perf: fix linearity issue in insertIfNew

.github/ISSUE_TEMPLATE/bug_report.md

@@ -9,15 +9,9 @@ assignees: ''
 
 ### Prerequisites
 
-Please put an X between the brackets as you perform the following steps:
-
-* [ ] Check that your issue is not already filed:
-      https://github.com/leanprover/lean4/issues
-* [ ] Reduce the issue to a minimal, self-contained, reproducible test case.
-      Avoid dependencies to Mathlib or Batteries.
-* [ ] Test your test case against the latest nightly release, for example on
-      https://live.lean-lang.org/#project=lean-nightly
-      (You can also use the settings there to switch to “Lean nightly”)
+* [ ] Put an X between the brackets on this line if you have done all of the following:
+    * Check that your issue is not already [filed](https://github.com/leanprover/lean4/issues).
+    * Reduce the issue to a minimal, self-contained, reproducible test case. Avoid dependencies to mathlib4 or std4.
 
 ### Description
 
@@ -39,8 +33,8 @@ Please put an X between the brackets as you perform the following steps:
 
 ### Versions
 
-[Output of `#eval Lean.versionString`]
-[OS version, if not using live.lean-lang.org.]
+[Output of `#eval Lean.versionString` or of `lean --version` in the folder that the issue occured in]
+[OS version]
 
 ### Additional Information
 

.github/workflows/actionlint.yml

@@ -15,7 +15,7 @@ jobs:
     runs-on: ubuntu-latest
     steps:
     - name: Checkout
-      uses: actions/checkout@v4
+      uses: actions/checkout@v3
     - name: actionlint
       uses: raven-actions/actionlint@v1
       with:

.github/workflows/check-stage0.yml

@@ -1,57 +0,0 @@
-name: Check for stage0 changes
-
-on:
-  merge_group:
-  pull_request:
-
-jobs:
-  check-stage0-on-queue:
-    runs-on: ubuntu-latest
-    steps:
-    - uses: actions/checkout@v4
-      with:
-        ref: ${{ github.event.pull_request.head.sha }}
-        filter: blob:none
-        fetch-depth: 0
-
-    - name: Find base commit
-      if: github.event_name == 'pull_request'
-      run: echo "BASE=$(git merge-base origin/${{ github.base_ref }} HEAD)" >> "$GITHUB_ENV"
-
-    - name: Identify stage0 changes
-      run: |
-        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"
-        else
-          echo "CHANGES=no" >> "$GITHUB_ENV"
-        fi
-      shell: bash
-
-    - if: github.event_name == 'pull_request'
-      name: Set label
-      uses: actions/github-script@v7
-      with:
-        script: |
-          const { owner, repo, number: issue_number  } = context.issue;
-          if (process.env.CHANGES == 'yes') {
-            await github.rest.issues.addLabels({ owner, repo, issue_number, labels: ['changes-stage0'] }).catch(() => {});
-          } else {
-            await github.rest.issues.removeLabel({ owner, repo, issue_number, name: 'changes-stage0' }).catch(() => {});
-          }
-
-    - if: env.CHANGES == 'yes'
-      name: Report changes
-      run: |
-        echo "Found changes to stage0/, please do not merge using the merge queue." | tee "$GITHUB_STEP_SUMMARY"
-        # shellcheck disable=SC2129
-        echo '```'                  >> "$GITHUB_STEP_SUMMARY"
-        cat  "$RUNNER_TEMP/stage0"  >> "$GITHUB_STEP_SUMMARY"
-        echo '```'                  >> "$GITHUB_STEP_SUMMARY"
-
-    - if: github.event_name == 'merge_group' && env.CHANGES == 'yes'
-      name: Fail when on the merge queue
-      run: exit 1

.github/workflows/ci.yml

@@ -6,20 +6,10 @@ on:
     tags:
       - '*'
   pull_request:
+    types: [opened, synchronize, reopened, labeled]
   merge_group:
   schedule:
     - cron: '0 7 * * *'  # 8AM CET/11PM PT
-  # for manual re-release of a nightly
-  workflow_dispatch:
-    inputs:
-      action:
-        description: 'Action'
-        required: true
-        default: 'release nightly'
-        type: choice
-        options:
-        - release nightly
-
 
 concurrency:
   group: ${{ github.workflow }}-${{ github.ref }}-${{ github.event_name }}
@@ -31,10 +21,8 @@ jobs:
   configure:
     runs-on: ubuntu-latest
     outputs:
-      # 0: PRs without special label
-      # 1: PRs with `merge-ci` label, merge queue checks, master commits
-      # 2: PRs with `release-ci` label, releases (incl. nightlies)
-      check-level: ${{ steps.set-level.outputs.check-level }}
+      # Should we run only a quick CI? Yes on a pull request without the full-ci label
+      quick: ${{ steps.set-quick.outputs.quick }}
       # The build matrix, dynamically generated here
       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
@@ -51,12 +39,164 @@ jobs:
       RELEASE_TAG: ${{ steps.set-release.outputs.RELEASE_TAG }}
 
     steps:
+      - name: Run quick CI?
+        id: set-quick
+        env:
+          quick: ${{
+            github.event_name == 'pull_request' && !contains( github.event.pull_request.labels.*.name, 'full-ci')
+           }}
+        run: |
+          echo "quick=${{env.quick}}" >> "$GITHUB_OUTPUT"
+
+      - name: Configure build matrix
+        id: set-matrix
+        uses: actions/github-script@v7
+        with:
+          script: |
+            const quick = ${{ steps.set-quick.outputs.quick }};
+            console.log(`quick: ${quick}`)
+            let matrix = [
+              {
+                // portable release build: use channel with older glibc (2.27)
+                "name": "Linux LLVM",
+                "os": "ubuntu-latest",
+                "release": false,
+                "quick": false,
+                "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
+                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
+                "binary-check": "ldd -v",
+                // foreign code may be linked against more recent glibc
+                // reverse-ffi needs to be updated to link to LLVM libraries
+                "CTEST_OPTIONS": "-E 'foreign|leanlaketest_reverse-ffi'",
+                "CMAKE_OPTIONS": "-DLLVM=ON -DLLVM_CONFIG=${GITHUB_WORKSPACE}/build/llvm-host/bin/llvm-config"
+              },
+              {
+                "name": "Linux release",
+                "os": "ubuntu-latest",
+                "release": true,
+                "quick": true,
+                "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
+                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
+                "binary-check": "ldd -v",
+                // foreign code may be linked against more recent glibc
+                "CTEST_OPTIONS": "-E 'foreign'"
+              },
+              {
+                "name": "Linux",
+                "os": "ubuntu-latest",
+                "check-stage3": true,
+                "test-speedcenter": true,
+                "quick": false,
+              },
+              {
+                "name": "Linux Debug",
+                "os": "ubuntu-latest",
+                "quick": false,
+                "CMAKE_OPTIONS": "-DCMAKE_BUILD_TYPE=Debug",
+                // exclude seriously slow tests
+                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
+              },
+              // TODO: suddenly started failing in CI
+              /*{
+                "name": "Linux fsanitize",
+                "os": "ubuntu-latest",
+                "quick": false,
+                // turn off custom allocator & symbolic functions to make LSAN do its magic
+                "CMAKE_OPTIONS": "-DLEAN_EXTRA_CXX_FLAGS=-fsanitize=address,undefined -DLEANC_EXTRA_FLAGS='-fsanitize=address,undefined -fsanitize-link-c++-runtime' -DSMALL_ALLOCATOR=OFF -DBSYMBOLIC=OFF",
+                // exclude seriously slow/problematic tests (laketests crash)
+                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
+              },*/
+              {
+                "name": "macOS",
+                "os": "macos-latest",
+                "release": true,
+                "quick": false,
+                "shell": "bash -euxo pipefail {0}",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-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
+              },
+              {
+                "name": "macOS aarch64",
+                "os": "macos-latest",
+                "release": true,
+                "quick": false,
+                "cross": true,
+                "cross_target": "aarch64-apple-darwin",
+                "shell": "bash -euxo pipefail {0}",
+                "CMAKE_OPTIONS": "-DUSE_GMP=OFF -DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-apple-darwin.tar.zst https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-apple-darwin.tar.zst",
+                "prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm-aarch64-* lean-llvm-x86_64-*",
+                "binary-check": "otool -L",
+                "tar": "gtar" // https://github.com/actions/runner-images/issues/2619
+              },
+              {
+                "name": "Windows",
+                "os": "windows-2022",
+                "release": true,
+                "quick": false,
+                "shell": "msys2 {0}",
+                "CMAKE_OPTIONS": "-G \"Unix Makefiles\" -DUSE_GMP=OFF",
+                // for reasons unknown, interactivetests are flaky on Windows
+                "CTEST_OPTIONS": "--repeat until-pass:2",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-w64-windows-gnu.tar.zst",
+                "prepare-llvm": "../script/prepare-llvm-mingw.sh lean-llvm*",
+                "binary-check": "ldd"
+              },
+              {
+                "name": "Linux aarch64",
+                "os": "ubuntu-latest",
+                "CMAKE_OPTIONS": "-DUSE_GMP=OFF -DLEAN_INSTALL_SUFFIX=-linux_aarch64",
+                "release": true,
+                "quick": false,
+                "cross": true,
+                "cross_target": "aarch64-unknown-linux-gnu",
+                "shell": "nix develop .#oldGlibcAArch -c bash -euxo pipefail {0}",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-linux-gnu.tar.zst",
+                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm-aarch64-* lean-llvm-x86_64-*"
+              },
+              {
+                "name": "Linux 32bit",
+                "os": "ubuntu-latest",
+                // Use 32bit on stage0 and stage1 to keep oleans compatible
+                "CMAKE_OPTIONS": "-DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_MMAP=OFF -DUSE_GMP=OFF -DLEAN_EXTRA_CXX_FLAGS='-m32' -DLEANC_OPTS='-m32' -DMMAP=OFF -DLEAN_INSTALL_SUFFIX=-linux_x86",
+                "cmultilib": true,
+                "release": true,
+                "quick": false,
+                "cross": true,
+                "shell": "bash -euxo pipefail {0}"
+              },
+              {
+                "name": "Web Assembly",
+                "os": "ubuntu-latest",
+                // Build a native 32bit binary in stage0 and use it to compile the oleans and the wasm build
+                "CMAKE_OPTIONS": "-DCMAKE_C_COMPILER_WORKS=1 -DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_CMAKE_CXX_COMPILER=clang++ -DSTAGE0_CMAKE_C_COMPILER=clang -DSTAGE0_CMAKE_EXECUTABLE_SUFFIX=\"\" -DUSE_GMP=OFF -DMMAP=OFF -DSTAGE0_MMAP=OFF -DCMAKE_AR=../emsdk/emsdk-main/upstream/emscripten/emar -DCMAKE_TOOLCHAIN_FILE=../emsdk/emsdk-main/upstream/emscripten/cmake/Modules/Platform/Emscripten.cmake -DLEAN_INSTALL_SUFFIX=-linux_wasm32",
+                "wasm": true,
+                "cmultilib": true,
+                "release": true,
+                "quick": false,
+                "cross": true,
+                "shell": "bash -euxo pipefail {0}",
+                // Just a few selected tests because wasm is slow
+                "CTEST_OPTIONS": "-R \"leantest_1007\\.lean|leantest_Format\\.lean|leanruntest\\_1037.lean|leanruntest_ac_rfl\\.lean\""
+              }
+            ];
+            console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`)
+            if (quick) {
+              return matrix.filter((job) => job.quick)
+            } else {
+              return matrix
+            }
+
       - name: Checkout
-        uses: actions/checkout@v4
+        uses: actions/checkout@v3
         # don't schedule nightlies on forks
-        if: github.event_name == 'schedule' && github.repository == 'leanprover/lean4' || inputs.action == 'release nightly'
+        if: github.event_name == 'schedule' && github.repository == 'leanprover/lean4'
       - name: Set Nightly
-        if: github.event_name == 'schedule' && github.repository == 'leanprover/lean4' || inputs.action == 'release nightly'
+        if: github.event_name == 'schedule' && github.repository == 'leanprover/lean4'
         id: set-nightly
         run: |
           if [[ -n '${{ secrets.PUSH_NIGHTLY_TOKEN }}' ]]; then
@@ -101,170 +241,6 @@ jobs:
             echo "Tag ${TAG_NAME} did not match SemVer regex."
           fi
 
-      - name: Set check level
-        id: set-level
-        # We do not use github.event.pull_request.labels.*.name here because
-        # re-running a run does not update that list, and we do want to be able to
-        # rerun the workflow run after setting the `release-ci`/`merge-ci` labels.
-        run: |
-          check_level=0
-
-          if [[ -n "${{ steps.set-nightly.outputs.nightly }}" || -n "${{ steps.set-release.outputs.RELEASE_TAG }}" ]]; then
-            check_level=2
-          elif [[ "${{ github.event_name }}" != "pull_request" ]]; then
-            check_level=1
-          else
-            labels="$(gh api repos/${{ github.repository_owner }}/${{ github.event.repository.name }}/pulls/${{ github.event.pull_request.number }}) --jq '.labels'"
-            if echo "$labels" | grep -q "release-ci"; then
-              check_level=2
-            elif echo "$labels" | grep -q "merge-ci"; then
-              check_level=1
-            fi
-          fi
-
-          echo "check-level=$check_level" >> "$GITHUB_OUTPUT"
-        env:
-          GH_TOKEN: ${{ github.token }}
-
-      - name: Configure build matrix
-        id: set-matrix
-        uses: actions/github-script@v7
-        with:
-          script: |
-            const level = ${{ steps.set-level.outputs.check-level }};
-            console.log(`level: ${level}`);
-            // use large runners where available (original repo)
-            let large = ${{ github.repository == 'leanprover/lean4' }};
-            let matrix = [
-              {
-                // portable release build: use channel with older glibc (2.27)
-                "name": "Linux LLVM",
-                "os": "ubuntu-latest",
-                "release": false,
-                "check-level": 2,
-                "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
-                "binary-check": "ldd -v",
-                // foreign code may be linked against more recent glibc
-                // reverse-ffi needs to be updated to link to LLVM libraries
-                "CTEST_OPTIONS": "-E 'foreign|leanlaketest_reverse-ffi'",
-                "CMAKE_OPTIONS": "-DLLVM=ON -DLLVM_CONFIG=${GITHUB_WORKSPACE}/build/llvm-host/bin/llvm-config"
-              },
-              {
-                "name": "Linux release",
-                "os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
-                "release": true,
-                "check-level": 0,
-                "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
-                "binary-check": "ldd -v",
-                // foreign code may be linked against more recent glibc
-                "CTEST_OPTIONS": "-E 'foreign'"
-              },
-              {
-                "name": "Linux",
-                "os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
-                "check-stage3": level >= 2,
-                "test-speedcenter": level >= 2,
-                "check-level": 1,
-              },
-              {
-                "name": "Linux Debug",
-                "os": "ubuntu-latest",
-                "check-level": 2,
-                "CMAKE_PRESET": "debug",
-                // exclude seriously slow tests
-                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
-              },
-              // TODO: suddenly started failing in CI
-              /*{
-                "name": "Linux fsanitize",
-                "os": "ubuntu-latest",
-                "check-level": 2,
-                // turn off custom allocator & symbolic functions to make LSAN do its magic
-                "CMAKE_PRESET": "sanitize",
-                // exclude seriously slow/problematic tests (laketests crash)
-                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
-              },*/
-              {
-                "name": "macOS",
-                "os": "macos-13",
-                "release": true,
-                "check-level": 2,
-                "shell": "bash -euxo pipefail {0}",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-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
-              },
-              {
-                "name": "macOS aarch64",
-                "os": "macos-14",
-                "CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
-                "release": true,
-                "check-level": 1,
-                "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
-              },
-              {
-                "name": "Windows",
-                "os": "windows-2022",
-                "release": true,
-                "check-level": 2,
-                "shell": "msys2 {0}",
-                "CMAKE_OPTIONS": "-G \"Unix Makefiles\" -DUSE_GMP=OFF",
-                // for reasons unknown, interactivetests are flaky on Windows
-                "CTEST_OPTIONS": "--repeat until-pass:2",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-w64-windows-gnu.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-mingw.sh lean-llvm*",
-                "binary-check": "ldd"
-              },
-              {
-                "name": "Linux aarch64",
-                "os": "ubuntu-latest",
-                "CMAKE_OPTIONS": "-DUSE_GMP=OFF -DLEAN_INSTALL_SUFFIX=-linux_aarch64",
-                "release": true,
-                "check-level": 2,
-                "cross": true,
-                "cross_target": "aarch64-unknown-linux-gnu",
-                "shell": "nix develop .#oldGlibcAArch -c bash -euxo pipefail {0}",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-linux-gnu.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm-aarch64-* lean-llvm-x86_64-*"
-              },
-              {
-                "name": "Linux 32bit",
-                "os": "ubuntu-latest",
-                // Use 32bit on stage0 and stage1 to keep oleans compatible
-                "CMAKE_OPTIONS": "-DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_MMAP=OFF -DUSE_GMP=OFF -DLEAN_EXTRA_CXX_FLAGS='-m32' -DLEANC_OPTS='-m32' -DMMAP=OFF -DLEAN_INSTALL_SUFFIX=-linux_x86",
-                "cmultilib": true,
-                "release": true,
-                "check-level": 2,
-                "cross": true,
-                "shell": "bash -euxo pipefail {0}"
-              },
-              {
-                "name": "Web Assembly",
-                "os": "ubuntu-latest",
-                // Build a native 32bit binary in stage0 and use it to compile the oleans and the wasm build
-                "CMAKE_OPTIONS": "-DCMAKE_C_COMPILER_WORKS=1 -DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_CMAKE_CXX_COMPILER=clang++ -DSTAGE0_CMAKE_C_COMPILER=clang -DSTAGE0_CMAKE_EXECUTABLE_SUFFIX=\"\" -DUSE_GMP=OFF -DMMAP=OFF -DSTAGE0_MMAP=OFF -DCMAKE_AR=../emsdk/emsdk-main/upstream/emscripten/emar -DCMAKE_TOOLCHAIN_FILE=../emsdk/emsdk-main/upstream/emscripten/cmake/Modules/Platform/Emscripten.cmake -DLEAN_INSTALL_SUFFIX=-linux_wasm32",
-                "wasm": true,
-                "cmultilib": true,
-                "release": true,
-                "check-level": 2,
-                "cross": true,
-                "shell": "bash -euxo pipefail {0}",
-                // Just a few selected tests because wasm is slow
-                "CTEST_OPTIONS": "-R \"leantest_1007\\.lean|leantest_Format\\.lean|leanruntest\\_1037.lean|leanruntest_ac_rfl\\.lean\""
-              }
-            ];
-            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'
@@ -291,34 +267,28 @@ jobs:
       CXX: c++
       MACOSX_DEPLOYMENT_TARGET: 10.15
     steps:
+      - name: Checkout
+        uses: actions/checkout@v3
+        with:
+          submodules: true
+          # 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: Install Nix
-        uses: DeterminateSystems/nix-installer-action@main
-        if: runner.os == 'Linux' && !matrix.cmultilib
+        uses: cachix/install-nix-action@v18
+        with:
+          install_url: https://releases.nixos.org/nix/nix-2.12.0/install
+        if: matrix.os == 'ubuntu-latest' && !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 git: zip: unzip: diffutils: binutils: tree: zstd tar:"
-        if: runner.os == 'Windows'
+          # `:p` means prefix with appropriate msystem prefix
+          pacboy: "make python cmake:p clang:p ccache:p gmp:p git zip unzip diffutils binutils tree zstd:p tar"
+        if: matrix.os == 'windows-2022'
       - name: Install Brew Packages
         run: |
           brew install ccache tree zstd coreutils gmp
-        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 overriden)
+        if: matrix.os == 'macos-latest'
       - name: Setup emsdk
         uses: mymindstorm/setup-emsdk@v12
         with:
@@ -334,22 +304,26 @@ jobs:
         uses: actions/cache@v3
         with:
           path: .ccache
-          key: ${{ matrix.name }}-build-v3-${{ github.event.pull_request.head.sha }}
+          key: ${{ matrix.name }}-build-v3-${{ github.sha }}
           # fall back to (latest) previous cache
           restore-keys: |
             ${{ matrix.name }}-build-v3
-      # open nix-shell once for initial setup
       - name: Setup
         run: |
-          ccache --zero-stats
-        if: runner.os == 'Linux'
-      - name: Set up NPROC
+          # open nix-shell once for initial setup
+          true
+        if: matrix.os == 'ubuntu-latest'
+      - name: Set up core dumps
         run: |
-          echo "NPROC=$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4)" >> $GITHUB_ENV
+          mkdir -p $PWD/coredumps
+          # store in current directory, for easy uploading together with binary
+          echo $PWD/coredumps/%e.%p.%t | sudo tee /proc/sys/kernel/core_pattern
+        if: matrix.os == 'ubuntu-latest'
       - name: Build
         run: |
           mkdir build
           cd build
+          ulimit -c unlimited # coredumps
           # arguments passed to `cmake`
           # this also enables githash embedding into stage 1 library
           OPTIONS=(-DCHECK_OLEAN_VERSION=ON)
@@ -375,11 +349,9 @@ jobs:
             OPTIONS+=(-DLEAN_SPECIAL_VERSION_DESC=${{ 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
+          cmake .. ${{ matrix.CMAKE_OPTIONS }} ${OPTIONS[@]+"${OPTIONS[@]}"} -DLEAN_INSTALL_PREFIX=$PWD/..
+          make -j4
+          make install
       - name: Check Binaries
         run: ${{ matrix.binary-check }} lean-*/bin/* || true
       - name: List Install Tree
@@ -397,7 +369,7 @@ jobs:
           else
             ${{ matrix.tar || 'tar' }} cf - $dir | zstd -T0 --no-progress -o pack/$dir.tar.zst
           fi
-      - uses: actions/upload-artifact@v4
+      - uses: actions/upload-artifact@v3
         if: matrix.release
         with:
           name: build-${{ matrix.name }}
@@ -407,43 +379,71 @@ jobs:
           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
+          cd build/stage1
+          ulimit -c unlimited # coredumps
+          # exclude nonreproducible test
+          ctest -j4 --progress --output-junit test-results.xml --output-on-failure ${{ matrix.CTEST_OPTIONS }} < /dev/null
+        if: (matrix.wasm || !matrix.cross) && needs.configure.outputs.quick == 'false'
       - 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'
+        if: always() && (matrix.wasm || !matrix.cross) && needs.configure.outputs.quick == 'false'
       - name: Check Test Binary
         run: ${{ matrix.binary-check }} tests/compiler/534.lean.out
-        if: (!matrix.cross) && steps.test.conclusion != 'skipped'
+        if: ${{ !matrix.cross && needs.configure.outputs.quick == 'false' }}
       - name: Build Stage 2
         run: |
-          make -C build -j$NPROC stage2
+          cd build
+          ulimit -c unlimited # coredumps
+          make -j4 stage2
         if: matrix.test-speedcenter
       - name: Check Stage 3
         run: |
-          make -C build -j$NPROC check-stage3
+          cd build
+          ulimit -c unlimited # coredumps
+          make -j4 check-stage3
         if: matrix.test-speedcenter
       - name: Test Speedcenter Benchmarks
         run: |
-          # Necessary for some timing metrics but does not work on Namespace runners
-          # and we just want to test that the benchmarks run at all here
-          #echo -1 | sudo tee /proc/sys/kernel/perf_event_paranoid
+          echo -1 | sudo tee /proc/sys/kernel/perf_event_paranoid
           export BUILD=$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: |
+          cd build
+          ulimit -c unlimited # coredumps
           # 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
+          make update-stage0 && rm -rf ./stage* && make -j4
+        if: matrix.name == 'Linux' && needs.configure.outputs.quick == 'false'
       - name: CCache stats
         run: ccache -s
+      - name: Show stacktrace for coredumps
+        if: ${{ failure() && matrix.os == 'ubuntu-latest' }}
+        run: |
+          for c in coredumps/*; do
+            progbin="$(file $c | sed "s/.*execfn: '\([^']*\)'.*/\1/")"
+            echo bt | $GDB/bin/gdb -q $progbin $c || true
+          done
+      # has not been used in a long while, would need to be adapted to new
+      # shared libs
+      #- name: Upload coredumps
+      #  uses: actions/upload-artifact@v3
+      #  if: ${{ failure() && matrix.os == 'ubuntu-latest' }}
+      #  with:
+      #    name: coredumps-${{ matrix.name }}
+      #    path: |
+      #      ./coredumps
+      #      ./build/stage0/bin/lean
+      #      ./build/stage0/lib/lean/libleanshared.so
+      #      ./build/stage1/bin/lean
+      #      ./build/stage1/lib/lean/libleanshared.so
+      #      ./build/stage2/bin/lean
+      #      ./build/stage2/lib/lean/libleanshared.so
 
   # This job collects results from all the matrix jobs
   # This can be made the “required” job, instead of listing each
@@ -455,24 +455,12 @@ jobs:
     # mark as merely cancelled not failed if builds are cancelled
     if: ${{ !cancelled() }}
     steps:
-    - if: ${{ contains(needs.*.result, 'failure') && github.repository == 'leanprover/lean4' && github.ref_name == 'master' }}
-      uses: zulip/github-actions-zulip/send-message@v1
-      with:
-        api-key: ${{ secrets.ZULIP_BOT_KEY }}
-        email: "github-actions-bot@lean-fro.zulipchat.com"
-        organization-url: "https://lean-fro.zulipchat.com"
-        to: "infrastructure"
-        topic: "Github actions"
-        type: "stream"
-        content: |
-          A build of `${{ github.ref_name }}`, triggered by event `${{ github.event_name }}`, [failed](https://github.com/${{ github.repository }}/actions/runs/${{ github.run_id }}).
     - if: contains(needs.*.result, 'failure')
       uses: actions/github-script@v7
       with:
         script: |
             core.setFailed('Some jobs failed')
 
-
   # This job creates releases from tags
   # (whether they are "unofficial" releases for experiments, or official releases when the tag is "v" followed by a semver string.)
   # We do not attempt to automatically construct a changelog here:
@@ -482,7 +470,7 @@ jobs:
     runs-on: ubuntu-latest
     needs: build
     steps:
-      - uses: actions/download-artifact@v4
+      - uses: actions/download-artifact@v3
         with:
           path: artifacts
       - name: Release
@@ -490,14 +478,8 @@ jobs:
         with:
           files: artifacts/*/*
           fail_on_unmatched_files: true
-          prerelease: ${{ !startsWith(github.ref, 'refs/tags/v') || contains(github.ref, '-rc') }}
         env:
           GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
-      - name: Update release.lean-lang.org
-        run: |
-          gh workflow -R leanprover/release-index run update-index.yml
-        env:
-          GITHUB_TOKEN: ${{ secrets.RELEASE_INDEX_TOKEN }}
 
   # This job creates nightly releases during the cron job.
   # It is responsible for creating the tag, and automatically generating a changelog.
@@ -507,12 +489,12 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - name: Checkout
-        uses: actions/checkout@v4
+        uses: actions/checkout@v3
         with:
           # needed for tagging
           fetch-depth: 0
           token: ${{ secrets.PUSH_NIGHTLY_TOKEN }}
-      - uses: actions/download-artifact@v4
+      - uses: actions/download-artifact@v3
         with:
           path: artifacts
       - name: Prepare Nightly Release
@@ -540,13 +522,3 @@ jobs:
           repository: ${{ github.repository_owner }}/lean4-nightly
         env:
           GITHUB_TOKEN: ${{ secrets.PUSH_NIGHTLY_TOKEN }}
-      - name: Update release.lean-lang.org
-        run: |
-          gh workflow -R leanprover/release-index run update-index.yml
-        env:
-          GITHUB_TOKEN: ${{ secrets.RELEASE_INDEX_TOKEN }}
-      - name: Update toolchain on mathlib4's nightly-testing branch
-        run: |
-          gh workflow -R leanprover-community/mathlib4 run nightly_bump_toolchain.yml
-        env:
-          GITHUB_TOKEN: ${{ secrets.MATHLIB4_BOT }}

.github/workflows/copyright-header.yml

@@ -10,7 +10,7 @@ jobs:
 
     - name: Verify .lean files start with a copyright header.
       run: |
-        FILES=$(find ./src -type d \( -path "./src/lake/examples" -o -path "./src/lake/tests" \) -prune -o -type f -name "*.lean" -exec perl -ne 'BEGIN { $/ = undef; } print "$ARGV\n" if !m{\A/-\nCopyright}; exit;' {} \;)
+        FILES=$(find . -type d \( -path "./tests" -o -path "./doc" -o -path "./src/lake/examples" -o -path "./src/lake/tests" -o -path "./build" -o -path "./nix" \) -prune -o -type f -name "*.lean" -exec perl -ne 'BEGIN { $/ = undef; } print "$ARGV\n" if !m{\A/-\nCopyright}; exit;' {} \;)
         if [ -n "$FILES" ]; then
           echo "Found .lean files which do not have a copyright header:"
           echo "$FILES"

.github/workflows/jira.yml

@@ -1,34 +0,0 @@
-name: Jira sync
-
-on:
-  issues:
-    types: [closed]
-
-jobs:
-  jira-sync:
-    runs-on: ubuntu-latest
-
-    steps:
-      - name: Move Jira issue to Done
-        env:
-          JIRA_API_TOKEN: ${{ secrets.JIRA_API_TOKEN }}
-          JIRA_USERNAME: ${{ secrets.JIRA_USERNAME }}
-          JIRA_BASE_URL: ${{ secrets.JIRA_BASE_URL }}
-        run: |
-          issue_number=${{ github.event.issue.number }}
-
-          jira_issue_key=$(curl -s -u "${JIRA_USERNAME}:${JIRA_API_TOKEN}" \
-            -X GET -H "Content-Type: application/json" \
-            "${JIRA_BASE_URL}/rest/api/2/search?jql=summary~\"${issue_number}\"" | \
-            jq -r '.issues[0].key')
-
-          if [ -z "$jira_issue_key" ]; then
-            exit
-          fi
-
-          curl -s -u "${JIRA_USERNAME}:${JIRA_API_TOKEN}" \
-            -X POST -H "Content-Type: application/json" \
-            --data "{\"transition\": {\"id\": \"41\"}}" \
-            "${JIRA_BASE_URL}/rest/api/2/issue/${jira_issue_key}/transitions"
-
-          echo "Moved Jira issue ${jira_issue_key} to Done"

.github/workflows/nix-ci.yml

@@ -6,6 +6,7 @@ on:
     tags:
       - '*'
   pull_request:
+    types: [opened, synchronize, reopened, labeled]
   merge_group:
 
 concurrency:
@@ -13,36 +14,18 @@ concurrency:
   cancel-in-progress: true
 
 jobs:
-  # see ci.yml
-  configure:
-    runs-on: ubuntu-latest
-    outputs:
-      matrix: ${{ steps.set-matrix.outputs.result }}
-    steps:
-      - name: Configure build matrix
-        id: set-matrix
-        uses: actions/github-script@v7
-        with:
-          script: |
-            let large = ${{ github.repository == 'leanprover/lean4' }};
-            let matrix = [
-              {
-                "name": "Nix Linux",
-                "os": large ? "nscloud-ubuntu-22.04-amd64-8x8" : "ubuntu-latest",
-              }
-            ];
-            console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`);
-            return matrix;
-
   Build:
-    needs: [configure]
     runs-on: ${{ matrix.os }}
     defaults:
       run:
         shell: nix run .#ciShell -- bash -euxo pipefail {0}
     strategy:
       matrix:
-        include: ${{fromJson(needs.configure.outputs.matrix)}}
+        include:
+          - name: Nix Linux
+            os: ubuntu-latest
+          #- name: Nix macOS
+          #  os: macos-latest
       # complete all jobs
       fail-fast: false
     name: ${{ matrix.name }}
@@ -50,7 +33,7 @@ jobs:
       NIX_BUILD_ARGS: --print-build-logs --fallback
     steps:
       - name: Checkout
-        uses: actions/checkout@v4
+        uses: actions/checkout@v3
         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 }}
@@ -103,7 +86,7 @@ jobs:
         continue-on-error: true
       - name: Build manual
         run: |
-          nix build $NIX_BUILD_ARGS --update-input lean --no-write-lock-file ./doc#{lean-mdbook,leanInk,alectryon,inked} -o push-doc
+          nix build $NIX_BUILD_ARGS --update-input lean --no-write-lock-file ./doc#{lean-mdbook,leanInk,alectryon,test,inked} -o push-doc
           nix build $NIX_BUILD_ARGS --update-input lean --no-write-lock-file ./doc
           # https://github.com/netlify/cli/issues/1809
           cp -r --dereference ./result ./dist
@@ -146,3 +129,5 @@ jobs:
       - name: Fixup CCache Cache
         run: |
           sudo chown -R $USER /nix/var/cache
+      - name: CCache stats
+        run: CCACHE_DIR=/nix/var/cache/ccache nix run .#nixpkgs.ccache -- -s

.github/workflows/pr-release.yml

@@ -126,11 +126,11 @@ jobs:
           if [ "$NIGHTLY_SHA" = "$MERGE_BASE_SHA" ]; then
             echo "The merge base of this PR coincides with the nightly release"
 
-            BATTERIES_REMOTE_TAGS="$(git ls-remote https://github.com/leanprover-community/batteries.git nightly-testing-"$MOST_RECENT_NIGHTLY")"
+            STD_REMOTE_TAGS="$(git ls-remote https://github.com/leanprover/std4.git nightly-testing-"$MOST_RECENT_NIGHTLY")"
             MATHLIB_REMOTE_TAGS="$(git ls-remote https://github.com/leanprover-community/mathlib4.git nightly-testing-"$MOST_RECENT_NIGHTLY")"
 
-            if [[ -n "$BATTERIES_REMOTE_TAGS" ]]; then
-              echo "... and Batteries has a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
+            if [[ -n "$STD_REMOTE_TAGS" ]]; then
+              echo "... and Std has a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
               MESSAGE=""
 
               if [[ -n "$MATHLIB_REMOTE_TAGS" ]]; then
@@ -140,8 +140,8 @@ jobs:
                 MESSAGE="- ❗ Mathlib CI can not be attempted yet, as the \`nightly-testing-$MOST_RECENT_NIGHTLY\` tag does not exist there yet. We will retry when you push more commits. If you rebase your branch onto \`nightly-with-mathlib\`, Mathlib CI should run now."
               fi
             else
-              echo "... but Batteries does not yet have a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
-              MESSAGE="- ❗ Batteries CI can not be attempted yet, as the \`nightly-testing-$MOST_RECENT_NIGHTLY\` tag does not exist there yet. We will retry when you push more commits. If you rebase your branch onto \`nightly-with-mathlib\`, Batteries CI should run now."
+              echo "... but Std does not yet have a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
+              MESSAGE="- ❗ Std CI can not be attempted yet, as the \`nightly-testing-$MOST_RECENT_NIGHTLY\` tag does not exist there yet. We will retry when you push more commits. If you rebase your branch onto \`nightly-with-mathlib\`, Std CI should run now."
             fi
 
           else
@@ -150,8 +150,8 @@ jobs:
             git -C lean4.git log -10 origin/master
 
             git -C lean4.git fetch origin nightly-with-mathlib 
-            NIGHTLY_WITH_MATHLIB_SHA="$(git -C lean4.git rev-parse "origin/nightly-with-mathlib")"
-            MESSAGE="- ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the \`nightly-with-mathlib\` branch. Try \`git rebase $MERGE_BASE_SHA --onto $NIGHTLY_WITH_MATHLIB_SHA\`."
+            NIGHTLY_WITH_MATHLIB_SHA="$(git -C lean4.git rev-parse "nightly-with-mathlib")"
+            MESSAGE="- ❗ Std/Mathlib CI will not be attempted unless your PR branches off the \`nightly-with-mathlib\` branch. Try \`git rebase $MERGE_BASE_SHA --onto $NIGHTLY_WITH_MATHLIB_SHA\`."
           fi
 
           if [[ -n "$MESSAGE" ]]; then
@@ -223,27 +223,27 @@ jobs:
               description: description,
             });
 
-      # We next automatically create a Batteries branch using this toolchain.
-      # Batteries doesn't itself have a mechanism to report results of CI from this branch back to Lean
-      # Instead this is taken care of by Mathlib CI, which will fail if Batteries fails.
+      # We next automatically create a Std branch using this toolchain.
+      # Std doesn't itself have a mechanism to report results of CI from this branch back to Lean
+      # Instead this is taken care of by Mathlib CI, which will fail if Std fails.
       - name: Cleanup workspace
         if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
         run: |
           sudo rm -rf ./*
 
-      # Checkout the Batteries repository with all branches
-      - name: Checkout Batteries repository
+      # Checkout the Std repository with all branches
+      - name: Checkout Std repository
         if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
-        uses: actions/checkout@v4
+        uses: actions/checkout@v3
         with:
-          repository: leanprover-community/batteries
+          repository: leanprover/std4
           token: ${{ secrets.MATHLIB4_BOT }}
           ref: nightly-testing
           fetch-depth: 0 # This ensures we check out all tags and branches.
 
       - name: Check if tag exists
         if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
-        id: check_batteries_tag
+        id: check_std_tag
         run: |
           git config user.name "leanprover-community-mathlib4-bot"
           git config user.email "leanprover-community-mathlib4-bot@users.noreply.github.com"
@@ -251,7 +251,7 @@ jobs:
           if git ls-remote --heads --tags --exit-code origin "nightly-testing-${MOST_RECENT_NIGHTLY}" >/dev/null; then
             BASE="nightly-testing-${MOST_RECENT_NIGHTLY}"
           else
-            echo "This shouldn't be possible: couldn't find a 'nightly-testing-${MOST_RECENT_NIGHTLY}' tag at Batteries. Falling back to 'nightly-testing'."
+            echo "This shouldn't be possible: couldn't find a 'nightly-testing-${MOST_RECENT_NIGHTLY}' tag at Std. Falling back to 'nightly-testing'."
             BASE=nightly-testing
           fi
 
@@ -268,7 +268,7 @@ jobs:
           else
             echo "Branch already exists, pushing an empty commit."
             git switch lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}
-            # The Batteries `nightly-testing` or `nightly-testing-YYYY-MM-DD` branch may have moved since this branch was created, so merge their changes.
+            # The Std `nightly-testing` or `nightly-testing-YYYY-MM-DD` branch may have moved since this branch was created, so merge their changes.
             # (This should no longer be possible once `nightly-testing-YYYY-MM-DD` is a tag, but it is still safe to merge.)
             git merge "$BASE" --strategy-option ours --no-commit --allow-unrelated-histories
             git commit --allow-empty -m "Trigger CI for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
@@ -291,20 +291,13 @@ jobs:
       # Checkout the mathlib4 repository with all branches
       - name: Checkout mathlib4 repository
         if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
-        uses: actions/checkout@v4
+        uses: actions/checkout@v3
         with:
           repository: leanprover-community/mathlib4
           token: ${{ secrets.MATHLIB4_BOT }}
           ref: nightly-testing
           fetch-depth: 0 # This ensures we check out all tags and branches.
 
-      - name: install elan
-        run: |
-          set -o pipefail
-          curl -sSfL https://github.com/leanprover/elan/releases/download/v3.0.0/elan-x86_64-unknown-linux-gnu.tar.gz | tar xz
-          ./elan-init -y --default-toolchain none
-          echo "$HOME/.elan/bin" >> "${GITHUB_PATH}"
-
       - name: Check if tag exists
         if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
         id: check_mathlib_tag
@@ -328,9 +321,8 @@ jobs:
             git switch -c lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }} "$BASE"
             echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}" > lean-toolchain
             git add lean-toolchain
-            sed -i 's,require "leanprover-community" / "batteries" @ ".\+",require "leanprover-community" / "batteries" @ "git#nightly-testing-'"${MOST_RECENT_NIGHTLY}"'",' lakefile.lean
-            lake update batteries
-            git add lakefile.lean lake-manifest.json
+            sed -i "s/require std from git \"https:\/\/github.com\/leanprover\/std4\" @ \".\+\"/require std from git \"https:\/\/github.com\/leanprover\/std4\" @ \"nightly-testing-${MOST_RECENT_NIGHTLY}\"/" lakefile.lean
+            git add lakefile.lean
             git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
           else
             echo "Branch already exists, pushing an empty commit."

.github/workflows/restart-on-label.yml

@@ -1,33 +0,0 @@
-name: Restart by label
-on:
-  pull_request_target:
-    types:
-      - unlabeled
-      - labeled
-jobs:
-  restart-on-label:
-    runs-on: ubuntu-latest
-    if: contains(github.event.label.name, 'merge-ci') || contains(github.event.label.name, 'release-ci')
-    steps:
-    - run: |
-        # Finding latest CI workflow run on current pull request
-        # (unfortunately cannot search by PR number, only base branch,
-        # and that is't even unique given PRs from forks, but the risk
-        # of confusion is low and the danger is mild)
-        run_id=$(gh run list -e pull_request -b "$head_ref" --workflow 'CI' --limit 1 \
-          --limit 1 --json databaseId --jq '.[0].databaseId')
-        echo "Run id: ${run_id}"
-        gh run view "$run_id"
-        echo "Cancelling (just in case)"
-        gh run cancel "$run_id" || echo "(failed)"
-        echo "Waiting for 30s"
-        sleep 30
-        gh run view "$run_id"
-        echo "Rerunning"
-        gh run rerun "$run_id"
-        gh run view "$run_id"
-      shell: bash
-      env:
-        head_ref: ${{ github.head_ref }}
-        GH_TOKEN: ${{ github.token }}
-        GH_REPO: ${{ github.repository }}

.github/workflows/update-stage0.yml

@@ -23,7 +23,7 @@ jobs:
     # This action should push to an otherwise protected branch, so it
     # uses a deploy key with write permissions, as suggested at
     # https://stackoverflow.com/a/76135647/946226
-    - uses: actions/checkout@v4
+    - uses: actions/checkout@v3
       with:
         ssh-key: ${{secrets.STAGE0_SSH_KEY}}
     - run: echo "should_update_stage0=yes" >> "$GITHUB_ENV"

.gitignore

@@ -4,10 +4,8 @@
 *.lock
 .lake
 lake-manifest.json
-/build
-/src/lakefile.toml
-/tests/lakefile.toml
-/lakefile.toml
+build
+!/src/lake/Lake/Build
 GPATH
 GRTAGS
 GSYMS

CMakePresets.json

@@ -1,83 +0,0 @@
-{
-  "version": 2,
-  "cmakeMinimumRequired": {
-    "major": 3,
-    "minor": 10,
-    "patch": 0
-  },
-  "configurePresets": [
-    {
-      "name": "release",
-      "displayName": "Default development optimized build config",
-      "generator": "Unix Makefiles",
-      "binaryDir": "${sourceDir}/build/release"
-    },
-    {
-      "name": "debug",
-      "displayName": "Debug build config",
-      "cacheVariables": {
-        "CMAKE_BUILD_TYPE": "Debug"
-      },
-      "generator": "Unix Makefiles",
-      "binaryDir": "${sourceDir}/build/debug"
-    },
-    {
-      "name": "sanitize",
-      "displayName": "Sanitize build config",
-      "cacheVariables": {
-        "LEAN_EXTRA_CXX_FLAGS": "-fsanitize=address,undefined",
-        "LEANC_EXTRA_FLAGS": "-fsanitize=address,undefined -fsanitize-link-c++-runtime",
-        "SMALL_ALLOCATOR": "OFF",
-        "BSYMBOLIC": "OFF"
-      },
-      "generator": "Unix Makefiles",
-      "binaryDir": "${sourceDir}/build/sanitize"
-    },
-    {
-      "name": "sandebug",
-      "inherits": ["debug", "sanitize"],
-      "displayName": "Sanitize+debug build config",
-      "binaryDir": "${sourceDir}/build/sandebug"
-    }
-  ],
-  "buildPresets": [
-    {
-      "name": "release",
-      "configurePreset": "release"
-    },
-    {
-      "name": "debug",
-      "configurePreset": "debug"
-    },
-    {
-      "name": "sanitize",
-      "configurePreset": "sanitize"
-    },
-    {
-      "name": "sandebug",
-      "configurePreset": "sandebug"
-    }
-  ],
-  "testPresets": [
-    {
-      "name": "release",
-      "configurePreset": "release",
-      "output": {"outputOnFailure": true, "shortProgress": true}
-    },
-    {
-      "name": "debug",
-      "configurePreset": "debug",
-      "inherits": "release"
-    },
-    {
-      "name": "sanitize",
-      "configurePreset": "sanitize",
-      "inherits": "release"
-    },
-    {
-      "name": "sandebug",
-      "configurePreset": "sandebug",
-      "inherits": "release"
-    }
-  ]
-}

CODEOWNERS

@@ -6,6 +6,7 @@
 
 /.github/ @Kha @semorrison
 /RELEASES.md @semorrison
+/src/Init/IO.lean @joehendrix
 /src/kernel/ @leodemoura
 /src/lake/ @tydeu
 /src/Lean/Compiler/ @leodemoura
@@ -19,11 +20,7 @@
 /src/Lean/PrettyPrinter/Delaborator/ @kmill
 /src/Lean/Server/ @mhuisi
 /src/Lean/Widget/ @Vtec234
-/src/Init/Data/ @semorrison
-/src/Init/Data/Array/Lemmas.lean @digama0
-/src/Init/Data/List/Lemmas.lean @digama0
-/src/Init/Data/List/BasicAux.lean @digama0
-/src/Init/Data/Array/Subarray.lean @david-christiansen
+/src/runtime/io.cpp @joehendrix
 /src/Lean/Elab/Tactic/RCases.lean @digama0
 /src/Init/RCases.lean @digama0
 /src/Lean/Elab/Tactic/Ext.lean @digama0
@@ -42,4 +39,3 @@
 /src/Lean/Elab/Tactic/Guard.lean @digama0
 /src/Init/Guard.lean @digama0
 /src/Lean/Server/CodeActions/ @digama0
-/src/Std/ @TwoFX

CONTRIBUTING.md

@@ -63,20 +63,6 @@ Because the change will be squashed, there is no need to polish the commit messa
 Reviews and Feedback:
 ----
 
-The lean4 repo is managed by the Lean FRO's *triage team* that aims to provide initial feedback on new bug reports, PRs, and RFCs weekly.
-This feedback generally consists of prioritizing the ticket using one of the following categories:
-* label `P-high`: We will work on this issue
-* label `P-medium`: We may work on this issue if we find the time
-* label `P-low`: We are not planning to work on this issue
-* *closed*: This issue is already fixed, it is not an issue, or is not sufficiently compatible with our roadmap for the project and we will not work on it nor accept external contributions on it
-
-For *bug reports*, the listed priority reflects our commitment to fixing the issue.
-It is generally indicative but not necessarily identical to the priority an external contribution addressing this bug would receive.
-For *PRs* and *RFCs*, the priority reflects our commitment to reviewing them and getting them to an acceptable state.
-Accepted RFCs are marked with the label `RFC accepted` and afterwards assigned a new "implementation" priority as with bug reports.
-
-General guidelines for interacting with reviews and feedback:
-
 **Be Patient**: Given the limited number of full-time maintainers and the volume of PRs, reviews may take some time.
 
 **Engage Constructively**: Always approach feedback positively and constructively. Remember, reviews are about ensuring the best quality for the project, not personal criticism.

README.md

@@ -22,4 +22,4 @@ Please read our [Contribution Guidelines](CONTRIBUTING.md) first.
 
 # Building from Source
 
-See [Building Lean](https://lean-lang.org/lean4/doc/make/index.html) (documentation source: [doc/make/index.md](doc/make/index.md)).
+See [Building Lean](https://lean-lang.org/lean4/doc/make/index.html).

doc/BoolExpr.lean

@@ -1,4 +1,4 @@
-open Batteries
+open Std
 open Lean
 
 inductive BoolExpr where

doc/char.md

@@ -1,11 +1 @@
 # Characters
-
-A value of type `Char`, also known as a character, is a [Unicode scalar value](https://www.unicode.org/glossary/#unicode_scalar_value). It is represented using an unsigned 32-bit integer and is statically guaranteed to be a valid Unicode scalar value.
-
-Syntactically, character literals are enclosed in single quotes.
-```lean
-#eval 'a' -- 'a'
-#eval '∀' -- '∀'
-```
-
-Characters are ordered and can be decidably compared using the relational operators `=`, `<`, `≤`, `>`, `≥`.

doc/dev/bootstrap.md

@@ -75,28 +75,14 @@ The github repository will automatically update stage0 on `master` once
 
 If you have write access to the lean4 repository, you can also also manually
 trigger that process, for example to be able to use new features in the compiler itself.
-You can do that on <https://github.com/leanprover/lean4/actions/workflows/update-stage0.yml>
+You can do that on <https://github.com/nomeata/lean4/actions/workflows/update-stage0.yml>
 or using Github CLI with
 ```
 gh workflow run update-stage0.yml
 ```
 
-Leaving stage0 updates to the CI automation is preferable, but should you need
-to do it locally, you can use `make update-stage0-commit` in `build/release` to
-update `stage0` from `stage1` or `make -C stageN update-stage0-commit` to
-update from another stage. This command will automatically stage the updated files
-and introduce a commit,so make sure to commit your work before that.
-
-If you rebased the branch (either onto a newer version of `master`, or fixing
-up some commits prior to the stage0 update, recreate the stage0 update commits.
-The script `script/rebase-stage0.sh` can be used for that.
-
-The CI should prevent PRs with changes to stage0 (besides `stdlib_flags.h`)
-from entering `master` through the (squashing!) merge queue, and label such PRs
-with the `changes-stage0` label. Such PRs should have a cleaned up history,
-with separate stage0 update commits; then coordinate with the admins to merge
-your PR using rebase merge, bypassing the merge queue.
-
+Leaving stage0 updates to the CI automation is preferable, but should you need to do it locally, you can use `make update-stage0-commit` in `build/release` to update `stage0` from `stage1` or `make -C stageN update-stage0-commit` to update from another stage.
+This command will automatically stage the updated files and introduce a commit, so make sure to commit your work before that. Then coordinate with the admins to not squash your PR so that stage 0 updates are preserved as separate commits.
 
 ## Further Bootstrapping Complications
 

doc/dev/ffi.md

@@ -53,59 +53,10 @@ In the case of `@[extern]` all *irrelevant* types are removed first; see next se
   Its runtime value is either a pointer to an opaque bignum object or, if the lowest bit of the "pointer" is 1 (`lean_is_scalar`), an encoded unboxed natural number (`lean_box`/`lean_unbox`).
 * A universe `Sort u`, type constructor `... → Sort u`, or proposition `p : Prop` is *irrelevant* and is either statically erased (see above) or represented as a `lean_object *` with the runtime value `lean_box(0)`
 * Any other type is represented by `lean_object *`.
-  Its runtime value is a pointer to an object of a subtype of `lean_object` (see the "Inductive types" section below) or the unboxed value `lean_box(cidx)` for the `cidx`th constructor of an inductive type if this constructor does not have any relevant parameters.
+  Its runtime value is a pointer to an object of a subtype of `lean_object` (see respective declarations in `lean.h`) or the unboxed value `lean_box(cidx)` for the `cidx`th constructor of an inductive type if this constructor does not have any relevant parameters.
 
   Example: the runtime value of `u : Unit` is always `lean_box(0)`.
 
-#### Inductive types
-
-For inductive types which are in the fallback `lean_object *` case above and not trivial constructors, the type is stored as a `lean_ctor_object`, and `lean_is_ctor` will return true. A `lean_ctor_object` stores the constructor index in the header, and the fields are stored in the `m_objs` portion of the object.
-
-The memory order of the fields is derived from the types and order of the fields in the declaration. They are ordered as follows:
-
-* Non-scalar fields stored as `lean_object *`
-* Fields of type `USize`
-* Other scalar fields, in decreasing order by size
-
-Within each group the fields are ordered in declaration order. **Warning**: Trivial wrapper types still count toward a field being treated as non-scalar for this purpose.
-
-* To access fields of the first kind, use `lean_ctor_get(val, i)` to get the `i`th non-scalar field.
-* To access `USize` fields, use `lean_ctor_get_usize(val, n+i)` to get the `i`th usize field and `n` is the total number of fields of the first kind.
-* To access other scalar fields, use `lean_ctor_get_uintN(val, off)` or `lean_ctor_get_usize(val, off)` as appropriate. Here `off` is the byte offset of the field in the structure, starting at `n*sizeof(void*)` where `n` is the number of fields of the first two kinds.
-
-For example, a structure such as
-```lean
-structure S where
-  ptr_1 : Array Nat
-  usize_1 : USize
-  sc64_1 : UInt64
-  ptr_2 : { x : UInt64 // x > 0 } -- wrappers don't count as scalars
-  sc64_2 : Float -- `Float` is 64 bit
-  sc8_1 : Bool
-  sc16_1 : UInt16
-  sc8_2 : UInt8
-  sc64_3 : UInt64
-  usize_2 : USize
-  ptr_3 : Char -- trivial wrapper around `UInt32`
-  sc32_1 : UInt32
-  sc16_2 : UInt16
-```
-would get re-sorted into the following memory order:
-
-* `S.ptr_1` - `lean_ctor_get(val, 0)`
-* `S.ptr_2` - `lean_ctor_get(val, 1)`
-* `S.ptr_3` - `lean_ctor_get(val, 2)`
-* `S.usize_1` - `lean_ctor_get_usize(val, 3)`
-* `S.usize_2` - `lean_ctor_get_usize(val, 4)`
-* `S.sc64_1` - `lean_ctor_get_uint64(val, sizeof(void*)*5)`
-* `S.sc64_2` - `lean_ctor_get_float(val, sizeof(void*)*5 + 8)`
-* `S.sc64_3` - `lean_ctor_get_uint64(val, sizeof(void*)*5 + 16)`
-* `S.sc32_1` - `lean_ctor_get_uint32(val, sizeof(void*)*5 + 24)`
-* `S.sc16_1` - `lean_ctor_get_uint16(val, sizeof(void*)*5 + 28)`
-* `S.sc16_2` - `lean_ctor_get_uint16(val, sizeof(void*)*5 + 30)`
-* `S.sc8_1` - `lean_ctor_get_uint8(val, sizeof(void*)*5 + 32)`
-* `S.sc8_2` - `lean_ctor_get_uint8(val, sizeof(void*)*5 + 33)`
-
 ### Borrowing
 
 By default, all `lean_object *` parameters of an `@[extern]` function are considered *owned*, i.e. the external code is passed a "virtual RC token" and is responsible for passing this token along to another consuming function (exactly once) or freeing it via `lean_dec`.

doc/dev/release_checklist.md

@@ -5,11 +5,7 @@ See below for the checklist for release candidates.
 
 We'll use `v4.6.0` as the intended release version as a running example.
 
-- One week before the planned release, ensure that
-  (1) someone has written the release notes and
-  (2) someone has written the first draft of the release blog post.
-  If there is any material in `./releases_drafts/` on the `releases/v4.6.0` branch, then the release notes are not done.
-  (See the section "Writing the release notes".)
+- One week before the planned release, ensure that someone has written the first draft of the release blog post
 - `git checkout releases/v4.6.0`
   (This branch should already exist, from the release candidates.)
 - `git pull`
@@ -17,8 +13,15 @@ We'll use `v4.6.0` as the intended release version as a running example.
   - `set(LEAN_VERSION_MINOR 6)` (for whichever `6` is appropriate)
   - `set(LEAN_VERSION_IS_RELEASE 1)`
   - (both of these should already be in place from the release candidates)
+- It is possible that the `v4.6.0` section of `RELEASES.md` is out of sync between
+  `releases/v4.6.0` and `master`. This should be reconciled:
+  - Run `git diff master RELEASES.md`.
+  - You should expect to see additons on `master` in the `v4.7.0-rc1` section; ignore these.
+    (i.e. the new release notes for the upcoming release candidate).
+  - Reconcile discrepancies in the `v4.6.0` section,
+    usually via copy and paste and a commit to `releases/v4.6.0`.
 - `git tag v4.6.0`
-- `git push $REMOTE v4.6.0`, where `$REMOTE` is the upstream Lean repository (e.g., `origin`, `upstream`)
+- `git push origin v4.6.0`
 - Now wait, while CI runs.
   - You can monitor this at `https://github.com/leanprover/lean4/actions/workflows/ci.yml`,
     looking for the `v4.6.0` tag.
@@ -27,85 +30,56 @@ We'll use `v4.6.0` as the intended release version as a running example.
     you may want to start on the release candidate checklist now.
 - Go to https://github.com/leanprover/lean4/releases and verify that the `v4.6.0` release appears.
   - Edit the release notes on Github to select the "Set as the latest release".
-  - Follow the instructions in creating a release candidate for the "GitHub release notes" step,
-    now that we have a written `RELEASES.md` section.
-    Do a quick sanity check.
+  - Copy and paste the Github release notes from the previous releases candidate for this version
+    (e.g. `v4.6.0-rc1`), and quickly sanity check.
 - Next, we will move a curated list of downstream repos to the latest stable release.
   - For each of the repositories listed below:
-    - Make a PR to `master`/`main` changing the toolchain to `v4.6.0`
-      - Update the toolchain file
-      - In the Lakefile, if there are dependencies on specific version tags of dependencies that you've already pushed as part of this process, update them to the new tag.
-        If they depend on `main` or `master`, don't change this; you've just updated the dependency, so it will work and be saved in the manifest
-      - Run `lake update`
-      - The PR title should be "chore: bump toolchain to v4.6.0".
-    - Merge the PR once CI completes.
-    - Create the tag `v4.6.0` from `master`/`main` and push it.
-    - Merge the tag `v4.6.0` into the `stable` branch and push it.
+    - Make a PR to `master`/`main` changing the toolchain to `v4.6.0`.
+      The PR title should be "chore: bump toolchain to v4.6.0".
+      Since the `v4.6.0` release should be functionally identical to the last release candidate,
+      which the repository should already be on, this PR is a no-op besides changing the toolchain.
+    - Once this is merged, create the tag `v4.6.0` from `master`/`main` and push it.
+    - Merge the tag `v4.6.0` into the stable branch.
   - We do this for the repositories:
     - [lean4checker](https://github.com/leanprover/lean4checker)
-      - No dependencies
-      - Toolchain bump PR
-      - Create and push the tag
-      - Merge the tag into `stable`
-    - [Batteries](https://github.com/leanprover-community/batteries)
-      - No dependencies
-      - Toolchain bump PR
-      - Create and push the tag
-      - Merge the tag into `stable`
+      - `lean4checker` uses a different version tagging scheme: use `toolchain/v4.6.0` rather than `v4.6.0`.
+    - [Std](https://github.com/leanprover-community/repl)
     - [ProofWidgets4](https://github.com/leanprover-community/ProofWidgets4)
-      - Dependencies: `Batteries`
-      - Note on versions and branches:
-        - `ProofWidgets` uses a sequential version tagging scheme, e.g. `v0.0.29`,
-          which does not refer to the toolchain being used.
-        - Make a new release in this sequence after merging the toolchain bump PR.
-        - `ProofWidgets` does not maintain a `stable` branch.
-      - Toolchain bump PR
-      - Create and push the tag, following the version convention of the repository
+      - `ProofWidgets` uses a sequential version tagging scheme, e.g. `v0.0.29`,
+        which does not refer to the toolchain being used.
+      - Make a new release in this sequence after merging the toolchain bump PR.
+      - `ProofWidgets` does not maintain a `stable` branch.
     - [Aesop](https://github.com/leanprover-community/aesop)
-      - Dependencies: `Batteries`
-      - Toolchain bump PR including updated Lake manifest
-      - Create and push the tag
-      - Merge the tag into `stable`
-    - [doc-gen4](https://github.com/leanprover/doc-gen4)
-      - Dependencies: exist, but they're not part of the release workflow
-      - Toolchain bump PR including updated Lake manifest
-      - Create and push the tag
-      - There is no `stable` branch; skip this step
-    - [import-graph](https://github.com/leanprover-community/import-graph)
-      - Toolchain bump PR including updated Lake manifest
-      - Create and push the tag
-      - There is no `stable` branch; skip this step
     - [Mathlib](https://github.com/leanprover-community/mathlib4)
-      - Dependencies: `Aesop`, `ProofWidgets4`, `lean4checker`, `Batteries`, `doc-gen4`, `import-graph`
-      - Toolchain bump PR notes:
-        - In addition to updating the `lean-toolchain` and `lakefile.lean`,
-          in `.github/workflows/lean4checker.yml` update the line
-          `git checkout v4.6.0` to the appropriate tag. 
-        - Push the PR branch to the main Mathlib repository rather than a fork, or CI may not work reliably
-        - Create and push the tag
-        - Create a new branch from the tag, push it, and open a pull request against `stable`.
-          Coordinate with a Mathlib maintainer to get this merged.
+      - In addition to updating the `lean-toolchain` and `lakefile.lean`,
+        in `.github/workflows/build.yml.in` in the `lean4checker` section update the line
+        `git checkout toolchain/v4.6.0` to the appropriate tag,
+        and then run `.github/workflows/mk_build_yml.sh`.
     - [REPL](https://github.com/leanprover-community/repl)
-      - Dependencies: `Mathlib` (for test code)
       - Note that there are two copies of `lean-toolchain`/`lakefile.lean`:
-        in the root, and in `test/Mathlib/`. Edit both, and run `lake update` in both directories.
-      - Toolchain bump PR including updated Lake manifest
-      - Create and push the tag
-      - Merge the tag into `stable`
-- The `v4.6.0` section of `RELEASES.md` is out of sync between
-  `releases/v4.6.0` and `master`. This should be reconciled:
-  - Replace the `v4.6.0` section on `master` with the `v4.6.0` section on `releases/v4.6.0`
-    and commit this to `master`.
+        in the root, and in `test/Mathlib/`.
+  - Note that there are dependencies between these packages:
+    you should update the lakefile so that you are using the `v4.6.0` tag of upstream repositories
+    (or the sequential tag for `ProofWidgets4`), and run `lake update` before committing.
+  - This means that this process is sequential; each repository must have its bump PR merged,
+    and the new tag pushed, before you can make the PR for the downstream repositories.
+    - `lean4checker` has no dependencies
+    - `Std` has no dependencies
+    - `Aesop` depends on `Std`
+    - `ProofWidgets4` depends on `Std`
+    - `Mathlib` depends on `Aesop`, `ProofWidgets4`, and `lean4checker` (and transitively on `Std`)
+    - `REPL` depends on `Mathlib` (this dependency is only for testing).
 - Merge the release announcement PR for the Lean website - it will be deployed automatically
 - Finally, make an announcement!
   This should go in https://leanprover.zulipchat.com/#narrow/stream/113486-announce, with topic `v4.6.0`.
   Please see previous announcements for suggested language.
   You will want a few bullet points for main topics from the release notes.
   Link to the blog post from the Zulip announcement.
-- Make sure that whoever is handling social media knows the release is out.
+  Please also make sure that whoever is handling social media knows the release is out.
 
 ## Optimistic(?) time estimates:
 - Initial checks and push the tag: 30 minutes.
+- Note that if `RELEASES.md` has discrepancies this could take longer!
 - Waiting for the release: 60 minutes.
 - Fixing release notes: 10 minutes.
 - Bumping toolchains in downstream repositories, up to creating the Mathlib PR: 30 minutes.
@@ -121,8 +95,8 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
 
 - Decide which nightly release you want to turn into a release candidate.
   We will use `nightly-2024-02-29` in this example.
-- It is essential that Batteries and Mathlib already have reviewed branches compatible with this nightly.
-  - Check that both Batteries and Mathlib's `bump/v4.7.0` branch contain `nightly-2024-02-29`
+- It is essential that Std and Mathlib already have reviewed branches compatible with this nightly.
+  - Check that both Std and Mathlib's `bump/v4.7.0` branch contain `nightly-2024-02-29`
     in their `lean-toolchain`.
   - The steps required to reach that state are beyond the scope of this checklist, but see below!
 - Create the release branch from this nightly tag:
@@ -132,25 +106,34 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
     git checkout nightly-2024-02-29
     git checkout -b releases/v4.7.0
     ```
-- In `RELEASES.md` replace `Development in progress` in the `v4.7.0` section with `Release notes to be written.`
-- We will rely on automatically generated release notes for release candidates,
-  and the written release notes will be used for stable versions only.
-  It is essential to choose the nightly that will become the release candidate as early as possible, to avoid confusion.
+- In `RELEASES.md` remove `(development in progress)` from the `v4.7.0` section header.
+- Our current goal is to have written release notes only about major language features or breaking changes,
+  and to rely on automatically generated release notes for bugfixes and minor changes.
+  - Do not wait on `RELEASES.md` being perfect before creating the `release/v4.7.0` branch. It is essential to choose the nightly which will become the release candidate as early as possible, to avoid confusion.
+  - If there are major changes not reflected in `RELEASES.md` already, you may need to solicit help from the authors.
+  - Minor changes and bug fixes do not need to be documented in `RELEASES.md`: they will be added automatically on the Github release page.
+  - Commit your changes to `RELEASES.md`, and push.
+  - Remember that changes to `RELEASES.md` after you have branched `releases/v4.7.0` should also be cherry-picked back to `master`.
 - In `src/CMakeLists.txt`,
   - verify that you see `set(LEAN_VERSION_MINOR 7)` (for whichever `7` is appropriate); this should already have been updated when the development cycle began.
   - `set(LEAN_VERSION_IS_RELEASE 1)` (this should be a change; on `master` and nightly releases it is always `0`).
   - Commit your changes to `src/CMakeLists.txt`, and push.
 - `git tag v4.7.0-rc1`
 - `git push origin v4.7.0-rc1`
-- Ping the FRO Zulip that release notes need to be written. The release notes do not block completing the rest of this checklist.
 - Now wait, while CI runs.
   - You can monitor this at `https://github.com/leanprover/lean4/actions/workflows/ci.yml`, looking for the `v4.7.0-rc1` tag.
   - This step can take up to an hour.
-- (GitHub release notes) Once the release appears at https://github.com/leanprover/lean4/releases/
-  - Verify that the release is marked as a prerelease (this should have been done automatically by the CI release job).
-  - In the "previous tag" dropdown, select `v4.6.0`, and click "Generate release notes".
-    This will add a list of all the commits since the last stable version.
+- Once the release appears at https://github.com/leanprover/lean4/releases/
+  - Edit the release notes on Github to select the "Set as a pre-release box".
+  - Copy the section of `RELEASES.md` for this version into the Github release notes.
+  - Use the title "Changes since v4.6.0 (from RELEASES.md)"
+  - Then in the "previous tag" dropdown, select `v4.6.0`, and click "Generate release notes".
+  - This will add a list of all the commits since the last stable version.
+    - Delete anything already mentioned in the hand-written release notes above.
     - Delete "update stage0" commits, and anything with a completely inscrutable commit message.
+    - Briefly rearrange the remaining items by category (e.g. `simp`, `lake`, `bug fixes`),
+      but for minor items don't put any work in expanding on commit messages.
+  - (How we want to release notes to look is evolving: please update this section if it looks wrong!)
 - Next, we will move a curated list of downstream repos to the release candidate.
   - This assumes that there is already a *reviewed* branch `bump/v4.7.0` on each repository
     containing the required adaptations (or no adaptations are required).
@@ -171,10 +154,7 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
   - We do this for the same list of repositories as for stable releases, see above.
     As above, there are dependencies between these, and so the process above is iterative.
     It greatly helps if you can merge the `bump/v4.7.0` PRs yourself!
-    It is essential for Mathlib CI that you then create the next `bump/v4.8.0` branch
-    for the next development cycle.
-    Set the `lean-toolchain` file on this branch to same `nightly` you used for this release.
-  - For Batteries/Aesop/Mathlib, which maintain a `nightly-testing` branch, make sure there is a tag
+  - For Std/Aesop/Mathlib, which maintain a `nightly-testing` branch, make sure there is a tag
     `nightly-testing-2024-02-29` with date corresponding to the nightly used for the release
     (create it if not), and then on the `nightly-testing` branch `git reset --hard master`, and force push.
 - Make an announcement!
@@ -184,19 +164,8 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
   Please also make sure that whoever is handling social media knows the release is out.
 - Begin the next development cycle (i.e. for `v4.8.0`) on the Lean repository, by making a PR that:
   - Updates `src/CMakeLists.txt` to say `set(LEAN_VERSION_MINOR 8)`
-  - Replaces the "release notes will be copied" text in the `v4.6.0` section of `RELEASES.md` with the
-    finalized release notes from the `releases/v4.6.0` branch.
-  - Replaces the "development in progress" in the `v4.7.0` section of `RELEASES.md` with
-    ```
-    Release candidate, release notes will be copied from `branch releases/v4.7.0` once completed.
-    ```
-    and inserts the following section before that section:
-    ```
-    v4.8.0
-    ----------
-    Development in progress.
-    ```
-  - Removes all the entries from the `./releases_drafts/` folder.
+  - Removes `(in development)` from the section heading in `RELEASES.md` for `v4.7.0`,
+    and creates a new `v4.8.0 (in development)` section heading.
 
 ## Time estimates:
 Slightly longer than the corresponding steps for a stable release.
@@ -207,7 +176,7 @@ In particular, updating the downstream repositories is significantly more work
 # Preparing `bump/v4.7.0` branches
 
 While not part of the release process per se,
-this is a brief summary of the work that goes into updating Batteries/Aesop/Mathlib to new versions.
+this is a brief summary of the work that goes into updating Std/Aesop/Mathlib to new versions.
 
 Please read https://leanprover-community.github.io/contribute/tags_and_branches.html
 
@@ -221,30 +190,12 @@ Please read https://leanprover-community.github.io/contribute/tags_and_branches.
   * This can either be done by the person managing this process directly,
     or by soliciting assistance from authors of files, or generally helpful people on Zulip!
 * Each repo has a `bump/v4.7.0` which accumulates reviewed changes adapting to new versions.
-* Once `nightly-testing` is working on a given nightly, say `nightly-2024-02-15`, we will create a PR to `bump/v4.7.0`.
-* For Mathlib, there is a script in `scripts/create-adaptation-pr.sh` that automates this process.
-* For Batteries and Aesop it is currently manual.
-* For all of these repositories, the process is the same:
+* Once `nightly-testing` is working on a given nightly, say `nightly-2024-02-15`, we:
   * Make sure `bump/v4.7.0` is up to date with `master` (by merging `master`, no PR necessary)
   * Create from `bump/v4.7.0` a `bump/nightly-2024-02-15` branch.
-  * In that branch, `git merge nightly-testing` to bring across changes from `nightly-testing`.
+  * In that branch, `git merge --squash nightly-testing` to bring across changes from `nightly-testing`.
   * Sanity check changes, commit, and make a PR to `bump/v4.7.0` from the `bump/nightly-2024-02-15` branch.
-  * Solicit review, merge the PR into `bump/v4.7.0`.
+  * Solicit review, merge the PR into `bump/v4,7,0`.
 * It is always okay to merge in the following directions:
   `master` -> `bump/v4.7.0` -> `bump/nightly-2024-02-15` -> `nightly-testing`.
   Please remember to push any merges you make to intermediate steps!
-
-# Writing the release notes
-
-We are currently trying a system where release notes are compiled all at once from someone looking through the commit history.
-The exact steps are a work in progress.
-Here is the general idea:
-
-* The work is done right on the `releases/v4.6.0` branch sometime after it is created but before the stable release is made.
-  The release notes for `v4.6.0` will later be copied to `master` when we begin a new development cycle.
-* There can be material for release notes entries in commit messages.
-* There can also be pre-written entries in `./releases_drafts`, which should be all incorporated in the release notes and then deleted from the branch.
-  See `./releases_drafts/README.md` for more information.
-* The release notes should be written from a downstream expert user's point of view.
-
-This section will be updated when the next release notes are written (for `v4.10.0`).

doc/examples/Certora2022/ex8.lean

@@ -4,16 +4,16 @@ def ack : Nat → Nat → Nat
   | 0,   y   => y+1
   | x+1, 0   => ack x 1
   | x+1, y+1 => ack x (ack (x+1) y)
-termination_by x y => (x, y)
+termination_by ack x y => (x, y)
 
 def sum (a : Array Int) : Int :=
   let rec go (i : Nat) :=
-     if _ : i < a.size then
+     if i < a.size then
         a[i] + go (i+1)
      else
         0
-  termination_by a.size - i
   go 0
+termination_by go i => a.size - i
 
 set_option pp.proofs true
 #print sum.go

doc/examples/ICERM2022/ctor.lean

@@ -4,42 +4,43 @@ open Lean Meta
 
 def ctor (mvarId : MVarId) (idx : Nat) : MetaM (List MVarId) := do
   /- Set `MetaM` context using `mvarId` -/
-  mvarId.withContext do
+  withMVarContext mvarId do 
     /- Fail if the metavariable is already assigned. -/
-    mvarId.checkNotAssigned `ctor
+    checkNotAssigned mvarId `ctor
     /- Retrieve the target type, instantiateMVars, and use `whnf`. -/
-    let target ← mvarId.getType'
+    let target ← getMVarType' mvarId
     let .const declName us := target.getAppFn
       | throwTacticEx `ctor mvarId "target is not an inductive datatype"
     let .inductInfo { ctors, .. } ← getConstInfo declName
       | throwTacticEx `ctor mvarId "target is not an inductive datatype"
     if idx = 0 then
-      throwTacticEx `ctor mvarId "invalid index, it must be > 0"
+      throwTacticEx `ctor mvarId "invalid index, it must be > 0"  
     else if h : idx - 1 < ctors.length then
-      mvarId.apply (.const ctors[idx - 1] us)
+      apply mvarId (.const ctors[idx - 1] us)
     else
-      throwTacticEx `ctor mvarId "invalid index, inductive datatype has only {ctors.length} contructors"
+      throwTacticEx `ctor mvarId "invalid index, inductive datatype has only {ctors.length} contructors"  
 
 open Elab Tactic
 
-elab "ctor" idx:num : tactic =>
+elab "ctor" idx:num : tactic => 
   liftMetaTactic (ctor · idx.getNat)
 
-example (p : Prop) : p := by
+example (p : Prop) : p := by 
   ctor 1 -- Error
 
-example (h : q) : p ∨ q := by
+example (h : q) : p ∨ q := by 
   ctor 0 -- Error
   exact h
 
-example (h : q) : p ∨ q := by
+example (h : q) : p ∨ q := by 
   ctor 3 -- Error
   exact h
 
-example (h : q) : p ∨ q := by
+example (h : q) : p ∨ q := by 
   ctor 2
   exact h
 
-example (h : q) : p ∨ q := by
+example (h : q) : p ∨ q := by 
   ctor 1
-  exact h -- Error
+  exact h -- Error 
+

doc/examples/ICERM2022/meta.lean

@@ -5,15 +5,15 @@ open Lean Meta
 def ex1 (declName : Name) : MetaM Unit := do
   let info ← getConstInfo declName
   IO.println s!"{declName} : {← ppExpr info.type}"
-  if let some val := info.value? then
+  if let some val := info.value? then 
     IO.println s!"{declName} : {← ppExpr val}"
-
+    
 #eval ex1 ``Nat
 
 def ex2 (declName : Name) : MetaM Unit := do
   let info ← getConstInfo declName
   trace[Meta.debug] "{declName} : {info.type}"
-  if let some val := info.value? then
+  if let some val := info.value? then 
     trace[Meta.debug] "{declName} : {val}"
 
 #eval ex2 ``Add.add
@@ -30,9 +30,9 @@ def ex3 (declName : Name) : MetaM Unit := do
       trace[Meta.debug] "{x} : {← inferType x}"
 
 def myMin [LT α] [DecidableRel (α := α) (·<·)] (a b : α) : α :=
-  if a < b then
+  if a < b then 
     a
-  else
+  else 
     b
 
 set_option trace.Meta.debug true in
@@ -40,7 +40,7 @@ set_option trace.Meta.debug true in
 
 def ex4 : MetaM Unit := do
   let nat := mkConst ``Nat
-  withLocalDeclD `a nat fun a =>
+  withLocalDeclD `a nat fun a => 
   withLocalDeclD `b nat fun b => do
     let e ← mkAppM ``HAdd.hAdd #[a, b]
     trace[Meta.debug] "{e} : {← inferType e}"
@@ -66,17 +66,15 @@ open Elab Term
 
 def ex5 : TermElabM Unit := do
   let nat := Lean.mkConst ``Nat
-  withLocalDeclD `a nat fun a => do
+  withLocalDeclD `a nat fun a => do 
   withLocalDeclD `b nat fun b => do
     let ab ← mkAppM ``HAdd.hAdd #[a, b]
-    let abStx ← exprToSyntax ab
-    let aStx ← exprToSyntax a
-    let stx ← `(fun x => if x < 10 then $abStx + x else x + $aStx)
+    let stx ← `(fun x => if x < 10 then $(← exprToSyntax ab) + x else x + $(← exprToSyntax a))
     let e ← elabTerm stx none
     trace[Meta.debug] "{e} : {← inferType e}"
     let e := mkApp e (mkNatLit 5)
     let e ← whnf e
     trace[Meta.debug] "{e}"
-
+       
 set_option trace.Meta.debug true in
 #eval ex5

doc/examples/NFM2022/nfm8.lean

@@ -4,16 +4,16 @@ def ack : Nat → Nat → Nat
   | 0,   y   => y+1
   | x+1, 0   => ack x 1
   | x+1, y+1 => ack x (ack (x+1) y)
-termination_by x y => (x, y)
+termination_by ack x y => (x, y)
 
 def sum (a : Array Int) : Int :=
   let rec go (i : Nat) :=
-     if _ : i < a.size then
+     if i < a.size then
         a[i] + go (i+1)
      else
         0
-  termination_by a.size - i
   go 0
+termination_by go i => a.size - i
 
 set_option pp.proofs true
 #print sum.go

doc/examples/compiler/.gitignore

@@ -1 +0,0 @@
-build

doc/examples/interp.lean

@@ -149,4 +149,4 @@ def fact : Expr ctx (Ty.fn Ty.int Ty.int) :=
            (op (·*·) (delay fun _ => app fact (op (·-·) (var stop) (val 1))) (var stop)))
   decreasing_by sorry
 
-#eval! fact.interp Env.nil 10
+#eval fact.interp Env.nil 10

doc/examples/test_single.sh

@@ -1,4 +1,4 @@
 #!/usr/bin/env bash
 source ../../tests/common.sh
 
-exec_check lean -Dlinter.all=false "$f"
+exec_check lean -j 0 -Dlinter.all=false "$f"

doc/flake.lock

@@ -18,15 +18,12 @@
       }
     },
     "flake-utils": {
-      "inputs": {
-        "systems": "systems"
-      },
       "locked": {
-        "lastModified": 1710146030,
-        "narHash": "sha256-SZ5L6eA7HJ/nmkzGG7/ISclqe6oZdOZTNoesiInkXPQ=",
+        "lastModified": 1656928814,
+        "narHash": "sha256-RIFfgBuKz6Hp89yRr7+NR5tzIAbn52h8vT6vXkYjZoM=",
         "owner": "numtide",
         "repo": "flake-utils",
-        "rev": "b1d9ab70662946ef0850d488da1c9019f3a9752a",
+        "rev": "7e2a3b3dfd9af950a856d66b0a7d01e3c18aa249",
         "type": "github"
       },
       "original": {
@@ -38,12 +35,13 @@
     "lean": {
       "inputs": {
         "flake-utils": "flake-utils",
-        "nixpkgs": "nixpkgs",
-        "nixpkgs-old": "nixpkgs-old"
+        "lean4-mode": "lean4-mode",
+        "nix": "nix",
+        "nixpkgs": "nixpkgs_2"
       },
       "locked": {
         "lastModified": 0,
-        "narHash": "sha256-saRAtQ6VautVXKDw1XH35qwP0KEBKTKZbg/TRa4N9Vw=",
+        "narHash": "sha256-YnYbmG0oou1Q/GE4JbMNb8/yqUVXBPIvcdQQJHBqtPk=",
         "path": "../.",
         "type": "path"
       },
@@ -52,6 +50,22 @@
         "type": "path"
       }
     },
+    "lean4-mode": {
+      "flake": false,
+      "locked": {
+        "lastModified": 1659020985,
+        "narHash": "sha256-+dRaXB7uvN/weSZiKcfSKWhcdJVNg9Vg8k0pJkDNjpc=",
+        "owner": "leanprover",
+        "repo": "lean4-mode",
+        "rev": "37d5c99b7b29c80ab78321edd6773200deb0bca6",
+        "type": "github"
+      },
+      "original": {
+        "owner": "leanprover",
+        "repo": "lean4-mode",
+        "type": "github"
+      }
+    },
     "leanInk": {
       "flake": false,
       "locked": {
@@ -69,6 +83,22 @@
         "type": "github"
       }
     },
+    "lowdown-src": {
+      "flake": false,
+      "locked": {
+        "lastModified": 1633514407,
+        "narHash": "sha256-Dw32tiMjdK9t3ETl5fzGrutQTzh2rufgZV4A/BbxuD4=",
+        "owner": "kristapsdz",
+        "repo": "lowdown",
+        "rev": "d2c2b44ff6c27b936ec27358a2653caaef8f73b8",
+        "type": "github"
+      },
+      "original": {
+        "owner": "kristapsdz",
+        "repo": "lowdown",
+        "type": "github"
+      }
+    },
     "mdBook": {
       "flake": false,
       "locked": {
@@ -85,13 +115,65 @@
         "type": "github"
       }
     },
+    "nix": {
+      "inputs": {
+        "lowdown-src": "lowdown-src",
+        "nixpkgs": "nixpkgs",
+        "nixpkgs-regression": "nixpkgs-regression"
+      },
+      "locked": {
+        "lastModified": 1657097207,
+        "narHash": "sha256-SmeGmjWM3fEed3kQjqIAO8VpGmkC2sL1aPE7kKpK650=",
+        "owner": "NixOS",
+        "repo": "nix",
+        "rev": "f6316b49a0c37172bca87ede6ea8144d7d89832f",
+        "type": "github"
+      },
+      "original": {
+        "owner": "NixOS",
+        "repo": "nix",
+        "type": "github"
+      }
+    },
     "nixpkgs": {
       "locked": {
-        "lastModified": 1710889954,
-        "narHash": "sha256-Pr6F5Pmd7JnNEMHHmspZ0qVqIBVxyZ13ik1pJtm2QXk=",
+        "lastModified": 1653988320,
+        "narHash": "sha256-ZaqFFsSDipZ6KVqriwM34T739+KLYJvNmCWzErjAg7c=",
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "7872526e9c5332274ea5932a0c3270d6e4724f3b",
+        "rev": "2fa57ed190fd6c7c746319444f34b5917666e5c1",
+        "type": "github"
+      },
+      "original": {
+        "owner": "NixOS",
+        "ref": "nixos-22.05-small",
+        "repo": "nixpkgs",
+        "type": "github"
+      }
+    },
+    "nixpkgs-regression": {
+      "locked": {
+        "lastModified": 1643052045,
+        "narHash": "sha256-uGJ0VXIhWKGXxkeNnq4TvV3CIOkUJ3PAoLZ3HMzNVMw=",
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "215d4d0fd80ca5163643b03a33fde804a29cc1e2",
+        "type": "github"
+      },
+      "original": {
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "215d4d0fd80ca5163643b03a33fde804a29cc1e2",
+        "type": "github"
+      }
+    },
+    "nixpkgs_2": {
+      "locked": {
+        "lastModified": 1657208011,
+        "narHash": "sha256-BlIFwopAykvdy1DYayEkj6ZZdkn+cVgPNX98QVLc0jM=",
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "2770cc0b1e8faa0e20eb2c6aea64c256a706d4f2",
         "type": "github"
       },
       "original": {
@@ -101,23 +183,6 @@
         "type": "github"
       }
     },
-    "nixpkgs-old": {
-      "flake": false,
-      "locked": {
-        "lastModified": 1581379743,
-        "narHash": "sha256-i1XCn9rKuLjvCdu2UeXKzGLF6IuQePQKFt4hEKRU5oc=",
-        "owner": "NixOS",
-        "repo": "nixpkgs",
-        "rev": "34c7eb7545d155cc5b6f499b23a7cb1c96ab4d59",
-        "type": "github"
-      },
-      "original": {
-        "owner": "NixOS",
-        "ref": "nixos-19.03",
-        "repo": "nixpkgs",
-        "type": "github"
-      }
-    },
     "root": {
       "inputs": {
         "alectryon": "alectryon",
@@ -129,21 +194,6 @@
         "leanInk": "leanInk",
         "mdBook": "mdBook"
       }
-    },
-    "systems": {
-      "locked": {
-        "lastModified": 1681028828,
-        "narHash": "sha256-Vy1rq5AaRuLzOxct8nz4T6wlgyUR7zLU309k9mBC768=",
-        "owner": "nix-systems",
-        "repo": "default",
-        "rev": "da67096a3b9bf56a91d16901293e51ba5b49a27e",
-        "type": "github"
-      },
-      "original": {
-        "owner": "nix-systems",
-        "repo": "default",
-        "type": "github"
-      }
     }
   },
   "root": "root",

doc/flake.nix

@@ -17,7 +17,7 @@
   };
 
   outputs = inputs@{ self, ... }: inputs.flake-utils.lib.eachDefaultSystem (system:
-    with inputs.lean.packages.${system}.deprecated; with nixpkgs;
+    with inputs.lean.packages.${system}; with nixpkgs;
     let
       doc-src = lib.sourceByRegex ../. ["doc.*" "tests(/lean(/beginEndAsMacro.lean)?)?"];
     in {
@@ -44,6 +44,21 @@
           mdbook build -d $out
         '';
       };
+      # We use a separate derivation instead of `checkPhase` so we can push it but not `doc` to the binary cache
+      test = stdenv.mkDerivation {
+        name ="lean-doc-test";
+        src = doc-src;
+        buildInputs = [ lean-mdbook stage1.Lean.lean-package strace ];
+        patchPhase = ''
+          cd doc
+          patchShebangs test
+        '';
+        buildPhase = ''
+          mdbook test
+          touch $out
+        '';
+        dontInstall = true;
+      };
       leanInk = (buildLeanPackage {
         name = "Main";
         src = inputs.leanInk;

doc/int.md

@@ -13,7 +13,7 @@ Recall that nonnegative numerals are considered to be a `Nat` if there are no ty
 
 The operator `/` for `Int` implements integer division.
 ```lean
-#eval -10 / 4 -- -3
+#eval -10 / 4 -- -2
 ```
 
 Similar to `Nat`, the internal representation of `Int` is optimized. Small integers are

doc/latex/lean4.py

@@ -0,0 +1,100 @@
+# -*- coding: utf-8 -*-
+"""
+    pygments.lexers.theorem
+    ~~~~~~~~~~~~~~~~~~~~~~~
+
+    Lexers for theorem-proving languages.
+
+    :copyright: Copyright 2006-2017 by the Pygments team, see AUTHORS.
+    :license: BSD, see LICENSE for details.
+"""
+
+import re
+
+from pygments.lexer import RegexLexer, default, words
+from pygments.token import Text, Comment, Operator, Keyword, Name, String, \
+    Number, Punctuation, Generic
+
+__all__ = ['Lean4Lexer']
+
+class Lean4Lexer(RegexLexer):
+    """
+    For the `Lean 4 <https://github.com/leanprover/lean4>`_
+    theorem prover.
+
+    .. versionadded:: 2.0
+    """
+    name = 'Lean4'
+    aliases = ['lean4']
+    filenames = ['*.lean']
+    mimetypes = ['text/x-lean']
+
+    flags = re.MULTILINE | re.UNICODE
+
+    keywords1 = (
+        'import', 'abbreviation', 'opaque_hint', 'tactic_hint', 'definition',
+        'renaming', 'inline', 'hiding', 'parameter', 'lemma', 'variable',
+        'theorem', 'axiom', 'inductive', 'structure', 'universe', 'alias',
+        'help', 'options', 'precedence', 'postfix', 'prefix',
+        'infix', 'infixl', 'infixr', 'notation', '#eval',
+        '#check', '#reduce', '#exit', 'coercion', 'end', 'private', 'using', 'namespace',
+        'including', 'instance', 'section', 'context', 'protected', 'expose',
+        'export', 'set_option', 'extends', 'open', 'example',
+        'constant', 'constants', 'print', 'opaque', 'reducible', 'irreducible',
+        'def', 'macro', 'elab', 'syntax', 'macro_rules', 'reduce', 'where',
+        'abbrev', 'noncomputable', 'class', 'attribute', 'synth', 'mutual',
+    )
+
+    keywords2 = (
+        'forall', 'fun', 'Pi', 'obtain', 'from', 'have', 'show', 'assume',
+        'take', 'let', 'if', 'else', 'then', 'by', 'in', 'with', 'begin',
+        'proof', 'qed', 'calc', 'match', 'nomatch', 'do', 'at',
+    )
+
+    keywords3 = (
+        # Sorts
+        'Type', 'Prop', 'Sort',
+    )
+
+    operators = (
+        u'!=', u'#', u'&', u'&&', u'*', u'+', u'-', u'/', u'@', u'!', u'`',
+        u'-.', u'->', u'.', u'..', u'...', u'::', u':>', u';', u';;', u'<',
+        u'<-', u'=', u'==', u'>', u'_', u'|', u'||', u'~', u'=>', u'<=', u'>=',
+        u'/\\', u'\\/', u'∀', u'Π', u'λ', u'↔', u'∧', u'∨', u'≠', u'≤', u'≥',
+        u'¬', u'⁻¹', u'⬝', u'▸', u'→', u'∃', u'ℕ', u'ℤ', u'≈', u'×', u'⌞',
+        u'⌟', u'≡', u'⟨', u'⟩',
+    )
+
+    punctuation = (u'(', u')', u':', u'{', u'}', u'[', u']', u'⦃', u'⦄',
+                   u':=', u',')
+
+    tokens = {
+        'root': [
+            (r'\s+', Text),
+            (r'/-', Comment, 'comment'),
+            (r'--.*?$', Comment.Single),
+            (words(keywords1, prefix=r'\b', suffix=r'\b'), Keyword.Namespace),
+            (words(keywords2, prefix=r'\b', suffix=r'\b'), Keyword),
+            (words(keywords3, prefix=r'\b', suffix=r'\b'), Keyword.Type),
+            (words(operators), Name.Builtin.Pseudo),
+            (words(punctuation), Operator),
+            (u"[A-Za-z_\u03b1-\u03ba\u03bc-\u03fb\u1f00-\u1ffe\u2100-\u214f]"
+             u"[A-Za-z_'\u03b1-\u03ba\u03bc-\u03fb\u1f00-\u1ffe\u2070-\u2079"
+             u"\u207f-\u2089\u2090-\u209c\u2100-\u214f0-9]*", Name),
+            (r'\d+', Number.Integer),
+            (r'"', String.Double, 'string'),
+            (r'[~?][a-z][\w\']*:', Name.Variable)
+        ],
+        'comment': [
+            # Multiline Comments
+            (r'[^/-]', Comment.Multiline),
+            (r'/-', Comment.Multiline, '#push'),
+            (r'-/', Comment.Multiline, '#pop'),
+            (r'[/-]', Comment.Multiline)
+        ],
+        'string': [
+            (r'[^\\"]+', String.Double),
+            (r'\\[n"\\]', String.Escape),
+            ('"', String.Double, '#pop'),
+        ],
+    }

doc/make/index.md

@@ -1,7 +1,3 @@
-These are instructions to set up a working development environment for those who wish to make changes to Lean itself. It is part of the [Development Guide](doc/dev/index.md).
-
-We strongly suggest that new users instead follow the [Quickstart](doc/quickstart.md) to get started using Lean, since this sets up an environment that can automatically manage multiple Lean toolchain versions, which is necessary when working within the Lean ecosystem.
-
 Requirements
 ------------
 
@@ -21,27 +17,39 @@ Platform-Specific Setup
 Generic Build Instructions
 --------------------------
 
-Setting up a basic parallelized release build:
+Setting up a basic release build:
 
 ```bash
-git clone https://github.com/leanprover/lean4
+git clone https://github.com/leanprover/lean4 --recurse-submodules
 cd lean4
-cmake --preset release
-make -C build/release -j$(nproc)  # see below for macOS
+mkdir -p build/release
+cd build/release
+cmake ../..
+make
 ```
-You can replace `$(nproc)`, which is not available on macOS and some alternative shells, with the desired parallelism amount.
+
+For regular development, we recommend running
+```bash
+git config submodule.recurse true
+```
+in the checkout so that `--recurse-submodules` doesn't have to be
+specified with `git pull/checkout/...`.
 
 The above commands will compile the Lean library and binaries into the
-`stage1` subfolder; see below for details.
+`stage1` subfolder; see below for details. Add `-j N` for an
+appropriate `N` to `make` for a parallel build.
 
-You should not usually run `cmake --install` after a successful build.
+For example, on an AMD Ryzen 9 `make` takes 00:04:55, whereas `make -j 10`
+takes 00:01:38.  Your results may vary depending on the speed of your hard
+drive.
+
+You should not usually run `make install` after a successful build.
 See [Dev setup using elan](../dev/index.md#dev-setup-using-elan) on how to properly set up your editor to use the correct stage depending on the source directory.
 
 Useful CMake Configuration Settings
 -----------------------------------
 
-Pass these along with the `cmake --preset release` command.
-There are also two alternative presets that combine some of these options you can use instead of `release`: `debug` and `sandebug` (sanitize + debug).
+Pass these along with the `cmake ../..` command.
 
 * `-D CMAKE_BUILD_TYPE=`\
   Select the build type. Valid values are `RELEASE` (default), `DEBUG`,

doc/make/msvc.md

@@ -0,0 +1,39 @@
+# Compiling Lean with Visual Studio
+
+WARNING: Compiling Lean with Visual Studio doesn't currently work.
+There's an ongoing effort to port Lean to Visual Studio.
+The instructions below are for VS 2017.
+
+In the meantime you can use [MSYS2](msys2.md) or [WSL](wsl.md).
+
+## Installing dependencies
+
+First, install `vcpkg` from https://github.com/Microsoft/vcpkg if you haven't
+done so already.
+Then, open a console in the directory you cloned `vcpkg` to, and type:
+`vcpkg install mpir` for the 32-bit library or
+`vcpkg install mpir:x64-windows` for the x64 one.
+
+In Visual Studio, use the "open folder" feature and open the Lean directory.
+Go to the `CMake->Change CMake Settings` menu. File `CMakeSettings.json` opens.
+In each of the targets, add the following snippet (i.e., after every
+`ctestCommandArgs`):
+
+```json
+    "variables": [
+      {
+        "name": "CMAKE_TOOLCHAIN_FILE",
+        "value": "C:\\path\\to\\vcpkg\\scripts\\buildsystems\\vcpkg.cmake"
+      }
+    ]
+```
+
+## Enable Intellisense
+
+In Visual Studio, press Ctrl+Q and type `CppProperties.json` and press Enter.
+Ensure `includePath` variables include `"${workspaceRoot}\\src"`.
+
+
+## Build Lean
+
+Press F7.

doc/make/msys2.md

@@ -38,9 +38,10 @@ cmake --version
 Then follow the [generic build instructions](index.md) in the MSYS2
 MinGW shell, using:
 ```
-cmake --preset release -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++
+cmake ../.. -G "Unix Makefiles"  -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++
 ```
-instead of `cmake --preset release`. This will use the clang compiler instead of gcc, which is required with msys2.
+instead of `cmake ../..`. This ensures that cmake will call `sh` instead of `cmd.exe`
+for script tasks and it will use the clang compiler instead of gcc, which is required.
 
 ## Install lean
 

doc/make/osx-10.9.md

@@ -1,4 +1,4 @@
-# Install Packages on OS X 14.5
+# Install Packages on OS X 10.9
 
 We assume that you are using [homebrew][homebrew] as a package manager.
 
@@ -22,7 +22,7 @@ brew install gcc
 ```
 To install clang++-3.5 via homebrew, please execute:
 ```bash
-brew install llvm
+brew install llvm --with-clang --with-asan
 ```
 To use compilers other than the default one (Apple's clang++), you
 need to use `-DCMAKE_CXX_COMPILER` option to specify the compiler

doc/monads/states.lean

@@ -15,7 +15,7 @@ data type containing several important pieces of information. First and foremost
 current player, and it has a random generator.
 -/
 
-open Batteries (HashMap)
+open Std (HashMap)
 abbrev TileIndex := Nat × Nat -- a 2D index
 
 inductive TileState where

doc/quickstart.md

@@ -7,17 +7,12 @@ See [Setup](./setup.md) for supported platforms and other ways to set up Lean 4.
 
 1. Launch VS Code and install the `lean4` extension by clicking on the "Extensions" sidebar entry and searching for "lean4".
 
-   ![installing the vscode-lean4 extension](images/code-ext.png)
+    ![installing the vscode-lean4 extension](images/code-ext.png)
 
-1. Open the Lean 4 setup guide by creating a new text file using "File > New Text File" (`Ctrl+N` / `Cmd+N`), clicking on the ∀-symbol in the top right and selecting "Documentation… > Docs: Show Setup Guide".
+1. Open the Lean 4 setup guide by creating a new text file using "File > New Text File" (`Ctrl+N`), clicking on the ∀-symbol in the top right and selecting "Documentation… > Setup: Show Setup Guide".
 
-   ![show setup guide](images/show-setup-guide.png)
+    ![show setup guide](images/show-setup-guide.png)
 
-1. Follow the Lean 4 setup guide. It will:
+1. Follow the Lean 4 setup guide. It will walk you through learning resources for Lean 4, teach you how to set up Lean's dependencies on your platform, install Lean 4 for you at the click of a button and help you set up your first project.
 
-   - walk you through learning resources for Lean,
-   - teach you how to set up Lean's dependencies on your platform,
-   - install Lean 4 for you at the click of a button,
-   - help you set up your first project.
-
-   ![setup guide](images/setup_guide.png)
+    ![setup guide](images/setup_guide.png)

doc/setup.md

@@ -6,7 +6,6 @@ Platforms built & tested by our CI, available as binary releases via elan (see b
 
 * x86-64 Linux with glibc 2.27+
 * x86-64 macOS 10.15+
-* aarch64 (Apple Silicon) macOS 10.15+
 * x86-64 Windows 10+
 
 ### Tier 2
@@ -17,6 +16,7 @@ Releases may be silently broken due to the lack of automated testing.
 Issue reports and fixes are welcome.
 
 * aarch64 Linux with glibc 2.27+
+* aarch64 (Apple Silicon) macOS
 * x86 (32-bit) Linux
 * Emscripten Web Assembly
 

doc/syntax_highlight_in_latex.md

@@ -43,8 +43,7 @@ $ pdflatex test.tex
 
 ## Example with `minted`
 
-First [install Pygments](https://pygments.org/download/) (version 2.18 or newer).
-Then save the following sample LaTeX file `test.tex` into the same directory:
+First [install Pygments](https://pygments.org/download/). Then save [`lean4.py`](https://raw.githubusercontent.com/leanprover/lean4/master/doc/latex/lean4.py), which contains an version of the Lean highlighter updated for Lean 4, and the following sample LaTeX file `test.tex` into the same directory:
 
 ```latex
 \documentclass{article}
@@ -52,8 +51,9 @@ Then save the following sample LaTeX file `test.tex` into the same directory:
 % switch to a monospace font supporting more Unicode characters
 \setmonofont{FreeMono}
 \usepackage{minted}
-\newmintinline[lean]{lean4}{bgcolor=white}
-\newminted[leancode]{lean4}{fontsize=\footnotesize}
+% instruct minted to use our local theorem.py
+\newmintinline[lean]{lean4.py:Lean4Lexer -x}{bgcolor=white}
+\newminted[leancode]{lean4.py:Lean4Lexer -x}{fontsize=\footnotesize}
 \usemintedstyle{tango}  % a nice, colorful theme
 
 \begin{document}
@@ -67,6 +67,9 @@ theorem funext {f₁ f₂ : ∀ (x : α), β x} (h : ∀ x, f₁ x = f₂ x) : f
 \end{document}
 ```
 
+If your version of `minted` is v2.7 or newer, but before v3.0,
+you will additionally need to follow the workaround described in https://github.com/gpoore/minted/issues/360.
+
 You can then compile `test.tex` by executing the following command:
 
 ```bash
@@ -78,14 +81,11 @@ Some remarks:
  - either `xelatex` or `lualatex` is required to handle Unicode characters in the code.
  - `--shell-escape` is needed to allow `xelatex` to execute `pygmentize` in a shell.
  - If the chosen monospace font is missing some Unicode symbols, you can direct them to be displayed using a fallback font or other replacement LaTeX code.
-   ``` latex
-   \usepackage{newunicodechar}
-   \newfontfamily{\freeserif}{DejaVu Sans}
-   \newunicodechar{✝}{\freeserif{✝}}
-   \newunicodechar{𝓞}{\ensuremath{\mathcal{O}}}
-   ```
- - If you are using an old version of Pygments, you can copy 
-   [`lean.py`](https://raw.githubusercontent.com/pygments/pygments/master/pygments/lexers/lean.py) into your working directory,
-   and use `lean4.py:Lean4Lexer -x` instead of `lean4` above.
-   If your version of `minted` is v2.7 or newer, but before v3.0,
-   you will additionally need to follow the workaround described in https://github.com/gpoore/minted/issues/360.
+``` latex
+\usepackage{newunicodechar}
+\newfontfamily{\freeserif}{DejaVu Sans}
+\newunicodechar{✝}{\freeserif{✝}}
+\newunicodechar{𝓞}{\ensuremath{\mathcal{O}}}
+```
+ - minted has a "helpful" feature that draws red boxes around characters the chosen lexer doesn't recognize.
+ Since the Lean lexer cannot encompass all user-defined syntax, it is advisable to [work around](https://tex.stackexchange.com/a/343506/14563) this feature.

flake.lock

@@ -1,5 +1,21 @@
 {
   "nodes": {
+    "flake-compat": {
+      "flake": false,
+      "locked": {
+        "lastModified": 1673956053,
+        "narHash": "sha256-4gtG9iQuiKITOjNQQeQIpoIB6b16fm+504Ch3sNKLd8=",
+        "owner": "edolstra",
+        "repo": "flake-compat",
+        "rev": "35bb57c0c8d8b62bbfd284272c928ceb64ddbde9",
+        "type": "github"
+      },
+      "original": {
+        "owner": "edolstra",
+        "repo": "flake-compat",
+        "type": "github"
+      }
+    },
     "flake-utils": {
       "inputs": {
         "systems": "systems"
@@ -18,18 +34,71 @@
         "type": "github"
       }
     },
-    "nixpkgs": {
+    "lean4-mode": {
+      "flake": false,
       "locked": {
-        "lastModified": 1710889954,
-        "narHash": "sha256-Pr6F5Pmd7JnNEMHHmspZ0qVqIBVxyZ13ik1pJtm2QXk=",
+        "lastModified": 1709737301,
+        "narHash": "sha256-uT9JN2kLNKJK9c/S/WxLjiHmwijq49EgLb+gJUSDpz0=",
+        "owner": "leanprover",
+        "repo": "lean4-mode",
+        "rev": "f1f24c15134dee3754b82c9d9924866fe6bc6b9f",
+        "type": "github"
+      },
+      "original": {
+        "owner": "leanprover",
+        "repo": "lean4-mode",
+        "type": "github"
+      }
+    },
+    "libgit2": {
+      "flake": false,
+      "locked": {
+        "lastModified": 1697646580,
+        "narHash": "sha256-oX4Z3S9WtJlwvj0uH9HlYcWv+x1hqp8mhXl7HsLu2f0=",
+        "owner": "libgit2",
+        "repo": "libgit2",
+        "rev": "45fd9ed7ae1a9b74b957ef4f337bc3c8b3df01b5",
+        "type": "github"
+      },
+      "original": {
+        "owner": "libgit2",
+        "repo": "libgit2",
+        "type": "github"
+      }
+    },
+    "nix": {
+      "inputs": {
+        "flake-compat": "flake-compat",
+        "libgit2": "libgit2",
+        "nixpkgs": "nixpkgs",
+        "nixpkgs-regression": "nixpkgs-regression"
+      },
+      "locked": {
+        "lastModified": 1711102798,
+        "narHash": "sha256-CXOIJr8byjolqG7eqCLa+Wfi7rah62VmLoqSXENaZnw=",
         "owner": "NixOS",
-        "repo": "nixpkgs",
-        "rev": "7872526e9c5332274ea5932a0c3270d6e4724f3b",
+        "repo": "nix",
+        "rev": "a22328066416650471c3545b0b138669ea212ab4",
         "type": "github"
       },
       "original": {
         "owner": "NixOS",
-        "ref": "nixpkgs-unstable",
+        "repo": "nix",
+        "type": "github"
+      }
+    },
+    "nixpkgs": {
+      "locked": {
+        "lastModified": 1709083642,
+        "narHash": "sha256-7kkJQd4rZ+vFrzWu8sTRtta5D1kBG0LSRYAfhtmMlSo=",
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "b550fe4b4776908ac2a861124307045f8e717c8e",
+        "type": "github"
+      },
+      "original": {
+        "owner": "NixOS",
+        "ref": "release-23.11",
         "repo": "nixpkgs",
         "type": "github"
       }
@@ -51,10 +120,44 @@
         "type": "github"
       }
     },
+    "nixpkgs-regression": {
+      "locked": {
+        "lastModified": 1643052045,
+        "narHash": "sha256-uGJ0VXIhWKGXxkeNnq4TvV3CIOkUJ3PAoLZ3HMzNVMw=",
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "215d4d0fd80ca5163643b03a33fde804a29cc1e2",
+        "type": "github"
+      },
+      "original": {
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "215d4d0fd80ca5163643b03a33fde804a29cc1e2",
+        "type": "github"
+      }
+    },
+    "nixpkgs_2": {
+      "locked": {
+        "lastModified": 1710889954,
+        "narHash": "sha256-Pr6F5Pmd7JnNEMHHmspZ0qVqIBVxyZ13ik1pJtm2QXk=",
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "7872526e9c5332274ea5932a0c3270d6e4724f3b",
+        "type": "github"
+      },
+      "original": {
+        "owner": "NixOS",
+        "ref": "nixpkgs-unstable",
+        "repo": "nixpkgs",
+        "type": "github"
+      }
+    },
     "root": {
       "inputs": {
         "flake-utils": "flake-utils",
-        "nixpkgs": "nixpkgs",
+        "lean4-mode": "lean4-mode",
+        "nix": "nix",
+        "nixpkgs": "nixpkgs_2",
         "nixpkgs-old": "nixpkgs-old"
       }
     },

flake.nix

@@ -1,55 +1,96 @@
 {
-  description = "Lean development flake. Not intended for end users.";
+  description = "Lean interactive theorem prover";
 
   inputs.nixpkgs.url = "github:NixOS/nixpkgs/nixpkgs-unstable";
   # old nixpkgs used for portable release with older glibc (2.27)
   inputs.nixpkgs-old.url = "github:NixOS/nixpkgs/nixos-19.03";
   inputs.nixpkgs-old.flake = false;
   inputs.flake-utils.url = "github:numtide/flake-utils";
+  inputs.nix.url = "github:NixOS/nix";
+  inputs.lean4-mode = {
+    url = "github:leanprover/lean4-mode";
+    flake = false;
+  };
+  # used *only* by `stage0-from-input` below
+  #inputs.lean-stage0 = {
+  #  url = github:leanprover/lean4;
+  #  inputs.nixpkgs.follows = "nixpkgs";
+  #  inputs.flake-utils.follows = "flake-utils";
+  #  inputs.nix.follows = "nix";
+  #  inputs.lean4-mode.follows = "lean4-mode";
+  #};
 
-  outputs = { self, nixpkgs, nixpkgs-old, flake-utils, ... }@inputs: flake-utils.lib.eachDefaultSystem (system:
+  outputs = { self, nixpkgs, nixpkgs-old, flake-utils, nix, lean4-mode, ... }@inputs: flake-utils.lib.eachDefaultSystem (system:
     let
-      pkgs = import nixpkgs { inherit system; };
+      pkgs = import nixpkgs {
+        inherit system;
+        # for `vscode-with-extensions`
+        config.allowUnfree = true;
+      };
       # An old nixpkgs for creating releases with an old glibc
       pkgsDist-old = import nixpkgs-old { inherit system; };
       # An old nixpkgs for creating releases with an old glibc
       pkgsDist-old-aarch = import nixpkgs-old { localSystem.config = "aarch64-unknown-linux-gnu"; };
 
-      lean-packages = pkgs.callPackage (./nix/packages.nix) { src = ./.; };
+      lean-packages = pkgs.callPackage (./nix/packages.nix) { src = ./.; inherit nix lean4-mode; };
 
       devShellWithDist = pkgsDist: pkgs.mkShell.override {
-          stdenv = pkgs.overrideCC pkgs.stdenv lean-packages.llvmPackages.clang;
-        } ({
-          buildInputs = with pkgs; [
-            cmake gmp ccache
-            lean-packages.llvmPackages.llvm  # llvm-symbolizer for asan/lsan
-            gdb
-            # TODO: only add when proven to not affect the flakification
-            #pkgs.python3
-            tree  # for CI
-          ];
-          # https://github.com/NixOS/nixpkgs/issues/60919
-          hardeningDisable = [ "all" ];
-          # more convenient `ctest` output
-          CTEST_OUTPUT_ON_FAILURE = 1;
-        } // pkgs.lib.optionalAttrs pkgs.stdenv.isLinux {
-          GMP = pkgsDist.gmp.override { withStatic = true; };
-          GLIBC = pkgsDist.glibc;
-          GLIBC_DEV = pkgsDist.glibc.dev;
-          GCC_LIB = pkgsDist.gcc.cc.lib;
-          ZLIB = pkgsDist.zlib;
-          GDB = pkgsDist.gdb;
-        });
+	  stdenv = pkgs.overrideCC pkgs.stdenv lean-packages.llvmPackages.clang;
+	} ({
+	  buildInputs = with pkgs; [
+	    cmake gmp ccache
+	    lean-packages.llvmPackages.llvm  # llvm-symbolizer for asan/lsan
+	    # TODO: only add when proven to not affect the flakification
+	    #pkgs.python3
+	  ];
+	  # https://github.com/NixOS/nixpkgs/issues/60919
+	  hardeningDisable = [ "all" ];
+	  # more convenient `ctest` output
+	  CTEST_OUTPUT_ON_FAILURE = 1;
+	} // pkgs.lib.optionalAttrs pkgs.stdenv.isLinux {
+	  GMP = pkgsDist.gmp.override { withStatic = true; };
+	  GLIBC = pkgsDist.glibc;
+	  GLIBC_DEV = pkgsDist.glibc.dev;
+	  GCC_LIB = pkgsDist.gcc.cc.lib;
+	  ZLIB = pkgsDist.zlib;
+	  GDB = pkgsDist.gdb;
+	});
     in {
-      packages = {
-        # to be removed when Nix CI is not needed anymore
-        inherit (lean-packages) cacheRoots test update-stage0-commit ciShell;
-        deprecated = lean-packages;
+      packages = lean-packages // rec {
+        debug = lean-packages.override { debug = true; };
+        stage0debug = lean-packages.override { stage0debug = true; };
+        asan = lean-packages.override { extraCMakeFlags = [ "-DLEAN_EXTRA_CXX_FLAGS=-fsanitize=address" "-DLEANC_EXTRA_FLAGS=-fsanitize=address" "-DSMALL_ALLOCATOR=OFF" "-DSYMBOLIC=OFF" ]; };
+        asandebug = asan.override { debug = true; };
+        tsan = lean-packages.override {
+          extraCMakeFlags = [ "-DLEAN_EXTRA_CXX_FLAGS=-fsanitize=thread" "-DLEANC_EXTRA_FLAGS=-fsanitize=thread" "-DCOMPRESSED_OBJECT_HEADER=OFF" ];
+          stage0 = (lean-packages.override {
+            # Compressed headers currently trigger data race reports in tsan.
+            # Turn them off for stage 0 as well so stage 1 can read its own stdlib.
+            extraCMakeFlags = [ "-DCOMPRESSED_OBJECT_HEADER=OFF" ];
+          }).stage1;
+        };
+        tsandebug = tsan.override { debug = true; };
+        stage0-from-input = lean-packages.override {
+          stage0 = pkgs.writeShellScriptBin "lean" ''
+            exec ${inputs.lean-stage0.packages.${system}.lean}/bin/lean -Dinterpreter.prefer_native=false "$@"
+          '';
+        };
+        inherit self;
       };
+      defaultPackage = lean-packages.lean-all;
 
       # The default development shell for working on lean itself
       devShells.default = devShellWithDist pkgs;
       devShells.oldGlibc = devShellWithDist pkgsDist-old;
       devShells.oldGlibcAArch = devShellWithDist pkgsDist-old-aarch;
-    });
+
+      checks.lean = lean-packages.test;
+    }) // rec {
+      templates.pkg = {
+        path = ./nix/templates/pkg;
+        description = "A custom Lean package";
+      };
+
+      defaultTemplate = templates.pkg;
+    };
 }

nix/bootstrap.nix

@@ -2,7 +2,7 @@
   stdenv, lib, cmake, gmp, git, gnumake, bash, buildLeanPackage, writeShellScriptBin, runCommand, symlinkJoin, lndir, perl, gnused, darwin, llvmPackages, linkFarmFromDrvs,
   ... } @ args:
 with builtins;
-lib.warn "The Nix-based build is deprecated" rec {
+rec {
   inherit stdenv;
   sourceByRegex = p: rs: lib.sourceByRegex p (map (r: "(/src/)?${r}") rs);
   buildCMake = args: stdenv.mkDerivation ({
@@ -87,8 +87,7 @@ lib.warn "The Nix-based build is deprecated" rec {
         leanFlags = [ "-DwarningAsError=true" ];
       } // args);
       Init' = build { name = "Init"; deps = []; };
-      Std' = build { name = "Std"; deps = [ Init' ]; };
-      Lean' = build { name = "Lean"; deps = [ Std' ]; };
+      Lean' = build { name = "Lean"; deps = [ Init' ]; };
       attachSharedLib = sharedLib: pkg: pkg // {
         inherit sharedLib;
         mods = mapAttrs (_: m: m // { inherit sharedLib; propagatedLoadDynlibs = []; }) pkg.mods;
@@ -96,8 +95,7 @@ lib.warn "The Nix-based build is deprecated" rec {
     in (all: all // all.lean) rec {
       inherit (Lean) emacs-dev emacs-package vscode-dev vscode-package;
       Init = attachSharedLib leanshared Init';
-      Std = attachSharedLib leanshared Std' // { allExternalDeps = [ Init ]; };
-      Lean = attachSharedLib leanshared Lean' // { allExternalDeps = [ Std ]; };
+      Lean = attachSharedLib leanshared Lean' // { allExternalDeps = [ Init ]; };
       Lake = build {
         name = "Lake";
         src = src + "/src/lake";
@@ -111,24 +109,23 @@ lib.warn "The Nix-based build is deprecated" rec {
         linkFlags = lib.optional stdenv.isLinux "-rdynamic";
         src = src + "/src/lake";
       };
-      stdlib = [ Init Std Lean Lake ];
+      stdlib = [ Init Lean Lake ];
       modDepsFiles = symlinkJoin { name = "modDepsFiles"; paths = map (l: l.modDepsFile) (stdlib ++ [ Leanc ]); };
       depRoots = symlinkJoin { name = "depRoots"; paths = map (l: l.depRoots) stdlib; };
       iTree = symlinkJoin { name = "ileans"; paths = map (l: l.iTree) stdlib; };
       Leanc = build { name = "Leanc"; src = lean-bin-tools-unwrapped.leanc_src; deps = stdlib; roots = [ "Leanc" ]; };
-      stdlibLinkFlags = "${lib.concatMapStringsSep " " (l: "-L${l.staticLib}") stdlib} -L${leancpp}/lib/lean";
+      stdlibLinkFlags = "-L${Init.staticLib} -L${Lean.staticLib} -L${Lake.staticLib} -L${leancpp}/lib/lean";
       libInit_shared = runCommand "libInit_shared" { buildInputs = [ stdenv.cc ]; libName = "libInit_shared${stdenv.hostPlatform.extensions.sharedLibrary}"; } ''
         mkdir $out
-        touch empty.c
-        ${stdenv.cc}/bin/cc -shared -o $out/$libName empty.c
+        LEAN_CC=${stdenv.cc}/bin/cc ${lean-bin-tools-unwrapped}/bin/leanc -shared -Wl,-Bsymbolic \
+          -Wl,--whole-archive -lInit ${leancpp}/lib/libleanrt_initial-exec.a -Wl,--no-whole-archive -lstdc++ -lm ${stdlibLinkFlags} \
+          $(${llvmPackages.libllvm.dev}/bin/llvm-config --ldflags --libs) \
+          -o $out/$libName
       '';
       leanshared = runCommand "leanshared" { buildInputs = [ stdenv.cc ]; libName = "libleanshared${stdenv.hostPlatform.extensions.sharedLibrary}"; } ''
         mkdir $out
-        LEAN_CC=${stdenv.cc}/bin/cc ${lean-bin-tools-unwrapped}/bin/leanc -shared ${lib.optionalString stdenv.isLinux "-Wl,-Bsymbolic"} \
-          ${if stdenv.isDarwin
-            then "-Wl,-force_load,${Init.staticLib}/libInit.a -Wl,-force_load,${Std.staticLib}/libStd.a -Wl,-force_load,${Lean.staticLib}/libLean.a -Wl,-force_load,${leancpp}/lib/lean/libleancpp.a ${leancpp}/lib/libleanrt_initial-exec.a -lc++"
-            else "-Wl,--whole-archive -lInit -lStd -lLean -lleancpp ${leancpp}/lib/libleanrt_initial-exec.a -Wl,--no-whole-archive -lstdc++"} \
-          -lm ${stdlibLinkFlags} \
+        LEAN_CC=${stdenv.cc}/bin/cc ${lean-bin-tools-unwrapped}/bin/leanc -shared -Wl,-Bsymbolic \
+          ${libInit_shared}/* -Wl,--whole-archive -lLean -lleancpp -Wl,--no-whole-archive -lstdc++ -lm ${stdlibLinkFlags} \
           $(${llvmPackages.libllvm.dev}/bin/llvm-config --ldflags --libs) \
           -o $out/$libName
       '';
@@ -154,9 +151,11 @@ lib.warn "The Nix-based build is deprecated" rec {
         '';
         meta.mainProgram = "lean";
       };
-      cacheRoots = linkFarmFromDrvs "cacheRoots" ([
+      cacheRoots = linkFarmFromDrvs "cacheRoots" [
         stage0 lean leanc lean-all iTree modDepsFiles depRoots Leanc.src
-      ] ++ map (lib: lib.oTree) stdlib);
+        # .o files are not a runtime dependency on macOS because of lack of thin archives
+        Lean.oTree Lake.oTree
+      ];
       test = buildCMake {
         name = "lean-test-${desc}";
         realSrc = lib.sourceByRegex src [ "src.*" "tests.*" ];
@@ -179,9 +178,9 @@ lib.warn "The Nix-based build is deprecated" rec {
         '';
       };
       update-stage0 =
-        let cTree = symlinkJoin { name = "cs"; paths = map (lib: lib.cTree) stdlib; }; in
+        let cTree = symlinkJoin { name = "cs"; paths = [ Init.cTree Lean.cTree ]; }; in
         writeShellScriptBin "update-stage0" ''
-          CSRCS=${cTree} CP_C_PARAMS="--dereference --no-preserve=all" ${src + "/script/lib/update-stage0"}
+          CSRCS=${cTree} CP_C_PARAMS="--dereference --no-preserve=all" ${src + "/script/update-stage0"}
         '';
       update-stage0-commit = writeShellScriptBin "update-stage0-commit" ''
         set -euo pipefail

nix/buildLeanPackage.nix

@@ -1,11 +1,11 @@
 { lean, lean-leanDeps ? lean, lean-final ? lean, leanc,
-  stdenv, lib, coreutils, gnused, writeShellScriptBin, bash, substituteAll, symlinkJoin, linkFarmFromDrvs,
+  stdenv, lib, coreutils, gnused, writeShellScriptBin, bash, lean-emacs, lean-vscode, nix, substituteAll, symlinkJoin, linkFarmFromDrvs,
   runCommand, darwin, mkShell, ... }:
 let lean-final' = lean-final; in
 lib.makeOverridable (
 { name, src, fullSrc ? src, srcPrefix ? "", srcPath ? "$PWD/${srcPrefix}",
   # Lean dependencies. Each entry should be an output of buildLeanPackage.
-  deps ? [ lean.Init lean.Std lean.Lean ],
+  deps ? [ lean.Lean ],
   # Static library dependencies. Each derivation `static` should contain a static library in the directory `${static}`.
   staticLibDeps ? [],
   # Whether to wrap static library inputs in a -Wl,--start-group [...] -Wl,--end-group to ensure dependencies are resolved.
@@ -197,6 +197,19 @@ with builtins; let
              then map (m: m.module) header.imports
              else abort "errors while parsing imports of ${mod}:\n${lib.concatStringsSep "\n" header.errors}";
     in mkMod mod (map (dep: if modDepsMap ? ${dep} then modCandidates.${dep} else externalModMap.${dep}) deps)) modDepsMap;
+  makeEmacsWrapper = name: emacs: lean: writeShellScriptBin name ''
+    ${emacs} --eval "(progn (setq lean4-rootdir \"${lean}\"))" "$@"
+  '';
+  makeVSCodeWrapper = name: lean: writeShellScriptBin name ''
+    PATH=${lean}/bin:$PATH ${lean-vscode}/bin/code "$@"
+  '';
+  printPaths = deps: writeShellScriptBin "print-paths" ''
+    echo '${toJSON {
+      oleanPath = [(depRoot "print-paths" deps)];
+      srcPath = ["."] ++ map (dep: dep.src) allExternalDeps;
+      loadDynlibPaths = map pathOfSharedLib (loadDynlibsOfDeps deps);
+    }}'
+  '';
   expandGlob = g:
     if typeOf g == "string" then [g]
     else if g.glob == "one" then [g.mod]
@@ -211,8 +224,7 @@ with builtins; let
   allLinkFlags = lib.foldr (shared: acc: acc ++ [ "-L${shared}" "-l${shared.linkName or shared.name}" ]) linkFlags allNativeSharedLibs;
 
   objects   = mapAttrs (_: m: m.obj) mods';
-  bintools = if stdenv.isDarwin then darwin.cctools else stdenv.cc.bintools.bintools;
-  staticLib = runCommand "${name}-lib" { buildInputs = [ bintools ]; } ''
+  staticLib = runCommand "${name}-lib" { buildInputs = [ stdenv.cc.bintools.bintools ]; } ''
     mkdir -p $out
     ar Trcs $out/lib${libName}.a ${lib.concatStringsSep " " (map (drv: "${drv}/${drv.oPath}") (attrValues objects))};
   '';
@@ -237,11 +249,55 @@ in rec {
     ${if stdenv.isDarwin then "-Wl,-force_load,${staticLib}/lib${libName}.a" else "-Wl,--whole-archive ${staticLib}/lib${libName}.a -Wl,--no-whole-archive"} \
     ${lib.concatStringsSep " " (map (d: "${d.sharedLib}/*") deps)}'';
   executable = lib.makeOverridable ({ withSharedStdlib ? true }: let
-      objPaths = map (drv: "${drv}/${drv.oPath}") (attrValues objects) ++ lib.optional withSharedStdlib "${lean-final.leanshared}/*";
+      objPaths = map (drv: "${drv}/${drv.oPath}") (attrValues objects) ++ lib.optional withSharedStdlib "${lean-final.libInit_shared}/* ${lean-final.leanshared}/*";
     in runCommand executableName { buildInputs = [ stdenv.cc leanc ]; } ''
       mkdir -p $out/bin
       leanc ${staticLibLinkWrapper (lib.concatStringsSep " " (objPaths ++ map (d: "${d}/*.a") allStaticLibDeps))} \
         -o $out/bin/${executableName} \
         ${lib.concatStringsSep " " allLinkFlags}
     '') {};
+
+  lean-package = writeShellScriptBin "lean" ''
+    LEAN_PATH=${modRoot}:$LEAN_PATH LEAN_SRC_PATH=$LEAN_SRC_PATH:${src} exec ${lean-final}/bin/lean "$@"
+  '';
+  emacs-package = makeEmacsWrapper "emacs-package" lean-package;
+  vscode-package = makeVSCodeWrapper "vscode-package" lean-package;
+
+  link-ilean = writeShellScriptBin "link-ilean" ''
+    dest=''${1:-.}
+    mkdir -p $dest/build/lib
+    ln -sf ${iTree}/* $dest/build/lib
+  '';
+
+  makePrintPathsFor = deps: mods: printPaths deps // mapAttrs (_: mod: makePrintPathsFor (deps ++ [mod]) mods) mods;
+  print-paths = makePrintPathsFor [] (mods' // externalModMap);
+  # `lean` wrapper that dynamically runs Nix for the actual `lean` executable so the same editor can be
+  # used for multiple projects/after upgrading the `lean` input/for editing both stage 1 and the tests
+  lean-bin-dev = substituteAll {
+    name = "lean";
+    dir = "bin";
+    src = ./lean-dev.in;
+    isExecutable = true;
+    srcRoot = fullSrc;  # use root flake.nix in case of Lean repo
+    inherit bash nix srcTarget srcArgs;
+  };
+  lake-dev = substituteAll {
+    name = "lake";
+    dir = "bin";
+    src = ./lake-dev.in;
+    isExecutable = true;
+    srcRoot = fullSrc;  # use root flake.nix in case of Lean repo
+    inherit bash nix srcTarget srcArgs;
+  };
+  lean-dev = symlinkJoin { name = "lean-dev"; paths = [ lean-bin-dev lake-dev ]; };
+  emacs-dev = makeEmacsWrapper "emacs-dev" "${lean-emacs}/bin/emacs" lean-dev;
+  emacs-path-dev = makeEmacsWrapper "emacs-path-dev" "emacs" lean-dev;
+  vscode-dev = makeVSCodeWrapper "vscode-dev" lean-dev;
+
+  devShell = mkShell {
+    buildInputs = [ nix ];
+    shellHook = ''
+      export LEAN_SRC_PATH="${srcPath}"
+    '';
+  };
 })

nix/packages.nix

@@ -1,6 +1,9 @@
-{ src, pkgs, ... } @ args:
+{ src, pkgs, nix, ... } @ args:
 with pkgs;
 let
+  nix-pinned = writeShellScriptBin "nix" ''
+    ${nix.packages.${system}.default}/bin/nix --experimental-features 'nix-command flakes' --extra-substituters https://lean4.cachix.org/ --option warn-dirty false "$@"
+  '';
   # https://github.com/NixOS/nixpkgs/issues/130963
   llvmPackages = if stdenv.isDarwin then llvmPackages_11 else llvmPackages_15;
   cc = (ccacheWrapper.override rec {
@@ -39,9 +42,40 @@ let
     inherit (lean) stdenv;
     lean = lean.stage1;
     inherit (lean.stage1) leanc;
+    inherit lean-emacs lean-vscode;
+    nix = nix-pinned;
   }));
+  lean4-mode = emacsPackages.melpaBuild {
+    pname = "lean4-mode";
+    version = "1";
+    commit = "1";
+    src = args.lean4-mode;
+    packageRequires = with pkgs.emacsPackages.melpaPackages; [ dash f flycheck magit-section lsp-mode s ];
+    recipe = pkgs.writeText "recipe" ''
+      (lean4-mode
+       :repo "leanprover/lean4-mode"
+       :fetcher github
+       :files ("*.el" "data"))
+    '';
+  };
+  lean-emacs = emacsWithPackages [ lean4-mode ];
+  # updating might be nicer by building from source from a flake input, but this is good enough for now
+  vscode-lean4 = vscode-utils.extensionFromVscodeMarketplace {
+      name = "lean4";
+      publisher = "leanprover";
+      version = "0.0.63";
+      sha256 = "sha256-kjEex7L0F2P4pMdXi4NIZ1y59ywJVubqDqsoYagZNkI=";
+  };
+  lean-vscode = vscode-with-extensions.override {
+    vscodeExtensions = [ vscode-lean4 ];
+  };
 in {
-  inherit cc buildLeanPackage llvmPackages;
+  inherit cc lean4-mode buildLeanPackage llvmPackages vscode-lean4;
+  lean = lean.stage1;
+  stage0print-paths = lean.stage1.Lean.print-paths;
+  HEAD-as-stage0 = (lean.stage1.Lean.overrideArgs { srcTarget = "..#stage0-from-input.stage0"; srcArgs = "(--override-input lean-stage0 ..\?rev=$(git rev-parse HEAD) -- -Dinterpreter.prefer_native=false \"$@\")"; });
+  HEAD-as-stage1 = (lean.stage1.Lean.overrideArgs { srcTarget = "..\?rev=$(git rev-parse HEAD)#stage0"; });
+  nix = nix-pinned;
   nixpkgs = pkgs;
   ciShell = writeShellScriptBin "ciShell" ''
     set -o pipefail
@@ -49,4 +83,5 @@ in {
     # prefix lines with cumulative and individual execution time
     "$@" |& ts -i "(%.S)]" | ts -s "[%M:%S"
   '';
-} // lean.stage1
+  vscode = lean-vscode;
+} // lean.stage1.Lean // lean.stage1 // lean

releases_drafts/README.md

@@ -1,22 +0,0 @@
-Draft release notes
--------------------
-
-This folder contains drafts of release notes for inclusion in `RELEASES.md`.
-During the process to create a release candidate, we look through all the commits that make up the release
-to prepare the release notes, and in that process we take these drafts into account.
-
-Guidelines:
-- You should prefer adding release notes to commit messages over adding anything to this folder.
-  A release note should briefly explain the impact of a change from a user's point of view.
-  Please mark these parts out with words such as **release notes** and/or **breaking changes**.
-- It is not necessary to add anything to this folder. It is meant for larger features that span multiple PRs,
-  or for anything that would be helpful when preparing the release notes that might be missed
-  by someone reading through the change log.
-- If the PR that adds a feature simultaneously adds a draft release note, including the PR number is not required
-  since it can be obtained from the git history for the file.
-
-When release notes are prepared, all the draft release notes are deleted from this folder.
-For release candidates beyond the first one, you can either update `RELEASE.md` directly
-or continue to add drafts.
-
-When a release is finalized, we will copy the completed release notes from `RELEASE.md` to the `master` branch.

releases_drafts/mutualStructural.md

@@ -1,65 +0,0 @@
-* Structural recursion can now be explicitly requested using
-  ```
-  termination_by structural x
-  ```
-  in analogy to the existing `termination_by x` syntax that causes well-founded recursion to be used.
-  (#4542)
-
-* The `termination_by?` syntax no longer forces the use of well-founded recursion, and when structural
-  recursion is inferred, will print the result using the `termination_by` syntax.
-
-* Mutual structural recursion is supported now. This supports both mutual recursion over a non-mutual
-  data type, as well as recursion over mutual or nested data types:
-
-  ```lean
-  mutual
-  def Even : Nat → Prop
-    | 0 => True
-    | n+1 => Odd n
-
-  def Odd : Nat → Prop
-    | 0 => False
-    | n+1 => Even n
-  end
-
-  mutual
-  inductive A
-  | other : B → A
-  | empty
-  inductive B
-  | other : A → B
-  | empty
-  end
-
-  mutual
-  def A.size : A → Nat
-  | .other b => b.size + 1
-  | .empty => 0
-
-  def B.size : B → Nat
-  | .other a => a.size + 1
-  | .empty => 0
-  end
-
-  inductive Tree where | node : List Tree → Tree
-
-  mutual
-  def Tree.size : Tree → Nat
-  | node ts => Tree.list_size ts
-
-  def Tree.list_size : List Tree → Nat
-  | [] => 0
-  | t::ts => Tree.size t + Tree.list_size ts
-  end
-  ```
-
-  Functional induction principles are generated for these functions as well (`A.size.induct`, `A.size.mutual_induct`).
-
-  Nested structural recursion is still not supported.
-
-  PRs #4639, #4715, #4642, #4656, #4684, #4715, #4728, #4575, #4731, #4658, #4734, #4738, #4718,
-  #4733, #4787, #4788, #4789, #4807, #4772
-
-* A bugfix in the structural recursion code may in some cases break existing code, when a parameter
-  of the type of the recursive argument is bound behind indices of that type. This can usually be
-  fixed by reordering the parameters of the function (PR #4672)

script/collideProfiles.lean

@@ -1,28 +0,0 @@
-import Lean.Util.Profiler
-
-/-!
-
-Usage:
-```sh
-lean --run ./script/collideProfiles.lean **/*.lean.json ... > merged.json
-```
-
-Merges multiple `trace.profiler.output` profiles into a single one while deduplicating samples with
-the same stack. This is useful for building cumulative profiles of medium-to-large projects because
-Firefox Profiler cannot handle hundreds of tracks and the deduplication will also ensure that the
-profile is small enough for uploading.
-
-As ordering of samples is not meaningful after this transformation, only "Call Tree" and "Flame
-Graph" are useful for such profiles.
--/
-
-open Lean
-
-def main (args : List String) : IO Unit := do
-  let profiles ← args.toArray.mapM fun path => do
-    let json ← IO.FS.readFile ⟨path⟩
-    let profile ← IO.ofExcept $ Json.parse json
-    IO.ofExcept <| fromJson? profile
-  -- NOTE: `collide` should not be interpreted
-  let profile := Firefox.Profile.collide profiles
-  IO.println <| Json.compress <| toJson profile

script/issues_summary.sh

@@ -1,39 +0,0 @@
-#!/bin/bash
-
-# https://chat.openai.com/share/7469c7c3-aceb-4d80-aee5-62982e1f1538
-
-# Output CSV Header
-echo '"Issue URL","Title","Days Since Creation","Days Since Last Update","Total Reactions","Assignee","Labels"'
-
-# Get the current date in YYYY-MM-DD format
-today=$(date +%Y-%m-%d)
-
-# Fetch only open issues (excluding PRs and closed issues) from the repository 'leanprover/lean4'
-issues=$(gh api repos/leanprover/lean4/issues --paginate --jq '.[] | select(.pull_request == null and .state == "open") | {url: .html_url, title: .title, created_at: (.created_at | split("T")[0]), updated_at: (.updated_at | split("T")[0]), number: .number, assignee: (.assignee.login // ""), labels: [.labels[].name] | join(",")}')
-
-# Process each JSON object
-echo "$issues" | while IFS= read -r issue; do
-    # Extract fields from JSON
-    url=$(echo "$issue" | jq -r '.url')
-    title=$(echo "$issue" | jq -r '.title')
-    created_at=$(echo "$issue" | jq -r '.created_at')
-    updated_at=$(echo "$issue" | jq -r '.updated_at')
-    issue_number=$(echo "$issue" | jq -r '.number')
-    assignee=$(echo "$issue" | jq -r '.assignee')
-    labels=$(echo "$issue" | jq -r '.labels')
-
-    # Calculate days since creation and update using macOS compatible date calculation
-    days_since_created=$(( ($(date -jf "%Y-%m-%d" "$today" +%s) - $(date -jf "%Y-%m-%d" "$created_at" +%s)) / 86400 ))
-    days_since_updated=$(( ($(date -jf "%Y-%m-%d" "$today" +%s) - $(date -jf "%Y-%m-%d" "$updated_at" +%s)) / 86400 ))
-
-    # Fetch the total number of reactions for each issue
-    reaction_data=$(gh api repos/leanprover/lean4/issues/$issue_number/reactions --paginate --jq 'length' 2>&1)
-    if [[ $reaction_data == *"Not Found"* ]]; then
-        total_reactions="Error fetching reactions"
-    else
-        total_reactions=$reaction_data
-    fi
-
-    # Format output as CSV by escaping quotes and delimiting with commas
-    echo "\"$url\",\"${title//\"/\"\"}\",\"$days_since_created\",\"$days_since_updated\",\"$total_reactions\",\"$assignee\",\"$labels\""
-done

script/lib/README.md

@@ -1,2 +0,0 @@
-This directory contains various scripts that are *not* meant to be called
-directly, but through other scripts or makefiles.

script/lib/rebase-editor.sh

@@ -1,19 +0,0 @@
-#!/usr/bin/env bash
-
-
-# Script internal to `./script/rebase-stage0.sh`
-
-# Determine OS type for sed in-place editing
-SED_CMD=("sed" "-i")
-if [[ "$OSTYPE" == "darwin"* ]]
-then
-    # macOS requires an empty string argument with -i for in-place editing
-    SED_CMD=("sed" "-i" "")
-fi
-
-if [ "$STAGE0_WITH_NIX" = true ]
-then
-  "${SED_CMD[@]}" '/chore: update stage0/ s,.*,x nix run .#update-stage0-commit,' "$1"
-else
-  "${SED_CMD[@]}" '/chore: update stage0/ s,.*,x make -j32 -C build/release update-stage0 \&\& git commit -m "chore: update stage0",' "$1"
-fi

script/lib/update-stage0

@@ -1,33 +0,0 @@
-#!/usr/bin/env bash
-set -euo pipefail
-
-rm -r stage0 || true
-# don't copy untracked files
-# `:!` is git glob flavor for exclude patterns
-for f in $(git ls-files src ':!:src/lake/*' ':!:src/Leanc.lean'); do
-    if [[ $f == *.lean ]]; then
-        f=${f#src/}
-        f=${f%.lean}.c
-        mkdir -p $(dirname stage0/stdlib/$f)
-        cp ${CP_C_PARAMS:-} $CSRCS/$f stage0/stdlib/$f
-    else
-        mkdir -p $(dirname stage0/$f)
-        cp $f stage0/$f
-    fi
-done
-
-# special handling for Lake files due to its nested directory
-# copy the README to ensure the `stage0/src/lake` directory is comitted
-for f in $(git ls-files 'src/lake/Lake/*' src/lake/Lake.lean src/lake/README.md ':!:src/lakefile.toml'); do
-    if [[ $f == *.lean ]]; then
-        f=${f#src/lake}
-        f=${f%.lean}.c
-        mkdir -p $(dirname stage0/stdlib/$f)
-        cp ${CP_C_PARAMS:-} $CSRCS/$f stage0/stdlib/$f
-    else
-        mkdir -p $(dirname stage0/$f)
-        cp $f stage0/$f
-    fi
-done
-
-git add stage0

script/rebase-stage0.sh

@@ -1,24 +0,0 @@
-#!/usr/bin/env bash
-
-# This script rebases onto the given branch/commit, and updates
-# all `chore: update stage0` commits along the way.
-
-# Whether to use nix or make to update stage0
-if [ "$1" = "-nix" ]
-then
-   export STAGE0_WITH_NIX=true
-   shift
-fi
-
-# Check if an argument is provided
-if [ "$#" -eq 0 ]; then
-    echo "Usage: $0 [-nix] <options to git rebase -i>"
-    exit 1
-fi
-
-REPO_ROOT=$(git rev-parse --show-toplevel)
-
-# Run git rebase in interactive mode, but automatically edit the todo list
-# using the defined GIT_SEQUENCE_EDITOR command
-GIT_SEQUENCE_EDITOR="$REPO_ROOT/script/lib/rebase-editor.sh" git rebase -i "$@"
-

script/update-stage0

@@ -0,0 +1,18 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+rm -r stage0 || true
+# don't copy untracked files
+# `:!` is git glob flavor for exclude patterns
+for f in $(git ls-files src ':!:src/lake/*' ':!:src/Leanc.lean'); do
+    if [[ $f == *.lean ]]; then
+        f=${f#src/}
+        f=${f%.lean}.c
+        mkdir -p $(dirname stage0/stdlib/$f)
+        cp ${CP_C_PARAMS:-} $CSRCS/$f stage0/stdlib/$f
+    else
+        mkdir -p $(dirname stage0/$f)
+        cp $f stage0/$f
+    fi
+done
+git add stage0

src/CMakeLists.txt

@@ -1,6 +1,5 @@
 cmake_minimum_required(VERSION 3.10)
 cmake_policy(SET CMP0054 NEW)
-cmake_policy(SET CMP0110 NEW)
 if(NOT (${CMAKE_GENERATOR} MATCHES "Unix Makefiles"))
   message(FATAL_ERROR "The only supported CMake generator at the moment is 'Unix Makefiles'")
 endif()
@@ -10,7 +9,7 @@ endif()
 include(ExternalProject)
 project(LEAN CXX C)
 set(LEAN_VERSION_MAJOR 4)
-set(LEAN_VERSION_MINOR 11)
+set(LEAN_VERSION_MINOR 8)
 set(LEAN_VERSION_PATCH 0)
 set(LEAN_VERSION_IS_RELEASE 0)  # This number is 1 in the release revision, and 0 otherwise.
 set(LEAN_SPECIAL_VERSION_DESC "" CACHE STRING "Additional version description like 'nightly-2018-03-11'")
@@ -74,7 +73,6 @@ option(USE_GMP "USE_GMP" ON)
 
 # development-specific options
 option(CHECK_OLEAN_VERSION "Only load .olean files compiled with the current version of Lean" OFF)
-option(USE_LAKE "Use Lake instead of lean.mk for building core libs from language server" OFF)
 
 set(LEAN_EXTRA_MAKE_OPTS  ""                           CACHE STRING "extra options to lean --make")
 set(LEANC_CC              ${CMAKE_C_COMPILER}          CACHE STRING "C compiler to use in `leanc`")
@@ -301,11 +299,11 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Darwin")
     cmake_path(GET ZLIB_LIBRARY PARENT_PATH ZLIB_LIBRARY_PARENT_PATH)
     string(APPEND LEANSHARED_LINKER_FLAGS " -L ${ZLIB_LIBRARY_PARENT_PATH}")
   endif()
-  string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " -lleancpp -lInit -lStd -lLean -lleanrt")
+  string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " -lleancpp -lInit -lLean -lleanrt")
 elseif(${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
-  string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " -lleancpp -lInit -lStd -lLean -lnodefs.js -lleanrt")
+  string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " -lleancpp -lInit -lLean -lnodefs.js -lleanrt")
 else()
-  string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " -Wl,--start-group -lleancpp -lLean -Wl,--end-group -lStd -Wl,--start-group -lInit -lleanrt -Wl,--end-group")
+  string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " -Wl,--start-group -lleancpp -lLean -Wl,--end-group -Wl,--start-group -lInit -lleanrt -Wl,--end-group")
 endif()
 
 set(LEAN_CXX_STDLIB "-lstdc++" CACHE STRING "C++ stdlib linker flags")
@@ -317,12 +315,6 @@ endif()
 string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " ${LEAN_CXX_STDLIB}")
 string(APPEND TOOLCHAIN_SHARED_LINKER_FLAGS " ${LEAN_CXX_STDLIB}")
 
-# in local builds, link executables and not just dynlibs against C++ stdlib as well,
-# which is required for e.g. asan
-if(NOT LEAN_STANDALONE)
-  string(APPEND CMAKE_EXE_LINKER_FLAGS " ${LEAN_CXX_STDLIB}")
-endif()
-
 # flags for user binaries = flags for toolchain binaries + Lake
 string(APPEND LEANC_STATIC_LINKER_FLAGS " ${TOOLCHAIN_STATIC_LINKER_FLAGS} -lLake")
 
@@ -511,15 +503,15 @@ file(RELATIVE_PATH LIB ${LEAN_SOURCE_DIR} ${CMAKE_BINARY_DIR}/lib)
 
 # set up libInit_shared only on Windows; see also stdlib.make.in
 if(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
-  set(INIT_SHARED_LINKER_FLAGS "-Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libInit.a.export ${CMAKE_BINARY_DIR}/lib/temp/libStd.a.export ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a -Wl,--no-whole-archive -Wl,--out-implib,${CMAKE_BINARY_DIR}/lib/lean/libInit_shared.dll.a")
+  set(INIT_SHARED_LINKER_FLAGS "-Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libInit.a.export ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a -Wl,--no-whole-archive -Wl,--out-implib,${CMAKE_BINARY_DIR}/lib/lean/libInit_shared.dll.a")
 endif()
 
 if(${CMAKE_SYSTEM_NAME} MATCHES "Darwin")
-  set(LEANSHARED_LINKER_FLAGS "-Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libInit.a -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libStd.a -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libLean.a -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libleancpp.a ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a ${LEANSHARED_LINKER_FLAGS}")
+  set(LEANSHARED_LINKER_FLAGS "-Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libInit.a -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libLean.a -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libleancpp.a ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a ${LEANSHARED_LINKER_FLAGS}")
 elseif(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
   set(LEANSHARED_LINKER_FLAGS "-Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libLean.a.export -lleancpp -Wl,--no-whole-archive -lInit_shared -Wl,--out-implib,${CMAKE_BINARY_DIR}/lib/lean/libleanshared.dll.a")
 else()
-  set(LEANSHARED_LINKER_FLAGS "-Wl,--whole-archive -lInit -lStd -lLean -lleancpp -Wl,--no-whole-archive ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a ${LEANSHARED_LINKER_FLAGS}")
+  set(LEANSHARED_LINKER_FLAGS "-Wl,--whole-archive -lInit -lLean -lleancpp -Wl,--no-whole-archive ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a ${LEANSHARED_LINKER_FLAGS}")
 endif()
 
 if (${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
@@ -541,7 +533,7 @@ add_custom_target(make_stdlib ALL
   # The actual rule is in a separate makefile because we want to prefix it with '+' to use the Make job server
   # for a parallelized nested build, but CMake doesn't let us do that.
   # We use `lean` from the previous stage, but `leanc`, headers, etc. from the current stage
-  COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make Init Std Lean
+  COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make Init Lean
   VERBATIM)
 
 # if we have LLVM enabled, then build `lean.h.bc` which has the LLVM bitcode
@@ -579,7 +571,11 @@ else()
   string(APPEND CMAKE_EXE_LINKER_FLAGS " -lInit_shared -lleanshared")
 endif()
 
-if(NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
+if(${STAGE} GREATER 0 AND NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
+  if(NOT EXISTS ${LEAN_SOURCE_DIR}/lake/Lake.lean)
+    message(FATAL_ERROR "src/lake does not exist. Please check out the Lake submodule using `git submodule update --init src/lake`.")
+  endif()
+
   add_custom_target(lake ALL
     WORKING_DIRECTORY ${LEAN_SOURCE_DIR}
     DEPENDS leanshared
@@ -589,7 +585,7 @@ endif()
 
 if(PREV_STAGE)
   add_custom_target(update-stage0
-    COMMAND bash -c 'CSRCS=${CMAKE_BINARY_DIR}/lib/temp script/lib/update-stage0'
+    COMMAND bash -c 'CSRCS=${CMAKE_BINARY_DIR}/lib/temp script/update-stage0'
     DEPENDS make_stdlib
     WORKING_DIRECTORY "${LEAN_SOURCE_DIR}/..")
 
@@ -656,9 +652,3 @@ endif()
 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 ${CMAKE_BINARY_DIR}/stdlib.make)
-
-if(USE_LAKE AND STAGE EQUAL 1)
-  configure_file(${LEAN_SOURCE_DIR}/lakefile.toml.in ${LEAN_SOURCE_DIR}/lakefile.toml)
-  configure_file(${LEAN_SOURCE_DIR}/lakefile.toml.in ${LEAN_SOURCE_DIR}/../tests/lakefile.toml)
-  configure_file(${LEAN_SOURCE_DIR}/lakefile.toml.in ${LEAN_SOURCE_DIR}/../lakefile.toml)
-endif()

src/Init.lean

@@ -34,4 +34,3 @@ import Init.BinderPredicates
 import Init.Ext
 import Init.Omega
 import Init.MacroTrace
-import Init.Grind

src/Init/ByCases.lean

@@ -63,12 +63,3 @@ theorem ite_some_none_eq_none [Decidable P] :
 @[simp] theorem ite_some_none_eq_some [Decidable P] :
     (if P then some x else none) = some y ↔ P ∧ x = y := by
   split <;> simp_all
-
--- This is not marked as `simp` as it is already handled by `dite_eq_right_iff`.
-theorem dite_some_none_eq_none [Decidable P] {x : P → α} :
-    (if h : P then some (x h) else none) = none ↔ ¬P := by
-  simp
-
-@[simp] theorem dite_some_none_eq_some [Decidable P] {x : P → α} {y : α} :
-    (if h : P then some (x h) else none) = some y ↔ ∃ h : P, x h = y := by
-  by_cases h : P <;> simp [h]

src/Init/Classical.lean

@@ -15,13 +15,6 @@ namespace Classical
 noncomputable def indefiniteDescription {α : Sort u} (p : α → Prop) (h : ∃ x, p x) : {x // p x} :=
   choice <| let ⟨x, px⟩ := h; ⟨⟨x, px⟩⟩
 
-/--
-Given that there exists an element satisfying `p`, returns one such element.
-
-This is a straightforward consequence of, and equivalent to, `Classical.choice`.
-
-See also `choose_spec`, which asserts that the returned value has property `p`.
--/
 noncomputable def choose {α : Sort u} {p : α → Prop} (h : ∃ x, p x) : α :=
   (indefiniteDescription p h).val
 

src/Init/Control/Basic.lean

@@ -20,29 +20,8 @@ def Functor.discard {f : Type u → Type v} {α : Type u} [Functor f] (x : f α)
 
 export Functor (discard)
 
-/--
-An `Alternative` functor is an `Applicative` functor that can "fail" or be "empty"
-and a binary operation `<|>` that “collects values” or finds the “left-most success”.
-
-Important instances include
-* `Option`, where `failure := none` and `<|>` returns the left-most `some`.
-* Parser combinators typically provide an `Applicative` instance for error-handling and
-  backtracking.
-  
-Error recovery and state can interact subtly. For example, the implementation of `Alternative` for `OptionT (StateT σ Id)` keeps modifications made to the state while recovering from failure, while `StateT σ (OptionT Id)` discards them.
--/
--- NB: List instance is in mathlib. Once upstreamed, add
--- * `List`, where `failure` is the empty list and `<|>` concatenates.
 class Alternative (f : Type u → Type v) extends Applicative f : Type (max (u+1) v) where
-  /--
-  Produces an empty collection or recoverable failure.  The `<|>` operator collects values or recovers
-  from failures. See `Alternative` for more details.
-  -/
   failure : {α : Type u} → f α
-  /--
-  Depending on the `Alternative` instance, collects values or recovers from `failure`s by
-  returning the leftmost success. Can be written using the `<|>` operator syntax.
-  -/
   orElse  : {α : Type u} → f α → (Unit → f α) → f α
 
 instance (f : Type u → Type v) (α : Type u) [Alternative f] : OrElse (f α) := ⟨Alternative.orElse⟩
@@ -51,15 +30,9 @@ variable {f : Type u → Type v} [Alternative f] {α : Type u}
 
 export Alternative (failure)
 
-/--
-If the proposition `p` is true, does nothing, else fails (using `failure`).
--/
 @[always_inline, inline] def guard {f : Type → Type v} [Alternative f] (p : Prop) [Decidable p] : f Unit :=
   if p then pure () else failure
 
-/--
-Returns `some x` if `f` succeeds with value `x`, else returns `none`.
--/
 @[always_inline, inline] def optional (x : f α) : f (Option α) :=
   some <$> x <|> pure none
 

src/Init/Control/Except.lean

@@ -131,7 +131,7 @@ protected def adapt {ε' α : Type u} (f : ε → ε') : ExceptT ε m α → Exc
 end ExceptT
 
 @[always_inline]
-instance (m : Type u → Type v) (ε₁ : Type u) (ε₂ : Type u) [MonadExceptOf ε₁ m] : MonadExceptOf ε₁ (ExceptT ε₂ m) where
+instance (m : Type u → Type v) (ε₁ : Type u) (ε₂ : Type u) [Monad m] [MonadExceptOf ε₁ m] : MonadExceptOf ε₁ (ExceptT ε₂ m) where
   throw e := ExceptT.mk <| throwThe ε₁ e
   tryCatch x handle := ExceptT.mk <| tryCatchThe ε₁ x handle
 

src/Init/Control/Lawful/Basic.lean

@@ -9,18 +9,9 @@ import Init.Meta
 
 open Function
 
-@[simp] theorem monadLift_self {m : Type u → Type v} (x : m α) : monadLift x = x :=
+@[simp] theorem monadLift_self [Monad m] (x : m α) : monadLift x = x :=
   rfl
 
-/--
-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
   map_const          : (Functor.mapConst : α → f β → f α) = Functor.map ∘ const β
   id_map   (x : f α) : id <$> x = x
@@ -33,16 +24,6 @@ attribute [simp] id_map
 @[simp] theorem id_map' [Functor m] [LawfulFunctor m] (x : m α) : (fun a => a) <$> x = x :=
   id_map x
 
-/--
-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] extends LawfulFunctor f : Prop where
   seqLeft_eq  (x : f α) (y : f β)     : x <* y = const β <$> x <*> y
   seqRight_eq (x : f α) (y : f β)     : x *> y = const α id <$> x <*> y
@@ -61,18 +42,6 @@ attribute [simp] map_pure seq_pure
 @[simp] theorem pure_id_seq [Applicative f] [LawfulApplicative f] (x : f α) : pure id <*> x = x := by
   simp [pure_seq]
 
-/--
-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 containing useful defaults for many fields.
--/
 class LawfulMonad (m : Type u → Type v) [Monad m] extends LawfulApplicative m : Prop where
   bind_pure_comp (f : α → β) (x : m α) : x >>= (fun a => pure (f a)) = f <$> x
   bind_map       {α β : Type u} (f : m (α → β)) (x : m α) : f >>= (. <$> x) = f <*> x

src/Init/Control/Lawful/Instances.lean

@@ -14,7 +14,7 @@ open Function
 
 namespace ExceptT
 
-theorem ext {x y : ExceptT ε m α} (h : x.run = y.run) : x = y := by
+theorem ext [Monad m] {x y : ExceptT ε m α} (h : x.run = y.run) : x = y := by
   simp [run] at h
   assumption
 
@@ -50,7 +50,7 @@ theorem run_bind [Monad m] (x : ExceptT ε m α)
 protected theorem seq_eq {α β ε : Type u} [Monad m] (mf : ExceptT ε m (α → β)) (x : ExceptT ε m α) : mf <*> x = mf >>= fun f => f <$> x :=
   rfl
 
-protected theorem bind_pure_comp [Monad m] (f : α → β) (x : ExceptT ε m α) : x >>= pure ∘ f = f <$> x := by
+protected theorem bind_pure_comp [Monad m] [LawfulMonad m] (f : α → β) (x : ExceptT ε m α) : x >>= pure ∘ f = f <$> x := by
   intros; rfl
 
 protected theorem seqLeft_eq {α β ε : Type u} {m : Type u → Type v} [Monad m] [LawfulMonad m] (x : ExceptT ε m α) (y : ExceptT ε m β) : x <* y = const β <$> x <*> y := by
@@ -188,23 +188,23 @@ theorem ext {x y : StateT σ m α} (h : ∀ s, x.run s = y.run s) : x = y :=
 
 @[simp] theorem run_lift {α σ : Type u} [Monad m] (x : m α) (s : σ) : (StateT.lift x : StateT σ m α).run s = x >>= fun a => pure (a, s) := rfl
 
-theorem run_bind_lift {α σ : Type u} [Monad m] [LawfulMonad m] (x : m α) (f : α → StateT σ m β) (s : σ) : (StateT.lift x >>= f).run s = x >>= fun a => (f a).run s := by
+@[simp] theorem run_bind_lift {α σ : Type u} [Monad m] [LawfulMonad m] (x : m α) (f : α → StateT σ m β) (s : σ) : (StateT.lift x >>= f).run s = x >>= fun a => (f a).run s := by
   simp [StateT.lift, StateT.run, bind, StateT.bind]
 
 @[simp] theorem run_monadLift {α σ : Type u} [Monad m] [MonadLiftT n m] (x : n α) (s : σ) : (monadLift x : StateT σ m α).run s = (monadLift x : m α) >>= fun a => pure (a, s) := rfl
 
-@[simp] theorem run_monadMap [MonadFunctor n m] (f : {β : Type u} → n β → n β) (x : StateT σ m α) (s : σ) :
-    (monadMap @f x : StateT σ m α).run s = monadMap @f (x.run s) := rfl
+@[simp] theorem run_monadMap [Monad m] [MonadFunctor n m] (f : {β : Type u} → n β → n β) (x : StateT σ m α) (s : σ)
+    : (monadMap @f x : StateT σ m α).run s = monadMap @f (x.run s) := rfl
 
 @[simp] theorem run_seq {α β σ : Type u} [Monad m] [LawfulMonad m] (f : StateT σ m (α → β)) (x : StateT σ m α) (s : σ) : (f <*> x).run s = (f.run s >>= fun fs => (fun (p : α × σ) => (fs.1 p.1, p.2)) <$> x.run fs.2) := by
   show (f >>= fun g => g <$> x).run s = _
   simp
 
-@[simp] theorem run_seqRight [Monad m] (x : StateT σ m α) (y : StateT σ m β) (s : σ) : (x *> y).run s = (x.run s >>= fun p => y.run p.2) := by
+@[simp] theorem run_seqRight [Monad m] [LawfulMonad m] (x : StateT σ m α) (y : StateT σ m β) (s : σ) : (x *> y).run s = (x.run s >>= fun p => y.run p.2) := by
   show (x >>= fun _ => y).run s = _
   simp
 
-@[simp] theorem run_seqLeft {α β σ : Type u} [Monad m] (x : StateT σ m α) (y : StateT σ m β) (s : σ) : (x <* y).run s = (x.run s >>= fun p => y.run p.2 >>= fun p' => pure (p.1, p'.2)) := by
+@[simp] theorem run_seqLeft {α β σ : Type u} [Monad m] [LawfulMonad m] (x : StateT σ m α) (y : StateT σ m β) (s : σ) : (x <* y).run s = (x.run s >>= fun p => y.run p.2 >>= fun p' => pure (p.1, p'.2)) := by
   show (x >>= fun a => y >>= fun _ => pure a).run s = _
   simp
 
@@ -235,13 +235,13 @@ end StateT
 
 instance : LawfulMonad (EStateM ε σ) := .mk'
   (id_map := fun x => funext <| fun s => by
-    dsimp only [EStateM.instMonad, EStateM.map]
+    dsimp only [EStateM.instMonadEStateM, EStateM.map]
     match x s with
     | .ok _ _ => rfl
     | .error _ _ => rfl)
   (pure_bind := fun _ _ => rfl)
   (bind_assoc := fun x _ _ => funext <| fun s => by
-    dsimp only [EStateM.instMonad, EStateM.bind]
+    dsimp only [EStateM.instMonadEStateM, EStateM.bind]
     match x s with
     | .ok _ _ => rfl
     | .error _ _ => rfl)

src/Init/Control/Option.lean

@@ -10,7 +10,7 @@ import Init.Control.Except
 
 universe u v
 
-instance : ToBool (Option α) := ⟨Option.isSome⟩
+instance : ToBool (Option α) := ⟨Option.toBool⟩
 
 def OptionT (m : Type u → Type v) (α : Type u) : Type v :=
   m (Option α)
@@ -67,7 +67,7 @@ instance : MonadExceptOf Unit (OptionT m) where
   throw    := fun _ => OptionT.fail
   tryCatch := OptionT.tryCatch
 
-instance (ε : Type u) [MonadExceptOf ε m] : MonadExceptOf ε (OptionT m) where
+instance (ε : Type u) [Monad m] [MonadExceptOf ε m] : MonadExceptOf ε (OptionT m) where
   throw e           := OptionT.mk <| throwThe ε e
   tryCatch x handle := OptionT.mk <| tryCatchThe ε x handle
 

src/Init/Control/Reader.lean

@@ -32,7 +32,7 @@ instance : MonadControl m (ReaderT ρ m) where
   restoreM x _ := x
 
 @[always_inline]
-instance ReaderT.tryFinally [MonadFinally m] : MonadFinally (ReaderT ρ m) where
+instance ReaderT.tryFinally [MonadFinally m] [Monad m] : MonadFinally (ReaderT ρ m) where
   tryFinally' x h ctx := tryFinally' (x ctx) (fun a? => h a? ctx)
 
 @[reducible] def ReaderM (ρ : Type u) := ReaderT ρ Id

src/Init/Control/State.lean

@@ -87,7 +87,7 @@ protected def lift {α : Type u} (t : m α) : StateT σ m α :=
 instance : MonadLift m (StateT σ m) := ⟨StateT.lift⟩
 
 @[always_inline]
-instance (σ m) : MonadFunctor m (StateT σ m) := ⟨fun f x s => f (x s)⟩
+instance (σ m) [Monad m] : MonadFunctor m (StateT σ m) := ⟨fun f x s => f (x s)⟩
 
 @[always_inline]
 instance (ε) [MonadExceptOf ε m] : MonadExceptOf ε (StateT σ m) := {

src/Init/Control/StateCps.lean

@@ -14,18 +14,16 @@ def StateCpsT (σ : Type u) (m : Type u → Type v) (α : Type u) := (δ : Type
 
 namespace StateCpsT
 
-variable {α σ : Type u} {m : Type u → Type v}
-
 @[always_inline, inline]
-def runK (x : StateCpsT σ m α) (s : σ) (k : α → σ → m β) : m β :=
+def runK {α σ : Type u} {m : Type u → Type v}  (x : StateCpsT σ m α) (s : σ) (k : α → σ → m β) : m β :=
   x _ s k
 
 @[always_inline, inline]
-def run [Monad m] (x : StateCpsT σ m α) (s : σ) : m (α × σ) :=
+def run {α σ : Type u} {m : Type u → Type v} [Monad m] (x : StateCpsT σ m α) (s : σ) : m (α × σ) :=
   runK x s (fun a s => pure (a, s))
 
 @[always_inline, inline]
-def run' [Monad m] (x : StateCpsT σ m α) (s : σ) : m α :=
+def run' {α σ : Type u} {m : Type u → Type v}  [Monad m] (x : StateCpsT σ m α) (s : σ) : m α :=
   runK x s (fun a _ => pure a)
 
 @[always_inline]
@@ -50,29 +48,29 @@ protected def lift [Monad m] (x : m α) : StateCpsT σ m α :=
 instance [Monad m] : MonadLift m (StateCpsT σ m) where
   monadLift := StateCpsT.lift
 
-@[simp] theorem runK_pure (a : α) (s : σ) (k : α → σ → m β) : (pure a : StateCpsT σ m α).runK s k = k a s := rfl
+@[simp] theorem runK_pure {m : Type u → Type v} (a : α) (s : σ) (k : α → σ → m β) : (pure a : StateCpsT σ m α).runK s k = k a s := rfl
 
-@[simp] theorem runK_get (s : σ) (k : σ → σ → m β) : (get : StateCpsT σ m σ).runK s k = k s s := rfl
+@[simp] theorem runK_get {m : Type u → Type v} (s : σ) (k : σ → σ → m β) : (get : StateCpsT σ m σ).runK s k = k s s := rfl
 
-@[simp] theorem runK_set (s s' : σ) (k : PUnit → σ → m β) : (set s' : StateCpsT σ m PUnit).runK s k = k ⟨⟩ s' := rfl
+@[simp] theorem runK_set {m : Type u → Type v} (s s' : σ) (k : PUnit → σ → m β) : (set s' : StateCpsT σ m PUnit).runK s k = k ⟨⟩ s' := rfl
 
-@[simp] theorem runK_modify (f : σ → σ) (s : σ) (k : PUnit → σ → m β) : (modify f : StateCpsT σ m PUnit).runK s k = k ⟨⟩ (f s) := rfl
+@[simp] theorem runK_modify {m : Type u → Type v} (f : σ → σ) (s : σ) (k : PUnit → σ → m β) : (modify f : StateCpsT σ m PUnit).runK s k = k ⟨⟩ (f s) := rfl
 
-@[simp] theorem runK_lift [Monad m] (x : m α) (s : σ) (k : α → σ → m β) : (StateCpsT.lift x : StateCpsT σ m α).runK s k = x >>= (k . s) := rfl
+@[simp] theorem runK_lift {α σ : Type u} [Monad m] (x : m α) (s : σ) (k : α → σ → m β) : (StateCpsT.lift x : StateCpsT σ m α).runK s k = x >>= (k . s) := rfl
 
-@[simp] theorem runK_monadLift [Monad m] [MonadLiftT n m] (x : n α) (s : σ) (k : α → σ → m β)
+@[simp] theorem runK_monadLift {σ : Type u} [Monad m] [MonadLiftT n m] (x : n α) (s : σ) (k : α → σ → m β)
     : (monadLift x : StateCpsT σ m α).runK s k = (monadLift x : m α) >>= (k . s) := rfl
 
-@[simp] theorem runK_bind_pure (a : α) (f : α → StateCpsT σ m β) (s : σ) (k : β → σ → m γ) : (pure a >>= f).runK s k = (f a).runK s k := rfl
+@[simp] theorem runK_bind_pure {α σ : Type u} [Monad m] (a : α) (f : α → StateCpsT σ m β) (s : σ) (k : β → σ → m γ) : (pure a >>= f).runK s k = (f a).runK s k := rfl
 
-@[simp] theorem runK_bind_lift [Monad m] (x : m α) (f : α → StateCpsT σ m β) (s : σ) (k : β → σ → m γ)
+@[simp] theorem runK_bind_lift {α σ : Type u} [Monad m] (x : m α) (f : α → StateCpsT σ m β) (s : σ) (k : β → σ → m γ)
     : (StateCpsT.lift x >>= f).runK s k = x >>= fun a => (f a).runK s k := rfl
 
-@[simp] theorem runK_bind_get (f : σ → StateCpsT σ m β) (s : σ) (k : β → σ → m γ) : (get >>= f).runK s k = (f s).runK s k := rfl
+@[simp] theorem runK_bind_get {σ : Type u} [Monad m] (f : σ → StateCpsT σ m β) (s : σ) (k : β → σ → m γ) : (get >>= f).runK s k = (f s).runK s k := rfl
 
-@[simp] theorem runK_bind_set (f : PUnit → StateCpsT σ m β) (s s' : σ) (k : β → σ → m γ) : (set s' >>= f).runK s k = (f ⟨⟩).runK s' k := rfl
+@[simp] theorem runK_bind_set {σ : Type u} [Monad m] (f : PUnit → StateCpsT σ m β) (s s' : σ) (k : β → σ → m γ) : (set s' >>= f).runK s k = (f ⟨⟩).runK s' k := rfl
 
-@[simp] theorem runK_bind_modify (f : σ → σ) (g : PUnit → StateCpsT σ m β) (s : σ) (k : β → σ → m γ) : (modify f >>= g).runK s k = (g ⟨⟩).runK (f s) k := rfl
+@[simp] theorem runK_bind_modify {σ : Type u} [Monad m] (f : σ → σ) (g : PUnit → StateCpsT σ m β) (s : σ) (k : β → σ → m γ) : (modify f >>= g).runK s k = (g ⟨⟩).runK (f s) k := rfl
 
 @[simp] theorem run_eq [Monad m] (x : StateCpsT σ m α) (s : σ) : x.run s = x.runK s (fun a s => pure (a, s)) := rfl
 

src/Init/Control/StateRef.lean

@@ -34,22 +34,22 @@ protected def lift (x : m α) : StateRefT' ω σ m α :=
 
 instance [Monad m] : Monad (StateRefT' ω σ m) := inferInstanceAs (Monad (ReaderT _ _))
 instance : MonadLift m (StateRefT' ω σ m) := ⟨StateRefT'.lift⟩
-instance (σ m) : MonadFunctor m (StateRefT' ω σ m) := inferInstanceAs (MonadFunctor m (ReaderT _ _))
+instance (σ m) [Monad m] : MonadFunctor m (StateRefT' ω σ m) := inferInstanceAs (MonadFunctor m (ReaderT _ _))
 instance [Alternative m] [Monad m] : Alternative (StateRefT' ω σ m) := inferInstanceAs (Alternative (ReaderT _ _))
 
 @[inline]
-protected def get [MonadLiftT (ST ω) m] : StateRefT' ω σ m σ :=
+protected def get [Monad m] [MonadLiftT (ST ω) m] : StateRefT' ω σ m σ :=
   fun ref => ref.get
 
 @[inline]
-protected def set [MonadLiftT (ST ω) m] (s : σ) : StateRefT' ω σ m PUnit :=
+protected def set [Monad m] [MonadLiftT (ST ω) m] (s : σ) : StateRefT' ω σ m PUnit :=
   fun ref => ref.set s
 
 @[inline]
-protected def modifyGet [MonadLiftT (ST ω) m] (f : σ → α × σ) : StateRefT' ω σ m α :=
+protected def modifyGet [Monad m] [MonadLiftT (ST ω) m] (f : σ → α × σ) : StateRefT' ω σ m α :=
   fun ref => ref.modifyGet f
 
-instance [MonadLiftT (ST ω) m] : MonadStateOf σ (StateRefT' ω σ m) where
+instance [MonadLiftT (ST ω) m] [Monad m] : MonadStateOf σ (StateRefT' ω σ m) where
   get       := StateRefT'.get
   set       := StateRefT'.set
   modifyGet := StateRefT'.modifyGet
@@ -64,5 +64,5 @@ end StateRefT'
 instance (ω σ : Type) (m : Type → Type) : MonadControl m (StateRefT' ω σ m) :=
   inferInstanceAs (MonadControl m (ReaderT _ _))
 
-instance {m : Type → Type} {ω σ : Type} [MonadFinally m] : MonadFinally (StateRefT' ω σ m) :=
+instance {m : Type → Type} {ω σ : Type} [MonadFinally m] [Monad m] : MonadFinally (StateRefT' ω σ m) :=
   inferInstanceAs (MonadFinally (ReaderT _ _))

src/Init/Core.lean

@@ -468,13 +468,11 @@ class Singleton (α : outParam <| Type u) (β : Type v) where
 export Singleton (singleton)
 
 /-- `insert x ∅ = {x}` -/
-class LawfulSingleton (α : Type u) (β : Type v) [EmptyCollection β] [Insert α β] [Singleton α β] :
+class IsLawfulSingleton (α : Type u) (β : Type v) [EmptyCollection β] [Insert α β] [Singleton α β] :
     Prop where
   /-- `insert x ∅ = {x}` -/
   insert_emptyc_eq (x : α) : (insert x ∅ : β) = singleton x
-export LawfulSingleton (insert_emptyc_eq)
-
-attribute [simp] insert_emptyc_eq
+export IsLawfulSingleton (insert_emptyc_eq)
 
 /-- Type class used to implement the notation `{ a ∈ c | p a }` -/
 class Sep (α : outParam <| Type u) (γ : Type v) where
@@ -644,7 +642,7 @@ instance : LawfulBEq String := inferInstance
 
 /-! # Logical connectives and equality -/
 
-@[inherit_doc True.intro] theorem trivial : True := ⟨⟩
+@[inherit_doc True.intro] def trivial : True := ⟨⟩
 
 theorem mt {a b : Prop} (h₁ : a → b) (h₂ : ¬b) : ¬a :=
   fun ha => h₂ (h₁ ha)
@@ -703,7 +701,7 @@ theorem Ne.elim (h : a ≠ b) : a = b → False := h
 
 theorem Ne.irrefl (h : a ≠ a) : False := h rfl
 
-@[symm] theorem Ne.symm (h : a ≠ b) : b ≠ a := fun h₁ => h (h₁.symm)
+theorem Ne.symm (h : a ≠ b) : b ≠ a := fun h₁ => h (h₁.symm)
 
 theorem ne_comm {α} {a b : α} : a ≠ b ↔ b ≠ a := ⟨Ne.symm, Ne.symm⟩
 
@@ -756,7 +754,7 @@ noncomputable def HEq.elim {α : Sort u} {a : α} {p : α → Sort v} {b : α} (
 theorem HEq.subst {p : (T : Sort u) → T → Prop} (h₁ : HEq a b) (h₂ : p α a) : p β b :=
   HEq.ndrecOn h₁ h₂
 
-@[symm] theorem HEq.symm (h : HEq a b) : HEq b a :=
+theorem HEq.symm (h : HEq a b) : HEq b a :=
   h.rec (HEq.refl a)
 
 theorem heq_of_eq (h : a = a') : HEq a a' :=
@@ -812,15 +810,15 @@ instance : Trans Iff Iff Iff where
 theorem Eq.comm {a b : α} : a = b ↔ b = a := Iff.intro Eq.symm Eq.symm
 theorem eq_comm {a b : α} : a = b ↔ b = a := Eq.comm
 
-@[symm] theorem Iff.symm (h : a ↔ b) : b ↔ a := Iff.intro h.mpr h.mp
+theorem Iff.symm (h : a ↔ b) : b ↔ a := Iff.intro h.mpr h.mp
 theorem Iff.comm: (a ↔ b) ↔ (b ↔ a) := Iff.intro Iff.symm Iff.symm
 theorem iff_comm : (a ↔ b) ↔ (b ↔ a) := Iff.comm
 
-@[symm] theorem And.symm : a ∧ b → b ∧ a := fun ⟨ha, hb⟩ => ⟨hb, ha⟩
+theorem And.symm : a ∧ b → b ∧ a := fun ⟨ha, hb⟩ => ⟨hb, ha⟩
 theorem And.comm : a ∧ b ↔ b ∧ a := Iff.intro And.symm And.symm
 theorem and_comm : a ∧ b ↔ b ∧ a := And.comm
 
-@[symm] theorem Or.symm : a ∨ b → b ∨ a := .rec .inr .inl
+theorem Or.symm : a ∨ b → b ∨ a := .rec .inr .inl
 theorem Or.comm : a ∨ b ↔ b ∨ a := Iff.intro Or.symm Or.symm
 theorem or_comm : a ∨ b ↔ b ∨ a := Or.comm
 
@@ -1091,23 +1089,19 @@ def InvImage {α : Sort u} {β : Sort v} (r : β → β → Prop) (f : α → β
   fun a₁ a₂ => r (f a₁) (f a₂)
 
 /--
-The transitive closure `TransGen r` of a relation `r` is the smallest relation which is
-transitive and contains `r`. `TransGen r a z` if and only if there exists a sequence
+The transitive closure `r⁺` of a relation `r` is the smallest relation which is
+transitive and contains `r`. `r⁺ a z` if and only if there exists a sequence
 `a r b r ... r z` of length at least 1 connecting `a` to `z`.
 -/
-inductive Relation.TransGen {α : Sort u} (r : α → α → Prop) : α → α → Prop
-  /-- If `r a b` then `TransGen r a b`. This is the base case of the transitive closure. -/
-  | single {a b} : r a b → TransGen r a b
+inductive TC {α : Sort u} (r : α → α → Prop) : α → α → Prop where
+  /-- If `r a b` then `r⁺ a b`. This is the base case of the transitive closure. -/
+  | base  : ∀ a b, r a b → TC r a b
   /-- The transitive closure is transitive. -/
-  | tail {a b c} : TransGen r a b → r b c → TransGen r a c
-
-/-- Deprecated synonym for `Relation.TransGen`. -/
-@[deprecated Relation.TransGen (since := "2024-07-16")] abbrev TC := @Relation.TransGen
+  | trans : ∀ a b c, TC r a b → TC r b c → TC r a c
 
 /-! # Subtype -/
 
 namespace Subtype
-
 theorem existsOfSubtype {α : Type u} {p : α → Prop} : { x // p x } → Exists (fun x => p x)
   | ⟨a, h⟩ => ⟨a, h⟩
 
@@ -1120,6 +1114,9 @@ theorem eta (a : {x // p x}) (h : p (val a)) : mk (val a) h = a := by
   cases a
   exact rfl
 
+instance {α : Type u} {p : α → Prop} {a : α} (h : p a) : Inhabited {x // p x} where
+  default := ⟨a, h⟩
+
 instance {α : Type u} {p : α → Prop} [DecidableEq α] : DecidableEq {x : α // p x} :=
   fun ⟨a, h₁⟩ ⟨b, h₂⟩ =>
     if h : a = b then isTrue (by subst h; exact rfl)
@@ -1179,7 +1176,7 @@ def Prod.lexLt [LT α] [LT β] (s : α × β) (t : α × β) : Prop :=
   s.1 < t.1 ∨ (s.1 = t.1 ∧ s.2 < t.2)
 
 instance Prod.lexLtDec
-    [LT α] [LT β] [DecidableEq α]
+    [LT α] [LT β] [DecidableEq α] [DecidableEq β]
     [(a b : α) → Decidable (a < b)] [(a b : β) → Decidable (a < b)]
     : (s t : α × β) → Decidable (Prod.lexLt s t) :=
   fun _ _ => inferInstanceAs (Decidable (_ ∨ _))
@@ -1197,20 +1194,11 @@ def Prod.map {α₁ : Type u₁} {α₂ : Type u₂} {β₁ : Type v₁} {β₂
     (f : α₁ → α₂) (g : β₁ → β₂) : α₁ × β₁ → α₂ × β₂
   | (a, b) => (f a, g b)
 
-@[simp] theorem Prod.map_apply (f : α → β) (g : γ → δ) (x) (y) :
-    Prod.map f g (x, y) = (f x, g y) := rfl
-@[simp] theorem Prod.map_fst (f : α → β) (g : γ → δ) (x) : (Prod.map f g x).1 = f x.1 := rfl
-@[simp] theorem Prod.map_snd (f : α → β) (g : γ → δ) (x) : (Prod.map f g x).2 = g x.2 := rfl
-
 /-! # Dependent products -/
 
-theorem Exists.of_psigma_prop {α : Sort u} {p : α → Prop} : (PSigma (fun x => p x)) → Exists (fun x => p x)
+theorem ex_of_PSigma {α : Type u} {p : α → Prop} : (PSigma (fun x => p x)) → Exists (fun x => p x)
   | ⟨x, hx⟩ => ⟨x, hx⟩
 
-@[deprecated Exists.of_psigma_prop (since := "2024-07-27")]
-theorem ex_of_PSigma {α : Type u} {p : α → Prop} : (PSigma (fun x => p x)) → Exists (fun x => p x) :=
-  Exists.of_psigma_prop
-
 protected theorem PSigma.eta {α : Sort u} {β : α → Sort v} {a₁ a₂ : α} {b₁ : β a₁} {b₂ : β a₂}
     (h₁ : a₁ = a₂) (h₂ : Eq.ndrec b₁ h₁ = b₂) : PSigma.mk a₁ b₁ = PSigma.mk a₂ b₂ := by
   subst h₁
@@ -1372,9 +1360,6 @@ theorem iff_false_right (ha : ¬a) : (b ↔ a) ↔ ¬b := Iff.comm.trans (iff_fa
 theorem of_iff_true    (h : a ↔ True) : a := h.mpr trivial
 theorem iff_true_intro (h : a) : a ↔ True := iff_of_true h trivial
 
-theorem eq_iff_true_of_subsingleton [Subsingleton α] (x y : α) : x = y ↔ True :=
-  iff_true_intro (Subsingleton.elim ..)
-
 theorem not_of_iff_false : (p ↔ False) → ¬p := Iff.mp
 theorem iff_false_intro (h : ¬a) : a ↔ False := iff_of_false h id
 
@@ -1552,7 +1537,7 @@ protected abbrev rec
     (q : Quot r) : motive q :=
   Eq.ndrecOn (Quot.liftIndepPr1 f h q) ((lift (Quot.indep f) (Quot.indepCoherent f h) q).2)
 
-@[inherit_doc Quot.rec, elab_as_elim] protected abbrev recOn
+@[inherit_doc Quot.rec] protected abbrev recOn
     (q : Quot r)
     (f : (a : α) → motive (Quot.mk r a))
     (h : (a b : α) → (p : r a b) → Eq.ndrec (f a) (sound p) = f b)
@@ -1563,7 +1548,7 @@ protected abbrev rec
 Dependent induction principle for a quotient, when the target type is a `Subsingleton`.
 In this case the quotient's side condition is trivial so any function can be lifted.
 -/
-@[elab_as_elim] protected abbrev recOnSubsingleton
+protected abbrev recOnSubsingleton
     [h : (a : α) → Subsingleton (motive (Quot.mk r a))]
     (q : Quot r)
     (f : (a : α) → motive (Quot.mk r a))
@@ -1880,7 +1865,7 @@ instance : Subsingleton (Squash α) where
 /--
 `Antisymm (·≤·)` says that `(·≤·)` is antisymmetric, that is, `a ≤ b → b ≤ a → a = b`.
 -/
-class Antisymm {α : Sort u} (r : α → α → Prop) : Prop where
+class Antisymm {α : Sort u} (r : α → α → Prop) where
   /-- An antisymmetric relation `(·≤·)` satisfies `a ≤ b → b ≤ a → a = b`. -/
   antisymm {a b : α} : r a b → r b a → a = b
 
@@ -2055,8 +2040,4 @@ class LawfulCommIdentity (op : α → α → α) (o : outParam α) [hc : Commuta
   left_id a := Eq.trans (hc.comm o a) (right_id a)
   right_id a := Eq.trans (hc.comm a o) (left_id a)
 
-instance : Commutative Or := ⟨fun _ _ => propext or_comm⟩
-instance : Commutative And := ⟨fun _ _ => propext and_comm⟩
-instance : Commutative Iff := ⟨fun _ _ => propext iff_comm⟩
-
 end Std

src/Init/Data.lean

@@ -14,7 +14,6 @@ import Init.Data.String
 import Init.Data.List
 import Init.Data.Int
 import Init.Data.Array
-import Init.Data.Array.Subarray.Split
 import Init.Data.ByteArray
 import Init.Data.FloatArray
 import Init.Data.Fin
@@ -35,5 +34,3 @@ import Init.Data.Queue
 import Init.Data.Channel
 import Init.Data.Cast
 import Init.Data.Sum
-import Init.Data.BEq
-import Init.Data.Subtype

src/Init/Data/AC.lean

@@ -146,8 +146,8 @@ theorem Context.evalList_mergeIdem (ctx : Context α) (h : ContextInformation.is
     | nil =>
       simp [mergeIdem, mergeIdem.loop]
       split
-      next h₂ => simp [evalList, h₂, h.1, EvalInformation.evalOp]
-      next => rfl
+      case inl h₂ => simp [evalList, h₂, h.1, EvalInformation.evalOp]
+      rfl
     | cons z zs =>
       by_cases h₂ : x = y
       case pos =>
@@ -191,11 +191,11 @@ theorem Context.evalList_insert
     . simp [evalList, h.1, EvalInformation.evalOp]
   | step y z zs ih =>
     simp [insert] at *; split
-    next => rfl
-    next =>
+    case inl => rfl
+    case inr =>
       split
-      next => simp [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]
-      next => simp_all [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]
+      case inl => simp [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]
+      case inr => simp_all [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]
 
 theorem Context.evalList_sort_congr
   (ctx : Context α)

src/Init/Data/Array.lean

@@ -10,7 +10,5 @@ import Init.Data.Array.BinSearch
 import Init.Data.Array.InsertionSort
 import Init.Data.Array.DecidableEq
 import Init.Data.Array.Mem
-import Init.Data.Array.Attach
 import Init.Data.Array.BasicAux
 import Init.Data.Array.Lemmas
-import Init.Data.Array.TakeDrop

src/Init/Data/Array/Attach.lean

@@ -1,29 +0,0 @@
-/-
-Copyright (c) 2021 Floris van Doorn. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Joachim Breitner, Mario Carneiro
--/
-prelude
-import Init.Data.Array.Mem
-import Init.Data.List.Attach
-
-namespace Array
-
-/--
-Unsafe implementation of `attachWith`, taking advantage of the fact that the representation of
-`Array {x // P x}` is the same as the input `Array α`.
--/
-@[inline] private unsafe def attachWithImpl
-    (xs : Array α) (P : α → Prop) (_ : ∀ x ∈ xs, P x) : Array {x // P x} := unsafeCast xs
-
-/-- `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.data.attachWith P fun x h => H x (Array.Mem.mk h)⟩
-
-/-- `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
-
-end Array

src/Init/Data/Array/Basic.lean

@@ -31,7 +31,6 @@ def ofFn {n} (f : Fin n → α) : Array α := go 0 (mkEmpty n) where
   go (i : Nat) (acc : Array α) : Array α :=
     if h : i < n then go (i+1) (acc.push (f ⟨i, h⟩)) else acc
 termination_by n - i
-decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 /-- The array `#[0, 1, ..., n - 1]`. -/
 def range (n : Nat) : Array Nat :=
@@ -44,29 +43,24 @@ instance : EmptyCollection (Array α) := ⟨Array.empty⟩
 instance : Inhabited (Array α) where
   default := Array.empty
 
-@[simp] def isEmpty (a : Array α) : Bool :=
+def isEmpty (a : Array α) : Bool :=
   a.size = 0
 
 def singleton (v : α) : Array α :=
   mkArray 1 v
 
-/-- Low-level version of `size` that directly queries the C array object cached size.
-    While this is not provable, `usize` always returns the exact size of the array since
-    the implementation only supports arrays of size less than `USize.size`.
--/
-@[extern "lean_array_size", simp]
-def usize (a : @& Array α) : USize := a.size.toUSize
-
 /-- Low-level version of `fget` which is as fast as a C array read.
    `Fin` values are represented as tag pointers in the Lean runtime. Thus,
    `fget` may be slightly slower than `uget`. -/
-@[extern "lean_array_uget", simp]
+@[extern "lean_array_uget"]
 def uget (a : @& Array α) (i : USize) (h : i.toNat < a.size) : α :=
   a[i.toNat]
 
 instance : GetElem (Array α) USize α fun xs i => i.toNat < xs.size where
   getElem xs i h := xs.uget i h
 
+instance : LawfulGetElem (Array α) USize α fun xs i => i.toNat < xs.size where
+
 def back [Inhabited α] (a : Array α) : α :=
   a.get! (a.size - 1)
 
@@ -108,7 +102,7 @@ def swap (a : Array α) (i j : @& Fin a.size) : Array α :=
   a'.set (size_set a i v₂ ▸ j) v₁
 
 /--
-Swaps two entries in an array, or returns the array unchanged if either index is out of bounds.
+Swaps two entries in an array, or panics if either index is out of bounds.
 
 This will perform the update destructively provided that `a` has a reference
 count of 1 when called.
@@ -181,7 +175,7 @@ def modifyOp (self : Array α) (idx : Nat) (f : α → α) : Array α :=
 
   This kind of low level trick can be removed with a little bit of compiler support. For example, if the compiler simplifies `as.size < usizeSz` to true. -/
 @[inline] unsafe def forInUnsafe {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (b : β) (f : α → β → m (ForInStep β)) : m β :=
-  let sz := as.usize
+  let sz := USize.ofNat as.size
   let rec @[specialize] loop (i : USize) (b : β) : m β := do
     if i < sz then
       let a := as.uget i lcProof
@@ -287,7 +281,7 @@ def foldrM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α
 /-- See comment at `forInUnsafe` -/
 @[inline]
 unsafe def mapMUnsafe {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m β) (as : Array α) : m (Array β) :=
-  let sz := as.usize
+  let sz := USize.ofNat as.size
   let rec @[specialize] map (i : USize) (r : Array NonScalar) : m (Array PNonScalar.{v}) := do
     if i < sz then
      let v    := r.uget i lcProof
@@ -312,7 +306,6 @@ def mapM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α
     else
       pure r
   termination_by as.size - i
-  decreasing_by simp_wf; decreasing_trivial_pre_omega
   map 0 (mkEmpty as.size)
 
 @[inline]
@@ -385,7 +378,6 @@ def anyM {α : Type u} {m : Type → Type w} [Monad m] (p : α → m Bool) (as :
       else
         pure false
       termination_by stop - j
-      decreasing_by simp_wf; decreasing_trivial_pre_omega
     loop start
   if h : stop ≤ as.size then
     any stop h
@@ -471,7 +463,6 @@ def findIdx? {α : Type u} (as : Array α) (p : α → Bool) : Option Nat :=
       if p as[j] then some j else loop (j + 1)
     else none
     termination_by as.size - j
-    decreasing_by simp_wf; decreasing_trivial_pre_omega
   loop 0
 
 def getIdx? [BEq α] (a : Array α) (v : α) : Option Nat :=
@@ -486,7 +477,7 @@ def all (as : Array α) (p : α → Bool) (start := 0) (stop := as.size) : Bool
   Id.run <| as.allM p start stop
 
 def contains [BEq α] (as : Array α) (a : α) : Bool :=
-  as.any (· == a)
+  as.any fun b => a == b
 
 def elem [BEq α] (a : α) (as : Array α) : Bool :=
   as.contains a
@@ -566,7 +557,6 @@ def isEqvAux (a b : Array α) (hsz : a.size = b.size) (p : α → α → Bool) (
   else
     true
 termination_by a.size - i
-decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 @[inline] def isEqv (a b : Array α) (p : α → α → Bool) : Bool :=
   if h : a.size = b.size then
@@ -671,7 +661,6 @@ def indexOfAux [BEq α] (a : Array α) (v : α) (i : Nat) : Option (Fin a.size)
     else indexOfAux a v (i+1)
   else none
 termination_by a.size - i
-decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 def indexOf? [BEq α] (a : Array α) (v : α) : Option (Fin a.size) :=
   indexOfAux a v 0
@@ -714,7 +703,6 @@ def popWhile (p : α → Bool) (as : Array α) : Array α :=
   else
     as
 termination_by as.size
-decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 def takeWhile (p : α → Bool) (as : Array α) : Array α :=
   let rec go (i : Nat) (r : Array α) : Array α :=
@@ -727,7 +715,6 @@ def takeWhile (p : α → Bool) (as : Array α) : Array α :=
     else
       r
     termination_by as.size - i
-    decreasing_by simp_wf; decreasing_trivial_pre_omega
   go 0 #[]
 
 /-- Remove the element at a given index from an array without bounds checks, using a `Fin` index.
@@ -738,15 +725,16 @@ def feraseIdx (a : Array α) (i : Fin a.size) : Array α :=
   if h : i.val + 1 < a.size then
     let a' := a.swap ⟨i.val + 1, h⟩ i
     let i' : Fin a'.size := ⟨i.val + 1, by simp [a', h]⟩
+    have : a'.size - i' < a.size - i := by
+      simp [a', Nat.sub_succ_lt_self _ _ i.isLt]
     a'.feraseIdx i'
   else
     a.pop
 termination_by a.size - i.val
-decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ i.isLt
 
 theorem size_feraseIdx (a : Array α) (i : Fin a.size) : (a.feraseIdx i).size = a.size - 1 := by
   induction a, i using Array.feraseIdx.induct with
-  | @case1 a i h a' _ ih =>
+  | @case1 a i h a' _ _ ih =>
     unfold feraseIdx
     simp [h, a', ih]
   | case2 a i h =>
@@ -775,7 +763,6 @@ def erase [BEq α] (as : Array α) (a : α) : Array α :=
     else
       as
     termination_by j.1
-    decreasing_by simp_wf; decreasing_trivial_pre_omega
   let j := as.size
   let as := as.push a
   loop as ⟨j, size_push .. ▸ j.lt_succ_self⟩
@@ -796,11 +783,11 @@ def toArrayLit (a : Array α) (n : Nat) (hsz : a.size = n) : Array α :=
 theorem ext' {as bs : Array α} (h : as.data = bs.data) : as = bs := by
   cases as; cases bs; simp at h; rw [h]
 
-@[simp] theorem toArrayAux_eq (as : List α) (acc : Array α) : (as.toArrayAux acc).data = acc.data ++ as := by
+theorem toArrayAux_eq (as : List α) (acc : Array α) : (as.toArrayAux acc).data = acc.data ++ as := by
   induction as generalizing acc <;> simp [*, List.toArrayAux, Array.push, List.append_assoc, List.concat_eq_append]
 
 theorem data_toArray (as : List α) : as.toArray.data = as := by
-  simp [List.toArray, Array.mkEmpty]
+  simp [List.toArray, toArrayAux_eq, Array.mkEmpty]
 
 theorem toArrayLit_eq (as : Array α) (n : Nat) (hsz : as.size = n) : as = toArrayLit as n hsz := by
   apply ext'
@@ -829,7 +816,6 @@ def isPrefixOfAux [BEq α] (as bs : Array α) (hle : as.size ≤ bs.size) (i : N
   else
     true
 termination_by as.size - i
-decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 /-- Return true iff `as` is a prefix of `bs`.
 That is, `bs = as ++ t` for some `t : List α`.-/
@@ -851,7 +837,6 @@ private def allDiffAux [BEq α] (as : Array α) (i : Nat) : Bool :=
   else
     true
 termination_by as.size - i
-decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 def allDiff [BEq α] (as : Array α) : Bool :=
   allDiffAux as 0
@@ -867,7 +852,6 @@ def allDiff [BEq α] (as : Array α) : Bool :=
   else
     cs
 termination_by as.size - i
-decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 @[inline] def zipWith (as : Array α) (bs : Array β) (f : α → β → γ) : Array γ :=
   zipWithAux f as bs 0 #[]

src/Init/Data/Array/BasicAux.lean

@@ -9,7 +9,7 @@ import Init.Data.Nat.Linear
 import Init.NotationExtra
 
 theorem Array.of_push_eq_push {as bs : Array α} (h : as.push a = bs.push b) : as = bs ∧ a = b := by
-  simp only [push, mk.injEq] at h
+  simp [push] at h
   have ⟨h₁, h₂⟩ := List.of_concat_eq_concat h
   cases as; cases bs
   simp_all
@@ -48,7 +48,6 @@ where
       let b ← f as[i]
       go (i+1) ⟨acc.val.push b, by simp [acc.property]⟩ hlt
   termination_by as.size - i
-  decreasing_by decreasing_trivial_pre_omega
 
 @[inline] private unsafe def mapMonoMImp [Monad m] (as : Array α) (f : α → m α) : m (Array α) :=
   go 0 as

src/Init/Data/Array/DecidableEq.lean

@@ -21,25 +21,22 @@ theorem eq_of_isEqvAux [DecidableEq α] (a b : Array α) (hsz : a.size = b.size)
     subst heq
     exact absurd (Nat.lt_of_lt_of_le high low) (Nat.lt_irrefl j)
 termination_by a.size - i
-decreasing_by decreasing_trivial_pre_omega
-
 
 theorem eq_of_isEqv [DecidableEq α] (a b : Array α) : Array.isEqv a b (fun x y => x = y) → a = b := by
   simp [Array.isEqv]
   split
-  next hsz =>
+  case inr => intro; contradiction
+  case inl hsz =>
    intro h
    have aux := eq_of_isEqvAux a b hsz 0 (Nat.zero_le ..) h
    exact ext a b hsz fun i h _ => aux i (Nat.zero_le ..) _
-  next => intro; contradiction
 
 theorem isEqvAux_self [DecidableEq α] (a : Array α) (i : Nat) : Array.isEqvAux a a rfl (fun x y => x = y) i = true := by
   unfold Array.isEqvAux
   split
-  next h => simp [h, isEqvAux_self a (i+1)]
-  next h => simp [h]
+  case inl h => simp [h, isEqvAux_self a (i+1)]
+  case inr h => simp [h]
 termination_by a.size - i
-decreasing_by decreasing_trivial_pre_omega
 
 theorem isEqv_self [DecidableEq α] (a : Array α) : Array.isEqv a a (fun x y => x = y) = true := by
   simp [isEqv, isEqvAux_self]

src/Init/Data/Array/Lemmas.lean

@@ -5,8 +5,7 @@ Authors: Mario Carneiro
 -/
 prelude
 import Init.Data.Nat.MinMax
-import Init.Data.Nat.Lemmas
-import Init.Data.List.Monadic
+import Init.Data.List.Lemmas
 import Init.Data.Fin.Basic
 import Init.Data.Array.Mem
 import Init.TacticsExtra
@@ -14,32 +13,21 @@ import Init.TacticsExtra
 /-!
 ## Bootstrapping theorems about arrays
 
-This file contains some theorems about `Array` and `List` needed for `Init.Data.List.Impl`.
+This file contains some theorems about `Array` and `List` needed for `Std.List.Basic`.
 -/
 
 namespace Array
 
 attribute [simp] data_toArray uset
 
-@[simp] theorem singleton_def (v : α) : singleton v = #[v] := rfl
-
-@[simp] theorem toArray_data : (a : Array α) → a.data.toArray = a
-  | ⟨l⟩ => ext' (data_toArray l)
-
-@[simp] theorem data_length {l : Array α} : l.data.length = l.size := rfl
-
 @[simp] theorem mkEmpty_eq (α n) : @mkEmpty α n = #[] := rfl
 
 @[simp] theorem size_toArray (as : List α) : as.toArray.size = as.length := by simp [size]
 
 @[simp] theorem size_mk (as : List α) : (Array.mk as).size = as.length := by simp [size]
 
-theorem getElem_eq_data_getElem (a : Array α) (h : i < a.size) : a[i] = a.data[i] := by
-  by_cases i < a.size <;> (try simp [*]) <;> rfl
-
-@[deprecated getElem_eq_data_getElem (since := "2024-06-12")]
 theorem getElem_eq_data_get (a : Array α) (h : i < a.size) : a[i] = a.data.get ⟨i, h⟩ := by
-  simp [getElem_eq_data_getElem]
+  by_cases i < a.size <;> (try simp [*]) <;> rfl
 
 theorem foldlM_eq_foldlM_data.aux [Monad m]
     (f : β → α → m β) (arr : Array α) (i j) (H : arr.size ≤ i + j) (b) :
@@ -51,7 +39,7 @@ theorem foldlM_eq_foldlM_data.aux [Monad m]
     simp [foldlM_eq_foldlM_data.aux f arr i (j+1) H]
     rw (config := {occs := .pos [2]}) [← List.get_drop_eq_drop _ _ ‹_›]
     rfl
-  · rw [List.drop_of_length_le (Nat.ge_of_not_lt ‹_›)]; rfl
+  · rw [List.drop_length_le (Nat.ge_of_not_lt ‹_›)]; rfl
 
 theorem foldlM_eq_foldlM_data [Monad m]
     (f : β → α → m β) (init : β) (arr : Array α) :
@@ -118,11 +106,11 @@ theorem foldr_push (f : α → β → β) (init : β) (arr : Array α) (a : α)
 theorem get_push_lt (a : Array α) (x : α) (i : Nat) (h : i < a.size) :
     have : i < (a.push x).size := by simp [*, Nat.lt_succ_of_le, Nat.le_of_lt]
     (a.push x)[i] = a[i] := by
-  simp only [push, getElem_eq_data_getElem, List.concat_eq_append, List.getElem_append_left, h]
+  simp only [push, getElem_eq_data_get, List.concat_eq_append, List.get_append_left, h]
 
 @[simp] theorem get_push_eq (a : Array α) (x : α) : (a.push x)[a.size] = x := by
-  simp only [push, getElem_eq_data_getElem, List.concat_eq_append]
-  rw [List.getElem_append_right] <;> simp [getElem_eq_data_getElem, Nat.zero_lt_one]
+  simp only [push, getElem_eq_data_get, List.concat_eq_append]
+  rw [List.get_append_right] <;> simp [getElem_eq_data_get, Nat.zero_lt_one]
 
 theorem get_push (a : Array α) (x : α) (i : Nat) (h : i < (a.push x).size) :
     (a.push x)[i] = if h : i < a.size then a[i] else x := by
@@ -139,11 +127,9 @@ where
       mapM.map f arr i r = (arr.data.drop i).foldlM (fun bs a => bs.push <$> f a) r := by
     unfold mapM.map; split
     · rw [← List.get_drop_eq_drop _ i ‹_›]
-      simp only [aux (i + 1), map_eq_pure_bind, data_length, List.foldlM_cons, bind_assoc, pure_bind]
-      rfl
-    · rw [List.drop_of_length_le (Nat.ge_of_not_lt ‹_›)]; rfl
+      simp [aux (i+1), map_eq_pure_bind]; rfl
+    · rw [List.drop_length_le (Nat.ge_of_not_lt ‹_›)]; rfl
   termination_by arr.size - i
-  decreasing_by decreasing_trivial_pre_omega
 
 @[simp] theorem map_data (f : α → β) (arr : Array α) : (arr.map f).data = arr.data.map f := by
   rw [map, mapM_eq_foldlM]
@@ -153,8 +139,7 @@ where
   simp [H]
 
 @[simp] theorem size_map (f : α → β) (arr : Array α) : (arr.map f).size = arr.size := by
-  simp only [← data_length]
-  simp
+  simp [size]
 
 @[simp] theorem pop_data (arr : Array α) : arr.pop.data = arr.data.dropLast := rfl
 
@@ -202,8 +187,7 @@ theorem anyM_stop_le_start [Monad m] (p : α → m Bool) (as : Array α) (start
 theorem mem_def (a : α) (as : Array α) : a ∈ as ↔ a ∈ as.data :=
   ⟨fun | .mk h => h, Array.Mem.mk⟩
 
-/-! # get -/
-
+/-- # get -/
 @[simp] theorem get_eq_getElem (a : Array α) (i : Fin _) : a.get i = a[i.1] := rfl
 
 theorem getElem?_lt
@@ -220,7 +204,7 @@ theorem getElem?_len_le (a : Array α) {i : Nat} (h : a.size ≤ i) : a[i]? = no
 theorem getD_get? (a : Array α) (i : Nat) (d : α) :
   Option.getD a[i]? d = if p : i < a.size then a[i]'p else d := by
   if h : i < a.size then
-    simp [setD, h, getElem?_def]
+    simp [setD, h, getElem?]
   else
     have p : i ≥ a.size := Nat.le_of_not_gt h
     simp [setD, getElem?_len_le _ p, h]
@@ -233,16 +217,16 @@ theorem get!_eq_getD [Inhabited α] (a : Array α) : a.get! n = a.getD n default
 @[simp] theorem get!_eq_getElem? [Inhabited α] (a : Array α) (i : Nat) : a.get! i = (a.get? i).getD default := by
   by_cases p : i < a.size <;> simp [getD_get?, get!_eq_getD, p]
 
-/-! # set -/
+/-- # set -/
 
 @[simp] theorem getElem_set_eq (a : Array α) (i : Fin a.size) (v : α) {j : Nat}
       (eq : i.val = j) (p : j < (a.set i v).size) :
     (a.set i v)[j]'p = v := by
-  simp [set, getElem_eq_data_getElem, ←eq]
+  simp [set, getElem_eq_data_get, ←eq]
 
 @[simp] theorem getElem_set_ne (a : Array α) (i : Fin a.size) (v : α) {j : Nat} (pj : j < (a.set i v).size)
     (h : i.val ≠ j) : (a.set i v)[j]'pj = a[j]'(size_set a i v ▸ pj) := by
-  simp only [set, getElem_eq_data_getElem, List.getElem_set_ne h]
+  simp only [set, getElem_eq_data_get, List.get_set_ne _ h]
 
 theorem getElem_set (a : Array α) (i : Fin a.size) (v : α) (j : Nat)
     (h : j < (a.set i v).size) :
@@ -256,7 +240,7 @@ theorem getElem_set (a : Array α) (i : Fin a.size) (v : α) (j : Nat)
     (ne : i.val ≠ j) : (a.set i v)[j]? = a[j]? := by
   by_cases h : j < a.size <;> simp [getElem?_lt, getElem?_ge, Nat.ge_of_not_lt, ne, h]
 
-/-! # setD -/
+/- # setD -/
 
 @[simp] theorem set!_is_setD : @set! = @setD := rfl
 
@@ -282,793 +266,4 @@ theorem getElem?_setD_eq (a : Array α) {i : Nat} (p : i < a.size) (v : α) : (a
   by_cases h : i < a.size <;>
     simp [setD, Nat.not_lt_of_le, h,  getD_get?]
 
-/-! # ofFn -/
-
-@[simp] theorem size_ofFn_go {n} (f : Fin n → α) (i acc) :
-    (ofFn.go f i acc).size = acc.size + (n - i) := by
-  if hin : i < n then
-    unfold ofFn.go
-    have : 1 + (n - (i + 1)) = n - i :=
-      Nat.sub_sub .. ▸ Nat.add_sub_cancel' (Nat.le_sub_of_add_le (Nat.add_comm .. ▸ hin))
-    rw [dif_pos hin, size_ofFn_go f (i+1), size_push, Nat.add_assoc, this]
-  else
-    have : n - i = 0 := Nat.sub_eq_zero_of_le (Nat.le_of_not_lt hin)
-    unfold ofFn.go
-    simp [hin, this]
-termination_by n - i
-
-@[simp] theorem size_ofFn (f : Fin n → α) : (ofFn f).size = n := by simp [ofFn]
-
-theorem getElem_ofFn_go (f : Fin n → α) (i) {acc k}
-    (hki : k < n) (hin : i ≤ n) (hi : i = acc.size)
-    (hacc : ∀ j, ∀ hj : j < acc.size, acc[j] = f ⟨j, Nat.lt_of_lt_of_le hj (hi ▸ hin)⟩) :
-    haveI : acc.size + (n - acc.size) = n := Nat.add_sub_cancel' (hi ▸ hin)
-    (ofFn.go f i acc)[k]'(by simp [*]) = f ⟨k, hki⟩ := by
-  unfold ofFn.go
-  if hin : i < n then
-    have : 1 + (n - (i + 1)) = n - i :=
-      Nat.sub_sub .. ▸ Nat.add_sub_cancel' (Nat.le_sub_of_add_le (Nat.add_comm .. ▸ hin))
-    simp only [dif_pos hin]
-    rw [getElem_ofFn_go f (i+1) _ hin (by simp [*]) (fun j hj => ?hacc)]
-    cases (Nat.lt_or_eq_of_le <| Nat.le_of_lt_succ (by simpa using hj)) with
-    | inl hj => simp [get_push, hj, hacc j hj]
-    | inr hj => simp [get_push, *]
-  else
-    simp [hin, hacc k (Nat.lt_of_lt_of_le hki (Nat.le_of_not_lt (hi ▸ hin)))]
-termination_by n - i
-
-@[simp] theorem getElem_ofFn (f : Fin n → α) (i : Nat) (h) :
-    (ofFn f)[i] = f ⟨i, size_ofFn f ▸ h⟩ :=
-  getElem_ofFn_go _ _ _ (by simp) (by simp) nofun
-
-/-- # mkArray -/
-
-@[simp] theorem mkArray_data (n : Nat) (v : α) : (mkArray n v).data = List.replicate n v := rfl
-
-@[simp] theorem getElem_mkArray (n : Nat) (v : α) (h : i < (mkArray n v).size) :
-    (mkArray n v)[i] = v := by simp [Array.getElem_eq_data_getElem]
-
-/-- # mem -/
-
-theorem mem_data {a : α} {l : Array α} : a ∈ l.data ↔ a ∈ l := (mem_def _ _).symm
-
-theorem not_mem_nil (a : α) : ¬ a ∈ #[] := nofun
-
-/-- # get lemmas -/
-
-theorem getElem?_mem {l : Array α} {i : Fin l.size} : l[i] ∈ l := by
-  erw [Array.mem_def, getElem_eq_data_getElem]
-  apply List.get_mem
-
-theorem getElem_fin_eq_data_get (a : Array α) (i : Fin _) : a[i] = a.data.get i := rfl
-
-@[simp] theorem ugetElem_eq_getElem (a : Array α) {i : USize} (h : i.toNat < a.size) :
-  a[i] = a[i.toNat] := rfl
-
-theorem getElem?_eq_getElem (a : Array α) (i : Nat) (h : i < a.size) : a[i]? = a[i] :=
-  getElem?_pos ..
-
-theorem get?_len_le (a : Array α) (i : Nat) (h : a.size ≤ i) : a[i]? = none := by
-  simp [getElem?_neg, h]
-
-theorem getElem_mem_data (a : Array α) (h : i < a.size) : a[i] ∈ a.data := by
-  simp only [getElem_eq_data_getElem, List.getElem_mem]
-
-theorem getElem?_eq_data_get? (a : Array α) (i : Nat) : a[i]? = a.data.get? i := by
-  by_cases i < a.size <;> simp_all [getElem?_pos, getElem?_neg, List.get?_eq_get, eq_comm]; rfl
-
-theorem get?_eq_data_get? (a : Array α) (i : Nat) : a.get? i = a.data.get? i :=
-  getElem?_eq_data_get? ..
-
-theorem get!_eq_get? [Inhabited α] (a : Array α) : a.get! n = (a.get? n).getD default := by
-  simp [get!_eq_getD]
-
-@[simp] theorem back_eq_back? [Inhabited α] (a : Array α) : a.back = a.back?.getD default := by
-  simp [back, back?]
-
-@[simp] theorem back?_push (a : Array α) : (a.push x).back? = some x := by
-  simp [back?, getElem?_eq_data_get?]
-
-theorem back_push [Inhabited α] (a : Array α) : (a.push x).back = x := by simp
-
-theorem get?_push_lt (a : Array α) (x : α) (i : Nat) (h : i < a.size) :
-    (a.push x)[i]? = some a[i] := by
-  rw [getElem?_pos, get_push_lt]
-
-theorem get?_push_eq (a : Array α) (x : α) : (a.push x)[a.size]? = some x := by
-  rw [getElem?_pos, get_push_eq]
-
-theorem get?_push {a : Array α} : (a.push x)[i]? = if i = a.size then some x else a[i]? := by
-  match Nat.lt_trichotomy i a.size with
-  | Or.inl g =>
-    have h1 : i < a.size + 1 := by omega
-    have h2 : i ≠ a.size := by omega
-    simp [getElem?_def, size_push, g, h1, h2, get_push_lt]
-  | Or.inr (Or.inl heq) =>
-    simp [heq, getElem?_pos, get_push_eq]
-  | Or.inr (Or.inr g) =>
-    simp only [getElem?_def, size_push]
-    have h1 : ¬ (i < a.size) := by omega
-    have h2 : ¬ (i < a.size + 1) := by omega
-    have h3 : i ≠ a.size := by omega
-    simp [h1, h2, h3]
-
-@[simp] theorem get?_size {a : Array α} : a[a.size]? = none := by
-  simp only [getElem?_def, Nat.lt_irrefl, dite_false]
-
-@[simp] theorem data_set (a : Array α) (i v) : (a.set i v).data = a.data.set i.1 v := rfl
-
-theorem get_set_eq (a : Array α) (i : Fin a.size) (v : α) :
-    (a.set i v)[i.1] = v := by
-  simp only [set, getElem_eq_data_getElem, List.getElem_set_eq]
-
-theorem get?_set_eq (a : Array α) (i : Fin a.size) (v : α) :
-    (a.set i v)[i.1]? = v := by simp [getElem?_pos, i.2]
-
-@[simp] theorem get?_set_ne (a : Array α) (i : Fin a.size) {j : Nat} (v : α)
-    (h : i.1 ≠ j) : (a.set i v)[j]? = a[j]? := by
-  by_cases j < a.size <;> simp [getElem?_pos, getElem?_neg, *]
-
-theorem get?_set (a : Array α) (i : Fin a.size) (j : Nat) (v : α) :
-    (a.set i v)[j]? = if i.1 = j then some v else a[j]? := by
-  if h : i.1 = j then subst j; simp [*] else simp [*]
-
-theorem get_set (a : Array α) (i : Fin a.size) (j : Nat) (hj : j < a.size) (v : α) :
-    (a.set i v)[j]'(by simp [*]) = if i = j then v else a[j] := by
-  if h : i.1 = j then subst j; simp [*] else simp [*]
-
-@[simp] theorem get_set_ne (a : Array α) (i : Fin a.size) {j : Nat} (v : α) (hj : j < a.size)
-    (h : i.1 ≠ j) : (a.set i v)[j]'(by simp [*]) = a[j] := by
-  simp only [set, getElem_eq_data_getElem, List.getElem_set_ne h]
-
-theorem getElem_setD (a : Array α) (i : Nat) (v : α) (h : i < (setD a i v).size) :
-  (setD a i v)[i] = v := by
-  simp at h
-  simp only [setD, h, dite_true, get_set, ite_true]
-
-theorem set_set (a : Array α) (i : Fin a.size) (v v' : α) :
-    (a.set i v).set ⟨i, by simp [i.2]⟩ v' = a.set i v' := by simp [set, List.set_set]
-
-private theorem fin_cast_val (e : n = n') (i : Fin n) : e ▸ i = ⟨i.1, e ▸ i.2⟩ := by cases e; rfl
-
-theorem swap_def (a : Array α) (i j : Fin a.size) :
-    a.swap i j = (a.set i (a.get j)).set ⟨j.1, by simp [j.2]⟩ (a.get i) := by
-  simp [swap, fin_cast_val]
-
-theorem data_swap (a : Array α) (i j : Fin a.size) :
-    (a.swap i j).data = (a.data.set i (a.get j)).set j (a.get i) := by simp [swap_def]
-
-theorem get?_swap (a : Array α) (i j : Fin a.size) (k : Nat) : (a.swap i j)[k]? =
-    if j = k then some a[i.1] else if i = k then some a[j.1] else a[k]? := by
-  simp [swap_def, get?_set, ← getElem_fin_eq_data_get]
-
-@[simp] theorem swapAt_def (a : Array α) (i : Fin a.size) (v : α) :
-    a.swapAt i v = (a[i.1], a.set i v) := rfl
-
--- @[simp] -- FIXME: gives a weird linter error
-theorem swapAt!_def (a : Array α) (i : Nat) (v : α) (h : i < a.size) :
-    a.swapAt! i v = (a[i], a.set ⟨i, h⟩ v) := by simp [swapAt!, h]
-
-@[simp] theorem data_pop (a : Array α) : a.pop.data = a.data.dropLast := by simp [pop]
-
-@[simp] theorem pop_empty : (#[] : Array α).pop = #[] := rfl
-
-@[simp] theorem pop_push (a : Array α) : (a.push x).pop = a := by simp [pop]
-
-@[simp] theorem getElem_pop (a : Array α) (i : Nat) (hi : i < a.pop.size) :
-    a.pop[i] = a[i]'(Nat.lt_of_lt_of_le (a.size_pop ▸ hi) (Nat.sub_le _ _)) :=
-  List.getElem_dropLast ..
-
-theorem eq_empty_of_size_eq_zero {as : Array α} (h : as.size = 0) : as = #[] := by
-  apply ext
-  · simp [h]
-  · intros; contradiction
-
-theorem eq_push_pop_back_of_size_ne_zero [Inhabited α] {as : Array α} (h : as.size ≠ 0) :
-    as = as.pop.push as.back := by
-  apply ext
-  · simp [Nat.sub_add_cancel (Nat.zero_lt_of_ne_zero h)]
-  · intros i h h'
-    if hlt : i < as.pop.size then
-      rw [get_push_lt (h:=hlt), getElem_pop]
-    else
-      have heq : i = as.pop.size :=
-        Nat.le_antisymm (size_pop .. ▸ Nat.le_pred_of_lt h) (Nat.le_of_not_gt hlt)
-      cases heq; rw [get_push_eq, back, ←size_pop, get!_eq_getD, getD, dif_pos h]; rfl
-
-theorem eq_push_of_size_ne_zero {as : Array α} (h : as.size ≠ 0) :
-    ∃ (bs : Array α) (c : α), as = bs.push c :=
-  let _ : Inhabited α := ⟨as[0]⟩
-  ⟨as.pop, as.back, eq_push_pop_back_of_size_ne_zero h⟩
-
-theorem size_eq_length_data (as : Array α) : as.size = as.data.length := rfl
-
-@[simp] theorem size_swap! (a : Array α) (i j) :
-    (a.swap! i j).size = a.size := by unfold swap!; split <;> (try split) <;> simp [size_swap]
-
-@[simp] theorem size_reverse (a : Array α) : a.reverse.size = a.size := by
-  let rec go (as : Array α) (i j) : (reverse.loop as i j).size = as.size := by
-    rw [reverse.loop]
-    if h : i < j then
-      have := reverse.termination h
-      simp [(go · (i+1) ⟨j-1, ·⟩), h]
-    else simp [h]
-    termination_by j - i
-  simp only [reverse]; split <;> simp [go]
-
-@[simp] theorem size_range {n : Nat} : (range n).size = n := by
-  unfold range
-  induction n with
-  | zero      => simp [Nat.fold]
-  | succ k ih =>
-    rw [Nat.fold, flip]
-    simp only [mkEmpty_eq, size_push] at *
-    omega
-
-set_option linter.deprecated false in
-@[simp] theorem reverse_data (a : Array α) : a.reverse.data = a.data.reverse := by
-  let rec go (as : Array α) (i j hj)
-      (h : i + j + 1 = a.size) (h₂ : as.size = a.size)
-      (H : ∀ k, as.data.get? k = if i ≤ k ∧ k ≤ j then a.data.get? k else a.data.reverse.get? k)
-      (k) : (reverse.loop as i ⟨j, hj⟩).data.get? k = a.data.reverse.get? k := by
-    rw [reverse.loop]; dsimp; split <;> rename_i h₁
-    · have p := reverse.termination h₁
-      match j with | j+1 => ?_
-      simp only [Nat.add_sub_cancel] at p ⊢
-      rw [(go · (i+1) j)]
-      · rwa [Nat.add_right_comm i]
-      · simp [size_swap, h₂]
-      · intro k
-        rw [← getElem?_eq_data_get?, get?_swap]
-        simp only [H, getElem_eq_data_get, ← List.get?_eq_get, Nat.le_of_lt h₁, getElem?_eq_data_get?]
-        split <;> rename_i h₂
-        · simp only [← h₂, Nat.not_le.2 (Nat.lt_succ_self _), Nat.le_refl, and_false]
-          exact (List.get?_reverse' (j+1) i (Eq.trans (by simp_arith) h)).symm
-        split <;> rename_i h₃
-        · simp only [← h₃, Nat.not_le.2 (Nat.lt_succ_self _), Nat.le_refl, false_and]
-          exact (List.get?_reverse' i (j+1) (Eq.trans (by simp_arith) h)).symm
-        simp only [Nat.succ_le, Nat.lt_iff_le_and_ne.trans (and_iff_left h₃),
-          Nat.lt_succ.symm.trans (Nat.lt_iff_le_and_ne.trans (and_iff_left (Ne.symm h₂)))]
-    · rw [H]; split <;> rename_i h₂
-      · cases Nat.le_antisymm (Nat.not_lt.1 h₁) (Nat.le_trans h₂.1 h₂.2)
-        cases Nat.le_antisymm h₂.1 h₂.2
-        exact (List.get?_reverse' _ _ h).symm
-      · rfl
-    termination_by j - i
-  simp only [reverse]
-  split
-  · match a with | ⟨[]⟩ | ⟨[_]⟩ => rfl
-  · have := Nat.sub_add_cancel (Nat.le_of_not_le ‹_›)
-    refine List.ext_get? <| go _ _ _ _ (by simp [this]) rfl fun k => ?_
-    split
-    · rfl
-    · rename_i h
-      simp only [← show k < _ + 1 ↔ _ from Nat.lt_succ (n := a.size - 1), this, Nat.zero_le,
-        true_and, Nat.not_lt] at h
-      rw [List.get?_eq_none.2 ‹_›, List.get?_eq_none.2 (a.data.length_reverse ▸ ‹_›)]
-
-/-! ### foldl / foldr -/
-
--- This proof is the pure version of `Array.SatisfiesM_foldlM`,
--- reproduced to avoid a dependency on `SatisfiesM`.
-theorem foldl_induction
-    {as : Array α} (motive : Nat → β → Prop) {init : β} (h0 : motive 0 init) {f : β → α → β}
-    (hf : ∀ i : Fin as.size, ∀ b, motive i.1 b → motive (i.1 + 1) (f b as[i])) :
-    motive as.size (as.foldl f init) := by
-  let rec go {i j b} (h₁ : j ≤ as.size) (h₂ : as.size ≤ i + j) (H : motive j b) :
-    (motive as.size) (foldlM.loop (m := Id) f as as.size (Nat.le_refl _) i j b) := by
-    unfold foldlM.loop; split
-    · next hj =>
-      split
-      · cases Nat.not_le_of_gt (by simp [hj]) h₂
-      · exact go hj (by rwa [Nat.succ_add] at h₂) (hf ⟨j, hj⟩ b H)
-    · next hj => exact Nat.le_antisymm h₁ (Nat.ge_of_not_lt hj) ▸ H
-  simpa [foldl, foldlM] using go (Nat.zero_le _) (Nat.le_refl _) h0
-
--- This proof is the pure version of `Array.SatisfiesM_foldrM`,
--- reproduced to avoid a dependency on `SatisfiesM`.
-theorem foldr_induction
-    {as : Array α} (motive : Nat → β → Prop) {init : β} (h0 : motive as.size init) {f : α → β → β}
-    (hf : ∀ i : Fin as.size, ∀ b, motive (i.1 + 1) b → motive i.1 (f as[i] b)) :
-    motive 0 (as.foldr f init) := by
-  let rec go {i b} (hi : i ≤ as.size) (H : motive i b) :
-    (motive 0) (foldrM.fold (m := Id) f as 0 i hi b) := by
-    unfold foldrM.fold; simp; split
-    · next hi => exact (hi ▸ H)
-    · next hi =>
-      split; {simp at hi}
-      · next i hi' =>
-        exact go _ (hf ⟨i, hi'⟩ b H)
-  simp [foldr, foldrM]; split; {exact go _ h0}
-  · next h => exact (Nat.eq_zero_of_not_pos h ▸ h0)
-
-/-! ### map -/
-
-@[simp] theorem mem_map {f : α → β} {l : Array α} : b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b := by
-  simp only [mem_def, map_data, List.mem_map]
-
-theorem mapM_eq_mapM_data [Monad m] [LawfulMonad m] (f : α → m β) (arr : Array α) :
-    arr.mapM f = return mk (← arr.data.mapM f) := by
-  rw [mapM_eq_foldlM, foldlM_eq_foldlM_data, ← List.foldrM_reverse]
-  conv => rhs; rw [← List.reverse_reverse arr.data]
-  induction arr.data.reverse with
-  | nil => simp; rfl
-  | cons a l ih => simp [ih]; simp [map_eq_pure_bind, push]
-
-theorem mapM_map_eq_foldl (as : Array α) (f : α → β) (i) :
-    mapM.map (m := Id) f as i b = as.foldl (start := i) (fun r a => r.push (f a)) b := by
-  unfold mapM.map
-  split <;> rename_i h
-  · simp only [Id.bind_eq]
-    dsimp [foldl, Id.run, foldlM]
-    rw [mapM_map_eq_foldl, dif_pos (by omega), foldlM.loop, dif_pos h]
-    -- Calling `split` here gives a bad goal.
-    have : size as - i = Nat.succ (size as - i - 1) := by omega
-    rw [this]
-    simp [foldl, foldlM, Id.run, Nat.sub_add_eq]
-  · dsimp [foldl, Id.run, foldlM]
-    rw [dif_pos (by omega), foldlM.loop, dif_neg h]
-    rfl
-termination_by as.size - i
-
-theorem map_eq_foldl (as : Array α) (f : α → β) :
-    as.map f = as.foldl (fun r a => r.push (f a)) #[] :=
-  mapM_map_eq_foldl _ _ _
-
-theorem map_induction (as : Array α) (f : α → β) (motive : Nat → Prop) (h0 : motive 0)
-    (p : Fin as.size → β → Prop) (hs : ∀ i, motive i.1 → p i (f as[i]) ∧ motive (i+1)) :
-    motive as.size ∧
-      ∃ eq : (as.map f).size = as.size, ∀ i h, p ⟨i, h⟩ ((as.map f)[i]) := by
-  have t := foldl_induction (as := as) (β := Array β)
-    (motive := fun i arr => motive i ∧ arr.size = i ∧ ∀ i h2, p i arr[i.1])
-    (init := #[]) (f := fun r a => r.push (f a)) ?_ ?_
-  obtain ⟨m, eq, w⟩ := t
-  · refine ⟨m, by simpa [map_eq_foldl] using eq, ?_⟩
-    intro i h
-    simp [eq] at w
-    specialize w ⟨i, h⟩ h
-    simpa [map_eq_foldl] using w
-  · exact ⟨h0, rfl, nofun⟩
-  · intro i b ⟨m, ⟨eq, w⟩⟩
-    refine ⟨?_, ?_, ?_⟩
-    · exact (hs _ m).2
-    · simp_all
-    · intro j h
-      simp at h ⊢
-      by_cases h' : j < size b
-      · rw [get_push]
-        simp_all
-      · rw [get_push, dif_neg h']
-        simp only [show j = i by omega]
-        exact (hs _ m).1
-
-theorem map_spec (as : Array α) (f : α → β) (p : Fin as.size → β → Prop)
-    (hs : ∀ i, p i (f as[i])) :
-    ∃ eq : (as.map f).size = as.size, ∀ i h, p ⟨i, h⟩ ((as.map f)[i]) := by
-  simpa using map_induction as f (fun _ => True) trivial p (by simp_all)
-
-@[simp] theorem getElem_map (f : α → β) (as : Array α) (i : Nat) (h) :
-    ((as.map f)[i]) = f (as[i]'(size_map .. ▸ h)) := by
-  have := map_spec as f (fun i b => b = f (as[i]))
-  simp only [implies_true, true_implies] at this
-  obtain ⟨eq, w⟩ := this
-  apply w
-  simp_all
-
-/-! ### mapIdx -/
-
--- This could also be prove from `SatisfiesM_mapIdxM`.
-theorem mapIdx_induction (as : Array α) (f : Fin as.size → α → β)
-    (motive : Nat → Prop) (h0 : motive 0)
-    (p : Fin as.size → β → Prop)
-    (hs : ∀ i, motive i.1 → p i (f i as[i]) ∧ motive (i + 1)) :
-    motive as.size ∧ ∃ eq : (Array.mapIdx as f).size = as.size,
-      ∀ i h, p ⟨i, h⟩ ((Array.mapIdx as f)[i]) := by
-  let rec go {bs i j h} (h₁ : j = bs.size) (h₂ : ∀ i h h', p ⟨i, h⟩ bs[i]) (hm : motive j) :
-    let arr : Array β := Array.mapIdxM.map (m := Id) as f i j h bs
-    motive as.size ∧ ∃ eq : arr.size = as.size, ∀ i h, p ⟨i, h⟩ arr[i] := by
-    induction i generalizing j bs with simp [mapIdxM.map]
-    | zero =>
-      have := (Nat.zero_add _).symm.trans h
-      exact ⟨this ▸ hm, h₁ ▸ this, fun _ _ => h₂ ..⟩
-    | succ i ih =>
-      apply @ih (bs.push (f ⟨j, by omega⟩ as[j])) (j + 1) (by omega) (by simp; omega)
-      · intro i i_lt h'
-        rw [get_push]
-        split
-        · apply h₂
-        · simp only [size_push] at h'
-          obtain rfl : i = j := by omega
-          apply (hs ⟨i, by omega⟩ hm).1
-      · exact (hs ⟨j, by omega⟩ hm).2
-  simp [mapIdx, mapIdxM]; exact go rfl nofun h0
-
-theorem mapIdx_spec (as : Array α) (f : Fin as.size → α → β)
-    (p : Fin as.size → β → Prop) (hs : ∀ i, p i (f i as[i])) :
-    ∃ eq : (Array.mapIdx as f).size = as.size,
-      ∀ i h, p ⟨i, h⟩ ((Array.mapIdx as f)[i]) :=
-  (mapIdx_induction _ _ (fun _ => True) trivial p fun _ _ => ⟨hs .., trivial⟩).2
-
-@[simp] theorem size_mapIdx (a : Array α) (f : Fin a.size → α → β) : (a.mapIdx f).size = a.size :=
-  (mapIdx_spec (p := fun _ _ => True) (hs := fun _ => trivial)).1
-
-@[simp] theorem size_zipWithIndex (as : Array α) : as.zipWithIndex.size = as.size :=
-  Array.size_mapIdx _ _
-
-@[simp] theorem getElem_mapIdx (a : Array α) (f : Fin a.size → α → β) (i : Nat)
-    (h : i < (mapIdx a f).size) :
-    haveI : i < a.size := by simp_all
-    (a.mapIdx f)[i] = f ⟨i, this⟩ a[i] :=
-  (mapIdx_spec _ _ (fun i b => b = f i a[i]) fun _ => rfl).2 i _
-
-/-! ### modify -/
-
-@[simp] theorem size_modify (a : Array α) (i : Nat) (f : α → α) : (a.modify i f).size = a.size := by
-  unfold modify modifyM Id.run
-  split <;> simp
-
-theorem get_modify {arr : Array α} {x i} (h : i < arr.size) :
-    (arr.modify x f).get ⟨i, by simp [h]⟩ =
-    if x = i then f (arr.get ⟨i, h⟩) else arr.get ⟨i, h⟩ := by
-  simp [modify, modifyM, Id.run]; split
-  · simp [get_set _ _ _ h]; split <;> simp [*]
-  · rw [if_neg (mt (by rintro rfl; exact h) ‹_›)]
-
-/-! ### filter -/
-
-@[simp] theorem filter_data (p : α → Bool) (l : Array α) :
-    (l.filter p).data = l.data.filter p := by
-  dsimp only [filter]
-  rw [foldl_eq_foldl_data]
-  generalize l.data = l
-  suffices ∀ a, (List.foldl (fun r a => if p a = true then push r a else r) a l).data =
-      a.data ++ List.filter p l by
-    simpa using this #[]
-  induction l with simp
-  | cons => split <;> simp [*]
-
-@[simp] theorem filter_filter (q) (l : Array α) :
-    filter p (filter q l) = filter (fun a => p a ∧ q a) l := by
-  apply ext'
-  simp only [filter_data, List.filter_filter]
-
-@[simp] theorem mem_filter : x ∈ filter p as ↔ x ∈ as ∧ p x := by
-  simp only [mem_def, filter_data, List.mem_filter]
-
-theorem mem_of_mem_filter {a : α} {l} (h : a ∈ filter p l) : a ∈ l :=
-  (mem_filter.mp h).1
-
-/-! ### filterMap -/
-
-@[simp] theorem filterMap_data (f : α → Option β) (l : Array α) :
-    (l.filterMap f).data = l.data.filterMap f := by
-  dsimp only [filterMap, filterMapM]
-  rw [foldlM_eq_foldlM_data]
-  generalize l.data = l
-  have this : ∀ a : Array β, (Id.run (List.foldlM (m := Id) ?_ a l)).data =
-    a.data ++ List.filterMap f l := ?_
-  exact this #[]
-  induction l
-  · simp_all [Id.run]
-  · simp_all [Id.run, List.filterMap_cons]
-    split <;> simp_all
-
-@[simp] theorem mem_filterMap (f : α → Option β) (l : Array α) {b : β} :
-    b ∈ filterMap f l ↔ ∃ a, a ∈ l ∧ f a = some b := by
-  simp only [mem_def, filterMap_data, List.mem_filterMap]
-
-/-! ### empty -/
-
-theorem size_empty : (#[] : Array α).size = 0 := rfl
-
-theorem empty_data : (#[] : Array α).data = [] := rfl
-
-/-! ### append -/
-
-theorem push_eq_append_singleton (as : Array α) (x) : as.push x = as ++ #[x] := rfl
-
-@[simp] theorem mem_append {a : α} {s t : Array α} : a ∈ s ++ t ↔ a ∈ s ∨ a ∈ t := by
-  simp only [mem_def, append_data, List.mem_append]
-
-theorem size_append (as bs : Array α) : (as ++ bs).size = as.size + bs.size := by
-  simp only [size, append_data, List.length_append]
-
-theorem get_append_left {as bs : Array α} {h : i < (as ++ bs).size} (hlt : i < as.size) :
-    (as ++ bs)[i] = as[i] := by
-  simp only [getElem_eq_data_getElem]
-  have h' : i < (as.data ++ bs.data).length := by rwa [← data_length, append_data] at h
-  conv => rhs; rw [← List.getElem_append_left (bs := bs.data) (h' := h')]
-  apply List.get_of_eq; rw [append_data]
-
-theorem get_append_right {as bs : Array α} {h : i < (as ++ bs).size} (hle : as.size ≤ i)
-    (hlt : i - as.size < bs.size := Nat.sub_lt_left_of_lt_add hle (size_append .. ▸ h)) :
-    (as ++ bs)[i] = bs[i - as.size] := by
-  simp only [getElem_eq_data_getElem]
-  have h' : i < (as.data ++ bs.data).length := by rwa [← data_length, append_data] at h
-  conv => rhs; rw [← List.getElem_append_right (h' := h') (h := Nat.not_lt_of_ge hle)]
-  apply List.get_of_eq; rw [append_data]
-
-@[simp] theorem append_nil (as : Array α) : as ++ #[] = as := by
-  apply ext'; simp only [append_data, empty_data, List.append_nil]
-
-@[simp] theorem nil_append (as : Array α) : #[] ++ as = as := by
-  apply ext'; simp only [append_data, empty_data, List.nil_append]
-
-theorem append_assoc (as bs cs : Array α) : as ++ bs ++ cs = as ++ (bs ++ cs) := by
-  apply ext'; simp only [append_data, List.append_assoc]
-
-/-! ### extract -/
-
-theorem extract_loop_zero (as bs : Array α) (start : Nat) : extract.loop as 0 start bs = bs := by
-  rw [extract.loop]; split <;> rfl
-
-theorem extract_loop_succ (as bs : Array α) (size start : Nat) (h : start < as.size) :
-    extract.loop as (size+1) start bs = extract.loop as size (start+1) (bs.push as[start]) := by
-  rw [extract.loop, dif_pos h]; rfl
-
-theorem extract_loop_of_ge (as bs : Array α) (size start : Nat) (h : start ≥ as.size) :
-    extract.loop as size start bs = bs := by
-  rw [extract.loop, dif_neg (Nat.not_lt_of_ge h)]
-
-theorem extract_loop_eq_aux (as bs : Array α) (size start : Nat) :
-    extract.loop as size start bs = bs ++ extract.loop as size start #[] := by
-  induction size using Nat.recAux generalizing start bs with
-  | zero => rw [extract_loop_zero, extract_loop_zero, append_nil]
-  | succ size ih =>
-    if h : start < as.size then
-      rw [extract_loop_succ (h:=h), ih (bs.push _), push_eq_append_singleton]
-      rw [extract_loop_succ (h:=h), ih (#[].push _), push_eq_append_singleton, nil_append]
-      rw [append_assoc]
-    else
-      rw [extract_loop_of_ge (h:=Nat.le_of_not_lt h)]
-      rw [extract_loop_of_ge (h:=Nat.le_of_not_lt h)]
-      rw [append_nil]
-
-theorem extract_loop_eq (as bs : Array α) (size start : Nat) (h : start + size ≤ as.size) :
-  extract.loop as size start bs = bs ++ as.extract start (start + size) := by
-  simp [extract]; rw [extract_loop_eq_aux, Nat.min_eq_left h, Nat.add_sub_cancel_left]
-
-theorem size_extract_loop (as bs : Array α) (size start : Nat) :
-    (extract.loop as size start bs).size = bs.size + min size (as.size - start) := by
-  induction size using Nat.recAux generalizing start bs with
-  | zero => rw [extract_loop_zero, Nat.zero_min, Nat.add_zero]
-  | succ size ih =>
-    if h : start < as.size then
-      rw [extract_loop_succ (h:=h), ih, size_push, Nat.add_assoc, ←Nat.add_min_add_left,
-        Nat.sub_succ, Nat.one_add, Nat.one_add, Nat.succ_pred_eq_of_pos (Nat.sub_pos_of_lt h)]
-    else
-      have h := Nat.le_of_not_gt h
-      rw [extract_loop_of_ge (h:=h), Nat.sub_eq_zero_of_le h, Nat.min_zero, Nat.add_zero]
-
-@[simp] theorem size_extract (as : Array α) (start stop : Nat) :
-    (as.extract start stop).size = min stop as.size - start := by
-  simp [extract]; rw [size_extract_loop, size_empty, Nat.zero_add, Nat.sub_min_sub_right,
-    Nat.min_assoc, Nat.min_self]
-
-theorem get_extract_loop_lt_aux (as bs : Array α) (size start : Nat) (hlt : i < bs.size) :
-    i < (extract.loop as size start bs).size := by
-  rw [size_extract_loop]
-  apply Nat.lt_of_lt_of_le hlt
-  exact Nat.le_add_right ..
-
-theorem get_extract_loop_lt (as bs : Array α) (size start : Nat) (hlt : i < bs.size)
-    (h := get_extract_loop_lt_aux as bs size start hlt) :
-    (extract.loop as size start bs)[i] = bs[i] := by
-  apply Eq.trans _ (get_append_left (bs:=extract.loop as size start #[]) hlt)
-  · rw [size_append]; exact Nat.lt_of_lt_of_le hlt (Nat.le_add_right ..)
-  · congr; rw [extract_loop_eq_aux]
-
-theorem get_extract_loop_ge_aux (as bs : Array α) (size start : Nat) (hge : i ≥ bs.size)
-    (h : i < (extract.loop as size start bs).size) : start + i - bs.size < as.size := by
-  have h : i < bs.size + (as.size - start) := by
-      apply Nat.lt_of_lt_of_le h
-      rw [size_extract_loop]
-      apply Nat.add_le_add_left
-      exact Nat.min_le_right ..
-  rw [Nat.add_sub_assoc hge]
-  apply Nat.add_lt_of_lt_sub'
-  exact Nat.sub_lt_left_of_lt_add hge h
-
-theorem get_extract_loop_ge (as bs : Array α) (size start : Nat) (hge : i ≥ bs.size)
-    (h : i < (extract.loop as size start bs).size)
-    (h' := get_extract_loop_ge_aux as bs size start hge h) :
-    (extract.loop as size start bs)[i] = as[start + i - bs.size] := by
-  induction size using Nat.recAux generalizing start bs with
-  | zero =>
-    rw [size_extract_loop, Nat.zero_min, Nat.add_zero] at h
-    omega
-  | succ size ih =>
-    have : start < as.size := by
-      apply Nat.lt_of_le_of_lt (Nat.le_add_right start (i - bs.size))
-      rwa [← Nat.add_sub_assoc hge]
-    have : i < (extract.loop as size (start+1) (bs.push as[start])).size := by
-      rwa [← extract_loop_succ]
-    have heq : (extract.loop as (size+1) start bs)[i] =
-        (extract.loop as size (start+1) (bs.push as[start]))[i] := by
-      congr 1; rw [extract_loop_succ]
-    rw [heq]
-    if hi : bs.size = i then
-      cases hi
-      have h₁ : bs.size < (bs.push as[start]).size := by rw [size_push]; exact Nat.lt_succ_self ..
-      have h₂ : bs.size < (extract.loop as size (start+1) (bs.push as[start])).size := by
-        rw [size_extract_loop]; apply Nat.lt_of_lt_of_le h₁; exact Nat.le_add_right ..
-      have h : (extract.loop as size (start + 1) (push bs as[start]))[bs.size] = as[start] := by
-        rw [get_extract_loop_lt as (bs.push as[start]) size (start+1) h₁ h₂, get_push_eq]
-      rw [h]; congr; rw [Nat.add_sub_cancel]
-    else
-      have hge : bs.size + 1 ≤ i := Nat.lt_of_le_of_ne hge hi
-      rw [ih (bs.push as[start]) (start+1) ((size_push ..).symm ▸ hge)]
-      congr 1; rw [size_push, Nat.add_right_comm, Nat.add_sub_add_right]
-
-theorem get_extract_aux {as : Array α} {start stop : Nat} (h : i < (as.extract start stop).size) :
-    start + i < as.size := by
-  rw [size_extract] at h; apply Nat.add_lt_of_lt_sub'; apply Nat.lt_of_lt_of_le h
-  apply Nat.sub_le_sub_right; apply Nat.min_le_right
-
-@[simp] theorem get_extract {as : Array α} {start stop : Nat}
-    (h : i < (as.extract start stop).size) :
-    (as.extract start stop)[i] = as[start + i]'(get_extract_aux h) :=
-  show (extract.loop as (min stop as.size - start) start #[])[i]
-    = as[start + i]'(get_extract_aux h) by rw [get_extract_loop_ge]; rfl; exact Nat.zero_le _
-
-@[simp] theorem extract_all (as : Array α) : as.extract 0 as.size = as := by
-  apply ext
-  · rw [size_extract, Nat.min_self, Nat.sub_zero]
-  · intros; rw [get_extract]; congr; rw [Nat.zero_add]
-
-theorem extract_empty_of_stop_le_start (as : Array α) {start stop : Nat} (h : stop ≤ start) :
-    as.extract start stop = #[] := by
-  simp [extract]; rw [←Nat.sub_min_sub_right, Nat.sub_eq_zero_of_le h, Nat.zero_min,
-    extract_loop_zero]
-
-theorem extract_empty_of_size_le_start (as : Array α) {start stop : Nat} (h : as.size ≤ start) :
-    as.extract start stop = #[] := by
-  simp [extract]; rw [←Nat.sub_min_sub_right, Nat.sub_eq_zero_of_le h, Nat.min_zero,
-    extract_loop_zero]
-
-@[simp] theorem extract_empty (start stop : Nat) : (#[] : Array α).extract start stop = #[] :=
-  extract_empty_of_size_le_start _ (Nat.zero_le _)
-
-/-! ### any -/
-
--- Auxiliary for `any_iff_exists`.
-theorem anyM_loop_iff_exists (p : α → Bool) (as : Array α) (start stop) (h : stop ≤ as.size) :
-    anyM.loop (m := Id) p as stop h start = true ↔
-      ∃ i : Fin as.size, start ≤ ↑i ∧ ↑i < stop ∧ p as[i] = true := by
-  unfold anyM.loop
-  split <;> rename_i h₁
-  · dsimp
-    split <;> rename_i h₂
-    · simp only [true_iff]
-      refine ⟨⟨start, by omega⟩, by dsimp; omega, by dsimp; omega, h₂⟩
-    · rw [anyM_loop_iff_exists]
-      constructor
-      · rintro ⟨i, ge, lt, h⟩
-        have : start ≠ i := by rintro rfl; omega
-        exact ⟨i, by omega, lt, h⟩
-      · rintro ⟨i, ge, lt, h⟩
-        have : start ≠ i := by rintro rfl; erw [h] at h₂; simp_all
-        exact ⟨i, by omega, lt, h⟩
-  · simp
-    omega
-termination_by stop - start
-
--- This could also be proved from `SatisfiesM_anyM_iff_exists` in `Batteries.Data.Array.Init.Monadic`
-theorem any_iff_exists (p : α → Bool) (as : Array α) (start stop) :
-    any as p start stop ↔ ∃ i : Fin as.size, start ≤ i.1 ∧ i.1 < stop ∧ p as[i] := by
-  dsimp [any, anyM, Id.run]
-  split
-  · rw [anyM_loop_iff_exists]; rfl
-  · rw [anyM_loop_iff_exists]
-    constructor
-    · rintro ⟨i, ge, _, h⟩
-      exact ⟨i, by omega, by omega, h⟩
-    · rintro ⟨i, ge, _, h⟩
-      exact ⟨i, by omega, by omega, h⟩
-
-theorem any_eq_true (p : α → Bool) (as : Array α) :
-    any as p ↔ ∃ i : Fin as.size, p as[i] := by simp [any_iff_exists, Fin.isLt]
-
-theorem any_def {p : α → Bool} (as : Array α) : as.any p = as.data.any p := by
-  rw [Bool.eq_iff_iff, any_eq_true, List.any_eq_true]; simp only [List.mem_iff_get]
-  exact ⟨fun ⟨i, h⟩ => ⟨_, ⟨i, rfl⟩, h⟩, fun ⟨_, ⟨i, rfl⟩, h⟩ => ⟨i, h⟩⟩
-
-/-! ### all -/
-
-theorem all_eq_not_any_not (p : α → Bool) (as : Array α) (start stop) :
-    all as p start stop = !(any as (!p ·) start stop) := by
-  dsimp [all, allM]
-  rfl
-
-theorem all_iff_forall (p : α → Bool) (as : Array α) (start stop) :
-    all as p start stop ↔ ∀ i : Fin as.size, start ≤ i.1 ∧ i.1 < stop → p as[i] := by
-  rw [all_eq_not_any_not]
-  suffices ¬(any as (!p ·) start stop = true) ↔
-      ∀ i : Fin as.size, start ≤ i.1 ∧ i.1 < stop → p as[i] by
-    simp_all
-  rw [any_iff_exists]
-  simp
-
-theorem all_eq_true (p : α → Bool) (as : Array α) : all as p ↔ ∀ i : Fin as.size, p as[i] := by
-  simp [all_iff_forall, Fin.isLt]
-
-theorem all_def {p : α → Bool} (as : Array α) : as.all p = as.data.all p := by
-  rw [Bool.eq_iff_iff, all_eq_true, List.all_eq_true]; simp only [List.mem_iff_getElem]
-  constructor
-  · rintro w x ⟨r, h, rfl⟩
-    rw [← getElem_eq_data_getElem]
-    exact w ⟨r, h⟩
-  · intro w i
-    exact w as[i] ⟨i, i.2, (getElem_eq_data_getElem as i.2).symm⟩
-
-theorem all_eq_true_iff_forall_mem {l : Array α} : l.all p ↔ ∀ x, x ∈ l → p x := by
-  simp only [all_def, List.all_eq_true, mem_def]
-
-/-! ### contains -/
-
-theorem contains_def [DecidableEq α] {a : α} {as : Array α} : as.contains a ↔ a ∈ as := by
-  rw [mem_def, contains, any_def, List.any_eq_true]; simp [and_comm]
-
-instance [DecidableEq α] (a : α) (as : Array α) : Decidable (a ∈ as) :=
-  decidable_of_iff _ contains_def
-
-/-! ### swap -/
-
-open Fin
-
-@[simp] theorem get_swap_right (a : Array α) {i j : Fin a.size} : (a.swap i j)[j.val] = a[i] :=
-  by simp only [swap, fin_cast_val, get_eq_getElem, getElem_set_eq, getElem_fin]
-
-@[simp] theorem get_swap_left (a : Array α) {i j : Fin a.size} : (a.swap i j)[i.val] = a[j] :=
-  if he : ((Array.size_set _ _ _).symm ▸ j).val = i.val then by
-    simp only [←he, fin_cast_val, get_swap_right, getElem_fin]
-  else by
-    apply Eq.trans
-    · apply Array.get_set_ne
-      · simp only [size_set, Fin.isLt]
-      · assumption
-    · simp [get_set_ne]
-
-@[simp] theorem get_swap_of_ne (a : Array α) {i j : Fin a.size} (hp : p < a.size)
-    (hi : p ≠ i) (hj : p ≠ j) : (a.swap i j)[p]'(a.size_swap .. |>.symm ▸ hp) = a[p] := by
-  apply Eq.trans
-  · have : ((a.size_set i (a.get j)).symm ▸ j).val = j.val := by simp only [fin_cast_val]
-    apply Array.get_set_ne
-    · simp only [this]
-      apply Ne.symm
-      · assumption
-  · apply Array.get_set_ne
-    · apply Ne.symm
-      · assumption
-
-theorem get_swap (a : Array α) (i j : Fin a.size) (k : Nat) (hk: k < a.size) :
-    (a.swap i j)[k]'(by simp_all) = if k = i then a[j] else if k = j then a[i]  else a[k] := by
-  split
-  · simp_all only [get_swap_left]
-  · split <;> simp_all
-
-theorem get_swap' (a : Array α) (i j : Fin a.size) (k : Nat) (hk' : k < (a.swap i j).size) :
-    (a.swap i j)[k] = if k = i then a[j] else if k = j then a[i] else a[k]'(by simp_all) := by
-  apply get_swap
-
-@[simp] theorem swap_swap (a : Array α) {i j : Fin a.size} :
-    (a.swap i j).swap ⟨i.1, (a.size_swap ..).symm ▸i.2⟩ ⟨j.1, (a.size_swap ..).symm ▸j.2⟩ = a := by
-  apply ext
-  · simp only [size_swap]
-  · intros
-    simp only [get_swap']
-    split
-    · simp_all
-    · split <;> simp_all
-
-theorem swap_comm (a : Array α) {i j : Fin a.size} : a.swap i j = a.swap j i := by
-  apply ext
-  · simp only [size_swap]
-  · intros
-    simp only [get_swap']
-    split
-    · split <;> simp_all
-    · split <;> simp_all
-
-
 end Array

src/Init/Data/Array/Mem.lean

@@ -23,24 +23,17 @@ theorem sizeOf_lt_of_mem [SizeOf α] {as : Array α} (h : a ∈ as) : sizeOf a <
   cases as with | _ as =>
   exact Nat.lt_trans (List.sizeOf_lt_of_mem h.val) (by simp_arith)
 
-theorem sizeOf_get [SizeOf α] (as : Array α) (i : Fin as.size) : sizeOf (as.get i) < sizeOf as := by
+@[simp] theorem sizeOf_get [SizeOf α] (as : Array α) (i : Fin as.size) : sizeOf (as.get i) < sizeOf as := by
   cases as with | _ as =>
   exact Nat.lt_trans (List.sizeOf_get ..) (by simp_arith)
 
-@[simp] theorem sizeOf_getElem [SizeOf α] (as : Array α) (i : Nat) (h : i < as.size) :
-  sizeOf (as[i]'h) < sizeOf as := sizeOf_get _ _
-
 /-- This tactic, added to the `decreasing_trivial` toolbox, proves that
 `sizeOf arr[i] < sizeOf arr`, which is useful for well founded recursions
 over a nested inductive like `inductive T | mk : Array T → T`. -/
 macro "array_get_dec" : tactic =>
   `(tactic| first
-    -- subsumed by simp
-    -- | with_reducible apply sizeOf_get
-    -- | with_reducible apply sizeOf_getElem
-    | (with_reducible apply Nat.lt_trans (sizeOf_get ..)); simp_arith
-    | (with_reducible apply Nat.lt_trans (sizeOf_getElem ..)); simp_arith
-    )
+    | apply sizeOf_get
+    | apply Nat.lt_trans (sizeOf_get ..); simp_arith)
 
 macro_rules | `(tactic| decreasing_trivial) => `(tactic| array_get_dec)
 
@@ -50,10 +43,9 @@ provided that `a ∈ arr` which is useful for well founded recursions over a nes
 -- NB: This is analogue to tactic `sizeOf_list_dec`
 macro "array_mem_dec" : tactic =>
   `(tactic| first
-    | with_reducible apply Array.sizeOf_lt_of_mem; assumption; done
-    | with_reducible
-        apply Nat.lt_trans (Array.sizeOf_lt_of_mem ?h)
-        case' h => assumption
+    | apply Array.sizeOf_lt_of_mem; assumption; done
+    | apply Nat.lt_trans (Array.sizeOf_lt_of_mem ?h)
+      case' h => assumption
       simp_arith)
 
 macro_rules | `(tactic| decreasing_trivial) => `(tactic| array_mem_dec)

src/Init/Data/Array/QSort.lean

@@ -27,7 +27,6 @@ def qpartition (as : Array α) (lt : α → α → Bool) (lo hi : Nat) : Nat ×
       let as := as.swap! i hi
       (i, as)
     termination_by hi - j
-    decreasing_by all_goals simp_wf; decreasing_trivial_pre_omega
   loop as lo lo
 
 @[inline] partial def qsort (as : Array α) (lt : α → α → Bool) (low := 0) (high := as.size - 1) : Array α :=

src/Init/Data/Array/Subarray.lean

@@ -9,44 +9,31 @@ import Init.Data.Array.Basic
 universe u v w
 
 structure Subarray (α : Type u)  where
-  array : Array α
+  as : Array α
   start : Nat
   stop : Nat
-  start_le_stop : start ≤ stop
-  stop_le_array_size : stop ≤ array.size
-
-@[deprecated Subarray.array (since := "2024-04-13")]
-abbrev Subarray.as (s : Subarray α) : Array α := s.array
-
-@[deprecated Subarray.start_le_stop (since := "2024-04-13")]
-theorem Subarray.h₁ (s : Subarray α) : s.start ≤ s.stop := s.start_le_stop
-
-@[deprecated Subarray.stop_le_array_size (since := "2024-04-13")]
-theorem Subarray.h₂ (s : Subarray α) : s.stop ≤ s.array.size := s.stop_le_array_size
+  h₁ : start ≤ stop
+  h₂ : stop ≤ as.size
 
 namespace Subarray
 
 def size (s : Subarray α) : Nat :=
   s.stop - s.start
 
-theorem size_le_array_size {s : Subarray α} : s.size ≤ s.array.size := by
-  let {array, start, stop, start_le_stop, stop_le_array_size} := s
-  simp [size]
-  apply Nat.le_trans (Nat.sub_le stop start)
-  assumption
-
 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
+  have : s.start + i.val < s.as.size := by
+   apply Nat.lt_of_lt_of_le _ s.h₂
    have := i.isLt
    simp [size] at this
    rw [Nat.add_comm]
    exact Nat.add_lt_of_lt_sub this
-  s.array[s.start + i.val]
+  s.as[s.start + i.val]
 
 instance : GetElem (Subarray α) Nat α fun xs i => i < xs.size where
   getElem xs i h := xs.get ⟨i, h⟩
 
+instance : LawfulGetElem (Subarray α) Nat α fun xs i => i < xs.size where
+
 @[inline] def getD (s : Subarray α) (i : Nat) (v₀ : α) : α :=
   if h : i < s.size then s.get ⟨i, h⟩ else v₀
 
@@ -55,7 +42,7 @@ abbrev get! [Inhabited α] (s : Subarray α) (i : Nat) : α :=
 
 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) }
+    { s with start := s.start + 1, h₁ := Nat.le_of_lt_succ (Nat.add_lt_add_right h 1) }
   else
     s
 
@@ -63,7 +50,7 @@ def popFront (s : Subarray α) : Subarray α :=
   let sz := USize.ofNat s.stop
   let rec @[specialize] loop (i : USize) (b : β) : m β := do
     if i < sz then
-      let a := s.array.uget i lcProof
+      let a := s.as.uget i lcProof
       match (← f a b) with
       | ForInStep.done  b => pure b
       | ForInStep.yield b => loop (i+1) b
@@ -81,27 +68,27 @@ instance : ForIn m (Subarray α) α where
 
 @[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)
+  as.as.foldlM f (init := init) (start := as.start) (stop := as.stop)
 
 @[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)
+  as.as.foldrM f (init := init) (start := as.stop) (stop := as.start)
 
 @[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)
+  as.as.anyM p (start := as.start) (stop := as.stop)
 
 @[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)
+  as.as.allM p (start := as.start) (stop := as.stop)
 
 @[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)
+  as.as.forM f (start := as.start) (stop := as.stop)
 
 @[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)
+  as.as.forRevM f (start := as.stop) (stop := as.start)
 
 @[inline]
 def foldl {α : Type u} {β : Type v} (f : β → α → β) (init : β) (as : Subarray α) : β :=
@@ -148,25 +135,15 @@ variable {α : Type u}
 
 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
-      { array := as, start := start, stop := stop,
-        start_le_stop := h₁, stop_le_array_size := h₂ }
-    else
-      { array := as, start := stop, stop := stop,
-        start_le_stop := Nat.le_refl _, stop_le_array_size := h₂ }
+     if h₁ : start ≤ stop then
+       { as := as, start := start, stop := stop, h₁ := h₁, h₂ := h₂ }
+     else
+       { as := as, start := stop, stop := stop, h₁ := Nat.le_refl _, h₂ := h₂ }
   else
-    if h₁ : start ≤ as.size then
-      { array := as,
-        start := start,
-        stop := as.size,
-        start_le_stop := h₁,
-        stop_le_array_size := Nat.le_refl _ }
-    else
-      { array := as,
-        start := as.size,
-        stop := as.size,
-        start_le_stop := Nat.le_refl _,
-        stop_le_array_size := Nat.le_refl _ }
+     if h₁ : start ≤ as.size then
+       { as := as, start := start, stop := as.size, h₁ := h₁, h₂ := Nat.le_refl _ }
+     else
+       { as := as, start := as.size, stop := as.size, h₁ := Nat.le_refl _, h₂ := Nat.le_refl _ }
 
 @[coe]
 def ofSubarray (s : Subarray α) : Array α := Id.run do

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

@@ -1,71 +0,0 @@
-/-
-Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: David Thrane Christiansen
--/
-
-prelude
-import Init.Data.Array.Basic
-import Init.Data.Array.Subarray
-import Init.Omega
-
-/-
-This module contains splitting operations on subarrays that crucially rely on `omega` for proof
-automation. Placing them in another module breaks an import cycle, because `omega` itself uses the
-array library.
--/
-
-namespace Subarray
-/--
-Splits a subarray into two parts.
--/
-def split (s : Subarray α) (i : Fin s.size.succ) : (Subarray α × Subarray α) :=
-  let ⟨i', isLt⟩ := i
-  have := s.start_le_stop
-  have := s.stop_le_array_size
-  have : i' ≤ s.stop - s.start := Nat.lt_succ.mp isLt
-  have : s.start + i' ≤ s.stop := by omega
-  have : s.start + i' ≤ s.array.size := by omega
-  have : s.start + i' ≤ s.stop := by
-    simp only [size] at isLt
-    omega
-  let pre := {s with
-    stop := s.start + i',
-    start_le_stop := by omega,
-    stop_le_array_size := by assumption
-  }
-  let post := {s with
-    start := s.start + i'
-    start_le_stop := by assumption
-  }
-  (pre, post)
-
-/--
-Removes the first `i` elements of the subarray. If there are `i` or fewer elements, the resulting
-subarray is empty.
--/
-def drop (arr : Subarray α) (i : Nat) : Subarray α where
-  array := arr.array
-  start := min (arr.start + i) arr.stop
-  stop := arr.stop
-  start_le_stop := by
-    rw [Nat.min_def]
-    split <;> simp only [Nat.le_refl, *]
-  stop_le_array_size := arr.stop_le_array_size
-
-/--
-Keeps only the first `i` elements of the subarray. If there are `i` or fewer elements, the resulting
-subarray is empty.
--/
-def take (arr : Subarray α) (i : Nat) : Subarray α where
-  array := arr.array
-  start := arr.start
-  stop := min (arr.start + i) arr.stop
-  start_le_stop := by
-    have := arr.start_le_stop
-    rw [Nat.min_def]
-    split <;> omega
-  stop_le_array_size := by
-    have := arr.stop_le_array_size
-    rw [Nat.min_def]
-    split <;> omega

src/Init/Data/Array/TakeDrop.lean

@@ -1,17 +0,0 @@
-/-
-Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Markus Himmel
--/
-prelude
-import Init.Data.Array.Lemmas
-import Init.Data.List.Nat.TakeDrop
-
-namespace Array
-
-theorem exists_of_uset (self : Array α) (i d h) :
-    ∃ l₁ l₂, self.data = l₁ ++ self[i] :: l₂ ∧ List.length l₁ = i.toNat ∧
-      (self.uset i d h).data = l₁ ++ d :: l₂ := by
-  simpa [Array.getElem_eq_data_getElem] using List.exists_of_set _
-
-end Array

src/Init/Data/BEq.lean

@@ -1,60 +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, Markus Himmel
--/
-prelude
-import Init.Data.Bool
-
-set_option linter.missingDocs true
-
-/-- `PartialEquivBEq α` says that the `BEq` implementation is a
-partial equivalence relation, that is:
-* it is symmetric: `a == b → b == a`
-* it is transitive: `a == b → b == c → a == c`.
--/
-class PartialEquivBEq (α) [BEq α] : Prop where
-  /-- Symmetry for `BEq`. If `a == b` then `b == a`. -/
-  symm : (a : α) == b → b == a
-  /-- Transitivity for `BEq`. If `a == b` and `b == c` then `a == c`. -/
-  trans : (a : α) == b → b == c → a == c
-
-/-- `ReflBEq α` says that the `BEq` implementation is reflexive. -/
-class ReflBEq (α) [BEq α] : Prop where
-  /-- Reflexivity for `BEq`. -/
-  refl : (a : α) == a
-
-/-- `EquivBEq` says that the `BEq` implementation is an equivalence relation. -/
-class EquivBEq (α) [BEq α] extends PartialEquivBEq α, ReflBEq α : Prop
-
-@[simp]
-theorem BEq.refl [BEq α] [ReflBEq α] {a : α} : a == a :=
-  ReflBEq.refl
-
-theorem beq_of_eq [BEq α] [ReflBEq α] {a b : α} : a = b → a == b
-  | rfl => BEq.refl
-
-theorem BEq.symm [BEq α] [PartialEquivBEq α] {a b : α} : a == b → b == a :=
-  PartialEquivBEq.symm
-
-theorem BEq.comm [BEq α] [PartialEquivBEq α] {a b : α} : (a == b) = (b == a) :=
-  Bool.eq_iff_iff.2 ⟨BEq.symm, BEq.symm⟩
-
-theorem BEq.symm_false [BEq α] [PartialEquivBEq α] {a b : α} : (a == b) = false → (b == a) = false :=
-  BEq.comm (α := α) ▸ id
-
-theorem BEq.trans [BEq α] [PartialEquivBEq α] {a b c : α} : a == b → b == c → a == c :=
-  PartialEquivBEq.trans
-
-theorem BEq.neq_of_neq_of_beq [BEq α] [PartialEquivBEq α] {a b c : α} :
-    (a == b) = false → b == c → (a == c) = false :=
-  fun h₁ h₂ => Bool.eq_false_iff.2 fun h₃ => Bool.eq_false_iff.1 h₁ (BEq.trans h₃ (BEq.symm h₂))
-
-theorem BEq.neq_of_beq_of_neq [BEq α] [PartialEquivBEq α] {a b c : α} :
-    a == b → (b == c) = false → (a == c) = false :=
-  fun h₁ h₂ => Bool.eq_false_iff.2 fun h₃ => Bool.eq_false_iff.1 h₂ (BEq.trans (BEq.symm h₁) h₃)
-
-instance (priority := low) [BEq α] [LawfulBEq α] : EquivBEq α where
-  refl := LawfulBEq.rfl
-  symm h := (beq_iff_eq _ _).2 <| Eq.symm <| (beq_iff_eq _ _).1 h
-  trans hab hbc := (beq_iff_eq _ _).2 <| ((beq_iff_eq _ _).1 hab).trans <| (beq_iff_eq _ _).1 hbc

src/Init/Data/BitVec/Basic.lean

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Joe Hendrix, Wojciech Nawrocki, Leonardo de Moura, Mario Carneiro, Alex Keizer, Harun Khan, Abdalrhman M Mohamed
+Authors: Joe Hendrix, Wojciech Nawrocki, Leonardo de Moura, Mario Carneiro, Alex Keizer
 -/
 prelude
 import Init.Data.Fin.Basic
@@ -20,8 +20,6 @@ We define many of the bitvector operations from the
 of SMT-LIBv2.
 -/
 
-set_option linter.missingDocs true
-
 /--
 A bitvector of the specified width.
 
@@ -36,9 +34,8 @@ structure BitVec (w : Nat) where
   O(1), because we use `Fin` as the internal representation of a bitvector. -/
   toFin : Fin (2^w)
 
-/--
-Bitvectors have decidable equality. This should be used via the instance `DecidableEq (BitVec n)`.
--/
+@[deprecated] abbrev Std.BitVec := _root_.BitVec
+
 -- We manually derive the `DecidableEq` instances for `BitVec` because
 -- we want to have builtin support for bit-vector literals, and we
 -- need a name for this function to implement `canUnfoldAtMatcher` at `WHNF.lean`.
@@ -76,7 +73,7 @@ protected def toNat (a : BitVec n) : Nat := a.toFin.val
 /-- Return the bound in terms of toNat. -/
 theorem isLt (x : BitVec w) : x.toNat < 2^w := x.toFin.isLt
 
-@[deprecated isLt (since := "2024-03-12")]
+@[deprecated isLt]
 theorem toNat_lt (x : BitVec n) : x.toNat < 2^n := x.isLt
 
 /-- Theorem for normalizing the bit vector literal representation. -/
@@ -153,12 +150,12 @@ end Int
 section Syntax
 
 /-- Notation for bit vector literals. `i#n` is a shorthand for `BitVec.ofNat n i`. -/
-syntax:max num noWs "#" noWs term:max : term
-macro_rules | `($i:num#$n) => `(BitVec.ofNat $n $i)
+scoped syntax:max term:max noWs "#" noWs term:max : term
+macro_rules | `($i#$n) => `(BitVec.ofNat $n $i)
 
 /-- Unexpander for bit vector literals. -/
 @[app_unexpander BitVec.ofNat] def unexpandBitVecOfNat : Lean.PrettyPrinter.Unexpander
-  | `($(_) $n $i:num) => `($i:num#$n)
+  | `($(_) $n $i) => `($i#$n)
   | _ => throw ()
 
 /-- Notation for bit vector literals without truncation. `i#'lt` is a shorthand for `BitVec.ofNatLt i lt`. -/
@@ -200,7 +197,7 @@ instance : Add (BitVec n) := ⟨BitVec.add⟩
 Subtraction for bit vectors. This can be interpreted as either signed or unsigned subtraction
 modulo `2^n`.
 -/
-protected def sub (x y : BitVec n) : BitVec n := .ofNat n ((2^n - y.toNat) + x.toNat)
+protected def sub (x y : BitVec n) : BitVec n := .ofNat n (x.toNat + (2^n - y.toNat))
 instance : Sub (BitVec n) := ⟨BitVec.sub⟩
 
 /--
@@ -506,7 +503,7 @@ equivalent to `a * 2^s`, modulo `2^n`.
 
 SMT-Lib name: `bvshl` except this operator uses a `Nat` shift value.
 -/
-protected def shiftLeft (a : BitVec n) (s : Nat) : BitVec n := BitVec.ofNat n (a.toNat <<< s)
+protected def shiftLeft (a : BitVec n) (s : Nat) : BitVec n := (a.toNat <<< s)#n
 instance : HShiftLeft (BitVec w) Nat (BitVec w) := ⟨.shiftLeft⟩
 
 /--
@@ -536,11 +533,6 @@ def sshiftRight (a : BitVec n) (s : Nat) : BitVec n := .ofInt n (a.toInt >>> s)
 instance {n} : HShiftLeft  (BitVec m) (BitVec n) (BitVec m) := ⟨fun x y => x <<< y.toNat⟩
 instance {n} : HShiftRight (BitVec m) (BitVec n) (BitVec m) := ⟨fun x y => x >>> y.toNat⟩
 
-/-- Auxiliary function for `rotateLeft`, which does not take into account the case where
-the rotation amount is greater than the bitvector width. -/
-def rotateLeftAux (x : BitVec w) (n : Nat) : BitVec w :=
-  x <<< n ||| x >>> (w - n)
-
 /--
 Rotate left for bit vectors. All the bits of `x` are shifted to higher positions, with the top `n`
 bits wrapping around to fill the low bits.
@@ -550,15 +542,7 @@ rotateLeft  0b0011#4 3 = 0b1001
 ```
 SMT-Lib name: `rotate_left` except this operator uses a `Nat` shift amount.
 -/
-def rotateLeft (x : BitVec w) (n : Nat) : BitVec w := rotateLeftAux x (n % w)
-
-
-/--
-Auxiliary function for `rotateRight`, which does not take into account the case where
-the rotation amount is greater than the bitvector width.
--/
-def rotateRightAux (x : BitVec w) (n : Nat) : BitVec w :=
-  x >>> n ||| x <<< (w - n)
+def rotateLeft (x : BitVec w) (n : Nat) : BitVec w := x <<< n ||| x >>> (w - n)
 
 /--
 Rotate right for bit vectors. All the bits of `x` are shifted to lower positions, with the
@@ -569,7 +553,7 @@ rotateRight 0b01001#5 1 = 0b10100
 ```
 SMT-Lib name: `rotate_right` except this operator uses a `Nat` shift amount.
 -/
-def rotateRight (x : BitVec w) (n : Nat) : BitVec w := rotateRightAux x (n % w)
+def rotateRight (x : BitVec w) (n : Nat) : BitVec w := x >>> n ||| x <<< (w - n)
 
 /--
 Concatenation of bitvectors. This uses the "big endian" convention that the more significant
@@ -585,9 +569,11 @@ instance : HAppend (BitVec w) (BitVec v) (BitVec (w + v)) := ⟨.append⟩
 -- TODO: write this using multiplication
 /-- `replicate i x` concatenates `i` copies of `x` into a new vector of length `w*i`. -/
 def replicate : (i : Nat) → BitVec w → BitVec (w*i)
-  | 0,   _ => 0#0
+  | 0,   _ => 0
   | n+1, x =>
-    (x ++ replicate n x).cast (by rw [Nat.mul_succ]; omega)
+    have hEq : w + w*n = w*(n + 1) := by
+      rw [Nat.mul_add, Nat.add_comm, Nat.mul_one]
+    hEq ▸ (x ++ replicate n x)
 
 /-!
 ### Cons and Concat
@@ -614,13 +600,6 @@ theorem ofBool_append (msb : Bool) (lsbs : BitVec w) :
     ofBool msb ++ lsbs = (cons msb lsbs).cast (Nat.add_comm ..) :=
   rfl
 
-/--
-`twoPow w i` is the bitvector `2^i` if `i < w`, and `0` otherwise.
-That is, 2 to the power `i`.
-For the bitwise point of view, it has the `i`th bit as `1` and all other bits as `0`.
--/
-def twoPow (w : Nat) (i : Nat) : BitVec w := 1#w <<< i
-
 end bitwise
 
 section normalization_eqs

src/Init/Data/BitVec/Bitblast.lean

@@ -28,8 +28,6 @@ https://github.com/mhk119/lean-smt/blob/bitvec/Smt/Data/Bitwise.lean.
 
 -/
 
-set_option linter.missingDocs true
-
 open Nat Bool
 
 namespace Bool
@@ -100,37 +98,6 @@ theorem carry_succ (i : Nat) (x y : BitVec w) (c : Bool) :
     exact mod_two_pow_add_mod_two_pow_add_bool_lt_two_pow_succ ..
   cases x.toNat.testBit i <;> cases y.toNat.testBit i <;> (simp; omega)
 
-/--
-If `x &&& y = 0`, then the carry bit `(x + y + 0)` is always `false` for any index `i`.
-Intuitively, this is because a carry is only produced when at least two of `x`, `y`, and the
-previous carry are true. However, since `x &&& y = 0`, at most one of `x, y` can be true,
-and thus we never have a previous carry, which means that the sum cannot produce a carry.
--/
-theorem carry_of_and_eq_zero {x y : BitVec w} (h : x &&& y = 0#w) : carry i x y false = false := by
-  induction i with
-  | zero => simp
-  | succ i ih =>
-    replace h := congrArg (·.getLsb i) h
-    simp_all [carry_succ]
-
-/-- The final carry bit when computing `x + y + c` is `true` iff `x.toNat + y.toNat + c.toNat ≥ 2^w`. -/
-theorem carry_width {x y : BitVec w} :
-    carry w x y c = decide (x.toNat + y.toNat + c.toNat ≥ 2^w) := by
-  simp [carry]
-
-/--
-If `x &&& y = 0`, then addition does not overflow, and thus `(x + y).toNat = x.toNat + y.toNat`.
--/
-theorem toNat_add_of_and_eq_zero {x y : BitVec w} (h : x &&& y = 0#w) :
-    (x + y).toNat = x.toNat + y.toNat := by
-  rw [toNat_add]
-  apply Nat.mod_eq_of_lt
-  suffices ¬ decide (x.toNat + y.toNat + false.toNat ≥ 2^w) by
-    simp only [decide_eq_true_eq] at this
-    omega
-  rw [← carry_width]
-  simp [not_eq_true, carry_of_and_eq_zero h]
-
 /-- Carry function for bitwise addition. -/
 def adcb (x y c : Bool) : Bool × Bool := (atLeastTwo x y c, Bool.xor x (Bool.xor y c))
 
@@ -192,304 +159,4 @@ theorem add_eq_adc (w : Nat) (x y : BitVec w) : x + y = (adc x y false).snd := b
 theorem allOnes_sub_eq_not (x : BitVec w) : allOnes w - x = ~~~x := by
   rw [← add_not_self x, BitVec.add_comm, add_sub_cancel]
 
-/-- Addition of bitvectors is the same as bitwise or, if bitwise and is zero. -/
-theorem add_eq_or_of_and_eq_zero {w : Nat} (x y : BitVec w)
-    (h : x &&& y = 0#w) : x + y = x ||| y := by
-  rw [add_eq_adc, adc, iunfoldr_replace (fun _ => false) (x ||| y)]
-  · rfl
-  · simp only [adcb, atLeastTwo, Bool.and_false, Bool.or_false, bne_false, getLsb_or,
-    Prod.mk.injEq, and_eq_false_imp]
-    intros i
-    replace h : (x &&& y).getLsb i = (0#w).getLsb i := by rw [h]
-    simp only [getLsb_and, getLsb_zero, and_eq_false_imp] at h
-    constructor
-    · intros hx
-      simp_all [hx]
-    · by_cases hx : x.getLsb i <;> simp_all [hx]
-
-/-! ### Negation -/
-
-theorem bit_not_testBit (x : BitVec w) (i : Fin w) :
-  getLsb (((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd) i.val = !(getLsb x i.val) := by
-  apply iunfoldr_getLsb (fun _ => ()) i (by simp)
-
-theorem bit_not_add_self (x : BitVec w) :
-  ((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd + x  = -1 := by
-  simp only [add_eq_adc]
-  apply iunfoldr_replace_snd (fun _ => false) (-1) false rfl
-  intro i; simp only [ BitVec.not, adcb, testBit_toNat]
-  rw [iunfoldr_replace_snd (fun _ => ()) (((iunfoldr (fun i c => (c, !(x.getLsb i)))) ()).snd)]
-  <;> simp [bit_not_testBit, negOne_eq_allOnes, getLsb_allOnes]
-
-theorem bit_not_eq_not (x : BitVec w) :
-  ((iunfoldr (fun i c => (c, !(x.getLsb i)))) ()).snd = ~~~ x := by
-  simp [←allOnes_sub_eq_not, BitVec.eq_sub_iff_add_eq.mpr (bit_not_add_self x), ←negOne_eq_allOnes]
-
-theorem bit_neg_eq_neg (x : BitVec w) : -x = (adc (((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd) (BitVec.ofNat w 1) false).snd:= by
-  simp only [← add_eq_adc]
-  rw [iunfoldr_replace_snd ((fun _ => ())) (((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd) _ rfl]
-  · rw [BitVec.eq_sub_iff_add_eq.mpr (bit_not_add_self x), sub_toAdd, BitVec.add_comm _ (-x)]
-    simp [← sub_toAdd, BitVec.sub_add_cancel]
-  · simp [bit_not_testBit x _]
-
-/-! ### Inequalities (le / lt) -/
-
-theorem ult_eq_not_carry (x y : BitVec w) : x.ult y = !carry w x (~~~y) true := by
-  simp only [BitVec.ult, carry, toNat_mod_cancel, toNat_not, toNat_true, ge_iff_le, ← decide_not,
-    Nat.not_le, decide_eq_decide]
-  rw [Nat.mod_eq_of_lt (by omega)]
-  omega
-
-theorem ule_eq_not_ult (x y : BitVec w) : x.ule y = !y.ult x := by
-  simp [BitVec.ule, BitVec.ult, ← decide_not]
-
-theorem ule_eq_carry (x y : BitVec w) : x.ule y = carry w y (~~~x) true := by
-  simp [ule_eq_not_ult, ult_eq_not_carry]
-
-/-- If two bitvectors have the same `msb`, then signed and unsigned comparisons coincide -/
-theorem slt_eq_ult_of_msb_eq {x y : BitVec w} (h : x.msb = y.msb) :
-    x.slt y = x.ult y := by
-  simp only [BitVec.slt, toInt_eq_msb_cond, BitVec.ult, decide_eq_decide, h]
-  cases y.msb <;> simp
-
-/-- If two bitvectors have different `msb`s, then unsigned comparison is determined by this bit -/
-theorem ult_eq_msb_of_msb_neq {x y : BitVec w} (h : x.msb ≠ y.msb) :
-    x.ult y = y.msb := by
-  simp only [BitVec.ult, msb_eq_decide, ne_eq, decide_eq_decide] at *
-  omega
-
-/-- If two bitvectors have different `msb`s, then signed and unsigned comparisons are opposites -/
-theorem slt_eq_not_ult_of_msb_neq {x y : BitVec w} (h : x.msb ≠ y.msb) :
-    x.slt y = !x.ult y := by
-  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) :
-    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) :
-    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
-  simp only [BitVec.sle, BitVec.slt, ← decide_not, decide_eq_decide]; omega
-
-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]
-
-/-! ### mul recurrence for bitblasting -/
-
-/--
-A recurrence that describes multiplication as repeated addition.
-Is useful for bitblasting multiplication.
--/
-def mulRec (l r : BitVec w) (s : Nat) : BitVec w :=
-  let cur := if r.getLsb s then (l <<< s) else 0
-  match s with
-  | 0 => cur
-  | s + 1 => mulRec l r s + cur
-
-theorem mulRec_zero_eq (l r : BitVec w) :
-    mulRec l r 0 = if r.getLsb 0 then l else 0 := by
-  simp [mulRec]
-
-theorem mulRec_succ_eq (l r : BitVec w) (s : Nat) :
-    mulRec l r (s + 1) = mulRec l r s + if r.getLsb (s + 1) then (l <<< (s + 1)) else 0 := rfl
-
-/--
-Recurrence lemma: truncating to `i+1` bits and then zero extending to `w`
-equals truncating upto `i` bits `[0..i-1]`, and then adding the `i`th bit of `x`.
--/
-theorem zeroExtend_truncate_succ_eq_zeroExtend_truncate_add_twoPow (x : BitVec w) (i : Nat) :
-    zeroExtend w (x.truncate (i + 1)) =
-      zeroExtend w (x.truncate i) + (x &&& twoPow w i) := by
-  rw [add_eq_or_of_and_eq_zero]
-  · ext k
-    simp only [getLsb_zeroExtend, Fin.is_lt, decide_True, Bool.true_and, getLsb_or, getLsb_and]
-    by_cases hik : i = k
-    · subst hik
-      simp
-    · simp only [getLsb_twoPow, hik, decide_False, Bool.and_false, Bool.or_false]
-      by_cases hik' : k < (i + 1)
-      · have hik'' : k < i := by omega
-        simp [hik', hik'']
-      · have hik'' : ¬ (k < i) := by omega
-        simp [hik', hik'']
-  · ext k
-    simp
-    by_cases hi : x.getLsb i <;> simp [hi] <;> omega
-
-/--
-Recurrence lemma: multiplying `l` with the first `s` bits of `r` is the
-same as truncating `r` to `s` bits, then zero extending to the original length,
-and performing the multplication. -/
-theorem mulRec_eq_mul_signExtend_truncate (l r : BitVec w) (s : Nat) :
-    mulRec l r s = l * ((r.truncate (s + 1)).zeroExtend w) := by
-  induction s
-  case zero =>
-    simp only [mulRec_zero_eq, ofNat_eq_ofNat, Nat.reduceAdd]
-    by_cases r.getLsb 0
-    case pos hr =>
-      simp only [hr, ↓reduceIte, truncate, zeroExtend_one_eq_ofBool_getLsb_zero,
-        hr, ofBool_true, ofNat_eq_ofNat]
-      rw [zeroExtend_ofNat_one_eq_ofNat_one_of_lt (by omega)]
-      simp
-    case neg hr =>
-      simp [hr, zeroExtend_one_eq_ofBool_getLsb_zero]
-  case succ s' hs =>
-    rw [mulRec_succ_eq, hs]
-    have heq :
-      (if r.getLsb (s' + 1) = true then l <<< (s' + 1) else 0) =
-        (l * (r &&& (BitVec.twoPow w (s' + 1)))) := by
-      simp only [ofNat_eq_ofNat, and_twoPow]
-      by_cases hr : r.getLsb (s' + 1) <;> simp [hr]
-    rw [heq, ← BitVec.mul_add, ← zeroExtend_truncate_succ_eq_zeroExtend_truncate_add_twoPow]
-
-theorem getLsb_mul (x y : BitVec w) (i : Nat) :
-    (x * y).getLsb i = (mulRec x y w).getLsb i := by
-  simp only [mulRec_eq_mul_signExtend_truncate]
-  rw [truncate, ← truncate_eq_zeroExtend, ← truncate_eq_zeroExtend,
-    truncate_truncate_of_le]
-  · simp
-  · omega
-
-/-! ## shiftLeft recurrence for bitblasting -/
-
-/--
-`shiftLeftRec x y n` shifts `x` to the left by the first `n` bits of `y`.
-
-The theorem `shiftLeft_eq_shiftLeftRec` proves the equivalence of `(x <<< y)` and `shiftLeftRec`.
-
-Together with equations `shiftLeftRec_zero`, `shiftLeftRec_succ`,
-this allows us to unfold `shiftLeft` into a circuit for bitblasting.
- -/
-def shiftLeftRec (x : BitVec w₁) (y : BitVec w₂) (n : Nat) : BitVec w₁ :=
-  let shiftAmt := (y &&& (twoPow w₂ n))
-  match n with
-  | 0 => x <<< shiftAmt
-  | n + 1 => (shiftLeftRec x y n) <<< shiftAmt
-
-@[simp]
-theorem shiftLeftRec_zero {x : BitVec w₁} {y : BitVec w₂} :
-    shiftLeftRec x y 0 = x <<< (y &&& twoPow w₂ 0)  := by
-  simp [shiftLeftRec]
-
-@[simp]
-theorem shiftLeftRec_succ {x : BitVec w₁} {y : BitVec w₂} :
-    shiftLeftRec x y (n + 1) = (shiftLeftRec x y n) <<< (y &&& twoPow w₂ (n + 1)) := by
-  simp [shiftLeftRec]
-
-/--
-If `y &&& z = 0`, `x <<< (y ||| z) = x <<< y <<< z`.
-This follows as `y &&& z = 0` implies `y ||| z = y + z`,
-and thus `x <<< (y ||| z) = x <<< (y + z) = x <<< y <<< z`.
--/
-theorem shiftLeft_or_of_and_eq_zero {x : BitVec w₁} {y z : BitVec w₂}
-    (h : y &&& z = 0#w₂) :
-    x <<< (y ||| z) = x <<< y <<< z := by
-  rw [← add_eq_or_of_and_eq_zero _ _ h,
-    shiftLeft_eq', toNat_add_of_and_eq_zero h]
-  simp [shiftLeft_add]
-
-/--
-`shiftLeftRec x y n` shifts `x` to the left by the first `n` bits of `y`.
--/
-theorem shiftLeftRec_eq {x : BitVec w₁} {y : BitVec w₂} {n : Nat} :
-    shiftLeftRec x y n = x <<< (y.truncate (n + 1)).zeroExtend w₂ := by
-  induction n generalizing x y
-  case zero =>
-    ext i
-    simp only [shiftLeftRec_zero, twoPow_zero, Nat.reduceAdd, truncate_one,
-      and_one_eq_zeroExtend_ofBool_getLsb]
-  case succ n ih =>
-    simp only [shiftLeftRec_succ, and_twoPow]
-    rw [ih]
-    by_cases h : y.getLsb (n + 1)
-    · simp only [h, ↓reduceIte]
-      rw [zeroExtend_truncate_succ_eq_zeroExtend_truncate_or_twoPow_of_getLsb_true h,
-        shiftLeft_or_of_and_eq_zero]
-      simp
-    · simp only [h, false_eq_true, ↓reduceIte, shiftLeft_zero']
-      rw [zeroExtend_truncate_succ_eq_zeroExtend_truncate_of_getLsb_false (i := n + 1)]
-      simp [h]
-
-/--
-Show that `x <<< y` can be written in terms of `shiftLeftRec`.
-This can be unfolded in terms of `shiftLeftRec_zero`, `shiftLeftRec_succ` for bitblasting.
--/
-theorem shiftLeft_eq_shiftLeftRec (x : BitVec w₁) (y : BitVec w₂) :
-    x <<< y = shiftLeftRec x y (w₂ - 1) := by
-  rcases w₂ with rfl | w₂
-  · simp [of_length_zero]
-  · simp [shiftLeftRec_eq]
-
-/- ### Logical shift right (ushiftRight) recurrence for bitblasting -/
-
-/--
-`ushiftRightRec x y n` shifts `x` logically to the right by the first `n` bits of `y`.
-
-The theorem `shiftRight_eq_ushiftRightRec` proves the equivalence
-of `(x >>> y)` and `ushiftRightRec`.
-
-Together with equations `ushiftRightRec_zero`, `ushiftRightRec_succ`,
-this allows us to unfold `ushiftRight` into a circuit for bitblasting.
--/
-def ushiftRightRec (x : BitVec w₁) (y : BitVec w₂) (n : Nat) : BitVec w₁ :=
-  let shiftAmt := (y &&& (twoPow w₂ n))
-  match n with
-  | 0 => x >>> shiftAmt
-  | n + 1 => (ushiftRightRec x y n) >>> shiftAmt
-
-@[simp]
-theorem ushiftRightRec_zero (x : BitVec w₁) (y : BitVec w₂) :
-    ushiftRightRec x y 0 = x >>> (y &&& twoPow w₂ 0) := by
-  simp [ushiftRightRec]
-
-@[simp]
-theorem ushiftRightRec_succ (x : BitVec w₁) (y : BitVec w₂) :
-    ushiftRightRec x y (n + 1) = (ushiftRightRec x y n) >>> (y &&& twoPow w₂ (n + 1)) := by
-  simp [ushiftRightRec]
-
-/--
-If `y &&& z = 0`, `x >>> (y ||| z) = x >>> y >>> z`.
-This follows as `y &&& z = 0` implies `y ||| z = y + z`,
-and thus `x >>> (y ||| z) = x >>> (y + z) = x >>> y >>> z`.
--/
-theorem ushiftRight'_or_of_and_eq_zero {x : BitVec w₁} {y z : BitVec w₂}
-    (h : y &&& z = 0#w₂) :
-    x >>> (y ||| z) = x >>> y >>> z := by
-  simp [← add_eq_or_of_and_eq_zero _ _ h, toNat_add_of_and_eq_zero h, shiftRight_add]
-
-theorem ushiftRightRec_eq (x : BitVec w₁) (y : BitVec w₂) (n : Nat) :
-    ushiftRightRec x y n = x >>> (y.truncate (n + 1)).zeroExtend w₂ := by
-  induction n generalizing x y
-  case zero =>
-    ext i
-    simp only [ushiftRightRec_zero, twoPow_zero, Nat.reduceAdd,
-      and_one_eq_zeroExtend_ofBool_getLsb, truncate_one]
-  case succ n ih =>
-    simp only [ushiftRightRec_succ, and_twoPow]
-    rw [ih]
-    by_cases h : y.getLsb (n + 1) <;> simp only [h, ↓reduceIte]
-    · rw [zeroExtend_truncate_succ_eq_zeroExtend_truncate_or_twoPow_of_getLsb_true h,
-        ushiftRight'_or_of_and_eq_zero]
-      simp
-    · simp [zeroExtend_truncate_succ_eq_zeroExtend_truncate_of_getLsb_false, h]
-
-/--
-Show that `x >>> y` can be written in terms of `ushiftRightRec`.
-This can be unfolded in terms of `ushiftRightRec_zero`, `ushiftRightRec_succ` for bitblasting.
--/
-theorem shiftRight_eq_ushiftRightRec (x : BitVec w₁) (y : BitVec w₂) :
-    x >>> y = ushiftRightRec x y (w₂ - 1) := by
-  rcases w₂ with rfl | w₂
-  · simp [of_length_zero]
-  · simp [ushiftRightRec_eq]
-
 end BitVec

src/Init/Data/BitVec/Folds.lean

@@ -1,15 +1,13 @@
 /-
 Copyright (c) 2023 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Joe Hendrix, Harun Khan
+Authors: Joe Hendrix
 -/
 prelude
 import Init.Data.BitVec.Lemmas
 import Init.Data.Nat.Lemmas
 import Init.Data.Fin.Iterate
 
-set_option linter.missingDocs true
-
 namespace BitVec
 
 /--
@@ -50,51 +48,6 @@ private theorem iunfoldr.eq_test
     intro i
     simp_all [truncate_succ]
 
-theorem iunfoldr_getLsb' {f : Fin w → α → α × Bool} (state : Nat → α)
-    (ind : ∀(i : Fin w), (f i (state i.val)).fst = state (i.val+1)) :
-  (∀ i : Fin w, getLsb (iunfoldr f (state 0)).snd i.val = (f i (state i.val)).snd)
-  ∧ (iunfoldr f (state 0)).fst = state w := by
-  unfold iunfoldr
-  simp
-  apply Fin.hIterate_elim
-        (fun j (p : α × BitVec j) => (hj : j ≤ w) →
-         (∀ i : Fin j,  getLsb p.snd i.val = (f ⟨i.val, Nat.lt_of_lt_of_le i.isLt hj⟩ (state i.val)).snd)
-          ∧ p.fst = state j)
-  case hj => simp
-  case init =>
-    intro
-    apply And.intro
-    · intro i
-      have := Fin.size_pos i
-      contradiction
-    · rfl
-  case step =>
-    intro j ⟨s, v⟩ ih hj
-    apply And.intro
-    case left =>
-      intro i
-      simp only [getLsb_cons]
-      have hj2 : j.val ≤ w := by simp
-      cases (Nat.lt_or_eq_of_le (Nat.lt_succ.mp i.isLt)) with
-      | inl h3 => simp [if_neg, (Nat.ne_of_lt h3)]
-                  exact (ih hj2).1 ⟨i.val, h3⟩
-      | inr h3 => simp [h3, if_pos]
-                  cases (Nat.eq_zero_or_pos j.val) with
-                  | inl hj3 => congr
-                               rw [← (ih hj2).2]
-                  | inr hj3 => congr
-                               exact (ih hj2).2
-    case right =>
-      simp
-      have hj2 : j.val ≤ w := by simp
-      rw [← ind j, ← (ih hj2).2]
-
-
-theorem iunfoldr_getLsb {f : Fin w → α → α × Bool} (state : Nat → α) (i : Fin w)
-    (ind : ∀(i : Fin w), (f i (state i.val)).fst = state (i.val+1)) :
-  getLsb (iunfoldr f (state 0)).snd i.val = (f i (state i.val)).snd := by
-  exact (iunfoldr_getLsb' state ind).1 i
-
 /--
 Correctness theorem for `iunfoldr`.
 -/
@@ -105,11 +58,4 @@ theorem iunfoldr_replace
     iunfoldr f a = (state w, value) := by
   simp [iunfoldr.eq_test state value a init step]
 
-theorem iunfoldr_replace_snd
-  {f : Fin w → α → α × Bool} (state : Nat → α) (value : BitVec w) (a : α)
-    (init : state 0 = a)
-    (step : ∀(i : Fin w), f i (state i.val) = (state (i.val+1), value.getLsb i.val)) :
-    (iunfoldr f a).snd = value := by
-  simp [iunfoldr.eq_test state value a init step]
-
 end BitVec

src/Init/Data/BitVec/Lemmas.lean

@@ -1,18 +1,13 @@
 /-
 Copyright (c) 2023 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Joe Hendrix, Harun Khan, Alex Keizer, Abdalrhman M Mohamed,
-
+Authors: Joe Hendrix
 -/
 prelude
 import Init.Data.Bool
 import Init.Data.BitVec.Basic
 import Init.Data.Fin.Lemmas
 import Init.Data.Nat.Lemmas
-import Init.Data.Nat.Mod
-import Init.Data.Int.Bitwise.Lemmas
-
-set_option linter.missingDocs true
 
 namespace BitVec
 
@@ -108,13 +103,7 @@ theorem eq_of_getMsb_eq {x y : BitVec w}
     have q := pred ⟨w - 1 - i, q_lt⟩
     simpa [q_lt, Nat.sub_sub_self, r] using q
 
--- This cannot be a `@[simp]` lemma, as it would be tried at every term.
-theorem of_length_zero {x : BitVec 0} : x = 0#0 := by ext; simp
-
-@[simp] theorem toNat_zero_length (x : BitVec 0) : x.toNat = 0 := by simp [of_length_zero]
-theorem getLsb_zero_length (x : BitVec 0) : x.getLsb i = false := by simp
-theorem getMsb_zero_length (x : BitVec 0) : x.getMsb i = false := by simp
-@[simp] theorem msb_zero_length (x : BitVec 0) : x.msb = false := by simp [BitVec.msb, of_length_zero]
+@[simp] theorem of_length_zero {x : BitVec 0} : x = 0#0 := by ext; simp
 
 theorem eq_of_toFin_eq : ∀ {x y : BitVec w}, x.toFin = y.toFin → x = y
   | ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
@@ -141,19 +130,16 @@ theorem ofBool_eq_iff_eq : ∀(b b' : Bool), BitVec.ofBool b = BitVec.ofBool b'
   getLsb (x#'lt) i = x.testBit i := by
   simp [getLsb, BitVec.ofNatLt]
 
-@[simp, bv_toNat] theorem toNat_ofNat (x w : Nat) : (BitVec.ofNat w x).toNat = x % 2^w := by
+@[simp, bv_toNat] theorem toNat_ofNat (x w : Nat) : (x#w).toNat = x % 2^w := by
   simp [BitVec.toNat, BitVec.ofNat, Fin.ofNat']
 
-@[simp] theorem toFin_ofNat (x : Nat) : toFin (BitVec.ofNat w x) = Fin.ofNat' x (Nat.two_pow_pos w) := rfl
-
 -- Remark: we don't use `[simp]` here because simproc` subsumes it for literals.
 -- If `x` and `n` are not literals, applying this theorem eagerly may not be a good idea.
 theorem getLsb_ofNat (n : Nat) (x : Nat) (i : Nat) :
-  getLsb (BitVec.ofNat n x) i = (i < n && x.testBit i) := by
+  getLsb (x#n) i = (i < n && x.testBit i) := by
   simp [getLsb, BitVec.ofNat, Fin.val_ofNat']
 
-@[simp, deprecated toNat_ofNat (since := "2024-02-22")]
-theorem toNat_zero (n : Nat) : (0#n).toNat = 0 := by trivial
+@[simp, deprecated toNat_ofNat] theorem toNat_zero (n : Nat) : (0#n).toNat = 0 := by trivial
 
 @[simp] theorem getLsb_zero : (0#w).getLsb i = false := by simp [getLsb]
 
@@ -165,13 +151,6 @@ theorem toNat_zero (n : Nat) : (0#n).toNat = 0 := by trivial
 private theorem lt_two_pow_of_le {x m n : Nat} (lt : x < 2 ^ m) (le : m ≤ n) : x < 2 ^ n :=
   Nat.lt_of_lt_of_le lt (Nat.pow_le_pow_of_le_right (by trivial : 0 < 2) le)
 
-@[simp]
-theorem getLsb_ofBool (b : Bool) (i : Nat) : (BitVec.ofBool b).getLsb i = ((i = 0) && b) := by
-  rcases b with rfl | rfl
-  · simp [ofBool]
-  · simp only [ofBool, ofNat_eq_ofNat, cond_true, getLsb_ofNat, Bool.and_true]
-    by_cases hi : i = 0 <;> simp [hi] <;> omega
-
 /-! ### msb -/
 
 @[simp] theorem msb_zero : (0#w).msb = false := by simp [BitVec.msb, getMsb]
@@ -187,13 +166,15 @@ theorem msb_eq_getLsb_last (x : BitVec w) :
     x.getLsb (w-1) = decide (2 ^ (w-1) ≤ x.toNat) := by
   rcases w with rfl | w
   · simp
-  · simp only [getLsb, Nat.testBit_to_div_mod, Nat.succ_sub_succ_eq_sub, Nat.sub_zero]
+  · simp only [Nat.zero_lt_succ, decide_True, getLsb, Nat.testBit, Nat.succ_sub_succ_eq_sub,
+    Nat.sub_zero, Nat.and_one_is_mod, Bool.true_and, Nat.shiftRight_eq_div_pow]
     rcases (Nat.lt_or_ge (BitVec.toNat x) (2 ^ w)) with h | h
     · simp [Nat.div_eq_of_lt h, h]
     · simp only [h]
       rw [Nat.div_eq_sub_div (Nat.two_pow_pos w) h, Nat.div_eq_of_lt]
       · decide
-      · omega
+      · have : BitVec.toNat x < 2^w + 2^w := by simpa [Nat.pow_succ, Nat.mul_two] using x.isLt
+        omega
 
 @[bv_toNat] theorem getLsb_succ_last (x : BitVec (w + 1)) :
     x.getLsb w = decide (2 ^ w ≤ x.toNat) := getLsb_last x
@@ -233,29 +214,17 @@ theorem toInt_eq_toNat_cond (i : BitVec n) :
       if 2*i.toNat < 2^n then
         (i.toNat : Int)
       else
-        (i.toNat : Int) - (2^n : Nat) :=
-  rfl
-
-theorem msb_eq_false_iff_two_mul_lt (x : BitVec w) : x.msb = false ↔ 2 * x.toNat < 2^w := by
-  cases w <;> simp [Nat.pow_succ, Nat.mul_comm _ 2, msb_eq_decide]
-
-theorem msb_eq_true_iff_two_mul_ge (x : BitVec w) : x.msb = true ↔ 2 * x.toNat ≥ 2^w := by
-  simp [← Bool.ne_false_iff, msb_eq_false_iff_two_mul_lt]
-
-/-- Characterize `x.toInt` in terms of `x.msb`. -/
-theorem toInt_eq_msb_cond (x : BitVec w) :
-    x.toInt = if x.msb then (x.toNat : Int) - (2^w : Nat) else (x.toNat : Int) := by
-  simp only [BitVec.toInt, ← msb_eq_false_iff_two_mul_lt]
-  cases x.msb <;> rfl
-
+        (i.toNat : Int) - (2^n : Nat) := by
+  unfold BitVec.toInt
+  split <;> omega
 
 theorem toInt_eq_toNat_bmod (x : BitVec n) : x.toInt = Int.bmod x.toNat (2^n) := by
   simp only [toInt_eq_toNat_cond]
   split
-  next g =>
+  case inl g =>
     rw [Int.bmod_pos] <;> simp only [←Int.ofNat_emod, toNat_mod_cancel]
     omega
-  next g =>
+  case inr g =>
     rw [Int.bmod_neg] <;> simp only [←Int.ofNat_emod, toNat_mod_cancel]
     omega
 
@@ -269,12 +238,6 @@ theorem eq_of_toInt_eq {i j : BitVec n} : i.toInt = j.toInt → i = j := by
   have _jlt := j.isLt
   split <;> split <;> omega
 
-theorem toInt_inj (x y : BitVec n) : x.toInt = y.toInt ↔ x = y :=
-  Iff.intro eq_of_toInt_eq (congrArg BitVec.toInt)
-
-theorem toInt_ne (x y : BitVec n) : x.toInt ≠ y.toInt ↔ x ≠ y  := by
-  rw [Ne, toInt_inj]
-
 @[simp] theorem toNat_ofInt {n : Nat} (i : Int) :
   (BitVec.ofInt n i).toNat = (i % (2^n : Nat)).toNat := by
   unfold BitVec.ofInt
@@ -290,14 +253,8 @@ theorem toInt_ofNat {n : Nat} (x : Nat) :
   have p : 0 ≤ i % (2^n : Nat) := by omega
   simp [toInt_eq_toNat_bmod, Int.toNat_of_nonneg p]
 
-@[simp] theorem ofInt_natCast (w n : Nat) :
-  BitVec.ofInt w (n : Int) = BitVec.ofNat w n := rfl
-
 /-! ### zeroExtend and truncate -/
 
-theorem truncate_eq_zeroExtend {v : Nat} {x : BitVec w} :
-  truncate v x = zeroExtend v x := rfl
-
 @[simp, bv_toNat] theorem toNat_zeroExtend' {m n : Nat} (p : m ≤ n) (x : BitVec m) :
     (zeroExtend' p x).toNat = x.toNat := by
   unfold zeroExtend'
@@ -327,28 +284,31 @@ theorem zeroExtend'_eq {x : BitVec w} (h : w ≤ v) : x.zeroExtend' h = x.zeroEx
   let ⟨x, lt_n⟩ := x
   simp [truncate, zeroExtend]
 
-@[simp] theorem zeroExtend_zero (m n : Nat) : zeroExtend m 0#n = 0#m := by
+@[simp] theorem zeroExtend_zero (m n : Nat) : zeroExtend m (0#n) = 0#m := by
   apply eq_of_toNat_eq
   simp [toNat_zeroExtend]
 
-theorem truncate_eq (x : BitVec n) : truncate n x = x := zeroExtend_eq x
+@[simp] theorem truncate_eq (x : BitVec n) : truncate n x = x := zeroExtend_eq x
 
-@[simp] theorem ofNat_toNat (m : Nat) (x : BitVec n) : BitVec.ofNat m x.toNat = truncate m x := by
+@[simp] theorem ofNat_toNat (m : Nat) (x : BitVec n) : x.toNat#m = truncate m x := by
   apply eq_of_toNat_eq
   simp
 
 /-- Moves one-sided left toNat equality to BitVec equality. -/
 theorem toNat_eq_nat (x : BitVec w) (y : Nat)
-  : (x.toNat = y) ↔ (y < 2^w ∧ (x = BitVec.ofNat w y)) := by
+  : (x.toNat = y) ↔ (y < 2^w ∧ (x = y#w)) := by
   apply Iff.intro
   · intro eq
-    simp [←eq, x.isLt]
+    simp at eq
+    have lt := x.isLt
+    simp [eq] at lt
+    simp [←eq, lt, x.isLt]
   · intro eq
     simp [Nat.mod_eq_of_lt, eq]
 
 /-- Moves one-sided right toNat equality to BitVec equality. -/
 theorem nat_eq_toNat (x : BitVec w) (y : Nat)
-  : (y = x.toNat) ↔ (y < 2^w ∧ (x = BitVec.ofNat w y)) := by
+  : (y = x.toNat) ↔ (y < 2^w ∧ (x = y#w)) := by
   rw [@eq_comm _ _ x.toNat]
   apply toNat_eq_nat
 
@@ -376,7 +336,7 @@ theorem nat_eq_toNat (x : BitVec w) (y : Nat)
 @[simp] theorem getMsb_zeroExtend_add {x : BitVec w} (h : k ≤ i) :
     (x.zeroExtend (w + k)).getMsb i = x.getMsb (i - k) := by
   by_cases h : w = 0
-  · subst h; simp [of_length_zero]
+  · subst h; simp
   simp only [getMsb, getLsb_zeroExtend]
   by_cases h₁ : i < w + k <;> by_cases h₂ : i - k < w <;> by_cases h₃ : w + k - 1 - i < w + k
     <;> simp [h₁, h₂, h₃]
@@ -385,7 +345,7 @@ theorem nat_eq_toNat (x : BitVec w) (y : Nat)
   all_goals (first | apply getLsb_ge | apply Eq.symm; apply getLsb_ge)
     <;> omega
 
-theorem getLsb_truncate (m : Nat) (x : BitVec n) (i : Nat) :
+@[simp] theorem getLsb_truncate (m : Nat) (x : BitVec n) (i : Nat) :
     getLsb (truncate m x) i = (decide (i < m) && getLsb x i) :=
   getLsb_zeroExtend m x i
 
@@ -404,12 +364,6 @@ theorem msb_truncate (x : BitVec w) : (x.truncate (k + 1)).msb = x.getLsb k := b
     (x.truncate l).truncate k = x.truncate k :=
   zeroExtend_zeroExtend_of_le x h
 
-/--Truncating by the bitwidth has no effect. -/
-@[simp]
-theorem truncate_eq_self {x : BitVec w} : x.truncate w = x := by
-  ext i
-  simp [getLsb_zeroExtend]
-
 @[simp] theorem truncate_cast {h : w = v} : (cast h x).truncate k = x.truncate k := by
   apply eq_of_getLsb_eq
   simp
@@ -422,28 +376,6 @@ theorem msb_zeroExtend (x : BitVec w) : (x.zeroExtend v).msb = (decide (0 < v) &
 theorem msb_zeroExtend' (x : BitVec w) (h : w ≤ v) : (x.zeroExtend' h).msb = (decide (0 < v) && x.getLsb (v - 1)) := by
   rw [zeroExtend'_eq, msb_zeroExtend]
 
-/-- zero extending a bitvector to width 1 equals the boolean of the lsb. -/
-theorem zeroExtend_one_eq_ofBool_getLsb_zero (x : BitVec w) :
-    x.zeroExtend 1 = BitVec.ofBool (x.getLsb 0) := by
-  ext i
-  simp [getLsb_zeroExtend, Fin.fin_one_eq_zero i]
-
-/-- Zero extending `1#v` to `1#w` equals `1#w` when `v > 0`. -/
-theorem zeroExtend_ofNat_one_eq_ofNat_one_of_lt {v w : Nat} (hv : 0 < v) :
-    (BitVec.ofNat v 1).zeroExtend w = BitVec.ofNat w 1 := by
-  ext ⟨i, hilt⟩
-  simp only [getLsb_zeroExtend, hilt, decide_True, getLsb_ofNat, Bool.true_and,
-    Bool.and_iff_right_iff_imp, decide_eq_true_eq]
-  intros hi₁
-  have hv := Nat.testBit_one_eq_true_iff_self_eq_zero.mp hi₁
-  omega
-
-/-- Truncating to width 1 produces a bitvector equal to the least significant bit. -/
-theorem truncate_one {x : BitVec w} :
-    x.truncate 1 = ofBool (x.getLsb 0) := by
-  ext i
-  simp [show i = 0 by omega]
-
 /-! ## extractLsb -/
 
 @[simp]
@@ -452,7 +384,7 @@ protected theorem extractLsb_ofFin {n} (x : Fin (2^n)) (hi lo : Nat) :
 
 @[simp]
 protected theorem extractLsb_ofNat (x n : Nat) (hi lo : Nat) :
-  extractLsb hi lo (BitVec.ofNat n x) = .ofNat (hi - lo + 1) ((x % 2^n) >>> lo) := by
+  extractLsb hi lo x#n = .ofNat (hi - lo + 1) ((x % 2^n) >>> lo) := by
   apply eq_of_getLsb_eq
   intro ⟨i, _lt⟩
   simp [BitVec.ofNat]
@@ -503,11 +435,6 @@ protected theorem extractLsb_ofNat (x n : Nat) (hi lo : Nat) :
   ext
   simp
 
-theorem or_assoc (x y z : BitVec w) :
-    x ||| y ||| z = x ||| (y ||| z) := by
-  ext i
-  simp [Bool.or_assoc]
-
 /-! ### and -/
 
 @[simp] theorem toNat_and (x y : BitVec v) :
@@ -534,16 +461,6 @@ theorem or_assoc (x y z : BitVec w) :
   ext
   simp
 
-theorem and_assoc (x y z : BitVec w) :
-    x &&& y &&& z = x &&& (y &&& z) := by
-  ext i
-  simp [Bool.and_assoc]
-
-theorem and_comm (x y : BitVec w) :
-    x &&& y = y &&& x := by
-  ext i
-  simp [Bool.and_comm]
-
 /-! ### xor -/
 
 @[simp] theorem toNat_xor (x y : BitVec v) :
@@ -564,11 +481,6 @@ theorem and_comm (x y : BitVec w) :
   ext
   simp
 
-theorem xor_assoc (x y z : BitVec w) :
-    x ^^^ y ^^^ z = x ^^^ (y ^^^ z) := by
-  ext i
-  simp [Bool.xor_assoc]
-
 /-! ### not -/
 
 theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
@@ -621,7 +533,7 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
   ext
   simp_all [lt_of_getLsb]
 
-@[simp] theorem xor_cast {x y : BitVec w} (h : w = w') : cast h x ^^^ cast h y = cast h (x ^^^ y) := by
+@[simp] theorem xor_cast {x y : BitVec w} (h : w = w') : cast h x &&& cast h y = cast h (x &&& y) := by
   ext
   simp_all [lt_of_getLsb]
 
@@ -634,15 +546,6 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
 @[simp] theorem toFin_shiftLeft {n : Nat} (x : BitVec w) :
     BitVec.toFin (x <<< n) = Fin.ofNat' (x.toNat <<< n) (Nat.two_pow_pos w) := rfl
 
-@[simp]
-theorem shiftLeft_zero_eq (x : BitVec w) : x <<< 0 = x := by
-  apply eq_of_toNat_eq
-  simp
-
-@[simp]
-theorem zero_shiftLeft (n : Nat) : 0#w <<< n = 0#w := by
-  simp [bv_toNat]
-
 @[simp] theorem getLsb_shiftLeft (x : BitVec m) (n) :
     getLsb (x <<< n) i = (decide (i < m) && !decide (i < n) && getLsb x (i - n)) := by
   rw [← testBit_toNat, getLsb]
@@ -692,38 +595,6 @@ theorem shiftLeftZeroExtend_eq {x : BitVec w} :
     (shiftLeftZeroExtend x i).msb = x.msb := by
   simp [shiftLeftZeroExtend_eq, BitVec.msb]
 
-theorem shiftLeft_add {w : Nat} (x : BitVec w) (n m : Nat) :
-    x <<< (n + m) = (x <<< n) <<< m := by
-  ext i
-  simp only [getLsb_shiftLeft, Fin.is_lt, decide_True, Bool.true_and]
-  rw [show i - (n + m) = (i - m - n) by omega]
-  cases h₂ : decide (i < m) <;>
-  cases h₃ : decide (i - m < w) <;>
-  cases h₄ : decide (i - m < n) <;>
-  cases h₅ : decide (i < n + m) <;>
-    simp at * <;> omega
-
-@[deprecated shiftLeft_add (since := "2024-06-02")]
-theorem shiftLeft_shiftLeft {w : Nat} (x : BitVec w) (n m : Nat) :
-    (x <<< n) <<< m = x <<< (n + m) := by
-  rw [shiftLeft_add]
-
-/-! ### shiftLeft reductions from BitVec to Nat -/
-
-@[simp]
-theorem shiftLeft_eq' {x : BitVec w₁} {y : BitVec w₂} : x <<< y = x <<< y.toNat := by rfl
-
-@[simp]
-theorem shiftLeft_zero' {x : BitVec w₁} : x <<< 0#w₂ = x := by simp
-
-theorem shiftLeft_shiftLeft' {x : BitVec w₁} {y : BitVec w₂} {z : BitVec w₃} :
-    x <<< y <<< z = x <<< (y.toNat + z.toNat) := by
-  simp [shiftLeft_add]
-
-theorem getLsb_shiftLeft' {x : BitVec w₁} {y : BitVec w₂} {i : Nat} :
-    (x <<< y).getLsb i = (decide (i < w₁) && !decide (i < y.toNat) && x.getLsb (i - y.toNat)) := by
-  simp [shiftLeft_eq', getLsb_shiftLeft]
-
 /-! ### ushiftRight -/
 
 @[simp, bv_toNat] theorem toNat_ushiftRight (x : BitVec n) (i : Nat) :
@@ -733,133 +604,6 @@ theorem getLsb_shiftLeft' {x : BitVec w₁} {y : BitVec w₂} {i : Nat} :
     getLsb (x >>> i) j = getLsb x (i+j) := by
   unfold getLsb ; simp
 
-@[simp]
-theorem ushiftRight_zero_eq (x : BitVec w) : x >>> 0 = x := by
-  simp [bv_toNat]
-
-/-! ### ushiftRight reductions from BitVec to Nat -/
-
-@[simp]
-theorem ushiftRight_eq' (x : BitVec w₁) (y : BitVec w₂) :
-    x >>> y = x >>> y.toNat := by rfl
-
-/-! ### sshiftRight -/
-
-theorem sshiftRight_eq {x : BitVec n} {i : Nat} :
-    x.sshiftRight i = BitVec.ofInt n (x.toInt >>> i) := by
-  apply BitVec.eq_of_toInt_eq
-  simp [BitVec.sshiftRight]
-
-/-- if the msb is false, the arithmetic shift right equals logical shift right -/
-theorem sshiftRight_eq_of_msb_false {x : BitVec w} {s : Nat} (h : x.msb = false) :
-    (x.sshiftRight s) = x >>> s := by
-  apply BitVec.eq_of_toNat_eq
-  rw [BitVec.sshiftRight_eq, BitVec.toInt_eq_toNat_cond]
-  have hxbound : 2 * x.toNat < 2 ^ w := (BitVec.msb_eq_false_iff_two_mul_lt x).mp h
-  simp only [hxbound, ↓reduceIte, Int.natCast_shiftRight, Int.ofNat_eq_coe, ofInt_natCast,
-    toNat_ofNat, toNat_ushiftRight]
-  replace hxbound : x.toNat >>> s < 2 ^ w := by
-    rw [Nat.shiftRight_eq_div_pow]
-    exact Nat.lt_of_le_of_lt (Nat.div_le_self ..) x.isLt
-  apply Nat.mod_eq_of_lt hxbound
-
-/--
-If the msb is `true`, the arithmetic shift right equals negating,
-then logical shifting right, then negating again.
-The double negation preserves the lower bits that have been shifted,
-and the outer negation ensures that the high bits are '1'. -/
-theorem sshiftRight_eq_of_msb_true {x : BitVec w} {s : Nat} (h : x.msb = true) :
-    (x.sshiftRight s) = ~~~((~~~x) >>> s) := by
-  apply BitVec.eq_of_toNat_eq
-  rcases w with rfl | w
-  · simp
-  · rw [BitVec.sshiftRight_eq, BitVec.toInt_eq_toNat_cond]
-    have hxbound : (2 * x.toNat ≥ 2 ^ (w + 1)) := (BitVec.msb_eq_true_iff_two_mul_ge x).mp h
-    replace hxbound : ¬ (2 * x.toNat < 2 ^ (w + 1)) := by omega
-    simp only [hxbound, ↓reduceIte, toNat_ofInt, toNat_not, toNat_ushiftRight]
-    rw [← Int.subNatNat_eq_coe, Int.subNatNat_of_lt (by omega),
-        Nat.pred_eq_sub_one, Int.negSucc_shiftRight,
-        Int.emod_negSucc, Int.natAbs_ofNat, Nat.succ_eq_add_one,
-        Int.subNatNat_of_le (by omega), Int.toNat_ofNat, Nat.mod_eq_of_lt,
-        Nat.sub_right_comm]
-    omega
-    · rw [Nat.shiftRight_eq_div_pow]
-      apply Nat.lt_of_le_of_lt (Nat.div_le_self _ _) (by omega)
-
-theorem getLsb_sshiftRight (x : BitVec w) (s i : Nat) :
-    getLsb (x.sshiftRight s) i =
-      (!decide (w ≤ i) && if s + i < w then x.getLsb (s + i) else x.msb) := by
-  rcases hmsb : x.msb with rfl | rfl
-  · simp only [sshiftRight_eq_of_msb_false hmsb, getLsb_ushiftRight, Bool.if_false_right]
-    by_cases hi : i ≥ w
-    · simp only [hi, decide_True, Bool.not_true, Bool.false_and]
-      apply getLsb_ge
-      omega
-    · simp only [hi, decide_False, Bool.not_false, Bool.true_and, Bool.iff_and_self,
-        decide_eq_true_eq]
-      intros hlsb
-      apply BitVec.lt_of_getLsb _ _ hlsb
-  · by_cases hi : i ≥ w
-    · simp [hi]
-    · simp only [sshiftRight_eq_of_msb_true hmsb, getLsb_not, getLsb_ushiftRight, Bool.not_and,
-        Bool.not_not, hi, decide_False, Bool.not_false, Bool.if_true_right, Bool.true_and,
-        Bool.and_iff_right_iff_imp, Bool.or_eq_true, Bool.not_eq_true', decide_eq_false_iff_not,
-        Nat.not_lt, decide_eq_true_eq]
-      omega
-
-/-! ### signExtend -/
-
-/-- Equation theorem for `Int.sub` when both arguments are `Int.ofNat` -/
-private theorem Int.ofNat_sub_ofNat_of_lt {n m : Nat} (hlt : n < m) :
-    (n : Int) - (m : Int) = -(↑(m - 1 - n) + 1) := by
-  omega
-
-/-- Equation theorem for `Int.mod` -/
-private theorem Int.negSucc_emod (m : Nat) (n : Int) :
-    -(m + 1) % n = Int.subNatNat (Int.natAbs n) ((m % Int.natAbs n) + 1) := rfl
-
-/-- The sign extension is the same as zero extending when `msb = false`. -/
-theorem signExtend_eq_not_zeroExtend_not_of_msb_false {x : BitVec w} {v : Nat} (hmsb : x.msb = false) :
-    x.signExtend v = x.zeroExtend v := by
-  ext i
-  by_cases hv : i < v
-  · simp only [signExtend, getLsb, getLsb_zeroExtend, hv, decide_True, Bool.true_and, toNat_ofInt,
-      BitVec.toInt_eq_msb_cond, hmsb, ↓reduceIte]
-    rw [Int.ofNat_mod_ofNat, Int.toNat_ofNat, Nat.testBit_mod_two_pow]
-    simp [BitVec.testBit_toNat]
-  · simp only [getLsb_zeroExtend, hv, decide_False, Bool.false_and]
-    apply getLsb_ge
-    omega
-
-/--
-The sign extension is a bitwise not, followed by a zero extend, followed by another bitwise not
-when `msb = true`. The double bitwise not ensures that the high bits are '1',
-and the lower bits are preserved. -/
-theorem signExtend_eq_not_zeroExtend_not_of_msb_true {x : BitVec w} {v : Nat} (hmsb : x.msb = true) :
-    x.signExtend v = ~~~((~~~x).zeroExtend v) := by
-  apply BitVec.eq_of_toNat_eq
-  simp only [signExtend, BitVec.toInt_eq_msb_cond, toNat_ofInt, toNat_not,
-    toNat_truncate, hmsb, ↓reduceIte]
-  norm_cast
-  rw [Int.ofNat_sub_ofNat_of_lt, Int.negSucc_emod]
-  simp only [Int.natAbs_ofNat, Nat.succ_eq_add_one]
-  rw [Int.subNatNat_of_le]
-  · rw [Int.toNat_ofNat, Nat.add_comm, Nat.sub_add_eq]
-  · apply Nat.le_trans
-    · apply Nat.succ_le_of_lt
-      apply Nat.mod_lt
-      apply Nat.two_pow_pos
-    · apply Nat.le_refl
-  · omega
-
-@[simp] theorem getLsb_signExtend (x  : BitVec w) {v i : Nat} :
-    (x.signExtend v).getLsb i = (decide (i < v) && if i < w then x.getLsb i else x.msb) := by
-  rcases hmsb : x.msb with rfl | rfl
-  · rw [signExtend_eq_not_zeroExtend_not_of_msb_false hmsb]
-    by_cases (i < v) <;> by_cases (i < w) <;> simp_all <;> omega
-  · rw [signExtend_eq_not_zeroExtend_not_of_msb_true hmsb]
-    by_cases (i < v) <;> by_cases (i < w) <;> simp_all <;> omega
-
 /-! ### append -/
 
 theorem append_def (x : BitVec v) (y : BitVec w) :
@@ -936,16 +680,6 @@ theorem msb_append {x : BitVec w} {y : BitVec v} :
   simp only [getLsb_append, cond_eq_if]
   split <;> simp [*]
 
-theorem shiftRight_add {w : Nat} (x : BitVec w) (n m : Nat) :
-    x >>> (n + m) = (x >>> n) >>> m:= by
-  ext i
-  simp [Nat.add_assoc n m i]
-
-@[deprecated shiftRight_add (since := "2024-06-02")]
-theorem shiftRight_shiftRight {w : Nat} (x : BitVec w) (n m : Nat) :
-    (x >>> n) >>> m = x >>> (n + m) := by
-  rw [shiftRight_add]
-
 /-! ### rev -/
 
 theorem getLsb_rev (x : BitVec w) (i : Fin w) :
@@ -1083,56 +817,30 @@ Definition of bitvector addition as a nat.
   .ofFin x + y = .ofFin (x + y.toFin) := rfl
 @[simp] theorem add_ofFin (x : BitVec n) (y : Fin (2^n)) :
   x + .ofFin y = .ofFin (x.toFin + y) := rfl
-
-theorem ofNat_add {n} (x y : Nat) : BitVec.ofNat n (x + y) = BitVec.ofNat n x + BitVec.ofNat n y := by
+@[simp] theorem ofNat_add_ofNat {n} (x y : Nat) : x#n + y#n = (x + y)#n := by
   apply eq_of_toNat_eq ; simp [BitVec.ofNat]
 
-theorem ofNat_add_ofNat {n} (x y : Nat) : BitVec.ofNat n x + BitVec.ofNat n y = BitVec.ofNat n (x + y) :=
-  (ofNat_add x y).symm
-
 protected theorem add_assoc (x y z : BitVec n) : x + y + z = x + (y + z) := by
   apply eq_of_toNat_eq ; simp [Nat.add_assoc]
-instance : Std.Associative (α := BitVec n) (· + ·) := ⟨BitVec.add_assoc⟩
 
 protected theorem add_comm (x y : BitVec n) : x + y = y + x := by
   simp [add_def, Nat.add_comm]
-instance : Std.Commutative (α := BitVec n) (· + ·) := ⟨BitVec.add_comm⟩
 
 @[simp] protected theorem add_zero (x : BitVec n) : x + 0#n = x := by simp [add_def]
 
 @[simp] protected theorem zero_add (x : BitVec n) : 0#n + x = x := by simp [add_def]
-instance : Std.LawfulIdentity (α := BitVec n) (· + ·) 0#n where
-  left_id := BitVec.zero_add
-  right_id := BitVec.add_zero
 
 theorem truncate_add (x y : BitVec w) (h : i ≤ w) :
     (x + y).truncate i = x.truncate i + y.truncate i := by
   have dvd : 2^i ∣ 2^w := Nat.pow_dvd_pow _ h
   simp [bv_toNat, h, Nat.mod_mod_of_dvd _ dvd]
 
-@[simp, bv_toNat] theorem toInt_add (x y : BitVec w) :
-  (x + y).toInt = (x.toInt + y.toInt).bmod (2^w) := by
-  simp [toInt_eq_toNat_bmod]
-
-theorem ofInt_add {n} (x y : Int) : BitVec.ofInt n (x + y) =
-    BitVec.ofInt n x + BitVec.ofInt n y := by
-  apply eq_of_toInt_eq
-  simp
-
 /-! ### sub/neg -/
 
-theorem sub_def {n} (x y : BitVec n) : x - y = .ofNat n ((2^n - y.toNat) + x.toNat) := by rfl
-
-@[simp] theorem toNat_sub {n} (x y : BitVec n) :
-    (x - y).toNat = (((2^n - y.toNat) + x.toNat) % 2^n) := rfl
-
--- We prefer this lemma to `toNat_sub` for the `bv_toNat` simp set.
--- For reasons we don't yet understand, unfolding via `toNat_sub` sometimes
--- results in `omega` generating proof terms that are very slow in the kernel.
-@[bv_toNat] theorem toNat_sub' {n} (x y : BitVec n) :
-    (x - y).toNat = ((x.toNat + (2^n - y.toNat)) % 2^n) := by
-  rw [toNat_sub, Nat.add_comm]
+theorem sub_def {n} (x y : BitVec n) : x - y = .ofNat n (x.toNat + (2^n - y.toNat)) := by rfl
 
+@[simp, bv_toNat] theorem toNat_sub {n} (x y : BitVec n) :
+  (x - y).toNat = ((x.toNat + (2^n - y.toNat)) % 2^n) := rfl
 @[simp] theorem toFin_sub (x y : BitVec n) : (x - y).toFin = toFin x - toFin y := rfl
 
 @[simp] theorem ofFin_sub (x : Fin (2^n)) (y : BitVec n) : .ofFin x - y = .ofFin (x - y.toFin) :=
@@ -1141,46 +849,32 @@ theorem sub_def {n} (x y : BitVec n) : x - y = .ofNat n ((2^n - y.toNat) + x.toN
   rfl
 -- Remark: we don't use `[simp]` here because simproc` subsumes it for literals.
 -- If `x` and `n` are not literals, applying this theorem eagerly may not be a good idea.
-theorem ofNat_sub_ofNat {n} (x y : Nat) : BitVec.ofNat n x - BitVec.ofNat n y = .ofNat n ((2^n - y % 2^n) + x) := by
+theorem ofNat_sub_ofNat {n} (x y : Nat) : x#n - y#n = .ofNat n (x + (2^n - y % 2^n)) := by
   apply eq_of_toNat_eq ; simp [BitVec.ofNat]
 
-@[simp] protected theorem sub_zero (x : BitVec n) : x - 0#n = x := by apply eq_of_toNat_eq ; simp
+@[simp] protected theorem sub_zero (x : BitVec n) : x - (0#n) = x := by apply eq_of_toNat_eq ; simp
 
 @[simp] protected theorem sub_self (x : BitVec n) : x - x = 0#n := by
   apply eq_of_toNat_eq
   simp only [toNat_sub]
-  rw [Nat.add_comm, Nat.add_sub_of_le]
+  rw [Nat.add_sub_of_le]
   · simp
   · exact Nat.le_of_lt x.isLt
 
 @[simp, bv_toNat] theorem toNat_neg (x : BitVec n) : (- x).toNat = (2^n - x.toNat) % 2^n := by
   simp [Neg.neg, BitVec.neg]
 
-@[simp] theorem toFin_neg (x : BitVec n) :
-    (-x).toFin = Fin.ofNat' (2^n - x.toNat) (Nat.two_pow_pos _) :=
-  rfl
-
 theorem sub_toAdd {n} (x y : BitVec n) : x - y = x + - y := by
   apply eq_of_toNat_eq
   simp
-  rw [Nat.add_comm]
 
-@[simp] theorem neg_zero (n:Nat) : -BitVec.ofNat n 0 = BitVec.ofNat n 0 := by apply eq_of_toNat_eq ; simp
+@[simp] theorem neg_zero (n:Nat) : -0#n = 0#n := by apply eq_of_toNat_eq ; simp
 
 theorem add_sub_cancel (x y : BitVec w) : x + y - y = x := by
   apply eq_of_toNat_eq
-  have y_toNat_le := Nat.le_of_lt y.isLt
-  rw [toNat_sub, toNat_add, Nat.add_comm, Nat.mod_add_mod, Nat.add_assoc, ← Nat.add_sub_assoc y_toNat_le,
-      Nat.add_sub_cancel_left, Nat.add_mod_right, toNat_mod_cancel]
-
-theorem sub_add_cancel (x y : BitVec w) : x - y + y = x := by
-  rw [sub_toAdd, BitVec.add_assoc, BitVec.add_comm _ y,
-      ← BitVec.add_assoc, ← sub_toAdd, add_sub_cancel]
-
-theorem eq_sub_iff_add_eq {x y z : BitVec w} : x = z - y ↔ x + y = z := by
-  apply Iff.intro <;> intro h
-  · simp [h, sub_add_cancel]
-  · simp [←h, add_sub_cancel]
+  have y_toNat_le := Nat.le_of_lt y.toNat_lt
+  rw [toNat_sub, toNat_add, Nat.mod_add_mod, Nat.add_assoc, ← Nat.add_sub_assoc y_toNat_le,
+    Nat.add_sub_cancel_left, Nat.add_mod_right, toNat_mod_cancel]
 
 theorem negOne_eq_allOnes : -1#w = allOnes w := by
   apply eq_of_toNat_eq
@@ -1191,13 +885,6 @@ theorem negOne_eq_allOnes : -1#w = allOnes w := by
     have r : (2^w - 1) < 2^w := by omega
     simp [Nat.mod_eq_of_lt q, Nat.mod_eq_of_lt r]
 
-theorem neg_eq_not_add (x : BitVec w) : -x = ~~~x + 1 := by
-  apply eq_of_toNat_eq
-  simp only [toNat_neg, ofNat_eq_ofNat, toNat_add, toNat_not, toNat_ofNat, Nat.add_mod_mod]
-  congr
-  have hx : x.toNat < 2^w := x.isLt
-  rw [Nat.sub_sub, Nat.add_comm 1 x.toNat, ← Nat.sub_sub, Nat.sub_add_cancel (by omega)]
-
 /-! ### mul -/
 
 theorem mul_def {n} {x y : BitVec n} : x * y = (ofFin <| x.toFin * y.toFin) := by rfl
@@ -1224,27 +911,6 @@ instance : Std.Associative (fun (x y : BitVec w) => x * y) := ⟨BitVec.mul_asso
 instance : Std.LawfulCommIdentity (fun (x y : BitVec w) => x * y) (1#w) where
   right_id := BitVec.mul_one
 
-@[simp]
-theorem BitVec.mul_zero {x : BitVec w} : x * 0#w = 0#w := by
-  apply eq_of_toNat_eq
-  simp [toNat_mul]
-
-theorem BitVec.mul_add {x y z : BitVec w} :
-    x * (y + z) = x * y + x * z := by
-  apply eq_of_toNat_eq
-  simp only [toNat_mul, toNat_add, Nat.add_mod_mod, Nat.mod_add_mod]
-  rw [Nat.mul_mod, Nat.mod_mod (y.toNat + z.toNat),
-    ← Nat.mul_mod, Nat.mul_add]
-
-@[simp, bv_toNat] theorem toInt_mul (x y : BitVec w) :
-  (x * y).toInt = (x.toInt * y.toInt).bmod (2^w) := by
-  simp [toInt_eq_toNat_bmod]
-
-theorem ofInt_mul {n} (x y : Int) : BitVec.ofInt n (x * y) =
-    BitVec.ofInt n x * BitVec.ofInt n y := by
-  apply eq_of_toInt_eq
-  simp
-
 /-! ### le and lt -/
 
 @[bv_toNat] theorem le_def (x y : BitVec n) :
@@ -1254,7 +920,7 @@ theorem ofInt_mul {n} (x y : Int) : BitVec.ofInt n (x * y) =
   x ≤ BitVec.ofFin y ↔ x.toFin ≤ y := Iff.rfl
 @[simp] theorem ofFin_le (x : Fin (2^n)) (y : BitVec n) :
   BitVec.ofFin x ≤ y ↔ x ≤ y.toFin := Iff.rfl
-@[simp] theorem ofNat_le_ofNat {n} (x y : Nat) : (BitVec.ofNat n x) ≤ (BitVec.ofNat n y) ↔ x % 2^n ≤ y % 2^n := by
+@[simp] theorem ofNat_le_ofNat {n} (x y : Nat) : (x#n) ≤ (y#n) ↔ x % 2^n ≤ y % 2^n := by
   simp [le_def]
 
 @[bv_toNat] theorem lt_def (x y : BitVec n) :
@@ -1264,7 +930,7 @@ theorem ofInt_mul {n} (x y : Int) : BitVec.ofInt n (x * y) =
   x < BitVec.ofFin y ↔ x.toFin < y := Iff.rfl
 @[simp] theorem ofFin_lt (x : Fin (2^n)) (y : BitVec n) :
   BitVec.ofFin x < y ↔ x < y.toFin := Iff.rfl
-@[simp] theorem ofNat_lt_ofNat {n} (x y : Nat) : BitVec.ofNat n x < BitVec.ofNat n y ↔ x % 2^n < y % 2^n := by
+@[simp] theorem ofNat_lt_ofNat {n} (x y : Nat) : (x#n) < (y#n) ↔ x % 2^n < y % 2^n := by
   simp [lt_def]
 
 protected theorem lt_of_le_ne (x y : BitVec n) (h1 : x <= y) (h2 : ¬ x = y) : x < y := by
@@ -1277,7 +943,7 @@ protected theorem lt_of_le_ne (x y : BitVec n) (h1 : x <= y) (h2 : ¬ x = y) : x
 /-! ### intMax -/
 
 /-- The bitvector of width `w` that has the largest value when interpreted as an integer. -/
-def intMax (w : Nat) : BitVec w := BitVec.ofNat w (2^w - 1)
+def intMax (w : Nat) : BitVec w  := (2^w - 1)#w
 
 theorem getLsb_intMax_eq (w : Nat) : (intMax w).getLsb i = decide (i < w) := by
   simp [intMax, getLsb]
@@ -1304,311 +970,4 @@ theorem toNat_intMax_eq : (intMax w).toNat = 2^w - 1 := by
     (ofBoolListLE bs).getMsb i = (decide (i < bs.length) && bs.getD (bs.length - 1 - i) false) := by
   simp [getMsb_eq_getLsb]
 
-/-! # Rotate Left -/
-
-/-- rotateLeft is invariant under `mod` by the bitwidth. -/
-@[simp]
-theorem rotateLeft_mod_eq_rotateLeft {x : BitVec w} {r : Nat} :
-    x.rotateLeft (r % w) = x.rotateLeft r := by
-  simp only [rotateLeft, Nat.mod_mod]
-
-/-- `rotateLeft` equals the bit fiddling definition of `rotateLeftAux` when the rotation amount is
-smaller than the bitwidth. -/
-theorem rotateLeft_eq_rotateLeftAux_of_lt {x : BitVec w} {r : Nat} (hr : r < w) :
-    x.rotateLeft r = x.rotateLeftAux r := by
-  simp only [rotateLeft, Nat.mod_eq_of_lt hr]
-
-
-/--
-Accessing bits in `x.rotateLeft r` the range `[0, r)` is equal to
-accessing bits `x` in the range `[w - r, w)`.
-
-Proof by example:
-Let x := <6 5 4 3 2 1 0> : BitVec 7.
-x.rotateLeft 2 = (<6 5 | 4 3 2 1 0>).rotateLeft 2 = <3 2 1 0 | 6 5>
-
-(x.rotateLeft 2).getLsb ⟨i, i < 2⟩
-= <3 2 1 0 | 6 5>.getLsb ⟨i, i < 2⟩
-= <6 5>[i]
-= <6 5 | 4 3 2 1 0>[i + len(<4 3 2 1 0>)]
-= <6 5 | 4 3 2 1 0>[i + 7 - 2]
--/
-theorem getLsb_rotateLeftAux_of_le {x : BitVec w} {r : Nat} {i : Nat} (hi : i < r) :
-    (x.rotateLeftAux r).getLsb i = x.getLsb (w - r + i) := by
-  rw [rotateLeftAux, getLsb_or, getLsb_ushiftRight]
-  simp; omega
-
-/--
-Accessing bits in `x.rotateLeft r` the range `[r, w)` is equal to
-accessing bits `x` in the range `[0, w - r)`.
-
-Proof by example:
-Let x := <6 5 4 3 2 1 0> : BitVec 7.
-x.rotateLeft 2 = (<6 5 | 4 3 2 1 0>).rotateLeft 2 = <3 2 1 0 | 6 5>
-
-(x.rotateLeft 2).getLsb ⟨i, i ≥ 2⟩
-= <3 2 1 0 | 6 5>.getLsb ⟨i, i ≥ 2⟩
-= <3 2 1 0>[i - 2]
-= <6 5 | 3 2 1 0>[i - 2]
-
-Intuitively, grab the full width (7), then move the marker `|` by `r` to the right `(-2)`
-Then, access the bit at `i` from the right `(+i)`.
- -/
-theorem getLsb_rotateLeftAux_of_geq {x : BitVec w} {r : Nat} {i : Nat} (hi : i ≥ r) :
-    (x.rotateLeftAux r).getLsb i = (decide (i < w) && x.getLsb (i - r)) := by
-  rw [rotateLeftAux, getLsb_or]
-  suffices (x >>> (w - r)).getLsb i = false by
-    have hiltr : decide (i < r) = false := by
-      simp [hi]
-    simp [getLsb_shiftLeft, Bool.or_false, hi, hiltr, this]
-  simp only [getLsb_ushiftRight]
-  apply getLsb_ge
-  omega
-
-/-- When `r < w`, we give a formula for `(x.rotateRight r).getLsb i`. -/
-theorem getLsb_rotateLeft_of_le {x : BitVec w} {r i : Nat} (hr: r < w) :
-    (x.rotateLeft r).getLsb i =
-      cond (i < r)
-      (x.getLsb (w - r + i))
-      (decide (i < w) && x.getLsb (i - r)) := by
-  · rw [rotateLeft_eq_rotateLeftAux_of_lt hr]
-    by_cases h : i < r
-    · simp [h, getLsb_rotateLeftAux_of_le h]
-    · simp [h, getLsb_rotateLeftAux_of_geq <| Nat.ge_of_not_lt h]
-
-@[simp]
-theorem getLsb_rotateLeft {x : BitVec w} {r i : Nat}  :
-    (x.rotateLeft r).getLsb i =
-      cond (i < r % w)
-      (x.getLsb (w - (r % w) + i))
-      (decide (i < w) && x.getLsb (i - (r % w))) := by
-  rcases w with ⟨rfl, w⟩
-  · simp
-  · rw [← rotateLeft_mod_eq_rotateLeft, getLsb_rotateLeft_of_le (Nat.mod_lt _ (by omega))]
-
-/-! ## Rotate Right -/
-
-/--
-Accessing bits in `x.rotateRight r` the range `[0, w-r)` is equal to
-accessing bits `x` in the range `[r, w)`.
-
-Proof by example:
-Let x := <6 5 4 3 2 1 0> : BitVec 7.
-x.rotateRight 2 = (<6 5 4 3 2 | 1 0>).rotateRight 2 = <1 0 | 6 5 4 3 2>
-
-(x.rotateLeft 2).getLsb ⟨i, i ≤ 7 - 2⟩
-= <1 0 | 6 5 4 3 2>.getLsb ⟨i, i ≤ 7 - 2⟩
-= <6 5 4 3 2>.getLsb i
-= <6 5 4 3 2 | 1 0>[i + 2]
--/
-theorem getLsb_rotateRightAux_of_le {x : BitVec w} {r : Nat} {i : Nat} (hi : i < w - r) :
-    (x.rotateRightAux r).getLsb i = x.getLsb (r + i) := by
-  rw [rotateRightAux, getLsb_or, getLsb_ushiftRight]
-  suffices (x <<< (w - r)).getLsb i = false by
-    simp only [this, Bool.or_false]
-  simp only [getLsb_shiftLeft, Bool.and_eq_false_imp, Bool.and_eq_true, decide_eq_true_eq,
-    Bool.not_eq_true', decide_eq_false_iff_not, Nat.not_lt, and_imp]
-  omega
-
-/--
-Accessing bits in `x.rotateRight r` the range `[w-r, w)` is equal to
-accessing bits `x` in the range `[0, r)`.
-
-Proof by example:
-Let x := <6 5 4 3 2 1 0> : BitVec 7.
-x.rotateRight 2 = (<6 5 4 3 2 | 1 0>).rotateRight 2 = <1 0 | 6 5 4 3 2>
-
-(x.rotateLeft 2).getLsb ⟨i, i ≥ 7 - 2⟩
-= <1 0 | 6 5 4 3 2>.getLsb ⟨i, i ≤ 7 - 2⟩
-= <1 0>.getLsb (i - len(<6 5 4 3 2>)
-= <6 5 4 3 2 | 1 0> (i - len<6 4 4 3 2>)
- -/
-theorem getLsb_rotateRightAux_of_geq {x : BitVec w} {r : Nat} {i : Nat} (hi : i ≥ w - r) :
-    (x.rotateRightAux r).getLsb i = (decide (i < w) && x.getLsb (i - (w - r))) := by
-  rw [rotateRightAux, getLsb_or]
-  suffices (x >>> r).getLsb i = false by
-    simp only [this, getLsb_shiftLeft, Bool.false_or]
-    by_cases hiw : i < w
-    <;> simp [hiw, hi]
-  simp only [getLsb_ushiftRight]
-  apply getLsb_ge
-  omega
-
-/-- `rotateRight` equals the bit fiddling definition of `rotateRightAux` when the rotation amount is
-smaller than the bitwidth. -/
-theorem rotateRight_eq_rotateRightAux_of_lt {x : BitVec w} {r : Nat} (hr : r < w) :
-    x.rotateRight r = x.rotateRightAux r := by
-  simp only [rotateRight, Nat.mod_eq_of_lt hr]
-
-/-- rotateRight is invariant under `mod` by the bitwidth. -/
-@[simp]
-theorem rotateRight_mod_eq_rotateRight {x : BitVec w} {r : Nat} :
-    x.rotateRight (r % w) = x.rotateRight r := by
-  simp only [rotateRight, Nat.mod_mod]
-
-/-- When `r < w`, we give a formula for `(x.rotateRight r).getLsb i`. -/
-theorem getLsb_rotateRight_of_le {x : BitVec w} {r i : Nat} (hr: r < w) :
-    (x.rotateRight r).getLsb i =
-      cond (i < w - r)
-      (x.getLsb (r + i))
-      (decide (i < w) && x.getLsb (i - (w - r))) := by
-  · rw [rotateRight_eq_rotateRightAux_of_lt hr]
-    by_cases h : i < w - r
-    · simp [h, getLsb_rotateRightAux_of_le h]
-    · simp [h, getLsb_rotateRightAux_of_geq <| Nat.le_of_not_lt h]
-
-@[simp]
-theorem getLsb_rotateRight {x : BitVec w} {r i : Nat} :
-    (x.rotateRight r).getLsb i =
-      cond (i < w - (r % w))
-      (x.getLsb ((r % w) + i))
-      (decide (i < w) && x.getLsb (i - (w - (r % w)))) := by
-  rcases w with ⟨rfl, w⟩
-  · simp
-  · rw [← rotateRight_mod_eq_rotateRight, getLsb_rotateRight_of_le (Nat.mod_lt _ (by omega))]
-
-/- ## twoPow -/
-
-@[simp, bv_toNat]
-theorem toNat_twoPow (w : Nat) (i : Nat) : (twoPow w i).toNat = 2^i % 2^w := by
-  rcases w with rfl | w
-  · simp [Nat.mod_one]
-  · simp only [twoPow, toNat_shiftLeft, toNat_ofNat]
-    have h1 : 1 < 2 ^ (w + 1) := Nat.one_lt_two_pow (by omega)
-    rw [Nat.mod_eq_of_lt h1, Nat.shiftLeft_eq, Nat.one_mul]
-
-@[simp]
-theorem getLsb_twoPow (i j : Nat) : (twoPow w i).getLsb j = ((i < w) && (i = j)) := by
-  rcases w with rfl | w
-  · simp
-  · simp only [twoPow, getLsb_shiftLeft, getLsb_ofNat]
-    by_cases hj : j < i
-    · simp only [hj, decide_True, Bool.not_true, Bool.and_false, Bool.false_and, Bool.false_eq,
-      Bool.and_eq_false_imp, decide_eq_true_eq, decide_eq_false_iff_not]
-      omega
-    · by_cases hi : Nat.testBit 1 (j - i)
-      · obtain hi' := Nat.testBit_one_eq_true_iff_self_eq_zero.mp hi
-        have hij : j = i := by omega
-        simp_all
-      · have hij : i ≠ j := by
-          intro h; subst h
-          simp at hi
-        simp_all
-
-@[simp]
-theorem and_twoPow (x : BitVec w) (i : Nat) :
-    x &&& (twoPow w i) = if x.getLsb i then twoPow w i else 0#w := by
-  ext j
-  simp only [getLsb_and, getLsb_twoPow]
-  by_cases hj : i = j <;> by_cases hx : x.getLsb i <;> simp_all
-
-@[simp]
-theorem twoPow_and (x : BitVec w) (i : Nat) :
-    (twoPow w i) &&& x = if x.getLsb i then twoPow w i else 0#w := by
-  rw [BitVec.and_comm, and_twoPow]
-
-@[simp]
-theorem mul_twoPow_eq_shiftLeft (x : BitVec w) (i : Nat) :
-    x * (twoPow w i) = x <<< i := by
-  apply eq_of_toNat_eq
-  simp only [toNat_mul, toNat_twoPow, toNat_shiftLeft, Nat.shiftLeft_eq]
-  by_cases hi : i < w
-  · have hpow : 2^i < 2^w := Nat.pow_lt_pow_of_lt (by omega) (by omega)
-    rw [Nat.mod_eq_of_lt hpow]
-  · have hpow : 2 ^ i % 2 ^ w = 0 := by
-      rw [Nat.mod_eq_zero_of_dvd]
-      apply Nat.pow_dvd_pow 2 (by omega)
-    simp [Nat.mul_mod, hpow]
-
-theorem twoPow_zero {w : Nat} : twoPow w 0 = 1#w := by
-  apply eq_of_toNat_eq
-  simp
-
-@[simp]
-theorem getLsb_one {w i : Nat} : (1#w).getLsb i = (decide (0 < w) && decide (0 = i)) := by
-  rw [← twoPow_zero, getLsb_twoPow]
-
-/- ### zeroExtend, truncate, and bitwise operations -/
-
-/--
-When the `(i+1)`th bit of `x` is false,
-keeping the lower `(i + 1)` bits of `x` equals keeping the lower `i` bits.
--/
-theorem zeroExtend_truncate_succ_eq_zeroExtend_truncate_of_getLsb_false
-  {x : BitVec w} {i : Nat} (hx : x.getLsb i = false) :
-    zeroExtend w (x.truncate (i + 1)) =
-      zeroExtend w (x.truncate i) := by
-  ext k
-  simp only [getLsb_zeroExtend, Fin.is_lt, decide_True, Bool.true_and, getLsb_or, getLsb_and]
-  by_cases hik : i = k
-  · subst hik
-    simp [hx]
-  · by_cases hik' : k < i + 1 <;> simp [hik'] <;> omega
-
-/--
-When the `(i+1)`th bit of `x` is true,
-keeping the lower `(i + 1)` bits of `x` equalsk eeping the lower `i` bits
-and then performing bitwise-or with `twoPow i = (1 << i)`,
--/
-theorem zeroExtend_truncate_succ_eq_zeroExtend_truncate_or_twoPow_of_getLsb_true
-    {x : BitVec w} {i : Nat} (hx : x.getLsb i = true) :
-    zeroExtend w (x.truncate (i + 1)) =
-      zeroExtend w (x.truncate i) ||| (twoPow w i) := by
-  ext k
-  simp only [getLsb_zeroExtend, Fin.is_lt, decide_True, Bool.true_and, getLsb_or, getLsb_and]
-  by_cases hik : i = k
-  · subst hik
-    simp [hx]
-  · by_cases hik' : k < i + 1 <;> simp [hik, hik'] <;> omega
-
-/-- Bitwise and of `(x : BitVec w)` with `1#w` equals zero extending `x.lsb` to `w`. -/
-theorem and_one_eq_zeroExtend_ofBool_getLsb {x : BitVec w} :
-    (x &&& 1#w) = zeroExtend w (ofBool (x.getLsb 0)) := by
-  ext i
-  simp only [getLsb_and, getLsb_one, getLsb_zeroExtend, Fin.is_lt, decide_True, getLsb_ofBool,
-    Bool.true_and]
-  by_cases h : (0 = (i : Nat)) <;> simp [h] <;> omega
-
-@[simp]
-theorem replicate_zero_eq {x : BitVec w} : x.replicate 0 = 0#0 := by
-  simp [replicate]
-
-@[simp]
-theorem replicate_succ_eq {x : BitVec w} :
-    x.replicate (n + 1) =
-    (x ++ replicate n x).cast (by rw [Nat.mul_succ]; omega) := by
-  simp [replicate]
-
-/--
-If a number `w * n ≤ i < w * (n + 1)`, then `i - w * n` equals `i % w`.
-This is true by subtracting `w * n` from the inequality, giving
-`0 ≤ i - w * n < w`, which uniquely identifies `i % w`.
--/
-private theorem Nat.sub_mul_eq_mod_of_lt_of_le (hlo : w * n ≤ i) (hhi : i < w * (n + 1)) :
-    i - w * n = i % w := by
-  rw [Nat.mod_def]
-  congr
-  symm
-  apply Nat.div_eq_of_lt_le
-    (by rw [Nat.mul_comm]; omega)
-    (by rw [Nat.mul_comm]; omega)
-
-@[simp]
-theorem getLsb_replicate {n w : Nat} (x : BitVec w) :
-    (x.replicate n).getLsb i =
-    (decide (i < w * n) && x.getLsb (i % w)) := by
-  induction n generalizing x
-  case zero => simp
-  case succ n ih =>
-    simp only [replicate_succ_eq, getLsb_cast, getLsb_append]
-    by_cases hi : i < w * (n + 1)
-    · simp only [hi, decide_True, Bool.true_and]
-      by_cases hi' : i < w * n
-      · simp [hi', ih]
-      · simp only [hi', decide_False, cond_false]
-        rw [Nat.sub_mul_eq_mod_of_lt_of_le] <;> omega
-    · rw [Nat.mul_succ] at hi ⊢
-      simp only [show ¬i < w * n by omega, decide_False, cond_false, hi, Bool.false_and]
-      apply BitVec.getLsb_ge (x := x) (i := i - w * n) (ge := by omega)
-
 end BitVec

src/Init/Data/Bool.lean

@@ -52,8 +52,8 @@ theorem eq_iff_iff {a b : Bool} : a = b ↔ (a ↔ b) := by cases b <;> simp
 
 @[simp] theorem decide_eq_true  {b : Bool} [Decidable (b = true)]  : decide (b = true)  =  b := by cases b <;> simp
 @[simp] theorem decide_eq_false {b : Bool} [Decidable (b = false)] : decide (b = false) = !b := by cases b <;> simp
-theorem decide_true_eq  {b : Bool} [Decidable (true = b)]  : decide (true  = b) =  b := by cases b <;> simp
-theorem decide_false_eq {b : Bool} [Decidable (false = b)] : decide (false = b) = !b := by cases b <;> simp
+@[simp] theorem decide_true_eq  {b : Bool} [Decidable (true = b)]  : decide (true  = b) =  b := by cases b <;> simp
+@[simp] theorem decide_false_eq {b : Bool} [Decidable (false = b)] : decide (false = b) = !b := by cases b <;> simp
 
 /-! ### and -/
 
@@ -74,7 +74,6 @@ Added for confluence with `not_and_self` `and_not_self` on term
 @[simp] theorem eq_false_and_eq_true_self : ∀(b : Bool), (b = false ∧ b = true) ↔ False := by decide
 
 theorem and_comm : ∀ (x y : Bool), (x && y) = (y && x) := by decide
-instance : Std.Commutative (· && ·) := ⟨and_comm⟩
 
 theorem and_left_comm : ∀ (x y z : Bool), (x && (y && z)) = (y && (x && z)) := by decide
 theorem and_right_comm : ∀ (x y z : Bool), ((x && y) && z) = ((x && z) && y) := by decide
@@ -121,7 +120,6 @@ Needed for confluence of term `(a || b) ↔ a` which reduces to `(a || b) = a` v
 @[simp] theorem iff_or_self : ∀(a b : Bool), (b = (a || b)) ↔ (a → b) := by decide
 
 theorem or_comm : ∀ (x y : Bool), (x || y) = (y || x) := by decide
-instance : Std.Commutative (· || ·) := ⟨or_comm⟩
 
 theorem or_left_comm : ∀ (x y z : Bool), (x || (y || z)) = (y || (x || z)) := by decide
 theorem or_right_comm : ∀ (x y z : Bool), ((x || y) || z) = ((x || z) || y) := by decide
@@ -163,7 +161,7 @@ Consider the term: `¬((b && c) = true)`:
 -/
 @[simp] theorem and_eq_false_imp : ∀ (x y : Bool), (x && y) = false ↔ (x = true → y = false) := by decide
 
-theorem or_eq_true_iff : ∀ (x y : Bool), (x || y) = true ↔ x = true ∨ y = true := by simp
+@[simp] theorem or_eq_true_iff : ∀ (x y : Bool), (x || y) = true ↔ x = true ∨ y = true := by decide
 
 @[simp] theorem or_eq_false_iff : ∀ (x y : Bool), (x || y) = false ↔ x = false ∧ y = false := by decide
 
@@ -187,17 +185,13 @@ in false_eq and true_eq.
 
 @[simp] theorem true_beq  : ∀b, (true  == b) =  b := by decide
 @[simp] theorem false_beq : ∀b, (false == b) = !b := by decide
-instance : Std.LawfulIdentity (· == ·) true where
-  left_id := true_beq
-  right_id := beq_true
+@[simp] theorem beq_true  : ∀b, (b == true)  =  b := by decide
+@[simp] theorem beq_false : ∀b, (b == false) = !b := by decide
 
 @[simp] theorem true_bne  : ∀(b : Bool), (true  != b) = !b := by decide
 @[simp] theorem false_bne : ∀(b : Bool), (false != b) =  b := by decide
 @[simp] theorem bne_true  : ∀(b : Bool), (b != true)  = !b := by decide
 @[simp] theorem bne_false : ∀(b : Bool), (b != false) =  b := by decide
-instance : Std.LawfulIdentity (· != ·) false where
-  left_id := false_bne
-  right_id := bne_false
 
 @[simp] theorem not_beq_self : ∀ (x : Bool), ((!x) == x) = false := by decide
 @[simp] theorem beq_not_self : ∀ (x : Bool), (x   == !x) = false := by decide
@@ -220,13 +214,10 @@ due to `beq_iff_eq`.
 @[simp] theorem not_bne_not : ∀ (x y : Bool), ((!x) != (!y)) = (x != y) := by decide
 
 @[simp] theorem bne_assoc : ∀ (x y z : Bool), ((x != y) != z) = (x != (y != z)) := by decide
-instance : Std.Associative (· != ·) := ⟨bne_assoc⟩
 
 @[simp] theorem bne_left_inj  : ∀ (x y z : Bool), (x != y) = (x != z) ↔ y = z := by decide
 @[simp] theorem bne_right_inj : ∀ (x y z : Bool), (x != z) = (y != z) ↔ x = y := by decide
 
-theorem eq_not_of_ne : ∀ {x y : Bool}, x ≠ y → x = !y := by decide
-
 /-! ### coercision related normal forms -/
 
 theorem beq_eq_decide_eq [BEq α] [LawfulBEq α] [DecidableEq α] (a b : α) :
@@ -351,7 +342,7 @@ theorem and_or_inj_left_iff :
 /-! ## toNat -/
 
 /-- convert a `Bool` to a `Nat`, `false -> 0`, `true -> 1` -/
-def toNat (b : Bool) : Nat := cond b 1 0
+def toNat (b:Bool) : Nat := cond b 1 0
 
 @[simp] theorem toNat_false : false.toNat = 0 := rfl
 
@@ -360,8 +351,7 @@ def toNat (b : Bool) : Nat := cond b 1 0
 theorem toNat_le (c : Bool) : c.toNat ≤ 1 := by
   cases c <;> trivial
 
-@[deprecated toNat_le (since := "2024-02-23")]
-abbrev toNat_le_one := toNat_le
+@[deprecated toNat_le] abbrev toNat_le_one := toNat_le
 
 theorem toNat_lt (b : Bool) : b.toNat < 2 :=
   Nat.lt_succ_of_le (toNat_le _)
@@ -494,16 +484,6 @@ protected theorem cond_false {α : Type u} {a b : α} : cond false a b = b := co
 @[simp] theorem cond_true_same  : ∀(c b : Bool), cond c c b = (c || b) := by decide
 @[simp] theorem cond_false_same : ∀(c b : Bool), cond c b c = (c && b) := by decide
 
-theorem cond_pos {b : Bool} {a a' : α} (h : b = true) : (bif b then a else a') = a := by
-  rw [h, cond_true]
-
-theorem cond_neg {b : Bool} {a a' : α} (h : b = false) : (bif b then a else a') = a' := by
-  rw [h, cond_false]
-
-theorem apply_cond (f : α → β) {b : Bool} {a a' : α} :
-    f (bif b then a else a') = bif b then f a else f a' := by
-  cases b <;> simp
-
 /-# decidability -/
 
 protected theorem decide_coe (b : Bool) [Decidable (b = true)] : decide (b = true) = b := decide_eq_true

src/Init/Data/ByteArray/Basic.lean

@@ -37,10 +37,6 @@ def push : ByteArray → UInt8 → ByteArray
 def size : (@& ByteArray) → Nat
   | ⟨bs⟩ => bs.size
 
-@[extern "lean_sarray_size", simp]
-def usize (a : @& ByteArray) : USize :=
-  a.size.toUSize
-
 @[extern "lean_byte_array_uget"]
 def uget : (a : @& ByteArray) → (i : USize) → i.toNat < a.size → UInt8
   | ⟨bs⟩, i, h => bs[i]
@@ -56,9 +52,13 @@ def get : (a : @& ByteArray) → (@& Fin a.size) → UInt8
 instance : GetElem ByteArray Nat UInt8 fun xs i => i < xs.size where
   getElem xs i h := xs.get ⟨i, h⟩
 
+instance : LawfulGetElem ByteArray Nat UInt8 fun xs i => i < xs.size where
+
 instance : GetElem ByteArray USize UInt8 fun xs i => i.val < xs.size where
   getElem xs i h := xs.uget i h
 
+instance : LawfulGetElem ByteArray USize UInt8 fun xs i => i.val < xs.size where
+
 @[extern "lean_byte_array_set"]
 def set! : ByteArray → (@& Nat) → UInt8 → ByteArray
   | ⟨bs⟩, i, b => ⟨bs.set! i b⟩
@@ -96,24 +96,20 @@ protected def append (a : ByteArray) (b : ByteArray) : ByteArray :=
 
 instance : Append ByteArray := ⟨ByteArray.append⟩
 
-def toList (bs : ByteArray) : List UInt8 :=
+partial def toList (bs : ByteArray) : List UInt8 :=
   let rec loop (i : Nat) (r : List UInt8) :=
     if i < bs.size then
       loop (i+1) (bs.get! i :: r)
     else
       r.reverse
-    termination_by bs.size - i
-    decreasing_by decreasing_trivial_pre_omega
   loop 0 []
 
-@[inline] def findIdx? (a : ByteArray) (p : UInt8 → Bool) (start := 0) : Option Nat :=
+@[inline] partial def findIdx? (a : ByteArray) (p : UInt8 → Bool) (start := 0) : Option Nat :=
   let rec @[specialize] loop (i : Nat) :=
     if i < a.size then
       if p (a.get! i) then some i else loop (i+1)
     else
       none
-    termination_by a.size - i
-    decreasing_by decreasing_trivial_pre_omega
   loop start
 
 /--
@@ -123,7 +119,7 @@ def toList (bs : ByteArray) : List UInt8 :=
   TODO: avoid code duplication in the future after we improve the compiler.
 -/
 @[inline] unsafe def forInUnsafe {β : Type v} {m : Type v → Type w} [Monad m] (as : ByteArray) (b : β) (f : UInt8 → β → m (ForInStep β)) : m β :=
-  let sz := as.usize
+  let sz := USize.ofNat as.size
   let rec @[specialize] loop (i : USize) (b : β) : m β := do
     if i < sz then
       let a := as.uget i lcProof
@@ -191,121 +187,6 @@ def foldlM {β : Type v} {m : Type v → Type w} [Monad m] (f : β → UInt8 →
 def foldl {β : Type v} (f : β → UInt8 → β) (init : β) (as : ByteArray) (start := 0) (stop := as.size) : β :=
   Id.run <| as.foldlM f init start stop
 
-/-- Iterator over the bytes (`UInt8`) of a `ByteArray`.
-
-Typically created by `arr.iter`, where `arr` is a `ByteArray`.
-
-An iterator is *valid* if the position `i` is *valid* for the array `arr`, meaning `0 ≤ i ≤ arr.size`
-
-Most operations on iterators return arbitrary values if the iterator is not valid. The functions in
-the `ByteArray.Iterator` API should rule out the creation of invalid iterators, with two exceptions:
-
-- `Iterator.next iter` is invalid if `iter` is already at the end of the array (`iter.atEnd` is
-  `true`)
-- `Iterator.forward iter n`/`Iterator.nextn iter n` is invalid if `n` is strictly greater than the
-  number of remaining bytes.
--/
-structure Iterator where
-  /-- The array the iterator is for. -/
-  array : ByteArray
-  /-- The current position.
-
-  This position is not necessarily valid for the array, for instance if one keeps calling
-  `Iterator.next` when `Iterator.atEnd` is true. If the position is not valid, then the
-  current byte is `(default : UInt8)`. -/
-  idx : Nat
-  deriving Inhabited
-
-/-- Creates an iterator at the beginning of an array. -/
-def mkIterator (arr : ByteArray) : Iterator :=
-  ⟨arr, 0⟩
-
-@[inherit_doc mkIterator]
-abbrev iter := mkIterator
-
-/-- The size of an array iterator is the number of bytes remaining. -/
-instance : SizeOf Iterator where
-  sizeOf i := i.array.size - i.idx
-
-theorem Iterator.sizeOf_eq (i : Iterator) : sizeOf i = i.array.size - i.idx :=
-  rfl
-
-namespace Iterator
-
-/-- Number of bytes remaining in the iterator. -/
-def remainingBytes : Iterator → Nat
-  | ⟨arr, i⟩ => arr.size - i
-
-@[inherit_doc Iterator.idx]
-def pos := Iterator.idx
-
-/-- The byte at the current position.
-
-On an invalid position, returns `(default : UInt8)`. -/
-@[inline]
-def curr : Iterator → UInt8
-  | ⟨arr, i⟩ =>
-    if h:i < arr.size then
-      arr[i]'h
-    else
-      default
-
-/-- Moves the iterator's position forward by one byte, unconditionally.
-
-It is only valid to call this function if the iterator is not at the end of the array, *i.e.*
-`Iterator.atEnd` is `false`; otherwise, the resulting iterator will be invalid. -/
-@[inline]
-def next : Iterator → Iterator
-  | ⟨arr, i⟩ => ⟨arr, i + 1⟩
-
-/-- Decreases the iterator's position.
-
-If the position is zero, this function is the identity. -/
-@[inline]
-def prev : Iterator → Iterator
-  | ⟨arr, i⟩ => ⟨arr, i - 1⟩
-
-/-- True if the iterator is past the array's last byte. -/
-@[inline]
-def atEnd : Iterator → Bool
-  | ⟨arr, i⟩ => i ≥ arr.size
-
-/-- True if the iterator is not past the array's last byte. -/
-@[inline]
-def hasNext : Iterator → Bool
-  | ⟨arr, i⟩ => i < arr.size
-
-/-- True if the position is not zero. -/
-@[inline]
-def hasPrev : Iterator → Bool
-  | ⟨_, i⟩ => i > 0
-
-/-- Moves the iterator's position to the end of the array.
-
-Note that `i.toEnd.atEnd` is always `true`. -/
-@[inline]
-def toEnd : Iterator → Iterator
-  | ⟨arr, _⟩ => ⟨arr, arr.size⟩
-
-/-- Moves the iterator's position several bytes forward.
-
-The resulting iterator is only valid if the number of bytes to skip is less than or equal to
-the number of bytes left in the iterator. -/
-@[inline]
-def forward : Iterator → Nat → Iterator
-  | ⟨arr, i⟩, f => ⟨arr, i + f⟩
-
-@[inherit_doc forward, inline]
-def nextn : Iterator → Nat → Iterator := forward
-
-/-- Moves the iterator's position several bytes back.
-
-If asked to go back more bytes than available, stops at the beginning of the array. -/
-@[inline]
-def prevn : Iterator → Nat → Iterator
-  | ⟨arr, i⟩, f => ⟨arr, i - f⟩
-
-end Iterator
 end ByteArray
 
 def List.toByteArray (bs : List UInt8) : ByteArray :=

src/Init/Data/Char.lean

@@ -5,4 +5,3 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Init.Data.Char.Basic
-import Init.Data.Char.Lemmas

src/Init/Data/Char/Basic.lean

@@ -40,7 +40,7 @@ theorem isValidUInt32 (n : Nat) (h : isValidCharNat n) : n < UInt32.size := by
     apply Nat.lt_trans h₂
     decide
 
-theorem isValidChar_of_isValidCharNat (n : Nat) (h : isValidCharNat n) : isValidChar (UInt32.ofNat' n (isValidUInt32 n h)) :=
+theorem isValidChar_of_isValidChar_Nat (n : Nat) (h : isValidCharNat n) : isValidChar (UInt32.ofNat' n (isValidUInt32 n h)) :=
   match h with
   | Or.inl h        => Or.inl h
   | Or.inr ⟨h₁, h₂⟩ => Or.inr ⟨h₁, h₂⟩
@@ -52,13 +52,6 @@ theorem isValidChar_zero : isValidChar 0 :=
 @[inline] def toNat (c : Char) : Nat :=
   c.val.toNat
 
-/-- Convert a character into a `UInt8`, by truncating (reducing modulo 256) if necessary. -/
-@[inline] def toUInt8 (c : Char) : UInt8 :=
-  c.val.toUInt8
-
-/-- 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.1.2 (by decide))⟩
-
 instance : Inhabited Char where
   default := 'A'
 

src/Init/Data/Char/Lemmas.lean

@@ -1,39 +0,0 @@
-/-
-Copyright (c) 2024 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.Char.Basic
-import Init.Data.UInt.Lemmas
-
-namespace Char
-
-theorem le_def {a b : Char} : a ≤ b ↔ a.1 ≤ b.1 := .rfl
-theorem lt_def {a b : Char} : a < b ↔ a.1 < b.1 := .rfl
-theorem lt_iff_val_lt_val {a b : Char} : a < b ↔ a.val < b.val := Iff.rfl
-@[simp] protected theorem not_le {a b : Char} : ¬ a ≤ b ↔ b < a := UInt32.not_le
-@[simp] protected theorem not_lt {a b : Char} : ¬ a < b ↔ b ≤ a := UInt32.not_lt
-@[simp] protected theorem le_refl (a : Char) : a ≤ a := by simp [le_def]
-@[simp] protected theorem lt_irrefl (a : Char) : ¬ a < a := by simp
-protected theorem le_trans {a b c : Char} : a ≤ b → b ≤ c → a ≤ c := UInt32.le_trans
-protected theorem lt_trans {a b c : Char} : a < b → b < c → a < c := UInt32.lt_trans
-protected theorem le_total (a b : Char) : a ≤ b ∨ b ≤ a := UInt32.le_total a.1 b.1
-protected theorem lt_asymm {a b : Char} (h : a < b) : ¬ b < a := UInt32.lt_asymm h
-protected theorem ne_of_lt {a b : Char} (h : a < b) : a ≠ b := Char.ne_of_val_ne (UInt32.ne_of_lt h)
-
-theorem utf8Size_eq (c : Char) : c.utf8Size = 1 ∨ c.utf8Size = 2 ∨ c.utf8Size = 3 ∨ c.utf8Size = 4 := by
-  have := c.utf8Size_pos
-  have := c.utf8Size_le_four
-  omega
-
-@[simp] theorem ofNat_toNat (c : Char) : Char.ofNat c.toNat = c := by
-  rw [Char.ofNat, dif_pos]
-  rfl
-
-@[ext] protected theorem ext : {a b : Char} → a.val = b.val → a = b
-  | ⟨_,_⟩, ⟨_,_⟩, rfl => rfl
-
-end Char
-
-@[deprecated Char.utf8Size (since := "2024-06-04")] abbrev String.csize := Char.utf8Size

src/Init/Data/Fin/Basic.lean

@@ -13,40 +13,17 @@ namespace Fin
 instance coeToNat : CoeOut (Fin n) Nat :=
   ⟨fun v => v.val⟩
 
-/--
-From the empty type `Fin 0`, any desired result `α` can be derived. This is simlar to `Empty.elim`.
--/
 def elim0.{u} {α : Sort u} : Fin 0 → α
   | ⟨_, h⟩ => absurd h (not_lt_zero _)
 
-/--
-Returns the successor of the argument.
-
-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.succ
   | ⟨i, h⟩ => ⟨i+1, Nat.succ_lt_succ h⟩
 
 variable {n : Nat}
 
-/--
-Returns `a` modulo `n + 1` as a `Fin n.succ`.
--/
 protected def ofNat {n : Nat} (a : Nat) : Fin n.succ :=
   ⟨a % (n+1), Nat.mod_lt _ (Nat.zero_lt_succ _)⟩
 
-/--
-Returns `a` modulo `n` as a `Fin n`.
-
-The assumption `n > 0` ensures that `Fin n` is nonempty.
--/
 protected def ofNat' {n : Nat} (a : Nat) (h : n > 0) : Fin n :=
   ⟨a % n, Nat.mod_lt _ h⟩
 
@@ -56,34 +33,14 @@ 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` -/
 protected def add : Fin n → Fin n → Fin n
   | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a + b) % n, mlt h⟩
 
-/-- Multiplication modulo `n` -/
 protected def mul : Fin n → Fin n → Fin n
   | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a * b) % n, mlt h⟩
 
-/-- Subtraction modulo `n` -/
 protected def sub : Fin n → Fin n → Fin n
-  /-
-  The definition of `Fin.sub` has been updated to improve performance.
-  The right-hand-side of the following `match` was originally
-  ```
-  ⟨(a + (n - b)) % n, mlt h⟩
-  ```
-  This caused significant performance issues when testing definitional equality,
-  such as `x =?= x - 1` where `x : Fin n` and `n` is a big number,
-  as Lean spent a long time reducing
-  ```
-  ((n - 1) + x.val) % n
-  ```
-  For example, this was an issue for `Fin 2^64` (i.e., `UInt64`).
-  This change improves performance by leveraging the fact that `Nat.add` is defined
-  using recursion on the second argument.
-  See issue #4413.
-  -/
-  | ⟨a, h⟩, ⟨b, _⟩ => ⟨((n - b) + a) % n, mlt h⟩
+  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a + (n - b)) % n, mlt h⟩
 
 /-!
 Remark: land/lor can be defined without using (% n), but
@@ -210,7 +167,4 @@ theorem val_add_one_le_of_lt {n : Nat} {a b : Fin n} (h : a < b) : (a : Nat) + 1
 
 theorem val_add_one_le_of_gt {n : Nat} {a b : Fin n} (h : a > b) : (b : Nat) + 1 ≤ (a : Nat) := h
 
-theorem exists_iff {p : Fin n → Prop} : (Exists fun i => p i) ↔ Exists fun i => Exists fun h => p ⟨i, h⟩ :=
-  ⟨fun ⟨⟨i, hi⟩, hpi⟩ => ⟨i, hi, hpi⟩, fun ⟨i, hi, hpi⟩ => ⟨⟨i, hi⟩, hpi⟩⟩
-
 end Fin

src/Init/Data/Fin/Bitwise.lean

@@ -1,15 +0,0 @@
-/-
-Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Markus Himmel
--/
-prelude
-import Init.Data.Nat.Bitwise
-import Init.Data.Fin.Basic
-
-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)
-
-end Fin

src/Init/Data/Fin/Fold.lean

@@ -6,15 +6,12 @@ Authors: François G. Dorais
 prelude
 import Init.Data.Nat.Linear
 
-namespace Fin
-
 /-- 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)`  -/
   loop (x : α) (i : Nat) : α :=
     if h : i < n then loop (f x ⟨i, h⟩) (i+1) else x
   termination_by n - i
-  decreasing_by decreasing_trivial_pre_omega
 
 /-- 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
@@ -22,5 +19,3 @@ namespace Fin
   loop : {i // i ≤ n} → α → α
   | ⟨0, _⟩, x => x
   | ⟨i+1, h⟩, x => loop ⟨i, Nat.le_of_lt h⟩ (f ⟨i, h⟩ x)
-
-end Fin

src/Init/Data/Fin/Iterate.lean

@@ -23,7 +23,6 @@ def hIterateFrom (P : Nat → Sort _) {n} (f : ∀(i : Fin n), P i.val → P (i.
     have p : i = n := (or_iff_left g).mp (Nat.eq_or_lt_of_le ubnd)
     _root_.cast (congrArg P p) a
   termination_by n - i
-  decreasing_by decreasing_trivial_pre_omega
 
 /--
 `hIterate` is a heterogenous iterative operation that applies a

src/Init/Data/Fin/Lemmas.lean

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2022 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Mario Carneiro, Leonardo de Moura
+Authors: Mario Carneiro
 -/
 prelude
 import Init.Data.Fin.Basic
@@ -11,9 +11,6 @@ import Init.ByCases
 import Init.Conv
 import Init.Omega
 
--- Remove after the next stage0 update
-set_option allowUnsafeReducibility true
-
 namespace Fin
 
 /-- If you actually have an element of `Fin n`, then the `n` is always positive -/
@@ -24,7 +21,7 @@ theorem mod_def (a m : Fin n) : a % m = Fin.mk (a % m) (Nat.lt_of_le_of_lt (Nat.
 
 theorem mul_def (a b : Fin n) : a * b = Fin.mk ((a * b) % n) (Nat.mod_lt _ a.size_pos) := rfl
 
-theorem sub_def (a b : Fin n) : a - b = Fin.mk (((n - b) + a) % n) (Nat.mod_lt _ a.size_pos) := rfl
+theorem sub_def (a b : Fin n) : a - b = Fin.mk ((a + (n - b)) % n) (Nat.mod_lt _ a.size_pos) := rfl
 
 theorem size_pos' : ∀ [Nonempty (Fin n)], 0 < n | ⟨i⟩ => i.size_pos
 
@@ -37,28 +34,32 @@ theorem pos_iff_nonempty {n : Nat} : 0 < n ↔ Nonempty (Fin n) :=
 
 @[simp] protected theorem eta (a : Fin n) (h : a < n) : (⟨a, h⟩ : Fin n) = a := rfl
 
-@[ext] protected theorem ext {a b : Fin n} (h : (a : Nat) = b) : a = b := eq_of_val_eq h
+@[ext] theorem ext {a b : Fin n} (h : (a : Nat) = b) : a = b := eq_of_val_eq h
+
+theorem ext_iff {a b : Fin n} : a = b ↔ a.1 = b.1 := val_inj.symm
 
 theorem val_ne_iff {a b : Fin n} : a.1 ≠ b.1 ↔ a ≠ b := not_congr val_inj
 
+theorem exists_iff {p : Fin n → Prop} : (∃ i, p i) ↔ ∃ i h, p ⟨i, h⟩ :=
+  ⟨fun ⟨⟨i, hi⟩, hpi⟩ => ⟨i, hi, hpi⟩, fun ⟨i, hi, hpi⟩ => ⟨⟨i, hi⟩, hpi⟩⟩
+
 theorem forall_iff {p : Fin n → Prop} : (∀ i, p i) ↔ ∀ i h, p ⟨i, h⟩ :=
   ⟨fun h i hi => h ⟨i, hi⟩, fun h ⟨i, hi⟩ => h i hi⟩
 
 protected theorem mk.inj_iff {n a b : Nat} {ha : a < n} {hb : b < n} :
-    (⟨a, ha⟩ : Fin n) = ⟨b, hb⟩ ↔ a = b := Fin.ext_iff
+    (⟨a, ha⟩ : Fin n) = ⟨b, hb⟩ ↔ a = b := ext_iff
 
 theorem val_mk {m n : Nat} (h : m < n) : (⟨m, h⟩ : Fin n).val = m := rfl
 
 theorem eq_mk_iff_val_eq {a : Fin n} {k : Nat} {hk : k < n} :
-    a = ⟨k, hk⟩ ↔ (a : Nat) = k := Fin.ext_iff
+    a = ⟨k, hk⟩ ↔ (a : Nat) = k := ext_iff
 
 theorem mk_val (i : Fin n) : (⟨i, i.isLt⟩ : Fin n) = i := Fin.eta ..
 
 @[simp] theorem val_ofNat' (a : Nat) (is_pos : n > 0) :
   (Fin.ofNat' a is_pos).val = a % n := rfl
 
-@[deprecated ofNat'_zero_val (since := "2024-02-22")]
-theorem ofNat'_zero_val : (Fin.ofNat' 0 h).val = 0 := Nat.zero_mod _
+@[deprecated ofNat'_zero_val] theorem ofNat'_zero_val : (Fin.ofNat' 0 h).val = 0 := Nat.zero_mod _
 
 @[simp] theorem mod_val (a b : Fin n) : (a % b).val = a.val % b.val :=
   rfl
@@ -89,18 +90,6 @@ theorem lt_iff_val_lt_val {a b : Fin n} : a < b ↔ a.val < b.val := Iff.rfl
 
 @[simp] protected theorem not_lt {a b : Fin n} : ¬ a < b ↔ b ≤ a := Nat.not_lt
 
-@[simp] protected theorem le_refl (a : Fin n) : a ≤ a := by simp [le_def]
-
-@[simp] protected theorem lt_irrefl (a : Fin n) : ¬ a < a := by simp
-
-protected theorem le_trans {a b c : Fin n} : a ≤ b → b ≤ c → a ≤ c := Nat.le_trans
-
-protected theorem lt_trans {a b c : Fin n} : a < b → b < c → a < c := Nat.lt_trans
-
-protected theorem le_total (a b : Fin n) : a ≤ b ∨ b ≤ a := Nat.le_total a b
-
-protected theorem lt_asymm {a b : Fin n} (h : a < b) : ¬ b < a := Nat.lt_asymm h
-
 protected theorem ne_of_lt {a b : Fin n} (h : a < b) : a ≠ b := Fin.ne_of_val_ne (Nat.ne_of_lt h)
 
 protected theorem ne_of_gt {a b : Fin n} (h : a < b) : b ≠ a := Fin.ne_of_val_ne (Nat.ne_of_gt h)
@@ -143,7 +132,7 @@ theorem eq_succ_of_ne_zero {n : Nat} {i : Fin (n + 1)} (hi : i ≠ 0) : ∃ j :
 
 @[simp] theorem val_rev (i : Fin n) : rev i = n - (i + 1) := rfl
 
-@[simp] theorem rev_rev (i : Fin n) : rev (rev i) = i := Fin.ext <| by
+@[simp] theorem rev_rev (i : Fin n) : rev (rev i) = i := ext <| by
   rw [val_rev, val_rev, ← Nat.sub_sub, Nat.sub_sub_self (by exact i.2), Nat.add_sub_cancel]
 
 @[simp] theorem rev_le_rev {i j : Fin n} : rev i ≤ rev j ↔ j ≤ i := by
@@ -169,12 +158,12 @@ theorem le_last (i : Fin (n + 1)) : i ≤ last n := Nat.le_of_lt_succ i.is_lt
 theorem last_pos : (0 : Fin (n + 2)) < last (n + 1) := Nat.succ_pos _
 
 theorem eq_last_of_not_lt {i : Fin (n + 1)} (h : ¬(i : Nat) < n) : i = last n :=
-  Fin.ext <| Nat.le_antisymm (le_last i) (Nat.not_lt.1 h)
+  ext <| Nat.le_antisymm (le_last i) (Nat.not_lt.1 h)
 
 theorem val_lt_last {i : Fin (n + 1)} : i ≠ last n → (i : Nat) < n :=
   Decidable.not_imp_comm.1 eq_last_of_not_lt
 
-@[simp] theorem rev_last (n : Nat) : rev (last n) = 0 := Fin.ext <| by simp
+@[simp] theorem rev_last (n : Nat) : rev (last n) = 0 := ext <| by simp
 
 @[simp] theorem rev_zero (n : Nat) : rev 0 = last n := by
   rw [← rev_rev (last _), rev_last]
@@ -242,11 +231,11 @@ theorem zero_ne_one : (0 : Fin (n + 2)) ≠ 1 := Fin.ne_of_lt one_pos
 @[simp] theorem succ_lt_succ_iff {a b : Fin n} : a.succ < b.succ ↔ a < b := Nat.succ_lt_succ_iff
 
 @[simp] theorem succ_inj {a b : Fin n} : a.succ = b.succ ↔ a = b := by
-  refine ⟨fun h => Fin.ext ?_, congrArg _⟩
+  refine ⟨fun h => ext ?_, congrArg _⟩
   apply Nat.le_antisymm <;> exact succ_le_succ_iff.1 (h ▸ Nat.le_refl _)
 
 theorem succ_ne_zero {n} : ∀ k : Fin n, Fin.succ k ≠ 0
-  | ⟨k, _⟩, heq => Nat.succ_ne_zero k <| congrArg Fin.val heq
+  | ⟨k, _⟩, heq => Nat.succ_ne_zero k <| ext_iff.1 heq
 
 @[simp] theorem succ_zero_eq_one : Fin.succ (0 : Fin (n + 1)) = 1 := rfl
 
@@ -265,7 +254,7 @@ theorem one_lt_succ_succ (a : Fin n) : (1 : Fin (n + 2)) < a.succ.succ := by
   rw [← succ_zero_eq_one, succ_lt_succ_iff]; exact succ_pos a
 
 @[simp] theorem add_one_lt_iff {n : Nat} {k : Fin (n + 2)} : k + 1 < k ↔ k = last _ := by
-  simp only [lt_def, val_add, val_last, Fin.ext_iff]
+  simp only [lt_def, val_add, val_last, ext_iff]
   let ⟨k, hk⟩ := k
   match Nat.eq_or_lt_of_le (Nat.le_of_lt_succ hk) with
   | .inl h => cases h; simp [Nat.succ_pos]
@@ -283,7 +272,7 @@ theorem one_lt_succ_succ (a : Fin n) : (1 : Fin (n + 2)) < a.succ.succ := by
     split <;> simp [*, (Nat.succ_ne_zero _).symm, Nat.ne_of_gt (Nat.lt_succ_self _)]
 
 @[simp] theorem last_le_iff {n : Nat} {k : Fin (n + 1)} : last n ≤ k ↔ k = last n := by
-  rw [Fin.ext_iff, Nat.le_antisymm_iff, le_def, and_iff_right (by apply le_last)]
+  rw [ext_iff, Nat.le_antisymm_iff, le_def, and_iff_right (by apply le_last)]
 
 @[simp] theorem lt_add_one_iff {n : Nat} {k : Fin (n + 1)} : k < k + 1 ↔ k < last n := by
   rw [← Decidable.not_iff_not]; simp
@@ -304,10 +293,10 @@ theorem succ_succ_ne_one (a : Fin n) : Fin.succ (Fin.succ a) ≠ 1 :=
 @[simp] theorem castLE_mk (i n m : Nat) (hn : i < n) (h : n ≤ m) :
     castLE h ⟨i, hn⟩ = ⟨i, Nat.lt_of_lt_of_le hn h⟩ := rfl
 
-@[simp] theorem castLE_zero {n m : Nat} (h : n.succ ≤ m.succ) : castLE h 0 = 0 := by simp [Fin.ext_iff]
+@[simp] theorem castLE_zero {n m : Nat} (h : n.succ ≤ m.succ) : castLE h 0 = 0 := by simp [ext_iff]
 
 @[simp] theorem castLE_succ {m n : Nat} (h : m + 1 ≤ n + 1) (i : Fin m) :
-    castLE h i.succ = (castLE (Nat.succ_le_succ_iff.mp h) i).succ := by simp [Fin.ext_iff]
+    castLE h i.succ = (castLE (Nat.succ_le_succ_iff.mp h) i).succ := by simp [ext_iff]
 
 @[simp] theorem castLE_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) (i : Fin k) :
     Fin.castLE mn (Fin.castLE km i) = Fin.castLE (Nat.le_trans km mn) i :=
@@ -320,7 +309,7 @@ theorem succ_succ_ne_one (a : Fin n) : Fin.succ (Fin.succ a) ≠ 1 :=
 @[simp] theorem coe_cast (h : n = m) (i : Fin n) : (cast h i : Nat) = i := rfl
 
 @[simp] theorem cast_last {n' : Nat} {h : n + 1 = n' + 1} : cast h (last n) = last n' :=
-  Fin.ext (by rw [coe_cast, val_last, val_last, Nat.succ.inj h])
+  ext (by rw [coe_cast, val_last, val_last, Nat.succ.inj h])
 
 @[simp] theorem cast_mk (h : n = m) (i : Nat) (hn : i < n) : cast h ⟨i, hn⟩ = ⟨i, h ▸ hn⟩ := rfl
 
@@ -346,7 +335,7 @@ theorem castAdd_lt {m : Nat} (n : Nat) (i : Fin m) : (castAdd n i : Nat) < m :=
 
 /-- For rewriting in the reverse direction, see `Fin.cast_castAdd_left`. -/
 theorem castAdd_cast {n n' : Nat} (m : Nat) (i : Fin n') (h : n' = n) :
-    castAdd m (Fin.cast h i) = Fin.cast (congrArg (. + m) h) (castAdd m i) := Fin.ext rfl
+    castAdd m (Fin.cast h i) = Fin.cast (congrArg (. + m) h) (castAdd m i) := ext rfl
 
 theorem cast_castAdd_left {n n' m : Nat} (i : Fin n') (h : n' + m = n + m) :
     cast h (castAdd m i) = castAdd m (cast (Nat.add_right_cancel h) i) := rfl
@@ -376,7 +365,7 @@ theorem castSucc_lt_succ (i : Fin n) : Fin.castSucc i < i.succ :=
   lt_def.2 <| by simp only [coe_castSucc, val_succ, Nat.lt_succ_self]
 
 theorem le_castSucc_iff {i : Fin (n + 1)} {j : Fin n} : i ≤ Fin.castSucc j ↔ i < j.succ := by
-  simpa only [lt_def, le_def] using Nat.add_one_le_add_one_iff.symm
+  simpa [lt_def, le_def] using Nat.succ_le_succ_iff.symm
 
 theorem castSucc_lt_iff_succ_le {n : Nat} {i : Fin n} {j : Fin (n + 1)} :
     Fin.castSucc i < j ↔ i.succ ≤ j := .rfl
@@ -395,7 +384,7 @@ theorem castSucc_lt_iff_succ_le {n : Nat} {i : Fin n} {j : Fin (n + 1)} :
 @[simp] theorem castSucc_lt_castSucc_iff {a b : Fin n} :
     Fin.castSucc a < Fin.castSucc b ↔ a < b := .rfl
 
-theorem castSucc_inj {a b : Fin n} : castSucc a = castSucc b ↔ a = b := by simp [Fin.ext_iff]
+theorem castSucc_inj {a b : Fin n} : castSucc a = castSucc b ↔ a = b := by simp [ext_iff]
 
 theorem castSucc_lt_last (a : Fin n) : castSucc a < last n := a.is_lt
 
@@ -407,7 +396,7 @@ theorem castSucc_lt_last (a : Fin n) : castSucc a < last n := a.is_lt
 theorem castSucc_pos {i : Fin (n + 1)} (h : 0 < i) : 0 < castSucc i := by
   simpa [lt_def] using h
 
-@[simp] theorem castSucc_eq_zero_iff (a : Fin (n + 1)) : castSucc a = 0 ↔ a = 0 := by simp [Fin.ext_iff]
+@[simp] theorem castSucc_eq_zero_iff (a : Fin (n + 1)) : castSucc a = 0 ↔ a = 0 := by simp [ext_iff]
 
 theorem castSucc_ne_zero_iff (a : Fin (n + 1)) : castSucc a ≠ 0 ↔ a ≠ 0 :=
   not_congr <| castSucc_eq_zero_iff a
@@ -419,7 +408,7 @@ theorem castSucc_fin_succ (n : Nat) (j : Fin n) :
 theorem coeSucc_eq_succ {a : Fin n} : castSucc a + 1 = a.succ := by
   cases n
   · exact a.elim0
-  · simp [Fin.ext_iff, add_def, Nat.mod_eq_of_lt (Nat.succ_lt_succ a.is_lt)]
+  · simp [ext_iff, add_def, Nat.mod_eq_of_lt (Nat.succ_lt_succ a.is_lt)]
 
 theorem lt_succ {a : Fin n} : castSucc a < a.succ := by
   rw [castSucc, lt_def, coe_castAdd, val_succ]; exact Nat.lt_succ_self a.val
@@ -452,7 +441,7 @@ theorem cast_addNat_left {n n' m : Nat} (i : Fin n') (h : n' + m = n + m) :
 
 @[simp] theorem cast_addNat_right {n m m' : Nat} (i : Fin n) (h : n + m' = n + m) :
     cast h (addNat i m') = addNat i m :=
-  Fin.ext <| (congrArg ((· + ·) (i : Nat)) (Nat.add_left_cancel h) : _)
+  ext <| (congrArg ((· + ·) (i : Nat)) (Nat.add_left_cancel h) : _)
 
 @[simp] theorem coe_natAdd (n : Nat) {m : Nat} (i : Fin m) : (natAdd n i : Nat) = n + i := rfl
 
@@ -472,7 +461,7 @@ theorem cast_natAdd_right {n n' m : Nat} (i : Fin n') (h : m + n' = m + n) :
 
 @[simp] theorem cast_natAdd_left {n m m' : Nat} (i : Fin n) (h : m' + n = m + n) :
     cast h (natAdd m' i) = natAdd m i :=
-  Fin.ext <| (congrArg (· + (i : Nat)) (Nat.add_right_cancel h) : _)
+  ext <| (congrArg (· + (i : Nat)) (Nat.add_right_cancel h) : _)
 
 theorem castAdd_natAdd (p m : Nat) {n : Nat} (i : Fin n) :
     castAdd p (natAdd m i) = cast (Nat.add_assoc ..).symm (natAdd m (castAdd p i)) := rfl
@@ -482,27 +471,27 @@ theorem natAdd_castAdd (p m : Nat) {n : Nat} (i : Fin n) :
 
 theorem natAdd_natAdd (m n : Nat) {p : Nat} (i : Fin p) :
     natAdd m (natAdd n i) = cast (Nat.add_assoc ..) (natAdd (m + n) i) :=
-  Fin.ext <| (Nat.add_assoc ..).symm
+  ext <| (Nat.add_assoc ..).symm
 
 @[simp]
 theorem cast_natAdd_zero {n n' : Nat} (i : Fin n) (h : 0 + n = n') :
     cast h (natAdd 0 i) = cast ((Nat.zero_add _).symm.trans h) i :=
-  Fin.ext <| Nat.zero_add _
+  ext <| Nat.zero_add _
 
 @[simp]
 theorem cast_natAdd (n : Nat) {m : Nat} (i : Fin m) :
-    cast (Nat.add_comm ..) (natAdd n i) = addNat i n := Fin.ext <| Nat.add_comm ..
+    cast (Nat.add_comm ..) (natAdd n i) = addNat i n := ext <| Nat.add_comm ..
 
 @[simp]
 theorem cast_addNat {n : Nat} (m : Nat) (i : Fin n) :
-    cast (Nat.add_comm ..) (addNat i m) = natAdd m i := Fin.ext <| Nat.add_comm ..
+    cast (Nat.add_comm ..) (addNat i m) = natAdd m i := ext <| Nat.add_comm ..
 
 @[simp] theorem natAdd_last {m n : Nat} : natAdd n (last m) = last (n + m) := rfl
 
 theorem natAdd_castSucc {m n : Nat} {i : Fin m} : natAdd n (castSucc i) = castSucc (natAdd n i) :=
   rfl
 
-theorem rev_castAdd (k : Fin n) (m : Nat) : rev (castAdd m k) = addNat (rev k) m := Fin.ext <| by
+theorem rev_castAdd (k : Fin n) (m : Nat) : rev (castAdd m k) = addNat (rev k) m := ext <| by
   rw [val_rev, coe_castAdd, coe_addNat, val_rev, Nat.sub_add_comm (Nat.succ_le_of_lt k.is_lt)]
 
 theorem rev_addNat (k : Fin n) (m : Nat) : rev (addNat k m) = castAdd m (rev k) := by
@@ -532,7 +521,7 @@ theorem pred_eq_iff_eq_succ {n : Nat} (i : Fin (n + 1)) (hi : i ≠ 0) (j : Fin
 theorem pred_mk_succ (i : Nat) (h : i < n + 1) :
     Fin.pred ⟨i + 1, Nat.add_lt_add_right h 1⟩ (ne_of_val_ne (Nat.ne_of_gt (mk_succ_pos i h))) =
       ⟨i, h⟩ := by
-  simp only [Fin.ext_iff, coe_pred, Nat.add_sub_cancel]
+  simp only [ext_iff, coe_pred, Nat.add_sub_cancel]
 
 @[simp] theorem pred_mk_succ' (i : Nat) (h₁ : i + 1 < n + 1 + 1) (h₂) :
     Fin.pred ⟨i + 1, h₁⟩ h₂ = ⟨i, Nat.lt_of_succ_lt_succ h₁⟩ := pred_mk_succ i _
@@ -552,14 +541,14 @@ theorem pred_mk {n : Nat} (i : Nat) (h : i < n + 1) (w) : Fin.pred ⟨i, h⟩ w
     ∀ {a b : Fin (n + 1)} {ha : a ≠ 0} {hb : b ≠ 0}, a.pred ha = b.pred hb ↔ a = b
   | ⟨0, _⟩, _, ha, _ => by simp only [mk_zero, ne_eq, not_true] at ha
   | ⟨i + 1, _⟩, ⟨0, _⟩, _, hb => by simp only [mk_zero, ne_eq, not_true] at hb
-  | ⟨i + 1, hi⟩, ⟨j + 1, hj⟩, ha, hb => by simp [Fin.ext_iff, Nat.succ.injEq]
+  | ⟨i + 1, hi⟩, ⟨j + 1, hj⟩, ha, hb => by simp [ext_iff, Nat.succ.injEq]
 
 @[simp] theorem pred_one {n : Nat} :
     Fin.pred (1 : Fin (n + 2)) (Ne.symm (Fin.ne_of_lt one_pos)) = 0 := rfl
 
 theorem pred_add_one (i : Fin (n + 2)) (h : (i : Nat) < n + 1) :
     pred (i + 1) (Fin.ne_of_gt (add_one_pos _ (lt_def.2 h))) = castLT i h := by
-  rw [Fin.ext_iff, coe_pred, coe_castLT, val_add, val_one, Nat.mod_eq_of_lt, Nat.add_sub_cancel]
+  rw [ext_iff, coe_pred, coe_castLT, val_add, val_one, Nat.mod_eq_of_lt, Nat.add_sub_cancel]
   exact Nat.add_lt_add_right h 1
 
 @[simp] theorem coe_subNat (i : Fin (n + m)) (h : m ≤ i) : (i.subNat m h : Nat) = i - m := rfl
@@ -571,10 +560,10 @@ theorem pred_add_one (i : Fin (n + 2)) (h : (i : Nat) < n + 1) :
     pred (castSucc i.succ) (Fin.ne_of_gt (castSucc_pos i.succ_pos)) = castSucc i := rfl
 
 @[simp] theorem addNat_subNat {i : Fin (n + m)} (h : m ≤ i) : addNat (subNat m i h) m = i :=
-  Fin.ext <| Nat.sub_add_cancel h
+  ext <| Nat.sub_add_cancel h
 
 @[simp] theorem subNat_addNat (i : Fin n) (m : Nat) (h : m ≤ addNat i m := le_coe_addNat m i) :
-    subNat m (addNat i m) h = i := Fin.ext <| Nat.add_sub_cancel i m
+    subNat m (addNat i m) h = i := ext <| Nat.add_sub_cancel i m
 
 @[simp] theorem natAdd_subNat_cast {i : Fin (n + m)} (h : n ≤ i) :
     natAdd n (subNat n (cast (Nat.add_comm ..) i) h) = i := by simp [← cast_addNat]; rfl
@@ -613,7 +602,6 @@ A version of `Fin.succRec` taking `i : Fin n` as the first argument. -/
     @Fin.succRecOn (n + 1) i.succ motive zero succ = succ n i (Fin.succRecOn i zero succ) := by
   cases i; rfl
 
-
 /-- 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`.
@@ -622,12 +610,8 @@ and `succ` defines the inductive step using `motive i.castSucc`.
 @[elab_as_elim] def induction {motive : Fin (n + 1) → Sort _} (zero : motive 0)
     (succ : ∀ i : Fin n, motive (castSucc i) → motive i.succ) :
     ∀ i : Fin (n + 1), motive i
-  | ⟨i, hi⟩ => go i hi
-where
-  -- Use a curried function so that this is structurally recursive
-  go : ∀ (i : Nat) (hi : i < n + 1), motive ⟨i, hi⟩
-  | 0, hi => by rwa [Fin.mk_zero]
-  | i+1, hi => succ ⟨i, Nat.lt_of_succ_lt_succ hi⟩ (go i (Nat.lt_of_succ_lt hi))
+  | ⟨0, hi⟩ => by rwa [Fin.mk_zero]
+  | ⟨i+1, hi⟩ => succ ⟨i, Nat.lt_of_succ_lt_succ hi⟩ (induction zero succ ⟨i, Nat.lt_of_succ_lt hi⟩)
 
 @[simp] theorem induction_zero {motive : Fin (n + 1) → Sort _} (zero : motive 0)
     (hs : ∀ i : Fin n, motive (castSucc i) → motive i.succ) :
@@ -757,16 +741,16 @@ theorem addCases_right {m n : Nat} {motive : Fin (m + n) → Sort _} {left right
 
 /-! ### sub -/
 
-protected theorem coe_sub (a b : Fin n) : ((a - b : Fin n) : Nat) = ((n - b) + a) % n := by
+protected theorem coe_sub (a b : Fin n) : ((a - b : Fin n) : Nat) = (a + (n - b)) % n := by
   cases a; cases b; rfl
 
 @[simp] theorem ofNat'_sub (x : Nat) (lt : 0 < n) (y : Fin n) :
-    Fin.ofNat' x lt - y = Fin.ofNat' ((n - y.val) + x) lt := by
+    Fin.ofNat' x lt - y = Fin.ofNat' (x + (n - y.val)) lt := by
   apply Fin.eq_of_val_eq
   simp [Fin.ofNat', Fin.sub_def]
 
 @[simp] theorem sub_ofNat' (x : Fin n) (y : Nat) (lt : 0 < n) :
-    x - Fin.ofNat' y lt = Fin.ofNat' ((n - y % n) + x.val) lt := by
+    x - Fin.ofNat' y lt = Fin.ofNat' (x.val + (n - y % n)) lt := by
   apply Fin.eq_of_val_eq
   simp [Fin.ofNat', Fin.sub_def]
 
@@ -777,20 +761,17 @@ private theorem _root_.Nat.mod_eq_sub_of_lt_two_mul {x n} (h₁ : n ≤ x) (h₂
 theorem coe_sub_iff_le {a b : Fin n} : (↑(a - b) : Nat) = a - b ↔ b ≤ a := by
   rw [sub_def, le_def]
   dsimp only
-  if h : n ≤ (n - b) + a then
+  if h : n ≤ a + (n - b) then
     rw [Nat.mod_eq_sub_of_lt_two_mul h]
     all_goals omega
   else
     rw [Nat.mod_eq_of_lt]
     all_goals omega
 
-theorem sub_val_of_le {a b : Fin n} : b ≤ a → (a - b).val = a.val - b.val :=
-  coe_sub_iff_le.2
-
 theorem coe_sub_iff_lt {a b : Fin n} : (↑(a - b) : Nat) = n + a - b ↔ a < b := by
   rw [sub_def, lt_def]
   dsimp only
-  if h : n ≤ (n - b) + a then
+  if h : n ≤ a + (n - b) then
     rw [Nat.mod_eq_sub_of_lt_two_mul h]
     all_goals omega
   else
@@ -808,28 +789,47 @@ theorem coe_mul {n : Nat} : ∀ a b : Fin n, ((a * b : Fin n) : Nat) = a * b % n
 protected theorem mul_one (k : Fin (n + 1)) : k * 1 = k := by
   match n with
   | 0 => exact Subsingleton.elim (α := Fin 1) ..
-  | n+1 => simp [Fin.ext_iff, mul_def, Nat.mod_eq_of_lt (is_lt k)]
+  | n+1 => simp [ext_iff, mul_def, Nat.mod_eq_of_lt (is_lt k)]
 
 protected theorem mul_comm (a b : Fin n) : a * b = b * a :=
-  Fin.ext <| by rw [mul_def, mul_def, Nat.mul_comm]
-instance : Std.Commutative (α := Fin n) (· * ·) := ⟨Fin.mul_comm⟩
+  ext <| by rw [mul_def, mul_def, Nat.mul_comm]
 
 protected theorem mul_assoc (a b c : Fin n) : a * b * c = a * (b * c) := by
   apply eq_of_val_eq
   simp only [val_mul]
   rw [← Nat.mod_eq_of_lt a.isLt, ← Nat.mod_eq_of_lt b.isLt, ← Nat.mod_eq_of_lt c.isLt]
   simp only [← Nat.mul_mod, Nat.mul_assoc]
-instance : Std.Associative (α := Fin n) (· * ·) := ⟨Fin.mul_assoc⟩
 
 protected theorem one_mul (k : Fin (n + 1)) : (1 : Fin (n + 1)) * k = k := by
   rw [Fin.mul_comm, Fin.mul_one]
-instance : Std.LawfulIdentity (α := Fin (n + 1)) (· * ·) 1 where
-  left_id := Fin.one_mul
-  right_id := Fin.mul_one
 
-protected theorem mul_zero (k : Fin (n + 1)) : k * 0 = 0 := by simp [Fin.ext_iff, mul_def]
+protected theorem mul_zero (k : Fin (n + 1)) : k * 0 = 0 := by simp [ext_iff, mul_def]
 
 protected theorem zero_mul (k : Fin (n + 1)) : (0 : Fin (n + 1)) * k = 0 := by
-  simp [Fin.ext_iff, mul_def]
+  simp [ext_iff, mul_def]
 
 end Fin
+
+namespace USize
+
+@[simp] theorem lt_def {a b : USize} : a < b ↔ a.toNat < b.toNat := .rfl
+
+@[simp] theorem le_def {a b : USize} : a ≤ b ↔ a.toNat ≤ b.toNat := .rfl
+
+@[simp] theorem zero_toNat : (0 : USize).toNat = 0 := Nat.zero_mod _
+
+@[simp] theorem mod_toNat (a b : USize) : (a % b).toNat = a.toNat % b.toNat :=
+  Fin.mod_val ..
+
+@[simp] theorem div_toNat (a b : USize) : (a / b).toNat = a.toNat / b.toNat :=
+  Fin.div_val ..
+
+@[simp] theorem modn_toNat (a : USize) (b : Nat) : (a.modn b).toNat = a.toNat % b :=
+  Fin.modn_val ..
+
+theorem mod_lt (a b : USize) (h : 0 < b) : a % b < b := USize.modn_lt _ (by simp at h; exact h)
+
+theorem toNat.inj : ∀ {a b : USize}, a.toNat = b.toNat → a = b
+  | ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
+
+end USize

src/Init/Data/Float.lean

@@ -101,13 +101,13 @@ Returns an undefined value if `x` is not finite.
 instance : ToString Float where
   toString := Float.toString
 
-@[extern "lean_uint64_to_float"] opaque UInt64.toFloat (n : UInt64) : Float
-
 instance : Repr Float where
-  reprPrec n prec := if n < UInt64.toFloat 0 then Repr.addAppParen (toString n) prec else toString n
+  reprPrec n _ := Float.toString n
 
 instance : ReprAtom Float  := ⟨⟩
 
+@[extern "lean_uint64_to_float"] opaque UInt64.toFloat (n : UInt64) : Float
+
 @[extern "sin"] opaque Float.sin : Float → Float
 @[extern "cos"] opaque Float.cos : Float → Float
 @[extern "tan"] opaque Float.tan : Float → Float