feat: force-mathlib-ci label

.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

@@ -1,246 +0,0 @@
-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: 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 }}
-      - 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
-        if: matrix.name != 'Linux Lake'
-        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
-      - name: Cache
-        if: matrix.name == 'Linux Lake'
-        uses: actions/cache@v4
-        with:
-          path: |
-            .ccache
-            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: |
-            ${{ matrix.name }}-build-v3
-          save-always: true
-      # open nix-shell once for initial setup
-      - name: Setup
-        run: |
-          ccache --zero-stats
-        if: runner.os == 'Linux'
-      - name: Set up NPROC
-        run: |
-          echo "NPROC=$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4)" >> $GITHUB_ENV
-      - name: Build
-        run: |
-          ulimit -c unlimited  # coredumps
-          [ -d build ] || mkdir build
-          cd build
-          # arguments passed to `cmake`
-          # this also enables githash embedding into stage 1 library
-          OPTIONS=(-DCHECK_OLEAN_VERSION=ON)
-          OPTIONS+=(-DLEAN_EXTRA_MAKE_OPTS=-DwarningAsError=true)
-          if [[ -n '${{ 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 }}
-        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
-        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

.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?
@@ -137,7 +135,6 @@ 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 = [
               {
                 "name": "Linux LLVM",
@@ -166,16 +163,6 @@ jobs:
                 // foreign code may be linked against more recent glibc
                 "CTEST_OPTIONS": "-E 'foreign'"
               },
-              {
-                "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",
@@ -217,18 +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",
@@ -279,41 +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

CMakeLists.txt

@@ -15,7 +15,10 @@ foreach(var ${vars})
       # must forward options that generate incompatible .olean format
       list(APPEND STAGE0_ARGS "-D${var}=${${var}}")
     endif()
-    if("${var}" MATCHES "LLVM*|PKG_CONFIG|USE_LAKE")
+    if("${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 "CMAKE_.*") AND NOT ("${var}" MATCHES "CMAKE_BUILD_TYPE") AND NOT ("${var}" MATCHES "CMAKE_HOME_DIRECTORY"))
@@ -44,11 +47,10 @@ 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}
@@ -65,8 +67,8 @@ ExternalProject_add(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} ${STAGE0_ARGS}
   BUILD_ALWAYS ON  # cmake doesn't auto-detect changes without a download method
   INSTALL_COMMAND ""  # skip install
@@ -80,7 +82,6 @@ ExternalProject_add(stage1
   BUILD_ALWAYS ON
   INSTALL_COMMAND ""
   DEPENDS stage0
-  STEP_TARGETS configure
 )
 ExternalProject_add(stage2
   SOURCE_DIR "${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",
@@ -26,12 +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",
-        "BSYMBOLIC": "OFF",
-        "LEAN_TEST_VARS": "MAIN_STACK_SIZE=16000"
+        "BSYMBOLIC": "OFF"
       },
       "generator": "Unix Makefiles",
       "binaryDir": "${sourceDir}/build/sanitize"

doc/setup.md

@@ -7,7 +7,7 @@ Platforms built & tested by our CI, available as binary releases via elan (see b
 * x86-64 Linux with glibc 2.26+
 * 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
 

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"
       }
     },

flake.nix

@@ -8,8 +8,8 @@
   # 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:
@@ -63,7 +63,6 @@
           GLIBC_DEV = pkgsDist.glibc.dev;
           GCC_LIB = pkgsDist.gcc.cc.lib;
           ZLIB = pkgsDist.zlib;
-          # for CI coredumps
           GDB = pkgsDist.gdb;
         });
     in {

script/release_notes.py

@@ -170,12 +170,7 @@ 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()

src/CMakeLists.txt

@@ -455,20 +455,20 @@ 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")
@@ -515,16 +515,7 @@ 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")
 
@@ -551,9 +542,6 @@ 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}}")
@@ -766,12 +754,7 @@ 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)
@@ -802,32 +785,10 @@ 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/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
 

src/Init/Control/Basic.lean

@@ -42,9 +42,7 @@ instance (priority := 500) instForInOfForIn' [ForIn' m ρ α d] : ForIn m ρ α
   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 +51,14 @@ 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
@@ -137,13 +121,6 @@ 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 +131,6 @@ 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 +141,6 @@ 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 +256,21 @@ 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 +286,25 @@ 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/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. -/
   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.
-  -/
   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/Data/Array/Attach.lean

@@ -15,12 +15,13 @@ set_option linter.indexVariables true -- Enforce naming conventions for index va
 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
 
@@ -31,27 +32,14 @@ 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} :
@@ -109,7 +97,7 @@ 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) :
+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
 
@@ -120,13 +108,13 @@ theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a,
   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) :
+theorem map_pmap {p : α → Prop} (g : β → γ) (f : ∀ a, p a → β) (xs H) :
     map g (pmap f xs H) = pmap (fun a h => g (f a h)) xs H := by
   cases xs
   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
+theorem pmap_map {p : β → Prop} (g : ∀ b, p b → γ) (f : α → β) (xs 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
   simp [List.pmap_map]
 
@@ -153,13 +141,13 @@ theorem attachWith_congr {xs ys : Array α} (w : xs = ys) {P : α → Prop} {H :
   cases xs
   simp [attachWith_congr (List.push_toArray _ _)]
 
-theorem pmap_eq_map_attach {p : α → Prop} {f : ∀ a, p a → β} {xs : Array α} (H) :
+theorem pmap_eq_map_attach {p : α → Prop} (f : ∀ a, p a → β) (xs H) :
     pmap f xs H = xs.attach.map fun x => f x.1 (H _ x.2) := by
   cases xs
   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) :
+theorem pmap_eq_attachWith {p q : α → Prop} (f : ∀ a, p a → q a) (xs 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
   simp [List.pmap_eq_attachWith]
@@ -172,18 +160,17 @@ theorem attach_map_val (xs : Array α) (f : α → β) :
 @[deprecated attach_map_val (since := "2025-02-17")]
 abbrev attach_map_coe := @attach_map_val
 
--- 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 attachWith_map_val {p : α → Prop} {f : α → β} {xs : Array α} (H : ∀ a ∈ xs, p a) :
+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
 
 @[deprecated attachWith_map_val (since := "2025-02-17")]
 abbrev attachWith_map_coe := @attachWith_map_val
 
-theorem attachWith_map_subtype_val {p : α → Prop} {xs : Array α} (H : ∀ a ∈ xs, p a) :
+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
 
@@ -195,7 +182,7 @@ theorem mem_attach (xs : Array α) : ∀ x, x ∈ xs.attach
     exact m
 
 @[simp]
-theorem mem_attachWith {xs : Array α} {q : α → Prop} (H) (x : {x // q x}) :
+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
   simp
@@ -251,11 +238,10 @@ theorem attachWith_ne_empty_iff {xs : Array α} {P : α → Prop} {H : ∀ a ∈
   cases xs; simp
 
 @[simp]
-theorem getElem?_pmap {p : α → Prop} {f : ∀ a, p a → β} {xs : Array α} (h : ∀ a ∈ xs, p a) (i : Nat) :
+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
 
--- 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) :
@@ -285,37 +271,37 @@ 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) :
+@[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⟩)
         (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) :
+@[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⟩)
         (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) :
+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
   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) :
+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
   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 : 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
   subst w
   rcases xs with ⟨xs⟩
   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 : 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
   subst w
   rcases xs with ⟨xs⟩
@@ -331,7 +317,7 @@ 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} :
+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,
@@ -350,7 +336,7 @@ 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} :
+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,
@@ -359,31 +345,31 @@ theorem foldr_attach {xs : Array α} {f : α → β → β} {b : β} :
   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
+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 f h⟩) := by
   cases xs
   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 {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 f h))).map
       fun ⟨x, h⟩ => ⟨f x, h⟩ := by
   cases xs
   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} :
+    (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} :
+    (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
   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} :
+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
   ext <;> simp
@@ -395,14 +381,14 @@ theorem attach_filterMap {xs : Array α} {f : α → Option β} :
     (xs.filterMap f).attach = xs.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]
+  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
       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]
+  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`.
@@ -424,14 +410,14 @@ theorem filter_attachWith {q : α → Prop} {xs : Array α} {p : {x // q x} →
   cases xs
   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) :
+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
         (fun a _ => H₁ a a.2) := by
   cases xs
   simp [List.pmap_pmap, List.pmap_map]
 
-@[simp] theorem pmap_append {p : ι → Prop} {f : ∀ a : ι, p a → α} {xs ys : Array ι}
+@[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)) ++
@@ -440,13 +426,13 @@ theorem pmap_pmap {p : α → Prop} {q : β → Prop} {g : ∀ a, p a → β} {f
   cases ys
   simp
 
-theorem pmap_append' {p : α → Prop} {f : ∀ a : α, p a → β} {xs ys : Array α}
+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 _
+  pmap_append f xs ys _
 
-@[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 +446,12 @@ 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 +469,18 @@ 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
@@ -513,19 +499,19 @@ theorem back?_attach {xs : Array α} :
   simp
 
 @[simp]
-theorem countP_attach {xs : Array α} {p : α → Bool} :
+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
   simp [Function.comp_def]
 
 @[simp]
-theorem countP_attachWith {p : α → Prop} {q : α → Bool} {xs : Array α} {H : ∀ a ∈ xs, p a} :
+theorem countP_attachWith {p : α → Prop} (xs : Array α) (H : ∀ a ∈ xs, p a) (q : α → Bool) :
     (xs.attachWith p H).countP (fun a : {x // p x} => q a) = xs.countP q := by
   cases xs
   simp
 
 @[simp]
-theorem count_attach [DecidableEq α] {xs : Array α} {a : {x // x ∈ xs}} :
+theorem count_attach [DecidableEq α] (xs : Array α) (a : {x // x ∈ xs}) :
     xs.attach.count a = xs.count ↑a := by
   rcases xs with ⟨xs⟩
   simp only [List.attach_toArray, List.attachWith_mem_toArray, List.count_toArray]
@@ -534,12 +520,12 @@ theorem count_attach [DecidableEq α] {xs : Array α} {a : {x // x ∈ xs}} :
   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}} :
+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
   simp
 
-@[simp] theorem countP_pmap {p : α → Prop} {g : ∀ a, p a → β} {f : β → Bool} {xs : Array α} (H₁) :
+@[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 [pmap_eq_map_attach, countP_map, Function.comp_def]
@@ -556,25 +542,15 @@ 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)
 
-@[simp] theorem unattach_nil {p : α → Prop} : (#[] : Array { x // p x }).unattach = #[] := by
-  simp [unattach]
-
+@[simp] theorem unattach_nil {p : α → Prop} : (#[] : Array { x // p x }).unattach = #[] := rfl
 @[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 only [unattach, Array.map_push]
@@ -745,73 +721,71 @@ and simplifies these to the function directly taking the value.
     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} :
+@[wf_preprocess] theorem Array.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} :
+@[wf_preprocess] theorem Array.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} :
+@[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} :
+@[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} :
+@[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} :
+@[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} :
+@[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} :
+@[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} :
+@[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)} :
+@[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} :
+@[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} :
+@[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} :
+@[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} :
+@[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

@@ -17,7 +17,7 @@ theorem Array.of_push_eq_push {as bs : Array α} (h : as.push a = bs.push b) : a
   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, *]
@@ -35,14 +35,9 @@ 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 +66,11 @@ 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

@@ -29,16 +29,6 @@ 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 +39,6 @@ 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 +68,6 @@ 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 +81,6 @@ 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

@@ -42,35 +42,35 @@ 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} :
+    (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
   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 xs 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} :
+    (f : β → α → m β) (init : β) (xs : Array α) :
     xs.toList.foldlM f init = xs.foldlM f init := by
   simp [foldlM, foldlM_toList.aux]
 
-@[simp] theorem foldl_toList (f : β → α → β) {init : β} {xs : Array α} :
+@[simp] theorem foldl_toList (f : β → α → β) (init : β) (xs : Array α) :
     xs.toList.foldl f init = xs.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) :
+    (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
   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 xs · i)]
 
-theorem foldrM_eq_reverse_foldlM_toList [Monad m] {f : α → β → m β} {init : β} {xs : Array α} :
+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 _)
@@ -78,31 +78,31 @@ theorem foldrM_eq_reverse_foldlM_toList [Monad m] {f : α → β → m β} {init
   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} :
+    (f : α → β → m β) (init : β) (xs : Array α) :
     xs.toList.foldrM f init = xs.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} :
+@[simp] theorem foldr_toList (f : α → β → β) (init : β) (xs : Array α) :
     xs.toList.foldr f init = xs.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 (xs : Array α) (a : α) : (xs.push a).toList = xs.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 (xs : Array α) (l : List α) : xs.toListAppend l = xs.toList ++ l := by
   simp [toListAppend, ← foldr_toList]
 
-@[simp] theorem toListImpl_eq {xs : Array α} : xs.toListImpl = xs.toList := by
+@[simp] theorem toListImpl_eq (xs : Array α) : xs.toListImpl = xs.toList := by
   simp [toListImpl, ← foldr_toList]
 
-@[simp] theorem toList_pop {xs : Array α} : xs.pop.toList = xs.toList.dropLast := rfl
+@[simp] theorem toList_pop (xs : Array α) : xs.pop.toList = xs.toList.dropLast := rfl
 
 @[deprecated toList_pop (since := "2025-02-17")]
 abbrev pop_toList := @Array.toList_pop
 
-@[simp] theorem append_eq_append {xs ys : Array α} : xs.append ys = xs ++ ys := rfl
+@[simp] theorem append_eq_append (xs ys : Array α) : xs.append ys = xs ++ ys := rfl
 
-@[simp] theorem toList_append {xs ys : Array α} :
+@[simp] theorem toList_append (xs ys : Array α) :
     (xs ++ ys).toList = xs.toList ++ ys.toList := by
   rw [← append_eq_append]; unfold Array.append
   rw [← foldl_toList]
@@ -110,24 +110,25 @@ abbrev pop_toList := @Array.toList_pop
 
 @[simp] theorem toList_empty : (#[] : Array α).toList = [] := rfl
 
-@[simp] theorem append_empty {xs : Array α} : xs ++ #[] = xs := by
+@[simp] theorem append_empty (xs : Array α) : xs ++ #[] = xs := 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 (xs : Array α) : #[] ++ xs = xs := 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 (xs ys zs : Array α) : xs ++ ys ++ zs = xs ++ (ys ++ zs) := 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
+    (xs : Array α) (l : List α) : xs.appendList l = xs ++ l := rfl
 
-@[simp] theorem toList_appendList {xs : Array α} {l : List α} :
+@[simp] theorem toList_appendList (xs : Array α) (l : List α) :
     (xs ++ l).toList = xs.toList ++ l := by
   rw [← appendList_eq_append]; unfold Array.appendList
   induction l generalizing xs <;> simp [*]
@@ -137,23 +138,25 @@ 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} :
+    (f : α → β → m β) (init : β) (xs : Array α) :
     xs.foldrM f init = xs.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} :
+    (f : β → α → m β) (init : β) (xs : Array α) :
     xs.foldlM f init = xs.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} :
+theorem foldr_eq_foldr_toList
+    (f : α → β → β) (init : β) (xs : Array α) :
     xs.foldr f init = xs.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} :
+theorem foldl_eq_foldl_toList
+    (f : β → α → β) (init : β) (xs : Array α) :
     xs.foldl f init = xs.toList.foldl f init:= by
   simp
 

src/Init/Data/Array/Count.lean

@@ -21,9 +21,9 @@ open Nat
 /-! ### countP -/
 section countP
 
-variable {p q : α → Bool}
+variable (p q : α → Bool)
 
-@[simp] theorem _root_.List.countP_toArray {l : List α} : countP p l.toArray = l.countP p := by
+@[simp] theorem _root_.List.countP_toArray (l : List α) : countP p l.toArray = l.countP p := by
   simp [countP]
   induction l with
   | nil => rfl
@@ -31,32 +31,32 @@ variable {p q : α → Bool}
     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
+@[simp] theorem countP_toList (xs : Array α) : xs.toList.countP p = countP p xs := by
   cases xs
   simp
 
 @[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
+@[simp] theorem countP_push_of_pos (xs) (pa : p a) : countP p (xs.push a) = countP p xs + 1 := by
   rcases xs with ⟨xs⟩
   simp_all
 
-@[simp] theorem countP_push_of_neg {xs : Array α} (pa : ¬p a) : countP p (xs.push a) = countP p xs := by
+@[simp] theorem countP_push_of_neg (xs) (pa : ¬p a) : countP p (xs.push a) = countP p xs := by
   rcases xs with ⟨xs⟩
   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
+theorem countP_push (a : α) (xs) : countP p (xs.push a) = countP p xs + if p a then 1 else 0 := by
   rcases xs with ⟨xs⟩
   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
+theorem size_eq_countP_add_countP (xs) : xs.size = countP p xs + countP (fun a => ¬p a) xs := by
   rcases xs with ⟨xs⟩
   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
+theorem countP_eq_size_filter (xs) : countP p xs = (filter p xs).size := by
   rcases xs with ⟨xs⟩
   simp [List.countP_eq_length_filter]
 
@@ -68,7 +68,7 @@ theorem countP_le_size : countP p xs ≤ xs.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
+@[simp] theorem countP_append (xs ys) : countP p (xs ++ ys) = countP p xs + countP p ys := by
   rcases xs with ⟨xs⟩
   rcases ys with ⟨ys⟩
   simp
@@ -88,23 +88,21 @@ theorem countP_le_size : countP p xs ≤ xs.size := by
   rcases xs with ⟨xs⟩
   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) :
+theorem boole_getElem_le_countP (p : α → Bool) (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⟩
   simp [List.boole_getElem_le_countP]
 
-theorem countP_set {xs : Array α} {i : Nat} {a : α} (h : i < xs.size) :
+theorem countP_set (p : α → Bool) (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⟩
   simp [List.countP_set, h]
 
-theorem countP_filter {xs : Array α} :
+theorem countP_filter (xs : Array α) :
     countP p (filter q xs) = countP (fun a => p a && q a) xs := by
   rcases xs with ⟨xs⟩
   simp [List.countP_filter]
@@ -117,35 +115,37 @@ theorem countP_filter {xs : Array α} :
   funext xs
   simp
 
-@[simp] theorem countP_map {p : β → Bool} {f : α → β} {xs : Array α} :
+@[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 size_filterMap_eq_countP {f : α → Option β} {xs : Array α} :
+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⟩
   simp [List.length_filterMap_eq_countP]
 
-theorem countP_filterMap {p : β → Bool} {f : α → Option β} {xs : Array α} :
+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⟩
   simp [List.countP_filterMap]
 
-@[simp] theorem countP_flatten {xss : Array (Array α)} :
+@[simp] theorem countP_flatten (xss : Array (Array α)) :
     countP p xss.flatten = (xss.map (countP p)).sum := by
   cases xss using array₂_induction
   simp [List.countP_flatten, Function.comp_def]
 
-theorem countP_flatMap {p : β → Bool} {xs : Array α} {f : α → Array β} :
+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⟩
   simp [List.countP_flatMap, Function.comp_def]
 
-@[simp] theorem countP_reverse {xs : Array α} : countP p xs.reverse = countP p xs := by
+@[simp] theorem countP_reverse (xs : Array α) : countP p xs.reverse = countP p xs := by
   rcases xs with ⟨xs⟩
   simp [List.countP_reverse]
 
+variable {p q}
+
 theorem countP_mono_left (h : ∀ x ∈ xs, p x → q x) : countP p xs ≤ countP q xs := by
   rcases xs with ⟨xs⟩
   simpa using List.countP_mono_left (by simpa using h)
@@ -162,62 +162,62 @@ 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] 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_toList {xs : Array α} {a : α} : xs.toList.count a = xs.count a := by
+@[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
+@[simp] theorem count_empty (a : α) : count a #[] = 0 := rfl
 
-theorem count_push {a b : α} {xs : Array α} :
+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
   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) (xs : Array α) : count a xs = countP (· == a) xs := rfl
 theorem count_eq_countP' {a : α} : count a = countP (· == a) := by
   funext xs
   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) (xs : Array α) : count a xs ≤ xs.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) (xs : Array α) : count a xs ≤ count a (xs.push b) := by
   simp [count_push]
 
-theorem count_singleton {a b : α} : count a #[b] = if b == a then 1 else 0 := by
+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) : ∀ xs ys, count a (xs ++ ys) = count a xs + count a ys :=
+  countP_append _
 
-@[simp] theorem count_flatten {a : α} {xss : Array (Array α)} :
+@[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 [List.count_flatten, Function.comp_def]
 
-@[simp] theorem count_reverse {a : α} {xs : Array α} : count a xs.reverse = count a xs := by
+@[simp] theorem count_reverse (a : α) (xs : Array α) : count a xs.reverse = count a xs := by
   rcases xs with ⟨xs⟩
   simp
 
-theorem boole_getElem_le_count {xs : Array α} {i : Nat} {a : α} (h : i < xs.size) :
+theorem boole_getElem_le_count (a : α) (xs : Array α) (i : Nat) (h : i < xs.size) :
     (if xs[i] == a then 1 else 0) ≤ xs.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) :
+theorem count_set (a b : α) (xs : Array α) (i : Nat) (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
   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) (xs : Array α) : count a (xs.push a) = count a xs + 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) (xs : Array α) : count a (xs.push b) = count a xs := 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
@@ -241,49 +241,40 @@ theorem count_eq_size {xs : Array α} : count a xs = xs.size ↔ ∀ b ∈ xs, a
   · 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
+theorem filter_beq (xs : Array α) (a : α) : xs.filter (· == a) = mkArray (count a xs) a := by
   rcases xs with ⟨xs⟩
   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] (xs : Array α) (a : α) : xs.filter (· = a) = mkArray (count a xs) a :=
+  filter_beq xs 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
+theorem mkArray_count_eq_of_count_eq_size {xs : Array α} (h : count a xs = xs.size) :
+    mkArray (count a xs) a = xs := by
   rcases xs with ⟨xs⟩
   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 [List.count_filter, h]
 
-theorem count_le_count_map [DecidableEq β] {xs : Array α} {f : α → β} {x : α} :
+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⟩
   simp [List.count_le_count_map, countP_map]
 
-theorem count_filterMap {α} [BEq β] {b : β} {f : α → Option β} {xs : Array α} :
+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⟩
   simp [List.count_filterMap, countP_filterMap]
 
-theorem count_flatMap {α} [BEq β] {xs : Array α} {f : α → Array β} {x : β} :
+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]

src/Init/Data/Array/DecidableEq.lean

@@ -71,7 +71,7 @@ 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

src/Init/Data/Array/Erase.lean

@@ -21,7 +21,7 @@ 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⟩
@@ -46,7 +46,6 @@ theorem exists_of_eraseP {xs : Array α} {a} (hm : a ∈ xs) (hp : p a) :
   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 :=
@@ -70,13 +69,13 @@ theorem size_eraseP {xs : Array α} : (xs.eraseP p).size = if xs.any p then xs.s
     rw [eraseP_of_forall_getElem_not]
     simp_all
 
-theorem size_eraseP_le {xs : Array α} : (xs.eraseP p).size ≤ xs.size := by
+theorem size_eraseP_le (xs : Array α) : (xs.eraseP p).size ≤ xs.size := by
   rcases xs with ⟨xs⟩
-  simpa using List.length_eraseP_le
+  simpa using List.length_eraseP_le xs
 
-theorem le_size_eraseP {xs : Array α} : xs.size - 1 ≤ (xs.eraseP p).size := by
+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
+  simpa using List.le_length_eraseP xs
 
 theorem mem_of_mem_eraseP {xs : Array α} : a ∈ xs.eraseP p → a ∈ xs := by
   rcases xs with ⟨xs⟩
@@ -90,19 +89,19 @@ theorem mem_of_mem_eraseP {xs : Array α} : a ∈ xs.eraseP p → a ∈ xs := by
   rcases xs with ⟨xs⟩
   simp
 
-theorem eraseP_map {f : β → α} {xs : Array β} : (xs.map f).eraseP p = (xs.eraseP (p ∘ f)).map f := by
+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
+  simpa using List.eraseP_map f xs
 
-theorem eraseP_filterMap {f : α → Option β} {xs : Array α} :
+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
+  simpa using List.eraseP_filterMap f xs
 
-theorem eraseP_filter {f : α → Bool} {xs : Array α} :
+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
+  simpa using List.eraseP_filter f xs
 
 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
@@ -123,30 +122,21 @@ theorem eraseP_append {xs : Array α} {ys : Array α} :
   simp only [List.append_toArray, List.eraseP_toArray, List.eraseP_append, 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) ∨
@@ -176,12 +166,10 @@ theorem erase_of_not_mem [LawfulBEq α] {a : α} {xs : Array α} (h : a ∉ xs)
   rcases xs with ⟨xs⟩
   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⟩
   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⟩
   simp [List.erase_eq_eraseP]
@@ -205,19 +193,19 @@ theorem exists_erase_eq [LawfulBEq α] {a : α} {xs : Array α} (h : a ∈ xs) :
     (xs.erase a).size = xs.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} :
+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
   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
+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
+  simpa using List.length_erase_le a xs
 
-theorem le_size_erase [LawfulBEq α] {a : α} {xs : Array α} : xs.size - 1 ≤ (xs.erase a).size := by
+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
+  simpa using List.le_length_erase a xs
 
 theorem mem_of_mem_erase {a b : α} {xs : Array α} (h : a ∈ xs.erase b) : a ∈ xs := by
   rcases xs with ⟨xs⟩
@@ -231,10 +219,10 @@ theorem mem_of_mem_erase {a b : α} {xs : Array α} (h : a ∈ xs.erase b) : a
   rw [erase_eq_eraseP', eraseP_eq_self_iff]
   simp [forall_mem_ne']
 
-theorem erase_filter [LawfulBEq α] {f : α → Bool} {xs : Array α} :
+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
+  simpa using List.erase_filter f xs
 
 theorem erase_append_left [LawfulBEq α] {xs : Array α} (ys) (h : a ∈ xs) :
     (xs ++ ys).erase a = xs.erase a ++ ys := by
@@ -255,21 +243,16 @@ theorem erase_append [LawfulBEq α] {a : α} {xs ys : Array α} :
   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
-
--- 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} :
+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
+  simpa using List.erase_comm a b xs
 
 theorem erase_eq_iff [LawfulBEq α] {a : α} {xs : Array α} :
     xs.erase a = ys ↔
@@ -285,22 +268,16 @@ theorem erase_eq_iff [LawfulBEq α] {a : α} {xs : Array α} :
     · left; simp_all
     · right; refine ⟨a, as, h, rfl, bs, 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 -/
@@ -309,8 +286,7 @@ theorem eraseIdx_eq_eraseIdxIfInBounds {xs : Array α} {i : Nat} (h : i < xs.siz
     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
+theorem eraseIdx_eq_take_drop_succ (xs : Array α) (i : Nat) (h) : xs.eraseIdx i = xs.take i ++ xs.drop (i + 1) := by
   rcases xs with ⟨xs⟩
   simp only [List.size_toArray] at h
   simp only [List.eraseIdx_toArray, List.eraseIdx_eq_take_drop_succ, take_eq_extract,
@@ -319,24 +295,24 @@ theorem eraseIdx_eq_take_drop_succ {xs : Array α} {i : Nat} (h) :
   rw [List.take_of_length_le]
   simp
 
-theorem getElem?_eraseIdx {xs : Array α} {i : Nat} (h : i < xs.size) {j : Nat} :
+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⟩
   simp [List.getElem?_eraseIdx]
 
-theorem getElem?_eraseIdx_of_lt {xs : Array α} {i : Nat} (h : i < xs.size) {j : Nat} (h' : j < i) :
+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
   rw [getElem?_eraseIdx]
   simp [h']
 
-theorem getElem?_eraseIdx_of_ge {xs : Array α} {i : Nat} (h : i < xs.size) {j : Nat} (h' : i ≤ j) :
+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
   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) :
+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]
       else
@@ -377,15 +353,12 @@ theorem eraseIdx_append_of_length_le {xs : Array α} {k : Nat} (hk : xs.size ≤
   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⟩
   simp [List.mem_eraseIdx_iff_getElem, *]
@@ -394,18 +367,18 @@ theorem mem_eraseIdx_iff_getElem? {x : α} {xs : Array α} {k} {h} : x ∈ xs.er
   rcases xs with ⟨xs⟩
   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) :
+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⟩
   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) :
+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⟩
   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) :
+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⟩
   simp [List.getElem_eraseIdx_of_ge, *]

src/Init/Data/Array/Extract.lean

@@ -249,15 +249,12 @@ theorem extract_append_left {as bs : Array α} :
   · 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
+@[simp] theorem extract_mkArray {a : α} {n i j : Nat} :
+    (mkArray n a).extract i j = mkArray (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
+  · simp only [size_extract, size_mkArray] at h₁ h₂
+    simp only [getElem_extract, getElem_mkArray]
 
 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
@@ -322,32 +319,32 @@ theorem reverse_extract {as : Array α} {i j : Nat} :
 
 /-! ### takeWhile -/
 
-theorem takeWhile_map {f : α → β} {p : β → Bool} {as : Array α} :
+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} :
+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} :
+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} :
+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} :
+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} :
+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]
@@ -390,36 +387,24 @@ theorem popWhile_append {xs ys : Array α} :
   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] theorem takeWhile_mkArray_eq_filter (p : α → Bool) :
+    (mkArray n a).takeWhile p = (mkArray 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_mkArray (p : α → Bool) :
+    (mkArray n a).takeWhile p = if p a then mkArray n a else #[] := by
+  simp [takeWhile_mkArray_eq_filter, filter_mkArray]
 
-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] theorem popWhile_mkArray_eq_filter_not (p : α → Bool) :
+    (mkArray n a).popWhile p = (mkArray 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,
+theorem popWhile_mkArray (p : α → Bool) :
+    (mkArray n a).popWhile p = if p a then #[] else mkArray n a := by
+  simp only [popWhile_mkArray_eq_filter_not, size_mkArray, filter_mkArray, 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⟩

src/Init/Data/Array/FinRange.lean

@@ -12,32 +12,26 @@ set_option linter.indexVariables true -- Enforce naming conventions for index va
 
 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] 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] theorem getElem_finRange (i : Nat) (h : i < (Array.finRange n).size) :
+    (Array.finRange n)[i] = Fin.cast (size_finRange n) ⟨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
+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} :
+theorem finRange_succ_last (n) :
     Array.finRange (n+1) = (Array.finRange n).map Fin.castSucc ++ #[Fin.last n] := by
   ext
   · simp
@@ -47,7 +41,7 @@ theorem finRange_succ_last {n} :
     · simp_all
       omega
 
-theorem finRange_reverse {n} : (Array.finRange n).reverse = (Array.finRange n).map Fin.rev := by
+theorem finRange_reverse (n) : (Array.finRange n).reverse = (Array.finRange n).map Fin.rev := by
   ext i h
   · simp
   · simp

src/Init/Data/Array/Find.lean

@@ -21,10 +21,10 @@ open Nat
 
 /-! ### findSome? -/
 
-@[simp] theorem findSomeRev?_push_of_isSome {xs : Array α} (h : (f a).isSome) : (xs.push a).findSomeRev? f = f a := by
+@[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_isNone {xs : Array α} (h : (f a).isNone) : (xs.push a).findSomeRev? f = xs.findSomeRev? f := by
+@[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
 
 theorem exists_of_findSome?_eq_some {f : α → Option β} {xs : Array α} (w : xs.findSome? f = some b) :
@@ -48,31 +48,31 @@ theorem findSome?_eq_some_iff {f : α → Option β} {xs : Array α} {b : β} :
   · rintro ⟨xs, a, ys, h₀, h₁, h₂⟩
     exact ⟨xs.toList, a, ys.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
+@[simp] theorem findSome?_guard (xs : Array α) : findSome? (Option.guard fun x => p x) xs = find? p xs := by
   cases xs; 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 (xs : Array α) : find? p xs = findSome? (Option.guard fun x => p x) xs :=
+  (findSome?_guard xs).symm
 
-@[simp] theorem getElem?_zero_filterMap {f : α → Option β} {xs : Array α} : (xs.filterMap f)[0]? = xs.findSome? f := by
+@[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} {xs : Array α} (h) :
+@[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 back?_filterMap {f : α → Option β} {xs : Array α} : (xs.filterMap f).back? = xs.findSomeRev? f := by
+@[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 [Inhabited β] {f : α → Option β} {xs : Array α} :
+@[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 map_findSome? {f : α → Option β} {g : β → γ} {xs : Array α} :
+@[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
 
-theorem findSome?_map {f : β → γ} {xs : Array β} : findSome? p (xs.map f) = xs.findSome? (p ∘ f) := by
+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?_append {xs ys : Array α} : (xs ++ ys).findSome? f = (xs.findSome? f).or (ys.findSome? f) := by
@@ -99,45 +99,33 @@ theorem getElem_zero_flatten {xss : Array (Array α)} (h) :
   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 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) :
+@[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?_cons_of_neg {xs : Array α} (h : ¬p a) :
+@[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]
 
@@ -183,28 +171,28 @@ 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} :
+@[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} {xs : Array α} (h) :
+@[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 [List.getElem_zero_eq_head]
 
-@[simp] theorem back?_filter {p : α → Bool} {xs : Array α} : (xs.filter p).back? = xs.findRev? p := by
+@[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 [Inhabited α] {p : α → Bool} {xs : Array α} :
+@[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 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
 
@@ -214,7 +202,7 @@ theorem get_find?_mem {xs : Array α} (h) : (xs.find? p).get h ∈ xs := by
   cases ys
   simp
 
-@[simp] theorem find?_flatten {xss : Array (Array α)} {p : α → Bool} :
+@[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 [List.findSome?_map, Function.comp_def]
@@ -254,7 +242,7 @@ 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 +254,42 @@ 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
@@ -359,7 +329,7 @@ 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 +343,7 @@ 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)
 
@@ -404,7 +374,7 @@ 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} :
+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⟩
@@ -438,7 +408,7 @@ theorem false_of_mem_extract_findIdx {xs : Array α} {p : α → Bool} (h : x
 
 /-! ### 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} :
@@ -492,8 +462,7 @@ 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
+@[simp] theorem findIdx?_map (f : β → α) (xs : Array β) : findIdx? p (xs.map f) = xs.findIdx? (p ∘ f) := by
   rcases xs with ⟨xs⟩
   simp [List.findIdx?_map]
 
@@ -512,15 +481,12 @@ theorem findIdx?_flatten {xss : Array (Array α)} {p : α → Bool} :
   cases xss 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⟩
@@ -560,7 +526,7 @@ theorem findIdx?_eq_some_le_of_findIdx?_eq_some {xs : Array α} {p q : α → Bo
 
 /-! ### findFinIdx? -/
 
-@[simp] theorem findFinIdx?_empty {p : α → Bool} : findFinIdx? p #[] = none := by simp
+@[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} {xs ys : Array α} (w : xs = ys) :
@@ -629,7 +595,7 @@ 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
@@ -646,7 +612,7 @@ 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?_empty [BEq α] : (#[] : Array α).finIdxOf? a = none := rfl
 
 @[simp] theorem finIdxOf?_eq_none_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
     xs.finIdxOf? a = none ↔ a ∉ xs := by

src/Init/Data/Array/GetLit.lean

@@ -23,7 +23,7 @@ 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)
+  Array.ext xs ys (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
   | 0,     _,  acc => acc

src/Init/Data/Array/InsertIdx.lean

@@ -30,13 +30,13 @@ section InsertIdx
 
 variable {a : α}
 
-@[simp] theorem toList_insertIdx {xs : Array α} {i : Nat} {x : α} (h : i ≤ xs.size) :
+@[simp] theorem toList_insertIdx (xs : Array α) (i x) (h) :
     (xs.insertIdx i x h).toList = xs.toList.insertIdx i x := by
   rcases xs with ⟨xs⟩
   simp
 
 @[simp]
-theorem insertIdx_zero {xs : Array α} {x : α} : xs.insertIdx 0 x = #[x] ++ xs := by
+theorem insertIdx_zero (xs : Array α) (x : α) : xs.insertIdx 0 x = #[x] ++ xs := by
   rcases xs with ⟨xs⟩
   simp
 
@@ -44,7 +44,7 @@ theorem insertIdx_zero {xs : Array α} {x : α} : xs.insertIdx 0 x = #[x] ++ xs
   rcases xs with ⟨xs⟩
   simp [List.length_insertIdx, h]
 
-theorem eraseIdx_insertIdx {i : Nat} {xs : Array α} (h : i ≤ xs.size) :
+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⟩
   simp_all
@@ -54,27 +54,27 @@ 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) :
+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)
+  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⟩
   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
+theorem insertIdx_size_self (xs : Array α) (x : α) : xs.insertIdx xs.size x = xs.push x := by
   rcases xs with ⟨xs⟩
   simp
 

src/Init/Data/Array/InsertionSort.lean

@@ -9,12 +9,6 @@ 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
 where

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

@@ -14,12 +14,11 @@ set_option linter.indexVariables true -- Enforce naming conventions for index va
 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

@@ -14,18 +14,18 @@ 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] (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
 
-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} (xs : Array α) : xs.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
@@ -45,7 +45,7 @@ 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]
@@ -55,7 +55,7 @@ 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} :
+@[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
 
@@ -68,7 +68,7 @@ instance ltIrrefl [LT α] [Std.Irrefl (· < · : α → α → Prop)] : Std.Irre
 @[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 le_empty [LT α] {xs : Array α} : xs ≤ #[] ↔ xs = #[] := by
+@[simp] theorem le_empty [LT α] (xs : Array α) : xs ≤ #[] ↔ xs = #[] := by
   cases xs
   simp
 

src/Init/Data/Array/MapIdx.lean

@@ -42,66 +42,66 @@ 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) :
+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 :=
   (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} :
+@[simp] theorem size_mapFinIdx (xs : Array α) (f : (i : Nat) → α → (h : i < xs.size) → β) :
     (xs.mapFinIdx f).size = xs.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 (xs : Array α) (k : Nat) : (xs.zipIdx k).size = xs.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}
+@[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 _
+  (mapFinIdx_spec _ _ (fun i b h => b = f i xs[i] h) fun _ _ => rfl).2 i _
 
-@[simp] theorem getElem?_mapFinIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {i : Nat} :
+@[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 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} :
+@[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
   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}
+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_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) :
+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
+  (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) (xs : Array α) : (xs.mapIdx f).size = xs.size :=
   (mapIdx_spec (p := fun _ _ _ => True) (hs := fun _ _ => trivial)).1
 
-@[simp] theorem getElem_mapIdx {f : Nat → α → β} {xs : Array α} {i : Nat}
+@[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)
+  (mapIdx_spec _ _ (fun i b h => b = f i xs[i]) fun _ _ => rfl).2 i (by simp_all)
 
-@[simp] theorem getElem?_mapIdx {f : Nat → α → β} {xs : Array α} {i : Nat} :
+@[simp] theorem getElem?_mapIdx (f : Nat → α → β) (xs : Array α) (i : Nat) :
     (xs.mapIdx f)[i]? =
       xs[i]?.map (f i) := by
   simp [getElem?_def, size_mapIdx, getElem_mapIdx]
 
-@[simp] theorem toList_mapIdx {f : Nat → α → β} {xs : Array α} :
+@[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
   apply List.ext_getElem <;> simp
 
@@ -109,11 +109,11 @@ 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
 
@@ -123,7 +123,7 @@ namespace Array
 
 /-! ### zipIdx -/
 
-@[simp] theorem getElem_zipIdx {xs : Array α} {k : Nat} {i : Nat} (h : i < (xs.zipIdx k).size) :
+@[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 [zipIdx]
 
@@ -137,7 +137,7 @@ 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} :
+@[simp] theorem toList_zipIdx (xs : Array α) (k : Nat) :
     (xs.zipIdx k).toList = xs.toList.zipIdx k := by
   rcases xs with ⟨xs⟩
   simp
@@ -292,15 +292,12 @@ theorem mapFinIdx_eq_mapFinIdx_iff {xs : Array α} {f g : (i : Nat) → α → (
     (xs.mapFinIdx f).mapFinIdx g = xs.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
+theorem mapFinIdx_eq_mkArray_iff {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {b : β} :
+    xs.mapFinIdx f = mkArray xs.size b ↔ ∀ (i : Nat) (h : i < xs.size), f i xs[i] h = b := by
   rcases xs 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⟩
@@ -434,15 +431,12 @@ theorem mapIdx_eq_mapIdx_iff {xs : Array α} :
     (xs.mapIdx f).mapIdx g = xs.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
+theorem mapIdx_eq_mkArray_iff {xs : Array α} {f : Nat → α → β} {b : β} :
+    mapIdx f xs = mkArray xs.size b ↔ ∀ (i : Nat) (h : i < xs.size), f i xs[i] = b := by
   rcases xs with ⟨xs⟩
   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⟩
@@ -452,8 +446,8 @@ 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 +458,17 @@ 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
@@ -490,14 +484,14 @@ end List
 
 namespace Array
 
-theorem toList_mapFinIdxM [Monad m] [LawfulMonad m] {xs : Array α}
-    {f : (i : Nat) → α → (h : i < xs.size) → m β} :
+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
   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} :
+theorem toList_mapIdxM [Monad m] [LawfulMonad m] (xs : Array α)
+    (f : Nat → α → m β) :
     toList <$> xs.mapIdxM f = xs.toList.mapIdxM f := by
   rw [List.mapIdxM_toArray]
   simp only [Functor.map_map, id_map']

src/Init/Data/Array/Monadic.lean

@@ -23,20 +23,16 @@ 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
+@[simp] theorem mapM_id {xs : Array α} {f : α → Id β} : xs.mapM f = 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} :
+@[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_eq_foldlM_push [Monad m] [LawfulMonad m] {f : α → m β} {xs : Array α} :
+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']
@@ -53,21 +49,21 @@ theorem mapM_eq_foldlM_push [Monad m] [LawfulMonad m] {f : α → m β} {xs : Ar
 
 /-! ### 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} :
+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
   subst w
   cases xs
   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} :
+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
   subst w
   cases xs
   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} :
+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
   subst w
@@ -75,8 +71,8 @@ theorem foldlM_filterMap [Monad m] [LawfulMonad m] {f : α → Option β} {g :
   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} :
+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
   subst w
@@ -84,16 +80,16 @@ theorem foldrM_filterMap [Monad m] [LawfulMonad m] {f : α → Option β} {g :
   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} :
+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
   subst w
   cases xs
   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} :
+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
   subst w
@@ -101,7 +97,7 @@ theorem foldrM_filter [Monad m] [LawfulMonad m] {p : α → Bool} {g : α → β
   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 : 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
   subst w
@@ -109,8 +105,7 @@ theorem foldrM_filter [Monad m] [LawfulMonad m] {p : α → Bool} {g : α → β
   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 : 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
   subst w
@@ -125,13 +120,13 @@ 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} :
+@[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
 
-@[simp] theorem forM_map [Monad m] [LawfulMonad m] {xs : Array α} {g : α → β} {f : β → m PUnit} :
+@[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
@@ -153,7 +148,7 @@ 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) :
+    (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
         | .yield b => f a m b
@@ -164,29 +159,29 @@ theorem forIn'_eq_foldlM [Monad m] [LawfulMonad m]
 
 /-- 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) :
+    (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⟩
   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) :
+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⟩
   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) :
+    (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⟩
   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
+    (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 g h) y := by
   rcases xs with ⟨xs⟩
   simp
 
@@ -195,7 +190,7 @@ 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) :
+    (f : α → β → m (ForInStep β)) (init : β) (xs : Array α) :
     forIn xs init f = ForInStep.value <$>
       xs.foldlM (fun b a => match b with
         | .yield b => f a b
@@ -206,63 +201,37 @@ theorem forIn_eq_foldlM [Monad m] [LawfulMonad m]
 
 /-- 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) :
+    (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⟩
   simp [List.foldlM_map]
 
-@[simp] theorem forIn_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
-    {xs : Array α} (f : α → β → β) (init : β) :
+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⟩
   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) :
+    (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⟩
   simp [List.foldl_map]
 
 @[simp] theorem forIn_map [Monad m] [LawfulMonad m]
-    {xs : Array α} {g : α → β} {f : β → γ → m (ForInStep γ)} :
+    (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
-  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 +246,24 @@ 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 +276,12 @@ 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
@@ -353,22 +322,22 @@ namespace Array
   subst w
   simp [flatMapM, h]
 
-theorem toList_filterM [Monad m] [LawfulMonad m] {xs : Array α} {p : α → m Bool} :
+theorem toList_filterM [Monad m] [LawfulMonad m] (xs : Array α) (p : α → m Bool) :
     toList <$> xs.filterM p = xs.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} :
+theorem toList_filterRevM [Monad m] [LawfulMonad m] (xs : Array α) (p : α → m Bool) :
     toList <$> xs.filterRevM p = xs.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)} :
+theorem toList_filterMapM [Monad m] [LawfulMonad m] (xs : Array α) (f : α → m (Option β)) :
     toList <$> xs.filterMapM f = xs.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)} :
+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
   rw [List.flatMapM_toArray]
   simp only [Functor.map_map, id_map']
@@ -388,12 +357,12 @@ and simplifies these to the function directly taking the value.
   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
+@[wf_preprocess] theorem foldlM_wfParam [Monad m] (xs : Array α) (f : β → α → m β) :
+    (wfParam xs).foldlM f = xs.attach.unattach.foldlM f := 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⟩ =>
+@[wf_preprocess] theorem foldlM_unattach [Monad m] (P : α → Prop) (xs : Array (Subtype P)) (f : β → α → m β) :
+    xs.unattach.foldlM f = xs.foldlM fun b ⟨x, h⟩ =>
       binderNameHint b f <| binderNameHint x (f b) <| binderNameHint h () <|
       f b (wfParam x) := by
   simp [wfParam]
@@ -412,12 +381,12 @@ and simplifies these to the function directly taking the value.
   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
+@[wf_preprocess] theorem foldrM_wfParam [Monad m] [LawfulMonad m] (xs : Array α) (f : α → β → m β) :
+    (wfParam xs).foldrM f = xs.attach.unattach.foldrM f := 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 =>
+@[wf_preprocess] theorem foldrM_unattach [Monad m] [LawfulMonad m] (P : α → Prop) (xs : Array (Subtype P)) (f : α → β → m β) :
+    xs.unattach.foldrM f = xs.foldrM fun ⟨x, h⟩ b =>
       binderNameHint x f <| binderNameHint h () <| binderNameHint b (f x) <|
       f (wfParam x) b := by
   simp [wfParam]
@@ -433,11 +402,11 @@ and simplifies these to the function directly taking the value.
   simp
   rw [List.mapM_subtype hf]
 
-@[wf_preprocess] theorem mapM_wfParam [Monad m] [LawfulMonad m] {xs : Array α} {f : α → m β} :
+@[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} :
+@[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]
@@ -452,12 +421,12 @@ and simplifies these to the function directly taking the value.
 
 
 @[wf_preprocess] theorem filterMapM_wfParam [Monad m] [LawfulMonad m]
-    {xs : Array α} {f : α → m (Option β)} :
+    (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)} :
+    (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]
@@ -471,12 +440,12 @@ and simplifies these to the function directly taking the value.
   simp [hf]
 
 @[wf_preprocess] theorem flatMapM_wfParam [Monad m] [LawfulMonad m]
-    {xs : Array α} {f : α → m (Array β)} :
+    (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)} :
+    (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]

src/Init/Data/Array/OfFn.lean

@@ -16,10 +16,9 @@ set_option linter.indexVariables true -- Enforce naming conventions for index va
 
 namespace Array
 
-@[simp] theorem ofFn_zero {f : Fin 0 → α} : ofFn f = #[] := by
-  simp [ofFn, ofFn.go]
+@[simp] theorem ofFn_zero (f : Fin 0 → α) : ofFn f = #[] := rfl
 
-theorem ofFn_succ {f : Fin (n+1) → α} :
+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
@@ -30,10 +29,10 @@ theorem ofFn_succ {f : Fin (n+1) → α} :
       simp at h₁ h₂
       omega
 
-@[simp] theorem _root_.List.toArray_ofFn {f : Fin n → α} : (List.ofFn f).toArray = Array.ofFn f := by
+@[simp] theorem _rooy_.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
+@[simp] theorem toList_ofFn (f : Fin n → α) : (Array.ofFn f).toList = List.ofFn f := by
   apply List.ext_getElem <;> simp
 
 @[simp]
@@ -42,7 +41,7 @@ theorem ofFn_eq_empty_iff {f : Fin n → α} : ofFn f = #[] ↔ n = 0 := by
   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/QSort.lean

@@ -30,16 +30,6 @@ 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 +50,7 @@ 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

@@ -26,21 +26,20 @@ 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']
 
-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 +56,13 @@ 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 +73,13 @@ 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 +87,7 @@ 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 n : Nat} (h : a ≤ s) :
+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]
@@ -121,10 +120,10 @@ 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
@@ -133,7 +132,7 @@ theorem range_succ_eq_map {n : Nat} : range (n + 1) = #[0] ++ map succ (range n)
       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
@@ -142,7 +141,7 @@ theorem range'_eq_map_range {s n : Nat} : range' s n = map (s + ·) (range n) :=
 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 +149,11 @@ 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 (n m : Nat) : range (n + m) = range n ++ (range m).map (n + ·) := 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 n m).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 +162,9 @@ 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 (i n : Nat) : take (range n) i = range (min i n) := by
   ext <;> simp
 
 @[simp] theorem find?_range_eq_some {n : Nat} {i : Nat} {p : Nat → Bool} :
@@ -188,50 +187,48 @@ theorem zipIdx_eq_empty_iff {xs : Array α} {i : Nat} : xs.zipIdx i = #[] ↔ xs
   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 (xs : Array α) (i j) : (zipIdx xs i)[j]? = xs[j]?.map fun a => (a, i + j) := by
   simp [getElem?_def]
 
-theorem map_snd_add_zipIdx_eq_zipIdx {xs : Array α} {n k : Nat} :
+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) :=
   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
   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
   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' (xs : Array α) {i : Nat} : xs.zipIdx i = xs.zip (range' i xs.size) := by
   simp [zip_of_prod (zipIdx_map_fst _ _) (zipIdx_map_snd _ _)]
 
 @[simp]
-theorem unzip_zipIdx_eq_prod {xs : Array α} {i : Nat} :
+theorem unzip_zipIdx_eq_prod (xs : Array α) {i : Nat} :
     (xs.zipIdx i).unzip = (xs, range' i xs.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} :
+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
   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} :
+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
   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} :
@@ -250,13 +247,13 @@ theorem snd_lt_add_of_mem_zipIdx {x : α × Nat} {k : Nat} {xs : Array α} (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
   simpa [Nat.add_comm] using snd_lt_add_of_mem_zipIdx h
 
-theorem map_zipIdx {f : α → β} {xs : Array α} {k : Nat} :
+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
   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
+  zipIdx_map_fst k xs ▸ 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
@@ -273,12 +270,12 @@ 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} :
+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
   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

src/Init/Data/Array/Set.lean

@@ -11,16 +11,11 @@ set_option linter.indexVariables true -- Enforce naming conventions for index va
 
 
 /--
-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) :
@@ -28,15 +23,10 @@ def Array.set (xs : Array α) (i : @& Nat) (v : α) (h : i < xs.size := by get_e
   toList := xs.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)

src/Init/Data/Array/Subarray.lean

@@ -7,44 +7,18 @@ 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 +28,6 @@ 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 +40,12 @@ 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 +54,6 @@ 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 +68,6 @@ 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 +80,6 @@ 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 +88,46 @@ 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 +142,10 @@ 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 +155,6 @@ 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 +177,6 @@ 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 +186,8 @@ 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 +197,6 @@ 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

@@ -20,8 +20,7 @@ set_option linter.indexVariables true -- Enforce naming conventions for index va
 
 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

@@ -26,7 +26,7 @@ end List
 
 namespace Array
 
-theorem exists_of_uset {xs : Array α} {i d} (h) :
+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
   simpa only [ugetElem_eq_getElem, ← getElem_toList, uset, toList_set] using

src/Init/Data/Array/Zip.lean

@@ -22,19 +22,19 @@ open Nat
 
 /-! ### zipWith -/
 
-theorem zipWith_comm {f : α → β → γ} {as : Array α} {bs : Array β} :
+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
+  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} :
+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
   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
+theorem zipWith_self (f : α → α → δ) (xs : Array α) : zipWith f xs xs = xs.map fun a => f a a := by
   cases xs
   simp
 
@@ -74,31 +74,31 @@ 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} :
+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
   simp [List.zipWith_map]
 
-theorem zipWith_map_left {as : Array α} {bs : Array β} {f : α → α'} {g : α' → β → γ} :
+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
   simp [List.zipWith_map_left]
 
-theorem zipWith_map_right {as : Array α} {bs : Array β} {f : β → β'} {g : α → β' → γ} :
+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
   simp [List.zipWith_map_right]
 
-theorem zipWith_foldr_eq_zip_foldr {f : α → β → γ} {i : δ} :
+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
   simp [List.zipWith_foldr_eq_zip_foldr]
 
-theorem zipWith_foldl_eq_zip_foldl {f : α → β → γ} {i : δ} :
+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
@@ -108,7 +108,7 @@ theorem zipWith_foldl_eq_zip_foldl {f : α → β → γ} {i : δ} :
 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 map_zipWith {δ : Type _} {f : α → β} {g : γ → δ → α} {cs : Array γ} {ds : Array δ} :
+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
@@ -124,7 +124,7 @@ theorem extract_zipWith : (zipWith f as bs).extract i j = zipWith f (as.extract
   cases bs
   simp [List.drop_zipWith, List.take_zipWith]
 
-theorem zipWith_append {f : α → β → γ} {as as' : Array α} {bs bs' : Array β}
+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
@@ -149,20 +149,17 @@ theorem zipWith_eq_append_iff {f : α → β → γ} {as : Array α} {bs : Array
   · rintro ⟨⟨ws⟩, ⟨xs⟩, ⟨ys⟩, ⟨zs⟩, h, rfl, rfl, h₁, h₂⟩
     exact ⟨ws, xs, ys, zs, 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} :
+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
   simp [List.map_uncurry_zip_eq_zipWith]
 
-theorem map_zip_eq_zipWith {f : α × β → γ} {as : Array α} {bs : Array β} :
+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
@@ -203,21 +200,21 @@ theorem getElem_zip {as : Array α} {bs : Array β} {i : Nat} {h : i < (zip as b
       (as[i]'(lt_size_left_of_zip h), bs[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
+theorem zip_eq_zipWith (as : Array α) (bs : Array β) : zip as bs = zipWith Prod.mk as bs := by
   cases as
   cases bs
   simp [List.zip_eq_zipWith]
 
-theorem zip_map {f : α → γ} {g : β → δ} {as : Array α} {bs : Array β} :
+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
   simp [List.zip_map]
 
-theorem zip_map_left {f : α → γ} {as : Array α} {bs : Array β} :
+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_right {f : β → γ} {as : Array α} {bs : Array β} :
+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_append {as bs : Array α} {cs ds : Array β} (_h : as.size = cs.size) :
@@ -228,7 +225,7 @@ theorem zip_append {as bs : Array α} {cs ds : Array β} (_h : as.size = cs.size
   cases ds
   simp_all [List.zip_append]
 
-theorem zip_map' {f : α → β} {g : α → γ} {xs : Array α} :
+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
   simp [List.zip_map']
@@ -238,25 +235,25 @@ theorem of_mem_zip {a b} {as : Array α} {bs : Array β} : (a, b) ∈ zip as bs
   cases bs
   simpa using List.of_mem_zip
 
-theorem map_fst_zip {as : Array α} {bs : Array β} (h : as.size ≤ bs.size) :
+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
   simp_all [List.map_fst_zip]
 
-theorem map_snd_zip {as : Array α} {bs : Array β} (h : bs.size ≤ as.size) :
+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
   simp_all [List.map_snd_zip]
 
-theorem map_prod_left_eq_zip {xs : Array α} {f : α → β} :
+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
   rw [← zip_map']
   congr
   simp
 
-theorem map_prod_right_eq_zip {xs : Array α} {f : α → β} :
+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
   rw [← zip_map']
   congr
@@ -273,14 +270,11 @@ theorem zip_eq_append_iff {as : Array α} {bs : Array β} :
       ∃ as₁ as₂ bs₁ bs₂, as₁.size = bs₁.size ∧ as = as₁ ++ as₂ ∧ bs = bs₁ ++ bs₂ ∧ xs = zip as₁ bs₁ ∧ ys = zip as₂ bs₂ := 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} :
+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
@@ -298,37 +292,34 @@ 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} :
+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
   simp [List.zipWithAll_map]
 
-theorem zipWithAll_map_left {as : Array α} {bs : Array β} {f : α → α'} {g : Option α' → Option β → γ} :
+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
   simp [List.zipWithAll_map_left]
 
-theorem zipWithAll_map_right {as : Array α} {bs : Array β} {f : β → β'} {g : Option α → Option β' → γ} :
+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
   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} :
+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
   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
+    zipWithAll f (mkArray n a) (mkArray n b) = mkArray n (f a b) := by
   simp [← List.toArray_replicate]
 
-@[deprecated zipWithAll_replicate (since := "2025-03-18")]
-abbrev zipWithAll_mkArray := @zipWithAll_replicate
-
 /-! ### unzip -/
 
 @[simp] theorem unzip_fst : (unzip l).fst = l.map Prod.fst := by
@@ -337,11 +328,10 @@ 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
+theorem unzip_eq_map (xs : Array (α × β)) : unzip xs = (xs.map Prod.fst, xs.map Prod.snd) := by
   cases xs
   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
   simp only [List.unzip_toArray, Prod.map_fst, Prod.map_snd, List.zip_toArray, List.zip_unzip]
@@ -370,9 +360,6 @@ theorem zip_of_prod {as : Array α} {bs : Array β} {xs : Array (α × β)} (hl
     (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]
 
-@[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/BitVec/Basic.lean

@@ -18,7 +18,7 @@ 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
@@ -96,10 +96,16 @@ This will be renamed `getMsb` after the existing deprecated alias is removed.
 @[inline] def getLsbD (x : BitVec w) (i : Nat) : Bool :=
   x.toNat.testBit i
 
+@[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)
 
+@[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
 
@@ -196,7 +202,7 @@ section arithmetic
 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⟩
@@ -210,7 +216,7 @@ protected def abs (x : BitVec n) : BitVec n := if x.msb then .neg x else x
 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⟩
@@ -225,7 +231,7 @@ instance : Div (BitVec n) := ⟨.udiv⟩
 /--
 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)
@@ -233,10 +239,10 @@ instance : Mod (BitVec n) := ⟨.umod⟩
 
 /--
 Unsigned division for bit vectors using the
-[SMT-LIB convention](http://smtlib.cs.uiowa.edu/theories-FixedSizeBitVectors.shtml)
+[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
 
@@ -259,11 +265,11 @@ def sdiv (x y : BitVec n) : BitVec n :=
   | true,  true  => udiv (.neg x) (.neg y)
 
 /--
-Signed division for bit vectors using SMT-LIB rules for division by zero.
+Signed division for bit vectors using SMTLIB rules for division by zero.
 
 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
@@ -275,7 +281,7 @@ 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
@@ -287,7 +293,7 @@ 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
@@ -321,14 +327,14 @@ section relations
 /--
 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 bit vectors.
 
-SMT-LIB name: `bvule`.
+SMT-Lib name: `bvule`.
 -/
 protected def ule (x y : BitVec n) : Bool := x.toNat ≤ y.toNat
 
@@ -339,14 +345,14 @@ Signed less-than for bit vectors.
 BitVec.slt 6#4 7 = true
 BitVec.slt 7#4 8 = false
 ```
-SMT-LIB name: `bvslt`.
+SMT-Lib name: `bvslt`.
 -/
 protected def slt (x y : BitVec n) : Bool := x.toInt < y.toInt
 
 /--
 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
 
@@ -378,7 +384,7 @@ def extractLsb' (start len : Nat) (x : BitVec n) : BitVec len := .ofNat _ (x.toN
 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`.
 
-SMT-LIB name: `extract`.
+SMT-Lib name: `extract`.
 -/
 def extractLsb (hi lo : Nat) (x : BitVec n) : BitVec (hi - lo + 1) := extractLsb' lo _ x
 
@@ -409,7 +415,7 @@ 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`.
+SMT-Lib name: `zero_extend`.
 -/
 def setWidth (v : Nat) (x : BitVec w) : BitVec v :=
   if h : w ≤ v then
@@ -422,7 +428,7 @@ 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`.
+SMT-Lib name: `zero_extend`.
 -/
 abbrev zeroExtend := @setWidth
 
@@ -431,7 +437,7 @@ 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`.
+SMT-Lib name: `zero_extend`.
 -/
 abbrev truncate := @setWidth
 
@@ -439,7 +445,7 @@ abbrev truncate := @setWidth
 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.
 
-SMT-LIB name: `sign_extend`.
+SMT-Lib name: `sign_extend`.
 -/
 def signExtend (v : Nat) (x : BitVec w) : BitVec v := .ofInt v x.toInt
 
@@ -454,7 +460,7 @@ Bitwise AND for bit vectors.
 0b1010#4 &&& 0b0110#4 = 0b0010#4
 ```
 
-SMT-LIB name: `bvand`.
+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)
@@ -467,7 +473,7 @@ Bitwise OR for bit vectors.
 0b1010#4 ||| 0b0110#4 = 0b1110#4
 ```
 
-SMT-LIB name: `bvor`.
+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)
@@ -480,7 +486,7 @@ instance : OrOp (BitVec w) := ⟨.or⟩
 0b1010#4 ^^^ 0b0110#4 = 0b1100#4
 ```
 
-SMT-LIB name: `bvxor`.
+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)
@@ -492,7 +498,7 @@ Bitwise NOT for bit vectors.
 ```lean
 ~~~(0b0101#4) == 0b1010
 ```
-SMT-LIB name: `bvnot`.
+SMT-Lib name: `bvnot`.
 -/
 protected def not (x : BitVec n) : BitVec n := allOnes n ^^^ x
 instance : Complement (BitVec w) := ⟨.not⟩
@@ -501,7 +507,7 @@ instance : Complement (BitVec w) := ⟨.not⟩
 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⟩
@@ -510,7 +516,7 @@ instance : HShiftLeft (BitVec w) Nat (BitVec w) := ⟨.shiftLeft⟩
 (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
@@ -526,7 +532,7 @@ 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)
 
@@ -538,7 +544,7 @@ 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
 
@@ -554,7 +560,7 @@ bits wrapping around to fill the low bits.
 ```lean
 rotateLeft  0b0011#4 3 = 0b1001
 ```
-SMT-LIB name: `rotate_left` except this operator uses a `Nat` shift amount.
+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)
 
@@ -573,7 +579,7 @@ bottom `n` bits wrapping around to fill the high bits.
 ```lean
 rotateRight 0b01001#5 1 = 0b10100
 ```
-SMT-LIB name: `rotate_right` except this operator uses a `Nat` shift amount.
+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)
 
@@ -581,7 +587,7 @@ def rotateRight (x : BitVec w) (n : Nat) : BitVec w := rotateRightAux x (n % w)
 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`.
+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
@@ -678,40 +684,18 @@ def ofBoolListLE : (bs : List Bool) → BitVec bs.length
 
 /-- `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
 
 /-- `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))
 
-/-- `usubOverflow x y` returns `true` if the 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
-
-/-- `ssubOverflow x y` returns `true` if 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))
-
-/-- `negOverflow x` returns `true` if the negation of `x` results in overflow. 
-For a BitVec `x` with width `0 < w`, this only happens if `x = intMin`. 
-
-  SMT-Lib name: `bvnego`.
--/
-def negOverflow {w : Nat} (x : BitVec w) : Bool :=
-  x.toInt == - 2 ^ (w - 1)
-
 /- ### reverse -/
 
 /-- Reverse the bits in a bitvector. -/

src/Init/Data/BitVec/BasicAux.lean

@@ -35,7 +35,7 @@ section arithmetic
 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⟩

src/Init/Data/BitVec/Bitblast.lean

@@ -91,7 +91,7 @@ First, we prove bitvector lemmas to unfold a high-level operation (such as multi
 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 bitblasting 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]
@@ -483,39 +478,6 @@ 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} :
@@ -567,58 +529,25 @@ 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 bitblasting -/
 
 /--
@@ -706,12 +635,6 @@ 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]
@@ -1321,38 +1244,14 @@ 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) :
@@ -1395,313 +1294,4 @@ theorem eq_iff_eq_of_inv (f : α → BitVec w) (g : BitVec w → α) (h : ∀ x,
     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 [Classical.not_and_iff_not_or_not] using h)]
-
-/-! ### Lemmas that use Bitblasting 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]
-
 end BitVec

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
@@ -379,9 +367,7 @@ 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
@@ -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

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
@@ -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)
 
@@ -61,93 +50,55 @@ theorem isValidChar_of_isValidCharNat (n : Nat) (h : isValidCharNat n) : isValid
 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⟩
@@ -54,13 +53,7 @@ protected def ofNat {n : Nat} (a : Nat) : Fin (n + 1) :=
 
 -- 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]
+@[inline, inherit_doc val]
 protected def toNat (i : Fin n) : Nat :=
   i.val
 
@@ -72,34 +65,15 @@ private theorem mlt {b : Nat} : {a : Nat} → a < n → b % n < n
     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 +100,27 @@ 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 +174,39 @@ 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

@@ -127,33 +127,6 @@ 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 +670,12 @@ 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 +684,13 @@ 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 +705,9 @@ 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 +728,18 @@ 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 +777,9 @@ 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 +802,8 @@ 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 +816,8 @@ 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
@@ -162,95 +90,44 @@ 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
 
@@ -263,27 +140,15 @@ instance : ToString Float where
 @[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.
--/
+/-- 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` this is larger than the given value, or the largest `Float` this is smaller
+than the given value. -/
 @[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.
--/
+/-- 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` this is larger than the given value, or the largest `Float` this is smaller
+than the given value. -/
 @[extern "lean_usize_to_float"] opaque USize.toFloat (n : USize) : Float
 
 instance : Inhabited Float where
@@ -294,191 +159,30 @@ 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 +193,6 @@ 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
@@ -159,91 +83,44 @@ 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
 
@@ -254,37 +131,20 @@ instance : ToString Float32 where
 @[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.
--/
+/-- 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` this is larger than the given value, or the largest `Float32` this is smaller
+than the given value. -/
 @[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.
--/
+/-- 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` this is larger than the given value, or the largest `Float32` this is smaller
+than the given value. -/
 @[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.
--/
+/-- 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` this is larger than the given value, or the largest `Float32` this is smaller
+than the given value. -/
 @[extern "lean_usize_to_float32"] opaque USize.toFloat32 (n : USize) : Float32
 
 instance : Inhabited Float32 where
@@ -295,191 +155,30 @@ 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 +189,9 @@ 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
@@ -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

@@ -14,4 +14,3 @@ 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

@@ -26,27 +26,24 @@ 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 +78,15 @@ 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 +105,21 @@ 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 +132,15 @@ 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 +152,48 @@ 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 +206,6 @@ 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 +251,15 @@ 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 +269,8 @@ 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 +279,27 @@ 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 +311,14 @@ 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 +338,8 @@ 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 +347,12 @@ 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

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

@@ -5,13 +5,12 @@ Authors: Siddharth Bhat, Jeremy Avigad
 -/
 prelude
 import Init.Data.Nat.Bitwise.Lemmas
-import Init.Data.Int.Bitwise.Basic
+import Init.Data.Int.Bitwise
 import Init.Data.Int.DivMod.Lemmas
 
 namespace Int
 
 theorem shiftRight_eq (n : Int) (s : Nat) : n >>> s = Int.shiftRight n s := rfl
-
 @[simp]
 theorem natCast_shiftRight (n s : Nat) : (n : Int) >>> s = n >>> s := rfl
 
@@ -28,7 +27,7 @@ theorem shiftRight_eq_div_pow (m : Int) (n : Nat) :
     m >>> n = m / ((2 ^ n) : Nat) := by
   simp only [shiftRight_eq, Int.shiftRight, Nat.shiftRight_eq_div_pow]
   split
-  · simp; norm_cast
+  · simp
   · rw [negSucc_ediv _ (by norm_cast; exact Nat.pow_pos (Nat.zero_lt_two))]
     rfl
 
@@ -40,47 +39,4 @@ theorem zero_shiftRight (n : Nat) : (0 : Int) >>> n = 0 := by
 theorem shiftRight_zero (n : Int) : n >>> 0 = n := by
   simp [Int.shiftRight_eq_div_pow]
 
-theorem le_shiftRight_of_nonpos {n : Int} {s : Nat} (h : n ≤ 0) : n ≤ n >>> s := by
-  simp only [Int.shiftRight_eq, Int.shiftRight, Int.ofNat_eq_coe]
-  split
-  case _ _ _ m =>
-    simp only [ofNat_eq_coe] at h
-    by_cases hm : m = 0
-    · simp [hm]
-    · omega
-  case _ _ _ m =>
-    by_cases hm : m = 0
-    · simp [hm]
-    · have := Nat.shiftRight_le m s
-      omega
-
-theorem shiftRight_le_of_nonneg {n : Int} {s : Nat} (h : 0 ≤ n) : n >>> s ≤ n := by
-  simp only [Int.shiftRight_eq, Int.shiftRight, Int.ofNat_eq_coe]
-  split
-  case _ _ _ m =>
-    simp only [Int.ofNat_eq_coe] at h
-    by_cases hm : m = 0
-    · simp [hm]
-    · have := Nat.shiftRight_le m s
-      simp
-      omega
-  case _ _ _ m =>
-    omega
-
-theorem le_shiftRight_of_nonneg {n : Int} {s : Nat} (h : 0 ≤ n) : 0 ≤ (n >>> s) := by
-  rw [Int.shiftRight_eq_div_pow]
-  by_cases h' : s = 0
-  · simp [h', h]
-  · have := @Nat.pow_pos 2 s (by omega)
-    have := @Int.ediv_nonneg n (2^s) h (by norm_cast at *; omega)
-    norm_cast at *
-
-theorem shiftRight_le_of_nonpos {n : Int} {s : Nat} (h : n ≤ 0) : (n >>> s) ≤ 0 := by
-  rw [Int.shiftRight_eq_div_pow]
-  by_cases h' : s = 0
-  · simp [h', h]
-  · have : 1 < 2 ^ s := Nat.one_lt_two_pow (by omega)
-    have rl : n / 2 ^ s ≤ 0 := Int.ediv_nonpos_of_nonpos_of_neg (by omega) (by norm_cast at *; omega)
-    norm_cast at *
-
 end Int

src/Init/Data/Int/Compare.lean

@@ -1,74 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro, Paul Reichert
--/
-prelude
-import Init.Data.Ord
-import Init.Data.Int.Order
-
-/-! # Basic lemmas about comparing integers
-
-This file introduces some basic lemmas about `compare` as applied to integers.
-
-Import `Std.Classes.Ord` in order to obtain the `TransOrd` and `LawfulEqOrd` instances for `Int`.
--/
-namespace Int
-
-protected theorem lt_or_eq_of_le {n m : Int} (h : n ≤ m) : n < m ∨ n = m := by
-  omega
-
-protected theorem le_iff_lt_or_eq {n m : Int} : n ≤ m ↔ n < m ∨ n = m :=
-  ⟨Int.lt_or_eq_of_le, fun | .inl h => Int.le_of_lt h | .inr rfl => Int.le_refl _⟩
-
-theorem compare_eq_ite_lt (a b : Int) :
-    compare a b = if a < b then .lt else if b < a then .gt else .eq := by
-  simp only [compare, compareOfLessAndEq]
-  split
-  · rfl
-  · next h =>
-    match Int.lt_or_eq_of_le (Int.not_lt.1 h) with
-    | .inl h => simp [h, Int.ne_of_gt h]
-    | .inr rfl => simp
-
-theorem compare_eq_ite_le (a b : Int) :
-    compare a b = if a ≤ b then if b ≤ a then .eq else .lt else .gt := by
-  rw [compare_eq_ite_lt]
-  split
-  · next hlt => simp [Int.le_of_lt hlt, Int.not_le.2 hlt]
-  · next hge =>
-    split
-    · next hgt => simp [Int.le_of_lt hgt, Int.not_le.2 hgt]
-    · next hle => simp [Int.not_lt.1 hge, Int.not_lt.1 hle]
-
-protected theorem compare_swap (a b : Int) : (compare a b).swap = compare b a := by
-  simp only [compare_eq_ite_le]; (repeat' split) <;> try rfl
-  next h1 h2 => cases h1 (Int.le_of_not_le h2)
-
-protected theorem compare_eq_eq {a b : Int} : compare a b = .eq ↔ a = b := by
-  rw [compare_eq_ite_lt]; (repeat' split) <;> simp [Int.ne_of_lt, Int.ne_of_gt, *]
-  next hlt hgt => exact Int.le_antisymm (Int.not_lt.1 hgt) (Int.not_lt.1 hlt)
-
-protected theorem compare_eq_lt {a b : Int} : compare a b = .lt ↔ a < b := by
-  rw [compare_eq_ite_lt]; (repeat' split) <;> simp [*]
-
-protected theorem compare_eq_gt {a b : Int} : compare a b = .gt ↔ b < a := by
-  rw [compare_eq_ite_lt]; (repeat' split) <;> simp [Int.le_of_lt, *]
-
-protected theorem compare_ne_gt {a b : Int} : compare a b ≠ .gt ↔ a ≤ b := by
-  rw [compare_eq_ite_le]; (repeat' split) <;> simp [*]
-
-protected theorem compare_ne_lt {a b : Int} : compare a b ≠ .lt ↔ b ≤ a := by
-  rw [compare_eq_ite_le]; (repeat' split) <;> simp [Int.le_of_not_le, *]
-
-protected theorem isLE_compare {a b : Int} :
-    (compare a b).isLE ↔ a ≤ b := by
-  simp only [Int.compare_eq_ite_le]
-  repeat' split <;> simp_all
-
-protected theorem isGE_compare {a b : Int} :
-    (compare a b).isGE ↔ b ≤ a := by
-  rw [← Int.compare_swap, Ordering.isGE_swap]
-  exact Int.isLE_compare
-
-end Int

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

@@ -22,7 +22,7 @@ In early versions of Lean, the typeclasses provided by `/` and `%`
 were defined in terms of `tdiv` and `tmod`, and these were named simply as `div` and `mod`.
 
 However we decided it was better to use `ediv` and `emod` for the default typeclass instances,
-as they are consistent with the conventions used in SMT-LIB, and Mathlib,
+as they are consistent with the conventions used in SMTLib, and Mathlib,
 and often mathematical reasoning is easier with these conventions.
 At that time, we did not rename `div` and `mod` to `tdiv` and `tmod` (along with all their lemma).
 
@@ -38,29 +38,29 @@ This pair satisfies `0 ≤ emod x y < natAbs y` for `y ≠ 0`.
 -/
 
 /--
-Integer division that uses the E-rounding convention. Usually accessed via the `/` operator.
-Division by zero is defined to be zero, rather than an error.
+Integer division. This version of integer division uses the E-rounding convention
+(euclidean division), in which `Int.emod x y` satisfies `0 ≤ emod x y < natAbs y` for `y ≠ 0`
+and `Int.ediv` is the unique function satisfying `emod x y + (ediv x y) * y = x`.
 
-In the E-rounding convention (Euclidean division), `Int.emod x y` satisfies `0 ≤ Int.emod x y < Int.natAbs y`
-for `y ≠ 0` and `Int.ediv` is the unique function satisfying `Int.emod x y + (Int.edivx y) * y = x`
-for `y ≠ 0`.
-
-This means that `Int.ediv x y` is `⌊x / y⌋` when `y > 0` and `⌈x / y⌉` when `y < 0`.
-
-This function is overridden by the compiler with an efficient implementation. This definition is
-the logical model.
+This is the function powering the `/` notation on integers.
 
 Examples:
-* `(7 : Int) / (0 : Int) = 0`
-* `(0 : Int) / (7 : Int) = 0`
-* `(12 : Int) / (6 : Int) = 2`
-* `(12 : Int) / (-6 : Int) = -2`
-* `(-12 : Int) / (6 : Int) = -2`
-* `(-12 : Int) / (-6 : Int) = 2`
-* `(12 : Int) / (7 : Int) = 1`
-* `(12 : Int) / (-7 : Int) = -1`
-* `(-12 : Int) / (7 : Int) = -2`
-* `(-12 : Int) / (-7 : Int) = 2`
+```
+#eval (7 : Int) / (0 : Int) -- 0
+#eval (0 : Int) / (7 : Int) -- 0
+
+#eval (12 : Int) / (6 : Int) -- 2
+#eval (12 : Int) / (-6 : Int) -- -2
+#eval (-12 : Int) / (6 : Int) -- -2
+#eval (-12 : Int) / (-6 : Int) -- 2
+
+#eval (12 : Int) / (7 : Int) -- 1
+#eval (12 : Int) / (-7 : Int) -- -1
+#eval (-12 : Int) / (7 : Int) -- -2
+#eval (-12 : Int) / (-7 : Int) -- 2
+```
+
+Implemented by efficient native code.
 -/
 @[extern "lean_int_ediv"]
 def ediv : (@& Int) → (@& Int) → Int
@@ -71,26 +71,29 @@ def ediv : (@& Int) → (@& Int) → Int
   | -[m+1],  -[n+1]  => ofNat (succ (m / succ n))
 
 /--
-Integer modulus that uses the E-rounding convention. Usually accessed via the `%` operator.
+Integer modulus. This version of integer modulus uses the E-rounding convention
+(euclidean division), in which `Int.emod x y` satisfies `0 ≤ emod x y < natAbs y` for `y ≠ 0`
+and `Int.ediv` is the unique function satisfying `emod x y + (ediv x y) * y = x`.
 
-In the E-rounding convention (Euclidean division), `Int.emod x y` satisfies `0 ≤ Int.emod x y < Int.natAbs y`
-for `y ≠ 0` and `Int.ediv` is the unique function satisfying `Int.emod x y + (Int.edivx y) * y = x`
-for `y ≠ 0`.
-
-This function is overridden by the compiler with an efficient implementation. This definition is
-the logical model.
+This is the function powering the `%` notation on integers.
 
 Examples:
-* `(7 : Int) % (0 : Int) = 7`
-* `(0 : Int) % (7 : Int) = 0`
-* `(12 : Int) % (6 : Int) = 0`
-* `(12 : Int) % (-6 : Int) = 0`
-* `(-12 : Int) % (6 : Int) = 0`
-* `(-12 : Int) % (-6 : Int) = 0`
-* `(12 : Int) % (7 : Int) = 5`
-* `(12 : Int) % (-7 : Int) = 5`
-* `(-12 : Int) % (7 : Int) = 2`
-* `(-12 : Int) % (-7 : Int) = 2`
+```
+#eval (7 : Int) % (0 : Int) -- 7
+#eval (0 : Int) % (7 : Int) -- 0
+
+#eval (12 : Int) % (6 : Int) -- 0
+#eval (12 : Int) % (-6 : Int) -- 0
+#eval (-12 : Int) % (6 : Int) -- 0
+#eval (-12 : Int) % (-6 : Int) -- 0
+
+#eval (12 : Int) % (7 : Int) -- 5
+#eval (12 : Int) % (-7 : Int) -- 5
+#eval (-12 : Int) % (7 : Int) -- 2
+#eval (-12 : Int) % (-7 : Int) -- 2
+```
+
+Implemented by efficient native code.
 -/
 @[extern "lean_int_emod"]
 def emod : (@& Int) → (@& Int) → Int
@@ -98,19 +101,15 @@ def emod : (@& Int) → (@& Int) → Int
   | -[m+1],  n => subNatNat (natAbs n) (succ (m % natAbs n))
 
 /--
-The `Div Int` and `Mod Int` instances use `Int.ediv` and `Int.emod` for compatibility with SMT-LIB and
-because mathematical reasoning tends to be easier.
+The Div and Mod syntax uses ediv and emod for compatibility with SMTLIb and mathematical
+reasoning tends to be easier.
 -/
 instance : Div Int where
   div := Int.ediv
-/--
-The `Div Int` and `Mod Int` instances use `Int.ediv` and `Int.emod` for compatibility with SMT-LIB and
-because mathematical reasoning tends to be easier.
--/
 instance : Mod Int where
   mod := Int.emod
 
-@[norm_cast] theorem ofNat_ediv (m n : Nat) : (↑(m / n) : Int) = ↑m / ↑n := rfl
+@[simp, norm_cast] theorem ofNat_ediv (m n : Nat) : (↑(m / n) : Int) = ↑m / ↑n := rfl
 
 theorem ofNat_ediv_ofNat {a b : Nat} : (↑a / ↑b : Int) = (a / b : Nat) := rfl
 @[norm_cast]
@@ -123,27 +122,35 @@ theorem negSucc_emod_negSucc {a b : Nat} : -[a+1] % -[b+1] = subNatNat (b + 1) (
 /-! ### T-rounding division -/
 
 /--
-Integer division using the T-rounding convention.
+`tdiv` uses the [*"T-rounding"*][t-rounding]
+(**T**runcation-rounding) convention, meaning that it rounds toward
+zero. Also note that division by zero is defined to equal zero.
 
-In [the T-rounding convention][t-rounding] (division with truncation), all rounding is towards zero.
-Division by 0 is defined to be 0. In this convention, `Int.tmod a b + b * (Int.tdiv a b) = a`.
+  The relation between integer division and modulo is found in
+  `Int.tmod_add_tdiv` which states that
+  `tmod a b + b * (tdiv a b) = a`, unconditionally.
 
-[t-rounding]: https://dl.acm.org/doi/pdf/10.1145/128861.128862
+  [t-rounding]: https://dl.acm.org/doi/pdf/10.1145/128861.128862
+  [theo tmod_add_tdiv]: https://leanprover-community.github.io/mathlib4_docs/find/?pattern=Int.tmod_add_tdiv#doc
 
-This function is overridden by the compiler with an efficient implementation. This definition is the
-logical model.
+  Examples:
 
-Examples:
-* `(7 : Int).tdiv (0 : Int) = 0`
-* `(0 : Int).tdiv (7 : Int) = 0`
-* `(12 : Int).tdiv (6 : Int) = 2`
-* `(12 : Int).tdiv (-6 : Int) = -2`
-* `(-12 : Int).tdiv (6 : Int) = -2`
-* `(-12 : Int).tdiv (-6 : Int) = 2`
-* `(12 : Int).tdiv (7 : Int) = 1`
-* `(12 : Int).tdiv (-7 : Int) = -1`
-* `(-12 : Int).tdiv (7 : Int) = -1`
-* `(-12 : Int).tdiv (-7 : Int) = 1`
+  ```
+  #eval (7 : Int).tdiv (0 : Int) -- 0
+  #eval (0 : Int).tdiv (7 : Int) -- 0
+
+  #eval (12 : Int).tdiv (6 : Int) -- 2
+  #eval (12 : Int).tdiv (-6 : Int) -- -2
+  #eval (-12 : Int).tdiv (6 : Int) -- -2
+  #eval (-12 : Int).tdiv (-6 : Int) -- 2
+
+  #eval (12 : Int).tdiv (7 : Int) -- 1
+  #eval (12 : Int).tdiv (-7 : Int) -- -1
+  #eval (-12 : Int).tdiv (7 : Int) -- -1
+  #eval (-12 : Int).tdiv (-7 : Int) -- 1
+  ```
+
+  Implemented by efficient native code.
 -/
 @[extern "lean_int_div"]
 def tdiv : (@& Int) → (@& Int) → Int
@@ -152,32 +159,33 @@ def tdiv : (@& Int) → (@& Int) → Int
   | -[m +1], ofNat n => -ofNat (succ m / n)
   | -[m +1], -[n +1] =>  ofNat (succ m / succ n)
 
-/-- Integer modulo using the T-rounding convention.
+/-- Integer modulo. This function uses the
+  [*"T-rounding"*][t-rounding] (**T**runcation-rounding) convention
+  to pair with `Int.tdiv`, meaning that `tmod a b + b * (tdiv a b) = a`
+  unconditionally (see [`Int.tmod_add_tdiv`][theo tmod_add_tdiv]). In
+  particular, `a % 0 = a`.
 
-In [the T-rounding convention][t-rounding] (division with truncation), all rounding is towards zero.
-Division by 0 is defined to be 0 and `Int.tmod a 0 = a`.
+  [t-rounding]: https://dl.acm.org/doi/pdf/10.1145/128861.128862
+  [theo tmod_add_tdiv]: https://leanprover-community.github.io/mathlib4_docs/find/?pattern=Int.tmod_add_tdiv#doc
 
-In this convention, `Int.tmod a b + b * (Int.tdiv a b) = a`. Additionally,
-`Int.natAbs (Int.tmod a b) = Int.natAbs a % Int.natAbs b`, and when `b` does not divide `a`,
-`Int.tmod a b` has the same sign as `a`.
+  Examples:
 
-[t-rounding]: https://dl.acm.org/doi/pdf/10.1145/128861.128862
+  ```
+  #eval (7 : Int).tmod (0 : Int) -- 7
+  #eval (0 : Int).tmod (7 : Int) -- 0
 
-This function is overridden by the compiler with an efficient implementation. This definition is the
-logical model.
+  #eval (12 : Int).tmod (6 : Int) -- 0
+  #eval (12 : Int).tmod (-6 : Int) -- 0
+  #eval (-12 : Int).tmod (6 : Int) -- 0
+  #eval (-12 : Int).tmod (-6 : Int) -- 0
 
-Examples:
-* `(7 : Int).tmod (0 : Int) = 7`
-* `(0 : Int).tmod (7 : Int) = 0`
-* `(12 : Int).tmod (6 : Int) = 0`
-* `(12 : Int).tmod (-6 : Int) = 0`
-* `(-12 : Int).tmod (6 : Int) = 0`
-* `(-12 : Int).tmod (-6 : Int) = 0`
-* `(12 : Int).tmod (7 : Int) = 5`
-* `(12 : Int).tmod (-7 : Int) = 5`
-* `(-12 : Int).tmod (7 : Int) = -5`
-* `(-12 : Int).tmod (-7 : Int) = -5`
--/
+  #eval (12 : Int).tmod (7 : Int) -- 5
+  #eval (12 : Int).tmod (-7 : Int) -- 5
+  #eval (-12 : Int).tmod (7 : Int) -- -5
+  #eval (-12 : Int).tmod (-7 : Int) -- -5
+  ```
+
+  Implemented by efficient native code. -/
 @[extern "lean_int_mod"]
 def tmod : (@& Int) → (@& Int) → Int
   | ofNat m, ofNat n =>  ofNat (m % n)
@@ -192,22 +200,25 @@ This pair satisfies `fdiv x y = floor (x / y)`.
 -/
 
 /--
-Integer division using the F-rounding convention.
-
-In the F-rounding convention (flooring division), `Int.fdiv x y` satisfies `Int.fdiv x y = ⌊x / y⌋`
-and `Int.fmod` is the unique function satisfying `Int.fmod x y + (Int.fdiv x y) * y = x`.
+Integer division. This version of division uses the F-rounding convention
+(flooring division), in which `Int.fdiv x y` satisfies `fdiv x y = floor (x / y)`
+and `Int.fmod` is the unique function satisfying `fmod x y + (fdiv x y) * y = x`.
 
 Examples:
-* `(7 : Int).fdiv (0 : Int) = 0`
-* `(0 : Int).fdiv (7 : Int) = 0`
-* `(12 : Int).fdiv (6 : Int) = 2`
-* `(12 : Int).fdiv (-6 : Int) = -2`
-* `(-12 : Int).fdiv (6 : Int) = -2`
-* `(-12 : Int).fdiv (-6 : Int) = 2`
-* `(12 : Int).fdiv (7 : Int) = 1`
-* `(12 : Int).fdiv (-7 : Int) = -2`
-* `(-12 : Int).fdiv (7 : Int) = -2`
-* `(-12 : Int).fdiv (-7 : Int) = 1`
+```
+#eval (7 : Int).fdiv (0 : Int) -- 0
+#eval (0 : Int).fdiv (7 : Int) -- 0
+
+#eval (12 : Int).fdiv (6 : Int) -- 2
+#eval (12 : Int).fdiv (-6 : Int) -- -2
+#eval (-12 : Int).fdiv (6 : Int) -- -2
+#eval (-12 : Int).fdiv (-6 : Int) -- 2
+
+#eval (12 : Int).fdiv (7 : Int) -- 1
+#eval (12 : Int).fdiv (-7 : Int) -- -2
+#eval (-12 : Int).fdiv (7 : Int) -- -2
+#eval (-12 : Int).fdiv (-7 : Int) -- 1
+```
 -/
 def fdiv : Int → Int → Int
   | 0,       _       => 0
@@ -218,26 +229,26 @@ def fdiv : Int → Int → Int
   | -[m+1],  -[n+1]  => ofNat (succ m / succ n)
 
 /--
-Integer modulus using the F-rounding convention.
-
-In the F-rounding convention (flooring division), `Int.fdiv x y` satisfies `Int.fdiv x y = ⌊x / y⌋`
-and `Int.fmod` is the unique function satisfying `Int.fmod x y + (Int.fdiv x y) * y = x`.
+Integer modulus. This version of integer modulus uses the F-rounding convention
+(flooring division), in which `Int.fdiv x y` satisfies `fdiv x y = floor (x / y)`
+and `Int.fmod` is the unique function satisfying `fmod x y + (fdiv x y) * y = x`.
 
 Examples:
 
-* `(7 : Int).fmod (0 : Int) = 7`
-* `(0 : Int).fmod (7 : Int) = 0`
+```
+#eval (7 : Int).fmod (0 : Int) -- 7
+#eval (0 : Int).fmod (7 : Int) -- 0
 
-* `(12 : Int).fmod (6 : Int) = 0`
-* `(12 : Int).fmod (-6 : Int) = 0`
-* `(-12 : Int).fmod (6 : Int) = 0`
-* `(-12 : Int).fmod (-6 : Int) = 0`
-
-* `(12 : Int).fmod (7 : Int) = 5`
-* `(12 : Int).fmod (-7 : Int) = -2`
-* `(-12 : Int).fmod (7 : Int) = 2`
-* `(-12 : Int).fmod (-7 : Int) = -5`
+#eval (12 : Int).fmod (6 : Int) -- 0
+#eval (12 : Int).fmod (-6 : Int) -- 0
+#eval (-12 : Int).fmod (6 : Int) -- 0
+#eval (-12 : Int).fmod (-6 : Int) -- 0
 
+#eval (12 : Int).fmod (7 : Int) -- 5
+#eval (12 : Int).fmod (-7 : Int) -- -2
+#eval (-12 : Int).fmod (7 : Int) -- 2
+#eval (-12 : Int).fmod (-7 : Int) -- -5
+```
 -/
 def fmod : Int → Int → Int
   | 0,       _       => 0
@@ -264,24 +275,28 @@ This function is used in `omega` as well as signed bitvectors.
 -/
 
 /--
-Balanced modulus.
+Balanced modulus.  This version of integer modulus uses the
+balanced rounding convention, which guarantees that
+`-m/2 ≤ bmod x m < m/2` for `m ≠ 0` and `bmod x m` is congruent
+to `x` modulo `m`.
 
-This version of integer modulus uses the balanced rounding convention, which guarantees that
-`-m / 2 ≤ Int.bmod x m < m/2` for `m ≠ 0` and `Int.bmod x m` is congruent to `x` modulo `m`.
-
-If `m = 0`, then `Int.bmod x m = x`.
+If `m = 0`, then `bmod x m = x`.
 
 Examples:
-* `(7 : Int).bmod 0 = 7`
-* `(0 : Int).bmod 7 = 0`
-* `(12 : Int).bmod 6 = 0`
-* `(12 : Int).bmod 7 = -2`
-* `(12 : Int).bmod 8 = -4`
-* `(12 : Int).bmod 9 = 3`
-* `(-12 : Int).bmod 6 = 0`
-* `(-12 : Int).bmod 7 = 2`
-* `(-12 : Int).bmod 8 = -4`
-* `(-12 : Int).bmod 9 = -3`
+```
+#eval (7 : Int).bdiv 0 -- 0
+#eval (0 : Int).bdiv 7 -- 0
+
+#eval (12 : Int).bdiv 6 -- 2
+#eval (12 : Int).bdiv 7 -- 2
+#eval (12 : Int).bdiv 8 -- 2
+#eval (12 : Int).bdiv 9 -- 1
+
+#eval (-12 : Int).bdiv 6 -- -2
+#eval (-12 : Int).bdiv 7 -- -2
+#eval (-12 : Int).bdiv 8 -- -1
+#eval (-12 : Int).bdiv 9 -- -1
+```
 -/
 def bmod (x : Int) (m : Nat) : Int :=
   let r := x % m
@@ -291,21 +306,24 @@ def bmod (x : Int) (m : Nat) : Int :=
     r - m
 
 /--
-Balanced division.
-
-This returns the unique integer so that `b * (Int.bdiv a b) + Int.bmod a b = a`.
+Balanced division.  This returns the unique integer so that
+`b * (Int.bdiv a b) + Int.bmod a b = a`.
 
 Examples:
-* `(7 : Int).bdiv 0 = 0`
-* `(0 : Int).bdiv 7 = 0`
-* `(12 : Int).bdiv 6 = 2`
-* `(12 : Int).bdiv 7 = 2`
-* `(12 : Int).bdiv 8 = 2`
-* `(12 : Int).bdiv 9 = 1`
-* `(-12 : Int).bdiv 6 = -2`
-* `(-12 : Int).bdiv 7 = -2`
-* `(-12 : Int).bdiv 8 = -1`
-* `(-12 : Int).bdiv 9 = -1`
+```
+#eval (7 : Int).bmod 0 -- 7
+#eval (0 : Int).bmod 7 -- 0
+
+#eval (12 : Int).bmod 6 -- 0
+#eval (12 : Int).bmod 7 -- -2
+#eval (12 : Int).bmod 8 -- -4
+#eval (12 : Int).bmod 9 -- 3
+
+#eval (-12 : Int).bmod 6 -- 0
+#eval (-12 : Int).bmod 7 -- 2
+#eval (-12 : Int).bmod 8 -- -4
+#eval (-12 : Int).bmod 9 -- -3
+```
 -/
 def bdiv (x : Int) (m : Nat) : Int :=
   if m = 0 then

src/Init/Data/Int/DivMod/Bootstrap.lean

@@ -53,7 +53,7 @@ protected theorem dvd_mul_left (a b : Int) : b ∣ a * b := ⟨_, Int.mul_comm .
   constructor <;> exact fun ⟨k, e⟩ =>
     ⟨-k, by simp [e, Int.neg_mul, Int.mul_neg, Int.neg_neg]⟩
 
-@[simp] protected theorem dvd_neg {a b : Int} : a ∣ -b ↔ a ∣ b := by
+protected theorem dvd_neg {a b : Int} : a ∣ -b ↔ a ∣ b := by
   constructor <;> exact fun ⟨k, e⟩ =>
     ⟨-k, by simp [← e, Int.neg_mul, Int.mul_neg, Int.neg_neg]⟩
 
@@ -121,7 +121,7 @@ theorem emod_def (a b : Int) : a % b = a - b * (a / b) := by
 
 /-! ### `/` ediv -/
 
-@[simp] theorem ediv_neg : ∀ a b : Int, a / (-b) = -(a / b)
+@[simp] protected theorem ediv_neg : ∀ a b : Int, a / (-b) = -(a / b)
   | ofNat m, 0 => show ofNat (m / 0) = -↑(m / 0) by rw [Nat.div_zero]; rfl
   | ofNat _, -[_+1] => (Int.neg_neg _).symm
   | ofNat _, succ _ | -[_+1], 0 | -[_+1], succ _ | -[_+1], -[_+1] => rfl
@@ -158,10 +158,6 @@ theorem add_mul_ediv_right (a b : Int) {c : Int} (H : c ≠ 0) : (a + b * c) / c
       apply congrArg negSucc
       rw [Nat.mul_comm, Nat.sub_mul_div]; rwa [Nat.mul_comm]
 
-theorem add_mul_ediv_left (a : Int) {b : Int}
-    (c : Int) (H : b ≠ 0) : (a + b * c) / b = a / b + c :=
-  Int.mul_comm .. ▸ Int.add_mul_ediv_right _ _ H
-
 theorem add_ediv_of_dvd_right {a b c : Int} (H : c ∣ b) : (a + b) / c = a / c + b / c :=
   if h : c = 0 then by simp [h] else by
     let ⟨k, hk⟩ := H
@@ -183,6 +179,8 @@ theorem ediv_nonneg_iff_of_pos {a b : Int} (h : 0 < b) : 0 ≤ a / b ↔ 0 ≤ a
   match b, h with
   | Int.ofNat (b+1), _ =>
     rcases a with ⟨a⟩ <;> simp [Int.ediv]
+    norm_cast
+    simp
 
 @[deprecated ediv_nonneg_iff_of_pos (since := "2025-02-28")]
 abbrev div_nonneg_iff_of_pos := @ediv_nonneg_iff_of_pos
@@ -198,6 +196,16 @@ theorem emod_lt_of_pos (a : Int) {b : Int} (H : 0 < b) : a % b < b :=
   | ofNat _, _, ⟨_, rfl⟩ => ofNat_lt.2 (Nat.mod_lt _ (Nat.succ_pos _))
   | -[_+1], _, ⟨_, rfl⟩ => Int.sub_lt_self _ (ofNat_lt.2 <| Nat.succ_pos _)
 
+theorem mul_ediv_self_le {x k : Int} (h : k ≠ 0) : k * (x / k) ≤ x :=
+  calc k * (x / k)
+    _ ≤ k * (x / k) + x % k := Int.le_add_of_nonneg_right (emod_nonneg x h)
+    _ = x                   := ediv_add_emod _ _
+
+theorem lt_mul_ediv_self_add {x k : Int} (h : 0 < k) : x < k * (x / k) + k :=
+  calc x
+    _ = k * (x / k) + x % k := (ediv_add_emod _ _).symm
+    _ < k * (x / k) + k     := Int.add_lt_add_left (emod_lt_of_pos x h) _
+
 @[simp] theorem add_mul_emod_self {a b c : Int} : (a + b * c) % c = a % c :=
   if cz : c = 0 then by
     rw [cz, Int.mul_zero, Int.add_zero]
@@ -305,18 +313,6 @@ theorem emod_pos_of_not_dvd {a b : Int} (h : ¬ a ∣ b) : a = 0 ∨ 0 < b % a :
   · simp_all
   · exact Or.inr (Int.lt_iff_le_and_ne.mpr ⟨emod_nonneg b w, Ne.symm h⟩)
 
-/-! ### `/` and ordering -/
-
-theorem mul_ediv_self_le {x k : Int} (h : k ≠ 0) : k * (x / k) ≤ x :=
-  calc k * (x / k)
-    _ ≤ k * (x / k) + x % k := Int.le_add_of_nonneg_right (emod_nonneg x h)
-    _ = x                   := ediv_add_emod _ _
-
-theorem lt_mul_ediv_self_add {x k : Int} (h : 0 < k) : x < k * (x / k) + k :=
-  calc x
-    _ = k * (x / k) + x % k := (ediv_add_emod _ _).symm
-    _ < k * (x / k) + k     := Int.add_lt_add_left (emod_lt_of_pos x h) _
-
 /-! ### bmod -/
 
 @[simp] theorem bmod_emod : bmod x m % m = x % m := by

src/Init/Data/Int/Gcd.lean

@@ -11,30 +11,12 @@ import Init.Data.Int.DivMod.Lemmas
 
 /-!
 Definition and lemmas for gcd and lcm over Int
-
-## Future work
-Most of the material about `Nat.gcd` and `Nat.lcm` from `Init.Data.Nat.Gcd` and `Init.Data.Nat.Lcm`
-has analogues for `Int.gcd` and `Int.lcm` that should be added to this file.
 -/
 namespace Int
 
 /-! ## gcd -/
 
-/--
-Computes the greatest common divisor of two integers as a natural number. The GCD of two integers is
-the largest natural number that evenly divides both. However, the GCD of a number and `0` is the
-number's absolute value.
-
-This implementation uses `Nat.gcd`, which is overridden in both the kernel and the compiler to
-efficiently evaluate using arbitrary-precision arithmetic.
-
-Examples:
-* `Int.gcd 10 15 = 5`
-* `Int.gcd 10 (-15) = 5`
-* `Int.gcd (-6) (-9) = 3`
-* `Int.gcd 0 5 = 5`
-* `Int.gcd (-7) 0 = 7`
--/
+/-- Computes the greatest common divisor of two integers, as a `Nat`. -/
 def gcd (m n : Int) : Nat := m.natAbs.gcd n.natAbs
 
 theorem gcd_dvd_left {a b : Int} : (gcd a b : Int) ∣ a := by
@@ -55,18 +37,7 @@ theorem gcd_dvd_right {a b : Int} : (gcd a b : Int) ∣ b := by
 
 /-! ## lcm -/
 
-/--
-Computes the least common multiple of two integers as a natural number. The LCM of two integers is
-the smallest natural number that's evenly divisible by the absolute values of both.
-
-Examples:
- * `Int.lcm 9 6 = 18`
- * `Int.lcm 9 (-6) = 18`
- * `Int.lcm 9 3 = 9`
- * `Int.lcm 9 (-3) = 9`
- * `Int.lcm 0 3 = 0`
- * `Int.lcm (-3) 0 = 0`
--/
+/-- Computes the least common multiple of two integers, as a `Nat`. -/
 def lcm (m n : Int) : Nat := m.natAbs.lcm n.natAbs
 
 theorem lcm_ne_zero (hm : m ≠ 0) (hn : n ≠ 0) : lcm m n ≠ 0 := by

src/Init/Data/Int/Lemmas.lean

@@ -25,32 +25,31 @@ theorem subNatNat_of_sub_eq_succ {m n k : Nat} (h : n - m = succ k) : subNatNat
 
 @[norm_cast] theorem ofNat_add (n m : Nat) : (↑(n + m) : Int) = n + m := rfl
 @[norm_cast] theorem ofNat_mul (n m : Nat) : (↑(n * m) : Int) = n * m := rfl
-@[norm_cast] theorem ofNat_succ (n : Nat) : (succ n : Int) = n + 1 := rfl
+theorem ofNat_succ (n : Nat) : (succ n : Int) = n + 1 := rfl
 
-theorem neg_ofNat_zero : -((0 : Nat) : Int) = 0 := rfl
-theorem neg_ofNat_succ (n : Nat) : -(succ n : Int) = -[n+1] := rfl
-theorem neg_negSucc (n : Nat) : -(-[n+1]) = succ n := rfl
+@[local simp] theorem neg_ofNat_zero : -((0 : Nat) : Int) = 0 := rfl
+@[local simp] theorem neg_ofNat_succ (n : Nat) : -(succ n : Int) = -[n+1] := rfl
+@[local simp] theorem neg_negSucc (n : Nat) : -(-[n+1]) = succ n := rfl
+
+theorem negSucc_coe (n : Nat) : -[n+1] = -↑(n + 1) := rfl
 
 theorem negOfNat_eq : negOfNat n = -ofNat n := rfl
 
+/-! ## These are only for internal use -/
+
 @[simp] theorem add_def {a b : Int} : Int.add a b = a + b := rfl
-@[simp] theorem mul_def {a b : Int} : Int.mul a b = a * b := rfl
-
-/-!
-## These are only for internal use
-
-Ideally these could all be made private, but they are used in downstream libraries.
--/
 
 @[local simp] theorem ofNat_add_ofNat (m n : Nat) : (↑m + ↑n : Int) = ↑(m + n) := rfl
 @[local simp] theorem ofNat_add_negSucc (m n : Nat) : ↑m + -[n+1] = subNatNat m (succ n) := rfl
 @[local simp] theorem negSucc_add_ofNat (m n : Nat) : -[m+1] + ↑n = subNatNat n (succ m) := rfl
 @[local simp] theorem negSucc_add_negSucc (m n : Nat) : -[m+1] + -[n+1] = -[succ (m + n) +1] := rfl
 
+@[simp] theorem mul_def {a b : Int} : Int.mul a b = a * b := rfl
+
 @[local simp] theorem ofNat_mul_ofNat (m n : Nat) : (↑m * ↑n : Int) = ↑(m * n) := rfl
-@[local simp] private theorem ofNat_mul_negSucc' (m n : Nat) : ↑m * -[n+1] = negOfNat (m * succ n) := rfl
-@[local simp] private theorem negSucc_mul_ofNat' (m n : Nat) : -[m+1] * ↑n = negOfNat (succ m * n) := rfl
-@[local simp] private theorem negSucc_mul_negSucc' (m n : Nat) :
+@[local simp] theorem ofNat_mul_negSucc' (m n : Nat) : ↑m * -[n+1] = negOfNat (m * succ n) := rfl
+@[local simp] theorem negSucc_mul_ofNat' (m n : Nat) : -[m+1] * ↑n = negOfNat (succ m * n) := rfl
+@[local simp] theorem negSucc_mul_negSucc' (m n : Nat) :
     -[m+1] * -[n+1] = ofNat (succ m * succ n) := rfl
 
 /- ## some basic functions and properties -/
@@ -65,14 +64,11 @@ theorem negSucc_inj : negSucc m = negSucc n ↔ m = n := ⟨negSucc.inj, fun H =
 
 theorem negSucc_eq (n : Nat) : -[n+1] = -((n : Int) + 1) := rfl
 
-@[deprecated negSucc_eq (since := "2025-03-11")]
-theorem negSucc_coe (n : Nat) : -[n+1] = -↑(n + 1) := rfl
-
 @[simp] theorem negSucc_ne_zero (n : Nat) : -[n+1] ≠ 0 := nofun
 
 @[simp] theorem zero_ne_negSucc (n : Nat) : 0 ≠ -[n+1] := nofun
 
-@[simp, norm_cast] theorem cast_ofNat_Int :
+@[simp, norm_cast] theorem Nat.cast_ofNat_Int :
   (Nat.cast (no_index (OfNat.ofNat n)) : Int) = OfNat.ofNat n := rfl
 
 /- ## neg -/
@@ -82,7 +78,7 @@ theorem negSucc_coe (n : Nat) : -[n+1] = -↑(n + 1) := rfl
   | succ _ => rfl
   | -[_+1] => rfl
 
-@[simp] protected theorem neg_inj {a b : Int} : -a = -b ↔ a = b :=
+protected theorem neg_inj {a b : Int} : -a = -b ↔ a = b :=
   ⟨fun h => by rw [← Int.neg_neg a, ← Int.neg_neg b, h], congrArg _⟩
 
 @[simp] protected theorem neg_eq_zero : -a = 0 ↔ a = 0 := Int.neg_inj (b := 0)
@@ -90,13 +86,12 @@ theorem negSucc_coe (n : Nat) : -[n+1] = -↑(n + 1) := rfl
 protected theorem neg_ne_zero : -a ≠ 0 ↔ a ≠ 0 := not_congr Int.neg_eq_zero
 
 protected theorem sub_eq_add_neg {a b : Int} : a - b = a + -b := rfl
-protected theorem add_neg_eq_sub {a b : Int} : a + -b = a - b := rfl
 
 theorem add_neg_one (i : Int) : i + -1 = i - 1 := rfl
 
 /- ## basic properties of subNatNat -/
 
-@[elab_as_elim]
+-- @[elabAsElim] -- TODO(Mario): unexpected eliminator resulting type
 theorem subNatNat_elim (m n : Nat) (motive : Nat → Nat → Int → Prop)
     (hp : ∀ i n, motive (n + i) n i)
     (hn : ∀ i m, motive m (m + i + 1) -[i+1]) :
@@ -145,6 +140,29 @@ theorem subNatNat_of_lt {m n : Nat} (h : m < n) : subNatNat m n = -[pred (n - m)
     rw [Nat.sub_eq_iff_eq_add' h]
     simp
 
+/- # Additive group properties -/
+
+/- addition -/
+
+protected theorem add_comm : ∀ a b : Int, a + b = b + a
+  | ofNat n, ofNat m => by simp [Nat.add_comm]
+  | ofNat _, -[_+1]  => rfl
+  | -[_+1],  ofNat _ => rfl
+  | -[_+1],  -[_+1]  => by simp [Nat.add_comm]
+instance : Std.Commutative (α := Int) (· + ·) := ⟨Int.add_comm⟩
+
+@[simp] protected theorem add_zero : ∀ a : Int, a + 0 = a
+  | ofNat _ => rfl
+  | -[_+1]  => rfl
+
+@[simp] protected theorem zero_add (a : Int) : 0 + a = a := Int.add_comm .. ▸ a.add_zero
+instance : Std.LawfulIdentity (α := Int) (· + ·) 0 where
+  left_id := Int.zero_add
+  right_id := Int.add_zero
+
+theorem ofNat_add_negSucc_of_lt (h : m < n.succ) : ofNat m + -[n+1] = -[n - m+1] :=
+  show subNatNat .. = _ by simp [succ_sub (le_of_lt_succ h), subNatNat]
+
 theorem subNatNat_sub (h : n ≤ m) (k : Nat) : subNatNat (m - n) k = subNatNat m (k + n) := by
   rwa [← subNatNat_add_add _ _ n, Nat.sub_add_cancel]
 
@@ -173,34 +191,6 @@ theorem subNatNat_add_negSucc (m n k : Nat) :
       ← Nat.add_assoc, succ_sub_succ_eq_sub, Nat.add_comm n,Nat.add_sub_assoc (Nat.le_of_lt h'),
       Nat.add_comm]
 
-theorem subNatNat_self : ∀ n, subNatNat n n = 0
-  | 0      => rfl
-  | succ m => by rw [subNatNat_of_sub_eq_zero (Nat.sub_self ..), Nat.sub_self, ofNat_zero]
-
-/- # Additive group properties -/
-
-/- addition -/
-
-protected theorem add_comm : ∀ a b : Int, a + b = b + a
-  | ofNat n, ofNat m => by simp [Nat.add_comm]
-  | ofNat _, -[_+1]  => rfl
-  | -[_+1],  ofNat _ => rfl
-  | -[_+1],  -[_+1]  => by simp [Nat.add_comm]
-
-instance : Std.Commutative (α := Int) (· + ·) := ⟨Int.add_comm⟩
-
-@[simp] protected theorem add_zero : ∀ a : Int, a + 0 = a
-  | ofNat _ => rfl
-  | -[_+1]  => rfl
-
-@[simp] protected theorem zero_add (a : Int) : 0 + a = a := Int.add_comm .. ▸ a.add_zero
-instance : Std.LawfulIdentity (α := Int) (· + ·) 0 where
-  left_id := Int.zero_add
-  right_id := Int.add_zero
-
-theorem ofNat_add_negSucc_of_lt (h : m < n.succ) : ofNat m + -[n+1] = -[n - m+1] :=
-  show subNatNat .. = _ by simp [succ_sub (le_of_lt_succ h), subNatNat]
-
 protected theorem add_assoc : ∀ a b c : Int, a + b + c = a + (b + c)
   | (m:Nat), (n:Nat), _ => aux1 ..
   | Nat.cast m, b, Nat.cast k => by
@@ -232,12 +222,18 @@ protected theorem add_right_comm (a b c : Int) : a + b + c = a + c + b := by
 
 /- ## negation -/
 
-protected theorem add_left_neg : ∀ a : Int, -a + a = 0
+theorem subNatNat_self : ∀ n, subNatNat n n = 0
   | 0      => rfl
-  | succ m => by simp [neg_ofNat_succ]
-  | -[m+1] => by simp [neg_negSucc]
+  | succ m => by rw [subNatNat_of_sub_eq_zero (Nat.sub_self ..), Nat.sub_self, ofNat_zero]
 
-protected theorem add_right_neg (a : Int) : a + -a = 0 := by
+attribute [local simp] subNatNat_self
+
+@[local simp] protected theorem add_left_neg : ∀ a : Int, -a + a = 0
+  | 0      => rfl
+  | succ m => by simp
+  | -[m+1] => by simp
+
+@[local simp] protected theorem add_right_neg (a : Int) : a + -a = 0 := by
   rw [Int.add_comm, Int.add_left_neg]
 
 protected theorem neg_eq_of_add_eq_zero {a b : Int} (h : a + b = 0) : -a = b := by
@@ -268,22 +264,11 @@ protected theorem add_left_cancel {a b c : Int} (h : a + b = a + c) : b = c := b
   have h₁ : -a + (a + b) = -a + (a + c) := by rw [h]
   simp [← Int.add_assoc, Int.add_left_neg, Int.zero_add] at h₁; exact h₁
 
-protected theorem neg_add {a b : Int} : -(a + b) = -a + -b := by
+@[local simp] protected theorem neg_add {a b : Int} : -(a + b) = -a + -b := by
   apply Int.add_left_cancel (a := a + b)
   rw [Int.add_right_neg, Int.add_comm a, ← Int.add_assoc, Int.add_assoc b,
     Int.add_right_neg, Int.add_zero, Int.add_right_neg]
 
-/--
-If a predicate on the integers is invariant under negation,
-then it is sufficient to prove it for the nonnegative integers.
--/
-theorem wlog_sign {P : Int → Prop} (inv : ∀ i, P i ↔ P (-i)) (w : ∀ n : Nat, P n) (i : Int) : P i := by
-  cases i with
-  | ofNat n => exact w n
-  | negSucc n =>
-    rw [negSucc_eq, ← inv, ← ofNat_succ]
-    apply w
-
 /- ## subtraction -/
 
 @[simp] theorem negSucc_sub_one (n : Nat) : -[n+1] - 1 = -[n + 1 +1] := rfl
@@ -307,13 +292,13 @@ protected theorem sub_eq_zero {a b : Int} : a - b = 0 ↔ a = b :=
   ⟨Int.eq_of_sub_eq_zero, Int.sub_eq_zero_of_eq⟩
 
 protected theorem sub_sub (a b c : Int) : a - b - c = a - (b + c) := by
-  simp [Int.sub_eq_add_neg, Int.add_assoc, Int.neg_add]
+  simp [Int.sub_eq_add_neg, Int.add_assoc]
 
 protected theorem neg_sub (a b : Int) : -(a - b) = b - a := by
-  simp [Int.sub_eq_add_neg, Int.add_comm, Int.neg_add]
+  simp [Int.sub_eq_add_neg, Int.add_comm]
 
 protected theorem sub_sub_self (a b : Int) : a - (a - b) = b := by
-  simp [Int.sub_eq_add_neg, ← Int.add_assoc, Int.neg_add, Int.add_right_neg]
+  simp [Int.sub_eq_add_neg, ← Int.add_assoc]
 
 @[simp] protected theorem sub_neg (a b : Int) : a - -b = a + b := by simp [Int.sub_eq_add_neg]
 
@@ -324,7 +309,7 @@ protected theorem sub_sub_self (a b : Int) : a - (a - b) = b := by
   Int.add_neg_cancel_right a b
 
 protected theorem add_sub_assoc (a b c : Int) : a + b - c = a + (b - c) := by
-  rw [Int.sub_eq_add_neg, Int.add_assoc, Int.add_neg_eq_sub]
+  rw [Int.sub_eq_add_neg, Int.add_assoc, ← Int.sub_eq_add_neg]
 
 @[norm_cast] theorem ofNat_sub (h : m ≤ n) : ((n - m : Nat) : Int) = n - m := by
   match m with
@@ -333,7 +318,6 @@ protected theorem add_sub_assoc (a b c : Int) : a + b - c = a + (b - c) := by
     show ofNat (n - succ m) = subNatNat n (succ m)
     rw [subNatNat, Nat.sub_eq_zero_of_le h]
 
-@[deprecated negSucc_eq (since := "2025-03-11")]
 theorem negSucc_coe' (n : Nat) : -[n+1] = -↑n - 1 := by
   rw [Int.sub_eq_add_neg, ← Int.neg_add]; rfl
 
@@ -343,11 +327,11 @@ protected theorem subNatNat_eq_coe {m n : Nat} : subNatNat m n = ↑m - ↑n :=
     rw [Int.ofNat_add, Int.sub_eq_add_neg, Int.add_assoc, Int.add_left_comm,
       Int.add_right_neg, Int.add_zero]
   · intros i n
-    simp only [negSucc_eq, ofNat_add, ofNat_one, Int.sub_eq_add_neg, Int.neg_add, ← Int.add_assoc]
-    rw [Int.add_neg_eq_sub (a := n), ← ofNat_sub, Nat.sub_self, ofNat_zero, Int.zero_add]
+    simp only [negSucc_coe, ofNat_add, Int.sub_eq_add_neg, Int.neg_add, ← Int.add_assoc]
+    rw [← @Int.sub_eq_add_neg n, ← ofNat_sub, Nat.sub_self, ofNat_zero, Int.zero_add]
     apply Nat.le_refl
 
-@[simp] theorem toNat_sub (m n : Nat) : toNat (m - n) = m - n := by
+theorem toNat_sub (m n : Nat) : toNat (m - n) = m - n := by
   rw [← Int.subNatNat_eq_coe]
   refine subNatNat_elim m n (fun m n i => toNat i = m - n) (fun i n => ?_) (fun i n => ?_)
   · exact (Nat.add_sub_cancel_left ..).symm
@@ -363,9 +347,6 @@ theorem toNat_of_nonpos : ∀ {z : Int}, z ≤ 0 → z.toNat = 0
   norm_cast
   simp [eq_comm]
 
-@[simp] theorem negSucc_eq_neg_ofNat_iff {a b : Nat} : -[a+1] = - (b : Int) ↔ a + 1 = b := by
-  rw [eq_comm, neg_ofNat_eq_negSucc_iff, eq_comm]
-
 @[simp] theorem neg_ofNat_eq_negSucc_add_one_iff {a b : Nat} : - (a : Int) = -[b+1] + 1 ↔ a = b := by
   cases b with
   | zero => simp; norm_cast
@@ -374,33 +355,30 @@ theorem toNat_of_nonpos : ∀ {z : Int}, z ≤ 0 → z.toNat = 0
     norm_cast
     simp [eq_comm]
 
-@[simp] theorem negSucc_add_one_eq_neg_ofNat_iff {a b : Nat} : -[a+1] + 1 = - (b : Int) ↔ a = b := by
-  rw [eq_comm, neg_ofNat_eq_negSucc_add_one_iff, eq_comm]
-
 /- ## add/sub injectivity -/
 
-@[simp] protected theorem add_left_inj {i j : Int} (k : Int) : (i + k = j + k) ↔ i = j := by
+protected theorem add_left_inj {i j : Int} (k : Int) : (i + k = j + k) ↔ i = j := by
   apply Iff.intro
   · intro p
     rw [←Int.add_sub_cancel i k, ←Int.add_sub_cancel j k, p]
   · exact congrArg (· + k)
 
-@[simp] protected theorem add_right_inj {i j : Int} (k : Int) : (k + i = k + j) ↔ i = j := by
+protected theorem add_right_inj {i j : Int} (k : Int) : (k + i = k + j) ↔ i = j := by
   simp [Int.add_comm k, Int.add_left_inj]
 
-@[simp] protected theorem sub_right_inj {i j : Int} (k : Int) : (k - i = k - j) ↔ i = j := by
+protected theorem sub_right_inj {i j : Int} (k : Int) : (k - i = k - j) ↔ i = j := by
   simp [Int.sub_eq_add_neg, Int.neg_inj, Int.add_right_inj]
 
-@[simp] protected theorem sub_left_inj {i j : Int} (k : Int) : (i - k = j - k) ↔ i = j := by
+protected theorem sub_left_inj {i j : Int} (k : Int) : (i - k = j - k) ↔ i = j := by
   simp [Int.sub_eq_add_neg, Int.add_left_inj]
 
 /- ## Ring properties -/
 
-theorem ofNat_mul_negSucc (m n : Nat) : (m : Int) * -[n+1] = -↑(m * succ n) := rfl
+@[simp] theorem ofNat_mul_negSucc (m n : Nat) : (m : Int) * -[n+1] = -↑(m * succ n) := rfl
 
-theorem negSucc_mul_ofNat (m n : Nat) : -[m+1] * n = -↑(succ m * n) := rfl
+@[simp] theorem negSucc_mul_ofNat (m n : Nat) : -[m+1] * n = -↑(succ m * n) := rfl
 
-theorem negSucc_mul_negSucc (m n : Nat) : -[m+1] * -[n+1] = succ m * succ n := rfl
+@[simp] theorem negSucc_mul_negSucc (m n : Nat) : -[m+1] * -[n+1] = succ m * succ n := rfl
 
 protected theorem mul_comm (a b : Int) : a * b = b * a := by
   cases a <;> cases b <;> simp [Nat.mul_comm]
@@ -418,10 +396,11 @@ theorem negSucc_mul_negOfNat (m n : Nat) : -[m+1] * negOfNat n = ofNat (succ m *
 theorem negOfNat_mul_negSucc (m n : Nat) : negOfNat n * -[m+1] = ofNat (n * succ m) := by
   rw [Int.mul_comm, negSucc_mul_negOfNat, Nat.mul_comm]
 
-protected theorem mul_assoc (a b c : Int) : a * b * c = a * (b * c) := by
-  cases a <;> cases b <;> cases c <;>
-    simp [Nat.mul_assoc, ofNat_mul_negOfNat, negOfNat_mul_ofNat, negSucc_mul_negOfNat, negOfNat_mul_negSucc]
+attribute [local simp] ofNat_mul_negOfNat negOfNat_mul_ofNat
+  negSucc_mul_negOfNat negOfNat_mul_negSucc
 
+protected theorem mul_assoc (a b c : Int) : a * b * c = a * (b * c) := by
+  cases a <;> cases b <;> cases c <;> simp [Nat.mul_assoc]
 instance : Std.Associative (α := Int) (· * ·) := ⟨Int.mul_assoc⟩
 
 protected theorem mul_left_comm (a b c : Int) : a * (b * c) = b * (a * c) := by
@@ -439,7 +418,7 @@ theorem negOfNat_eq_subNatNat_zero (n) : negOfNat n = subNatNat 0 n := by cases
 theorem ofNat_mul_subNatNat (m n k : Nat) :
     m * subNatNat n k = subNatNat (m * n) (m * k) := by
   cases m with
-  | zero => simp [ofNat_zero, Int.zero_mul, Nat.zero_mul, subNatNat_self]
+  | zero => simp [ofNat_zero, Int.zero_mul, Nat.zero_mul]
   | succ m => cases n.lt_or_ge k with
     | inl h =>
       have h' : succ m * n < succ m * k := Nat.mul_lt_mul_of_pos_left h (Nat.succ_pos m)
@@ -467,7 +446,8 @@ theorem negSucc_mul_subNatNat (m n k : Nat) :
         Nat.mul_sub_left_distrib, ← succ_pred_eq_of_pos (Nat.sub_pos_of_lt h₁)]; rfl
     | inr h' => rw [Nat.le_antisymm h h', subNatNat_self, subNatNat_self, Int.mul_zero]
 
-attribute [local simp] ofNat_mul_subNatNat negOfNat_add negSucc_mul_subNatNat in
+attribute [local simp] ofNat_mul_subNatNat negOfNat_add negSucc_mul_subNatNat
+
 protected theorem mul_add : ∀ a b c : Int, a * (b + c) = a * b + a * c
   | (m:Nat), (n:Nat), (k:Nat) => by simp [Nat.left_distrib]
   | (m:Nat), (n:Nat), -[k+1]  => by
@@ -490,23 +470,21 @@ protected theorem neg_mul_eq_neg_mul (a b : Int) : -(a * b) = -a * b :=
 protected theorem neg_mul_eq_mul_neg (a b : Int) : -(a * b) = a * -b :=
   Int.neg_eq_of_add_eq_zero <| by rw [← Int.mul_add, Int.add_right_neg, Int.mul_zero]
 
--- Note, this is not a `@[simp]` lemma because it interferes with normalization in `simp +arith`.
-protected theorem neg_mul (a b : Int) : -a * b = -(a * b) :=
+@[simp] protected theorem neg_mul (a b : Int) : -a * b = -(a * b) :=
   (Int.neg_mul_eq_neg_mul a b).symm
 
--- Note, this is not a `@[simp]` lemma because it interferes with normalization in `simp +arith`.
-protected theorem mul_neg (a b : Int) : a * -b = -(a * b) :=
+@[simp] protected theorem mul_neg (a b : Int) : a * -b = -(a * b) :=
   (Int.neg_mul_eq_mul_neg a b).symm
 
-protected theorem neg_mul_neg (a b : Int) : -a * -b = a * b := by simp [Int.neg_mul, Int.mul_neg]
+protected theorem neg_mul_neg (a b : Int) : -a * -b = a * b := by simp
 
-protected theorem neg_mul_comm (a b : Int) : -a * b = a * -b := by simp [Int.neg_mul, Int.mul_neg]
+protected theorem neg_mul_comm (a b : Int) : -a * b = a * -b := by simp
 
 protected theorem mul_sub (a b c : Int) : a * (b - c) = a * b - a * c := by
-  simp [Int.sub_eq_add_neg, Int.mul_add, Int.mul_neg]
+  simp [Int.sub_eq_add_neg, Int.mul_add]
 
 protected theorem sub_mul (a b c : Int) : (a - b) * c = a * c - b * c := by
-  simp [Int.sub_eq_add_neg, Int.add_mul, Int.neg_mul]
+  simp [Int.sub_eq_add_neg, Int.add_mul]
 
 @[simp] protected theorem one_mul : ∀ a : Int, 1 * a = a
   | ofNat n => show ofNat (1 * n) = ofNat n by rw [Nat.one_mul]
@@ -517,9 +495,7 @@ instance : Std.LawfulIdentity (α := Int) (· * ·) 1 where
   left_id := Int.one_mul
   right_id := Int.mul_one
 
-@[simp] protected theorem mul_neg_one (a : Int) : a * -1 = -a := by rw [Int.mul_neg, Int.mul_one]
-
-@[simp] protected theorem neg_one_mul (a : Int) : -1 * a = -a := by rw [Int.neg_mul, Int.one_mul]
+protected theorem mul_neg_one (a : Int) : a * -1 = -a := by rw [Int.mul_neg, Int.mul_one]
 
 protected theorem neg_eq_neg_one_mul : ∀ a : Int, -a = -1 * a
   | 0      => rfl
@@ -568,18 +544,16 @@ The following lemmas are later subsumed by e.g. `Nat.cast_add` and `Nat.cast_mul
 but it is convenient to have these earlier, for users who only need `Nat` and `Int`.
 -/
 
-protected theorem natCast_zero : ((0 : Nat) : Int) = (0 : Int) := rfl
+theorem natCast_zero : ((0 : Nat) : Int) = (0 : Int) := rfl
 
-protected theorem natCast_one : ((1 : Nat) : Int) = (1 : Int) := rfl
+theorem natCast_one : ((1 : Nat) : Int) = (1 : Int) := rfl
 
-@[simp] protected theorem natCast_add (a b : Nat) : ((a + b : Nat) : Int) = (a : Int) + (b : Int) := by
+@[simp] theorem natCast_add (a b : Nat) : ((a + b : Nat) : Int) = (a : Int) + (b : Int) := by
   -- Note this only works because of local simp attributes in this file,
   -- so it still makes sense to tag the lemmas with `@[simp]`.
   simp
 
-protected theorem natCast_succ (n : Nat) : ((n + 1 : Nat) : Int) = (n : Int) + 1 := rfl
-
-@[simp] protected theorem natCast_mul (a b : Nat) : ((a * b : Nat) : Int) = (a : Int) * (b : Int) := by
+@[simp] theorem natCast_mul (a b : Nat) : ((a * b : Nat) : Int) = (a : Int) * (b : Int) := by
   simp
 
 end Int

src/Init/Data/Int/LemmasAux.lean

@@ -15,35 +15,6 @@ import Init.Omega
 
 namespace Int
 
-/-! ### miscellaneous lemmas -/
-
-@[simp] theorem natCast_le_zero : {n : Nat} → (n : Int) ≤ 0 ↔ n = 0 := by omega
-
-protected theorem sub_eq_iff_eq_add {b a c : Int} : a - b = c ↔ a = c + b := by omega
-protected theorem sub_eq_iff_eq_add' {b a c : Int} : a - b = c ↔ a = b + c := by omega
-
-@[simp] protected theorem neg_nonpos_iff (i : Int) : -i ≤ 0 ↔ 0 ≤ i := by omega
-
-@[simp] theorem zero_le_ofNat (n : Nat) : 0 ≤ ((no_index (OfNat.ofNat n)) : Int) :=
-  ofNat_nonneg _
-
-@[simp] theorem neg_natCast_le_natCast (n m : Nat) : -(n : Int) ≤ (m : Int) :=
-  Int.le_trans (by simp) (ofNat_zero_le m)
-
-@[simp] theorem neg_natCast_le_ofNat (n m : Nat) : -(n : Int) ≤ (no_index (OfNat.ofNat m)) :=
-  Int.le_trans (by simp) (ofNat_zero_le m)
-
-@[simp] theorem neg_ofNat_le_ofNat (n m : Nat) : -(no_index (OfNat.ofNat n)) ≤ (no_index (OfNat.ofNat m)) :=
-  Int.le_trans (by simp) (ofNat_zero_le m)
-
-@[simp] theorem neg_ofNat_le_natCast (n m : Nat) : -(no_index (OfNat.ofNat n)) ≤ (m : Int) :=
-  Int.le_trans (by simp) (ofNat_zero_le m)
-
-theorem neg_lt_self_iff {n : Int} : -n < n ↔ 0 < n := by
-  omega
-
-/-! ### toNat -/
-
 @[simp] theorem toNat_sub' (a : Int) (b : Nat) : (a - b).toNat = a.toNat - b := by
   symm
   simp only [Int.toNat]
@@ -68,21 +39,17 @@ theorem neg_lt_self_iff {n : Int} : -n < n ↔ 0 < n := by
   simp [toNat]
   split <;> simp_all <;> omega
 
+theorem bmod_neg_iff {m : Nat} {x : Int} (h2 : -m ≤ x) (h1 : x < m) :
+    (x.bmod m) < 0 ↔ (-(m / 2) ≤ x ∧ x < 0) ∨ ((m + 1) / 2 ≤ x) := by
+  simp only [Int.bmod_def]
+  by_cases xpos : 0 ≤ x
+  · rw [Int.emod_eq_of_lt xpos (by omega)]; omega
+  · rw [Int.add_emod_self.symm, Int.emod_eq_of_lt (by omega) (by omega)]; omega
+
+@[simp] theorem natCast_le_zero : {n : Nat} → (n : Int) ≤ 0 ↔ n = 0 := by omega
+
 @[simp] theorem toNat_eq_zero : ∀ {n : Int}, n.toNat = 0 ↔ n ≤ 0 := by omega
 
-@[simp] theorem toNat_le {m : Int} {n : Nat} : m.toNat ≤ n ↔ m ≤ n := by omega
-@[simp] theorem toNat_lt' {m : Int} {n : Nat} (hn : 0 < n) : m.toNat < n ↔ m < n := by omega
-
-theorem pos_iff_toNat_pos {n : Int} : 0 < n ↔ 0 < n.toNat := by
-  omega
-
-theorem ofNat_toNat_eq_self {a : Int} : a.toNat = a ↔ 0 ≤ a := by omega
-theorem eq_ofNat_toNat {a : Int} : a = a.toNat ↔ 0 ≤ a := by omega
-theorem toNat_le_toNat {n m : Int} (h : n ≤ m) : n.toNat ≤ m.toNat := by omega
-theorem toNat_lt_toNat {n m : Int} (hn : 0 < m) : n.toNat < m.toNat ↔ n < m := by omega
-
-/-! ### natAbs -/
-
 theorem eq_zero_of_dvd_of_natAbs_lt_natAbs {d n : Int} (h : d ∣ n) (h₁ : n.natAbs < d.natAbs) :
     n = 0 := by
   obtain ⟨a, rfl⟩ := h
@@ -90,53 +57,6 @@ theorem eq_zero_of_dvd_of_natAbs_lt_natAbs {d n : Int} (h : d ∣ n) (h₁ : n.n
   suffices ¬ 0 < a.natAbs by simp [Int.natAbs_eq_zero.1 (Nat.eq_zero_of_not_pos this)]
   exact fun h => Nat.lt_irrefl _ (Nat.lt_of_le_of_lt (Nat.le_mul_of_pos_right d.natAbs h) h₁)
 
-/-! ### min and max -/
-
-@[simp] protected theorem min_assoc : ∀ (a b c : Int), min (min a b) c = min a (min b c) := by omega
-instance : Std.Associative (α := Nat) min := ⟨Nat.min_assoc⟩
-
-@[simp] protected theorem min_self_assoc {m n : Int} : min m (min m n) = min m n := by
-  rw [← Int.min_assoc, Int.min_self]
-
-@[simp] protected theorem min_self_assoc' {m n : Int} : min n (min m n) = min n m := by
-  rw [Int.min_comm m n, ← Int.min_assoc, Int.min_self]
-
-@[simp] protected theorem max_assoc (a b c : Int) : max (max a b) c = max a (max b c) := by omega
-instance : Std.Associative (α := Nat) max := ⟨Nat.max_assoc⟩
-
-@[simp] protected theorem max_self_assoc {m n : Int} : max m (max m n) = max m n := by
-  rw [← Int.max_assoc, Int.max_self]
-
-@[simp] protected theorem max_self_assoc' {m n : Int} : max n (max m n) = max n m := by
-  rw [Int.max_comm m n, ← Int.max_assoc, Int.max_self]
-
-protected theorem max_min_distrib_left (a b c : Int) : max a (min b c) = min (max a b) (max a c) := by omega
-
-protected theorem min_max_distrib_left (a b c : Int) : min a (max b c) = max (min a b) (min a c) := by omega
-
-protected theorem max_min_distrib_right (a b c : Int) :
-    max (min a b) c = min (max a c) (max b c) := by omega
-
-protected theorem min_max_distrib_right (a b c : Int) :
-    min (max a b) c = max (min a c) (min b c) := by omega
-
-protected theorem sub_min_sub_right (a b c : Int) : min (a - c) (b - c) = min a b - c := by omega
-
-protected theorem sub_max_sub_right (a b c : Int) : max (a - c) (b - c) = max a b - c := by omega
-
-protected theorem sub_min_sub_left (a b c : Int) : min (a - b) (a - c) = a - max b c := by omega
-
-protected theorem sub_max_sub_left (a b c : Int) : max (a - b) (a - c) = a - min b c := by omega
-
-/-! ### bmod -/
-
-theorem bmod_neg_iff {m : Nat} {x : Int} (h2 : -m ≤ x) (h1 : x < m) :
-    (x.bmod m) < 0 ↔ (-(m / 2) ≤ x ∧ x < 0) ∨ ((m + 1) / 2 ≤ x) := by
-  simp only [Int.bmod_def]
-  by_cases xpos : 0 ≤ x
-  · rw [Int.emod_eq_of_lt xpos (by omega)]; omega
-  · rw [Int.add_emod_self.symm, Int.emod_eq_of_lt (by omega) (by omega)]; omega
-
 theorem bmod_eq_self_of_le {n : Int} {m : Nat} (hn' : -(m / 2) ≤ n) (hn : n < (m + 1) / 2) :
     n.bmod m = n := by
   rw [← Int.sub_eq_zero]
@@ -145,10 +65,4 @@ theorem bmod_eq_self_of_le {n : Int} {m : Nat} (hn' : -(m / 2) ≤ n) (hn : n <
   apply eq_zero_of_dvd_of_natAbs_lt_natAbs Int.dvd_bmod_sub_self
   omega
 
-theorem bmod_bmod_of_dvd {a : Int} {n m : Nat} (hnm : n ∣ m) :
-    (a.bmod m).bmod n = a.bmod n := by
-  rw [← Int.sub_eq_iff_eq_add.2 (bmod_add_bdiv a m).symm]
-  obtain ⟨k, rfl⟩ := hnm
-  simp [Int.mul_assoc]
-
 end Int

src/Init/Data/Int/Linear.lean

@@ -187,13 +187,14 @@ theorem cmod_gt_of_pos (a : Int) {b : Int} (h : 0 < b) : cmod a b > -b :=
 
 theorem cmod_nonpos (a : Int) {b : Int} (h : b ≠ 0) : cmod a b ≤ 0 := by
   have := Int.neg_le_neg (Int.emod_nonneg (-a) h)
-  simpa [cmod] using this
+  simp at this
+  assumption
 
 theorem cmod_eq_zero_iff_emod_eq_zero (a b : Int) : cmod a b = 0 ↔ a%b = 0 := by
   unfold cmod
   have := @Int.emod_eq_emod_iff_emod_sub_eq_zero  b b a
   simp at this
-  simp [Int.neg_emod_eq_sub_emod, ← this, Eq.comm]
+  simp [Int.neg_emod, ← this, Eq.comm]
 
 private abbrev div_mul_cancel_of_mod_zero :=
   @Int.ediv_mul_cancel_of_emod_eq_zero
@@ -250,24 +251,14 @@ def Poly.divCoeffs (k : Int) : Poly → Bool
 /--
 `p.mul k` multiplies all coefficients and constant of the polynomial `p` by `k`.
 -/
-def Poly.mul' (p : Poly) (k : Int) : Poly :=
+def Poly.mul (p : Poly) (k : Int) : Poly :=
   match p with
   | .num k' => .num (k*k')
-  | .add k' v p => .add (k*k') v (mul' p k)
-
-def Poly.mul (p : Poly) (k : Int) : Poly :=
-  if k == 0 then
-    .num 0
-  else
-    p.mul' k
+  | .add k' v p => .add (k*k') v (mul p k)
 
 @[simp] theorem Poly.denote_mul (ctx : Context) (p : Poly) (k : Int) : (p.mul k).denote ctx = k * p.denote ctx := by
-  simp [mul]
-  split
-  next => simp [*, denote]
-  next =>
-    induction p <;> simp [mul', denote, *]
-    rw [Int.mul_assoc, Int.mul_add]
+  induction p <;> simp [mul, denote, *]
+  rw [Int.mul_assoc, Int.mul_add]
 
 attribute [local simp] Int.add_comm Int.add_assoc Int.add_left_comm Int.add_mul Int.mul_add
 attribute [local simp] Poly.insert Poly.denote Poly.norm Poly.addConst
@@ -320,6 +311,7 @@ theorem Poly.denote_div_eq_of_divAll (ctx : Context) (p : Poly) (k : Int) : p.di
     replace h₁ := div_mul_cancel_of_mod_zero h₁
     have ih := ih h₂
     simp [ih]
+    apply congrArg (denote ctx p + ·)
     rw [Int.mul_right_comm, h₁]
 
 attribute [local simp] Poly.divCoeffs Poly.getConst
@@ -361,7 +353,7 @@ theorem Expr.denote_toPoly'_go (ctx : Context) (e : Expr) :
     simp only [mul_def, denote]
     rw [Int.mul_comm (denote _ _) _]
     simpa [Int.mul_assoc] using ih
-  | case10 k a ih => simp [toPoly'.go, ih, Int.neg_mul, Int.mul_neg]
+  | case10 k a ih => simp [toPoly'.go, ih]
 
 theorem Expr.denote_norm (ctx : Context) (e : Expr) : e.norm.denote ctx = e.denote ctx := by
   simp [norm, toPoly', Expr.denote_toPoly'_go]
@@ -419,7 +411,7 @@ theorem norm_eq_var_const (ctx : Context) (lhs rhs : Expr) (x : Var) (k : Int) (
   simp [norm_eq_var_const_cert] at h
   replace h := congrArg (Poly.denote ctx) h
   simp at h
-  rw [←Int.sub_eq_zero, h, Int.add_comm, Int.add_neg_eq_sub, Int.sub_eq_zero]
+  rw [←Int.sub_eq_zero, h, Int.add_comm, ← Int.sub_eq_add_neg, Int.sub_eq_zero]
 
 private theorem mul_eq_zero_iff (a k : Int) (h₁ : k > 0) : k * a = 0 ↔ a = 0 := by
   conv => lhs; rw [← Int.mul_zero k]
@@ -798,10 +790,10 @@ theorem dvd_solve_elim (ctx : Context) (d₁ : Int) (p₁ : Poly) (d₂ : Int) (
   simp [dvd_solve_elim_cert]
   split <;> simp
   next a₁ x₁ p₁ a₂ x₂ p₂ =>
-  intro _ hd _; subst x₁ p; simp [Int.neg_mul]
+  intro _ hd _; subst x₁ p; simp
   intro h₁ h₂
   rw [Int.add_comm] at h₁ h₂
-  rw [Int.add_neg_eq_sub]
+  rw [← Int.sub_eq_add_neg]
   exact dvd_solve_elim' hd h₁ h₂
 
 theorem dvd_norm (ctx : Context) (d : Int) (p₁ p₂ : Poly) : p₁.norm == p₂ → d ∣ p₁.denote' ctx → d ∣ p₂.denote' ctx := by
@@ -854,26 +846,6 @@ theorem le_combine (ctx : Context) (p₁ p₂ p₃ : Poly)
   · rw [← Int.zero_mul (Poly.denote ctx p₂)]; apply Int.mul_le_mul_of_nonpos_right <;> simp [*]
   · rw [← Int.zero_mul (Poly.denote ctx p₁)]; apply Int.mul_le_mul_of_nonpos_right <;> simp [*]
 
-def le_combine_coeff_cert (p₁ p₂ p₃ : Poly) (k : Int) : Bool :=
-  let a₁ := p₁.leadCoeff.natAbs
-  let a₂ := p₂.leadCoeff.natAbs
-  let p  := p₁.mul a₂ |>.combine (p₂.mul a₁)
-  k > 0 && (p.divCoeffs k && p₃ == p.div k)
-
-theorem le_combine_coeff (ctx : Context) (p₁ p₂ p₃ : Poly) (k : Int)
-    : le_combine_coeff_cert p₁ p₂ p₃ k → p₁.denote' ctx ≤ 0 → p₂.denote' ctx ≤ 0 → p₃.denote' ctx ≤ 0 := by
-  simp only [le_combine_coeff_cert, gt_iff_lt, Bool.and_eq_true, decide_eq_true_eq, beq_iff_eq, and_imp]
-  let a₁ := p₁.leadCoeff.natAbs
-  let a₂ := p₂.leadCoeff.natAbs
-  generalize h : (p₁.mul a₂ |>.combine (p₂.mul a₁)) = p
-  intro h₁ h₂ h₃ h₄ h₅
-  have := le_combine ctx p₁ p₂ p
-  simp only [le_combine_cert, beq_iff_eq] at this
-  have aux₁ := this h.symm h₄ h₅
-  have := le_coeff ctx p p₃ k
-  simp only [le_coeff_cert, gt_iff_lt, Bool.and_eq_true, decide_eq_true_eq, beq_iff_eq, and_imp] at this
-  exact this h₁ h₂ h₃ aux₁
-
 theorem le_unsat (ctx : Context) (p : Poly) : p.isUnsatLe → p.denote' ctx ≤ 0 → False := by
   simp [Poly.isUnsatLe]; split <;> simp
 
@@ -908,7 +880,7 @@ def Poly.coeff (p : Poly) (x : Var) : Int :=
   | .num _ => 0
 
 private theorem eq_add_coeff_insert (ctx : Context) (p : Poly) (x : Var) : p.denote ctx = (p.coeff x) * (x.denote ctx) + (p.insert (-p.coeff x) x).denote ctx := by
-  simp; rw [← Int.add_assoc, Int.neg_mul, Int.add_neg_cancel_right]
+  simp; rw [← Int.add_assoc, Int.add_neg_cancel_right]
 
 private theorem dvd_of_eq' {a x p : Int} : a*x + p = 0 → a ∣ p := by
   intro h
@@ -977,7 +949,7 @@ theorem eq_dvd_subst (ctx : Context) (x : Var) (p₁ : Poly) (d₂ : Int) (p₂
   have := eq_dvd_subst' h₁ h₂
   rw [Int.sub_eq_add_neg, Int.add_comm] at this
   apply abs_dvd
-  simp [this, Int.neg_mul]
+  simp [this]
 
 def eq_eq_subst_cert (x : Var) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly) : Bool :=
   let a := p₁.coeff x
@@ -1017,8 +989,10 @@ theorem eq_le_subst_nonpos (ctx : Context) (x : Var) (p₁ : Poly) (p₂ : Poly)
   intro h
   intro; subst p₃
   intro h₁ h₂
-  simp [*, -Int.neg_nonpos_iff, Int.neg_mul]
+  simp [*]
   replace h₂ := Int.mul_le_mul_of_nonpos_left h₂ h; simp at h₂; clear h
+  rw [← Int.neg_zero]
+  apply Int.neg_le_neg
   rw [Int.mul_comm]
   assumption
 
@@ -1029,7 +1003,7 @@ theorem eq_of_core (ctx : Context) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly)
     : eq_of_core_cert p₁ p₂ p₃ → p₁.denote' ctx = p₂.denote' ctx → p₃.denote' ctx = 0 := by
   simp [eq_of_core_cert]
   intro; subst p₃; simp
-  intro h; rw [h, Int.add_neg_eq_sub, Int.sub_self]
+  intro h; rw [h, ←Int.sub_eq_add_neg, Int.sub_self]
 
 def Poly.isUnsatDiseq (p : Poly) : Bool :=
   match p with
@@ -1069,7 +1043,7 @@ theorem diseq_of_core (ctx : Context) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly)
   simp [eq_of_core_cert]
   intro; subst p₃; simp
   intro h; rw [← Int.sub_eq_zero] at h
-  rw [Int.add_neg_eq_sub]; assumption
+  rw [←Int.sub_eq_add_neg]; assumption
 
 def eq_of_le_ge_cert (p₁ p₂ : Poly) : Bool :=
   p₂ == p₁.mul (-1)
@@ -1077,8 +1051,9 @@ def eq_of_le_ge_cert (p₁ p₂ : Poly) : Bool :=
 theorem eq_of_le_ge (ctx : Context) (p₁ : Poly) (p₂ : Poly)
     : eq_of_le_ge_cert p₁ p₂ → p₁.denote' ctx ≤ 0 → p₂.denote' ctx ≤ 0 → p₁.denote' ctx = 0 := by
   simp [eq_of_le_ge_cert]
-  intro; subst p₂; simp [-Int.neg_nonpos_iff]
+  intro; subst p₂; simp
   intro h₁ h₂
+  replace h₂ := Int.neg_le_of_neg_le h₂; simp at h₂
   simp [Int.eq_iff_le_and_ge, *]
 
 def le_of_le_diseq_cert (p₁ : Poly) (p₂ : Poly) (p₃ : Poly) : Bool :=
@@ -1127,16 +1102,6 @@ theorem orOver_resolve {n p} : OrOver (n+1) p → ¬ p n → OrOver n p := by
   · contradiction
   · assumption
 
-def OrOver_cases_type (n : Nat) (p : Nat → Prop) : Prop :=
-  match n with
-  | 0 => p 0
-  | n+1 => ¬ p (n+1) → OrOver_cases_type n p
-
-theorem orOver_cases {n p} : OrOver (n+1) p → OrOver_cases_type n p := by
-  induction n <;> simp [OrOver_cases_type]
-  next => exact orOver_one
-  next n ih => intro h₁ h₂; exact ih (orOver_resolve h₁ h₂)
-
 private theorem orOver_of_p {i n p} (h₁ : i < n) (h₂ : p i) : OrOver n p := by
   induction n
   next => simp at h₁
@@ -1153,10 +1118,12 @@ private theorem orOver_of_exists {n p} : (∃ k, k < n ∧ p k) → OrOver n p :
 private theorem ofNat_toNat {a : Int} : a ≥ 0 → Int.ofNat a.toNat = a := by cases a <;> simp
 private theorem cast_toNat {a : Int} : a ≥ 0 → a.toNat = a := by cases a <;> simp
 private theorem ofNat_lt {a : Int} {n : Nat} : a ≥ 0 → a < Int.ofNat n → a.toNat < n := by cases a <;> simp
-private theorem lcm_neg_left (a b : Int) : Int.lcm (-a) b = Int.lcm a b := by simp [Int.lcm]
-private theorem lcm_neg_right (a b : Int) : Int.lcm a (-b) = Int.lcm a b := by simp [Int.lcm]
-private theorem gcd_zero (a : Int) : Int.gcd a 0 = a.natAbs := by simp [Int.gcd]
-private theorem lcm_one (a : Int) : Int.lcm a 1 = a.natAbs := by simp [Int.lcm]
+@[local simp] private theorem lcm_neg_left (a b : Int) : Int.lcm (-a) b = Int.lcm a b := by simp [Int.lcm]
+@[local simp] private theorem lcm_neg_right (a b : Int) : Int.lcm a (-b) = Int.lcm a b := by simp [Int.lcm]
+@[local simp] private theorem gcd_neg_left (a b : Int) : Int.gcd (-a) b = Int.gcd a b := by simp [Int.gcd]
+@[local simp] private theorem gcd_neg_right (a b : Int) : Int.gcd a (-b) = Int.gcd a b := by simp [Int.gcd]
+@[local simp] private theorem gcd_zero (a : Int) : Int.gcd a 0 = a.natAbs := by simp [Int.gcd]
+@[local simp] private theorem lcm_one (a : Int) : Int.lcm a 1 = a.natAbs := by simp [Int.lcm]
 
 private theorem cooper_dvd_left_core
     {a b c d s p q x : Int} (a_neg : a < 0) (b_pos : 0 < b) (d_pos : 0 < d)
@@ -1246,7 +1213,7 @@ def cooper_dvd_left_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (b : Int) (p' :
   p₂.leadCoeff == b && p' == p₁.addConst (b*k)
 
 theorem cooper_dvd_left_split_ineq (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (k : Nat) (b : Int) (p' : Poly)
-    : cooper_dvd_left_split ctx p₁ p₂ p₃ d k → cooper_dvd_left_split_ineq_cert p₁ p₂ k b p' → p'.denote' ctx ≤ 0 := by
+    : cooper_dvd_left_split ctx p₁ p₂ p₃ d k → cooper_dvd_left_split_ineq_cert p₁ p₂ k b p' → p'.denote ctx ≤ 0 := by
   simp [cooper_dvd_left_split_ineq_cert, cooper_dvd_left_split]
   intros; subst p' b; simp [denote'_mul_combine_mul_addConst_eq]; assumption
 
@@ -1254,7 +1221,7 @@ def cooper_dvd_left_split_dvd1_cert (p₁ p' : Poly) (a : Int) (k : Int) : Bool
   a == p₁.leadCoeff && p' == p₁.tail.addConst k
 
 theorem cooper_dvd_left_split_dvd1 (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (k : Nat) (a : Int) (p' : Poly)
-    : cooper_dvd_left_split ctx p₁ p₂ p₃ d k → cooper_dvd_left_split_dvd1_cert p₁ p' a k → a ∣ p'.denote' ctx := by
+    : cooper_dvd_left_split ctx p₁ p₂ p₃ d k → cooper_dvd_left_split_dvd1_cert p₁ p' a k → a ∣ p'.denote ctx := by
   simp [cooper_dvd_left_split_dvd1_cert, cooper_dvd_left_split]
   intros; subst a p'; simp; assumption
 
@@ -1267,7 +1234,7 @@ def cooper_dvd_left_split_dvd2_cert (p₁ p₃ : Poly) (d : Int) (k : Nat) (d' :
   d' == a*d && p' == p₂.addConst (c*k)
 
 theorem cooper_dvd_left_split_dvd2 (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (k : Nat) (d' : Int) (p' : Poly)
-    : cooper_dvd_left_split ctx p₁ p₂ p₃ d k → cooper_dvd_left_split_dvd2_cert p₁ p₃ d k d' p' → d' ∣ p'.denote' ctx := by
+    : cooper_dvd_left_split ctx p₁ p₂ p₃ d k → cooper_dvd_left_split_dvd2_cert p₁ p₃ d k d' p' → d' ∣ p'.denote ctx := by
   simp [cooper_dvd_left_split_dvd2_cert, cooper_dvd_left_split]
   intros; subst d' p'; simp; assumption
 
@@ -1328,7 +1295,7 @@ def cooper_left_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (b : Int) (p' : Pol
   p₂.leadCoeff == b && p' == p₁.addConst (b*k)
 
 theorem cooper_left_split_ineq (ctx : Context) (p₁ p₂ : Poly) (k : Nat) (b : Int) (p' : Poly)
-    : cooper_left_split ctx p₁ p₂ k → cooper_left_split_ineq_cert p₁ p₂ k b p' → p'.denote' ctx ≤ 0 := by
+    : cooper_left_split ctx p₁ p₂ k → cooper_left_split_ineq_cert p₁ p₂ k b p' → p'.denote ctx ≤ 0 := by
   simp [cooper_left_split_ineq_cert, cooper_left_split]
   intros; subst p' b; simp [denote'_mul_combine_mul_addConst_eq]; assumption
 
@@ -1336,7 +1303,7 @@ def cooper_left_split_dvd_cert (p₁ p' : Poly) (a : Int) (k : Int) : Bool :=
   a == p₁.leadCoeff && p' == p₁.tail.addConst k
 
 theorem cooper_left_split_dvd (ctx : Context) (p₁ p₂ : Poly) (k : Nat) (a : Int) (p' : Poly)
-    : cooper_left_split ctx p₁ p₂ k → cooper_left_split_dvd_cert p₁ p' a k → a ∣ p'.denote' ctx := by
+    : cooper_left_split ctx p₁ p₂ k → cooper_left_split_dvd_cert p₁ p' a k → a ∣ p'.denote ctx := by
   simp [cooper_left_split_dvd_cert, cooper_left_split]
   intros; subst a p'; simp; assumption
 
@@ -1413,7 +1380,7 @@ def cooper_dvd_right_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (a : Int) (p'
   p₁.leadCoeff == a && p' == p₂.addConst ((-a)*k)
 
 theorem cooper_dvd_right_split_ineq (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (k : Nat) (a : Int) (p' : Poly)
-    : cooper_dvd_right_split ctx p₁ p₂ p₃ d k → cooper_dvd_right_split_ineq_cert p₁ p₂ k a p' → p'.denote' ctx ≤ 0 := by
+    : cooper_dvd_right_split ctx p₁ p₂ p₃ d k → cooper_dvd_right_split_ineq_cert p₁ p₂ k a p' → p'.denote ctx ≤ 0 := by
   simp [cooper_dvd_right_split_ineq_cert, cooper_dvd_right_split]
   intros; subst a p'; simp [denote'_mul_combine_mul_addConst_eq]; assumption
 
@@ -1421,7 +1388,7 @@ def cooper_dvd_right_split_dvd1_cert (p₂ p' : Poly) (b : Int) (k : Int) : Bool
   b == p₂.leadCoeff && p' == p₂.tail.addConst k
 
 theorem cooper_dvd_right_split_dvd1 (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (k : Nat) (b : Int) (p' : Poly)
-    : cooper_dvd_right_split ctx p₁ p₂ p₃ d k → cooper_dvd_right_split_dvd1_cert p₂ p' b k → b ∣ p'.denote' ctx := by
+    : cooper_dvd_right_split ctx p₁ p₂ p₃ d k → cooper_dvd_right_split_dvd1_cert p₂ p' b k → b ∣ p'.denote ctx := by
   simp [cooper_dvd_right_split_dvd1_cert, cooper_dvd_right_split]
   intros; subst b p'; simp; assumption
 
@@ -1434,7 +1401,7 @@ def cooper_dvd_right_split_dvd2_cert (p₂ p₃ : Poly) (d : Int) (k : Nat) (d'
   d' == b*d && p' == p₂.addConst ((-c)*k)
 
 theorem cooper_dvd_right_split_dvd2 (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (k : Nat) (d' : Int) (p' : Poly)
-    : cooper_dvd_right_split ctx p₁ p₂ p₃ d k → cooper_dvd_right_split_dvd2_cert p₂ p₃ d k d' p' → d' ∣ p'.denote' ctx := by
+    : cooper_dvd_right_split ctx p₁ p₂ p₃ d k → cooper_dvd_right_split_dvd2_cert p₂ p₃ d k d' p' → d' ∣ p'.denote ctx := by
   simp [cooper_dvd_right_split_dvd2_cert, cooper_dvd_right_split]
   intros; subst d' p'; simp; assumption
 
@@ -1494,7 +1461,7 @@ def cooper_right_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (a : Int) (p' : Po
   p₁.leadCoeff == a && p' == p₂.addConst ((-a)*k)
 
 theorem cooper_right_split_ineq (ctx : Context) (p₁ p₂ : Poly) (k : Nat) (a : Int) (p' : Poly)
-    : cooper_right_split ctx p₁ p₂ k → cooper_right_split_ineq_cert p₁ p₂ k a p' → p'.denote' ctx ≤ 0 := by
+    : cooper_right_split ctx p₁ p₂ k → cooper_right_split_ineq_cert p₁ p₂ k a p' → p'.denote ctx ≤ 0 := by
   simp [cooper_right_split_ineq_cert, cooper_right_split]
   intros; subst a p'; simp [denote'_mul_combine_mul_addConst_eq]; assumption
 
@@ -1502,300 +1469,10 @@ def cooper_right_split_dvd_cert (p₂ p' : Poly) (b : Int) (k : Int) : Bool :=
   b == p₂.leadCoeff && p' == p₂.tail.addConst k
 
 theorem cooper_right_split_dvd (ctx : Context) (p₁ p₂ : Poly) (k : Nat) (b : Int) (p' : Poly)
-    : cooper_right_split ctx p₁ p₂ k → cooper_right_split_dvd_cert p₂ p' b k → b ∣ p'.denote' ctx := by
+    : cooper_right_split ctx p₁ p₂ k → cooper_right_split_dvd_cert p₂ p' b k → b ∣ p'.denote ctx := by
   simp [cooper_right_split_dvd_cert, cooper_right_split]
   intros; subst b p'; simp; assumption
 
-private theorem one_emod_eq_one {a : Int} (h : a > 1) : 1 % a = 1 := by
-  have aux₁ := Int.ediv_add_emod 1 a
-  have : 1 / a = 0 := Int.ediv_eq_zero_of_lt (by decide) h
-  simp [this] at aux₁
-  assumption
-
-private theorem ex_of_dvd {α β a b d x : Int}
-    (h₀ : d > 1)
-    (h₁ : d ∣ a*x + b)
-    (h₂ : α * a + β * d = 1)
-    : ∃ k, x = k * d + (- α * b) % d := by
-  have ⟨k, h₁⟩ := h₁
-  have aux₁ : (α * a) % d = 1 := by
-    replace h₂ := congrArg (· % d) h₂; simp at h₂
-    rw [one_emod_eq_one h₀] at h₂
-    assumption
-  have : ((α * a) * x) % d = (- α * b) % d := by
-    replace h₁ := congrArg (α * ·) h₁; simp only at h₁
-    rw [Int.mul_add] at h₁
-    replace h₁ := congrArg (· - α * b) h₁; simp only [Int.add_sub_cancel] at h₁
-    rw [← Int.mul_assoc, Int.mul_left_comm, Int.sub_eq_add_neg] at h₁
-    replace h₁ := congrArg (· % d) h₁; simp only at h₁
-    rw [Int.add_emod, Int.mul_emod_right, Int.zero_add, Int.emod_emod, ← Int.neg_mul] at h₁
-    assumption
-  have : x % d = (- α * b) % d := by
-    rw [Int.mul_emod, aux₁, Int.one_mul, Int.emod_emod] at this
-    assumption
-  have : x = (x / d)*d + (- α * b) % d := by
-    conv => lhs; rw [← Int.ediv_add_emod x d]
-    rw [Int.mul_comm, this]
-  exists x / d
-
-private theorem cdiv_le {a d k : Int} : d > 0 → a ≤ k * d → cdiv a d ≤ k := by
-  intro h₁ h₂
-  simp [cdiv]
-  replace h₂ := Int.neg_le_neg h₂
-  rw [← Int.neg_mul] at h₂
-  replace h₂ := Int.le_ediv_of_mul_le h₁ h₂
-  replace h₂ := Int.neg_le_neg h₂
-  simp at h₂
-  assumption
-
-private theorem cooper_unsat'_helper {a b d c k x : Int}
-    (d_pos : d > 0)
-    (h₁ : x = k * d + c)
-    (h₂ : a ≤ x)
-    (h₃ : x ≤ b)
-    : ¬ b < (cdiv (a - c) d) * d + c := by
-  intro h₄
-  have aux₁ : cdiv (a - c) d ≤ k := by
-    rw [h₁] at h₂
-    replace h₂ := Int.sub_right_le_of_le_add h₂
-    exact cdiv_le d_pos h₂
-  have aux₂ : cdiv (a - c) d * d ≤ k * d := Int.mul_le_mul_of_nonneg_right aux₁ (Int.le_of_lt d_pos)
-  have aux₃ : cdiv (a - c) d * d + c ≤ k * d + c := Int.add_le_add_right aux₂ _
-  have aux₄ : cdiv (a - c) d * d + c ≤ x := by rw [←h₁] at aux₃; assumption
-  have aux₅ : cdiv (a - c) d * d + c ≤ b := Int.le_trans aux₄ h₃
-  have := Int.lt_of_le_of_lt aux₅ h₄
-  exact Int.lt_irrefl _ this
-
-private theorem cooper_unsat' {a c b d e α β x : Int}
-    (h₁ : d > 1)
-    (h₂ : d ∣ c*x + e)
-    (h₃ : α * c + β * d = 1)
-    (h₄ : (-1)*x + a ≤ 0)
-    (h₅ : x + b ≤ 0)
-    (h₆ : -b < cdiv (a - -α * e % d) d * d + -α * e % d)
-    : False := by
-  have ⟨k, h⟩ := ex_of_dvd h₁ h₂ h₃
-  have d_pos : d > 0 := Int.lt_trans (by decide) h₁
-  replace h₄ := Int.le_neg_add_of_add_le h₄; simp at h₄
-  replace h₅ := Int.neg_le_neg (Int.le_neg_add_of_add_le h₅); simp at h₅
-  have := cooper_unsat'_helper d_pos h h₄ h₅
-  exact this h₆
-
-abbrev Poly.casesOnAdd (p : Poly) (k : Int → Var → Poly → Bool) : Bool :=
-  p.casesOn (fun _  => false) k
-
-abbrev Poly.casesOnNum (p : Poly) (k : Int → Bool) : Bool :=
-  p.casesOn k (fun _ _ _ => false)
-
-def cooper_unsat_cert (p₁ p₂ p₃ : Poly) (d : Int) (α β : Int) : Bool :=
-  p₁.casesOnAdd fun k₁ x p₁ =>
-  p₂.casesOnAdd fun k₂ y p₂ =>
-  p₃.casesOnAdd fun c z p₃ =>
-  p₁.casesOnNum fun a =>
-  p₂.casesOnNum fun b =>
-  p₃.casesOnNum fun e =>
-  (k₁ == -1) |>.and (k₂ == 1) |>.and
-  (x == y) |>.and (x == z) |>.and
-  (d > 1) |>.and (α * c + β * d == 1) |>.and
-  (-b < cdiv (a - -α * e % d) d * d + -α * e % d)
-
-theorem cooper_unsat (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (α β : Int)
-   : cooper_unsat_cert p₁ p₂ p₃ d α β →
-     p₁.denote' ctx ≤ 0 → p₂.denote' ctx ≤ 0 → d ∣ p₃.denote' ctx → False := by
-  unfold cooper_unsat_cert <;> cases p₁ <;> cases p₂ <;> cases p₃ <;> simp only [Poly.casesOnAdd,
-    Bool.false_eq_true, Poly.denote'_add, mul_def, add_def, false_implies]
-  next k₁ x p₁ k₂ y p₂ c z p₃ =>
-  cases p₁ <;> cases p₂ <;> cases p₃ <;> simp only [Poly.casesOnNum, Int.reduceNeg,
-    Bool.and_eq_true, beq_iff_eq, decide_eq_true_eq, and_imp, Bool.false_eq_true,
-    mul_def, add_def, false_implies, Poly.denote]
-  next a b e =>
-  intro _ _ _ _; subst k₁ k₂ y z
-  intro h₁ h₃ h₆; generalize Var.denote ctx x = x'
-  intro h₄ h₅ h₂
-  rw [Int.one_mul] at h₅
-  exact cooper_unsat' h₁ h₂ h₃ h₄ h₅ h₆
-
-theorem ediv_emod (x y : Int) : -1 * x + y * (x / y) + x % y = 0 := by
-  rw [Int.add_assoc, Int.ediv_add_emod x y, Int.add_comm]
-  simp
-  rw [Int.add_neg_eq_sub, Int.sub_self]
-
-theorem emod_nonneg (x y : Int) : y != 0 → -1 * (x % y) ≤ 0 := by
-  simp; intro h
-  have := Int.neg_le_neg (Int.emod_nonneg x h)
-  simp at this
-  assumption
-
-def emod_le_cert (y n : Int) : Bool :=
-  y != 0 && n == 1 - y.natAbs
-
-theorem emod_le (x y : Int) (n : Int) : emod_le_cert y n → x % y + n ≤ 0 := by
-  simp [emod_le_cert]
-  intro h₁
-  cases Int.lt_or_gt_of_ne h₁
-  next h =>
-    rw [Int.ofNat_natAbs_of_nonpos (Int.le_of_lt h)]
-    simp only [Int.sub_neg]
-    intro; subst n
-    rw [Int.add_assoc, Int.add_left_comm]
-    apply Int.add_le_of_le_sub_left
-    rw [Int.zero_sub, Int.add_comm]
-    have : 0 < -y := by
-      have := Int.neg_lt_neg h
-      rw [Int.neg_zero] at this
-      assumption
-    have := Int.emod_lt_of_pos x this
-    rw [Int.emod_neg] at this
-    exact this
-  next h =>
-    rw [Int.natAbs_of_nonneg (Int.le_of_lt h)]
-    intro; subst n
-    rw [Int.sub_eq_add_neg, Int.add_assoc, Int.add_left_comm]
-    apply Int.add_le_of_le_sub_left
-    simp only [Int.add_comm, Int.sub_neg, Int.add_zero]
-    exact Int.emod_lt_of_pos x h
-
-theorem natCast_nonneg (x : Nat) : (-1:Int) * NatCast.natCast x ≤ 0 := by
-  simp
-
-theorem natCast_sub (x y : Nat)
-    : (NatCast.natCast (x - y) : Int)
-      =
-      if (NatCast.natCast y : Int) + (-1)*NatCast.natCast x ≤ 0 then
-        (NatCast.natCast x : Int) + -1*NatCast.natCast y
-      else
-        (0 : Int) := by
-  show (↑(x - y) : Int) = if (↑y : Int) + (-1)*↑x ≤ 0 then ↑x + (-1)*↑y else 0
-  rw [Int.neg_mul, ← Int.sub_eq_add_neg, Int.one_mul]
-  rw [Int.neg_mul, ← Int.sub_eq_add_neg, Int.one_mul]
-  split
-  next h =>
-    replace h := Int.le_of_sub_nonpos h
-    rw [Int.ofNat_le] at h
-    rw [Int.ofNat_sub h]
-  next h =>
-    have : ¬ (↑y : Int) ≤ ↑x := by
-      intro h
-      replace h := Int.sub_nonpos_of_le h
-      contradiction
-    rw [Int.ofNat_le] at this
-    rw [Lean.Omega.Int.ofNat_sub_eq_zero this]
-
-private theorem dvd_le_tight' {d p b₁ b₂ : Int} (hd : d > 0) (h₁ : d ∣ p + b₁) (h₂ : p + b₂ ≤ 0)
-    : p + (b₁ - d*((b₁-b₂) / d)) ≤ 0 := by
-  have ⟨k, h⟩ := h₁
-  replace h₁ : p = d*k - b₁ := by
-    replace h := congrArg (· - b₁) h
-    simp only [Int.add_sub_cancel] at h
-    assumption
-  replace h₂ : d*k - b₁ + b₂ ≤ 0 := by
-    rw [h₁] at h₂; assumption
-  have : d*k ≤ b₁ - b₂ := by
-    rw [Int.sub_eq_add_neg, Int.add_assoc, Lean.Omega.Int.add_le_zero_iff_le_neg,
-        Int.neg_add, Int.neg_neg, Int.add_neg_eq_sub] at h₂
-    assumption
-  replace this : k ≤ (b₁ - b₂)/d := by
-    rw [Int.mul_comm] at this; exact Int.le_ediv_of_mul_le hd this
-  replace this := Int.mul_le_mul_of_nonneg_left this (Int.le_of_lt hd)
-  rw [←h] at this
-  replace this := Int.sub_nonpos_of_le this
-  rw [Int.add_sub_assoc] at this
-  exact this
-
-private theorem eq_neg_addConst_add (ctx : Context) (p : Poly)
-    : p.denote' ctx = (p.addConst (-p.getConst)).denote' ctx + p.getConst := by
-  simp only [Poly.denote'_eq_denote, Poly.denote_addConst, Int.add_comm, Int.add_left_comm]
-  rw [Int.add_right_neg]
-  simp
-
-def dvd_le_tight_cert (d : Int) (p₁ p₂ p₃ : Poly) : Bool :=
-  let b₁ := p₁.getConst
-  let b₂ := p₂.getConst
-  let p  := p₁.addConst (-b₁)
-  d > 0 && (p₂ == p.addConst b₂ && p₃ == p.addConst (b₁ - d*((b₁ - b₂)/d)))
-
-theorem dvd_le_tight (ctx : Context) (d : Int) (p₁ p₂ p₃ : Poly)
-    : dvd_le_tight_cert d p₁ p₂ p₃ → d ∣ p₁.denote' ctx → p₂.denote' ctx ≤ 0 → p₃.denote' ctx ≤ 0 := by
-  simp only [dvd_le_tight_cert, gt_iff_lt, Bool.and_eq_true, decide_eq_true_eq, beq_iff_eq, and_imp]
-  generalize p₂.getConst = b₂
-  intro hd _ _; subst p₂ p₃
-  have := eq_neg_addConst_add ctx p₁
-  revert this
-  generalize p₁.getConst = b₁
-  generalize p₁.addConst (-b₁) = p
-  intro h₁; rw [h₁]; clear h₁
-  simp only [denote'_addConst_eq]
-  simp only [Poly.denote'_eq_denote]
-  exact dvd_le_tight' hd
-
-def dvd_neg_le_tight_cert (d : Int) (p₁ p₂ p₃ : Poly) : Bool :=
-  let b₁ := p₁.getConst
-  let b₂ := p₂.getConst
-  let p  := p₁.addConst (-b₁)
-  let b₁ := -b₁
-  let p  := p.mul (-1)
-  d > 0 && (p₂ == p.addConst b₂ && p₃ == p.addConst (b₁ - d*((b₁ - b₂)/d)))
-
-theorem Poly.mul_minus_one_getConst_eq (p : Poly) : (p.mul (-1)).getConst = -p.getConst := by
-  simp [Poly.mul, Poly.getConst]
-  induction p <;> simp [Poly.mul', Poly.getConst, *]
-
-theorem dvd_neg_le_tight (ctx : Context) (d : Int) (p₁ p₂ p₃ : Poly)
-    : dvd_neg_le_tight_cert d p₁ p₂ p₃ → d ∣ p₁.denote' ctx → p₂.denote' ctx ≤ 0 → p₃.denote' ctx ≤ 0 := by
-  simp only [dvd_neg_le_tight_cert, gt_iff_lt, Bool.and_eq_true, decide_eq_true_eq, beq_iff_eq, and_imp]
-  generalize p₂.getConst = b₂
-  intro hd _ _; subst p₂ p₃
-  simp only [Poly.denote'_eq_denote, Int.reduceNeg, Poly.denote_addConst, Poly.denote_mul,
-    Int.mul_add, Int.neg_mul, Int.one_mul, Int.mul_neg, Int.neg_neg, Int.add_comm, Int.add_assoc]
-  intro h₁ h₂
-  replace h₁ := Int.dvd_neg.mpr h₁
-  have := eq_neg_addConst_add ctx (p₁.mul (-1))
-  simp [Poly.mul_minus_one_getConst_eq] at this
-  rw [← Int.add_assoc] at this
-  rw [this] at h₁; clear this
-  rw [← Int.add_assoc]
-  revert h₁ h₂
-  generalize -Poly.denote ctx p₁ + p₁.getConst = p
-  generalize -p₁.getConst = b₁
-  intro h₁ h₂; rw [Int.add_comm] at h₁
-  exact dvd_le_tight' hd h₂ h₁
-
-theorem le_norm_expr (ctx : Context) (lhs rhs : Expr) (p : Poly)
-    : norm_eq_cert lhs rhs p → lhs.denote ctx ≤ rhs.denote ctx → p.denote' ctx ≤ 0 := by
-  intro h₁ h₂; rwa [norm_le ctx lhs rhs p h₁] at h₂
-
-def not_le_norm_expr_cert (lhs rhs : Expr) (p : Poly) : Bool :=
-  p == (((lhs.sub rhs).norm).mul (-1)).addConst 1
-
-theorem not_le_norm_expr (ctx : Context) (lhs rhs : Expr) (p : Poly)
-    : not_le_norm_expr_cert lhs rhs p → ¬ lhs.denote ctx ≤ rhs.denote ctx → p.denote' ctx ≤ 0 := by
-  simp [not_le_norm_expr_cert]
-  intro; subst p; simp
-  intro h
-  replace h := Int.sub_nonpos_of_le h
-  rw [Int.add_comm, Int.add_sub_assoc] at h
-  rw [Int.neg_sub]; assumption
-
-theorem dvd_norm_expr (ctx : Context) (d : Int) (e : Expr) (p : Poly)
-    : p == e.norm → d ∣ e.denote ctx → d ∣ p.denote' ctx := by
-  simp; intro; subst p; simp
-
-theorem eq_norm_expr (ctx : Context) (lhs rhs : Expr) (p : Poly)
-    : norm_eq_cert lhs rhs p → lhs.denote ctx = rhs.denote ctx → p.denote' ctx = 0 := by
-  intro h₁ h₂; rwa [norm_eq ctx lhs rhs p h₁] at h₂
-
-theorem not_eq_norm_expr (ctx : Context) (lhs rhs : Expr) (p : Poly)
-    : norm_eq_cert lhs rhs p → ¬ lhs.denote ctx = rhs.denote ctx → ¬ p.denote' ctx = 0 := by
-  simp [norm_eq_cert]
-  intro; subst p; simp
-  intro; rwa [Int.sub_eq_zero]
-
-theorem of_not_dvd (a b : Int) : a != 0 → ¬ (a ∣ b) → b % a > 0 := by
-  simp; intro h₁ h₂
-  replace h₂ := Int.emod_pos_of_not_dvd h₂
-  simp [h₁] at h₂
-  assumption
-
 end Int.Linear
 
 theorem Int.not_le_eq (a b : Int) : (¬a ≤ b) = (b + 1 ≤ a) := by

src/Init/Data/Int/OfNat.lean

@@ -1,90 +0,0 @@
-/-
-Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Init.Data.Int.Lemmas
-import Init.Data.Int.DivMod
-import Init.Data.RArray
-
-namespace Int.OfNat
-/-!
-Helper definitions and theorems for converting `Nat` expressions into `Int` one.
-We use them to implement the arithmetic theories in `grind`
--/
-
-abbrev Var := Nat
-abbrev Context := Lean.RArray Nat
-def Var.denote (ctx : Context) (v : Var) : Nat :=
-  ctx.get v
-
-inductive Expr where
-  | num  (v : Nat)
-  | var  (i : Var)
-  | add  (a b : Expr)
-  | mul  (a b : Expr)
-  | div  (a b : Expr)
-  | mod  (a b : Expr)
-  deriving BEq
-
-def Expr.denote (ctx : Context) : Expr → Nat
-  | .num k    => k
-  | .var v    => v.denote ctx
-  | .add a b  => Nat.add (denote ctx a) (denote ctx b)
-  | .mul a b  => Nat.mul (denote ctx a) (denote ctx b)
-  | .div a b  => Nat.div (denote ctx a) (denote ctx b)
-  | .mod a b  => Nat.mod (denote ctx a) (denote ctx b)
-
-def Expr.denoteAsInt (ctx : Context) : Expr → Int
-  | .num k    => Int.ofNat k
-  | .var v    => Int.ofNat (v.denote ctx)
-  | .add a b  => Int.add (denoteAsInt ctx a) (denoteAsInt ctx b)
-  | .mul a b  => Int.mul (denoteAsInt ctx a) (denoteAsInt ctx b)
-  | .div a b  => Int.ediv (denoteAsInt ctx a) (denoteAsInt ctx b)
-  | .mod a b  => Int.emod (denoteAsInt ctx a) (denoteAsInt ctx b)
-
-theorem Expr.denoteAsInt_eq (ctx : Context) (e : Expr) : e.denoteAsInt ctx = e.denote ctx := by
-  induction e <;> simp [denote, denoteAsInt, Int.ofNat_ediv, *] <;> rfl
-
-theorem Expr.eq (ctx : Context) (lhs rhs : Expr)
-    : (lhs.denote ctx = rhs.denote ctx) = (lhs.denoteAsInt ctx = rhs.denoteAsInt ctx) := by
-  simp [denoteAsInt_eq, Int.ofNat_inj]
-
-theorem Expr.le (ctx : Context) (lhs rhs : Expr)
-    : (lhs.denote ctx ≤ rhs.denote ctx) = (lhs.denoteAsInt ctx ≤ rhs.denoteAsInt ctx) := by
-  simp [denoteAsInt_eq, Int.ofNat_le]
-
-theorem of_le (ctx : Context) (lhs rhs : Expr)
-    : lhs.denote ctx ≤ rhs.denote ctx → lhs.denoteAsInt ctx ≤ rhs.denoteAsInt ctx := by
-  rw [Expr.le ctx lhs rhs]; simp
-
-theorem of_not_le (ctx : Context) (lhs rhs : Expr)
-    : ¬ lhs.denote ctx ≤ rhs.denote ctx → ¬ lhs.denoteAsInt ctx ≤ rhs.denoteAsInt ctx := by
-  rw [Expr.le ctx lhs rhs]; simp
-
-theorem of_dvd (ctx : Context) (d : Nat) (e : Expr)
-    : d ∣ e.denote ctx → Int.ofNat d ∣ e.denoteAsInt ctx := by
-  simp [Expr.denoteAsInt_eq, Int.ofNat_dvd]
-
-theorem of_eq (ctx : Context) (lhs rhs : Expr)
-    : lhs.denote ctx = rhs.denote ctx → lhs.denoteAsInt ctx = rhs.denoteAsInt ctx := by
-  rw [Expr.eq ctx lhs rhs]; simp
-
-theorem of_not_eq (ctx : Context) (lhs rhs : Expr)
-    : ¬ lhs.denote ctx = rhs.denote ctx → ¬ lhs.denoteAsInt ctx = rhs.denoteAsInt ctx := by
-  rw [Expr.eq ctx lhs rhs]; simp
-
-theorem ofNat_toNat (a : Int) : (NatCast.natCast a.toNat : Int) = if a ≤ 0 then 0 else a := by
-  split
-  next h =>
-    rw [Int.toNat_of_nonpos h]; rfl
-  next h =>
-    simp at h
-    have := Int.toNat_of_nonneg (Int.le_of_lt h)
-    assumption
-
-theorem Expr.denoteAsInt_nonneg (ctx : Context) (e : Expr) : e.denoteAsInt ctx ≥ 0 := by
-  simp [Expr.denoteAsInt_eq]
-
-end Int.OfNat

src/Init/Data/Int/Order.lean

@@ -33,18 +33,20 @@ theorem lt_iff_add_one_le {a b : Int} : a < b ↔ a + 1 ≤ b := .rfl
 theorem le.intro_sub {a b : Int} (n : Nat) (h : b - a = n) : a ≤ b := by
   simp [le_def, h]; constructor
 
+attribute [local simp] Int.add_left_neg Int.add_right_neg Int.neg_add
+
 theorem le.intro {a b : Int} (n : Nat) (h : a + n = b) : a ≤ b :=
-  le.intro_sub n <| by rw [← h, Int.add_comm]; simp [Int.sub_eq_add_neg, Int.add_assoc, Int.add_right_neg]
+  le.intro_sub n <| by rw [← h, Int.add_comm]; simp [Int.sub_eq_add_neg, Int.add_assoc]
 
 theorem le.dest_sub {a b : Int} (h : a ≤ b) : ∃ n : Nat, b - a = n := nonneg_def.1 h
 
 theorem le.dest {a b : Int} (h : a ≤ b) : ∃ n : Nat, a + n = b :=
   let ⟨n, h₁⟩ := le.dest_sub h
-  ⟨n, by rw [← h₁, Int.add_comm]; simp [Int.sub_eq_add_neg, Int.add_assoc, Int.add_left_neg]⟩
+  ⟨n, by rw [← h₁, Int.add_comm]; simp [Int.sub_eq_add_neg, Int.add_assoc]⟩
 
 protected theorem le_total (a b : Int) : a ≤ b ∨ b ≤ a :=
   (nonneg_or_nonneg_neg (b - a)).imp_right fun H => by
-    rwa [show -(b - a) = a - b by simp [Int.neg_add,Int.add_comm, Int.sub_eq_add_neg]] at H
+    rwa [show -(b - a) = a - b by simp [Int.add_comm, Int.sub_eq_add_neg]] at H
 
 @[simp, norm_cast] theorem ofNat_le {m n : Nat} : (↑m : Int) ≤ ↑n ↔ m ≤ n :=
   ⟨fun h =>
@@ -59,14 +61,14 @@ protected theorem le_total (a b : Int) : a ≤ b ∨ b ≤ a :=
 theorem eq_ofNat_of_zero_le {a : Int} (h : 0 ≤ a) : ∃ n : Nat, a = n := by
   have t := le.dest_sub h; rwa [Int.sub_zero] at t
 
-theorem eq_succ_of_zero_lt {a : Int} (h : 0 < a) : ∃ n : Nat, a = n + 1 :=
+theorem eq_succ_of_zero_lt {a : Int} (h : 0 < a) : ∃ n : Nat, a = n.succ :=
   let ⟨n, (h : ↑(1 + n) = a)⟩ := le.dest h
   ⟨n, by rw [Nat.add_comm] at h; exact h.symm⟩
 
-theorem lt_add_succ (a : Int) (n : Nat) : a < a + (n + 1) :=
-  le.intro n <| by rw [Int.add_comm, Int.add_left_comm]
+theorem lt_add_succ (a : Int) (n : Nat) : a < a + Nat.succ n :=
+  le.intro n <| by rw [Int.add_comm, Int.add_left_comm]; rfl
 
-theorem lt.intro {a b : Int} {n : Nat} (h : a + (n + 1) = b) : a < b :=
+theorem lt.intro {a b : Int} {n : Nat} (h : a + Nat.succ n = b) : a < b :=
   h ▸ lt_add_succ a n
 
 theorem lt.dest {a b : Int} (h : a < b) : ∃ n : Nat, a + Nat.succ n = b :=
@@ -115,7 +117,7 @@ protected theorem lt_iff_le_and_ne {a b : Int} : a < b ↔ a ≤ b ∧ a ≠ b :
   have : n ≠ 0 := aneb.imp fun eq => by rw [← hn, eq, ofNat_zero, Int.add_zero]
   apply lt.intro; rwa [← Nat.succ_pred_eq_of_pos (Nat.pos_of_ne_zero this)] at hn
 
-protected theorem lt_succ (a : Int) : a < a + 1 := Int.le_refl _
+theorem lt_succ (a : Int) : a < a + 1 := Int.le_refl _
 
 protected theorem zero_lt_one : (0 : Int) < 1 := ⟨_⟩
 
@@ -137,9 +139,6 @@ protected theorem not_le_of_gt {a b : Int} (h : b < a) : ¬a ≤ b :=
 @[simp] protected theorem not_lt {a b : Int} : ¬a < b ↔ b ≤ a :=
   by rw [← Int.not_le, Decidable.not_not]
 
-protected theorem le_of_not_gt {a b : Int} (h : ¬ a > b) : a ≤ b :=
-  Int.not_lt.mp h
-
 protected theorem lt_trichotomy (a b : Int) : a < b ∨ a = b ∨ b < a :=
   if eq : a = b then .inr <| .inl eq else
   if le : a ≤ b then .inl <| Int.lt_iff_le_and_ne.2 ⟨le, eq⟩ else
@@ -184,19 +183,61 @@ instance : Trans (α := Int) (· ≤ ·) (· < ·) (· < ·) := ⟨Int.lt_of_le_
 
 instance : Trans (α := Int) (· < ·) (· < ·) (· < ·) := ⟨Int.lt_trans⟩
 
-theorem eq_natAbs_of_nonneg {a : Int} (h : 0 ≤ a) : a = natAbs a := by
+protected theorem min_def (n m : Int) : min n m = if n ≤ m then n else m := rfl
+
+protected theorem max_def (n m : Int) : max n m = if n ≤ m then m else n := rfl
+
+protected theorem min_comm (a b : Int) : min a b = min b a := by
+  simp [Int.min_def]
+  by_cases h₁ : a ≤ b <;> by_cases h₂ : b ≤ a <;> simp [h₁, h₂]
+  · exact Int.le_antisymm h₁ h₂
+  · cases not_or_intro h₁ h₂ <| Int.le_total ..
+instance : Std.Commutative (α := Int) min := ⟨Int.min_comm⟩
+
+protected theorem min_le_right (a b : Int) : min a b ≤ b := by rw [Int.min_def]; split <;> simp [*]
+
+protected theorem min_le_left (a b : Int) : min a b ≤ a := Int.min_comm .. ▸ Int.min_le_right ..
+
+protected theorem min_eq_left {a b : Int} (h : a ≤ b) : min a b = a := by simp [Int.min_def, h]
+
+protected theorem min_eq_right {a b : Int} (h : b ≤ a) : min a b = b := by
+  rw [Int.min_comm a b]; exact Int.min_eq_left h
+
+protected theorem le_min {a b c : Int} : a ≤ min b c ↔ a ≤ b ∧ a ≤ c :=
+  ⟨fun h => ⟨Int.le_trans h (Int.min_le_left ..), Int.le_trans h (Int.min_le_right ..)⟩,
+   fun ⟨h₁, h₂⟩ => by rw [Int.min_def]; split <;> assumption⟩
+
+protected theorem max_comm (a b : Int) : max a b = max b a := by
+  simp only [Int.max_def]
+  by_cases h₁ : a ≤ b <;> by_cases h₂ : b ≤ a <;> simp [h₁, h₂]
+  · exact Int.le_antisymm h₂ h₁
+  · cases not_or_intro h₁ h₂ <| Int.le_total ..
+instance : Std.Commutative (α := Int) max := ⟨Int.max_comm⟩
+
+protected theorem le_max_left (a b : Int) : a ≤ max a b := by rw [Int.max_def]; split <;> simp [*]
+
+protected theorem le_max_right (a b : Int) : b ≤ max a b := Int.max_comm .. ▸ Int.le_max_left ..
+
+protected theorem max_le {a b c : Int} : max a b ≤ c ↔ a ≤ c ∧ b ≤ c :=
+  ⟨fun h => ⟨Int.le_trans (Int.le_max_left ..) h, Int.le_trans (Int.le_max_right ..) h⟩,
+   fun ⟨h₁, h₂⟩ => by rw [Int.max_def]; split <;> assumption⟩
+
+protected theorem max_eq_right {a b : Int} (h : a ≤ b) : max a b = b := by
+  simp [Int.max_def, h, Int.not_lt.2 h]
+
+protected theorem max_eq_left {a b : Int} (h : b ≤ a) : max a b = a := by
+  rw [← Int.max_comm b a]; exact Int.max_eq_right h
+
+theorem eq_natAbs_of_zero_le {a : Int} (h : 0 ≤ a) : a = natAbs a := by
   let ⟨n, e⟩ := eq_ofNat_of_zero_le h
   rw [e]; rfl
 
-@[deprecated eq_natAbs_of_nonneg (since := "2025-03-11")]
-abbrev eq_natAbs_of_zero_le := @eq_natAbs_of_nonneg
-
 theorem le_natAbs {a : Int} : a ≤ natAbs a :=
   match Int.le_total 0 a with
-  | .inl h => by rw [eq_natAbs_of_nonneg h]; apply Int.le_refl
+  | .inl h => by rw [eq_natAbs_of_zero_le h]; apply Int.le_refl
   | .inr h => Int.le_trans h (ofNat_zero_le _)
 
-@[simp] theorem negSucc_lt_zero (n : Nat) : -[n+1] < 0 :=
+theorem negSucc_lt_zero (n : Nat) : -[n+1] < 0 :=
   Int.not_le.1 fun h => let ⟨_, h⟩ := eq_ofNat_of_zero_le h; nomatch h
 
 theorem negSucc_le_zero (n : Nat) : -[n+1] ≤ 0 :=
@@ -205,6 +246,18 @@ theorem negSucc_le_zero (n : Nat) : -[n+1] ≤ 0 :=
 @[simp] theorem negSucc_not_nonneg (n : Nat) : 0 ≤ -[n+1] ↔ False := by
   simp only [Int.not_le, iff_false]; exact Int.negSucc_lt_zero n
 
+@[simp] theorem ofNat_max_zero (n : Nat) : (max (n : Int) 0) = n := by
+  rw [Int.max_eq_left (ofNat_zero_le n)]
+
+@[simp] theorem zero_max_ofNat (n : Nat) : (max 0 (n : Int)) = n := by
+  rw [Int.max_eq_right (ofNat_zero_le n)]
+
+@[simp] theorem negSucc_max_zero (n : Nat) : (max (Int.negSucc n) 0) = 0 := by
+  rw [Int.max_eq_right (negSucc_le_zero _)]
+
+@[simp] theorem zero_max_negSucc (n : Nat) : (max 0 (Int.negSucc n)) = 0 := by
+  rw [Int.max_eq_left (negSucc_le_zero _)]
+
 protected theorem add_le_add_left {a b : Int} (h : a ≤ b) (c : Int) : c + a ≤ c + b :=
   let ⟨n, hn⟩ := le.dest h; le.intro n <| by rw [Int.add_assoc, hn]
 
@@ -226,10 +279,10 @@ protected theorem le_of_add_le_add_left {a b c : Int} (h : a + b ≤ a + c) : b
 protected theorem le_of_add_le_add_right {a b c : Int} (h : a + b ≤ c + b) : a ≤ c :=
   Int.le_of_add_le_add_left (a := b) <| by rwa [Int.add_comm b a, Int.add_comm b c]
 
-@[simp] protected theorem add_le_add_iff_left (a : Int) : a + b ≤ a + c ↔ b ≤ c :=
+protected theorem add_le_add_iff_left (a : Int) : a + b ≤ a + c ↔ b ≤ c :=
   ⟨Int.le_of_add_le_add_left, (Int.add_le_add_left · _)⟩
 
-@[simp] protected theorem add_le_add_iff_right (c : Int) : a + c ≤ b + c ↔ a ≤ b :=
+protected theorem add_le_add_iff_right (c : Int) : a + c ≤ b + c ↔ a ≤ b :=
   ⟨Int.le_of_add_le_add_right, (Int.add_le_add_right · _)⟩
 
 protected theorem add_le_add {a b c d : Int} (h₁ : a ≤ b) (h₂ : c ≤ d) : a + c ≤ b + d :=
@@ -248,15 +301,6 @@ protected theorem neg_le_neg {a b : Int} (h : a ≤ b) : -b ≤ -a := by
   have : 0 + -b ≤ -a + b + -b := Int.add_le_add_right this (-b)
   rwa [Int.add_neg_cancel_right, Int.zero_add] at this
 
-@[simp] protected theorem neg_le_neg_iff {a b : Int} : -a ≤ -b ↔ b ≤ a :=
-  ⟨fun h => by simpa using Int.neg_le_neg h, Int.neg_le_neg⟩
-
-@[simp] protected theorem neg_le_zero_iff {a : Int} : -a ≤ 0 ↔ 0 ≤ a := by
-  rw [← Int.neg_zero, Int.neg_le_neg_iff, Int.neg_zero]
-
-@[simp] protected theorem zero_le_neg_iff {a : Int} : 0 ≤ -a ↔ a ≤ 0 := by
-  rw [← Int.neg_zero, Int.neg_le_neg_iff, Int.neg_zero]
-
 protected theorem le_of_neg_le_neg {a b : Int} (h : -b ≤ -a) : a ≤ b :=
   suffices - -a ≤ - -b by simp [Int.neg_neg] at this; assumption
   Int.neg_le_neg h
@@ -274,15 +318,6 @@ protected theorem neg_lt_neg {a b : Int} (h : a < b) : -b < -a := by
   have : 0 + -b < -a + b + -b := Int.add_lt_add_right this (-b)
   rwa [Int.add_neg_cancel_right, Int.zero_add] at this
 
-@[simp] protected theorem neg_lt_neg_iff {a b : Int} : -a < -b ↔ b < a :=
-  ⟨fun h => by simpa using Int.neg_lt_neg h, Int.neg_lt_neg⟩
-
-@[simp] protected theorem neg_lt_zero_iff {a : Int} : -a < 0 ↔ 0 < a := by
-  rw [← Int.neg_zero, Int.neg_lt_neg_iff, Int.neg_zero]
-
-@[simp] protected theorem zero_lt_neg_iff {a : Int} : 0 < -a ↔ a < 0 := by
-  rw [← Int.neg_zero, Int.neg_lt_neg_iff, Int.neg_zero]
-
 protected theorem neg_neg_of_pos {a : Int} (h : 0 < a) : -a < 0 := by
   have : -a < -0 := Int.neg_lt_neg h
   rwa [Int.neg_zero] at this
@@ -323,125 +358,9 @@ protected theorem sub_lt_self (a : Int) {b : Int} (h : 0 < b) : a - b < a :=
 
 theorem add_one_le_of_lt {a b : Int} (H : a < b) : a + 1 ≤ b := H
 
-protected theorem le_iff_lt_add_one {a b : Int} : a ≤ b ↔ a < b + 1 := by
-  rw [Int.lt_iff_add_one_le]
-  exact (Int.add_le_add_iff_right 1).symm
-
-/- ### min and max -/
-
-protected theorem min_def (n m : Int) : min n m = if n ≤ m then n else m := rfl
-
-protected theorem max_def (n m : Int) : max n m = if n ≤ m then m else n := rfl
-
-@[simp] protected theorem neg_min_neg (a b : Int) : min (-a) (-b) = -max a b := by
-  rw [Int.min_def, Int.max_def]
-  simp
-  split <;> rename_i h₁ <;> split <;> rename_i h₂
-  · simpa using Int.le_antisymm h₂ h₁
-  · simp
-  · simp
-  · simp only [Int.not_le] at h₁ h₂
-    exfalso
-    exact Int.lt_irrefl _ (Int.lt_trans h₁ h₂)
-
-@[simp] protected theorem min_add_right (a b c : Int) : min (a + c) (b + c) = min a b + c := by
-  rw [Int.min_def, Int.min_def]
-  simp only [Int.add_le_add_iff_right]
-  split <;> simp
-
-@[simp] protected theorem min_add_left (a b c : Int) : min (a + b) (a + c) = a + min b c := by
-  rw [Int.min_def, Int.min_def]
-  simp only [Int.add_le_add_iff_left]
-  split <;> simp
-
-protected theorem min_comm (a b : Int) : min a b = min b a := by
-  simp [Int.min_def]
-  by_cases h₁ : a ≤ b <;> by_cases h₂ : b ≤ a <;> simp [h₁, h₂]
-  · exact Int.le_antisymm h₁ h₂
-  · cases not_or_intro h₁ h₂ <| Int.le_total ..
-instance : Std.Commutative (α := Int) min := ⟨Int.min_comm⟩
-
-protected theorem min_le_right (a b : Int) : min a b ≤ b := by rw [Int.min_def]; split <;> simp [*]
-
-protected theorem min_le_left (a b : Int) : min a b ≤ a := Int.min_comm .. ▸ Int.min_le_right ..
-
-protected theorem min_eq_left {a b : Int} (h : a ≤ b) : min a b = a := by simp [Int.min_def, h]
-
-protected theorem min_eq_right {a b : Int} (h : b ≤ a) : min a b = b := by
-  rw [Int.min_comm a b]; exact Int.min_eq_left h
-
-protected theorem le_min {a b c : Int} : a ≤ min b c ↔ a ≤ b ∧ a ≤ c :=
-  ⟨fun h => ⟨Int.le_trans h (Int.min_le_left ..), Int.le_trans h (Int.min_le_right ..)⟩,
-   fun ⟨h₁, h₂⟩ => by rw [Int.min_def]; split <;> assumption⟩
-
-protected theorem lt_min {a b c : Int} : a < min b c ↔ a < b ∧ a < c := Int.le_min
-
-@[simp] protected theorem neg_max_neg (a b : Int) : max (-a) (-b) = -min a b := by
-  rw [Int.min_def, Int.max_def]
-  simp
-  split <;> rename_i h₁ <;> split <;> rename_i h₂
-  · simpa using Int.le_antisymm h₁ h₂
-  · simp
-  · simp
-  · simp only [Int.not_le] at h₁ h₂
-    exfalso
-    exact Int.lt_irrefl _ (Int.lt_trans h₁ h₂)
-
-@[simp] protected theorem max_add_right (a b c : Int) : max (a + c) (b + c) = max a b + c := by
-  rw [Int.max_def, Int.max_def]
-  simp only [Int.add_le_add_iff_right]
-  split <;> simp
-
-@[simp] protected theorem max_add_left (a b c : Int) : max (a + b) (a + c) = a + max b c := by
-  rw [Int.max_def, Int.max_def]
-  simp only [Int.add_le_add_iff_left]
-  split <;> simp
-
-protected theorem max_comm (a b : Int) : max a b = max b a := by
-  simp only [Int.max_def]
-  by_cases h₁ : a ≤ b <;> by_cases h₂ : b ≤ a <;> simp [h₁, h₂]
-  · exact Int.le_antisymm h₂ h₁
-  · cases not_or_intro h₁ h₂ <| Int.le_total ..
-instance : Std.Commutative (α := Int) max := ⟨Int.max_comm⟩
-
-protected theorem le_max_left (a b : Int) : a ≤ max a b := by rw [Int.max_def]; split <;> simp [*]
-
-protected theorem le_max_right (a b : Int) : b ≤ max a b := Int.max_comm .. ▸ Int.le_max_left ..
-
-protected theorem max_eq_right {a b : Int} (h : a ≤ b) : max a b = b := by
-  simp [Int.max_def, h, Int.not_lt.2 h]
-
-protected theorem max_eq_left {a b : Int} (h : b ≤ a) : max a b = a := by
-  rw [← Int.max_comm b a]; exact Int.max_eq_right h
-
-protected theorem max_le {a b c : Int} : max a b ≤ c ↔ a ≤ c ∧ b ≤ c :=
-  ⟨fun h => ⟨Int.le_trans (Int.le_max_left ..) h, Int.le_trans (Int.le_max_right ..) h⟩,
-   fun ⟨h₁, h₂⟩ => by rw [Int.max_def]; split <;> assumption⟩
-
-protected theorem max_lt {a b c : Int} : max a b < c ↔ a < c ∧ b < c := by
-  simp only [Int.lt_iff_add_one_le]
-  simpa using Int.max_le (a := a + 1) (b := b + 1) (c := c)
-
-@[simp] theorem ofNat_max_zero (n : Nat) : (max (n : Int) 0) = n := by
-  rw [Int.max_eq_left (ofNat_zero_le n)]
-
-@[simp] theorem zero_max_ofNat (n : Nat) : (max 0 (n : Int)) = n := by
-  rw [Int.max_eq_right (ofNat_zero_le n)]
-
-@[simp] theorem negSucc_max_zero (n : Nat) : (max (Int.negSucc n) 0) = 0 := by
-  rw [Int.max_eq_right (negSucc_le_zero _)]
-
-@[simp] theorem zero_max_negSucc (n : Nat) : (max 0 (Int.negSucc n)) = 0 := by
-  rw [Int.max_eq_left (negSucc_le_zero _)]
-
-@[simp] protected theorem min_self (a : Int) : min a a = a := Int.min_eq_left (Int.le_refl _)
-instance : Std.IdempotentOp (α := Int) min := ⟨Int.min_self⟩
-
-@[simp] protected theorem max_self (a : Int) : max a a = a := Int.max_eq_right (Int.le_refl _)
-instance : Std.IdempotentOp (α := Int) max := ⟨Int.max_self⟩
-
 /- ### Order properties and multiplication -/
 
+
 protected theorem mul_nonneg {a b : Int} (ha : 0 ≤ a) (hb : 0 ≤ b) : 0 ≤ a * b := by
   let ⟨n, hn⟩ := eq_ofNat_of_zero_le ha
   let ⟨m, hm⟩ := eq_ofNat_of_zero_le hb
@@ -450,8 +369,7 @@ protected theorem mul_nonneg {a b : Int} (ha : 0 ≤ a) (hb : 0 ≤ b) : 0 ≤ a
 protected theorem mul_pos {a b : Int} (ha : 0 < a) (hb : 0 < b) : 0 < a * b := by
   let ⟨n, hn⟩ := eq_succ_of_zero_lt ha
   let ⟨m, hm⟩ := eq_succ_of_zero_lt hb
-  rw [hn, hm]
-  apply ofNat_succ_pos
+  rw [hn, hm, ← ofNat_mul]; apply ofNat_succ_pos
 
 protected theorem mul_lt_mul_of_pos_left {a b c : Int}
   (h₁ : a < b) (h₂ : 0 < c) : c * a < c * b := by
@@ -507,7 +425,7 @@ protected theorem mul_le_mul_of_nonpos_left {a b c : Int}
 
 /- ## natAbs -/
 
-@[simp, norm_cast] theorem natAbs_ofNat (n : Nat) : natAbs ↑n = n := rfl
+@[simp] theorem natAbs_ofNat (n : Nat) : natAbs ↑n = n := rfl
 @[simp] theorem natAbs_negSucc (n : Nat) : natAbs -[n+1] = n.succ := rfl
 @[simp] theorem natAbs_zero : natAbs (0 : Int) = (0 : Nat) := rfl
 @[simp] theorem natAbs_one : natAbs (1 : Int) = (1 : Nat) := rfl
@@ -552,13 +470,6 @@ theorem natAbs_of_nonneg {a : Int} (H : 0 ≤ a) : (natAbs a : Int) = a :=
 theorem ofNat_natAbs_of_nonpos {a : Int} (H : a ≤ 0) : (natAbs a : Int) = -a := by
   rw [← natAbs_neg, natAbs_of_nonneg (Int.neg_nonneg_of_nonpos H)]
 
-theorem natAbs_sub_of_nonneg_of_le {a b : Int} (h₁ : 0 ≤ b) (h₂ : b ≤ a) :
-    (a - b).natAbs = a.natAbs - b.natAbs := by
-  rw [← Int.ofNat_inj]
-  rw [natAbs_of_nonneg, ofNat_sub, natAbs_of_nonneg (Int.le_trans h₁ h₂), natAbs_of_nonneg h₁]
-  · rwa [← Int.ofNat_le, natAbs_of_nonneg h₁, natAbs_of_nonneg (Int.le_trans h₁ h₂)]
-  · exact Int.sub_nonneg_of_le h₂
-
 /-! ### toNat -/
 
 theorem toNat_eq_max : ∀ a : Int, (toNat a : Int) = max a 0
@@ -581,8 +492,8 @@ theorem toNat_of_nonneg {a : Int} (h : 0 ≤ a) : (toNat a : Int) = a := by
 
 @[simp] theorem ofNat_toNat (a : Int) : (a.toNat : Int) = max a 0 := by
   match a with
-  | (n : Nat) => simp
-  | -(n + 1 : Nat) => norm_cast
+  | Int.ofNat n => simp
+  | Int.negSucc n => simp
 
 theorem self_le_toNat (a : Int) : a ≤ toNat a := by rw [toNat_eq_max]; apply Int.le_max_left
 
@@ -618,15 +529,12 @@ theorem toNat_sub_toNat_neg : ∀ n : Int, ↑n.toNat - ↑(-n).toNat = n
   | 0 => rfl
   | _+1 => rfl
 
-/-! ### toNat? -/
+/-! ### toNat' -/
 
-theorem mem_toNat? : ∀ {a : Int} {n : Nat}, toNat? a = some n ↔ a = n
-  | (m : Nat), n => by simp [toNat?, Int.ofNat_inj]
+theorem mem_toNat' : ∀ {a : Int} {n : Nat}, toNat' a = some n ↔ a = n
+  | (m : Nat), n => by simp [toNat', Int.ofNat_inj]
   | -[m+1], n => by constructor <;> nofun
 
-@[deprecated mem_toNat? (since := "2025-03-11")]
-abbrev mem_toNat' := @mem_toNat?
-
 /-! ## Order properties of the integers -/
 
 protected theorem le_of_not_le {a b : Int} : ¬ a ≤ b → b ≤ a := (Int.le_total a b).resolve_left
@@ -646,10 +554,10 @@ protected theorem lt_of_add_lt_add_left {a b c : Int} (h : a + b < a + c) : b <
 protected theorem lt_of_add_lt_add_right {a b c : Int} (h : a + b < c + b) : a < c :=
   Int.lt_of_add_lt_add_left (a := b) <| by rwa [Int.add_comm b a, Int.add_comm b c]
 
-@[simp] protected theorem add_lt_add_iff_left (a : Int) : a + b < a + c ↔ b < c :=
+protected theorem add_lt_add_iff_left (a : Int) : a + b < a + c ↔ b < c :=
   ⟨Int.lt_of_add_lt_add_left, (Int.add_lt_add_left · _)⟩
 
-@[simp] protected theorem add_lt_add_iff_right (c : Int) : a + c < b + c ↔ a < b :=
+protected theorem add_lt_add_iff_right (c : Int) : a + c < b + c ↔ a < b :=
   ⟨Int.lt_of_add_lt_add_right, (Int.add_lt_add_right · _)⟩
 
 protected theorem add_lt_add {a b c d : Int} (h₁ : a < b) (h₂ : c < d) : a + c < b + d :=
@@ -844,18 +752,6 @@ protected theorem sub_le_sub_right {a b : Int} (h : a ≤ b) (c : Int) : a - c
 protected theorem sub_le_sub {a b c d : Int} (hab : a ≤ b) (hcd : c ≤ d) : a - d ≤ b - c :=
   Int.add_le_add hab (Int.neg_le_neg hcd)
 
-protected theorem le_of_sub_le_sub_left {a b c : Int} (h : c - a ≤ c - b) : b ≤ a :=
-  Int.le_of_neg_le_neg <| Int.le_of_add_le_add_left h
-
-protected theorem le_of_sub_le_sub_right {a b c : Int} (h : a - c ≤ b - c) : a ≤ b :=
-  Int.le_of_add_le_add_right h
-
-@[simp] protected theorem sub_le_sub_left_iff {a b c : Int} : c - a ≤ c - b ↔ b ≤ a :=
-  ⟨Int.le_of_sub_le_sub_left, (Int.sub_le_sub_left · c)⟩
-
-@[simp] protected theorem sub_le_sub_right_iff {a b c : Int} : a - c ≤ b - c ↔ a ≤ b :=
-  ⟨Int.le_of_sub_le_sub_right, (Int.sub_le_sub_right · c)⟩
-
 protected theorem add_lt_of_lt_neg_add {a b c : Int} (h : b < -a + c) : a + b < c := by
   have h := Int.add_lt_add_left h a
   rwa [Int.add_neg_cancel_left] at h
@@ -964,11 +860,11 @@ protected theorem lt_of_sub_lt_sub_right {a b c : Int} (h : a - c < b - c) : a <
   ⟨Int.lt_of_sub_lt_sub_right, (Int.sub_lt_sub_right · c)⟩
 
 protected theorem sub_lt_sub_of_le_of_lt {a b c d : Int}
-    (hab : a ≤ b) (hcd : c < d) : a - d < b - c :=
+  (hab : a ≤ b) (hcd : c < d) : a - d < b - c :=
   Int.add_lt_add_of_le_of_lt hab (Int.neg_lt_neg hcd)
 
 protected theorem sub_lt_sub_of_lt_of_le {a b c d : Int}
-    (hab : a < b) (hcd : c ≤ d) : a - d < b - c :=
+  (hab : a < b) (hcd : c ≤ d) : a - d < b - c :=
   Int.add_lt_add_of_lt_of_le hab (Int.neg_le_neg hcd)
 
 protected theorem add_le_add_three {a b c d e f : Int}
@@ -1042,22 +938,6 @@ protected theorem mul_self_le_mul_self {a b : Int} (h1 : 0 ≤ a) (h2 : a ≤ b)
 protected theorem mul_self_lt_mul_self {a b : Int} (h1 : 0 ≤ a) (h2 : a < b) : a * a < b * b :=
   Int.mul_lt_mul' (Int.le_of_lt h2) h2 h1 (Int.lt_of_le_of_lt h1 h2)
 
-protected theorem nonneg_of_mul_nonneg_left {a b : Int}
-    (h : 0 ≤ a * b) (hb : 0 < b) : 0 ≤ a :=
-  Int.le_of_not_gt fun ha => Int.not_le_of_gt (Int.mul_neg_of_neg_of_pos ha hb) h
-
-protected theorem nonneg_of_mul_nonneg_right {a b : Int}
-    (h : 0 ≤ a * b) (ha : 0 < a) : 0 ≤ b :=
-  Int.le_of_not_gt fun hb => Int.not_le_of_gt (Int.mul_neg_of_pos_of_neg ha hb) h
-
-protected theorem nonpos_of_mul_nonpos_left {a b : Int}
-    (h : a * b ≤ 0) (hb : 0 < b) : a ≤ 0 :=
-  Int.le_of_not_gt fun ha : a > 0 => Int.not_le_of_gt (Int.mul_pos ha hb) h
-
-protected theorem nonpos_of_mul_nonpos_right {a b : Int}
-    (h : a * b ≤ 0) (ha : 0 < a) : b ≤ 0 :=
-  Int.le_of_not_gt fun hb : b > 0 => Int.not_le_of_gt (Int.mul_pos ha hb) h
-
 /- ## sign -/
 
 @[simp] theorem sign_zero : sign 0 = 0 := rfl
@@ -1108,10 +988,10 @@ theorem neg_of_sign_eq_neg_one : ∀ {a : Int}, sign a = -1 → a < 0
   | 0, h => nomatch h
   | -[_+1], _ => negSucc_lt_zero _
 
-@[simp] theorem sign_eq_one_iff_pos {a : Int} : sign a = 1 ↔ 0 < a :=
+theorem sign_eq_one_iff_pos {a : Int} : sign a = 1 ↔ 0 < a :=
   ⟨pos_of_sign_eq_one, sign_eq_one_of_pos⟩
 
-@[simp] theorem sign_eq_neg_one_iff_neg {a : Int} : sign a = -1 ↔ a < 0 :=
+theorem sign_eq_neg_one_iff_neg {a : Int} : sign a = -1 ↔ a < 0 :=
   ⟨neg_of_sign_eq_neg_one, sign_eq_neg_one_of_neg⟩
 
 @[simp] theorem sign_eq_zero_iff_zero {a : Int} : sign a = 0 ↔ a = 0 :=
@@ -1123,7 +1003,7 @@ theorem neg_of_sign_eq_neg_one : ∀ {a : Int}, sign a = -1 → a < 0
   | .ofNat (_ + 1) => rfl
   | .negSucc _ => rfl
 
-@[simp] theorem sign_nonneg_iff : 0 ≤ sign x ↔ 0 ≤ x := by
+@[simp] theorem sign_nonneg : 0 ≤ sign x ↔ 0 ≤ x := by
   match x with
   | 0 => rfl
   | .ofNat (_ + 1) =>
@@ -1131,26 +1011,6 @@ theorem neg_of_sign_eq_neg_one : ∀ {a : Int}, sign a = -1 → a < 0
     exact Int.le_add_one (ofNat_nonneg _)
   | .negSucc _ => simp +decide [sign]
 
-@[deprecated sign_nonneg_iff (since := "2025-03-11")] abbrev sign_nonneg := @sign_nonneg_iff
-
-@[simp] theorem sign_pos_iff : 0 < sign x ↔ 0 < x := by
-  match x with
-  | 0
-  | .ofNat (_ + 1) => simp
-  | .negSucc x => simp
-
-@[simp] theorem sign_nonpos_iff : sign x ≤ 0 ↔ x ≤ 0 := by
-  match x with
-  | 0 => rfl
-  | .ofNat (_ + 1) => simp
-  | .negSucc _ => simpa using negSucc_le_zero _
-
-@[simp] theorem sign_neg_iff : sign x < 0 ↔ x < 0 := by
-  match x with
-  | 0 => simp
-  | .ofNat (_ + 1) => simpa using le.intro_sub _ rfl
-  | .negSucc _ => simp
-
 @[simp] theorem mul_sign_self : ∀ i : Int, i * sign i = natAbs i
   | succ _ => Int.mul_one _
   | 0 => Int.mul_zero _
@@ -1161,12 +1021,6 @@ theorem neg_of_sign_eq_neg_one : ∀ {a : Int}, sign a = -1 → a < 0
 @[simp] theorem sign_mul_self : sign i * i = natAbs i := by
   rw [Int.mul_comm, mul_sign_self]
 
-theorem sign_trichotomy (a : Int) : sign a = 1 ∨ sign a = 0 ∨ sign a = -1 := by
-  match a with
-  | 0 => simp
-  | .ofNat (_ + 1) => simp
-  | .negSucc _ => simp
-
 /- ## natAbs -/
 
 theorem natAbs_ne_zero {a : Int} : a.natAbs ≠ 0 ↔ a ≠ 0 := not_congr Int.natAbs_eq_zero
@@ -1175,7 +1029,7 @@ theorem natAbs_mul_self : ∀ {a : Int}, ↑(natAbs a * natAbs a) = a * a
   | ofNat _ => rfl
   | -[_+1]  => rfl
 
-protected theorem eq_nat_or_neg (a : Int) : ∃ n : Nat, a = n ∨ a = -↑n := ⟨_, natAbs_eq a⟩
+theorem eq_nat_or_neg (a : Int) : ∃ n : Nat, a = n ∨ a = -↑n := ⟨_, natAbs_eq a⟩
 
 theorem natAbs_mul_natAbs_eq {a b : Int} {c : Nat}
     (h : a * b = (c : Int)) : a.natAbs * b.natAbs = c := by rw [← natAbs_mul, h, natAbs.eq_def]
@@ -1189,7 +1043,7 @@ theorem natAbs_eq_iff {a : Int} {n : Nat} : a.natAbs = n ↔ a = n ∨ a = -↑n
 theorem natAbs_add_le (a b : Int) : natAbs (a + b) ≤ natAbs a + natAbs b := by
   suffices ∀ a b : Nat, natAbs (subNatNat a b.succ) ≤ (a + b).succ by
     match a, b with
-    | (a:Nat), (b:Nat) => rw [← ofNat_add, natAbs_ofNat]; apply Nat.le_refl
+    | (a:Nat), (b:Nat) => rw [ofNat_add_ofNat, natAbs_ofNat]; apply Nat.le_refl
     | (a:Nat), -[b+1]  => rw [natAbs_ofNat, natAbs_negSucc]; apply this
     | -[a+1],  (b:Nat) =>
       rw [natAbs_negSucc, natAbs_ofNat, Nat.succ_add, Nat.add_comm a b]; apply this
@@ -1208,7 +1062,6 @@ theorem natAbs_add_le (a b : Int) : natAbs (a + b) ≤ natAbs a + natAbs b := by
 theorem natAbs_sub_le (a b : Int) : natAbs (a - b) ≤ natAbs a + natAbs b := by
   rw [← Int.natAbs_neg b]; apply natAbs_add_le
 
-@[deprecated negSucc_eq (since := "2025-03-11")]
 theorem negSucc_eq' (m : Nat) : -[m+1] = -m - 1 := by simp only [negSucc_eq, Int.neg_add]; rfl
 
 theorem natAbs_lt_natAbs_of_nonneg_of_lt {a b : Int}
@@ -1216,10 +1069,7 @@ theorem natAbs_lt_natAbs_of_nonneg_of_lt {a b : Int}
   match a, b, eq_ofNat_of_zero_le w₁, eq_ofNat_of_zero_le (Int.le_trans w₁ (Int.le_of_lt w₂)) with
   | _, _, ⟨_, rfl⟩, ⟨_, rfl⟩ => ofNat_lt.1 w₂
 
-theorem natAbs_eq_iff_mul_eq_zero : natAbs a = n ↔ (a - n) * (a + n) = 0 := by
+theorem eq_natAbs_iff_mul_eq_zero : natAbs a = n ↔ (a - n) * (a + n) = 0 := by
   rw [natAbs_eq_iff, Int.mul_eq_zero, ← Int.sub_neg, Int.sub_eq_zero, Int.sub_eq_zero]
 
-@[deprecated natAbs_eq_iff_mul_eq_zero (since := "2025-03-11")]
-abbrev eq_natAbs_iff_mul_eq_zero := @natAbs_eq_iff_mul_eq_zero
-
 end Int

src/Init/Data/Int/Pow.lean

@@ -11,22 +11,12 @@ namespace Int
 
 /-! # pow -/
 
-@[simp] protected theorem pow_zero (b : Int) : b^0 = 1 := rfl
+protected theorem pow_zero (b : Int) : b^0 = 1 := rfl
 
 protected theorem pow_succ (b : Int) (e : Nat) : b ^ (e+1) = (b ^ e) * b := rfl
 protected theorem pow_succ' (b : Int) (e : Nat) : b ^ (e+1) = b * (b ^ e) := by
   rw [Int.mul_comm, Int.pow_succ]
 
-protected theorem pow_pos {n : Int} {m : Nat} : 0 < n → 0 < n ^ m := by
-  induction m with
-  | zero => simp
-  | succ m ih => exact fun h => Int.mul_pos (ih h) h
-
-protected theorem pow_nonneg {n : Int} {m : Nat} : 0 ≤ n → 0 ≤ n ^ m := by
-  induction m with
-  | zero => simp
-  | succ m ih => exact fun h => Int.mul_nonneg (ih h) h
-
 @[deprecated Nat.pow_le_pow_left (since := "2025-02-17")]
 abbrev pow_le_pow_of_le_left := @Nat.pow_le_pow_left
 
@@ -37,11 +27,11 @@ abbrev pow_le_pow_of_le_right := @Nat.pow_le_pow_right
 abbrev pos_pow_of_pos := @Nat.pow_pos
 
 @[norm_cast]
-protected theorem natCast_pow (b n : Nat) : ((b^n : Nat) : Int) = (b : Int) ^ n := by
+theorem natCast_pow (b n : Nat) : ((b^n : Nat) : Int) = (b : Int) ^ n := by
   match n with
   | 0 => rfl
   | n + 1 =>
-    simp only [Nat.pow_succ, Int.pow_succ, Int.natCast_mul, Int.natCast_pow _ n]
+    simp only [Nat.pow_succ, Int.pow_succ, natCast_mul, natCast_pow _ n]
 
 @[simp]
 protected theorem two_pow_pred_sub_two_pow {w : Nat} (h : 0 < w) :

src/Init/Data/List/Attach.lean

@@ -13,44 +13,29 @@ set_option linter.indexVariables true -- Enforce naming conventions for index va
 
 namespace List
 
-/--
-Maps a partially defined function (defined on those terms of `α` that satisfy a predicate `P`) over
-a list `l : List α`, given a proof that every element of `l` in fact satisfies `P`.
-
-`O(|l|)`. `List.pmap`, named for “partial map,” is the equivalent of `List.map` for such partial
-functions.
--/
+/-- `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`. -/
 def pmap {P : α → Prop} (f : ∀ a, P a → β) : ∀ l : List α, (H : ∀ a ∈ l, P a) → List β
   | [], _ => []
   | a :: l, H => f a (forall_mem_cons.1 H).1 :: pmap f l (forall_mem_cons.1 H).2
 
 /--
-Unsafe implementation of `attachWith` that takes advantage of the fact that the representation of
+Unsafe implementation of `attachWith`, taking advantage of the fact that the representation of
 `List {x // P x}` is the same as the input `List α`.
+(Someday, the compiler might do this optimization automatically, but until then...)
 -/
 @[inline] private unsafe def attachWithImpl
     (l : List α) (P : α → Prop) (_ : ∀ x ∈ l, P x) : List {x // P x} := unsafeCast l
 
-/--
-“Attaches” individual proofs to a list of values that satisfy a predicate `P`, returning a list 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 `l` to produce a new list
+  with the same elements but in the type `{x // P x}`. -/
 @[implemented_by attachWithImpl] def attachWith
     (l : List α) (P : α → Prop) (H : ∀ x ∈ l, P x) : List {x // P x} := pmap Subtype.mk l H
 
-/--
-“Attaches” the proof that the elements of `l` are in fact elements of `l`, producing a new list with
-the same elements but in the subtype `{ x // x ∈ l }`.
-
-`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
-`List.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 `l` are in `l` to produce a new list
+  with the same elements but in the type `{x // x ∈ l}`. -/
 @[inline] def attach (l : List α) : List {x // x ∈ l} := attachWith l _ fun _ => id
 
 /-- Implementation of `pmap` using the zero-copy version of `attach`. -/
@@ -65,9 +50,9 @@ well-founded recursion mechanism to prove that the function terminates.
   | cons _ l', hL' => congrArg _ <| go l' fun _ hx => hL' (.tail _ hx)
   exact go l h'
 
-@[simp] theorem pmap_nil {P : α → Prop} {f : ∀ a, P a → β} : pmap f [] (by simp) = [] := rfl
+@[simp] theorem pmap_nil {P : α → Prop} (f : ∀ a, P a → β) : pmap f [] (by simp) = [] := rfl
 
-@[simp] theorem pmap_cons {P : α → Prop} {f : ∀ a, P a → β} {a : α} {l : List α} (h : ∀ b ∈ a :: l, P b) :
+@[simp] theorem pmap_cons {P : α → Prop} (f : ∀ a, P a → β) (a : α) (l : List α) (h : ∀ b ∈ a :: l, P b) :
     pmap f (a :: l) h = f a (forall_mem_cons.1 h).1 :: pmap f l (forall_mem_cons.1 h).2 := rfl
 
 @[simp] theorem attach_nil : ([] : List α).attach = [] := rfl
@@ -75,7 +60,7 @@ well-founded recursion mechanism to prove that the function terminates.
 @[simp] theorem attachWith_nil : ([] : List α).attachWith P H = [] := rfl
 
 @[simp]
-theorem pmap_eq_map {p : α → Prop} {f : α → β} {l : List α} (H) :
+theorem pmap_eq_map (p : α → Prop) (f : α → β) (l : List α) (H) :
     @pmap _ _ p (fun a _ => f a) l H = map f l := by
   induction l
   · rfl
@@ -86,18 +71,18 @@ theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a,
   induction l with
   | nil => rfl
   | cons x l ih =>
-    rw [pmap, pmap, h _ mem_cons_self, ih fun a ha => h a (mem_cons_of_mem _ ha)]
+    rw [pmap, pmap, h _ (mem_cons_self _ _), ih fun a ha => h a (mem_cons_of_mem _ ha)]
 
 @[deprecated pmap_congr_left (since := "2024-09-06")] abbrev pmap_congr := @pmap_congr_left
 
-theorem map_pmap {p : α → Prop} {g : β → γ} {f : ∀ a, p a → β} {l : List α} (H) :
+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
   induction l
   · rfl
   · simp only [*, pmap, map]
 
-theorem pmap_map {p : β → Prop} {g : ∀ b, p b → γ} {f : α → β} {l : List α} (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
+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
   induction l
   · rfl
   · simp only [*, pmap, map]
@@ -114,7 +99,7 @@ theorem attachWith_congr {l₁ l₂ : List α} (w : l₁ = l₂) {P : α → Pro
 
 @[simp] theorem attach_cons {x : α} {xs : List α} :
     (x :: xs).attach =
-      ⟨x, mem_cons_self⟩ :: xs.attach.map fun ⟨y, h⟩ => ⟨y, mem_cons_of_mem x h⟩ := by
+      ⟨x, mem_cons_self x xs⟩ :: xs.attach.map fun ⟨y, h⟩ => ⟨y, mem_cons_of_mem x h⟩ := by
   simp only [attach, attachWith, pmap, map_pmap, cons.injEq, true_and]
   apply pmap_congr_left
   intros a _ m' _
@@ -122,43 +107,42 @@ theorem attachWith_congr {l₁ l₂ : List α} (w : l₁ = l₂) {P : α → Pro
 
 @[simp]
 theorem attachWith_cons {x : α} {xs : List α} {p : α → Prop} (h : ∀ a ∈ x :: xs, p a) :
-    (x :: xs).attachWith p h = ⟨x, h x (mem_cons_self)⟩ ::
+    (x :: xs).attachWith p h = ⟨x, h x (mem_cons_self x xs)⟩ ::
       xs.attachWith p (fun a ha ↦ h a (mem_cons_of_mem x ha)) :=
   rfl
 
-theorem pmap_eq_map_attach {p : α → Prop} {f : ∀ a, p a → β} {l : List α} (H) :
+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
   rw [attach, attachWith, map_pmap]; exact pmap_congr_left l fun _ _ _ _ => rfl
 
 @[simp]
-theorem pmap_eq_attachWith {p q : α → Prop} {f : ∀ a, p a → q a} {l : List α} (H) :
+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
   induction l with
   | nil => rfl
   | cons a l ih =>
     simp [pmap, attachWith, ih]
 
-theorem attach_map_val {l : List α} {f : α → β} :
+theorem attach_map_val (l : List α) (f : α → β) :
     (l.attach.map fun (i : {i // i ∈ l}) => f i) = l.map f := by
-  rw [attach, attachWith, map_pmap]; exact pmap_eq_map _
+  rw [attach, attachWith, map_pmap]; exact pmap_eq_map _ _ _ _
 
 @[deprecated attach_map_val (since := "2025-02-17")]
 abbrev attach_map_coe := @attach_map_val
 
--- The argument `l : List α` is explicit to allow rewriting from right to left.
 theorem attach_map_subtype_val (l : List α) : l.attach.map Subtype.val = l :=
-  attach_map_val.trans (List.map_id _)
+  (attach_map_val _ _).trans (List.map_id _)
 
-theorem attachWith_map_val {p : α → Prop} {f : α → β} {l : List α} (H : ∀ a ∈ l, p a) :
+theorem attachWith_map_val {p : α → Prop} (f : α → β) (l : List α) (H : ∀ a ∈ l, p a) :
     ((l.attachWith p H).map fun (i : { i // p i}) => f i) = l.map f := by
-  rw [attachWith, map_pmap]; exact pmap_eq_map _
+  rw [attachWith, map_pmap]; exact pmap_eq_map _ _ _ _
 
 @[deprecated attachWith_map_val (since := "2025-02-17")]
 abbrev attachWith_map_coe := @attachWith_map_val
 
-theorem attachWith_map_subtype_val {p : α → Prop} {l : List α} (H : ∀ a ∈ l, p a) :
+theorem attachWith_map_subtype_val {p : α → Prop} (l : List α) (H : ∀ a ∈ l, p a) :
     (l.attachWith p H).map Subtype.val = l :=
-  (attachWith_map_val _).trans (List.map_id _)
+  (attachWith_map_val _ _ _).trans (List.map_id _)
 
 @[simp]
 theorem mem_attach (l : List α) : ∀ x, x ∈ l.attach
@@ -168,7 +152,7 @@ theorem mem_attach (l : List α) : ∀ x, x ∈ l.attach
     exact m
 
 @[simp]
-theorem mem_attachWith {l : List α} {q : α → Prop} (H) (x : {x // q x}) :
+theorem mem_attachWith (l : List α) {q : α → Prop} (H) (x : {x // q x}) :
     x ∈ l.attachWith q H ↔ x.1 ∈ l := by
   induction l with
   | nil => simp
@@ -241,7 +225,7 @@ theorem attachWith_ne_nil_iff {l : List α} {P : α → Prop} {H : ∀ a ∈ l,
 @[deprecated attach_ne_nil_iff (since := "2024-09-06")] abbrev attach_ne_nil := @attach_ne_nil_iff
 
 @[simp]
-theorem getElem?_pmap {p : α → Prop} {f : ∀ a, p a → β} {l : List α} (h : ∀ a ∈ l, p a) (i : Nat) :
+theorem getElem?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List 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
   induction l generalizing i with
   | nil => simp
@@ -258,7 +242,6 @@ theorem get?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h :
   simp only [get?_eq_getElem?]
   simp [getElem?_pmap, h]
 
--- The argument `f` is explicit to allow rewriting from right to left.
 @[simp]
 theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h : ∀ a ∈ l, p a) {i : Nat}
     (hn : i < (pmap f l h).length) :
@@ -304,19 +287,19 @@ theorem getElem_attach {xs : List α} {i : Nat} (h : i < xs.attach.length) :
     xs.attach[i] = ⟨xs[i]'(by simpa using h), getElem_mem (by simpa using h)⟩ :=
   getElem_attachWith h
 
-@[simp] theorem pmap_attach {l : List α} {p : {x // x ∈ l} → Prop} {f : ∀ a, p a → β} (H) :
+@[simp] theorem pmap_attach (l : List 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
   apply ext_getElem <;> simp
 
-@[simp] theorem pmap_attachWith {l : List α} {p : {x // q x} → Prop} {f : ∀ a, p a → β} (H₁ H₂) :
+@[simp] theorem pmap_attachWith (l : List 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
   apply ext_getElem <;> simp
 
-@[simp] theorem head?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp] theorem head?_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : List α)
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.pmap f H).head? = xs.attach.head?.map fun ⟨a, m⟩ => f a (H a m) := by
   induction xs with
@@ -325,7 +308,7 @@ theorem getElem_attach {xs : List α} {i : Nat} (h : i < xs.attach.length) :
     simp at ih
     simp [head?_pmap, ih]
 
-@[simp] theorem head_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp] theorem head_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : List α)
     (H : ∀ (a : α), a ∈ xs → P a) (h : xs.pmap f H ≠ []) :
     (xs.pmap f H).head h = f (xs.head (by simpa using h)) (H _ (head_mem _)) := by
   induction xs with
@@ -344,7 +327,7 @@ theorem getElem_attach {xs : List α} {i : Nat} (h : i < xs.attach.length) :
   | nil => simp at h
   | cons x xs => simp [head_attachWith, h]
 
-@[simp] theorem head?_attach {xs : List α} :
+@[simp] theorem head?_attach (xs : List α) :
     xs.attach.head? = xs.head?.pbind (fun a h => some ⟨a, mem_of_mem_head? h⟩) := by
   cases xs <;> simp_all
 
@@ -354,7 +337,7 @@ theorem getElem_attach {xs : List α} {i : Nat} (h : i < xs.attach.length) :
   | nil => simp at h
   | cons x xs => simp [head_attach, h]
 
-@[simp] theorem tail_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp] theorem tail_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : List α)
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.pmap f H).tail = xs.tail.pmap f (fun a h => H a (mem_of_mem_tail h)) := by
   cases xs <;> simp
@@ -364,29 +347,29 @@ theorem getElem_attach {xs : List α} {i : Nat} (h : i < xs.attach.length) :
     (xs.attachWith P H).tail = xs.tail.attachWith P (fun a h => H a (mem_of_mem_tail h)) := by
   cases xs <;> simp
 
-@[simp] theorem tail_attach {xs : List α} :
+@[simp] theorem tail_attach (xs : List α) :
     xs.attach.tail = xs.tail.attach.map (fun ⟨x, h⟩ => ⟨x, mem_of_mem_tail h⟩) := by
   cases xs <;> simp
 
-theorem foldl_pmap {l : List α} {P : α → Prop} {f : (a : α) → P a → β}
-    (H : ∀ (a : α), a ∈ l → P a) (g : γ → β → γ) (x : γ) :
+theorem foldl_pmap (l : List 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 {l : List α} {P : α → Prop} {f : (a : α) → P a → β}
-    (H : ∀ (a : α), a ∈ l → P a) (g : β → γ → γ) (x : γ) :
+theorem foldr_pmap (l : List 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
-    {l : List α} {q : α → Prop} (H : ∀ a, a ∈ l → q a) {f : β → { x // q x } → β} {b} :
+    (l : List α) {q : α → Prop} (H : ∀ a, a ∈ l → q a) {f : β → { x // q x} → β} {b} :
     (l.attachWith q H).foldl f b = l.attach.foldl (fun b ⟨a, h⟩ => f b ⟨a, H _ h⟩) b := by
   induction l generalizing b with
   | nil => simp
   | cons a l ih => simp [ih, foldl_map]
 
 @[simp] theorem foldr_attachWith
-    {l : List α} {q : α → Prop} (H : ∀ a, a ∈ l → q a) {f : { x // q x } → β → β} {b} :
+    (l : List α) {q : α → Prop} (H : ∀ a, a ∈ l → q a) {f : { x // q x} → β → β} {b} :
     (l.attachWith q H).foldr f b = l.attach.foldr (fun a acc => f ⟨a.1, H _ a.2⟩ acc) b := by
   induction l generalizing b with
   | nil => simp
@@ -402,7 +385,7 @@ 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 {l : List α} {f : β → α → β} {b : β} :
+theorem foldl_attach (l : List α) (f : β → α → β) (b : β) :
     l.attach.foldl (fun acc t => f acc t.1) b = l.foldl f b := by
   induction l generalizing b with
   | nil => simp
@@ -418,28 +401,28 @@ 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 {l : List α} {f : α → β → β} {b : β} :
+theorem foldr_attach (l : List α) (f : α → β → β) (b : β) :
     l.attach.foldr (fun t acc => f t.1 acc) b = l.foldr f b := by
   induction l generalizing b with
   | nil => simp
   | cons a l ih => rw [foldr_cons, attach_cons, foldr_cons, foldr_map, ih]
 
-theorem attach_map {l : List α} {f : α → β} :
-    (l.map f).attach = l.attach.map (fun ⟨x, h⟩ => ⟨f x, mem_map_of_mem h⟩) := by
+theorem attach_map {l : List α} (f : α → β) :
+    (l.map f).attach = l.attach.map (fun ⟨x, h⟩ => ⟨f x, mem_map_of_mem f h⟩) := by
   induction l <;> simp [*]
 
-theorem attachWith_map {l : List 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 h))).map
+theorem attachWith_map {l : List 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
   induction l <;> simp [*]
 
 @[simp] theorem map_attachWith {l : List α} {P : α → Prop} {H : ∀ (a : α), a ∈ l → P a}
-    {f : { x // P x } → β} :
+    (f : { x // P x } → β) :
     (l.attachWith P H).map f = l.attach.map fun ⟨x, h⟩ => f ⟨x, H _ h⟩ := by
   induction l <;> simp_all
 
 theorem map_attachWith_eq_pmap {l : List α} {P : α → Prop} {H : ∀ (a : α), a ∈ l → P a}
-    {f : { x // P x } → β} :
+    (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
   induction l with
@@ -450,7 +433,7 @@ theorem map_attachWith_eq_pmap {l : List α} {P : α → Prop} {H : ∀ (a : α)
     simp
 
 /-- See also `pmap_eq_map_attach` for writing `pmap` in terms of `map` and `attach`. -/
-theorem map_attach_eq_pmap {l : List α} {f : { x // x ∈ l } → β} :
+theorem map_attach_eq_pmap {l : List α} (f : { x // x ∈ l } → β) :
     l.attach.map f = l.pmap (fun a h => f ⟨a, h⟩) (fun _ => id) := by
   induction l with
   | nil => rfl
@@ -496,7 +479,7 @@ theorem attach_filterMap {l : List α} {f : α → Option β} :
 theorem attach_filter {l : List 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
-  rw [attach_congr (congrFun filterMap_eq_filter.symm _), attach_filterMap, map_filterMap]
+  rw [attach_congr (congrFun (filterMap_eq_filter _).symm _), attach_filterMap, map_filterMap]
   simp only [Option.guard]
   congr
   ext1
@@ -523,13 +506,13 @@ theorem filter_attachWith {q : α → Prop} {l : List α} {p : {x // q x} → Bo
     simp only [attachWith_cons, filter_cons]
     split <;> simp_all [Function.comp_def, filter_map]
 
-theorem pmap_pmap {p : α → Prop} {q : β → Prop} {g : ∀ a, p a → β} {f : ∀ b, q b → γ} {l} (H₁ H₂) :
+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
   simp [pmap_eq_map_attach, attach_map]
 
-@[simp] theorem pmap_append {p : ι → Prop} {f : ∀ a : ι, p a → α} {l₁ l₂ : List ι}
+@[simp] theorem pmap_append {p : ι → Prop} (f : ∀ a : ι, p a → α) (l₁ l₂ : List 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)) ++
@@ -540,13 +523,13 @@ theorem pmap_pmap {p : α → Prop} {q : β → Prop} {g : ∀ a, p a → β} {f
     dsimp only [pmap, cons_append]
     rw [ih]
 
-theorem pmap_append' {p : α → Prop} {f : ∀ a : α, p a → β} {l₁ l₂ : List α}
+theorem pmap_append' {p : α → Prop} (f : ∀ a : α, p a → β) (l₁ l₂ : List α)
     (h₁ : ∀ a ∈ l₁, p a) (h₂ : ∀ a ∈ l₂, p a) :
     ((l₁ ++ l₂).pmap f fun a ha => (List.mem_append.1 ha).elim (h₁ a) (h₂ a)) =
       l₁.pmap f h₁ ++ l₂.pmap f h₂ :=
-  pmap_append _
+  pmap_append f l₁ l₂ _
 
-@[simp] theorem attach_append {xs ys : List α} :
+@[simp] theorem attach_append (xs ys : List 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
   simp only [attach, attachWith, pmap, map_pmap, pmap_append]
@@ -559,12 +542,12 @@ theorem pmap_append' {p : α → Prop} {f : ∀ a : α, p a → β} {l₁ l₂ :
       ys.attachWith P (fun a h => H a (mem_append_right xs h)) := by
   simp only [attachWith, attach_append, map_pmap, pmap_append]
 
-@[simp] theorem pmap_reverse {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp] theorem pmap_reverse {P : α → Prop} (f : (a : α) → P a → β) (xs : List 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 : List α}
+theorem reverse_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : List 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]
@@ -580,21 +563,21 @@ theorem reverse_attachWith {P : α → Prop} {xs : List α}
     (xs.attachWith P H).reverse = (xs.reverse.attachWith P (fun a h => H a (by simpa using h))) :=
   reverse_pmap ..
 
-@[simp] theorem attach_reverse {xs : List α} :
+@[simp] theorem attach_reverse (xs : List α) :
     xs.reverse.attach = xs.attach.reverse.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
   simp only [attach, attachWith, reverse_pmap, map_pmap]
   apply pmap_congr_left
   intros
   rfl
 
-theorem reverse_attach {xs : List α} :
+theorem reverse_attach (xs : List α) :
     xs.attach.reverse = xs.reverse.attach.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
   simp only [attach, attachWith, reverse_pmap, map_pmap]
   apply pmap_congr_left
   intros
   rfl
 
-@[simp] theorem getLast?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp] theorem getLast?_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : List α)
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.pmap f H).getLast? = xs.attach.getLast?.map fun ⟨a, m⟩ => f a (H a m) := by
   simp only [getLast?_eq_head?_reverse]
@@ -602,7 +585,7 @@ theorem reverse_attach {xs : List α} :
   simp only [Option.map_map]
   congr
 
-@[simp] theorem getLast_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp] theorem getLast_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : List α)
     (H : ∀ (a : α), a ∈ xs → P a) (h : xs.pmap f H ≠ []) :
     (xs.pmap f H).getLast h = f (xs.getLast (by simpa using h)) (H _ (getLast_mem _)) := by
   simp only [getLast_eq_head_reverse]
@@ -631,26 +614,26 @@ theorem getLast_attach {xs : List α} (h : xs.attach ≠ []) :
   simp only [getLast_eq_head_reverse, reverse_attach, head_map, head_attach]
 
 @[simp]
-theorem countP_attach {l : List α} {p : α → Bool} :
+theorem countP_attach (l : List α) (p : α → Bool) :
     l.attach.countP (fun a : {x // x ∈ l} => p a) = l.countP p := by
   simp only [← Function.comp_apply (g := Subtype.val), ← countP_map, attach_map_subtype_val]
 
 @[simp]
-theorem countP_attachWith {p : α → Prop} {q : α → Bool} {l : List α} (H : ∀ a ∈ l, p a) :
+theorem countP_attachWith {p : α → Prop} (l : List 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
   simp only [← Function.comp_apply (g := Subtype.val), ← countP_map, attachWith_map_subtype_val]
 
 @[simp]
-theorem count_attach [DecidableEq α] {l : List α} {a : {x // x ∈ l}} :
+theorem count_attach [DecidableEq α] (l : List α) (a : {x // x ∈ l}) :
     l.attach.count a = l.count ↑a :=
-  Eq.trans (countP_congr fun _ _ => by simp [Subtype.ext_iff]) <| countP_attach
+  Eq.trans (countP_congr fun _ _ => by simp [Subtype.ext_iff]) <| countP_attach _ _
 
 @[simp]
-theorem count_attachWith [DecidableEq α] {p : α → Prop} {l : List α} (H : ∀ a ∈ l, p a) {a : {x // p x}} :
+theorem count_attachWith [DecidableEq α] {p : α → Prop} (l : List α) (H : ∀ a ∈ l, p a) (a : {x // p x}) :
     (l.attachWith p H).count a = l.count ↑a :=
-  Eq.trans (countP_congr fun _ _ => by simp [Subtype.ext_iff]) <| countP_attachWith _
+  Eq.trans (countP_congr fun _ _ => by simp [Subtype.ext_iff]) <| countP_attachWith _ _ _
 
-@[simp] theorem countP_pmap {p : α → Prop} {g : ∀ a, p a → β} {f : β → Bool} {l : List α} (H₁) :
+@[simp] theorem countP_pmap {p : α → Prop} (g : ∀ a, p a → β) (f : β → Bool) (l : List 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]
@@ -667,19 +650,11 @@ Further, we provide simp lemmas that push `unattach` inwards.
 -/
 
 /--
-Maps a list 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 an intermediate step by lemmas such as `map_subtype`,
+and is ideally subsequently simplified away by `unattach_attach`.
 
-This is the inverse of `List.attachWith` and a synonym for `l.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 [List.unattach, -List.map_subtype]`.
+If not, usually the right approach is `simp [List.unattach, -List.map_subtype]` to unfold.
 -/
 def unattach {α : Type _} {p : α → Prop} (l : List { x // p x }) : List α := l.map (·.val)
 
@@ -837,62 +812,62 @@ and simplifies these to the function directly taking the value.
 
 /-! ### Well-founded recursion preprocessing setup -/
 
-@[wf_preprocess] theorem map_wfParam {xs : List α} {f : α → β} :
+@[wf_preprocess] theorem map_wfParam (xs : List 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 : List (Subtype P)} {f : α → β} :
+@[wf_preprocess] theorem map_unattach (P : α → Prop) (xs : List (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 : List α} {f : β → α → β} {x : β} :
+@[wf_preprocess] theorem foldl_wfParam (xs : List 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 : List (Subtype P)} {f : β → α → β} {x : β} :
+@[wf_preprocess] theorem foldl_unattach (P : α → Prop) (xs : List (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 : List α} {f : α → β → β} {x : β} :
+@[wf_preprocess] theorem foldr_wfParam (xs : List 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 : List (Subtype P)} {f : α → β → β} {x : β} :
+@[wf_preprocess] theorem foldr_unattach (P : α → Prop) (xs : List (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 : List α} {f : α → Bool} :
+@[wf_preprocess] theorem filter_wfParam (xs : List 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 : List (Subtype P)} {f : α → Bool} :
+@[wf_preprocess] theorem filter_unattach (P : α → Prop) (xs : List (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 : List α} :
+@[wf_preprocess] theorem reverse_wfParam (xs : List α) :
     (wfParam xs).reverse = xs.attach.unattach.reverse := by simp [wfParam]
 
-@[wf_preprocess] theorem reverse_unattach {P : α → Prop} {xs : List (Subtype P)} :
+@[wf_preprocess] theorem reverse_unattach (P : α → Prop) (xs : List (Subtype P)) :
     xs.unattach.reverse = xs.reverse.unattach := by simp
 
-@[wf_preprocess] theorem filterMap_wfParam {xs : List α} {f : α → Option β} :
+@[wf_preprocess] theorem filterMap_wfParam (xs : List 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 : List (Subtype P)} {f : α → Option β} :
+@[wf_preprocess] theorem filterMap_unattach (P : α → Prop) (xs : List (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 : List α} {f : α → List β} :
+@[wf_preprocess] theorem flatMap_wfParam (xs : List α) (f : α → List β) :
     (wfParam xs).flatMap f = xs.attach.unattach.flatMap f := by
   simp [wfParam]
 
-@[wf_preprocess] theorem flatMap_unattach {P : α → Prop} {xs : List (Subtype P)} {f : α → List β} :
+@[wf_preprocess] theorem flatMap_unattach (P : α → Prop) (xs : List (Subtype P)) (f : α → List β) :
     xs.unattach.flatMap f = xs.flatMap fun ⟨x, h⟩ =>
       binderNameHint x f <| binderNameHint h () <| f (wfParam x) := by
   simp [wfParam]

src/Init/Data/List/BasicAux.lean

@@ -79,16 +79,10 @@ theorem get!_cons_zero [Inhabited α] (l : List α) (a : α) : (a::l).get! 0 = a
 /-! ### getD -/
 
 /--
-Returns the element at the provided index, counting from `0`. Returns `fallback` if the index is out
-of bounds.
+Returns the `i`-th element in the list (zero-based).
 
-To return an `Option` depending on whether the index is in bounds, use `as[i]?`. To panic if the
-index is out of bounds, use `as[i]!`.
-
-Examples:
- * `["spring", "summer", "fall", "winter"].getD 2 "never" = "fall"`
- * `["spring", "summer", "fall", "winter"].getD 0 "never" = "spring"`
- * `["spring", "summer", "fall", "winter"].getD 4 "never" = "never"`
+If the index is out of bounds (`i ≥ as.length`), this function returns `fallback`.
+See also `get?` and `get!`.
 -/
 def getD (as : List α) (i : Nat) (fallback : α) : α :=
   as[i]?.getD fallback
@@ -98,16 +92,10 @@ def getD (as : List α) (i : Nat) (fallback : α) : α :=
 /-! ### getLast! -/
 
 /--
-Returns the last element in the list. Panics and returns `default` if the list is empty.
+Returns the last element in the list.
 
-Safer alternatives include:
- * `getLast?`, which returns an `Option`,
- * `getLastD`, which takes a fallback value for empty lists, and
- * `getLast`, which requires a proof that the list is non-empty.
-
-Examples:
- * `["circle", "rectangle"].getLast! = "rectangle"`
- * `["circle"].getLast! = "circle"`
+If the list is empty, this function panics when executed, and returns `default`.
+See `getLast` and `getLastD` for safer alternatives.
 -/
 def getLast! [Inhabited α] : List α → α
   | []    => panic! "empty list"
@@ -118,12 +106,10 @@ def getLast! [Inhabited α] : List α → α
 /-! ### head! -/
 
 /--
-Returns the first element in the list. If the list is empty, panics and returns `default`.
+Returns the first element in the list.
 
-Safer alternatives include:
-  * `List.head`, which requires a proof that the list is non-empty,
-  * `List.head?`, which returns an `Option`, and
-  * `List.headD`, which returns an explicitly-provided fallback value on empty lists.
+If the list is empty, this function panics when executed, and returns `default`.
+See `head` and `headD` for safer alternatives.
 -/
 def head! [Inhabited α] : List α → α
   | []   => panic! "empty list"
@@ -132,17 +118,10 @@ def head! [Inhabited α] : List α → α
 /-! ### tail! -/
 
 /--
-Drops the first element of a nonempty list, returning the tail. If the list is empty, this function
-panics when executed and returns the empty list.
+Drops the first element of the list.
 
-Safer alternatives include
- * `tail`, which returns the empty list without panicking,
- * `tail?`, which returns an `Option`, and
- * `tailD`, which returns a fallback value when passed the empty list.
-
-Examples:
- * `["apple", "banana", "grape"].tail! = ["banana", "grape"]`
- * `["banana", "grape"].tail! = ["grape"]`
+If the list is empty, this function panics when executed, and returns the empty list.
+See `tail` and `tailD` for safer alternatives.
 -/
 def tail! : List α → List α
   | []    => panic! "empty list"
@@ -153,30 +132,17 @@ def tail! : List α → List α
 /-! ### partitionM -/
 
 /--
-Returns a pair of lists that together contain all the elements of `as`. The first list contains
-those elements for which the monadic predicate `p` returns `true`, and the second contains those for
-which `p` returns `false`. The list's elements are examined in order, from left to right.
+Monadic generalization of `List.partition`.
 
-This is a monadic version of `List.partition`.
-
-Example:
-```lean example
+This uses `Array.toList` and which isn't imported by `Init.Data.List.Basic` or `Init.Data.List.Control`.
+```
 def posOrNeg (x : Int) : Except String Bool :=
   if x > 0 then pure true
   else if x < 0 then pure false
   else throw "Zero is not positive or negative"
-```
-```lean example
-#eval [-1, 2, 3].partitionM posOrNeg
-```
-```output
-Except.ok ([2, 3], [-1])
-```
-```lean example
-#eval [0, 2, 3].partitionM posOrNeg
-```
-```output
-Except.error "Zero is not positive or negative"
+
+partitionM posOrNeg [-1, 2, 3] = Except.ok ([2, 3], [-1])
+partitionM posOrNeg [0, 2, 3] = Except.error "Zero is not positive or negative"
 ```
 -/
 @[inline] def partitionM [Monad m] (p : α → m Bool) (l : List α) : m (List α × List α) :=
@@ -196,12 +162,12 @@ where
 /-! ### partitionMap -/
 
 /--
-Applies a function that returns a disjoint union to each element of a list, collecting the `Sum.inl`
-and `Sum.inr` results into separate lists.
-
-Examples:
- * `[0, 1, 2, 3].partitionMap (fun x => if x % 2 = 0 then .inl x else .inr x) = ([0, 2], [1, 3])`
- * `[0, 1, 2, 3].partitionMap (fun x => if x = 0 then .inl x else .inr x) = ([0], [1, 2, 3])`
+Given a function `f : α → β ⊕ γ`, `partitionMap f l` maps the list by `f`
+whilst partitioning the result into a pair of lists, `List β × List γ`,
+partitioning the `.inl _` into the left list, and the `.inr _` into the right List.
+```
+partitionMap (id : Nat ⊕ Nat → Nat ⊕ Nat) [inl 0, inr 1, inl 2] = ([0, 2], [1])
+```
 -/
 @[inline] def partitionMap (f : α → β ⊕ γ) (l : List α) : List β × List γ := go l #[] #[] where
   /-- Auxiliary for `partitionMap`:
@@ -233,24 +199,14 @@ For verification purposes, `List.mapMono = List.map`.
       return b' :: bs'
 
 /--
-Applies a monadic function to each element of a list, returning the list 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 list if the result of each function call is
-pointer-equal to its argument.
+Monomorphic `List.mapM`. The internal implementation uses pointer equality, and does not allocate a new list
+if the result of each `f a` is a pointer equal value `a`.
 -/
 @[implemented_by mapMonoMImp] def mapMonoM [Monad m] (as : List α) (f : α → m α) : m (List α) :=
   match as with
   | [] => return []
   | a :: as => return (← f a) :: (← mapMonoM as f)
 
-/--
-Applies a function to each element of a list, returning the list 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 list if the result of each function call is
-pointer-equal to its argument.
-
-For verification purposes, `List.mapMono = List.map`.
--/
 def mapMono (as : List α) (f : α → α) : List α :=
   Id.run <| as.mapMonoM f
 

src/Init/Data/List/Control.lean

@@ -46,12 +46,11 @@ Users that want to use `mapM` with `Applicative` should use `mapA` instead.
 -/
 
 /--
-Applies the monadic action `f` to every element in the list, left-to-right, and returns the list of
+Applies the monadic action `f` on every element in the list, left-to-right, and returns the list of
 results.
 
-This implementation is tail recursive. `List.mapM'` is a a non-tail-recursive variant that may be
-more convenient to reason about. `List.forM` is the variant that discards the results and
-`List.mapA` is the variant that works with `Applicative`.
+See `List.forM` for the variant that discards the results.
+See `List.mapA` for the variant that works with `Applicative`.
 -/
 @[inline]
 def mapM {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f : α → m β) (as : List α) : m (List β) :=
@@ -61,15 +60,15 @@ def mapM {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f : α
   loop as []
 
 /--
-Applies the applicative action `f` on every element in the list, left-to-right, and returns the list
-of results.
+Applies the applicative action `f` on every element in the list, left-to-right, and returns the list of
+results.
 
-If `m` is also a `Monad`, then using `mapM` can be more efficient.
+NB: If `m` is also a `Monad`, then using `mapM` can be more efficient.
 
-See `List.forA` for the variant that discards the results. See `List.mapM` for the variant that
-works with `Monad`.
+See `List.forA` for the variant that discards the results.
+See `List.mapM` for the variant that works with `Monad`.
 
-This function is not tail-recursive, so it may fail with a stack overflow on long lists.
+**Warning**: this function is not tail-recursive, meaning that it may fail with a stack overflow on long lists.
 -/
 @[specialize]
 def mapA {m : Type u → Type v} [Applicative m] {α : Type w} {β : Type u} (f : α → m β) : List α → m (List β)
@@ -77,10 +76,10 @@ def mapA {m : Type u → Type v} [Applicative m] {α : Type w} {β : Type u} (f
   | a::as => List.cons <$> f a <*> mapA f as
 
 /--
-Applies the monadic action `f` to every element in the list, in order.
+Applies the monadic action `f` on every element in the list, left-to-right.
 
-`List.mapM` is a variant that collects results. `List.forA` is a variant that works on any
-`Applicative`.
+See `List.mapM` for the variant that collects results.
+See `List.forA` for the variant that works with `Applicative`.
 -/
 @[specialize]
 protected def forM {m : Type u → Type v} [Monad m] {α : Type w} (as : List α) (f : α → m PUnit) : m PUnit :=
@@ -89,11 +88,12 @@ protected def forM {m : Type u → Type v} [Monad m] {α : Type w} (as : List α
   | a :: as => do f a; List.forM as f
 
 /--
-Applies the applicative action `f` to every element in the list, in order.
+Applies the applicative action `f` on every element in the list, left-to-right.
 
-If `m` is also a `Monad`, then using `List.forM` can be more efficient.
+NB: If `m` is also a `Monad`, then using `forM` can be more efficient.
 
-`List.mapA` is a variant that collects results.
+See `List.mapA` for the variant that collects results.
+See `List.forM` for the variant that works with `Monad`.
 -/
 @[specialize]
 def forA {m : Type u → Type v} [Applicative m] {α : Type w} (as : List α) (f : α → m PUnit) : m PUnit :=
@@ -110,28 +110,8 @@ def filterAuxM {m : Type → Type v} [Monad m] {α : Type} (f : α → m Bool) :
     filterAuxM f t (cond b (h :: acc) acc)
 
 /--
-Applies the monadic predicate `p` to every element in the list, in order from left to right, and
-returns the list of elements for which `p` returns `true`.
-
-`O(|l|)`.
-
-Example:
-```lean example
-#eval [1, 2, 5, 2, 7, 7].filterM fun x => do
-  IO.println s!"Checking {x}"
-  return x < 3
-```
-```output
-Checking 1
-Checking 2
-Checking 5
-Checking 2
-Checking 7
-Checking 7
-```
-```output
-[1, 2, 2]
-```
+Applies the monadic predicate `p` on every element in the list, left-to-right, and returns those
+elements `x` for which `p x` returns `true`.
 -/
 @[inline]
 def filterM {m : Type → Type v} [Monad m] {α : Type} (p : α → m Bool) (as : List α) : m (List α) := do
@@ -139,56 +119,16 @@ def filterM {m : Type → Type v} [Monad m] {α : Type} (p : α → m Bool) (as
   pure as.reverse
 
 /--
-Applies the monadic predicate `p` on every element in the list in reverse order, from right to left,
-and returns those elements for which `p` returns `true`. The elements of the returned list are in
-the same order as in the input list.
-
-Example:
-```lean example
-#eval [1, 2, 5, 2, 7, 7].filterRevM fun x => do
-  IO.println s!"Checking {x}"
-  return x < 3
-```
-```output
-Checking 7
-Checking 7
-Checking 2
-Checking 5
-Checking 2
-Checking 1
-```
-```output
-[1, 2, 2]
-```
+Applies the monadic predicate `p` on every element in the list, right-to-left, and returns those
+elements `x` for which `p x` returns `true`.
 -/
 @[inline]
 def filterRevM {m : Type → Type v} [Monad m] {α : Type} (p : α → m Bool) (as : List α) : m (List α) :=
   filterAuxM p as.reverse []
 
 /--
-Applies a monadic function that returns an `Option` to each element of a list, collecting the
-non-`none` values.
-
-`O(|l|)`.
-
-Example:
-```lean example
-#eval [1, 2, 5, 2, 7, 7].filterMapM fun x => do
-  IO.println s!"Examining {x}"
-  if x > 2 then return some (2 * x)
-  else return none
-```
-```output
-Examining 1
-Examining 2
-Examining 5
-Examining 2
-Examining 7
-Examining 7
-```
-```output
-[10, 14, 14]
-```
+Applies the monadic function `f` on every element `x` in the list, left-to-right, and returns those
+results `y` for which `f x` returns `some y`.
 -/
 @[inline]
 def filterMapM {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f : α → m (Option β)) (as : List α) : m (List β) :=
@@ -201,8 +141,8 @@ def filterMapM {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f
   loop as []
 
 /--
-Applies a monadic function that returns a list to each element of a list, from left to right, and
-concatenates the resulting lists.
+Applies the monadic function `f` on every element `x` in the list, left-to-right, and returns the
+concatenation of the results.
 -/
 @[inline]
 def flatMapM {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f : α → m (List β)) (as : List α) : m (List β) :=
@@ -213,20 +153,14 @@ def flatMapM {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f :
       loop as (bs' :: bs)
   loop as []
 
-
 /--
-Folds a monadic function over a list from the left, accumulating a value starting with `init`. The
-accumulated value is combined with the each element of the list in order, using `f`.
-
-Example:
-```lean example
-example [Monad m] (f : α → β → m α) :
-    List.foldlM (m := m) f x₀ [a, b, c] = (do
-      let x₁ ← f x₀ a
-      let x₂ ← f x₁ b
-      let x₃ ← f x₂ c
-      pure x₃)
-  := by rfl
+Folds a monadic function over a list from left to right:
+```
+foldlM f x₀ [a, b, c] = do
+  let x₁ ← f x₀ a
+  let x₂ ← f x₁ b
+  let x₃ ← f x₂ c
+  pure x₃
 ```
 -/
 @[specialize]
@@ -236,97 +170,54 @@ def foldlM {m : Type u → Type v} [Monad m] {s : Type u} {α : Type w} : (f : s
     let s' ← f s a
     List.foldlM f s' as
 
-@[simp] theorem foldlM_nil [Monad m] {f : β → α → m β} {b : β} : [].foldlM f b = pure b := rfl
-@[simp] theorem foldlM_cons [Monad m] {f : β → α → m β} {b : β} {a : α} {l : List α} :
+@[simp] theorem foldlM_nil [Monad m] (f : β → α → m β) (b) : [].foldlM f b = pure b := rfl
+@[simp] theorem foldlM_cons [Monad m] (f : β → α → m β) (b) (a) (l : List α) :
     (a :: l).foldlM f b = f b a >>= l.foldlM f := by
   simp [List.foldlM]
 
 /--
-Folds a monadic function over a list from the right, accumulating a value starting with `init`. The
-accumulated value is combined with the each element of the list in reverse order, using `f`.
-
-Example:
-```lean example
-example [Monad m] (f : α → β → m β) :
-  List.foldrM (m := m) f x₀ [a, b, c] = (do
-    let x₁ ← f c x₀
-    let x₂ ← f b x₁
-    let x₃ ← f a x₂
-    pure x₃)
-  := by rfl
+Folds a monadic function over a list from right to left:
+```
+foldrM f x₀ [a, b, c] = do
+  let x₁ ← f c x₀
+  let x₂ ← f b x₁
+  let x₃ ← f a x₂
+  pure x₃
 ```
 -/
 @[inline]
 def foldrM {m : Type u → Type v} [Monad m] {s : Type u} {α : Type w} (f : α → s → m s) (init : s) (l : List α) : m s :=
   l.reverse.foldlM (fun s a => f a s) init
 
-@[simp] theorem foldrM_nil [Monad m] {f : α → β → m β} {b : β} : [].foldrM f b = pure b := rfl
+@[simp] theorem foldrM_nil [Monad m] (f : α → β → m β) (b) : [].foldrM f b = pure b := rfl
 
 /--
-Maps `f` over the list and collects the results with `<|>`. The result for the end of the list is
-`failure`.
-
-Examples:
- * `[[], [1, 2], [], [2]].firstM List.head? = some 1`
- * `[[], [], []].firstM List.head? = none`
- * `[].firstM List.head? = none`
+Maps `f` over the list and collects the results with `<|>`.
+```
+firstM f [a, b, c] = f a <|> f b <|> f c <|> failure
+```
 -/
 @[specialize]
 def firstM {m : Type u → Type v} [Alternative m] {α : Type w} {β : Type u} (f : α → m β) : List α → m β
   | []    => failure
   | a::as => f a <|> firstM f as
 
-/--
-Returns true if the monadic predicate `p` returns `true` for any element of `l`.
-
-`O(|l|)`. Short-circuits upon encountering the first `true`. The elements in `l` are examined in
-order from left to right.
--/
 @[specialize]
-def anyM {m : Type → Type u} [Monad m] {α : Type v} (p : α → m Bool) : (l : List α) → m Bool
+def anyM {m : Type → Type u} [Monad m] {α : Type v} (f : α → m Bool) : List α → m Bool
   | []    => pure false
   | a::as => do
-    match (← p a) with
+    match (← f a) with
     | true  => pure true
-    | false => anyM p as
+    | false => anyM f as
 
-/--
-Returns true if the monadic predicate `p` returns `true` for every element of `l`.
-
-`O(|l|)`. Short-circuits upon encountering the first `false`. The elements in `l` are examined in
-order from left to right.
--/
 @[specialize]
-def allM {m : Type → Type u} [Monad m] {α : Type v} (p : α → m Bool) : (l : List α) → m Bool
+def allM {m : Type → Type u} [Monad m] {α : Type v} (f : α → m Bool) : List α → m Bool
   | []    => pure true
   | a::as => do
-    match (← p a) with
-    | true  => allM p as
+    match (← f a) with
+    | true  => allM f as
     | false => pure false
 
-/--
-Returns the first element of the list for which the monadic predicate `p` returns `true`, or `none`
-if no such element is found. Elements of the list are checked in order.
-
-`O(|l|)`.
-
-Example:
-```lean example
-#eval [7, 6, 5, 8, 1, 2, 6].findM? fun i => do
-  if i < 5 then
-    return true
-  if i ≤ 6 then
-    IO.println s!"Almost! {i}"
-  return false
-```
-```output
-Almost! 6
-Almost! 5
-```
-```output
-some 1
-```
--/
 @[specialize]
 def findM? {m : Type → Type u} [Monad m] {α : Type} (p : α → m Bool) : List α → m (Option α)
   | []    => pure none
@@ -336,43 +227,15 @@ def findM? {m : Type → Type u} [Monad m] {α : Type} (p : α → m Bool) : Lis
     | false => findM? p as
 
 @[simp]
-theorem findM?_pure {m} [Monad m] [LawfulMonad m] (p : α → Bool) (as : List α) :
-    findM? (m := m) (pure <| p ·) as = pure (as.find? p) := by
+theorem findM?_id (p : α → Bool) (as : List α) : findM? (m := Id) p as = as.find? p := by
   induction as with
   | nil => rfl
   | cons a as ih =>
     simp only [findM?, find?]
     cases p a with
-    | true  => simp
-    | false => simp [ih]
+    | true  => rfl
+    | false => rw [ih]; rfl
 
-@[simp]
-theorem findM?_id (p : α → Bool) (as : List α) : findM? (m := Id) p as = as.find? p :=
-  findM?_pure _ _
-
-/--
-Returns the first non-`none` result of applying the monadic function `f` to each element of the
-list, in order. Returns `none` if `f` returns `none` for all elements.
-
-`O(|l|)`.
-
-Example:
-```lean example
-#eval [7, 6, 5, 8, 1, 2, 6].findSomeM? fun i => do
-  if i < 5 then
-    return some (i * 10)
-  if i ≤ 6 then
-    IO.println s!"Almost! {i}"
-  return none
-```
-```output
-Almost! 6
-Almost! 5
-```
-```output
-some 10
-```
--/
 @[specialize]
 def findSomeM? {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f : α → m (Option β)) : List α → m (Option β)
   | []    => pure none
@@ -382,21 +245,16 @@ def findSomeM? {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f
     | none   => findSomeM? f as
 
 @[simp]
-theorem findSomeM?_pure [Monad m] [LawfulMonad m] {f : α → Option β} {as : List α} :
-    findSomeM? (m := m) (pure <| f ·) as = pure (as.findSome? f) := by
+theorem findSomeM?_id (f : α → Option β) (as : List α) : findSomeM? (m := Id) f as = as.findSome? f := by
   induction as with
   | nil => rfl
   | cons a as ih =>
     simp only [findSomeM?, findSome?]
     cases f a with
-    | some b => simp
-    | none   => simp [ih]
+    | some b => rfl
+    | none   => rw [ih]; rfl
 
-@[simp]
-theorem findSomeM?_id {f : α → Option β} {as : List α} : findSomeM? (m := Id) f as = as.findSome? f :=
-  findSomeM?_pure
-
-theorem findM?_eq_findSomeM? [Monad m] [LawfulMonad m] {p : α → m Bool} {as : List α} :
+theorem findM?_eq_findSomeM? [Monad m] [LawfulMonad m] (p : α → m Bool) (as : List α) :
     as.findM? p = as.findSomeM? fun a => return if (← p a) then some a else none := by
   induction as with
   | nil => rfl
@@ -420,7 +278,7 @@ theorem findM?_eq_findSomeM? [Monad m] [LawfulMonad m] {p : α → m Bool} {as :
       match (← f a this b) with
       | ForInStep.done b  => pure b
       | ForInStep.yield b =>
-        have : Exists (fun bs => bs ++ as' = as) := have ⟨bs, h⟩ := h; ⟨bs ++ [a], by rw [← h, append_cons (bs := as')]⟩
+        have : Exists (fun bs => bs ++ as' = as) := have ⟨bs, h⟩ := h; ⟨bs ++ [a], by rw [← h, append_cons bs a as']⟩
         loop as' b this
   loop as init ⟨[], rfl⟩
 
@@ -432,10 +290,10 @@ instance : ForIn' m (List α) α inferInstance where
 -- We simplify `List.forIn'` to `forIn'`.
 @[simp] theorem forIn'_eq_forIn' [Monad m] : @List.forIn' α β m _ = forIn' := rfl
 
-@[simp] theorem forIn'_nil [Monad m] {f : (a : α) → a ∈ [] → β → m (ForInStep β)} {b : β} : forIn' [] b f = pure b :=
+@[simp] theorem forIn'_nil [Monad m] (f : (a : α) → a ∈ [] → β → m (ForInStep β)) (b : β) : forIn' [] b f = pure b :=
   rfl
 
-@[simp] theorem forIn_nil [Monad m] {f : α → β → m (ForInStep β)} {b : β} : forIn [] b f = pure b :=
+@[simp] theorem forIn_nil [Monad m] (f : α → β → m (ForInStep β)) (b : β) : forIn [] b f = pure b :=
   rfl
 
 instance : ForM m (List α) α where
@@ -444,9 +302,9 @@ instance : ForM m (List α) α where
 -- We simplify `List.forM` to `forM`.
 @[simp] theorem forM_eq_forM [Monad m] : @List.forM m _ α = forM := rfl
 
-@[simp] theorem forM_nil [Monad m] {f : α → m PUnit} : forM [] f = pure ⟨⟩ :=
+@[simp] theorem forM_nil  [Monad m] (f : α → m PUnit) : forM [] f = pure ⟨⟩ :=
   rfl
-@[simp] theorem forM_cons [Monad m] {f : α → m PUnit} {a : α} {as : List α} : forM (a::as) f = f a >>= fun _ => forM as f :=
+@[simp] theorem forM_cons [Monad m] (f : α → m PUnit) (a : α) (as : List α) : forM (a::as) f = f a >>= fun _ => forM as f :=
   rfl
 
 instance : Functor List where

src/Init/Data/List/Count.lean

@@ -20,11 +20,11 @@ open Nat
 /-! ### countP -/
 section countP
 
-variable {p q : α → Bool}
+variable (p q : α → Bool)
 
 @[simp] theorem countP_nil : countP p [] = 0 := rfl
 
-protected theorem countP_go_eq_add {l} : countP.go p l n = n + countP.go p l 0 := by
+protected theorem countP_go_eq_add (l) : countP.go p l n = n + countP.go p l 0 := by
   induction l generalizing n with
   | nil => rfl
   | cons hd _ ih =>
@@ -32,40 +32,40 @@ protected theorem countP_go_eq_add {l} : countP.go p l n = n + countP.go p l 0 :
     rw [ih (n := n + 1), ih (n := n), ih (n := 1)]
     if h : p hd then simp [h, Nat.add_assoc] else simp [h]
 
-@[simp] theorem countP_cons_of_pos {l} (pa : p a) : countP p (a :: l) = countP p l + 1 := by
+@[simp] theorem countP_cons_of_pos (l) (pa : p a) : countP p (a :: l) = countP p l + 1 := by
   have : countP.go p (a :: l) 0 = countP.go p l 1 := show cond .. = _ by rw [pa]; rfl
   unfold countP
   rw [this, Nat.add_comm, List.countP_go_eq_add]
 
-@[simp] theorem countP_cons_of_neg {l} (pa : ¬p a) : countP p (a :: l) = countP p l := by
+@[simp] theorem countP_cons_of_neg (l) (pa : ¬p a) : countP p (a :: l) = countP p l := by
   simp [countP, countP.go, pa]
 
-theorem countP_cons {a : α} {l : List α} : countP p (a :: l) = countP p l + if p a then 1 else 0 := by
+theorem countP_cons (a : α) (l) : countP p (a :: l) = countP p l + if p a then 1 else 0 := by
   by_cases h : p a <;> simp [h]
 
-@[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_cons]
 
-theorem length_eq_countP_add_countP (p : α → Bool) {l : List α} : length l = countP p l + countP (fun a => ¬p a) l := by
+theorem length_eq_countP_add_countP (l) : length l = countP p l + countP (fun a => ¬p a) l := by
   induction l with
   | nil => rfl
   | cons hd _ ih =>
     if h : p hd then
-      rw [countP_cons_of_pos h, countP_cons_of_neg _, length, ih]
+      rw [countP_cons_of_pos _ _ h, countP_cons_of_neg _ _ _, length, ih]
       · rw [Nat.add_assoc, Nat.add_comm _ 1, Nat.add_assoc]
       · simp [h]
     else
-      rw [countP_cons_of_pos (p := fun a => ¬p a), countP_cons_of_neg h, length, ih]
+      rw [countP_cons_of_pos (fun a => ¬p a) _ _, countP_cons_of_neg _ _ h, length, ih]
       · rfl
       · simp [h]
 
-theorem countP_eq_length_filter {l : List α} : countP p l = length (filter p l) := by
+theorem countP_eq_length_filter (l) : countP p l = length (filter p l) := by
   induction l with
   | nil => rfl
   | cons x l ih =>
     if h : p x
-    then rw [countP_cons_of_pos h, ih, filter_cons_of_pos h, length]
-    else rw [countP_cons_of_neg h, ih, filter_cons_of_neg h]
+    then rw [countP_cons_of_pos p l h, ih, filter_cons_of_pos h, length]
+    else rw [countP_cons_of_neg p l h, ih, filter_cons_of_neg h]
 
 theorem countP_eq_length_filter' : countP p = length ∘ filter p := by
   funext l
@@ -75,7 +75,7 @@ theorem countP_le_length : countP p l ≤ l.length := by
   simp only [countP_eq_length_filter]
   apply length_filter_le
 
-@[simp] theorem countP_append {l₁ l₂ : List α} : countP p (l₁ ++ l₂) = countP p l₁ + countP p l₂ := by
+@[simp] theorem countP_append (l₁ l₂) : countP p (l₁ ++ l₂) = countP p l₁ + countP p l₂ := by
   simp only [countP_eq_length_filter, filter_append, length_append]
 
 @[simp] theorem countP_pos_iff {p} : 0 < countP p l ↔ ∃ a ∈ l, p a := by
@@ -90,14 +90,14 @@ theorem countP_le_length : countP p l ≤ l.length := by
   simp only [countP_eq_length_filter, length_eq_zero_iff, filter_eq_nil_iff]
 
 @[simp] theorem countP_eq_length {p} : countP p l = l.length ↔ ∀ a ∈ l, p a := by
-  rw [countP_eq_length_filter, length_filter_eq_length_iff]
+  rw [countP_eq_length_filter, filter_length_eq_length]
 
-theorem countP_replicate {p : α → Bool} {a : α} {n : Nat} :
+theorem countP_replicate (p : α → Bool) (a : α) (n : Nat) :
     countP p (replicate n a) = if p a then n else 0 := by
   simp only [countP_eq_length_filter, filter_replicate]
   split <;> simp
 
-theorem boole_getElem_le_countP {p : α → Bool} {l : List α} {i : Nat} (h : i < l.length) :
+theorem boole_getElem_le_countP (p : α → Bool) (l : List α) (i : Nat) (h : i < l.length) :
     (if p l[i] then 1 else 0) ≤ l.countP p := by
   induction l generalizing i with
   | nil => simp at h
@@ -107,25 +107,25 @@ theorem boole_getElem_le_countP {p : α → Bool} {l : List α} {i : Nat} (h : i
     | succ i =>
       simp only [length_cons, add_one_lt_add_one_iff] at h
       simp only [getElem_cons_succ, countP_cons]
-      specialize ih h
+      specialize ih _ h
       exact le_add_right_of_le ih
 
 theorem Sublist.countP_le (s : l₁ <+ l₂) : countP p l₁ ≤ countP p l₂ := by
   simp only [countP_eq_length_filter]
   apply s.filter _ |>.length_le
 
-theorem IsPrefix.countP_le (s : l₁ <+: l₂) : countP p l₁ ≤ countP p l₂ := s.sublist.countP_le
-theorem IsSuffix.countP_le (s : l₁ <:+ l₂) : countP p l₁ ≤ countP p l₂ := s.sublist.countP_le
-theorem IsInfix.countP_le (s : l₁ <:+: l₂) : countP p l₁ ≤ countP p l₂ := s.sublist.countP_le
+theorem IsPrefix.countP_le (s : l₁ <+: l₂) : countP p l₁ ≤ countP p l₂ := s.sublist.countP_le _
+theorem IsSuffix.countP_le (s : l₁ <:+ l₂) : countP p l₁ ≤ countP p l₂ := s.sublist.countP_le _
+theorem IsInfix.countP_le (s : l₁ <:+: l₂) : countP p l₁ ≤ countP p l₂ := s.sublist.countP_le _
 
 -- See `Init.Data.List.Nat.Count` for `Sublist.le_countP : countP p l₂ - (l₂.length - l₁.length) ≤ countP p l₁`.
 
 theorem countP_tail_le (l) : countP p l.tail ≤ countP p l :=
-  (tail_sublist l).countP_le
+  (tail_sublist l).countP_le _
 
 -- See `Init.Data.List.Nat.Count` for `le_countP_tail : countP p l - 1 ≤ countP p l.tail`.
 
-theorem countP_filter {l : List α} :
+theorem countP_filter (l : List α) :
     countP p (filter q l) = countP (fun a => p a && q a) l := by
   simp only [countP_eq_length_filter, filter_filter]
 
@@ -137,12 +137,12 @@ theorem countP_filter {l : List α} :
   funext l
   simp
 
-@[simp] theorem countP_map {p : β → Bool} {f : α → β} :
-    ∀ {l}, countP p (map f l) = countP (p ∘ f) l
+@[simp] theorem countP_map (p : β → Bool) (f : α → β) :
+    ∀ l, countP p (map f l) = countP (p ∘ f) l
   | [] => rfl
-  | a :: l => by rw [map_cons, countP_cons, countP_cons, countP_map]; rfl
+  | a :: l => by rw [map_cons, countP_cons, countP_cons, countP_map p f l]; rfl
 
-theorem length_filterMap_eq_countP {f : α → Option β} {l : List α} :
+theorem length_filterMap_eq_countP (f : α → Option β) (l : List α) :
     (filterMap f l).length = countP (fun a => (f a).isSome) l := by
   induction l with
   | nil => rfl
@@ -150,7 +150,7 @@ theorem length_filterMap_eq_countP {f : α → Option β} {l : List α} :
     simp only [filterMap_cons, countP_cons]
     split <;> simp [ih, *]
 
-theorem countP_filterMap {p : β → Bool} {f : α → Option β} {l : List α} :
+theorem countP_filterMap (p : β → Bool) (f : α → Option β) (l : List α) :
     countP p (filterMap f l) = countP (fun a => ((f a).map p).getD false) l := by
   simp only [countP_eq_length_filter, filter_filterMap, ← filterMap_eq_filter]
   simp only [length_filterMap_eq_countP]
@@ -158,20 +158,22 @@ theorem countP_filterMap {p : β → Bool} {f : α → Option β} {l : List α}
   ext a
   simp +contextual [Option.getD_eq_iff, Option.isSome_eq_isSome]
 
-@[simp] theorem countP_flatten {l : List (List α)} :
+@[simp] theorem countP_flatten (l : List (List α)) :
     countP p l.flatten = (l.map (countP p)).sum := by
   simp only [countP_eq_length_filter, filter_flatten]
   simp [countP_eq_length_filter']
 
 @[deprecated countP_flatten (since := "2024-10-14")] abbrev countP_join := @countP_flatten
 
-theorem countP_flatMap {p : β → Bool} {l : List α} {f : α → List β} :
+theorem countP_flatMap (p : β → Bool) (l : List α) (f : α → List β) :
     countP p (l.flatMap f) = sum (map (countP p ∘ f) l) := by
   rw [List.flatMap, countP_flatten, map_map]
 
-@[simp] theorem countP_reverse {l : List α} : countP p l.reverse = countP p l := by
+@[simp] theorem countP_reverse (l : List α) : countP p l.reverse = countP p l := by
   simp [countP_eq_length_filter, filter_reverse]
 
+variable {p q}
+
 theorem countP_mono_left (h : ∀ x ∈ l, p x → q x) : countP p l ≤ countP q l := by
   induction l with
   | nil => apply Nat.le_refl
@@ -198,69 +200,71 @@ section count
 
 variable [BEq α]
 
-@[simp] theorem count_nil {a : α} : count a [] = 0 := rfl
+@[simp] theorem count_nil (a : α) : count a [] = 0 := rfl
 
-theorem count_cons {a b : α} {l : List α} :
+theorem count_cons (a b : α) (l : List α) :
     count a (b :: l) = count a l + if b == a then 1 else 0 := by
   simp [count, countP_cons]
 
-theorem count_eq_countP {a : α} {l : List α} : count a l = countP (· == a) l := rfl
+theorem count_eq_countP (a : α) (l : List α) : count a l = countP (· == a) l := rfl
 theorem count_eq_countP' {a : α} : count a = countP (· == a) := by
   funext l
   apply count_eq_countP
 
-theorem count_tail : ∀ {l : List α} {a : α} (h : l ≠ []),
+theorem count_tail : ∀ (l : List α) (a : α) (h : l ≠ []),
       l.tail.count a = l.count a - if l.head h == a then 1 else 0
   | _ :: _, a, _ => by simp [count_cons]
 
-theorem count_le_length {a : α} {l : List α} : count a l ≤ l.length := countP_le_length
+theorem count_le_length (a : α) (l : List α) : count a l ≤ l.length := countP_le_length _
 
-theorem Sublist.count_le (a : α) (h : l₁ <+ l₂) : count a l₁ ≤ count a l₂ := h.countP_le
+theorem Sublist.count_le (h : l₁ <+ l₂) (a : α) : count a l₁ ≤ count a l₂ := h.countP_le _
 
-theorem IsPrefix.count_le (a : α) (h : l₁ <+: l₂) : count a l₁ ≤ count a l₂ := h.sublist.count_le a
-theorem IsSuffix.count_le (a : α) (h : l₁ <:+ l₂) : count a l₁ ≤ count a l₂ := h.sublist.count_le a
-theorem IsInfix.count_le (a : α) (h : l₁ <:+: l₂) : count a l₁ ≤ count a l₂ := h.sublist.count_le a
+theorem IsPrefix.count_le (h : l₁ <+: l₂) (a : α) : count a l₁ ≤ count a l₂ := h.sublist.count_le _
+theorem IsSuffix.count_le (h : l₁ <:+ l₂) (a : α) : count a l₁ ≤ count a l₂ := h.sublist.count_le _
+theorem IsInfix.count_le (h : l₁ <:+: l₂) (a : α) : count a l₁ ≤ count a l₂ := h.sublist.count_le _
 
 -- See `Init.Data.List.Nat.Count` for `Sublist.le_count : count a l₂ - (l₂.length - l₁.length) ≤ countP a l₁`.
 
-theorem count_tail_le {a : α} {l : List α} : count a l.tail ≤ count a l :=
-  (tail_sublist l).count_le a
+theorem count_tail_le (a : α) (l) : count a l.tail ≤ count a l :=
+  (tail_sublist l).count_le _
 
 -- See `Init.Data.List.Nat.Count` for `le_count_tail : count a l - 1 ≤ count a l.tail`.
 
-theorem count_le_count_cons {a b : α} {l : List α} : count a l ≤ count a (b :: l) :=
-  (sublist_cons_self _ _).count_le a
+theorem count_le_count_cons (a b : α) (l : List α) : count a l ≤ count a (b :: l) :=
+  (sublist_cons_self _ _).count_le _
 
-theorem count_singleton {a b : α} : count a [b] = if b == a then 1 else 0 := by
+theorem count_singleton (a b : α) : count a [b] = if b == a then 1 else 0 := by
   simp [count_cons]
 
-@[simp] theorem count_append {a : α} {l₁ l₂ : List α} : count a (l₁ ++ l₂) = count a l₁ + count a l₂ :=
-  countP_append
+@[simp] theorem count_append (a : α) : ∀ l₁ l₂, count a (l₁ ++ l₂) = count a l₁ + count a l₂ :=
+  countP_append _
 
-theorem count_flatten {a : α} {l : List (List α)} : count a l.flatten = (l.map (count a)).sum := by
+theorem count_flatten (a : α) (l : List (List α)) : count a l.flatten = (l.map (count a)).sum := by
   simp only [count_eq_countP, countP_flatten, count_eq_countP']
 
 @[deprecated count_flatten (since := "2024-10-14")] abbrev count_join := @count_flatten
 
-@[simp] theorem count_reverse {a : α} {l : List α} : count a l.reverse = count a l := by
+@[simp] theorem count_reverse (a : α) (l : List α) : count a l.reverse = count a l := by
   simp only [count_eq_countP, countP_eq_length_filter, filter_reverse, length_reverse]
 
-theorem boole_getElem_le_count {a : α} {l : List α} {i : Nat} (h : i < l.length) :
+theorem boole_getElem_le_count (a : α) (l : List α) (i : Nat) (h : i < l.length) :
     (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)
 
 variable [LawfulBEq α]
 
-@[simp] theorem count_cons_self {a : α} {l : List α} : count a (a :: l) = count a l + 1 := by
+@[simp] theorem count_cons_self (a : α) (l : List α) : count a (a :: l) = count a l + 1 := by
   simp [count_cons]
 
-@[simp] theorem count_cons_of_ne (h : b ≠ a) {l : List α} : count a (b :: l) = count a l := by
-  simp [count_cons, h]
+@[simp] theorem count_cons_of_ne (h : a ≠ b) (l : List α) : count a (b :: l) = count a l := by
+  simp only [count_cons, cond_eq_if, beq_iff_eq]
+  split <;> simp_all
 
-theorem count_singleton_self {a : α} : count a [a] = 1 := by simp
+theorem count_singleton_self (a : α) : count a [a] = 1 := by simp
 
-theorem count_concat_self {a : α} {l : List α} : count a (concat l a) = count a l + 1 := by simp
+theorem count_concat_self (a : α) (l : List α) :
+    count a (concat l a) = (count a l) + 1 := by simp
 
 @[simp]
 theorem count_pos_iff {a : α} {l : List α} : 0 < count a l ↔ a ∈ l := by
@@ -286,40 +290,41 @@ theorem count_eq_length {l : List α} : count a l = l.length ↔ ∀ b ∈ l, a
   · 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 :=
+@[simp] theorem count_replicate_self (a : α) (n : Nat) : count a (replicate n a) = n :=
   (count_eq_length.2 <| fun _ h => (eq_of_mem_replicate h).symm).trans (length_replicate ..)
 
-theorem count_replicate {a b : α} {n : Nat} : count a (replicate n b) = if b == a then n else 0 := by
+theorem count_replicate (a b : α) (n : Nat) : count a (replicate n b) = if b == a then n else 0 := by
   split <;> (rename_i h; simp only [beq_iff_eq] at h)
   · exact ‹b = a› ▸ count_replicate_self ..
   · exact count_eq_zero.2 <| mt eq_of_mem_replicate (Ne.symm h)
 
-theorem filter_beq {l : List α} (a : α) : l.filter (· == a) = replicate (count a l) a := by
+theorem filter_beq (l : List α) (a : α) : l.filter (· == a) = replicate (count a l) a := by
   simp only [count, countP_eq_length_filter, eq_replicate_iff, mem_filter, beq_iff_eq]
   exact ⟨trivial, fun _ h => h.2⟩
 
-theorem filter_eq {α} [DecidableEq α] {l : List α} (a : α) : l.filter (· = a) = replicate (count a l) a :=
-  filter_beq a
+theorem filter_eq {α} [DecidableEq α] (l : List α) (a : α) : l.filter (· = a) = replicate (count a l) a :=
+  filter_beq l a
 
 theorem le_count_iff_replicate_sublist {l : List α} : n ≤ count a l ↔ replicate n a <+ l := by
   refine ⟨fun h => ?_, fun h => ?_⟩
-  · exact ((replicate_sublist_replicate a).2 h).trans <| filter_beq a ▸ filter_sublist
+  · exact ((replicate_sublist_replicate a).2 h).trans <| filter_beq l a ▸ filter_sublist _
   · simpa only [count_replicate_self] using h.count_le a
 
 theorem replicate_count_eq_of_count_eq_length {l : List α} (h : count a l = length l) :
     replicate (count a l) a = l :=
-  (le_count_iff_replicate_sublist.mp (Nat.le_refl _)).eq_of_length <| length_replicate.trans h
+  (le_count_iff_replicate_sublist.mp (Nat.le_refl _)).eq_of_length <|
+    (length_replicate (count a l) a).trans h
 
 @[simp] theorem count_filter {l : List α} (h : p a) : count a (filter p l) = count a l := by
   rw [count, countP_filter]; congr; funext b
   simp; rintro rfl; exact h
 
-theorem count_le_count_map [DecidableEq β] {l : List α} {f : α → β} {x : α} :
+theorem count_le_count_map [DecidableEq β] (l : List α) (f : α → β) (x : α) :
     count x l ≤ count (f x) (map f l) := by
   rw [count, count, countP_map]
   apply countP_mono_left; simp +contextual
 
-theorem count_filterMap {α} [BEq β] {b : β} {f : α → Option β} {l : List α} :
+theorem count_filterMap {α} [BEq β] (b : β) (f : α → Option β) (l : List α) :
     count b (filterMap f l) = countP (fun a => f a == some b) l := by
   rw [count_eq_countP, countP_filterMap]
   congr
@@ -328,11 +333,11 @@ theorem count_filterMap {α} [BEq β] {b : β} {f : α → Option β} {l : List
   · simp
   · simp
 
-theorem count_flatMap {α} [BEq β] {l : List α} {f : α → List β} {x : β} :
-    count x (l.flatMap f) = sum (map (count x ∘ f) l) := countP_flatMap
+theorem count_flatMap {α} [BEq β] (l : List α) (f : α → List β) (x : β) :
+    count x (l.flatMap f) = sum (map (count x ∘ f) l) := countP_flatMap _ _ _
 
-theorem count_erase {a b : α} :
-    ∀ {l : List α}, count a (l.erase b) = count a l - if b == a then 1 else 0
+theorem count_erase (a b : α) :
+    ∀ l : List α, count a (l.erase b) = count a l - if b == a then 1 else 0
   | [] => by simp
   | c :: l => by
     rw [erase_cons]
@@ -341,17 +346,17 @@ theorem count_erase {a b : α} :
       rw [if_pos hc_beq, hc, count_cons, Nat.add_sub_cancel]
     else
       have hc_beq := beq_false_of_ne hc
-      simp only [hc_beq, if_false, count_cons, count_cons, count_erase, reduceCtorEq]
+      simp only [hc_beq, if_false, count_cons, count_cons, count_erase a b l, reduceCtorEq]
       if ha : b = a then
         rw [ha, eq_comm] at hc
         rw [if_pos (beq_iff_eq.2 ha), if_neg (by simpa using Ne.symm hc), Nat.add_zero, Nat.add_zero]
       else
         rw [if_neg (by simpa using ha), Nat.sub_zero, Nat.sub_zero]
 
-@[simp] theorem count_erase_self {a : α} {l : List α} :
+@[simp] theorem count_erase_self (a : α) (l : List α) :
     count a (List.erase l a) = count a l - 1 := by rw [count_erase, if_pos (by simp)]
 
-@[simp] theorem count_erase_of_ne (ab : a ≠ b) {l : List α} : count a (l.erase b) = count a l := by
+@[simp] theorem count_erase_of_ne (ab : a ≠ b) (l : List α) : count a (l.erase b) = count a l := by
   rw [count_erase, if_neg (by simpa using ab.symm), Nat.sub_zero]
 
 end count

src/Init/Data/List/Erase.lean

@@ -23,7 +23,7 @@ open Nat
 
 @[simp] theorem eraseP_nil : [].eraseP p = [] := rfl
 
-theorem eraseP_cons {a : α} {l : List α} :
+theorem eraseP_cons (a : α) (l : List α) :
     (a :: l).eraseP p = bif p a then l else a :: l.eraseP p := rfl
 
 @[simp] theorem eraseP_cons_of_pos {l : List α} {p} (h : p a) : (a :: l).eraseP p = l := by
@@ -75,7 +75,6 @@ theorem exists_of_eraseP : ∀ {l : List α} {a} (_ : a ∈ l) (_ : p a),
         ⟨c, b::l₁, l₂, (forall_mem_cons ..).2 ⟨pb, h₁⟩,
           h₂, by rw [h₃, cons_append], by simp [pb, h₄]⟩
 
--- The arguments are explicit here, so this lemma can be used as a case split.
 theorem exists_or_eq_self_of_eraseP (p) (l : List α) :
     l.eraseP p = l ∨
     ∃ a l₁ l₂, (∀ b ∈ l₁, ¬p b) ∧ p a ∧ l = l₁ ++ a :: l₂ ∧ l.eraseP p = l₁ ++ l₂ :=
@@ -99,32 +98,32 @@ theorem length_eraseP {l : List α} : (l.eraseP p).length = if l.any p then l.le
     rw [eraseP_of_forall_not]
     simp_all
 
-theorem eraseP_sublist {l : List α} : l.eraseP p <+ l := by
+theorem eraseP_sublist (l : List α) : l.eraseP p <+ l := by
   match exists_or_eq_self_of_eraseP p l with
   | .inl h => rw [h]; apply Sublist.refl
   | .inr ⟨c, l₁, l₂, _, _, h₃, h₄⟩ => rw [h₄, h₃]; simp
 
-theorem eraseP_subset {l : List α} : l.eraseP p ⊆ l := eraseP_sublist.subset
+theorem eraseP_subset (l : List α) : l.eraseP p ⊆ l := (eraseP_sublist l).subset
 
 protected theorem Sublist.eraseP : l₁ <+ l₂ → l₁.eraseP p <+ l₂.eraseP p
   | .slnil => Sublist.refl _
   | .cons a s => by
     by_cases h : p a
-    · simpa [h] using s.eraseP.trans eraseP_sublist
+    · simpa [h] using s.eraseP.trans (eraseP_sublist _)
     · simpa [h] using s.eraseP.cons _
   | .cons₂ a s => by
     by_cases h : p a
     · simpa [h] using s
     · simpa [h] using s.eraseP
 
-theorem length_eraseP_le {l : List α} : (l.eraseP p).length ≤ l.length :=
-  eraseP_sublist.length_le
+theorem length_eraseP_le (l : List α) : (l.eraseP p).length ≤ l.length :=
+  l.eraseP_sublist.length_le
 
-theorem le_length_eraseP {l : List α} : l.length - 1 ≤ (l.eraseP p).length := by
+theorem le_length_eraseP (l : List α) : l.length - 1 ≤ (l.eraseP p).length := by
   rw [length_eraseP]
   split <;> simp
 
-theorem mem_of_mem_eraseP {l : List α} : a ∈ l.eraseP p → a ∈ l := (eraseP_subset ·)
+theorem mem_of_mem_eraseP {l : List α} : a ∈ l.eraseP p → a ∈ l := (eraseP_subset _ ·)
 
 @[simp] theorem mem_eraseP_of_neg {l : List α} (pa : ¬p a) : a ∈ l.eraseP p ↔ a ∈ l := by
   refine ⟨mem_of_mem_eraseP, fun al => ?_⟩
@@ -136,7 +135,7 @@ theorem mem_of_mem_eraseP {l : List α} : a ∈ l.eraseP p → a ∈ l := (erase
     simp [this] at al; simp [al]
 
 @[simp] theorem eraseP_eq_self_iff {p} {l : List α} : l.eraseP p = l ↔ ∀ a ∈ l, ¬ p a := by
-  rw [← Sublist.length_eq eraseP_sublist, length_eraseP]
+  rw [← Sublist.length_eq (eraseP_sublist l), length_eraseP]
   split <;> rename_i h
   · simp only [any_eq_true, length_eq_zero_iff] at h
     constructor
@@ -144,11 +143,11 @@ theorem mem_of_mem_eraseP {l : List α} : a ∈ l.eraseP p → a ∈ l := (erase
     · intro; obtain ⟨x, m, h⟩ := h; simp_all
   · simp_all
 
-theorem eraseP_map {f : β → α} : ∀ {l : List β}, (map f l).eraseP p = map f (l.eraseP (p ∘ f))
+theorem eraseP_map (f : β → α) : ∀ (l : List β), (map f l).eraseP p = map f (l.eraseP (p ∘ f))
   | [] => rfl
-  | b::l => by by_cases h : p (f b) <;> simp [h, eraseP_map, eraseP_cons_of_pos]
+  | b::l => by by_cases h : p (f b) <;> simp [h, eraseP_map f l, eraseP_cons_of_pos]
 
-theorem eraseP_filterMap {f : α → Option β} : ∀ {l : List α},
+theorem eraseP_filterMap (f : α → Option β) : ∀ (l : List α),
     (filterMap f l).eraseP p = filterMap f (l.eraseP (fun x => match f x with | some y => p y | none => false))
   | [] => rfl
   | a::l => by
@@ -162,7 +161,7 @@ theorem eraseP_filterMap {f : α → Option β} : ∀ {l : List α},
       · simp only [w, cond_false]
         rw [filterMap_cons_some h, eraseP_filterMap]
 
-theorem eraseP_filter {f : α → Bool} {l : List α} :
+theorem eraseP_filter (f : α → Bool) (l : List α) :
     (filter f l).eraseP p = filter f (l.eraseP (fun x => p x && f x)) := by
   rw [← filterMap_eq_filter, eraseP_filterMap]
   congr
@@ -183,7 +182,7 @@ theorem eraseP_append_right :
   | _ :: _, _, h => by
     simp [(forall_mem_cons.1 h).1, eraseP_append_right _ (forall_mem_cons.1 h).2]
 
-theorem eraseP_append {l₁ l₂ : List α} :
+theorem eraseP_append (l₁ l₂ : List α) :
     (l₁ ++ l₂).eraseP p = if l₁.any p then l₁.eraseP p ++ l₂ else l₁ ++ l₂.eraseP p := by
   split <;> rename_i h
   · simp only [any_eq_true] at h
@@ -193,7 +192,7 @@ theorem eraseP_append {l₁ l₂ : List α} :
     rw [eraseP_append_right _]
     simp_all
 
-theorem eraseP_replicate {n : Nat} {a : α} {p : α → Bool} :
+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
   induction n with
   | zero => simp
@@ -256,7 +255,7 @@ theorem eraseP_eq_iff {p} {l : List α} :
         simp_all
 
 theorem Pairwise.eraseP (q) : Pairwise p l → Pairwise p (l.eraseP q) :=
-  Pairwise.sublist <| eraseP_sublist
+  Pairwise.sublist <| eraseP_sublist _
 
 theorem Nodup.eraseP (p) : Nodup l → Nodup (l.eraseP p) :=
   Pairwise.eraseP p
@@ -275,11 +274,11 @@ theorem eraseP_comm {l : List α} (h : ∀ a ∈ l, ¬ p a ∨ ¬ q a) :
       · simp [h₁, h₂, ih (fun b m => h b (mem_cons_of_mem _ m))]
       · simp [h₁, h₂, ih (fun b m => h b (mem_cons_of_mem _ m))]
 
-theorem head_eraseP_mem {xs : List α} {p : α → Bool} (h) : (xs.eraseP p).head h ∈ xs :=
-  eraseP_sublist.head_mem h
+theorem head_eraseP_mem (xs : List α) (p : α → Bool) (h) : (xs.eraseP p).head h ∈ xs :=
+  (eraseP_sublist xs).head_mem h
 
-theorem getLast_eraseP_mem {xs : List α} {p : α → Bool} (h) : (xs.eraseP p).getLast h ∈ xs :=
-  eraseP_sublist.getLast_mem h
+theorem getLast_eraseP_mem (xs : List α) (p : α → Bool) (h) : (xs.eraseP p).getLast h ∈ xs :=
+  (eraseP_sublist xs).getLast_mem h
 
 theorem eraseP_eq_eraseIdx {xs : List α} {p : α → Bool} :
     xs.eraseP p = match xs.findIdx? p with
@@ -300,8 +299,6 @@ theorem eraseP_eq_eraseIdx {xs : List α} {p : α → Bool} :
 section erase
 variable [BEq α]
 
--- The arguments are explicit to allow determining the type,
--- and to allow rewriting from right to left.
 @[simp] theorem erase_cons_head [LawfulBEq α] (a : α) (l : List α) : (a :: l).erase a = l := by
   simp [erase_cons]
 
@@ -314,7 +311,6 @@ theorem erase_of_not_mem [LawfulBEq α] {a : α} : ∀ {l : List α}, a ∉ l
     rw [mem_cons, not_or] at h
     simp only [erase_cons, if_neg, erase_of_not_mem h.2, beq_iff_eq, Ne.symm h.1, not_false_eq_true]
 
--- The arguments are intentionally explicit.
 theorem erase_eq_eraseP' (a : α) (l : List α) : l.erase a = l.eraseP (· == a) := by
   induction l
   · simp
@@ -322,11 +318,10 @@ theorem erase_eq_eraseP' (a : α) (l : List α) : l.erase a = l.eraseP (· == a)
     rw [erase_cons, eraseP_cons, ih]
     if h : b == a then simp [h] else simp [h]
 
--- The arguments are intentionally explicit.
-theorem erase_eq_eraseP [LawfulBEq α] (a : α) : ∀ (l : List α), l.erase a = l.eraseP (a == ·)
+theorem erase_eq_eraseP [LawfulBEq α] (a : α) : ∀ l : List α,  l.erase a = l.eraseP (a == ·)
   | [] => rfl
   | b :: l => by
-    if h : a = b then simp [h] else simp [h, Ne.symm h, erase_eq_eraseP (l := l)]
+    if h : a = b then simp [h] else simp [h, Ne.symm h, erase_eq_eraseP a l]
 
 @[simp] theorem erase_eq_nil_iff [LawfulBEq α] {xs : List α} {a : α} :
     xs.erase a = [] ↔ xs = [] ∨ xs = [a] := by
@@ -353,15 +348,15 @@ theorem exists_erase_eq [LawfulBEq α] {a : α} {l : List α} (h : a ∈ l) :
     length (l.erase a) = length l - 1 := by
   rw [erase_eq_eraseP]; exact length_eraseP_of_mem h (beq_self_eq_true a)
 
-theorem length_erase [LawfulBEq α] {a : α} {l : List α} :
+theorem length_erase [LawfulBEq α] (a : α) (l : List α) :
     length (l.erase a) = if a ∈ l then length l - 1 else length l := by
   rw [erase_eq_eraseP, length_eraseP]
   split <;> split <;> simp_all
 
-theorem erase_sublist {a : α} {l : List α} : l.erase a <+ l :=
+theorem erase_sublist (a : α) (l : List α) : l.erase a <+ l :=
   erase_eq_eraseP' a l ▸ eraseP_sublist ..
 
-theorem erase_subset {a : α} {l : List α} : l.erase a ⊆ l := erase_sublist.subset
+theorem erase_subset (a : α) (l : List α) : l.erase a ⊆ l := (erase_sublist a l).subset
 
 theorem Sublist.erase (a : α) {l₁ l₂ : List α} (h : l₁ <+ l₂) : l₁.erase a <+ l₂.erase a := by
   simp only [erase_eq_eraseP']; exact h.eraseP
@@ -369,14 +364,14 @@ theorem Sublist.erase (a : α) {l₁ l₂ : List α} (h : l₁ <+ l₂) : l₁.e
 theorem IsPrefix.erase (a : α) {l₁ l₂ : List α} (h : l₁ <+: l₂) : l₁.erase a <+: l₂.erase a := by
   simp only [erase_eq_eraseP']; exact h.eraseP
 
-theorem length_erase_le {a : α} {l : List α} : (l.erase a).length ≤ l.length :=
-  erase_sublist.length_le
+theorem length_erase_le (a : α) (l : List α) : (l.erase a).length ≤ l.length :=
+  (erase_sublist a l).length_le
 
-theorem le_length_erase [LawfulBEq α] {a : α} {l : List α} : l.length - 1 ≤ (l.erase a).length := by
+theorem le_length_erase [LawfulBEq α] (a : α) (l : List α) : l.length - 1 ≤ (l.erase a).length := by
   rw [length_erase]
   split <;> simp
 
-theorem mem_of_mem_erase {a b : α} {l : List α} (h : a ∈ l.erase b) : a ∈ l := erase_subset h
+theorem mem_of_mem_erase {a b : α} {l : List α} (h : a ∈ l.erase b) : a ∈ l := erase_subset _ _ h
 
 @[simp] theorem mem_erase_of_ne [LawfulBEq α] {a b : α} {l : List α} (ab : a ≠ b) :
     a ∈ l.erase b ↔ a ∈ l :=
@@ -386,7 +381,7 @@ theorem mem_of_mem_erase {a b : α} {l : List α} (h : a ∈ l.erase b) : a ∈
   rw [erase_eq_eraseP', eraseP_eq_self_iff]
   simp [forall_mem_ne']
 
-theorem erase_filter [LawfulBEq α] {f : α → Bool} {l : List α} :
+theorem erase_filter [LawfulBEq α] (f : α → Bool) (l : List α) :
     (filter f l).erase a = filter f (l.erase a) := by
   induction l with
   | nil => rfl
@@ -417,14 +412,12 @@ theorem erase_append [LawfulBEq α] {a : α} {l₁ l₂ : List α} :
     (l₁ ++ l₂).erase a = if a ∈ l₁ then l₁.erase a ++ l₂ else l₁ ++ l₂.erase a := by
   simp [erase_eq_eraseP, eraseP_append]
 
-theorem erase_replicate [LawfulBEq α] {n : Nat} {a b : α} :
+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
   rw [erase_eq_eraseP]
   simp [eraseP_replicate]
 
--- 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) {l : List α} :
+theorem erase_comm [LawfulBEq α] (a b : α) (l : List α) :
     (l.erase a).erase b = (l.erase b).erase a := by
   if ab : a == b then rw [eq_of_beq ab] else ?_
   if ha : a ∈ l then ?_ else
@@ -464,7 +457,7 @@ theorem erase_eq_iff [LawfulBEq α] {a : α} {l : List α} :
   simp_all
 
 theorem Pairwise.erase [LawfulBEq α] {l : List α} (a) : Pairwise p l → Pairwise p (l.erase a) :=
-  Pairwise.sublist <| erase_sublist
+  Pairwise.sublist <| erase_sublist _ _
 
 theorem Nodup.erase_eq_filter [LawfulBEq α] {l} (d : Nodup l) (a : α) : l.erase a = l.filter (· != a) := by
   induction d with
@@ -489,10 +482,10 @@ theorem Nodup.erase [LawfulBEq α] (a : α) : Nodup l → Nodup (l.erase a) :=
   Pairwise.erase a
 
 theorem head_erase_mem (xs : List α) (a : α) (h) : (xs.erase a).head h ∈ xs :=
-  erase_sublist.head_mem h
+  (erase_sublist a xs).head_mem h
 
 theorem getLast_erase_mem (xs : List α) (a : α) (h) : (xs.erase a).getLast h ∈ xs :=
-  erase_sublist.getLast_mem h
+  (erase_sublist a xs).getLast_mem h
 
 theorem erase_eq_eraseIdx (l : List α) (a : α) :
     l.erase a = match l.idxOf? a with
@@ -511,7 +504,7 @@ end erase
 
 /-! ### eraseIdx -/
 
-theorem length_eraseIdx {l : List α} {i : Nat} :
+theorem length_eraseIdx (l : List α) (i : Nat) :
     (l.eraseIdx i).length = if i < l.length then l.length - 1 else l.length := by
   induction l generalizing i with
   | nil => simp
@@ -528,7 +521,7 @@ theorem length_eraseIdx_of_lt {l : List α} {i} (h : i < length l) :
     (l.eraseIdx i).length = length l - 1 := by
   simp [length_eraseIdx, h]
 
-@[simp] theorem eraseIdx_zero {l : List α} : eraseIdx l 0 = l.tail := by cases l <;> rfl
+@[simp] theorem eraseIdx_zero (l : List α) : eraseIdx l 0 = tail l := by cases l <;> rfl
 
 theorem eraseIdx_eq_take_drop_succ :
     ∀ (l : List α) (i : Nat), l.eraseIdx i = l.take i ++ l.drop (i + 1)
@@ -559,13 +552,12 @@ abbrev eraseIdx_ne_nil := @eraseIdx_ne_nil_iff
 theorem eraseIdx_sublist : ∀ (l : List α) (k : Nat), eraseIdx l k <+ l
   | [], _ => by simp
   | a::l, 0 => by simp
-  | a::l, k + 1 => by simp [eraseIdx_sublist]
+  | a::l, k + 1 => by simp [eraseIdx_sublist l k]
 
 theorem mem_of_mem_eraseIdx {l : List α} {i : Nat} {a : α} (h : a ∈ l.eraseIdx i) : a ∈ l :=
   (eraseIdx_sublist _ _).mem h
 
-theorem eraseIdx_subset {l : List α} {k : Nat} : eraseIdx l k ⊆ l :=
-  (eraseIdx_sublist _ _).subset
+theorem eraseIdx_subset (l : List α) (k : Nat) : eraseIdx l k ⊆ l := (eraseIdx_sublist l k).subset
 
 @[simp]
 theorem eraseIdx_eq_self : ∀ {l : List α} {k : Nat}, eraseIdx l k = l ↔ length l ≤ k
@@ -576,11 +568,9 @@ theorem eraseIdx_eq_self : ∀ {l : List α} {k : Nat}, eraseIdx l k = l ↔ len
 theorem eraseIdx_of_length_le {l : List α} {k : Nat} (h : length l ≤ k) : eraseIdx l k = l := by
   rw [eraseIdx_eq_self.2 h]
 
--- Arguments are intentionally explicit.
 theorem length_eraseIdx_le (l : List α) (i : Nat) : length (l.eraseIdx i) ≤ length l :=
-  (eraseIdx_sublist _ _).length_le
+  (eraseIdx_sublist l i).length_le
 
--- Arguments are intentionally explicit.
 theorem le_length_eraseIdx (l : List α) (i : Nat) : length l - 1 ≤ length (l.eraseIdx i) := by
   rw [length_eraseIdx]
   split <;> simp
@@ -633,7 +623,7 @@ protected theorem IsPrefix.eraseIdx {l l' : List α} (h : l <+: l') (k : Nat) :
 -- `Init/Data/List/Nat/Basic.lean`.
 
 theorem erase_eq_eraseIdx_of_idxOf [BEq α] [LawfulBEq α]
-    {l : List α} {a : α} {i : Nat} (w : l.idxOf a = i) :
+    (l : List α) (a : α) (i : Nat) (w : l.idxOf a = i) :
     l.erase a = l.eraseIdx i := by
   subst w
   rw [erase_eq_iff]

src/Init/Data/List/FinRange.lean

@@ -11,28 +11,22 @@ set_option linter.indexVariables true -- Enforce naming conventions for index va
 
 namespace List
 
-/--
-Lists all elements of `Fin n` in order, starting at `0`.
-
-Examples:
- * `List.finRange 0 = ([] : List (Fin 0))`
- * `List.finRange 2 = ([0, 1] : List (Fin 2))`
--/
+/-- `finRange n` lists all elements of `Fin n` in order -/
 def finRange (n : Nat) : List (Fin n) := ofFn fun i => i
 
-@[simp] theorem length_finRange {n : Nat} : (List.finRange n).length = n := by
+@[simp] theorem length_finRange (n) : (List.finRange n).length = n := by
   simp [List.finRange]
 
-@[simp] theorem getElem_finRange {i : Nat} (h : i < (List.finRange n).length) :
-    (finRange n)[i] = Fin.cast length_finRange ⟨i, h⟩ := by
+@[simp] theorem getElem_finRange (i : Nat) (h : i < (List.finRange n).length) :
+    (finRange n)[i] = Fin.cast (length_finRange n) ⟨i, h⟩ := by
   simp [List.finRange]
 
 @[simp] theorem finRange_zero : finRange 0 = [] := by simp [finRange, ofFn]
 
-theorem finRange_succ {n} : finRange (n+1) = 0 :: (finRange n).map Fin.succ := by
+theorem finRange_succ (n) : finRange (n+1) = 0 :: (finRange n).map Fin.succ := by
   apply List.ext_getElem; simp; intro i; cases i <;> simp
 
-theorem finRange_succ_last {n} :
+theorem finRange_succ_last (n) :
     finRange (n+1) = (finRange n).map Fin.castSucc ++ [Fin.last n] := by
   apply List.ext_getElem
   · simp
@@ -43,7 +37,7 @@ theorem finRange_succ_last {n} :
     · rfl
     · next h => exact Fin.eq_last_of_not_lt h
 
-theorem finRange_reverse {n} : (finRange n).reverse = (finRange n).map Fin.rev := by
+theorem finRange_reverse (n) : (finRange n).reverse = (finRange n).map Fin.rev := by
   induction n with
   | zero => simp
   | succ n ih =>

src/Init/Data/List/Find.lean

@@ -25,11 +25,11 @@ open Nat
 
 /-! ### findSome? -/
 
-@[simp] theorem findSome?_cons_of_isSome {l} (h : (f a).isSome) : findSome? f (a :: l) = f a := by
+@[simp] theorem findSome?_cons_of_isSome (l) (h : (f a).isSome) : findSome? f (a :: l) = f a := by
   simp only [findSome?]
   split <;> simp_all
 
-@[simp] theorem findSome?_cons_of_isNone {l} (h : (f a).isNone) : findSome? f (a :: l) = findSome? f l := by
+@[simp] theorem findSome?_cons_of_isNone (l) (h : (f a).isNone) : findSome? f (a :: l) = findSome? f l := by
   simp only [findSome?]
   split <;> simp_all
 
@@ -89,7 +89,7 @@ theorem findSome?_eq_some_iff {f : α → Option β} {l : List α} {b : β} :
           obtain ⟨⟨rfl, rfl⟩, rfl⟩ := h₁
           exact ⟨l₁, a, l₂, rfl, h₂, fun a' w => h₃ a' (mem_cons_of_mem p w)⟩
 
-@[simp] theorem findSome?_guard {l : List α} : findSome? (Option.guard fun x => p x) l = find? p l := by
+@[simp] theorem findSome?_guard (l : List α) : findSome? (Option.guard fun x => p x) l = find? p l := by
   induction l with
   | nil => simp
   | cons x xs ih =>
@@ -101,33 +101,33 @@ theorem findSome?_eq_some_iff {f : α → Option β} {l : List α} {b : β} :
     · simp only [Option.guard_eq_none] at h
       simp [ih, h]
 
-theorem find?_eq_findSome?_guard {l : List α} : find? p l = findSome? (Option.guard fun x => p x) l :=
-  findSome?_guard.symm
+theorem find?_eq_findSome?_guard (l : List α) : find? p l = findSome? (Option.guard fun x => p x) l :=
+  (findSome?_guard l).symm
 
-@[simp] theorem head?_filterMap {f : α → Option β} {l : List α} : (l.filterMap f).head? = l.findSome? f := by
+@[simp] theorem head?_filterMap (f : α → Option β) (l : List α) : (l.filterMap f).head? = l.findSome? f := by
   induction l with
   | nil => simp
   | cons x xs ih =>
     simp only [filterMap_cons, findSome?_cons]
     split <;> simp [*]
 
-@[simp] theorem head_filterMap {f : α → Option β} {l : List α} (h) :
+@[simp] theorem head_filterMap (f : α → Option β) (l : List α) (h) :
     (l.filterMap f).head h = (l.findSome? f).get (by simp_all [Option.isSome_iff_ne_none]) := by
   simp [head_eq_iff_head?_eq_some]
 
-@[simp] theorem getLast?_filterMap {f : α → Option β} {l : List α} : (l.filterMap f).getLast? = l.reverse.findSome? f := by
+@[simp] theorem getLast?_filterMap (f : α → Option β) (l : List α) : (l.filterMap f).getLast? = l.reverse.findSome? f := by
   rw [getLast?_eq_head?_reverse]
   simp [← filterMap_reverse]
 
-@[simp] theorem getLast_filterMap {f : α → Option β} {l : List α} (h) :
+@[simp] theorem getLast_filterMap (f : α → Option β) (l : List α) (h) :
     (l.filterMap f).getLast h = (l.reverse.findSome? f).get (by simp_all [Option.isSome_iff_ne_none]) := by
   simp [getLast_eq_iff_getLast?_eq_some]
 
-@[simp] theorem map_findSome? {f : α → Option β} {g : β → γ} {l : List α} :
+@[simp] theorem map_findSome? (f : α → Option β) (g : β → γ) (l : List α) :
     (l.findSome? f).map g = l.findSome? (Option.map g ∘ f) := by
   induction l <;> simp [findSome?_cons]; split <;> simp [*]
 
-theorem findSome?_map {f : β → γ} {l : List β} : findSome? p (l.map f) = l.findSome? (p ∘ f) := by
+theorem findSome?_map (f : β → γ) (l : List β) : findSome? p (l.map f) = l.findSome? (p ∘ f) := by
   induction l with
   | nil => simp
   | cons x xs ih =>
@@ -202,14 +202,14 @@ theorem IsInfix.findSome?_eq_none {l₁ l₂ : List α} {f : α → Option β} (
 
 /-! ### find? -/
 
-@[simp] theorem find?_singleton {a : α} {p : α → Bool} : [a].find? p = if p a then some a else none := by
+@[simp] theorem find?_singleton (a : α) (p : α → Bool) : [a].find? p = if p a then some a else none := by
   simp only [find?]
   split <;> simp_all
 
-@[simp] theorem find?_cons_of_pos {l} (h : p a) : find? p (a :: l) = some a := by
+@[simp] theorem find?_cons_of_pos (l) (h : p a) : find? p (a :: l) = some a := by
   simp [find?, h]
 
-@[simp] theorem find?_cons_of_neg {l} (h : ¬p a) : find? p (a :: l) = find? p l := by
+@[simp] theorem find?_cons_of_neg (l) (h : ¬p a) : find? p (a :: l) = find? p l := by
   simp [find?, h]
 
 @[simp] theorem find?_eq_none : find? p l = none ↔ ∀ x ∈ l, ¬ p x := by
@@ -230,7 +230,7 @@ theorem find?_eq_some_iff_append :
         cases as with
         | nil => simp_all
         | cons a as =>
-          specialize h₂ a mem_cons_self
+          specialize h₂ a (mem_cons_self _ _)
           simp only [cons_append] at h₁
           obtain ⟨rfl, -⟩ := h₁
           simp_all
@@ -279,7 +279,7 @@ theorem mem_of_find?_eq_some : ∀ {l}, find? p l = some a → a ∈ l
     · exact H ▸ .head _
     · exact .tail _ (mem_of_find?_eq_some H)
 
-theorem get_find?_mem {xs : List α} {p : α → Bool} (h) : (xs.find? p).get h ∈ xs := by
+theorem get_find?_mem (xs : List α) (p : α → Bool) (h) : (xs.find? p).get h ∈ xs := by
   induction xs with
   | nil => simp at h
   | cons x xs ih =>
@@ -290,7 +290,7 @@ theorem get_find?_mem {xs : List α} {p : α → Bool} (h) : (xs.find? p).get h
       right
       apply ih
 
-@[simp] theorem find?_filter {xs : List α} {p : α → Bool} {q : α → Bool} :
+@[simp] theorem find?_filter (xs : List α) (p : α → Bool) (q : α → Bool) :
     (xs.filter p).find? q = xs.find? (fun a => p a ∧ q a) := by
   induction xs with
   | nil => simp
@@ -300,22 +300,22 @@ theorem get_find?_mem {xs : List α} {p : α → Bool} (h) : (xs.find? p).get h
     · simp only [find?_cons]
       split <;> simp_all
 
-@[simp] theorem head?_filter {p : α → Bool} {l : List α} : (l.filter p).head? = l.find? p := by
+@[simp] theorem head?_filter (p : α → Bool) (l : List α) : (l.filter p).head? = l.find? p := by
   rw [← filterMap_eq_filter, head?_filterMap, findSome?_guard]
 
-@[simp] theorem head_filter {p : α → Bool} {l : List α} (h) :
+@[simp] theorem head_filter (p : α → Bool) (l : List α) (h) :
     (l.filter p).head h = (l.find? p).get (by simp_all [Option.isSome_iff_ne_none]) := by
   simp [head_eq_iff_head?_eq_some]
 
-@[simp] theorem getLast?_filter {p : α → Bool} {l : List α} : (l.filter p).getLast? = l.reverse.find? p := by
+@[simp] theorem getLast?_filter (p : α → Bool) (l : List α) : (l.filter p).getLast? = l.reverse.find? p := by
   rw [getLast?_eq_head?_reverse]
   simp [← filter_reverse]
 
-@[simp] theorem getLast_filter {p : α → Bool} {l : List α} (h) :
+@[simp] theorem getLast_filter (p : α → Bool) (l : List α) (h) :
     (l.filter p).getLast h = (l.reverse.find? p).get (by simp_all [Option.isSome_iff_ne_none]) := by
   simp [getLast_eq_iff_getLast?_eq_some]
 
-@[simp] theorem find?_filterMap {xs : List α} {f : α → Option β} {p : β → Bool} :
+@[simp] theorem find?_filterMap (xs : List α) (f : α → Option β) (p : β → Bool) :
     (xs.filterMap f).find? p = (xs.find? (fun a => (f a).any p)).bind f := by
   induction xs with
   | nil => simp
@@ -325,7 +325,7 @@ theorem get_find?_mem {xs : List α} {p : α → Bool} (h) : (xs.find? p).get h
     · simp only [find?_cons]
       split <;> simp_all
 
-@[simp] theorem find?_map {f : β → α} {l : List β} : find? p (l.map f) = (l.find? (p ∘ f)).map f := by
+@[simp] theorem find?_map (f : β → α) (l : List β) : find? p (l.map f) = (l.find? (p ∘ f)).map f := by
   induction l with
   | nil => simp
   | cons x xs ih =>
@@ -339,7 +339,7 @@ theorem get_find?_mem {xs : List α} {p : α → Bool} (h) : (xs.find? p).get h
     simp only [cons_append, find?]
     by_cases h : p x <;> simp [h, ih]
 
-@[simp] theorem find?_flatten {xss : List (List α)} {p : α → Bool} :
+@[simp] theorem find?_flatten (xss : List (List α)) (p : α → Bool) :
     xss.flatten.find? p = xss.findSome? (·.find? p) := by
   induction xss with
   | nil => simp
@@ -397,7 +397,7 @@ theorem find?_flatten_eq_some_iff {xs : List (List 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 : List α} {f : α → List β} {p : β → Bool} :
+@[simp] theorem find?_flatMap (xs : List α) (f : α → List β) (p : β → Bool) :
     (xs.flatMap f).find? p = xs.findSome? (fun x => (f x).find? p) := by
   simp [flatMap_def, findSome?_map]; rfl
 
@@ -441,7 +441,7 @@ abbrev find?_replicate_eq_none := @find?_replicate_eq_none_iff
 @[deprecated find?_replicate_eq_some_iff (since := "2025-02-03")]
 abbrev find?_replicate_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?_replicate (n : Nat) (a : α) (p : α → Bool) (h) : ((replicate n a).find? p).get h = a := by
   cases n with
   | zero => simp at h
   | succ n => simp
@@ -476,8 +476,8 @@ theorem IsInfix.find?_eq_none {l₁ l₂ : List α} {p : α → Bool} (h : l₁
     List.find? p l₂ = none → List.find? p l₁ = none :=
   h.sublist.find?_eq_none
 
-theorem find?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
-    (H : ∀ (a : α), a ∈ xs → P a) {p : β → Bool} :
+theorem find?_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : List 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
@@ -516,7 +516,7 @@ private theorem findIdx?_go_eq {p : α → Bool} {xs : List α} {i : Nat} :
 
 /-! ### findIdx -/
 
-theorem findIdx_cons {p : α → Bool} {b : α} {l : List α} :
+theorem findIdx_cons (p : α → Bool) (b : α) (l : List α) :
     (b :: l).findIdx p = bif p b then 0 else (l.findIdx p) + 1 := by
   cases H : p b with
   | true => simp [H, findIdx, findIdx.go]
@@ -540,6 +540,11 @@ theorem findIdx_getElem {xs : List α} {w : xs.findIdx p < xs.length} :
     p xs[xs.findIdx p] :=
   xs.findIdx_of_getElem?_eq_some (getElem?_eq_getElem w)
 
+@[deprecated findIdx_getElem (since := "2024-08-12")]
+theorem findIdx_get {xs : List α} {w : xs.findIdx p < xs.length} :
+    p (xs.get ⟨xs.findIdx p, w⟩) :=
+  xs.findIdx_of_getElem?_eq_some (getElem?_eq_getElem w)
+
 theorem findIdx_lt_length_of_exists {xs : List α} (h : ∃ x ∈ xs, p x) :
     xs.findIdx p < xs.length := by
   induction xs with
@@ -572,7 +577,7 @@ theorem findIdx_eq_length_of_false {p : α → Bool} {xs : List α} (h : ∀ x
   rw [findIdx_eq_length]
   exact h
 
-theorem findIdx_le_length {p : α → Bool} {xs : List α} : xs.findIdx p ≤ xs.length := by
+theorem findIdx_le_length (p : α → Bool) {xs : List α} : xs.findIdx p ≤ xs.length := by
   by_cases e : ∃ x ∈ xs, p x
   · exact Nat.le_of_lt (findIdx_lt_length_of_exists e)
   · simp at e
@@ -589,7 +594,7 @@ theorem findIdx_lt_length {p : α → Bool} {xs : List α} :
 
 /-- `p` does not hold for elements with indices less than `xs.findIdx p`. -/
 theorem not_of_lt_findIdx {p : α → Bool} {xs : List α} {i : Nat} (h : i < xs.findIdx p) :
-    p (xs[i]'(Nat.le_trans h findIdx_le_length)) = false := by
+    p (xs[i]'(Nat.le_trans h (findIdx_le_length p))) = false := by
   revert i
   induction xs with
   | nil => intro i h; rw [findIdx_nil] at h; simp at h
@@ -638,7 +643,7 @@ theorem findIdx_eq {p : α → Bool} {xs : List α} {i : Nat} (h : i < xs.length
   simp at h3
   simp_all [not_of_lt_findIdx h3]
 
-theorem findIdx_append {p : α → Bool} {l₁ l₂ : List α} :
+theorem findIdx_append (p : α → Bool) (l₁ l₂ : List α) :
     (l₁ ++ l₂).findIdx p =
       if l₁.findIdx p < l₁.length then l₁.findIdx p else l₂.findIdx p + l₁.length := by
   induction l₁ with
@@ -813,7 +818,7 @@ theorem of_findIdx?_eq_none {xs : List α} {p : α → Bool} (w : xs.findIdx? p
 @[deprecated of_findIdx?_eq_none (since := "2025-02-02")]
 abbrev findIdx?_of_eq_none := @of_findIdx?_eq_none
 
-@[simp] theorem findIdx?_map {f : β → α} {l : List β} : findIdx? p (l.map f) = l.findIdx? (p ∘ f) := by
+@[simp] theorem findIdx?_map (f : β → α) (l : List β) : findIdx? p (l.map f) = l.findIdx? (p ∘ f) := by
   induction l with
   | nil => simp
   | cons x xs ih =>
@@ -1066,7 +1071,7 @@ theorem idxOf?_eq_map_finIdxOf?_val [BEq α] {xs : List α} {a : α} :
 
 @[simp] theorem finIdxOf?_nil [BEq α] : ([] : List α).finIdxOf? a = none := rfl
 
-@[simp] theorem finIdxOf?_cons [BEq α] {a : α} {xs : List α} :
+@[simp] theorem finIdxOf?_cons [BEq α] (a : α) (xs : List α) :
     (a :: xs).finIdxOf? b =
       if a == b then some ⟨0, by simp⟩ else (xs.finIdxOf? b).map (·.succ) := by
   simp [finIdxOf?]
@@ -1092,7 +1097,7 @@ The lemmas below should be made consistent with those for `findIdx?` (and proved
 
 @[simp] theorem idxOf?_nil [BEq α] : ([] : List α).idxOf? a = none := rfl
 
-theorem idxOf?_cons [BEq α] {a : α} {xs : List α} {b : α} :
+theorem idxOf?_cons [BEq α] (a : α) (xs : List α) (b : α) :
     (a :: xs).idxOf? b = if a == b then some 0 else (xs.idxOf? b).map (· + 1) := by
   simp [idxOf?]
 
@@ -1117,7 +1122,7 @@ variable [BEq α] [LawfulBEq α]
 @[simp] theorem lookup_cons_self  {k : α} : ((k,b) :: es).lookup k = some b := by
   simp [lookup_cons]
 
-theorem lookup_eq_findSome? {l : List (α × β)} {k : α} :
+theorem lookup_eq_findSome? (l : List (α × β)) (k : α) :
     l.lookup k = l.findSome? fun p => if k == p.1 then some p.2 else none := by
   induction l with
   | nil => rfl

src/Init/Data/List/Impl.lean

@@ -17,8 +17,7 @@ then at runtime you will get non-tail recursive versions of the following defini
 -/
 
 set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
--- TODO: restore after an update-stage0
--- set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
 
 namespace List
 
@@ -50,16 +49,7 @@ The following operations are given `@[csimp]` replacements below:
 
 /-! ### set -/
 
-/--
-Replaces the value at (zero-based) index `n` in `l` with `a`. If the index is out of bounds, then
-the list is returned unmodified.
-
-This is a tail-recursive version of `List.set` that's used at runtime.
-
-Examples:
-* `["water", "coffee", "soda", "juice"].set 1 "tea" = ["water", "tea", "soda", "juice"]`
-* `["water", "coffee", "soda", "juice"].set 4 "tea" = ["water", "coffee", "soda", "juice"]`
--/
+/-- Tail recursive version of `List.set`. -/
 @[inline] def setTR (l : List α) (n : Nat) (a : α) : List α := go l n #[] where
   /-- Auxiliary for `setTR`: `setTR.go l a xs n acc = acc.toList ++ set xs a`,
   unless `n ≥ l.length` in which case it returns `l` -/
@@ -79,22 +69,7 @@ Examples:
 
 /-! ### filterMap -/
 
-
-/--
-Applies a function that returns an `Option` to each element of a list, collecting the non-`none`
-values.
-
-`O(|l|)`. This is a tail-recursive version of `List.filterMap`, used at runtime.
-
-Example:
-```lean example
-#eval [1, 2, 5, 2, 7, 7].filterMapTR fun x =>
-  if x > 2 then some (2 * x) else none
-```
-```output
-[10, 14, 14]
-```
--/
+/-- Tail recursive version of `filterMap`. -/
 @[inline] def filterMapTR (f : α → Option β) (l : List α) : List β := go l #[] where
   /-- Auxiliary for `filterMap`: `filterMap.go f l = acc.toList ++ filterMap f l` -/
   @[specialize] go : List α → Array β → List β
@@ -115,17 +90,7 @@ Example:
 
 /-! ### foldr -/
 
-/--
-Folds a function over a list from the right, accumulating a value starting with `init`. The
-accumulated value is combined with the each element of the list in reverse order, using `f`.
-
-`O(|l|)`. This is the tail-recursive replacement for `List.foldr` in runtime code.
-
-Examples:
- * `[a, b, c].foldrTR f init  = f a (f b (f c init))`
- * `[1, 2, 3].foldrTR (toString · ++ ·) "" = "123"`
- * `[1, 2, 3].foldrTR (s!"({·} {·})") "!" = "(1 (2 (3 !)))"`
--/
+/-- Tail recursive version of `List.foldr`. -/
 @[specialize] def foldrTR (f : α → β → β) (init : β) (l : List α) : β := l.toArray.foldr f init
 
 @[csimp] theorem foldr_eq_foldrTR : @foldr = @foldrTR := by
@@ -133,16 +98,7 @@ Examples:
 
 /-! ### flatMap  -/
 
-/--
-Applies a function that returns a list to each element of a list, and concatenates the resulting
-lists.
-
-This is the tail-recursive version of `List.flatMap` that's used at runtime.
-
-Examples:
-* `[2, 3, 2].flatMapTR List.range = [0, 1, 0, 1, 2, 0, 1]`
-* `["red", "blue"].flatMapTR String.toList = ['r', 'e', 'd', 'b', 'l', 'u', 'e']`
--/
+/-- Tail recursive version of `List.flatMap`. -/
 @[inline] def flatMapTR (f : α → List β) (as : List α) : List β := go as #[] where
   /-- Auxiliary for `flatMap`: `flatMap.go f as = acc.toList ++ bind f as` -/
   @[specialize] go : List α → Array β → List β
@@ -158,15 +114,7 @@ Examples:
 
 /-! ### flatten -/
 
-/--
-Concatenates a list of lists into a single list, preserving the order of the elements.
-
-`O(|flatten L|)`. This is a tail-recursive version of `List.flatten`, used in runtime code.
-
-Examples:
-* `[["a"], ["b", "c"]].flattenTR = ["a", "b", "c"]`
-* `[["a"], [], ["b", "c"], ["d", "e", "f"]].flattenTR = ["a", "b", "c", "d", "e", "f"]`
--/
+/-- Tail recursive version of `List.flatten`. -/
 @[inline] def flattenTR (l : List (List α)) : List α := l.flatMapTR id
 
 @[csimp] theorem flatten_eq_flattenTR : @flatten = @flattenTR := by
@@ -176,16 +124,7 @@ Examples:
 
 /-! ### take -/
 
-/--
-Extracts the first `n` elements of `xs`, or the whole list if `n` is greater than `xs.length`.
-
-`O(min n |xs|)`. This is a tail-recursive version of `List.take`, used at runtime.
-
-Examples:
-* `[a, b, c, d, e].takeTR 0 = []`
-* `[a, b, c, d, e].takeTR 3 = [a, b, c]`
-* `[a, b, c, d, e].takeTR 6 = [a, b, c, d, e]`
--/
+/-- Tail recursive version of `List.take`. -/
 @[inline] def takeTR (n : Nat) (l : List α) : List α := go l n #[] where
   /-- Auxiliary for `take`: `take.go l xs n acc = acc.toList ++ take n xs`,
   unless `n ≥ xs.length` in which case it returns `l`. -/
@@ -207,17 +146,7 @@ Examples:
 
 /-! ### takeWhile -/
 
-
-/--
- Returns the longest initial segment of `xs` for which `p` returns true.
-
-`O(|xs|)`. This is a tail-recursive version of `List.take`, used at runtime.
-
-Examples:
-* `[7, 6, 4, 8].takeWhileTR (· > 5) = [7, 6]`
-* `[7, 6, 6, 5].takeWhileTR (· > 5) = [7, 6, 6]`
-* `[7, 6, 6, 8].takeWhileTR (· > 5) = [7, 6, 6, 8]`
--/
+/-- Tail recursive version of `List.takeWhile`. -/
 @[inline] def takeWhileTR (p : α → Bool) (l : List α) : List α := go l #[] where
   /-- Auxiliary for `takeWhile`: `takeWhile.go p l xs acc = acc.toList ++ takeWhile p xs`,
   unless no element satisfying `p` is found in `xs` in which case it returns `l`. -/
@@ -240,16 +169,7 @@ Examples:
 
 /-! ### dropLast -/
 
-/--
-Removes the last element of the list, if one exists.
-
-This is a tail-recursive version of `List.dropLast`, used at runtime.
-
-Examples:
-* `[].dropLastTR = []`
-* `["tea"].dropLastTR = []`
-* `["tea", "coffee", "juice"].dropLastTR = ["tea", "coffee"]`
--/
+/-- Tail recursive version of `dropLast`. -/
 @[inline] def dropLastTR (l : List α) : List α := l.toArray.pop.toList
 
 @[csimp] theorem dropLast_eq_dropLastTR : @dropLast = @dropLastTR := by
@@ -259,16 +179,7 @@ Examples:
 
 /-! ### replace -/
 
-/--
-Replaces the first element of the list `l` that is equal to `a` with `b`. If no element is equal to
-`a`, then the list is returned unchanged.
-
-`O(|l|)`. This is a tail-recursive version of `List.replace` that's used in runtime code.
-
-Examples:
-* `[1, 4, 2, 3, 3, 7].replaceTR 3 6 = [1, 4, 2, 6, 3, 7]`
-* `[1, 4, 2, 3, 3, 7].replaceTR 5 6 = [1, 4, 2, 3, 3, 7]`
--/
+/-- Tail recursive version of `List.replace`. -/
 @[inline] def replaceTR [BEq α] (l : List α) (b c : α) : List α := go l #[] where
   /-- Auxiliary for `replace`: `replace.go l b c xs acc = acc.toList ++ replace xs b c`,
   unless `b` is not found in `xs` in which case it returns `l`. -/
@@ -291,76 +202,42 @@ Examples:
 
 /-! ### modify -/
 
-/--
-Replaces the element at the given index, if it exists, with the result of applying `f` to it.
-
-This is a tail-recursive version of `List.modify`.
-
-Examples:
- * `[1, 2, 3].modifyTR 0 (· * 10) = [10, 2, 3]`
- * `[1, 2, 3].modifyTR 2 (· * 10) = [1, 2, 30]`
- * `[1, 2, 3].modifyTR 3 (· * 10) = [1, 2, 3]`
--/
-def modifyTR (l : List α) (i : Nat) (f : α → α) : List α := go l i #[] where
-  /-- Auxiliary for `modifyTR`: `modifyTR.go f l i acc = acc.toList ++ modify f i l`. -/
+/-- Tail-recursive version of `modify`. -/
+def modifyTR (f : α → α) (n : Nat) (l : List α) : List α := go l n #[] where
+  /-- Auxiliary for `modifyTR`: `modifyTR.go f l n acc = acc.toList ++ modify f n l`. -/
   go : List α → Nat → Array α → List α
   | [], _, acc => acc.toList
   | a :: l, 0, acc => acc.toListAppend (f a :: l)
-  | a :: l, i+1, acc => go l i (acc.push a)
+  | a :: l, n+1, acc => go l n (acc.push a)
 
-theorem modifyTR_go_eq : ∀ l i, modifyTR.go f l i acc = acc.toList ++ modify l i f
-  | [], i => by cases i <;> simp [modifyTR.go, modify]
+theorem modifyTR_go_eq : ∀ l i, modifyTR.go f l i acc = acc.toList ++ modify f i l
+  | [], n => by cases n <;> simp [modifyTR.go, modify]
   | a :: l, 0 => by simp [modifyTR.go, modify]
-  | a :: l, i+1 => by simp [modifyTR.go, modify, modifyTR_go_eq l]
+  | a :: l, n+1 => by simp [modifyTR.go, modify, modifyTR_go_eq l]
 
 @[csimp] theorem modify_eq_modifyTR : @modify = @modifyTR := by
-  funext α l i f; simp [modifyTR, modifyTR_go_eq]
+  funext α f n l; simp [modifyTR, modifyTR_go_eq]
 
 /-! ### insertIdx -/
 
-/--
-Inserts an element into a list at the specified index. If the index is greater than the length of
-the list, then the list is returned unmodified.
-
-In other words, the new element is inserted into the list `l` after the first `i` elements of `l`.
-
-This is a tail-recursive version of `List.insertIdx`, used at runtime.
-
-Examples:
- * `["tues", "thur", "sat"].insertIdxTR 1 "wed" = ["tues", "wed", "thur", "sat"]`
- * `["tues", "thur", "sat"].insertIdxTR 2 "wed" = ["tues", "thur", "wed", "sat"]`
- * `["tues", "thur", "sat"].insertIdxTR 3 "wed" = ["tues", "thur", "sat", "wed"]`
- * `["tues", "thur", "sat"].insertIdxTR 4 "wed" = ["tues", "thur", "sat"]`
-
--/
-@[inline] def insertIdxTR (l : List α) (n : Nat) (a : α) : List α := go n l #[] where
+/-- Tail-recursive version of `insertIdx`. -/
+@[inline] def insertIdxTR (n : Nat) (a : α) (l : List α) : List α := go n l #[] where
   /-- Auxiliary for `insertIdxTR`: `insertIdxTR.go a n l acc = acc.toList ++ insertIdx n a l`. -/
   go : Nat → List α → Array α → List α
   | 0, l, acc => acc.toListAppend (a :: l)
   | _, [], acc => acc.toList
   | n+1, a :: l, acc => go n l (acc.push a)
 
-theorem insertIdxTR_go_eq : ∀ i l, insertIdxTR.go a i l acc = acc.toList ++ insertIdx l i a
+theorem insertIdxTR_go_eq : ∀ i l, insertIdxTR.go a i l acc = acc.toList ++ insertIdx i a l
   | 0, l | _+1, [] => by simp [insertIdxTR.go, insertIdx]
   | n+1, a :: l => by simp [insertIdxTR.go, insertIdx, insertIdxTR_go_eq n l]
 
 @[csimp] theorem insertIdx_eq_insertIdxTR : @insertIdx = @insertIdxTR := by
-  funext α l i a; simp [insertIdxTR, insertIdxTR_go_eq]
+  funext α f n l; simp [insertIdxTR, insertIdxTR_go_eq]
 
 /-! ### erase -/
 
-/--
-Removes the first occurrence of `a` from `l`. If `a` does not occur in `l`, the list is returned
-unmodified.
-
-`O(|l|)`.
-
-This is a tail-recursive version of `List.erase`, used in runtime code.
-
-Examples:
-* `[1, 5, 3, 2, 5].eraseTR 5 = [1, 3, 2, 5]`
-* `[1, 5, 3, 2, 5].eraseTR 6 = [1, 5, 3, 2, 5]`
--/
+/-- Tail recursive version of `List.erase`. -/
 @[inline] def eraseTR [BEq α] (l : List α) (a : α) : List α := go l #[] where
   /-- Auxiliary for `eraseTR`: `eraseTR.go l a xs acc = acc.toList ++ erase xs a`,
   unless `a` is not present in which case it returns `l` -/
@@ -380,17 +257,7 @@ Examples:
     · rw [IH] <;> simp_all
     · simp
 
-/--
-Removes the first element of a list for which `p` returns `true`. If no element satisfies `p`, then
-the list is returned unchanged.
-
-This is a tail-recursive version of `eraseP`, used at runtime.
-
-Examples:
-  * `[2, 1, 2, 1, 3, 4].erasePTR (· < 2) = [2, 2, 1, 3, 4]`
-  * `[2, 1, 2, 1, 3, 4].erasePTR (· > 2) = [2, 1, 2, 1, 4]`
-  * `[2, 1, 2, 1, 3, 4].erasePTR (· > 8) = [2, 1, 2, 1, 3, 4]`
--/
+/-- Tail-recursive version of `eraseP`. -/
 @[inline] def erasePTR (p : α → Bool) (l : List α) : List α := go l #[] where
   /-- Auxiliary for `erasePTR`: `erasePTR.go p l xs acc = acc.toList ++ eraseP p xs`,
   unless `xs` does not contain any elements satisfying `p`, where it returns `l`. -/
@@ -410,20 +277,7 @@ Examples:
 
 /-! ### eraseIdx -/
 
-
-/--
-Removes the element at the specified index. If the index is out of bounds, the list is returned
-unmodified.
-
-`O(i)`.
-
-This is a tail-recursive version of `List.eraseIdx`, used at runtime.
-
-Examples:
-* `[0, 1, 2, 3, 4].eraseIdxTR 0 = [1, 2, 3, 4]`
-* `[0, 1, 2, 3, 4].eraseIdxTR 1 = [0, 2, 3, 4]`
-* `[0, 1, 2, 3, 4].eraseIdxTR 5 = [0, 1, 2, 3, 4]`
--/
+/-- Tail recursive version of `List.eraseIdx`. -/
 @[inline] def eraseIdxTR (l : List α) (n : Nat) : List α := go l n #[] where
   /-- Auxiliary for `eraseIdxTR`: `eraseIdxTR.go l n xs acc = acc.toList ++ eraseIdx xs a`,
   unless `a` is not present in which case it returns `l` -/
@@ -449,18 +303,7 @@ Examples:
 
 /-! ### zipWith -/
 
-/--
-Applies a function to the corresponding elements of two lists, stopping at the end of the shorter
-list.
-
-`O(min |xs| |ys|)`. This is a tail-recursive version of `List.zipWith` that's used at runtime.
-
-Examples:
-* `[1, 2].zipWithTR (· + ·) [5, 6] = [6, 8]`
-* `[1, 2, 3].zipWithTR (· + ·) [5, 6, 10] = [6, 8, 13]`
-* `[].zipWithTR (· + ·) [5, 6] = []`
-* `[x₁, x₂, x₃].zipWithTR f [y₁, y₂, y₃, y₄] = [f x₁ y₁, f x₂ y₂, f x₃ y₃]`
--/
+/-- Tail recursive version of `List.zipWith`. -/
 @[inline] def zipWithTR (f : α → β → γ) (as : List α) (bs : List β) : List γ := go as bs #[] where
   /-- Auxiliary for `zipWith`: `zipWith.go f as bs acc = acc.toList ++ zipWith f as bs` -/
   go : List α → List β → Array γ → List γ
@@ -478,16 +321,7 @@ Examples:
 
 /-! ### zipIdx -/
 
-
-/--
-Pairs each element of a list with its index, optionally starting from an index other than `0`.
-
-`O(|l|)`. This is a tail-recursive version of `List.zipIdx` that's used at runtime.
-
-Examples:
-* `[a, b, c].zipIdxTR = [(a, 0), (b, 1), (c, 2)]`
-* `[a, b, c].zipIdxTR 5 = [(a, 5), (b, 6), (c, 7)]`
--/
+/-- Tail recursive version of `List.zipIdx`. -/
 def zipIdxTR (l : List α) (n : Nat := 0) : List (α × Nat) :=
   let as := l.toArray
   (as.foldr (fun a (n, acc) => (n-1, (a, n-1) :: acc)) (n + as.size, [])).2
@@ -529,18 +363,8 @@ theorem enumFrom_eq_enumFromTR : @enumFrom = @enumFromTR := by
 /-! ### intercalate -/
 
 set_option linter.listVariables false in
-/--
-Alternates the lists in `xs` with the separator `sep`.
-
-This is a tail-recursive version of `List.intercalate` used at runtime.
-
-Examples:
-* `List.intercalateTR sep [] = []`
-* `List.intercalateTR sep [a] = a`
-* `List.intercalateTR sep [a, b] = a ++ sep ++ b`
-* `List.intercalateTR sep [a, b, c] = a ++ sep ++ b ++ sep ++ c`
--/
-def intercalateTR (sep : List α) : (xs : List (List α)) → List α
+/-- Tail recursive version of `List.intercalate`. -/
+def intercalateTR (sep : List α) : List (List α) → List α
   | [] => []
   | [x] => x
   | x::xs => go sep.toArray x xs #[]

src/Init/Data/List/Lex.lean

@@ -14,11 +14,11 @@ namespace List
 
 /-! ### Lexicographic ordering -/
 
-@[simp] theorem lex_lt [LT α] {l₁ l₂ : List α} : Lex (· < ·) l₁ l₂ ↔ l₁ < l₂ := Iff.rfl
-@[simp] theorem not_lex_lt [LT α] {l₁ l₂ : List α} : ¬ Lex (· < ·) l₁ l₂ ↔ l₂ ≤ l₁ := Iff.rfl
+@[simp] theorem lex_lt [LT α] (l₁ l₂ : List α) : Lex (· < ·) l₁ l₂ ↔ l₁ < l₂ := Iff.rfl
+@[simp] theorem not_lex_lt [LT α] (l₁ l₂ : List α) : ¬ Lex (· < ·) l₁ l₂ ↔ l₂ ≤ l₁ := 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
 
@@ -49,7 +49,7 @@ instance ltIrrefl [LT α] [Std.Irrefl (· < · : α → α → Prop)] : Std.Irre
   · rintro rfl
     exact not_lex_nil
 
-@[simp] theorem le_nil [LT α] {l : List α} : l ≤ [] ↔ l = [] := not_nil_lex_iff
+@[simp] theorem le_nil [LT α] (l : List α) : l ≤ [] ↔ l = [] := not_nil_lex_iff
 
 -- This is named with a prime to avoid conflict with `lex [] (b :: bs) lt = true`.
 -- Better naming for the `Lex` vs `lex` distinction would be welcome.

src/Init/Data/List/MapIdx.lean

@@ -19,11 +19,8 @@ namespace List
 /-! ## Operations using indexes -/
 
 /--
-Applies a function to each element of the list along with the index at which that element is found,
-returning the list of results. In addition to the index, the function is also provided with a proof
-that the index is valid.
-
-`List.mapIdx` is a variant that does not provide the function with evidence that the index is valid.
+Given a list `as = [a₀, a₁, ...]` and a function `f : (i : Nat) → α → (h : i < as.length) → β`, returns the list
+`[f 0 a₀ ⋯, f 1 a₁ ⋯, ...]`.
 -/
 @[inline] def mapFinIdx (as : List α) (f : (i : Nat) → α → (h : i < as.length) → β) : List β :=
   go as #[] (by simp)
@@ -36,11 +33,8 @@ where
     go as (acc.push (f acc.size a (by simp at h; omega))) (by simp at h ⊢; omega)
 
 /--
-Applies a function to each element of the list along with the index at which that element is found,
-returning the list of results.
-
-`List.mapFinIdx` is a variant that additionally provides the function with a proof that the index
-is valid.
+Given a function `f : Nat → α → β` and `as : List α`, `as = [a₀, a₁, ...]`, returns the list
+`[f 0 a₀, f 1 a₁, ...]`.
 -/
 @[inline] def mapIdx (f : Nat → α → β) (as : List α) : List β := go as #[] where
   /-- Auxiliary for `mapIdx`:
@@ -50,12 +44,8 @@ is valid.
   | a :: as, acc => go as (acc.push (f acc.size a))
 
 /--
-Applies a monadic function to each element of the list along with the index at which that element is
-found, returning the list of results. In addition to the index, the function is also provided with a
-proof that the index is valid.
-
-`List.mapIdxM` is a variant that does not provide the function with evidence that the index is
-valid.
+Given a list `as = [a₀, a₁, ...]` and a monadic function `f : (i : Nat) → α → (h : i < as.length) → m β`,
+returns the list `[f 0 a₀ ⋯, f 1 a₁ ⋯, ...]`.
 -/
 @[inline] def mapFinIdxM [Monad m] (as : List α) (f : (i : Nat) → α → (h : i < as.length) → m β) : m (List β) :=
   go as #[] (by simp)
@@ -68,11 +58,8 @@ where
     go as (acc.push (← f acc.size a (by simp at h; omega))) (by simp at h ⊢; omega)
 
 /--
-Applies a monadic function to each element of the list along with the index at which that element is
-found, returning the list of results.
-
-`List.mapFinIdxM` is a variant that additionally provides the function with a proof that the index
-is valid.
+Given a monadic function `f : Nat → α → m β` and `as : List α`, `as = [a₀, a₁, ...]`,
+returns the list `[f 0 a₀, f 1 a₁, ...]`.
 -/
 @[inline] def mapIdxM [Monad m] (f : Nat → α → m β) (as : List α) : m (List β) := go as #[] where
   /-- Auxiliary for `mapIdxM`:
@@ -490,9 +477,9 @@ theorem mapIdx_eq_mapIdx_iff {l : List α} :
   cases l with
   | nil => simp at h
   | cons _ _ =>
-    simp only [← getElem_cons_length rfl]
+    simp only [← getElem_cons_length _ _ _ rfl]
     simp only [mapIdx_cons]
-    simp only [← getElem_cons_length rfl]
+    simp only [← getElem_cons_length _ _ _ rfl]
     simp only [← mapIdx_cons, getElem_mapIdx]
     simp