test: try? exact

.github/workflows/awaiting-mathlib.yml

@@ -1,20 +0,0 @@
-name: Check awaiting-mathlib label
-
-on:
-  merge_group:
-  pull_request:
-    types: [opened, synchronize, reopened, labeled, unlabeled]
-
-jobs:
-  check-awaiting-mathlib:
-    runs-on: ubuntu-latest
-    steps:
-      - name: Check awaiting-mathlib label
-        if: github.event_name == 'pull_request'
-        uses: actions/github-script@v7
-        with:
-          script: |
-            const { labels } = context.payload.pull_request;
-            if (labels.some(label => label.name == "awaiting-mathlib") && !labels.some(label => label.name == "builds-mathlib")) {
-              core.setFailed('PR is marked "awaiting-mathlib" but "builds-mathlib" label has not been applied yet by the bot');
-            }

.github/workflows/build-template.yml

@@ -1,251 +0,0 @@
-# instantiated by ci.yml
-name: build-template
-on:
-  workflow_call:
-    inputs:
-      check-level:
-        type: string
-        required: true
-      config:
-        type: string
-        required: true
-      nightly:
-        type: string
-        required: true
-      LEAN_VERSION_MAJOR:
-        type: string
-        required: true
-      LEAN_VERSION_MINOR:
-        type: string
-        required: true
-      LEAN_VERSION_PATCH:
-        type: string
-        required: true
-      LEAN_SPECIAL_VERSION_DESC:
-        type: string
-        required: true
-      RELEASE_TAG:
-        type: string
-        required: true
-
-jobs:
-  build:
-    if: github.event_name != 'schedule' || github.repository == 'leanprover/lean4'
-    strategy:
-      matrix:
-        include: ${{fromJson(inputs.config)}}
-      # complete all jobs
-      fail-fast: false
-    runs-on: ${{ matrix.os }}
-    defaults:
-      run:
-        shell: ${{ matrix.shell || 'nix develop -c bash -euxo pipefail {0}' }}
-    name: ${{ matrix.name }}
-    env:
-      # must be inside workspace
-      CCACHE_DIR: ${{ github.workspace }}/.ccache
-      CCACHE_COMPRESS: true
-      # current cache limit
-      CCACHE_MAXSIZE: 600M
-      # squelch error message about missing nixpkgs channel
-      NIX_BUILD_SHELL: bash
-      LSAN_OPTIONS: max_leaks=10
-      # somehow MinGW clang64 (or cmake?) defaults to `g++` even though it doesn't exist
-      CXX: c++
-      MACOSX_DEPLOYMENT_TARGET: 10.15
-    steps:
-      - name: Install Nix
-        uses: DeterminateSystems/nix-installer-action@main
-        if: runner.os == 'Linux' && !matrix.cmultilib
-      - name: Install MSYS2
-        uses: msys2/setup-msys2@v2
-        with:
-          msystem: clang64
-          # `:` means do not prefix with msystem
-          pacboy: "make: python: cmake clang ccache gmp libuv git: zip: unzip: diffutils: binutils: tree: zstd tar:"
-        if: runner.os == 'Windows'
-      - name: Install Brew Packages
-        run: |
-          brew install ccache tree zstd coreutils gmp libuv
-        if: runner.os == 'macOS'
-      - name: Checkout
-        uses: actions/checkout@v4
-        with:
-          # the default is to use a virtual merge commit between the PR and master: just use the PR
-          ref: ${{ github.event.pull_request.head.sha }}
-      - name: Open Nix shell once
-        run: true
-        if: runner.os == 'Linux'
-      # Do check out some CI-relevant files from virtual merge commit to accommodate CI changes on
-      # master (as the workflow files themselves are always taken from the merge)
-      # (needs to be after "Install *" to use the right shell)
-      - name: CI Merge Checkout
-        run: |
-          git fetch --depth=1 origin ${{ github.sha }}
-          git checkout FETCH_HEAD flake.nix flake.lock
-        if: github.event_name == 'pull_request'
-      # (needs to be after "Checkout" so files don't get overridden)
-      - name: Setup emsdk
-        uses: mymindstorm/setup-emsdk@v14
-        with:
-          version: 3.1.44
-          actions-cache-folder: emsdk
-        if: matrix.wasm
-      - name: Install 32bit c libs
-        run: |
-          sudo dpkg --add-architecture i386
-          sudo apt-get update
-          sudo apt-get install -y gcc-multilib g++-multilib ccache libuv1-dev:i386 pkgconf:i386
-        if: matrix.cmultilib
-      - name: Cache
-        id: restore-cache
-        if: matrix.name != 'Linux Lake'
-        uses: actions/cache/restore@v4
-        with:
-          # NOTE: must be in sync with `save` below
-          path: |
-            .ccache
-            ${{ matrix.name == 'Linux Lake' && 'build/stage1/**/*.trace
-            build/stage1/**/*.olean
-            build/stage1/**/*.ilean
-            build/stage1/**/*.c
-            build/stage1/**/*.c.o*' || '' }}
-          key: ${{ matrix.name }}-build-v3-${{ github.event.pull_request.head.sha }}
-          # fall back to (latest) previous cache
-          restore-keys: |
-            ${{ matrix.name }}-build-v3
-      # open nix-shell once for initial setup
-      - name: Setup
-        run: |
-          ccache --zero-stats
-        if: runner.os == 'Linux'
-      - name: Set up NPROC
-        run: |
-          echo "NPROC=$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4)" >> $GITHUB_ENV
-      - name: Build
-        run: |
-          ulimit -c unlimited  # coredumps
-          [ -d build ] || mkdir build
-          cd build
-          # arguments passed to `cmake`
-          # this also enables githash embedding into stage 1 library
-          OPTIONS=(-DCHECK_OLEAN_VERSION=ON)
-          OPTIONS+=(-DLEAN_EXTRA_MAKE_OPTS=-DwarningAsError=true)
-          if [[ -n '${{ matrix.cross_target }}' ]]; then
-            # used by `prepare-llvm`
-            export EXTRA_FLAGS=--target=${{ matrix.cross_target }}
-            OPTIONS+=(-DLEAN_PLATFORM_TARGET=${{ matrix.cross_target }})
-          fi
-          if [[ -n '${{ matrix.prepare-llvm }}' ]]; then
-            wget -q ${{ matrix.llvm-url }}
-            PREPARE="$(${{ matrix.prepare-llvm }})"
-            eval "OPTIONS+=($PREPARE)"
-          fi
-          if [[ -n '${{ matrix.release }}' && -n '${{ inputs.nightly }}' ]]; then
-            OPTIONS+=(-DLEAN_SPECIAL_VERSION_DESC=${{ inputs.nightly }})
-          fi
-          if [[ -n '${{ matrix.release }}' && -n '${{ inputs.RELEASE_TAG }}' ]]; then
-            OPTIONS+=(-DLEAN_VERSION_MAJOR=${{ inputs.LEAN_VERSION_MAJOR }})
-            OPTIONS+=(-DLEAN_VERSION_MINOR=${{ inputs.LEAN_VERSION_MINOR }})
-            OPTIONS+=(-DLEAN_VERSION_PATCH=${{ inputs.LEAN_VERSION_PATCH }})
-            OPTIONS+=(-DLEAN_VERSION_IS_RELEASE=1)
-            OPTIONS+=(-DLEAN_SPECIAL_VERSION_DESC=${{ inputs.LEAN_SPECIAL_VERSION_DESC }})
-          fi
-          # contortion to support empty OPTIONS with old macOS bash
-          cmake .. --preset ${{ matrix.CMAKE_PRESET || 'release' }} -B . ${{ matrix.CMAKE_OPTIONS }} ${OPTIONS[@]+"${OPTIONS[@]}"} -DLEAN_INSTALL_PREFIX=$PWD/..
-          time make -j$NPROC
-      - name: Install
-        run: |
-          make -C build install
-      - name: Check Binaries
-        run: ${{ matrix.binary-check }} lean-*/bin/* || true
-      - name: Count binary symbols
-        run: |
-          for f in lean-*/bin/*; do
-            echo "$f: $(nm $f | grep " T " | wc -l) exported symbols"
-          done
-        if: matrix.name == 'Windows'
-      - name: List Install Tree
-        run: |
-          # omit contents of Init/, ...
-          tree --du -h lean-*-* | grep -E ' (Init|Lean|Lake|LICENSE|[a-z])'
-      - name: Pack
-        run: |
-          dir=$(echo lean-*-*)
-          mkdir pack
-          # high-compression tar.zst + zip for release, fast tar.zst otherwise
-          if [[ '${{ startsWith(github.ref, 'refs/tags/') && matrix.release }}' == true || -n '${{ inputs.nightly }}' || -n '${{ inputs.RELEASE_TAG }}' ]]; then
-            ${{ matrix.tar || 'tar' }} cf - $dir | zstd -T0 --no-progress -19 -o pack/$dir.tar.zst
-            zip -rq pack/$dir.zip $dir
-          else
-            ${{ matrix.tar || 'tar' }} cf - $dir | zstd -T0 --no-progress -o pack/$dir.tar.zst
-          fi
-      - uses: actions/upload-artifact@v4
-        if: matrix.release
-        with:
-          name: build-${{ matrix.name }}
-          path: pack/*
-      - name: Lean stats
-        run: |
-          build/stage1/bin/lean --stats src/Lean.lean
-        if: ${{ !matrix.cross }}
-      - name: Test
-        id: test
-        run: |
-          ulimit -c unlimited  # coredumps
-          time ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/stage1 -j$NPROC --output-junit test-results.xml ${{ matrix.CTEST_OPTIONS }} --timeout 200
-        if: (matrix.wasm || !matrix.cross) && inputs.check-level >= 1
-      - name: Test Summary
-        uses: test-summary/action@v2
-        with:
-          paths: build/stage1/test-results.xml
-        # prefix `if` above with `always` so it's run even if tests failed
-        if: always() && steps.test.conclusion != 'skipped'
-      - name: Check Test Binary
-        run: ${{ matrix.binary-check }} tests/compiler/534.lean.out
-        if: (!matrix.cross) && steps.test.conclusion != 'skipped'
-      - name: Build Stage 2
-        run: |
-          make -C build -j$NPROC stage2
-        if: matrix.test-speedcenter
-      - name: Check Stage 3
-        run: |
-          make -C build -j$NPROC check-stage3
-        if: matrix.test-speedcenter
-      - name: Test Speedcenter Benchmarks
-        run: |
-          # Necessary for some timing metrics but does not work on Namespace runners
-          # and we just want to test that the benchmarks run at all here
-          #echo -1 | sudo tee /proc/sys/kernel/perf_event_paranoid
-          export BUILD=$PWD/build PATH=$PWD/build/stage1/bin:$PATH
-          cd tests/bench
-          nix shell .#temci -c temci exec --config speedcenter.yaml --included_blocks fast --runs 1
-        if: matrix.test-speedcenter
-      - name: Check rebootstrap
-        run: |
-          # clean rebuild in case of Makefile changes
-          make -C build update-stage0 && rm -rf build/stage* && make -C build -j$NPROC
-        if: matrix.name == 'Linux' && inputs.check-level >= 1
-      - name: CCache stats
-        if: always()
-        run: ccache -s
-      - name: Show stacktrace for coredumps
-        if: failure() && runner.os == 'Linux'
-        run: |
-          for c in $(find . -name core); do
-            progbin="$(file $c | sed "s/.*execfn: '\([^']*\)'.*/\1/")"
-            echo bt | $GDB/bin/gdb -q $progbin $c || true
-          done
-      - name: Save Cache
-        if: always() && steps.restore-cache.outputs.cache-hit != 'true'
-        uses: actions/cache/save@v4
-        with:
-          # NOTE: must be in sync with `restore` above
-          path: |
-            .ccache
-            ${{ matrix.name == 'Linux Lake' && 'build/stage1/**/*.trace
-            build/stage1/**/*.olean
-            build/stage1/**/*.ilean
-            build/stage1/**/*.c
-            build/stage1/**/*.c.o*' || '' }}
-          key: ${{ steps.restore-cache.outputs.cache-primary-key }}

.github/workflows/check-stage0.yml

@@ -20,7 +20,9 @@ jobs:
 
     - name: Identify stage0 changes
       run: |
-        git diff "${BASE:-HEAD^}..HEAD" --name-only -- stage0/stdlib > "$RUNNER_TEMP/stage0" || true
+        git diff "${BASE:-HEAD^}..HEAD" --name-only -- stage0 |
+          grep -v -x -F $'stage0/src/stdlib_flags.h\nstage0/src/lean.mk.in' \
+          > "$RUNNER_TEMP/stage0" || true
         if test -s "$RUNNER_TEMP/stage0"
         then
           echo "CHANGES=yes" >> "$GITHUB_ENV"

.github/workflows/ci.yml

@@ -36,9 +36,7 @@ jobs:
       # 2: PRs with `release-ci` label, releases (incl. nightlies)
       check-level: ${{ steps.set-level.outputs.check-level }}
       # The build matrix, dynamically generated here
-      matrix: ${{ steps.set-matrix.outputs.matrix }}
-      # secondary build jobs that should not block the CI success/merge queue
-      matrix-secondary: ${{ steps.set-matrix.outputs.matrix-secondary }}
+      matrix: ${{ steps.set-matrix.outputs.result }}
       # Should we make a nightly release? If so, this output contains the lean version string, else it is empty
       nightly: ${{ steps.set-nightly.outputs.nightly }}
       # Should this be the CI for a tagged release?
@@ -137,9 +135,9 @@ jobs:
             console.log(`level: ${level}`);
             // use large runners where available (original repo)
             let large = ${{ github.repository == 'leanprover/lean4' }};
-            const isPr = "${{ github.event_name }}" == "pull_request";
             let matrix = [
               {
+                // portable release build: use channel with older glibc (2.27)
                 "name": "Linux LLVM",
                 "os": "ubuntu-latest",
                 "release": false,
@@ -154,7 +152,6 @@ jobs:
                 "CMAKE_OPTIONS": "-DLLVM=ON -DLLVM_CONFIG=${GITHUB_WORKSPACE}/build/llvm-host/bin/llvm-config"
               },
               {
-                // portable release build: use channel with older glibc (2.26)
                 "name": "Linux release",
                 "os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
                 "release": true,
@@ -166,19 +163,6 @@ jobs:
                 // foreign code may be linked against more recent glibc
                 "CTEST_OPTIONS": "-E 'foreign'"
               },
-              // deactivated due to bugs
-              /*
-              {
-                "name": "Linux Lake",
-                "os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
-                // just a secondary PR build job for now
-                "check-level": isPr ? 0 : 3,
-                "secondary": true,
-                "CMAKE_OPTIONS": "-DUSE_LAKE=ON",
-                // TODO: why does this fail?
-                "CTEST_OPTIONS": "-E 'scopedMacros'"
-              },
-              */
               {
                 "name": "Linux",
                 "os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
@@ -220,18 +204,12 @@ jobs:
                 "os": "macos-14",
                 "CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
                 "release": true,
+                "check-level": 0,
                 "shell": "bash -euxo pipefail {0}",
                 "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-apple-darwin.tar.zst",
                 "prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm*",
                 "binary-check": "otool -L",
-                "tar": "gtar", // https://github.com/actions/runner-images/issues/2619
-                // Special handling for MacOS aarch64, we want:
-                // 1. To run it in PRs so Mac devs get PR toolchains (so secondary is sufficient)
-                // 2. To skip it in merge queues as it takes longer than the Linux build and adds
-                //    little value in the merge queue
-                // 3. To run it in release (obviously)
-                "check-level": isPr ? 0 : 2,
-                "secondary": isPr,
+                "tar": "gtar" // https://github.com/actions/runner-images/issues/2619
               },
               {
                 "name": "Windows",
@@ -282,41 +260,196 @@ jobs:
               //   "CTEST_OPTIONS": "-R \"leantest_1007\\.lean|leantest_Format\\.lean|leanruntest\\_1037.lean|leanruntest_ac_rfl\\.lean|leanruntest_tempfile.lean\\.|leanruntest_libuv\\.lean\""
               // }
             ];
-            console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`);
-            matrix = matrix.filter((job) => level >= job["check-level"]);
-            core.setOutput('matrix', matrix.filter((job) => !job["secondary"]));
-            core.setOutput('matrix-secondary', matrix.filter((job) => job["secondary"]));
+            console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`)
+            return matrix.filter((job) => level >= job["check-level"])
 
   build:
+    needs: [configure]
     if: github.event_name != 'schedule' || github.repository == 'leanprover/lean4'
-    needs: [configure]
-    uses: ./.github/workflows/build-template.yml
-    with:
-      config: ${{needs.configure.outputs.matrix}}
-      check-level: ${{ needs.configure.outputs.check-level }}
-      nightly: ${{ needs.configure.outputs.nightly }}
-      LEAN_VERSION_MAJOR: ${{ needs.configure.outputs.LEAN_VERSION_MAJOR }}
-      LEAN_VERSION_MINOR: ${{ needs.configure.outputs.LEAN_VERSION_MINOR }}
-      LEAN_VERSION_PATCH: ${{ needs.configure.outputs.LEAN_VERSION_PATCH }}
-      LEAN_SPECIAL_VERSION_DESC: ${{ needs.configure.outputs.LEAN_SPECIAL_VERSION_DESC }}
-      RELEASE_TAG: ${{ needs.configure.outputs.RELEASE_TAG }}
-    secrets: inherit
-
-  # build jobs that should not be considered by `all-done` below
-  build-secondary:
-    needs: [configure]
-    if: needs.configure.outputs.matrix-secondary != '[]'
-    uses: ./.github/workflows/build-template.yml
-    with:
-      config: ${{needs.configure.outputs.matrix-secondary}}
-      check-level: ${{ needs.configure.outputs.check-level }}
-      nightly: ${{ needs.configure.outputs.nightly }}
-      LEAN_VERSION_MAJOR: ${{ needs.configure.outputs.LEAN_VERSION_MAJOR }}
-      LEAN_VERSION_MINOR: ${{ needs.configure.outputs.LEAN_VERSION_MINOR }}
-      LEAN_VERSION_PATCH: ${{ needs.configure.outputs.LEAN_VERSION_PATCH }}
-      LEAN_SPECIAL_VERSION_DESC: ${{ needs.configure.outputs.LEAN_SPECIAL_VERSION_DESC }}
-      RELEASE_TAG: ${{ needs.configure.outputs.RELEASE_TAG }}
-    secrets: inherit
+    strategy:
+      matrix:
+        include: ${{fromJson(needs.configure.outputs.matrix)}}
+      # complete all jobs
+      fail-fast: false
+    runs-on: ${{ matrix.os }}
+    defaults:
+      run:
+        shell: ${{ matrix.shell || 'nix develop -c bash -euxo pipefail {0}' }}
+    name: ${{ matrix.name }}
+    env:
+      # must be inside workspace
+      CCACHE_DIR: ${{ github.workspace }}/.ccache
+      CCACHE_COMPRESS: true
+      # current cache limit
+      CCACHE_MAXSIZE: 200M
+      # squelch error message about missing nixpkgs channel
+      NIX_BUILD_SHELL: bash
+      LSAN_OPTIONS: max_leaks=10
+      # somehow MinGW clang64 (or cmake?) defaults to `g++` even though it doesn't exist
+      CXX: c++
+      MACOSX_DEPLOYMENT_TARGET: 10.15
+    steps:
+      - name: Install Nix
+        uses: DeterminateSystems/nix-installer-action@main
+        if: runner.os == 'Linux' && !matrix.cmultilib
+      - name: Install MSYS2
+        uses: msys2/setup-msys2@v2
+        with:
+          msystem: clang64
+          # `:` means do not prefix with msystem
+          pacboy: "make: python: cmake clang ccache gmp libuv git: zip: unzip: diffutils: binutils: tree: zstd tar:"
+        if: runner.os == 'Windows'
+      - name: Install Brew Packages
+        run: |
+          brew install ccache tree zstd coreutils gmp libuv
+        if: runner.os == 'macOS'
+      - name: Checkout
+        uses: actions/checkout@v4
+        with:
+          # the default is to use a virtual merge commit between the PR and master: just use the PR
+          ref: ${{ github.event.pull_request.head.sha }}
+      # Do check out some CI-relevant files from virtual merge commit to accommodate CI changes on
+      # master (as the workflow files themselves are always taken from the merge)
+      # (needs to be after "Install *" to use the right shell)
+      - name: CI Merge Checkout
+        run: |
+          git fetch --depth=1 origin ${{ github.sha }}
+          git checkout FETCH_HEAD flake.nix flake.lock
+        if: github.event_name == 'pull_request'
+      # (needs to be after "Checkout" so files don't get overridden)
+      - name: Setup emsdk
+        uses: mymindstorm/setup-emsdk@v14
+        with:
+          version: 3.1.44
+          actions-cache-folder: emsdk
+        if: matrix.wasm
+      - name: Install 32bit c libs
+        run: |
+          sudo dpkg --add-architecture i386
+          sudo apt-get update
+          sudo apt-get install -y gcc-multilib g++-multilib ccache libuv1-dev:i386 pkgconf:i386
+        if: matrix.cmultilib
+      - name: Cache
+        uses: actions/cache@v4
+        with:
+          path: .ccache
+          key: ${{ matrix.name }}-build-v3-${{ github.event.pull_request.head.sha }}
+          # fall back to (latest) previous cache
+          restore-keys: |
+            ${{ matrix.name }}-build-v3
+          save-always: true
+      # open nix-shell once for initial setup
+      - name: Setup
+        run: |
+          ccache --zero-stats
+        if: runner.os == 'Linux'
+      - name: Set up NPROC
+        run: |
+          echo "NPROC=$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4)" >> $GITHUB_ENV
+      - name: Build
+        run: |
+          mkdir build
+          cd build
+          # arguments passed to `cmake`
+          # this also enables githash embedding into stage 1 library
+          OPTIONS=(-DCHECK_OLEAN_VERSION=ON)
+          OPTIONS+=(-DLEAN_EXTRA_MAKE_OPTS=-DwarningAsError=true)
+          if [[ -n '${{ matrix.cross_target }}' ]]; then
+            # used by `prepare-llvm`
+            export EXTRA_FLAGS=--target=${{ matrix.cross_target }}
+            OPTIONS+=(-DLEAN_PLATFORM_TARGET=${{ matrix.cross_target }})
+          fi
+          if [[ -n '${{ matrix.prepare-llvm }}' ]]; then
+            wget -q ${{ matrix.llvm-url }}
+            PREPARE="$(${{ matrix.prepare-llvm }})"
+            eval "OPTIONS+=($PREPARE)"
+          fi
+          if [[ -n '${{ matrix.release }}' && -n '${{ needs.configure.outputs.nightly }}' ]]; then
+            OPTIONS+=(-DLEAN_SPECIAL_VERSION_DESC=${{ needs.configure.outputs.nightly }})
+          fi
+          if [[ -n '${{ matrix.release }}' && -n '${{ needs.configure.outputs.RELEASE_TAG }}' ]]; then
+            OPTIONS+=(-DLEAN_VERSION_MAJOR=${{ needs.configure.outputs.LEAN_VERSION_MAJOR }})
+            OPTIONS+=(-DLEAN_VERSION_MINOR=${{ needs.configure.outputs.LEAN_VERSION_MINOR }})
+            OPTIONS+=(-DLEAN_VERSION_PATCH=${{ needs.configure.outputs.LEAN_VERSION_PATCH }})
+            OPTIONS+=(-DLEAN_VERSION_IS_RELEASE=1)
+            OPTIONS+=(-DLEAN_SPECIAL_VERSION_DESC=${{ needs.configure.outputs.LEAN_SPECIAL_VERSION_DESC }})
+          fi
+          # contortion to support empty OPTIONS with old macOS bash
+          cmake .. --preset ${{ matrix.CMAKE_PRESET || 'release' }} -B . ${{ matrix.CMAKE_OPTIONS }} ${OPTIONS[@]+"${OPTIONS[@]}"} -DLEAN_INSTALL_PREFIX=$PWD/..
+          time make -j$NPROC
+      - name: Install
+        run: |
+          make -C build install
+      - name: Check Binaries
+        run: ${{ matrix.binary-check }} lean-*/bin/* || true
+      - name: Count binary symbols
+        run: |
+          for f in lean-*/bin/*; do
+            echo "$f: $(nm $f | grep " T " | wc -l) exported symbols"
+          done
+        if: matrix.name == 'Windows'
+      - name: List Install Tree
+        run: |
+          # omit contents of Init/, ...
+          tree --du -h lean-*-* | grep -E ' (Init|Lean|Lake|LICENSE|[a-z])'
+      - name: Pack
+        run: |
+          dir=$(echo lean-*-*)
+          mkdir pack
+          # high-compression tar.zst + zip for release, fast tar.zst otherwise
+          if [[ '${{ startsWith(github.ref, 'refs/tags/') && matrix.release }}' == true || -n '${{ needs.configure.outputs.nightly }}' || -n '${{ needs.configure.outputs.RELEASE_TAG }}' ]]; then
+            ${{ matrix.tar || 'tar' }} cf - $dir | zstd -T0 --no-progress -19 -o pack/$dir.tar.zst
+            zip -rq pack/$dir.zip $dir
+          else
+            ${{ matrix.tar || 'tar' }} cf - $dir | zstd -T0 --no-progress -o pack/$dir.tar.zst
+          fi
+      - uses: actions/upload-artifact@v4
+        if: matrix.release
+        with:
+          name: build-${{ matrix.name }}
+          path: pack/*
+      - name: Lean stats
+        run: |
+          build/stage1/bin/lean --stats src/Lean.lean
+        if: ${{ !matrix.cross }}
+      - name: Test
+        id: test
+        run: |
+          time ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/stage1 -j$NPROC --output-junit test-results.xml ${{ matrix.CTEST_OPTIONS }}
+        if: (matrix.wasm || !matrix.cross) && needs.configure.outputs.check-level >= 1
+      - name: Test Summary
+        uses: test-summary/action@v2
+        with:
+          paths: build/stage1/test-results.xml
+        # prefix `if` above with `always` so it's run even if tests failed
+        if: always() && steps.test.conclusion != 'skipped'
+      - name: Check Test Binary
+        run: ${{ matrix.binary-check }} tests/compiler/534.lean.out
+        if: (!matrix.cross) && steps.test.conclusion != 'skipped'
+      - name: Build Stage 2
+        run: |
+          make -C build -j$NPROC stage2
+        if: matrix.test-speedcenter
+      - name: Check Stage 3
+        run: |
+          make -C build -j$NPROC check-stage3
+        if: matrix.test-speedcenter
+      - name: Test Speedcenter Benchmarks
+        run: |
+          # Necessary for some timing metrics but does not work on Namespace runners
+          # and we just want to test that the benchmarks run at all here
+          #echo -1 | sudo tee /proc/sys/kernel/perf_event_paranoid
+          export BUILD=$PWD/build PATH=$PWD/build/stage1/bin:$PATH
+          cd tests/bench
+          nix shell .#temci -c temci exec --config speedcenter.yaml --included_blocks fast --runs 1
+        if: matrix.test-speedcenter
+      - name: Check rebootstrap
+        run: |
+          # clean rebuild in case of Makefile changes
+          make -C build update-stage0 && rm -rf build/stage* && make -C build -j$NPROC
+        if: matrix.name == 'Linux' && needs.configure.outputs.check-level >= 1
+      - name: CCache stats
+        run: ccache -s
 
   # This job collects results from all the matrix jobs
   # This can be made the "required" job, instead of listing each

.github/workflows/pr-release.yml

@@ -34,7 +34,7 @@ jobs:
       - name: Download artifact from the previous workflow.
         if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
         id: download-artifact
-        uses: dawidd6/action-download-artifact@v9 # https://github.com/marketplace/actions/download-workflow-artifact
+        uses: dawidd6/action-download-artifact@v8 # https://github.com/marketplace/actions/download-workflow-artifact
         with:
           run_id: ${{ github.event.workflow_run.id }}
           path: artifacts
@@ -155,20 +155,6 @@ jobs:
           fi
 
           if [[ -n "$MESSAGE" ]]; then
-            # Check if force-mathlib-ci label is present
-            LABELS="$(curl --retry 3 --location --silent \
-                          -H "Authorization: token ${{ secrets.MATHLIB4_COMMENT_BOT }}" \
-                          -H "Accept: application/vnd.github.v3+json" \
-                          "https://api.github.com/repos/leanprover/lean4/issues/${{ steps.workflow-info.outputs.pullRequestNumber }}/labels" \
-                          | jq -r '.[].name')"
-            
-            if echo "$LABELS" | grep -q "^force-mathlib-ci$"; then
-              echo "force-mathlib-ci label detected, forcing CI despite issues"
-              MESSAGE="Forcing Mathlib CI because the \`force-mathlib-ci\` label is present, despite problem: $MESSAGE"
-              FORCE_CI=true
-            else
-              MESSAGE="$MESSAGE You can force Mathlib CI using the \`force-mathlib-ci\` label."
-            fi
 
             echo "Checking existing messages"
 
@@ -215,12 +201,7 @@ jobs:
             else
               echo "The message already exists in the comment body."
             fi
-
-            if [[ "$FORCE_CI" == "true" ]]; then
-              echo "mathlib_ready=true" >> "$GITHUB_OUTPUT"
-            else
-              echo "mathlib_ready=false" >> "$GITHUB_OUTPUT"
-            fi
+            echo "mathlib_ready=false" >> "$GITHUB_OUTPUT"
           else
             echo "mathlib_ready=true" >> "$GITHUB_OUTPUT"
           fi
@@ -271,7 +252,7 @@ jobs:
           if git ls-remote --heads --tags --exit-code origin "nightly-testing-${MOST_RECENT_NIGHTLY}" >/dev/null; then
             BASE="nightly-testing-${MOST_RECENT_NIGHTLY}"
           else
-            echo "Couldn't find a 'nightly-testing-${MOST_RECENT_NIGHTLY}' tag at Batteries. Falling back to 'nightly-testing'."
+            echo "This shouldn't be possible: couldn't find a 'nightly-testing-${MOST_RECENT_NIGHTLY}' tag at Batteries. Falling back to 'nightly-testing'."
             BASE=nightly-testing
           fi
 
@@ -335,7 +316,7 @@ jobs:
           if git ls-remote --heads --tags --exit-code origin "nightly-testing-${MOST_RECENT_NIGHTLY}" >/dev/null; then
             BASE="nightly-testing-${MOST_RECENT_NIGHTLY}"
           else
-            echo "Couldn't find a 'nightly-testing-${MOST_RECENT_NIGHTLY}' branch at Mathlib. Falling back to 'nightly-testing'."
+            echo "This shouldn't be possible: couldn't find a 'nightly-testing-${MOST_RECENT_NIGHTLY}' branch at Mathlib. Falling back to 'nightly-testing'."
             BASE=nightly-testing
           fi
 

CMakeLists.txt

@@ -1,7 +1,4 @@
 cmake_minimum_required(VERSION 3.11)
-
-option(USE_MIMALLOC "use mimalloc" ON)
-
 # store all variables passed on the command line into CL_ARGS so we can pass them to the stage builds
 # https://stackoverflow.com/a/48555098/161659
 # MUST be done before call to 'project'
@@ -17,12 +14,13 @@ foreach(var ${vars})
     if("${var}" MATCHES "USE_GMP|CHECK_OLEAN_VERSION")
       # must forward options that generate incompatible .olean format
       list(APPEND STAGE0_ARGS "-D${var}=${${var}}")
-    elseif("${var}" MATCHES "LLVM*|PKG_CONFIG|USE_LAKE|USE_MIMALLOC")
+    endif()
+    if("${var}" MATCHES "LLVM*")
+      list(APPEND STAGE0_ARGS "-D${var}=${${var}}")
+    endif()
+    if("${var}" MATCHES "PKG_CONFIG*")
       list(APPEND STAGE0_ARGS "-D${var}=${${var}}")
     endif()
-  elseif("${var}" MATCHES "USE_MIMALLOC")
-    list(APPEND CL_ARGS "-D${var}=${${var}}")
-    list(APPEND STAGE0_ARGS "-D${var}=${${var}}")
   elseif(("${var}" MATCHES "CMAKE_.*") AND NOT ("${var}" MATCHES "CMAKE_BUILD_TYPE") AND NOT ("${var}" MATCHES "CMAKE_HOME_DIRECTORY"))
     list(APPEND PLATFORM_ARGS "-D${var}=${${var}}")
   endif()
@@ -49,41 +47,28 @@ if (NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
     if(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
       string(APPEND CADICAL_CXXFLAGS " -DNUNLOCKED")
     endif()
-    string(APPEND CADICAL_CXXFLAGS " -DNCLOSEFROM")
     ExternalProject_add(cadical
       PREFIX cadical
       GIT_REPOSITORY https://github.com/arminbiere/cadical
-      GIT_TAG rel-2.1.2
+      GIT_TAG rel-1.9.5
       CONFIGURE_COMMAND ""
       # https://github.com/arminbiere/cadical/blob/master/BUILD.md#manual-build
       BUILD_COMMAND $(MAKE) -f ${CMAKE_SOURCE_DIR}/src/cadical.mk CMAKE_EXECUTABLE_SUFFIX=${CMAKE_EXECUTABLE_SUFFIX} CXX=${CADICAL_CXX} CXXFLAGS=${CADICAL_CXXFLAGS}
       BUILD_IN_SOURCE ON
       INSTALL_COMMAND "")
     set(CADICAL ${CMAKE_BINARY_DIR}/cadical/cadical${CMAKE_EXECUTABLE_SUFFIX} CACHE FILEPATH "path to cadical binary" FORCE)
-    list(APPEND EXTRA_DEPENDS cadical)
+    set(EXTRA_DEPENDS "cadical")
   endif()
   list(APPEND CL_ARGS -DCADICAL=${CADICAL})
 endif()
 
-if (USE_MIMALLOC)
-  ExternalProject_add(mimalloc
-    PREFIX mimalloc
-    GIT_REPOSITORY https://github.com/microsoft/mimalloc
-    GIT_TAG v2.2.3
-    # just download, we compile it as part of each stage as it is small
-    CONFIGURE_COMMAND ""
-    BUILD_COMMAND ""
-    INSTALL_COMMAND "")
-  list(APPEND EXTRA_DEPENDS mimalloc)
-endif()
-
 ExternalProject_add(stage0
   SOURCE_DIR "${LEAN_SOURCE_DIR}/stage0"
   SOURCE_SUBDIR src
   BINARY_DIR stage0
   # do not rebuild stage0 when git hash changes; it's not from this commit anyway
-  # (however, CI will override this as we need to embed the githash into the stage 1 library built
-  # by stage 0)
+  # (however, `CHECK_OLEAN_VERSION=ON` in CI will override this as we need to
+  # embed the githash into the stage 1 library built by stage 0)
   CMAKE_ARGS -DSTAGE=0 -DUSE_GITHASH=OFF ${PLATFORM_ARGS} ${STAGE0_ARGS}
   BUILD_ALWAYS ON  # cmake doesn't auto-detect changes without a download method
   INSTALL_COMMAND ""  # skip install
@@ -97,7 +82,6 @@ ExternalProject_add(stage1
   BUILD_ALWAYS ON
   INSTALL_COMMAND ""
   DEPENDS stage0
-  STEP_TARGETS configure
 )
 ExternalProject_add(stage2
   SOURCE_DIR "${LEAN_SOURCE_DIR}"

CMakePresets.json

@@ -16,7 +16,6 @@
       "name": "debug",
       "displayName": "Debug build config",
       "cacheVariables": {
-        "LEAN_EXTRA_CXX_FLAGS": "-DLEAN_DEFAULT_THREAD_STACK_SIZE=16*1024*1024",
         "CMAKE_BUILD_TYPE": "Debug"
       },
       "generator": "Unix Makefiles",
@@ -26,13 +25,10 @@
       "name": "sanitize",
       "displayName": "Sanitize build config",
       "cacheVariables": {
-        "LEAN_EXTRA_CXX_FLAGS": "-fsanitize=address,undefined -DLEAN_DEFAULT_THREAD_STACK_SIZE=16*1024*1024",
-        "LEANC_EXTRA_CC_FLAGS": "-fsanitize=address,undefined",
-        "LEAN_EXTRA_LINKER_FLAGS": "-fsanitize=address,undefined -fsanitize-link-c++-runtime",
+        "LEAN_EXTRA_CXX_FLAGS": "-fsanitize=address,undefined",
+        "LEANC_EXTRA_CC_FLAGS": "-fsanitize=address,undefined -fsanitize-link-c++-runtime",
         "SMALL_ALLOCATOR": "OFF",
-        "USE_MIMALLOC": "OFF",
-        "BSYMBOLIC": "OFF",
-        "LEAN_TEST_VARS": "MAIN_STACK_SIZE=16000"
+        "BSYMBOLIC": "OFF"
       },
       "generator": "Unix Makefiles",
       "binaryDir": "${sourceDir}/build/sanitize"

doc/declarations.md

@@ -764,12 +764,11 @@ Structures and Records
 The ``structure`` command in Lean is used to define an inductive data type with a single constructor and to define its projections at the same time. The syntax is as follows:
 
 ```
-structure Foo (a : α) : Sort u extends Bar, Baz :=
+structure Foo (a : α) extends Bar, Baz : Sort u :=
 constructor :: (field₁ : β₁) ... (fieldₙ : βₙ)
 ```
 
-Here ``(a : α)`` is a telescope, that is, the parameters to the inductive definition. The name ``constructor`` followed by the double colon is optional; if it is not present, the name ``mk`` is used by default. The keyword ``extends`` followed by a list of previously defined structures is also optional; if it is present, an instance of each of these structures is included among the fields to ``Foo``, and the types ``βᵢ`` can refer to their fields as well. The output type, ``Sort u``, can be omitted, in which case Lean infers to smallest non-``Prop`` sort possible (unless all the fields are ``Prop``, in which case it infers ``Prop``).
-Finally, ``(field₁ : β₁) ... (fieldₙ : βₙ)`` is a telescope relative to ``(a : α)`` and the fields in ``bar`` and ``baz``.
+Here ``(a : α)`` is a telescope, that is, the parameters to the inductive definition. The name ``constructor`` followed by the double colon is optional; if it is not present, the name ``mk`` is used by default. The keyword ``extends`` followed by a list of previously defined structures is also optional; if it is present, an instance of each of these structures is included among the fields to ``Foo``, and the types ``βᵢ`` can refer to their fields as well. The output type, ``Sort u``, can be omitted, in which case Lean infers to smallest non-``Prop`` sort possible. Finally, ``(field₁ : β₁) ... (fieldₙ : βₙ)`` is a telescope relative to ``(a : α)`` and the fields in ``bar`` and ``baz``.
 
 The declaration above is syntactic sugar for an inductive type declaration, and so results in the addition of the following constants to the environment:
 

doc/dev/release_checklist.md

@@ -5,7 +5,7 @@ See below for the checklist for release candidates.
 
 We'll use `v4.6.0` as the intended release version as a running example.
 
-- Run `script/release_checklist.py v4.6.0` to check the status of the release.
+- Run `scripts/release_checklist.py v4.6.0` to check the status of the release.
   This script is purely informational, idempotent, and safe to run at any stage of the release process.
 - `git checkout releases/v4.6.0`
   (This branch should already exist, from the release candidates.)
@@ -13,8 +13,7 @@ We'll use `v4.6.0` as the intended release version as a running example.
 - In `src/CMakeLists.txt`, verify you see
   - `set(LEAN_VERSION_MINOR 6)` (for whichever `6` is appropriate)
   - `set(LEAN_VERSION_IS_RELEASE 1)`
-  - (all of these should already be in place from the release candidates)
-
+  - (both of these should already be in place from the release candidates)
 - `git tag v4.6.0`
 - `git push $REMOTE v4.6.0`, where `$REMOTE` is the upstream Lean repository (e.g., `origin`, `upstream`)
 - Now wait, while CI runs.
@@ -42,10 +41,6 @@ We'll use `v4.6.0` as the intended release version as a running example.
   - In order to have the access rights to push to these repositories and merge PRs,
     you will need to be a member of the `lean-release-managers` team at both `leanprover-community` and `leanprover`.
     Contact Kim Morrison (@kim-em) to arrange access.
-  - There is an experimental script that will guide you through the steps for each of the repositories below.
-    The script should be invoked as
-    `script/release_steps.py vx.y.x <repo>` where `<repo>` is a case-insensitive substring of the repo name.
-    For example: `script/release_steps.py v4.6.0 batt` will guide you through the steps for the Batteries repository.
   - For each of the repositories listed below:
     - Make a PR to `master`/`main` changing the toolchain to `v4.6.0`
       - The usual branch name would be `bump_to_v4.6.0`.
@@ -85,11 +80,6 @@ We'll use `v4.6.0` as the intended release version as a running example.
       - Toolchain bump PR including updated Lake manifest
       - Create and push the tag
       - There is no `stable` branch; skip this step
-    - [Reference Manual](https://github.com/leanprover/reference-manual)
-      - Dependencies: Verso
-      - Toolchain bump PR including updated Lake manifest
-      - Pushing the tag (whether for an RC or a final) triggers a deployment.
-      - There is no `stable` branch; skip this step
     - [Cli](https://github.com/leanprover/lean4-cli)
       - No dependencies
       - Toolchain bump PR
@@ -133,10 +123,6 @@ We'll use `v4.6.0` as the intended release version as a running example.
       - Toolchain bump PR including updated Lake manifest
       - Create and push the tag
       - Merge the tag into `stable`
-- An awkward situtation that sometimes occurs (e.g. with Verso) is that one of these upstream dependencies has
-  already moved its `master`/`main` branch to a nightly toolchain that comes *after* the stable toolchain we are
-  targeting. In this case it is necessary to create a branch `releases/v4.6.0` from the last commit which was on
-  an earlier toolchain, move that branch to the stable toolchain, and create the toolchain tag from that branch.
 - Run `script/release_checklist.py v4.6.0` again to check that everything is in order.
 - Finally, make an announcement!
   This should go in https://leanprover.zulipchat.com/#narrow/stream/113486-announce, with topic `v4.6.0`.
@@ -174,7 +160,6 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
     git fetch nightly tag nightly-2024-02-29
     git checkout nightly-2024-02-29
     git checkout -b releases/v4.7.0
-    git push --set-upstream origin releases/v4.18.0
     ```
 - In `RELEASES.md` replace `Development in progress` in the `v4.7.0` section with `Release notes to be written.`
 - In `src/CMakeLists.txt`,
@@ -184,7 +169,6 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
 - `git tag v4.7.0-rc1`
 - `git push origin v4.7.0-rc1`
 - Now wait, while CI runs.
-  - The CI setup parses the tag to discover the `-rc1` special description, and passes it to `cmake` using a `-D` option. The `-rc1` doesn't need to be placed in the configuration file.
   - You can monitor this at `https://github.com/leanprover/lean4/actions/workflows/ci.yml`, looking for the `v4.7.0-rc1` tag.
   - This step can take up to an hour.
 - (GitHub release notes) Once the release appears at https://github.com/leanprover/lean4/releases/
@@ -228,8 +212,20 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
   You will want a few bullet points for main topics from the release notes.
   Please also make sure that whoever is handling social media knows the release is out.
 - Begin the next development cycle (i.e. for `v4.8.0`) on the Lean repository, by making a PR that:
-  - Uses branch name `dev_cycle_v4.8`.
   - Updates `src/CMakeLists.txt` to say `set(LEAN_VERSION_MINOR 8)`
+  - Replaces the "release notes will be copied" text in the `v4.6.0` section of `RELEASES.md` with the
+    finalized release notes from the `releases/v4.6.0` branch.
+  - Replaces the "development in progress" in the `v4.7.0` section of `RELEASES.md` with
+    ```
+    Release candidate, release notes will be copied from the branch `releases/v4.7.0` once completed.
+    ```
+    and inserts the following section before that section:
+    ```
+    v4.8.0
+    ----------
+    Development in progress.
+    ```
+  - Removes all the entries from the `./releases_drafts/` folder.
   - Titled "chore: begin development cycle for v4.8.0"
 
 

doc/examples/bintree.lean

@@ -179,7 +179,7 @@ local macro "have_eq " lhs:term:max rhs:term:max : tactic =>
   `(tactic|
     (have h : $lhs = $rhs :=
        -- TODO: replace with linarith
-       by simp +arith at *; apply Nat.le_antisymm <;> assumption
+       by simp_arith at *; apply Nat.le_antisymm <;> assumption
      try subst $lhs))
 
 /-!

doc/setup.md

@@ -4,10 +4,10 @@
 
 Platforms built & tested by our CI, available as binary releases via elan (see below)
 
-* x86-64 Linux with glibc 2.26+
+* x86-64 Linux with glibc 2.27+
 * x86-64 macOS 10.15+
 * aarch64 (Apple Silicon) macOS 10.15+
-* x86-64 Windows 11 (any version), Windows 10 (version 1903 or higher), Windows Server 2022, Windows Server 2025
+* x86-64 Windows 11 (any version), Windows 10 (version 1903 or higher), Windows Server 2022
 
 ### Tier 2
 

doc/std/naming.md

@@ -57,13 +57,13 @@ for deciding where to place a theorem, and is, on occasion, a good reason to dup
 New types that are added will usually be placed in the `Std` namespace and in the `Std/` source directory, unless there are good reasons to place
 them elsewhere.
 
-Inside the `Std` namespace, all internal declarations should be `private` or else have a name component that clearly marks them as internal, preferably
+Inside the  `Std`, all internal declarations should be `private` or else have a name component that clearly marks them as internal, preferably
 `Internal`.
 
 
 ## Naming convention for data
 
-When defining data, i.e., a (possibly 0-ary) function whose codomain is not Sort u, but has type Type u for some u, it should be named in lowerCamelCase. Examples include `List.append` and `List.isPrefixOf`.
+When defining data, i.e., a (possibly 0-ary) function whose codomain is not Sort u, but has type Type u for some u, it should be named in lowerCamelCase. Examples include List.append and List.isPrefixOf.
 If your data is morally fully specified by its type, then use the naming procedure for theorems described below and convert the result to lower camel case.
 
 If your function returns an `Option`, consider adding `?` as a suffix. If your function may panic, consider adding `!` as a suffix. In many cases, there will be multiple variants of a function; one returning an option, one that may panic and possibly one that takes a proof argument.
@@ -187,12 +187,10 @@ There are certain special “keywords” that may appear in identifiers.
 | `distrib` | Theorems of the form `f (g a b) = g (f a) (f b)` | `Nat.add_left_distrib` |
 | `self` | May be used if a variable appears multiple times in the conclusion | `List.mem_cons_self` |
 | `inj` | Theorems of the form `f a = f b ↔ a = b`. | `Int.neg_inj`, `Nat.add_left_inj` |
-| `cancel` | Theorems which have one of the forms `f a = f b → a = b` or `g (f a) = a`, where `f` and `g` usually involve a binary operator | `Nat.add_sub_cancel` |
+| `cancel` | Theorems which have one of the forms `f a = f b →a = b` or `g (f a) = a`, where `f` and `g` usually involve a binary operator | `Nat.add_sub_cancel` |
 | `cancel_iff` | Same as `inj`, but with different conventions for left and right (see below) | `Nat.add_right_cancel_iff` |
-| `ext` | Theorems of the form `f a = f b → a = b`, where `f` usually involves some kind of projection | `List.ext_getElem`
-| `mono` | Theorems of the form `a R b → f a R f b`, where `R` is a transitive relation | `List.countP_mono_left`
 
-### Left and right
+## Left and right
 
 The keywords left and right are useful to disambiguate symmetric variants of theorems.
 
@@ -223,10 +221,6 @@ theorem Nat.add_sub_self_right (a b : Nat) : (a + b) - b = a := sorry
 theorem Nat.add_sub_cancel (n m : Nat) : (n + m) - m = n := sorry
 ```
 
-## Primed names
-
-Avoid disambiguating variants of a concept by appending the `'` character (e.g., introducing both `BitVec.sshiftRight` and `BitVec.sshiftRight'`), as it is impossible to tell the difference without looking at the type signature, the documentation or even the code, and even if you know what the two variants are there is no way to tell which is which. Prefer descriptive pairs `BitVec.sshiftRightNat`/`BitVec.sshiftRight`.
-
 ## Acronyms
 
 For acronyms which are three letters or shorter, all letters should use the same case as dictated by the convention. For example, `IO` is a correct name for a type and the name `IO.Ref` may become `IORef` when used as part of a definition name and `ioRef` when used as part of a theorem name.
@@ -234,27 +228,3 @@ For acronyms which are three letters or shorter, all letters should use the same
 For acronyms which are at least four letters long, switch to lower case starting from the second letter. For example, `Json` is a correct name for a type, as is `JsonRPC`.
 
 If an acronym is typically spelled using mixed case, this mixed spelling may be used in identifiers (for example `Std.Net.IPv4Addr`).
-
-## Simp sets
-
-Simp sets centered around a conversion function should be called `source_to_target`. For example, a simp set for the `BitVec.toNat` function, which goes from `BitVec` to
-`Nat`, should be called `bitvec_to_nat`.
-
-## Variable names
-
-We make the following recommendations for variable names, but without insisting on them:
-* Simple hypotheses should be named `h`, `h'`, or using a numerical sequence `h₁`, `h₂`, etc.
-* Another common name for a simple hypothesis is `w` (for "witness").
-* `List`s should be named `l`, `l'`, `l₁`, etc, or `as`, `bs`, etc.
-  (Use of `as`, `bs` is encouraged when the lists are of different types, e.g. `as : List α` and `bs : List β`.)
-  `xs`, `ys`, `zs` are allowed, but it is better if these are reserved for `Array` and `Vector`.
-  A list of lists may be named `L`.
-* `Array`s should be named `xs`, `ys`, `zs`, although `as`, `bs` are encouraged when the arrays are of different types, e.g. `as : Array α` and `bs : Array β`.
-  An array of arrays may be named `xss`.
-* `Vector`s should be named `xs`, `ys`, `zs`, although `as`, `bs` are encouraged when the vectors are of different types, e.g. `as : Vector α n` and `bs : Vector β n`.
-  A vector of vectors may be named `xss`.
-* A common exception for `List` / `Array` / `Vector` is to use `acc` for an accumulator in a recursive function.
-* `i`, `j`, `k` are preferred for numerical indices.
-  Descriptive names such as `start`, `stop`, `lo`, and `hi` are encouraged when they increase readability.
-* `n`, `m` are preferred for sizes, e.g. in `Vector α n` or `xs.size = n`.
-* `w` is preferred for the width of a `BitVec`.

doc/std/style.md

@@ -122,8 +122,6 @@ example : Vector Nat :=
 
 Every file should start with a copyright header, imports (in the standard library, this always includes a `prelude` declaration) and a module documentation string. There should not be a blank line between the copyright header and the imports. There should be a blank line between the imports and the module documentation string.
 
-If you explicitly declare universe variables, do so at the top of the file, after the module documentation.
-
 Correct:
 ```lean
 /-
@@ -139,8 +137,6 @@ import Init.Data.List.Find
 /-!
 **# Lemmas about `List.eraseP` and `List.erase`.**
 -/
-
-universe u u'
 ```
 
 Syntax that is not supposed to be user-facing must be scoped. New public syntax must always be discussed explicitly in an RFC.
@@ -289,15 +285,6 @@ structure Iterator where
 deriving Inhabited
 ```
 
-## Notation and Unicode
-
-We generally prefer to use notation as available. We usually prefer the Unicode versions of notations over non-Unicode alternatives.
-
-There are some rules and exceptions regarding specific notations which are listed below:
-
-* Sigma types: use `(a : α) × β a` instead of `Σ a, β a` or `Sigma β`.
-* Function arrows: use `fun a => f x` instead of `fun x ↦ f x` or `λ x => f x` or any other variant.
-
 ## Language constructs
 
 ### Pattern matching, induction etc.
@@ -417,35 +404,6 @@ instance [Inhabited α] : Inhabited (Descr α β σ) where
   }
 ```
 
-### Declaring structures
-
-When defining structure types, do not parenthesize structure fields.
-
-When declaring a structure type with a custom constructor name, put the custom name on its own line, indented like the
-structure fields, and add a documentation comment.
-
-Correct:
-
-```lean
-/--
-A bitvector of the specified width.
-
-This is represented as the underlying `Nat` number in both the runtime
-and the kernel, inheriting all the special support for `Nat`.
--/
-structure BitVec (w : Nat) where
-  /--
-  Constructs a `BitVec w` from a number less than `2^w`.
-  O(1), because we use `Fin` as the internal representation of a bitvector.
-  -/
-  ofFin ::
-  /--
-  Interprets a bitvector as a number less than `2^w`.
-  O(1), because we use `Fin` as the internal representation of a bitvector.
-  -/
-  toFin : Fin (2 ^ w)
-```
-
 ## Tactic proofs
 
 Tactic proofs are the most common thing to break during any kind of upgrade, so it is important to write them in a way that minimizes the likelihood of proofs breaking and that makes it easy to debug breakages if they do occur.
@@ -466,8 +424,6 @@ Prefer highly automated tactics (like `grind` and `omega`) over low-level proofs
 
 ## `do` notation
 
-The `do` keyword goes on the same line as the corresponding `:=` (or `=>`, or similar). `Id.run do` should be treated as if it was a bare `do`.
-
 Use early `return` statements to reduce nesting depth and make the non-exceptional control flow of a function easier to see.
 
 Alternatives for `let` matches may be placed in the same line or in the next line, indented by two spaces. If the term that is
@@ -499,24 +455,3 @@ def getFunDecl (fvarId : FVarId) : CompilerM FunDecl := do
   return decl
 ```
 
-Correct:
-```lean
-def tagUntaggedGoals (parentTag : Name) (newSuffix : Name) (newGoals : List MVarId) : TacticM Unit := do
-  let mctx ← getMCtx
-  let mut numAnonymous := 0
-  for g in newGoals do
-    if mctx.isAnonymousMVar g then
-      numAnonymous := numAnonymous + 1
-  modifyMCtx fun mctx => Id.run do
-    let mut mctx := mctx
-    let mut idx  := 1
-    for g in newGoals do
-      if mctx.isAnonymousMVar g then
-        if numAnonymous == 1 then
-          mctx := mctx.setMVarUserName g parentTag
-        else
-          mctx := mctx.setMVarUserName g (parentTag ++ newSuffix.appendIndexAfter idx)
-        idx := idx + 1
-    pure mctx
-```
-

flake.lock

@@ -36,17 +36,17 @@
     },
     "nixpkgs-cadical": {
       "locked": {
-        "lastModified": 1740791350,
-        "narHash": "sha256-igS2Z4tVw5W/x3lCZeeadt0vcU9fxtetZ/RyrqsCRQ0=",
+        "lastModified": 1722221733,
+        "narHash": "sha256-sga9SrrPb+pQJxG1ttJfMPheZvDOxApFfwXCFO0H9xw=",
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "199169a2135e6b864a888e89a2ace345703c025d",
+        "rev": "12bf09802d77264e441f48e25459c10c93eada2e",
         "type": "github"
       },
       "original": {
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "199169a2135e6b864a888e89a2ace345703c025d",
+        "rev": "12bf09802d77264e441f48e25459c10c93eada2e",
         "type": "github"
       }
     },
@@ -67,30 +67,12 @@
         "type": "github"
       }
     },
-    "nixpkgs-older": {
-      "flake": false,
-      "locked": {
-        "lastModified": 1523316493,
-        "narHash": "sha256-5qJS+i5ECICPAKA6FhPLIWkhPKDnOZsZbh2PHYF1Kbs=",
-        "owner": "NixOS",
-        "repo": "nixpkgs",
-        "rev": "0b307aa73804bbd7a7172899e59ae0b8c347a62d",
-        "type": "github"
-      },
-      "original": {
-        "owner": "NixOS",
-        "repo": "nixpkgs",
-        "rev": "0b307aa73804bbd7a7172899e59ae0b8c347a62d",
-        "type": "github"
-      }
-    },
     "root": {
       "inputs": {
         "flake-utils": "flake-utils",
         "nixpkgs": "nixpkgs",
         "nixpkgs-cadical": "nixpkgs-cadical",
-        "nixpkgs-old": "nixpkgs-old",
-        "nixpkgs-older": "nixpkgs-older"
+        "nixpkgs-old": "nixpkgs-old"
       }
     },
     "systems": {

flake.nix

@@ -5,20 +5,17 @@
   # old nixpkgs used for portable release with older glibc (2.27)
   inputs.nixpkgs-old.url = "github:NixOS/nixpkgs/nixos-19.03";
   inputs.nixpkgs-old.flake = false;
-  # old nixpkgs used for portable release with older glibc (2.26)
-  inputs.nixpkgs-older.url = "github:NixOS/nixpkgs/0b307aa73804bbd7a7172899e59ae0b8c347a62d";
-  inputs.nixpkgs-older.flake = false;
-  # for cadical 2.1.2; sync with CMakeLists.txt by taking commit from https://www.nixhub.io/packages/cadical
-  inputs.nixpkgs-cadical.url = "github:NixOS/nixpkgs/199169a2135e6b864a888e89a2ace345703c025d";
+  # for cadical 1.9.5; sync with CMakeLists.txt
+  inputs.nixpkgs-cadical.url = "github:NixOS/nixpkgs/12bf09802d77264e441f48e25459c10c93eada2e";
   inputs.flake-utils.url = "github:numtide/flake-utils";
 
-  outputs = inputs: inputs.flake-utils.lib.eachDefaultSystem (system:
+  outputs = { self, nixpkgs, nixpkgs-old, flake-utils, ... }@inputs: flake-utils.lib.eachDefaultSystem (system:
     let
-      pkgs = import inputs.nixpkgs { inherit system; };
+      pkgs = import nixpkgs { inherit system; };
       # An old nixpkgs for creating releases with an old glibc
-      pkgsDist-old = import inputs.nixpkgs-older { inherit system; };
+      pkgsDist-old = import nixpkgs-old { inherit system; };
       # An old nixpkgs for creating releases with an old glibc
-      pkgsDist-old-aarch = import inputs.nixpkgs-old { localSystem.config = "aarch64-unknown-linux-gnu"; };
+      pkgsDist-old-aarch = import nixpkgs-old { localSystem.config = "aarch64-unknown-linux-gnu"; };
       pkgsCadical = import inputs.nixpkgs-cadical { inherit system; };
       cadical = if pkgs.stdenv.isLinux then
         # use statically-linked cadical on Linux to avoid glibc versioning troubles
@@ -63,7 +60,6 @@
           GLIBC_DEV = pkgsDist.glibc.dev;
           GCC_LIB = pkgsDist.gcc.cc.lib;
           ZLIB = pkgsDist.zlib;
-          # for CI coredumps
           GDB = pkgsDist.gdb;
         });
     in {

nix/bootstrap.nix

@@ -17,7 +17,7 @@ lib.warn "The Nix-based build is deprecated" rec {
     '';
   } // args // {
     src = args.realSrc or (sourceByRegex args.src [ "[a-z].*" "CMakeLists\.txt" ]);
-    cmakeFlags = ["-DSMALL_ALLOCATOR=ON" "-DUSE_MIMALLOC=OFF"] ++ (args.cmakeFlags or [ "-DSTAGE=1" "-DPREV_STAGE=./faux-prev-stage" "-DUSE_GITHASH=OFF" "-DCADICAL=${cadical}/bin/cadical" ]) ++ (args.extraCMakeFlags or extraCMakeFlags) ++ lib.optional (args.debug or debug) [ "-DCMAKE_BUILD_TYPE=Debug" ];
+    cmakeFlags = (args.cmakeFlags or [ "-DSTAGE=1" "-DPREV_STAGE=./faux-prev-stage" "-DUSE_GITHASH=OFF" "-DCADICAL=${cadical}/bin/cadical" ]) ++ (args.extraCMakeFlags or extraCMakeFlags) ++ lib.optional (args.debug or debug) [ "-DCMAKE_BUILD_TYPE=Debug" ];
     preConfigure = args.preConfigure or "" + ''
       # ignore absence of submodule
       sed -i 's!lake/Lake.lean!!' CMakeLists.txt

releases_drafts/environment.md

@@ -1,6 +0,0 @@
-**Breaking Changes**
-
-* The functions `Lean.Environment.importModules` and `Lean.Environment.finalizeImport` have been extended with a new parameter `loadExts : Bool := false` that enables environment extension state loading.
-  Their previous behavior corresponds to setting the flag to `true` but is only safe to do in combination with `enableInitializersExecution`; see also the `importModules` docstring.
-  The new default value `false` ensures the functions can be used correctly multiple times within the same process when environment extension access is not needed.
-  The wrapper function `Lean.Environment.withImportModules` now always calls `importModules` with `loadExts := false` as it is incompatible with extension loading.

script/benchReelabRss.lean

@@ -1,70 +0,0 @@
-import Lean.Data.Lsp
-open Lean
-open Lean.Lsp
-open Lean.JsonRpc
-
-/-!
-Tests language server memory use by repeatedly re-elaborate a given file.
-
-NOTE: only works on Linux for now.
-
-HACK: The line that is to be prepended with a space is hard-coded below to be sufficiently far down
-not to touch the imports for usual files.
--/
-
-def main (args : List String) : IO Unit := do
-  let leanCmd :: file :: iters :: args := args | panic! "usage: script <lean> <file> <#iterations> <server-args>..."
-  let uri := s!"file:///{file}"
-  Ipc.runWith leanCmd (#["--worker", "-DstderrAsMessages=false"] ++ args ++ #[uri]) do
-  -- for use with heaptrack:
-  --Ipc.runWith "heaptrack" (#[leanCmd, "--worker", "-DstderrAsMessages=false"] ++ args ++ #[uri]) do
-  --  -- heaptrack has no quiet mode??
-  --  let _ ← (← Ipc.stdout).getLine
-  --  let _ ← (← Ipc.stdout).getLine
-    let capabilities := {
-      textDocument? := some {
-        completion? := some {
-          completionItem? := some {
-            insertReplaceSupport? := true
-          }
-        }
-      }
-    }
-    Ipc.writeRequest ⟨0, "initialize", { capabilities : InitializeParams }⟩
-
-    let text ← IO.FS.readFile file
-    let mut requestNo : Nat := 1
-    let mut versionNo : Nat := 1
-    Ipc.writeNotification ⟨"textDocument/didOpen", {
-      textDocument := { uri := uri, languageId := "lean", version := 1, text := text } : DidOpenTextDocumentParams }⟩
-    for i in [0:iters.toNat!] do
-      if i > 0 then
-        versionNo := versionNo + 1
-        let pos := { line := 19, character := 0 }
-        let params : DidChangeTextDocumentParams := {
-          textDocument := {
-            uri      := uri
-            version? := versionNo
-          }
-          contentChanges := #[TextDocumentContentChangeEvent.rangeChange {
-            start := pos
-            «end» := pos
-          } " "]
-        }
-        let params := toJson params
-        Ipc.writeNotification ⟨"textDocument/didChange", params⟩
-        requestNo := requestNo + 1
-
-      let diags ← Ipc.collectDiagnostics requestNo uri versionNo
-      if let some diags := diags then
-        for diag in diags.param.diagnostics do
-          IO.eprintln diag.message
-      requestNo := requestNo + 1
-
-      let status ← IO.FS.readFile s!"/proc/{(← read).pid}/status"
-      for line in status.splitOn "\n" |>.filter (·.startsWith "RssAnon") do
-        IO.eprintln line
-
-    let _ ← Ipc.collectDiagnostics requestNo uri versionNo
-    (← Ipc.stdin).writeLspMessage (Message.notification "exit" none)
-    discard <| Ipc.waitForExit

script/merge_remote.py

@@ -1,167 +0,0 @@
-#!/usr/bin/env python3
-
-"""
-Merge a tag into a branch on a GitHub repository.
-
-This script checks if a specified tag can be merged cleanly into a branch and performs
-the merge if possible. If the merge cannot be done cleanly, it prints a helpful message.
-
-Usage:
-    python3 merge_remote.py <org/repo> <branch> <tag>
-
-Arguments:
-    org/repo: GitHub repository in the format 'organization/repository'
-    branch: The target branch to merge into
-    tag: The tag to merge from
-
-Example:
-    python3 merge_remote.py leanprover/mathlib4 stable v4.6.0
-
-The script uses the GitHub CLI (`gh`), so make sure it's installed and authenticated.
-"""
-
-import argparse
-import subprocess
-import sys
-import tempfile
-import os
-import shutil
-
-
-def run_command(command, check=True, capture_output=True):
-    """Run a shell command and return the result."""
-    try:
-        result = subprocess.run(
-            command,
-            check=check,
-            shell=True,
-            text=True,
-            capture_output=capture_output
-        )
-        return result
-    except subprocess.CalledProcessError as e:
-        if capture_output:
-            print(f"Command failed: {command}")
-            print(f"Error: {e.stderr}")
-        return e
-
-
-def clone_repo(repo, temp_dir):
-    """Clone the repository to a temporary directory using shallow clone."""
-    print(f"Shallow cloning {repo}...")
-    # Keep the shallow clone for efficiency
-    clone_result = run_command(f"gh repo clone {repo} {temp_dir} -- --depth=1", check=False)
-    if clone_result.returncode != 0:
-        print(f"Failed to clone repository {repo}.")
-        print(f"Error: {clone_result.stderr}")
-        return False
-    return True
-
-
-def check_and_merge(repo, branch, tag, temp_dir):
-    """Check if tag can be merged into branch and perform the merge if possible."""
-    # Change to the temporary directory
-    os.chdir(temp_dir)
-    
-    # First fetch the specific remote branch with its history
-    print(f"Fetching branch '{branch}'...")
-    fetch_branch = run_command(f"git fetch origin {branch}:refs/remotes/origin/{branch} --update-head-ok")
-    if fetch_branch.returncode != 0:
-        print(f"Error: Failed to fetch branch '{branch}'.")
-        return False
-    
-    # Then fetch the specific tag
-    print(f"Fetching tag '{tag}'...")
-    fetch_tag = run_command(f"git fetch origin tag {tag}")
-    if fetch_tag.returncode != 0:
-        print(f"Error: Failed to fetch tag '{tag}'.")
-        return False
-    
-    # Check if branch exists now that we've fetched it
-    branch_check = run_command(f"git branch -r | grep origin/{branch}")
-    if branch_check.returncode != 0:
-        print(f"Error: Branch '{branch}' does not exist in repository.")
-        return False
-
-    # Check if tag exists
-    tag_check = run_command(f"git tag -l {tag}")
-    if tag_check.returncode != 0 or not tag_check.stdout.strip():
-        print(f"Error: Tag '{tag}' does not exist in repository.")
-        return False
-
-    # Checkout the branch
-    print(f"Checking out branch '{branch}'...")
-    checkout_result = run_command(f"git checkout -b {branch} origin/{branch}")
-    if checkout_result.returncode != 0:
-        return False
-
-    # Try merging the tag in a dry-run to check if it can be merged cleanly
-    print(f"Checking if {tag} can be merged cleanly into {branch}...")
-    merge_check = run_command(f"git merge --no-commit --no-ff {tag}", check=False)
-    
-    if merge_check.returncode != 0:
-        print(f"Cannot merge {tag} cleanly into {branch}.")
-        print("Merge conflicts would occur. Aborting merge.")
-        run_command("git merge --abort")
-        return False
-    
-    # Abort the test merge
-    run_command("git reset --hard HEAD")
-    
-    # Now perform the actual merge and push to remote
-    print(f"Merging {tag} into {branch}...")
-    merge_result = run_command(f"git merge {tag} --no-edit")
-    if merge_result.returncode != 0:
-        print(f"Failed to merge {tag} into {branch}.")
-        return False
-    
-    print(f"Pushing changes to remote...")
-    push_result = run_command(f"git push origin {branch}")
-    if push_result.returncode != 0:
-        print(f"Failed to push changes to remote.")
-        return False
-    
-    print(f"Successfully merged {tag} into {branch} and pushed to remote.")
-    return True
-
-
-def main():
-    parser = argparse.ArgumentParser(
-        description="Merge a tag into a branch on a GitHub repository.",
-        formatter_class=argparse.RawDescriptionHelpFormatter,
-        epilog="""
-Examples:
-  %(prog)s leanprover/mathlib4 stable v4.6.0    Merge tag v4.6.0 into stable branch
-
-The script will:
-1. Clone the repository
-2. Check if the tag and branch exist
-3. Check if the tag can be merged cleanly into the branch
-4. Perform the merge and push to remote if possible
-        """
-    )
-    parser.add_argument("repo", help="GitHub repository in the format 'organization/repository'")
-    parser.add_argument("branch", help="The target branch to merge into")
-    parser.add_argument("tag", help="The tag to merge from")
-    
-    args = parser.parse_args()
-    
-    # Create a temporary directory for the repository
-    temp_dir = tempfile.mkdtemp()
-    try:
-        # Clone the repository
-        if not clone_repo(args.repo, temp_dir):
-            sys.exit(1)
-        
-        # Check if the tag can be merged and perform the merge
-        if not check_and_merge(args.repo, args.branch, args.tag, temp_dir):
-            sys.exit(1)
-        
-    finally:
-        # Clean up the temporary directory
-        print(f"Cleaning up temporary files...")
-        shutil.rmtree(temp_dir)
-
-
-if __name__ == "__main__":
-    main() 

script/prepare-llvm-mingw.sh

@@ -25,10 +25,7 @@ cp llvm/lib/clang/*/include/{std*,__std*,limits}.h stage1/include/clang
 echo '
 // https://docs.microsoft.com/en-us/windows/win32/api/errhandlingapi/nf-errhandlingapi-seterrormode
 #define SEM_FAILCRITICALERRORS 0x0001
-__declspec(dllimport) __stdcall unsigned int SetErrorMode(unsigned int uMode);
-// https://docs.microsoft.com/en-us/windows/console/setconsoleoutputcp
-#define CP_UTF8 65001
-__declspec(dllimport) __stdcall int SetConsoleOutputCP(unsigned int wCodePageID);' > stage1/include/clang/windows.h
+__declspec(dllimport) __stdcall unsigned int SetErrorMode(unsigned int uMode);' > stage1/include/clang/windows.h
 # COFF dependencies
 cp /clang64/lib/{crtbegin,crtend,crt2,dllcrt2}.o stage1/lib/
 # runtime

script/release_checklist.py

@@ -7,13 +7,6 @@ import base64
 import subprocess
 import sys
 import os
-# Import run_command from merge_remote.py
-from merge_remote import run_command
-
-def debug(verbose, message):
-    """Print debug message if verbose mode is enabled."""
-    if verbose:
-        print(f"    [DEBUG] {message}")
 
 def parse_repos_config(file_path):
     with open(file_path, "r") as f:
@@ -92,12 +85,9 @@ def parse_version(version_str):
 
 def is_version_gte(version1, version2):
     """Check if version1 >= version2, including proper handling of release candidates."""
-    # Check if version1 is a nightly toolchain
-    if version1.startswith("leanprover/lean4:nightly-"):
-        return False
     return parse_version(version1) >= parse_version(version2)
 
-def is_merged_into_stable(repo_url, tag_name, stable_branch, github_token, verbose=False):
+def is_merged_into_stable(repo_url, tag_name, stable_branch, github_token):
     # First get the commit SHA for the tag
     api_base = repo_url.replace("https://github.com/", "https://api.github.com/repos/")
     headers = {'Authorization': f'token {github_token}'} if github_token else {}
@@ -105,7 +95,6 @@ def is_merged_into_stable(repo_url, tag_name, stable_branch, github_token, verbo
     # Get tag's commit SHA
     tag_response = requests.get(f"{api_base}/git/refs/tags/{tag_name}", headers=headers)
     if tag_response.status_code != 200:
-        debug(verbose, f"Could not fetch tag {tag_name}, status code: {tag_response.status_code}")
         return False
     
     # Handle both single object and array responses
@@ -114,48 +103,22 @@ def is_merged_into_stable(repo_url, tag_name, stable_branch, github_token, verbo
         # Find the exact matching tag in the list
         matching_tags = [tag for tag in tag_data if tag['ref'] == f'refs/tags/{tag_name}']
         if not matching_tags:
-            debug(verbose, f"No matching tag found for {tag_name} in response list")
             return False
         tag_sha = matching_tags[0]['object']['sha']
     else:
         tag_sha = tag_data['object']['sha']
-    
-    # Check if the tag is an annotated tag and get the actual commit SHA
-    if tag_data.get('object', {}).get('type') == 'tag' or (
-        isinstance(tag_data, list) and 
-        matching_tags and 
-        matching_tags[0].get('object', {}).get('type') == 'tag'):
-        
-        # Get the commit that this tag points to
-        tag_obj_response = requests.get(f"{api_base}/git/tags/{tag_sha}", headers=headers)
-        if tag_obj_response.status_code == 200:
-            tag_obj = tag_obj_response.json()
-            if 'object' in tag_obj and tag_obj['object']['type'] == 'commit':
-                commit_sha = tag_obj['object']['sha']
-                debug(verbose, f"Tag is annotated. Resolved commit SHA: {commit_sha}")
-                tag_sha = commit_sha  # Use the actual commit SHA
-    
+
     # Get commits on stable branch containing this SHA
     commits_response = requests.get(
         f"{api_base}/commits?sha={stable_branch}&per_page=100",
         headers=headers
     )
     if commits_response.status_code != 200:
-        debug(verbose, f"Could not fetch commits for branch {stable_branch}, status code: {commits_response.status_code}")
         return False
 
     # Check if any commit in stable's history matches our tag's SHA
     stable_commits = [commit['sha'] for commit in commits_response.json()]
-    
-    is_merged = tag_sha in stable_commits
-    
-    debug(verbose, f"Tag SHA: {tag_sha}")
-    debug(verbose, f"First 5 stable commits: {stable_commits[:5]}")
-    debug(verbose, f"Total stable commits fetched: {len(stable_commits)}")
-    if not is_merged:
-        debug(verbose, f"Tag SHA not found in first {len(stable_commits)} commits of stable branch")
-    
-    return is_merged
+    return tag_sha in stable_commits
 
 def is_release_candidate(version):
     return "-rc" in version
@@ -215,75 +178,51 @@ def check_bump_branch_toolchain(url, bump_branch, github_token):
     print(f"  ✅ Bump branch correctly uses toolchain: {content}")
     return True
 
-def pr_exists_with_title(repo_url, title, github_token):
-    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + "/pulls"
-    headers = {'Authorization': f'token {github_token}'} if github_token else {}
-    params = {'state': 'open'}
-    response = requests.get(api_url, headers=headers, params=params)
-    if response.status_code != 200:
-        return None
-    pull_requests = response.json()
-    for pr in pull_requests:
-        if pr['title'] == title:
-            return pr['number'], pr['html_url']
-    return None
-
 def main():
-    parser = argparse.ArgumentParser(description="Check release status of Lean4 repositories")
-    parser.add_argument("toolchain", help="The toolchain version to check (e.g., v4.6.0)")
-    parser.add_argument("--verbose", "-v", action="store_true", help="Enable verbose debugging output")
-    parser.add_argument("--dry-run", action="store_true", help="Dry run mode (no actions taken)")
-    args = parser.parse_args()
-
     github_token = get_github_token()
-    toolchain = args.toolchain
-    verbose = args.verbose
-    # dry_run = args.dry_run  # Not used yet but available for future implementation
-    
+
+    if len(sys.argv) != 2:
+        print("Usage: python3 release_checklist.py <toolchain>")
+        sys.exit(1)
+
+    toolchain = sys.argv[1]
     stripped_toolchain = strip_rc_suffix(toolchain)
     lean_repo_url = "https://github.com/leanprover/lean4"
 
-    # Track repository status
-    repo_status = {}  # Will store True for success, False for failure
-
-    # Preliminary checks for lean4 itself
+    # Preliminary checks
     print("\nPerforming preliminary checks...")
-    lean4_success = True
 
     # Check for branch releases/v4.Y.0
     version_major, version_minor, _ = map(int, stripped_toolchain.lstrip('v').split('.'))
     branch_name = f"releases/v{version_major}.{version_minor}.0"
-    if not branch_exists(lean_repo_url, branch_name, github_token):
-        print(f"  ❌ Branch {branch_name} does not exist")
-        lean4_success = False
-    else:
+    if branch_exists(lean_repo_url, branch_name, github_token):
         print(f"  ✅ Branch {branch_name} exists")
+
         # Check CMake version settings
-        if not check_cmake_version(lean_repo_url, branch_name, version_major, version_minor, github_token):
-            lean4_success = False
-
-    # Check for tag and release page
-    if not tag_exists(lean_repo_url, toolchain, github_token):
-        print(f"  ❌ Tag {toolchain} does not exist.")
-        lean4_success = False
+        check_cmake_version(lean_repo_url, branch_name, version_major, version_minor, github_token)
     else:
+        print(f"  ❌ Branch {branch_name} does not exist")
+
+    # Check for tag v4.X.Y(-rcZ)
+    if tag_exists(lean_repo_url, toolchain, github_token):
         print(f"  ✅ Tag {toolchain} exists")
-
-    if not release_page_exists(lean_repo_url, toolchain, github_token):
-        print(f"  ❌ Release page for {toolchain} does not exist")
-        lean4_success = False
     else:
+        print(f"  ❌ Tag {toolchain} does not exist.")
+
+    # Check for release page
+    if release_page_exists(lean_repo_url, toolchain, github_token):
         print(f"  ✅ Release page for {toolchain} exists")
+
+        # Check the first line of the release notes
         release_notes = get_release_notes(lean_repo_url, toolchain, github_token)
-        if not (release_notes and toolchain in release_notes.splitlines()[0].strip()):
+        if release_notes and toolchain in release_notes.splitlines()[0].strip():
+            print(f"  ✅ Release notes look good.")
+        else:
             previous_minor_version = version_minor - 1
             previous_release = f"v{version_major}.{previous_minor_version}.0"
             print(f"  ❌ Release notes not published. Please run `script/release_notes.py --since {previous_release}` on branch `{branch_name}`.")
-            lean4_success = False
-        else:
-            print(f"  ✅ Release notes look good.")
-
-    repo_status["lean4"] = lean4_success
+    else:
+        print(f"  ❌ Release page for {toolchain} does not exist")
 
     # Load repositories and perform further checks
     print("\nChecking repositories...")
@@ -294,100 +233,50 @@ def main():
     for repo in repos:
         name = repo["name"]
         url = repo["url"]
-        org_repo = extract_org_repo_from_url(url)
         branch = repo["branch"]
         check_stable = repo["stable-branch"]
         check_tag = repo.get("toolchain-tag", True)
         check_bump = repo.get("bump-branch", False)
-        dependencies = repo.get("dependencies", [])
 
         print(f"\nRepository: {name}")
 
-        # Check if any dependencies have failed
-        failed_deps = [dep for dep in dependencies if dep in repo_status and not repo_status[dep]]
-        if failed_deps:
-            print(f"  🟡  Dependencies not ready: {', '.join(failed_deps)}")
-            repo_status[name] = False
-            continue
-
-        # Initialize success flag for this repo
-        success = True
-
         # Check if branch is on at least the target toolchain
         lean_toolchain_content = get_branch_content(url, branch, "lean-toolchain", github_token)
         if lean_toolchain_content is None:
             print(f"  ❌ No lean-toolchain file found in {branch} branch")
-            repo_status[name] = False
             continue
-        
+
         on_target_toolchain = is_version_gte(lean_toolchain_content.strip(), toolchain)
         if not on_target_toolchain:
             print(f"  ❌ Not on target toolchain (needs ≥ {toolchain}, but {branch} is on {lean_toolchain_content.strip()})")
-            pr_title = f"chore: bump toolchain to {toolchain}"
-            pr_info = pr_exists_with_title(url, pr_title, github_token)
-            if pr_info:
-                pr_number, pr_url = pr_info
-                print(f"  ✅ PR with title '{pr_title}' exists: #{pr_number} ({pr_url})")
-            else:
-                print(f"  ❌ PR with title '{pr_title}' does not exist")
-                print(f"     Run `script/release_steps.py {toolchain} {name}` to create it")
-            repo_status[name] = False
             continue
         print(f"  ✅ On compatible toolchain (>= {toolchain})")
 
+        # Only check for tag if toolchain-tag is true
         if check_tag:
-            tag_exists_initially = tag_exists(url, toolchain, github_token)
-            if not tag_exists_initially:                
-                if args.dry_run:
-                    print(f"  ❌ Tag {toolchain} does not exist. Run `script/push_repo_release_tag.py {org_repo} {branch} {toolchain}`.")
-                    repo_status[name] = False
-                    continue
-                else:
-                    print(f"  … Tag {toolchain} does not exist. Running `script/push_repo_release_tag.py {org_repo} {branch} {toolchain}`...")
-                    
-                    # Run the script to create the tag
-                    subprocess.run(["script/push_repo_release_tag.py", org_repo, branch, toolchain])
-                    
-                    # Check again if the tag exists now
-                    if not tag_exists(url, toolchain, github_token):
-                        print(f"  ❌ Manual intervention required.")
-                        repo_status[name] = False
-                        continue
-            
-            # This will print in all successful cases - whether tag existed initially or was created successfully
-            print(f"  ✅ Tag {toolchain} exists")
+            if not tag_exists(url, toolchain, github_token):
+                print(f"  ❌ Tag {toolchain} does not exist. Run `script/push_repo_release_tag.py {extract_org_repo_from_url(url)} {branch} {toolchain}`.")
+            else:
+                print(f"  ✅ Tag {toolchain} exists")
 
+        # Only check merging into stable if stable-branch is true and not a release candidate
         if check_stable and not is_release_candidate(toolchain):
-            if not is_merged_into_stable(url, toolchain, "stable", github_token, verbose):
-                org_repo = extract_org_repo_from_url(url)
+            if not is_merged_into_stable(url, toolchain, "stable", github_token):
                 print(f"  ❌ Tag {toolchain} is not merged into stable")
-                print(f"     Run `script/merge_remote.py {org_repo} stable {toolchain}` to merge it")
-                repo_status[name] = False
-                continue
-            print(f"  ✅ Tag {toolchain} is merged into stable")
+            else:
+                print(f"  ✅ Tag {toolchain} is merged into stable")
 
+        # Check for bump branch if configured
         if check_bump:
             next_version = get_next_version(toolchain)
             bump_branch = f"bump/{next_version}"
-            if not branch_exists(url, bump_branch, github_token):
-                if args.dry_run:
-                    print(f"  ❌ Bump branch {bump_branch} does not exist. Run `gh api -X POST /repos/{org_repo}/git/refs -f ref=refs/heads/{bump_branch} -f sha=$(gh api /repos/{org_repo}/git/refs/heads/{branch} --jq .object.sha)` to create it.")
-                    repo_status[name] = False
-                    continue
-                print(f"  … Bump branch {bump_branch} does not exist. Creating it...")
-                result = run_command(f"gh api -X POST /repos/{org_repo}/git/refs -f ref=refs/heads/{bump_branch} -f sha=$(gh api /repos/{org_repo}/git/refs/heads/{branch} --jq .object.sha)", check=False)
-                if result.returncode != 0:
-                    print(f"  ❌ Failed to create bump branch {bump_branch}")
-                    repo_status[name] = False
-                    continue
-            print(f"  ✅ Bump branch {bump_branch} exists")
-            if not check_bump_branch_toolchain(url, bump_branch, github_token):
-                repo_status[name] = False
-                continue
+            if branch_exists(url, bump_branch, github_token):
+                print(f"  ✅ Bump branch {bump_branch} exists")
+                check_bump_branch_toolchain(url, bump_branch, github_token)
+            else:
+                print(f"  ❌ Bump branch {bump_branch} does not exist")
 
-        repo_status[name] = success
-
-    # Final check for lean4 master branch
+    # Check lean4 master branch for next development cycle
     print("\nChecking lean4 master branch configuration...")
     next_version = get_next_version(toolchain)
     next_minor = int(next_version.split('.')[1])

script/release_notes.py

@@ -65,21 +65,20 @@ def format_markdown_description(pr_number, description):
     link = f"[#{pr_number}](https://github.com/leanprover/lean4/pull/{pr_number})"
     return f"{link} {description}"
 
-def commit_types():
-    # see doc/dev/commit_convention.md
-    return ['feat', 'fix', 'doc', 'style', 'refactor', 'test', 'chore', 'perf']
-
 def count_commit_types(commits):
     counts = {
         'total': len(commits),
+        'feat': 0,
+        'fix': 0,
+        'refactor': 0,
+        'doc': 0,
+        'chore': 0
     }
-    for commit_type in commit_types():
-        counts[commit_type] = 0
     
     for _, first_line, _ in commits:
-        for commit_type in commit_types():
-            if first_line.startswith(f'{commit_type}:'):
-                counts[commit_type] += 1
+        for commit_type in ['feat:', 'fix:', 'refactor:', 'doc:', 'chore:']:
+            if first_line.startswith(commit_type):
+                counts[commit_type.rstrip(':')] += 1
                 break
     
     return counts
@@ -159,9 +158,8 @@ def main():
     counts = count_commit_types(commits)
     print(f"For this release, {counts['total']} changes landed. "
           f"In addition to the {counts['feat']} feature additions and {counts['fix']} fixes listed below "
-          f"there were {counts['refactor']} refactoring changes, {counts['doc']} documentation improvements, "
-          f"{counts['perf']} performance improvements, {counts['test']} improvements to the test suite "
-          f"and {counts['style'] + counts['chore']} other changes.\n")
+          f"there were {counts['refactor']} refactoring changes, {counts['doc']} documentation improvements "
+          f"and {counts['chore']} chores.\n")
 
     section_order = sort_sections_order()
     sorted_changelog = sorted(changelog.items(), key=lambda item: section_order.index(format_section_title(item[0])) if format_section_title(item[0]) in section_order else len(section_order))
@@ -170,12 +168,7 @@ def main():
         section_title = format_section_title(label) if label != "Uncategorised" else "Uncategorised"
         print(f"## {section_title}\n")
         for _, entry in sorted(entries, key=lambda x: x[0]):
-            # Split entry into lines and indent all lines after the first
-            lines = entry.splitlines()
-            print(f"* {lines[0]}")
-            for line in lines[1:]:
-                print(f"  {line}")
-            print()  # Empty line after each entry
+            print(f"* {entry}\n")
 
 if __name__ == "__main__":
     main()

script/release_repos.yml

@@ -63,9 +63,7 @@ repositories:
     toolchain-tag: true
     stable-branch: false
     branch: main
-    dependencies:
-      - Cli
-      - Batteries
+    dependencies: []
 
   - name: plausible
     url: https://github.com/leanprover-community/plausible
@@ -87,7 +85,6 @@ repositories:
       - Batteries
       - doc-gen4
       - import-graph
-      - plausible
 
   - name: REPL
     url: https://github.com/leanprover-community/repl

script/release_steps.py

@@ -1,154 +0,0 @@
-#!/usr/bin/env python3
-
-"""
-Generate release steps script for Lean4 repositories.
-
-This script helps automate the release process for Lean4 and its dependent repositories
-by generating step-by-step instructions for updating toolchains, creating tags,
-and managing branches.
-
-Usage:
-    python3 release_steps.py <version> <repo>
-
-Arguments:
-    version: The version to set in the lean-toolchain file (e.g., v4.6.0)
-    repo: A substring of the repository name as specified in release_repos.yml
-
-Example:
-    python3 release_steps.py v4.6.0 mathlib
-    python3 release_steps.py v4.6.0 batt
-
-The script reads repository configurations from release_repos.yml in the same directory.
-Each repository may have specific requirements for:
-- Branch management
-- Toolchain updates
-- Dependency updates
-- Tagging conventions
-- Stable branch handling
-"""
-
-import argparse
-import yaml
-import os
-import sys
-import re
-
-def load_repos_config(file_path):
-    with open(file_path, "r") as f:
-        return yaml.safe_load(f)["repositories"]
-
-def find_repo(repo_substring, config):
-    pattern = re.compile(re.escape(repo_substring), re.IGNORECASE)
-    matching_repos = [r for r in config if pattern.search(r["name"])]
-    if not matching_repos:
-        print(f"Error: No repository matching '{repo_substring}' found in configuration.")
-        sys.exit(1)
-    if len(matching_repos) > 1:
-        print(f"Error: Multiple repositories matching '{repo_substring}' found in configuration: {', '.join(r['name'] for r in matching_repos)}")
-        sys.exit(1)
-    return matching_repos[0]
-
-def generate_script(repo, version, config):
-    repo_config = find_repo(repo, config)
-    repo_name = repo_config['name']
-    repo_url = repo_config['url']
-    # Extract the last component of the URL, removing the .git extension if present
-    repo_dir = repo_url.split('/')[-1].replace('.git', '')
-    default_branch = repo_config.get("branch", "main")
-    dependencies = repo_config.get("dependencies", [])
-    requires_tagging = repo_config.get("toolchain-tag", True)
-    has_stable_branch = repo_config.get("stable-branch", True)
-
-    script_lines = [
-        f"cd {repo_dir}",
-        "git fetch",
-        f"git checkout {default_branch} && git pull",
-        f"git checkout -b bump_to_{version}",
-        f"echo leanprover/lean4:{version} > lean-toolchain",
-    ]
-
-    # Special cases for specific repositories
-    if repo_name == "REPL":
-        script_lines.extend([
-            "lake update",
-            "cd test/Mathlib",
-            f"perl -pi -e 's/rev = \"v\\d+\\.\\d+\\.\\d+(-rc\\d+)?\"/rev = \"{version}\"/g' lakefile.toml",
-            f"echo leanprover/lean4:{version} > lean-toolchain",
-            "lake update",
-            "cd ../..",
-            "./test.sh"
-        ])
-    elif dependencies:
-        script_lines.append('echo "Please update the dependencies in lakefile.{lean,toml}"')
-        script_lines.append("lake update")
-
-    script_lines.append("")
-
-    script_lines.extend([
-        f'git commit -am "chore: bump toolchain to {version}"',
-        ""
-    ])
-
-    if re.search(r'rc\d+$', version) and repo_name in ["Batteries", "Mathlib"]:
-        script_lines.extend([
-            "echo 'This repo has nightly-testing infrastructure'",
-            f"git merge origin/bump/{version.split('-rc')[0]}",
-            "echo 'Please resolve any conflicts.'",
-            ""
-        ])
-    if repo_name != "Mathlib":
-        script_lines.extend([
-            "lake build && if lake check-test; then lake test; fi",
-            ""
-        ])
-
-    script_lines.extend([
-        'gh pr create --title "chore: bump toolchain to ' + version + '" --body ""',
-        "echo 'Please review the PR and merge it.'",
-        ""
-    ])
-
-    # Special cases for specific repositories
-    if repo_name == "ProofWidgets4":
-        script_lines.append(f"echo 'Note: Follow the version convention of the repository for tagging.'")
-    elif requires_tagging:
-        script_lines.append(f"git checkout {default_branch} && git pull")
-        script_lines.append(f'[ "$(cat lean-toolchain)" = "leanprover/lean4:{version}" ] && git tag -a {version} -m \'Release {version}\' && git push origin --tags || echo "Error: lean-toolchain does not contain expected version {version}"')
-
-    if has_stable_branch:
-        script_lines.extend([
-            "git checkout stable && git pull",
-            f"git merge {version} --no-edit",
-            "git push origin stable"
-        ])
-
-    return "\n".join(script_lines)
-
-def main():
-    parser = argparse.ArgumentParser(
-        description="Generate release steps script for Lean4 repositories.",
-        formatter_class=argparse.RawDescriptionHelpFormatter,
-        epilog="""
-Examples:
-  %(prog)s v4.6.0 mathlib    Generate steps for updating Mathlib to v4.6.0
-  %(prog)s v4.6.0 batt       Generate steps for updating Batteries to v4.6.0
-  
-The script will generate shell commands to:
-1. Update the lean-toolchain file
-2. Create appropriate branches and commits
-3. Create pull requests
-4. Create version tags
-5. Update stable branches where applicable"""
-    )
-    parser.add_argument("version", help="The version to set in the lean-toolchain file (e.g., v4.6.0)")
-    parser.add_argument("repo", help="A substring of the repository name as specified in release_repos.yml")
-    args = parser.parse_args()
-
-    config_path = os.path.join(os.path.dirname(__file__), "release_repos.yml")
-    config = load_repos_config(config_path)
-
-    script = generate_script(args.repo, args.version, config)
-    print(script)
-
-if __name__ == "__main__":
-    main()

src/CMakeLists.txt

@@ -10,7 +10,7 @@ endif()
 include(ExternalProject)
 project(LEAN CXX C)
 set(LEAN_VERSION_MAJOR 4)
-set(LEAN_VERSION_MINOR 20)
+set(LEAN_VERSION_MINOR 18)
 set(LEAN_VERSION_PATCH 0)
 set(LEAN_VERSION_IS_RELEASE 0)  # This number is 1 in the release revision, and 0 otherwise.
 set(LEAN_SPECIAL_VERSION_DESC "" CACHE STRING "Additional version description like 'nightly-2018-03-11'")
@@ -20,11 +20,6 @@ if (LEAN_SPECIAL_VERSION_DESC)
 elseif (NOT LEAN_VERSION_IS_RELEASE)
   string(APPEND LEAN_VERSION_STRING "-pre")
 endif()
-if (LEAN_VERSION_IS_RELEASE)
-  set(LEAN_MANUAL_ROOT "https://lean-lang.org/doc/reference/${LEAN_VERSION_STRING}/")
-else()
-  set(LEAN_MANUAL_ROOT "")
-endif()
 
 set(LEAN_PLATFORM_TARGET "" CACHE STRING "LLVM triple of the target platform")
 if (NOT LEAN_PLATFORM_TARGET)
@@ -74,13 +69,12 @@ option(TRACK_LIVE_EXPRS    "TRACK_LIVE_EXPRS" OFF)
 option(CUSTOM_ALLOCATORS   "CUSTOM_ALLOCATORS" ON)
 option(SAVE_SNAPSHOT       "SAVE_SNAPSHOT" ON)
 option(SAVE_INFO           "SAVE_INFO" ON)
-option(SMALL_ALLOCATOR     "SMALL_ALLOCATOR" OFF)
+option(SMALL_ALLOCATOR     "SMALL_ALLOCATOR" ON)
 option(MMAP                "MMAP" ON)
 option(LAZY_RC             "LAZY_RC" OFF)
 option(RUNTIME_STATS       "RUNTIME_STATS" OFF)
 option(BSYMBOLIC "Link with -Bsymbolic to reduce call overhead in shared libraries (Linux)" ON)
 option(USE_GMP "USE_GMP" ON)
-option(USE_MIMALLOC "use mimalloc" ON)
 
 # development-specific options
 option(CHECK_OLEAN_VERSION "Only load .olean files compiled with the current version of Lean" OFF)
@@ -93,11 +87,6 @@ if ("${LAZY_RC}" MATCHES "ON")
   set(LEAN_LAZY_RC "#define LEAN_LAZY_RC")
 endif()
 
-if (USE_MIMALLOC)
-  set(SMALL_ALLOCATOR OFF)
-  set(LEAN_MIMALLOC "#define LEAN_MIMALLOC")
-endif()
-
 if ("${SMALL_ALLOCATOR}" MATCHES "ON")
   set(LEAN_SMALL_ALLOCATOR "#define LEAN_SMALL_ALLOCATOR")
 endif()
@@ -155,12 +144,11 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
   # do not import the world from windows.h using appropriately named flag
   string(APPEND LEAN_EXTRA_CXX_FLAGS " -D WIN32_LEAN_AND_MEAN")
   # DLLs must go next to executables on Windows
-  set(CMAKE_RELATIVE_LIBRARY_OUTPUT_DIRECTORY "bin")
+  set(CMAKE_LIBRARY_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/bin")
 else()
-  set(CMAKE_RELATIVE_LIBRARY_OUTPUT_DIRECTORY "lib/lean")
+  set(CMAKE_LIBRARY_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/lib/lean")
 endif()
 
-set(CMAKE_LIBRARY_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/${CMAKE_RELATIVE_LIBRARY_OUTPUT_DIRECTORY}")
 set(CMAKE_ARCHIVE_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/lib/lean")
 
 # OSX default thread stack size is very small. Moreover, in Debug mode, each new stack frame consumes a lot of extra memory.
@@ -466,20 +454,20 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Linux")
   string(APPEND CMAKE_CXX_FLAGS " -fPIC -ftls-model=initial-exec")
   string(APPEND LEANC_EXTRA_CC_FLAGS " -fPIC")
   string(APPEND TOOLCHAIN_SHARED_LINKER_FLAGS " -Wl,-rpath=\\$$ORIGIN/..:\\$$ORIGIN")
-  string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/lean/libLake.a.export -Wl,--no-whole-archive")
-  string(APPEND CMAKE_EXE_LINKER_FLAGS " -Wl,-rpath=$ORIGIN/../lib:$ORIGIN/../lib/lean")
+  string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libLake.a.export -Wl,--no-whole-archive")
+  string(APPEND CMAKE_EXE_LINKER_FLAGS " -Wl,-rpath=\\\$ORIGIN/../lib:\\\$ORIGIN/../lib/lean")
 elseif(${CMAKE_SYSTEM_NAME} MATCHES "Darwin")
   string(APPEND CMAKE_CXX_FLAGS " -ftls-model=initial-exec")
   string(APPEND INIT_SHARED_LINKER_FLAGS " -install_name @rpath/libInit_shared.dylib")
   string(APPEND LEANSHARED_1_LINKER_FLAGS " -install_name @rpath/libleanshared_1.dylib")
   string(APPEND LEANSHARED_LINKER_FLAGS " -install_name @rpath/libleanshared.dylib")
-  string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libLake.a.export -install_name @rpath/libLake_shared.dylib")
+  string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/temp/libLake.a.export -install_name @rpath/libLake_shared.dylib")
   string(APPEND CMAKE_EXE_LINKER_FLAGS " -Wl,-rpath,@executable_path/../lib -Wl,-rpath,@executable_path/../lib/lean")
 elseif(${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
   string(APPEND CMAKE_CXX_FLAGS " -fPIC")
   string(APPEND LEANC_EXTRA_CC_FLAGS " -fPIC")
 elseif(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
-  string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,--out-implib,${CMAKE_BINARY_DIR}/lib/lean/libLake_shared.dll.a -Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/lean/libLake.a.export -Wl,--no-whole-archive")
+  string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,--out-implib,${CMAKE_BINARY_DIR}/lib/lean/libLake_shared.dll.a -Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libLake.a.export -Wl,--no-whole-archive")
 endif()
 
 if(${CMAKE_SYSTEM_NAME} MATCHES "Linux")
@@ -526,16 +514,7 @@ if(USE_GITHASH)
     message(STATUS "git commit sha1: ${GIT_SHA1}")
   endif()
 else()
-  if(USE_LAKE AND ${STAGE} EQUAL 0)
-    # we need to embed *some* hash for Lake to invalidate stage 1 on stage 0 changes
-    execute_process(
-        COMMAND git ls-tree HEAD "${CMAKE_CURRENT_SOURCE_DIR}/../../stage0" --object-only
-        OUTPUT_VARIABLE GIT_SHA1
-        OUTPUT_STRIP_TRAILING_WHITESPACE)
-    message(STATUS "stage0 sha1: ${GIT_SHA1}")
-  else()
-    set(GIT_SHA1 "")
-  endif()
+  set(GIT_SHA1 "")
 endif()
 configure_file("${LEAN_SOURCE_DIR}/githash.h.in" "${LEAN_BINARY_DIR}/githash.h")
 
@@ -554,9 +533,6 @@ else()
   set(LEAN_IS_STAGE0 "#define LEAN_IS_STAGE0 0")
 endif()
 configure_file("${LEAN_SOURCE_DIR}/config.h.in" "${LEAN_BINARY_DIR}/include/lean/config.h")
-if (USE_MIMALLOC)
-  file(COPY "${LEAN_BINARY_DIR}/../mimalloc/src/mimalloc/include/mimalloc.h" DESTINATION "${LEAN_BINARY_DIR}/include/lean")
-endif()
 install(DIRECTORY ${LEAN_BINARY_DIR}/include/ DESTINATION include)
 configure_file(${LEAN_SOURCE_DIR}/lean.mk.in ${LEAN_BINARY_DIR}/share/lean/lean.mk)
 install(DIRECTORY ${LEAN_BINARY_DIR}/share/ DESTINATION share)
@@ -565,9 +541,6 @@ include_directories(${LEAN_SOURCE_DIR})
 include_directories(${CMAKE_BINARY_DIR})  # version.h etc., "private" headers
 include_directories(${CMAKE_BINARY_DIR}/include)  # config.h etc., "public" headers
 
-# Lean code only needs this one include
-string(APPEND LEANC_OPTS " -I${CMAKE_BINARY_DIR}/include")
-
 # Use CMake profile C++ flags for building Lean libraries, but do not embed in `leanc`
 string(TOUPPER "${CMAKE_BUILD_TYPE}" uppercase_CMAKE_BUILD_TYPE)
 string(APPEND LEANC_OPTS " ${CMAKE_CXX_FLAGS_${uppercase_CMAKE_BUILD_TYPE}}")
@@ -780,12 +753,7 @@ add_custom_target(clean-olean
   DEPENDS clean-stdlib)
 
 install(DIRECTORY "${CMAKE_BINARY_DIR}/lib/" DESTINATION lib
-  PATTERN temp
-  PATTERN "*.export"
-  PATTERN "*.hash"
-  PATTERN "*.trace"
-  PATTERN "*.rsp"
-  EXCLUDE)
+  PATTERN temp EXCLUDE)
 
 # symlink source into expected installation location for go-to-definition, if file system allows it
 file(MAKE_DIRECTORY ${CMAKE_BINARY_DIR}/src)
@@ -816,32 +784,10 @@ if(LEAN_INSTALL_PREFIX)
 endif()
 
 # Escape for `make`. Yes, twice.
-string(REPLACE "$" "\\\$$" CMAKE_EXE_LINKER_FLAGS_MAKE "${CMAKE_EXE_LINKER_FLAGS}")
+string(REPLACE "$" "$$" CMAKE_EXE_LINKER_FLAGS_MAKE "${CMAKE_EXE_LINKER_FLAGS}")
 string(REPLACE "$" "$$" CMAKE_EXE_LINKER_FLAGS_MAKE_MAKE "${CMAKE_EXE_LINKER_FLAGS_MAKE}")
 configure_file(${LEAN_SOURCE_DIR}/stdlib.make.in ${CMAKE_BINARY_DIR}/stdlib.make)
 
-# hacky
-function(toml_escape IN OUTVAR)
-  if(IN)
-    string(STRIP "${IN}" OUT)
-    string(REPLACE " " "\", \"" OUT "${OUT}")
-    set(${OUTVAR} "\"${OUT}\"" PARENT_SCOPE)
-  endif()
-endfunction()
-string(REPLACE "ROOT" "${CMAKE_BINARY_DIR}" LEANC_CC "${LEANC_CC}")
-string(REPLACE "ROOT" "${CMAKE_BINARY_DIR}" LEANC_INTERNAL_FLAGS "${LEANC_INTERNAL_FLAGS}")
-string(REPLACE "ROOT" "${CMAKE_BINARY_DIR}" LEANC_INTERNAL_LINKER_FLAGS "${LEANC_INTERNAL_LINKER_FLAGS}")
-set(LEANC_OPTS_TOML "${LEANC_OPTS} ${LEANC_EXTRA_CC_FLAGS} ${LEANC_INTERNAL_FLAGS}")
-set(LINK_OPTS_TOML "${LEANC_INTERNAL_LINKER_FLAGS} -L${CMAKE_BINARY_DIR}/lib/lean ${LEAN_EXTRA_LINKER_FLAGS}")
-
-toml_escape("${LEAN_EXTRA_MAKE_OPTS}" LEAN_EXTRA_OPTS_TOML)
-toml_escape("${LEANC_OPTS_TOML}" LEANC_OPTS_TOML)
-toml_escape("${LINK_OPTS_TOML}" LINK_OPTS_TOML)
-
-if(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
-  set(LAKE_LIB_PREFIX "lib")
-endif()
-
 if(USE_LAKE AND STAGE EQUAL 1)
   configure_file(${LEAN_SOURCE_DIR}/lakefile.toml.in ${LEAN_SOURCE_DIR}/lakefile.toml)
   configure_file(${LEAN_SOURCE_DIR}/lakefile.toml.in ${LEAN_SOURCE_DIR}/../tests/lakefile.toml)

src/Init.lean

@@ -40,4 +40,3 @@ import Init.Syntax
 import Init.Internal
 import Init.Try
 import Init.BinderNameHint
-import Init.Task

src/Init/BinderNameHint.lean

@@ -31,12 +31,8 @@ example (names : List String) : names.all (fun name => "Waldo".isPrefixOf name)
 If `binder` is not a binder, then the name of `v` attains a macro scope. This only matters when the
 resulting term is used in a non-hygienic way, e.g. in termination proofs for well-founded recursion.
 
-This gadget is supported by
-* `simp`, `dsimp` and `rw` in the right-hand-side of an equation
-* `simp` in the assumptions of congruence rules
-
-It is ineffective in other positions (hyptheses of rewrite rules) or when used by other tactics
-(e.g. `apply`).
+This gadget is supported by `simp`, `dsimp` and `rw` in the right-hand-side of an equation, but not
+in hypotheses or by other tactics.
 -/
 @[simp ↓]
 def binderNameHint {α : Sort u} {β : Sort v} {γ : Sort w} (v : α) (binder : β) (e : γ) : γ := e

src/Init/ByCases.lean

@@ -38,8 +38,7 @@ theorem apply_ite (f : α → β) (P : Prop) [Decidable P] (x y : α) :
   apply_dite f P (fun _ => x) (fun _ => y)
 
 /-- A `dite` whose results do not actually depend on the condition may be reduced to an `ite`. -/
-@[simp] theorem dite_eq_ite [Decidable P] :
-  (dite P (fun _ => a) (fun _ => b)) = ite P a b := rfl
+@[simp] theorem dite_eq_ite [Decidable P] : (dite P (fun _ => a) fun _ => b) = ite P a b := rfl
 
 @[deprecated "Use `ite_eq_right_iff`" (since := "2024-09-18")]
 theorem ite_some_none_eq_none [Decidable P] :

src/Init/Classical.lean

@@ -175,10 +175,7 @@ theorem or_iff_not_imp_right : a ∨ b ↔ (¬b → a) := Decidable.or_iff_not_i
 
 theorem not_imp_iff_and_not : ¬(a → b) ↔ a ∧ ¬b := Decidable.not_imp_iff_and_not
 
-theorem not_and_iff_not_or_not : ¬(a ∧ b) ↔ ¬a ∨ ¬b := Decidable.not_and_iff_not_or_not
-
-@[deprecated not_and_iff_not_or_not (since := "2025-03-18")]
-abbrev not_and_iff_or_not_not := @not_and_iff_not_or_not
+theorem not_and_iff_or_not_not : ¬(a ∧ b) ↔ ¬a ∨ ¬b := Decidable.not_and_iff_or_not_not
 
 theorem not_iff : ¬(a ↔ b) ↔ (¬a ↔ b) := Decidable.not_iff
 
@@ -198,7 +195,7 @@ end Classical
 /- Export for Mathlib compat. -/
 export Classical (imp_iff_right_iff imp_and_neg_imp_iff and_or_imp not_imp)
 
-/-- Extract an element from an existential statement, using `Classical.choose`. -/
+/-- Extract an element from a existential statement, using `Classical.choose`. -/
 -- This enables projection notation.
 @[reducible] noncomputable def Exists.choose {p : α → Prop} (P : ∃ a, p a) : α := Classical.choose P
 

src/Init/Control/Basic.lean

@@ -5,7 +5,6 @@ Author: Leonardo de Moura, Sebastian Ullrich
 -/
 prelude
 import Init.Core
-import Init.BinderNameHint
 
 universe u v w
 
@@ -36,15 +35,7 @@ instance (priority := 500) instForInOfForIn' [ForIn' m ρ α d] : ForIn m ρ α
   simp [h]
   rfl
 
-@[wf_preprocess] theorem forIn_eq_forin' [d : Membership α ρ] [ForIn' m ρ α d] {β} [Monad m]
-    (x : ρ) (b : β) (f : (a : α) → β → m (ForInStep β)) :
-    forIn x b f = forIn' x b (fun x h => binderNameHint x f <| binderNameHint h () <| f x) := by
-  simp [binderNameHint]
-  rfl -- very strange why `simp` did not close it
-
-/--
-Extracts the value from a `ForInStep`, ignoring whether it is `ForInStep.done` or `ForInStep.yield`.
--/
+/-- Extract the value from a `ForInStep`, ignoring whether it is `done` or `yield`. -/
 def ForInStep.value (x : ForInStep α) : α :=
   match x with
   | ForInStep.done b => b
@@ -53,28 +44,14 @@ def ForInStep.value (x : ForInStep α) : α :=
 @[simp] theorem ForInStep.value_done (b : β) : (ForInStep.done b).value = b := rfl
 @[simp] theorem ForInStep.value_yield (b : β) : (ForInStep.yield b).value = b := rfl
 
-/--
-Maps a function over a functor, with parameters swapped so that the function comes last.
-
-This function is `Functor.map` with the parameters reversed, typically used via the `<&>` operator.
--/
 @[reducible]
 def Functor.mapRev {f : Type u → Type v} [Functor f] {α β : Type u} : f α → (α → β) → f β :=
   fun a f => f <$> a
 
-@[inherit_doc Functor.mapRev]
 infixr:100 " <&> " => Functor.mapRev
 
 recommended_spelling "mapRev" for "<&>" in [Functor.mapRev, «term_<&>_»]
 
-/--
-Discards the value in a functor, retaining the functor's structure.
-
-Discarding values is especially useful when using `Applicative` functors or `Monad`s to implement
-effects, and some operation should be carried out only for its effects. In `do`-notation, statements
-whose values are discarded must return `Unit`, and `discard` can be used to explicitly discard their
-values.
--/
 @[always_inline, inline]
 def Functor.discard {f : Type u → Type v} {α : Type u} [Functor f] (x : f α) : f PUnit :=
   Functor.mapConst PUnit.unit x
@@ -94,7 +71,7 @@ Error recovery and state can interact subtly. For example, the implementation of
 -/
 -- NB: List instance is in mathlib. Once upstreamed, add
 -- * `List`, where `failure` is the empty list and `<|>` concatenates.
-class Alternative (f : Type u → Type v) : Type (max (u+1) v) extends Applicative f where
+class Alternative (f : Type u → Type v) extends Applicative f : Type (max (u+1) v) where
   /--
   Produces an empty collection or recoverable failure.  The `<|>` operator collects values or recovers
   from failures. See `Alternative` for more details.
@@ -137,13 +114,6 @@ instance : ToBool Bool where
   | true  => t
   | false => f
 
-/--
-Converts the result of the monadic action `x` to a `Bool`. If it is `true`, returns it and ignores
-`y`; otherwise, runs `y` and returns its result.
-
-This a monadic counterpart to the short-circuiting `||` operator, usually accessed via the `<||>`
-operator.
--/
 @[macro_inline] def orM {m : Type u → Type v} {β : Type u} [Monad m] [ToBool β] (x y : m β) : m β := do
   let b ← x
   match toBool b with
@@ -154,13 +124,6 @@ infixr:30 " <||> " => orM
 
 recommended_spelling "orM" for "<||>" in [orM, «term_<||>_»]
 
-/--
-Converts the result of the monadic action `x` to a `Bool`. If it is `true`, returns `y`; otherwise,
-returns the original result of `x`.
-
-This a monadic counterpart to the short-circuiting `&&` operator, usually accessed via the `<&&>`
-operator.
--/
 @[macro_inline] def andM {m : Type u → Type v} {β : Type u} [Monad m] [ToBool β] (x y : m β) : m β := do
   let b ← x
   match toBool b with
@@ -171,9 +134,6 @@ infixr:35 " <&&> " => andM
 
 recommended_spelling "andM" for "<&&>" in [andM, «term_<&&>_»]
 
-/--
-Runs a monadic action and returns the negation of its result.
--/
 @[macro_inline] def notM {m : Type → Type v} [Applicative m] (x : m Bool) : m Bool :=
   not <$> x
 
@@ -289,61 +249,21 @@ Using `control` means that `runInBase` can be used multiple times.
 -/
 
 
-/--
-A way to lift a computation from one monad to another while providing the lifted computation with a
-means of interpreting computations from the outer monad. This provides a means of lifting
-higher-order operations automatically.
+/-- MonadControl is a way of stating that the monad `m` can be 'run inside' the monad `n`.
+
+This is the same as [`MonadBaseControl`](https://hackage.haskell.org/package/monad-control-1.0.3.1/docs/Control-Monad-Trans-Control.html#t:MonadBaseControl) in Haskell.
+To learn about `MonadControl`, see the comment above this docstring.
 
-Clients should typically use `control` or `controlAt`, which request an instance of `MonadControlT`:
-the reflexive, transitive closure of `MonadControl`. New instances should be defined for
-`MonadControl` itself.
 -/
--- This is the same as
--- [`MonadBaseControl`](https://hackage.haskell.org/package/monad-control-1.0.3.1/docs/Control-Monad-Trans-Control.html#t:MonadBaseControl)
--- in Haskell.
 class MonadControl (m : semiOutParam (Type u → Type v)) (n : Type u → Type w) where
-  /--
-  A type that can be used to reconstruct both a returned value and any state used by the outer
-  monad.
-  -/
   stM      : Type u → Type u
-  /--
-  Lifts an action from the inner monad `m` to the outer monad `n`. The inner monad has access to a
-  reverse lifting operator that can run an `n` action, returning a value and state together.
-  -/
   liftWith : {α : Type u} → (({β : Type u} → n β → m (stM β)) → m α) → n α
-  /--
-  Lifts a monadic action that returns a state and a value in the inner monad to an action in the
-  outer monad. The extra state information is used to restore the results of effects from the
-  reverse lift passed to `liftWith`'s parameter.
-  -/
   restoreM : {α : Type u} → m (stM α) → n α
 
-/--
-A way to lift a computation from one monad to another while providing the lifted computation with a
-means of interpreting computations from the outer monad. This provides a means of lifting
-higher-order operations automatically.
-
-Clients should typically use `control` or `controlAt`, which request an instance of `MonadControlT`:
-the reflexive, transitive closure of `MonadControl`. New instances should be defined for
-`MonadControl` itself.
--/
+/-- Transitive closure of MonadControl. -/
 class MonadControlT (m : Type u → Type v) (n : Type u → Type w) where
-  /--
-  A type that can be used to reconstruct both a returned value and any state used by the outer
-  monad.
-  -/
   stM      : Type u → Type u
-  /--
-  Lifts an action from the inner monad `m` to the outer monad `n`. The inner monad has access to a
-  reverse lifting operator that can run an `n` action, returning a value and state together.
-  -/
   liftWith : {α : Type u} → (({β : Type u} → n β → m (stM β)) → m α) → n α
-  /--
-  Lifts a monadic action that returns a state and a value in the inner monad to an action in the
-  outer monad. The extra state information is used to restore the results of effects from the
-  reverse lift passed to `liftWith`'s parameter.
-  -/
   restoreM {α : Type u} : stM α → n α
 
 export MonadControlT (stM liftWith restoreM)
@@ -359,48 +279,25 @@ instance (m : Type u → Type v) [Pure m] : MonadControlT m m where
   liftWith f := f fun x => x
   restoreM x := pure x
 
-/--
-Lifts an operation from an inner monad to an outer monad, providing it with a reverse lifting
-operator that allows outer monad computations to be run in the inner monad. The lifted operation is
-required to return extra information that is required in order to reconstruct the reverse lift's
-effects in the outer monad; this extra information is determined by `stM`.
-
-This function takes the inner monad as an explicit parameter. Use `control` to infer the monad.
--/
 @[always_inline, inline]
 def controlAt (m : Type u → Type v) {n : Type u → Type w} [MonadControlT m n] [Bind n] {α : Type u}
     (f : ({β : Type u} → n β → m (stM m n β)) → m (stM m n α)) : n α :=
   liftWith f >>= restoreM
 
-/--
-Lifts an operation from an inner monad to an outer monad, providing it with a reverse lifting
-operator that allows outer monad computations to be run in the inner monad. The lifted operation is
-required to return extra information that is required in order to reconstruct the reverse lift's
-effects in the outer monad; this extra information is determined by `stM`.
-
-This function takes the inner monad as an implicit parameter. Use `controlAt` to specify it
-explicitly.
--/
 @[always_inline, inline]
 def control {m : Type u → Type v} {n : Type u → Type w} [MonadControlT m n] [Bind n] {α : Type u}
     (f : ({β : Type u} → n β → m (stM m n β)) → m (stM m n α)) : n α :=
   controlAt m f
 
 /--
-Overloaded monadic iteration over some container type.
-
-An instance of `ForM m γ α` describes how to iterate a monadic operator over a container of type `γ`
-with elements of type `α` in the monad `m`. The element type should be uniquely determined by the
-monad and the container.
-
-Use `ForM.forIn` to construct a `ForIn` instance from a `ForM` instance, thus enabling the use of
-the `for` operator in `do`-notation.
+  Typeclass for the polymorphic `forM` operation described in the "do unchained" paper.
+  Remark:
+  - `γ` is a "container" type of elements of type `α`.
+  - `α` is treated as an output parameter by the typeclass resolution procedure.
+    That is, it tries to find an instance using only `m` and `γ`.
 -/
 class ForM (m : Type u → Type v) (γ : Type w₁) (α : outParam (Type w₂)) where
-  /--
-  Runs the monadic action `f` on each element of the collection `coll`.
-  -/
-  forM [Monad m] (coll : γ) (f : α → m PUnit) : m PUnit
+  forM [Monad m] : γ → (α → m PUnit) → m PUnit
 
 export ForM (forM)
 

src/Init/Control/EState.lean

@@ -29,11 +29,8 @@ namespace EStateM
 
 variable {ε σ α β : Type u}
 
-/--
-Alternative orElse operator that allows callers to select which exception should be used when both
-operations fail. The default is to use the first exception since the standard `orElse` uses the
-second.
--/
+/-- Alternative orElse operator that allows to select which exception should be used.
+    The default is to use the first exception since the standard `orElse` uses the second. -/
 @[always_inline, inline]
 protected def orElse' {δ} [Backtrackable δ σ] (x₁ x₂ : EStateM ε σ α) (useFirstEx := true) : EStateM ε σ α := fun s =>
   let d := Backtrackable.save s;
@@ -57,11 +54,6 @@ instance : MonadFinally (EStateM ε σ) := {
       | Result.error e₂ s => Result.error e₂ s
 }
 
-/--
-Converts a state monad action into a state monad action with exceptions.
-
-The resulting action does not throw an exception.
--/
 @[always_inline, inline] def fromStateM {ε σ α : Type} (x : StateM σ α) : EStateM ε σ α := fun s =>
   match x.run s with
   | (a, s') => EStateM.Result.ok a s'

src/Init/Control/Except.lean

@@ -13,20 +13,10 @@ import Init.Coe
 namespace Except
 variable {ε : Type u}
 
-/--
-A successful computation in the `Except ε` monad: `a` is returned, and no exception is thrown.
--/
 @[always_inline, inline]
 protected def pure (a : α) : Except ε α :=
   Except.ok a
 
-/--
-Transforms a successful result with a function, doing nothing when an exception is thrown.
-
-Examples:
- * `(pure 2 : Except String Nat).map toString = pure 2`
- * `(throw "Error" : Except String Nat).map toString = throw "Error"`
--/
 @[always_inline, inline]
 protected def map (f : α → β) : Except ε α → Except ε β
   | Except.error err => Except.error err
@@ -37,78 +27,36 @@ protected def map (f : α → β) : Except ε α → Except ε β
   intro e
   simp [Except.map]; cases e <;> rfl
 
-/--
-Transforms exceptions with a function, doing nothing on successful results.
-
-Examples:
- * `(pure 2 : Except String Nat).mapError (·.length) = pure 2`
- * `(throw "Error" : Except String Nat).mapError (·.length) = throw 5`
--/
 @[always_inline, inline]
 protected def mapError (f : ε → ε') : Except ε α → Except ε' α
   | Except.error err => Except.error <| f err
   | Except.ok v      => Except.ok v
 
-/--
-Sequences two operations that may throw exceptions, allowing the second to depend on the value
-returned by the first.
-
-If the first operation throws an exception, then it is the result of the computation. If the first
-succeeds but the second throws an exception, then that exception is the result. If both succeed,
-then the result is the result of the second computation.
-
-This is the implementation of the `>>=` operator for `Except ε`.
--/
 @[always_inline, inline]
 protected def bind (ma : Except ε α) (f : α → Except ε β) : Except ε β :=
   match ma with
   | Except.error err => Except.error err
   | Except.ok v      => f v
 
-/-- Returns `true` if the value is `Except.ok`, `false` otherwise. -/
+/-- Returns true if the value is `Except.ok`, false otherwise. -/
 @[always_inline, inline]
 protected def toBool : Except ε α → Bool
   | Except.ok _    => true
   | Except.error _ => false
 
-@[inherit_doc Except.toBool]
 abbrev isOk : Except ε α → Bool := Except.toBool
 
-/--
-Returns `none` if an exception was thrown, or `some` around the value on success.
-
-Examples:
- * `(pure 10 : Except String Nat).toOption = some 10`
- * `(throw "Failure" : Except String Nat).toOption = none`
--/
 @[always_inline, inline]
 protected def toOption : Except ε α → Option α
   | Except.ok a    => some a
   | Except.error _ => none
 
-/--
-Handles exceptions thrown in the `Except ε` monad.
-
-If `ma` is successful, its result is returned. If it throws an exception, then `handle` is invoked
-on the exception's value.
-
-Examples:
- * `(pure 2 : Except String Nat).tryCatch (pure ·.length) = pure 2`
- * `(throw "Error" : Except String Nat).tryCatch (pure ·.length) = pure 5`
- * `(throw "Error" : Except String Nat).tryCatch (fun x => throw ("E: " ++ x)) = throw "E: Error"`
--/
 @[always_inline, inline]
 protected def tryCatch (ma : Except ε α) (handle : ε → Except ε α) : Except ε α :=
   match ma with
   | Except.ok a    => Except.ok a
   | Except.error e => handle e
 
-/--
-Recovers from exceptions thrown in the `Except ε` monad. Typically used via the `<|>` operator.
-
-`Except.tryCatch` is a related operator that allows the recovery procedure to depend on _which_
-exception was thrown.
--/
 def orElseLazy (x : Except ε α) (y : Unit → Except ε α) : Except ε α :=
   match x with
   | Except.ok a    => Except.ok a
@@ -122,26 +70,12 @@ instance : Monad (Except ε) where
 
 end Except
 
-/--
-Adds exceptions of type `ε` to a monad `m`.
--/
 def ExceptT (ε : Type u) (m : Type u → Type v) (α : Type u) : Type v :=
   m (Except ε α)
 
-/--
-Use a monadic action that may return an exception's value as an action in the transformed monad that
-may throw the corresponding exception.
-
-This is the inverse of `ExceptT.run`.
--/
 @[always_inline, inline]
 def ExceptT.mk {ε : Type u} {m : Type u → Type v} {α : Type u} (x : m (Except ε α)) : ExceptT ε m α := x
 
-/--
-Use a monadic action that may throw an exception as an action that may return an exception's value.
-
-This is the inverse of `ExceptT.mk`.
--/
 @[always_inline, inline]
 def ExceptT.run {ε : Type u} {m : Type u → Type v} {α : Type u} (x : ExceptT ε m α) : m (Except ε α) := x
 
@@ -149,41 +83,25 @@ namespace ExceptT
 
 variable {ε : Type u} {m : Type u → Type v} [Monad m]
 
-/--
-Returns the value `a` without throwing exceptions or having any other effect.
--/
 @[always_inline, inline]
 protected def pure {α : Type u} (a : α) : ExceptT ε m α :=
   ExceptT.mk <| pure (Except.ok a)
 
-/--
-Handles exceptions thrown by an action that can have no effects _other_ than throwing exceptions.
--/
 @[always_inline, inline]
 protected def bindCont {α β : Type u} (f : α → ExceptT ε m β) : Except ε α → m (Except ε β)
   | Except.ok a    => f a
   | Except.error e => pure (Except.error e)
 
-/--
-Sequences two actions that may throw exceptions. Typically used via `do`-notation or the `>>=`
-operator.
--/
 @[always_inline, inline]
 protected def bind {α β : Type u} (ma : ExceptT ε m α) (f : α → ExceptT ε m β) : ExceptT ε m β :=
   ExceptT.mk <| ma >>= ExceptT.bindCont f
 
-/--
-Transforms a successful computation's value using `f`. Typically used via the `<$>` operator.
--/
 @[always_inline, inline]
 protected def map {α β : Type u} (f : α → β) (x : ExceptT ε m α) : ExceptT ε m β :=
   ExceptT.mk <| x >>= fun a => match a with
     | (Except.ok a)    => pure <| Except.ok (f a)
     | (Except.error e) => pure <| Except.error e
 
-/--
-Runs a computation from an underlying monad in the transformed monad with exceptions.
--/
 @[always_inline, inline]
 protected def lift {α : Type u} (t : m α) : ExceptT ε m α :=
   ExceptT.mk <| Except.ok <$> t
@@ -192,9 +110,6 @@ protected def lift {α : Type u} (t : m α) : ExceptT ε m α :=
 instance : MonadLift (Except ε) (ExceptT ε m) := ⟨fun e => ExceptT.mk <| pure e⟩
 instance : MonadLift m (ExceptT ε m) := ⟨ExceptT.lift⟩
 
-/--
-Handles exceptions produced in the `ExceptT ε` transformer.
--/
 @[always_inline, inline]
 protected def tryCatch {α : Type u} (ma : ExceptT ε m α) (handle : ε → ExceptT ε m α) : ExceptT ε m α :=
   ExceptT.mk <| ma >>= fun res => match res with
@@ -209,11 +124,6 @@ instance : Monad (ExceptT ε m) where
   bind := ExceptT.bind
   map  := ExceptT.map
 
-/--
-Transforms exceptions using the function `f`.
-
-This is the `ExceptT` version of `Except.mapError`.
--/
 @[always_inline, inline]
 protected def adapt {ε' α : Type u} (f : ε → ε') : ExceptT ε m α → ExceptT ε' m α := fun x =>
   ExceptT.mk <| Except.mapError f <$> x
@@ -240,12 +150,8 @@ instance (ε) : MonadExceptOf ε (Except ε) where
 namespace MonadExcept
 variable {ε : Type u} {m : Type v → Type w}
 
-/--
-An alternative unconditional error recovery operator that allows callers to specify which exception
-to throw in cases where both operations throw exceptions.
-
-By default, the first is thrown, because the `<|>` operator throws the second.
--/
+/-- Alternative orelse operator that allows to select which exception should be used.
+    The default is to use the first exception since the standard `orelse` uses the second. -/
 @[always_inline, inline]
 def orelse' [MonadExcept ε m] {α : Type v} (t₁ t₂ : m α) (useFirstEx := true) : m α :=
   tryCatch t₁ fun e₁ => tryCatch t₂ fun e₂ => throw (if useFirstEx then e₁ else e₂)
@@ -265,24 +171,13 @@ instance (ε : Type u) (m : Type u → Type v) [Monad m] : MonadControl m (Excep
   liftWith f := liftM <| f fun x => x.run
   restoreM x := x
 
-/--
-Monads that provide the ability to ensure an action happens, regardless of exceptions or other
-failures.
-
-`MonadFinally.tryFinally'` is used to desugar `try ... finally ...` syntax.
--/
 class MonadFinally (m : Type u → Type v) where
-  /--
-  Runs an action, ensuring that some other action always happens afterward.
-
-  More specifically, `tryFinally' x f` runs `x` and then the “finally” computation `f`. If `x`
-  succeeds with some value `a : α`, `f (some a)` is returned. If `x` fails for `m`'s definition of
-  failure, `f none` is returned.
-
-  `tryFinally'` can be thought of as performing the same role as a `finally` block in an imperative
-  programming language.
-  -/
-  tryFinally' {α β} : (x : m α) → (f : Option α → m β) → m (α × β)
+  /-- `tryFinally' x f` runs `x` and then the "finally" computation `f`.
+  When `x` succeeds with `a : α`, `f (some a)` is returned. If `x` fails
+  for `m`'s definition of failure, `f none` is returned. Hence `tryFinally'`
+  can be thought of as performing the same role as a `finally` block in
+  an imperative programming language. -/
+  tryFinally' {α β} : m α → (Option α → m β) → m (α × β)
 
 export MonadFinally (tryFinally')
 

src/Init/Control/ExceptCps.lean

@@ -10,37 +10,19 @@ import Init.Control.Lawful.Basic
 The Exception monad transformer using CPS style.
 -/
 
-/--
-Adds exceptions of type `ε` to a monad `m`.
-
-Instead of using `Except ε` to model exceptions, this implementation uses continuation passing
-style. This has different performance characteristics from `ExceptT ε`.
--/
 def ExceptCpsT (ε : Type u) (m : Type u → Type v) (α : Type u) := (β : Type u) → (α → m β) → (ε → m β) → m β
 
 namespace ExceptCpsT
 
-/--
-Use a monadic action that may throw an exception as an action that may return an exception's value.
--/
 @[always_inline, inline]
 def run {ε α : Type u} [Monad m] (x : ExceptCpsT ε m α) : m (Except ε α) :=
   x _ (fun a => pure (Except.ok a)) (fun e => pure (Except.error e))
 
 set_option linter.unusedVariables false in  -- `s` unused
-/--
-Use a monadic action that may throw an exception by providing explicit success and failure
-continuations.
--/
 @[always_inline, inline]
 def runK {ε α : Type u} (x : ExceptCpsT ε m α) (s : ε) (ok : α → m β) (error : ε → m β) : m β :=
   x _ ok error
 
-/--
-Returns the value of a computation, forgetting whether it was an exception or a success.
-
-This corresponds to early return.
--/
 @[always_inline, inline]
 def runCatch [Monad m] (x : ExceptCpsT α m α) : m α :=
   x α pure pure
@@ -58,9 +40,6 @@ instance : MonadExceptOf ε (ExceptCpsT ε m) where
   throw e  := fun _ _ k => k e
   tryCatch x handle := fun _ k₁ k₂ => x _ k₁ (fun e => handle e _ k₁ k₂)
 
-/--
-Run an action from the transformed monad in the exception monad.
--/
 @[always_inline, inline]
 def lift [Monad m] (x : m α) : ExceptCpsT ε m α :=
   fun _ k _ => x >>= k

src/Init/Control/Id.lean

@@ -10,28 +10,6 @@ import Init.Core
 
 universe u
 
-/--
-The identity function on types, used primarily for its `Monad` instance.
-
-The identity monad is useful together with monad transformers to construct monads for particular
-purposes. Additionally, it can be used with `do`-notation in order to use control structures such as
-local mutability, `for`-loops, and early returns in code that does not otherwise use monads.
-
-Examples:
-```lean example
-def containsFive (xs : List Nat) : Bool := Id.run do
-  for x in xs do
-    if x == 5 then return true
-  return false
-```
-
-```lean example
-#eval containsFive [1, 3, 5, 7]
-```
-```output
-true
-```
--/
 def Id (type : Type u) : Type u := type
 
 namespace Id
@@ -42,18 +20,9 @@ instance : Monad Id where
   bind x f := f x
   map f x := f x
 
-/--
-The identity monad has a `bind` operator.
--/
 def hasBind : Bind Id :=
   inferInstance
 
-/--
-Runs a computation in the identity monad.
-
-This function is the identity function. Because its parameter has type `Id α`, it causes
-`do`-notation in its arguments to use the `Monad Id` instance.
--/
 @[always_inline, inline]
 protected def run (x : Id α) : α := x
 

src/Init/Control/Lawful/Basic.lean

@@ -13,26 +13,17 @@ open Function
   rfl
 
 /--
-A functor satisfies the functor laws.
-
-The `Functor` class contains the operations of a functor, but does not require that instances
-prove they satisfy the laws of a functor. A `LawfulFunctor` instance includes proofs that the laws
-are satisfied. Because `Functor` instances may provide optimized implementations of `mapConst`,
-`LawfulFunctor` instances must also prove that the optimized implementation is equivalent to the
-standard implementation.
+The `Functor` typeclass only contains the operations of a functor.
+`LawfulFunctor` further asserts that these operations satisfy the laws of a functor,
+including the preservation of the identity and composition laws:
+```
+id <$> x = x
+(h ∘ g) <$> x = h <$> g <$> x
+```
 -/
 class LawfulFunctor (f : Type u → Type v) [Functor f] : Prop where
-  /--
-  The `mapConst` implementation is equivalent to the default implementation.
-  -/
   map_const          : (Functor.mapConst : α → f β → f α) = Functor.map ∘ const β
-  /--
-  The `map` implementation preserves identity.
-  -/
   id_map   (x : f α) : id <$> x = x
-  /--
-  The `map` implementation preserves function composition.
-  -/
   comp_map (g : α → β) (h : β → γ) (x : f α) : (h ∘ g) <$> x = h <$> g <$> x
 
 export LawfulFunctor (map_const id_map comp_map)
@@ -47,48 +38,21 @@ attribute [simp] id_map
   (comp_map _ _ _).symm
 
 /--
-An applicative functor satisfies the laws of an applicative functor.
-
-The `Applicative` class contains the operations of an applicative functor, but does not require that
-instances prove they satisfy the laws of an applicative functor. A `LawfulApplicative` instance
-includes proofs that the laws are satisfied.
-
-Because `Applicative` instances may provide optimized implementations of `seqLeft` and `seqRight`,
-`LawfulApplicative` instances must also prove that the optimized implementation is equivalent to the
-standard implementation.
+The `Applicative` typeclass only contains the operations of an applicative functor.
+`LawfulApplicative` further asserts that these operations satisfy the laws of an applicative functor:
+```
+pure id <*> v = v
+pure (·∘·) <*> u <*> v <*> w = u <*> (v <*> w)
+pure f <*> pure x = pure (f x)
+u <*> pure y = pure (· y) <*> u
+```
 -/
-class LawfulApplicative (f : Type u → Type v) [Applicative f] : Prop extends LawfulFunctor f where
-  /-- `seqLeft` is equivalent to the default implementation. -/
+class LawfulApplicative (f : Type u → Type v) [Applicative f] extends LawfulFunctor f : Prop where
   seqLeft_eq  (x : f α) (y : f β)     : x <* y = const β <$> x <*> y
-  /-- `seqRight` is equivalent to the default implementation. -/
   seqRight_eq (x : f α) (y : f β)     : x *> y = const α id <$> x <*> y
-  /--
-  `pure` before `seq` is equivalent to `Functor.map`.
-
-  This means that `pure` really is pure when occurring immediately prior to `seq`.
-   -/
   pure_seq    (g : α → β) (x : f α)   : pure g <*> x = g <$> x
-
-  /--
-  Mapping a function over the result of `pure` is equivalent to applying the function under `pure`.
-
-  This means that `pure` really is pure with respect to `Functor.map`.
-  -/
   map_pure    (g : α → β) (x : α)     : g <$> (pure x : f α) = pure (g x)
-
-  /--
-  `pure` after `seq` is equivalent to `Functor.map`.
-
-  This means that `pure` really is pure when occurring just after `seq`.
-  -/
   seq_pure    {α β : Type u} (g : f (α → β)) (x : α) : g <*> pure x = (fun h => h x) <$> g
-
-  /--
-  `seq` is associative.
-
-  Changing the nesting of `seq` calls while maintaining the order of computations results in an
-  equivalent computation. This means that `seq` is not doing any more than sequencing.
-  -/
   seq_assoc   {α β γ : Type u} (x : f α) (g : f (α → β)) (h : f (β → γ)) : h <*> (g <*> x) = ((@comp α β γ) <$> h) <*> g <*> x
   comp_map g h x := (by
     repeat rw [← pure_seq]
@@ -102,36 +66,21 @@ attribute [simp] map_pure seq_pure
   simp [pure_seq]
 
 /--
-Lawful monads are those that satisfy a certain behavioral specification. While all instances of
-`Monad` should satisfy these laws, not all implementations are required to prove this.
+The `Monad` typeclass only contains the operations of a monad.
+`LawfulMonad` further asserts that these operations satisfy the laws of a monad,
+including associativity and identity laws for `bind`:
+```
+pure x >>= f = f x
+x >>= pure = x
+x >>= f >>= g = x >>= (fun x => f x >>= g)
+```
 
-`LawfulMonad.mk'` is an alternative constructor that contains useful defaults for many fields.
+`LawfulMonad.mk'` is an alternative constructor containing useful defaults for many fields.
 -/
-class LawfulMonad (m : Type u → Type v) [Monad m] : Prop extends LawfulApplicative m where
-  /--
-  A `bind` followed by `pure` composed with a function is equivalent to a functorial map.
-
-  This means that `pure` really is pure after a `bind` and has no effects.
-  -/
+class LawfulMonad (m : Type u → Type v) [Monad m] extends LawfulApplicative m : Prop where
   bind_pure_comp (f : α → β) (x : m α) : x >>= (fun a => pure (f a)) = f <$> x
-  /--
-  A `bind` followed by a functorial map is equivalent to `Applicative` sequencing.
-
-  This means that the effect sequencing from `Monad` and `Applicative` are the same.
-  -/
   bind_map       {α β : Type u} (f : m (α → β)) (x : m α) : f >>= (. <$> x) = f <*> x
-  /--
-  `pure` followed by `bind` is equivalent to function application.
-
-  This means that `pure` really is pure before a `bind` and has no effects.
-  -/
   pure_bind      (x : α) (f : α → m β) : pure x >>= f = f x
-  /--
-  `bind` is associative.
-
-  Changing the nesting of `bind` calls while maintaining the order of computations results in an
-  equivalent computation. This means that `bind` is not doing more than data-dependent sequencing.
-  -/
   bind_assoc     (x : m α) (f : α → m β) (g : β → m γ) : x >>= f >>= g = x >>= fun x => f x >>= g
   map_pure g x    := (by rw [← bind_pure_comp, pure_bind])
   seq_pure g x    := (by rw [← bind_map]; simp [map_pure, bind_pure_comp])

src/Init/Control/Option.lean

@@ -8,22 +8,13 @@ import Init.Data.Option.Basic
 import Init.Control.Basic
 import Init.Control.Except
 
-set_option linter.missingDocs true
-
 universe u v
 
 instance : ToBool (Option α) := ⟨Option.isSome⟩
 
-/--
-Adds the ability to fail to a monad. Unlike ordinary exceptions, there is no way to signal why a
-failure occurred.
--/
 def OptionT (m : Type u → Type v) (α : Type u) : Type v :=
   m (Option α)
 
-/--
-Executes an action that might fail in the underlying monad `m`, returning `none` in case of failure.
--/
 @[always_inline, inline]
 def OptionT.run {m : Type u → Type v} {α : Type u} (x : OptionT m α) : m (Option α) :=
   x
@@ -31,25 +22,15 @@ def OptionT.run {m : Type u → Type v} {α : Type u} (x : OptionT m α) : m (Op
 namespace OptionT
 variable {m : Type u → Type v} [Monad m] {α β : Type u}
 
-/--
-Converts an action that returns an `Option` into one that might fail, with `none` indicating
-failure.
--/
 protected def mk (x : m (Option α)) : OptionT m α :=
   x
 
-/--
-Sequences two potentially-failing actions. The second action is run only if the first succeeds.
--/
 @[always_inline, inline]
 protected def bind (x : OptionT m α) (f : α → OptionT m β) : OptionT m β := OptionT.mk do
   match (← x) with
   | some a => f a
   | none   => pure none
 
-/--
-Succeeds with the provided value.
--/
 @[always_inline, inline]
 protected def pure (a : α) : OptionT m α := OptionT.mk do
   pure (some a)
@@ -59,17 +40,11 @@ instance : Monad (OptionT m) where
   pure := OptionT.pure
   bind := OptionT.bind
 
-/--
-Recovers from failures. Typically used via the `<|>` operator.
--/
 @[always_inline, inline] protected def orElse (x : OptionT m α) (y : Unit → OptionT m α) : OptionT m α := OptionT.mk do
   match (← x) with
   | some a => pure (some a)
   | _      => y ()
 
-/--
-A recoverable failure.
--/
 @[always_inline, inline] protected def fail : OptionT m α := OptionT.mk do
   pure none
 
@@ -77,12 +52,6 @@ instance : Alternative (OptionT m) where
   failure := OptionT.fail
   orElse  := OptionT.orElse
 
-/--
-Converts a computation from the underlying monad into one that could fail, even though it does not.
-
-This function is typically implicitly accessed via a `MonadLiftT` instance as part of [automatic
-lifting](lean-manual://section/monad-lifting).
--/
 @[always_inline, inline] protected def lift (x : m α) : OptionT m α := OptionT.mk do
   return some (← x)
 
@@ -90,9 +59,6 @@ instance : MonadLift m (OptionT m) := ⟨OptionT.lift⟩
 
 instance : MonadFunctor m (OptionT m) := ⟨fun f x => f x⟩
 
-/--
-Handles failures by treating them as exceptions of type `Unit`.
--/
 @[always_inline, inline] protected def tryCatch (x : OptionT m α) (handle : Unit → OptionT m α) : OptionT m α := OptionT.mk do
   let some a ← x | handle ()
   pure a

src/Init/Control/Reader.lean

@@ -10,21 +10,12 @@ import Init.Control.Basic
 import Init.Control.Id
 import Init.Control.Except
 
-set_option linter.missingDocs true
-
 namespace ReaderT
 
-/--
-Recovers from errors. The same local value is provided to both branches. Typically used via the
-`<|>` operator.
--/
 @[always_inline, inline]
 protected def orElse [Alternative m] (x₁ : ReaderT ρ m α) (x₂ : Unit → ReaderT ρ m α) : ReaderT ρ m α :=
   fun s => x₁ s <|> x₂ () s
 
-/--
-Fails with a recoverable error.
--/
 @[always_inline, inline]
 protected def failure [Alternative m] : ReaderT ρ m α :=
   fun _ => failure
@@ -44,8 +35,4 @@ instance : MonadControl m (ReaderT ρ m) where
 instance ReaderT.tryFinally [MonadFinally m] : MonadFinally (ReaderT ρ m) where
   tryFinally' x h ctx := tryFinally' (x ctx) (fun a? => h a? ctx)
 
-/--
-A monad with access to a read-only value of type `ρ`. The value can be locally overridden by
-`withReader`, but it cannot be mutated.
--/
 @[reducible] def ReaderM (ρ : Type u) := ReaderT ρ Id

src/Init/Control/State.lean

@@ -9,42 +9,19 @@ prelude
 import Init.Control.Basic
 import Init.Control.Id
 import Init.Control.Except
-
-set_option linter.missingDocs true
-
 universe u v w
 
-/--
-Adds a mutable state of type `σ` to a monad.
-
-Actions in the resulting monad are functions that take an initial state and return, in `m`, a tuple
-of a value and a state.
--/
 def StateT (σ : Type u) (m : Type u → Type v) (α : Type u) : Type (max u v) :=
   σ → m (α × σ)
 
-/--
-Executes an action from a monad with added state in the underlying monad `m`. Given an initial
-state, it returns a value paired with the final state.
--/
 @[always_inline, inline]
 def StateT.run {σ : Type u} {m : Type u → Type v} {α : Type u} (x : StateT σ m α) (s : σ) : m (α × σ) :=
   x s
 
-/--
-Executes an action from a monad with added state in the underlying monad `m`. Given an initial
-state, it returns a value, discarding the final state.
--/
 @[always_inline, inline]
 def StateT.run' {σ : Type u} {m : Type u → Type v} [Functor m] {α : Type u} (x : StateT σ m α) (s : σ) : m α :=
   (·.1) <$> x s
 
-/--
-A tuple-based state monad.
-
-Actions in `StateM σ` are functions that take an initial state and return a value paired with a
-final state.
--/
 @[reducible]
 def StateM (σ α : Type u) : Type u := StateT σ Id α
 
@@ -61,23 +38,14 @@ section
 variable {σ : Type u} {m : Type u → Type v}
 variable [Monad m] {α β : Type u}
 
-/--
-Returns the given value without modifying the state. Typically used via `Pure.pure`.
--/
 @[always_inline, inline]
 protected def pure (a : α) : StateT σ m α :=
   fun s => pure (a, s)
 
-/--
-Sequences two actions. Typically used via the `>>=` operator.
--/
 @[always_inline, inline]
 protected def bind (x : StateT σ m α) (f : α → StateT σ m β) : StateT σ m β :=
   fun s => do let (a, s) ← x s; f a s
 
-/--
-Modifies the value returned by a computation. Typically used via the `<$>` operator.
--/
 @[always_inline, inline]
 protected def map (f : α → β) (x : StateT σ m α) : StateT σ m β :=
   fun s => do let (a, s) ← x s; pure (f a, s)
@@ -88,17 +56,10 @@ instance : Monad (StateT σ m) where
   bind := StateT.bind
   map  := StateT.map
 
-/--
-Recovers from errors. The state is rolled back on error recovery. Typically used via the `<|>`
-operator.
--/
 @[always_inline, inline]
 protected def orElse [Alternative m] {α : Type u} (x₁ : StateT σ m α) (x₂ : Unit → StateT σ m α) : StateT σ m α :=
   fun s => x₁ s <|> x₂ () s
 
-/--
-Fails with a recoverable error. The state is rolled back on error recovery.
--/
 @[always_inline, inline]
 protected def failure [Alternative m] {α : Type u} : StateT σ m α :=
   fun _ => failure
@@ -107,40 +68,18 @@ instance [Alternative m] : Alternative (StateT σ m) where
   failure := StateT.failure
   orElse  := StateT.orElse
 
-/--
-Retrieves the current value of the monad's mutable state.
-
-This increments the reference count of the state, which may inhibit in-place updates.
--/
 @[always_inline, inline]
 protected def get : StateT σ m σ :=
   fun s => pure (s, s)
 
-/--
-Replaces the mutable state with a new value.
--/
 @[always_inline, inline]
 protected def set : σ → StateT σ m PUnit :=
   fun s' _ => pure (⟨⟩, s')
 
-/--
-Applies a function to the current state that both computes a new state and a value. The new state
-replaces the current state, and the value is returned.
-
-It is equivalent to `do let (a, s) := f (← StateT.get); StateT.set s; pure a`. However, using
-`StateT.modifyGet` may lead to better performance because it doesn't add a new reference to the
-state value, and additional references can inhibit in-place updates of data.
--/
 @[always_inline, inline]
 protected def modifyGet (f : σ → α × σ) : StateT σ m α :=
   fun s => pure (f s)
 
-/--
-Runs an action from the underlying monad in the monad with state. The state is not modified.
-
-This function is typically implicitly accessed via a `MonadLiftT` instance as part of [automatic
-lifting](lean-manual://section/monad-lifting).
--/
 @[always_inline, inline]
 protected def lift {α : Type u} (t : m α) : StateT σ m α :=
   fun s => do let a ← t; pure (a, s)
@@ -159,9 +98,7 @@ instance (ε) [MonadExceptOf ε m] : MonadExceptOf ε (StateT σ m) := {
 end
 end StateT
 
-/--
-Creates a suitable implementation of `ForIn.forIn` from a `ForM` instance.
--/
+/-- Adapter to create a ForIn instance from a ForM instance -/
 @[always_inline, inline]
 def ForM.forIn [Monad m] [ForM (StateT β (ExceptT β m)) ρ α]
     (x : ρ) (b : β) (f : α → β → m (ForInStep β)) : m β := do

src/Init/Control/StateCps.lean

@@ -6,45 +6,24 @@ Authors: Leonardo de Moura
 prelude
 import Init.Control.Lawful.Basic
 
-set_option linter.missingDocs true
-
 /-!
 The State monad transformer using CPS style.
 -/
 
-/--
-An alternative implementation of a state monad transformer that internally uses continuation passing
-style instead of tuples.
--/
 def StateCpsT (σ : Type u) (m : Type u → Type v) (α : Type u) := (δ : Type u) → σ → (α → σ → m δ) → m δ
 
 namespace StateCpsT
 
 variable {α σ : Type u} {m : Type u → Type v}
 
-/--
-Runs a stateful computation that's represented using continuation passing style by providing it with
-an initial state and a continuation.
--/
 @[always_inline, inline]
 def runK (x : StateCpsT σ m α) (s : σ) (k : α → σ → m β) : m β :=
   x _ s k
 
-/--
-Executes an action from a monad with added state in the underlying monad `m`. Given an initial
-state, it returns a value paired with the final state.
-
-While the state is internally represented in continuation passing style, the resulting value is the
-same as for a non-CPS state monad.
--/
 @[always_inline, inline]
 def run [Monad m] (x : StateCpsT σ m α) (s : σ) : m (α × σ) :=
   runK x s (fun a s => pure (a, s))
 
-/--
-Executes an action from a monad with added state in the underlying monad `m`. Given an initial
-state, it returns a value, discarding the final state.
--/
 @[always_inline, inline]
 def run' [Monad m] (x : StateCpsT σ m α) (s : σ) : m α :=
   runK x s (fun a _ => pure a)
@@ -64,12 +43,6 @@ instance : MonadStateOf σ (StateCpsT σ m) where
   set s := fun _ _ k => k ⟨⟩ s
   modifyGet f := fun _ s k => let (a, s) := f s; k a s
 
-/--
-Runs an action from the underlying monad in the monad with state. The state is not modified.
-
-This function is typically implicitly accessed via a `MonadLiftT` instance as part of [automatic
-lifting](lean-manual://section/monad-lifting).
--/
 @[always_inline, inline]
 protected def lift [Monad m] (x : m α) : StateCpsT σ m α :=
   fun _ s k => x >>= (k . s)

src/Init/Control/StateRef.lean

@@ -8,23 +8,10 @@ The State monad transformer using IO references.
 prelude
 import Init.System.ST
 
-set_option linter.missingDocs true
-
-/--
-A state monad that uses an actual mutable reference cell (i.e. an `ST.Ref ω σ`).
-
-The macro `StateRefT σ m α` infers `ω` from `m`. It should normally be used instead.
--/
 def StateRefT' (ω : Type) (σ : Type) (m : Type → Type) (α : Type) : Type := ReaderT (ST.Ref ω σ) m α
 
 /-! Recall that `StateRefT` is a macro that infers `ω` from the `m`. -/
 
-/--
-Executes an action from a monad with added state in the underlying monad `m`. Given an initial
-state, it returns a value paired with the final state.
-
-The monad `m` must support `ST` effects in order to create and mutate reference cells.
--/
 @[always_inline, inline]
 def StateRefT'.run {ω σ : Type} {m : Type → Type} [Monad m] [MonadLiftT (ST ω) m] {α : Type} (x : StateRefT' ω σ m α) (s : σ) : m (α × σ) := do
   let ref ← ST.mkRef s
@@ -32,12 +19,6 @@ def StateRefT'.run {ω σ : Type} {m : Type → Type} [Monad m] [MonadLiftT (ST
   let s ← ref.get
   pure (a, s)
 
-/--
-Executes an action from a monad with added state in the underlying monad `m`. Given an initial
-state, it returns a value, discarding the final state.
-
-The monad `m` must support `ST` effects in order to create and mutate reference cells.
--/
 @[always_inline, inline]
 def StateRefT'.run' {ω σ : Type} {m : Type → Type} [Monad m] [MonadLiftT (ST ω) m] {α : Type} (x : StateRefT' ω σ m α) (s : σ) : m α := do
   let (a, _) ← x.run s
@@ -46,12 +27,6 @@ def StateRefT'.run' {ω σ : Type} {m : Type → Type} [Monad m] [MonadLiftT (ST
 namespace StateRefT'
 variable {ω σ : Type} {m : Type → Type} {α : Type}
 
-/--
-Runs an action from the underlying monad in the monad with state. The state is not modified.
-
-This function is typically implicitly accessed via a `MonadLiftT` instance as part of [automatic
-lifting](lean-manual://section/monad-lifting).
--/
 @[always_inline, inline]
 protected def lift (x : m α) : StateRefT' ω σ m α :=
   fun _ => x
@@ -61,30 +36,14 @@ instance : MonadLift m (StateRefT' ω σ m) := ⟨StateRefT'.lift⟩
 instance (σ m) : MonadFunctor m (StateRefT' ω σ m) := inferInstanceAs (MonadFunctor m (ReaderT _ _))
 instance [Alternative m] [Monad m] : Alternative (StateRefT' ω σ m) := inferInstanceAs (Alternative (ReaderT _ _))
 
-/--
-Retrieves the current value of the monad's mutable state.
-
-This increments the reference count of the state, which may inhibit in-place updates.
--/
 @[inline]
 protected def get [MonadLiftT (ST ω) m] : StateRefT' ω σ m σ :=
   fun ref => ref.get
 
-/--
-Replaces the mutable state with a new value.
--/
 @[inline]
 protected def set [MonadLiftT (ST ω) m] (s : σ) : StateRefT' ω σ m PUnit :=
   fun ref => ref.set s
 
-/--
-Applies a function to the current state that both computes a new state and a value. The new state
-replaces the current state, and the value is returned.
-
-It is equivalent to a `get` followed by a `set`. However, using `modifyGet` may lead to higher
-performance because it doesn't add a new reference to the state value. Additional references can
-inhibit in-place updates of data.
--/
 @[inline]
 protected def modifyGet [MonadLiftT (ST ω) m] (f : σ → α × σ) : StateRefT' ω σ m α :=
   fun ref => ref.modifyGet f

src/Init/Conv.lean

@@ -306,10 +306,6 @@ syntax (name := first) "first " withPosition((ppDedent(ppLine) colGe "| " convSe
 /-- `try tac` runs `tac` and succeeds even if `tac` failed. -/
 macro "try " t:convSeq : conv => `(conv| first | $t | skip)
 
-/--
-`tac <;> tac'` runs `tac` on the main goal and `tac'` on each produced goal, concatenating all goals
-produced by `tac'`.
--/
 macro:1 x:conv tk:" <;> " y:conv:0 : conv =>
   `(conv| tactic' => (conv' => $x:conv) <;>%$tk (conv' => $y:conv))
 

src/Init/Data/AC.lean

@@ -39,7 +39,7 @@ class EvalInformation (α : Sort u) (β : Sort v) where
   evalVar : α → Nat → β
 
 def Context.var (ctx : Context α) (idx : Nat) : Variable ctx.op :=
-  ctx.vars[idx]?.getD ⟨ctx.arbitrary, none⟩
+  ctx.vars.getD idx ⟨ctx.arbitrary, none⟩
 
 instance : ContextInformation (Context α) where
   isNeutral ctx x := ctx.var x |>.neutral.isSome

src/Init/Data/Array.lean

@@ -27,4 +27,3 @@ import Init.Data.Array.Range
 import Init.Data.Array.Erase
 import Init.Data.Array.Zip
 import Init.Data.Array.InsertIdx
-import Init.Data.Array.Extract

src/Init/Data/Array/Attach.lean

@@ -9,20 +9,18 @@ import Init.Data.Array.Lemmas
 import Init.Data.Array.Count
 import Init.Data.List.Attach
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 namespace Array
 
 /--
-Maps a partially defined function (defined on those terms of `α` that satisfy a predicate `P`) over
-an array `xs : Array α`, given a proof that every element of `xs` in fact satisfies `P`.
+`O(n)`. Partial map. If `f : Π a, P a → β` is a partial function defined on
+`a : α` satisfying `P`, then `pmap f l h` is essentially the same as `map f l`
+but is defined only when all members of `l` satisfy `P`, using the proof
+to apply `f`.
 
-`Array.pmap`, named for “partial map,” is the equivalent of `Array.map` for such partial functions.
+We replace this at runtime with a more efficient version via the `csimp` lemma `pmap_eq_pmapImpl`.
 -/
-
-def pmap {P : α → Prop} (f : ∀ a, P a → β) (xs : Array α) (H : ∀ a ∈ xs, P a) : Array β :=
-  (xs.toList.pmap f (fun a m => H a (mem_def.mpr m))).toArray
+def pmap {P : α → Prop} (f : ∀ a, P a → β) (l : Array α) (H : ∀ a ∈ l, P a) : Array β :=
+  (l.toList.pmap f (fun a m => H a (mem_def.mpr m))).toArray
 
 /--
 Unsafe implementation of `attachWith`, taking advantage of the fact that the representation of
@@ -31,27 +29,14 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
 @[inline] private unsafe def attachWithImpl
     (xs : Array α) (P : α → Prop) (_ : ∀ x ∈ xs, P x) : Array {x // P x} := unsafeCast xs
 
-/--
-“Attaches” individual proofs to an array of values that satisfy a predicate `P`, returning an array
-of elements in the corresponding subtype `{ x // P x }`.
-
-`O(1)`.
--/
+/-- `O(1)`. "Attach" a proof `P x` that holds for all the elements of `xs` to produce a new array
+  with the same elements but in the type `{x // P x}`. -/
 @[implemented_by attachWithImpl] def attachWith
     (xs : Array α) (P : α → Prop) (H : ∀ x ∈ xs, P x) : Array {x // P x} :=
   ⟨xs.toList.attachWith P fun x h => H x (Array.Mem.mk h)⟩
 
-/--
-“Attaches” the proof that the elements of `xs` are in fact elements of `xs`, producing a new array with
-the same elements but in the subtype `{ x // x ∈ xs }`.
-
-`O(1)`.
-
-This function is primarily used to allow definitions by [well-founded
-recursion](lean-manual://section/well-founded-recursion) that use higher-order functions (such as
-`Array.map`) to prove that an value taken from a list is smaller than the list. This allows the
-well-founded recursion mechanism to prove that the function terminates.
--/
+/-- `O(1)`. "Attach" the proof that the elements of `xs` are in `xs` to produce a new array
+  with the same elements but in the type `{x // x ∈ xs}`. -/
 @[inline] def attach (xs : Array α) : Array {x // x ∈ xs} := xs.attachWith _ fun _ => id
 
 @[simp] theorem _root_.List.attachWith_toArray {l : List α} {P : α → Prop} {H : ∀ x ∈ l.toArray, P x} :
@@ -66,35 +51,35 @@ well-founded recursion mechanism to prove that the function terminates.
     l.toArray.pmap f H = (l.pmap f (by simpa using H)).toArray := by
   simp [pmap]
 
-@[simp] theorem toList_attachWith {xs : Array α} {P : α → Prop} {H : ∀ x ∈ xs, P x} :
-   (xs.attachWith P H).toList = xs.toList.attachWith P (by simpa [mem_toList] using H) := by
+@[simp] theorem toList_attachWith {l : Array α} {P : α → Prop} {H : ∀ x ∈ l, P x} :
+   (l.attachWith P H).toList = l.toList.attachWith P (by simpa [mem_toList] using H) := by
   simp [attachWith]
 
-@[simp] theorem toList_attach {xs : Array α} :
-    xs.attach.toList = xs.toList.attachWith (· ∈ xs) (by simp [mem_toList]) := by
+@[simp] theorem toList_attach {α : Type _} {l : Array α} :
+    l.attach.toList = l.toList.attachWith (· ∈ l) (by simp [mem_toList]) := by
   simp [attach]
 
-@[simp] theorem toList_pmap {xs : Array α} {P : α → Prop} {f : ∀ a, P a → β} {H : ∀ a ∈ xs, P a} :
-    (xs.pmap f H).toList = xs.toList.pmap f (fun a m => H a (mem_def.mpr m)) := by
+@[simp] theorem toList_pmap {l : Array α} {P : α → Prop} {f : ∀ a, P a → β} {H : ∀ a ∈ l, P a} :
+    (l.pmap f H).toList = l.toList.pmap f (fun a m => H a (mem_def.mpr m)) := by
   simp [pmap]
 
 /-- Implementation of `pmap` using the zero-copy version of `attach`. -/
-@[inline] private def pmapImpl {P : α → Prop} (f : ∀ a, P a → β) (xs : Array α) (H : ∀ a ∈ xs, P a) :
-    Array β := (xs.attachWith _ H).map fun ⟨x, h'⟩ => f x h'
+@[inline] private def pmapImpl {P : α → Prop} (f : ∀ a, P a → β) (l : Array α) (H : ∀ a ∈ l, P a) :
+    Array β := (l.attachWith _ H).map fun ⟨x, h'⟩ => f x h'
 
 @[csimp] private theorem pmap_eq_pmapImpl : @pmap = @pmapImpl := by
-  funext α β p f xs H
-  cases xs
-  simp only [pmap, pmapImpl, List.attachWith_toArray, List.map_toArray, mk.injEq, List.map_attachWith_eq_pmap]
+  funext α β p f L h'
+  cases L
+  simp only [pmap, pmapImpl, List.attachWith_toArray, List.map_toArray, mk.injEq, List.map_attachWith]
   apply List.pmap_congr_left
   intro a m h₁ h₂
   congr
 
 @[simp] theorem pmap_empty {P : α → Prop} (f : ∀ a, P a → β) : pmap f #[] (by simp) = #[] := rfl
 
-@[simp] theorem pmap_push {P : α → Prop} (f : ∀ a, P a → β) (a : α) (xs : Array α) (h : ∀ b ∈ xs.push a, P b) :
-    pmap f (xs.push a) h =
-      (pmap f xs (fun a m => by simp at h; exact h a (.inl m))).push (f a (h a (by simp))) := by
+@[simp] theorem pmap_push {P : α → Prop} (f : ∀ a, P a → β) (a : α) (l : Array α) (h : ∀ b ∈ l.push a, P b) :
+    pmap f (l.push a) h =
+      (pmap f l (fun a m => by simp at h; exact h a (.inl m))).push (f a (h a (by simp))) := by
   simp [pmap]
 
 @[simp] theorem attach_empty : (#[] : Array α).attach = #[] := rfl
@@ -109,160 +94,159 @@ well-founded recursion mechanism to prove that the function terminates.
   simp
 
 @[simp]
-theorem pmap_eq_map {p : α → Prop} {f : α → β} {xs : Array α} (H) :
-    @pmap _ _ p (fun a _ => f a) xs H = map f xs := by
-  cases xs; simp
+theorem pmap_eq_map (p : α → Prop) (f : α → β) (l : Array α) (H) :
+    @pmap _ _ p (fun a _ => f a) l H = map f l := by
+  cases l; simp
 
-theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a, q a → β} (xs : Array α) {H₁ H₂}
-    (h : ∀ a ∈ xs, ∀ (h₁ h₂), f a h₁ = g a h₂) : pmap f xs H₁ = pmap g xs H₂ := by
-  cases xs
+theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a, q a → β} (l : Array α) {H₁ H₂}
+    (h : ∀ a ∈ l, ∀ (h₁ h₂), f a h₁ = g a h₂) : pmap f l H₁ = pmap g l H₂ := by
+  cases l
   simp only [mem_toArray] at h
   simp only [List.pmap_toArray, mk.injEq]
   rw [List.pmap_congr_left _ h]
 
-theorem map_pmap {p : α → Prop} {g : β → γ} {f : ∀ a, p a → β} {xs : Array α} (H) :
-    map g (pmap f xs H) = pmap (fun a h => g (f a h)) xs H := by
-  cases xs
+theorem map_pmap {p : α → Prop} (g : β → γ) (f : ∀ a, p a → β) (l H) :
+    map g (pmap f l H) = pmap (fun a h => g (f a h)) l H := by
+  cases l
   simp [List.map_pmap]
 
-theorem pmap_map {p : β → Prop} {g : ∀ b, p b → γ} {f : α → β} {xs : Array α} (H) :
-    pmap g (map f xs) H = pmap (fun a h => g (f a) h) xs fun _ h => H _ (mem_map_of_mem h) := by
-  cases xs
+theorem pmap_map {p : β → Prop} (g : ∀ b, p b → γ) (f : α → β) (l H) :
+    pmap g (map f l) H = pmap (fun a h => g (f a) h) l fun _ h => H _ (mem_map_of_mem _ h) := by
+  cases l
   simp [List.pmap_map]
 
-theorem attach_congr {xs ys : Array α} (h : xs = ys) :
-    xs.attach = ys.attach.map (fun x => ⟨x.1, h ▸ x.2⟩) := by
+theorem attach_congr {l₁ l₂ : Array α} (h : l₁ = l₂) :
+    l₁.attach = l₂.attach.map (fun x => ⟨x.1, h ▸ x.2⟩) := by
   subst h
   simp
 
-theorem attachWith_congr {xs ys : Array α} (w : xs = ys) {P : α → Prop} {H : ∀ x ∈ xs, P x} :
-    xs.attachWith P H = ys.attachWith P fun _ h => H _ (w ▸ h) := by
+theorem attachWith_congr {l₁ l₂ : Array α} (w : l₁ = l₂) {P : α → Prop} {H : ∀ x ∈ l₁, P x} :
+    l₁.attachWith P H = l₂.attachWith P fun _ h => H _ (w ▸ h) := by
   subst w
   simp
 
-@[simp] theorem attach_push {a : α} {xs : Array α} :
-    (xs.push a).attach =
-      (xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_push_of_mem a h⟩)).push ⟨a, by simp⟩ := by
-  cases xs
+@[simp] theorem attach_push {a : α} {l : Array α} :
+    (l.push a).attach =
+      (l.attach.map (fun ⟨x, h⟩ => ⟨x, mem_push_of_mem a h⟩)).push ⟨a, by simp⟩ := by
+  cases l
   rw [attach_congr (List.push_toArray _ _)]
   simp [Function.comp_def]
 
-@[simp] theorem attachWith_push {a : α} {xs : Array α} {P : α → Prop} {H : ∀ x ∈ xs.push a, P x} :
-    (xs.push a).attachWith P H =
-      (xs.attachWith P (fun x h => by simp at H; exact H x (.inl h))).push ⟨a, H a (by simp)⟩ := by
-  cases xs
+@[simp] theorem attachWith_push {a : α} {l : Array α} {P : α → Prop} {H : ∀ x ∈ l.push a, P x} :
+    (l.push a).attachWith P H =
+      (l.attachWith P (fun x h => by simp at H; exact H x (.inl h))).push ⟨a, H a (by simp)⟩ := by
+  cases l
   simp [attachWith_congr (List.push_toArray _ _)]
 
-theorem pmap_eq_map_attach {p : α → Prop} {f : ∀ a, p a → β} {xs : Array α} (H) :
-    pmap f xs H = xs.attach.map fun x => f x.1 (H _ x.2) := by
-  cases xs
+theorem pmap_eq_map_attach {p : α → Prop} (f : ∀ a, p a → β) (l H) :
+    pmap f l H = l.attach.map fun x => f x.1 (H _ x.2) := by
+  cases l
   simp [List.pmap_eq_map_attach]
 
 @[simp]
-theorem pmap_eq_attachWith {p q : α → Prop} {f : ∀ a, p a → q a} {xs : Array α} (H) :
-    pmap (fun a h => ⟨a, f a h⟩) xs H = xs.attachWith q (fun x h => f x (H x h)) := by
-  cases xs
+theorem pmap_eq_attachWith {p q : α → Prop} (f : ∀ a, p a → q a) (l H) :
+    pmap (fun a h => ⟨a, f a h⟩) l H = l.attachWith q (fun x h => f x (H x h)) := by
+  cases l
   simp [List.pmap_eq_attachWith]
 
-theorem attach_map_val (xs : Array α) (f : α → β) :
-    (xs.attach.map fun (i : {i // i ∈ xs}) => f i) = xs.map f := by
-  cases xs
+theorem attach_map_coe (l : Array α) (f : α → β) :
+    (l.attach.map fun (i : {i // i ∈ l}) => f i) = l.map f := by
+  cases l
   simp
 
-@[deprecated attach_map_val (since := "2025-02-17")]
-abbrev attach_map_coe := @attach_map_val
+theorem attach_map_val (l : Array α) (f : α → β) : (l.attach.map fun i => f i.val) = l.map f :=
+  attach_map_coe _ _
 
--- The argument `xs : Array α` is explicit to allow rewriting from right to left.
-theorem attach_map_subtype_val (xs : Array α) : xs.attach.map Subtype.val = xs := by
-  cases xs; simp
+theorem attach_map_subtype_val (l : Array α) : l.attach.map Subtype.val = l := by
+  cases l; simp
 
-theorem attachWith_map_val {p : α → Prop} {f : α → β} {xs : Array α} (H : ∀ a ∈ xs, p a) :
-    ((xs.attachWith p H).map fun (i : { i // p i}) => f i) = xs.map f := by
-  cases xs; simp
+theorem attachWith_map_coe {p : α → Prop} (f : α → β) (l : Array α) (H : ∀ a ∈ l, p a) :
+    ((l.attachWith p H).map fun (i : { i // p i}) => f i) = l.map f := by
+  cases l; simp
 
-@[deprecated attachWith_map_val (since := "2025-02-17")]
-abbrev attachWith_map_coe := @attachWith_map_val
+theorem attachWith_map_val {p : α → Prop} (f : α → β) (l : Array α) (H : ∀ a ∈ l, p a) :
+    ((l.attachWith p H).map fun i => f i.val) = l.map f :=
+  attachWith_map_coe _ _ _
 
-theorem attachWith_map_subtype_val {p : α → Prop} {xs : Array α} (H : ∀ a ∈ xs, p a) :
-    (xs.attachWith p H).map Subtype.val = xs := by
-  cases xs; simp
+theorem attachWith_map_subtype_val {p : α → Prop} (l : Array α) (H : ∀ a ∈ l, p a) :
+    (l.attachWith p H).map Subtype.val = l := by
+  cases l; simp
 
 @[simp]
-theorem mem_attach (xs : Array α) : ∀ x, x ∈ xs.attach
+theorem mem_attach (l : Array α) : ∀ x, x ∈ l.attach
   | ⟨a, h⟩ => by
     have := mem_map.1 (by rw [attach_map_subtype_val] <;> exact h)
     rcases this with ⟨⟨_, _⟩, m, rfl⟩
     exact m
 
 @[simp]
-theorem mem_attachWith {xs : Array α} {q : α → Prop} (H) (x : {x // q x}) :
-    x ∈ xs.attachWith q H ↔ x.1 ∈ xs := by
-  cases xs
+theorem mem_attachWith (l : Array α) {q : α → Prop} (H) (x : {x // q x}) :
+    x ∈ l.attachWith q H ↔ x.1 ∈ l := by
+  cases l
   simp
 
 @[simp]
-theorem mem_pmap {p : α → Prop} {f : ∀ a, p a → β} {xs H b} :
-    b ∈ pmap f xs H ↔ ∃ (a : _) (h : a ∈ xs), f a (H a h) = b := by
+theorem mem_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H b} :
+    b ∈ pmap f l H ↔ ∃ (a : _) (h : a ∈ l), f a (H a h) = b := by
   simp only [pmap_eq_map_attach, mem_map, mem_attach, true_and, Subtype.exists, eq_comm]
 
-theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {xs H} {a} (h : a ∈ xs) :
-    f a (H a h) ∈ pmap f xs H := by
+theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {l H} {a} (h : a ∈ l) :
+    f a (H a h) ∈ pmap f l H := by
   rw [mem_pmap]
   exact ⟨a, h, rfl⟩
 
 @[simp]
-theorem size_pmap {p : α → Prop} {f : ∀ a, p a → β} {xs H} : (pmap f xs H).size = xs.size := by
-  cases xs; simp
+theorem size_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H} : (pmap f l H).size = l.size := by
+  cases l; simp
 
 @[simp]
-theorem size_attach {xs : Array α} : xs.attach.size = xs.size := by
-  cases xs; simp
+theorem size_attach {L : Array α} : L.attach.size = L.size := by
+  cases L; simp
 
 @[simp]
-theorem size_attachWith {p : α → Prop} {xs : Array α} {H} : (xs.attachWith p H).size = xs.size := by
-  cases xs; simp
+theorem size_attachWith {p : α → Prop} {l : Array α} {H} : (l.attachWith p H).size = l.size := by
+  cases l; simp
 
 @[simp]
-theorem pmap_eq_empty_iff {p : α → Prop} {f : ∀ a, p a → β} {xs H} : pmap f xs H = #[] ↔ xs = #[] := by
-  cases xs; simp
+theorem pmap_eq_empty_iff {p : α → Prop} {f : ∀ a, p a → β} {l H} : pmap f l H = #[] ↔ l = #[] := by
+  cases l; simp
 
 theorem pmap_ne_empty_iff {P : α → Prop} (f : (a : α) → P a → β) {xs : Array α}
     (H : ∀ (a : α), a ∈ xs → P a) : xs.pmap f H ≠ #[] ↔ xs ≠ #[] := by
   cases xs; simp
 
-theorem pmap_eq_self {xs : Array α} {p : α → Prop} {hp : ∀ (a : α), a ∈ xs → p a}
-    {f : (a : α) → p a → α} : xs.pmap f hp = xs ↔ ∀ a (h : a ∈ xs), f a (hp a h) = a := by
-  cases xs; simp [List.pmap_eq_self]
+theorem pmap_eq_self {l : Array α} {p : α → Prop} {hp : ∀ (a : α), a ∈ l → p a}
+    {f : (a : α) → p a → α} : l.pmap f hp = l ↔ ∀ a (h : a ∈ l), f a (hp a h) = a := by
+  cases l; simp [List.pmap_eq_self]
 
 @[simp]
-theorem attach_eq_empty_iff {xs : Array α} : xs.attach = #[] ↔ xs = #[] := by
-  cases xs; simp
+theorem attach_eq_empty_iff {l : Array α} : l.attach = #[] ↔ l = #[] := by
+  cases l; simp
 
-theorem attach_ne_empty_iff {xs : Array α} : xs.attach ≠ #[] ↔ xs ≠ #[] := by
-  cases xs; simp
+theorem attach_ne_empty_iff {l : Array α} : l.attach ≠ #[] ↔ l ≠ #[] := by
+  cases l; simp
 
 @[simp]
-theorem attachWith_eq_empty_iff {xs : Array α} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
-    xs.attachWith P H = #[] ↔ xs = #[] := by
-  cases xs; simp
+theorem attachWith_eq_empty_iff {l : Array α} {P : α → Prop} {H : ∀ a ∈ l, P a} :
+    l.attachWith P H = #[] ↔ l = #[] := by
+  cases l; simp
 
-theorem attachWith_ne_empty_iff {xs : Array α} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
-    xs.attachWith P H ≠ #[] ↔ xs ≠ #[] := by
-  cases xs; simp
+theorem attachWith_ne_empty_iff {l : Array α} {P : α → Prop} {H : ∀ a ∈ l, P a} :
+    l.attachWith P H ≠ #[] ↔ l ≠ #[] := by
+  cases l; simp
 
 @[simp]
-theorem getElem?_pmap {p : α → Prop} {f : ∀ a, p a → β} {xs : Array α} (h : ∀ a ∈ xs, p a) (i : Nat) :
-    (pmap f xs h)[i]? = Option.pmap f xs[i]? fun x H => h x (mem_of_getElem? H) := by
-  cases xs; simp
+theorem getElem?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : Array α} (h : ∀ a ∈ l, p a) (i : Nat) :
+    (pmap f l h)[i]? = Option.pmap f l[i]? fun x H => h x (mem_of_getElem? H) := by
+  cases l; simp
 
--- The argument `f` is explicit to allow rewriting from right to left.
 @[simp]
-theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {xs : Array α} (h : ∀ a ∈ xs, p a) {i : Nat}
-    (hi : i < (pmap f xs h).size) :
-    (pmap f xs h)[i] =
-      f (xs[i]'(@size_pmap _ _ p f xs h ▸ hi))
-        (h _ (getElem_mem (@size_pmap _ _ p f xs h ▸ hi))) := by
-  cases xs; simp
+theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : Array α} (h : ∀ a ∈ l, p a) {i : Nat}
+    (hi : i < (pmap f l h).size) :
+    (pmap f l h)[i] =
+      f (l[i]'(@size_pmap _ _ p f l h ▸ hi))
+        (h _ (getElem_mem (@size_pmap _ _ p f l h ▸ hi))) := by
+  cases l; simp
 
 @[simp]
 theorem getElem?_attachWith {xs : Array α} {i : Nat} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
@@ -285,40 +269,40 @@ theorem getElem_attach {xs : Array α} {i : Nat} (h : i < xs.attach.size) :
     xs.attach[i] = ⟨xs[i]'(by simpa using h), getElem_mem (by simpa using h)⟩ :=
   getElem_attachWith h
 
-@[simp] theorem pmap_attach {xs : Array α} {p : {x // x ∈ xs} → Prop} {f : ∀ a, p a → β} (H) :
-    pmap f xs.attach H =
-      xs.pmap (P := fun a => ∃ h : a ∈ xs, p ⟨a, h⟩)
+@[simp] theorem pmap_attach (l : Array α) {p : {x // x ∈ l} → Prop} (f : ∀ a, p a → β) (H) :
+    pmap f l.attach H =
+      l.pmap (P := fun a => ∃ h : a ∈ l, p ⟨a, h⟩)
         (fun a h => f ⟨a, h.1⟩ h.2) (fun a h => ⟨h, H ⟨a, h⟩ (by simp)⟩) := by
   ext <;> simp
 
-@[simp] theorem pmap_attachWith {xs : Array α} {p : {x // q x} → Prop} {f : ∀ a, p a → β} (H₁ H₂) :
-    pmap f (xs.attachWith q H₁) H₂ =
-      xs.pmap (P := fun a => ∃ h : q a, p ⟨a, h⟩)
+@[simp] theorem pmap_attachWith (l : Array α) {p : {x // q x} → Prop} (f : ∀ a, p a → β) (H₁ H₂) :
+    pmap f (l.attachWith q H₁) H₂ =
+      l.pmap (P := fun a => ∃ h : q a, p ⟨a, h⟩)
         (fun a h => f ⟨a, h.1⟩ h.2) (fun a h => ⟨H₁ _ h, H₂ ⟨a, H₁ _ h⟩ (by simpa)⟩) := by
   ext <;> simp
 
-theorem foldl_pmap {xs : Array α} {P : α → Prop} {f : (a : α) → P a → β}
-    (H : ∀ (a : α), a ∈ xs → P a) (g : γ → β → γ) (x : γ) :
-    (xs.pmap f H).foldl g x = xs.attach.foldl (fun acc a => g acc (f a.1 (H _ a.2))) x := by
+theorem foldl_pmap (l : Array α) {P : α → Prop} (f : (a : α) → P a → β)
+  (H : ∀ (a : α), a ∈ l → P a) (g : γ → β → γ) (x : γ) :
+    (l.pmap f H).foldl g x = l.attach.foldl (fun acc a => g acc (f a.1 (H _ a.2))) x := by
   rw [pmap_eq_map_attach, foldl_map]
 
-theorem foldr_pmap {xs : Array α} {P : α → Prop} {f : (a : α) → P a → β}
-    (H : ∀ (a : α), a ∈ xs → P a) (g : β → γ → γ) (x : γ) :
-    (xs.pmap f H).foldr g x = xs.attach.foldr (fun a acc => g (f a.1 (H _ a.2)) acc) x := by
+theorem foldr_pmap (l : Array α) {P : α → Prop} (f : (a : α) → P a → β)
+  (H : ∀ (a : α), a ∈ l → P a) (g : β → γ → γ) (x : γ) :
+    (l.pmap f H).foldr g x = l.attach.foldr (fun a acc => g (f a.1 (H _ a.2)) acc) x := by
   rw [pmap_eq_map_attach, foldr_map]
 
 @[simp] theorem foldl_attachWith
-    {xs : Array α} {q : α → Prop} (H : ∀ a, a ∈ xs → q a) {f : β → { x // q x} → β} {b} (w : stop = xs.size) :
-    (xs.attachWith q H).foldl f b 0 stop = xs.attach.foldl (fun b ⟨a, h⟩ => f b ⟨a, H _ h⟩) b := by
+    (l : Array α) {q : α → Prop} (H : ∀ a, a ∈ l → q a) {f : β → { x // q x} → β} {b} (w : stop = l.size) :
+    (l.attachWith q H).foldl f b 0 stop = l.attach.foldl (fun b ⟨a, h⟩ => f b ⟨a, H _ h⟩) b := by
   subst w
-  rcases xs with ⟨xs⟩
+  rcases l with ⟨l⟩
   simp [List.foldl_attachWith, List.foldl_map]
 
 @[simp] theorem foldr_attachWith
-    {xs : Array α} {q : α → Prop} (H : ∀ a, a ∈ xs → q a) {f : { x // q x} → β → β} {b} (w : start = xs.size) :
-    (xs.attachWith q H).foldr f b start 0 = xs.attach.foldr (fun a acc => f ⟨a.1, H _ a.2⟩ acc) b := by
+    (l : Array α) {q : α → Prop} (H : ∀ a, a ∈ l → q a) {f : { x // q x} → β → β} {b} (w : start = l.size) :
+    (l.attachWith q H).foldr f b start 0 = l.attach.foldr (fun a acc => f ⟨a.1, H _ a.2⟩ acc) b := by
   subst w
-  rcases xs with ⟨xs⟩
+  rcases l with ⟨l⟩
   simp [List.foldr_attachWith, List.foldr_map]
 
 /--
@@ -331,10 +315,10 @@ Unfortunately this can't be applied by `simp` because of the higher order unific
 and even when rewriting we need to specify the function explicitly.
 See however `foldl_subtype` below.
 -/
-theorem foldl_attach {xs : Array α} {f : β → α → β} {b : β} :
-    xs.attach.foldl (fun acc t => f acc t.1) b = xs.foldl f b := by
-  rcases xs with ⟨xs⟩
-  simp only [List.attach_toArray, List.attachWith_mem_toArray, List.size_toArray,
+theorem foldl_attach (l : Array α) (f : β → α → β) (b : β) :
+    l.attach.foldl (fun acc t => f acc t.1) b = l.foldl f b := by
+  rcases l with ⟨l⟩
+  simp only [List.attach_toArray, List.attachWith_mem_toArray, List.map_attach, size_toArray,
     List.length_pmap, List.foldl_toArray', mem_toArray, List.foldl_subtype]
   congr
   ext
@@ -350,103 +334,95 @@ Unfortunately this can't be applied by `simp` because of the higher order unific
 and even when rewriting we need to specify the function explicitly.
 See however `foldr_subtype` below.
 -/
-theorem foldr_attach {xs : Array α} {f : α → β → β} {b : β} :
-    xs.attach.foldr (fun t acc => f t.1 acc) b = xs.foldr f b := by
-  rcases xs with ⟨xs⟩
-  simp only [List.attach_toArray, List.attachWith_mem_toArray, List.size_toArray,
+theorem foldr_attach (l : Array α) (f : α → β → β) (b : β) :
+    l.attach.foldr (fun t acc => f t.1 acc) b = l.foldr f b := by
+  rcases l with ⟨l⟩
+  simp only [List.attach_toArray, List.attachWith_mem_toArray, List.map_attach, size_toArray,
     List.length_pmap, List.foldr_toArray', mem_toArray, List.foldr_subtype]
   congr
   ext
   simpa using fun a => List.mem_of_getElem? a
 
-theorem attach_map {xs : Array α} {f : α → β} :
-    (xs.map f).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨f x, mem_map_of_mem h⟩) := by
-  cases xs
+theorem attach_map {l : Array α} (f : α → β) :
+    (l.map f).attach = l.attach.map (fun ⟨x, h⟩ => ⟨f x, mem_map_of_mem f h⟩) := by
+  cases l
   ext <;> simp
 
-theorem attachWith_map {xs : Array α} {f : α → β} {P : β → Prop} (H : ∀ (b : β), b ∈ xs.map f → P b) :
-    (xs.map f).attachWith P H = (xs.attachWith (P ∘ f) (fun _ h => H _ (mem_map_of_mem h))).map
+theorem attachWith_map {l : Array α} (f : α → β) {P : β → Prop} {H : ∀ (b : β), b ∈ l.map f → P b} :
+    (l.map f).attachWith P H = (l.attachWith (P ∘ f) (fun _ h => H _ (mem_map_of_mem f h))).map
       fun ⟨x, h⟩ => ⟨f x, h⟩ := by
-  cases xs
+  cases l
   simp [List.attachWith_map]
 
-@[simp] theorem map_attachWith {xs : Array α} {P : α → Prop} {H : ∀ (a : α), a ∈ xs → P a}
-    {f : { x // P x } → β} :
-    (xs.attachWith P H).map f = xs.attach.map fun ⟨x, h⟩ => f ⟨x, H _ h⟩ := by
-  cases xs <;> simp_all
-
-theorem map_attachWith_eq_pmap {xs : Array α} {P : α → Prop} {H : ∀ (a : α), a ∈ xs → P a}
-    {f : { x // P x } → β} :
-    (xs.attachWith P H).map f =
-      xs.pmap (fun a (h : a ∈ xs ∧ P a) => f ⟨a, H _ h.1⟩) (fun a h => ⟨h, H a h⟩) := by
-  cases xs
+theorem map_attachWith {l : Array α} {P : α → Prop} {H : ∀ (a : α), a ∈ l → P a}
+    (f : { x // P x } → β) :
+    (l.attachWith P H).map f =
+      l.pmap (fun a (h : a ∈ l ∧ P a) => f ⟨a, H _ h.1⟩) (fun a h => ⟨h, H a h⟩) := by
+  cases l
   ext <;> simp
 
 /-- See also `pmap_eq_map_attach` for writing `pmap` in terms of `map` and `attach`. -/
-theorem map_attach_eq_pmap {xs : Array α} {f : { x // x ∈ xs } → β} :
-    xs.attach.map f = xs.pmap (fun a h => f ⟨a, h⟩) (fun _ => id) := by
-  cases xs
+theorem map_attach {l : Array α} (f : { x // x ∈ l } → β) :
+    l.attach.map f = l.pmap (fun a h => f ⟨a, h⟩) (fun _ => id) := by
+  cases l
   ext <;> simp
 
-@[deprecated map_attach_eq_pmap (since := "2025-02-09")]
-abbrev map_attach := @map_attach_eq_pmap
-
-theorem attach_filterMap {xs : Array α} {f : α → Option β} :
-    (xs.filterMap f).attach = xs.attach.filterMap
+theorem attach_filterMap {l : Array α} {f : α → Option β} :
+    (l.filterMap f).attach = l.attach.filterMap
       fun ⟨x, h⟩ => (f x).pbind (fun b m => some ⟨b, mem_filterMap.mpr ⟨x, h, m⟩⟩) := by
-  cases xs
-  rw [attach_congr List.filterMap_toArray]
+  cases l
+  rw [attach_congr (List.filterMap_toArray f _)]
   simp [List.attach_filterMap, List.map_filterMap, Function.comp_def]
 
-theorem attach_filter {xs : Array α} (p : α → Bool) :
-    (xs.filter p).attach = xs.attach.filterMap
+theorem attach_filter {l : Array α} (p : α → Bool) :
+    (l.filter p).attach = l.attach.filterMap
       fun x => if w : p x.1 then some ⟨x.1, mem_filter.mpr ⟨x.2, w⟩⟩ else none := by
-  cases xs
-  rw [attach_congr List.filter_toArray]
+  cases l
+  rw [attach_congr (List.filter_toArray p _)]
   simp [List.attach_filter, List.map_filterMap, Function.comp_def]
 
 -- We are still missing here `attachWith_filterMap` and `attachWith_filter`.
 
 @[simp]
-theorem filterMap_attachWith {q : α → Prop} {xs : Array α} {f : {x // q x} → Option β} (H)
-    (w : stop = (xs.attachWith q H).size) :
-    (xs.attachWith q H).filterMap f 0 stop = xs.attach.filterMap (fun ⟨x, h⟩ => f ⟨x, H _ h⟩) := by
+theorem filterMap_attachWith {q : α → Prop} {l : Array α} {f : {x // q x} → Option β} (H)
+    (w : stop = (l.attachWith q H).size) :
+    (l.attachWith q H).filterMap f 0 stop = l.attach.filterMap (fun ⟨x, h⟩ => f ⟨x, H _ h⟩) := by
   subst w
-  cases xs
+  cases l
   simp [Function.comp_def]
 
 @[simp]
-theorem filter_attachWith {q : α → Prop} {xs : Array α} {p : {x // q x} → Bool} (H)
-    (w : stop = (xs.attachWith q H).size) :
-    (xs.attachWith q H).filter p 0 stop =
-      (xs.attach.filter (fun ⟨x, h⟩ => p ⟨x, H _ h⟩)).map (fun ⟨x, h⟩ => ⟨x, H _ h⟩) := by
+theorem filter_attachWith {q : α → Prop} {l : Array α} {p : {x // q x} → Bool} (H)
+    (w : stop = (l.attachWith q H).size) :
+    (l.attachWith q H).filter p 0 stop =
+      (l.attach.filter (fun ⟨x, h⟩ => p ⟨x, H _ h⟩)).map (fun ⟨x, h⟩ => ⟨x, H _ h⟩) := by
   subst w
-  cases xs
+  cases l
   simp [Function.comp_def, List.filter_map]
 
-theorem pmap_pmap {p : α → Prop} {q : β → Prop} {g : ∀ a, p a → β} {f : ∀ b, q b → γ} {xs} (H₁ H₂) :
-    pmap f (pmap g xs H₁) H₂ =
-      pmap (α := { x // x ∈ xs }) (fun a h => f (g a h) (H₂ (g a h) (mem_pmap_of_mem a.2))) xs.attach
+theorem pmap_pmap {p : α → Prop} {q : β → Prop} (g : ∀ a, p a → β) (f : ∀ b, q b → γ) (l H₁ H₂) :
+    pmap f (pmap g l H₁) H₂ =
+      pmap (α := { x // x ∈ l }) (fun a h => f (g a h) (H₂ (g a h) (mem_pmap_of_mem a.2))) l.attach
         (fun a _ => H₁ a a.2) := by
-  cases xs
+  cases l
   simp [List.pmap_pmap, List.pmap_map]
 
-@[simp] theorem pmap_append {p : ι → Prop} {f : ∀ a : ι, p a → α} {xs ys : Array ι}
-    (h : ∀ a ∈ xs ++ ys, p a) :
-    (xs ++ ys).pmap f h =
-      (xs.pmap f fun a ha => h a (mem_append_left ys ha)) ++
-        ys.pmap f fun a ha => h a (mem_append_right xs ha) := by
-  cases xs
-  cases ys
+@[simp] theorem pmap_append {p : ι → Prop} (f : ∀ a : ι, p a → α) (l₁ l₂ : Array ι)
+    (h : ∀ a ∈ l₁ ++ l₂, p a) :
+    (l₁ ++ l₂).pmap f h =
+      (l₁.pmap f fun a ha => h a (mem_append_left l₂ ha)) ++
+        l₂.pmap f fun a ha => h a (mem_append_right l₁ ha) := by
+  cases l₁
+  cases l₂
   simp
 
-theorem pmap_append' {p : α → Prop} {f : ∀ a : α, p a → β} {xs ys : Array α}
-    (h₁ : ∀ a ∈ xs, p a) (h₂ : ∀ a ∈ ys, p a) :
-    ((xs ++ ys).pmap f fun a ha => (mem_append.1 ha).elim (h₁ a) (h₂ a)) =
-      xs.pmap f h₁ ++ ys.pmap f h₂ :=
-  pmap_append _
+theorem pmap_append' {p : α → Prop} (f : ∀ a : α, p a → β) (l₁ l₂ : Array α)
+    (h₁ : ∀ a ∈ l₁, p a) (h₂ : ∀ a ∈ l₂, p a) :
+    ((l₁ ++ l₂).pmap f fun a ha => (mem_append.1 ha).elim (h₁ a) (h₂ a)) =
+      l₁.pmap f h₁ ++ l₂.pmap f h₂ :=
+  pmap_append f l₁ l₂ _
 
-@[simp] theorem attach_append {xs ys : Array α} :
+@[simp] theorem attach_append (xs ys : Array α) :
     (xs ++ ys).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_append_left ys h⟩) ++
       ys.attach.map fun ⟨x, h⟩ => ⟨x, mem_append_right xs h⟩ := by
   cases xs
@@ -460,12 +436,12 @@ theorem pmap_append' {p : α → Prop} {f : ∀ a : α, p a → β} {xs ys : Arr
       ys.attachWith P (fun a h => H a (mem_append_right xs h)) := by
   simp [attachWith, attach_append, map_pmap, pmap_append]
 
-@[simp] theorem pmap_reverse {P : α → Prop} {f : (a : α) → P a → β} {xs : Array α}
+@[simp] theorem pmap_reverse {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
     (H : ∀ (a : α), a ∈ xs.reverse → P a) :
     xs.reverse.pmap f H = (xs.pmap f (fun a h => H a (by simpa using h))).reverse := by
   induction xs <;> simp_all
 
-theorem reverse_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : Array α}
+theorem reverse_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.pmap f H).reverse = xs.reverse.pmap f (fun a h => H a (by simpa using h)) := by
   rw [pmap_reverse]
@@ -483,18 +459,18 @@ theorem reverse_attachWith {P : α → Prop} {xs : Array α}
   cases xs
   simp
 
-@[simp] theorem attach_reverse {xs : Array α} :
+@[simp] theorem attach_reverse (xs : Array α) :
     xs.reverse.attach = xs.attach.reverse.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
   cases xs
-  rw [attach_congr List.reverse_toArray]
+  rw [attach_congr (List.reverse_toArray _)]
   simp
 
-theorem reverse_attach {xs : Array α} :
+theorem reverse_attach (xs : Array α) :
     xs.attach.reverse = xs.reverse.attach.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
   cases xs
   simp
 
-@[simp] theorem back?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : Array α}
+@[simp] theorem back?_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.pmap f H).back? = xs.attach.back?.map fun ⟨a, m⟩ => f a (H a m) := by
   cases xs
@@ -513,35 +489,35 @@ theorem back?_attach {xs : Array α} :
   simp
 
 @[simp]
-theorem countP_attach {xs : Array α} {p : α → Bool} :
-    xs.attach.countP (fun a : {x // x ∈ xs} => p a) = xs.countP p := by
-  cases xs
+theorem countP_attach (l : Array α) (p : α → Bool) :
+    l.attach.countP (fun a : {x // x ∈ l} => p a) = l.countP p := by
+  cases l
   simp [Function.comp_def]
 
 @[simp]
-theorem countP_attachWith {p : α → Prop} {q : α → Bool} {xs : Array α} {H : ∀ a ∈ xs, p a} :
-    (xs.attachWith p H).countP (fun a : {x // p x} => q a) = xs.countP q := by
-  cases xs
+theorem countP_attachWith {p : α → Prop} (l : Array α) (H : ∀ a ∈ l, p a) (q : α → Bool) :
+    (l.attachWith p H).countP (fun a : {x // p x} => q a) = l.countP q := by
+  cases l
   simp
 
 @[simp]
-theorem count_attach [DecidableEq α] {xs : Array α} {a : {x // x ∈ xs}} :
-    xs.attach.count a = xs.count ↑a := by
-  rcases xs with ⟨xs⟩
+theorem count_attach [DecidableEq α] (l : Array α) (a : {x // x ∈ l}) :
+    l.attach.count a = l.count ↑a := by
+  rcases l with ⟨l⟩
   simp only [List.attach_toArray, List.attachWith_mem_toArray, List.count_toArray]
-  rw [List.map_attach_eq_pmap, List.count_eq_countP]
+  rw [List.map_attach, List.count_eq_countP]
   simp only [Subtype.beq_iff]
   rw [List.countP_pmap, List.countP_attach (p := (fun x => x == a.1)), List.count]
 
 @[simp]
-theorem count_attachWith [DecidableEq α] {p : α → Prop} {xs : Array α} (H : ∀ a ∈ xs, p a) {a : {x // p x}} :
-    (xs.attachWith p H).count a = xs.count ↑a := by
-  cases xs
+theorem count_attachWith [DecidableEq α] {p : α → Prop} (l : Array α) (H : ∀ a ∈ l, p a) (a : {x // p x}) :
+    (l.attachWith p H).count a = l.count ↑a := by
+  cases l
   simp
 
-@[simp] theorem countP_pmap {p : α → Prop} {g : ∀ a, p a → β} {f : β → Bool} {xs : Array α} (H₁) :
-    (xs.pmap g H₁).countP f =
-      xs.attach.countP (fun ⟨a, m⟩ => f (g a (H₁ a m))) := by
+@[simp] theorem countP_pmap {p : α → Prop} (g : ∀ a, p a → β) (f : β → Bool) (l : Array α) (H₁) :
+    (l.pmap g H₁).countP f =
+      l.attach.countP (fun ⟨a, m⟩ => f (g a (H₁ a m))) := by
   simp [pmap_eq_map_attach, countP_map, Function.comp_def]
 
 /-! ## unattach
@@ -556,63 +532,49 @@ Further, we provide simp lemmas that push `unattach` inwards.
 -/
 
 /--
-Maps an array of terms in a subtype to the corresponding terms in the type by forgetting that they
-satisfy the predicate.
+A synonym for `l.map (·.val)`. Mostly this should not be needed by users.
+It is introduced as in intermediate step by lemmas such as `map_subtype`,
+and is ideally subsequently simplified away by `unattach_attach`.
 
-This is the inverse of `Array.attachWith` and a synonym for `xs.map (·.val)`.
-
-Mostly this should not be needed by users. It is introduced as an intermediate step by lemmas such
-as `map_subtype`, and is ideally subsequently simplified away by `unattach_attach`.
-
-This function is usually inserted automatically by Lean as an intermediate step while proving
-termination. It is rarely used explicitly in code. It is introduced as an intermediate step during
-the elaboration of definitions by [well-founded
-recursion](lean-manual://section/well-founded-recursion). If this function is encountered in a proof
-state, the right approach is usually the tactic `simp [Array.unattach, -Array.map_subtype]`.
+If not, usually the right approach is `simp [Array.unattach, -Array.map_subtype]` to unfold.
 -/
-def unattach {α : Type _} {p : α → Prop} (xs : Array { x // p x }) : Array α := xs.map (·.val)
+def unattach {α : Type _} {p : α → Prop} (l : Array { x // p x }) : Array α := l.map (·.val)
 
-@[simp] theorem unattach_nil {p : α → Prop} : (#[] : Array { x // p x }).unattach = #[] := by
-  simp [unattach]
-
-@[simp] theorem unattach_push {p : α → Prop} {a : { x // p x }} {xs : Array { x // p x }} :
-    (xs.push a).unattach = xs.unattach.push a.1 := by
+@[simp] theorem unattach_nil {p : α → Prop} : (#[] : Array { x // p x }).unattach = #[] := rfl
+@[simp] theorem unattach_push {p : α → Prop} {a : { x // p x }} {l : Array { x // p x }} :
+    (l.push a).unattach = l.unattach.push a.1 := by
   simp only [unattach, Array.map_push]
 
-@[simp] theorem mem_unattach {p : α → Prop} {xs : Array { x // p x }} {a} :
-    a ∈ xs.unattach ↔ ∃ h : p a, ⟨a, h⟩ ∈ xs := by
-  simp only [unattach, mem_map, Subtype.exists, exists_and_right, exists_eq_right]
-
-@[simp] theorem size_unattach {p : α → Prop} {xs : Array { x // p x }} :
-    xs.unattach.size = xs.size := by
+@[simp] theorem size_unattach {p : α → Prop} {l : Array { x // p x }} :
+    l.unattach.size = l.size := by
   unfold unattach
   simp
 
-@[simp] theorem _root_.List.unattach_toArray {p : α → Prop} {xs : List { x // p x }} :
-    xs.toArray.unattach = xs.unattach.toArray := by
+@[simp] theorem _root_.List.unattach_toArray {p : α → Prop} {l : List { x // p x }} :
+    l.toArray.unattach = l.unattach.toArray := by
   simp only [unattach, List.map_toArray, List.unattach]
 
-@[simp] theorem toList_unattach {p : α → Prop} {xs : Array { x // p x }} :
-    xs.unattach.toList = xs.toList.unattach := by
+@[simp] theorem toList_unattach {p : α → Prop} {l : Array { x // p x }} :
+    l.unattach.toList = l.toList.unattach := by
   simp only [unattach, toList_map, List.unattach]
 
-@[simp] theorem unattach_attach {xs : Array α} : xs.attach.unattach = xs := by
-  cases xs
+@[simp] theorem unattach_attach {l : Array α} : l.attach.unattach = l := by
+  cases l
   simp only [List.attach_toArray, List.unattach_toArray, List.unattach_attachWith]
 
-@[simp] theorem unattach_attachWith {p : α → Prop} {xs : Array α}
-    {H : ∀ a ∈ xs, p a} :
-    (xs.attachWith p H).unattach = xs := by
-  cases xs
+@[simp] theorem unattach_attachWith {p : α → Prop} {l : Array α}
+    {H : ∀ a ∈ l, p a} :
+    (l.attachWith p H).unattach = l := by
+  cases l
   simp
 
-@[simp] theorem getElem?_unattach {p : α → Prop} {xs : Array { x // p x }} (i : Nat) :
-    xs.unattach[i]? = xs[i]?.map Subtype.val := by
+@[simp] theorem getElem?_unattach {p : α → Prop} {l : Array { x // p x }} (i : Nat) :
+    l.unattach[i]? = l[i]?.map Subtype.val := by
   simp [unattach]
 
 @[simp] theorem getElem_unattach
-    {p : α → Prop} {xs : Array { x // p x }} (i : Nat) (h : i < xs.unattach.size) :
-    xs.unattach[i] = (xs[i]'(by simpa using h)).1 := by
+    {p : α → Prop} {l : Array { x // p x }} (i : Nat) (h : i < l.unattach.size) :
+    l.unattach[i] = (l[i]'(by simpa using h)).1 := by
   simp [unattach]
 
 /-! ### Recognizing higher order functions using a function that only depends on the value. -/
@@ -621,20 +583,20 @@ def unattach {α : Type _} {p : α → Prop} (xs : Array { x // p x }) : Array
 This lemma identifies folds over arrays of subtypes, where the function only depends on the value, not the proposition,
 and simplifies these to the function directly taking the value.
 -/
-theorem foldl_subtype {p : α → Prop} {xs : Array { x // p x }}
+theorem foldl_subtype {p : α → Prop} {l : Array { x // p x }}
     {f : β → { x // p x } → β} {g : β → α → β} {x : β}
     (hf : ∀ b x h, f b ⟨x, h⟩ = g b x) :
-    xs.foldl f x = xs.unattach.foldl g x := by
-  cases xs
+    l.foldl f x = l.unattach.foldl g x := by
+  cases l
   simp only [List.foldl_toArray', List.unattach_toArray]
   rw [List.foldl_subtype] -- Why can't simp do this?
   simp [hf]
 
 /-- Variant of `foldl_subtype` with side condition to check `stop = l.size`. -/
-@[simp] theorem foldl_subtype' {p : α → Prop} {xs : Array { x // p x }}
+@[simp] theorem foldl_subtype' {p : α → Prop} {l : Array { x // p x }}
     {f : β → { x // p x } → β} {g : β → α → β} {x : β}
-    (hf : ∀ b x h, f b ⟨x, h⟩ = g b x) (h : stop = xs.size) :
-    xs.foldl f x 0 stop = xs.unattach.foldl g x := by
+    (hf : ∀ b x h, f b ⟨x, h⟩ = g b x) (h : stop = l.size) :
+    l.foldl f x 0 stop = l.unattach.foldl g x := by
   subst h
   rwa [foldl_subtype]
 
@@ -642,20 +604,20 @@ theorem foldl_subtype {p : α → Prop} {xs : Array { x // p x }}
 This lemma identifies folds over arrays of subtypes, where the function only depends on the value, not the proposition,
 and simplifies these to the function directly taking the value.
 -/
-theorem foldr_subtype {p : α → Prop} {xs : Array { x // p x }}
+theorem foldr_subtype {p : α → Prop} {l : Array { x // p x }}
     {f : { x // p x } → β → β} {g : α → β → β} {x : β}
     (hf : ∀ x h b, f ⟨x, h⟩ b = g x b) :
-    xs.foldr f x = xs.unattach.foldr g x := by
-  cases xs
+    l.foldr f x = l.unattach.foldr g x := by
+  cases l
   simp only [List.foldr_toArray', List.unattach_toArray]
   rw [List.foldr_subtype]
   simp [hf]
 
 /-- Variant of `foldr_subtype` with side condition to check `stop = l.size`. -/
-@[simp] theorem foldr_subtype' {p : α → Prop} {xs : Array { x // p x }}
+@[simp] theorem foldr_subtype' {p : α → Prop} {l : Array { x // p x }}
     {f : { x // p x } → β → β} {g : α → β → β} {x : β}
-    (hf : ∀ x h b, f ⟨x, h⟩ b = g x b) (h : start = xs.size) :
-    xs.foldr f x start 0 = xs.unattach.foldr g x := by
+    (hf : ∀ x h b, f ⟨x, h⟩ b = g x b) (h : start = l.size) :
+    l.foldr f x start 0 = l.unattach.foldr g x := by
   subst h
   rwa [foldr_subtype]
 
@@ -663,155 +625,66 @@ theorem foldr_subtype {p : α → Prop} {xs : Array { x // p x }}
 This lemma identifies maps over arrays of subtypes, where the function only depends on the value, not the proposition,
 and simplifies these to the function directly taking the value.
 -/
-@[simp] theorem map_subtype {p : α → Prop} {xs : Array { x // p x }}
+@[simp] theorem map_subtype {p : α → Prop} {l : Array { x // p x }}
     {f : { x // p x } → β} {g : α → β} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
-    xs.map f = xs.unattach.map g := by
-  cases xs
+    l.map f = l.unattach.map g := by
+  cases l
   simp only [List.map_toArray, List.unattach_toArray]
   rw [List.map_subtype]
   simp [hf]
 
-@[simp] theorem filterMap_subtype {p : α → Prop} {xs : Array { x // p x }}
+@[simp] theorem filterMap_subtype {p : α → Prop} {l : Array { x // p x }}
     {f : { x // p x } → Option β} {g : α → Option β} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
-    xs.filterMap f = xs.unattach.filterMap g := by
-  cases xs
-  simp only [List.size_toArray, List.filterMap_toArray', List.unattach_toArray, List.length_unattach,
+    l.filterMap f = l.unattach.filterMap g := by
+  cases l
+  simp only [size_toArray, List.filterMap_toArray', List.unattach_toArray, List.length_unattach,
     mk.injEq]
   rw [List.filterMap_subtype]
   simp [hf]
 
-
-@[simp] theorem flatMap_subtype {p : α → Prop} {xs : Array { x // p x }}
-    {f : { x // p x } → Array β} {g : α → Array β} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
-    (xs.flatMap f) = xs.unattach.flatMap g := by
-  cases xs
-  simp only [List.size_toArray, List.flatMap_toArray, List.unattach_toArray, List.length_unattach,
-    mk.injEq]
-  rw [List.flatMap_subtype]
-  simp [hf]
-
-@[simp] theorem findSome?_subtype {p : α → Prop} {xs : Array { x // p x }}
+@[simp] theorem findSome?_subtype {p : α → Prop} {l : Array { x // p x }}
     {f : { x // p x } → Option β} {g : α → Option β} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
-    xs.findSome? f = xs.unattach.findSome? g := by
-  cases xs
+    l.findSome? f = l.unattach.findSome? g := by
+  cases l
   simp
   rw [List.findSome?_subtype hf]
 
-@[simp] theorem find?_subtype {p : α → Prop} {xs : Array { x // p x }}
+@[simp] theorem find?_subtype {p : α → Prop} {l : Array { x // p x }}
     {f : { x // p x } → Bool} {g : α → Bool} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
-    (xs.find? f).map Subtype.val = xs.unattach.find? g := by
-  cases xs
+    (l.find? f).map Subtype.val = l.unattach.find? g := by
+  cases l
   simp
   rw [List.find?_subtype hf]
 
-@[simp] theorem all_subtype {p : α → Prop} {xs : Array { x // p x }} {f : { x // p x } → Bool} {g : α → Bool}
-    (hf : ∀ x h, f ⟨x, h⟩ = g x) (w : stop = xs.size) :
-    xs.all f 0 stop = xs.unattach.all g := by
-  subst w
-  rcases xs with ⟨xs⟩
-  simp [hf]
-
-@[simp] theorem any_subtype {p : α → Prop} {xs : Array { x // p x }} {f : { x // p x } → Bool} {g : α → Bool}
-    (hf : ∀ x h, f ⟨x, h⟩ = g x) (w : stop = xs.size) :
-    xs.any f 0 stop = xs.unattach.any g := by
-  subst w
-  rcases xs with ⟨xs⟩
-  simp [hf]
-
 /-! ### Simp lemmas pushing `unattach` inwards. -/
 
-@[simp] theorem unattach_filter {p : α → Prop} {xs : Array { x // p x }}
+@[simp] theorem unattach_filter {p : α → Prop} {l : Array { x // p x }}
     {f : { x // p x } → Bool} {g : α → Bool} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
-    (xs.filter f).unattach = xs.unattach.filter g := by
-  cases xs
+    (l.filter f).unattach = l.unattach.filter g := by
+  cases l
   simp [hf]
 
-@[simp] theorem unattach_reverse {p : α → Prop} {xs : Array { x // p x }} :
-    xs.reverse.unattach = xs.unattach.reverse := by
-  cases xs
+@[simp] theorem unattach_reverse {p : α → Prop} {l : Array { x // p x }} :
+    l.reverse.unattach = l.unattach.reverse := by
+  cases l
   simp
 
-@[simp] theorem unattach_append {p : α → Prop} {xs₁ xs₂ : Array { x // p x }} :
-    (xs₁ ++ xs₂).unattach = xs₁.unattach ++ xs₂.unattach := by
-  cases xs₁
-  cases xs₂
+@[simp] theorem unattach_append {p : α → Prop} {l₁ l₂ : Array { x // p x }} :
+    (l₁ ++ l₂).unattach = l₁.unattach ++ l₂.unattach := by
+  cases l₁
+  cases l₂
   simp
 
-@[simp] theorem unattach_flatten {p : α → Prop} {xs : Array (Array { x // p x })} :
-    xs.flatten.unattach = (xs.map unattach).flatten := by
+@[simp] theorem unattach_flatten {p : α → Prop} {l : Array (Array { x // p x })} :
+    l.flatten.unattach = (l.map unattach).flatten := by
   unfold unattach
-  cases xs using array₂_induction
+  cases l using array₂_induction
   simp only [flatten_toArray, List.map_map, Function.comp_def, List.map_id_fun', id_eq,
     List.map_toArray, List.map_flatten, map_subtype, map_id_fun', List.unattach_toArray, mk.injEq]
   simp only [List.unattach]
 
-@[simp] theorem unattach_replicate {p : α → Prop} {n : Nat} {x : { x // p x }} :
-    (Array.replicate n x).unattach = Array.replicate n x.1 := by
+@[simp] theorem unattach_mkArray {p : α → Prop} {n : Nat} {x : { x // p x }} :
+    (Array.mkArray n x).unattach = Array.mkArray n x.1 := by
   simp [unattach]
 
-@[deprecated unattach_replicate (since := "2025-03-18")]
-abbrev unattach_mkArray := @unattach_replicate
-
-/-! ### Well-founded recursion preprocessing setup -/
-
-@[wf_preprocess] theorem map_wfParam {xs : Array α} {f : α → β} :
-    (wfParam xs).map f = xs.attach.unattach.map f := by
-  simp [wfParam]
-
-@[wf_preprocess] theorem map_unattach {P : α → Prop} {xs : Array (Subtype P)} {f : α → β} :
-    xs.unattach.map f = xs.map fun ⟨x, h⟩ =>
-      binderNameHint x f <| binderNameHint h () <| f (wfParam x) := by
-  simp [wfParam]
-
-@[wf_preprocess] theorem foldl_wfParam {xs : Array α} {f : β → α → β} {x : β} :
-    (wfParam xs).foldl f x = xs.attach.unattach.foldl f x := by
-  simp [wfParam]
-
-@[wf_preprocess] theorem foldl_unattach {P : α → Prop} {xs : Array (Subtype P)} {f : β → α → β} {x : β} :
-    xs.unattach.foldl f x = xs.foldl (fun s ⟨x, h⟩ =>
-      binderNameHint s f <| binderNameHint x (f s) <| binderNameHint h () <| f s (wfParam x)) x := by
-  simp [wfParam]
-
-@[wf_preprocess] theorem foldr_wfParam {xs : Array α} {f : α → β → β} {x : β} :
-    (wfParam xs).foldr f x = xs.attach.unattach.foldr f x := by
-  simp [wfParam]
-
-@[wf_preprocess] theorem foldr_unattach {P : α → Prop} {xs : Array (Subtype P)} {f : α → β → β} {x : β} :
-    xs.unattach.foldr f x = xs.foldr (fun ⟨x, h⟩ s =>
-      binderNameHint x f <| binderNameHint s (f x) <| binderNameHint h () <| f (wfParam x) s) x := by
-  simp [wfParam]
-
-@[wf_preprocess] theorem filter_wfParam {xs : Array α} {f : α → Bool} :
-    (wfParam xs).filter f = xs.attach.unattach.filter f:= by
-  simp [wfParam]
-
-@[wf_preprocess] theorem filter_unattach {P : α → Prop} {xs : Array (Subtype P)} {f : α → Bool} :
-    xs.unattach.filter f = (xs.filter (fun ⟨x, h⟩ =>
-      binderNameHint x f <| binderNameHint h () <| f (wfParam x))).unattach := by
-  simp [wfParam]
-
-@[wf_preprocess] theorem reverse_wfParam {xs : Array α} :
-    (wfParam xs).reverse = xs.attach.unattach.reverse := by simp [wfParam]
-
-@[wf_preprocess] theorem reverse_unattach {P : α → Prop} {xs : Array (Subtype P)} :
-    xs.unattach.reverse = xs.reverse.unattach := by simp
-
-@[wf_preprocess] theorem filterMap_wfParam {xs : Array α} {f : α → Option β} :
-    (wfParam xs).filterMap f = xs.attach.unattach.filterMap f := by
-  simp [wfParam]
-
-@[wf_preprocess] theorem filterMap_unattach {P : α → Prop} {xs : Array (Subtype P)} {f : α → Option β} :
-    xs.unattach.filterMap f = xs.filterMap fun ⟨x, h⟩ =>
-      binderNameHint x f <| binderNameHint h () <| f (wfParam x) := by
-  simp [wfParam]
-
-@[wf_preprocess] theorem flatMap_wfParam {xs : Array α} {f : α → Array β} :
-    (wfParam xs).flatMap f = xs.attach.unattach.flatMap f := by
-  simp [wfParam]
-
-@[wf_preprocess] theorem flatMap_unattach {P : α → Prop} {xs : Array (Subtype P)} {f : α → Array β} :
-    xs.unattach.flatMap f = xs.flatMap fun ⟨x, h⟩ =>
-      binderNameHint x f <| binderNameHint h () <| f (wfParam x) := by
-  simp [wfParam]
-
 end Array

src/Init/Data/Array/BasicAux.lean

@@ -8,25 +8,22 @@ import Init.Data.Array.Basic
 import Init.Data.Nat.Linear
 import Init.NotationExtra
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 theorem Array.of_push_eq_push {as bs : Array α} (h : as.push a = bs.push b) : as = bs ∧ a = b := by
   simp only [push, mk.injEq] at h
   have ⟨h₁, h₂⟩ := List.of_concat_eq_concat h
   cases as; cases bs
   simp_all
 
-private theorem List.size_toArrayAux {as : List α} {bs : Array α} : (as.toArrayAux bs).size = as.length + bs.size := by
+private theorem List.size_toArrayAux (as : List α) (bs : Array α) : (as.toArrayAux bs).size = as.length + bs.size := by
   induction as generalizing bs with
   | nil => simp [toArrayAux]
-  | cons a as ih => simp +arith [toArrayAux, *]
+  | cons a as ih => simp_arith [toArrayAux, *]
 
 private theorem List.of_toArrayAux_eq_toArrayAux {as bs : List α} {cs ds : Array α} (h : as.toArrayAux cs = bs.toArrayAux ds) (hlen : cs.size = ds.size) : as = bs ∧ cs = ds := by
   match as, bs with
   | [], []    => simp [toArrayAux] at h; simp [h]
-  | a::as, [] => simp [toArrayAux] at h; rw [← h] at hlen; simp +arith [size_toArrayAux] at hlen
-  | [], b::bs => simp [toArrayAux] at h; rw [h] at hlen; simp +arith [size_toArrayAux] at hlen
+  | a::as, [] => simp [toArrayAux] at h; rw [← h] at hlen; simp_arith [size_toArrayAux] at hlen
+  | [], b::bs => simp [toArrayAux] at h; rw [h] at hlen; simp_arith [size_toArrayAux] at hlen
   | a::as, b::bs =>
     simp [toArrayAux] at h
     have : (cs.push a).size = (ds.push b).size := by simp [*]
@@ -35,14 +32,9 @@ private theorem List.of_toArrayAux_eq_toArrayAux {as bs : List α} {cs ds : Arra
     have := Array.of_push_eq_push ih₂
     simp [this]
 
-theorem List.toArray_eq_toArray_eq {as bs : List α} : (as.toArray = bs.toArray) = (as = bs) := by
+theorem List.toArray_eq_toArray_eq (as bs : List α) : (as.toArray = bs.toArray) = (as = bs) := by
   simp
 
-/--
-Applies the monadic action `f` to every element in the array, left-to-right, and returns the array
-of results. Furthermore, the resulting array's type guarantees that it contains the same number of
-elements as the input array.
--/
 def Array.mapM' [Monad m] (f : α → m β) (as : Array α) : m { bs : Array β // bs.size = as.size } :=
   go 0 ⟨mkEmpty as.size, rfl⟩ (by simp)
 where
@@ -71,19 +63,11 @@ where
       return as
 
 /--
-Applies a monadic function to each element of an array, returning the array of results. The function is
-monomorphic: it is required to return a value of the same type. The internal implementation uses
-pointer equality, and does not allocate a new array if the result of each function call is
-pointer-equal to its argument.
+Monomorphic `Array.mapM`. The internal implementation uses pointer equality, and does not allocate a new array
+if the result of each `f a` is a pointer equal value `a`.
 -/
 @[implemented_by mapMonoMImp] def Array.mapMonoM [Monad m] (as : Array α) (f : α → m α) : m (Array α) :=
   as.mapM f
 
-/--
-Applies a function to each element of an array, returning the array of results. The function is
-monomorphic: it is required to return a value of the same type. The internal implementation uses
-pointer equality, and does not allocate a new array if the result of each function call is
-pointer-equal to its argument.
--/
 @[inline] def Array.mapMono (as : Array α) (f : α → α) : Array α :=
   Id.run <| as.mapMonoM f

src/Init/Data/Array/BinSearch.lean

@@ -5,13 +5,9 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Init.Data.Array.Basic
-import Init.Data.Int.DivMod.Lemmas
 import Init.Omega
 universe u v
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
--- We do not use `linter.indexVariables` here as it is helpful to name the index variables as `lo`, `mid`, and `hi`.
-
 namespace Array
 
 @[specialize] def binSearchAux {α : Type u} {β : Type v} (lt : α → α → Bool) (found : Option α → β) (as : Array α) (k : α) :
@@ -29,16 +25,6 @@ namespace Array
     else found (some a)
 termination_by lo hi => hi.1 - lo.1
 
-/--
-Binary search for an element equivalent to `k` in the sorted array `as`. Returns the element from
-the array, if it is found, or `none` otherwise.
-
-The array `as` must be sorted according to the comparison operator `lt`, which should be a total
-order.
-
-The optional parameters `lo` and `hi` determine the region of the array indices to be searched. Both
-are inclusive, and default to searching the entire array.
--/
 @[inline] def binSearch {α : Type} (as : Array α) (k : α) (lt : α → α → Bool) (lo := 0) (hi := as.size - 1) : Option α :=
   if h : lo < as.size then
     let hi := if hi < as.size then hi else as.size - 1
@@ -49,16 +35,6 @@ are inclusive, and default to searching the entire array.
   else
     none
 
-/--
-Binary search for an element equivalent to `k` in the sorted array `as`. Returns `true` if the
-element is found, or `false` otherwise.
-
-The array `as` must be sorted according to the comparison operator `lt`, which should be a total
-order.
-
-The optional parameters `lo` and `hi` determine the region of the array indices to be searched. Both
-are inclusive, and default to searching the entire array.
--/
 @[inline] def binSearchContains {α : Type} (as : Array α) (k : α) (lt : α → α → Bool) (lo := 0) (hi := as.size - 1) : Bool :=
   if h : lo < as.size then
     let hi := if hi < as.size then hi else as.size - 1
@@ -88,16 +64,6 @@ are inclusive, and default to searching the entire array.
       as.modifyM mid <| fun v => merge v
 termination_by lo hi => hi.1 - lo.1
 
-/--
-Inserts an element `k` into a sorted array `as` such that the resulting array is sorted.
-
-The ordering predicate `lt` should be a total order on elements, and the array `as` should be sorted
-with respect to `lt`.
-
-If an element that `lt` equates to `k` is already present in `as`, then `merge` is applied to the
-existing element to determine the value of that position in the resulting array. If no element equal
-to `k` is present, then `add` is used to determine the value to be inserted.
--/
 @[specialize] def binInsertM {α : Type u} {m : Type u → Type v} [Monad m]
     (lt : α → α → Bool)
     (merge : α → m α)
@@ -111,21 +77,6 @@ to `k` is present, then `add` is used to determine the value to be inserted.
   else if !lt k as[as.size - 1] then as.modifyM (as.size - 1) <| merge
   else binInsertAux lt merge add as k ⟨0, by omega⟩ ⟨as.size - 1, by omega⟩ (by simp) (by simpa using h')
 
-/--
-Inserts an element into a sorted array such that the resulting array is sorted. If the element is
-already present in the array, it is not inserted.
-
-The ordering predicate `lt` should be a total order on elements, and the array `as` should be sorted
-with respect to `lt`.
-
-`Array.binInsertM` is a more general operator that provides greater control over the handling of
-duplicate elements in addition to running in a monad.
-
-Examples:
-* `#[0, 1, 3, 5].binInsert (· < ·) 2 = #[0, 1, 2, 3, 5]`
-* `#[0, 1, 3, 5].binInsert (· < ·) 1 = #[0, 1, 3, 5]`
-* `#[].binInsert (· < ·) 1 = #[1]`
--/
 @[inline] def binInsert {α : Type u} (lt : α → α → Bool) (as : Array α) (k : α) : Array α :=
   Id.run <| binInsertM lt (fun _ => k) (fun _ => k) as k
 

src/Init/Data/Array/Bootstrap.lean

@@ -13,148 +13,122 @@ import Init.Data.List.TakeDrop
 This file contains some theorems about `Array` and `List` needed for `Init.Data.List.Impl`.
 -/
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 namespace Array
 
-/--
-Use the indexing notation `a[i]` instead.
-
-Access an element from an array without needing a runtime bounds checks,
-using a `Nat` index and a proof that it is in bounds.
-
-This function does not use `get_elem_tactic` to automatically find the proof that
-the index is in bounds. This is because the tactic itself needs to look up values in
-arrays.
--/
-@[deprecated "Use indexing notation `as[i]` instead" (since := "2025-02-17")]
-def get {α : Type u} (a : @& Array α) (i : @& Nat) (h : LT.lt i a.size) : α :=
-  a.toList.get ⟨i, h⟩
-
-/--
-Use the indexing notation `a[i]!` instead.
-
-Access an element from an array, or panic if the index is out of bounds.
--/
-@[deprecated "Use indexing notation `as[i]!` instead" (since := "2025-02-17")]
-def get! {α : Type u} [Inhabited α] (a : @& Array α) (i : @& Nat) : α :=
-  Array.getD a i default
-
 theorem foldlM_toList.aux [Monad m]
-    {f : β → α → m β} {xs : Array α} {i j} (H : xs.size ≤ i + j) {b} :
-    foldlM.loop f xs xs.size (Nat.le_refl _) i j b = (xs.toList.drop j).foldlM f b := by
+    (f : β → α → m β) (arr : Array α) (i j) (H : arr.size ≤ i + j) (b) :
+    foldlM.loop f arr arr.size (Nat.le_refl _) i j b = (arr.toList.drop j).foldlM f b := by
   unfold foldlM.loop
   split; split
   · cases Nat.not_le_of_gt ‹_› (Nat.zero_add _ ▸ H)
   · rename_i i; rw [Nat.succ_add] at H
-    simp [foldlM_toList.aux (j := j+1) H]
+    simp [foldlM_toList.aux f arr i (j+1) H]
     rw (occs := [2]) [← List.getElem_cons_drop_succ_eq_drop ‹_›]
     rfl
   · rw [List.drop_of_length_le (Nat.ge_of_not_lt ‹_›)]; rfl
 
 @[simp] theorem foldlM_toList [Monad m]
-    {f : β → α → m β} {init : β} {xs : Array α} :
-    xs.toList.foldlM f init = xs.foldlM f init := by
+    (f : β → α → m β) (init : β) (arr : Array α) :
+    arr.toList.foldlM f init = arr.foldlM f init := by
   simp [foldlM, foldlM_toList.aux]
 
-@[simp] theorem foldl_toList (f : β → α → β) {init : β} {xs : Array α} :
-    xs.toList.foldl f init = xs.foldl f init :=
+@[simp] theorem foldl_toList (f : β → α → β) (init : β) (arr : Array α) :
+    arr.toList.foldl f init = arr.foldl f init :=
   List.foldl_eq_foldlM .. ▸ foldlM_toList ..
 
 theorem foldrM_eq_reverse_foldlM_toList.aux [Monad m]
-    {f : α → β → m β} {xs : Array α} {init : β} {i} (h) :
-    (xs.toList.take i).reverse.foldlM (fun x y => f y x) init = foldrM.fold f xs 0 i h init := by
+    (f : α → β → m β) (arr : Array α) (init : β) (i h) :
+    (arr.toList.take i).reverse.foldlM (fun x y => f y x) init = foldrM.fold f arr 0 i h init := by
   unfold foldrM.fold
   match i with
   | 0 => simp [List.foldlM, List.take]
-  | i+1 => rw [← List.take_concat_get h]; simp [← aux]
+  | i+1 => rw [← List.take_concat_get _ _ h]; simp [← (aux f arr · i)]
 
-theorem foldrM_eq_reverse_foldlM_toList [Monad m] {f : α → β → m β} {init : β} {xs : Array α} :
-    xs.foldrM f init = xs.toList.reverse.foldlM (fun x y => f y x) init := by
-  have : xs = #[] ∨ 0 < xs.size :=
-    match xs with | ⟨[]⟩ => .inl rfl | ⟨a::l⟩ => .inr (Nat.zero_lt_succ _)
-  match xs, this with | _, .inl rfl => rfl | xs, .inr h => ?_
+theorem foldrM_eq_reverse_foldlM_toList [Monad m] (f : α → β → m β) (init : β) (arr : Array α) :
+    arr.foldrM f init = arr.toList.reverse.foldlM (fun x y => f y x) init := by
+  have : arr = #[] ∨ 0 < arr.size :=
+    match arr with | ⟨[]⟩ => .inl rfl | ⟨a::l⟩ => .inr (Nat.zero_lt_succ _)
+  match arr, this with | _, .inl rfl => rfl | arr, .inr h => ?_
   simp [foldrM, h, ← foldrM_eq_reverse_foldlM_toList.aux, List.take_length]
 
 @[simp] theorem foldrM_toList [Monad m]
-    {f : α → β → m β} {init : β} {xs : Array α} :
-    xs.toList.foldrM f init = xs.foldrM f init := by
+    (f : α → β → m β) (init : β) (arr : Array α) :
+    arr.toList.foldrM f init = arr.foldrM f init := by
   rw [foldrM_eq_reverse_foldlM_toList, List.foldlM_reverse]
 
-@[simp] theorem foldr_toList (f : α → β → β) {init : β} {xs : Array α} :
-    xs.toList.foldr f init = xs.foldr f init :=
+@[simp] theorem foldr_toList (f : α → β → β) (init : β) (arr : Array α) :
+    arr.toList.foldr f init = arr.foldr f init :=
   List.foldr_eq_foldrM .. ▸ foldrM_toList ..
 
-@[simp] theorem push_toList {xs : Array α} {a : α} : (xs.push a).toList = xs.toList ++ [a] := by
+@[simp] theorem push_toList (arr : Array α) (a : α) : (arr.push a).toList = arr.toList ++ [a] := by
   simp [push, List.concat_eq_append]
 
-@[simp] theorem toListAppend_eq {xs : Array α} {l : List α} : xs.toListAppend l = xs.toList ++ l := by
+@[simp] theorem toListAppend_eq (arr : Array α) (l) : arr.toListAppend l = arr.toList ++ l := by
   simp [toListAppend, ← foldr_toList]
 
-@[simp] theorem toListImpl_eq {xs : Array α} : xs.toListImpl = xs.toList := by
+@[simp] theorem toListImpl_eq (arr : Array α) : arr.toListImpl = arr.toList := by
   simp [toListImpl, ← foldr_toList]
 
-@[simp] theorem toList_pop {xs : Array α} : xs.pop.toList = xs.toList.dropLast := rfl
+@[simp] theorem pop_toList (arr : Array α) : arr.pop.toList = arr.toList.dropLast := rfl
 
-@[deprecated toList_pop (since := "2025-02-17")]
-abbrev pop_toList := @Array.toList_pop
+@[simp] theorem append_eq_append (arr arr' : Array α) : arr.append arr' = arr ++ arr' := rfl
 
-@[simp] theorem append_eq_append {xs ys : Array α} : xs.append ys = xs ++ ys := rfl
-
-@[simp] theorem toList_append {xs ys : Array α} :
-    (xs ++ ys).toList = xs.toList ++ ys.toList := by
+@[simp] theorem toList_append (arr arr' : Array α) :
+    (arr ++ arr').toList = arr.toList ++ arr'.toList := by
   rw [← append_eq_append]; unfold Array.append
   rw [← foldl_toList]
-  induction ys.toList generalizing xs <;> simp [*]
+  induction arr'.toList generalizing arr <;> simp [*]
 
 @[simp] theorem toList_empty : (#[] : Array α).toList = [] := rfl
 
-@[simp] theorem append_empty {xs : Array α} : xs ++ #[] = xs := by
+@[simp] theorem append_empty (as : Array α) : as ++ #[] = as := by
   apply ext'; simp only [toList_append, toList_empty, List.append_nil]
 
 @[deprecated append_empty (since := "2025-01-13")]
 abbrev append_nil := @append_empty
 
-@[simp] theorem empty_append {xs : Array α} : #[] ++ xs = xs := by
+@[simp] theorem empty_append (as : Array α) : #[] ++ as = as := by
   apply ext'; simp only [toList_append, toList_empty, List.nil_append]
 
 @[deprecated empty_append (since := "2025-01-13")]
 abbrev nil_append := @empty_append
 
-@[simp] theorem append_assoc {xs ys zs : Array α} : xs ++ ys ++ zs = xs ++ (ys ++ zs) := by
+@[simp] theorem append_assoc (as bs cs : Array α) : as ++ bs ++ cs = as ++ (bs ++ cs) := by
   apply ext'; simp only [toList_append, List.append_assoc]
 
-@[simp] theorem appendList_eq_append {xs : Array α} {l : List α} : xs.appendList l = xs ++ l := rfl
+@[simp] theorem appendList_eq_append
+    (arr : Array α) (l : List α) : arr.appendList l = arr ++ l := rfl
 
-@[simp] theorem toList_appendList {xs : Array α} {l : List α} :
-    (xs ++ l).toList = xs.toList ++ l := by
+@[simp] theorem toList_appendList (arr : Array α) (l : List α) :
+    (arr ++ l).toList = arr.toList ++ l := by
   rw [← appendList_eq_append]; unfold Array.appendList
-  induction l generalizing xs <;> simp [*]
+  induction l generalizing arr <;> simp [*]
 
 @[deprecated toList_appendList (since := "2024-12-11")]
 abbrev appendList_toList := @toList_appendList
 
 @[deprecated "Use the reverse direction of `foldrM_toList`." (since := "2024-11-13")]
 theorem foldrM_eq_foldrM_toList [Monad m]
-    {f : α → β → m β} {init : β} {xs : Array α} :
-    xs.foldrM f init = xs.toList.foldrM f init := by
+    (f : α → β → m β) (init : β) (arr : Array α) :
+    arr.foldrM f init = arr.toList.foldrM f init := by
   simp
 
 @[deprecated "Use the reverse direction of `foldlM_toList`." (since := "2024-11-13")]
 theorem foldlM_eq_foldlM_toList [Monad m]
-    {f : β → α → m β} {init : β} {xs : Array α} :
-    xs.foldlM f init = xs.toList.foldlM f init:= by
+    (f : β → α → m β) (init : β) (arr : Array α) :
+    arr.foldlM f init = arr.toList.foldlM f init:= by
   simp
 
 @[deprecated "Use the reverse direction of `foldr_toList`." (since := "2024-11-13")]
-theorem foldr_eq_foldr_toList {f : α → β → β} {init : β} {xs : Array α} :
-    xs.foldr f init = xs.toList.foldr f init := by
+theorem foldr_eq_foldr_toList
+    (f : α → β → β) (init : β) (arr : Array α) :
+    arr.foldr f init = arr.toList.foldr f init := by
   simp
 
 @[deprecated "Use the reverse direction of `foldl_toList`." (since := "2024-11-13")]
-theorem foldl_eq_foldl_toList {f : β → α → β} {init : β} {xs : Array α} :
-    xs.foldl f init = xs.toList.foldl f init:= by
+theorem foldl_eq_foldl_toList
+    (f : β → α → β) (init : β) (arr : Array α) :
+    arr.foldl f init = arr.toList.foldl f init:= by
   simp
 
 @[deprecated foldlM_toList (since := "2024-09-09")]
@@ -179,7 +153,7 @@ abbrev push_data := @push_toList
 abbrev toList_eq := @toListImpl_eq
 
 @[deprecated pop_toList (since := "2024-09-09")]
-abbrev pop_data := @toList_pop
+abbrev pop_data := @pop_toList
 
 @[deprecated toList_append (since := "2024-09-09")]
 abbrev append_data := @toList_append

src/Init/Data/Array/Count.lean

@@ -11,9 +11,6 @@ import Init.Data.List.Nat.Count
 # Lemmas about `Array.countP` and `Array.count`.
 -/
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 namespace Array
 
 open Nat
@@ -21,136 +18,124 @@ open Nat
 /-! ### countP -/
 section countP
 
-variable {p q : α → Bool}
-
-@[simp] theorem _root_.List.countP_toArray {l : List α} : countP p l.toArray = l.countP p := by
-  simp [countP]
-  induction l with
-  | nil => rfl
-  | cons hd tl ih =>
-    simp only [List.foldr_cons, ih, List.countP_cons]
-    split <;> simp_all
-
-@[simp] theorem countP_toList {xs : Array α} : xs.toList.countP p = countP p xs := by
-  cases xs
-  simp
+variable (p q : α → Bool)
 
 @[simp] theorem countP_empty : countP p #[] = 0 := rfl
 
-@[simp] theorem countP_push_of_pos {xs : Array α} (pa : p a) : countP p (xs.push a) = countP p xs + 1 := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem countP_push_of_pos (l) (pa : p a) : countP p (l.push a) = countP p l + 1 := by
+  rcases l with ⟨l⟩
   simp_all
 
-@[simp] theorem countP_push_of_neg {xs : Array α} (pa : ¬p a) : countP p (xs.push a) = countP p xs := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem countP_push_of_neg (l) (pa : ¬p a) : countP p (l.push a) = countP p l := by
+  rcases l with ⟨l⟩
   simp_all
 
-theorem countP_push {a : α} {xs : Array α} : countP p (xs.push a) = countP p xs + if p a then 1 else 0 := by
-  rcases xs with ⟨xs⟩
+theorem countP_push (a : α) (l) : countP p (l.push a) = countP p l + if p a then 1 else 0 := by
+  rcases l with ⟨l⟩
   simp_all
 
-@[simp] theorem countP_singleton {a : α} : countP p #[a] = if p a then 1 else 0 := by
+@[simp] theorem countP_singleton (a : α) : countP p #[a] = if p a then 1 else 0 := by
   simp [countP_push]
 
-theorem size_eq_countP_add_countP {xs : Array α} : xs.size = countP p xs + countP (fun a => ¬p a) xs := by
-  rcases xs with ⟨xs⟩
+theorem size_eq_countP_add_countP (l) : l.size = countP p l + countP (fun a => ¬p a) l := by
+  cases l
   simp [List.length_eq_countP_add_countP (p := p)]
 
-theorem countP_eq_size_filter {xs : Array α} : countP p xs = (filter p xs).size := by
-  rcases xs with ⟨xs⟩
+theorem countP_eq_size_filter (l) : countP p l = (filter p l).size := by
+  cases l
   simp [List.countP_eq_length_filter]
 
 theorem countP_eq_size_filter' : countP p = size ∘ filter p := by
-  funext xs
+  funext l
   apply countP_eq_size_filter
 
-theorem countP_le_size : countP p xs ≤ xs.size := by
+theorem countP_le_size : countP p l ≤ l.size := by
   simp only [countP_eq_size_filter]
   apply size_filter_le
 
-@[simp] theorem countP_append {xs ys : Array α} : countP p (xs ++ ys) = countP p xs + countP p ys := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
+@[simp] theorem countP_append (l₁ l₂) : countP p (l₁ ++ l₂) = countP p l₁ + countP p l₂ := by
+  cases l₁
+  cases l₂
   simp
 
-@[simp] theorem countP_pos_iff {p} : 0 < countP p xs ↔ ∃ a ∈ xs, p a := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem countP_pos_iff {p} : 0 < countP p l ↔ ∃ a ∈ l, p a := by
+  cases l
   simp
 
-@[simp] theorem one_le_countP_iff {p} : 1 ≤ countP p xs ↔ ∃ a ∈ xs, p a :=
+@[simp] theorem one_le_countP_iff {p} : 1 ≤ countP p l ↔ ∃ a ∈ l, p a :=
   countP_pos_iff
 
-@[simp] theorem countP_eq_zero {p} : countP p xs = 0 ↔ ∀ a ∈ xs, ¬p a := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem countP_eq_zero {p} : countP p l = 0 ↔ ∀ a ∈ l, ¬p a := by
+  cases l
   simp
 
-@[simp] theorem countP_eq_size {p} : countP p xs = xs.size ↔ ∀ a ∈ xs, p a := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem countP_eq_size {p} : countP p l = l.size ↔ ∀ a ∈ l, p a := by
+  cases l
   simp
 
-theorem countP_replicate {a : α} {n : Nat} : countP p (replicate n a) = if p a then n else 0 := by
+theorem countP_mkArray (p : α → Bool) (a : α) (n : Nat) :
+    countP p (mkArray n a) = if p a then n else 0 := by
   simp [← List.toArray_replicate, List.countP_replicate]
 
-@[deprecated countP_replicate (since := "2025-03-18")]
-abbrev countP_mkArray := @countP_replicate
-
-theorem boole_getElem_le_countP {xs : Array α} {i : Nat} (h : i < xs.size) :
-    (if p xs[i] then 1 else 0) ≤ xs.countP p := by
-  rcases xs with ⟨xs⟩
+theorem boole_getElem_le_countP (p : α → Bool) (l : Array α) (i : Nat) (h : i < l.size) :
+    (if p l[i] then 1 else 0) ≤ l.countP p := by
+  cases l
   simp [List.boole_getElem_le_countP]
 
-theorem countP_set {xs : Array α} {i : Nat} {a : α} (h : i < xs.size) :
-    (xs.set i a).countP p = xs.countP p - (if p xs[i] then 1 else 0) + (if p a then 1 else 0) := by
-  rcases xs with ⟨xs⟩
+theorem countP_set (p : α → Bool) (l : Array α) (i : Nat) (a : α) (h : i < l.size) :
+    (l.set i a).countP p = l.countP p - (if p l[i] then 1 else 0) + (if p a then 1 else 0) := by
+  cases l
   simp [List.countP_set, h]
 
-theorem countP_filter {xs : Array α} :
-    countP p (filter q xs) = countP (fun a => p a && q a) xs := by
-  rcases xs with ⟨xs⟩
+theorem countP_filter (l : Array α) :
+    countP p (filter q l) = countP (fun a => p a && q a) l := by
+  cases l
   simp [List.countP_filter]
 
 @[simp] theorem countP_true : (countP fun (_ : α) => true) = size := by
-  funext xs
+  funext l
   simp
 
 @[simp] theorem countP_false : (countP fun (_ : α) => false) = Function.const _ 0 := by
-  funext xs
+  funext l
   simp
 
-@[simp] theorem countP_map {p : β → Bool} {f : α → β} {xs : Array α} :
-    countP p (map f xs) = countP (p ∘ f) xs := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem countP_map (p : β → Bool) (f : α → β) (l : Array α) :
+    countP p (map f l) = countP (p ∘ f) l := by
+  cases l
   simp
 
-theorem size_filterMap_eq_countP {f : α → Option β} {xs : Array α} :
-    (filterMap f xs).size = countP (fun a => (f a).isSome) xs := by
-  rcases xs with ⟨xs⟩
+theorem size_filterMap_eq_countP (f : α → Option β) (l : Array α) :
+    (filterMap f l).size = countP (fun a => (f a).isSome) l := by
+  cases l
   simp [List.length_filterMap_eq_countP]
 
-theorem countP_filterMap {p : β → Bool} {f : α → Option β} {xs : Array α} :
-    countP p (filterMap f xs) = countP (fun a => ((f a).map p).getD false) xs := by
-  rcases xs with ⟨xs⟩
+theorem countP_filterMap (p : β → Bool) (f : α → Option β) (l : Array α) :
+    countP p (filterMap f l) = countP (fun a => ((f a).map p).getD false) l := by
+  cases l
   simp [List.countP_filterMap]
 
-@[simp] theorem countP_flatten {xss : Array (Array α)} :
-    countP p xss.flatten = (xss.map (countP p)).sum := by
-  cases xss using array₂_induction
+@[simp] theorem countP_flatten (l : Array (Array α)) :
+    countP p l.flatten = (l.map (countP p)).sum := by
+  cases l using array₂_induction
   simp [List.countP_flatten, Function.comp_def]
 
-theorem countP_flatMap {p : β → Bool} {xs : Array α} {f : α → Array β} :
-    countP p (xs.flatMap f) = sum (map (countP p ∘ f) xs) := by
-  rcases xs with ⟨xs⟩
+theorem countP_flatMap (p : β → Bool) (l : Array α) (f : α → Array β) :
+    countP p (l.flatMap f) = sum (map (countP p ∘ f) l) := by
+  cases l
   simp [List.countP_flatMap, Function.comp_def]
 
-@[simp] theorem countP_reverse {xs : Array α} : countP p xs.reverse = countP p xs := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem countP_reverse (l : Array α) : countP p l.reverse = countP p l := by
+  cases l
   simp [List.countP_reverse]
 
-theorem countP_mono_left (h : ∀ x ∈ xs, p x → q x) : countP p xs ≤ countP q xs := by
-  rcases xs with ⟨xs⟩
+variable {p q}
+
+theorem countP_mono_left (h : ∀ x ∈ l, p x → q x) : countP p l ≤ countP q l := by
+  cases l
   simpa using List.countP_mono_left (by simpa using h)
 
-theorem countP_congr (h : ∀ x ∈ xs, p x ↔ q x) : countP p xs = countP q xs :=
+theorem countP_congr (h : ∀ x ∈ l, p x ↔ q x) : countP p l = countP q l :=
   Nat.le_antisymm
     (countP_mono_left fun x hx => (h x hx).1)
     (countP_mono_left fun x hx => (h x hx).2)
@@ -162,131 +147,114 @@ section count
 
 variable [BEq α]
 
-@[simp] theorem _root_.List.count_toArray {l : List α} {a : α} : count a l.toArray = l.count a := by
-  simp [count, List.count_eq_countP]
+@[simp] theorem count_empty (a : α) : count a #[] = 0 := rfl
 
-@[simp] theorem count_toList {xs : Array α} {a : α} : xs.toList.count a = xs.count a := by
-  cases xs
-  simp
-
-@[simp] theorem count_empty {a : α} : count a #[] = 0 := rfl
-
-theorem count_push {a b : α} {xs : Array α} :
-    count a (xs.push b) = count a xs + if b == a then 1 else 0 := by
+theorem count_push (a b : α) (l : Array α) :
+    count a (l.push b) = count a l + if b == a then 1 else 0 := by
   simp [count, countP_push]
 
-theorem count_eq_countP {a : α} {xs : Array α} : count a xs = countP (· == a) xs := rfl
+theorem count_eq_countP (a : α) (l : Array α) : count a l = countP (· == a) l := rfl
 theorem count_eq_countP' {a : α} : count a = countP (· == a) := by
-  funext xs
+  funext l
   apply count_eq_countP
 
-theorem count_le_size {a : α} {xs : Array α} : count a xs ≤ xs.size := countP_le_size
+theorem count_le_size (a : α) (l : Array α) : count a l ≤ l.size := countP_le_size _
 
-theorem count_le_count_push {a b : α} {xs : Array α} : count a xs ≤ count a (xs.push b) := by
+theorem count_le_count_push (a b : α) (l : Array α) : count a l ≤ count a (l.push b) := by
   simp [count_push]
 
-theorem count_singleton {a b : α} : count a #[b] = if b == a then 1 else 0 := by
+@[simp] theorem count_singleton (a b : α) : count a #[b] = if b == a then 1 else 0 := by
   simp [count_eq_countP]
 
-@[simp] theorem count_append {a : α} {xs ys : Array α} : count a (xs ++ ys) = count a xs + count a ys :=
-  countP_append
+@[simp] theorem count_append (a : α) : ∀ l₁ l₂, count a (l₁ ++ l₂) = count a l₁ + count a l₂ :=
+  countP_append _
 
-@[simp] theorem count_flatten {a : α} {xss : Array (Array α)} :
-    count a xss.flatten = (xss.map (count a)).sum := by
-  cases xss using array₂_induction
+@[simp] theorem count_flatten (a : α) (l : Array (Array α)) :
+    count a l.flatten = (l.map (count a)).sum := by
+  cases l using array₂_induction
   simp [List.count_flatten, Function.comp_def]
 
-@[simp] theorem count_reverse {a : α} {xs : Array α} : count a xs.reverse = count a xs := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem count_reverse (a : α) (l : Array α) : count a l.reverse = count a l := by
+  cases l
   simp
 
-theorem boole_getElem_le_count {xs : Array α} {i : Nat} {a : α} (h : i < xs.size) :
-    (if xs[i] == a then 1 else 0) ≤ xs.count a := by
+theorem boole_getElem_le_count (a : α) (l : Array α) (i : Nat) (h : i < l.size) :
+    (if l[i] == a then 1 else 0) ≤ l.count a := by
   rw [count_eq_countP]
-  apply boole_getElem_le_countP (p := (· == a))
+  apply boole_getElem_le_countP (· == a)
 
-theorem count_set {xs : Array α} {i : Nat} {a b : α} (h : i < xs.size) :
-    (xs.set i a).count b = xs.count b - (if xs[i] == b then 1 else 0) + (if a == b then 1 else 0) := by
+theorem count_set (a b : α) (l : Array α) (i : Nat) (h : i < l.size) :
+    (l.set i a).count b = l.count b - (if l[i] == b then 1 else 0) + (if a == b then 1 else 0) := by
   simp [count_eq_countP, countP_set, h]
 
 variable [LawfulBEq α]
 
-@[simp] theorem count_push_self {a : α} {xs : Array α} : count a (xs.push a) = count a xs + 1 := by
+@[simp] theorem count_push_self (a : α) (l : Array α) : count a (l.push a) = count a l + 1 := by
   simp [count_push]
 
-@[simp] theorem count_push_of_ne {xs : Array α} (h : b ≠ a) : count a (xs.push b) = count a xs := by
+@[simp] theorem count_push_of_ne (h : b ≠ a) (l : Array α) : count a (l.push b) = count a l := by
   simp_all [count_push, h]
 
-theorem count_singleton_self {a : α} : count a #[a] = 1 := by simp
+theorem count_singleton_self (a : α) : count a #[a] = 1 := by simp
 
 @[simp]
-theorem count_pos_iff {a : α} {xs : Array α} : 0 < count a xs ↔ a ∈ xs := by
+theorem count_pos_iff {a : α} {l : Array α} : 0 < count a l ↔ a ∈ l := by
   simp only [count, countP_pos_iff, beq_iff_eq, exists_eq_right]
 
-@[simp] theorem one_le_count_iff {a : α} {xs : Array α} : 1 ≤ count a xs ↔ a ∈ xs :=
+@[simp] theorem one_le_count_iff {a : α} {l : Array α} : 1 ≤ count a l ↔ a ∈ l :=
   count_pos_iff
 
-theorem count_eq_zero_of_not_mem {a : α} {xs : Array α} (h : a ∉ xs) : count a xs = 0 :=
+theorem count_eq_zero_of_not_mem {a : α} {l : Array α} (h : a ∉ l) : count a l = 0 :=
   Decidable.byContradiction fun h' => h <| count_pos_iff.1 (Nat.pos_of_ne_zero h')
 
-theorem not_mem_of_count_eq_zero {a : α} {xs : Array α} (h : count a xs = 0) : a ∉ xs :=
+theorem not_mem_of_count_eq_zero {a : α} {l : Array α} (h : count a l = 0) : a ∉ l :=
   fun h' => Nat.ne_of_lt (count_pos_iff.2 h') h.symm
 
-theorem count_eq_zero {xs : Array α} : count a xs = 0 ↔ a ∉ xs :=
+theorem count_eq_zero {l : Array α} : count a l = 0 ↔ a ∉ l :=
   ⟨not_mem_of_count_eq_zero, count_eq_zero_of_not_mem⟩
 
-theorem count_eq_size {xs : Array α} : count a xs = xs.size ↔ ∀ b ∈ xs, a = b := by
+theorem count_eq_size {l : Array α} : count a l = l.size ↔ ∀ b ∈ l, a = b := by
   rw [count, countP_eq_size]
   refine ⟨fun h b hb => Eq.symm ?_, fun h b hb => ?_⟩
   · simpa using h b hb
   · rw [h b hb, beq_self_eq_true]
 
-@[simp] theorem count_replicate_self {a : α} {n : Nat} : count a (replicate n a) = n := by
+@[simp] theorem count_mkArray_self (a : α) (n : Nat) : count a (mkArray n a) = n := by
   simp [← List.toArray_replicate]
 
-@[deprecated count_replicate_self (since := "2025-03-18")]
-abbrev count_mkArray_self := @count_replicate_self
-
-theorem count_replicate {a b : α} {n : Nat} : count a (replicate n b) = if b == a then n else 0 := by
+theorem count_mkArray (a b : α) (n : Nat) : count a (mkArray n b) = if b == a then n else 0 := by
   simp [← List.toArray_replicate, List.count_replicate]
 
-@[deprecated count_replicate (since := "2025-03-18")]
-abbrev count_mkArray := @count_replicate
-
-theorem filter_beq {xs : Array α} (a : α) : xs.filter (· == a) = replicate (count a xs) a := by
-  rcases xs with ⟨xs⟩
+theorem filter_beq (l : Array α) (a : α) : l.filter (· == a) = mkArray (count a l) a := by
+  cases l
   simp [List.filter_beq]
 
-theorem filter_eq {α} [DecidableEq α] {xs : Array α} (a : α) : xs.filter (· = a) = replicate (count a xs) a :=
-  filter_beq a
+theorem filter_eq {α} [DecidableEq α] (l : Array α) (a : α) : l.filter (· = a) = mkArray (count a l) a :=
+  filter_beq l a
 
-theorem replicate_count_eq_of_count_eq_size {xs : Array α} (h : count a xs = xs.size) :
-    replicate (count a xs) a = xs := by
-  rcases xs with ⟨xs⟩
+theorem mkArray_count_eq_of_count_eq_size {l : Array α} (h : count a l = l.size) :
+    mkArray (count a l) a = l := by
+  cases l
   rw [← toList_inj]
   simp [List.replicate_count_eq_of_count_eq_length (by simpa using h)]
 
-@[deprecated replicate_count_eq_of_count_eq_size (since := "2025-03-18")]
-abbrev mkArray_count_eq_of_count_eq_size := @replicate_count_eq_of_count_eq_size
-
-@[simp] theorem count_filter {xs : Array α} (h : p a) : count a (filter p xs) = count a xs := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem count_filter {l : Array α} (h : p a) : count a (filter p l) = count a l := by
+  cases l
   simp [List.count_filter, h]
 
-theorem count_le_count_map [DecidableEq β] {xs : Array α} {f : α → β} {x : α} :
-    count x xs ≤ count (f x) (map f xs) := by
-  rcases xs with ⟨xs⟩
+theorem count_le_count_map [DecidableEq β] (l : Array α) (f : α → β) (x : α) :
+    count x l ≤ count (f x) (map f l) := by
+  cases l
   simp [List.count_le_count_map, countP_map]
 
-theorem count_filterMap {α} [BEq β] {b : β} {f : α → Option β} {xs : Array α} :
-    count b (filterMap f xs) = countP (fun a => f a == some b) xs := by
-  rcases xs with ⟨xs⟩
+theorem count_filterMap {α} [BEq β] (b : β) (f : α → Option β) (l : Array α) :
+    count b (filterMap f l) = countP (fun a => f a == some b) l := by
+  cases l
   simp [List.count_filterMap, countP_filterMap]
 
-theorem count_flatMap {α} [BEq β] {xs : Array α} {f : α → Array β} {x : β} :
-    count x (xs.flatMap f) = sum (map (count x ∘ f) xs) := by
-  rcases xs with ⟨xs⟩
-  simp [List.count_flatMap, countP_flatMap, Function.comp_def]
+theorem count_flatMap {α} [BEq β] (l : Array α) (f : α → Array β) (x : β) :
+    count x (l.flatMap f) = sum (map (count x ∘ f) l) := by
+  simp [count_eq_countP, countP_flatMap, Function.comp_def]
 
 -- FIXME these theorems can be restored once `List.erase` and `Array.erase` have been related.
 

src/Init/Data/Array/DecidableEq.lean

@@ -9,9 +9,6 @@ import Init.Data.BEq
 import Init.Data.List.Nat.BEq
 import Init.ByCases
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 namespace Array
 
 private theorem rel_of_isEqvAux
@@ -71,7 +68,7 @@ theorem isEqv_eq_decide (xs ys : Array α) (r) :
 
 theorem eq_of_isEqv [DecidableEq α] (xs ys : Array α) (h : Array.isEqv xs ys (fun x y => x = y)) : xs = ys := by
   have ⟨h, h'⟩ := rel_of_isEqv h
-  exact ext h (fun i lt _ => by simpa using h' i lt)
+  exact ext _ _ h (fun i lt _ => by simpa using h' i lt)
 
 private theorem isEqvAux_self (r : α → α → Bool) (hr : ∀ a, r a a) (xs : Array α) (i : Nat) (h : i ≤ xs.size) :
     Array.isEqvAux xs xs rfl r i h = true := by
@@ -87,9 +84,9 @@ theorem isEqv_self [DecidableEq α] (xs : Array α) : Array.isEqv xs xs (· = ·
   simp [isEqv, isEqvAux_self]
 
 instance [DecidableEq α] : DecidableEq (Array α) :=
-  fun xs ys =>
-    match h:isEqv xs ys (fun a b => a = b) with
-    | true  => isTrue (eq_of_isEqv xs ys h)
+  fun a b =>
+    match h:isEqv a b (fun a b => a = b) with
+    | true  => isTrue (eq_of_isEqv a b h)
     | false => isFalse fun h' => by subst h'; rw [isEqv_self] at h; contradiction
 
 theorem beq_eq_decide [BEq α] (xs ys : Array α) :

src/Init/Data/Array/Erase.lean

@@ -12,22 +12,19 @@ import Init.Data.List.Nat.Basic
 # Lemmas about `Array.eraseP`, `Array.erase`, and `Array.eraseIdx`.
 -/
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 namespace Array
 
 open Nat
 
 /-! ### eraseP -/
 
-@[simp] theorem eraseP_empty : #[].eraseP p = #[] := by simp
+@[simp] theorem eraseP_empty : #[].eraseP p = #[] := rfl
 
-theorem eraseP_of_forall_mem_not {xs : Array α} (h : ∀ a, a ∈ xs → ¬p a) : xs.eraseP p = xs := by
-  rcases xs with ⟨xs⟩
+theorem eraseP_of_forall_mem_not {l : Array α} (h : ∀ a, a ∈ l → ¬p a) : l.eraseP p = l := by
+  cases l
   simp_all [List.eraseP_of_forall_not]
 
-theorem eraseP_of_forall_getElem_not {xs : Array α} (h : ∀ i, (h : i < xs.size) → ¬p xs[i]) : xs.eraseP p = xs :=
+theorem eraseP_of_forall_getElem_not {l : Array α} (h : ∀ i, (h : i < l.size) → ¬p l[i]) : l.eraseP p = l :=
   eraseP_of_forall_mem_not fun a m => by
     rw [mem_iff_getElem] at m
     obtain ⟨i, w, rfl⟩ := m
@@ -40,131 +37,121 @@ theorem eraseP_of_forall_getElem_not {xs : Array α} (h : ∀ i, (h : i < xs.siz
 theorem eraseP_ne_empty_iff {xs : Array α} {p : α → Bool} : xs.eraseP p ≠ #[] ↔ xs ≠ #[] ∧ ∀ x, p x → xs ≠ #[x] := by
   simp
 
-theorem exists_of_eraseP {xs : Array α} {a} (hm : a ∈ xs) (hp : p a) :
-    ∃ a ys zs, (∀ b ∈ ys, ¬p b) ∧ p a ∧ xs = ys.push a ++ zs ∧ xs.eraseP p = ys ++ zs := by
-  rcases xs with ⟨xs⟩
+theorem exists_of_eraseP {l : Array α} {a} (hm : a ∈ l) (hp : p a) :
+    ∃ a l₁ l₂, (∀ b ∈ l₁, ¬p b) ∧ p a ∧ l = l₁.push a ++ l₂ ∧ l.eraseP p = l₁ ++ l₂ := by
+  rcases l with ⟨l⟩
   obtain ⟨a, l₁, l₂, h₁, h₂, rfl, h₃⟩ := List.exists_of_eraseP (by simpa using hm) (hp)
   refine ⟨a, ⟨l₁⟩, ⟨l₂⟩, by simpa using h₁, h₂, by simp, by simpa using h₃⟩
 
--- The arguments are explicit here, so this lemma can be used as a case split.
-theorem exists_or_eq_self_of_eraseP (p) (xs : Array α) :
-    xs.eraseP p = xs ∨
-    ∃ a ys zs, (∀ b ∈ ys, ¬p b) ∧ p a ∧ xs = ys.push a ++ zs ∧ xs.eraseP p = ys ++ zs :=
-  if h : ∃ a ∈ xs, p a then
+theorem exists_or_eq_self_of_eraseP (p) (l : Array α) :
+    l.eraseP p = l ∨
+    ∃ a l₁ l₂, (∀ b ∈ l₁, ¬p b) ∧ p a ∧ l = l₁.push a ++ l₂ ∧ l.eraseP p = l₁ ++ l₂ :=
+  if h : ∃ a ∈ l, p a then
     let ⟨_, ha, pa⟩ := h
     .inr (exists_of_eraseP ha pa)
   else
     .inl (eraseP_of_forall_mem_not (h ⟨·, ·, ·⟩))
 
-@[simp] theorem size_eraseP_of_mem {xs : Array α} (al : a ∈ xs) (pa : p a) :
-    (xs.eraseP p).size = xs.size - 1 := by
-  let ⟨_, ys, zs, _, _, e₁, e₂⟩ := exists_of_eraseP al pa
+@[simp] theorem size_eraseP_of_mem {l : Array α} (al : a ∈ l) (pa : p a) :
+    (l.eraseP p).size = l.size - 1 := by
+  let ⟨_, l₁, l₂, _, _, e₁, e₂⟩ := exists_of_eraseP al pa
   rw [e₂]; simp [size_append, e₁]; omega
 
-theorem size_eraseP {xs : Array α} : (xs.eraseP p).size = if xs.any p then xs.size - 1 else xs.size := by
+theorem size_eraseP {l : Array α} : (l.eraseP p).size = if l.any p then l.size - 1 else l.size := by
   split <;> rename_i h
   · simp only [any_eq_true] at h
     obtain ⟨i, h, w⟩ := h
-    simp [size_eraseP_of_mem (xs := xs) (by simp) w]
+    simp [size_eraseP_of_mem (l := l) (by simp) w]
   · simp only [any_eq_true] at h
     rw [eraseP_of_forall_getElem_not]
     simp_all
 
-theorem size_eraseP_le {xs : Array α} : (xs.eraseP p).size ≤ xs.size := by
-  rcases xs with ⟨xs⟩
-  simpa using List.length_eraseP_le
+theorem size_eraseP_le (l : Array α) : (l.eraseP p).size ≤ l.size := by
+  rcases l with ⟨l⟩
+  simpa using List.length_eraseP_le l
 
-theorem le_size_eraseP {xs : Array α} : xs.size - 1 ≤ (xs.eraseP p).size := by
-  rcases xs with ⟨xs⟩
-  simpa using List.le_length_eraseP
+theorem le_size_eraseP (l : Array α) : l.size - 1 ≤ (l.eraseP p).size := by
+  rcases l with ⟨l⟩
+  simpa using List.le_length_eraseP l
 
-theorem mem_of_mem_eraseP {xs : Array α} : a ∈ xs.eraseP p → a ∈ xs := by
-  rcases xs with ⟨xs⟩
+theorem mem_of_mem_eraseP {l : Array α} : a ∈ l.eraseP p → a ∈ l := by
+  rcases l with ⟨l⟩
   simpa using List.mem_of_mem_eraseP
 
-@[simp] theorem mem_eraseP_of_neg {xs : Array α} (pa : ¬p a) : a ∈ xs.eraseP p ↔ a ∈ xs := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem mem_eraseP_of_neg {l : Array α} (pa : ¬p a) : a ∈ l.eraseP p ↔ a ∈ l := by
+  rcases l with ⟨l⟩
   simpa using List.mem_eraseP_of_neg pa
 
-@[simp] theorem eraseP_eq_self_iff {xs : Array α} : xs.eraseP p = xs ↔ ∀ a ∈ xs, ¬ p a := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem eraseP_eq_self_iff {p} {l : Array α} : l.eraseP p = l ↔ ∀ a ∈ l, ¬ p a := by
+  rcases l with ⟨l⟩
   simp
 
-theorem eraseP_map {f : β → α} {xs : Array β} : (xs.map f).eraseP p = (xs.eraseP (p ∘ f)).map f := by
-  rcases xs with ⟨xs⟩
-  simpa using List.eraseP_map
+theorem eraseP_map (f : β → α) (l : Array β) : (map f l).eraseP p = map f (l.eraseP (p ∘ f)) := by
+  rcases l with ⟨l⟩
+  simpa using List.eraseP_map f l
 
-theorem eraseP_filterMap {f : α → Option β} {xs : Array α} :
-    (filterMap f xs).eraseP p = filterMap f (xs.eraseP (fun x => match f x with | some y => p y | none => false)) := by
-  rcases xs with ⟨xs⟩
-  simpa using List.eraseP_filterMap
+theorem eraseP_filterMap (f : α → Option β) (l : Array α) :
+    (filterMap f l).eraseP p = filterMap f (l.eraseP (fun x => match f x with | some y => p y | none => false)) := by
+  rcases l with ⟨l⟩
+  simpa using List.eraseP_filterMap f l
 
-theorem eraseP_filter {f : α → Bool} {xs : Array α} :
-    (filter f xs).eraseP p = filter f (xs.eraseP (fun x => p x && f x)) := by
-  rcases xs with ⟨xs⟩
-  simpa using List.eraseP_filter
+theorem eraseP_filter (f : α → Bool) (l : Array α) :
+    (filter f l).eraseP p = filter f (l.eraseP (fun x => p x && f x)) := by
+  rcases l with ⟨l⟩
+  simpa using List.eraseP_filter f l
 
-theorem eraseP_append_left {a : α} (pa : p a) {xs : Array α} {ys : Array α} (h : a ∈ xs) :
-    (xs ++ ys).eraseP p = xs.eraseP p ++ ys := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
-  simpa using List.eraseP_append_left pa ys (by simpa using h)
+theorem eraseP_append_left {a : α} (pa : p a) {l₁ : Array α} l₂ (h : a ∈ l₁) :
+    (l₁ ++ l₂).eraseP p = l₁.eraseP p ++ l₂ := by
+  rcases l₁ with ⟨l₁⟩
+  rcases l₂ with ⟨l₂⟩
+  simpa using List.eraseP_append_left pa l₂ (by simpa using h)
 
-theorem eraseP_append_right {xs : Array α} ys (h : ∀ b ∈ xs, ¬p b) :
-    (xs ++ ys).eraseP p = xs ++ ys.eraseP p := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
-  simpa using List.eraseP_append_right ys (by simpa using h)
+theorem eraseP_append_right {l₁ : Array α} l₂ (h : ∀ b ∈ l₁, ¬p b) :
+    (l₁ ++ l₂).eraseP p = l₁ ++ l₂.eraseP p := by
+  rcases l₁ with ⟨l₁⟩
+  rcases l₂ with ⟨l₂⟩
+  simpa using List.eraseP_append_right l₂ (by simpa using h)
 
-theorem eraseP_append {xs : Array α} {ys : Array α} :
-    (xs ++ ys).eraseP p = if xs.any p then xs.eraseP p ++ ys else xs ++ ys.eraseP p := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
-  simp only [List.append_toArray, List.eraseP_toArray, List.eraseP_append, List.any_toArray]
+theorem eraseP_append (l₁ l₂ : Array α) :
+    (l₁ ++ l₂).eraseP p = if l₁.any p then l₁.eraseP p ++ l₂ else l₁ ++ l₂.eraseP p := by
+  rcases l₁ with ⟨l₁⟩
+  rcases l₂ with ⟨l₂⟩
+  simp only [List.append_toArray, List.eraseP_toArray, List.eraseP_append l₁ l₂, List.any_toArray']
   split <;> simp
 
-theorem eraseP_replicate {n : Nat} {a : α} {p : α → Bool} :
-    (replicate n a).eraseP p = if p a then replicate (n - 1) a else replicate n a := by
+theorem eraseP_mkArray (n : Nat) (a : α) (p : α → Bool) :
+    (mkArray n a).eraseP p = if p a then mkArray (n - 1) a else mkArray n a := by
   simp only [← List.toArray_replicate, List.eraseP_toArray, List.eraseP_replicate]
   split <;> simp
 
-@[deprecated eraseP_replicate (since := "2025-03-18")]
-abbrev eraseP_mkArray := @eraseP_replicate
-
-@[simp] theorem eraseP_replicate_of_pos {n : Nat} {a : α} (h : p a) :
-    (replicate n a).eraseP p = replicate (n - 1) a := by
+@[simp] theorem eraseP_mkArray_of_pos {n : Nat} {a : α} (h : p a) :
+    (mkArray n a).eraseP p = mkArray (n - 1) a := by
   simp only [← List.toArray_replicate, List.eraseP_toArray]
   simp [h]
 
-@[deprecated eraseP_replicate_of_pos (since := "2025-03-18")]
-abbrev eraseP_mkArray_of_pos := @eraseP_replicate_of_pos
-
-@[simp] theorem eraseP_replicate_of_neg {n : Nat} {a : α} (h : ¬p a) :
-    (replicate n a).eraseP p = replicate n a := by
+@[simp] theorem eraseP_mkArray_of_neg {n : Nat} {a : α} (h : ¬p a) :
+    (mkArray n a).eraseP p = mkArray n a := by
   simp only [← List.toArray_replicate, List.eraseP_toArray]
   simp [h]
 
-@[deprecated eraseP_replicate_of_neg (since := "2025-03-18")]
-abbrev eraseP_mkArray_of_neg := @eraseP_replicate_of_neg
-
-theorem eraseP_eq_iff {p} {xs : Array α} :
-    xs.eraseP p = ys ↔
-      ((∀ a ∈ xs, ¬ p a) ∧ xs = ys) ∨
-        ∃ a as bs, (∀ b ∈ as, ¬ p b) ∧ p a ∧ xs = as.push a ++ bs ∧ ys = as ++ bs := by
-  rcases xs with ⟨l⟩
-  rcases ys with ⟨ys⟩
+theorem eraseP_eq_iff {p} {l : Array α} :
+    l.eraseP p = l' ↔
+      ((∀ a ∈ l, ¬ p a) ∧ l = l') ∨
+        ∃ a l₁ l₂, (∀ b ∈ l₁, ¬ p b) ∧ p a ∧ l = l₁.push a ++ l₂ ∧ l' = l₁ ++ l₂ := by
+  rcases l with ⟨l⟩
+  rcases l' with ⟨l'⟩
   simp [List.eraseP_eq_iff]
   constructor
-  · rintro (h | ⟨a, l₁, h₁, h₂, ⟨l, rfl, rfl⟩⟩)
+  · rintro (h | ⟨a, l₁, h₁, h₂, ⟨x, rfl, rfl⟩⟩)
     · exact Or.inl h
-    · exact Or.inr ⟨a, ⟨l₁⟩, by simpa using h₁, h₂, ⟨⟨l⟩, by simp⟩⟩
-  · rintro (h | ⟨a, ⟨l₁⟩, h₁, h₂, ⟨⟨l⟩, rfl, rfl⟩⟩)
+    · exact Or.inr ⟨a, ⟨l₁⟩, by simpa using h₁, h₂, ⟨⟨x⟩, by simp⟩⟩
+  · rintro (h | ⟨a, ⟨l₁⟩, h₁, h₂, ⟨⟨x⟩, rfl, rfl⟩⟩)
     · exact Or.inl h
-    · exact Or.inr ⟨a, l₁, by simpa using h₁, h₂, ⟨l, by simp⟩⟩
+    · exact Or.inr ⟨a, l₁, by simpa using h₁, h₂, ⟨x, by simp⟩⟩
 
-theorem eraseP_comm {xs : Array α} (h : ∀ a ∈ xs, ¬ p a ∨ ¬ q a) :
-    (xs.eraseP p).eraseP q = (xs.eraseP q).eraseP p := by
-  rcases xs with ⟨xs⟩
+theorem eraseP_comm {l : Array α} (h : ∀ a ∈ l, ¬ p a ∨ ¬ q a) :
+    (l.eraseP p).eraseP q = (l.eraseP q).eraseP p := by
+  rcases l with ⟨l⟩
   simpa using List.eraseP_comm (by simpa using h)
 
 /-! ### erase -/
@@ -172,18 +159,16 @@ theorem eraseP_comm {xs : Array α} (h : ∀ a ∈ xs, ¬ p a ∨ ¬ q a) :
 section erase
 variable [BEq α]
 
-theorem erase_of_not_mem [LawfulBEq α] {a : α} {xs : Array α} (h : a ∉ xs) : xs.erase a = xs := by
-  rcases xs with ⟨xs⟩
+theorem erase_of_not_mem [LawfulBEq α] {a : α} {l : Array α} (h : a ∉ l) : l.erase a = l := by
+  rcases l with ⟨l⟩
   simp [List.erase_of_not_mem (by simpa using h)]
 
--- The arguments are intentionally explicit.
-theorem erase_eq_eraseP' (a : α) (xs : Array α) : xs.erase a = xs.eraseP (· == a) := by
-  rcases xs with ⟨xs⟩
+theorem erase_eq_eraseP' (a : α) (l : Array α) : l.erase a = l.eraseP (· == a) := by
+  rcases l with ⟨l⟩
   simp [List.erase_eq_eraseP']
 
--- The arguments are intentionally explicit.
-theorem erase_eq_eraseP [LawfulBEq α] (a : α) (xs : Array α) : xs.erase a = xs.eraseP (a == ·) := by
-  rcases xs with ⟨xs⟩
+theorem erase_eq_eraseP [LawfulBEq α] (a : α) (l : Array α) : l.erase a = l.eraseP (a == ·) := by
+  rcases l with ⟨l⟩
   simp [List.erase_eq_eraseP]
 
 @[simp] theorem erase_eq_empty_iff [LawfulBEq α] {xs : Array α} {a : α} :
@@ -196,239 +181,220 @@ theorem erase_ne_empty_iff [LawfulBEq α] {xs : Array α} {a : α} :
   rcases xs with ⟨xs⟩
   simp [List.erase_ne_nil_iff]
 
-theorem exists_erase_eq [LawfulBEq α] {a : α} {xs : Array α} (h : a ∈ xs) :
-    ∃ ys zs, a ∉ ys ∧ xs = ys.push a ++ zs ∧ xs.erase a = ys ++ zs := by
-  let ⟨_, ys, zs, h₁, e, h₂, h₃⟩ := exists_of_eraseP h (beq_self_eq_true _)
-  rw [erase_eq_eraseP]; exact ⟨ys, zs, fun h => h₁ _ h (beq_self_eq_true _), eq_of_beq e ▸ h₂, h₃⟩
+theorem exists_erase_eq [LawfulBEq α] {a : α} {l : Array α} (h : a ∈ l) :
+    ∃ l₁ l₂, a ∉ l₁ ∧ l = l₁.push a ++ l₂ ∧ l.erase a = l₁ ++ l₂ := by
+  let ⟨_, l₁, l₂, h₁, e, h₂, h₃⟩ := exists_of_eraseP h (beq_self_eq_true _)
+  rw [erase_eq_eraseP]; exact ⟨l₁, l₂, fun h => h₁ _ h (beq_self_eq_true _), eq_of_beq e ▸ h₂, h₃⟩
 
-@[simp] theorem size_erase_of_mem [LawfulBEq α] {a : α} {xs : Array α} (h : a ∈ xs) :
-    (xs.erase a).size = xs.size - 1 := by
+@[simp] theorem size_erase_of_mem [LawfulBEq α] {a : α} {l : Array α} (h : a ∈ l) :
+    (l.erase a).size = l.size - 1 := by
   rw [erase_eq_eraseP]; exact size_eraseP_of_mem h (beq_self_eq_true a)
 
-theorem size_erase [LawfulBEq α] {a : α} {xs : Array α} :
-    (xs.erase a).size = if a ∈ xs then xs.size - 1 else xs.size := by
+theorem size_erase [LawfulBEq α] (a : α) (l : Array α) :
+    (l.erase a).size = if a ∈ l then l.size - 1 else l.size := by
   rw [erase_eq_eraseP, size_eraseP]
   congr
   simp [mem_iff_getElem, eq_comm (a := a)]
 
-theorem size_erase_le {a : α} {xs : Array α} : (xs.erase a).size ≤ xs.size := by
-  rcases xs with ⟨xs⟩
-  simpa using List.length_erase_le
+theorem size_erase_le (a : α) (l : Array α) : (l.erase a).size ≤ l.size := by
+  rcases l with ⟨l⟩
+  simpa using List.length_erase_le a l
 
-theorem le_size_erase [LawfulBEq α] {a : α} {xs : Array α} : xs.size - 1 ≤ (xs.erase a).size := by
-  rcases xs with ⟨xs⟩
-  simpa using List.le_length_erase
+theorem le_size_erase [LawfulBEq α] (a : α) (l : Array α) : l.size - 1 ≤ (l.erase a).size := by
+  rcases l with ⟨l⟩
+  simpa using List.le_length_erase a l
 
-theorem mem_of_mem_erase {a b : α} {xs : Array α} (h : a ∈ xs.erase b) : a ∈ xs := by
-  rcases xs with ⟨xs⟩
+theorem mem_of_mem_erase {a b : α} {l : Array α} (h : a ∈ l.erase b) : a ∈ l := by
+  rcases l with ⟨l⟩
   simpa using List.mem_of_mem_erase (by simpa using h)
 
-@[simp] theorem mem_erase_of_ne [LawfulBEq α] {a b : α} {xs : Array α} (ab : a ≠ b) :
-    a ∈ xs.erase b ↔ a ∈ xs :=
-  erase_eq_eraseP b xs ▸ mem_eraseP_of_neg (mt eq_of_beq ab.symm)
+@[simp] theorem mem_erase_of_ne [LawfulBEq α] {a b : α} {l : Array α} (ab : a ≠ b) :
+    a ∈ l.erase b ↔ a ∈ l :=
+  erase_eq_eraseP b l ▸ mem_eraseP_of_neg (mt eq_of_beq ab.symm)
 
-@[simp] theorem erase_eq_self_iff [LawfulBEq α] {xs : Array α} : xs.erase a = xs ↔ a ∉ xs := by
+@[simp] theorem erase_eq_self_iff [LawfulBEq α] {l : Array α} : l.erase a = l ↔ a ∉ l := by
   rw [erase_eq_eraseP', eraseP_eq_self_iff]
   simp [forall_mem_ne']
 
-theorem erase_filter [LawfulBEq α] {f : α → Bool} {xs : Array α} :
-    (filter f xs).erase a = filter f (xs.erase a) := by
-  rcases xs with ⟨xs⟩
-  simpa using List.erase_filter
+theorem erase_filter [LawfulBEq α] (f : α → Bool) (l : Array α) :
+    (filter f l).erase a = filter f (l.erase a) := by
+  rcases l with ⟨l⟩
+  simpa using List.erase_filter f l
 
-theorem erase_append_left [LawfulBEq α] {xs : Array α} (ys) (h : a ∈ xs) :
-    (xs ++ ys).erase a = xs.erase a ++ ys := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
-  simpa using List.erase_append_left ys (by simpa using h)
+theorem erase_append_left [LawfulBEq α] {l₁ : Array α} (l₂) (h : a ∈ l₁) :
+    (l₁ ++ l₂).erase a = l₁.erase a ++ l₂ := by
+  rcases l₁ with ⟨l₁⟩
+  rcases l₂ with ⟨l₂⟩
+  simpa using List.erase_append_left l₂ (by simpa using h)
 
-theorem erase_append_right [LawfulBEq α] {a : α} {xs : Array α} (ys : Array α) (h : a ∉ xs) :
-    (xs ++ ys).erase a = (xs ++ ys.erase a) := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
-  simpa using List.erase_append_right ys (by simpa using h)
+theorem erase_append_right [LawfulBEq α] {a : α} {l₁ : Array α} (l₂ : Array α) (h : a ∉ l₁) :
+    (l₁ ++ l₂).erase a = (l₁ ++ l₂.erase a) := by
+  rcases l₁ with ⟨l₁⟩
+  rcases l₂ with ⟨l₂⟩
+  simpa using List.erase_append_right l₂ (by simpa using h)
 
-theorem erase_append [LawfulBEq α] {a : α} {xs ys : Array α} :
-    (xs ++ ys).erase a = if a ∈ xs then xs.erase a ++ ys else xs ++ ys.erase a := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
+theorem erase_append [LawfulBEq α] {a : α} {l₁ l₂ : Array α} :
+    (l₁ ++ l₂).erase a = if a ∈ l₁ then l₁.erase a ++ l₂ else l₁ ++ l₂.erase a := by
+  rcases l₁ with ⟨l₁⟩
+  rcases l₂ with ⟨l₂⟩
   simp only [List.append_toArray, List.erase_toArray, List.erase_append, mem_toArray]
   split <;> simp
 
-theorem erase_replicate [LawfulBEq α] {n : Nat} {a b : α} :
-    (replicate n a).erase b = if b == a then replicate (n - 1) a else replicate n a := by
+theorem erase_mkArray [LawfulBEq α] (n : Nat) (a b : α) :
+    (mkArray n a).erase b = if b == a then mkArray (n - 1) a else mkArray n a := by
   simp only [← List.toArray_replicate, List.erase_toArray]
   simp only [List.erase_replicate, beq_iff_eq, List.toArray_replicate]
   split <;> simp
 
-@[deprecated erase_replicate (since := "2025-03-18")]
-abbrev erase_mkArray := @erase_replicate
+theorem erase_comm [LawfulBEq α] (a b : α) (l : Array α) :
+    (l.erase a).erase b = (l.erase b).erase a := by
+  rcases l with ⟨l⟩
+  simpa using List.erase_comm a b l
 
--- The arguments `a b` are explicit,
--- so they can be specified to prevent `simp` repeatedly applying the lemma.
-theorem erase_comm [LawfulBEq α] (a b : α) {xs : Array α} :
-    (xs.erase a).erase b = (xs.erase b).erase a := by
-  rcases xs with ⟨xs⟩
-  simpa using List.erase_comm a b
-
-theorem erase_eq_iff [LawfulBEq α] {a : α} {xs : Array α} :
-    xs.erase a = ys ↔
-      (a ∉ xs ∧ xs = ys) ∨
-        ∃ as bs, a ∉ as ∧ xs = as.push a ++ bs ∧ ys = as ++ bs := by
+theorem erase_eq_iff [LawfulBEq α] {a : α} {l : Array α} :
+    l.erase a = l' ↔
+      (a ∉ l ∧ l = l') ∨
+        ∃ l₁ l₂, a ∉ l₁ ∧ l = l₁.push a ++ l₂ ∧ l' = l₁ ++ l₂ := by
   rw [erase_eq_eraseP', eraseP_eq_iff]
   simp only [beq_iff_eq, forall_mem_ne', exists_and_left]
   constructor
-  · rintro (⟨h, rfl⟩ | ⟨a', as, h, rfl, bs, rfl, rfl⟩)
+  · rintro (⟨h, rfl⟩ | ⟨a', l', h, rfl, x, rfl, rfl⟩)
     · left; simp_all
-    · right; refine ⟨as, h, bs, by simp⟩
-  · rintro (⟨h, rfl⟩ | ⟨as, h, bs, rfl, rfl⟩)
+    · right; refine ⟨l', h, x, by simp⟩
+  · rintro (⟨h, rfl⟩ | ⟨l₁, h, x, rfl, rfl⟩)
     · left; simp_all
-    · right; refine ⟨a, as, h, rfl, bs, by simp⟩
+    · right; refine ⟨a, l₁, h, rfl, x, by simp⟩
 
-@[simp] theorem erase_replicate_self [LawfulBEq α] {a : α} :
-    (replicate n a).erase a = replicate (n - 1) a := by
+@[simp] theorem erase_mkArray_self [LawfulBEq α] {a : α} :
+    (mkArray n a).erase a = mkArray (n - 1) a := by
   simp only [← List.toArray_replicate, List.erase_toArray]
   simp [List.erase_replicate]
 
-@[deprecated erase_replicate_self (since := "2025-03-18")]
-abbrev erase_mkArray_self := @erase_replicate_self
-
-@[simp] theorem erase_replicate_ne [LawfulBEq α] {a b : α} (h : !b == a) :
-    (replicate n a).erase b = replicate n a := by
+@[simp] theorem erase_mkArray_ne [LawfulBEq α] {a b : α} (h : !b == a) :
+    (mkArray n a).erase b = mkArray n a := by
   rw [erase_of_not_mem]
   simp_all
 
-@[deprecated erase_replicate_ne (since := "2025-03-18")]
-abbrev erase_mkArray_ne := @erase_replicate_ne
-
 end erase
 
 /-! ### eraseIdx -/
 
-theorem eraseIdx_eq_eraseIdxIfInBounds {xs : Array α} {i : Nat} (h : i < xs.size) :
-    xs.eraseIdx i h = xs.eraseIdxIfInBounds i := by
-  simp [eraseIdxIfInBounds, h]
-
-theorem eraseIdx_eq_take_drop_succ {xs : Array α} {i : Nat} (h) :
-    xs.eraseIdx i h = xs.take i ++ xs.drop (i + 1) := by
-  rcases xs with ⟨xs⟩
-  simp only [List.size_toArray] at h
+theorem eraseIdx_eq_take_drop_succ (l : Array α) (i : Nat) (h) : l.eraseIdx i = l.take i ++ l.drop (i + 1) := by
+  rcases l with ⟨l⟩
+  simp only [size_toArray] at h
   simp only [List.eraseIdx_toArray, List.eraseIdx_eq_take_drop_succ, take_eq_extract,
     List.extract_toArray, List.extract_eq_drop_take, Nat.sub_zero, List.drop_zero, drop_eq_extract,
-    List.size_toArray, List.append_toArray, mk.injEq, List.append_cancel_left_eq]
+    size_toArray, List.append_toArray, mk.injEq, List.append_cancel_left_eq]
   rw [List.take_of_length_le]
   simp
 
-theorem getElem?_eraseIdx {xs : Array α} {i : Nat} (h : i < xs.size) {j : Nat} :
-    (xs.eraseIdx i)[j]? = if j < i then xs[j]? else xs[j + 1]? := by
-  rcases xs with ⟨xs⟩
+theorem getElem?_eraseIdx (l : Array α) (i : Nat) (h : i < l.size) (j : Nat) :
+    (l.eraseIdx i)[j]? = if j < i then l[j]? else l[j + 1]? := by
+  rcases l with ⟨l⟩
   simp [List.getElem?_eraseIdx]
 
-theorem getElem?_eraseIdx_of_lt {xs : Array α} {i : Nat} (h : i < xs.size) {j : Nat} (h' : j < i) :
-    (xs.eraseIdx i)[j]? = xs[j]? := by
+theorem getElem?_eraseIdx_of_lt (l : Array α) (i : Nat) (h : i < l.size) (j : Nat) (h' : j < i) :
+    (l.eraseIdx i)[j]? = l[j]? := by
   rw [getElem?_eraseIdx]
   simp [h']
 
-theorem getElem?_eraseIdx_of_ge {xs : Array α} {i : Nat} (h : i < xs.size) {j : Nat} (h' : i ≤ j) :
-    (xs.eraseIdx i)[j]? = xs[j + 1]? := by
+theorem getElem?_eraseIdx_of_ge (l : Array α) (i : Nat) (h : i < l.size) (j : Nat) (h' : i ≤ j) :
+    (l.eraseIdx i)[j]? = l[j + 1]? := by
   rw [getElem?_eraseIdx]
   simp only [dite_eq_ite, ite_eq_right_iff]
   intro h'
   omega
 
-theorem getElem_eraseIdx {xs : Array α} {i : Nat} (h : i < xs.size) {j : Nat} (h' : j < (xs.eraseIdx i).size) :
-    (xs.eraseIdx i)[j] = if h'' : j < i then
-        xs[j]
+theorem getElem_eraseIdx (l : Array α) (i : Nat) (h : i < l.size) (j : Nat) (h' : j < (l.eraseIdx i).size) :
+    (l.eraseIdx i)[j] = if h'' : j < i then
+        l[j]
       else
-        xs[j + 1]'(by rw [size_eraseIdx] at h'; omega) := by
+        l[j + 1]'(by rw [size_eraseIdx] at h'; omega) := by
   apply Option.some.inj
   rw [← getElem?_eq_getElem, getElem?_eraseIdx]
   split <;> simp
 
-@[simp] theorem eraseIdx_eq_empty_iff {xs : Array α} {i : Nat} {h} : xs.eraseIdx i = #[] ↔ xs.size = 1 ∧ i = 0 := by
-  rcases xs with ⟨xs⟩
-  simp only [List.eraseIdx_toArray, mk.injEq, List.eraseIdx_eq_nil_iff, List.size_toArray,
+@[simp] theorem eraseIdx_eq_empty_iff {l : Array α} {i : Nat} {h} : eraseIdx l i = #[] ↔ l.size = 1 ∧ i = 0 := by
+  rcases l with ⟨l⟩
+  simp only [List.eraseIdx_toArray, mk.injEq, List.eraseIdx_eq_nil_iff, size_toArray,
     or_iff_right_iff_imp]
   rintro rfl
   simp_all
 
-theorem eraseIdx_ne_empty_iff {xs : Array α} {i : Nat} {h} : xs.eraseIdx i ≠ #[] ↔ 2 ≤ xs.size := by
-  rcases xs with ⟨_ | ⟨a, (_ | ⟨b, l⟩)⟩⟩
+theorem eraseIdx_ne_empty_iff {l : Array α} {i : Nat} {h} : eraseIdx l i ≠ #[] ↔ 2 ≤ l.size := by
+  rcases l with ⟨_ | ⟨a, (_ | ⟨b, l⟩)⟩⟩
   · simp
   · simp at h
     simp [h]
   · simp
 
-theorem mem_of_mem_eraseIdx {xs : Array α} {i : Nat} {h} {a : α} (h : a ∈ xs.eraseIdx i) : a ∈ xs := by
-  rcases xs with ⟨xs⟩
+theorem mem_of_mem_eraseIdx {l : Array α} {i : Nat} {h} {a : α} (h : a ∈ l.eraseIdx i) : a ∈ l := by
+  rcases l with ⟨l⟩
   simpa using List.mem_of_mem_eraseIdx (by simpa using h)
 
-theorem eraseIdx_append_of_lt_size {xs : Array α} {k : Nat} (hk : k < xs.size) (ys : Array α) (h) :
-    eraseIdx (xs ++ ys) k = eraseIdx xs k ++ ys := by
-  rcases xs with ⟨l⟩
-  rcases ys with ⟨l'⟩
+theorem eraseIdx_append_of_lt_size {l : Array α} {k : Nat} (hk : k < l.size) (l' : Array α) (h) :
+    eraseIdx (l ++ l') k = eraseIdx l k ++ l' := by
+  rcases l with ⟨l⟩
+  rcases l' with ⟨l'⟩
   simp at hk
   simp [List.eraseIdx_append_of_lt_length, *]
 
-theorem eraseIdx_append_of_length_le {xs : Array α} {k : Nat} (hk : xs.size ≤ k) (ys : Array α) (h) :
-    eraseIdx (xs ++ ys) k = xs ++ eraseIdx ys (k - xs.size) (by simp at h; omega) := by
-  rcases xs with ⟨l⟩
-  rcases ys with ⟨l'⟩
+theorem eraseIdx_append_of_length_le {l : Array α} {k : Nat} (hk : l.size ≤ k) (l' : Array α) (h) :
+    eraseIdx (l ++ l') k = l ++ eraseIdx l' (k - l.size) (by simp at h; omega) := by
+  rcases l with ⟨l⟩
+  rcases l' with ⟨l'⟩
   simp at hk
   simp [List.eraseIdx_append_of_length_le, *]
 
-theorem eraseIdx_replicate {n : Nat} {a : α} {k : Nat} {h} :
-    (replicate n a).eraseIdx k = replicate (n - 1) a := by
+theorem eraseIdx_mkArray {n : Nat} {a : α} {k : Nat} {h} :
+    (mkArray n a).eraseIdx k = mkArray (n - 1) a := by
   simp at h
   simp only [← List.toArray_replicate, List.eraseIdx_toArray]
   simp [List.eraseIdx_replicate, h]
 
-@[deprecated eraseIdx_replicate (since := "2025-03-18")]
-abbrev eraseIdx_mkArray := @eraseIdx_replicate
-
-theorem mem_eraseIdx_iff_getElem {x : α} {xs : Array α} {k} {h} : x ∈ xs.eraseIdx k h ↔ ∃ i w, i ≠ k ∧ xs[i]'w = x := by
-  rcases xs with ⟨xs⟩
+theorem mem_eraseIdx_iff_getElem {x : α} {l} {k} {h} : x ∈ eraseIdx l k h ↔ ∃ i w, i ≠ k ∧ l[i]'w = x := by
+  rcases l with ⟨l⟩
   simp [List.mem_eraseIdx_iff_getElem, *]
 
-theorem mem_eraseIdx_iff_getElem? {x : α} {xs : Array α} {k} {h} : x ∈ xs.eraseIdx k h ↔ ∃ i ≠ k, xs[i]? = some x := by
-  rcases xs with ⟨xs⟩
+theorem mem_eraseIdx_iff_getElem? {x : α} {l} {k} {h} : x ∈ eraseIdx l k h ↔ ∃ i ≠ k, l[i]? = some x := by
+  rcases l with ⟨l⟩
   simp [List.mem_eraseIdx_iff_getElem?, *]
 
-theorem erase_eq_eraseIdx_of_idxOf [BEq α] [LawfulBEq α] {xs : Array α} {a : α} {i : Nat} (w : xs.idxOf a = i) (h : i < xs.size) :
-    xs.erase a = xs.eraseIdx i := by
-  rcases xs with ⟨xs⟩
+theorem erase_eq_eraseIdx_of_idxOf [BEq α] [LawfulBEq α] (l : Array α) (a : α) (i : Nat) (w : l.idxOf a = i) (h : i < l.size) :
+    l.erase a = l.eraseIdx i := by
+  rcases l with ⟨l⟩
   simp at w
   simp [List.erase_eq_eraseIdx_of_idxOf, *]
 
-theorem getElem_eraseIdx_of_lt {xs : Array α} {i : Nat} (w : i < xs.size) {j : Nat} (h : j < (xs.eraseIdx i).size) (h' : j < i) :
-    (xs.eraseIdx i)[j] = xs[j] := by
-  rcases xs with ⟨xs⟩
+theorem getElem_eraseIdx_of_lt (l : Array α) (i : Nat) (w : i < l.size) (j : Nat) (h : j < (l.eraseIdx i).size) (h' : j < i) :
+    (l.eraseIdx i)[j] = l[j] := by
+  rcases l with ⟨l⟩
   simp [List.getElem_eraseIdx_of_lt, *]
 
-theorem getElem_eraseIdx_of_ge {xs : Array α} {i : Nat} (w : i < xs.size) {j : Nat} (h : j < (xs.eraseIdx i).size) (h' : i ≤ j) :
-    (xs.eraseIdx i)[j] = xs[j + 1]'(by simp at h; omega) := by
-  rcases xs with ⟨xs⟩
+theorem getElem_eraseIdx_of_ge (l : Array α) (i : Nat) (w : i < l.size) (j : Nat) (h : j < (l.eraseIdx i).size) (h' : i ≤ j) :
+    (l.eraseIdx i)[j] = l[j + 1]'(by simp at h; omega) := by
+  rcases l with ⟨l⟩
   simp [List.getElem_eraseIdx_of_ge, *]
 
-theorem eraseIdx_set_eq {xs : Array α} {i : Nat} {a : α} {h : i < xs.size} :
-    (xs.set i a).eraseIdx i (by simp; omega) = xs.eraseIdx i := by
-  rcases xs with ⟨xs⟩
+theorem eraseIdx_set_eq {l : Array α} {i : Nat} {a : α} {h : i < l.size} :
+    (l.set i a).eraseIdx i (by simp; omega) = l.eraseIdx i := by
+  rcases l with ⟨l⟩
   simp [List.eraseIdx_set_eq, *]
 
-theorem eraseIdx_set_lt {xs : Array α} {i : Nat} {w : i < xs.size} {j : Nat} {a : α} (h : j < i) :
-    (xs.set i a).eraseIdx j (by simp; omega) = (xs.eraseIdx j).set (i - 1) a (by simp; omega) := by
-  rcases xs with ⟨xs⟩
+theorem eraseIdx_set_lt {l : Array α} {i : Nat} {w : i < l.size} {j : Nat} {a : α} (h : j < i) :
+    (l.set i a).eraseIdx j (by simp; omega) = (l.eraseIdx j).set (i - 1) a (by simp; omega) := by
+  rcases l with ⟨l⟩
   simp [List.eraseIdx_set_lt, *]
 
-theorem eraseIdx_set_gt {xs : Array α} {i : Nat} {j : Nat} {a : α} (h : i < j) {w : j < xs.size} :
-    (xs.set i a).eraseIdx j (by simp; omega) = (xs.eraseIdx j).set i a (by simp; omega) := by
-  rcases xs with ⟨xs⟩
+theorem eraseIdx_set_gt {l : Array α} {i : Nat} {j : Nat} {a : α} (h : i < j) {w : j < l.size} :
+    (l.set i a).eraseIdx j (by simp; omega) = (l.eraseIdx j).set i a (by simp; omega) := by
+  rcases l with ⟨l⟩
   simp [List.eraseIdx_set_gt, *]
 
 @[simp] theorem set_getElem_succ_eraseIdx_succ
-    {xs : Array α} {i : Nat} (h : i + 1 < xs.size) :
-    (xs.eraseIdx (i + 1)).set i xs[i + 1] (by simp; omega) = xs.eraseIdx i := by
-  rcases xs with ⟨xs⟩
+    {l : Array α} {i : Nat} (h : i + 1 < l.size) :
+    (l.eraseIdx (i + 1)).set i l[i + 1] (by simp; omega) = l.eraseIdx i := by
+  rcases l with ⟨l⟩
   simp [List.set_getElem_succ_eraseIdx_succ, *]
 
 end Array

src/Init/Data/Array/Extract.lean

@@ -1,445 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison
--/
-prelude
-import Init.Data.Array.Lemmas
-import Init.Data.List.Nat.TakeDrop
-
-/-!
-# Lemmas about `Array.extract`
-
-This file follows the contents of `Init.Data.List.TakeDrop` and `Init.Data.List.Nat.TakeDrop`.
--/
-
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
-open Nat
-namespace Array
-
-/-! ### extract -/
-
-@[simp] theorem extract_of_size_lt {as : Array α} {i j : Nat} (h : as.size < j) :
-    as.extract i j = as.extract i as.size := by
-  ext l h₁ h₂
-  · simp
-    omega
-  · simp only [size_extract] at h₁ h₂
-    simp [h]
-
-theorem size_extract_le {as : Array α} {i j : Nat} :
-    (as.extract i j).size ≤ j - i := by
-  simp
-  omega
-
-theorem size_extract_le' {as : Array α} {i j : Nat} :
-    (as.extract i j).size ≤ as.size - i := by
-  simp
-  omega
-
-theorem size_extract_of_le {as : Array α} {i j : Nat} (h : j ≤ as.size) :
-    (as.extract i j).size = j - i := by
-  simp
-  omega
-
-@[simp]
-theorem extract_push {as : Array α} {b : α} {start stop : Nat} (h : stop ≤ as.size) :
-    (as.push b).extract start stop = as.extract start stop := by
-  ext i h₁ h₂
-  · simp
-    omega
-  · simp only [size_extract, size_push] at h₁ h₂
-    simp only [getElem_extract, getElem_push]
-    rw [dif_pos (by omega)]
-
-@[simp]
-theorem extract_eq_pop {as : Array α} {stop : Nat} (h : stop = as.size - 1) :
-    as.extract 0 stop = as.pop := by
-  ext i h₁ h₂
-  · simp
-    omega
-  · simp only [size_extract, size_pop] at h₁ h₂
-    simp [getElem_extract, getElem_pop]
-
-@[simp]
-theorem extract_append_extract {as : Array α} {i j k : Nat} :
-    as.extract i j ++ as.extract j k = as.extract (min i j) (max j k) := by
-  ext l h₁ h₂
-  · simp
-    omega
-  · simp only [size_append, size_extract] at h₁ h₂
-    simp only [getElem_append, size_extract, getElem_extract]
-    split <;>
-    · congr 1
-      omega
-
-@[simp]
-theorem extract_eq_empty_iff {as : Array α} :
-    as.extract i j = #[] ↔ min j as.size ≤ i := by
-  constructor
-  · intro h
-    replace h := congrArg Array.size h
-    simp at h
-    omega
-  · intro h
-    exact eq_empty_of_size_eq_zero (by simp; omega)
-
-theorem extract_eq_empty_of_le {as : Array α} (h : min j as.size ≤ i) :
-    as.extract i j = #[] :=
-  extract_eq_empty_iff.2 h
-
-theorem lt_of_extract_ne_empty {as : Array α} (h : as.extract i j ≠ #[]) :
-    i < min j as.size :=
-  gt_of_not_le (mt extract_eq_empty_of_le h)
-
-@[simp]
-theorem extract_eq_self_iff {as : Array α} :
-    as.extract i j = as ↔ as.size = 0 ∨ i = 0 ∧ as.size ≤ j := by
-  constructor
-  · intro h
-    replace h := congrArg Array.size h
-    simp at h
-    omega
-  · intro h
-    ext l h₁ h₂
-    · simp
-      omega
-    · simp only [size_extract] at h₁
-      simp only [getElem_extract]
-      congr 1
-      omega
-
-theorem extract_eq_self_of_le {as : Array α} (h : as.size ≤ j) :
-    as.extract 0 j = as :=
-  extract_eq_self_iff.2 (.inr ⟨rfl, h⟩)
-
-theorem le_of_extract_eq_self {as : Array α} (h : as.extract i j = as) :
-    as.size ≤ j := by
-  replace h := congrArg Array.size h
-  simp at h
-  omega
-
-@[simp]
-theorem extract_size_left {as : Array α} :
-    as.extract as.size j = #[] := by
-  simp
-  omega
-
-@[simp]
-theorem push_extract_getElem {as : Array α} {i j : Nat} (h : j < as.size) :
-    (as.extract i j).push as[j] = as.extract (min i j) (j + 1) := by
-  ext l h₁ h₂
-  · simp
-    omega
-  · simp only [size_push, size_extract] at h₁ h₂
-    simp only [getElem_push, size_extract, getElem_extract]
-    split <;>
-    · congr
-      omega
-
-theorem extract_succ_right {as : Array α} {i j : Nat} (w : i < j + 1) (h : j < as.size) :
-    as.extract i (j + 1) = (as.extract i j).push as[j] := by
-  ext l h₁ h₂
-  · simp
-    omega
-  · simp only [size_extract, push_extract_getElem] at h₁ h₂
-    simp only [getElem_extract, push_extract_getElem]
-    congr
-    omega
-
-theorem extract_sub_one {as : Array α} {i j : Nat} (h : j < as.size) :
-    as.extract i (j - 1) = (as.extract i j).pop := by
-  ext l h₁ h₂
-  · simp
-    omega
-  · simp only [size_extract, size_pop] at h₁ h₂
-    simp only [getElem_extract, getElem_pop]
-
-@[simp]
-theorem getElem?_extract_of_lt {as : Array α} {i j k : Nat} (h : k < min j as.size - i) :
-    (as.extract i j)[k]? = some (as[i + k]'(by omega)) := by
-  simp [getElem?_extract, h]
-
-theorem getElem?_extract_of_succ {as : Array α} {j : Nat} :
-    (as.extract 0 (j + 1))[j]? = as[j]? := by
-  simp [getElem?_extract]
-  omega
-
-@[simp] theorem extract_extract {as : Array α} {i j k l : Nat} :
-    (as.extract i j).extract k l = as.extract (i + k) (min (i + l) j) := by
-  ext m h₁ h₂
-  · simp
-    omega
-  · simp only [size_extract] at h₁ h₂
-    simp [Nat.add_assoc]
-
-theorem extract_eq_empty_of_eq_empty {as : Array α} {i j : Nat} (h : as = #[]) :
-    as.extract i j = #[] := by
-  simp [h]
-
-theorem ne_empty_of_extract_ne_empty {as : Array α} {i j : Nat} (h : as.extract i j ≠ #[]) :
-    as ≠ #[] :=
-  mt extract_eq_empty_of_eq_empty h
-
-theorem extract_set {as : Array α} {i j k : Nat} (h : k < as.size) {a : α} :
-    (as.set k a).extract i j =
-      if _ : k < i then
-        as.extract i j
-      else if _ : k < min j as.size then
-        (as.extract i j).set (k - i) a (by simp; omega)
-      else as.extract i j := by
-  split
-  · ext l h₁ h₂
-    · simp
-    · simp at h₁ h₂
-      simp [getElem_set]
-      omega
-  · split
-    · ext l h₁ h₂
-      · simp
-      · simp only [getElem_extract, getElem_set]
-        split
-        · rw [if_pos]; omega
-        · rw [if_neg]; omega
-    · ext l h₁ h₂
-      · simp
-      · simp at h₁ h₂
-        simp [getElem_set]
-        omega
-
-theorem set_extract {as : Array α} {i j k : Nat} (h : k < (as.extract i j).size) {a : α} :
-    (as.extract i j).set k a = (as.set (i + k) a (by simp at h; omega)).extract i j := by
-  ext l h₁ h₂
-  · simp
-  · simp_all [getElem_set]
-
-@[simp]
-theorem extract_append {as bs : Array α} {i j : Nat} :
-    (as ++ bs).extract i j = as.extract i j ++ bs.extract (i - as.size) (j - as.size) := by
-  ext l h₁ h₂
-  · simp
-    omega
-  · simp only [size_extract, size_append] at h₁ h₂
-    simp only [getElem_extract, getElem_append, size_extract]
-    split
-    · split
-      · rfl
-      · omega
-    · split
-      · omega
-      · congr 1
-        omega
-
-theorem extract_append_left {as bs : Array α} :
-    (as ++ bs).extract 0 as.size = as.extract 0 as.size := by
-  simp
-
-@[simp] theorem extract_append_right {as bs : Array α} :
-    (as ++ bs).extract as.size (as.size + i) = bs.extract 0 i := by
-  simp only [extract_append, extract_size_left, Nat.sub_self, empty_append]
-  congr 1
-  omega
-
-@[simp] theorem map_extract {as : Array α} {i j : Nat} :
-    (as.extract i j).map f = (as.map f).extract i j := by
-  ext l h₁ h₂
-  · simp
-  · simp only [size_map, size_extract] at h₁ h₂
-    simp only [getElem_map, getElem_extract]
-
-@[simp] theorem extract_replicate {a : α} {n i j : Nat} :
-    (replicate n a).extract i j = replicate (min j n - i) a := by
-  ext l h₁ h₂
-  · simp
-  · simp only [size_extract, size_replicate] at h₁ h₂
-    simp only [getElem_extract, getElem_replicate]
-
-@[deprecated extract_replicate (since := "2025-03-18")]
-abbrev extract_mkArray := @extract_replicate
-
-theorem extract_eq_extract_right {as : Array α} {i j j' : Nat} :
-    as.extract i j = as.extract i j' ↔ min (j - i) (as.size - i) = min (j' - i) (as.size - i) := by
-  rcases as with ⟨as⟩
-  simp
-
-theorem extract_eq_extract_left {as : Array α} {i i' j : Nat} :
-    as.extract i j = as.extract i' j ↔ min j as.size - i = min j as.size - i' := by
-  constructor
-  · intro h
-    replace h := congrArg Array.size h
-    simpa using h
-  · intro h
-    ext l h₁ h₂
-    · simpa
-    · simp only [size_extract] at h₁ h₂
-      simp only [getElem_extract]
-      congr 1
-      omega
-
-theorem extract_add_left {as : Array α} {i j k : Nat} :
-    as.extract (i + j) k = (as.extract i k).extract j (k - i) := by
-  simp [extract_eq_extract_right]
-  omega
-
-theorem mem_extract_iff_getElem {as : Array α} {a : α} {i j : Nat} :
-    a ∈ as.extract i j ↔ ∃ (k : Nat) (hm : k < min j as.size - i), as[i + k] = a := by
-  rcases as with ⟨as⟩
-  simp [List.mem_take_iff_getElem]
-  constructor <;>
-  · rintro ⟨k, h, rfl⟩
-    exact ⟨k, by omega, rfl⟩
-
-theorem set_eq_push_extract_append_extract {as : Array α} {i : Nat} (h : i < as.size) {a : α} :
-    as.set i a = (as.extract 0 i).push a ++ (as.extract (i + 1) as.size) := by
-  rcases as with ⟨as⟩
-  simp at h
-  simp [List.set_eq_take_append_cons_drop, h, List.take_of_length_le]
-
-theorem extract_reverse {as : Array α} {i j : Nat} :
-    as.reverse.extract i j = (as.extract (as.size - j) (as.size - i)).reverse := by
-  ext l h₁ h₂
-  · simp
-    omega
-  · simp only [size_extract, size_reverse] at h₁ h₂
-    simp only [getElem_extract, getElem_reverse, size_extract]
-    congr 1
-    omega
-
-theorem reverse_extract {as : Array α} {i j : Nat} :
-    (as.extract i j).reverse = as.reverse.extract (as.size - j) (as.size - i) := by
-  rw [extract_reverse]
-  simp
-  by_cases h : j ≤ as.size
-  · have : as.size - (as.size - j) = j := by omega
-    simp [this, extract_eq_extract_left]
-    omega
-  · have : as.size - (as.size - j) = as.size := by omega
-    simp only [Nat.not_le] at h
-    simp [h, this, extract_eq_extract_left]
-    omega
-
-/-! ### takeWhile -/
-
-theorem takeWhile_map {f : α → β} {p : β → Bool} {as : Array α} :
-    (as.map f).takeWhile p = (as.takeWhile (p ∘ f)).map f := by
-  rcases as with ⟨as⟩
-  simp [List.takeWhile_map]
-
-theorem popWhile_map {f : α → β} {p : β → Bool} {as : Array α} :
-    (as.map f).popWhile p = (as.popWhile (p ∘ f)).map f := by
-  rcases as with ⟨as⟩
-  simp [List.dropWhile_map, ← List.map_reverse]
-
-theorem takeWhile_filterMap {f : α → Option β} {p : β → Bool} {as : Array α} :
-    (as.filterMap f).takeWhile p = (as.takeWhile fun a => (f a).all p).filterMap f := by
-  rcases as with ⟨as⟩
-  simp [List.takeWhile_filterMap]
-
-theorem popWhile_filterMap {f : α → Option β} {p : β → Bool} {as : Array α} :
-    (as.filterMap f).popWhile p = (as.popWhile fun a => (f a).all p).filterMap f := by
-  rcases as with ⟨as⟩
-  simp [List.dropWhile_filterMap, ← List.filterMap_reverse]
-
-theorem takeWhile_filter {p q : α → Bool} {as : Array α} :
-    (as.filter p).takeWhile q = (as.takeWhile fun a => !p a || q a).filter p := by
-  rcases as with ⟨as⟩
-  simp [List.takeWhile_filter]
-
-theorem popWhile_filter {p q : α → Bool} {as : Array α} :
-    (as.filter p).popWhile q = (as.popWhile fun a => !p a || q a).filter p := by
-  rcases as with ⟨as⟩
-  simp [List.dropWhile_filter, ← List.filter_reverse]
-
-theorem takeWhile_append {xs ys : Array α} :
-    (xs ++ ys).takeWhile p =
-      if (xs.takeWhile p).size = xs.size then xs ++ ys.takeWhile p else xs.takeWhile p := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
-  simp only [List.append_toArray, List.takeWhile_toArray, List.takeWhile_append, List.size_toArray]
-  split <;> rfl
-
-@[simp] theorem takeWhile_append_of_pos {p : α → Bool} {xs ys : Array α} (h : ∀ a ∈ xs, p a) :
-    (xs ++ ys).takeWhile p = xs ++ ys.takeWhile p := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
-  simp at h
-  simp [List.takeWhile_append_of_pos h]
-
-theorem popWhile_append {xs ys : Array α} :
-    (xs ++ ys).popWhile p =
-      if (ys.popWhile p).isEmpty then xs.popWhile p else xs ++ ys.popWhile p := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
-  simp only [List.append_toArray, List.popWhile_toArray, List.reverse_append, List.dropWhile_append,
-    List.isEmpty_iff, List.isEmpty_toArray, List.isEmpty_reverse]
-  -- Why do these not fire with `simp`?
-  rw [List.popWhile_toArray, List.isEmpty_toArray, List.isEmpty_reverse]
-  split
-  · rfl
-  · simp
-
-@[simp] theorem popWhile_append_of_pos {p : α → Bool} {xs ys : Array α} (h : ∀ a ∈ ys, p a) :
-    (xs ++ ys).popWhile p = xs.popWhile p := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
-  simp at h
-  simp only [List.append_toArray, List.popWhile_toArray, List.reverse_append, mk.injEq,
-    List.reverse_inj]
-  rw [List.dropWhile_append_of_pos]
-  simpa
-
-@[simp] theorem takeWhile_replicate_eq_filter {p : α → Bool} :
-    (replicate n a).takeWhile p = (replicate n a).filter p := by
-  simp [← List.toArray_replicate]
-
-@[deprecated takeWhile_replicate_eq_filter (since := "2025-03-18")]
-abbrev takeWhile_mkArray_eq_filter := @takeWhile_replicate_eq_filter
-
-theorem takeWhile_replicate {p : α → Bool} :
-    (replicate n a).takeWhile p = if p a then replicate n a else #[] := by
-  simp [takeWhile_replicate_eq_filter, filter_replicate]
-
-@[deprecated takeWhile_replicate (since := "2025-03-18")]
-abbrev takeWhile_mkArray := @takeWhile_replicate
-
-@[simp] theorem popWhile_replicate_eq_filter_not {p : α → Bool} :
-    (replicate n a).popWhile p = (replicate n a).filter (fun a => !p a) := by
-  simp [← List.toArray_replicate, ← List.filter_reverse]
-
-@[deprecated popWhile_replicate_eq_filter_not (since := "2025-03-18")]
-abbrev popWhile_mkArray_eq_filter_not := @popWhile_replicate_eq_filter_not
-
-theorem popWhile_replicate {p : α → Bool} :
-    (replicate n a).popWhile p = if p a then #[] else replicate n a := by
-  simp only [popWhile_replicate_eq_filter_not, size_replicate, filter_replicate, Bool.not_eq_eq_eq_not,
-    Bool.not_true]
-  split <;> simp_all
-
-@[deprecated popWhile_replicate (since := "2025-03-18")]
-abbrev popWhile_mkArray := @popWhile_replicate
-
-theorem extract_takeWhile {as : Array α} {i : Nat} :
-    (as.takeWhile p).extract 0 i = (as.extract 0 i).takeWhile p := by
-  rcases as with ⟨as⟩
-  simp [List.take_takeWhile]
-
-@[simp] theorem all_takeWhile {as : Array α} :
-    (as.takeWhile p).all p = true := by
-  rcases as with ⟨as⟩
-  rw [List.takeWhile_toArray] -- Not sure why this doesn't fire with `simp`.
-  simp
-
-@[simp] theorem any_popWhile {as : Array α} :
-    (as.popWhile p).any (fun a => !p a) = !as.all p := by
-  rcases as with ⟨as⟩
-  rw [List.popWhile_toArray] -- Not sure why this doesn't fire with `simp`.
-  simp
-
-theorem takeWhile_eq_extract_findIdx_not {xs : Array α} {p : α → Bool} :
-    takeWhile p xs = xs.extract 0 (xs.findIdx (fun a => !p a)) := by
-  rcases xs with ⟨xs⟩
-  simp [List.takeWhile_eq_take_findIdx_not]
-
-end Array

src/Init/Data/Array/FinRange.lean

@@ -5,52 +5,10 @@ Authors: François G. Dorais
 -/
 prelude
 import Init.Data.List.FinRange
-import Init.Data.Array.OfFn
-
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
 
 namespace Array
 
-/--
-Returns an array of all elements of `Fin n` in order, starting at `0`.
-
-Examples:
- * `Array.finRange 0 = (#[] : Array (Fin 0))`
- * `Array.finRange 2 = (#[0, 1] : Array (Fin 2))`
--/
+/-- `finRange n` is the array of all elements of `Fin n` in order. -/
 protected def finRange (n : Nat) : Array (Fin n) := ofFn fun i => i
 
-@[simp] theorem size_finRange {n} : (Array.finRange n).size = n := by
-  simp [Array.finRange]
-
-@[simp] theorem getElem_finRange {i : Nat} (h : i < (Array.finRange n).size) :
-    (Array.finRange n)[i] = Fin.cast size_finRange ⟨i, h⟩ := by
-  simp [Array.finRange]
-
-@[simp] theorem finRange_zero : Array.finRange 0 = #[] := by simp [Array.finRange]
-
-theorem finRange_succ {n} : Array.finRange (n+1) = #[0] ++ (Array.finRange n).map Fin.succ := by
-  ext
-  · simp [Nat.add_comm]
-  · simp [getElem_append]
-    split <;>
-    · simp; omega
-
-theorem finRange_succ_last {n} :
-    Array.finRange (n+1) = (Array.finRange n).map Fin.castSucc ++ #[Fin.last n] := by
-  ext
-  · simp
-  · simp [getElem_push]
-    split
-    · simp
-    · simp_all
-      omega
-
-theorem finRange_reverse {n} : (Array.finRange n).reverse = (Array.finRange n).map Fin.rev := by
-  ext i h
-  · simp
-  · simp
-    omega
-
 end Array

src/Init/Data/Array/Find.lean

@@ -13,136 +13,127 @@ import Init.Data.Array.Range
 # Lemmas about `Array.findSome?`, `Array.find?, `Array.findIdx`, `Array.findIdx?`, `Array.idxOf`.
 -/
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
 namespace Array
 
 open Nat
 
 /-! ### findSome? -/
 
-@[simp] theorem findSomeRev?_push_of_isSome {xs : Array α} (h : (f a).isSome) : (xs.push a).findSomeRev? f = f a := by
-  cases xs; simp_all
+@[simp] theorem findSomeRev?_push_of_isSome (l : Array α) (h : (f a).isSome) : (l.push a).findSomeRev? f = f a := by
+  cases l; simp_all
 
-@[simp] theorem findSomeRev?_push_of_isNone {xs : Array α} (h : (f a).isNone) : (xs.push a).findSomeRev? f = xs.findSomeRev? f := by
-  cases xs; simp_all
+@[simp] theorem findSomeRev?_push_of_isNone (l : Array α) (h : (f a).isNone) : (l.push a).findSomeRev? f = l.findSomeRev? f := by
+  cases l; simp_all
 
-theorem exists_of_findSome?_eq_some {f : α → Option β} {xs : Array α} (w : xs.findSome? f = some b) :
-    ∃ a, a ∈ xs ∧ f a = b := by
-  cases xs; simp_all [List.exists_of_findSome?_eq_some]
+theorem exists_of_findSome?_eq_some {f : α → Option β} {l : Array α} (w : l.findSome? f = some b) :
+    ∃ a, a ∈ l ∧ f a = b := by
+  cases l; simp_all [List.exists_of_findSome?_eq_some]
 
-@[simp] theorem findSome?_eq_none_iff : findSome? p xs = none ↔ ∀ x ∈ xs, p x = none := by
-  cases xs; simp
+@[simp] theorem findSome?_eq_none_iff : findSome? p l = none ↔ ∀ x ∈ l, p x = none := by
+  cases l; simp
 
-@[simp] theorem findSome?_isSome_iff {f : α → Option β} {xs : Array α} :
-    (xs.findSome? f).isSome ↔ ∃ x, x ∈ xs ∧ (f x).isSome := by
-  cases xs; simp
+@[simp] theorem findSome?_isSome_iff {f : α → Option β} {l : Array α} :
+    (l.findSome? f).isSome ↔ ∃ x, x ∈ l ∧ (f x).isSome := by
+  cases l; simp
 
-theorem findSome?_eq_some_iff {f : α → Option β} {xs : Array α} {b : β} :
-    xs.findSome? f = some b ↔ ∃ (ys : Array α) (a : α) (zs : Array α), xs = ys.push a ++ zs ∧ f a = some b ∧ ∀ x ∈ ys, f x = none := by
-  cases xs
+theorem findSome?_eq_some_iff {f : α → Option β} {l : Array α} {b : β} :
+    l.findSome? f = some b ↔ ∃ (l₁ : Array α) (a : α) (l₂ : Array α), l = l₁.push a ++ l₂ ∧ f a = some b ∧ ∀ x ∈ l₁, f x = none := by
+  cases l
   simp only [List.findSome?_toArray, List.findSome?_eq_some_iff]
   constructor
   · rintro ⟨l₁, a, l₂, rfl, h₁, h₂⟩
     exact ⟨l₁.toArray, a, l₂.toArray, by simp_all⟩
-  · rintro ⟨xs, a, ys, h₀, h₁, h₂⟩
-    exact ⟨xs.toList, a, ys.toList, by simpa using congrArg toList h₀, h₁, by simpa⟩
+  · rintro ⟨l₁, a, l₂, h₀, h₁, h₂⟩
+    exact ⟨l₁.toList, a, l₂.toList, by simpa using congrArg toList h₀, h₁, by simpa⟩
 
-@[simp] theorem findSome?_guard {xs : Array α} : findSome? (Option.guard fun x => p x) xs = find? p xs := by
-  cases xs; simp
+@[simp] theorem findSome?_guard (l : Array α) : findSome? (Option.guard fun x => p x) l = find? p l := by
+  cases l; simp
 
-theorem find?_eq_findSome?_guard {xs : Array α} : find? p xs = findSome? (Option.guard fun x => p x) xs :=
-  findSome?_guard.symm
+theorem find?_eq_findSome?_guard (l : Array α) : find? p l = findSome? (Option.guard fun x => p x) l :=
+  (findSome?_guard l).symm
 
-@[simp] theorem getElem?_zero_filterMap {f : α → Option β} {xs : Array α} : (xs.filterMap f)[0]? = xs.findSome? f := by
-  cases xs; simp [← List.head?_eq_getElem?]
+@[simp] theorem getElem?_zero_filterMap (f : α → Option β) (l : Array α) : (l.filterMap f)[0]? = l.findSome? f := by
+  cases l; simp [← List.head?_eq_getElem?]
 
-@[simp] theorem getElem_zero_filterMap {f : α → Option β} {xs : Array α} (h) :
-    (xs.filterMap f)[0] = (xs.findSome? f).get (by cases xs; simpa [List.length_filterMap_eq_countP] using h) := by
-  cases xs; simp [← List.head_eq_getElem, ← getElem?_zero_filterMap]
+@[simp] theorem getElem_zero_filterMap (f : α → Option β) (l : Array α) (h) :
+    (l.filterMap f)[0] = (l.findSome? f).get (by cases l; simpa [List.length_filterMap_eq_countP] using h) := by
+  cases l; simp [← List.head_eq_getElem, ← getElem?_zero_filterMap]
 
-@[simp] theorem back?_filterMap {f : α → Option β} {xs : Array α} : (xs.filterMap f).back? = xs.findSomeRev? f := by
-  cases xs; simp
+@[simp] theorem back?_filterMap (f : α → Option β) (l : Array α) : (l.filterMap f).back? = l.findSomeRev? f := by
+  cases l; simp
 
-@[simp] theorem back!_filterMap [Inhabited β] {f : α → Option β} {xs : Array α} :
-    (xs.filterMap f).back! = (xs.findSomeRev? f).getD default := by
-  cases xs; simp
+@[simp] theorem back!_filterMap [Inhabited β] (f : α → Option β) (l : Array α) :
+    (l.filterMap f).back! = (l.findSomeRev? f).getD default := by
+  cases l; simp
 
-@[simp] theorem map_findSome? {f : α → Option β} {g : β → γ} {xs : Array α} :
-    (xs.findSome? f).map g = xs.findSome? (Option.map g ∘ f) := by
-  cases xs; simp
+@[simp] theorem map_findSome? (f : α → Option β) (g : β → γ) (l : Array α) :
+    (l.findSome? f).map g = l.findSome? (Option.map g ∘ f) := by
+  cases l; simp
 
-theorem findSome?_map {f : β → γ} {xs : Array β} : findSome? p (xs.map f) = xs.findSome? (p ∘ f) := by
-  cases xs; simp [List.findSome?_map]
+theorem findSome?_map (f : β → γ) (l : Array β) : findSome? p (l.map f) = l.findSome? (p ∘ f) := by
+  cases l; simp [List.findSome?_map]
 
-theorem findSome?_append {xs ys : Array α} : (xs ++ ys).findSome? f = (xs.findSome? f).or (ys.findSome? f) := by
-  cases xs; cases ys; simp [List.findSome?_append]
+theorem findSome?_append {l₁ l₂ : Array α} : (l₁ ++ l₂).findSome? f = (l₁.findSome? f).or (l₂.findSome? f) := by
+  cases l₁; cases l₂; simp [List.findSome?_append]
 
-theorem getElem?_zero_flatten (xss : Array (Array α)) :
-    (flatten xss)[0]? = xss.findSome? fun xs => xs[0]? := by
-  cases xss using array₂_induction
+theorem getElem?_zero_flatten (L : Array (Array α)) :
+    (flatten L)[0]? = L.findSome? fun l => l[0]? := by
+  cases L using array₂_induction
   simp [← List.head?_eq_getElem?, List.head?_flatten, List.findSome?_map, Function.comp_def]
 
-theorem getElem_zero_flatten.proof {xss : Array (Array α)} (h : 0 < xss.flatten.size) :
-    (xss.findSome? fun xs => xs[0]?).isSome := by
-  cases xss using array₂_induction
+theorem getElem_zero_flatten.proof {L : Array (Array α)} (h : 0 < L.flatten.size) :
+    (L.findSome? fun l => l[0]?).isSome := by
+  cases L using array₂_induction
   simp only [List.findSome?_toArray, List.findSome?_map, Function.comp_def, List.getElem?_toArray,
     List.findSome?_isSome_iff, isSome_getElem?]
-  simp only [flatten_toArray_map_toArray, List.size_toArray, List.length_flatten,
+  simp only [flatten_toArray_map_toArray, size_toArray, List.length_flatten,
     Nat.sum_pos_iff_exists_pos, List.mem_map] at h
   obtain ⟨_, ⟨xs, m, rfl⟩, h⟩ := h
   exact ⟨xs, m, by simpa using h⟩
 
-theorem getElem_zero_flatten {xss : Array (Array α)} (h) :
-    (flatten xss)[0] = (xss.findSome? fun xs => xs[0]?).get (getElem_zero_flatten.proof h) := by
-  have t := getElem?_zero_flatten xss
+theorem getElem_zero_flatten {L : Array (Array α)} (h) :
+    (flatten L)[0] = (L.findSome? fun l => l[0]?).get (getElem_zero_flatten.proof h) := by
+  have t := getElem?_zero_flatten L
   simp [getElem?_eq_getElem, h] at t
   simp [← t]
 
-theorem findSome?_replicate : findSome? f (replicate n a) = if n = 0 then none else f a := by
+theorem back?_flatten {L : Array (Array α)} :
+    (flatten L).back? = (L.findSomeRev? fun l => l.back?) := by
+  cases L using array₂_induction
+  simp [List.getLast?_flatten, ← List.map_reverse, List.findSome?_map, Function.comp_def]
+
+theorem findSome?_mkArray : findSome? f (mkArray n a) = if n = 0 then none else f a := by
   simp [← List.toArray_replicate, List.findSome?_replicate]
 
-@[deprecated findSome?_replicate (since := "2025-03-18")]
-abbrev findSome?_mkArray := @findSome?_replicate
-
-@[simp] theorem findSome?_replicate_of_pos (h : 0 < n) : findSome? f (replicate n a) = f a := by
-  simp [findSome?_replicate, Nat.ne_of_gt h]
-
-@[deprecated findSome?_replicate_of_pos (since := "2025-03-18")]
-abbrev findSome?_mkArray_of_pos := @findSome?_replicate_of_pos
+@[simp] theorem findSome?_mkArray_of_pos (h : 0 < n) : findSome? f (mkArray n a) = f a := by
+  simp [findSome?_mkArray, Nat.ne_of_gt h]
 
 -- Argument is unused, but used to decide whether `simp` should unfold.
-@[simp] theorem findSome?_replicate_of_isSome (_ : (f a).isSome) :
-   findSome? f (replicate n a) = if n = 0 then none else f a := by
-  simp [findSome?_replicate]
+@[simp] theorem findSome?_mkArray_of_isSome (_ : (f a).isSome) :
+   findSome? f (mkArray n a) = if n = 0 then none else f a := by
+  simp [findSome?_mkArray]
 
-@[deprecated findSome?_replicate_of_isSome (since := "2025-03-18")]
-abbrev findSome?_mkArray_of_isSome := @findSome?_replicate_of_isSome
-
-@[simp] theorem findSome?_replicate_of_isNone (h : (f a).isNone) :
-    findSome? f (replicate n a) = none := by
+@[simp] theorem findSome?_mkArray_of_isNone (h : (f a).isNone) :
+    findSome? f (mkArray n a) = none := by
   rw [Option.isNone_iff_eq_none] at h
-  simp [findSome?_replicate, h]
-
-@[deprecated findSome?_replicate_of_isNone (since := "2025-03-18")]
-abbrev findSome?_mkArray_of_isNone := @findSome?_replicate_of_isNone
+  simp [findSome?_mkArray, h]
 
 /-! ### find? -/
 
-@[simp] theorem find?_singleton {a : α} {p : α → Bool} :
+@[simp] theorem find?_singleton (a : α) (p : α → Bool) :
     #[a].find? p = if p a then some a else none := by
   simp [singleton_eq_toArray_singleton]
 
-@[simp] theorem findRev?_push_of_pos {xs : Array α} (h : p a) :
-    findRev? p (xs.push a) = some a := by
-  cases xs; simp [h]
+@[simp] theorem findRev?_push_of_pos (l : Array α) (h : p a) :
+    findRev? p (l.push a) = some a := by
+  cases l; simp [h]
 
-@[simp] theorem findRev?_cons_of_neg {xs : Array α} (h : ¬p a) :
-    findRev? p (xs.push a) = findRev? p xs := by
-  cases xs; simp [h]
+@[simp] theorem findRev?_cons_of_neg (l : Array α) (h : ¬p a) :
+    findRev? p (l.push a) = findRev? p l := by
+  cases l; simp [h]
 
-@[simp] theorem find?_eq_none : find? p xs = none ↔ ∀ x ∈ xs, ¬ p x := by
-  cases xs; simp
+@[simp] theorem find?_eq_none : find? p l = none ↔ ∀ x ∈ l, ¬ p x := by
+  cases l; simp
 
 theorem find?_eq_some_iff_append {xs : Array α} :
     xs.find? p = some b ↔ p b ∧ ∃ (as bs : Array α), xs = as.push b ++ bs ∧ ∀ a ∈ as, !p a := by
@@ -151,10 +142,10 @@ theorem find?_eq_some_iff_append {xs : Array α} :
     Bool.not_true, exists_and_right, and_congr_right_iff]
   intro w
   constructor
-  · rintro ⟨as, ⟨⟨xs, rfl⟩, h⟩⟩
-    exact ⟨as.toArray, ⟨xs.toArray, by simp⟩ , by simpa using h⟩
-  · rintro ⟨as, ⟨⟨⟨l⟩, h'⟩, h⟩⟩
-    exact ⟨as.toList, ⟨l, by simpa using congrArg Array.toList h'⟩,
+  · rintro ⟨as, ⟨⟨x, rfl⟩, h⟩⟩
+    exact ⟨as.toArray, ⟨x.toArray, by simp⟩ , by simpa using h⟩
+  · rintro ⟨as, ⟨⟨x, h'⟩, h⟩⟩
+    exact ⟨as.toList, ⟨x.toList, by simpa using congrArg Array.toList h'⟩,
       by simpa using h⟩
 
 @[simp]
@@ -183,44 +174,44 @@ theorem get_find?_mem {xs : Array α} (h) : (xs.find? p).get h ∈ xs := by
     (xs.filter p).find? q = xs.find? (fun a => p a ∧ q a) := by
   cases xs; simp
 
-@[simp] theorem getElem?_zero_filter {p : α → Bool} {xs : Array α} :
-    (xs.filter p)[0]? = xs.find? p := by
-  cases xs; simp [← List.head?_eq_getElem?]
+@[simp] theorem getElem?_zero_filter (p : α → Bool) (l : Array α) :
+    (l.filter p)[0]? = l.find? p := by
+  cases l; simp [← List.head?_eq_getElem?]
 
-@[simp] theorem getElem_zero_filter {p : α → Bool} {xs : Array α} (h) :
-    (xs.filter p)[0] =
-      (xs.find? p).get (by cases xs; simpa [← List.countP_eq_length_filter] using h) := by
-  cases xs
+@[simp] theorem getElem_zero_filter (p : α → Bool) (l : Array α) (h) :
+    (l.filter p)[0] =
+      (l.find? p).get (by cases l; simpa [← List.countP_eq_length_filter] using h) := by
+  cases l
   simp [List.getElem_zero_eq_head]
 
-@[simp] theorem back?_filter {p : α → Bool} {xs : Array α} : (xs.filter p).back? = xs.findRev? p := by
-  cases xs; simp
+@[simp] theorem back?_filter (p : α → Bool) (l : Array α) : (l.filter p).back? = l.findRev? p := by
+  cases l; simp
 
-@[simp] theorem back!_filter [Inhabited α] {p : α → Bool} {xs : Array α} :
-    (xs.filter p).back! = (xs.findRev? p).get! := by
-  cases xs; simp [Option.get!_eq_getD]
+@[simp] theorem back!_filter [Inhabited α] (p : α → Bool) (l : Array α) :
+    (l.filter p).back! = (l.findRev? p).get! := by
+  cases l; simp [Option.get!_eq_getD]
 
-@[simp] theorem find?_filterMap {xs : Array α} {f : α → Option β} {p : β → Bool} :
+@[simp] theorem find?_filterMap (xs : Array α) (f : α → Option β) (p : β → Bool) :
     (xs.filterMap f).find? p = (xs.find? (fun a => (f a).any p)).bind f := by
   cases xs; simp
 
-@[simp] theorem find?_map {f : β → α} {xs : Array β} :
+@[simp] theorem find?_map (f : β → α) (xs : Array β) :
     find? p (xs.map f) = (xs.find? (p ∘ f)).map f := by
   cases xs; simp
 
-@[simp] theorem find?_append {xs ys : Array α} :
-    (xs ++ ys).find? p = (xs.find? p).or (ys.find? p) := by
-  cases xs
-  cases ys
+@[simp] theorem find?_append {l₁ l₂ : Array α} :
+    (l₁ ++ l₂).find? p = (l₁.find? p).or (l₂.find? p) := by
+  cases l₁
+  cases l₂
   simp
 
-@[simp] theorem find?_flatten {xss : Array (Array α)} {p : α → Bool} :
-    xss.flatten.find? p = xss.findSome? (·.find? p) := by
-  cases xss using array₂_induction
+@[simp] theorem find?_flatten (xs : Array (Array α)) (p : α → Bool) :
+    xs.flatten.find? p = xs.findSome? (·.find? p) := by
+  cases xs using array₂_induction
   simp [List.findSome?_map, Function.comp_def]
 
-theorem find?_flatten_eq_none_iff {xss : Array (Array α)} {p : α → Bool} :
-    xss.flatten.find? p = none ↔ ∀ ys ∈ xss, ∀ x ∈ ys, !p x := by
+theorem find?_flatten_eq_none_iff {xs : Array (Array α)} {p : α → Bool} :
+    xs.flatten.find? p = none ↔ ∀ ys ∈ xs, ∀ x ∈ ys, !p x := by
   simp
 
 @[deprecated find?_flatten_eq_none_iff (since := "2025-02-03")]
@@ -231,12 +222,12 @@ If `find? p` returns `some a` from `xs.flatten`, then `p a` holds, and
 some array in `xs` contains `a`, and no earlier element of that array satisfies `p`.
 Moreover, no earlier array in `xs` has an element satisfying `p`.
 -/
-theorem find?_flatten_eq_some_iff {xss : Array (Array α)} {p : α → Bool} {a : α} :
-    xss.flatten.find? p = some a ↔
+theorem find?_flatten_eq_some_iff {xs : Array (Array α)} {p : α → Bool} {a : α} :
+    xs.flatten.find? p = some a ↔
       p a ∧ ∃ (as : Array (Array α)) (ys zs : Array α) (bs : Array (Array α)),
-        xss = as.push (ys.push a ++ zs) ++ bs ∧
-        (∀ ws ∈ as, ∀ x ∈ ws, !p x) ∧ (∀ x ∈ ys, !p x) := by
-  cases xss using array₂_induction
+        xs = as.push (ys.push a ++ zs) ++ bs ∧
+        (∀ a ∈ as, ∀ x ∈ a, !p x) ∧ (∀ x ∈ ys, !p x) := by
+  cases xs using array₂_induction
   simp only [flatten_toArray_map_toArray, List.find?_toArray, List.find?_flatten_eq_some_iff]
   simp only [Bool.not_eq_eq_eq_not, Bool.not_true, exists_and_right, and_congr_right_iff]
   intro w
@@ -254,7 +245,7 @@ theorem find?_flatten_eq_some_iff {xss : Array (Array α)} {p : α → Bool} {a
 @[deprecated find?_flatten_eq_some_iff (since := "2025-02-03")]
 abbrev find?_flatten_eq_some := @find?_flatten_eq_some_iff
 
-@[simp] theorem find?_flatMap {xs : Array α} {f : α → Array β} {p : β → Bool} :
+@[simp] theorem find?_flatMap (xs : Array α) (f : α → Array β) (p : β → Bool) :
     (xs.flatMap f).find? p = xs.findSome? (fun x => (f x).find? p) := by
   cases xs
   simp [List.find?_flatMap, Array.flatMap_toArray]
@@ -266,60 +257,42 @@ theorem find?_flatMap_eq_none_iff {xs : Array α} {f : α → Array β} {p : β
 @[deprecated find?_flatMap_eq_none_iff (since := "2025-02-03")]
 abbrev find?_flatMap_eq_none := @find?_flatMap_eq_none_iff
 
-theorem find?_replicate :
-    find? p (replicate n a) = if n = 0 then none else if p a then some a else none := by
+theorem find?_mkArray :
+    find? p (mkArray n a) = if n = 0 then none else if p a then some a else none := by
   simp [← List.toArray_replicate, List.find?_replicate]
 
-@[deprecated find?_replicate (since := "2025-03-18")]
-abbrev find?_mkArray := @find?_replicate
+@[simp] theorem find?_mkArray_of_length_pos (h : 0 < n) :
+    find? p (mkArray n a) = if p a then some a else none := by
+  simp [find?_mkArray, Nat.ne_of_gt h]
 
-@[simp] theorem find?_replicate_of_size_pos (h : 0 < n) :
-    find? p (replicate n a) = if p a then some a else none := by
-  simp [find?_replicate, Nat.ne_of_gt h]
+@[simp] theorem find?_mkArray_of_pos (h : p a) :
+    find? p (mkArray n a) = if n = 0 then none else some a := by
+  simp [find?_mkArray, h]
 
-@[deprecated find?_replicate_of_size_pos (since := "2025-03-18")]
-abbrev find?_mkArray_of_length_pos := @find?_replicate_of_size_pos
-
-@[simp] theorem find?_replicate_of_pos (h : p a) :
-    find? p (replicate n a) = if n = 0 then none else some a := by
-  simp [find?_replicate, h]
-
-@[deprecated find?_replicate_of_pos (since := "2025-03-18")]
-abbrev find?_mkArray_of_pos := @find?_replicate_of_pos
-
-@[simp] theorem find?_replicate_of_neg (h : ¬ p a) : find? p (replicate n a) = none := by
-  simp [find?_replicate, h]
-
-@[deprecated find?_replicate_of_neg (since := "2025-03-18")]
-abbrev find?_mkArray_of_neg := @find?_replicate_of_neg
+@[simp] theorem find?_mkArray_of_neg (h : ¬ p a) : find? p (mkArray n a) = none := by
+  simp [find?_mkArray, h]
 
 -- This isn't a `@[simp]` lemma since there is already a lemma for `l.find? p = none` for any `l`.
-theorem find?_replicate_eq_none_iff {n : Nat} {a : α} {p : α → Bool} :
-    (replicate n a).find? p = none ↔ n = 0 ∨ !p a := by
+theorem find?_mkArray_eq_none_iff {n : Nat} {a : α} {p : α → Bool} :
+    (mkArray n a).find? p = none ↔ n = 0 ∨ !p a := by
   simp [← List.toArray_replicate, List.find?_replicate_eq_none_iff, Classical.or_iff_not_imp_left]
 
-@[deprecated find?_replicate_eq_none_iff (since := "2025-03-18")]
-abbrev find?_mkArray_eq_none_iff := @find?_replicate_eq_none_iff
+@[deprecated find?_mkArray_eq_none_iff (since := "2025-02-03")]
+abbrev find?_mkArray_eq_none := @find?_mkArray_eq_none_iff
 
-@[simp] theorem find?_replicate_eq_some_iff {n : Nat} {a b : α} {p : α → Bool} :
-    (replicate n a).find? p = some b ↔ n ≠ 0 ∧ p a ∧ a = b := by
+@[simp] theorem find?_mkArray_eq_some_iff {n : Nat} {a b : α} {p : α → Bool} :
+    (mkArray n a).find? p = some b ↔ n ≠ 0 ∧ p a ∧ a = b := by
   simp [← List.toArray_replicate]
 
-@[deprecated find?_replicate_eq_some_iff (since := "2025-03-18")]
-abbrev find?_mkArray_eq_some_iff := @find?_replicate_eq_some_iff
+@[deprecated find?_mkArray_eq_some_iff (since := "2025-02-03")]
+abbrev find?_mkArray_eq_some := @find?_mkArray_eq_some_iff
 
-@[deprecated find?_replicate_eq_some_iff (since := "2025-02-03")]
-abbrev find?_mkArray_eq_some := @find?_replicate_eq_some_iff
-
-@[simp] theorem get_find?_replicate {n : Nat} {a : α} {p : α → Bool} (h) :
-    ((replicate n a).find? p).get h = a := by
+@[simp] theorem get_find?_mkArray (n : Nat) (a : α) (p : α → Bool) (h) :
+    ((mkArray n a).find? p).get h = a := by
   simp [← List.toArray_replicate]
 
-@[deprecated get_find?_replicate (since := "2025-03-18")]
-abbrev get_find?_mkArray := @get_find?_replicate
-
-theorem find?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : Array α}
-    (H : ∀ (a : α), a ∈ xs → P a) {p : β → Bool} :
+theorem find?_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
+    (H : ∀ (a : α), a ∈ xs → P a) (p : β → Bool) :
     (xs.pmap f H).find? p = (xs.attach.find? (fun ⟨a, m⟩ => p (f a (H a m)))).map fun ⟨a, m⟩ => f a (H a m) := by
   simp only [pmap_eq_map_attach, find?_map]
   rfl
@@ -329,6 +302,24 @@ theorem find?_eq_some_iff_getElem {xs : Array α} {p : α → Bool} {b : α} :
   rcases xs with ⟨xs⟩
   simp [List.find?_eq_some_iff_getElem]
 
+/-! ### findFinIdx? -/
+
+@[simp] theorem findFinIdx?_empty {p : α → Bool} : findFinIdx? p #[] = none := rfl
+
+-- We can't mark this as a `@[congr]` lemma since the head of the RHS is not `findFinIdx?`.
+theorem findFinIdx?_congr {p : α → Bool} {l₁ : Array α} {l₂ : Array α} (w : l₁ = l₂) :
+    findFinIdx? p l₁ = (findFinIdx? p l₂).map (fun i => i.cast (by simp [w])) := by
+  subst w
+  simp
+
+@[simp] theorem findFinIdx?_subtype {p : α → Prop} {l : Array { x // p x }}
+    {f : { x // p x } → Bool} {g : α → Bool} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
+    l.findFinIdx? f = (l.unattach.findFinIdx? g).map (fun i => i.cast (by simp)) := by
+  cases l
+  simp only [List.findFinIdx?_toArray, hf, List.findFinIdx?_subtype]
+  rw [findFinIdx?_congr List.unattach_toArray]
+  simp [Function.comp_def]
+
 /-! ### findIdx -/
 
 theorem findIdx_of_getElem?_eq_some {xs : Array α} (w : xs[xs.findIdx p]? = some y) : p y := by
@@ -359,7 +350,7 @@ theorem findIdx_eq_size_of_false {p : α → Bool} {xs : Array α} (h : ∀ x
   rcases xs with ⟨xs⟩
   simp_all
 
-theorem findIdx_le_size {p : α → Bool} {xs : Array α} : xs.findIdx p ≤ xs.size := by
+theorem findIdx_le_size (p : α → Bool) {xs : Array α} : xs.findIdx p ≤ xs.size := by
   by_cases e : ∃ x ∈ xs, p x
   · exact Nat.le_of_lt (findIdx_lt_size_of_exists e)
   · simp at e
@@ -373,7 +364,7 @@ theorem findIdx_lt_size {p : α → Bool} {xs : Array α} :
 
 /-- `p` does not hold for elements with indices less than `xs.findIdx p`. -/
 theorem not_of_lt_findIdx {p : α → Bool} {xs : Array α} {i : Nat} (h : i < xs.findIdx p) :
-    p (xs[i]'(Nat.le_trans h findIdx_le_size)) = false := by
+    p (xs[i]'(Nat.le_trans h (findIdx_le_size p))) = false := by
   rcases xs with ⟨xs⟩
   simpa using List.not_of_lt_findIdx (by simpa using h)
 
@@ -404,41 +395,26 @@ theorem findIdx_eq {p : α → Bool} {xs : Array α} {i : Nat} (h : i < xs.size)
   simp at h3
   simp_all [not_of_lt_findIdx h3]
 
-theorem findIdx_append {p : α → Bool} {xs ys : Array α} :
-    (xs ++ ys).findIdx p =
-      if xs.findIdx p < xs.size then xs.findIdx p else ys.findIdx p + xs.size := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
+theorem findIdx_append (p : α → Bool) (l₁ l₂ : Array α) :
+    (l₁ ++ l₂).findIdx p =
+      if l₁.findIdx p < l₁.size then l₁.findIdx p else l₂.findIdx p + l₁.size := by
+  rcases l₁ with ⟨l₁⟩
+  rcases l₂ with ⟨l₂⟩
   simp [List.findIdx_append]
 
-theorem findIdx_le_findIdx {xs : Array α} {p q : α → Bool} (h : ∀ x ∈ xs, p x → q x) : xs.findIdx q ≤ xs.findIdx p := by
-  rcases xs with ⟨xs⟩
+theorem findIdx_le_findIdx {l : Array α} {p q : α → Bool} (h : ∀ x ∈ l, p x → q x) : l.findIdx q ≤ l.findIdx p := by
+  rcases l with ⟨l⟩
   simp_all [List.findIdx_le_findIdx]
 
-@[simp] theorem findIdx_subtype {p : α → Prop} {xs : Array { x // p x }}
+@[simp] theorem findIdx_subtype {p : α → Prop} {l : Array { x // p x }}
     {f : { x // p x } → Bool} {g : α → Bool} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
-    xs.findIdx f = xs.unattach.findIdx g := by
-  cases xs
+    l.findIdx f = l.unattach.findIdx g := by
+  cases l
   simp [hf]
 
-theorem false_of_mem_extract_findIdx {xs : Array α} {p : α → Bool} (h : x ∈ xs.extract 0 (xs.findIdx p)) :
-    p x = false := by
-  rcases xs with ⟨xs⟩
-  exact List.false_of_mem_take_findIdx (by simpa using h)
-
-@[simp] theorem findIdx_extract {xs : Array α} {i : Nat} {p : α → Bool} :
-    (xs.extract 0 i).findIdx p = min i (xs.findIdx p) := by
-  cases xs
-  simp
-
-@[simp] theorem min_findIdx_findIdx {xs : Array α} {p q : α → Bool} :
-    min (xs.findIdx p) (xs.findIdx q) = xs.findIdx (fun a => p a || q a) := by
-  cases xs
-  simp
-
 /-! ### findIdx? -/
 
-@[simp] theorem findIdx?_empty : (#[] : Array α).findIdx? p = none := by simp
+@[simp] theorem findIdx?_empty : (#[] : Array α).findIdx? p = none := rfl
 
 @[simp]
 theorem findIdx?_eq_none_iff {xs : Array α} {p : α → Bool} :
@@ -492,9 +468,8 @@ theorem of_findIdx?_eq_none {xs : Array α} {p : α → Bool} (w : xs.findIdx? p
   rcases xs with ⟨xs⟩
   simpa using List.of_findIdx?_eq_none (by simpa using w)
 
-@[simp] theorem findIdx?_map {f : β → α} {xs : Array β} {p : α → Bool} :
-    findIdx? p (xs.map f) = xs.findIdx? (p ∘ f) := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem findIdx?_map (f : β → α) (l : Array β) : findIdx? p (l.map f) = l.findIdx? (p ∘ f) := by
+  rcases l with ⟨l⟩
   simp [List.findIdx?_map]
 
 @[simp] theorem findIdx?_append :
@@ -504,23 +479,20 @@ theorem of_findIdx?_eq_none {xs : Array α} {p : α → Bool} (w : xs.findIdx? p
   rcases ys with ⟨ys⟩
   simp [List.findIdx?_append]
 
-theorem findIdx?_flatten {xss : Array (Array α)} {p : α → Bool} :
-    xss.flatten.findIdx? p =
-      (xss.findIdx? (·.any p)).map
-        fun i => ((xss.take i).map Array.size).sum +
-          (xss[i]?.map fun xs => xs.findIdx p).getD 0 := by
-  cases xss using array₂_induction
+theorem findIdx?_flatten {l : Array (Array α)} {p : α → Bool} :
+    l.flatten.findIdx? p =
+      (l.findIdx? (·.any p)).map
+        fun i => ((l.take i).map Array.size).sum +
+          (l[i]?.map fun xs => xs.findIdx p).getD 0 := by
+  cases l using array₂_induction
   simp [List.findIdx?_flatten, Function.comp_def]
 
-@[simp] theorem findIdx?_replicate :
-    (replicate n a).findIdx? p = if 0 < n ∧ p a then some 0 else none := by
+@[simp] theorem findIdx?_mkArray :
+    (mkArray n a).findIdx? p = if 0 < n ∧ p a then some 0 else none := by
   rw [← List.toArray_replicate]
   simp only [List.findIdx?_toArray]
   simp
 
-@[deprecated findIdx?_replicate (since := "2025-03-18")]
-abbrev findIdx?_mkArray := @findIdx?_replicate
-
 theorem findIdx?_eq_findSome?_zipIdx {xs : Array α} {p : α → Bool} :
     xs.findIdx? p = xs.zipIdx.findSome? fun ⟨a, i⟩ => if p a then some i else none := by
   rcases xs with ⟨xs⟩
@@ -547,66 +519,20 @@ theorem findIdx?_eq_some_le_of_findIdx?_eq_some {xs : Array α} {p q : α → Bo
   rcases xs with ⟨xs⟩
   simp [List.findIdx?_eq_some_le_of_findIdx?_eq_some (by simpa using w) (by simpa using h)]
 
-@[simp] theorem findIdx?_subtype {p : α → Prop} {xs : Array { x // p x }}
+@[simp] theorem findIdx?_subtype {p : α → Prop} {l : Array { x // p x }}
     {f : { x // p x } → Bool} {g : α → Bool} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
-    xs.findIdx? f = xs.unattach.findIdx? g := by
-  cases xs
+    l.findIdx? f = l.unattach.findIdx? g := by
+  cases l
   simp [hf]
 
-@[simp] theorem findIdx?_take {xs : Array α} {i : Nat} {p : α → Bool} :
-    (xs.take i).findIdx? p = (xs.findIdx? p).bind (Option.guard (fun j => j < i)) := by
-  cases xs
-  simp
-
-/-! ### findFinIdx? -/
-
-@[simp] theorem findFinIdx?_empty {p : α → Bool} : findFinIdx? p #[] = none := by simp
-
--- We can't mark this as a `@[congr]` lemma since the head of the RHS is not `findFinIdx?`.
-theorem findFinIdx?_congr {p : α → Bool} {xs ys : Array α} (w : xs = ys) :
-    findFinIdx? p xs = (findFinIdx? p ys).map (fun i => i.cast (by simp [w])) := by
-  subst w
-  simp
-
-theorem findFinIdx?_eq_pmap_findIdx? {xs : Array α} {p : α → Bool} :
-    xs.findFinIdx? p =
-      (xs.findIdx? p).pmap
-        (fun i m => by simp [findIdx?_eq_some_iff_getElem] at m; exact ⟨i, m.choose⟩)
-        (fun i h => h) := by
-  simp [findIdx?_eq_map_findFinIdx?_val, Option.pmap_map]
-
-@[simp] theorem findFinIdx?_eq_none_iff {xs : Array α} {p : α → Bool} :
-    xs.findFinIdx? p = none ↔ ∀ x, x ∈ xs → ¬ p x := by
-  simp [findFinIdx?_eq_pmap_findIdx?]
-
-@[simp]
-theorem findFinIdx?_eq_some_iff {xs : Array α} {p : α → Bool} {i : Fin xs.size} :
-    xs.findFinIdx? p = some i ↔
-      p xs[i] ∧ ∀ j (hji : j < i), ¬p (xs[j]'(Nat.lt_trans hji i.2)) := by
-  simp only [findFinIdx?_eq_pmap_findIdx?, Option.pmap_eq_some_iff, findIdx?_eq_some_iff_getElem,
-    Bool.not_eq_true, Option.mem_def, exists_and_left, and_exists_self, Fin.getElem_fin]
-  constructor
-  · rintro ⟨a, ⟨h, w₁, w₂⟩, rfl⟩
-    exact ⟨w₁, fun j hji => by simpa using w₂ j hji⟩
-  · rintro ⟨h, w⟩
-    exact ⟨i, ⟨i.2, h, fun j hji => w ⟨j, by omega⟩ hji⟩, rfl⟩
-
-@[simp] theorem findFinIdx?_subtype {p : α → Prop} {xs : Array { x // p x }}
-    {f : { x // p x } → Bool} {g : α → Bool} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
-    xs.findFinIdx? f = (xs.unattach.findFinIdx? g).map (fun i => i.cast (by simp)) := by
-  cases xs
-  simp only [List.findFinIdx?_toArray, hf, List.findFinIdx?_subtype]
-  rw [findFinIdx?_congr List.unattach_toArray]
-  simp [Function.comp_def]
-
 /-! ### idxOf
 
 The verification API for `idxOf` is still incomplete.
 The lemmas below should be made consistent with those for `findIdx` (and proved using them).
 -/
 
-theorem idxOf_append [BEq α] [LawfulBEq α] {xs ys : Array α} {a : α} :
-    (xs ++ ys).idxOf a = if a ∈ xs then xs.idxOf a else ys.idxOf a + xs.size := by
+theorem idxOf_append [BEq α] [LawfulBEq α] {l₁ l₂ : Array α} {a : α} :
+    (l₁ ++ l₂).idxOf a = if a ∈ l₁ then l₁.idxOf a else l₂.idxOf a + l₁.size := by
   rw [idxOf, findIdx_append]
   split <;> rename_i h
   · rw [if_pos]
@@ -614,12 +540,12 @@ theorem idxOf_append [BEq α] [LawfulBEq α] {xs ys : Array α} {a : α} :
   · rw [if_neg]
     simpa using h
 
-theorem idxOf_eq_size [BEq α] [LawfulBEq α] {xs : Array α} (h : a ∉ xs) : xs.idxOf a = xs.size := by
-  rcases xs with ⟨xs⟩
+theorem idxOf_eq_size [BEq α] [LawfulBEq α] {l : Array α} (h : a ∉ l) : l.idxOf a = l.size := by
+  rcases l with ⟨l⟩
   simp [List.idxOf_eq_length (by simpa using h)]
 
-theorem idxOf_lt_length [BEq α] [LawfulBEq α] {xs : Array α} (h : a ∈ xs) : xs.idxOf a < xs.size := by
-  rcases xs with ⟨xs⟩
+theorem idxOf_lt_length [BEq α] [LawfulBEq α] {l : Array α} (h : a ∈ l) : l.idxOf a < l.size := by
+  rcases l with ⟨l⟩
   simp [List.idxOf_lt_length (by simpa using h)]
 
 
@@ -629,33 +555,17 @@ The verification API for `idxOf?` is still incomplete.
 The lemmas below should be made consistent with those for `findIdx?` (and proved using them).
 -/
 
-@[simp] theorem idxOf?_empty [BEq α] : (#[] : Array α).idxOf? a = none := by simp
+@[simp] theorem idxOf?_empty [BEq α] : (#[] : Array α).idxOf? a = none := rfl
 
-@[simp] theorem idxOf?_eq_none_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
-    xs.idxOf? a = none ↔ a ∉ xs := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem idxOf?_eq_none_iff [BEq α] [LawfulBEq α] {l : Array α} {a : α} :
+    l.idxOf? a = none ↔ a ∉ l := by
+  rcases l with ⟨l⟩
   simp [List.idxOf?_eq_none_iff]
 
-/-! ### finIdxOf?
-
-The verification API for `finIdxOf?` is still incomplete.
-The lemmas below should be made consistent with those for `findFinIdx?` (and proved using them).
--/
+/-! ### finIdxOf? -/
 
 theorem idxOf?_eq_map_finIdxOf?_val [BEq α] {xs : Array α} {a : α} :
     xs.idxOf? a = (xs.finIdxOf? a).map (·.val) := by
   simp [idxOf?, finIdxOf?, findIdx?_eq_map_findFinIdx?_val]
 
-@[simp] theorem finIdxOf?_empty [BEq α] : (#[] : Array α).finIdxOf? a = none := by simp
-
-@[simp] theorem finIdxOf?_eq_none_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
-    xs.finIdxOf? a = none ↔ a ∉ xs := by
-  rcases xs with ⟨xs⟩
-  simp [List.finIdxOf?_eq_none_iff]
-
-@[simp] theorem finIdxOf?_eq_some_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} {i : Fin xs.size} :
-    xs.finIdxOf? a = some i ↔ xs[i] = a ∧ ∀ j (_ : j < i), ¬xs[j] = a := by
-  rcases xs with ⟨xs⟩
-  simp [List.finIdxOf?_eq_some_iff]
-
 end Array

src/Init/Data/Array/GetLit.lean

@@ -7,43 +7,40 @@ Authors: Leonardo de Moura
 prelude
 import Init.Data.Array.Basic
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 namespace Array
 
 /-! ### getLit -/
 
 -- auxiliary declaration used in the equation compiler when pattern matching array literals.
-abbrev getLit {α : Type u} {n : Nat} (xs : Array α) (i : Nat) (h₁ : xs.size = n) (h₂ : i < n) : α :=
+abbrev getLit {α : Type u} {n : Nat} (a : Array α) (i : Nat) (h₁ : a.size = n) (h₂ : i < n) : α :=
   have := h₁.symm ▸ h₂
-  xs[i]
+  a[i]
 
 theorem extLit {n : Nat}
-    (xs ys : Array α)
-    (hsz₁ : xs.size = n) (hsz₂ : ys.size = n)
-    (h : (i : Nat) → (hi : i < n) → xs.getLit i hsz₁ hi = ys.getLit i hsz₂ hi) : xs = ys :=
-  Array.ext (hsz₁.trans hsz₂.symm) fun i hi₁ _ => h i (hsz₁ ▸ hi₁)
+    (a b : Array α)
+    (hsz₁ : a.size = n) (hsz₂ : b.size = n)
+    (h : (i : Nat) → (hi : i < n) → a.getLit i hsz₁ hi = b.getLit i hsz₂ hi) : a = b :=
+  Array.ext a b (hsz₁.trans hsz₂.symm) fun i hi₁ _ => h i (hsz₁ ▸ hi₁)
 
-def toListLitAux (xs : Array α) (n : Nat) (hsz : xs.size = n) : ∀ (i : Nat), i ≤ xs.size → List α → List α
+def toListLitAux (a : Array α) (n : Nat) (hsz : a.size = n) : ∀ (i : Nat), i ≤ a.size → List α → List α
   | 0,     _,  acc => acc
-  | (i+1), hi, acc => toListLitAux xs n hsz i (Nat.le_of_succ_le hi) (xs.getLit i hsz (Nat.lt_of_lt_of_eq (Nat.lt_of_lt_of_le (Nat.lt_succ_self i) hi) hsz) :: acc)
+  | (i+1), hi, acc => toListLitAux a n hsz i (Nat.le_of_succ_le hi) (a.getLit i hsz (Nat.lt_of_lt_of_eq (Nat.lt_of_lt_of_le (Nat.lt_succ_self i) hi) hsz) :: acc)
 
-def toArrayLit (xs : Array α) (n : Nat) (hsz : xs.size = n) : Array α :=
-  List.toArray <| toListLitAux xs n hsz n (hsz ▸ Nat.le_refl _) []
+def toArrayLit (a : Array α) (n : Nat) (hsz : a.size = n) : Array α :=
+  List.toArray <| toListLitAux a n hsz n (hsz ▸ Nat.le_refl _) []
 
-theorem toArrayLit_eq (xs : Array α) (n : Nat) (hsz : xs.size = n) : xs = toArrayLit xs n hsz := by
+theorem toArrayLit_eq (as : Array α) (n : Nat) (hsz : as.size = n) : as = toArrayLit as n hsz := by
   apply ext'
-  simp [toArrayLit, List.toList_toArray]
-  have hle : n ≤ xs.size := hsz ▸ Nat.le_refl _
-  have hge : xs.size ≤ n := hsz ▸ Nat.le_refl _
+  simp [toArrayLit, toList_toArray]
+  have hle : n ≤ as.size := hsz ▸ Nat.le_refl _
+  have hge : as.size ≤ n := hsz ▸ Nat.le_refl _
   have := go n hle
   rw [List.drop_eq_nil_of_le hge] at this
   rw [this]
 where
-  getLit_eq (xs : Array α) (i : Nat) (h₁ : xs.size = n) (h₂ : i < n) : xs.getLit i h₁ h₂ = getElem xs.toList i ((id (α := xs.toList.length = n) h₁) ▸ h₂) :=
+  getLit_eq (as : Array α) (i : Nat) (h₁ : as.size = n) (h₂ : i < n) : as.getLit i h₁ h₂ = getElem as.toList i ((id (α := as.toList.length = n) h₁) ▸ h₂) :=
     rfl
-  go (i : Nat) (hi : i ≤ xs.size) : toListLitAux xs n hsz i hi (xs.toList.drop i) = xs.toList := by
+  go (i : Nat) (hi : i ≤ as.size) : toListLitAux as n hsz i hi (as.toList.drop i) = as.toList := by
     induction i <;> simp only [List.drop, toListLitAux, getLit_eq, List.getElem_cons_drop_succ_eq_drop, *]
 
 end Array

src/Init/Data/Array/InsertIdx.lean

@@ -13,9 +13,6 @@ import Init.Data.List.Nat.InsertIdx
 Proves various lemmas about `Array.insertIdx`.
 -/
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 open Function
 
 open Nat
@@ -30,23 +27,23 @@ section InsertIdx
 
 variable {a : α}
 
-@[simp] theorem toList_insertIdx {xs : Array α} {i : Nat} {x : α} (h : i ≤ xs.size) :
-    (xs.insertIdx i x h).toList = xs.toList.insertIdx i x := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem toList_insertIdx (a : Array α) (i x) (h) :
+    (a.insertIdx i x h).toList = a.toList.insertIdx i x := by
+  rcases a with ⟨a⟩
   simp
 
 @[simp]
-theorem insertIdx_zero {xs : Array α} {x : α} : xs.insertIdx 0 x = #[x] ++ xs := by
-  rcases xs with ⟨xs⟩
+theorem insertIdx_zero (s : Array α) (x : α) : s.insertIdx 0 x = #[x] ++ s := by
+  cases s
   simp
 
-@[simp] theorem size_insertIdx {xs : Array α} (h : i ≤ xs.size) : (xs.insertIdx i a).size = xs.size + 1 := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem size_insertIdx {as : Array α} (h : n ≤ as.size) : (as.insertIdx n a).size = as.size + 1 := by
+  cases as
   simp [List.length_insertIdx, h]
 
-theorem eraseIdx_insertIdx {i : Nat} {xs : Array α} (h : i ≤ xs.size) :
-    (xs.insertIdx i a).eraseIdx i (by simp; omega) = xs := by
-  rcases xs with ⟨xs⟩
+theorem eraseIdx_insertIdx (i : Nat) (l : Array α) (h : i ≤ l.size) :
+    (l.insertIdx i a).eraseIdx i (by simp; omega) = l := by
+  cases l
   simp_all
 
 theorem insertIdx_eraseIdx_of_ge {as : Array α}
@@ -54,77 +51,77 @@ theorem insertIdx_eraseIdx_of_ge {as : Array α}
     (as.eraseIdx i).insertIdx j a =
       (as.insertIdx (j + 1) a (by simp at w₂; omega)).eraseIdx i (by simp_all; omega) := by
   cases as
-  simpa using List.insertIdx_eraseIdx_of_ge (by simpa) (by simpa)
+  simpa using List.insertIdx_eraseIdx_of_ge _ _ _ (by simpa) (by simpa)
 
 theorem insertIdx_eraseIdx_of_le {as : Array α}
     (w₁ : i < as.size) (w₂ : j ≤ (as.eraseIdx i).size) (h : j ≤ i) :
     (as.eraseIdx i).insertIdx j a =
       (as.insertIdx j a (by simp at w₂; omega)).eraseIdx (i + 1) (by simp_all) := by
   cases as
-  simpa using List.insertIdx_eraseIdx_of_le (by simpa) (by simpa)
+  simpa using List.insertIdx_eraseIdx_of_le _ _ _ (by simpa) (by simpa)
 
-theorem insertIdx_comm (a b : α) {i j : Nat} {xs : Array α} (_ : i ≤ j) (_ : j ≤ xs.size) :
-    (xs.insertIdx i a).insertIdx (j + 1) b (by simpa) =
-      (xs.insertIdx j b).insertIdx i a (by simp; omega) := by
-  rcases xs with ⟨xs⟩
-  simpa using List.insertIdx_comm a b (by simpa) (by simpa)
+theorem insertIdx_comm (a b : α) (i j : Nat) (l : Array α) (_ : i ≤ j) (_ : j ≤ l.size) :
+    (l.insertIdx i a).insertIdx (j + 1) b (by simpa) =
+      (l.insertIdx j b).insertIdx i a (by simp; omega) := by
+  cases l
+  simpa using List.insertIdx_comm a b i j _ (by simpa) (by simpa)
 
-theorem mem_insertIdx {xs : Array α} {h : i ≤ xs.size} : a ∈ xs.insertIdx i b h ↔ a = b ∨ a ∈ xs := by
-  rcases xs with ⟨xs⟩
+theorem mem_insertIdx {l : Array α} {h : i ≤ l.size} : a ∈ l.insertIdx i b h ↔ a = b ∨ a ∈ l := by
+  cases l
   simpa using List.mem_insertIdx (by simpa)
 
 @[simp]
-theorem insertIdx_size_self {xs : Array α} {x : α} : xs.insertIdx xs.size x = xs.push x := by
-  rcases xs with ⟨xs⟩
+theorem insertIdx_size_self (l : Array α) (x : α) : l.insertIdx l.size x = l.push x := by
+  cases l
   simp
 
-theorem getElem_insertIdx {xs : Array α} {x : α} {i k : Nat} (w : i ≤ xs.size) (h : k < (xs.insertIdx i x).size) :
-    (xs.insertIdx i x)[k] =
+theorem getElem_insertIdx {as : Array α} {x : α} {i k : Nat} (w : i ≤ as.size) (h : k < (as.insertIdx i x).size) :
+    (as.insertIdx i x)[k] =
       if h₁ : k < i then
-        xs[k]'(by simp [size_insertIdx] at h; omega)
+        as[k]'(by simp [size_insertIdx] at h; omega)
       else
         if h₂ : k = i then
           x
         else
-          xs[k-1]'(by simp [size_insertIdx] at h; omega) := by
-  cases xs
+          as[k-1]'(by simp [size_insertIdx] at h; omega) := by
+  cases as
   simp [List.getElem_insertIdx, w]
 
-theorem getElem_insertIdx_of_lt {xs : Array α} {x : α} {i k : Nat} (w : i ≤ xs.size) (h : k < i) :
-    (xs.insertIdx i x)[k]'(by simp; omega) = xs[k] := by
+theorem getElem_insertIdx_of_lt {as : Array α} {x : α} {i k : Nat} (w : i ≤ as.size) (h : k < i) :
+    (as.insertIdx i x)[k]'(by simp; omega) = as[k] := by
   simp [getElem_insertIdx, w, h]
 
-theorem getElem_insertIdx_self {xs : Array α} {x : α} {i : Nat} (w : i ≤ xs.size) :
-    (xs.insertIdx i x)[i]'(by simp; omega) = x := by
+theorem getElem_insertIdx_self {as : Array α} {x : α} {i : Nat} (w : i ≤ as.size) :
+    (as.insertIdx i x)[i]'(by simp; omega) = x := by
   simp [getElem_insertIdx, w]
 
-theorem getElem_insertIdx_of_gt {xs : Array α} {x : α} {i k : Nat} (w : k ≤ xs.size) (h : k > i) :
-    (xs.insertIdx i x)[k]'(by simp; omega) = xs[k - 1]'(by omega) := by
+theorem getElem_insertIdx_of_gt {as : Array α} {x : α} {i k : Nat} (w : k ≤ as.size) (h : k > i) :
+    (as.insertIdx i x)[k]'(by simp; omega) = as[k - 1]'(by omega) := by
   simp [getElem_insertIdx, w, h]
   rw [dif_neg (by omega), dif_neg (by omega)]
 
-theorem getElem?_insertIdx {xs : Array α} {x : α} {i k : Nat} (h : i ≤ xs.size) :
-    (xs.insertIdx i x)[k]? =
+theorem getElem?_insertIdx {l : Array α} {x : α} {i k : Nat} (h : i ≤ l.size) :
+    (l.insertIdx i x)[k]? =
       if k < i then
-        xs[k]?
+        l[k]?
       else
         if k = i then
-          if k ≤ xs.size then some x else none
+          if k ≤ l.size then some x else none
         else
-          xs[k-1]? := by
-  cases xs
+          l[k-1]? := by
+  cases l
   simp [List.getElem?_insertIdx, h]
 
-theorem getElem?_insertIdx_of_lt {xs : Array α} {x : α} {i k : Nat} (w : i ≤ xs.size) (h : k < i) :
-    (xs.insertIdx i x)[k]? = xs[k]? := by
+theorem getElem?_insertIdx_of_lt {l : Array α} {x : α} {i k : Nat} (w : i ≤ l.size) (h : k < i) :
+    (l.insertIdx i x)[k]? = l[k]? := by
   rw [getElem?_insertIdx, if_pos h]
 
-theorem getElem?_insertIdx_self {xs : Array α} {x : α} {i : Nat} (w : i ≤ xs.size) :
-    (xs.insertIdx i x)[i]? = some x := by
+theorem getElem?_insertIdx_self {l : Array α} {x : α} {i : Nat} (w : i ≤ l.size) :
+    (l.insertIdx i x)[i]? = some x := by
   rw [getElem?_insertIdx, if_neg (by omega), if_pos rfl, if_pos w]
 
-theorem getElem?_insertIdx_of_ge {xs : Array α} {x : α} {i k : Nat} (w : i < k) (h : k ≤ xs.size) :
-    (xs.insertIdx i x)[k]? = xs[k - 1]? := by
+theorem getElem?_insertIdx_of_ge {l : Array α} {x : α} {i k : Nat} (w : i < k) (h : k ≤ l.size) :
+    (l.insertIdx i x)[k]? = l[k - 1]? := by
   rw [getElem?_insertIdx, if_neg (by omega), if_neg (by omega)]
 
 end InsertIdx

src/Init/Data/Array/InsertionSort.lean

@@ -6,32 +6,23 @@ Authors: Leonardo de Moura
 prelude
 import Init.Data.Array.Basic
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
-/--
-Sorts an array using insertion sort.
-
-The optional parameter `lt` specifies an ordering predicate. It defaults to `LT.lt`, which must be
-decidable to be used for sorting.
--/
-@[inline] def Array.insertionSort (xs : Array α) (lt : α → α → Bool := by exact (· < ·)) : Array α :=
-  traverse xs 0 xs.size
+@[inline] def Array.insertionSort (a : Array α) (lt : α → α → Bool := by exact (· < ·)) : Array α :=
+  traverse a 0 a.size
 where
-  @[specialize] traverse (xs : Array α) (i : Nat) (fuel : Nat) : Array α :=
+  @[specialize] traverse (a : Array α) (i : Nat) (fuel : Nat) : Array α :=
     match fuel with
-    | 0      => xs
+    | 0      => a
     | fuel+1 =>
-      if h : i < xs.size then
-        traverse (swapLoop xs i h) (i+1) fuel
+      if h : i < a.size then
+        traverse (swapLoop a i h) (i+1) fuel
       else
-        xs
-  @[specialize] swapLoop (xs : Array α) (j : Nat) (h : j < xs.size) : Array α :=
+        a
+  @[specialize] swapLoop (a : Array α) (j : Nat) (h : j < a.size) : Array α :=
     match (generalizing := false) he:j with -- using `generalizing` because we don't want to refine the type of `h`
-    | 0    => xs
+    | 0    => a
     | j'+1 =>
-      have h' : j' < xs.size := by subst j; exact Nat.lt_trans (Nat.lt_succ_self _) h
-      if lt xs[j] xs[j'] then
-        swapLoop (xs.swap j j') j' (by rw [size_swap]; assumption; done)
+      have h' : j' < a.size := by subst j; exact Nat.lt_trans (Nat.lt_succ_self _) h
+      if lt a[j] a[j'] then
+        swapLoop (a.swap j j') j' (by rw [size_swap]; assumption; done)
       else
-        xs
+        a

src/Init/Data/Array/Lex/Basic.lean

@@ -8,18 +8,17 @@ import Init.Data.Array.Basic
 import Init.Data.Nat.Lemmas
 import Init.Data.Range
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+-- set_option linter.listName true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+-- set_option linter.indexVariables true -- Enforce naming conventions for index variables.
 
 namespace Array
 
 /--
-Compares arrays lexicographically with respect to a comparison `lt` on their elements.
+Lexicographic comparator for arrays.
 
-Specifically, `Array.lex as bs lt` is true if
-* `bs` is larger than `as` and `as` is pairwise equivalent via `==` to the initial segment of `bs`,
-  or
-* there is an index `i` such that `lt as[i] bs[i]`, and for all `j < i`, `as[j] == bs[j]`.
+`lex as bs lt` is true if
+- `bs` is larger than `as` and `as` is pairwise equivalent via `==` to the initial segment of `bs`, or
+- there is an index `i` such that `lt as[i] bs[i]`, and for all `j < i`, `as[j] == bs[j]`.
 -/
 def lex [BEq α] (as bs : Array α) (lt : α → α → Bool := by exact (· < ·)) : Bool := Id.run do
   for h : i in [0 : min as.size bs.size] do

src/Init/Data/Array/Lex/Lemmas.lean

@@ -7,25 +7,22 @@ prelude
 import Init.Data.Array.Lemmas
 import Init.Data.List.Lex
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 namespace Array
 
 /-! ### Lexicographic ordering -/
 
-@[simp] theorem _root_.List.lt_toArray [LT α] {l₁ l₂ : List α} : l₁.toArray < l₂.toArray ↔ l₁ < l₂ := Iff.rfl
-@[simp] theorem _root_.List.le_toArray [LT α] {l₁ l₂ : List α} : l₁.toArray ≤ l₂.toArray ↔ l₁ ≤ l₂ := Iff.rfl
+@[simp] theorem _root_.List.lt_toArray [LT α] (l₁ l₂ : List α) : l₁.toArray < l₂.toArray ↔ l₁ < l₂ := Iff.rfl
+@[simp] theorem _root_.List.le_toArray [LT α] (l₁ l₂ : List α) : l₁.toArray ≤ l₂.toArray ↔ l₁ ≤ l₂ := Iff.rfl
 
-@[simp] theorem lt_toList [LT α] {xs ys : Array α} : xs.toList < ys.toList ↔ xs < ys := Iff.rfl
-@[simp] theorem le_toList [LT α] {xs ys : Array α} : xs.toList ≤ ys.toList ↔ xs ≤ ys := Iff.rfl
+@[simp] theorem lt_toList [LT α] (l₁ l₂ : Array α) : l₁.toList < l₂.toList ↔ l₁ < l₂ := Iff.rfl
+@[simp] theorem le_toList [LT α] (l₁ l₂ : Array α) : l₁.toList ≤ l₂.toList ↔ l₁ ≤ l₂ := Iff.rfl
 
-protected theorem not_lt_iff_ge [LT α] {l₁ l₂ : List α} : ¬ l₁ < l₂ ↔ l₂ ≤ l₁ := Iff.rfl
-protected theorem not_le_iff_gt [DecidableEq α] [LT α] [DecidableLT α] {l₁ l₂ : List α} :
+protected theorem not_lt_iff_ge [LT α] (l₁ l₂ : List α) : ¬ l₁ < l₂ ↔ l₂ ≤ l₁ := Iff.rfl
+protected theorem not_le_iff_gt [DecidableEq α] [LT α] [DecidableLT α] (l₁ l₂ : List α) :
     ¬ l₁ ≤ l₂ ↔ l₂ < l₁ :=
   Decidable.not_not
 
-@[simp] theorem lex_empty [BEq α] {lt : α → α → Bool} {xs : Array α} : xs.lex #[] lt = false := by
+@[simp] theorem lex_empty [BEq α] {lt : α → α → Bool} (l : Array α) : l.lex #[] lt = false := by
   simp [lex, Id.run]
 
 @[simp] theorem singleton_lex_singleton [BEq α] {lt : α → α → Bool} : #[a].lex #[b] lt = lt a b := by
@@ -36,7 +33,7 @@ private theorem cons_lex_cons [BEq α] {lt : α → α → Bool} {a b : α} {xs
      (#[a] ++ xs).lex (#[b] ++ ys) lt =
        (lt a b || a == b && xs.lex ys lt) := by
   simp only [lex, Id.run]
-  simp only [Std.Range.forIn'_eq_forIn'_range', size_append, List.size_toArray, List.length_singleton,
+  simp only [Std.Range.forIn'_eq_forIn'_range', size_append, size_toArray, List.length_singleton,
     Nat.add_comm 1]
   simp [Nat.add_min_add_right, List.range'_succ, getElem_append_left, List.range'_succ_left,
     getElem_append_right]
@@ -45,7 +42,7 @@ private theorem cons_lex_cons [BEq α] {lt : α → α → Bool} {a b : α} {xs
     cases a == b <;> simp
   · simp
 
-@[simp] theorem _root_.List.lex_toArray [BEq α] {lt : α → α → Bool} {l₁ l₂ : List α} :
+@[simp] theorem _root_.List.lex_toArray [BEq α] (lt : α → α → Bool) (l₁ l₂ : List α) :
     l₁.toArray.lex l₂.toArray lt = l₁.lex l₂ lt := by
   induction l₁ generalizing l₂ with
   | nil => cases l₂ <;> simp [lex, Id.run]
@@ -55,35 +52,35 @@ private theorem cons_lex_cons [BEq α] {lt : α → α → Bool} {a b : α} {xs
     | cons y l₂ =>
       rw [List.toArray_cons, List.toArray_cons y, cons_lex_cons, List.lex, ih]
 
-@[simp] theorem lex_toList [BEq α] {lt : α → α → Bool} {xs ys : Array α} :
-    xs.toList.lex ys.toList lt = xs.lex ys lt := by
-  cases xs <;> cases ys <;> simp
+@[simp] theorem lex_toList [BEq α] (lt : α → α → Bool) (l₁ l₂ : Array α) :
+    l₁.toList.lex l₂.toList lt = l₁.lex l₂ lt := by
+  cases l₁ <;> cases l₂ <;> simp
 
-protected theorem lt_irrefl [LT α] [Std.Irrefl (· < · : α → α → Prop)] (xs : Array α) : ¬ xs < xs :=
-  List.lt_irrefl xs.toList
+protected theorem lt_irrefl [LT α] [Std.Irrefl (· < · : α → α → Prop)] (l : Array α) : ¬ l < l :=
+  List.lt_irrefl l.toList
 
 instance ltIrrefl [LT α] [Std.Irrefl (· < · : α → α → Prop)] : Std.Irrefl (α := Array α) (· < ·) where
   irrefl := Array.lt_irrefl
 
-@[simp] theorem not_lt_empty [LT α] (xs : Array α) : ¬ xs < #[] := List.not_lt_nil xs.toList
-@[simp] theorem empty_le [LT α] (xs : Array α) : #[] ≤ xs := List.nil_le xs.toList
+@[simp] theorem not_lt_empty [LT α] (l : Array α) : ¬ l < #[] := List.not_lt_nil l.toList
+@[simp] theorem empty_le [LT α] (l : Array α) : #[] ≤ l := List.nil_le l.toList
 
-@[simp] theorem le_empty [LT α] {xs : Array α} : xs ≤ #[] ↔ xs = #[] := by
-  cases xs
+@[simp] theorem le_empty [LT α] (l : Array α) : l ≤ #[] ↔ l = #[] := by
+  cases l
   simp
 
-@[simp] theorem empty_lt_push [LT α] (xs : Array α) (a : α) : #[] < xs.push a := by
-  rcases xs with (_ | ⟨x, xs⟩) <;> simp
+@[simp] theorem empty_lt_push [LT α] (l : Array α) (a : α) : #[] < l.push a := by
+  rcases l with (_ | ⟨x, l⟩) <;> simp
 
-protected theorem le_refl [LT α] [i₀ : Std.Irrefl (· < · : α → α → Prop)] (xs : Array α) : xs ≤ xs :=
-  List.le_refl xs.toList
+protected theorem le_refl [LT α] [i₀ : Std.Irrefl (· < · : α → α → Prop)] (l : Array α) : l ≤ l :=
+  List.le_refl l.toList
 
 instance [LT α] [Std.Irrefl (· < · : α → α → Prop)] : Std.Refl (· ≤ · : Array α → Array α → Prop) where
   refl := Array.le_refl
 
 protected theorem lt_trans [LT α]
     [i₁ : Trans (· < · : α → α → Prop) (· < ·) (· < ·)]
-    {xs ys zs : Array α} (h₁ : xs < ys) (h₂ : ys < zs) : xs < zs :=
+    {l₁ l₂ l₃ : Array α} (h₁ : l₁ < l₂) (h₂ : l₂ < l₃) : l₁ < l₃ :=
   List.lt_trans h₁ h₂
 
 instance [LT α] [Trans (· < · : α → α → Prop) (· < ·) (· < ·)] :
@@ -95,7 +92,7 @@ protected theorem lt_of_le_of_lt [DecidableEq α] [LT α] [DecidableLT α]
     [i₁ : Std.Asymm (· < · : α → α → Prop)]
     [i₂ : Std.Antisymm (¬ · < · : α → α → Prop)]
     [i₃ : Trans (¬ · < · : α → α → Prop) (¬ · < ·) (¬ · < ·)]
-    {xs ys zs : Array α} (h₁ : xs ≤ ys) (h₂ : ys < zs) : xs < zs :=
+    {l₁ l₂ l₃ : Array α} (h₁ : l₁ ≤ l₂) (h₂ : l₂ < l₃) : l₁ < l₃ :=
   List.lt_of_le_of_lt h₁ h₂
 
 protected theorem le_trans [DecidableEq α] [LT α] [DecidableLT α]
@@ -103,7 +100,7 @@ protected theorem le_trans [DecidableEq α] [LT α] [DecidableLT α]
     [Std.Asymm (· < · : α → α → Prop)]
     [Std.Antisymm (¬ · < · : α → α → Prop)]
     [Trans (¬ · < · : α → α → Prop) (¬ · < ·) (¬ · < ·)]
-    {xs ys zs : Array α} (h₁ : xs ≤ ys) (h₂ : ys ≤ zs) : xs ≤ zs :=
+    {l₁ l₂ l₃ : Array α} (h₁ : l₁ ≤ l₂) (h₂ : l₂ ≤ l₃) : l₁ ≤ l₃ :=
   fun h₃ => h₁ (Array.lt_of_le_of_lt h₂ h₃)
 
 instance [DecidableEq α] [LT α] [DecidableLT α]
@@ -116,7 +113,7 @@ instance [DecidableEq α] [LT α] [DecidableLT α]
 
 protected theorem lt_asymm [LT α]
     [i : Std.Asymm (· < · : α → α → Prop)]
-    {xs ys : Array α} (h : xs < ys) : ¬ ys < xs := List.lt_asymm h
+    {l₁ l₂ : Array α} (h : l₁ < l₂) : ¬ l₂ < l₁ := List.lt_asymm h
 
 instance [DecidableEq α] [LT α] [DecidableLT α]
     [Std.Asymm (· < · : α → α → Prop)] :
@@ -124,26 +121,26 @@ instance [DecidableEq α] [LT α] [DecidableLT α]
   asymm _ _ := Array.lt_asymm
 
 protected theorem le_total [DecidableEq α] [LT α] [DecidableLT α]
-    [i : Std.Total (¬ · < · : α → α → Prop)] (xs ys : Array α) : xs ≤ ys ∨ ys ≤ xs :=
-  List.le_total xs.toList ys.toList
+    [i : Std.Total (¬ · < · : α → α → Prop)] (l₁ l₂ : Array α) : l₁ ≤ l₂ ∨ l₂ ≤ l₁ :=
+  List.le_total _ _
 
 @[simp] protected theorem not_lt [LT α]
-    {xs ys : Array α} : ¬ xs < ys ↔ ys ≤ xs := Iff.rfl
+    {l₁ l₂ : Array α} : ¬ l₁ < l₂ ↔ l₂ ≤ l₁ := Iff.rfl
 
 @[simp] protected theorem not_le [DecidableEq α] [LT α] [DecidableLT α]
-    {xs ys : Array α} : ¬ ys ≤ xs ↔ xs < ys := Decidable.not_not
+    {l₁ l₂ : Array α} : ¬ l₂ ≤ l₁ ↔ l₁ < l₂ := Decidable.not_not
 
 protected theorem le_of_lt [DecidableEq α] [LT α] [DecidableLT α]
     [i : Std.Total (¬ · < · : α → α → Prop)]
-    {xs ys : Array α} (h : xs < ys) : xs ≤ ys :=
+    {l₁ l₂ : Array α} (h : l₁ < l₂) : l₁ ≤ l₂ :=
   List.le_of_lt h
 
 protected theorem le_iff_lt_or_eq [DecidableEq α] [LT α] [DecidableLT α]
     [Std.Irrefl (· < · : α → α → Prop)]
     [Std.Antisymm (¬ · < · : α → α → Prop)]
     [Std.Total (¬ · < · : α → α → Prop)]
-    {xs ys : Array α} : xs ≤ ys ↔ xs < ys ∨ xs = ys := by
-  simpa using List.le_iff_lt_or_eq (l₁ := xs.toList) (l₂ := ys.toList)
+    {l₁ l₂ : Array α} : l₁ ≤ l₂ ↔ l₁ < l₂ ∨ l₁ = l₂ := by
+  simpa using List.le_iff_lt_or_eq (l₁ := l₁.toList) (l₂ := l₂.toList)
 
 instance [DecidableEq α] [LT α] [DecidableLT α]
     [Std.Total (¬ · < · : α → α → Prop)] :
@@ -151,22 +148,22 @@ instance [DecidableEq α] [LT α] [DecidableLT α]
   total := Array.le_total
 
 @[simp] theorem lex_eq_true_iff_lt [DecidableEq α] [LT α] [DecidableLT α]
-    {xs ys : Array α} : lex xs ys = true ↔ xs < ys := by
-  cases xs
-  cases ys
+    {l₁ l₂ : Array α} : lex l₁ l₂ = true ↔ l₁ < l₂ := by
+  cases l₁
+  cases l₂
   simp
 
 @[simp] theorem lex_eq_false_iff_ge [DecidableEq α] [LT α] [DecidableLT α]
-    {xs ys : Array α} : lex xs ys = false ↔ ys ≤ xs := by
-  cases xs
-  cases ys
+    {l₁ l₂ : Array α} : lex l₁ l₂ = false ↔ l₂ ≤ l₁ := by
+  cases l₁
+  cases l₂
   simp [List.not_lt_iff_ge]
 
 instance [DecidableEq α] [LT α] [DecidableLT α] : DecidableLT (Array α) :=
-  fun xs ys => decidable_of_iff (lex xs ys = true) lex_eq_true_iff_lt
+  fun l₁ l₂ => decidable_of_iff (lex l₁ l₂ = true) lex_eq_true_iff_lt
 
 instance [DecidableEq α] [LT α] [DecidableLT α] : DecidableLE (Array α) :=
-  fun xs ys => decidable_of_iff (lex ys xs = false) lex_eq_false_iff_ge
+  fun l₁ l₂ => decidable_of_iff (lex l₂ l₁ = false) lex_eq_false_iff_ge
 
 /--
 `l₁` is lexicographically less than `l₂` if either
@@ -214,58 +211,58 @@ theorem lex_eq_false_iff_exists [BEq α] [PartialEquivBEq α] (lt : α → α
   cases l₂
   simp_all [List.lex_eq_false_iff_exists]
 
-protected theorem lt_iff_exists [DecidableEq α] [LT α] [DecidableLT α] {xs ys : Array α} :
-    xs < ys ↔
-      (xs = ys.take xs.size ∧ xs.size < ys.size) ∨
-        (∃ (i : Nat) (h₁ : i < xs.size) (h₂ : i < ys.size),
+protected theorem lt_iff_exists [DecidableEq α] [LT α] [DecidableLT α] {l₁ l₂ : Array α} :
+    l₁ < l₂ ↔
+      (l₁ = l₂.take l₁.size ∧ l₁.size < l₂.size) ∨
+        (∃ (i : Nat) (h₁ : i < l₁.size) (h₂ : i < l₂.size),
           (∀ j, (hj : j < i) →
-            xs[j]'(Nat.lt_trans hj h₁) = ys[j]'(Nat.lt_trans hj h₂)) ∧ xs[i] < ys[i]) := by
-  cases xs
-  cases ys
+            l₁[j]'(Nat.lt_trans hj h₁) = l₂[j]'(Nat.lt_trans hj h₂)) ∧ l₁[i] < l₂[i]) := by
+  cases l₁
+  cases l₂
   simp [List.lt_iff_exists]
 
 protected theorem le_iff_exists [DecidableEq α] [LT α] [DecidableLT α]
     [Std.Irrefl (· < · : α → α → Prop)]
     [Std.Asymm (· < · : α → α → Prop)]
-    [Std.Antisymm (¬ · < · : α → α → Prop)] {xs ys : Array α} :
-    xs ≤ ys ↔
-      (xs = ys.take xs.size) ∨
-        (∃ (i : Nat) (h₁ : i < xs.size) (h₂ : i < ys.size),
+    [Std.Antisymm (¬ · < · : α → α → Prop)] {l₁ l₂ : Array α} :
+    l₁ ≤ l₂ ↔
+      (l₁ = l₂.take l₁.size) ∨
+        (∃ (i : Nat) (h₁ : i < l₁.size) (h₂ : i < l₂.size),
           (∀ j, (hj : j < i) →
-            xs[j]'(Nat.lt_trans hj h₁) = ys[j]'(Nat.lt_trans hj h₂)) ∧ xs[i] < ys[i]) := by
-  cases xs
-  cases ys
+            l₁[j]'(Nat.lt_trans hj h₁) = l₂[j]'(Nat.lt_trans hj h₂)) ∧ l₁[i] < l₂[i]) := by
+  cases l₁
+  cases l₂
   simp [List.le_iff_exists]
 
-theorem append_left_lt [LT α] {xs ys zs : Array α} (h : ys < zs) :
-    xs ++ ys < xs ++ zs := by
-  cases xs
-  cases ys
-  cases zs
+theorem append_left_lt [LT α] {l₁ l₂ l₃ : Array α} (h : l₂ < l₃) :
+    l₁ ++ l₂ < l₁ ++ l₃ := by
+  cases l₁
+  cases l₂
+  cases l₃
   simpa using List.append_left_lt h
 
 theorem append_left_le [DecidableEq α] [LT α] [DecidableLT α]
     [Std.Irrefl (· < · : α → α → Prop)]
     [Std.Asymm (· < · : α → α → Prop)]
     [Std.Antisymm (¬ · < · : α → α → Prop)]
-    {xs ys zs : Array α} (h : ys ≤ zs) :
-    xs ++ ys ≤ xs ++ zs := by
-  cases xs
-  cases ys
-  cases zs
+    {l₁ l₂ l₃ : Array α} (h : l₂ ≤ l₃) :
+    l₁ ++ l₂ ≤ l₁ ++ l₃ := by
+  cases l₁
+  cases l₂
+  cases l₃
   simpa using List.append_left_le h
 
 theorem le_append_left [LT α] [Std.Irrefl (· < · : α → α → Prop)]
-    {xs ys : Array α} : xs ≤ xs ++ ys := by
-  cases xs
-  cases ys
+    {l₁ l₂ : Array α} : l₁ ≤ l₁ ++ l₂ := by
+  cases l₁
+  cases l₂
   simpa using List.le_append_left
 
 protected theorem map_lt [LT α] [LT β]
-    {xs ys : Array α} {f : α → β} (w : ∀ x y, x < y → f x < f y) (h : xs < ys) :
-    map f xs < map f ys := by
-  cases xs
-  cases ys
+    {l₁ l₂ : Array α} {f : α → β} (w : ∀ x y, x < y → f x < f y) (h : l₁ < l₂) :
+    map f l₁ < map f l₂ := by
+  cases l₁
+  cases l₂
   simpa using List.map_lt w h
 
 protected theorem map_le [DecidableEq α] [LT α] [DecidableLT α] [DecidableEq β] [LT β] [DecidableLT β]
@@ -275,10 +272,10 @@ protected theorem map_le [DecidableEq α] [LT α] [DecidableLT α] [DecidableEq
     [Std.Irrefl (· < · : β → β → Prop)]
     [Std.Asymm (· < · : β → β → Prop)]
     [Std.Antisymm (¬ · < · : β → β → Prop)]
-    {xs ys : Array α} {f : α → β} (w : ∀ x y, x < y → f x < f y) (h : xs ≤ ys) :
-    map f xs ≤ map f ys := by
-  cases xs
-  cases ys
+    {l₁ l₂ : Array α} {f : α → β} (w : ∀ x y, x < y → f x < f y) (h : l₁ ≤ l₂) :
+    map f l₁ ≤ map f l₂ := by
+  cases l₁
+  cases l₂
   simpa using List.map_le w h
 
 end Array

src/Init/Data/Array/MapIdx.lean

@@ -6,32 +6,28 @@ Authors: Mario Carneiro, Kim Morrison
 prelude
 import Init.Data.Array.Lemmas
 import Init.Data.Array.Attach
-import Init.Data.Array.OfFn
 import Init.Data.List.MapIdx
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 namespace Array
 
 /-! ### mapFinIdx -/
 
 -- This could also be proved from `SatisfiesM_mapIdxM` in Batteries.
-theorem mapFinIdx_induction (xs : Array α) (f : (i : Nat) → α → (h : i < xs.size) → β)
+theorem mapFinIdx_induction (as : Array α) (f : (i : Nat) → α → (h : i < as.size) → β)
     (motive : Nat → Prop) (h0 : motive 0)
-    (p : (i : Nat) → β → (h : i < xs.size) → Prop)
-    (hs : ∀ i h, motive i → p i (f i xs[i] h) h ∧ motive (i + 1)) :
-    motive xs.size ∧ ∃ eq : (Array.mapFinIdx xs f).size = xs.size,
-      ∀ i h, p i ((Array.mapFinIdx xs f)[i]) h := by
+    (p : (i : Nat) → β → (h : i < as.size) → Prop)
+    (hs : ∀ i h, motive i → p i (f i as[i] h) h ∧ motive (i + 1)) :
+    motive as.size ∧ ∃ eq : (Array.mapFinIdx as f).size = as.size,
+      ∀ i h, p i ((Array.mapFinIdx as f)[i]) h := by
   let rec go {bs i j h} (h₁ : j = bs.size) (h₂ : ∀ i h h', p i bs[i] h) (hm : motive j) :
-    let as : Array β := Array.mapFinIdxM.map (m := Id) xs f i j h bs
-    motive xs.size ∧ ∃ eq : as.size = xs.size, ∀ i h, p i as[i] h := by
+    let arr : Array β := Array.mapFinIdxM.map (m := Id) as f i j h bs
+    motive as.size ∧ ∃ eq : arr.size = as.size, ∀ i h, p i arr[i] h := by
     induction i generalizing j bs with simp [mapFinIdxM.map]
     | zero =>
       have := (Nat.zero_add _).symm.trans h
       exact ⟨this ▸ hm, h₁ ▸ this, fun _ _ => h₂ ..⟩
     | succ i ih =>
-      apply @ih (bs.push (f j xs[j] (by omega))) (j + 1) (by omega) (by simp; omega)
+      apply @ih (bs.push (f j as[j] (by omega))) (j + 1) (by omega) (by simp; omega)
       · intro i i_lt h'
         rw [getElem_push]
         split
@@ -42,78 +38,78 @@ theorem mapFinIdx_induction (xs : Array α) (f : (i : Nat) → α → (h : i < x
       · exact (hs j (by omega) hm).2
   simp [mapFinIdx, mapFinIdxM]; exact go rfl nofun h0
 
-theorem mapFinIdx_spec {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β}
-    {p : (i : Nat) → β → (h : i < xs.size) → Prop} (hs : ∀ i h, p i (f i xs[i] h) h) :
-    ∃ eq : (Array.mapFinIdx xs f).size = xs.size,
-      ∀ i h, p i ((Array.mapFinIdx xs f)[i]) h :=
+theorem mapFinIdx_spec (as : Array α) (f : (i : Nat) → α → (h : i < as.size) → β)
+    (p : (i : Nat) → β → (h : i < as.size) → Prop) (hs : ∀ i h, p i (f i as[i] h) h) :
+    ∃ eq : (Array.mapFinIdx as f).size = as.size,
+      ∀ i h, p i ((Array.mapFinIdx as f)[i]) h :=
   (mapFinIdx_induction _ _ (fun _ => True) trivial p fun _ _ _ => ⟨hs .., trivial⟩).2
 
-@[simp] theorem size_mapFinIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
-    (xs.mapFinIdx f).size = xs.size :=
+@[simp] theorem size_mapFinIdx (a : Array α) (f : (i : Nat) → α → (h : i < a.size) → β) :
+    (a.mapFinIdx f).size = a.size :=
   (mapFinIdx_spec (p := fun _ _ _ => True) (hs := fun _ _ => trivial)).1
 
-@[simp] theorem size_zipIdx {xs : Array α} {k : Nat} : (xs.zipIdx k).size = xs.size :=
-  Array.size_mapFinIdx
+@[simp] theorem size_zipIdx (as : Array α) (k : Nat) : (as.zipIdx k).size = as.size :=
+  Array.size_mapFinIdx _ _
 
 @[deprecated size_zipIdx (since := "2025-01-21")] abbrev size_zipWithIndex := @size_zipIdx
 
-@[simp] theorem getElem_mapFinIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {i : Nat}
-    (h : i < (xs.mapFinIdx f).size) :
-    (xs.mapFinIdx f)[i] = f i (xs[i]'(by simp_all)) (by simp_all) :=
-  (mapFinIdx_spec (p := fun i b h => b = f i xs[i] h) fun _ _ => rfl).2 i _
+@[simp] theorem getElem_mapFinIdx (a : Array α) (f : (i : Nat) → α → (h : i < a.size) → β) (i : Nat)
+    (h : i < (mapFinIdx a f).size) :
+    (a.mapFinIdx f)[i] = f i (a[i]'(by simp_all))  (by simp_all) :=
+  (mapFinIdx_spec _ _ (fun i b h => b = f i a[i] h) fun _ _ => rfl).2 i _
 
-@[simp] theorem getElem?_mapFinIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {i : Nat} :
-    (xs.mapFinIdx f)[i]? =
-      xs[i]?.pbind fun b h => f i b (getElem?_eq_some_iff.1 h).1 := by
+@[simp] theorem getElem?_mapFinIdx (a : Array α) (f : (i : Nat) → α → (h : i < a.size) → β) (i : Nat) :
+    (a.mapFinIdx f)[i]? =
+      a[i]?.pbind fun b h => f i b (getElem?_eq_some_iff.1 h).1 := by
   simp only [getElem?_def, size_mapFinIdx, getElem_mapFinIdx]
   split <;> simp_all
 
-@[simp] theorem toList_mapFinIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
-    (xs.mapFinIdx f).toList = xs.toList.mapFinIdx (fun i a h => f i a (by simpa)) := by
+@[simp] theorem toList_mapFinIdx (a : Array α) (f : (i : Nat) → α → (h : i < a.size) → β) :
+    (a.mapFinIdx f).toList = a.toList.mapFinIdx (fun i a h => f i a (by simpa)) := by
   apply List.ext_getElem <;> simp
 
 /-! ### mapIdx -/
 
-theorem mapIdx_induction {f : Nat → α → β} {xs : Array α}
-    {motive : Nat → Prop} (h0 : motive 0)
-    {p : (i : Nat) → β → (h : i < xs.size) → Prop}
-    (hs : ∀ i h, motive i → p i (f i xs[i]) h ∧ motive (i + 1)) :
-    motive xs.size ∧ ∃ eq : (xs.mapIdx f).size = xs.size,
-      ∀ i h, p i ((xs.mapIdx f)[i]) h :=
-  mapFinIdx_induction xs (fun i a _ => f i a) motive h0 p hs
+theorem mapIdx_induction (f : Nat → α → β) (as : Array α)
+    (motive : Nat → Prop) (h0 : motive 0)
+    (p : (i : Nat) → β → (h : i < as.size) → Prop)
+    (hs : ∀ i h, motive i → p i (f i as[i]) h ∧ motive (i + 1)) :
+    motive as.size ∧ ∃ eq : (as.mapIdx f).size = as.size,
+      ∀ i h, p i ((as.mapIdx f)[i]) h :=
+  mapFinIdx_induction as (fun i a _ => f i a) motive h0 p hs
 
-theorem mapIdx_spec {f : Nat → α → β} {xs : Array α}
-    {p : (i : Nat) → β → (h : i < xs.size) → Prop} (hs : ∀ i h, p i (f i xs[i]) h) :
-    ∃ eq : (xs.mapIdx f).size = xs.size,
-      ∀ i h, p i ((xs.mapIdx f)[i]) h :=
-  (mapIdx_induction (motive := fun _ => True) trivial fun _ _ _ => ⟨hs .., trivial⟩).2
+theorem mapIdx_spec (f : Nat → α → β) (as : Array α)
+    (p : (i : Nat) → β → (h : i < as.size) → Prop) (hs : ∀ i h, p i (f i as[i]) h) :
+    ∃ eq : (as.mapIdx f).size = as.size,
+      ∀ i h, p i ((as.mapIdx f)[i]) h :=
+  (mapIdx_induction _ _ (fun _ => True) trivial p fun _ _ _ => ⟨hs .., trivial⟩).2
 
-@[simp] theorem size_mapIdx {f : Nat → α → β} {xs : Array α} : (xs.mapIdx f).size = xs.size :=
+@[simp] theorem size_mapIdx (f : Nat → α → β) (as : Array α) : (as.mapIdx f).size = as.size :=
   (mapIdx_spec (p := fun _ _ _ => True) (hs := fun _ _ => trivial)).1
 
-@[simp] theorem getElem_mapIdx {f : Nat → α → β} {xs : Array α} {i : Nat}
-    (h : i < (xs.mapIdx f).size) :
-    (xs.mapIdx f)[i] = f i (xs[i]'(by simp_all)) :=
-  (mapIdx_spec (p := fun i b h => b = f i xs[i]) fun _ _ => rfl).2 i (by simp_all)
+@[simp] theorem getElem_mapIdx (f : Nat → α → β) (as : Array α) (i : Nat)
+    (h : i < (as.mapIdx f).size) :
+    (as.mapIdx f)[i] = f i (as[i]'(by simp_all)) :=
+  (mapIdx_spec _ _ (fun i b h => b = f i as[i]) fun _ _ => rfl).2 i (by simp_all)
 
-@[simp] theorem getElem?_mapIdx {f : Nat → α → β} {xs : Array α} {i : Nat} :
-    (xs.mapIdx f)[i]? =
-      xs[i]?.map (f i) := by
+@[simp] theorem getElem?_mapIdx (f : Nat → α → β) (as : Array α) (i : Nat) :
+    (as.mapIdx f)[i]? =
+      as[i]?.map (f i) := by
   simp [getElem?_def, size_mapIdx, getElem_mapIdx]
 
-@[simp] theorem toList_mapIdx {f : Nat → α → β} {xs : Array α} :
-    (xs.mapIdx f).toList = xs.toList.mapIdx (fun i a => f i a) := by
+@[simp] theorem toList_mapIdx (f : Nat → α → β) (as : Array α) :
+    (as.mapIdx f).toList = as.toList.mapIdx (fun i a => f i a) := by
   apply List.ext_getElem <;> simp
 
 end Array
 
 namespace List
 
-@[simp] theorem mapFinIdx_toArray {l : List α} {f : (i : Nat) → α → (h : i < l.length) → β} :
+@[simp] theorem mapFinIdx_toArray (l : List α) (f : (i : Nat) → α → (h : i < l.length) → β) :
     l.toArray.mapFinIdx f = (l.mapFinIdx f).toArray := by
   ext <;> simp
 
-@[simp] theorem mapIdx_toArray {f : Nat → α → β} {l : List α} :
+@[simp] theorem mapIdx_toArray (f : Nat → α → β) (l : List α) :
     l.toArray.mapIdx f = (l.mapIdx f).toArray := by
   ext <;> simp
 
@@ -123,8 +119,8 @@ namespace Array
 
 /-! ### zipIdx -/
 
-@[simp] theorem getElem_zipIdx {xs : Array α} {k : Nat} {i : Nat} (h : i < (xs.zipIdx k).size) :
-    (xs.zipIdx k)[i] = (xs[i]'(by simp_all), k + i) := by
+@[simp] theorem getElem_zipIdx (a : Array α) (k : Nat) (i : Nat) (h : i < (a.zipIdx k).size) :
+    (a.zipIdx k)[i] = (a[i]'(by simp_all), k + i) := by
   simp [zipIdx]
 
 @[deprecated getElem_zipIdx (since := "2025-01-21")]
@@ -137,35 +133,35 @@ abbrev getElem_zipWithIndex := @getElem_zipIdx
 @[deprecated zipIdx_toArray (since := "2025-01-21")]
 abbrev zipWithIndex_toArray := @zipIdx_toArray
 
-@[simp] theorem toList_zipIdx {xs : Array α} {k : Nat} :
-    (xs.zipIdx k).toList = xs.toList.zipIdx k := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem toList_zipIdx (a : Array α) (k : Nat) :
+    (a.zipIdx k).toList = a.toList.zipIdx k := by
+  rcases a with ⟨a⟩
   simp
 
 @[deprecated toList_zipIdx (since := "2025-01-21")]
 abbrev toList_zipWithIndex := @toList_zipIdx
 
-theorem mk_mem_zipIdx_iff_le_and_getElem?_sub {k i : Nat} {x : α} {xs : Array α} :
-    (x, i) ∈ xs.zipIdx k ↔ k ≤ i ∧ xs[i - k]? = some x := by
-  rcases xs with ⟨xs⟩
+theorem mk_mem_zipIdx_iff_le_and_getElem?_sub {k i : Nat} {x : α} {l : Array α} :
+    (x, i) ∈ zipIdx l k ↔ k ≤ i ∧ l[i - k]? = some x := by
+  rcases l with ⟨l⟩
   simp [List.mk_mem_zipIdx_iff_le_and_getElem?_sub]
 
 /-- Variant of `mk_mem_zipIdx_iff_le_and_getElem?_sub` specialized at `k = 0`,
 to avoid the inequality and the subtraction. -/
-theorem mk_mem_zipIdx_iff_getElem? {x : α} {i : Nat} {xs : Array α} :
-    (x, i) ∈ xs.zipIdx ↔ xs[i]? = x := by
+theorem mk_mem_zipIdx_iff_getElem? {x : α} {i : Nat} {l : Array α} :
+    (x, i) ∈ l.zipIdx ↔ l[i]? = x := by
   rw [mk_mem_zipIdx_iff_le_and_getElem?_sub]
   simp
 
-theorem mem_zipIdx_iff_le_and_getElem?_sub {x : α × Nat} {xs : Array α} {k : Nat} :
-    x ∈ xs.zipIdx k ↔ k ≤ x.2 ∧ xs[x.2 - k]? = some x.1 := by
+theorem mem_zipIdx_iff_le_and_getElem?_sub {x : α × Nat} {l : Array α} {k : Nat} :
+    x ∈ zipIdx l k ↔ k ≤ x.2 ∧ l[x.2 - k]? = some x.1 := by
   cases x
   simp [mk_mem_zipIdx_iff_le_and_getElem?_sub]
 
 /-- Variant of `mem_zipIdx_iff_le_and_getElem?_sub` specialized at `k = 0`,
 to avoid the inequality and the subtraction. -/
-theorem mem_zipIdx_iff_getElem? {x : α × Nat} {xs : Array α} :
-    x ∈ xs.zipIdx ↔ xs[x.2]? = some x.1 := by
+theorem mem_zipIdx_iff_getElem? {x : α × Nat} {l : Array α} :
+    x ∈ l.zipIdx ↔ l[x.2]? = some x.1 := by
   rw [mk_mem_zipIdx_iff_getElem?]
 
 @[deprecated mk_mem_zipIdx_iff_getElem? (since := "2025-01-21")]
@@ -186,31 +182,31 @@ abbrev mem_zipWithIndex_iff_getElem? := @mem_zipIdx_iff_getElem?
 theorem mapFinIdx_empty {f : (i : Nat) → α → (h : i < 0) → β} : mapFinIdx #[] f = #[] :=
   rfl
 
-theorem mapFinIdx_eq_ofFn {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
-    xs.mapFinIdx f = Array.ofFn fun i : Fin xs.size => f i xs[i] i.2 := by
-  cases xs
+theorem mapFinIdx_eq_ofFn {as : Array α} {f : (i : Nat) → α → (h : i < as.size) → β} :
+    as.mapFinIdx f = Array.ofFn fun i : Fin as.size => f i as[i] i.2 := by
+  cases as
   simp [List.mapFinIdx_eq_ofFn]
 
-theorem mapFinIdx_append {xs ys : Array α} {f : (i : Nat) → α → (h : i < (xs ++ ys).size) → β} :
-    (xs ++ ys).mapFinIdx f =
-      xs.mapFinIdx (fun i a h => f i a (by simp; omega)) ++
-        ys.mapFinIdx (fun i a h => f (i + xs.size) a (by simp; omega)) := by
-  cases xs
-  cases ys
+theorem mapFinIdx_append {K L : Array α} {f : (i : Nat) → α → (h : i < (K ++ L).size) → β} :
+    (K ++ L).mapFinIdx f =
+      K.mapFinIdx (fun i a h => f i a (by simp; omega)) ++
+        L.mapFinIdx (fun i a h => f (i + K.size) a (by simp; omega)) := by
+  cases K
+  cases L
   simp [List.mapFinIdx_append]
 
 @[simp]
-theorem mapFinIdx_push {xs : Array α} {a : α} {f : (i : Nat) → α → (h : i < (xs.push a).size) → β} :
-    mapFinIdx (xs.push a) f =
-      (mapFinIdx xs (fun i a h => f i a (by simp; omega))).push (f xs.size a (by simp)) := by
+theorem mapFinIdx_push {l : Array α} {a : α} {f : (i : Nat) → α → (h : i < (l.push a).size) → β} :
+    mapFinIdx (l.push a) f =
+      (mapFinIdx l (fun i a h => f i a (by simp; omega))).push (f l.size a (by simp)) := by
   simp [← append_singleton, mapFinIdx_append]
 
 theorem mapFinIdx_singleton {a : α} {f : (i : Nat) → α → (h : i < 1) → β} :
     #[a].mapFinIdx f = #[f 0 a (by simp)] := by
   simp
 
-theorem mapFinIdx_eq_zipIdx_map {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
-    xs.mapFinIdx f = xs.zipIdx.attach.map
+theorem mapFinIdx_eq_zipIdx_map {l : Array α} {f : (i : Nat) → α → (h : i < l.size) → β} :
+    l.mapFinIdx f = l.zipIdx.attach.map
       fun ⟨⟨x, i⟩, m⟩ =>
         f i x (by simp [mk_mem_zipIdx_iff_getElem?, getElem?_eq_some_iff] at m; exact m.1) := by
   ext <;> simp
@@ -219,44 +215,44 @@ theorem mapFinIdx_eq_zipIdx_map {xs : Array α} {f : (i : Nat) → α → (h : i
 abbrev mapFinIdx_eq_zipWithIndex_map := @mapFinIdx_eq_zipIdx_map
 
 @[simp]
-theorem mapFinIdx_eq_empty_iff {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
-    xs.mapFinIdx f = #[] ↔ xs = #[] := by
-  cases xs
+theorem mapFinIdx_eq_empty_iff {l : Array α} {f : (i : Nat) → α → (h : i < l.size) → β} :
+    l.mapFinIdx f = #[] ↔ l = #[] := by
+  cases l
   simp
 
-theorem mapFinIdx_ne_empty_iff {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
-    xs.mapFinIdx f ≠ #[] ↔ xs ≠ #[] := by
+theorem mapFinIdx_ne_empty_iff {l : Array α} {f : (i : Nat) → α → (h : i < l.size) → β} :
+    l.mapFinIdx f ≠ #[] ↔ l ≠ #[] := by
   simp
 
-theorem exists_of_mem_mapFinIdx {b : β} {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β}
-    (h : b ∈ xs.mapFinIdx f) : ∃ (i : Nat) (h : i < xs.size), f i xs[i] h = b := by
-  rcases xs with ⟨xs⟩
+theorem exists_of_mem_mapFinIdx {b : β} {l : Array α} {f : (i : Nat) → α → (h : i < l.size) → β}
+    (h : b ∈ l.mapFinIdx f) : ∃ (i : Nat) (h : i < l.size), f i l[i] h = b := by
+  rcases l with ⟨l⟩
   exact List.exists_of_mem_mapFinIdx (by simpa using h)
 
-@[simp] theorem mem_mapFinIdx {b : β} {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
-    b ∈ xs.mapFinIdx f ↔ ∃ (i : Nat) (h : i < xs.size), f i xs[i] h = b := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem mem_mapFinIdx {b : β} {l : Array α} {f : (i : Nat) → α → (h : i < l.size) → β} :
+    b ∈ l.mapFinIdx f ↔ ∃ (i : Nat) (h : i < l.size), f i l[i] h = b := by
+  rcases l with ⟨l⟩
   simp
 
-theorem mapFinIdx_eq_iff {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {ys : Array β} :
-    xs.mapFinIdx f = ys ↔ ∃ h : ys.size = xs.size, ∀ (i : Nat) (h : i < xs.size), ys[i] = f i xs[i] h := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
+theorem mapFinIdx_eq_iff {l : Array α} {f : (i : Nat) → α → (h : i < l.size) → β} :
+    l.mapFinIdx f = l' ↔ ∃ h : l'.size = l.size, ∀ (i : Nat) (h : i < l.size), l'[i] = f i l[i] h := by
+  rcases l with ⟨l⟩
+  rcases l' with ⟨l'⟩
   simpa using List.mapFinIdx_eq_iff
 
-@[simp] theorem mapFinIdx_eq_singleton_iff {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {b : β} :
-    xs.mapFinIdx f = #[b] ↔ ∃ (a : α) (w : xs = #[a]), f 0 a (by simp [w]) = b := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem mapFinIdx_eq_singleton_iff {l : Array α} {f : (i : Nat) → α → (h : i < l.size) → β} {b : β} :
+    l.mapFinIdx f = #[b] ↔ ∃ (a : α) (w : l = #[a]), f 0 a (by simp [w]) = b := by
+  rcases l with ⟨l⟩
   simp
 
-theorem mapFinIdx_eq_append_iff {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {ys zs : Array β} :
-    xs.mapFinIdx f = ys ++ zs ↔
-      ∃ (ys' : Array α) (zs' : Array α) (w : xs = ys' ++ zs'),
-        ys'.mapFinIdx (fun i a h => f i a (by simp [w]; omega)) = ys ∧
-        zs'.mapFinIdx (fun i a h => f (i + ys'.size) a (by simp [w]; omega)) = zs := by
-  rcases xs with ⟨l⟩
-  rcases ys with ⟨l₁⟩
-  rcases zs with ⟨l₂⟩
+theorem mapFinIdx_eq_append_iff {l : Array α} {f : (i : Nat) → α → (h : i < l.size) → β} {l₁ l₂ : Array β} :
+    l.mapFinIdx f = l₁ ++ l₂ ↔
+      ∃ (l₁' : Array α) (l₂' : Array α) (w : l = l₁' ++ l₂'),
+        l₁'.mapFinIdx (fun i a h => f i a (by simp [w]; omega)) = l₁ ∧
+        l₂'.mapFinIdx (fun i a h => f (i + l₁'.size) a (by simp [w]; omega)) = l₂ := by
+  rcases l with ⟨l⟩
+  rcases l₁ with ⟨l₁⟩
+  rcases l₂ with ⟨l₂⟩
   simp only [List.mapFinIdx_toArray, List.append_toArray, mk.injEq, List.mapFinIdx_eq_append_iff,
     toArray_eq_append_iff]
   constructor
@@ -268,42 +264,39 @@ theorem mapFinIdx_eq_append_iff {xs : Array α} {f : (i : Nat) → α → (h : i
     obtain rfl := h₂
     refine ⟨l₁, l₂, by simp_all⟩
 
-theorem mapFinIdx_eq_push_iff {xs : Array α} {b : β} {f : (i : Nat) → α → (h : i < xs.size) → β} :
-    xs.mapFinIdx f = ys.push b ↔
-      ∃ (zs : Array α) (a : α) (w : xs = zs.push a),
-        zs.mapFinIdx (fun i a h => f i a (by simp [w]; omega)) = ys ∧ b = f (xs.size - 1) a (by simp [w]) := by
+theorem mapFinIdx_eq_push_iff {l : Array α} {b : β} {f : (i : Nat) → α → (h : i < l.size) → β} :
+    l.mapFinIdx f = l₂.push b ↔
+      ∃ (l₁ : Array α) (a : α) (w : l = l₁.push a),
+        l₁.mapFinIdx (fun i a h => f i a (by simp [w]; omega)) = l₂ ∧ b = f (l.size - 1) a (by simp [w]) := by
   rw [push_eq_append, mapFinIdx_eq_append_iff]
   constructor
-  · rintro ⟨ys', zs', rfl, rfl, h₂⟩
+  · rintro ⟨l₁, l₂, rfl, rfl, h₂⟩
     simp only [mapFinIdx_eq_singleton_iff, Nat.zero_add] at h₂
     obtain ⟨a, rfl, rfl⟩ := h₂
-    exact ⟨ys', a, by simp⟩
-  · rintro ⟨zs, a, rfl, rfl, rfl⟩
-    exact ⟨zs, #[a], by simp⟩
+    exact ⟨l₁, a, by simp⟩
+  · rintro ⟨l₁, a, rfl, rfl, rfl⟩
+    exact ⟨l₁, #[a], by simp⟩
 
-theorem mapFinIdx_eq_mapFinIdx_iff {xs : Array α} {f g : (i : Nat) → α → (h : i < xs.size) → β} :
-    xs.mapFinIdx f = xs.mapFinIdx g ↔ ∀ (i : Nat) (h : i < xs.size), f i xs[i] h = g i xs[i] h := by
+theorem mapFinIdx_eq_mapFinIdx_iff {l : Array α} {f g : (i : Nat) → α → (h : i < l.size) → β} :
+    l.mapFinIdx f = l.mapFinIdx g ↔ ∀ (i : Nat) (h : i < l.size), f i l[i] h = g i l[i] h := by
   rw [eq_comm, mapFinIdx_eq_iff]
   simp
 
-@[simp] theorem mapFinIdx_mapFinIdx {xs : Array α}
-    {f : (i : Nat) → α → (h : i < xs.size) → β}
-    {g : (i : Nat) → β → (h : i < (xs.mapFinIdx f).size) → γ} :
-    (xs.mapFinIdx f).mapFinIdx g = xs.mapFinIdx (fun i a h => g i (f i a h) (by simpa using h)) := by
+@[simp] theorem mapFinIdx_mapFinIdx {l : Array α}
+    {f : (i : Nat) → α → (h : i < l.size) → β}
+    {g : (i : Nat) → β → (h : i < (l.mapFinIdx f).size) → γ} :
+    (l.mapFinIdx f).mapFinIdx g = l.mapFinIdx (fun i a h => g i (f i a h) (by simpa using h)) := by
   simp [mapFinIdx_eq_iff]
 
-theorem mapFinIdx_eq_replicate_iff {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {b : β} :
-    xs.mapFinIdx f = replicate xs.size b ↔ ∀ (i : Nat) (h : i < xs.size), f i xs[i] h = b := by
-  rcases xs with ⟨l⟩
+theorem mapFinIdx_eq_mkArray_iff {l : Array α} {f : (i : Nat) → α → (h : i < l.size) → β} {b : β} :
+    l.mapFinIdx f = mkArray l.size b ↔ ∀ (i : Nat) (h : i < l.size), f i l[i] h = b := by
+  rcases l with ⟨l⟩
   rw [← toList_inj]
   simp [List.mapFinIdx_eq_replicate_iff]
 
-@[deprecated mapFinIdx_eq_replicate_iff (since := "2025-03-18")]
-abbrev mapFinIdx_eq_mkArray_iff := @mapFinIdx_eq_replicate_iff
-
-@[simp] theorem mapFinIdx_reverse {xs : Array α} {f : (i : Nat) → α → (h : i < xs.reverse.size) → β} :
-    xs.reverse.mapFinIdx f = (xs.mapFinIdx (fun i a h => f (xs.size - 1 - i) a (by simp; omega))).reverse := by
-  rcases xs with ⟨l⟩
+@[simp] theorem mapFinIdx_reverse {l : Array α} {f : (i : Nat) → α → (h : i < l.reverse.size) → β} :
+    l.reverse.mapFinIdx f = (l.mapFinIdx (fun i a h => f (l.size - 1 - i) a (by simp; omega))).reverse := by
+  rcases l with ⟨l⟩
   simp [List.mapFinIdx_reverse]
 
 /-! ### mapIdx -/
@@ -312,52 +305,52 @@ abbrev mapFinIdx_eq_mkArray_iff := @mapFinIdx_eq_replicate_iff
 theorem mapIdx_empty {f : Nat → α → β} : mapIdx f #[] = #[] :=
   rfl
 
-@[simp] theorem mapFinIdx_eq_mapIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {g : Nat → α → β}
-    (h : ∀ (i : Nat) (h : i < xs.size), f i xs[i] h = g i xs[i]) :
-    xs.mapFinIdx f = xs.mapIdx g := by
+@[simp] theorem mapFinIdx_eq_mapIdx {l : Array α} {f : (i : Nat) → α → (h : i < l.size) → β} {g : Nat → α → β}
+    (h : ∀ (i : Nat) (h : i < l.size), f i l[i] h = g i l[i]) :
+    l.mapFinIdx f = l.mapIdx g := by
   simp_all [mapFinIdx_eq_iff]
 
-theorem mapIdx_eq_mapFinIdx {xs : Array α} {f : Nat → α → β} :
-    xs.mapIdx f = xs.mapFinIdx (fun i a _ => f i a) := by
+theorem mapIdx_eq_mapFinIdx {l : Array α} {f : Nat → α → β} :
+    l.mapIdx f = l.mapFinIdx (fun i a _ => f i a) := by
   simp [mapFinIdx_eq_mapIdx]
 
-theorem mapIdx_eq_zipIdx_map {xs : Array α} {f : Nat → α → β} :
-    xs.mapIdx f = xs.zipIdx.map fun ⟨a, i⟩ => f i a := by
+theorem mapIdx_eq_zipIdx_map {l : Array α} {f : Nat → α → β} :
+    l.mapIdx f = l.zipIdx.map fun ⟨a, i⟩ => f i a := by
   ext <;> simp
 
 @[deprecated mapIdx_eq_zipIdx_map (since := "2025-01-21")]
 abbrev mapIdx_eq_zipWithIndex_map := @mapIdx_eq_zipIdx_map
 
-theorem mapIdx_append {xs ys : Array α} :
-    (xs ++ ys).mapIdx f = xs.mapIdx f ++ ys.mapIdx (fun i => f (i + xs.size)) := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
+theorem mapIdx_append {K L : Array α} :
+    (K ++ L).mapIdx f = K.mapIdx f ++ L.mapIdx fun i => f (i + K.size) := by
+  rcases K with ⟨K⟩
+  rcases L with ⟨L⟩
   simp [List.mapIdx_append]
 
 @[simp]
-theorem mapIdx_push {xs : Array α} {a : α} :
-    mapIdx f (xs.push a) = (mapIdx f xs).push (f xs.size a) := by
+theorem mapIdx_push {l : Array α} {a : α} :
+    mapIdx f (l.push a) = (mapIdx f l).push (f l.size a) := by
   simp [← append_singleton, mapIdx_append]
 
 theorem mapIdx_singleton {a : α} : mapIdx f #[a] = #[f 0 a] := by
   simp
 
 @[simp]
-theorem mapIdx_eq_empty_iff {xs : Array α} : mapIdx f xs = #[] ↔ xs = #[] := by
-  rcases xs with ⟨xs⟩
+theorem mapIdx_eq_empty_iff {l : Array α} : mapIdx f l = #[] ↔ l = #[] := by
+  rcases l with ⟨l⟩
   simp
 
-theorem mapIdx_ne_empty_iff {xs : Array α} :
-    mapIdx f xs ≠ #[] ↔ xs ≠ #[] := by
+theorem mapIdx_ne_empty_iff {l : Array α} :
+    mapIdx f l ≠ #[] ↔ l ≠ #[] := by
   simp
 
-theorem exists_of_mem_mapIdx {b : β} {xs : Array α}
-    (h : b ∈ mapIdx f xs) : ∃ (i : Nat) (h : i < xs.size), f i xs[i] = b := by
+theorem exists_of_mem_mapIdx {b : β} {l : Array α}
+    (h : b ∈ mapIdx f l) : ∃ (i : Nat) (h : i < l.size), f i l[i] = b := by
   rw [mapIdx_eq_mapFinIdx] at h
   simpa [Fin.exists_iff] using exists_of_mem_mapFinIdx h
 
-@[simp] theorem mem_mapIdx {b : β} {xs : Array α} :
-    b ∈ mapIdx f xs ↔ ∃ (i : Nat) (h : i < xs.size), f i xs[i] = b := by
+@[simp] theorem mem_mapIdx {b : β} {l : Array α} :
+    b ∈ mapIdx f l ↔ ∃ (i : Nat) (h : i < l.size), f i l[i] = b := by
   constructor
   · intro h
     exact exists_of_mem_mapIdx h
@@ -365,95 +358,87 @@ theorem exists_of_mem_mapIdx {b : β} {xs : Array α}
     rw [mem_iff_getElem]
     exact ⟨i, by simpa using h, by simp⟩
 
-theorem mapIdx_eq_push_iff {xs : Array α} {b : β} :
-    mapIdx f xs = ys.push b ↔
-      ∃ (a : α) (zs : Array α), xs = zs.push a ∧ mapIdx f zs = ys ∧ f zs.size a = b := by
+theorem mapIdx_eq_push_iff {l : Array α} {b : β} :
+    mapIdx f l = l₂.push b ↔
+      ∃ (a : α) (l₁ : Array α), l = l₁.push a ∧ mapIdx f l₁ = l₂ ∧ f l₁.size a = b := by
   rw [mapIdx_eq_mapFinIdx, mapFinIdx_eq_push_iff]
   simp only [mapFinIdx_eq_mapIdx, exists_and_left, exists_prop]
   constructor
-  · rintro ⟨zs, rfl, a, rfl, rfl⟩
-    exact ⟨a, zs, by simp⟩
-  · rintro ⟨a, zs, rfl, rfl, rfl⟩
-    exact ⟨zs, rfl, a, by simp⟩
+  · rintro ⟨l₁, rfl, a, rfl, rfl⟩
+    exact ⟨a, l₁, by simp⟩
+  · rintro ⟨a, l₁, rfl, rfl, rfl⟩
+    exact ⟨l₁, rfl, a, by simp⟩
 
-@[simp] theorem mapIdx_eq_singleton_iff {xs : Array α} {f : Nat → α → β} {b : β} :
-    mapIdx f xs = #[b] ↔ ∃ (a : α), xs = #[a] ∧ f 0 a = b := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem mapIdx_eq_singleton_iff {l : Array α} {f : Nat → α → β} {b : β} :
+    mapIdx f l = #[b] ↔ ∃ (a : α), l = #[a] ∧ f 0 a = b := by
+  rcases l with ⟨l⟩
   simp [List.mapIdx_eq_singleton_iff]
 
-theorem mapIdx_eq_append_iff {xs : Array α} {f : Nat → α → β} {ys zs : Array β} :
-    mapIdx f xs = ys ++ zs ↔
-      ∃ (xs' : Array α) (zs' : Array α), xs = xs' ++ zs' ∧
-        xs'.mapIdx f = ys ∧
-        zs'.mapIdx (fun i => f (i + xs'.size)) = zs := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
-  rcases zs with ⟨zs⟩
+theorem mapIdx_eq_append_iff {l : Array α} {f : Nat → α → β} {l₁ l₂ : Array β} :
+    mapIdx f l = l₁ ++ l₂ ↔
+      ∃ (l₁' : Array α) (l₂' : Array α), l = l₁' ++ l₂' ∧
+        l₁'.mapIdx f = l₁ ∧
+        l₂'.mapIdx (fun i => f (i + l₁'.size)) = l₂ := by
+  rcases l with ⟨l⟩
+  rcases l₁ with ⟨l₁⟩
+  rcases l₂ with ⟨l₂⟩
   simp only [List.mapIdx_toArray, List.append_toArray, mk.injEq, List.mapIdx_eq_append_iff,
     toArray_eq_append_iff]
   constructor
   · rintro ⟨l₁, l₂, rfl, rfl, rfl⟩
     exact ⟨l₁.toArray, l₂.toArray, by simp⟩
   · rintro ⟨⟨l₁⟩, ⟨l₂⟩, rfl, h₁, h₂⟩
-    simp only [List.mapIdx_toArray, mk.injEq, List.size_toArray] at h₁ h₂
+    simp only [List.mapIdx_toArray, mk.injEq, size_toArray] at h₁ h₂
     obtain rfl := h₁
     obtain rfl := h₂
     exact ⟨l₁, l₂, by simp⟩
 
-theorem mapIdx_eq_iff {xs : Array α} : mapIdx f xs = ys ↔ ∀ i : Nat, ys[i]? = xs[i]?.map (f i) := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
+theorem mapIdx_eq_iff {l : Array α} : mapIdx f l = l' ↔ ∀ i : Nat, l'[i]? = l[i]?.map (f i) := by
+  rcases l with ⟨l⟩
+  rcases l' with ⟨l'⟩
   simp [List.mapIdx_eq_iff]
 
-theorem mapIdx_eq_mapIdx_iff {xs : Array α} :
-    mapIdx f xs = mapIdx g xs ↔ ∀ i : Nat, (h : i < xs.size) → f i xs[i] = g i xs[i] := by
-  rcases xs with ⟨xs⟩
+theorem mapIdx_eq_mapIdx_iff {l : Array α} :
+    mapIdx f l = mapIdx g l ↔ ∀ i : Nat, (h : i < l.size) → f i l[i] = g i l[i] := by
+  rcases l with ⟨l⟩
   simp [List.mapIdx_eq_mapIdx_iff]
 
-@[simp] theorem mapIdx_set {xs : Array α} {i : Nat} {h : i < xs.size} {a : α} :
-    (xs.set i a).mapIdx f = (xs.mapIdx f).set i (f i a) (by simpa) := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem mapIdx_set {l : Array α} {i : Nat} {h : i < l.size} {a : α} :
+    (l.set i a).mapIdx f = (l.mapIdx f).set i (f i a) (by simpa) := by
+  rcases l with ⟨l⟩
   simp [List.mapIdx_set]
 
-@[simp] theorem mapIdx_setIfInBounds {xs : Array α} {i : Nat} {a : α} :
-    (xs.setIfInBounds i a).mapIdx f = (xs.mapIdx f).setIfInBounds i (f i a) := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem mapIdx_setIfInBounds {l : Array α} {i : Nat} {a : α} :
+    (l.setIfInBounds i a).mapIdx f = (l.mapIdx f).setIfInBounds i (f i a) := by
+  rcases l with ⟨l⟩
   simp [List.mapIdx_set]
 
-@[simp] theorem back?_mapIdx {xs : Array α} {f : Nat → α → β} :
-    (mapIdx f xs).back? = (xs.back?).map (f (xs.size - 1)) := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem back?_mapIdx {l : Array α} {f : Nat → α → β} :
+    (mapIdx f l).back? = (l.back?).map (f (l.size - 1)) := by
+  rcases l with ⟨l⟩
   simp [List.getLast?_mapIdx]
 
-@[simp] theorem back_mapIdx {xs : Array α} {f : Nat → α → β} (h) :
-    (xs.mapIdx f).back h = f (xs.size - 1) (xs.back (by simpa using h)) := by
-  rcases xs with ⟨xs⟩
-  simp [List.getLast_mapIdx]
-
-@[simp] theorem mapIdx_mapIdx {xs : Array α} {f : Nat → α → β} {g : Nat → β → γ} :
-    (xs.mapIdx f).mapIdx g = xs.mapIdx (fun i => g i ∘ f i) := by
+@[simp] theorem mapIdx_mapIdx {l : Array α} {f : Nat → α → β} {g : Nat → β → γ} :
+    (l.mapIdx f).mapIdx g = l.mapIdx (fun i => g i ∘ f i) := by
   simp [mapIdx_eq_iff]
 
-theorem mapIdx_eq_replicate_iff {xs : Array α} {f : Nat → α → β} {b : β} :
-    mapIdx f xs = replicate xs.size b ↔ ∀ (i : Nat) (h : i < xs.size), f i xs[i] = b := by
-  rcases xs with ⟨xs⟩
+theorem mapIdx_eq_mkArray_iff {l : Array α} {f : Nat → α → β} {b : β} :
+    mapIdx f l = mkArray l.size b ↔ ∀ (i : Nat) (h : i < l.size), f i l[i] = b := by
+  rcases l with ⟨l⟩
   rw [← toList_inj]
   simp [List.mapIdx_eq_replicate_iff]
 
-@[deprecated mapIdx_eq_replicate_iff (since := "2025-03-18")]
-abbrev mapIdx_eq_mkArray_iff := @mapIdx_eq_replicate_iff
-
-@[simp] theorem mapIdx_reverse {xs : Array α} {f : Nat → α → β} :
-    xs.reverse.mapIdx f = (mapIdx (fun i => f (xs.size - 1 - i)) xs).reverse := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem mapIdx_reverse {l : Array α} {f : Nat → α → β} :
+    l.reverse.mapIdx f = (mapIdx (fun i => f (l.size - 1 - i)) l).reverse := by
+  rcases l with ⟨l⟩
   simp [List.mapIdx_reverse]
 
 end Array
 
 namespace List
 
-theorem mapFinIdxM_toArray [Monad m] [LawfulMonad m] {l : List α}
-    {f : (i : Nat) → α → (h : i < l.length) → m β} :
+theorem mapFinIdxM_toArray [Monad m] [LawfulMonad m] (l : List α)
+    (f : (i : Nat) → α → (h : i < l.length) → m β) :
     l.toArray.mapFinIdxM f = toArray <$> l.mapFinIdxM f := by
   let rec go (i : Nat) (acc : Array β) (inv : i + acc.size = l.length) :
       Array.mapFinIdxM.map l.toArray f i acc.size inv acc
@@ -464,17 +449,17 @@ theorem mapFinIdxM_toArray [Monad m] [LawfulMonad m] {l : List α}
       rw [Nat.zero_add] at inv
       simp only [Array.mapFinIdxM.map, inv, drop_length, mapFinIdxM.go, map_pure]
     | k + 1 =>
-      conv => enter [2, 2, 3]; rw [← getElem_cons_drop (by omega)]
+      conv => enter [2, 2, 3]; rw [← getElem_cons_drop l acc.size (by omega)]
       simp only [Array.mapFinIdxM.map, mapFinIdxM.go, _root_.map_bind]
       congr; funext x
-      conv => enter [1, 4]; rw [← Array.size_push x]
-      conv => enter [2, 2, 3]; rw [← Array.size_push x]
+      conv => enter [1, 4]; rw [← Array.size_push _ x]
+      conv => enter [2, 2, 3]; rw [← Array.size_push _ x]
       refine go k (acc.push x) _
   simp only [Array.mapFinIdxM, mapFinIdxM]
   exact go _ #[] _
 
-theorem mapIdxM_toArray [Monad m] [LawfulMonad m] {l : List α}
-    {f : Nat → α → m β} :
+theorem mapIdxM_toArray [Monad m] [LawfulMonad m] (l : List α)
+    (f : Nat → α → m β) :
     l.toArray.mapIdxM f = toArray <$> l.mapIdxM f := by
   let rec go (bs : List α) (acc : Array β) (inv : bs.length + acc.size = l.length) :
       mapFinIdxM.go l (fun i a h => f i a) bs acc inv = mapIdxM.go f bs acc := by
@@ -490,15 +475,15 @@ end List
 
 namespace Array
 
-theorem toList_mapFinIdxM [Monad m] [LawfulMonad m] {xs : Array α}
-    {f : (i : Nat) → α → (h : i < xs.size) → m β} :
-    toList <$> xs.mapFinIdxM f = xs.toList.mapFinIdxM f := by
+theorem toList_mapFinIdxM [Monad m] [LawfulMonad m] (l : Array α)
+    (f : (i : Nat) → α → (h : i < l.size) → m β) :
+    toList <$> l.mapFinIdxM f = l.toList.mapFinIdxM f := by
   rw [List.mapFinIdxM_toArray]
   simp only [Functor.map_map, id_map']
 
-theorem toList_mapIdxM [Monad m] [LawfulMonad m] {xs : Array α}
-    {f : Nat → α → m β} :
-    toList <$> xs.mapIdxM f = xs.toList.mapIdxM f := by
+theorem toList_mapIdxM [Monad m] [LawfulMonad m] (l : Array α)
+    (f : Nat → α → m β) :
+    toList <$> l.mapIdxM f = l.toList.mapIdxM f := by
   rw [List.mapIdxM_toArray]
   simp only [Functor.map_map, id_map']
 

src/Init/Data/Array/Mem.lean

@@ -8,18 +8,15 @@ import Init.Data.Array.Basic
 import Init.Data.Nat.Linear
 import Init.Data.List.BasicAux
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 namespace Array
 
 theorem sizeOf_lt_of_mem [SizeOf α] {as : Array α} (h : a ∈ as) : sizeOf a < sizeOf as := by
   cases as with | _ as =>
-  exact Nat.lt_trans (List.sizeOf_lt_of_mem h.val) (by simp +arith)
+  exact Nat.lt_trans (List.sizeOf_lt_of_mem h.val) (by simp_arith)
 
-theorem sizeOf_get [SizeOf α] (as : Array α) (i : Nat) (h : i < as.size) : sizeOf as[i] < sizeOf as := by
+theorem sizeOf_get [SizeOf α] (as : Array α) (i : Nat) (h : i < as.size) : sizeOf (as.get i h) < sizeOf as := by
   cases as with | _ as =>
-  simpa using Nat.lt_trans (List.sizeOf_get _ ⟨i, h⟩) (by simp +arith)
+  simpa using Nat.lt_trans (List.sizeOf_get _ ⟨i, h⟩) (by simp_arith)
 
 @[simp] theorem sizeOf_getElem [SizeOf α] (as : Array α) (i : Nat) (h : i < as.size) :
   sizeOf (as[i]'h) < sizeOf as := sizeOf_get _ _ h
@@ -32,8 +29,8 @@ macro "array_get_dec" : tactic =>
     -- subsumed by simp
     -- | with_reducible apply sizeOf_get
     -- | with_reducible apply sizeOf_getElem
-    | (with_reducible apply Nat.lt_of_lt_of_le (sizeOf_get ..)); simp +arith
-    | (with_reducible apply Nat.lt_of_lt_of_le (sizeOf_getElem ..)); simp +arith
+    | (with_reducible apply Nat.lt_of_lt_of_le (sizeOf_get ..)); simp_arith
+    | (with_reducible apply Nat.lt_of_lt_of_le (sizeOf_getElem ..)); simp_arith
     )
 
 macro_rules | `(tactic| decreasing_trivial) => `(tactic| array_get_dec)
@@ -48,7 +45,7 @@ macro "array_mem_dec" : tactic =>
     | with_reducible
         apply Nat.lt_of_lt_of_le (Array.sizeOf_lt_of_mem ?h)
         case' h => assumption
-      simp +arith)
+      simp_arith)
 
 macro_rules | `(tactic| decreasing_trivial) => `(tactic| array_mem_dec)
 

src/Init/Data/Array/Monadic.lean

@@ -12,9 +12,6 @@ import Init.Data.List.Monadic
 # Lemmas about `Array.forIn'` and `Array.forIn`.
 -/
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 namespace Array
 
 open Nat
@@ -23,98 +20,90 @@ open Nat
 
 /-! ### mapM -/
 
-@[simp] theorem mapM_pure [Monad m] [LawfulMonad m] {xs : Array α} {f : α → β} :
-    xs.mapM (m := m) (pure <| f ·) = pure (xs.map f) := by
-  induction xs; simp_all
-
-@[simp] theorem mapM_id {xs : Array α} {f : α → Id β} : xs.mapM f = xs.map f :=
-  mapM_pure
-
-@[simp] theorem mapM_append [Monad m] [LawfulMonad m] {f : α → m β} {xs ys : Array α} :
-    (xs ++ ys).mapM f = (return (← xs.mapM f) ++ (← ys.mapM f)) := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
+@[simp] theorem mapM_append [Monad m] [LawfulMonad m] (f : α → m β) {l₁ l₂ : Array α} :
+    (l₁ ++ l₂).mapM f = (return (← l₁.mapM f) ++ (← l₂.mapM f)) := by
+  rcases l₁ with ⟨l₁⟩
+  rcases l₂ with ⟨l₂⟩
   simp
 
-theorem mapM_eq_foldlM_push [Monad m] [LawfulMonad m] {f : α → m β} {xs : Array α} :
-    mapM f xs = xs.foldlM (fun acc a => return (acc.push (← f a))) #[] := by
-  rcases xs with ⟨xs⟩
-  simp only [List.mapM_toArray, bind_pure_comp, List.size_toArray, List.foldlM_toArray']
+theorem mapM_eq_foldlM_push [Monad m] [LawfulMonad m] (f : α → m β) (l : Array α) :
+    mapM f l = l.foldlM (fun acc a => return (acc.push (← f a))) #[] := by
+  rcases l with ⟨l⟩
+  simp only [List.mapM_toArray, bind_pure_comp, size_toArray, List.foldlM_toArray']
   rw [List.mapM_eq_reverse_foldlM_cons]
   simp only [bind_pure_comp, Functor.map_map]
-  suffices ∀ (l), (fun l' => l'.reverse.toArray) <$> List.foldlM (fun acc a => (fun a => a :: acc) <$> f a) l xs =
-      List.foldlM (fun acc a => acc.push <$> f a) l.reverse.toArray xs by
+  suffices ∀ (k), (fun a => a.reverse.toArray) <$> List.foldlM (fun acc a => (fun a => a :: acc) <$> f a) k l =
+      List.foldlM (fun acc a => acc.push <$> f a) k.reverse.toArray l by
     exact this []
-  intro l
-  induction xs generalizing l with
+  intro k
+  induction l generalizing k with
   | nil => simp
   | cons a as ih =>
     simp [ih, List.foldlM_cons]
 
 /-! ### foldlM and foldrM -/
 
-theorem foldlM_map [Monad m] {f : β₁ → β₂} {g : α → β₂ → m α} {xs : Array β₁} {init : α} {w : stop = xs.size} :
-    (xs.map f).foldlM g init 0 stop = xs.foldlM (fun x y => g x (f y)) init 0 stop := by
+theorem foldlM_map [Monad m] (f : β₁ → β₂) (g : α → β₂ → m α) (l : Array β₁) (init : α) (w : stop = l.size) :
+    (l.map f).foldlM g init 0 stop = l.foldlM (fun x y => g x (f y)) init 0 stop := by
   subst w
-  cases xs
+  cases l
   simp [List.foldlM_map]
 
-theorem foldrM_map [Monad m] [LawfulMonad m] {f : β₁ → β₂} {g : β₂ → α → m α} {xs : Array β₁}
-    {init : α} {w : start = xs.size} :
-    (xs.map f).foldrM g init start 0 = xs.foldrM (fun x y => g (f x) y) init start 0 := by
+theorem foldrM_map [Monad m] [LawfulMonad m] (f : β₁ → β₂) (g : β₂ → α → m α) (l : Array β₁)
+    (init : α) (w : start = l.size) :
+    (l.map f).foldrM g init start 0 = l.foldrM (fun x y => g (f x) y) init start 0 := by
   subst w
-  cases xs
+  cases l
   simp [List.foldrM_map]
 
-theorem foldlM_filterMap [Monad m] [LawfulMonad m] {f : α → Option β} {g : γ → β → m γ} {xs : Array α}
-    {init : γ} {w : stop = (xs.filterMap f).size} :
-    (xs.filterMap f).foldlM g init 0 stop =
-      xs.foldlM (fun x y => match f y with | some b => g x b | none => pure x) init := by
+theorem foldlM_filterMap [Monad m] [LawfulMonad m] (f : α → Option β) (g : γ → β → m γ)
+    (l : Array α) (init : γ) (w : stop = (l.filterMap f).size) :
+    (l.filterMap f).foldlM g init 0 stop =
+      l.foldlM (fun x y => match f y with | some b => g x b | none => pure x) init := by
   subst w
-  cases xs
+  cases l
   simp [List.foldlM_filterMap]
   rfl
 
-theorem foldrM_filterMap [Monad m] [LawfulMonad m] {f : α → Option β} {g : β → γ → m γ} {xs : Array α}
-    {init : γ} {w : start = (xs.filterMap f).size} :
-    (xs.filterMap f).foldrM g init start 0 =
-      xs.foldrM (fun x y => match f x with | some b => g b y | none => pure y) init := by
+theorem foldrM_filterMap [Monad m] [LawfulMonad m] (f : α → Option β) (g : β → γ → m γ)
+    (l : Array α) (init : γ) (w : start = (l.filterMap f).size) :
+    (l.filterMap f).foldrM g init start 0 =
+      l.foldrM (fun x y => match f x with | some b => g b y | none => pure y) init := by
   subst w
-  cases xs
+  cases l
   simp [List.foldrM_filterMap]
   rfl
 
-theorem foldlM_filter [Monad m] [LawfulMonad m] {p : α → Bool} {g : β → α → m β} {xs : Array α}
-    {init : β} {w : stop = (xs.filter p).size} :
-    (xs.filter p).foldlM g init 0 stop =
-      xs.foldlM (fun x y => if p y then g x y else pure x) init := by
+theorem foldlM_filter [Monad m] [LawfulMonad m] (p : α → Bool) (g : β → α → m β)
+    (l : Array α) (init : β) (w : stop = (l.filter p).size) :
+    (l.filter p).foldlM g init 0 stop =
+      l.foldlM (fun x y => if p y then g x y else pure x) init := by
   subst w
-  cases xs
+  cases l
   simp [List.foldlM_filter]
 
-theorem foldrM_filter [Monad m] [LawfulMonad m] {p : α → Bool} {g : α → β → m β} {xs : Array α}
-    {init : β} {w : start = (xs.filter p).size} :
-    (xs.filter p).foldrM g init start 0 =
-      xs.foldrM (fun x y => if p x then g x y else pure y) init := by
+theorem foldrM_filter [Monad m] [LawfulMonad m] (p : α → Bool) (g : α → β → m β)
+    (l : Array α) (init : β) (w : start = (l.filter p).size) :
+    (l.filter p).foldrM g init start 0 =
+      l.foldrM (fun x y => if p x then g x y else pure y) init := by
   subst w
-  cases xs
+  cases l
   simp [List.foldrM_filter]
 
 @[simp] theorem foldlM_attachWith [Monad m]
-    {xs : Array α} {q : α → Prop} (H : ∀ a, a ∈ xs → q a) {f : β → { x // q x} → m β} {b} (w : stop = xs.size):
-    (xs.attachWith q H).foldlM f b 0 stop =
-      xs.attach.foldlM (fun b ⟨a, h⟩ => f b ⟨a, H _ h⟩) b := by
+    (l : Array α) {q : α → Prop} (H : ∀ a, a ∈ l → q a) {f : β → { x // q x} → m β} {b} (w : stop = l.size):
+    (l.attachWith q H).foldlM f b 0 stop =
+      l.attach.foldlM (fun b ⟨a, h⟩ => f b ⟨a, H _ h⟩) b := by
   subst w
-  rcases xs with ⟨xs⟩
+  rcases l with ⟨l⟩
   simp [List.foldlM_map]
 
 @[simp] theorem foldrM_attachWith [Monad m] [LawfulMonad m]
-    {xs : Array α} {q : α → Prop} (H : ∀ a, a ∈ xs → q a) {f : { x // q x} → β → m β} {b}
-    {w : start = xs.size} :
-    (xs.attachWith q H).foldrM f b start 0 =
-      xs.attach.foldrM (fun a acc => f ⟨a.1, H _ a.2⟩ acc) b := by
+    (l : Array α) {q : α → Prop} (H : ∀ a, a ∈ l → q a) {f : { x // q x} → β → m β} {b} (w : start = l.size):
+    (l.attachWith q H).foldrM f b start 0 =
+      l.attach.foldrM (fun a acc => f ⟨a.1, H _ a.2⟩ acc) b := by
   subst w
-  rcases xs with ⟨xs⟩
+  rcases l with ⟨l⟩
   simp [List.foldrM_map]
 
 /-! ### forM -/
@@ -125,15 +114,15 @@ theorem foldrM_filter [Monad m] [LawfulMonad m] {p : α → Bool} {g : α → β
   cases as <;> cases bs
   simp_all
 
-@[simp] theorem forM_append [Monad m] [LawfulMonad m] {xs ys : Array α} {f : α → m PUnit} :
-    forM (xs ++ ys) f = (do forM xs f; forM ys f) := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
+@[simp] theorem forM_append [Monad m] [LawfulMonad m] (l₁ l₂ : Array α) (f : α → m PUnit) :
+    forM (l₁ ++ l₂) f = (do forM l₁ f; forM l₂ f) := by
+  rcases l₁ with ⟨l₁⟩
+  rcases l₂ with ⟨l₂⟩
   simp
 
-@[simp] theorem forM_map [Monad m] [LawfulMonad m] {xs : Array α} {g : α → β} {f : β → m PUnit} :
-    forM (xs.map g) f = forM xs (fun a => f (g a)) := by
-  rcases xs with ⟨xs⟩
+@[simp] theorem forM_map [Monad m] [LawfulMonad m] (l : Array α) (g : α → β) (f : β → m PUnit) :
+    forM (l.map g) f = forM l (fun a => f (g a)) := by
+  cases l
   simp
 
 /-! ### forIn' -/
@@ -153,41 +142,41 @@ We can express a for loop over an array as a fold,
 in which whenever we reach `.done b` we keep that value through the rest of the fold.
 -/
 theorem forIn'_eq_foldlM [Monad m] [LawfulMonad m]
-    {xs : Array α} (f : (a : α) → a ∈ xs → β → m (ForInStep β)) (init : β) :
-    forIn' xs init f = ForInStep.value <$>
-      xs.attach.foldlM (fun b ⟨a, m⟩ => match b with
+    (l : Array α) (f : (a : α) → a ∈ l → β → m (ForInStep β)) (init : β) :
+    forIn' l init f = ForInStep.value <$>
+      l.attach.foldlM (fun b ⟨a, m⟩ => match b with
         | .yield b => f a m b
         | .done b => pure (.done b)) (ForInStep.yield init) := by
-  rcases xs with ⟨xs⟩
+  cases l
   simp [List.forIn'_eq_foldlM, List.foldlM_map]
   congr
 
 /-- We can express a for loop over an array which always yields as a fold. -/
 @[simp] theorem forIn'_yield_eq_foldlM [Monad m] [LawfulMonad m]
-    {xs : Array α} (f : (a : α) → a ∈ xs → β → m γ) (g : (a : α) → a ∈ xs → β → γ → β) (init : β) :
-    forIn' xs init (fun a m b => (fun c => .yield (g a m b c)) <$> f a m b) =
-      xs.attach.foldlM (fun b ⟨a, m⟩ => g a m b <$> f a m b) init := by
-  rcases xs with ⟨xs⟩
+    (l : Array α) (f : (a : α) → a ∈ l → β → m γ) (g : (a : α) → a ∈ l → β → γ → β) (init : β) :
+    forIn' l init (fun a m b => (fun c => .yield (g a m b c)) <$> f a m b) =
+      l.attach.foldlM (fun b ⟨a, m⟩ => g a m b <$> f a m b) init := by
+  cases l
   simp [List.foldlM_map]
 
-@[simp] theorem forIn'_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
-    {xs : Array α} (f : (a : α) → a ∈ xs → β → β) (init : β) :
-    forIn' xs init (fun a m b => pure (.yield (f a m b))) =
-      pure (f := m) (xs.attach.foldl (fun b ⟨a, h⟩ => f a h b) init) := by
-  rcases xs with ⟨xs⟩
+theorem forIn'_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
+    (l : Array α) (f : (a : α) → a ∈ l → β → β) (init : β) :
+    forIn' l init (fun a m b => pure (.yield (f a m b))) =
+      pure (f := m) (l.attach.foldl (fun b ⟨a, h⟩ => f a h b) init) := by
+  cases l
   simp [List.forIn'_pure_yield_eq_foldl, List.foldl_map]
 
 @[simp] theorem forIn'_yield_eq_foldl
-    {xs : Array α} (f : (a : α) → a ∈ xs → β → β) (init : β) :
-    forIn' (m := Id) xs init (fun a m b => .yield (f a m b)) =
-      xs.attach.foldl (fun b ⟨a, h⟩ => f a h b) init := by
-  rcases xs with ⟨xs⟩
+    (l : Array α) (f : (a : α) → a ∈ l → β → β) (init : β) :
+    forIn' (m := Id) l init (fun a m b => .yield (f a m b)) =
+      l.attach.foldl (fun b ⟨a, h⟩ => f a h b) init := by
+  cases l
   simp [List.foldl_map]
 
 @[simp] theorem forIn'_map [Monad m] [LawfulMonad m]
-    {xs : Array α} (g : α → β) (f : (b : β) → b ∈ xs.map g → γ → m (ForInStep γ)) :
-    forIn' (xs.map g) init f = forIn' xs init fun a h y => f (g a) (mem_map_of_mem h) y := by
-  rcases xs with ⟨xs⟩
+    (l : Array α) (g : α → β) (f : (b : β) → b ∈ l.map g → γ → m (ForInStep γ)) :
+    forIn' (l.map g) init f = forIn' l init fun a h y => f (g a) (mem_map_of_mem g h) y := by
+  cases l
   simp
 
 /--
@@ -195,74 +184,48 @@ We can express a for loop over an array as a fold,
 in which whenever we reach `.done b` we keep that value through the rest of the fold.
 -/
 theorem forIn_eq_foldlM [Monad m] [LawfulMonad m]
-    {xs : Array α} (f : α → β → m (ForInStep β)) (init : β) :
-    forIn xs init f = ForInStep.value <$>
-      xs.foldlM (fun b a => match b with
+    (f : α → β → m (ForInStep β)) (init : β) (l : Array α) :
+    forIn l init f = ForInStep.value <$>
+      l.foldlM (fun b a => match b with
         | .yield b => f a b
         | .done b => pure (.done b)) (ForInStep.yield init) := by
-  rcases xs with ⟨xs⟩
-  simp only [List.forIn_toArray, List.forIn_eq_foldlM, List.size_toArray, List.foldlM_toArray']
+  cases l
+  simp only [List.forIn_toArray, List.forIn_eq_foldlM, size_toArray, List.foldlM_toArray']
   congr
 
 /-- We can express a for loop over an array which always yields as a fold. -/
 @[simp] theorem forIn_yield_eq_foldlM [Monad m] [LawfulMonad m]
-    {xs : Array α} (f : α → β → m γ) (g : α → β → γ → β) (init : β) :
-    forIn xs init (fun a b => (fun c => .yield (g a b c)) <$> f a b) =
-      xs.foldlM (fun b a => g a b <$> f a b) init := by
-  rcases xs with ⟨xs⟩
+    (l : Array α) (f : α → β → m γ) (g : α → β → γ → β) (init : β) :
+    forIn l init (fun a b => (fun c => .yield (g a b c)) <$> f a b) =
+      l.foldlM (fun b a => g a b <$> f a b) init := by
+  cases l
   simp [List.foldlM_map]
 
-@[simp] theorem forIn_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
-    {xs : Array α} (f : α → β → β) (init : β) :
-    forIn xs init (fun a b => pure (.yield (f a b))) =
-      pure (f := m) (xs.foldl (fun b a => f a b) init) := by
-  rcases xs with ⟨xs⟩
+theorem forIn_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
+    (l : Array α) (f : α → β → β) (init : β) :
+    forIn l init (fun a b => pure (.yield (f a b))) =
+      pure (f := m) (l.foldl (fun b a => f a b) init) := by
+  cases l
   simp [List.forIn_pure_yield_eq_foldl, List.foldl_map]
 
 @[simp] theorem forIn_yield_eq_foldl
-    {xs : Array α} (f : α → β → β) (init : β) :
-    forIn (m := Id) xs init (fun a b => .yield (f a b)) =
-      xs.foldl (fun b a => f a b) init := by
-  rcases xs with ⟨xs⟩
+    (l : Array α) (f : α → β → β) (init : β) :
+    forIn (m := Id) l init (fun a b => .yield (f a b)) =
+      l.foldl (fun b a => f a b) init := by
+  cases l
   simp [List.foldl_map]
 
 @[simp] theorem forIn_map [Monad m] [LawfulMonad m]
-    {xs : Array α} {g : α → β} {f : β → γ → m (ForInStep γ)} :
-    forIn (xs.map g) init f = forIn xs init fun a y => f (g a) y := by
-  rcases xs with ⟨xs⟩
-  simp
-
-/-! ### allM and anyM -/
-
-@[simp] theorem anyM_pure [Monad m] [LawfulMonad m] {p : α → Bool} {xs : Array α} :
-    xs.anyM (m := m) (pure <| p ·) = pure (xs.any p) := by
-  cases xs
-  simp
-
-@[simp] theorem allM_pure [Monad m] [LawfulMonad m] {p : α → Bool} {xs : Array α} :
-    xs.allM (m := m) (pure <| p ·) = pure (xs.all p) := by
-  cases xs
-  simp
-
-/-! ### findM? and findSomeM? -/
-
-@[simp]
-theorem findM?_pure {m} [Monad m] [LawfulMonad m] {p : α → Bool} {xs : Array α} :
-    findM? (m := m) (pure <| p ·) xs = pure (xs.find? p) := by
-  cases xs
-  simp
-
-@[simp]
-theorem findSomeM?_pure [Monad m] [LawfulMonad m] {f : α → Option β} {xs : Array α} :
-    findSomeM? (m := m) (pure <| f ·) xs = pure (xs.findSome? f) := by
-  cases xs
+    (l : Array α) (g : α → β) (f : β → γ → m (ForInStep γ)) :
+    forIn (l.map g) init f = forIn l init fun a y => f (g a) y := by
+  cases l
   simp
 
 end Array
 
 namespace List
 
-theorem filterM_toArray [Monad m] [LawfulMonad m] {l : List α} {p : α → m Bool} :
+theorem filterM_toArray [Monad m] [LawfulMonad m] (l : List α) (p : α → m Bool) :
     l.toArray.filterM p = toArray <$> l.filterM p := by
   simp only [Array.filterM, filterM, foldlM_toArray, bind_pure_comp, Functor.map_map]
   conv => lhs; rw [← reverse_nil]
@@ -277,24 +240,24 @@ theorem filterM_toArray [Monad m] [LawfulMonad m] {l : List α} {p : α → m Bo
       exact ih (x :: acc)
 
 /-- Variant of `filterM_toArray` with a side condition for the stop position. -/
-@[simp] theorem filterM_toArray' [Monad m] [LawfulMonad m] {l : List α} {p : α → m Bool} (w : stop = l.length) :
+@[simp] theorem filterM_toArray' [Monad m] [LawfulMonad m] (l : List α) (p : α → m Bool) (w : stop = l.length) :
     l.toArray.filterM p 0 stop = toArray <$> l.filterM p := by
   subst w
   rw [filterM_toArray]
 
-theorem filterRevM_toArray [Monad m] [LawfulMonad m] {l : List α} {p : α → m Bool} :
+theorem filterRevM_toArray [Monad m] [LawfulMonad m] (l : List α) (p : α → m Bool) :
     l.toArray.filterRevM p = toArray <$> l.filterRevM p := by
   simp [Array.filterRevM, filterRevM]
   rw [← foldlM_reverse, ← foldlM_toArray, ← Array.filterM, filterM_toArray]
   simp only [filterM, bind_pure_comp, Functor.map_map, reverse_toArray, reverse_reverse]
 
 /-- Variant of `filterRevM_toArray` with a side condition for the start position. -/
-@[simp] theorem filterRevM_toArray' [Monad m] [LawfulMonad m] {l : List α} {p : α → m Bool} (w : start = l.length) :
+@[simp] theorem filterRevM_toArray' [Monad m] [LawfulMonad m] (l : List α) (p : α → m Bool) (w : start = l.length) :
     l.toArray.filterRevM p start 0 = toArray <$> l.filterRevM p := by
   subst w
   rw [filterRevM_toArray]
 
-theorem filterMapM_toArray [Monad m] [LawfulMonad m] {l : List α} {f : α → m (Option β)} :
+theorem filterMapM_toArray [Monad m] [LawfulMonad m] (l : List α) (f : α → m (Option β)) :
     l.toArray.filterMapM f = toArray <$> l.filterMapM f := by
   simp [Array.filterMapM, filterMapM]
   conv => lhs; rw [← reverse_nil]
@@ -307,12 +270,12 @@ theorem filterMapM_toArray [Monad m] [LawfulMonad m] {l : List α} {f : α → m
     · simp only [pure_bind]; rw [← List.reverse_cons]; exact ih _
 
 /-- Variant of `filterMapM_toArray` with a side condition for the stop position. -/
-@[simp] theorem filterMapM_toArray' [Monad m] [LawfulMonad m] {l : List α} {f : α → m (Option β)} (w : stop = l.length) :
+@[simp] theorem filterMapM_toArray' [Monad m] [LawfulMonad m] (l : List α) (f : α → m (Option β)) (w : stop = l.length) :
     l.toArray.filterMapM f 0 stop = toArray <$> l.filterMapM f := by
   subst w
   rw [filterMapM_toArray]
 
-@[simp] theorem flatMapM_toArray [Monad m] [LawfulMonad m] {l : List α} {f : α → m (Array β)} :
+@[simp] theorem flatMapM_toArray [Monad m] [LawfulMonad m] (l : List α) (f : α → m (Array β)) :
     l.toArray.flatMapM f = toArray <$> l.flatMapM (fun a => Array.toList <$> f a) := by
   simp only [Array.flatMapM, bind_pure_comp, foldlM_toArray, flatMapM]
   conv => lhs; arg 2; change [].reverse.flatten.toArray
@@ -321,7 +284,7 @@ theorem filterMapM_toArray [Monad m] [LawfulMonad m] {l : List α} {f : α → m
   | nil => simp only [foldlM_nil, flatMapM.loop, map_pure]
   | cons x xs ih =>
     simp only [foldlM_cons, bind_map_left, flatMapM.loop, _root_.map_bind]
-    congr; funext xs
+    congr; funext a
     conv => lhs; rw [Array.toArray_append, ← flatten_concat, ← reverse_cons]
     exact ih _
 
@@ -353,23 +316,23 @@ namespace Array
   subst w
   simp [flatMapM, h]
 
-theorem toList_filterM [Monad m] [LawfulMonad m] {xs : Array α} {p : α → m Bool} :
-    toList <$> xs.filterM p = xs.toList.filterM p := by
+theorem toList_filterM [Monad m] [LawfulMonad m] (a : Array α) (p : α → m Bool) :
+    toList <$> a.filterM p = a.toList.filterM p := by
   rw [List.filterM_toArray]
   simp only [Functor.map_map, id_map']
 
-theorem toList_filterRevM [Monad m] [LawfulMonad m] {xs : Array α} {p : α → m Bool} :
-    toList <$> xs.filterRevM p = xs.toList.filterRevM p := by
+theorem toList_filterRevM [Monad m] [LawfulMonad m] (a : Array α) (p : α → m Bool) :
+    toList <$> a.filterRevM p = a.toList.filterRevM p := by
   rw [List.filterRevM_toArray]
   simp only [Functor.map_map, id_map']
 
-theorem toList_filterMapM [Monad m] [LawfulMonad m] {xs : Array α} {f : α → m (Option β)} :
-    toList <$> xs.filterMapM f = xs.toList.filterMapM f := by
+theorem toList_filterMapM [Monad m] [LawfulMonad m] (a : Array α) (f : α → m (Option β)) :
+    toList <$> a.filterMapM f = a.toList.filterMapM f := by
   rw [List.filterMapM_toArray]
   simp only [Functor.map_map, id_map']
 
-theorem toList_flatMapM [Monad m] [LawfulMonad m] {xs : Array α} {f : α → m (Array β)} :
-    toList <$> xs.flatMapM f = xs.toList.flatMapM (fun a => toList <$> f a) := by
+theorem toList_flatMapM [Monad m] [LawfulMonad m] (a : Array α) (f : α → m (Array β)) :
+    toList <$> a.flatMapM f = a.toList.flatMapM (fun a => toList <$> f a) := by
   rw [List.flatMapM_toArray]
   simp only [Functor.map_map, id_map']
 
@@ -379,106 +342,53 @@ theorem toList_flatMapM [Monad m] [LawfulMonad m] {xs : Array α} {f : α → m
 This lemma identifies monadic folds over lists of subtypes, where the function only depends on the value, not the proposition,
 and simplifies these to the function directly taking the value.
 -/
-@[simp] theorem foldlM_subtype [Monad m] {p : α → Prop} {xs : Array { x // p x }}
+@[simp] theorem foldlM_subtype [Monad m] {p : α → Prop} {l : Array { x // p x }}
     {f : β → { x // p x } → m β} {g : β → α → m β} {x : β}
-    (hf : ∀ b x h, f b ⟨x, h⟩ = g b x) (w : stop = xs.size) :
-    xs.foldlM f x 0 stop = xs.unattach.foldlM g x 0 stop := by
+    (hf : ∀ b x h, f b ⟨x, h⟩ = g b x) (w : stop = l.size) :
+    l.foldlM f x 0 stop = l.unattach.foldlM g x 0 stop := by
   subst w
-  rcases xs with ⟨l⟩
+  rcases l with ⟨l⟩
   simp
   rw [List.foldlM_subtype hf]
 
-@[wf_preprocess] theorem foldlM_wfParam [Monad m] {xs : Array α} {f : β → α → m β} {init : β} :
-    (wfParam xs).foldlM f init = xs.attach.unattach.foldlM f init := by
-  simp [wfParam]
-
-@[wf_preprocess] theorem foldlM_unattach [Monad m] {P : α → Prop} {xs : Array (Subtype P)} {f : β → α → m β} {init : β} :
-    xs.unattach.foldlM f init = xs.foldlM (init := init) fun b ⟨x, h⟩ =>
-      binderNameHint b f <| binderNameHint x (f b) <| binderNameHint h () <|
-      f b (wfParam x) := by
-  simp [wfParam]
-
 /--
 This lemma identifies monadic folds over lists of subtypes, where the function only depends on the value, not the proposition,
 and simplifies these to the function directly taking the value.
 -/
-@[simp] theorem foldrM_subtype [Monad m] [LawfulMonad m] {p : α → Prop} {xs : Array { x // p x }}
+@[simp] theorem foldrM_subtype [Monad m] [LawfulMonad m] {p : α → Prop} {l : Array { x // p x }}
     {f : { x // p x } → β → m β} {g : α → β → m β} {x : β}
-    (hf : ∀ x h b, f ⟨x, h⟩ b = g x b) (w : start = xs.size) :
-    xs.foldrM f x start 0 = xs.unattach.foldrM g x start 0:= by
+    (hf : ∀ x h b, f ⟨x, h⟩ b = g x b) (w : start = l.size) :
+    l.foldrM f x start 0 = l.unattach.foldrM g x start 0:= by
   subst w
-  rcases xs with ⟨xs⟩
+  rcases l with ⟨l⟩
   simp
   rw [List.foldrM_subtype hf]
 
-
-@[wf_preprocess] theorem foldrM_wfParam [Monad m] [LawfulMonad m] {xs : Array α} {f : α → β → m β} {init : β} :
-    (wfParam xs).foldrM f init = xs.attach.unattach.foldrM f init := by
-  simp [wfParam]
-
-@[wf_preprocess] theorem foldrM_unattach [Monad m] [LawfulMonad m] {P : α → Prop} {xs : Array (Subtype P)} {f : α → β → m β} {init : β} :
-    xs.unattach.foldrM f init = xs.foldrM (init := init) fun ⟨x, h⟩ b =>
-      binderNameHint x f <| binderNameHint h () <| binderNameHint b (f x) <|
-      f (wfParam x) b := by
-  simp [wfParam]
-
 /--
 This lemma identifies monadic maps over lists of subtypes, where the function only depends on the value, not the proposition,
 and simplifies these to the function directly taking the value.
 -/
-@[simp] theorem mapM_subtype [Monad m] [LawfulMonad m] {p : α → Prop} {xs : Array { x // p x }}
+@[simp] theorem mapM_subtype [Monad m] [LawfulMonad m] {p : α → Prop} {l : Array { x // p x }}
     {f : { x // p x } → m β} {g : α → m β} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
-    xs.mapM f = xs.unattach.mapM g := by
-  rcases xs with ⟨xs⟩
+    l.mapM f = l.unattach.mapM g := by
+  rcases l with ⟨l⟩
   simp
   rw [List.mapM_subtype hf]
 
-@[wf_preprocess] theorem mapM_wfParam [Monad m] [LawfulMonad m] {xs : Array α} {f : α → m β} :
-    (wfParam xs).mapM f = xs.attach.unattach.mapM f := by
-  simp [wfParam]
-
-@[wf_preprocess] theorem mapM_unattach [Monad m] [LawfulMonad m] {P : α → Prop} {xs : Array (Subtype P)} {f : α → m β} :
-    xs.unattach.mapM f = xs.mapM fun ⟨x, h⟩ =>
-      binderNameHint x f <| binderNameHint h () <| f (wfParam x) := by
-  simp [wfParam]
-
-@[simp] theorem filterMapM_subtype [Monad m] [LawfulMonad m] {p : α → Prop} {xs : Array { x // p x }}
-    {f : { x // p x } → m (Option β)} {g : α → m (Option β)} (hf : ∀ x h, f ⟨x, h⟩ = g x) (w : stop = xs.size) :
-    xs.filterMapM f 0 stop = xs.unattach.filterMapM g := by
+@[simp] theorem filterMapM_subtype [Monad m] [LawfulMonad m] {p : α → Prop} {l : Array { x // p x }}
+    {f : { x // p x } → m (Option β)} {g : α → m (Option β)} (hf : ∀ x h, f ⟨x, h⟩ = g x) (w : stop = l.size) :
+    l.filterMapM f 0 stop = l.unattach.filterMapM g := by
   subst w
-  rcases xs with ⟨xs⟩
+  rcases l with ⟨l⟩
   simp
   rw [List.filterMapM_subtype hf]
 
-
-@[wf_preprocess] theorem filterMapM_wfParam [Monad m] [LawfulMonad m]
-    {xs : Array α} {f : α → m (Option β)} :
-    (wfParam xs).filterMapM f = xs.attach.unattach.filterMapM f := by
-  simp [wfParam]
-
-@[wf_preprocess] theorem filterMapM_unattach [Monad m] [LawfulMonad m]
-    {P : α → Prop} {xs : Array (Subtype P)} {f : α → m (Option β)} :
-    xs.unattach.filterMapM f = xs.filterMapM fun ⟨x, h⟩ =>
-      binderNameHint x f <| binderNameHint h () <| f (wfParam x) := by
-  simp [wfParam]
-
-@[simp] theorem flatMapM_subtype [Monad m] [LawfulMonad m] {p : α → Prop} {xs : Array { x // p x }}
+@[simp] theorem flatMapM_subtype [Monad m] [LawfulMonad m] {p : α → Prop} {l : Array { x // p x }}
     {f : { x // p x } → m (Array β)} {g : α → m (Array β)} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
-    (xs.flatMapM f) = xs.unattach.flatMapM g := by
-  rcases xs with ⟨xs⟩
+    (l.flatMapM f) = l.unattach.flatMapM g := by
+  rcases l with ⟨l⟩
   simp
   rw [List.flatMapM_subtype]
   simp [hf]
 
-@[wf_preprocess] theorem flatMapM_wfParam [Monad m] [LawfulMonad m]
-    {xs : Array α} {f : α → m (Array β)} :
-    (wfParam xs).flatMapM f = xs.attach.unattach.flatMapM f := by
-  simp [wfParam]
-
-@[wf_preprocess] theorem flatMapM_unattach [Monad m] [LawfulMonad m]
-    {P : α → Prop} {xs : Array (Subtype P)} {f : α → m (Array β)} :
-    xs.unattach.flatMapM f = xs.flatMapM fun ⟨x, h⟩ =>
-      binderNameHint x f <| binderNameHint h () <| f (wfParam x) := by
-  simp [wfParam]
-
 end Array

src/Init/Data/Array/OfFn.lean

@@ -11,38 +11,15 @@ import Init.Data.List.OfFn
 # Theorems about `Array.ofFn`
 -/
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 namespace Array
 
-@[simp] theorem ofFn_zero {f : Fin 0 → α} : ofFn f = #[] := by
-  simp [ofFn, ofFn.go]
-
-theorem ofFn_succ {f : Fin (n+1) → α} :
-    ofFn f = (ofFn (fun (i : Fin n) => f i.castSucc)).push (f ⟨n, by omega⟩) := by
-  ext i h₁ h₂
-  · simp
-  · simp [getElem_push]
-    split <;> rename_i h₃
-    · rfl
-    · congr
-      simp at h₁ h₂
-      omega
-
-@[simp] theorem _root_.List.toArray_ofFn {f : Fin n → α} : (List.ofFn f).toArray = Array.ofFn f := by
-  ext <;> simp
-
-@[simp] theorem toList_ofFn {f : Fin n → α} : (Array.ofFn f).toList = List.ofFn f := by
-  apply List.ext_getElem <;> simp
-
 @[simp]
 theorem ofFn_eq_empty_iff {f : Fin n → α} : ofFn f = #[] ↔ n = 0 := by
   rw [← Array.toList_inj]
   simp
 
 @[simp 500]
-theorem mem_ofFn {n} {f : Fin n → α} {a : α} : a ∈ ofFn f ↔ ∃ i, f i = a := by
+theorem mem_ofFn {n} (f : Fin n → α) (a : α) : a ∈ ofFn f ↔ ∃ i, f i = a := by
   constructor
   · intro w
     obtain ⟨i, h, rfl⟩ := getElem_of_mem w

src/Init/Data/Array/Perm.lean

@@ -7,9 +7,6 @@ prelude
 import Init.Data.List.Nat.Perm
 import Init.Data.Array.Lemmas
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 namespace Array
 
 open List
@@ -30,38 +27,38 @@ theorem perm_iff_toList_perm {as bs : Array α} : as ~ bs ↔ as.toList ~ bs.toL
 @[simp] theorem perm_toArray (as bs : List α) : as.toArray ~ bs.toArray ↔ as ~ bs := by
   simp [perm_iff_toList_perm]
 
-@[simp, refl] protected theorem Perm.refl (xs : Array α) : xs ~ xs := by
-  cases xs
+@[simp, refl] protected theorem Perm.refl (l : Array α) : l ~ l := by
+  cases l
   simp
 
-protected theorem Perm.rfl {xs : List α} : xs ~ xs := .refl _
+protected theorem Perm.rfl {l : List α} : l ~ l := .refl _
 
-theorem Perm.of_eq {xs ys : Array α} (h : xs = ys) : xs ~ ys := h ▸ .rfl
+theorem Perm.of_eq {l₁ l₂ : Array α} (h : l₁ = l₂) : l₁ ~ l₂ := h ▸ .rfl
 
-protected theorem Perm.symm {xs ys : Array α} (h : xs ~ ys) : ys ~ xs := by
-  cases xs; cases ys
+protected theorem Perm.symm {l₁ l₂ : Array α} (h : l₁ ~ l₂) : l₂ ~ l₁ := by
+  cases l₁; cases l₂
   simp only [perm_toArray] at h
   simpa using h.symm
 
-protected theorem Perm.trans {xs ys zs : Array α} (h₁ : xs ~ ys) (h₂ : ys ~ zs) : xs ~ zs := by
-  cases xs; cases ys; cases zs
+protected theorem Perm.trans {l₁ l₂ l₃ : Array α} (h₁ : l₁ ~ l₂) (h₂ : l₂ ~ l₃) : l₁ ~ l₃ := by
+  cases l₁; cases l₂; cases l₃
   simp only [perm_toArray] at h₁ h₂
   simpa using h₁.trans h₂
 
 instance : Trans (Perm (α := α)) (Perm (α := α)) (Perm (α := α)) where
   trans h₁ h₂ := Perm.trans h₁ h₂
 
-theorem perm_comm {xs ys : Array α} : xs ~ ys ↔ ys ~ xs := ⟨Perm.symm, Perm.symm⟩
+theorem perm_comm {l₁ l₂ : Array α} : l₁ ~ l₂ ↔ l₂ ~ l₁ := ⟨Perm.symm, Perm.symm⟩
 
-theorem Perm.push (x y : α) {xs ys : Array α} (p : xs ~ ys) :
-    (xs.push x).push y ~ (ys.push y).push x := by
-  cases xs; cases ys
+theorem Perm.push (x y : α) {l₁ l₂ : Array α} (p : l₁ ~ l₂) :
+    (l₁.push x).push y ~ (l₂.push y).push x := by
+  cases l₁; cases l₂
   simp only [perm_toArray] at p
   simp only [push_toArray, List.append_assoc, singleton_append, perm_toArray]
   exact p.append (Perm.swap' _ _ Perm.nil)
 
-theorem swap_perm {xs : Array α} {i j : Nat} (h₁ : i < xs.size) (h₂ : j < xs.size) :
-    xs.swap i j ~ xs := by
+theorem swap_perm {as : Array α} {i j : Nat} (h₁ : i < as.size) (h₂ : j < as.size) :
+    as.swap i j ~ as := by
   simp only [swap, perm_iff_toList_perm, toList_set]
   apply set_set_perm
 

src/Init/Data/Array/QSort.lean

@@ -7,9 +7,6 @@ prelude
 import Init.Data.Vector.Basic
 import Init.Data.Ord
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
--- We do not enable `linter.indexVariables` because it is helpful to name index variables `lo`, `mid`, `hi`, etc.
-
 namespace Array
 
 private def qpartition {n} (as : Vector α n) (lt : α → α → Bool) (lo hi : Nat)
@@ -30,16 +27,6 @@ private def qpartition {n} (as : Vector α n) (lt : α → α → Bool) (lo hi :
       (⟨i, ilo⟩, as.swap i hi)
   loop as lo lo
 
-/--
-Sorts an array using the Quicksort algorithm.
-
-The optional parameter `lt` specifies an ordering predicate. It defaults to `LT.lt`, which must be
-decidable to be used for sorting. Use `Array.qsortOrd` to sort the array according to the `Ord α`
-instance.
-
-The optional parameters `low` and `high` delimit the region of the array that is sorted. Both are
-inclusive, and default to sorting the entire array.
--/
 @[inline] def qsort (as : Array α) (lt : α → α → Bool := by exact (· < ·))
     (low := 0) (high := as.size - 1) : Array α :=
   let rec @[specialize] sort {n} (as : Vector α n) (lo hi : Nat)
@@ -60,7 +47,7 @@ inclusive, and default to sorting the entire array.
 
 set_option linter.unusedVariables.funArgs false in
 /--
-Sorts an array using the Quicksort algorithm, using `Ord.compare` to compare elements.
+Sort an array using `compare` to compare elements.
 -/
 def qsortOrd [ord : Ord α] (xs : Array α) : Array α :=
   xs.qsort fun x y => compare x y |>.isLT

src/Init/Data/Array/Range.lean

@@ -15,9 +15,6 @@ import Init.Data.List.Nat.Range
 
 -/
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 namespace Array
 
 open Nat
@@ -26,21 +23,20 @@ open Nat
 
 /-! ### range' -/
 
-theorem range'_succ {s n step} : range' s (n + 1) step = #[s] ++ range' (s + step) n step := by
+theorem range'_succ (s n step) : range' s (n + 1) step = #[s] ++ range' (s + step) n step := by
   rw [← toList_inj]
   simp [List.range'_succ]
 
 @[simp] theorem range'_eq_empty_iff : range' s n step = #[] ↔ n = 0 := by
-  rw [← size_eq_zero_iff, size_range']
+  rw [← size_eq_zero, size_range']
 
-theorem range'_ne_empty_iff : range' s n step ≠ #[] ↔ n ≠ 0 := by
+theorem range'_ne_empty_iff (s : Nat) {n step : Nat} : range' s n step ≠ #[] ↔ n ≠ 0 := by
   cases n <;> simp
 
 @[simp] theorem range'_zero : range' s 0 step = #[] := by
   simp
 
-@[simp] theorem range'_one {s step : Nat} : range' s 1 step = #[s] := by
-  simp [range', ofFn, ofFn.go]
+@[simp] theorem range'_one {s step : Nat} : range' s 1 step = #[s] := rfl
 
 @[simp] theorem range'_inj : range' s n = range' s' n' ↔ n = n' ∧ (n = 0 ∨ s = s') := by
   rw [← toList_inj]
@@ -57,13 +53,13 @@ theorem mem_range' {n} : m ∈ range' s n step ↔ ∃ i < n, m = s + step * i :
 theorem pop_range' : (range' s n step).pop = range' s (n - 1) step := by
   ext <;> simp
 
-theorem map_add_range' {a} (s n step) : map (a + ·) (range' s n step) = range' (a + s) n step := by
+theorem map_add_range' (a) (s n step) : map (a + ·) (range' s n step) = range' (a + s) n step := by
   ext <;> simp <;> omega
 
 theorem range'_succ_left : range' (s + 1) n step = (range' s n step).map (· + 1) := by
   ext <;> simp <;> omega
 
-theorem range'_append {s m n step : Nat} :
+theorem range'_append (s m n step : Nat) :
     range' s m step ++ range' (s + step * m) n step = range' s (m + n) step := by
   ext i h₁ h₂
   · simp
@@ -74,13 +70,13 @@ theorem range'_append {s m n step : Nat} :
     have : step * m ≤ step * i := by exact mul_le_mul_left step h
     omega
 
-@[simp] theorem range'_append_1 {s m n : Nat} :
-    range' s m ++ range' (s + m) n = range' s (m + n) := by simpa using range'_append (step := 1)
+@[simp] theorem range'_append_1 (s m n : Nat) :
+    range' s m ++ range' (s + m) n = range' s (m + n) := by simpa using range'_append s m n 1
 
-theorem range'_concat {s n : Nat} : range' s (n + 1) step = range' s n step ++ #[s + step * n] := by
-  simpa using range'_append.symm
+theorem range'_concat (s n : Nat) : range' s (n + 1) step = range' s n step ++ #[s + step * n] := by
+  exact (range'_append s n 1 step).symm
 
-theorem range'_1_concat {s n : Nat} : range' s (n + 1) = range' s n ++ #[s + n] := by
+theorem range'_1_concat (s n : Nat) : range' s (n + 1) = range' s n ++ #[s + n] := by
   simp [range'_concat]
 
 @[simp] theorem mem_range'_1 : m ∈ range' s n ↔ s ≤ m ∧ m < s + n := by
@@ -88,7 +84,7 @@ theorem range'_1_concat {s n : Nat} : range' s (n + 1) = range' s n ++ #[s + n]
     fun ⟨i, h, e⟩ => e ▸ ⟨Nat.le_add_right .., Nat.add_lt_add_left h _⟩,
     fun ⟨h₁, h₂⟩ => ⟨m - s, Nat.sub_lt_left_of_lt_add h₁ h₂, (Nat.add_sub_cancel' h₁).symm⟩⟩
 
-theorem map_sub_range' {a s : Nat} (h : a ≤ s) (n : Nat) :
+theorem map_sub_range' (a s n : Nat) (h : a ≤ s) :
     map (· - a) (range' s n step) = range' (s - a) n step := by
   conv => lhs; rw [← Nat.add_sub_cancel' h]
   rw [← map_add_range', map_map, (?_ : _∘_ = _), map_id]
@@ -121,28 +117,28 @@ theorem erase_range' :
 
 /-! ### range -/
 
-theorem range_eq_range' {n : Nat} : range n = range' 0 n := by
+theorem range_eq_range' (n : Nat) : range n = range' 0 n := by
   simp [range, range']
 
-theorem range_succ_eq_map {n : Nat} : range (n + 1) = #[0] ++ map succ (range n) := by
+theorem range_succ_eq_map (n : Nat) : range (n + 1) = #[0] ++ map succ (range n) := by
   ext i h₁ h₂
   · simp
     omega
-  · simp only [getElem_range, getElem_append, List.size_toArray, List.length_cons, List.length_nil,
+  · simp only [getElem_range, getElem_append, size_toArray, List.length_cons, List.length_nil,
       Nat.zero_add, lt_one_iff, List.getElem_toArray, List.getElem_singleton, getElem_map,
       succ_eq_add_one, dite_eq_ite]
     split <;> omega
 
-theorem range'_eq_map_range {s n : Nat} : range' s n = map (s + ·) (range n) := by
+theorem range'_eq_map_range (s n : Nat) : range' s n = map (s + ·) (range n) := by
   rw [range_eq_range', map_add_range']; rfl
 
 @[simp] theorem range_eq_empty_iff {n : Nat} : range n = #[] ↔ n = 0 := by
-  rw [← size_eq_zero_iff, size_range]
+  rw [← size_eq_zero, size_range]
 
 theorem range_ne_empty_iff {n : Nat} : range n ≠ #[] ↔ n ≠ 0 := by
   cases n <;> simp
 
-theorem range_succ {n : Nat} : range (succ n) = range n ++ #[n] := by
+theorem range_succ (n : Nat) : range (succ n) = range n ++ #[n] := by
   ext i h₁ h₂
   · simp
   · simp only [succ_eq_add_one, size_range] at h₁
@@ -150,11 +146,11 @@ theorem range_succ {n : Nat} : range (succ n) = range n ++ #[n] := by
       dite_eq_ite]
     split <;> omega
 
-theorem range_add {n m : Nat} : range (n + m) = range n ++ (range m).map (n + ·) := by
+theorem range_add (a b : Nat) : range (a + b) = range a ++ (range b).map (a + ·) := by
   rw [← range'_eq_map_range]
-  simpa [range_eq_range', Nat.add_comm] using (range'_append_1 (s := 0)).symm
+  simpa [range_eq_range', Nat.add_comm] using (range'_append_1 0 a b).symm
 
-theorem reverse_range' {s n : Nat} : reverse (range' s n) = map (s + n - 1 - ·) (range n) := by
+theorem reverse_range' (s n : Nat) : reverse (range' s n) = map (s + n - 1 - ·) (range n) := by
   simp [← toList_inj, List.reverse_range']
 
 @[simp]
@@ -163,9 +159,9 @@ theorem mem_range {m n : Nat} : m ∈ range n ↔ m < n := by
 
 theorem not_mem_range_self {n : Nat} : n ∉ range n := by simp
 
-theorem self_mem_range_succ {n : Nat} : n ∈ range (n + 1) := by simp
+theorem self_mem_range_succ (n : Nat) : n ∈ range (n + 1) := by simp
 
-@[simp] theorem take_range {i n : Nat} : take (range n) i = range (min i n) := by
+@[simp] theorem take_range (m n : Nat) : take (range n) m = range (min m n) := by
   ext <;> simp
 
 @[simp] theorem find?_range_eq_some {n : Nat} {i : Nat} {p : Nat → Bool} :
@@ -183,84 +179,82 @@ theorem erase_range : (range n).erase i = range (min n i) ++ range' (i + 1) (n -
 /-! ### zipIdx -/
 
 @[simp]
-theorem zipIdx_eq_empty_iff {xs : Array α} {i : Nat} : xs.zipIdx i = #[] ↔ xs = #[] := by
-  cases xs
+theorem zipIdx_eq_empty_iff {l : Array α} {n : Nat} : l.zipIdx n = #[] ↔ l = #[] := by
+  cases l
   simp
 
 @[simp]
-theorem getElem?_zipIdx {xs : Array α} {i j} : (zipIdx xs i)[j]? = xs[j]?.map fun a => (a, i + j) := by
+theorem getElem?_zipIdx (l : Array α) (n m) : (zipIdx l n)[m]? = l[m]?.map fun a => (a, n + m) := by
   simp [getElem?_def]
 
-theorem map_snd_add_zipIdx_eq_zipIdx {xs : Array α} {n k : Nat} :
-    map (Prod.map id (· + n)) (zipIdx xs k) = zipIdx xs (n + k) :=
+theorem map_snd_add_zipIdx_eq_zipIdx (l : Array α) (n k : Nat) :
+    map (Prod.map id (· + n)) (zipIdx l k) = zipIdx l (n + k) :=
   ext_getElem? fun i ↦ by simp [(· ∘ ·), Nat.add_comm, Nat.add_left_comm]; rfl
 
--- Arguments are explicit for parity with `zipIdx_map_fst`.
 @[simp]
-theorem zipIdx_map_snd (i) (xs : Array α) : map Prod.snd (zipIdx xs i) = range' i xs.size := by
-  cases xs
+theorem zipIdx_map_snd (n) (l : Array α) : map Prod.snd (zipIdx l n) = range' n l.size := by
+  cases l
   simp
 
--- Arguments are explicit so we can rewrite from right to left.
 @[simp]
-theorem zipIdx_map_fst (i) (xs : Array α) : map Prod.fst (zipIdx xs i) = xs := by
-  cases xs
+theorem zipIdx_map_fst (n) (l : Array α) : map Prod.fst (zipIdx l n) = l := by
+  cases l
   simp
 
-theorem zipIdx_eq_zip_range' {xs : Array α} {i : Nat} : xs.zipIdx i = xs.zip (range' i xs.size) := by
+theorem zipIdx_eq_zip_range' (l : Array α) {n : Nat} : l.zipIdx n = l.zip (range' n l.size) := by
   simp [zip_of_prod (zipIdx_map_fst _ _) (zipIdx_map_snd _ _)]
 
 @[simp]
-theorem unzip_zipIdx_eq_prod {xs : Array α} {i : Nat} :
-    (xs.zipIdx i).unzip = (xs, range' i xs.size) := by
+theorem unzip_zipIdx_eq_prod (l : Array α) {n : Nat} :
+    (l.zipIdx n).unzip = (l, range' n l.size) := by
   simp only [zipIdx_eq_zip_range', unzip_zip, size_range']
 
 /-- Replace `zipIdx` with a starting index `n+1` with `zipIdx` starting from `n`,
 followed by a `map` increasing the indices by one. -/
-theorem zipIdx_succ {xs : Array α} {i : Nat} :
-    xs.zipIdx (i + 1) = (xs.zipIdx i).map (fun ⟨a, j⟩ => (a, j + 1)) := by
-  cases xs
+theorem zipIdx_succ (l : Array α) (n : Nat) :
+    l.zipIdx (n + 1) = (l.zipIdx n).map (fun ⟨a, i⟩ => (a, i + 1)) := by
+  cases l
   simp [List.zipIdx_succ]
 
 /-- Replace `zipIdx` with a starting index with `zipIdx` starting from 0,
 followed by a `map` increasing the indices. -/
-theorem zipIdx_eq_map_add {xs : Array α} {i : Nat} :
-    xs.zipIdx i = (xs.zipIdx 0).map (fun ⟨a, j⟩ => (a, i + j)) := by
-  cases xs
+theorem zipIdx_eq_map_add (l : Array α) (n : Nat) :
+    l.zipIdx n = l.zipIdx.map (fun ⟨a, i⟩ => (a, n + i)) := by
+  cases l
   simp only [zipIdx_toArray, List.map_toArray, mk.injEq]
   rw [List.zipIdx_eq_map_add]
 
 @[simp]
-theorem zipIdx_singleton {x : α} {k : Nat} : zipIdx #[x] k = #[(x, k)] :=
+theorem zipIdx_singleton (x : α) (k : Nat) : zipIdx #[x] k = #[(x, k)] :=
   rfl
 
-theorem mk_add_mem_zipIdx_iff_getElem? {k i : Nat} {x : α} {xs : Array α} :
-    (x, k + i) ∈ zipIdx xs k ↔ xs[i]? = some x := by
+theorem mk_add_mem_zipIdx_iff_getElem? {k i : Nat} {x : α} {l : Array α} :
+    (x, k + i) ∈ zipIdx l k ↔ l[i]? = some x := by
   simp [mem_iff_getElem?, and_left_comm]
 
-theorem le_snd_of_mem_zipIdx {x : α × Nat} {k : Nat} {xs : Array α} (h : x ∈ zipIdx xs k) :
+theorem le_snd_of_mem_zipIdx {x : α × Nat} {k : Nat} {l : Array α} (h : x ∈ zipIdx l k) :
     k ≤ x.2 :=
   (mk_mem_zipIdx_iff_le_and_getElem?_sub.1 h).1
 
-theorem snd_lt_add_of_mem_zipIdx {x : α × Nat} {k : Nat} {xs : Array α} (h : x ∈ zipIdx xs k) :
-    x.2 < k + xs.size := by
+theorem snd_lt_add_of_mem_zipIdx {x : α × Nat} {l : Array α} {k : Nat} (h : x ∈ zipIdx l k) :
+    x.2 < k + l.size := by
   rcases mem_iff_getElem.1 h with ⟨i, h', rfl⟩
   simpa using h'
 
-theorem snd_lt_of_mem_zipIdx {x : α × Nat} {k : Nat} {xs : Array α} (h : x ∈ zipIdx xs k) : x.2 < xs.size + k := by
+theorem snd_lt_of_mem_zipIdx {x : α × Nat} {l : Array α} {k : Nat} (h : x ∈ l.zipIdx k) : x.2 < l.size + k := by
   simpa [Nat.add_comm] using snd_lt_add_of_mem_zipIdx h
 
-theorem map_zipIdx {f : α → β} {xs : Array α} {k : Nat} :
-    map (Prod.map f id) (zipIdx xs k) = zipIdx (xs.map f) k := by
-  cases xs
+theorem map_zipIdx (f : α → β) (l : Array α) (k : Nat) :
+    map (Prod.map f id) (zipIdx l k) = zipIdx (l.map f) k := by
+  cases l
   simp [List.map_zipIdx]
 
-theorem fst_mem_of_mem_zipIdx {x : α × Nat} {xs : Array α} {k : Nat} (h : x ∈ zipIdx xs k) : x.1 ∈ xs :=
-  zipIdx_map_fst k xs ▸ mem_map_of_mem h
+theorem fst_mem_of_mem_zipIdx {x : α × Nat} {l : Array α} {k : Nat} (h : x ∈ zipIdx l k) : x.1 ∈ l :=
+  zipIdx_map_fst k l ▸ mem_map_of_mem _ h
 
-theorem fst_eq_of_mem_zipIdx {x : α × Nat} {xs : Array α} {k : Nat} (h : x ∈ zipIdx xs k) :
-    x.1 = xs[x.2 - k]'(by have := le_snd_of_mem_zipIdx h; have := snd_lt_add_of_mem_zipIdx h; omega) := by
-  cases xs
+theorem fst_eq_of_mem_zipIdx {x : α × Nat} {l : Array α} {k : Nat} (h : x ∈ zipIdx l k) :
+    x.1 = l[x.2 - k]'(by have := le_snd_of_mem_zipIdx h; have := snd_lt_add_of_mem_zipIdx h; omega) := by
+  cases l
   exact List.fst_eq_of_mem_zipIdx (by simpa using h)
 
 theorem mem_zipIdx {x : α} {i : Nat} {xs : Array α} {k : Nat} (h : (x, i) ∈ xs.zipIdx k) :
@@ -273,30 +267,30 @@ theorem mem_zipIdx' {x : α} {i : Nat} {xs : Array α} (h : (x, i) ∈ xs.zipIdx
     i < xs.size ∧ x = xs[i]'(by have := le_snd_of_mem_zipIdx h; have := snd_lt_add_of_mem_zipIdx h; omega) :=
   ⟨by simpa using snd_lt_add_of_mem_zipIdx h, fst_eq_of_mem_zipIdx h⟩
 
-theorem zipIdx_map {xs : Array α} {k : Nat} {f : α → β} :
-    zipIdx (xs.map f) k = (zipIdx xs k).map (Prod.map f id) := by
-  cases xs
+theorem zipIdx_map (l : Array α) (k : Nat) (f : α → β) :
+    zipIdx (l.map f) k = (zipIdx l k).map (Prod.map f id) := by
+  cases l
   simp [List.zipIdx_map]
 
-theorem zipIdx_append {xs ys : Array α} {k : Nat} :
+theorem zipIdx_append (xs ys : Array α) (k : Nat) :
     zipIdx (xs ++ ys) k = zipIdx xs k ++ zipIdx ys (k + xs.size) := by
   cases xs
   cases ys
   simp [List.zipIdx_append]
 
-theorem zipIdx_eq_append_iff {xs : Array α} {k : Nat} :
-    zipIdx xs k = ys ++ zs ↔
-      ∃ ys' zs', xs = ys' ++ zs' ∧ ys = zipIdx ys' k ∧ zs = zipIdx zs' (k + ys'.size) := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
-  rcases zs with ⟨zs⟩
+theorem zipIdx_eq_append_iff {l : Array α} {k : Nat} :
+    zipIdx l k = l₁ ++ l₂ ↔
+      ∃ l₁' l₂', l = l₁' ++ l₂' ∧ l₁ = zipIdx l₁' k ∧ l₂ = zipIdx l₂' (k + l₁'.size) := by
+  rcases l with ⟨l⟩
+  rcases l₁ with ⟨l₁⟩
+  rcases l₂ with ⟨l₂⟩
   simp only [zipIdx_toArray, List.append_toArray, mk.injEq, List.zipIdx_eq_append_iff,
     toArray_eq_append_iff]
   constructor
   · rintro ⟨l₁', l₂', rfl, rfl, rfl⟩
     exact ⟨⟨l₁'⟩, ⟨l₂'⟩, by simp⟩
   · rintro ⟨⟨l₁'⟩, ⟨l₂'⟩, rfl, h⟩
-    simp only [zipIdx_toArray, mk.injEq, List.size_toArray] at h
+    simp only [zipIdx_toArray, mk.injEq, size_toArray] at h
     obtain ⟨rfl, rfl⟩ := h
     exact ⟨l₁', l₂', by simp⟩
 

src/Init/Data/Array/Set.lean

@@ -6,40 +6,27 @@ Authors: Leonardo de Moura, Mario Carneiro
 prelude
 import Init.Tactics
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 
 /--
-Replaces the element at a given index in an array.
+Set an element in an array, using a proof that the index is in bounds.
+(This proof can usually be omitted, and will be synthesized automatically.)
 
-No bounds check is performed, but the function requires a proof that the index is in bounds. This
-proof can usually be omitted, and will be synthesized automatically.
-
-The array is modified in-place if there are no other references to it.
-
-Examples:
-* `#[0, 1, 2].set 1 5 = #[0, 5, 2]`
-* `#["orange", "apple"].set 1 "grape" = #["orange", "grape"]`
+This will perform the update destructively provided that `a` has a reference
+count of 1 when called.
 -/
 @[extern "lean_array_fset"]
-def Array.set (xs : Array α) (i : @& Nat) (v : α) (h : i < xs.size := by get_elem_tactic) :
+def Array.set (a : Array α) (i : @& Nat) (v : α) (h : i < a.size := by get_elem_tactic) :
     Array α where
-  toList := xs.toList.set i v
+  toList := a.toList.set i v
 
 /--
-Replaces the element at the provided index in an array. The array is returned unmodified if the
-index is out of bounds.
+Set an element in an array, or do nothing if the index is out of bounds.
 
-The array is modified in-place if there are no other references to it.
-
-Examples:
-* `#[0, 1, 2].setIfInBounds 1 5 = #[0, 5, 2]`
-* `#["orange", "apple"].setIfInBounds 1 "grape" = #["orange", "grape"]`
-* `#["orange", "apple"].setIfInBounds 5 "grape" = #["orange", "apple"]`
+This will perform the update destructively provided that `a` has a reference
+count of 1 when called.
 -/
-@[inline] def Array.setIfInBounds (xs : Array α) (i : Nat) (v : α) : Array α :=
-  dite (LT.lt i xs.size) (fun h => xs.set i v h) (fun _ => xs)
+@[inline] def Array.setIfInBounds (a : Array α) (i : Nat) (v : α) : Array α :=
+  dite (LT.lt i a.size) (fun h => a.set i v h) (fun _ => a)
 
 @[deprecated Array.setIfInBounds (since := "2024-11-24")] abbrev Array.setD := @Array.setIfInBounds
 
@@ -50,5 +37,5 @@ This will perform the update destructively provided that `a` has a reference
 count of 1 when called.
 -/
 @[extern "lean_array_set"]
-def Array.set! (xs : Array α) (i : @& Nat) (v : α) : Array α :=
-  Array.setIfInBounds xs i v
+def Array.set! (a : Array α) (i : @& Nat) (v : α) : Array α :=
+  Array.setIfInBounds a i v

src/Init/Data/Array/Subarray.lean

@@ -6,45 +6,17 @@ Authors: Leonardo de Moura
 prelude
 import Init.Data.Array.Basic
 
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-set_option linter.missingDocs true
-
 universe u v w
 
-/--
-A region of some underlying array.
-
-A subarray contains an array together with the start and end indices of a region of interest.
-Subarrays can be used to avoid copying or allocating space, while being more convenient than
-tracking the bounds by hand. The region of interest consists of every index that is both greater
-than or equal to `start` and strictly less than `stop`.
--/
-structure Subarray (α : Type u) where
-  /-- The underlying array. -/
+structure Subarray (α : Type u)  where
   array : Array α
-  /-- The starting index of the region of interest (inclusive). -/
   start : Nat
-  /-- The ending index of the region of interest (exclusive). -/
   stop : Nat
-  /--
-  The starting index is no later than the ending index.
-
-  The ending index is exclusive. If the starting and ending indices are equal, then the subarray is
-  empty.
-  -/
   start_le_stop : start ≤ stop
-  /-- The stopping index is no later than the end of the array.
-
-  The ending index is exclusive. If it is equal to the size of the array, then the last element of
-  the array is in the subarray.
-  -/
   stop_le_array_size : stop ≤ array.size
 
 namespace Subarray
 
-/--
-Computes the size of the subarray.
--/
 def size (s : Subarray α) : Nat :=
   s.stop - s.start
 
@@ -54,11 +26,6 @@ theorem size_le_array_size {s : Subarray α} : s.size ≤ s.array.size := by
   apply Nat.le_trans (Nat.sub_le stop start)
   assumption
 
-/--
-Extracts an element from the subarray.
-
-The index is relative to the start of the subarray, rather than the underlying array.
--/
 def get (s : Subarray α) (i : Fin s.size) : α :=
   have : s.start + i.val < s.array.size := by
    apply Nat.lt_of_lt_of_le _ s.stop_le_array_size
@@ -71,33 +38,12 @@ def get (s : Subarray α) (i : Fin s.size) : α :=
 instance : GetElem (Subarray α) Nat α fun xs i => i < xs.size where
   getElem xs i h := xs.get ⟨i, h⟩
 
-/--
-Extracts an element from the subarray, or returns a default value `v₀` when the index is out of
-bounds.
-
-The index is relative to the start and end of the subarray, rather than the underlying array.
--/
 @[inline] def getD (s : Subarray α) (i : Nat) (v₀ : α) : α :=
   if h : i < s.size then s[i] else v₀
 
-/--
-Extracts an element from the subarray, or returns a default value when the index is out of bounds.
-
-The index is relative to the start and end of the subarray, rather than the underlying array. The
-default value is that provided by the `Inhabited α` instance.
--/
 abbrev get! [Inhabited α] (s : Subarray α) (i : Nat) : α :=
   getD s i default
 
-/--
-Shrinks the subarray by incrementing its starting index if possible, returning it unchanged if not.
-
-Examples:
- * `#[1,2,3].toSubarray.popFront.toArray = #[2, 3]`
- * `#[1,2,3].toSubarray.popFront.popFront.toArray = #[3]`
- * `#[1,2,3].toSubarray.popFront.popFront.popFront.toArray = #[]`
- * `#[1,2,3].toSubarray.popFront.popFront.popFront.popFront.toArray = #[]`
--/
 def popFront (s : Subarray α) : Subarray α :=
   if h : s.start < s.stop then
     { s with start := s.start + 1, start_le_stop := Nat.le_of_lt_succ (Nat.add_lt_add_right h 1) }
@@ -106,8 +52,6 @@ def popFront (s : Subarray α) : Subarray α :=
 
 /--
 The empty subarray.
-
-This empty subarray is backed by an empty array.
 -/
 protected def empty : Subarray α where
   array := #[]
@@ -122,12 +66,6 @@ instance : EmptyCollection (Subarray α) :=
 instance : Inhabited (Subarray α) :=
   ⟨{}⟩
 
-/--
-The run-time implementation of `ForIn.forIn` for `Subarray`, which allows it to be used with `for`
-loops in `do`-notation.
-
-This definition replaces `Subarray.forIn`.
--/
 @[inline] unsafe def forInUnsafe {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (s : Subarray α) (b : β) (f : α → β → m (ForInStep β)) : m β :=
   let sz := USize.ofNat s.stop
   let rec @[specialize] loop (i : USize) (b : β) : m β := do
@@ -140,10 +78,6 @@ This definition replaces `Subarray.forIn`.
       pure b
   loop (USize.ofNat s.start) b
 
-/--
-The implementation of `ForIn.forIn` for `Subarray`, which allows it to be used with `for` loops in
-`do`-notation.
--/
 -- TODO: provide reference implementation
 @[implemented_by Subarray.forInUnsafe]
 protected opaque forIn {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (s : Subarray α) (b : β) (f : α → β → m (ForInStep β)) : m β :=
@@ -152,197 +86,46 @@ protected opaque forIn {α : Type u} {β : Type v} {m : Type v → Type w} [Mona
 instance : ForIn m (Subarray α) α where
   forIn := Subarray.forIn
 
-/--
-Folds a monadic operation from left to right over the elements in a subarray.
-
-An accumulator of type `β` is constructed by starting with `init` and monadically combining each
-element of the subarray with the current accumulator value in turn. The monad in question may permit
-early termination or repetition.
-
-Examples:
-```lean example
-#eval #["red", "green", "blue"].toSubarray.foldlM (init := "") fun acc x => do
-  let l ← Option.guard (· ≠ 0) x.length
-  return s!"{acc}({l}){x} "
-```
-```output
-some "(3)red (5)green (4)blue "
-```
-```lean example
-#eval #["red", "green", "blue"].toSubarray.foldlM (init := 0) fun acc x => do
-  let l ← Option.guard (· ≠ 5) x.length
-  return s!"{acc}({l}){x} "
-```
-```output
-none
-```
--/
 @[inline]
 def foldlM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : β → α → m β) (init : β) (as : Subarray α) : m β :=
   as.array.foldlM f (init := init) (start := as.start) (stop := as.stop)
 
-/--
-Folds a monadic operation from right to left over the elements in a subarray.
-
-An accumulator of type `β` is constructed by starting with `init` and monadically combining each
-element of the subarray with the current accumulator value in turn, moving from the end to the
-start. The monad in question may permit early termination or repetition.
-
-Examples:
-```lean example
-#eval #["red", "green", "blue"].toSubarray.foldrM (init := "") fun x acc => do
-  let l ← Option.guard (· ≠ 0) x.length
-  return s!"{acc}({l}){x} "
-```
-```output
-some "(4)blue (5)green (3)red "
-```
-```lean example
-#eval #["red", "green", "blue"].toSubarray.foldrM (init := 0) fun x acc => do
-  let l ← Option.guard (· ≠ 5) x.length
-  return s!"{acc}({l}){x} "
-```
-```output
-none
-```
--/
 @[inline]
 def foldrM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → β → m β) (init : β) (as : Subarray α) : m β :=
   as.array.foldrM f (init := init) (start := as.stop) (stop := as.start)
 
-/--
-Checks whether any of the elements in a subarray satisfy a monadic Boolean predicate.
-
-The elements are tested starting at the lowest index and moving up. The search terminates as soon as
-an element that satisfies the predicate is found.
-
-Example:
-```lean example
-#eval #["red", "green", "blue", "orange"].toSubarray.popFront.anyM fun x => do
-  IO.println x
-  pure (x == "blue")
-```
-```output
-green
-blue
-```
-```output
-true
-```
--/
 @[inline]
 def anyM {α : Type u} {m : Type → Type w} [Monad m] (p : α → m Bool) (as : Subarray α) : m Bool :=
   as.array.anyM p (start := as.start) (stop := as.stop)
 
-/--
-Checks whether all of the elements in a subarray satisfy a monadic Boolean predicate.
-
-The elements are tested starting at the lowest index and moving up. The search terminates as soon as
-an element that does not satisfy the predicate is found.
-
-Example:
-```lean example
-#eval #["red", "green", "blue", "orange"].toSubarray.popFront.allM fun x => do
-  IO.println x
-  pure (x.length == 5)
-```
-```output
-green
-blue
-```
-```output
-false
-```
--/
 @[inline]
 def allM {α : Type u} {m : Type → Type w} [Monad m] (p : α → m Bool) (as : Subarray α) : m Bool :=
   as.array.allM p (start := as.start) (stop := as.stop)
 
-/--
-Runs a monadic action on each element of a subarray.
-
-The elements are processed starting at the lowest index and moving up.
--/
 @[inline]
 def forM {α : Type u} {m : Type v → Type w} [Monad m] (f : α → m PUnit) (as : Subarray α) : m PUnit :=
   as.array.forM f (start := as.start) (stop := as.stop)
 
-/--
-Runs a monadic action on each element of a subarray, in reverse order.
-
-The elements are processed starting at the highest index and moving down.
--/
 @[inline]
 def forRevM {α : Type u} {m : Type v → Type w} [Monad m] (f : α → m PUnit) (as : Subarray α) : m PUnit :=
   as.array.forRevM f (start := as.stop) (stop := as.start)
 
-/--
-Folds an operation from left to right over the elements in a subarray.
-
-An accumulator of type `β` is constructed by starting with `init` and combining each
-element of the subarray with the current accumulator value in turn.
-
-Examples:
- * `#["red", "green", "blue"].toSubarray.foldl (· + ·.length) 0 = 12`
- * `#["red", "green", "blue"].toSubarray.popFront.foldl (· + ·.length) 0 = 9`
--/
 @[inline]
 def foldl {α : Type u} {β : Type v} (f : β → α → β) (init : β) (as : Subarray α) : β :=
   Id.run <| as.foldlM f (init := init)
 
-/--
-Folds an operation from right to left over the elements in a subarray.
-
-An accumulator of type `β` is constructed by starting with `init` and combining each element of the
-subarray with the current accumulator value in turn, moving from the end to the start.
-
-Examples:
- * `#eval #["red", "green", "blue"].toSubarray.foldr (·.length + ·) 0 = 12`
- * `#["red", "green", "blue"].toSubarray.popFront.foldlr (·.length + ·) 0 = 9`
--/
 @[inline]
 def foldr {α : Type u} {β : Type v} (f : α → β → β) (init : β) (as : Subarray α) : β :=
   Id.run <| as.foldrM f (init := init)
 
-/--
-Checks whether any of the elements in a subarray satisfy a Boolean predicate.
-
-The elements are tested starting at the lowest index and moving up. The search terminates as soon as
-an element that satisfies the predicate is found.
--/
 @[inline]
 def any {α : Type u} (p : α → Bool) (as : Subarray α) : Bool :=
   Id.run <| as.anyM p
 
-/--
-Checks whether all of the elements in a subarray satisfy a Boolean predicate.
-
-The elements are tested starting at the lowest index and moving up. The search terminates as soon as
-an element that does not satisfy the predicate is found.
--/
 @[inline]
 def all {α : Type u} (p : α → Bool) (as : Subarray α) : Bool :=
   Id.run <| as.allM p
 
-/--
-Applies a monadic function to each element in a subarray in reverse order, stopping at the first
-element for which the function succeeds by returning a value other than `none`. The succeeding value
-is returned, or `none` if there is no success.
-
-Example:
-```lean example
-#eval #["red", "green", "blue"].toSubarray.findSomeRevM? fun x => do
-  IO.println x
-  return Option.guard (· = 5) x.length
-```
-```output
-blue
-green
-```
-```output
-some 5
-```
--/
 @[inline]
 def findSomeRevM? {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Subarray α) (f : α → m (Option β)) : m (Option β) :=
   let rec @[specialize] find : (i : Nat) → i ≤ as.size → m (Option β)
@@ -357,39 +140,10 @@ def findSomeRevM? {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m]
         find i this
   find as.size (Nat.le_refl _)
 
-/--
-Applies a monadic Boolean predicate to each element in a subarray in reverse order, stopping at the
-first element that satisfies the predicate. The element that satisfies the predicate is returned, or
-`none` if no element satisfies it.
-
-Example:
-```lean example
-#eval #["red", "green", "blue"].toSubarray.findRevM? fun x => do
-  IO.println x
-  return (x.length = 5)
-```
-```output
-blue
-green
-```
-```output
-some 5
-```
--/
 @[inline]
 def findRevM? {α : Type} {m : Type → Type w} [Monad m] (as : Subarray α) (p : α → m Bool) : m (Option α) :=
   as.findSomeRevM? fun a => return if (← p a) then some a else none
 
-/--
-Tests each element in a subarray with a Boolean predicate in reverse order, stopping at the first
-element that satisfies the predicate. The element that satisfies the predicate is returned, or
-`none` if no element satisfies the predicate.
-
-Examples:
- * `#["red", "green", "blue"].toSubarray.findRev? (·.length ≠ 4) = some "green"`
- * `#["red", "green", "blue"].toSubarray.findRev? (fun _ => true) = some "blue"`
- * `#["red", "green", "blue"].toSubarray 0 0 |>.findRev? (fun _ => true) = none`
--/
 @[inline]
 def findRev? {α : Type} (as : Subarray α) (p : α → Bool) : Option α :=
   Id.run <| as.findRevM? p
@@ -399,12 +153,6 @@ end Subarray
 namespace Array
 variable {α : Type u}
 
-/--
-Returns a subarray of an array, with the given bounds.
-
-If `start` or `stop` are not valid bounds for a subarray, then they are clamped to array's size.
-Additionally, the starting index is clamped to the ending index.
--/
 def toSubarray (as : Array α) (start : Nat := 0) (stop : Nat := as.size) : Subarray α :=
   if h₂ : stop ≤ as.size then
     if h₁ : start ≤ stop then
@@ -427,9 +175,6 @@ def toSubarray (as : Array α) (start : Nat := 0) (stop : Nat := as.size) : Suba
         start_le_stop := Nat.le_refl _,
         stop_le_array_size := Nat.le_refl _ }
 
-/--
-Allocates a new array that contains the contents of the subarray.
--/
 @[coe]
 def ofSubarray (s : Subarray α) : Array α := Id.run do
   let mut as := mkEmpty (s.stop - s.start)
@@ -439,11 +184,8 @@ def ofSubarray (s : Subarray α) : Array α := Id.run do
 
 instance : Coe (Subarray α) (Array α) := ⟨ofSubarray⟩
 
-/-- A subarray with the provided bounds.-/
 syntax:max term noWs "[" withoutPosition(term ":" term) "]" : term
-/-- A subarray with the provided lower bound that extends to the rest of the array. -/
 syntax:max term noWs "[" withoutPosition(term ":") "]" : term
-/-- A subarray with the provided upper bound, starting at the index 0. -/
 syntax:max term noWs "[" withoutPosition(":" term) "]" : term
 
 macro_rules
@@ -453,7 +195,6 @@ macro_rules
 
 end Array
 
-@[inherit_doc Array.ofSubarray]
 def Subarray.toArray (s : Subarray α) : Array α :=
   Array.ofSubarray s
 

src/Init/Data/Array/Subarray/Split.lean

@@ -15,13 +15,9 @@ automation. Placing them in another module breaks an import cycle, because `omeg
 array library.
 -/
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 namespace Subarray
 /--
-Splits a subarray into two parts, the first of which contains the first `i` elements and the second
-of which contains the remainder.
+Splits a subarray into two parts.
 -/
 def split (s : Subarray α) (i : Fin s.size.succ) : (Subarray α × Subarray α) :=
   let ⟨i', isLt⟩ := i

src/Init/Data/Array/TakeDrop.lean

@@ -7,28 +7,11 @@ prelude
 import Init.Data.Array.Lemmas
 import Init.Data.List.Nat.TakeDrop
 
-/-!
-These lemmas are used in the internals of HashMap.
-They should find a new home and/or be reformulated.
--/
-
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
-namespace List
-
-theorem exists_of_set {i : Nat} {a' : α} {l : List α} (h : i < l.length) :
-    ∃ l₁ l₂, l = l₁ ++ l[i] :: l₂ ∧ l₁.length = i ∧ l.set i a' = l₁ ++ a' :: l₂ := by
-  refine ⟨l.take i, l.drop (i + 1), ⟨by simp, ⟨length_take_of_le (Nat.le_of_lt h), ?_⟩⟩⟩
-  simp [set_eq_take_append_cons_drop, h]
-
-end List
-
 namespace Array
 
-theorem exists_of_uset {xs : Array α} {i d} (h) :
-    ∃ l₁ l₂, xs.toList = l₁ ++ xs[i] :: l₂ ∧ List.length l₁ = i.toNat ∧
-      (xs.uset i d h).toList = l₁ ++ d :: l₂ := by
+theorem exists_of_uset (self : Array α) (i d h) :
+    ∃ l₁ l₂, self.toList = l₁ ++ self[i] :: l₂ ∧ List.length l₁ = i.toNat ∧
+      (self.uset i d h).toList = l₁ ++ d :: l₂ := by
   simpa only [ugetElem_eq_getElem, ← getElem_toList, uset, toList_set] using
     List.exists_of_set _
 

src/Init/Data/Array/Zip.lean

@@ -11,9 +11,6 @@ import Init.Data.List.Zip
 # Lemmas about `Array.zip`, `Array.zipWith`, `Array.zipWithAll`, and `Array.unzip`.
 -/
 
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
 namespace Array
 
 open Nat
@@ -22,20 +19,20 @@ open Nat
 
 /-! ### zipWith -/
 
-theorem zipWith_comm {f : α → β → γ} {as : Array α} {bs : Array β} :
-    zipWith f as bs = zipWith (fun b a => f a b) bs as := by
-  cases as
-  cases bs
-  simpa using List.zipWith_comm
+theorem zipWith_comm (f : α → β → γ) (la : Array α) (lb : Array β) :
+    zipWith f la lb = zipWith (fun b a => f a b) lb la := by
+  cases la
+  cases lb
+  simpa using List.zipWith_comm _ _ _
 
-theorem zipWith_comm_of_comm {f : α → α → β} (comm : ∀ x y : α, f x y = f y x) {xs ys : Array α} :
-    zipWith f xs ys = zipWith f ys xs := by
+theorem zipWith_comm_of_comm (f : α → α → β) (comm : ∀ x y : α, f x y = f y x) (l l' : Array α) :
+    zipWith f l l' = zipWith f l' l := by
   rw [zipWith_comm]
   simp only [comm]
 
 @[simp]
-theorem zipWith_self {f : α → α → δ} {xs : Array α} : zipWith f xs xs = xs.map fun a => f a a := by
-  cases xs
+theorem zipWith_self (f : α → α → δ) (l : Array α) : zipWith f l l = l.map fun a => f a a := by
+  cases l
   simp
 
 /--
@@ -57,15 +54,15 @@ theorem getElem?_zipWith' {f : α → β → γ} {i : Nat} :
   cases l₂
   simp [List.getElem?_zipWith']
 
-theorem getElem?_zipWith_eq_some {f : α → β → γ} {as : Array α} {bs : Array β} {z : γ} {i : Nat} :
-    (zipWith f as bs)[i]? = some z ↔
-      ∃ x y, as[i]? = some x ∧ bs[i]? = some y ∧ f x y = z := by
-  cases as
-  cases bs
+theorem getElem?_zipWith_eq_some {f : α → β → γ} {l₁ : Array α} {l₂ : Array β} {z : γ} {i : Nat} :
+    (zipWith f l₁ l₂)[i]? = some z ↔
+      ∃ x y, l₁[i]? = some x ∧ l₂[i]? = some y ∧ f x y = z := by
+  cases l₁
+  cases l₂
   simp [List.getElem?_zipWith_eq_some]
 
-theorem getElem?_zip_eq_some {as : Array α} {bs : Array β} {z : α × β} {i : Nat} :
-    (zip as bs)[i]? = some z ↔ as[i]? = some z.1 ∧ bs[i]? = some z.2 := by
+theorem getElem?_zip_eq_some {l₁ : Array α} {l₂ : Array β} {z : α × β} {i : Nat} :
+    (zip l₁ l₂)[i]? = some z ↔ l₁[i]? = some z.1 ∧ l₂[i]? = some z.2 := by
   cases z
   rw [zip, getElem?_zipWith_eq_some]; constructor
   · rintro ⟨x, y, h₀, h₁, h₂⟩
@@ -74,217 +71,211 @@ theorem getElem?_zip_eq_some {as : Array α} {bs : Array β} {z : α × β} {i :
     exact ⟨_, _, h₀, h₁, rfl⟩
 
 @[simp]
-theorem zipWith_map {μ} {f : γ → δ → μ} {g : α → γ} {h : β → δ} {as : Array α} {bs : Array β} :
-    zipWith f (as.map g) (bs.map h) = zipWith (fun a b => f (g a) (h b)) as bs := by
-  cases as
-  cases bs
+theorem zipWith_map {μ} (f : γ → δ → μ) (g : α → γ) (h : β → δ) (l₁ : Array α) (l₂ : Array β) :
+    zipWith f (l₁.map g) (l₂.map h) = zipWith (fun a b => f (g a) (h b)) l₁ l₂ := by
+  cases l₁
+  cases l₂
   simp [List.zipWith_map]
 
-theorem zipWith_map_left {as : Array α} {bs : Array β} {f : α → α'} {g : α' → β → γ} :
-    zipWith g (as.map f) bs = zipWith (fun a b => g (f a) b) as bs := by
-  cases as
-  cases bs
+theorem zipWith_map_left (l₁ : Array α) (l₂ : Array β) (f : α → α') (g : α' → β → γ) :
+    zipWith g (l₁.map f) l₂ = zipWith (fun a b => g (f a) b) l₁ l₂ := by
+  cases l₁
+  cases l₂
   simp [List.zipWith_map_left]
 
-theorem zipWith_map_right {as : Array α} {bs : Array β} {f : β → β'} {g : α → β' → γ} :
-    zipWith g as (bs.map f) = zipWith (fun a b => g a (f b)) as bs := by
-  cases as
-  cases bs
+theorem zipWith_map_right (l₁ : Array α) (l₂ : Array β) (f : β → β') (g : α → β' → γ) :
+    zipWith g l₁ (l₂.map f) = zipWith (fun a b => g a (f b)) l₁ l₂ := by
+  cases l₁
+  cases l₂
   simp [List.zipWith_map_right]
 
-theorem zipWith_foldr_eq_zip_foldr {f : α → β → γ} {i : δ} :
-    (zipWith f as bs).foldr g i = (zip as bs).foldr (fun p r => g (f p.1 p.2) r) i := by
-  cases as
-  cases bs
+theorem zipWith_foldr_eq_zip_foldr {f : α → β → γ} (i : δ):
+    (zipWith f l₁ l₂).foldr g i = (zip l₁ l₂).foldr (fun p r => g (f p.1 p.2) r) i := by
+  cases l₁
+  cases l₂
   simp [List.zipWith_foldr_eq_zip_foldr]
 
-theorem zipWith_foldl_eq_zip_foldl {f : α → β → γ} {i : δ} :
-    (zipWith f as bs).foldl g i = (zip as bs).foldl (fun r p => g r (f p.1 p.2)) i := by
-  cases as
-  cases bs
+theorem zipWith_foldl_eq_zip_foldl {f : α → β → γ} (i : δ):
+    (zipWith f l₁ l₂).foldl g i = (zip l₁ l₂).foldl (fun r p => g r (f p.1 p.2)) i := by
+  cases l₁
+  cases l₂
   simp [List.zipWith_foldl_eq_zip_foldl]
 
 @[simp]
-theorem zipWith_eq_empty_iff {f : α → β → γ} {as : Array α} {bs : Array β} : zipWith f as bs = #[] ↔ as = #[] ∨ bs = #[] := by
-  cases as <;> cases bs <;> simp
+theorem zipWith_eq_empty_iff {f : α → β → γ} {l l'} : zipWith f l l' = #[] ↔ l = #[] ∨ l' = #[] := by
+  cases l <;> cases l' <;> simp
 
-theorem map_zipWith {δ : Type _} {f : α → β} {g : γ → δ → α} {cs : Array γ} {ds : Array δ} :
-    map f (zipWith g cs ds) = zipWith (fun x y => f (g x y)) cs ds := by
-  cases cs
-  cases ds
+theorem map_zipWith {δ : Type _} (f : α → β) (g : γ → δ → α) (l : Array γ) (l' : Array δ) :
+    map f (zipWith g l l') = zipWith (fun x y => f (g x y)) l l' := by
+  cases l
+  cases l'
   simp [List.map_zipWith]
 
-theorem take_zipWith : (zipWith f as bs).take i = zipWith f (as.take i) (bs.take i) := by
-  cases as
-  cases bs
+theorem take_zipWith : (zipWith f l l').take n = zipWith f (l.take n) (l'.take n) := by
+  cases l
+  cases l'
   simp [List.take_zipWith]
 
-theorem extract_zipWith : (zipWith f as bs).extract i j = zipWith f (as.extract i j) (bs.extract i j) := by
-  cases as
-  cases bs
+theorem extract_zipWith : (zipWith f l l').extract m n = zipWith f (l.extract m n) (l'.extract m n) := by
+  cases l
+  cases l'
   simp [List.drop_zipWith, List.take_zipWith]
 
-theorem zipWith_append {f : α → β → γ} {as as' : Array α} {bs bs' : Array β}
-    (h : as.size = bs.size) :
-    zipWith f (as ++ as') (bs ++ bs') = zipWith f as bs ++ zipWith f as' bs' := by
-  cases as
-  cases bs
-  cases as'
-  cases bs'
+theorem zipWith_append (f : α → β → γ) (l la : Array α) (l' lb : Array β)
+    (h : l.size = l'.size) :
+    zipWith f (l ++ la) (l' ++ lb) = zipWith f l l' ++ zipWith f la lb := by
+  cases l
+  cases l'
+  cases la
+  cases lb
   simp at h
   simp [List.zipWith_append, h]
 
-theorem zipWith_eq_append_iff {f : α → β → γ} {as : Array α} {bs : Array β} :
-    zipWith f as bs = xs ++ ys ↔
-      ∃ as₁ as₂ bs₁ bs₂, as₁.size = bs₁.size ∧ as = as₁ ++ as₂ ∧ bs = bs₁ ++ bs₂ ∧ xs = zipWith f as₁ bs₁ ∧ ys = zipWith f as₂ bs₂ := by
-  cases as
-  cases bs
-  cases xs
-  cases ys
+theorem zipWith_eq_append_iff {f : α → β → γ} {l₁ : Array α} {l₂ : Array β} :
+    zipWith f l₁ l₂ = l₁' ++ l₂' ↔
+      ∃ w x y z, w.size = y.size ∧ l₁ = w ++ x ∧ l₂ = y ++ z ∧ l₁' = zipWith f w y ∧ l₂' = zipWith f x z := by
+  cases l₁
+  cases l₂
+  cases l₁'
+  cases l₂'
   simp only [List.zipWith_toArray, List.append_toArray, mk.injEq, List.zipWith_eq_append_iff,
     toArray_eq_append_iff]
   constructor
-  · rintro ⟨ws, xs, ys, zs, h, rfl, rfl, rfl, rfl⟩
-    exact ⟨ws.toArray, xs.toArray, ys.toArray, zs.toArray, by simp [h]⟩
-  · rintro ⟨⟨ws⟩, ⟨xs⟩, ⟨ys⟩, ⟨zs⟩, h, rfl, rfl, h₁, h₂⟩
-    exact ⟨ws, xs, ys, zs, by simp_all⟩
+  · rintro ⟨w, x, y, z, h, rfl, rfl, rfl, rfl⟩
+    exact ⟨w.toArray, x.toArray, y.toArray, z.toArray, by simp [h]⟩
+  · rintro ⟨⟨w⟩, ⟨x⟩, ⟨y⟩, ⟨z⟩, h, rfl, rfl, h₁, h₂⟩
+    exact ⟨w, x, y, z, by simp_all⟩
 
-@[simp] theorem zipWith_replicate {a : α} {b : β} {m n : Nat} :
-    zipWith f (replicate m a) (replicate n b) = replicate (min m n) (f a b) := by
+@[simp] theorem zipWith_mkArray {a : α} {b : β} {m n : Nat} :
+    zipWith f (mkArray m a) (mkArray n b) = mkArray (min m n) (f a b) := by
   simp [← List.toArray_replicate]
 
-@[deprecated zipWith_replicate (since := "2025-03-18")]
-abbrev zipWith_mkArray := @zipWith_replicate
-
-theorem map_uncurry_zip_eq_zipWith {f : α → β → γ} {as : Array α} {bs : Array β} :
-    map (Function.uncurry f) (as.zip bs) = zipWith f as bs := by
-  cases as
-  cases bs
+theorem map_uncurry_zip_eq_zipWith (f : α → β → γ) (l : Array α) (l' : Array β) :
+    map (Function.uncurry f) (l.zip l') = zipWith f l l' := by
+  cases l
+  cases l'
   simp [List.map_uncurry_zip_eq_zipWith]
 
-theorem map_zip_eq_zipWith {f : α × β → γ} {as : Array α} {bs : Array β} :
-    map f (as.zip bs) = zipWith (Function.curry f) as bs := by
-  cases as
-  cases bs
+theorem map_zip_eq_zipWith (f : α × β → γ) (l : Array α) (l' : Array β) :
+    map f (l.zip l') = zipWith (Function.curry f) l l' := by
+  cases l
+  cases l'
   simp [List.map_zip_eq_zipWith]
 
-theorem lt_size_left_of_zipWith {f : α → β → γ} {i : Nat} {as : Array α} {bs : Array β}
-    (h : i < (zipWith f as bs).size) : i < as.size := by rw [size_zipWith] at h; omega
+theorem lt_size_left_of_zipWith {f : α → β → γ} {i : Nat} {l : Array α} {l' : Array β}
+    (h : i < (zipWith f l l').size) : i < l.size := by rw [size_zipWith] at h; omega
 
-theorem lt_size_right_of_zipWith {f : α → β → γ} {i : Nat} {as : Array α} {bs : Array β}
-    (h : i < (zipWith f as bs).size) : i < bs.size := by rw [size_zipWith] at h; omega
+theorem lt_size_right_of_zipWith {f : α → β → γ} {i : Nat} {l : Array α} {l' : Array β}
+    (h : i < (zipWith f l l').size) : i < l'.size := by rw [size_zipWith] at h; omega
 
-theorem zipWith_eq_zipWith_take_min (as : Array α) (bs : Array β) :
-    zipWith f as bs = zipWith f (as.take (min as.size bs.size)) (bs.take (min as.size bs.size)) := by
-  cases as
-  cases bs
+theorem zipWith_eq_zipWith_take_min (l₁ : Array α) (l₂ : Array β) :
+    zipWith f l₁ l₂ = zipWith f (l₁.take (min l₁.size l₂.size)) (l₂.take (min l₁.size l₂.size)) := by
+  cases l₁
+  cases l₂
   simp
   rw [List.zipWith_eq_zipWith_take_min]
 
-theorem reverse_zipWith (h : as.size = bs.size) :
-    (zipWith f as bs).reverse = zipWith f as.reverse bs.reverse := by
-  cases as
-  cases bs
+theorem reverse_zipWith (h : l.size = l'.size) :
+    (zipWith f l l').reverse = zipWith f l.reverse l'.reverse := by
+  cases l
+  cases l'
   simp [List.reverse_zipWith (by simpa using h)]
 
 /-! ### zip -/
 
-theorem lt_size_left_of_zip {i : Nat} {as : Array α} {bs : Array β} (h : i < (zip as bs).size) :
-    i < as.size :=
+theorem lt_size_left_of_zip {i : Nat} {l : Array α} {l' : Array β} (h : i < (zip l l').size) :
+    i < l.size :=
   lt_size_left_of_zipWith h
 
-theorem lt_size_right_of_zip {i : Nat} {as : Array α} {bs : Array β} (h : i < (zip as bs).size) :
-    i < bs.size :=
+theorem lt_size_right_of_zip {i : Nat} {l : Array α} {l' : Array β} (h : i < (zip l l').size) :
+    i < l'.size :=
   lt_size_right_of_zipWith h
 
 @[simp]
-theorem getElem_zip {as : Array α} {bs : Array β} {i : Nat} {h : i < (zip as bs).size} :
-    (zip as bs)[i] =
-      (as[i]'(lt_size_left_of_zip h), bs[i]'(lt_size_right_of_zip h)) :=
+theorem getElem_zip {l : Array α} {l' : Array β} {i : Nat} {h : i < (zip l l').size} :
+    (zip l l')[i] =
+      (l[i]'(lt_size_left_of_zip h), l'[i]'(lt_size_right_of_zip h)) :=
   getElem_zipWith (hi := by simpa using h)
 
-theorem zip_eq_zipWith {as : Array α} {bs : Array β} : zip as bs = zipWith Prod.mk as bs := by
-  cases as
-  cases bs
+theorem zip_eq_zipWith (l₁ : Array α) (l₂ : Array β) : zip l₁ l₂ = zipWith Prod.mk l₁ l₂ := by
+  cases l₁
+  cases l₂
   simp [List.zip_eq_zipWith]
 
-theorem zip_map {f : α → γ} {g : β → δ} {as : Array α} {bs : Array β} :
-    zip (as.map f) (bs.map g) = (zip as bs).map (Prod.map f g) := by
-  cases as
-  cases bs
+theorem zip_map (f : α → γ) (g : β → δ) (l₁ : Array α) (l₂ : Array β) :
+    zip (l₁.map f) (l₂.map g) = (zip l₁ l₂).map (Prod.map f g) := by
+  cases l₁
+  cases l₂
   simp [List.zip_map]
 
-theorem zip_map_left {f : α → γ} {as : Array α} {bs : Array β} :
-    zip (as.map f) bs = (zip as bs).map (Prod.map f id) := by rw [← zip_map, map_id]
+theorem zip_map_left (f : α → γ) (l₁ : Array α) (l₂ : Array β) :
+    zip (l₁.map f) l₂ = (zip l₁ l₂).map (Prod.map f id) := by rw [← zip_map, map_id]
 
-theorem zip_map_right {f : β → γ} {as : Array α} {bs : Array β} :
-    zip as (bs.map f) = (zip as bs).map (Prod.map id f) := by rw [← zip_map, map_id]
+theorem zip_map_right (f : β → γ) (l₁ : Array α) (l₂ : Array β) :
+    zip l₁ (l₂.map f) = (zip l₁ l₂).map (Prod.map id f) := by rw [← zip_map, map_id]
 
-theorem zip_append {as bs : Array α} {cs ds : Array β} (_h : as.size = cs.size) :
-    zip (as ++ bs) (cs ++ ds) = zip as cs ++ zip bs ds := by
-  cases as
-  cases cs
-  cases bs
-  cases ds
+theorem zip_append {l₁ r₁ : Array α} {l₂ r₂ : Array β} (_h : l₁.size = l₂.size) :
+    zip (l₁ ++ r₁) (l₂ ++ r₂) = zip l₁ l₂ ++ zip r₁ r₂ := by
+  cases l₁
+  cases l₂
+  cases r₁
+  cases r₂
   simp_all [List.zip_append]
 
-theorem zip_map' {f : α → β} {g : α → γ} {xs : Array α} :
-    zip (xs.map f) (xs.map g) = xs.map fun a => (f a, g a) := by
-  cases xs
+theorem zip_map' (f : α → β) (g : α → γ) (l : Array α) :
+    zip (l.map f) (l.map g) = l.map fun a => (f a, g a) := by
+  cases l
   simp [List.zip_map']
 
-theorem of_mem_zip {a b} {as : Array α} {bs : Array β} : (a, b) ∈ zip as bs → a ∈ as ∧ b ∈ bs := by
-  cases as
-  cases bs
+theorem of_mem_zip {a b} {l₁ : Array α} {l₂ : Array β} : (a, b) ∈ zip l₁ l₂ → a ∈ l₁ ∧ b ∈ l₂ := by
+  cases l₁
+  cases l₂
   simpa using List.of_mem_zip
 
-theorem map_fst_zip {as : Array α} {bs : Array β} (h : as.size ≤ bs.size) :
-    map Prod.fst (zip as bs) = as := by
-  cases as
-  cases bs
+theorem map_fst_zip (l₁ : Array α) (l₂ : Array β) (h : l₁.size ≤ l₂.size) :
+    map Prod.fst (zip l₁ l₂) = l₁ := by
+  cases l₁
+  cases l₂
   simp_all [List.map_fst_zip]
 
-theorem map_snd_zip {as : Array α} {bs : Array β} (h : bs.size ≤ as.size) :
-    map Prod.snd (zip as bs) = bs := by
-  cases as
-  cases bs
+theorem map_snd_zip (l₁ : Array α) (l₂ : Array β) (h : l₂.size ≤ l₁.size) :
+    map Prod.snd (zip l₁ l₂) = l₂ := by
+  cases l₁
+  cases l₂
   simp_all [List.map_snd_zip]
 
-theorem map_prod_left_eq_zip {xs : Array α} {f : α → β} :
-    (xs.map fun x => (x, f x)) = xs.zip (xs.map f) := by
+theorem map_prod_left_eq_zip {l : Array α} (f : α → β) :
+    (l.map fun x => (x, f x)) = l.zip (l.map f) := by
   rw [← zip_map']
   congr
   simp
 
-theorem map_prod_right_eq_zip {xs : Array α} {f : α → β} :
-    (xs.map fun x => (f x, x)) = (xs.map f).zip xs := by
+theorem map_prod_right_eq_zip {l : Array α} (f : α → β) :
+    (l.map fun x => (f x, x)) = (l.map f).zip l := by
   rw [← zip_map']
   congr
   simp
 
-@[simp] theorem zip_eq_empty_iff {as : Array α} {bs : Array β} :
-    zip as bs = #[] ↔ as = #[] ∨ bs = #[] := by
-  cases as
-  cases bs
+@[simp] theorem zip_eq_empty_iff {l₁ : Array α} {l₂ : Array β} :
+    zip l₁ l₂ = #[] ↔ l₁ = #[] ∨ l₂ = #[] := by
+  cases l₁
+  cases l₂
   simp [List.zip_eq_nil_iff]
 
-theorem zip_eq_append_iff {as : Array α} {bs : Array β} :
-    zip as bs = xs ++ ys ↔
-      ∃ as₁ as₂ bs₁ bs₂, as₁.size = bs₁.size ∧ as = as₁ ++ as₂ ∧ bs = bs₁ ++ bs₂ ∧ xs = zip as₁ bs₁ ∧ ys = zip as₂ bs₂ := by
+theorem zip_eq_append_iff {l₁ : Array α} {l₂ : Array β} :
+    zip l₁ l₂ = l₁' ++ l₂' ↔
+      ∃ w x y z, w.size = y.size ∧ l₁ = w ++ x ∧ l₂ = y ++ z ∧ l₁' = zip w y ∧ l₂' = zip x z := by
   simp [zip_eq_zipWith, zipWith_eq_append_iff]
 
-@[simp] theorem zip_replicate {a : α} {b : β} {m n : Nat} :
-    zip (replicate m a) (replicate n b) = replicate (min m n) (a, b) := by
+@[simp] theorem zip_mkArray {a : α} {b : β} {m n : Nat} :
+    zip (mkArray m a) (mkArray n b) = mkArray (min m n) (a, b) := by
   simp [← List.toArray_replicate]
 
-@[deprecated zip_replicate (since := "2025-03-18")]
-abbrev zip_mkArray := @zip_replicate
-
-theorem zip_eq_zip_take_min {as : Array α} {bs : Array β} :
-    zip as bs = zip (as.take (min as.size bs.size)) (bs.take (min as.size bs.size)) := by
-  cases as
-  cases bs
-  simp only [List.zip_toArray, List.size_toArray, List.take_toArray, mk.injEq]
+theorem zip_eq_zip_take_min (l₁ : Array α) (l₂ : Array β) :
+    zip l₁ l₂ = zip (l₁.take (min l₁.size l₂.size)) (l₂.take (min l₁.size l₂.size)) := by
+  cases l₁
+  cases l₂
+  simp only [List.zip_toArray, size_toArray, List.take_toArray, mk.injEq]
   rw [List.zip_eq_zip_take_min]
 
 
@@ -298,36 +289,34 @@ theorem getElem?_zipWithAll {f : Option α → Option β → γ} {i : Nat} :
   simp [List.getElem?_zipWithAll]
   rfl
 
-theorem zipWithAll_map {μ} {f : Option γ → Option δ → μ} {g : α → γ} {h : β → δ} {as : Array α} {bs : Array β} :
-    zipWithAll f (as.map g) (bs.map h) = zipWithAll (fun a b => f (g <$> a) (h <$> b)) as bs := by
-  cases as
-  cases bs
+theorem zipWithAll_map {μ} (f : Option γ → Option δ → μ) (g : α → γ) (h : β → δ) (l₁ : Array α) (l₂ : Array β) :
+    zipWithAll f (l₁.map g) (l₂.map h) = zipWithAll (fun a b => f (g <$> a) (h <$> b)) l₁ l₂ := by
+  cases l₁
+  cases l₂
   simp [List.zipWithAll_map]
 
-theorem zipWithAll_map_left {as : Array α} {bs : Array β} {f : α → α'} {g : Option α' → Option β → γ} :
-    zipWithAll g (as.map f) bs = zipWithAll (fun a b => g (f <$> a) b) as bs := by
-  cases as
-  cases bs
+theorem zipWithAll_map_left (l₁ : Array α) (l₂ : Array β) (f : α → α') (g : Option α' → Option β → γ) :
+    zipWithAll g (l₁.map f) l₂ = zipWithAll (fun a b => g (f <$> a) b) l₁ l₂ := by
+  cases l₁
+  cases l₂
   simp [List.zipWithAll_map_left]
 
-theorem zipWithAll_map_right {as : Array α} {bs : Array β} {f : β → β'} {g : Option α → Option β' → γ} :
-    zipWithAll g as (bs.map f) = zipWithAll (fun a b => g a (f <$> b)) as bs := by
-  cases as
-  cases bs
+theorem zipWithAll_map_right (l₁ : Array α) (l₂ : Array β) (f : β → β') (g : Option α → Option β' → γ) :
+    zipWithAll g l₁ (l₂.map f) = zipWithAll (fun a b => g a (f <$> b)) l₁ l₂ := by
+  cases l₁
+  cases l₂
   simp [List.zipWithAll_map_right]
 
-theorem map_zipWithAll {δ : Type _} {f : α → β} {g : Option γ → Option δ → α} {cs : Array γ} {ds : Array δ} :
-    map f (zipWithAll g cs ds) = zipWithAll (fun x y => f (g x y)) cs ds := by
-  cases cs
-  cases ds
+theorem map_zipWithAll {δ : Type _} (f : α → β) (g : Option γ → Option δ → α) (l : Array γ) (l' : Array δ) :
+    map f (zipWithAll g l l') = zipWithAll (fun x y => f (g x y)) l l' := by
+  cases l
+  cases l'
   simp [List.map_zipWithAll]
 
-@[simp] theorem zipWithAll_replicate {a : α} {b : β} {n : Nat} :
-    zipWithAll f (replicate n a) (replicate n b) = replicate n (f a b) := by
-  simp [← List.toArray_replicate]
 
-@[deprecated zipWithAll_replicate (since := "2025-03-18")]
-abbrev zipWithAll_mkArray := @zipWithAll_replicate
+@[simp] theorem zipWithAll_replicate {a : α} {b : β} {n : Nat} :
+    zipWithAll f (mkArray n a) (mkArray n b) = mkArray n (f a b) := by
+  simp [← List.toArray_replicate]
 
 /-! ### unzip -/
 
@@ -337,42 +326,38 @@ abbrev zipWithAll_mkArray := @zipWithAll_replicate
 @[simp] theorem unzip_snd : (unzip l).snd = l.map Prod.snd := by
   induction l <;> simp_all
 
-theorem unzip_eq_map {xs : Array (α × β)} : unzip xs = (xs.map Prod.fst, xs.map Prod.snd) := by
-  cases xs
+theorem unzip_eq_map (l : Array (α × β)) : unzip l = (l.map Prod.fst, l.map Prod.snd) := by
+  cases l
   simp [List.unzip_eq_map]
 
--- The argument `xs` is explicit so we can rewrite from right to left.
-theorem zip_unzip (xs : Array (α × β)) : zip (unzip xs).1 (unzip xs).2 = xs := by
-  cases xs
+theorem zip_unzip (l : Array (α × β)) : zip (unzip l).1 (unzip l).2 = l := by
+  cases l
   simp only [List.unzip_toArray, Prod.map_fst, Prod.map_snd, List.zip_toArray, List.zip_unzip]
 
-theorem unzip_zip_left {as : Array α} {bs : Array β} (h : as.size ≤ bs.size) :
-    (unzip (zip as bs)).1 = as := by
-  cases as
-  cases bs
-  simp_all only [List.size_toArray, List.zip_toArray, List.unzip_toArray, Prod.map_fst,
+theorem unzip_zip_left {l₁ : Array α} {l₂ : Array β} (h : l₁.size ≤ l₂.size) :
+    (unzip (zip l₁ l₂)).1 = l₁ := by
+  cases l₁
+  cases l₂
+  simp_all only [size_toArray, List.zip_toArray, List.unzip_toArray, Prod.map_fst,
     List.unzip_zip_left]
 
-theorem unzip_zip_right {as : Array α} {bs : Array β} (h : bs.size ≤ as.size) :
-    (unzip (zip as bs)).2 = bs := by
-  cases as
-  cases bs
-  simp_all only [List.size_toArray, List.zip_toArray, List.unzip_toArray, Prod.map_snd,
+theorem unzip_zip_right {l₁ : Array α} {l₂ : Array β} (h : l₂.size ≤ l₁.size) :
+    (unzip (zip l₁ l₂)).2 = l₂ := by
+  cases l₁
+  cases l₂
+  simp_all only [size_toArray, List.zip_toArray, List.unzip_toArray, Prod.map_snd,
     List.unzip_zip_right]
 
-theorem unzip_zip {as : Array α} {bs : Array β} (h : as.size = bs.size) :
-    unzip (zip as bs) = (as, bs) := by
-  cases as
-  cases bs
-  simp_all only [List.size_toArray, List.zip_toArray, List.unzip_toArray, List.unzip_zip, Prod.map_apply]
+theorem unzip_zip {l₁ : Array α} {l₂ : Array β} (h : l₁.size = l₂.size) :
+    unzip (zip l₁ l₂) = (l₁, l₂) := by
+  cases l₁
+  cases l₂
+  simp_all only [size_toArray, List.zip_toArray, List.unzip_toArray, List.unzip_zip, Prod.map_apply]
 
-theorem zip_of_prod {as : Array α} {bs : Array β} {xs : Array (α × β)} (hl : xs.map Prod.fst = as)
-    (hr : xs.map Prod.snd = bs) : xs = as.zip bs := by
-  rw [← hl, ← hr, ← zip_unzip xs, ← unzip_fst, ← unzip_snd, zip_unzip, zip_unzip]
+theorem zip_of_prod {l : Array α} {l' : Array β} {lp : Array (α × β)} (hl : lp.map Prod.fst = l)
+    (hr : lp.map Prod.snd = l') : lp = l.zip l' := by
+  rw [← hl, ← hr, ← zip_unzip lp, ← unzip_fst, ← unzip_snd, zip_unzip, zip_unzip]
 
-@[simp] theorem unzip_replicate {n : Nat} {a : α} {b : β} :
-    unzip (replicate n (a, b)) = (replicate n a, replicate n b) := by
+@[simp] theorem unzip_mkArray {n : Nat} {a : α} {b : β} :
+    unzip (mkArray n (a, b)) = (mkArray n a, mkArray n b) := by
   ext1 <;> simp
-
-@[deprecated unzip_replicate (since := "2025-03-18")]
-abbrev unzip_mkArray := @unzip_replicate

src/Init/Data/BEq.lean

@@ -25,7 +25,7 @@ class ReflBEq (α) [BEq α] : Prop where
   refl : (a : α) == a
 
 /-- `EquivBEq` says that the `BEq` implementation is an equivalence relation. -/
-class EquivBEq (α) [BEq α] : Prop extends PartialEquivBEq α, ReflBEq α
+class EquivBEq (α) [BEq α] extends PartialEquivBEq α, ReflBEq α : Prop
 
 @[simp]
 theorem BEq.refl [BEq α] [ReflBEq α] {a : α} : a == a :=
@@ -49,14 +49,6 @@ theorem BEq.symm_false [BEq α] [PartialEquivBEq α] {a b : α} : (a == b) = fal
 theorem BEq.trans [BEq α] [PartialEquivBEq α] {a b c : α} : a == b → b == c → a == c :=
   PartialEquivBEq.trans
 
-theorem BEq.congr_left [BEq α] [PartialEquivBEq α] {a b c : α} (h : a == b) :
-    (a == c) = (b == c) :=
-  Bool.eq_iff_iff.mpr ⟨BEq.trans (BEq.symm h), BEq.trans h⟩
-
-theorem BEq.congr_right [BEq α] [PartialEquivBEq α] {a b c : α} (h : b == c) :
-    (a == b) = (a == c) :=
-  Bool.eq_iff_iff.mpr ⟨fun h' => BEq.trans h' h, fun h' => BEq.trans h' (BEq.symm h)⟩
-
 theorem BEq.neq_of_neq_of_beq [BEq α] [PartialEquivBEq α] {a b c : α} :
     (a == b) = false → b == c → (a == c) = false :=
   fun h₁ h₂ => Bool.eq_false_iff.2 fun h₃ => Bool.eq_false_iff.1 h₁ (BEq.trans h₃ (BEq.symm h₂))

src/Init/Data/BitVec/Basic.lean

@@ -18,24 +18,20 @@ operations on `Fin` are already defined. Some other possible representations are
 
 We define many of the bitvector operations from the
 [`QF_BV` logic](https://smtlib.cs.uiowa.edu/logics-all.shtml#QF_BV).
-of SMT-LIB v2.
+of SMT-LIBv2.
 -/
 
 set_option linter.missingDocs true
 
 namespace BitVec
 
-@[inline, deprecated BitVec.ofNatLT (since := "2025-02-13"), inherit_doc BitVec.ofNatLT]
-protected def ofNatLt {n : Nat} (i : Nat) (p : i < 2 ^ n) : BitVec n :=
-  BitVec.ofNatLT i p
-
 section Nat
 
 instance natCastInst : NatCast (BitVec w) := ⟨BitVec.ofNat w⟩
 
-/-- Theorem for normalizing the bitvector literal representation. -/
+/-- Theorem for normalizing the bit vector literal representation. -/
 -- TODO: This needs more usage data to assess which direction the simp should go.
-@[simp, bitvec_to_nat] theorem ofNat_eq_ofNat : @OfNat.ofNat (BitVec n) i _ = .ofNat n i := rfl
+@[simp, bv_toNat] theorem ofNat_eq_ofNat : @OfNat.ofNat (BitVec n) i _ = .ofNat n i := rfl
 
 -- Note. Mathlib would like this to go the other direction.
 @[simp] theorem natCast_eq_ofNat (w x : Nat) : @Nat.cast (BitVec w) _ x = .ofNat w x := rfl
@@ -48,7 +44,7 @@ section subsingleton
 instance : Subsingleton (BitVec 0) where
   allEq := by intro ⟨0, _⟩ ⟨0, _⟩; rfl
 
-/-- The empty bitvector. -/
+/-- The empty bitvector -/
 abbrev nil : BitVec 0 := 0
 
 /-- Every bitvector of length 0 is equal to `nil`, i.e., there is only one empty bitvector -/
@@ -58,49 +54,55 @@ end subsingleton
 
 section zero_allOnes
 
-/-- Returns a bitvector of size `n` where all bits are `0`. -/
-protected def zero (n : Nat) : BitVec n := .ofNatLT 0 (Nat.two_pow_pos n)
+/-- Return a bitvector `0` of size `n`. This is the bitvector with all zero bits. -/
+protected def zero (n : Nat) : BitVec n := .ofNatLt 0 (Nat.two_pow_pos n)
 instance : Inhabited (BitVec n) where default := .zero n
 
-/-- Returns a bitvector of size `n` where all bits are `1`. -/
+/-- Bit vector of size `n` where all bits are `1`s -/
 def allOnes (n : Nat) : BitVec n :=
-  .ofNatLT (2^n - 1) (Nat.le_of_eq (Nat.sub_add_cancel (Nat.two_pow_pos n)))
+  .ofNatLt (2^n - 1) (Nat.le_of_eq (Nat.sub_add_cancel (Nat.two_pow_pos n)))
 
 end zero_allOnes
 
 section getXsb
 
 /--
-Returns the `i`th least significant bit.
+Return the `i`-th least significant bit.
 
 This will be renamed `getLsb` after the existing deprecated alias is removed.
 -/
 @[inline] def getLsb' (x : BitVec w) (i : Fin w) : Bool := x.toNat.testBit i
 
-/-- Returns the `i`th least significant bit, or `none` if `i ≥ w`. -/
+/-- Return the `i`-th least significant bit or `none` if `i ≥ w`. -/
 @[inline] def getLsb? (x : BitVec w) (i : Nat) : Option Bool :=
   if h : i < w then some (getLsb' x ⟨i, h⟩) else none
 
 /--
-Returns the `i`th most significant bit.
+Return the `i`-th most significant bit.
 
-This will be renamed `BitVec.getMsb` after the existing deprecated alias is removed.
+This will be renamed `getMsb` after the existing deprecated alias is removed.
 -/
 @[inline] def getMsb' (x : BitVec w) (i : Fin w) : Bool := x.getLsb' ⟨w-1-i, by omega⟩
 
-/-- Returns the `i`th most significant bit or `none` if `i ≥ w`. -/
+/-- Return the `i`-th most significant bit or `none` if `i ≥ w`. -/
 @[inline] def getMsb? (x : BitVec w) (i : Nat) : Option Bool :=
   if h : i < w then some (getMsb' x ⟨i, h⟩) else none
 
-/-- Returns the `i`th least significant bit or `false` if `i ≥ w`. -/
+/-- Return the `i`-th least significant bit or `false` if `i ≥ w`. -/
 @[inline] def getLsbD (x : BitVec w) (i : Nat) : Bool :=
   x.toNat.testBit i
 
-/-- Returns the `i`th most significant bit, or `false` if `i ≥ w`. -/
+@[deprecated getLsbD (since := "2024-08-29"), inherit_doc getLsbD]
+def getLsb (x : BitVec w) (i : Nat) : Bool := x.getLsbD i
+
+/-- Return the `i`-th most significant bit or `false` if `i ≥ w`. -/
 @[inline] def getMsbD (x : BitVec w) (i : Nat) : Bool :=
   i < w && x.getLsbD (w-1-i)
 
-/-- Returns the most significant bit in a bitvector. -/
+@[deprecated getMsbD (since := "2024-08-29"), inherit_doc getMsbD]
+def getMsb (x : BitVec w) (i : Nat) : Bool := x.getMsbD i
+
+/-- Return most-significant bit in bitvector. -/
 @[inline] protected def msb (x : BitVec n) : Bool := getMsbD x 0
 
 end getXsb
@@ -121,7 +123,6 @@ instance : GetElem (BitVec w) Nat Bool fun _ i => i < w where
 theorem getElem_eq_testBit_toNat (x : BitVec w) (i : Nat) (h : i < w) :
   x[i] = x.toNat.testBit i := rfl
 
-@[simp]
 theorem getLsbD_eq_getElem {x : BitVec w} {i : Nat} (h : i < w) :
     x.getLsbD i = x[i] := rfl
 
@@ -129,23 +130,15 @@ end getElem
 
 section Int
 
-/--
-Interprets the bitvector as an integer stored in two's complement form.
--/
+/-- Interpret the bitvector as an integer stored in two's complement form. -/
 protected def toInt (x : BitVec n) : Int :=
   if 2 * x.toNat < 2^n then
     x.toNat
   else
     (x.toNat : Int) - (2^n : Nat)
 
-/--
-Converts an integer to its two's complement representation as a bitvector of the given width `n`,
-over- and underflowing as needed.
-
-The underlying `Nat` is `(2^n + (i mod 2^n)) mod 2^n`. Converting the bitvector back to an `Int`
-with `BitVec.toInt` results in the value `i.bmod (2^n)`.
--/
-protected def ofInt (n : Nat) (i : Int) : BitVec n := .ofNatLT (i % (Int.ofNat (2^n))).toNat (by
+/-- The `BitVec` with value `(2^n + (i mod 2^n)) mod 2^n`.  -/
+protected def ofInt (n : Nat) (i : Int) : BitVec n := .ofNatLt (i % (Int.ofNat (2^n))).toNat (by
   apply (Int.toNat_lt _).mpr
   · apply Int.emod_lt_of_pos
     exact Int.ofNat_pos.mpr (Nat.two_pow_pos _)
@@ -160,7 +153,7 @@ end Int
 
 section Syntax
 
-/-- Notation for bitvector literals. `i#n` is a shorthand for `BitVec.ofNat n i`. -/
+/-- Notation for bit vector literals. `i#n` is a shorthand for `BitVec.ofNat n i`. -/
 syntax:max num noWs "#" noWs term:max : term
 macro_rules | `($i:num#$n) => `(BitVec.ofNat $n $i)
 
@@ -169,17 +162,17 @@ recommended_spelling "zero" for "0#n" in [BitVec.ofNat, «term__#__»]
 /-- not `ofNat_one` -/
 recommended_spelling "one" for "1#n" in [BitVec.ofNat, «term__#__»]
 
-/-- Unexpander for bitvector literals. -/
+/-- Unexpander for bit vector literals. -/
 @[app_unexpander BitVec.ofNat] def unexpandBitVecOfNat : Lean.PrettyPrinter.Unexpander
   | `($(_) $n $i:num) => `($i:num#$n)
   | _ => throw ()
 
-/-- Notation for bitvector literals without truncation. `i#'lt` is a shorthand for `BitVec.ofNatLT i lt`. -/
+/-- Notation for bit vector literals without truncation. `i#'lt` is a shorthand for `BitVec.ofNatLt i lt`. -/
 scoped syntax:max term:max noWs "#'" noWs term:max : term
-macro_rules | `($i#'$p) => `(BitVec.ofNatLT $i $p)
+macro_rules | `($i#'$p) => `(BitVec.ofNatLt $i $p)
 
-/-- Unexpander for bitvector literals without truncation. -/
-@[app_unexpander BitVec.ofNatLT] def unexpandBitVecOfNatLt : Lean.PrettyPrinter.Unexpander
+/-- Unexpander for bit vector literals without truncation. -/
+@[app_unexpander BitVec.ofNatLt] def unexpandBitVecOfNatLt : Lean.PrettyPrinter.Unexpander
   | `($(_) $i $p) => `($i#'$p)
   | _ => throw ()
 
@@ -187,11 +180,7 @@ end Syntax
 
 section repr_toString
 
-/--
-Converts a bitvector into a fixed-width hexadecimal number with enough digits to represent it.
-
-If `n` is `0`, then one digit is returned. Otherwise, `⌊(n + 3) / 4⌋` digits are returned.
--/
+/-- Convert bitvector into a fixed-width hex number. -/
 protected def toHex {n : Nat} (x : BitVec n) : String :=
   let s := (Nat.toDigits 16 x.toNat).asString
   let t := (List.replicate ((n+3) / 4 - s.length) '0').asString
@@ -205,63 +194,63 @@ end repr_toString
 section arithmetic
 
 /--
-Negation of bitvectors. This can be interpreted as either signed or unsigned negation modulo `2^n`.
-Usually accessed via the `-` prefix operator.
+Negation for bit vectors. This can be interpreted as either signed or unsigned negation
+modulo `2^n`.
 
-SMT-LIB name: `bvneg`.
+SMT-Lib name: `bvneg`.
 -/
 protected def neg (x : BitVec n) : BitVec n := .ofNat n (2^n - x.toNat)
 instance : Neg (BitVec n) := ⟨.neg⟩
 
 /--
-Returns the absolute value of a signed bitvector.
+Return the absolute value of a signed bitvector.
 -/
 protected def abs (x : BitVec n) : BitVec n := if x.msb then .neg x else x
 
 /--
-Multiplies two bitvectors. This can be interpreted as either signed or unsigned multiplication
-modulo `2^n`. Usually accessed via the `*` operator.
+Multiplication for bit vectors. This can be interpreted as either signed or unsigned
+multiplication modulo `2^n`.
 
-SMT-LIB name: `bvmul`.
+SMT-Lib name: `bvmul`.
 -/
 protected def mul (x y : BitVec n) : BitVec n := BitVec.ofNat n (x.toNat * y.toNat)
 instance : Mul (BitVec n) := ⟨.mul⟩
 
 /--
-Unsigned division of bitvectors using the Lean convention where division by zero returns zero.
-Usually accessed via the `/` operator.
+Unsigned division for bit vectors using the Lean convention where division by zero returns zero.
 -/
 def udiv (x y : BitVec n) : BitVec n :=
   (x.toNat / y.toNat)#'(Nat.lt_of_le_of_lt (Nat.div_le_self _ _) x.isLt)
 instance : Div (BitVec n) := ⟨.udiv⟩
 
 /--
-Unsigned modulo for bitvectors. Usually accessed via the `%` operator.
+Unsigned modulo for bit vectors.
 
-SMT-LIB name: `bvurem`.
+SMT-Lib name: `bvurem`.
 -/
 def umod (x y : BitVec n) : BitVec n :=
   (x.toNat % y.toNat)#'(Nat.lt_of_le_of_lt (Nat.mod_le _ _) x.isLt)
 instance : Mod (BitVec n) := ⟨.umod⟩
 
 /--
-Unsigned division of bitvectors using the
-[SMT-LIB convention](http://smtlib.cs.uiowa.edu/theories-FixedSizeBitVectors.shtml),
-where division by zero returns `BitVector.allOnes n`.
+Unsigned division for bit vectors using the
+[SMT-Lib convention](http://smtlib.cs.uiowa.edu/theories-FixedSizeBitVectors.shtml)
+where division by zero returns the `allOnes` bitvector.
 
-SMT-LIB name: `bvudiv`.
+SMT-Lib name: `bvudiv`.
 -/
 def smtUDiv (x y : BitVec n) : BitVec n := if y = 0 then allOnes n else udiv x y
 
 /--
-Signed T-division (using the truncating rounding convention) for bitvectors. This function obeys the
-Lean convention that division by zero returns zero.
+Signed t-division for bit vectors using the Lean convention where division
+by zero returns zero.
 
-Examples:
-* `(7#4).sdiv 2 = 3#4`
-* `(-9#4).sdiv 2 = -4#4`
-* `(5#4).sdiv -2 = -2#4`
-* `(-7#4).sdiv (-2) = 3#4`
+```lean
+sdiv 7#4 2 = 3#4
+sdiv (-9#4) 2 = -4#4
+sdiv 5#4 -2 = -2#4
+sdiv (-7#4) (-2) = 3#4
+```
 -/
 def sdiv (x y : BitVec n) : BitVec n :=
   match x.msb, y.msb with
@@ -271,13 +260,11 @@ def sdiv (x y : BitVec n) : BitVec n :=
   | true,  true  => udiv (.neg x) (.neg y)
 
 /--
-Signed division for bitvectors using the SMT-LIB using the
-[SMT-LIB convention](http://smtlib.cs.uiowa.edu/theories-FixedSizeBitVectors.shtml),
-where division by zero returns `BitVector.allOnes n`.
+Signed division for bit vectors using SMTLIB rules for division by zero.
 
-Specifically, `x.smtSDiv 0 = if x >= 0 then -1 else 1`
+Specifically, `smtSDiv x 0 = if x >= 0 then -1 else 1`
 
-SMT-LIB name: `bvsdiv`.
+SMT-Lib name: `bvsdiv`.
 -/
 def smtSDiv (x y : BitVec n) : BitVec n :=
   match x.msb, y.msb with
@@ -289,7 +276,7 @@ def smtSDiv (x y : BitVec n) : BitVec n :=
 /--
 Remainder for signed division rounding to zero.
 
-SMT-LIB name: `bvsrem`.
+SMT_Lib name: `bvsrem`.
 -/
 def srem (x y : BitVec n) : BitVec n :=
   match x.msb, y.msb with
@@ -301,7 +288,7 @@ def srem (x y : BitVec n) : BitVec n :=
 /--
 Remainder for signed division rounded to negative infinity.
 
-SMT-LIB name: `bvsmod`.
+SMT_Lib name: `bvsmod`.
 -/
 def smod (x y : BitVec m) : BitVec m :=
   match x.msb, y.msb with
@@ -319,7 +306,7 @@ end arithmetic
 
 section bool
 
-/-- Turns a `Bool` into a bitvector of length `1`. -/
+/-- Turn a `Bool` into a bitvector of length `1` -/
 def ofBool (b : Bool) : BitVec 1 := cond b 1 0
 
 @[simp] theorem ofBool_false : ofBool false = 0 := by trivial
@@ -333,34 +320,34 @@ end bool
 section relations
 
 /--
-Unsigned less-than for bitvectors.
+Unsigned less-than for bit vectors.
 
-SMT-LIB name: `bvult`.
+SMT-Lib name: `bvult`.
 -/
 protected def ult (x y : BitVec n) : Bool := x.toNat < y.toNat
 
 /--
-Unsigned less-than-or-equal-to for bitvectors.
+Unsigned less-than-or-equal-to for bit vectors.
 
-SMT-LIB name: `bvule`.
+SMT-Lib name: `bvule`.
 -/
 protected def ule (x y : BitVec n) : Bool := x.toNat ≤ y.toNat
 
 /--
-Signed less-than for bitvectors.
+Signed less-than for bit vectors.
 
-SMT-LIB name: `bvslt`.
-
-Examples:
- * `BitVec.slt 6#4 7 = true`
- * `BitVec.slt 7#4 8 = false`
+```lean
+BitVec.slt 6#4 7 = true
+BitVec.slt 7#4 8 = false
+```
+SMT-Lib name: `bvslt`.
 -/
 protected def slt (x y : BitVec n) : Bool := x.toInt < y.toInt
 
 /--
-Signed less-than-or-equal-to for bitvectors.
+Signed less-than-or-equal-to for bit vectors.
 
-SMT-LIB name: `bvsle`.
+SMT-Lib name: `bvsle`.
 -/
 protected def sle (x y : BitVec n) : Bool := x.toInt ≤ y.toInt
 
@@ -368,14 +355,8 @@ end relations
 
 section cast
 
-/--
-If two natural numbers `n` and `m` are equal, then a bitvector of width `n` is also a bitvector of
-width `m`.
-
-Using `x.cast eq` should be preferred over `eq ▸ x` because there are special-purpose `simp` lemmas
-that can more consistently simplify `BitVec.cast` away.
--/
-@[inline] protected def cast (eq : n = m) (x : BitVec n) : BitVec m := .ofNatLT x.toNat (eq ▸ x.isLt)
+/-- `cast eq x` embeds `x` into an equal `BitVec` type. -/
+@[inline] protected def cast (eq : n = m) (x : BitVec n) : BitVec m := .ofNatLt x.toNat (eq ▸ x.isLt)
 
 @[simp] theorem cast_ofNat {n m : Nat} (h : n = m) (x : Nat) :
     (BitVec.ofNat n x).cast h = BitVec.ofNat m x := by
@@ -388,36 +369,34 @@ that can more consistently simplify `BitVec.cast` away.
 @[simp] theorem cast_eq {n : Nat} (h : n = n) (x : BitVec n) : x.cast h = x := rfl
 
 /--
-Extracts the bits `start` to `start + len - 1` from a bitvector of size `n` to yield a
-new bitvector of size `len`. If `start + len > n`, then the bitvector is zero-extended.
+Extraction of bits `start` to `start + len - 1` from a bit vector of size `n` to yield a
+new bitvector of size `len`. If `start + len > n`, then the vector will be zero-padded in the
+high bits.
 -/
 def extractLsb' (start len : Nat) (x : BitVec n) : BitVec len := .ofNat _ (x.toNat >>> start)
 
 /--
-Extracts the bits from `hi` down to `lo` (both inclusive) from a bitvector, which is implicitly
-zero-extended if necessary.
+Extraction of bits `hi` (inclusive) down to `lo` (inclusive) from a bit vector of size `n` to
+yield a new bitvector of size `hi - lo + 1`.
 
-The resulting bitvector has size `hi - lo + 1`.
-
-SMT-LIB name: `extract`.
+SMT-Lib name: `extract`.
 -/
 def extractLsb (hi lo : Nat) (x : BitVec n) : BitVec (hi - lo + 1) := extractLsb' lo _ x
 
 /--
-Increases the width of a bitvector to one that is at least as large by zero-extending it.
-
-This is a constant-time operation because the underlying `Nat` is unmodified; because the new width
-is at least as large as the old one, no overflow is possible.
+A version of `setWidth` that requires a proof the new width is at least as large,
+and is a computational noop.
 -/
 def setWidth' {n w : Nat} (le : n ≤ w) (x : BitVec n) : BitVec w :=
   x.toNat#'(by
     apply Nat.lt_of_lt_of_le x.isLt
-    exact Nat.pow_le_pow_right (by trivial) le)
+    exact Nat.pow_le_pow_of_le_right (by trivial) le)
 
 @[deprecated setWidth' (since := "2024-09-18"), inherit_doc setWidth'] abbrev zeroExtend' := @setWidth'
 
 /--
-Returns `zeroExtend (w+n) x <<< n` without needing to compute `x % 2^(2+n)`.
+`shiftLeftZeroExtend x n` returns `zeroExtend (w+n) x <<< n` without
+needing to compute `x % 2^(2+n)`.
 -/
 def shiftLeftZeroExtend (msbs : BitVec w) (m : Nat) : BitVec (w + m) :=
   let shiftLeftLt {x : Nat} (p : x < 2^w) (m : Nat) : x <<< m < 2^(w + m) := by
@@ -426,20 +405,12 @@ def shiftLeftZeroExtend (msbs : BitVec w) (m : Nat) : BitVec (w + m) :=
         exact (Nat.two_pow_pos m)
   (msbs.toNat <<< m)#'(shiftLeftLt msbs.isLt m)
 
-
 /--
-Transforms a bitvector of length `w` into a bitvector of length `v`, padding with `0` as needed.
+Transform `x` of length `w` into a bitvector of length `v`, by either:
+- zero extending, that is, adding zeros in the high bits until it has length `v`, if `v > w`, or
+- truncating the high bits, if `v < w`.
 
-The specific behavior depends on the relationship between the starting width `w` and the final width
-`v`:
- * If `v > w`, it is zero-extended; the high bits are padded with zeroes until the bitvector has `v`
-   bits.
- * If `v = w`, the bitvector is returned unchanged.
- * If `v < w`, the high bits are truncated.
-
-`BitVec.setWidth`, `BitVec.zeroExtend`, and `BitVec.truncate` are aliases for this operation.
-
-SMT-LIB name: `zero_extend`.
+SMT-Lib name: `zero_extend`.
 -/
 def setWidth (v : Nat) (x : BitVec w) : BitVec v :=
   if h : w ≤ v then
@@ -447,19 +418,29 @@ def setWidth (v : Nat) (x : BitVec w) : BitVec v :=
   else
     .ofNat v x.toNat
 
-@[inherit_doc setWidth]
+/--
+Transform `x` of length `w` into a bitvector of length `v`, by either:
+- zero extending, that is, adding zeros in the high bits until it has length `v`, if `v > w`, or
+- truncating the high bits, if `v < w`.
+
+SMT-Lib name: `zero_extend`.
+-/
 abbrev zeroExtend := @setWidth
 
-@[inherit_doc setWidth]
+/--
+Transform `x` of length `w` into a bitvector of length `v`, by either:
+- zero extending, that is, adding zeros in the high bits until it has length `v`, if `v > w`, or
+- truncating the high bits, if `v < w`.
+
+SMT-Lib name: `zero_extend`.
+-/
 abbrev truncate := @setWidth
 
 /--
-Transforms a bitvector of length `w` into a bitvector of length `v`, padding as needed with the most
-significant bit's value.
+Sign extend a vector of length `w`, extending with `i` additional copies of the most significant
+bit in `x`. If `x` is an empty vector, then the sign is treated as zero.
 
-If `x` is an empty bitvector, then the sign is treated as zero.
-
-SMT-LIB name: `sign_extend`.
+SMT-Lib name: `sign_extend`.
 -/
 def signExtend (v : Nat) (x : BitVec w) : BitVec v := .ofInt v x.toInt
 
@@ -468,68 +449,69 @@ end cast
 section bitwise
 
 /--
-Bitwise and for bitvectors. Usually accessed via the `&&&` operator.
+Bitwise AND for bit vectors.
 
-SMT-LIB name: `bvand`.
+```lean
+0b1010#4 &&& 0b0110#4 = 0b0010#4
+```
 
-Example:
- * `0b1010#4 &&& 0b0110#4 = 0b0010#4`
+SMT-Lib name: `bvand`.
 -/
 protected def and (x y : BitVec n) : BitVec n :=
   (x.toNat &&& y.toNat)#'(Nat.and_lt_two_pow x.toNat y.isLt)
 instance : AndOp (BitVec w) := ⟨.and⟩
 
 /--
-Bitwise or for bitvectors. Usually accessed via the `|||` operator.
+Bitwise OR for bit vectors.
 
-SMT-LIB name: `bvor`.
+```lean
+0b1010#4 ||| 0b0110#4 = 0b1110#4
+```
 
-Example:
- * `0b1010#4 ||| 0b0110#4 = 0b1110#4`
+SMT-Lib name: `bvor`.
 -/
 protected def or (x y : BitVec n) : BitVec n :=
   (x.toNat ||| y.toNat)#'(Nat.or_lt_two_pow x.isLt y.isLt)
 instance : OrOp (BitVec w) := ⟨.or⟩
 
 /--
-Bitwise xor for bitvectors. Usually accessed via the `^^^` operator.
+ Bitwise XOR for bit vectors.
 
-SMT-LIB name: `bvxor`.
+```lean
+0b1010#4 ^^^ 0b0110#4 = 0b1100#4
+```
 
-Example:
- * `0b1010#4 ^^^ 0b0110#4 = 0b1100#4`
+SMT-Lib name: `bvxor`.
 -/
 protected def xor (x y : BitVec n) : BitVec n :=
   (x.toNat ^^^ y.toNat)#'(Nat.xor_lt_two_pow x.isLt y.isLt)
 instance : Xor (BitVec w) := ⟨.xor⟩
 
 /--
-Bitwise complement for bitvectors. Usually accessed via the `~~~` prefix operator.
+Bitwise NOT for bit vectors.
 
-SMT-LIB name: `bvnot`.
-
-Example:
- * `~~~(0b0101#4) == 0b1010`
+```lean
+~~~(0b0101#4) == 0b1010
+```
+SMT-Lib name: `bvnot`.
 -/
 protected def not (x : BitVec n) : BitVec n := allOnes n ^^^ x
 instance : Complement (BitVec w) := ⟨.not⟩
 
 /--
-Shifts a bitvector to the left. The low bits are filled with zeros. As a numeric operation, this is
+Left shift for bit vectors. The low bits are filled with zeros. As a numeric operation, this is
 equivalent to `x * 2^s`, modulo `2^n`.
 
-SMT-LIB name: `bvshl` except this operator uses a `Nat` shift value.
+SMT-Lib name: `bvshl` except this operator uses a `Nat` shift value.
 -/
 protected def shiftLeft (x : BitVec n) (s : Nat) : BitVec n := BitVec.ofNat n (x.toNat <<< s)
 instance : HShiftLeft (BitVec w) Nat (BitVec w) := ⟨.shiftLeft⟩
 
 /--
-Shifts a bitvector to the right. This is a logical right shift - the high bits are filled with
-zeros.
-
+(Logical) right shift for bit vectors. The high bits are filled with zeros.
 As a numeric operation, this is equivalent to `x / 2^s`, rounding down.
 
-SMT-LIB name: `bvlshr` except this operator uses a `Nat` shift value.
+SMT-Lib name: `bvlshr` except this operator uses a `Nat` shift value.
 -/
 def ushiftRight (x : BitVec n) (s : Nat) : BitVec n :=
   (x.toNat >>> s)#'(by
@@ -541,12 +523,11 @@ def ushiftRight (x : BitVec n) (s : Nat) : BitVec n :=
 instance : HShiftRight (BitVec w) Nat (BitVec w) := ⟨.ushiftRight⟩
 
 /--
-Shifts a bitvector to the right. This is an arithmetic right shift - the high bits are filled with
-most significant bit's value.
-
+Arithmetic right shift for bit vectors. The high bits are filled with the
+most-significant bit.
 As a numeric operation, this is equivalent to `x.toInt >>> s`.
 
-SMT-LIB name: `bvashr` except this operator uses a `Nat` shift value.
+SMT-Lib name: `bvashr` except this operator uses a `Nat` shift value.
 -/
 def sshiftRight (x : BitVec n) (s : Nat) : BitVec n := .ofInt n (x.toInt >>> s)
 
@@ -554,12 +535,11 @@ instance {n} : HShiftLeft  (BitVec m) (BitVec n) (BitVec m) := ⟨fun x y => x <
 instance {n} : HShiftRight (BitVec m) (BitVec n) (BitVec m) := ⟨fun x y => x >>> y.toNat⟩
 
 /--
-Shifts a bitvector to the right. This is an arithmetic right shift - the high bits are filled with
-most significant bit's value.
-
+Arithmetic right shift for bit vectors. The high bits are filled with the
+most-significant bit.
 As a numeric operation, this is equivalent to `a.toInt >>> s.toNat`.
 
-SMT-LIB name: `bvashr`.
+SMT-Lib name: `bvashr`.
 -/
 def sshiftRight' (a : BitVec n) (s : BitVec m) : BitVec n := a.sshiftRight s.toNat
 
@@ -569,15 +549,13 @@ def rotateLeftAux (x : BitVec w) (n : Nat) : BitVec w :=
   x <<< n ||| x >>> (w - n)
 
 /--
-Rotates the bits in a bitvector to the left.
+Rotate left for bit vectors. All the bits of `x` are shifted to higher positions, with the top `n`
+bits wrapping around to fill the low bits.
 
-All the bits of `x` are shifted to higher positions, with the top `n` bits wrapping around to fill
-the vacated low bits.
-
-SMT-LIB name: `rotate_left`, except this operator uses a `Nat` shift amount.
-
-Example:
- * `(0b0011#4).rotateLeft 3 = 0b1001`
+```lean
+rotateLeft  0b0011#4 3 = 0b1001
+```
+SMT-Lib name: `rotate_left` except this operator uses a `Nat` shift amount.
 -/
 def rotateLeft (x : BitVec w) (n : Nat) : BitVec w := rotateLeftAux x (n % w)
 
@@ -590,26 +568,21 @@ def rotateRightAux (x : BitVec w) (n : Nat) : BitVec w :=
   x >>> n ||| x <<< (w - n)
 
 /--
-Rotates the bits in a bitvector to the right.
+Rotate right for bit vectors. All the bits of `x` are shifted to lower positions, with the
+bottom `n` bits wrapping around to fill the high bits.
 
-All the bits of `x` are shifted to lower positions, with the bottom `n` bits wrapping around to fill
-the vacated high bits.
-
-SMT-LIB name: `rotate_right`, except this operator uses a `Nat` shift amount.
-
-Example:
- * `rotateRight 0b01001#5 1 = 0b10100`
+```lean
+rotateRight 0b01001#5 1 = 0b10100
+```
+SMT-Lib name: `rotate_right` except this operator uses a `Nat` shift amount.
 -/
 def rotateRight (x : BitVec w) (n : Nat) : BitVec w := rotateRightAux x (n % w)
 
 /--
-Concatenates two bitvectors using the “big-endian” convention that the more significant
-input is on the left. Usually accessed via the `++` operator.
+Concatenation of bitvectors. This uses the "big endian" convention that the more significant
+input is on the left, so `0xAB#8 ++ 0xCD#8 = 0xABCD#16`.
 
-SMT-LIB name: `concat`.
-
-Example:
- * `0xAB#8 ++ 0xCD#8 = 0xABCD#16`.
+SMT-Lib name: `concat`.
 -/
 def append (msbs : BitVec n) (lsbs : BitVec m) : BitVec (n+m) :=
   shiftLeftZeroExtend msbs m ||| setWidth' (Nat.le_add_left m n) lsbs
@@ -617,7 +590,7 @@ def append (msbs : BitVec n) (lsbs : BitVec m) : BitVec (n+m) :=
 instance : HAppend (BitVec w) (BitVec v) (BitVec (w + v)) := ⟨.append⟩
 
 -- TODO: write this using multiplication
-/-- Concatenates `i` copies of `x` into a new vector of length `w * i`. -/
+/-- `replicate i x` concatenates `i` copies of `x` into a new vector of length `w*i`. -/
 def replicate : (i : Nat) → BitVec w → BitVec (w*i)
   | 0,   _ => 0#0
   | n+1, x =>
@@ -636,18 +609,14 @@ result of appending a single bit to the front in the naive implementation).
 def concat {n} (msbs : BitVec n) (lsb : Bool) : BitVec (n+1) := msbs ++ (ofBool lsb)
 
 /--
-Shifts all bits of `x` to the left by `1` and sets the least significant bit to `b`.
-
-This is a non-dependent version of `BitVec.concat` that does not change the total bitwidth.
+`x.shiftConcat b` shifts all bits of `x` to the left by `1` and sets the least significant bit to `b`.
+It is a non-dependent version of `concat` that does not change the total bitwidth.
 -/
 def shiftConcat (x : BitVec n) (b : Bool) : BitVec n :=
   (x.concat b).truncate n
 
-/--
-Prepends a single bit to the front of a bitvector, using big-endian order (see `append`).
-
-The new bit is the most significant bit.
--/
+/-- Prepend a single bit to the front of a bitvector, using big endian order (see `append`).
+    That is, the new bit is the most significant bit. -/
 def cons {n} (msb : Bool) (lsbs : BitVec n) : BitVec (n+1) :=
   ((ofBool msb) ++ lsbs).cast (Nat.add_comm ..)
 
@@ -660,18 +629,15 @@ theorem ofBool_append (msb : Bool) (lsbs : BitVec w) :
   rfl
 
 /--
-`twoPow w i` is the bitvector `2^i` if `i < w`, and `0` otherwise. In other words, it is 2 to the
-power `i`.
-
-From the bitwise point of view, it has the `i`th bit as `1` and all other bits as `0`.
+`twoPow w i` is the bitvector `2^i` if `i < w`, and `0` otherwise.
+That is, 2 to the power `i`.
+For the bitwise point of view, it has the `i`th bit as `1` and all other bits as `0`.
 -/
 def twoPow (w : Nat) (i : Nat) : BitVec w := 1#w <<< i
 
 end bitwise
 
-/--
-Computes a hash of a bitvector, combining 64-bit words using `mixHash`.
--/
+/-- Compute a hash of a bitvector, combining 64-bit words using `mixHash`. -/
 def hash (bv : BitVec n) : UInt64 :=
   if n ≤ 64 then
     bv.toFin.val.toUInt64
@@ -699,63 +665,35 @@ section normalization_eqs
 @[simp] theorem zero_eq                                   : BitVec.zero n = 0#n               := rfl
 end normalization_eqs
 
-/-- Converts a list of `Bool`s into a big-endian `BitVec`. -/
+/-- Converts a list of `Bool`s to a big-endian `BitVec`. -/
 def ofBoolListBE : (bs : List Bool) → BitVec bs.length
 | [] => 0#0
 | b :: bs => cons b (ofBoolListBE bs)
 
-/-- Converts a list of `Bool`s into a little-endian `BitVec`. -/
+/-- Converts a list of `Bool`s to a little-endian `BitVec`. -/
 def ofBoolListLE : (bs : List Bool) → BitVec bs.length
 | [] => 0#0
 | b :: bs => concat (ofBoolListLE bs) b
 
 /-! ## Overflow -/
 
-/--
-Checks whether addition of `x` and `y` results in *unsigned* overflow.
+/-- `uaddOverflow x y` returns `true` if addition of `x` and `y` results in *unsigned* overflow.
 
-SMT-LIB name: `bvuaddo`.
+  SMT-Lib name: `bvuaddo`.
 -/
 def uaddOverflow {w : Nat} (x y : BitVec w) : Bool := x.toNat + y.toNat ≥ 2 ^ w
 
-/--
-Checks whether addition of `x` and `y` results in *signed* overflow, treating `x` and `y` as 2's
-complement signed bitvectors.
+/-- `saddOverflow x y` returns `true` if addition of `x` and `y` results in *signed* overflow,
+treating `x` and `y` as 2's complement signed bitvectors.
 
-SMT-LIB name: `bvsaddo`.
+  SMT-Lib name: `bvsaddo`.
 -/
 def saddOverflow {w : Nat} (x y : BitVec w) : Bool :=
   (x.toInt + y.toInt ≥ 2 ^ (w - 1)) || (x.toInt + y.toInt < - 2 ^ (w - 1))
 
-/--
-Checks whether subtraction of `x` and `y` results in *unsigned* overflow.
-
-SMT-Lib name: `bvusubo`.
--/
-def usubOverflow {w : Nat} (x y : BitVec w) : Bool := x.toNat < y.toNat
-
-/--
-Checks whether the subtraction of `x` and `y` results in *signed* overflow, treating `x` and `y` as
-2's complement signed bitvectors.
-
-SMT-Lib name: `bvssubo`.
--/
-def ssubOverflow {w : Nat} (x y : BitVec w) : Bool :=
-  (x.toInt - y.toInt ≥ 2 ^ (w - 1)) || (x.toInt - y.toInt < - 2 ^ (w - 1))
-
-/--
-Checks whether the negation of a bitvector results in overflow.
-
-For a bitvector `x` with nonzero width, this only happens if `x = intMin`.
-
-SMT-Lib name: `bvnego`.
--/
-def negOverflow {w : Nat} (x : BitVec w) : Bool :=
-  x.toInt == - 2 ^ (w - 1)
-
 /- ### reverse -/
 
-/-- Reverses the bits in a bitvector. -/
+/-- Reverse the bits in a bitvector. -/
 def reverse : {w : Nat} → BitVec w → BitVec w
   | 0, x => x
   | w + 1, x => concat (reverse (x.truncate w)) (x.msb)

src/Init/Data/BitVec/BasicAux.lean

@@ -17,9 +17,7 @@ namespace BitVec
 
 section Nat
 
-/--
-The bitvector with value `i mod 2^n`.
--/
+/-- The `BitVec` with value `i mod 2^n`. -/
 @[match_pattern]
 protected def ofNat (n : Nat) (i : Nat) : BitVec n where
   toFin := Fin.ofNat' (2^n) i
@@ -34,18 +32,17 @@ end Nat
 section arithmetic
 
 /--
-Adds two bitvectors. This can be interpreted as either signed or unsigned addition modulo `2^n`.
-Usually accessed via the `+` operator.
+Addition for bit vectors. This can be interpreted as either signed or unsigned addition
+modulo `2^n`.
 
-SMT-LIB name: `bvadd`.
+SMT-Lib name: `bvadd`.
 -/
 protected def add (x y : BitVec n) : BitVec n := .ofNat n (x.toNat + y.toNat)
 instance : Add (BitVec n) := ⟨BitVec.add⟩
 
 /--
-Subtracts one bitvector from another. This can be interpreted as either signed or unsigned subtraction
-modulo `2^n`. Usually accessed via the `-` operator.
-
+Subtraction for bit vectors. This can be interpreted as either signed or unsigned subtraction
+modulo `2^n`.
 -/
 protected def sub (x y : BitVec n) : BitVec n := .ofNat n ((2^n - y.toNat) + x.toNat)
 instance : Sub (BitVec n) := ⟨BitVec.sub⟩

src/Init/Data/BitVec/Bitblast.lean

@@ -9,7 +9,7 @@ import Init.Data.Nat.Mod
 import Init.Data.Int.LemmasAux
 
 /-!
-# Bit blasting of bitvectors
+# Bitblasting of bitvectors
 
 This module provides theorems for showing the equivalence between BitVec operations using
 the `Fin 2^n` representation and Boolean vectors.  It is still under development, but
@@ -19,21 +19,21 @@ as vectors of bits into proofs about Lean `BitVec` values.
 The module is named for the bit-blasting operation in an SMT solver that converts bitvector
 expressions into expressions about individual bits in each vector.
 
-### Example: How bit blasting works for multiplication
+### Example: How bitblasting works for multiplication
 
-We explain how the lemmas here are used for bit blasting,
+We explain how the lemmas here are used for bitblasting,
 by using multiplication as a prototypical example.
-Other bit blasters for other operations follow the same pattern.
-To bit blast a multiplication of the form `x * y`,
+Other bitblasters for other operations follow the same pattern.
+To bitblast a multiplication of the form `x * y`,
 we must unfold the above into a form that the SAT solver understands.
 
-We assume that the solver already knows how to bit blast addition.
+We assume that the solver already knows how to bitblast addition.
 This is known to `bv_decide`, by exploiting the lemma `add_eq_adc`,
 which says that `x + y : BitVec w` equals `(adc x y false).2`,
 where `adc` builds an add-carry circuit in terms of the primitive operations
 (bitwise and, bitwise or, bitwise xor) that bv_decide already understands.
-In this way, we layer bit blasters on top of each other,
-by reducing the multiplication bit blaster to an addition operation.
+In this way, we layer bitblasters on top of each other,
+by reducing the multiplication bitblaster to an addition operation.
 
 The core lemma is given by `getLsbD_mul`:
 
@@ -65,7 +65,7 @@ mulRec_succ_eq
 By repeatedly applying the lemmas `mulRec_zero_eq` and `mulRec_succ_eq`,
 one obtains a circuit for multiplication.
 Note that this circuit uses `BitVec.add`, `BitVec.getLsbD`, `BitVec.shiftLeft`.
-Here, `BitVec.add` and `BitVec.shiftLeft` are (recursively) bit blasted by `bv_decide`,
+Here, `BitVec.add` and `BitVec.shiftLeft` are (recursively) bitblasted by `bv_decide`,
 using the lemmas `add_eq_adc` and `shiftLeft_eq_shiftLeftRec`,
 and `BitVec.getLsbD` is a primitive that `bv_decide` knows how to reduce to SAT.
 
@@ -88,10 +88,10 @@ computes the correct value for multiplication.
 
 To zoom out, therefore, we follow two steps:
 First, we prove bitvector lemmas to unfold a high-level operation (such as multiplication)
-into already bit blastable operations (such as addition and left shift).
+into already bitblastable operations (such as addition and left shift).
 We then use these lemmas to prove the correctness of the circuit that `bv_decide` builds.
 
-We use this workflow to implement bit blasting for all SMT-LIB v2 operations.
+We use this workflow to implement bitblasting for all SMT-LIB2 operations.
 
 ## Main results
 * `x + y : BitVec w` is `(adc x y false).2`.
@@ -109,12 +109,7 @@ open Nat Bool
 
 namespace Bool
 
-/--
-At least two out of three Booleans are true.
-
-This function is typically used to model addition of binary numbers, to combine a carry bit with two
-addend bits.
--/
+/-- At least two out of three booleans are true. -/
 abbrev atLeastTwo (a b c : Bool) : Bool := a && b || a && c || b && c
 
 @[simp] theorem atLeastTwo_false_left  : atLeastTwo false b c = (b && c) := by simp [atLeastTwo]
@@ -149,7 +144,7 @@ private theorem testBit_limit {x i : Nat} (x_lt_succ : x < 2^(i+1)) :
         exfalso
         apply Nat.lt_irrefl
         calc x < 2^(i+1) := x_lt_succ
-             _ ≤ 2 ^ j := Nat.pow_le_pow_right Nat.zero_lt_two x_lt
+             _ ≤ 2 ^ j := Nat.pow_le_pow_of_le_right Nat.zero_lt_two x_lt
              _ ≤ x := testBit_implies_ge jp
 
 private theorem mod_two_pow_succ (x i : Nat) :
@@ -290,7 +285,7 @@ theorem adc_spec (x y : BitVec w) (c : Bool) :
     simp [carry, Nat.mod_one]
     cases c <;> rfl
   case step =>
-    simp [adcb, Prod.mk.injEq, carry_succ, getElem_add_add_bool]
+    simp [adcb, Prod.mk.injEq, carry_succ, getLsbD_add_add_bool]
 
 theorem add_eq_adc (w : Nat) (x y : BitVec w) : x + y = (adc x y false).snd := by
   simp [adc_spec]
@@ -300,7 +295,7 @@ theorem add_eq_adc (w : Nat) (x y : BitVec w) : x + y = (adc x y false).snd := b
 theorem getMsbD_add {i : Nat} {i_lt : i < w} {x y : BitVec w} :
     getMsbD (x + y) i =
       Bool.xor (getMsbD x i) (Bool.xor (getMsbD y i) (carry (w - 1 - i) x y false)) := by
-  simp [getMsbD, getElem_add, i_lt, show w - 1 - i < w by omega]
+  simp [getMsbD, getLsbD_add, i_lt, show w - 1 - i < w by omega]
 
 theorem msb_add {w : Nat} {x y: BitVec w} :
     (x + y).msb =
@@ -364,25 +359,24 @@ theorem msb_sub {x y: BitVec w} :
 /-! ### Negation -/
 
 theorem bit_not_testBit (x : BitVec w) (i : Fin w) :
-  (((iunfoldr (fun (i : Fin w) c => (c, !(x[i.val])))) ()).snd)[i.val] = !(getLsbD x i.val) := by
+  getLsbD (((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsbD i)))) ()).snd) i.val = !(getLsbD x i.val) := by
   apply iunfoldr_getLsbD (fun _ => ()) i (by simp)
 
 theorem bit_not_add_self (x : BitVec w) :
-  ((iunfoldr (fun (i : Fin w) c => (c, !(x[i.val])))) ()).snd + x  = -1 := by
+  ((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsbD i)))) ()).snd + x  = -1 := by
   simp only [add_eq_adc]
   apply iunfoldr_replace_snd (fun _ => false) (-1) false rfl
-  intro i; simp only [adcb, Fin.is_lt, getLsbD_eq_getElem, atLeastTwo_false_right, bne_false,
-    ofNat_eq_ofNat, Fin.getElem_fin, Prod.mk.injEq, and_eq_false_imp]
-  rw [iunfoldr_replace_snd (fun _ => ()) (((iunfoldr (fun i c => (c, !(x[i.val])))) ()).snd)]
-  <;> simp [bit_not_testBit, negOne_eq_allOnes, getElem_allOnes]
+  intro i; simp only [ BitVec.not, adcb, testBit_toNat]
+  rw [iunfoldr_replace_snd (fun _ => ()) (((iunfoldr (fun i c => (c, !(x.getLsbD i)))) ()).snd)]
+  <;> simp [bit_not_testBit, negOne_eq_allOnes, getLsbD_allOnes]
 
 theorem bit_not_eq_not (x : BitVec w) :
-  ((iunfoldr (fun i c => (c, !(x[i])))) ()).snd = ~~~ x := by
+  ((iunfoldr (fun i c => (c, !(x.getLsbD i)))) ()).snd = ~~~ x := by
   simp [←allOnes_sub_eq_not, BitVec.eq_sub_iff_add_eq.mpr (bit_not_add_self x), ←negOne_eq_allOnes]
 
-theorem bit_neg_eq_neg (x : BitVec w) : -x = (adc (((iunfoldr (fun (i : Fin w) c => (c, !(x[i.val])))) ()).snd) (BitVec.ofNat w 1) false).snd:= by
+theorem bit_neg_eq_neg (x : BitVec w) : -x = (adc (((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsbD i)))) ()).snd) (BitVec.ofNat w 1) false).snd:= by
   simp only [← add_eq_adc]
-  rw [iunfoldr_replace_snd ((fun _ => ())) (((iunfoldr (fun (i : Fin w) c => (c, !(x[i.val])))) ()).snd) _ rfl]
+  rw [iunfoldr_replace_snd ((fun _ => ())) (((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsbD i)))) ()).snd) _ rfl]
   · rw [BitVec.eq_sub_iff_add_eq.mpr (bit_not_add_self x), sub_toAdd, BitVec.add_comm _ (-x)]
     simp [← sub_toAdd, BitVec.sub_add_cancel]
   · simp [bit_not_testBit x _]
@@ -483,39 +477,6 @@ theorem msb_neg {w : Nat} {x : BitVec w} :
         case zero => exact hmsb
         case succ => exact getMsbD_x _ hi (by omega)
 
-/-- This is false if `v < w` and `b = intMin`. See also `signExtend_neg_of_ne_intMin`. -/
-@[simp] theorem signExtend_neg_of_le {v w : Nat} (h : w ≤ v) (b : BitVec v) :
-    (-b).signExtend w = -b.signExtend w := by
-  apply BitVec.eq_of_getElem_eq
-  intro i hi
-  simp only [getElem_signExtend, getElem_neg]
-  rw [dif_pos (by omega), dif_pos (by omega)]
-  simp only [getLsbD_signExtend, Bool.and_eq_true, decide_eq_true_eq, Bool.ite_eq_true_distrib,
-    Bool.bne_right_inj, decide_eq_decide]
-  exact ⟨fun ⟨j, hj₁, hj₂⟩ => ⟨j, ⟨hj₁, ⟨by omega, by rwa [if_pos (by omega)]⟩⟩⟩,
-    fun ⟨j, hj₁, hj₂, hj₃⟩ => ⟨j, hj₁, by rwa [if_pos (by omega)] at hj₃⟩⟩
-
-/-- This is false if `v < w` and `b = intMin`. See also `signExtend_neg_of_le`. -/
-@[simp] theorem signExtend_neg_of_ne_intMin {v w : Nat} (b : BitVec v) (hb : b ≠ intMin v) :
-    (-b).signExtend w = -b.signExtend w := by
-  refine (by omega : w ≤ v ∨ v < w).elim (fun h => signExtend_neg_of_le h b) (fun h => ?_)
-  apply BitVec.eq_of_toInt_eq
-  rw [toInt_signExtend_of_le (by omega), toInt_neg_of_ne_intMin hb, toInt_neg_of_ne_intMin,
-    toInt_signExtend_of_le (by omega)]
-  apply ne_of_apply_ne BitVec.toInt
-  rw [toInt_signExtend_of_le (by omega), toInt_intMin_of_pos (by omega)]
-  have := b.le_two_mul_toInt
-  have : -2 ^ w < -2 ^ v := by
-    apply Int.neg_lt_neg
-    norm_cast
-    rwa [Nat.pow_lt_pow_iff_right (by omega)]
-  have : 2 * b.toInt ≠ -2 ^ w := by omega
-  rw [(show w = w - 1 + 1 by omega), Int.pow_succ] at this
-  omega
-
-@[simp] theorem BitVec.setWidth_neg_of_le {x : BitVec v} (h : w ≤ v) : BitVec.setWidth w (-x) = -BitVec.setWidth w x := by
-  simp [← BitVec.signExtend_eq_setWidth_of_le _ h, BitVec.signExtend_neg_of_le h]
-
 /-! ### abs -/
 
 theorem msb_abs {w : Nat} {x : BitVec w} :
@@ -567,64 +528,30 @@ theorem slt_eq_not_ult_of_msb_neq {x y : BitVec w} (h : x.msb ≠ y.msb) :
   simp only [BitVec.slt, toInt_eq_msb_cond, Bool.eq_not_of_ne h, ult_eq_msb_of_msb_neq h]
   cases y.msb <;> (simp; omega)
 
-theorem slt_eq_ult {x y : BitVec w} :
+theorem slt_eq_ult (x y : BitVec w) :
     x.slt y = (x.msb != y.msb).xor (x.ult y) := by
   by_cases h : x.msb = y.msb
   · simp [h, slt_eq_ult_of_msb_eq]
   · have h' : x.msb != y.msb := by simp_all
     simp [slt_eq_not_ult_of_msb_neq h, h']
 
-theorem slt_eq_not_carry {x y : BitVec w} :
+theorem slt_eq_not_carry (x y : BitVec w) :
     x.slt y = (x.msb == y.msb).xor (carry w x (~~~y) true) := by
   simp only [slt_eq_ult, bne, ult_eq_not_carry]
   cases x.msb == y.msb <;> simp
 
-theorem sle_eq_not_slt {x y : BitVec w} : x.sle y = !y.slt x := by
+theorem sle_eq_not_slt (x y : BitVec w) : x.sle y = !y.slt x := by
   simp only [BitVec.sle, BitVec.slt, ← decide_not, decide_eq_decide]; omega
 
-theorem zero_sle_eq_not_msb {w : Nat} {x : BitVec w} : BitVec.sle 0#w x = !x.msb := by
-  rw [sle_eq_not_slt, BitVec.slt_zero_eq_msb]
-
-theorem zero_sle_iff_msb_eq_false {w : Nat} {x : BitVec w} : BitVec.sle 0#w x ↔ x.msb = false := by
-  simp [zero_sle_eq_not_msb]
-
-theorem toNat_toInt_of_sle {w : Nat} {x : BitVec w} (hx : BitVec.sle 0#w x) : x.toInt.toNat = x.toNat :=
-  toNat_toInt_of_msb x (zero_sle_iff_msb_eq_false.1 hx)
-
-theorem sle_eq_carry {x y : BitVec w} :
+theorem sle_eq_carry (x y : BitVec w) :
     x.sle y = !((x.msb == y.msb).xor (carry w y (~~~x) true)) := by
   rw [sle_eq_not_slt, slt_eq_not_carry, beq_comm]
 
-theorem neg_slt_zero (h : 0 < w) {x : BitVec w} :
-    (-x).slt 0#w = ((x == intMin w) || (0#w).slt x) := by
-  rw [slt_zero_eq_msb, msb_neg, slt_eq_sle_and_ne, zero_sle_eq_not_msb]
-  apply Bool.eq_iff_iff.2
-  cases hmsb : x.msb with
-  | false => simpa [ne_intMin_of_msb_eq_false h hmsb] using Decidable.not_iff_not.2 (eq_comm)
-  | true =>
-    simp only [Bool.bne_true, Bool.not_and, Bool.or_eq_true, Bool.not_eq_eq_eq_not, Bool.not_true,
-      bne_eq_false_iff_eq, Bool.false_and, Bool.or_false, beq_iff_eq,
-      _root_.or_iff_right_iff_imp]
-    rintro rfl
-    simp at hmsb
-
-theorem neg_sle_zero (h : 0 < w) {x : BitVec w} :
-    (-x).sle 0#w = (x == intMin w || (0#w).sle x) := by
-  rw [sle_eq_slt_or_eq, neg_slt_zero h, sle_eq_slt_or_eq]
-  simp [Bool.beq_eq_decide_eq (-x), Bool.beq_eq_decide_eq _ x, Eq.comm (a := x), Bool.or_assoc]
-
-theorem sle_eq_ule {x y : BitVec w} : x.sle y = (x.msb != y.msb ^^ x.ule y) := by
-  rw [sle_eq_not_slt, slt_eq_ult, ← Bool.xor_not, ← ule_eq_not_ult, bne_comm]
-
-theorem sle_eq_ule_of_msb_eq {x y : BitVec w} (h : x.msb = y.msb) : x.sle y = x.ule y := by
-  simp [BitVec.sle_eq_ule, h]
-
-/-! ### mul recurrence for bit blasting -/
+/-! ### mul recurrence for bitblasting -/
 
 /--
 A recurrence that describes multiplication as repeated addition.
-
-This function is useful for bit blasting multiplication.
+Is useful for bitblasting multiplication.
 -/
 def mulRec (x y : BitVec w) (s : Nat) : BitVec w :=
   let cur := if y.getLsbD s then (x <<< s) else 0
@@ -648,18 +575,16 @@ theorem setWidth_setWidth_succ_eq_setWidth_setWidth_add_twoPow (x : BitVec w) (i
       setWidth w (x.setWidth i) + (x &&& twoPow w i) := by
   rw [add_eq_or_of_and_eq_zero]
   · ext k h
-    simp only [getElem_setWidth, getLsbD_setWidth, h, getLsbD_eq_getElem, getElem_or, getElem_and,
-      getElem_twoPow]
+    simp only [getLsbD_setWidth, h, decide_true, Bool.true_and, getLsbD_or, getLsbD_and]
     by_cases hik : i = k
     · subst hik
       simp [h]
-    · by_cases hik' : k < (i + 1)
+    · simp only [getLsbD_twoPow, hik, decide_false, Bool.and_false, Bool.or_false]
+      by_cases hik' : k < (i + 1)
       · have hik'' : k < i := by omega
         simp [hik', hik'']
-        omega
       · have hik'' : ¬ (k < i) := by omega
         simp [hik', hik'']
-        omega
   · ext k
     simp only [and_twoPow, getLsbD_and, getLsbD_setWidth, Fin.is_lt, decide_true, Bool.true_and,
       getLsbD_zero, and_eq_false_imp, and_eq_true, decide_eq_true_eq, and_imp]
@@ -707,12 +632,6 @@ theorem getLsbD_mul (x y : BitVec w) (i : Nat) :
   · simp
   · omega
 
-theorem mul_eq_mulRec {x y : BitVec w} :
-    x * y = mulRec x y w := by
-  apply eq_of_getLsbD_eq
-  intro i hi
-  apply getLsbD_mul
-
 theorem getMsbD_mul (x y : BitVec w) (i : Nat) :
     (x * y).getMsbD i = (mulRec x y w).getMsbD i := by
   simp only [mulRec_eq_mul_signExtend_setWidth]
@@ -724,16 +643,15 @@ theorem getElem_mul {x y : BitVec w} {i : Nat} (h : i < w) :
     (x * y)[i] = (mulRec x y w)[i] := by
   simp [mulRec_eq_mul_signExtend_setWidth]
 
-/-! ## shiftLeft recurrence for bit blasting -/
+/-! ## shiftLeft recurrence for bitblasting -/
 
 /--
-Shifts `x` to the left by the first `n` bits of `y`.
+`shiftLeftRec x y n` shifts `x` to the left by the first `n` bits of `y`.
 
-The theorem `BitVec.shiftLeft_eq_shiftLeftRec` proves the equivalence of `(x <<< y)` and
-`BitVec.shiftLeftRec x y`.
+The theorem `shiftLeft_eq_shiftLeftRec` proves the equivalence of `(x <<< y)` and `shiftLeftRec`.
 
-Together with equations `BitVec.shiftLeftRec_zero` and `BitVec.shiftLeftRec_succ`, this allows
-`BitVec.shiftLeft` to be unfolded into a circuit for bit blasting.
+Together with equations `shiftLeftRec_zero`, `shiftLeftRec_succ`,
+this allows us to unfold `shiftLeft` into a circuit for bitblasting.
  -/
 def shiftLeftRec (x : BitVec w₁) (y : BitVec w₂) (n : Nat) : BitVec w₁ :=
   let shiftAmt := (y &&& (twoPow w₂ n))
@@ -787,7 +705,7 @@ theorem shiftLeftRec_eq {x : BitVec w₁} {y : BitVec w₂} {n : Nat} :
 
 /--
 Show that `x <<< y` can be written in terms of `shiftLeftRec`.
-This can be unfolded in terms of `shiftLeftRec_zero`, `shiftLeftRec_succ` for bit blasting.
+This can be unfolded in terms of `shiftLeftRec_zero`, `shiftLeftRec_succ` for bitblasting.
 -/
 theorem shiftLeft_eq_shiftLeftRec (x : BitVec w₁) (y : BitVec w₂) :
     x <<< y = shiftLeftRec x y (w₂ - 1) := by
@@ -795,7 +713,7 @@ theorem shiftLeft_eq_shiftLeftRec (x : BitVec w₁) (y : BitVec w₂) :
   · simp [of_length_zero]
   · simp [shiftLeftRec_eq]
 
-/-! # udiv/urem recurrence for bit blasting
+/-! # udiv/urem recurrence for bitblasting
 
 In order to prove the correctness of the division algorithm on the integers,
 one shows that `n.div d = q` and `n.mod d = r` iff `n = d * q + r` and `0 ≤ r < d`.
@@ -986,7 +904,7 @@ The input to the shift subtractor is a legal input to `divrem`, and we also need
 input bit to perform shift subtraction on, and thus we need `0 < wn`.
 -/
 structure DivModState.Poised {w : Nat} (args : DivModArgs w) (qr : DivModState w)
-  extends DivModState.Lawful args qr where
+  extends DivModState.Lawful args qr : Type where
   /-- Only perform a round of shift-subtract if we have dividend bits. -/
   hwn_lt : 0 < qr.wn
 
@@ -1002,9 +920,8 @@ def DivModState.wr_lt_w {qr : DivModState w} (h : qr.Poised args) : qr.wr < w :=
 /-! ### Division shift subtractor -/
 
 /--
-One round of the division algorithm. It tries to perform a subtract shift.
-
-This should only be called when `r.msb = false`, so it will not overflow.
+One round of the division algorithm, that tries to perform a subtract shift.
+Note that this should only be called when `r.msb = false`, so we will not overflow.
 -/
 def divSubtractShift (args : DivModArgs w) (qr : DivModState w) : DivModState w :=
   let {n, d} := args
@@ -1094,7 +1011,7 @@ theorem lawful_divSubtractShift (qr : DivModState w) (h : qr.Poised args) :
 
 /-! ### Core division algorithm circuit -/
 
-/-- A recursive definition of division for bit blasting, in terms of a shift-subtraction circuit. -/
+/-- A recursive definition of division for bitblasting, in terms of a shift-subtraction circuit. -/
 def divRec {w : Nat} (m : Nat) (args : DivModArgs w) (qr : DivModState w) :
     DivModState w :=
   match m with
@@ -1114,10 +1031,11 @@ theorem divRec_succ (m : Nat) (args : DivModArgs w) (qr : DivModState w) :
 theorem lawful_divRec {args : DivModArgs w} {qr : DivModState w}
     (h : DivModState.Lawful args qr) :
     DivModState.Lawful args (divRec qr.wn args qr) := by
-  induction hm : qr.wn generalizing qr with
-  | zero =>
+  generalize hm : qr.wn = m
+  induction m generalizing qr
+  case zero =>
     exact h
-  | succ wn' ih =>
+  case succ wn' ih =>
     simp only [divRec_succ]
     apply ih
     · apply lawful_divSubtractShift
@@ -1131,10 +1049,11 @@ theorem lawful_divRec {args : DivModArgs w} {qr : DivModState w}
 @[simp]
 theorem wn_divRec (args : DivModArgs w) (qr : DivModState w) :
     (divRec qr.wn args qr).wn = 0 := by
-  induction hm : qr.wn generalizing qr with
-  | zero =>
+  generalize hm : qr.wn = m
+  induction m generalizing qr
+  case zero =>
     assumption
-  | succ wn' ih =>
+  case succ wn' ih =>
     apply ih
     simp only [divSubtractShift, hm]
     split <;> rfl
@@ -1191,12 +1110,10 @@ theorem getMsbD_udiv (n d : BitVec w) (hd : 0#w < d)  (i : Nat) :
 /- ### Arithmetic shift right (sshiftRight) recurrence -/
 
 /--
-Shifts `x` arithmetically (signed) to the right by the first `n` bits of `y`.
-
-The theorem `BitVec.sshiftRight_eq_sshiftRightRec` proves the equivalence of `(x.sshiftRight y)` and
-`BitVec.sshiftRightRec x y`. Together with equations `BitVec.sshiftRightRec_zero`, and
-`BitVec.sshiftRightRec_succ`, this allows `BitVec.sshiftRight` to be unfolded into a circuit for
-bit blasting.
+`sshiftRightRec x y n` shifts `x` arithmetically/signed to the right by the first `n` bits of `y`.
+The theorem `sshiftRight_eq_sshiftRightRec` proves the equivalence of `(x.sshiftRight y)` and `sshiftRightRec`.
+Together with equations `sshiftRightRec_zero`, `sshiftRightRec_succ`,
+this allows us to unfold `sshiftRight` into a circuit for bitblasting.
 -/
 def sshiftRightRec (x : BitVec w₁) (y : BitVec w₂) (n : Nat) : BitVec w₁ :=
   let shiftAmt := (y &&& (twoPow w₂ n))
@@ -1243,7 +1160,7 @@ theorem sshiftRightRec_eq (x : BitVec w₁) (y : BitVec w₂) (n : Nat) :
 
 /--
 Show that `x.sshiftRight y` can be written in terms of `sshiftRightRec`.
-This can be unfolded in terms of `sshiftRightRec_zero_eq`, `sshiftRightRec_succ_eq` for bit blasting.
+This can be unfolded in terms of `sshiftRightRec_zero_eq`, `sshiftRightRec_succ_eq` for bitblasting.
 -/
 theorem sshiftRight_eq_sshiftRightRec (x : BitVec w₁) (y : BitVec w₂) :
     (x.sshiftRight' y).getLsbD i = (sshiftRightRec x y (w₂ - 1)).getLsbD i := by
@@ -1251,16 +1168,16 @@ theorem sshiftRight_eq_sshiftRightRec (x : BitVec w₁) (y : BitVec w₂) :
   · simp [of_length_zero]
   · simp [sshiftRightRec_eq]
 
-/- ### Logical shift right (ushiftRight) recurrence for bit blasting -/
+/- ### Logical shift right (ushiftRight) recurrence for bitblasting -/
 
 /--
-Shifts `x` logically to the right by the first `n` bits of `y`.
+`ushiftRightRec x y n` shifts `x` logically to the right by the first `n` bits of `y`.
 
-The theorem `BitVec.shiftRight_eq_ushiftRightRec` proves the equivalence
-of `(x >>> y)` and `BitVec.ushiftRightRec`.
+The theorem `shiftRight_eq_ushiftRightRec` proves the equivalence
+of `(x >>> y)` and `ushiftRightRec`.
 
-Together with equations `BitVec.ushiftRightRec_zero` and `BitVec.ushiftRightRec_succ`,
-this allows `BitVec.ushiftRight` to be unfolded into a circuit for bit blasting.
+Together with equations `ushiftRightRec_zero`, `ushiftRightRec_succ`,
+this allows us to unfold `ushiftRight` into a circuit for bitblasting.
 -/
 def ushiftRightRec (x : BitVec w₁) (y : BitVec w₂) (n : Nat) : BitVec w₁ :=
   let shiftAmt := (y &&& (twoPow w₂ n))
@@ -1306,7 +1223,7 @@ theorem ushiftRightRec_eq (x : BitVec w₁) (y : BitVec w₂) (n : Nat) :
 
 /--
 Show that `x >>> y` can be written in terms of `ushiftRightRec`.
-This can be unfolded in terms of `ushiftRightRec_zero`, `ushiftRightRec_succ` for bit blasting.
+This can be unfolded in terms of `ushiftRightRec_zero`, `ushiftRightRec_succ` for bitblasting.
 -/
 theorem shiftRight_eq_ushiftRightRec (x : BitVec w₁) (y : BitVec w₂) :
     x >>> y = ushiftRightRec x y (w₂ - 1) := by
@@ -1326,38 +1243,14 @@ theorem saddOverflow_eq {w : Nat} (x y : BitVec w) :
   simp only [saddOverflow]
   rcases w with _|w
   · revert x y; decide
-  · have := le_two_mul_toInt (x := x); have := two_mul_toInt_lt (x := x)
-    have := le_two_mul_toInt (x := y); have := two_mul_toInt_lt (x := y)
+  · have := le_toInt (x := x); have := toInt_lt (x := x)
+    have := le_toInt (x := y); have := toInt_lt (x := y)
     simp only [← decide_or, msb_eq_toInt, decide_beq_decide, toInt_add, ← decide_not, ← decide_and,
       decide_eq_decide]
     rw_mod_cast [Int.bmod_neg_iff (by omega) (by omega)]
     simp
     omega
 
-theorem usubOverflow_eq {w : Nat} (x y : BitVec w) :
-    usubOverflow x y = decide (x < y) := rfl
-
-theorem ssubOverflow_eq {w : Nat} (x y : BitVec w) :
-    ssubOverflow x y = ((!x.msb && y.msb && (x - y).msb) || (x.msb && !y.msb && !(x - y).msb)) := by
-  simp only [ssubOverflow]
-  rcases w with _|w
-  · simp [BitVec.of_length_zero]
-  · have h₁ := BitVec.toInt_sub_toInt_lt_twoPow_iff (x := x) (y := y)
-    have h₂ := BitVec.twoPow_le_toInt_sub_toInt_iff (x := x) (y := y)
-    simp only [Nat.add_one_sub_one] at h₁ h₂
-    simp only [Nat.add_one_sub_one, ge_iff_le, msb_eq_toInt, ← decide_not, Int.not_lt, toInt_sub]
-    simp only [bool_to_prop]
-    omega
-
-theorem negOverflow_eq {w : Nat} (x : BitVec w) :
-    (negOverflow x) = (decide (0 < w) && (x == intMin w)) := by
-  simp only [negOverflow]
-  rcases w with _|w
-  · simp [toInt_of_zero_length, Int.min_eq_right]
-  · suffices - 2 ^ w = (intMin (w + 1)).toInt by simp [beq_eq_decide_eq, ← toInt_inj, this]
-    simp only [toInt_intMin, Nat.add_one_sub_one, Int.ofNat_emod, Int.neg_inj]
-    rw_mod_cast [Nat.mod_eq_of_lt (by simp [Nat.pow_lt_pow_succ])]
-
 /- ### umod -/
 
 theorem getElem_umod {n d : BitVec w} (hi : i < w) :
@@ -1387,387 +1280,4 @@ theorem getMsbD_umod {n d : BitVec w}:
     simp [BitVec.getMsbD_eq_getLsbD, hi]
   · simp [show w ≤ i by omega]
 
-
-/-! ### Mappings to and from BitVec -/
-
-theorem eq_iff_eq_of_inv (f : α → BitVec w) (g : BitVec w → α) (h : ∀ x, g (f x) = x) :
-    ∀ x y, x = y ↔ f x = f y := by
-  intro x y
-  constructor
-  · intro h'
-    rw [h']
-  · intro h'
-    have := congrArg g h'
-    simpa [h] using this
-
-@[simp]
-theorem ne_intMin_of_lt_of_msb_false {x : BitVec w} (hw : 0 < w) (hx : x.msb = false) :
-    x ≠ intMin w := by
-  have := toNat_lt_of_msb_false hx
-  simp [toNat_eq, Nat.two_pow_pred_mod_two_pow hw]
-  omega
-
-@[simp]
-theorem ne_zero_of_msb_true {x : BitVec w} (hx : x.msb = true) :
-    x ≠ 0#w := by
-  have := Nat.two_pow_pos (w-1)
-  have := le_toNat_of_msb_true hx
-  simp [toNat_eq]
-  omega
-
-@[simp]
-theorem msb_neg_of_ne_intMin_of_ne_zero {x : BitVec w} (h : x ≠ intMin w) (h' : x ≠ 0#w) :
-    (-x).msb = !x.msb := by
-  simp only [msb_neg, bool_to_prop]
-  simp [h, h']
-
-@[simp]
-theorem udiv_intMin_of_msb_false {x : BitVec w} (h : x.msb = false) :
-    x / intMin w = 0#w := by
-  by_cases hw : w = 0
-  · subst hw
-    decide +revert
-  have wpos : 0 < w := by omega
-  have := Nat.two_pow_pos (w-1)
-  simp [toNat_eq, wpos]
-  rw [Nat.div_eq_zero_iff_lt (by omega)]
-  exact toNat_lt_of_msb_false h
-
-theorem sdiv_intMin {x : BitVec w} :
-    x.sdiv (intMin w) = if x = intMin w then 1#w else 0#w := by
-  by_cases hw : w = 0
-  · subst hw
-    decide +revert
-  have wpos : 0 < w := by omega
-  by_cases h : x = intMin w
-  · subst h
-    simp
-    omega
-  · simp only [sdiv_eq, msb_intMin, show 0 < w by omega, h]
-    have := Nat.two_pow_pos (w-1)
-    by_cases hx : x.msb
-    · simp [msb_neg_of_ne_intMin_of_ne_zero (by simp [h])
-        (BitVec.ne_zero_of_msb_true hx), hx]
-    · simp [hx]
-
-theorem sdiv_neg {x y : BitVec w} (h : y ≠ intMin w) :
-    x.sdiv (-y) = -(x.sdiv y) := by
-  by_cases h' : y = 0#w
-  · subst h'
-    simp
-  · simp only [BitVec.sdiv, msb_neg_of_ne_intMin_of_ne_zero h (by simp [h'])]
-    cases x.msb <;> cases y.msb <;> simp
-
-theorem neg_sdiv {x y : BitVec w} (h : x ≠ intMin w) :
-    (-x).sdiv y = -(x.sdiv y) := by
-  by_cases hx0 : x = 0#w
-  · subst hx0
-    simp
-  · simp only [BitVec.sdiv, msb_neg_of_ne_intMin_of_ne_zero h (by simp [hx0])]
-    cases x.msb <;> cases y.msb <;> simp
-
-theorem neg_sdiv_neg {x y : BitVec w} (h : x ≠ intMin w) :
-    (-x).sdiv (-y) = x.sdiv y := by
-  by_cases h' : y = intMin w
-  · subst h'
-    simp [sdiv_intMin, neg_intMin]
-  · by_cases hy0 : y = 0#w
-    · subst hy0
-      simp
-    · by_cases hx0 : x = 0#w
-      · subst hx0
-        simp
-      · simp only [BitVec.sdiv,
-           msb_neg_of_ne_intMin_of_ne_zero h  (by simp [hx0]),
-           msb_neg_of_ne_intMin_of_ne_zero h' (by simp [hy0])]
-        cases x.msb <;> cases y.msb <;> simp
-
-theorem intMin_eq_neg_two_pow : intMin w = BitVec.ofInt w (-2 ^ (w - 1)) := by
-  apply BitVec.eq_of_toInt_eq
-  refine (Nat.eq_zero_or_pos w).elim (by rintro rfl; simp [BitVec.toInt_zero_length]) (fun hw => ?_)
-  rw [BitVec.toInt_intMin_of_pos hw, BitVec.toInt_ofInt_eq_self hw (Int.le_refl _)]
-  have := Nat.two_pow_pos (w - 1)
-  norm_cast
-  omega
-
-theorem toInt_intMin_eq_bmod : (intMin w).toInt = (-2 ^ (w - 1)).bmod (2 ^ w) := by
-  rw [intMin_eq_neg_two_pow, toInt_ofInt]
-
-@[simp]
-theorem toInt_bmod_cancel(b : BitVec w) : b.toInt.bmod (2 ^ w) = b.toInt := by
-  rw [toInt_eq_toNat_bmod, Int.bmod_bmod]
-
-theorem sdiv_ne_intMin_of_ne_intMin {x y : BitVec w} (h : x ≠ intMin w) :
-    x.sdiv y ≠ intMin w := by
-  by_cases hw : w = 0
-  · subst hw
-    simp [BitVec.eq_nil x] at h
-    contradiction
-  simp only [sdiv, udiv_eq, neg_eq]
-  by_cases hx : x.msb <;> by_cases hy : y.msb
-  <;> simp only [hx, hy, neg_ne_intMin_inj]
-  <;> simp only [Bool.not_eq_true] at hx hy
-  <;> apply ne_intMin_of_lt_of_msb_false (by omega)
-  <;> rw [msb_udiv]
-  <;> try simp only [hx, Bool.false_and]
-  · simp [h, ne_zero_of_msb_true, hx]
-  · simp [h, ne_zero_of_msb_true, hx]
-
-theorem toInt_eq_neg_toNat_neg_of_msb_true {x : BitVec w} (h : x.msb = true) :
-    x.toInt = -((-x).toNat) := by
-  simp only [toInt_eq_msb_cond, h, ↓reduceIte, toNat_neg, Int.ofNat_emod]
-  norm_cast
-  rw [Nat.mod_eq_of_lt]
-  · omega
-  · have := @BitVec.isLt w x
-    have ne_zero := ne_zero_of_msb_true h
-    simp only [ne_eq, toNat_eq, toNat_ofNat, zero_mod] at ne_zero
-    omega
-
-theorem toInt_eq_neg_toNat_neg_of_nonpos {x : BitVec w} (h : x = 0#w ∨ x.msb = true) :
-    x.toInt = -((-x).toNat) := by
-  cases h
-  case inl h' =>
-    simp [h']
-  case inr h' =>
-    simp [toInt_eq_neg_toNat_neg_of_msb_true h']
-
-theorem intMin_udiv_eq_intMin_iff (x : BitVec w) :
-    intMin w / x = intMin w ↔ x = 1#w := by
-  by_cases hw : w = 0;   subst hw; decide +revert
-  by_cases hx : x = 1#w; subst hx; simp
-  have wpos : 0 < w := by omega
-
-  have : 0 ≤ (2 ^ (w - 1) / x.toNat) := by simp
-  have := Nat.two_pow_pos (w - 1)
-
-  constructor
-  · intro h
-    rw [← toInt_inj, toInt_eq_msb_cond] at h
-    have : (intMin w / x).msb = false := by simp [msb_udiv, msb_intMin,  wpos, hx]
-    simp [this, wpos, toInt_intMin] at h
-    omega
-  · intro h
-    subst h
-    simp
-
-theorem intMin_udiv_ne_zero_of_ne_zero {b : BitVec w} (hb : b.msb = false) (hb0 : b ≠ 0#w) :
-    intMin w / b ≠ 0#w := by
-  by_cases hw : w = 0;   subst hw; decide +revert
-  have wpos : 0 < w := by omega
-
-  simp [toNat_eq] at hb0
-  have := @Nat.div_eq_zero_iff_lt b.toNat (2 ^ (w-1)) (by omega)
-  have := toNat_lt_of_msb_false hb
-
-  simp [toNat_eq, wpos]
-  omega
-
-theorem toInt_sdiv_of_ne_or_ne (a b : BitVec w) (h : a ≠ intMin w ∨ b ≠ -1#w) :
-    (a.sdiv b).toInt = a.toInt.tdiv b.toInt := by
-  by_cases hw0 : w = 0;   subst hw0; decide +revert
-  by_cases hw1 : w = 1;   subst hw1; decide +revert
-  by_cases ha0 : a = 0#w; subst ha0; simp
-  by_cases hb0 : b = 0#w; subst hb0; simp
-  by_cases hb1 : b = 1#w; subst hb1; simp [show 1 < w by omega]
-
-  have wpos : 0 < w := by omega
-  have := Nat.two_pow_pos (w - 1)
-
-  by_cases hbintMin : b = intMin w
-  · simp only [ne_eq, Decidable.not_not] at hbintMin
-    subst hbintMin
-    have toIntA_lt := @BitVec.toInt_lt w a; norm_cast at toIntA_lt
-    have le_toIntA := @BitVec.le_toInt w a; norm_cast at le_toIntA
-    simp only [sdiv_intMin, h, ↓reduceIte, toInt_zero, toInt_intMin, wpos,
-      Nat.two_pow_pred_mod_two_pow, Int.tdiv_neg]
-    · by_cases ha_intMin : a = intMin w
-      · simp only [ha_intMin, ↓reduceIte, show 1 < w by omega, toInt_one, toInt_intMin, wpos,
-          Nat.two_pow_pred_mod_two_pow, Int.neg_tdiv, Int.neg_neg]
-        rw [Int.tdiv_self (by omega)]
-      · by_cases ha_nonneg : 0 ≤ a.toInt
-        · simp [Int.tdiv_eq_zero_of_lt ha_nonneg (by norm_cast at *), ha_intMin]
-        · simp only [ne_eq, ← toInt_inj, toInt_intMin, wpos, Nat.two_pow_pred_mod_two_pow] at h
-          rw [← Int.neg_tdiv, Int.tdiv_eq_zero_of_lt (by omega)]
-          · simp [ha_intMin]
-          · simp [wpos, ← toInt_ne, toInt_intMin] at ha_intMin
-            omega
-
-  · by_cases ha : a.msb <;> by_cases hb : b.msb
-    <;> simp only [not_eq_true] at ha hb
-    · simp only [sdiv_eq, ha, hb, udiv_eq]
-      rw [toInt_eq_neg_toNat_neg_of_nonpos (x := a) (by simp [ha]),
-        toInt_eq_neg_toNat_neg_of_nonpos (x := b) (by simp [hb]),
-        Int.neg_tdiv_neg, Int.tdiv_eq_ediv_of_nonneg (by omega)]
-      rw [toInt_eq_toNat_of_msb]
-      · rfl
-      · by_cases ha_intMin : a = intMin w
-        · simp only [ha_intMin, ne_eq, not_true_eq_false, _root_.false_or] at h
-          simp [msb_udiv, neg_eq_iff_eq_neg, h]
-        · simp [msb_udiv, ha_intMin, ha]
-    · have sdiv_toInt_of_msb_true_of_msb_false :
-          (a.sdiv b).toInt = -((-a).toNat / b.toNat) := by
-        simp only [sdiv_eq, ha, hb, udiv_eq]
-        rw [toInt_eq_neg_toNat_neg_of_nonpos]
-        · rw [neg_neg, toNat_udiv, toNat_neg, Int.ofNat_emod, Int.neg_inj]
-          norm_cast
-        · rw [neg_eq_zero_iff]
-          by_cases h' : -a / b = 0#w
-          · simp [h']
-          · by_cases ha_intMin : a = intMin w
-            · have ry := (intMin_udiv_eq_intMin_iff b).mp
-              simp only [hb1, imp_false] at ry
-              simp [msb_udiv, ha_intMin, hb1, ry, intMin_udiv_ne_zero_of_ne_zero, hb, hb0]
-            · have := @BitVec.ne_intMin_of_lt_of_msb_false w ((-a) / b) wpos (by simp [ha, ha0, ha_intMin])
-              simp [msb_neg, h', this, ha, ha_intMin]
-      rw [toInt_eq_toNat_of_msb hb, toInt_eq_neg_toNat_neg_of_msb_true ha, Int.neg_tdiv,
-        Int.tdiv_eq_ediv_of_nonneg (by omega), sdiv_toInt_of_msb_true_of_msb_false]
-    · rw [← @BitVec.neg_neg w (a.sdiv b), ← sdiv_neg hbintMin]
-      have hmb : (-b).msb = false := by simp [hbintMin, hb]
-      rw [toInt_neg_of_ne_intMin]
-      · simp [sdiv, ha, hmb]
-        rw [toInt_udiv_of_msb ha, toInt_eq_toNat_of_msb ha]
-        rw [toInt_eq_neg_toNat_neg_of_msb_true hb, Int.tdiv_neg, Int.tdiv_eq_ediv_of_nonneg (by omega)]
-      · apply sdiv_ne_intMin_of_ne_intMin
-        apply ne_intMin_of_lt_of_msb_false (by omega) ha
-    · rw [sdiv, Int.tdiv_cases, udiv_eq, neg_eq, if_pos (toInt_nonneg_of_msb_false ha),
-        if_pos (toInt_nonneg_of_msb_false hb), ha, hb, toInt_udiv_of_msb ha,
-        toInt_eq_toNat_of_msb ha, toInt_eq_toNat_of_msb hb]
-
-theorem intMin_sdiv_neg_one : (intMin w).sdiv (-1#w) = intMin w := by
-  refine (Nat.eq_zero_or_pos w).elim (by rintro rfl; exact Subsingleton.elim _ _) (fun hw => ?_)
-  apply BitVec.eq_of_toNat_eq
-  rw [sdiv]
-  simp [msb_intMin, hw, negOne_eq_allOnes, msb_allOnes]
-  have : 2 ≤ 2 ^ w := Nat.pow_one 2 ▸ (Nat.pow_le_pow_iff_right (by omega)).2 (by omega)
-  rw [Nat.sub_sub_self (by omega), Nat.mod_eq_of_lt, Nat.div_one]
-  omega
-
-theorem toInt_sdiv (a b : BitVec w) : (a.sdiv b).toInt = (a.toInt.tdiv b.toInt).bmod (2 ^ w) := by
-  by_cases h : a = intMin w ∧ b = -1#w
-  · rcases h with ⟨rfl, rfl⟩
-    rw [BitVec.intMin_sdiv_neg_one]
-    refine (Nat.eq_zero_or_pos w).elim (by rintro rfl; simp [toInt_of_zero_length]) (fun hw => ?_)
-    rw [toInt_intMin_of_pos hw, negOne_eq_allOnes, toInt_allOnes, if_pos hw, Int.tdiv_neg,
-      Int.tdiv_one, Int.neg_neg, Int.bmod_eq_neg (Int.pow_nonneg (by omega))]
-    conv => lhs; rw [(by omega: w = (w - 1) + 1)]
-    simp [Nat.pow_succ, Int.natCast_pow, Int.mul_comm]
-  · rw [← toInt_bmod_cancel]
-    rw [BitVec.toInt_sdiv_of_ne_or_ne _ _ (by simpa only [Decidable.not_and_iff_not_or_not] using h)]
-
-theorem msb_umod_eq_false_of_left {x : BitVec w} (hx : x.msb = false) (y : BitVec w) : (x % y).msb = false := by
-  rw [msb_eq_false_iff_two_mul_lt] at hx ⊢
-  rw [toNat_umod]
-  refine Nat.lt_of_le_of_lt ?_ hx
-  rw [Nat.mul_le_mul_left_iff (by decide)]
-  exact Nat.mod_le _ _
-
-theorem msb_umod_of_le_of_ne_zero_of_le {x y : BitVec w}
-    (hx : x ≤ intMin w) (hy : y ≠ 0#w) (hy' : y ≤ intMin w) : (x % y).msb = false := by
-  simp only [msb_umod, Bool.and_eq_false_imp, Bool.or_eq_false_iff, decide_eq_false_iff_not,
-    BitVec.not_lt, beq_eq_false_iff_ne, ne_eq, hy, not_false_eq_true, _root_.and_true]
-  intro h
-  rw [← intMin_le_iff_msb_eq_true (length_pos_of_ne hy)] at h
-  rwa [BitVec.le_antisymm hx h]
-
-@[simp]
-theorem toInt_srem (x y : BitVec w) : (x.srem y).toInt = x.toInt.tmod y.toInt := by
-  rw [srem_eq]
-  by_cases hyz : y = 0#w
-  · simp only [hyz, ofNat_eq_ofNat, msb_zero, umod_zero, neg_zero, neg_neg, toInt_zero, Int.tmod_zero]
-    cases x.msb <;> rfl
-  cases h : x.msb
-  · cases h' : y.msb
-    · dsimp only
-      rw [toInt_eq_toNat_of_msb (msb_umod_eq_false_of_left h y), toNat_umod]
-      rw [toInt_eq_toNat_of_msb h, toInt_eq_toNat_of_msb h', ← Int.ofNat_tmod]
-    · dsimp only
-      rw [toInt_eq_toNat_of_msb (msb_umod_eq_false_of_left h _), toNat_umod]
-      rw [toInt_eq_toNat_of_msb h, toInt_eq_neg_toNat_neg_of_msb_true h']
-      rw [Int.tmod_neg, ← Int.ofNat_tmod]
-  · cases h' : y.msb
-    · dsimp only
-      rw [toInt_eq_neg_toNat_neg_of_msb_true h, toInt_eq_toNat_of_msb h', Int.neg_tmod]
-      rw [← Int.ofNat_tmod, ← toNat_umod, toInt_neg_eq_of_msb ?msb, toInt_eq_toNat_of_msb ?msb]
-      rw [BitVec.msb_umod_of_le_of_ne_zero_of_le (neg_le_intMin_of_msb_eq_true h) hyz]
-      exact le_intMin_of_msb_eq_false h'
-    · dsimp only
-      rw [toInt_eq_neg_toNat_neg_of_msb_true h, toInt_eq_neg_toNat_neg_of_msb_true h', Int.neg_tmod, Int.tmod_neg]
-      rw [← Int.ofNat_tmod, ← toNat_umod, toInt_neg_eq_of_msb ?msb', toInt_eq_toNat_of_msb ?msb']
-      rw [BitVec.msb_umod_of_le_of_ne_zero_of_le (neg_le_intMin_of_msb_eq_true h)
-        ((not_congr neg_eq_zero_iff).mpr hyz)]
-      exact neg_le_intMin_of_msb_eq_true h'
-
-/-! ### Lemmas that use bit blasting circuits -/
-
-theorem add_sub_comm {x y : BitVec w} : x + y - z = x - z + y := by
-  apply eq_of_toNat_eq
-  simp only [toNat_sub, toNat_add, add_mod_mod, mod_add_mod]
-  congr 1
-  omega
-
-theorem sub_add_comm {x y : BitVec w} : x - y + z = x + z - y := by
-  rw [add_sub_comm]
-
-theorem not_add_one {x : BitVec w} : ~~~ (x + 1#w) = ~~~ x - 1#w := by
-  rw [not_eq_neg_add, not_eq_neg_add, neg_add]
-
-theorem not_add_eq_not_neg {x y : BitVec w} : ~~~ (x + y) = ~~~ x - y := by
-  rw [not_eq_neg_add, not_eq_neg_add, neg_add]
-  simp only [sub_toAdd]
-  rw [BitVec.add_assoc, @BitVec.add_comm _ (-y), ← BitVec.add_assoc]
-
-theorem not_sub_one_eq_not_add_one {x : BitVec w} : ~~~ (x - 1#w) = ~~~ x + 1#w := by
-  rw [not_eq_neg_add, not_eq_neg_add, neg_sub,
-    BitVec.add_sub_cancel, BitVec.sub_add_cancel]
-
-theorem not_sub_eq_not_add {x y : BitVec w} : ~~~ (x - y) = ~~~ x + y := by
-  rw [BitVec.sub_toAdd, not_add_eq_not_neg, sub_neg]
-
-/-- The value of `(carry i x y false)` can be computed by truncating `x` and `y`
-to `len` bits where `len ≥ i`. -/
-theorem carry_extractLsb'_eq_carry {w i len : Nat} (hi : i < len)
-    {x y : BitVec w} {b : Bool}:
-    (carry i (extractLsb' 0 len x) (extractLsb' 0 len y) b)
-    = (carry i x y b) := by
-  simp only [carry, extractLsb'_toNat, shiftRight_zero, toNat_false, Nat.add_zero, ge_iff_le,
-    decide_eq_decide]
-  have : 2 ^ i ∣ 2^len := by
-    apply Nat.pow_dvd_pow
-    omega
-  rw [Nat.mod_mod_of_dvd _ this, Nat.mod_mod_of_dvd _ this]
-
-/--
-The `[0..len)` low bits of `x + y` can be computed by truncating `x` and `y`
-to `len` bits and then adding.
--/
-theorem extractLsb'_add {w len : Nat} {x y : BitVec w} (hlen : len ≤ w) :
-    (x + y).extractLsb' 0 len = x.extractLsb' 0 len + y.extractLsb' 0 len := by
-  ext i hi
-  rw [getElem_extractLsb', Nat.zero_add, getLsbD_add (by omega)]
-  simp [getElem_add, carry_extractLsb'_eq_carry hi, getElem_extractLsb', Nat.zero_add]
-
-/-- `extractLsb'` commutes with multiplication. -/
-theorem extractLsb'_mul {w len} {x y : BitVec w} (hlen : len ≤ w) :
-    (x * y).extractLsb' 0 len = (x.extractLsb' 0 len) * (y.extractLsb' 0 len) := by
-  simp [← setWidth_eq_extractLsb' hlen, setWidth_mul _ _ hlen]
-
-/-- Adding bitvectors that are zero in complementary positions equals concatenation. -/
-theorem append_add_append_eq_append {v w : Nat} {x : BitVec v} {y : BitVec w} :
-    (x ++ 0#w) + (0#v ++ y) = x ++ y := by
-  rw [add_eq_or_of_and_eq_zero] <;> ext i <;> simp
-
-/-- Heuristically, `y <<< x` is much larger than `x`,
-and hence low bits of `y <<< x`. Thus, `x + (y <<< x) = x ||| (y <<< x).` -/
-theorem add_shifLeft_eq_or_shiftLeft {x y : BitVec w} :
-    x + (y <<< x) =  x ||| (y <<< x) := by
-  rw [add_eq_or_of_and_eq_zero]
-  ext i hi
-  simp only [shiftLeft_eq', getElem_and, getElem_shiftLeft, getElem_zero, and_eq_false_imp,
-    not_eq_eq_eq_not, Bool.not_true, decide_eq_false_iff_not, Nat.not_lt]
-  intros hxi hxval
-  have : 2^i ≤ x.toNat := two_pow_le_toNat_of_getElem_eq_true hi hxi
-  have : i < 2^i := by exact Nat.lt_two_pow_self
-  omega
-
 end BitVec

src/Init/Data/BitVec/Folds.lean

@@ -13,18 +13,15 @@ set_option linter.missingDocs true
 namespace BitVec
 
 /--
-Constructs a bitvector by iteratively computing a state for each bit using the function `f`,
-starting with the initial state `s`. At each step, the prior state and the current bit index are
-passed to `f`, and it produces a bit along with the next state value. These bits are assembled into
-the final bitvector.
+iunfoldr is an iterative operation that applies a function `f` repeatedly.
 
-It produces a sequence of state values `[s_0, s_1 .. s_w]` and a bitvector `v` where `f i s_i =
-(s_{i+1}, b_i)` and `b_i` is bit `i`th least-significant bit in `v` (e.g., `getLsb v i = b_i`).
+It produces a sequence of state values `[s_0, s_1 .. s_w]` and a bitvector
+`v` where `f i s_i = (s_{i+1}, b_i)` and `b_i` is bit `i`th least-significant bit
+in `v` (e.g., `getLsb v i = b_i`).
 
-The theorem `iunfoldr_replace` allows uses of `BitVec.iunfoldr` to be replaced wiht declarative
-specifications that are easier to reason about.
+Theorems involving `iunfoldr` can be eliminated using `iunfoldr_replace` below.
 -/
-def iunfoldr (f : Fin w → α → α × Bool) (s : α) : α × BitVec w :=
+def iunfoldr (f : Fin w -> α → α × Bool) (s : α) : α × BitVec w :=
   Fin.hIterate (fun i => α × BitVec i) (s, nil) fun i q =>
     (fun p => ⟨p.fst, cons p.snd q.snd⟩) (f i q.fst)
 
@@ -99,24 +96,19 @@ theorem iunfoldr_getLsbD {f : Fin w → α → α × Bool} (state : Nat → α)
   exact (iunfoldr_getLsbD' state ind).1 i
 
 /--
-Given a function `state` that provides the correct state for every potential iteration count and a
-function that computes these states from the correct initial state, the result of applying
-`BitVec.iunfoldr f` to the initial state is the state corresponding to the bitvector's width paired
-with the bitvector that consists of each computed bit.
-
-This theorem can be used to prove properties of functions that are defined using `BitVec.iunfoldr`.
+Correctness theorem for `iunfoldr`.
 -/
 theorem iunfoldr_replace
     {f : Fin w → α → α × Bool} (state : Nat → α) (value : BitVec w) (a : α)
     (init : state 0 = a)
-    (step : ∀(i : Fin w), f i (state i.val) = (state (i.val+1), value[i.val])) :
+    (step : ∀(i : Fin w), f i (state i.val) = (state (i.val+1), value.getLsbD i.val)) :
     iunfoldr f a = (state w, value) := by
   simp [iunfoldr.eq_test state value a init step]
 
 theorem iunfoldr_replace_snd
   {f : Fin w → α → α × Bool} (state : Nat → α) (value : BitVec w) (a : α)
     (init : state 0 = a)
-    (step : ∀(i : Fin w), f i (state i.val) = (state (i.val+1), value[i.val])) :
+    (step : ∀(i : Fin w), f i (state i.val) = (state (i.val+1), value.getLsbD i.val)) :
     (iunfoldr f a).snd = value := by
   simp [iunfoldr.eq_test state value a init step]
 

src/Init/Data/Bool.lean

@@ -9,19 +9,7 @@ import Init.NotationExtra
 
 namespace Bool
 
-/--
-Boolean “exclusive or”. `xor x y` can be written `x ^^ y`.
-
-`x ^^ y` is `true` when precisely one of `x` or `y` is `true`. Unlike `and` and `or`, it does not
-have short-circuiting behavior, because one argument's value never determines the final value. Also
-unlike `and` and `or`, there is no commonly-used corresponding propositional connective.
-
-Examples:
- * `false ^^ false = false`
- * `true ^^ false = true`
- * `false ^^ true = true`
- * `true ^^ true = false`
--/
+/-- Boolean exclusive or -/
 abbrev xor : Bool → Bool → Bool := bne
 
 @[inherit_doc] infixl:33 " ^^ " => xor
@@ -379,19 +367,17 @@ theorem and_or_inj_left_iff :
 
 /-! ## toNat -/
 
-/--
-Converts `true` to `1` and `false` to `0`.
--/
+/-- convert a `Bool` to a `Nat`, `false -> 0`, `true -> 1` -/
 def toNat (b : Bool) : Nat := cond b 1 0
 
-@[simp, bitvec_to_nat] theorem toNat_false : false.toNat = 0 := rfl
+@[simp, bv_toNat] theorem toNat_false : false.toNat = 0 := rfl
 
-@[simp, bitvec_to_nat] theorem toNat_true : true.toNat = 1 := rfl
+@[simp, bv_toNat] theorem toNat_true : true.toNat = 1 := rfl
 
 theorem toNat_le (c : Bool) : c.toNat ≤ 1 := by
   cases c <;> trivial
 
-@[bitvec_to_nat]
+@[bv_toNat]
 theorem toNat_lt (b : Bool) : b.toNat < 2 :=
   Nat.lt_succ_of_le (toNat_le _)
 
@@ -402,9 +388,7 @@ theorem toNat_lt (b : Bool) : b.toNat < 2 :=
 
 /-! ## toInt -/
 
-/--
-Converts `true` to `1` and `false` to `0`.
--/
+/-- convert a `Bool` to an `Int`, `false -> 0`, `true -> 1` -/
 def toInt (b : Bool) : Int := cond b 1 0
 
 @[simp] theorem toInt_false : false.toInt = 0 := rfl
@@ -555,8 +539,8 @@ theorem cond_decide {α} (p : Prop) [Decidable p] (t e : α) :
 @[simp] theorem cond_eq_false_distrib : ∀(c t f : Bool),
     (cond c t f = false) = ite (c = true) (t = false) (f = false) := by decide
 
-protected theorem cond_true  {α : Sort u} {a b : α} : cond true  a b = a := cond_true  a b
-protected theorem cond_false {α : Sort u} {a b : α} : cond false a b = b := cond_false a b
+protected theorem cond_true  {α : Type u} {a b : α} : cond true  a b = a := cond_true  a b
+protected theorem cond_false {α : Type u} {a b : α} : cond false a b = b := cond_false a b
 
 @[simp] theorem cond_true_left   : ∀(c f : Bool), cond c true f  = ( c || f) := by decide
 @[simp] theorem cond_false_left  : ∀(c f : Bool), cond c false f = (!c && f) := by decide
@@ -596,13 +580,17 @@ protected theorem decide_coe (b : Bool) [Decidable (b = true)] : decide (b = tru
     decide (p ↔ q) = (decide p == decide q) := by
   cases dp with | _ p => simp [p]
 
-@[bool_to_prop]
-theorem and_eq_decide (p q : Bool) : (p && q) = decide (p ∧ q) := by simp
+@[boolToPropSimps]
+theorem and_eq_decide (p q : Prop) [dpq : Decidable (p ∧ q)] [dp : Decidable p] [dq : Decidable q] :
+    (p && q) = decide (p ∧ q) := by
+  cases dp with | _ p => simp [p]
 
-@[bool_to_prop]
-theorem or_eq_decide (p q : Bool) : (p || q) = decide (p ∨ q) := by simp
+@[boolToPropSimps]
+theorem or_eq_decide (p q : Prop) [dpq : Decidable (p ∨ q)] [dp : Decidable p] [dq : Decidable q] :
+    (p || q) = decide (p ∨ q) := by
+  cases dp with | _ p => simp [p]
 
-@[bool_to_prop]
+@[boolToPropSimps]
 theorem decide_beq_decide (p q : Prop) [dpq : Decidable (p ↔ q)] [dp : Decidable p] [dq : Decidable q] :
     (decide p == decide q) = decide (p ↔ q) := by
   cases dp with | _ p => simp [p]

src/Init/Data/ByteArray/Basic.lean

@@ -18,13 +18,10 @@ attribute [extern "lean_byte_array_data"] ByteArray.data
 
 namespace ByteArray
 @[extern "lean_mk_empty_byte_array"]
-def emptyWithCapacity (c : @& Nat) : ByteArray :=
+def mkEmpty (c : @& Nat) : ByteArray :=
   { data := #[] }
 
-@[deprecated emptyWithCapacity (since := "2025-03-12")]
-abbrev mkEmpty := emptyWithCapacity
-
-def empty : ByteArray := emptyWithCapacity 0
+def empty : ByteArray := mkEmpty 0
 
 instance : Inhabited ByteArray where
   default := empty
@@ -50,7 +47,7 @@ def uget : (a : @& ByteArray) → (i : USize) → (h : i.toNat < a.size := by ge
 
 @[extern "lean_byte_array_get"]
 def get! : (@& ByteArray) → (@& Nat) → UInt8
-  | ⟨bs⟩, i => bs[i]!
+  | ⟨bs⟩, i => bs.get! i
 
 @[extern "lean_byte_array_fget"]
 def get : (a : @& ByteArray) → (i : @& Nat) → (h : i < a.size := by get_elem_tactic) → UInt8
@@ -59,7 +56,7 @@ def get : (a : @& ByteArray) → (i : @& Nat) → (h : i < a.size := by get_elem
 instance : GetElem ByteArray Nat UInt8 fun xs i => i < xs.size where
   getElem xs i h := xs.get i
 
-instance : GetElem ByteArray USize UInt8 fun xs i => i.toFin < xs.size where
+instance : GetElem ByteArray USize UInt8 fun xs i => i.val < xs.size where
   getElem xs i h := xs.uget i h
 
 @[extern "lean_byte_array_set"]
@@ -337,9 +334,6 @@ def prevn : Iterator → Nat → Iterator
 end Iterator
 end ByteArray
 
-/--
-Converts a list of bytes into a `ByteArray`.
--/
 def List.toByteArray (bs : List UInt8) : ByteArray :=
   let rec loop
     | [],    r => r

src/Init/Data/Cast.lean

@@ -44,26 +44,25 @@ Nat → Nat → ...`. Sometimes we also need to declare the `CoeHTCT`
 instance if we need to shadow another coercion.
 -/
 
-/--
-The canonical homomorphism `Nat → R`. In most use cases, the target type will have a (semi)ring
-structure, and this homomorphism should be a (semi)ring homomorphism.
-
-`NatCast` and `IntCast` exist to allow different libraries with their own types that can be notated
-as natural numbers to have consistent `simp` normal forms without needing to create coercion
-simplification sets that are aware of all combinations. Libraries should make it easy to work with
-`NatCast` where possible. For instance, in Mathlib there will be such a homomorphism (and thus a
-`NatCast R` instance) whenever `R` is an additive monoid with a `1`.
-
-The prototypical example is `Int.ofNat`.
--/
+/-- Type class for the canonical homomorphism `Nat → R`. -/
 class NatCast (R : Type u) where
   /-- The canonical map `Nat → R`. -/
   protected natCast : Nat → R
 
 instance : NatCast Nat where natCast n := n
 
-@[coe, reducible, match_pattern, inherit_doc NatCast]
-protected def Nat.cast {R : Type u} [NatCast R] : Nat → R :=
+/--
+Canonical homomorphism from `Nat` to a type `R`.
+
+It contains just the function, with no axioms.
+In practice, the target type will likely have a (semi)ring structure,
+and this homomorphism should be a ring homomorphism.
+
+The prototypical example is `Int.ofNat`.
+
+This class and `IntCast` exist to allow different libraries with their own types that can be notated as natural numbers to have consistent `simp` normal forms without needing to create coercion simplification sets that are aware of all combinations. Libraries should make it easy to work with `NatCast` where possible. For instance, in Mathlib there will be such a homomorphism (and thus a `NatCast R` instance) whenever `R` is an additive monoid with a `1`.
+-/
+@[coe, reducible, match_pattern] protected def Nat.cast {R : Type u} [NatCast R] : Nat → R :=
   NatCast.natCast
 
 -- see the notes about coercions into arbitrary types in the module doc-string

src/Init/Data/Char/Basic.lean

@@ -15,15 +15,7 @@ Note that values in `[0xd800, 0xdfff]` are reserved for [UTF-16 surrogate pairs]
 
 namespace Char
 
-/--
-One character is less than another if its code point is strictly less than the other's.
--/
 protected def lt (a b : Char) : Prop := a.val < b.val
-
-/--
-One character is less than or equal to another if its code point is less than or equal to the
-other's.
--/
 protected def le (a b : Char) : Prop := a.val ≤ b.val
 
 instance : LT Char := ⟨Char.lt⟩
@@ -35,10 +27,7 @@ instance (a b : Char) :  Decidable (a < b) :=
 instance (a b : Char) : Decidable (a ≤ b) :=
   UInt32.decLe _ _
 
-/--
-True for natural numbers that are valid [Unicode scalar
-values](https://www.unicode.org/glossary/#unicode_scalar_value).
--/
+/-- Determines if the given nat is a valid [Unicode scalar value](https://www.unicode.org/glossary/#unicode_scalar_value).-/
 abbrev isValidCharNat (n : Nat) : Prop :=
   n < 0xd800 ∨ (0xdfff < n ∧ n < 0x110000)
 
@@ -51,103 +40,65 @@ theorem isValidUInt32 (n : Nat) (h : isValidCharNat n) : n < UInt32.size := by
     apply Nat.lt_trans h₂
     decide
 
-theorem isValidChar_of_isValidCharNat (n : Nat) (h : isValidCharNat n) : isValidChar (UInt32.ofNatLT n (isValidUInt32 n h)) :=
+theorem isValidChar_of_isValidCharNat (n : Nat) (h : isValidCharNat n) : isValidChar (UInt32.ofNat' n (isValidUInt32 n h)) :=
   match h with
   | Or.inl h =>
-    Or.inl (UInt32.ofNatLT_lt_of_lt _ (by decide) h)
+    Or.inl (UInt32.ofNat'_lt_of_lt _ (by decide) h)
   | Or.inr ⟨h₁, h₂⟩ =>
-    Or.inr ⟨UInt32.lt_ofNatLT_of_lt _ (by decide) h₁, UInt32.ofNatLT_lt_of_lt _ (by decide) h₂⟩
+    Or.inr ⟨UInt32.lt_ofNat'_of_lt _ (by decide) h₁, UInt32.ofNat'_lt_of_lt _ (by decide) h₂⟩
 
 theorem isValidChar_zero : isValidChar 0 :=
   Or.inl (by decide)
 
-/--
-The character's Unicode code point as a `Nat`.
--/
+/-- Underlying unicode code point as a `Nat`. -/
 @[inline] def toNat (c : Char) : Nat :=
   c.val.toNat
 
-/--
-Converts a character into a `UInt8` that contains its code point.
-
-If the code point is larger than 255, it is truncated (reduced modulo 256).
--/
+/-- Convert a character into a `UInt8`, by truncating (reducing modulo 256) if necessary. -/
 @[inline] def toUInt8 (c : Char) : UInt8 :=
   c.val.toUInt8
 
-/--
-Converts an 8-bit unsigned integer into a character.
-
-The integer's value is interpreted as a Unicode code point.
--/
+/-- The numbers from 0 to 256 are all valid UTF-8 characters, so we can embed one in the other. -/
 def ofUInt8 (n : UInt8) : Char := ⟨n.toUInt32, .inl (Nat.lt_trans n.toBitVec.isLt (by decide))⟩
 
 instance : Inhabited Char where
   default := 'A'
 
-/--
-Returns `true` if the character is a space `(' ', U+0020)`, a tab `('\t', U+0009)`, a carriage
-return `('\r', U+000D)`, or a newline `('\n', U+000A)`.
--/
+/-- Is the character a space (U+0020) a tab (U+0009), a carriage return (U+000D) or a newline (U+000A)? -/
 @[inline] def isWhitespace (c : Char) : Bool :=
   c = ' ' || c = '\t' || c = '\r' || c = '\n'
 
-/--
-Returns `true` if the character is a uppercase ASCII letter.
-
-The uppercase ASCII letters are the following: `ABCDEFGHIJKLMNOPQRSTUVWXYZ`.
--/
+/-- Is the character in `ABCDEFGHIJKLMNOPQRSTUVWXYZ`? -/
 @[inline] def isUpper (c : Char) : Bool :=
   c.val ≥ 65 && c.val ≤ 90
 
-/--
-Returns `true` if the character is a lowercase ASCII letter.
-
-The lowercase ASCII letters are the following: `abcdefghijklmnopqrstuvwxyz`.
--/
+/-- Is the character in `abcdefghijklmnopqrstuvwxyz`? -/
 @[inline] def isLower (c : Char) : Bool :=
   c.val ≥ 97 && c.val ≤ 122
 
-/--
-Returns `true` if the character is an ASCII letter.
-
-The ASCII letters are the following: `ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz`.
--/
+/-- Is the character in `ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz`? -/
 @[inline] def isAlpha (c : Char) : Bool :=
   c.isUpper || c.isLower
 
-/--
-Returns `true` if the character is an ASCII digit.
-
-The ASCII digits are the following: `0123456789`.
--/
+/-- Is the character in `0123456789`? -/
 @[inline] def isDigit (c : Char) : Bool :=
   c.val ≥ 48 && c.val ≤ 57
 
-/--
-Returns `true` if the character is an ASCII letter or digit.
-
-The ASCII letters are the following: `ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz`.
-The ASCII digits are the following: `0123456789`.
--/
+/-- Is the character in `ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789`? -/
 @[inline] def isAlphanum (c : Char) : Bool :=
   c.isAlpha || c.isDigit
 
-/--
-Converts an uppercase ASCII letter to the corresponding lowercase letter. Letters outside the ASCII
-alphabet are returned unchanged.
+/-- Convert an upper case character to its lower case character.
 
-The uppercase ASCII letters are the following: `ABCDEFGHIJKLMNOPQRSTUVWXYZ`.
+Only works on basic latin letters.
 -/
 def toLower (c : Char) : Char :=
   let n := toNat c;
   if n >= 65 ∧ n <= 90 then ofNat (n + 32) else c
 
-/--
-Converts a lowercase ASCII letter to the corresponding uppercase letter. Letters outside the ASCII
-alphabet are returned unchanged.
+/-- Convert a lower case character to its upper case character.
 
-The lowercase ASCII letters are the following: `abcdefghijklmnopqrstuvwxyz`.
+Only works on basic latin letters.
 -/
 def toUpper (c : Char) : Char :=
   let n := toNat c;

src/Init/Data/Fin/Basic.lean

@@ -14,23 +14,22 @@ instance coeToNat : CoeOut (Fin n) Nat :=
   ⟨fun v => v.val⟩
 
 /--
-The type `Fin 0` is uninhabited, so it can be used to derive any result whatsoever.
-
-This is similar to `Empty.elim`. It can be thought of as a compiler-checked assertion that a code
-path is unreachable, or a logical contradiction from which `False` and thus anything else could be
-derived.
+From the empty type `Fin 0`, any desired result `α` can be derived. This is similar to `Empty.elim`.
 -/
 def elim0.{u} {α : Sort u} : Fin 0 → α
   | ⟨_, h⟩ => absurd h (not_lt_zero _)
 
 /--
-The successor, with an increased bound.
+Returns the successor of the argument.
 
-This differs from adding `1`, which instead wraps around.
-
-Examples:
- * `(2 : Fin 3).succ = (3 : Fin 4)`
- * `(2 : Fin 3) + 1 = (0 : Fin 3)`
+The bound in the result type is increased:
+```
+(2 : Fin 3).succ = (3 : Fin 4)
+```
+This differs from addition, which wraps around:
+```
+(2 : Fin 3) + 1 = (0 : Fin 3)
+```
 -/
 def succ : Fin n → Fin (n + 1)
   | ⟨i, h⟩ => ⟨i+1, Nat.succ_lt_succ h⟩
@@ -52,54 +51,21 @@ Returns `a` modulo `n + 1` as a `Fin n.succ`.
 protected def ofNat {n : Nat} (a : Nat) : Fin (n + 1) :=
   ⟨a % (n+1), Nat.mod_lt _ (Nat.zero_lt_succ _)⟩
 
--- We provide this because other similar types have a `toNat` function, but `simp` rewrites
--- `i.toNat` to `i.val`.
-/--
-Extracts the underlying `Nat` value.
-
-This function is a synonym for `Fin.val`, which is the simp normal form. `Fin.val` is also a
-coercion, so values of type `Fin n` are automatically converted to `Nat`s as needed.
--/
-@[inline]
-protected def toNat (i : Fin n) : Nat :=
-  i.val
-
-@[simp] theorem toNat_eq_val {i : Fin n} : i.toNat = i.val := rfl
-
 private theorem mlt {b : Nat} : {a : Nat} → a < n → b % n < n
   | 0,   h => Nat.mod_lt _ h
   | _+1, h =>
     have : n > 0 := Nat.lt_trans (Nat.zero_lt_succ _) h;
     Nat.mod_lt _ this
 
-/--
-Addition modulo `n`, usually invoked via the `+` operator.
-
-Examples:
- * `(2 : Fin 8) + (2 : Fin 8) = (4 : Fin 8)`
- * `(2 : Fin 3) + (2 : Fin 3) = (1 : Fin 3)`
--/
+/-- Addition modulo `n` -/
 protected def add : Fin n → Fin n → Fin n
   | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a + b) % n, mlt h⟩
 
-/--
-Multiplication modulo `n`, usually invoked via the `*` operator.
-
-Examples:
- * `(2 : Fin 10) * (2 : Fin 10) = (4 : Fin 10)`
- * `(2 : Fin 10) * (7 : Fin 10) = (4 : Fin 10)`
- * `(3 : Fin 10) * (7 : Fin 10) = (1 : Fin 10)`
--/
+/-- Multiplication modulo `n` -/
 protected def mul : Fin n → Fin n → Fin n
   | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a * b) % n, mlt h⟩
 
-/--
-Subtraction modulo `n`, usually invoked via the `-` operator.
-
-Examples:
- * `(5 : Fin 11) - (3 : Fin 11) = (2 : Fin 11)`
- * `(3 : Fin 11) - (5 : Fin 11) = (9 : Fin 11)`
--/
+/-- Subtraction modulo `n` -/
 protected def sub : Fin n → Fin n → Fin n
   /-
   The definition of `Fin.sub` has been updated to improve performance.
@@ -126,76 +92,27 @@ we are trying to minimize the number of Nat theorems
 needed to bootstrap Lean.
 -/
 
-/--
-Modulus of bounded numbers, usually invoked via the `%` operator.
-
-The resulting value is that computed by the `%` operator on `Nat`.
--/
 protected def mod : Fin n → Fin n → Fin n
   | ⟨a, h⟩, ⟨b, _⟩ => ⟨a % b,  Nat.lt_of_le_of_lt (Nat.mod_le _ _) h⟩
 
-/--
-Division of bounded numbers, usually invoked via the `/` operator.
-
-The resulting value is that computed by the `/` operator on `Nat`. In particular, the result of
-division by `0` is `0`.
-
-Examples:
- * `(5 : Fin 10) / (2 : Fin 10) = (2 : Fin 10)`
- * `(5 : Fin 10) / (0 : Fin 10) = (0 : Fin 10)`
- * `(5 : Fin 10) / (7 : Fin 10) = (0 : Fin 10)`
--/
 protected def div : Fin n → Fin n → Fin n
   | ⟨a, h⟩, ⟨b, _⟩ => ⟨a / b, Nat.lt_of_le_of_lt (Nat.div_le_self _ _) h⟩
 
-/--
-Modulus of bounded numbers with respect to a `Nat`.
-
-The resulting value is that computed by the `%` operator on `Nat`.
--/
 def modn : Fin n → Nat → Fin n
   | ⟨a, h⟩, m => ⟨a % m, Nat.lt_of_le_of_lt (Nat.mod_le _ _) h⟩
 
-/--
-Bitwise and.
--/
 def land : Fin n → Fin n → Fin n
   | ⟨a, h⟩, ⟨b, _⟩ => ⟨(Nat.land a b) % n, mlt h⟩
 
-/--
-Bitwise or.
--/
 def lor : Fin n → Fin n → Fin n
   | ⟨a, h⟩, ⟨b, _⟩ => ⟨(Nat.lor a b) % n, mlt h⟩
 
-/--
-Bitwise xor (“exclusive or”).
--/
 def xor : Fin n → Fin n → Fin n
   | ⟨a, h⟩, ⟨b, _⟩ => ⟨(Nat.xor a b) % n, mlt h⟩
 
-/--
-Bitwise left shift of bounded numbers, with wraparound on overflow.
-
-Examples:
- * `(1 : Fin 10) <<< (1 : Fin 10) = (2 : Fin 10)`
- * `(1 : Fin 10) <<< (3 : Fin 10) = (8 : Fin 10)`
- * `(1 : Fin 10) <<< (4 : Fin 10) = (6 : Fin 10)`
--/
 def shiftLeft : Fin n → Fin n → Fin n
   | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a <<< b) % n, mlt h⟩
 
-/--
-Bitwise right shift of bounded numbers.
-
-This operator corresponds to logical rather than arithmetic bit shifting. The new bits are always
-`0`.
-
-Examples:
- * `(15 : Fin 16) >>> (1 : Fin 16) = (7 : Fin 16)`
- * `(15 : Fin 16) >>> (2 : Fin 16) = (3 : Fin 16)`
- * `(15 : Fin 17) >>> (2 : Fin 17) = (3 : Fin 17)`
--/
 def shiftRight : Fin n → Fin n → Fin n
   | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a >>> b) % n, mlt h⟩
 
@@ -249,125 +166,39 @@ theorem val_lt_of_le (i : Fin b) (h : b ≤ n) : i.val < n :=
 protected theorem pos (i : Fin n) : 0 < n :=
   Nat.lt_of_le_of_lt (Nat.zero_le _) i.2
 
-/--
-The greatest value of `Fin (n+1)`, namely `n`.
-
-Examples:
- * `Fin.last 4 = (4 : Fin 5)`
- * `(Fin.last 0).val = (0 : Nat)`
--/
+/-- The greatest value of `Fin (n+1)`. -/
 @[inline] def last (n : Nat) : Fin (n + 1) := ⟨n, n.lt_succ_self⟩
 
-/--
-Replaces the bound with another that is suitable for the value.
-
-The proof embedded in `i` can be used to cast to a larger bound even if the concrete value is not
-known.
-
-Examples:
-```lean example
-example : Fin 12 := (7 : Fin 10).castLT (by decide : 7 < 12)
-```
-```lean example
-example (i : Fin 10) : Fin 12 :=
-  i.castLT <| by
-    cases i; simp; omega
-```
--/
+/-- `castLT i h` embeds `i` into a `Fin` where `h` proves it belongs into.  -/
 @[inline] def castLT (i : Fin m) (h : i.1 < n) : Fin n := ⟨i.1, h⟩
 
-/--
-Coarsens a bound to one at least as large.
-
-See also `Fin.castAdd` for a version that represents the larger bound with addition rather than an
-explicit inequality proof.
--/
+/-- `castLE h i` embeds `i` into a larger `Fin` type.  -/
 @[inline] def castLE (h : n ≤ m) (i : Fin n) : Fin m := ⟨i, Nat.lt_of_lt_of_le i.2 h⟩
 
-/--
-Uses a proof that two bounds are equal to allow a value bounded by one to be used with the other.
-
-In other words, when `eq : n = m`, `Fin.cast eq i` converts `i : Fin n` into a `Fin m`.
--/
+/-- `cast eq i` embeds `i` into an equal `Fin` type. -/
 @[inline] protected def cast (eq : n = m) (i : Fin n) : Fin m := ⟨i, eq ▸ i.2⟩
 
-/--
-Coarsens a bound to one at least as large.
-
-See also `Fin.natAdd` and `Fin.addNat` for addition functions that increase the bound, and
-`Fin.castLE` for a version that uses an explicit inequality proof.
--/
+/-- `castAdd m i` embeds `i : Fin n` in `Fin (n+m)`. See also `Fin.natAdd` and `Fin.addNat`. -/
 @[inline] def castAdd (m) : Fin n → Fin (n + m) :=
   castLE <| Nat.le_add_right n m
 
-/--
-Coarsens a bound by one.
--/
+/-- `castSucc i` embeds `i : Fin n` in `Fin (n+1)`. -/
 @[inline] def castSucc : Fin n → Fin (n + 1) := castAdd 1
 
-/--
-Adds a natural number to a `Fin`, increasing the bound.
-
-This is a generalization of `Fin.succ`.
-
-`Fin.natAdd` is a version of this function that takes its `Nat` parameter first.
-
-Examples:
- * `Fin.addNat (5 : Fin 8) 3 = (8 : Fin 11)`
- * `Fin.addNat (0 : Fin 8) 1 = (1 : Fin 9)`
- * `Fin.addNat (1 : Fin 8) 2 = (3 : Fin 10)`
-
--/
+/-- `addNat m i` adds `m` to `i`, generalizes `Fin.succ`. -/
 def addNat (i : Fin n) (m) : Fin (n + m) := ⟨i + m, Nat.add_lt_add_right i.2 _⟩
 
-/--
-Adds a natural number to a `Fin`, increasing the bound.
-
-This is a generalization of `Fin.succ`.
-
-`Fin.addNat` is a version of this function that takes its `Nat` parameter second.
-
-Examples:
- * `Fin.natAdd 3 (5 : Fin 8) = (8 : Fin 11)`
- * `Fin.natAdd 1 (0 : Fin 8) = (1 : Fin 9)`
- * `Fin.natAdd 1 (2 : Fin 8) = (3 : Fin 9)`
--/
+/-- `natAdd n i` adds `n` to `i` "on the left". -/
 def natAdd (n) (i : Fin m) : Fin (n + m) := ⟨n + i, Nat.add_lt_add_left i.2 _⟩
 
-/--
-Replaces a value with its difference from the largest value in the type.
-
-Considering the values of `Fin n` as a sequence `0`, `1`, …, `n-2`, `n-1`, `Fin.rev` finds the
-corresponding element of the reversed sequence. In other words, it maps `0` to `n-1`, `1` to `n-2`,
-..., and `n-1` to `0`.
-
-Examples:
- * `(5 : Fin 6).rev = (0 : Fin 6)`
- * `(0 : Fin 6).rev = (5 : Fin 6)`
- * `(2 : Fin 5).rev = (2 : Fin 5)`
--/
+/-- Maps `0` to `n-1`, `1` to `n-2`, ..., `n-1` to `0`. -/
 @[inline] def rev (i : Fin n) : Fin n := ⟨n - (i + 1), Nat.sub_lt i.pos (Nat.succ_pos _)⟩
 
-/--
-Subtraction of a natural number from a `Fin`, with the bound narrowed.
-
-This is a generalization of `Fin.pred`. It is guaranteed to not underflow or wrap around.
-
-Examples:
- * `(5 : Fin 9).subNat 2 (by decide) = (3 : Fin 7)`
- * `(5 : Fin 9).subNat 0 (by decide) = (5 : Fin 9)`
- * `(3 : Fin 9).subNat 3 (by decide) = (0 : Fin 6)`
--/
+/-- `subNat i h` subtracts `m` from `i`, generalizes `Fin.pred`. -/
 @[inline] def subNat (m) (i : Fin (n + m)) (h : m ≤ i) : Fin n :=
   ⟨i - m, Nat.sub_lt_right_of_lt_add h i.2⟩
 
-/--
-The predecessor of a non-zero element of `Fin (n+1)`, with the bound decreased.
-
-Examples:
- * `(4 : Fin 8).pred (by decide) = (3 : Fin 7)`
- * `(1 : Fin 2).pred (by decide) = (0 : Fin 1)`
--/
+/-- Predecessor of a nonzero element of `Fin (n+1)`. -/
 @[inline] def pred {n : Nat} (i : Fin (n + 1)) (h : i ≠ 0) : Fin n :=
   subNat 1 i <| Nat.pos_of_ne_zero <| mt (Fin.eq_of_val_eq (j := 0)) h
 

src/Init/Data/Fin/Bitwise.lean

@@ -12,31 +12,4 @@ namespace Fin
 @[simp] theorem and_val (a b : Fin n) : (a &&& b).val = a.val &&& b.val :=
   Nat.mod_eq_of_lt (Nat.lt_of_le_of_lt Nat.and_le_left a.isLt)
 
-@[simp] theorem or_val_of_two_pow {w} (a b : Fin (2 ^ w)) : (a ||| b).val = a.val ||| b.val :=
-  Nat.mod_eq_of_lt (Nat.or_lt_two_pow a.isLt b.isLt)
-
-@[simp] theorem or_val_of_uInt8Size (a b : Fin UInt8.size) : (a ||| b).val = a.val ||| b.val := or_val_of_two_pow (w := 8) a b
-@[simp] theorem or_val_of_uInt16Size (a b : Fin UInt16.size) : (a ||| b).val = a.val ||| b.val := or_val_of_two_pow (w := 16) a b
-@[simp] theorem or_val_of_uInt32Size (a b : Fin UInt32.size) : (a ||| b).val = a.val ||| b.val := or_val_of_two_pow (w := 32) a b
-@[simp] theorem or_val_of_uInt64Size (a b : Fin UInt64.size) : (a ||| b).val = a.val ||| b.val := or_val_of_two_pow (w := 64) a b
-@[simp] theorem or_val_of_uSizeSize (a b : Fin USize.size) : (a ||| b).val = a.val ||| b.val := or_val_of_two_pow a b
-
-theorem or_val (a b : Fin n) : (a ||| b).val = (a.val ||| b.val) % n := rfl
-
-@[simp] theorem xor_val_of_two_pow {w} (a b : Fin (2 ^ w)) : (a ^^^ b).val = a.val ^^^ b.val :=
-  Nat.mod_eq_of_lt (Nat.xor_lt_two_pow a.isLt b.isLt)
-
-@[simp] theorem xor_val_of_uInt8Size (a b : Fin UInt8.size) : (a ^^^ b).val = a.val ^^^ b.val := xor_val_of_two_pow (w := 8) a b
-@[simp] theorem xor_val_of_uInt16Size (a b : Fin UInt16.size) : (a ^^^ b).val = a.val ^^^ b.val := xor_val_of_two_pow (w := 16) a b
-@[simp] theorem xor_val_of_uInt32Size (a b : Fin UInt32.size) : (a ^^^ b).val = a.val ^^^ b.val := xor_val_of_two_pow (w := 32) a b
-@[simp] theorem xor_val_of_uInt64Size (a b : Fin UInt64.size) : (a ^^^ b).val = a.val ^^^ b.val := xor_val_of_two_pow (w := 64) a b
-@[simp] theorem xor_val_of_uSizeSize (a b : Fin USize.size) : (a ^^^ b).val = a.val ^^^ b.val := xor_val_of_two_pow a b
-
-theorem xor_val (a b : Fin n) : (a ^^^ b).val = (a.val ^^^ b.val) % n := rfl
-
-@[simp] theorem shiftLeft_val (a b : Fin n) : (a <<< b).val = (a.val <<< b.val) % n := rfl
-
-@[simp] theorem shiftRight_val (a b : Fin n) : (a >>> b).val = a.val >>> b.val :=
-  Nat.mod_eq_of_lt (Nat.lt_of_le_of_lt (Nat.shiftRight_le _ _) a.isLt)
-
 end Fin

src/Init/Data/Fin/Fold.lean

@@ -10,26 +10,14 @@ import Init.Data.Fin.Lemmas
 
 namespace Fin
 
-/--
-Combine all the values that can be represented by `Fin n` with an initial value, starting at `0` and
-nesting to the left.
-
-Example:
- * `Fin.foldl 3 (· + ·.val) (0 : Nat) = ((0 + (0 : Fin 3).val) + (1 : Fin 3).val) + (2 : Fin 3).val`
--/
+/-- Folds over `Fin n` from the left: `foldl 3 f x = f (f (f x 0) 1) 2`. -/
 @[inline] def foldl (n) (f : α → Fin n → α) (init : α) : α := loop init 0 where
   /-- Inner loop for `Fin.foldl`. `Fin.foldl.loop n f x i = f (f (f x i) ...) (n-1)`  -/
   @[semireducible, specialize] loop (x : α) (i : Nat) : α :=
     if h : i < n then loop (f x ⟨i, h⟩) (i+1) else x
   termination_by n - i
 
-/--
-Combine all the values that can be represented by `Fin n` with an initial value, starting at `n - 1`
-and nesting to the right.
-
-Example:
- * `Fin.foldr 3 (·.val + ·) (0 : Nat) = (0 : Fin 3).val + ((1 : Fin 3).val + ((2 : Fin 3).val + 0))`
--/
+/-- Folds over `Fin n` from the right: `foldr 3 f x = f 0 (f 1 (f 2 x))`. -/
 @[inline] def foldr (n) (f : Fin n → α → α) (init : α) : α := loop n (Nat.le_refl n) init where
   /-- Inner loop for `Fin.foldr`. `Fin.foldr.loop n f i x = f 0 (f ... (f (i-1) x))`  -/
   @[specialize] loop : (i : _) → i ≤ n → α → α
@@ -38,9 +26,7 @@ Example:
   termination_by structural i => i
 
 /--
-Folds a monadic function over all the values in `Fin n` from left to right, starting with `0`.
-
-It is the sequence of steps:
+Folds a monadic function over `Fin n` from left to right:
 ```
 Fin.foldlM n f x₀ = do
   let x₁ ← f x₀ 0
@@ -67,9 +53,7 @@ Fin.foldlM n f x₀ = do
   decreasing_by decreasing_trivial_pre_omega
 
 /--
-Folds a monadic function over `Fin n` from right to left, starting with `n-1`.
-
-It is the sequence of steps:
+Folds a monadic function over `Fin n` from right to left:
 ```
 Fin.foldrM n f xₙ = do
   let xₙ₋₁ ← f (n-1) xₙ
@@ -141,9 +125,7 @@ theorem foldrM_loop [Monad m] [LawfulMonad m] (f : Fin (n+1) → α → m α) (x
   | zero =>
     rw [foldrM_loop_zero, foldrM_loop_succ, pure_bind]
     conv => rhs; rw [←bind_pure (f 0 x)]
-    congr
-    funext
-    try simp only [foldrM.loop] -- the try makes this proof work with and without opaque wf rec
+    congr; funext
   | succ i ih =>
     rw [foldrM_loop_succ, foldrM_loop_succ, bind_assoc]
     congr; funext; exact ih ..

src/Init/Data/Fin/Iterate.lean

@@ -10,18 +10,10 @@ import Init.Data.Fin.Basic
 namespace Fin
 
 /--
-Applies an index-dependent function `f` to all of the values in `[i:n]`, starting at `i` with an
-initial accumulator `a`.
+`hIterateFrom f i bnd a` applies `f` over indices `[i:n]` to compute `P n`
+from `P i`.
 
-Concretely, `Fin.hIterateFrom P f i a` is equal to
-```lean
-  a |> f i |> f (i + 1) |> ... |> f (n - 1)
-```
-
-Theorems about `Fin.hIterateFrom` can be proven using the general theorem `Fin.hIterateFrom_elim` or
-other more specialized theorems.
-
-`Fin.hIterate` is a variant that always starts at `0`.
+See `hIterate` below for more details.
 -/
 def hIterateFrom (P : Nat → Sort _) {n} (f : ∀(i : Fin n), P i.val → P (i.val+1))
       (i : Nat) (ubnd : i ≤ n) (a : P i) : P n :=
@@ -34,18 +26,20 @@ def hIterateFrom (P : Nat → Sort _) {n} (f : ∀(i : Fin n), P i.val → P (i.
   decreasing_by decreasing_trivial_pre_omega
 
 /--
-Applies an index-dependent function to all the values less than the given bound `n`, starting at
-`0` with an accumulator.
+`hIterate` is a heterogeneous iterative operation that applies a
+index-dependent function `f` to a value `init : P start` a total of
+`stop - start` times to produce a value of type `P stop`.
 
-Concretely, `Fin.hIterate P init f` is equal to
+Concretely, `hIterate start stop f init` is equal to
 ```lean
-  init |> f 0 |> f 1 |> ... |> f (n-1)
+  init |> f start _ |> f (start+1) _ ... |> f (end-1) _
 ```
 
-Theorems about `Fin.hIterate` can be proven using the general theorem `Fin.hIterate_elim` or other more
-specialized theorems.
+Because it is heterogeneous and must return a value of type `P stop`,
+`hIterate` requires proof that `start ≤ stop`.
 
-`Fin.hIterateFrom` is a variant that takes a custom starting value instead of `0`.
+One can prove properties of `hIterate` using the general theorem
+`hIterate_elim` or other more specialized theorems.
  -/
 def hIterate (P : Nat → Sort _) {n : Nat} (init : P 0) (f : ∀(i : Fin n), P i.val → P (i.val+1)) :
     P n :=

src/Init/Data/Fin/Lemmas.lean

@@ -45,7 +45,6 @@ theorem val_ne_iff {a b : Fin n} : a.1 ≠ b.1 ↔ a ≠ b := not_congr val_inj
 theorem forall_iff {p : Fin n → Prop} : (∀ i, p i) ↔ ∀ i h, p ⟨i, h⟩ :=
   ⟨fun h i hi => h ⟨i, hi⟩, fun h ⟨i, hi⟩ => h i hi⟩
 
-/-- Restatement of `Fin.mk.injEq` as an `iff`. -/
 protected theorem mk.inj_iff {n a b : Nat} {ha : a < n} {hb : b < n} :
     (⟨a, ha⟩ : Fin n) = ⟨b, hb⟩ ↔ a = b := Fin.ext_iff
 
@@ -56,14 +55,6 @@ theorem eq_mk_iff_val_eq {a : Fin n} {k : Nat} {hk : k < n} :
 
 theorem mk_val (i : Fin n) : (⟨i, i.isLt⟩ : Fin n) = i := Fin.eta ..
 
-@[simp] theorem mk_eq_zero {n a : Nat} {ha : a < n} [NeZero n] :
-    (⟨a, ha⟩ : Fin n) = 0 ↔ a = 0 :=
-  mk.inj_iff
-
-@[simp] theorem zero_eq_mk {n a : Nat} {ha : a < n} [NeZero n] :
-    0 = (⟨a, ha⟩ : Fin n) ↔ a = 0 := by
-  simp [eq_comm]
-
 @[simp] theorem val_ofNat' (n : Nat) [NeZero n] (a : Nat) :
   (Fin.ofNat' n a).val = a % n := rfl
 
@@ -127,33 +118,6 @@ protected theorem ne_of_gt {a b : Fin n} (h : a < b) : b ≠ a := Fin.ne_of_val_
 
 protected theorem le_of_lt {a b : Fin n} (h : a < b) : a ≤ b := Nat.le_of_lt h
 
-protected theorem lt_of_le_of_lt {a b c : Fin n} : a ≤ b → b < c → a < c := Nat.lt_of_le_of_lt
-
-protected theorem lt_of_lt_of_le {a b c : Fin n} : a < b → b ≤ c → a < c := Nat.lt_of_lt_of_le
-
-protected theorem le_rfl {a : Fin n} : a ≤ a := Nat.le_refl _
-
-protected theorem lt_iff_le_and_ne {a b : Fin n} : a < b ↔ a ≤ b ∧ a ≠ b := by
-  rw [← val_ne_iff]; exact Nat.lt_iff_le_and_ne
-
-protected theorem lt_or_lt_of_ne {a b : Fin n} (h : a ≠ b) : a < b ∨ b < a :=
-  Nat.lt_or_lt_of_ne <| val_ne_iff.2 h
-
-protected theorem lt_or_le (a b : Fin n) : a < b ∨ b ≤ a := Nat.lt_or_ge _ _
-
-protected theorem le_or_lt (a b : Fin n) : a ≤ b ∨ b < a := (b.lt_or_le a).symm
-
-protected theorem le_of_eq {a b : Fin n} (hab : a = b) : a ≤ b :=
-  Nat.le_of_eq <| congrArg val hab
-
-protected theorem ge_of_eq {a b : Fin n} (hab : a = b) : b ≤ a := Fin.le_of_eq hab.symm
-
-protected theorem eq_or_lt_of_le {a b : Fin n} : a ≤ b → a = b ∨ a < b := by
-  rw [Fin.ext_iff]; exact Nat.eq_or_lt_of_le
-
-protected theorem lt_or_eq_of_le {a b : Fin n} : a ≤ b → a < b ∨ a = b := by
-  rw [Fin.ext_iff]; exact Nat.lt_or_eq_of_le
-
 theorem is_le (i : Fin (n + 1)) : i ≤ n := Nat.le_of_lt_succ i.is_lt
 
 @[simp] theorem is_le' {a : Fin n} : a ≤ n := Nat.le_of_lt a.is_lt
@@ -697,20 +661,12 @@ theorem pred_add_one (i : Fin (n + 2)) (h : (i : Nat) < n + 1) :
 @[simp] theorem natAdd_subNat_cast {i : Fin (n + m)} (h : n ≤ i) :
     natAdd n (subNat n (i.cast (Nat.add_comm ..)) h) = i := by simp [← cast_addNat]
 
-/-! ### Recursion and induction principles -/
+/-! ### recursion and induction principles -/
 
-/--
-An induction principle for `Fin` that considers a given `i : Fin n` as given by a sequence of `i`
-applications of `Fin.succ`.
-
-The cases in the induction are:
- * `zero` demonstrates the motive for `(0 : Fin (n + 1))` for all bounds `n`
- * `succ` demonstrates the motive for `Fin.succ` applied to an arbitrary `Fin` for an arbitrary
-   bound `n`
-
-Unlike `Fin.induction`, the motive quantifies over the bound, and the bound varies at each inductive
-step. `Fin.succRecOn` is a version of this induction principle that takes the `Fin` argument first.
--/
+/-- Define `motive n i` by induction on `i : Fin n` interpreted as `(0 : Fin (n - i)).succ.succ…`.
+This function has two arguments: `zero n` defines `0`-th element `motive (n+1) 0` of an
+`(n+1)`-tuple, and `succ n i` defines `(i+1)`-st element of `(n+1)`-tuple based on `n`, `i`, and
+`i`-th element of `n`-tuple. -/
 -- FIXME: Performance review
 @[elab_as_elim] def succRec {motive : ∀ n, Fin n → Sort _}
     (zero : ∀ n, motive n.succ (0 : Fin (n + 1)))
@@ -719,18 +675,13 @@ step. `Fin.succRecOn` is a version of this induction principle that takes the `F
   | Nat.succ n, ⟨0, _⟩ => by rw [mk_zero]; exact zero n
   | Nat.succ _, ⟨Nat.succ i, h⟩ => succ _ _ (succRec zero succ ⟨i, Nat.lt_of_succ_lt_succ h⟩)
 
-/--
-An induction principle for `Fin` that considers a given `i : Fin n` as given by a sequence of `i`
-applications of `Fin.succ`.
+/-- Define `motive n i` by induction on `i : Fin n` interpreted as `(0 : Fin (n - i)).succ.succ…`.
+This function has two arguments:
+`zero n` defines the `0`-th element `motive (n+1) 0` of an `(n+1)`-tuple, and
+`succ n i` defines the `(i+1)`-st element of an `(n+1)`-tuple based on `n`, `i`,
+and the `i`-th element of an `n`-tuple.
 
-The cases in the induction are:
- * `zero` demonstrates the motive for `(0 : Fin (n + 1))` for all bounds `n`
- * `succ` demonstrates the motive for `Fin.succ` applied to an arbitrary `Fin` for an arbitrary
-   bound `n`
-
-Unlike `Fin.induction`, the motive quantifies over the bound, and the bound varies at each inductive
-step. `Fin.succRec` is a version of this induction principle that takes the `Fin` argument last.
--/
+A version of `Fin.succRec` taking `i : Fin n` as the first argument. -/
 -- FIXME: Performance review
 @[elab_as_elim] def succRecOn {n : Nat} (i : Fin n) {motive : ∀ n, Fin n → Sort _}
     (zero : ∀ n, motive (n + 1) 0) (succ : ∀ n i, motive n i → motive (Nat.succ n) i.succ) :
@@ -745,17 +696,9 @@ step. `Fin.succRec` is a version of this induction principle that takes the `Fin
   cases i; rfl
 
 
-/--
-Proves a statement by induction on the underlying `Nat` value in a `Fin (n + 1)`.
-
-For the induction:
- * `zero` is the base case, demonstrating `motive 0`.
- * `succ` is the inductive step, assuming the motive for `i : Fin n` (lifted to `Fin (n + 1)` with
-   `Fin.castSucc`) and demonstrating it for `i.succ`.
-
-`Fin.inductionOn` is a version of this induction principle that takes the `Fin` as its first
-parameter, `Fin.cases` is the corresponding case analysis operator, and `Fin.reverseInduction` is a
-version that starts at the greatest value instead of `0`.
+/-- Define `motive i` by induction on `i : Fin (n + 1)` via induction on the underlying `Nat` value.
+This function has two arguments: `zero` handles the base case on `motive 0`,
+and `succ` defines the inductive step using `motive i.castSucc`.
 -/
 -- FIXME: Performance review
 @[elab_as_elim] def induction {motive : Fin (n + 1) → Sort _} (zero : motive 0)
@@ -776,30 +719,18 @@ where
     (succ : ∀ i : Fin n, motive (castSucc i) → motive i.succ) (i : Fin n) :
     induction (motive := motive) zero succ i.succ = succ i (induction zero succ (castSucc i)) := rfl
 
-/--
-Proves a statement by induction on the underlying `Nat` value in a `Fin (n + 1)`.
+/-- Define `motive i` by induction on `i : Fin (n + 1)` via induction on the underlying `Nat` value.
+This function has two arguments: `zero` handles the base case on `motive 0`,
+and `succ` defines the inductive step using `motive i.castSucc`.
 
-For the induction:
- * `zero` is the base case, demonstrating `motive 0`.
- * `succ` is the inductive step, assuming the motive for `i : Fin n` (lifted to `Fin (n + 1)` with
-   `Fin.castSucc`) and demonstrating it for `i.succ`.
-
-`Fin.induction` is a version of this induction principle that takes the `Fin` as its last
-parameter.
+A version of `Fin.induction` taking `i : Fin (n + 1)` as the first argument.
 -/
 -- FIXME: Performance review
 @[elab_as_elim] def inductionOn (i : Fin (n + 1)) {motive : Fin (n + 1) → Sort _} (zero : motive 0)
     (succ : ∀ i : Fin n, motive (castSucc i) → motive i.succ) : motive i := induction zero succ i
 
-/--
-Proves a statement by cases on the underlying `Nat` value in a `Fin (n + 1)`.
-
-The two cases are:
- * `zero`, used when the value is of the form `(0 : Fin (n + 1))`
- * `succ`, used when the value is of the form `(j : Fin n).succ`
-
-The corresponding induction principle is `Fin.induction`.
--/
+/-- Define `f : Π i : Fin n.succ, motive i` by separately handling the cases `i = 0` and
+`i = j.succ`, `j : Fin n`. -/
 @[elab_as_elim] def cases {motive : Fin (n + 1) → Sort _}
     (zero : motive 0) (succ : ∀ i : Fin n, motive i.succ) :
     ∀ i : Fin (n + 1), motive i := induction zero fun i _ => succ i
@@ -837,14 +768,9 @@ theorem fin_two_eq_of_eq_zero_iff : ∀ {a b : Fin 2}, (a = 0 ↔ b = 0) → a =
   simp only [forall_fin_two]; decide
 
 /--
-Proves a statement by reverse induction on the underlying `Nat` value in a `Fin (n + 1)`.
-
-For the induction:
- * `last` is the base case, demonstrating `motive (Fin.last n)`.
- * `cast` is the inductive step, assuming the motive for `(j : Fin n).succ` and demonstrating it for
-    the predecessor `j.castSucc`.
-
-`Fin.induction` is the non-reverse induction principle.
+Define `motive i` by reverse induction on `i : Fin (n + 1)` via induction on the underlying `Nat`
+value. This function has two arguments: `last` handles the base case on `motive (Fin.last n)`,
+and `cast` defines the inductive step using `motive i.succ`, inducting downwards.
 -/
 @[elab_as_elim] def reverseInduction {motive : Fin (n + 1) → Sort _} (last : motive (Fin.last n))
     (cast : ∀ i : Fin n, motive i.succ → motive (castSucc i)) (i : Fin (n + 1)) : motive i :=
@@ -867,16 +793,8 @@ decreasing_by decreasing_with
       succ i (reverseInduction zero succ i.succ) := by
   rw [reverseInduction, dif_neg (Fin.ne_of_lt (Fin.castSucc_lt_last i))]; rfl
 
-/--
-Proves a statement by cases on the underlying `Nat` value in a `Fin (n + 1)`, checking whether the
-value is the greatest representable or a predecessor of some other.
-
-The two cases are:
- * `last`, used when the value is `Fin.last n`
- * `cast`, used when the value is of the form `(j : Fin n).succ`
-
-The corresponding induction principle is `Fin.reverseInduction`.
--/
+/-- Define `f : Π i : Fin n.succ, motive i` by separately handling the cases `i = Fin.last n` and
+`i = j.castSucc`, `j : Fin n`. -/
 @[elab_as_elim] def lastCases {n : Nat} {motive : Fin (n + 1) → Sort _} (last : motive (Fin.last n))
     (cast : ∀ i : Fin n, motive (castSucc i)) (i : Fin (n + 1)) : motive i :=
   reverseInduction last (fun i _ => cast i) i
@@ -889,16 +807,8 @@ The corresponding induction principle is `Fin.reverseInduction`.
     (i : Fin n) : (Fin.lastCases last cast (Fin.castSucc i) : motive (Fin.castSucc i)) = cast i :=
   reverseInduction_castSucc ..
 
-/--
-A case analysis operator for `i : Fin (m + n)` that separately handles the cases where `i < m` and
-where `m ≤ i < m + n`.
-
-The first case, where `i < m`, is handled by `left`. In this case, `i` can be represented as
-`Fin.castAdd n (j : Fin m)`.
-
-The second case, where `m ≤ i < m + n`, is handled by `right`. In this case, `i` can be represented
-as `Fin.natAdd m (j : Fin n)`.
--/
+/-- Define `f : Π i : Fin (m + n), motive i` by separately handling the cases `i = castAdd n i`,
+`j : Fin m` and `i = natAdd m j`, `j : Fin n`. -/
 @[elab_as_elim] def addCases {m n : Nat} {motive : Fin (m + n) → Sort u}
     (left : ∀ i, motive (castAdd n i)) (right : ∀ i, motive (natAdd m i))
     (i : Fin (m + n)) : motive i :=

src/Init/Data/Fin/Log2.lean

@@ -6,20 +6,4 @@ Authors: Henrik Böving
 prelude
 import Init.Data.Nat.Log2
 
-set_option linter.missingDocs true
-
-/--
-Logarithm base 2 for bounded numbers.
-
-The resulting value is the same as that computed by `Nat.log2`. In particular, the result for `0` is
-`0`.
-
-Examples:
- * `(8 : Fin 10).log2 = (3 : Fin 10)`
- * `(7 : Fin 10).log2 = (2 : Fin 10)`
- * `(4 : Fin 10).log2 = (2 : Fin 10)`
- * `(3 : Fin 10).log2 = (1 : Fin 10)`
- * `(1 : Fin 10).log2 = (0 : Fin 10)`
- * `(0 : Fin 10).log2 = (0 : Fin 10)`
--/
 def Fin.log2 (n : Fin m) : Fin m := ⟨Nat.log2 n.val, Nat.lt_of_le_of_lt (Nat.log2_le_self n.val) n.isLt⟩

src/Init/Data/Float.lean

@@ -26,97 +26,43 @@ opaque floatSpec : FloatSpec := {
   decLe := fun _ _ => inferInstanceAs (Decidable True)
 }
 
-/--
-64-bit floating-point numbers.
-
-`Float` corresponds to the IEEE 754 *binary64* format (`double` in C or `f64` in Rust).
-Floating-point numbers are a finite representation of a subset of the real numbers, extended with
-extra “sentinel” values that represent undefined and infinite results as well as separate positive
-and negative zeroes. Arithmetic on floating-point numbers approximates the corresponding operations
-on the real numbers by rounding the results to numbers that are representable, propagating error and
-infinite values.
-
-Floating-point numbers include [subnormal numbers](https://en.wikipedia.org/wiki/Subnormal_number).
-Their special values are:
- * `NaN`, which denotes a class of “not a number” values that result from operations such as
-   dividing zero by zero, and
- * `Inf` and `-Inf`, which represent positive and infinities that result from dividing non-zero
-   values by zero.
--/
+/-- Native floating point type, corresponding to the IEEE 754 *binary64* format
+(`double` in C or `f64` in Rust). -/
 structure Float where
   val : floatSpec.float
 
 instance : Nonempty Float := ⟨{ val := floatSpec.val }⟩
 
-/--
-Adds two 64-bit floating-point numbers according to IEEE 754. Typically used via the `+` operator.
-
-This function does not reduce in the kernel. It is compiled to the C addition operator.
--/
 @[extern "lean_float_add"] opaque Float.add : Float → Float → Float
-/--
-Subtracts 64-bit floating-point numbers according to IEEE 754. Typically used via the `-` operator.
-
-This function does not reduce in the kernel. It is compiled to the C subtraction operator.
--/
 @[extern "lean_float_sub"] opaque Float.sub : Float → Float → Float
-/--
-Multiplies 64-bit floating-point numbers according to IEEE 754. Typically used via the `*` operator.
-
-This function does not reduce in the kernel. It is compiled to the C multiplication operator.
--/
 @[extern "lean_float_mul"] opaque Float.mul : Float → Float → Float
-/--
-Divides 64-bit floating-point numbers according to IEEE 754. Typically used via the `/` operator.
-
-In Lean, division by zero typically yields zero. For `Float`, it instead yields either `Inf`,
-`-Inf`, or `NaN`.
-
-This function does not reduce in the kernel. It is compiled to the C division operator.
--/
 @[extern "lean_float_div"] opaque Float.div : Float → Float → Float
-/--
-Negates 64-bit floating-point numbers according to IEEE 754. Typically used via the `-` prefix
-operator.
-
-This function does not reduce in the kernel. It is compiled to the C negation operator.
--/
 @[extern "lean_float_negate"] opaque Float.neg : Float → Float
 
 set_option bootstrap.genMatcherCode false
-/--
-Strict inequality of floating-point numbers. Typically used via the `<` operator.
--/
 def Float.lt : Float → Float → Prop := fun a b =>
   match a, b with
   | ⟨a⟩, ⟨b⟩ => floatSpec.lt a b
 
-/--
-Non-strict inequality of floating-point numbers. Typically used via the `≤` operator.
--/
 def Float.le : Float → Float → Prop := fun a b =>
   floatSpec.le a.val b.val
 
 /--
-Bit-for-bit conversion from `UInt64`. Interprets a `UInt64` as a `Float`, ignoring the numeric value
-and treating the `UInt64`'s bit pattern as a `Float`.
+Raw transmutation from `UInt64`.
 
-`Float`s and `UInt64`s have the same endianness on all supported platforms. IEEE 754 very precisely
-specifies the bit layout of floats.
-
-This function does not reduce in the kernel.
+Floats and UInts have the same endianness on all supported platforms.
+IEEE 754 very precisely specifies the bit layout of floats.
 -/
 @[extern "lean_float_of_bits"] opaque Float.ofBits : UInt64 → Float
 
 /--
-Bit-for-bit conversion to `UInt64`. Interprets a `Float` as a `UInt64`, ignoring the numeric value
-and treating the `Float`'s bit pattern as a `UInt64`.
+Raw transmutation to `UInt64`.
 
-`Float`s and `UInt64`s have the same endianness on all supported platforms. IEEE 754 very precisely
-specifies the bit layout of floats.
+Floats and UInts have the same endianness on all supported platforms.
+IEEE 754 very precisely specifies the bit layout of floats.
 
-This function is distinct from `Float.toUInt64`, which attempts to preserve the numeric value rather
-than reinterpreting the bit pattern.
+Note that this function is distinct from `Float.toUInt64`, which attempts
+to preserve the numeric value, and not the bitwise value.
 -/
 @[extern "lean_float_to_bits"] opaque Float.toBits : Float → UInt64
 
@@ -128,33 +74,15 @@ instance : Neg Float := ⟨Float.neg⟩
 instance : LT Float  := ⟨Float.lt⟩
 instance : LE Float  := ⟨Float.le⟩
 
-/--
-Checks whether two floating-point numbers are equal according to IEEE 754.
-
-Floating-point equality does not correspond with propositional equality. In particular, it is not
-reflexive since `NaN != NaN`, and it is not a congruence because `0.0 == -0.0`, but
-`1.0 / 0.0 != 1.0 / -0.0`.
-
-This function does not reduce in the kernel. It is compiled to the C equality operator.
--/
+/-- Note: this is not reflexive since `NaN != NaN`.-/
 @[extern "lean_float_beq"] opaque Float.beq (a b : Float) : Bool
 
 instance : BEq Float := ⟨Float.beq⟩
 
-/--
-Compares two floating point numbers for strict inequality.
-
-This function does not reduce in the kernel. It is compiled to the C inequality operator.
--/
 @[extern "lean_float_decLt"] opaque Float.decLt (a b : Float) : Decidable (a < b) :=
   match a, b with
   | ⟨a⟩, ⟨b⟩ => floatSpec.decLt a b
 
-/--
-Compares two floating point numbers for non-strict inequality.
-
-This function does not reduce in the kernel. It is compiled to the C inequality operator.
--/
 @[extern "lean_float_decLe"] opaque Float.decLe (a b : Float) : Decidable (a ≤ b) :=
   match a, b with
   | ⟨a⟩, ⟨b⟩ => floatSpec.decLe a b
@@ -162,129 +90,51 @@ This function does not reduce in the kernel. It is compiled to the C inequality
 instance floatDecLt (a b : Float) : Decidable (a < b) := Float.decLt a b
 instance floatDecLe (a b : Float) : Decidable (a ≤ b) := Float.decLe a b
 
-/--
-Converts a floating-point number to a string.
-
-This function does not reduce in the kernel.
--/
 @[extern "lean_float_to_string"] opaque Float.toString : Float → String
-
-/--
-Converts a floating-point number to an 8-bit unsigned integer.
-
-If the given `Float` is non-negative, truncates the value to a positive integer, rounding down and
-clamping to the range of `UInt8`. Returns `0` if the `Float` is negative or `NaN`, and returns the
-largest `UInt8` value (i.e. `UInt8.size - 1`) if the float is larger than it.
-
-This function does not reduce in the kernel.
+/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
+If negative or NaN, returns `0`.
+If larger than the maximum value for `UInt8` (including Inf), returns the maximum value of `UInt8`
+(i.e. `UInt8.size - 1`).
 -/
 @[extern "lean_float_to_uint8"] opaque Float.toUInt8 : Float → UInt8
-/--
-Converts a floating-point number to a 16-bit unsigned integer.
-
-If the given `Float` is non-negative, truncates the value to a positive integer, rounding down and
-clamping to the range of `UInt16`. Returns `0` if the `Float` is negative or `NaN`, and returns the
-largest `UInt16` value (i.e. `UInt16.size - 1`) if the float is larger than it.
-
-This function does not reduce in the kernel.
+/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
+If negative or NaN, returns `0`.
+If larger than the maximum value for `UInt16` (including Inf), returns the maximum value of `UInt16`
+(i.e. `UInt16.size - 1`).
 -/
 @[extern "lean_float_to_uint16"] opaque Float.toUInt16 : Float → UInt16
-/--
-Converts a floating-point number to a 32-bit unsigned integer.
-
-If the given `Float` is non-negative, truncates the value to a positive integer, rounding down and
-clamping to the range of `UInt32`. Returns `0` if the `Float` is negative or `NaN`, and returns the
-largest `UInt32` value (i.e. `UInt32.size - 1`) if the float is larger than it.
-
-This function does not reduce in the kernel.
+/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
+If negative or NaN, returns `0`.
+If larger than the maximum value for `UInt32` (including Inf), returns the maximum value of `UInt32`
+(i.e. `UInt32.size - 1`).
 -/
 @[extern "lean_float_to_uint32"] opaque Float.toUInt32 : Float → UInt32
-/--
-Converts a floating-point number to a 64-bit unsigned integer.
-
-If the given `Float` is non-negative, truncates the value to a positive integer, rounding down and
-clamping to the range of `UInt64`. Returns `0` if the `Float` is negative or `NaN`, and returns the
-largest `UInt64` value (i.e. `UInt64.size - 1`) if the float is larger than it.
-
-This function does not reduce in the kernel.
+/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
+If negative or NaN, returns `0`.
+If larger than the maximum value for `UInt64` (including Inf), returns the maximum value of `UInt64`
+(i.e. `UInt64.size - 1`).
 -/
 @[extern "lean_float_to_uint64"] opaque Float.toUInt64 : Float → UInt64
-/--
-Converts a floating-point number to a word-sized unsigned integer.
-
-If the given `Float` is non-negative, truncates the value to a positive integer, rounding down and
-clamping to the range of `USize`. Returns `0` if the `Float` is negative or `NaN`, and returns the
-largest `USize` value (i.e. `USize.size - 1`) if the float is larger than it.
-
-This function does not reduce in the kernel.
+/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
+If negative or NaN, returns `0`.
+If larger than the maximum value for `USize` (including Inf), returns the maximum value of `USize`
+(i.e. `USize.size - 1`). This value is platform dependent).
 -/
 @[extern "lean_float_to_usize"] opaque Float.toUSize : Float → USize
 
-/--
-Checks whether a floating point number is `NaN` (“not a number”) value.
-
-`NaN` values result from operations that might otherwise be errors, such as dividing zero by zero.
-
-This function does not reduce in the kernel. It is compiled to the C operator `isnan`.
--/
 @[extern "lean_float_isnan"] opaque Float.isNaN : Float → Bool
-
-/--
-Checks whether a floating-point number is finite, that is, whether it is normal, subnormal, or zero,
-but not infinite or `NaN`.
-
-This function does not reduce in the kernel. It is compiled to the C operator `isfinite`.
--/
 @[extern "lean_float_isfinite"] opaque Float.isFinite : Float → Bool
-
-/--
-Checks whether a floating-point number is a positive or negative infinite number, but not a finite
-number or `NaN`.
-
-This function does not reduce in the kernel. It is compiled to the C operator `isinf`.
--/
 @[extern "lean_float_isinf"] opaque Float.isInf : Float → Bool
-
-/--
-Splits the given float `x` into a significand/exponent pair `(s, i)` such that `x = s * 2^i` where
-`s ∈ (-1;-0.5] ∪ [0.5; 1)`. Returns an undefined value if `x` is not finite.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`frexp`.
+/-- Splits the given float `x` into a significand/exponent pair `(s, i)`
+such that `x = s * 2^i` where `s ∈ (-1;-0.5] ∪ [0.5; 1)`.
+Returns an undefined value if `x` is not finite.
 -/
 @[extern "lean_float_frexp"] opaque Float.frExp : Float → Float × Int
 
 instance : ToString Float where
   toString := Float.toString
 
-/-- Obtains the `Float` whose value is the same as the given `UInt8`. -/
-@[extern "lean_uint8_to_float"] opaque UInt8.toFloat (n : UInt8) : Float
-/-- Obtains the `Float` whose value is the same as the given `UInt16`. -/
-@[extern "lean_uint16_to_float"] opaque UInt16.toFloat (n : UInt16) : Float
-/-- Obtains the `Float` whose value is the same as the given `UInt32`. -/
-@[extern "lean_uint32_to_float"] opaque UInt32.toFloat (n : UInt32) : Float
-/--
-Obtains a `Float` whose value is near the given `UInt64`.
-
-It will be exactly the value of the given `UInt64` if such a `Float` exists. If no such `Float`
-exists, the returned value will either be the smallest `Float` that is larger than the given value,
-or the largest `Float` that is smaller than the given value.
-
-This function is opaque in the kernel, but is overridden at runtime with an efficient
-implementation.
--/
 @[extern "lean_uint64_to_float"] opaque UInt64.toFloat (n : UInt64) : Float
-/--
-Obtains a `Float` whose value is near the given `USize`.
-
-It will be exactly the value of the given `USize` if such a `Float` exists. If no such `Float`
-exists, the returned value will either be the smallest `Float` that is larger than the given value,
-or the largest `Float` that is smaller than the given value.
-
-This function is opaque in the kernel, but is overridden at runtime with an efficient
-implementation.
--/
-@[extern "lean_usize_to_float"] opaque USize.toFloat (n : USize) : Float
 
 instance : Inhabited Float where
   default := UInt64.toFloat 0
@@ -294,191 +144,30 @@ instance : Repr Float where
 
 instance : ReprAtom Float  := ⟨⟩
 
-/--
-Computes the sine of a floating-point number in radians.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`sin`.
--/
 @[extern "sin"] opaque Float.sin : Float → Float
-/--
-Computes the cosine of a floating-point number in radians.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`cos`.
--/
 @[extern "cos"] opaque Float.cos : Float → Float
-/--
-Computes the tangent of a floating-point number in radians.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`tan`.
--/
 @[extern "tan"] opaque Float.tan : Float → Float
-/--
-Computes the arc sine (inverse sine) of a floating-point number in radians.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`asin`.
--/
 @[extern "asin"] opaque Float.asin : Float → Float
-/--
-Computes the arc cosine (inverse cosine) of a floating-point number in radians.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`acos`.
--/
 @[extern "acos"] opaque Float.acos : Float → Float
-/--
-Computes the arc tangent (inverse tangent) of a floating-point number in radians.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`atan`.
--/
 @[extern "atan"] opaque Float.atan : Float → Float
-/--
-Computes the arc tangent (inverse tangent) of `y / x` in radians, in the range `-π`–`π`. The signs
-of the arguments determine the quadrant of the result.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`atan2`.
--/
-@[extern "atan2"] opaque Float.atan2 (y x : Float) : Float
-/--
-Computes the hyperbolic sine of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`sinh`.
--/
+@[extern "atan2"] opaque Float.atan2 : Float → Float → Float
 @[extern "sinh"] opaque Float.sinh : Float → Float
-/--
-Computes the hyperbolic cosine of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`cosh`.
--/
 @[extern "cosh"] opaque Float.cosh : Float → Float
-/--
-Computes the hyperbolic tangent of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`tanh`.
--/
 @[extern "tanh"] opaque Float.tanh : Float → Float
-/--
-Computes the hyperbolic arc sine (inverse sine) of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`asinh`.
--/
 @[extern "asinh"] opaque Float.asinh : Float → Float
-/--
-Computes the hyperbolic arc cosine (inverse cosine) of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`acosh`.
--/
 @[extern "acosh"] opaque Float.acosh : Float → Float
-/--
-Computes the hyperbolic arc tangent (inverse tangent) of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`atanh`.
--/
 @[extern "atanh"] opaque Float.atanh : Float → Float
-/--
-Computes the exponential `e^x` of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`exp`.
--/
-@[extern "exp"] opaque Float.exp (x : Float) : Float
-/--
-Computes the base-2 exponential `2^x` of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`exp2`.
--/
-@[extern "exp2"] opaque Float.exp2 (x : Float) : Float
-/--
-Computes the natural logarithm `ln x` of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`log`.
--/
-@[extern "log"] opaque Float.log (x : Float) : Float
-/--
-Computes the base-2 logarithm of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`log2`.
--/
+@[extern "exp"] opaque Float.exp : Float → Float
+@[extern "exp2"] opaque Float.exp2 : Float → Float
+@[extern "log"] opaque Float.log : Float → Float
 @[extern "log2"] opaque Float.log2 : Float → Float
-/--
-Computes the base-10 logarithm of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`log10`.
--/
 @[extern "log10"] opaque Float.log10 : Float → Float
-/--
-Raises one floating-point number to the power of another. Typically used via the `^` operator.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`pow`.
--/
 @[extern "pow"] opaque Float.pow : Float → Float → Float
-/--
-Computes the square root of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`sqrt`.
--/
 @[extern "sqrt"] opaque Float.sqrt : Float → Float
-/--
-Computes the cube root of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`cbrt`.
--/
 @[extern "cbrt"] opaque Float.cbrt : Float → Float
-/--
-Computes the ceiling of a floating-point number, which is the smallest integer that's no smaller
-than the given number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`ceil`.
-
-Examples:
- * `Float.ceil 1.5 = 2`
- * `Float.ceil (-1.5) = (-1)`
--/
 @[extern "ceil"] opaque Float.ceil : Float → Float
-/--
-Computes the floor of a floating-point number, which is the largest integer that's no larger
-than the given number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`floor`.
-
-Examples:
- * `Float.floor 1.5 = 1`
- * `Float.floor (-1.5) = (-2)`
--/
 @[extern "floor"] opaque Float.floor : Float → Float
-/--
-Rounds to the nearest integer, rounding away from zero at half-way points.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`round`.
--/
 @[extern "round"] opaque Float.round : Float → Float
-/--
-Computes the absolute value of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`fabs`.
--/
 @[extern "fabs"] opaque Float.abs : Float → Float
 
 instance : HomogeneousPow Float := ⟨Float.pow⟩
@@ -489,8 +178,6 @@ instance : Max Float := maxOfLe
 
 /--
 Efficiently computes `x * 2^i`.
-
-This function does not reduce in the kernel.
 -/
 @[extern "lean_float_scaleb"]
 opaque Float.scaleB (x : Float) (i : @& Int) : Float

src/Init/Data/Float32.lean

@@ -19,101 +19,43 @@ opaque float32Spec : FloatSpec := {
   decLe := fun _ _ => inferInstanceAs (Decidable True)
 }
 
-/--
-32-bit floating-point numbers.
-
-`Float32` corresponds to the IEEE 754 *binary32* format (`float` in C or `f32` in Rust).
-Floating-point numbers are a finite representation of a subset of the real numbers, extended with
-extra “sentinel” values that represent undefined and infinite results as well as separate positive
-and negative zeroes. Arithmetic on floating-point numbers approximates the corresponding operations
-on the real numbers by rounding the results to numbers that are representable, propagating error and
-infinite values.
-
-Floating-point numbers include [subnormal numbers](https://en.wikipedia.org/wiki/Subnormal_number).
-Their special values are:
- * `NaN`, which denotes a class of “not a number” values that result from operations such as
-   dividing zero by zero, and
- * `Inf` and `-Inf`, which represent positive and infinities that result from dividing non-zero
-   values by zero.
-
--/
+/-- Native floating point type, corresponding to the IEEE 754 *binary32* format
+(`float` in C or `f32` in Rust). -/
 structure Float32 where
   val : float32Spec.float
 
 instance : Nonempty Float32 := ⟨{ val := float32Spec.val }⟩
 
-/--
-Adds two 32-bit floating-point numbers according to IEEE 754. Typically used via the `+` operator.
-
-This function does not reduce in the kernel. It is compiled to the C addition operator.
--/
 @[extern "lean_float32_add"] opaque Float32.add : Float32 → Float32 → Float32
-/--
-Subtracts 32-bit floating-point numbers according to IEEE 754. Typically used via the `-` operator.
-
-This function does not reduce in the kernel. It is compiled to the C subtraction operator.
--/
 @[extern "lean_float32_sub"] opaque Float32.sub : Float32 → Float32 → Float32
-/--
-Multiplies 32-bit floating-point numbers according to IEEE 754. Typically used via the `*` operator.
-
-This function does not reduce in the kernel. It is compiled to the C multiplication operator.
--/
 @[extern "lean_float32_mul"] opaque Float32.mul : Float32 → Float32 → Float32
-/--
-Divides 32-bit floating-point numbers according to IEEE 754. Typically used via the `/` operator.
-
-In Lean, division by zero typically yields zero. For `Float32`, it instead yields either `Inf`,
-`-Inf`, or `NaN`.
-
-This function does not reduce in the kernel. It is compiled to the C division operator.
--/
 @[extern "lean_float32_div"] opaque Float32.div : Float32 → Float32 → Float32
-/--
-Negates 32-bit floating-point numbers according to IEEE 754. Typically used via the `-` prefix
-operator.
-
-This function does not reduce in the kernel. It is compiled to the C negation operator.
--/
 @[extern "lean_float32_negate"] opaque Float32.neg : Float32 → Float32
 
 set_option bootstrap.genMatcherCode false
-/--
-Strict inequality of floating-point numbers. Typically used via the `<` operator.
--/
 def Float32.lt : Float32 → Float32 → Prop := fun a b =>
   match a, b with
   | ⟨a⟩, ⟨b⟩ => float32Spec.lt a b
 
-/--
-Non-strict inequality of floating-point numbers. Typically used via the `≤` operator.
--/
 def Float32.le : Float32 → Float32 → Prop := fun a b =>
   float32Spec.le a.val b.val
 
 /--
-Bit-for-bit conversion from `UInt32`. Interprets a `UInt32` as a `Float32`, ignoring the numeric
-value and treating the `UInt32`'s bit pattern as a `Float32`.
+Raw transmutation from `UInt32`.
 
-`Float32`s and `UInt32`s have the same endianness on all supported platforms. IEEE 754 very
-precisely specifies the bit layout of floats.
-
-This function does not reduce in the kernel.
+Float32s and UInts have the same endianness on all supported platforms.
+IEEE 754 very precisely specifies the bit layout of floats.
 -/
 @[extern "lean_float32_of_bits"] opaque Float32.ofBits : UInt32 → Float32
 
-
 /--
-Bit-for-bit conversion to `UInt32`. Interprets a `Float32` as a `UInt32`, ignoring the numeric value
-and treating the `Float32`'s bit pattern as a `UInt32`.
+Raw transmutation to `UInt32`.
 
-`Float32`s and `UInt32`s have the same endianness on all supported platforms. IEEE 754 very
-precisely specifies the bit layout of floats.
+Float32s and UInts have the same endianness on all supported platforms.
+IEEE 754 very precisely specifies the bit layout of floats.
 
-This function is distinct from `Float.toUInt32`, which attempts to preserve the numeric value rather
-than reinterpreting the bit pattern.
-
-This function does not reduce in the kernel.
+Note that this function is distinct from `Float32.toUInt32`, which attempts
+to preserve the numeric value, and not the bitwise value.
 -/
 @[extern "lean_float32_to_bits"] opaque Float32.toBits : Float32 → UInt32
 
@@ -125,33 +67,15 @@ instance : Neg Float32 := ⟨Float32.neg⟩
 instance : LT Float32  := ⟨Float32.lt⟩
 instance : LE Float32  := ⟨Float32.le⟩
 
-/--
-Checks whether two floating-point numbers are equal according to IEEE 754.
-
-Floating-point equality does not correspond with propositional equality. In particular, it is not
-reflexive since `NaN != NaN`, and it is not a congruence because `0.0 == -0.0`, but
-`1.0 / 0.0 != 1.0 / -0.0`.
-
-This function does not reduce in the kernel. It is compiled to the C equality operator.
--/
+/-- Note: this is not reflexive since `NaN != NaN`.-/
 @[extern "lean_float32_beq"] opaque Float32.beq (a b : Float32) : Bool
 
 instance : BEq Float32 := ⟨Float32.beq⟩
 
-/--
-Compares two floating point numbers for strict inequality.
-
-This function does not reduce in the kernel. It is compiled to the C inequality operator.
--/
 @[extern "lean_float32_decLt"] opaque Float32.decLt (a b : Float32) : Decidable (a < b) :=
   match a, b with
   | ⟨a⟩, ⟨b⟩ => float32Spec.decLt a b
 
-/--
-Compares two floating point numbers for non-strict inequality.
-
-This function does not reduce in the kernel. It is compiled to the C inequality operator.
--/
 @[extern "lean_float32_decLe"] opaque Float32.decLe (a b : Float32) : Decidable (a ≤ b) :=
   match a, b with
   | ⟨a⟩, ⟨b⟩ => float32Spec.decLe a b
@@ -159,133 +83,51 @@ This function does not reduce in the kernel. It is compiled to the C inequality
 instance float32DecLt (a b : Float32) : Decidable (a < b) := Float32.decLt a b
 instance float32DecLe (a b : Float32) : Decidable (a ≤ b) := Float32.decLe a b
 
-/--
-Converts a floating-point number to a string.
-
-This function does not reduce in the kernel.
--/
 @[extern "lean_float32_to_string"] opaque Float32.toString : Float32 → String
-/--
-Converts a floating-point number to an 8-bit unsigned integer.
-
-If the given `Float32` is non-negative, truncates the value to a positive integer, rounding down and
-clamping to the range of `UInt8`. Returns `0` if the `Float32` is negative or `NaN`, and returns the
-largest `UInt8` value (i.e. `UInt8.size - 1`) if the float is larger than it.
-
-This function does not reduce in the kernel.
+/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
+If negative or NaN, returns `0`.
+If larger than the maximum value for `UInt8` (including Inf), returns the maximum value of `UInt8`
+(i.e. `UInt8.size - 1`).
 -/
 @[extern "lean_float32_to_uint8"] opaque Float32.toUInt8 : Float32 → UInt8
-/--
-Converts a floating-point number to a 16-bit unsigned integer.
-
-If the given `Float32` is non-negative, truncates the value to a positive integer, rounding down and
-clamping to the range of `UInt16`. Returns `0` if the `Float32` is negative or `NaN`, and returns
-the largest `UInt16` value (i.e. `UInt16.size - 1`) if the float is larger than it.
-
-This function does not reduce in the kernel.
+/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
+If negative or NaN, returns `0`.
+If larger than the maximum value for `UInt16` (including Inf), returns the maximum value of `UInt16`
+(i.e. `UInt16.size - 1`).
 -/
 @[extern "lean_float32_to_uint16"] opaque Float32.toUInt16 : Float32 → UInt16
-/--
-Converts a floating-point number to a 32-bit unsigned integer.
-
-If the given `Float32` is non-negative, truncates the value to a positive integer, rounding down and
-clamping to the range of `UInt32`. Returns `0` if the `Float32` is negative or `NaN`, and returns
-the largest `UInt32` value (i.e. `UInt32.size - 1`) if the float is larger than it.
-
-This function does not reduce in the kernel.
+/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
+If negative or NaN, returns `0`.
+If larger than the maximum value for `UInt32` (including Inf), returns the maximum value of `UInt32`
+(i.e. `UInt32.size - 1`).
 -/
 @[extern "lean_float32_to_uint32"] opaque Float32.toUInt32 : Float32 → UInt32
-/--
-Converts a floating-point number to a 64-bit unsigned integer.
-
-If the given `Float32` is non-negative, truncates the value to a positive integer, rounding down and
-clamping to the range of `UInt64`. Returns `0` if the `Float32` is negative or `NaN`, and returns
-the largest `UInt64` value (i.e. `UInt64.size - 1`) if the float is larger than it.
-
-This function does not reduce in the kernel.
+/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
+If negative or NaN, returns `0`.
+If larger than the maximum value for `UInt64` (including Inf), returns the maximum value of `UInt64`
+(i.e. `UInt64.size - 1`).
 -/
 @[extern "lean_float32_to_uint64"] opaque Float32.toUInt64 : Float32 → UInt64
-/--
-Converts a floating-point number to a word-sized unsigned integer.
-
-If the given `Float32` is non-negative, truncates the value to a positive integer, rounding down and
-clamping to the range of `USize`. Returns `0` if the `Float32` is negative or `NaN`, and returns the
-largest `USize` value (i.e. `USize.size - 1`) if the float is larger than it.
-
-This function does not reduce in the kernel.
+/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
+If negative or NaN, returns `0`.
+If larger than the maximum value for `USize` (including Inf), returns the maximum value of `USize`
+(i.e. `USize.size - 1`). This value is platform dependent).
 -/
 @[extern "lean_float32_to_usize"] opaque Float32.toUSize : Float32 → USize
 
-/--
-Checks whether a floating point number is `NaN` ("not a number") value.
-
-`NaN` values result from operations that might otherwise be errors, such as dividing zero by zero.
-
-This function does not reduce in the kernel. It is compiled to the C operator `isnan`.
--/
 @[extern "lean_float32_isnan"] opaque Float32.isNaN : Float32 → Bool
-/--
-Checks whether a floating-point number is finite, that is, whether it is normal, subnormal, or zero,
-but not infinite or `NaN`.
-
-This function does not reduce in the kernel. It is compiled to the C operator `isfinite`.
--/
 @[extern "lean_float32_isfinite"] opaque Float32.isFinite : Float32 → Bool
-/--
-Checks whether a floating-point number is a positive or negative infinite number, but not a finite
-number or `NaN`.
-
-This function does not reduce in the kernel. It is compiled to the C operator `isinf`.
--/
 @[extern "lean_float32_isinf"] opaque Float32.isInf : Float32 → Bool
-/--
-Splits the given float `x` into a significand/exponent pair `(s, i)` such that `x = s * 2^i` where
-`s ∈ (-1;-0.5] ∪ [0.5; 1)`. Returns an undefined value if `x` is not finite.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`frexp`.
+/-- Splits the given float `x` into a significand/exponent pair `(s, i)`
+such that `x = s * 2^i` where `s ∈ (-1;-0.5] ∪ [0.5; 1)`.
+Returns an undefined value if `x` is not finite.
 -/
 @[extern "lean_float32_frexp"] opaque Float32.frExp : Float32 → Float32 × Int
 
 instance : ToString Float32 where
   toString := Float32.toString
 
-/-- Obtains the `Float32` whose value is the same as the given `UInt8`. -/
-@[extern "lean_uint8_to_float32"] opaque UInt8.toFloat32 (n : UInt8) : Float32
-/-- Obtains the `Float32` whose value is the same as the given `UInt16`. -/
-@[extern "lean_uint16_to_float32"] opaque UInt16.toFloat32 (n : UInt16) : Float32
-/--
-Obtains a `Float32` whose value is near the given `UInt32`.
-
-It will be exactly the value of the given `UInt32` if such a `Float32` exists. If no such `Float32`
-exists, the returned value will either be the smallest `Float32` that is larger than the given
-value, or the largest `Float32` that is smaller than the given value.
-
-This function is opaque in the kernel, but is overridden at runtime with an efficient
-implementation.
--/
-@[extern "lean_uint32_to_float32"] opaque UInt32.toFloat32 (n : UInt32) : Float32
-/--
-Obtains a `Float32` whose value is near the given `UInt64`.
-
-It will be exactly the value of the given `UInt64` if such a `Float32` exists. If no such `Float32`
-exists, the returned value will either be the smallest `Float32` that is larger than the given
-value, or the largest `Float32` that is smaller than the given value.
-
-This function is opaque in the kernel, but is overridden at runtime with an efficient
-implementation.
--/
 @[extern "lean_uint64_to_float32"] opaque UInt64.toFloat32 (n : UInt64) : Float32
-/-- Obtains a `Float32` whose value is near the given `USize`.
-
-It will be exactly the value of the given `USize` if such a `Float32` exists. If no such `Float32`
-exists, the returned value will either be the smallest `Float32` that is larger than the given
-value, or the largest `Float32` that is smaller than the given value.
-
-This function is opaque in the kernel, but is overridden at runtime with an efficient
-implementation.
--/
-@[extern "lean_usize_to_float32"] opaque USize.toFloat32 (n : USize) : Float32
 
 instance : Inhabited Float32 where
   default := UInt64.toFloat32 0
@@ -295,191 +137,30 @@ instance : Repr Float32 where
 
 instance : ReprAtom Float32  := ⟨⟩
 
-/--
-Computes the sine of a floating-point number in radians.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`sinf`.
--/
 @[extern "sinf"] opaque Float32.sin : Float32 → Float32
-/--
-Computes the cosine of a floating-point number in radians.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`cosf`.
--/
 @[extern "cosf"] opaque Float32.cos : Float32 → Float32
-/--
-Computes the tangent of a floating-point number in radians.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`tanf`.
--/
 @[extern "tanf"] opaque Float32.tan : Float32 → Float32
-/--
-Computes the arc sine (inverse sine) of a floating-point number in radians.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`asinf`.
--/
 @[extern "asinf"] opaque Float32.asin : Float32 → Float32
-/--
-Computes the arc cosine (inverse cosine) of a floating-point number in radians.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`acosf`.
--/
 @[extern "acosf"] opaque Float32.acos : Float32 → Float32
-/--
-Computes the arc tangent (inverse tangent) of a floating-point number in radians.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`atanf`.
--/
 @[extern "atanf"] opaque Float32.atan : Float32 → Float32
-/--
-Computes the arc tangent (inverse tangent) of `y / x` in radians, in the range `-π`–`π`. The signs
-of the arguments determine the quadrant of the result.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`atan2f`.
--/
 @[extern "atan2f"] opaque Float32.atan2 : Float32 → Float32 → Float32
-/--
-Computes the hyperbolic sine of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`sinhf`.
--/
 @[extern "sinhf"] opaque Float32.sinh : Float32 → Float32
-/--
-Computes the hyperbolic cosine of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`coshf`.
--/
 @[extern "coshf"] opaque Float32.cosh : Float32 → Float32
-/--
-Computes the hyperbolic tangent of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`tanhf`.
--/
 @[extern "tanhf"] opaque Float32.tanh : Float32 → Float32
-/--
-Computes the hyperbolic arc sine (inverse sine) of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`asinhf`.
--/
 @[extern "asinhf"] opaque Float32.asinh : Float32 → Float32
-/--
-Computes the hyperbolic arc cosine (inverse cosine) of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`acoshf`.
--/
 @[extern "acoshf"] opaque Float32.acosh : Float32 → Float32
-/--
-Computes the hyperbolic arc tangent (inverse tangent) of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`atanhf`.
--/
 @[extern "atanhf"] opaque Float32.atanh : Float32 → Float32
-/--
-Computes the exponential `e^x` of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`expf`.
--/
 @[extern "expf"] opaque Float32.exp : Float32 → Float32
-/--
-Computes the base-2 exponential `2^x` of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`exp2f`.
--/
 @[extern "exp2f"] opaque Float32.exp2 : Float32 → Float32
-/--
-Computes the natural logarithm `ln x` of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`logf`.
--/
 @[extern "logf"] opaque Float32.log : Float32 → Float32
-/--
-Computes the base-2 logarithm of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`log2f`.
--/
 @[extern "log2f"] opaque Float32.log2 : Float32 → Float32
-/--
-Computes the base-10 logarithm of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`log10f`.
--/
 @[extern "log10f"] opaque Float32.log10 : Float32 → Float32
-/--
-Raises one floating-point number to the power of another. Typically used via the `^` operator.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`powf`.
--/
 @[extern "powf"] opaque Float32.pow : Float32 → Float32 → Float32
-/--
-Computes the square root of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`sqrtf`.
--/
 @[extern "sqrtf"] opaque Float32.sqrt : Float32 → Float32
-/--
-Computes the cube root of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`cbrtf`.
--/
 @[extern "cbrtf"] opaque Float32.cbrt : Float32 → Float32
-/--
-Computes the ceiling of a floating-point number, which is the smallest integer that's no smaller
-than the given number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`ceilf`.
-
-Examples:
- * `Float32.ceil 1.5 = 2`
- * `Float32.ceil (-1.5) = (-1)`
--/
 @[extern "ceilf"] opaque Float32.ceil : Float32 → Float32
-/--
-Computes the floor of a floating-point number, which is the largest integer that's no larger
-than the given number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`floorf`.
-
-Examples:
- * `Float32.floor 1.5 = 1`
- * `Float32.floor (-1.5) = (-2)`
--/
 @[extern "floorf"] opaque Float32.floor : Float32 → Float32
-/--
-Rounds to the nearest integer, rounding away from zero at half-way points.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`roundf`.
--/
 @[extern "roundf"] opaque Float32.round : Float32 → Float32
-/--
-Computes the absolute value of a floating-point number.
-
-This function does not reduce in the kernel. It is implemented in compiled code by the C function
-`fabsf`.
--/
 @[extern "fabsf"] opaque Float32.abs : Float32 → Float32
 
 instance : HomogeneousPow Float32 := ⟨Float32.pow⟩
@@ -490,22 +171,9 @@ instance : Max Float32 := maxOfLe
 
 /--
 Efficiently computes `x * 2^i`.
-
-This function does not reduce in the kernel.
 -/
 @[extern "lean_float32_scaleb"]
 opaque Float32.scaleB (x : Float32) (i : @& Int) : Float32
 
-/--
-Converts a 32-bit floating-point number to a 64-bit floating-point number.
-
-This function does not reduce in the kernel.
--/
 @[extern "lean_float32_to_float"] opaque Float32.toFloat : Float32 → Float
-/--
-Converts a 64-bit floating-point number to a 32-bit floating-point number.
-This may lose precision.
-
-This function does not reduce in the kernel.
--/
 @[extern "lean_float_to_float32"] opaque Float.toFloat32 : Float → Float32

src/Init/Data/FloatArray/Basic.lean

@@ -17,14 +17,11 @@ attribute [extern "lean_float_array_data"] FloatArray.data
 
 namespace FloatArray
 @[extern "lean_mk_empty_float_array"]
-def emptyWithCapacity (c : @& Nat) : FloatArray :=
+def mkEmpty (c : @& Nat) : FloatArray :=
   { data := #[] }
 
-@[deprecated emptyWithCapacity (since := "2025-03-12")]
-abbrev mkEmpty := emptyWithCapacity
-
 def empty : FloatArray :=
-  emptyWithCapacity 0
+  mkEmpty 0
 
 instance : Inhabited FloatArray where
   default := empty
@@ -50,11 +47,11 @@ def uget : (a : @& FloatArray) → (i : USize) → i.toNat < a.size → Float
 
 @[extern "lean_float_array_fget"]
 def get : (ds : @& FloatArray) → (i : @& Nat) → (h : i < ds.size := by get_elem_tactic) → Float
-  | ⟨ds⟩, i, h => ds[i]
+  | ⟨ds⟩, i, h => ds.get i h
 
 @[extern "lean_float_array_get"]
 def get! : (@& FloatArray) → (@& Nat) → Float
-  | ⟨ds⟩, i => ds[i]!
+  | ⟨ds⟩, i => ds.get! i
 
 def get? (ds : FloatArray) (i : Nat) : Option Float :=
   if h : i < ds.size then
@@ -65,7 +62,7 @@ def get? (ds : FloatArray) (i : Nat) : Option Float :=
 instance : GetElem FloatArray Nat Float fun xs i => i < xs.size where
   getElem xs i h := xs.get i h
 
-instance : GetElem FloatArray USize Float fun xs i => i.toNat < xs.size where
+instance : GetElem FloatArray USize Float fun xs i => i.val < xs.size where
   getElem xs i h := xs.uget i h
 
 @[extern "lean_float_array_uset"]
@@ -167,9 +164,6 @@ def foldl {β : Type v} (f : β → Float → β) (init : β) (as : FloatArray)
 
 end FloatArray
 
-/--
-Converts a list of floats into a `FloatArray`.
--/
 def List.toFloatArray (ds : List Float) : FloatArray :=
   let rec loop
     | [],    r => r

src/Init/Data/Format/Instances.lean

@@ -23,12 +23,6 @@ instance [ToFormat α] : ToFormat (List α) where
 instance [ToFormat α] : ToFormat (Array α) where
   format a := "#" ++ format a.toList
 
-/--
-Formats an optional value, with no expectation that the Lean parser should be able to parse the
-result.
-
-This function is usually accessed through the `ToFormat (Option α)` instance.
--/
 def Option.format {α : Type u} [ToFormat α] : Option α → Format
   | none   => "none"
   | some a => "some " ++ Std.format a
@@ -39,10 +33,6 @@ instance {α : Type u} [ToFormat α] : ToFormat (Option α) :=
 instance {α : Type u} {β : Type v} [ToFormat α] [ToFormat β] : ToFormat (Prod α β) where
   format := fun (a, b) => Format.paren <| format a ++ "," ++ Format.line ++ format b
 
-/--
-Converts a string to a pretty-printer document, replacing newlines in the string with
-`Std.Format.line`.
--/
 def String.toFormat (s : String) : Std.Format :=
   Std.Format.joinSep (s.splitOn "\n") Std.Format.line
 

src/Init/Data/Function.lean

@@ -9,23 +9,10 @@ import Init.Core
 
 namespace Function
 
-/--
-Transforms a function from pairs into an equivalent two-parameter function.
-
-Examples:
- * `Function.curry (fun (x, y) => x + y) 3 5 = 8`
- * `Function.curry Prod.swap 3 "five" = ("five", 3)`
--/
 @[inline]
 def curry : (α × β → φ) → α → β → φ := fun f a b => f (a, b)
 
-/--
-Transforms a two-parameter function into an equivalent function from pairs.
-
-Examples:
- * `Function.uncurry List.drop (1, ["a", "b", "c"]) = ["b", "c"]`
- * `[("orange", 2), ("android", 3) ].map (Function.uncurry String.take) = ["or", "and"]`
--/
+/-- Interpret a function with two arguments as a function on `α × β` -/
 @[inline]
 def uncurry : (α → β → φ) → α × β → φ := fun f a => f a.1 a.2
 

src/Init/Data/Hashable.lean

@@ -75,19 +75,13 @@ instance (P : Prop) : Hashable P where
 @[always_inline, inline] def hash64 (u : UInt64) : UInt64 :=
   mixHash u 11
 
-/--
-The `BEq α` and `Hashable α` instances on `α` are compatible. This means that that `a == b` implies
-`hash a = hash b`.
-
-This is automatic if the `BEq` instance is lawful.
+/-- `LawfulHashable α` says that the `BEq α` and `Hashable α` instances on `α` are compatible, i.e.,
+that `a == b` implies `hash a = hash b`. This is automatic if the `BEq` instance is lawful.
 -/
 class LawfulHashable (α : Type u) [BEq α] [Hashable α] where
   /-- If `a == b`, then `hash a = hash b`. -/
   hash_eq (a b : α) : a == b → hash a = hash b
 
-/--
-A lawful hash function respects its Boolean equality test.
--/
 theorem hash_eq [BEq α] [Hashable α] [LawfulHashable α] {a b : α} : a == b → hash a = hash b :=
   LawfulHashable.hash_eq a b
 

src/Init/Data/Int.lean

@@ -7,11 +7,10 @@ prelude
 import Init.Data.Int.Basic
 import Init.Data.Int.Bitwise
 import Init.Data.Int.DivMod
+import Init.Data.Int.DivModLemmas
 import Init.Data.Int.Gcd
 import Init.Data.Int.Lemmas
 import Init.Data.Int.LemmasAux
 import Init.Data.Int.Order
 import Init.Data.Int.Pow
 import Init.Data.Int.Cooper
-import Init.Data.Int.Linear
-import Init.Data.Int.OfNat

src/Init/Data/Int/Basic.lean

@@ -17,36 +17,31 @@ open Nat
 This file defines the `Int` type as well as
 
 * coercions, conversions, and compatibility with numeric literals,
-* basic arithmetic operations add/sub/mul/pow,
+* basic arithmetic operations add/sub/mul/div/mod/pow,
 * a few `Nat`-related operations such as `negOfNat` and `subNatNat`,
 * relations `<`/`≤`/`≥`/`>`, the `NonNeg` property and `min`/`max`,
 * decidability of equality, relations and `NonNeg`.
-
-Division and modulus operations are defined in `Init.Data.Int.DivMod.Basic`.
 -/
 
 /--
-The integers.
+The type of integers. It is defined as an inductive type based on the
+natural number type `Nat` featuring two constructors: "a natural
+number is an integer", and "the negation of a successor of a natural
+number is an integer". The former represents integers between `0`
+(inclusive) and `∞`, and the latter integers between `-∞` and `-1`
+(inclusive).
 
-This type is special-cased by the compiler and overridden with an efficient implementation. The
-runtime has a special representation for `Int` that stores “small” signed numbers directly, while
-larger numbers use a fast arbitrary-precision arithmetic library (usually
-[GMP](https://gmplib.org/)). A “small number” is an integer that can be encoded with one fewer bits
-than the platform's pointer size (i.e. 63 bits on 64-bit architectures and 31 bits on 32-bit
-architectures).
+This type is special-cased by the compiler. The runtime has a special
+representation for `Int` which stores "small" signed numbers directly,
+and larger numbers use an arbitrary precision "bignum" library
+(usually [GMP](https://gmplib.org/)). A "small number" is an integer
+that can be encoded with 63 bits (31 bits on 32-bits architectures).
 -/
 inductive Int : Type where
-  /--
-  A natural number is an integer.
-
-  This constructor covers the non-negative integers (from `0` to `∞`).
-  -/
+  /-- A natural number is an integer (`0` to `∞`). -/
   | ofNat   : Nat → Int
-  /--
-  The negation of the successor of a natural number is an integer.
-
-  This constructor covers the negative integers (from `-1` to `-∞`).
-  -/
+  /-- The negation of the successor of a natural number is an integer
+    (`-1` to `-∞`). -/
   | negSucc : Nat → Int
 
 attribute [extern "lean_nat_to_int"] Int.ofNat
@@ -81,29 +76,15 @@ protected theorem zero_ne_one : (0 : Int) ≠ 1 := nofun
 
 theorem ofNat_two : ((2 : Nat) : Int) = 2 := rfl
 
-/--
-Negation of natural numbers.
-
-Examples:
- * `Int.negOfNat 6 = -6`
- * `Int.negOfNat 0 = 0`
--/
+/-- Negation of a natural number. -/
 def negOfNat : Nat → Int
   | 0      => 0
   | succ m => negSucc m
 
 set_option bootstrap.genMatcherCode false in
-/--
-Negation of integers, usually accessed via the `-` prefix operator.
+/-- Negation of an integer.
 
-This function is overridden by the compiler with an efficient implementation. This definition is
-the logical model.
-
-Examples:
- * `-(6 : Int) = -6`
- * `-(-6 : Int) = 6`
- * `(12 : Int).neg = -12`
--/
+  Implemented by efficient native code. -/
 @[extern "lean_int_neg"]
 protected def neg (n : @& Int) : Int :=
   match n with
@@ -122,30 +103,21 @@ protected def neg (n : @& Int) : Int :=
 instance instNegInt : Neg Int where
   neg := Int.neg
 
-/--
-Non-truncating subtraction of two natural numbers.
-
-Examples:
- * `Int.subNatNat 5 2 = 3`
- * `Int.subNatNat 2 5 = -3`
- * `Int.subNatNat 0 13 = -13`
--/
+/-- Subtraction of two natural numbers. -/
 def subNatNat (m n : Nat) : Int :=
   match (n - m : Nat) with
   | 0        => ofNat (m - n)  -- m ≥ n
   | (succ k) => negSucc k
 
 set_option bootstrap.genMatcherCode false in
-/--
-Addition of integers, usually accessed via the `+` operator.
+/-- Addition of two integers.
 
-This function is overridden by the compiler with an efficient implementation. This definition is
-the logical model.
+  ```
+  #eval (7 : Int) + (6 : Int) -- 13
+  #eval (6 : Int) + (-6 : Int) -- 0
+  ```
 
-Examples:
- * `(7 : Int) + (6 : Int) = 13`
- * `(6 : Int) + (-6 : Int) = 0`
--/
+  Implemented by efficient native code. -/
 @[extern "lean_int_add"]
 protected def add (m n : @& Int) : Int :=
   match m, n with
@@ -158,17 +130,15 @@ instance : Add Int where
   add := Int.add
 
 set_option bootstrap.genMatcherCode false in
-/--
-Multiplication of integers, usually accessed via the `*` operator.
+/-- Multiplication of two integers.
 
-This function is overridden by the compiler with an efficient implementation. This definition is
-the logical model.
+  ```
+  #eval (63 : Int) * (6 : Int) -- 378
+  #eval (6 : Int) * (-6 : Int) -- -36
+  #eval (7 : Int) * (0 : Int) -- 0
+  ```
 
-Examples:
- * `(63 : Int) * (6 : Int) = 378`
- * `(6 : Int) * (-6 : Int) = -36`
- * `(7 : Int) * (0 : Int) = 0`
--/
+  Implemented by efficient native code. -/
 @[extern "lean_int_mul"]
 protected def mul (m n : @& Int) : Int :=
   match m, n with
@@ -180,65 +150,48 @@ protected def mul (m n : @& Int) : Int :=
 instance : Mul Int where
   mul := Int.mul
 
+/-- Subtraction of two integers.
 
-/--
-Subtraction of integers, usually accessed via the `-` operator.
+  ```
+  #eval (63 : Int) - (6 : Int) -- 57
+  #eval (7 : Int) - (0 : Int) -- 7
+  #eval (0 : Int) - (7 : Int) -- -7
+  ```
 
-This function is overridden by the compiler with an efficient implementation. This definition is
-the logical model.
-
-Examples:
-* `(63 : Int) - (6 : Int) = 57`
-* `(7 : Int) - (0 : Int) = 7`
-* `(0 : Int) - (7 : Int) = -7`
--/
+  Implemented by efficient native code. -/
 @[extern "lean_int_sub"]
 protected def sub (m n : @& Int) : Int := m + (- n)
 
 instance : Sub Int where
   sub := Int.sub
 
-/--
-An integer is non-negative if it is equal to a natural number.
--/
+/-- A proof that an `Int` is non-negative. -/
 inductive NonNeg : Int → Prop where
-  /--
-  For all natural numbers `n`, `Int.ofNat n` is non-negative.
-  -/
+  /-- Sole constructor, proving that `ofNat n` is positive. -/
   | mk (n : Nat) : NonNeg (ofNat n)
 
-/--
-Non-strict inequality of integers, usually accessed via the `≤` operator.
-
-`a ≤ b` is defined as `b - a ≥ 0`, using `Int.NonNeg`.
--/
+/-- Definition of `a ≤ b`, encoded as `b - a ≥ 0`. -/
 protected def le (a b : Int) : Prop := NonNeg (b - a)
 
 instance instLEInt : LE Int where
   le := Int.le
 
-/--
-Strict inequality of integers, usually accessed via the `<` operator.
-
-`a < b` when `a + 1 ≤ b`.
--/
+/-- Definition of `a < b`, encoded as `a + 1 ≤ b`. -/
 protected def lt (a b : Int) : Prop := (a + 1) ≤ b
 
 instance instLTInt : LT Int where
   lt := Int.lt
 
 set_option bootstrap.genMatcherCode false in
-/--
-Decides whether two integers are equal. Usually accessed via the `DecidableEq Int` instance.
+/-- Decides equality between two `Int`s.
 
-This function is overridden by the compiler with an efficient implementation. This definition is the
-logical model.
+  ```
+  #eval (7 : Int) = (3 : Int) + (4 : Int) -- true
+  #eval (6 : Int) = (3 : Int) * (2 : Int) -- true
+  #eval ¬ (6 : Int) = (3 : Int) -- true
+  ```
 
-Examples:
-* `show (7 : Int) = (3 : Int) + (4 : Int) by decide`
-* `if (6 : Int) = (3 : Int) * (2 : Int) then "yes" else "no" = "yes"`
-* `(¬ (6 : Int) = (3 : Int)) = true`
--/
+  Implemented by efficient native code. -/
 @[extern "lean_int_dec_eq"]
 protected def decEq (a b : @& Int) : Decidable (a = b) :=
   match a, b with
@@ -251,7 +204,6 @@ protected def decEq (a b : @& Int) : Decidable (a = b) :=
     | isTrue h  => isTrue  <| h ▸ rfl
     | isFalse h => isFalse <| fun h' => Int.noConfusion h' (fun h' => absurd h' h)
 
-@[inherit_doc Int.decEq]
 instance : DecidableEq Int := Int.decEq
 
 set_option bootstrap.genMatcherCode false in
@@ -297,17 +249,15 @@ instance decLt (a b : @& Int) : Decidable (a < b) :=
   decNonneg _
 
 set_option bootstrap.genMatcherCode false in
-/--
-The absolute value of an integer is its distance from `0`.
+/-- Absolute value (`Nat`) of an integer.
 
-This function is overridden by the compiler with an efficient implementation. This definition is
-the logical model.
+  ```
+  #eval (7 : Int).natAbs -- 7
+  #eval (0 : Int).natAbs -- 0
+  #eval (-11 : Int).natAbs -- 11
+  ```
 
-Examples:
- * `(7 : Int).natAbs = 7`
- * `(0 : Int).natAbs = 0`
- * `((-11 : Int).natAbs = 11`
--/
+  Implemented by efficient native code. -/
 @[extern "lean_nat_abs"]
 def natAbs (m : @& Int) : Nat :=
   match m with
@@ -317,17 +267,8 @@ def natAbs (m : @& Int) : Nat :=
 /-! ## sign -/
 
 /--
-Returns the “sign” of the integer as another integer:
- * `1` for positive numbers,
- * `-1` for negative numbers, and
- * `0` for `0`.
-
-Examples:
- * `Int.sign 34 = 1`
- * `Int.sign 2 = 1`
- * `Int.sign 0 = 0`
- * `Int.sign -1 = -1`
- * `Int.sign -362 = -1`
+Returns the "sign" of the integer as another integer: `1` for positive numbers,
+`-1` for negative numbers, and `0` for `0`.
 -/
 def sign : Int → Int
   | Int.ofNat (succ _) => 1
@@ -336,33 +277,27 @@ def sign : Int → Int
 
 /-! ## Conversion -/
 
-/--
-Converts an integer into a natural number. Negative numbers are converted to `0`.
+/-- Turns an integer into a natural number, negative numbers become
+  `0`.
 
-Examples:
-* `(7 : Int).toNat = 7`
-* `(0 : Int).toNat = 0`
-* `(-7 : Int).toNat = 0`
+  ```
+  #eval (7 : Int).toNat -- 7
+  #eval (0 : Int).toNat -- 0
+  #eval (-7 : Int).toNat -- 0
+  ```
 -/
 def toNat : Int → Nat
   | ofNat n   => n
   | negSucc _ => 0
 
 /--
-Converts an integer into a natural number. Returns `none` for negative numbers.
-
-Examples:
-* `(7 : Int).toNat? = some 7`
-* `(0 : Int).toNat? = some 0`
-* `(-7 : Int).toNat? = none`
+* If `n : Nat`, then `int.toNat' n = some n`
+* If `n : Int` is negative, then `int.toNat' n = none`.
 -/
-def toNat? : Int → Option Nat
+def toNat' : Int → Option Nat
   | (n : Nat) => some n
   | -[_+1] => none
 
-@[deprecated toNat? (since := "2025-03-11"), inherit_doc toNat?]
-abbrev toNat' := toNat?
-
 /-! ## divisibility -/
 
 /--
@@ -374,14 +309,14 @@ instance : Dvd Int where
 
 /-! ## Powers -/
 
-/--
-Power of an integer to a natural number, usually accessed via the `^` operator.
+/-- Power of an integer to some natural number.
 
-Examples:
-* `(2 : Int) ^ 4 = 16`
-* `(10 : Int) ^ 0 = 1`
-* `(0 : Int) ^ 10 = 0`
-* `(-7 : Int) ^ 3 = -343`
+  ```
+  #eval (2 : Int) ^ 4 -- 16
+  #eval (10 : Int) ^ 0 -- 1
+  #eval (0 : Int) ^ 10 -- 0
+  #eval (-7 : Int) ^ 3 -- -343
+  ```
 -/
 protected def pow (m : Int) : Nat → Int
   | 0      => 1
@@ -401,14 +336,8 @@ instance : Max Int := maxOfLe
 end Int
 
 /--
-The canonical homomorphism `Int → R`. In most use cases, the target type will have a ring structure,
-and this homomorphism should be a ring homomorphism.
-
-`IntCast` and `NatCast` exist to allow different libraries with their own types that can be notated
-as natural numbers to have consistent `simp` normal forms without needing to create coercion
-simplification sets that are aware of all combinations. Libraries should make it easy to work with
-`IntCast` where possible. For instance, in Mathlib there will be such a homomorphism (and thus an
-`IntCast R` instance) whenever `R` is an additive group with a `1`.
+The canonical homomorphism `Int → R`.
+In most use cases `R` will have a ring structure and this will be a ring homomorphism.
 -/
 class IntCast (R : Type u) where
   /-- The canonical map `Int → R`. -/
@@ -416,8 +345,12 @@ class IntCast (R : Type u) where
 
 instance : IntCast Int where intCast n := n
 
-@[coe, reducible, match_pattern, inherit_doc IntCast]
-protected def Int.cast {R : Type u} [IntCast R] : Int → R :=
+/--
+Apply the canonical homomorphism from `Int` to a type `R` from an `IntCast R` instance.
+
+In Mathlib there will be such a homomorphism whenever `R` is an additive group with a `1`.
+-/
+@[coe, reducible, match_pattern] protected def Int.cast {R : Type u} [IntCast R] : Int → R :=
   IntCast.intCast
 
 -- see the notes about coercions into arbitrary types in the module doc-string

src/Init/Data/Int/Bitwise.lean

@@ -1,8 +1,50 @@
 /-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Copyright (c) 2022 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison
+Authors: Mario Carneiro
 -/
 prelude
-import Init.Data.Int.Bitwise.Basic
-import Init.Data.Int.Bitwise.Lemmas
+import Init.Data.Int.Basic
+import Init.Data.Nat.Bitwise.Basic
+
+namespace Int
+
+/-! ## bit operations -/
+
+/--
+Bitwise not
+
+Interprets the integer as an infinite sequence of bits in two's complement
+and complements each bit.
+```
+~~~(0:Int) = -1
+~~~(1:Int) = -2
+~~~(-1:Int) = 0
+```
+-/
+protected def not : Int -> Int
+  | Int.ofNat n => Int.negSucc n
+  | Int.negSucc n => Int.ofNat n
+
+instance : Complement Int := ⟨.not⟩
+
+/--
+Bitwise shift right.
+
+Conceptually, this treats the integer as an infinite sequence of bits in two's
+complement and shifts the value to the right.
+
+```lean
+( 0b0111:Int) >>> 1 =  0b0011
+( 0b1000:Int) >>> 1 =  0b0100
+(-0b1000:Int) >>> 1 = -0b0100
+(-0b0111:Int) >>> 1 = -0b0100
+```
+-/
+protected def shiftRight : Int → Nat → Int
+  | Int.ofNat n, s => Int.ofNat (n >>> s)
+  | Int.negSucc n, s => Int.negSucc (n >>> s)
+
+instance : HShiftRight Int Nat Int := ⟨.shiftRight⟩
+
+end Int

src/Init/Data/Int/Bitwise/Basic.lean

@@ -1,48 +0,0 @@
-/-
-Copyright (c) 2022 Mario Carneiro. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Mario Carneiro
--/
-prelude
-import Init.Data.Int.Basic
-import Init.Data.Nat.Bitwise.Basic
-
-namespace Int
-
-/-! ## bit operations -/
-
-/--
-Bitwise not, usually accessed via the `~~~` prefix operator.
-
-Interprets the integer as an infinite sequence of bits in two's complement and complements each bit.
-
-Examples:
- * `~~~(0 : Int) = -1`
- * `~~~(1 : Int) = -2`
- * `~~~(-1 : Int) = 0`
--/
-protected def not : Int → Int
-  | Int.ofNat n => Int.negSucc n
-  | Int.negSucc n => Int.ofNat n
-
-instance : Complement Int := ⟨.not⟩
-
-/--
-Bitwise right shift, usually accessed via the `>>>` operator.
-
-Interprets the integer as an infinite sequence of bits in two's complement and shifts the value to
-the right.
-
-Examples:
-* `( 0b0111 : Int) >>> 1 =  0b0011`
-* `( 0b1000 : Int) >>> 1 =  0b0100`
-* `(-0b1000 : Int) >>> 1 = -0b0100`
-* `(-0b0111 : Int) >>> 1 = -0b0100`
--/
-protected def shiftRight : Int → Nat → Int
-  | Int.ofNat n, s => Int.ofNat (n >>> s)
-  | Int.negSucc n, s => Int.negSucc (n >>> s)
-
-instance : HShiftRight Int Nat Int := ⟨.shiftRight⟩
-
-end Int