doc-string

This PR refactors the `NoNatZeroDivisors` to make sure it will work with
the new `Semiring` support.

.github/workflows/build-template.yml

@@ -82,7 +82,7 @@ jobs:
       - name: CI Merge Checkout
         run: |
           git fetch --depth=1 origin ${{ github.sha }}
-          git checkout FETCH_HEAD flake.nix flake.lock script/prepare-*
+          git checkout FETCH_HEAD flake.nix flake.lock script/prepare-* tests/lean/run/importStructure.lean
         if: github.event_name == 'pull_request'
       # (needs to be after "Checkout" so files don't get overridden)
       - name: Setup emsdk
@@ -104,12 +104,12 @@ jobs:
           # NOTE: must be in sync with `save` below
           path: |
             .ccache
-            ${{ matrix.name == 'Linux Lake' && 'build/stage1/**/*.trace
-            build/stage1/**/*.olean
+            ${{ matrix.name == 'Linux Lake' && false && 'build/stage1/**/*.trace
+            build/stage1/**/*.olean*
             build/stage1/**/*.ilean
             build/stage1/**/*.c
             build/stage1/**/*.c.o*' || '' }}
-          key: ${{ matrix.name }}-build-v3-${{ github.event.pull_request.head.sha }}
+          key: ${{ matrix.name }}-build-v3-${{ github.sha }}
           # fall back to (latest) previous cache
           restore-keys: |
             ${{ matrix.name }}-build-v3
@@ -127,9 +127,12 @@ jobs:
           [ -d build ] || mkdir build
           cd build
           # arguments passed to `cmake`
-          # this also enables githash embedding into stage 1 library
-          OPTIONS=(-DCHECK_OLEAN_VERSION=ON)
-          OPTIONS+=(-DLEAN_EXTRA_MAKE_OPTS=-DwarningAsError=true)
+          OPTIONS=(-DLEAN_EXTRA_MAKE_OPTS=-DwarningAsError=true)
+          if [[ -n '${{ matrix.release }}' ]]; then
+            # this also enables githash embedding into stage 1 library, which prohibits reusing
+            # `.olean`s across commits, so we don't do it in the fast non-release CI
+            OPTIONS+=(-DCHECK_OLEAN_VERSION=ON)
+          fi
           if [[ -n '${{ matrix.cross_target }}' ]]; then
             # used by `prepare-llvm`
             export EXTRA_FLAGS=--target=${{ matrix.cross_target }}
@@ -193,7 +196,7 @@ jobs:
         run: |
           ulimit -c unlimited  # coredumps
           time ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/stage1 -j$NPROC --output-junit test-results.xml ${{ matrix.CTEST_OPTIONS }}
-        if: (matrix.wasm || !matrix.cross) && (inputs.check-level >= 1 || matrix.name == 'Linux release')
+        if: (matrix.wasm || !matrix.cross) && (inputs.check-level >= 1 || matrix.test)
       - name: Test Summary
         uses: test-summary/action@v2
         with:
@@ -210,7 +213,7 @@ jobs:
       - name: Check Stage 3
         run: |
           make -C build -j$NPROC check-stage3
-        if: matrix.test-speedcenter
+        if: matrix.check-stage3
       - name: Test Speedcenter Benchmarks
         run: |
           # Necessary for some timing metrics but does not work on Namespace runners
@@ -224,7 +227,7 @@ jobs:
         run: |
           # clean rebuild in case of Makefile changes
           make -C build update-stage0 && rm -rf build/stage* && make -C build -j$NPROC
-        if: matrix.name == 'Linux' && inputs.check-level >= 1
+        if: matrix.check-rebootstrap
       - name: CCache stats
         if: always()
         run: ccache -s
@@ -242,8 +245,8 @@ jobs:
           # NOTE: must be in sync with `restore` above
           path: |
             .ccache
-            ${{ matrix.name == 'Linux Lake' && 'build/stage1/**/*.trace
-            build/stage1/**/*.olean
+            ${{ matrix.name == 'Linux Lake' && false && 'build/stage1/**/*.trace
+            build/stage1/**/*.olean*
             build/stage1/**/*.ilean
             build/stage1/**/*.c
             build/stage1/**/*.c.o*' || '' }}

.github/workflows/ci.yml

@@ -103,6 +103,13 @@ jobs:
             echo "Tag ${TAG_NAME} did not match SemVer regex."
           fi
 
+      - name: Check for custom releases (e.g., not in the main lean repository)
+        if: startsWith(github.ref, 'refs/tags/') && github.repository != 'leanprover/lean4'
+        id: set-release-custom
+        run: |
+          TAG_NAME="${GITHUB_REF##*/}"
+          echo "RELEASE_TAG=$TAG_NAME" >> "$GITHUB_OUTPUT"
+
       - name: Set check level
         id: set-level
         # We do not use github.event.pull_request.labels.*.name here because
@@ -111,7 +118,7 @@ jobs:
         run: |
           check_level=0
 
-          if [[ -n "${{ steps.set-nightly.outputs.nightly }}" || -n "${{ steps.set-release.outputs.RELEASE_TAG }}" ]]; then
+          if [[ -n "${{ steps.set-nightly.outputs.nightly }}" || -n "${{ steps.set-release.outputs.RELEASE_TAG }}" || -n "${{ steps.set-release-custom.outputs.RELEASE_TAG }}" ]]; then
             check_level=2
           elif [[ "${{ github.event_name }}" != "pull_request" ]]; then
             check_level=1
@@ -157,9 +164,15 @@ jobs:
               {
                 // portable release build: use channel with older glibc (2.26)
                 "name": "Linux release",
-                "os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
+                "os": large && level < 2 ? "nscloud-ubuntu-22.04-amd64-4x16" : "ubuntu-latest",
                 "release": true,
-                "check-level": 0,
+                // Special handling for release jobs. We want:
+                // 1. To run it in PRs so developrs get PR toolchains (so secondary is sufficient)
+                // 2. To skip it in merge queues as it takes longer than the
+                //    Linux lake build and adds little value in the merge queue
+                // 3. To run it in release (obviously)
+                "check-level": isPr ? 0 : 2,
+                "secondary": isPr,
                 "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
                 "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-linux-gnu.tar.zst",
                 "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
@@ -169,21 +182,14 @@ jobs:
               },
               {
                 "name": "Linux Lake",
-                "os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
+                "os": large ? "nscloud-ubuntu-22.04-amd64-8x16" : "ubuntu-latest",
                 "check-level": 0,
-                // just a secondary build job for now until false positives can be excluded
-                "secondary": true,
-                "CMAKE_OPTIONS": "-DUSE_LAKE=ON",
-                // TODO: importStructure is not compatible with .olean caching
-                // TODO: why does scopedMacros fail?
-                "CTEST_OPTIONS": "-E 'scopedMacros|importStructure'"
-              },
-              {
-                "name": "Linux",
-                "os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
+                "test": true,
+                "check-rebootstrap": level >= 1,
                 "check-stage3": level >= 2,
-                "test-speedcenter": level >= 2,
-                "check-level": 1,
+                // NOTE: `test-speedcenter` currently seems to be broken on `ubuntu-latest`
+                "test-speedcenter": large && level >= 2,
+                "CMAKE_OPTIONS": "-DUSE_LAKE=ON",
               },
               {
                 "name": "Linux Reldebug",
@@ -216,7 +222,8 @@ jobs:
               },
               {
                 "name": "macOS aarch64",
-                "os": "macos-14",
+                // standard GH runner only comes with 7GB so use large runner if possible
+                "os": large ? "nscloud-macos-sonoma-arm64-6x14" : "macos-14",
                 "CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
                 "release": true,
                 "shell": "bash -euxo pipefail {0}",
@@ -224,11 +231,7 @@ jobs:
                 "prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm*",
                 "binary-check": "otool -L",
                 "tar": "gtar", // https://github.com/actions/runner-images/issues/2619
-                // Special handling for MacOS aarch64, we want:
-                // 1. To run it in PRs so Mac devs get PR toolchains (so secondary is sufficient)
-                // 2. To skip it in merge queues as it takes longer than the Linux build and adds
-                //    little value in the merge queue
-                // 3. To run it in release (obviously)
+                // See above for release job levels
                 "check-level": isPr ? 0 : 2,
                 "secondary": isPr,
               },
@@ -247,7 +250,7 @@ jobs:
               },
               {
                 "name": "Linux aarch64",
-                "os": "nscloud-ubuntu-22.04-arm64-4x8",
+                "os": "nscloud-ubuntu-22.04-arm64-4x16",
                 "CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-linux_aarch64",
                 "release": true,
                 "check-level": 2,
@@ -357,7 +360,7 @@ jobs:
         with:
           path: artifacts
       - name: Release
-        uses: softprops/action-gh-release@v2
+        uses: softprops/action-gh-release@da05d552573ad5aba039eaac05058a918a7bf631
         with:
           files: artifacts/*/*
           fail_on_unmatched_files: true
@@ -401,7 +404,7 @@ jobs:
           echo -e "\n*Full commit log*\n" >> diff.md
           git log --oneline "$last_tag"..HEAD | sed 's/^/* /' >> diff.md
       - name: Release Nightly
-        uses: softprops/action-gh-release@v2
+        uses: softprops/action-gh-release@da05d552573ad5aba039eaac05058a918a7bf631
         with:
           body_path: diff.md
           prerelease: true

.github/workflows/pr-release.yml

@@ -34,7 +34,7 @@ jobs:
       - name: Download artifact from the previous workflow.
         if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
         id: download-artifact
-        uses: dawidd6/action-download-artifact@v9 # https://github.com/marketplace/actions/download-workflow-artifact
+        uses: dawidd6/action-download-artifact@v10 # https://github.com/marketplace/actions/download-workflow-artifact
         with:
           run_id: ${{ github.event.workflow_run.id }}
           path: artifacts
@@ -48,19 +48,30 @@ jobs:
           git -C lean4.git remote add origin https://github.com/${{ github.repository_owner }}/lean4.git
           git -C lean4.git fetch -n origin master
           git -C lean4.git fetch -n origin "${{ steps.workflow-info.outputs.sourceHeadSha }}"
+          
+          # Create both the original tag and the SHA-suffixed tag
+          SHORT_SHA="${{ steps.workflow-info.outputs.sourceHeadSha }}"
+          SHORT_SHA="${SHORT_SHA:0:7}"
+          
+          # Export the short SHA for use in subsequent steps
+          echo "SHORT_SHA=${SHORT_SHA}" >> "$GITHUB_ENV"
+
           git -C lean4.git tag -f pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }} "${{ steps.workflow-info.outputs.sourceHeadSha }}"
+          git -C lean4.git tag -f pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-"${SHORT_SHA}" "${{ steps.workflow-info.outputs.sourceHeadSha }}"
+          
           git -C lean4.git remote add pr-releases https://foo:'${{ secrets.PR_RELEASES_TOKEN }}'@github.com/${{ github.repository_owner }}/lean4-pr-releases.git
           git -C lean4.git push -f pr-releases pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}
+          git -C lean4.git push -f pr-releases pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-"${SHORT_SHA}"
       - name: Delete existing release if present
         if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
         run: |
-          # Try to delete any existing release for the current PR.
+          # Try to delete any existing release for the current PR (just the version without the SHA suffix).
           gh release delete --repo ${{ github.repository_owner }}/lean4-pr-releases pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }} -y || true
         env:
           GH_TOKEN: ${{ secrets.PR_RELEASES_TOKEN }}
-      - name: Release
+      - name: Release (short format)
         if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
-        uses: softprops/action-gh-release@v2
+        uses: softprops/action-gh-release@da05d552573ad5aba039eaac05058a918a7bf631
         with:
           name: Release for PR ${{ steps.workflow-info.outputs.pullRequestNumber }}
           # There are coredumps files here as well, but all in deeper subdirectories.
@@ -73,7 +84,22 @@ jobs:
           # The token used here must have `workflow` privileges.
           GITHUB_TOKEN: ${{ secrets.PR_RELEASES_TOKEN }}
 
-      - name: Report release status
+      - name: Release (SHA-suffixed format)
+        if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
+        uses: softprops/action-gh-release@da05d552573ad5aba039eaac05058a918a7bf631
+        with:
+          name: Release for PR ${{ steps.workflow-info.outputs.pullRequestNumber }} (${{ steps.workflow-info.outputs.sourceHeadSha }})
+          # There are coredumps files here as well, but all in deeper subdirectories.
+          files: artifacts/*/*
+          fail_on_unmatched_files: true
+          draft: false
+          tag_name: pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}
+          repository: ${{ github.repository_owner }}/lean4-pr-releases
+        env:
+          # The token used here must have `workflow` privileges.
+          GITHUB_TOKEN: ${{ secrets.PR_RELEASES_TOKEN }}
+
+      - name: Report release status (short format)
         if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
         uses: actions/github-script@v7
         with:
@@ -87,6 +113,20 @@ jobs:
               description: "${{ github.repository_owner }}/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}",
             });
 
+      - name: Report release status (SHA-suffixed format)
+        if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
+        uses: actions/github-script@v7
+        with:
+          script: |
+            await github.rest.repos.createCommitStatus({
+              owner: context.repo.owner,
+              repo: context.repo.repo,
+              sha: "${{ steps.workflow-info.outputs.sourceHeadSha }}",
+              state: "success",
+              context: "PR toolchain (SHA-suffixed)",
+              description: "${{ github.repository_owner }}/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}",
+            });
+
       - name: Add label
         if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
         uses: actions/github-script@v7
@@ -282,16 +322,18 @@ jobs:
           if [ "$EXISTS" = "0" ]; then
             echo "Branch does not exist, creating it."
             git switch -c lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }} "$BASE"
-            echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}" > lean-toolchain
+            echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
             git add lean-toolchain
             git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
           else
-            echo "Branch already exists, pushing an empty commit."
+            echo "Branch already exists, updating lean-toolchain."
             git switch lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}
             # The Batteries `nightly-testing` or `nightly-testing-YYYY-MM-DD` branch may have moved since this branch was created, so merge their changes.
             # (This should no longer be possible once `nightly-testing-YYYY-MM-DD` is a tag, but it is still safe to merge.)
             git merge "$BASE" --strategy-option ours --no-commit --allow-unrelated-histories
-            git commit --allow-empty -m "Trigger CI for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
+            echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
+            git add lean-toolchain
+            git commit -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
           fi
 
       - name: Push changes
@@ -346,21 +388,23 @@ jobs:
           if [ "$EXISTS" = "0" ]; then
             echo "Branch does not exist, creating it."
             git switch -c lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }} "$BASE"
-            echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}" > lean-toolchain
+            echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
             git add lean-toolchain
             sed -i 's,require "leanprover-community" / "batteries" @ git ".\+",require "leanprover-community" / "batteries" @ git "lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}",' lakefile.lean
             lake update batteries
             git add lakefile.lean lake-manifest.json
             git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
           else
-            echo "Branch already exists, merging $BASE and bumping Batteries."
+            echo "Branch already exists, updating lean-toolchain and bumping Batteries."
             git switch lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}
             # The Mathlib `nightly-testing` branch or `nightly-testing-YYYY-MM-DD` tag 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 "$BASE" --strategy-option ours --no-commit --allow-unrelated-histories
+            echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
+            git add lean-toolchain
             lake update batteries
             git add lake-manifest.json
-            git commit --allow-empty -m "Trigger CI for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
+            git commit -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
           fi
 
       - name: Push changes

.gitignore

@@ -6,7 +6,6 @@
 lake-manifest.json
 /build
 /src/lakefile.toml
-/tests/lakefile.toml
 /lakefile.toml
 GPATH
 GRTAGS

doc/dev/release_checklist.md

@@ -50,7 +50,7 @@ We'll use `v4.6.0` as the intended release version as a running example.
     - Re-running `script/release_checklist.py` will then create the tag `v4.6.0` from `master`/`main` and push it (unless `toolchain-tag: false` in the `release_repos.yml` file)
     - `script/release_checklist.py` will then merge the tag `v4.6.0` into the `stable` branch and push it (unless `stable-branch: false` in the `release_repos.yml` file).
   - Special notes on repositories with exceptional requirements:
-    - `doc-gen4` has addition dependencies which we do not update at each toolchain release, although occasionally these break and need to be updated manually.
+    - `doc-gen4` has additional dependencies which we do not update at each toolchain release, although occasionally these break and need to be updated manually.
     - `verso`:
       - The `subverso` dependency is unusual in that it needs to be compatible with _every_ Lean release simultaneously.
         Usually you don't need to do anything.
@@ -94,6 +94,8 @@ We'll use `v4.6.0` as the intended release version as a running example.
 
 This checklist walks you through creating the first release candidate for a version of Lean.
 
+For subsequent release candidates, the process is essentially the same, but we start out with the `releases/v4.7.0` branch already created.
+
 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.
@@ -112,7 +114,7 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
     git fetch nightly tag nightly-2024-02-29
     git checkout nightly-2024-02-29
     git checkout -b releases/v4.7.0
-    git push --set-upstream origin releases/v4.18.0
+    git push --set-upstream origin releases/v4.7.0
     ```
 - 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.

script/bench.sh

@@ -0,0 +1,9 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+# We benchmark against stage 2 to test new optimizations.
+timeout -s KILL 1h time bash -c 'mkdir -p build/release; cd build/release; cmake ../.. && make -j$(nproc) stage2' 1>&2
+export PATH=$PWD/build/release/stage2/bin:$PATH
+cd tests/bench
+timeout -s KILL 1h time temci exec --config speedcenter.yaml --in speedcenter.exec.velcom.yaml 1>&2
+temci report run_output.yaml --reporter codespeed2

script/prepare-llvm-mingw.sh

@@ -50,5 +50,4 @@ echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='--sysroot ROOT -L ROOT/lib -Wl,-Bstatic
 # when not using the above flags, link GMP dynamically/as usual. Always link ICU dynamically.
 echo -n " -DLEAN_EXTRA_LINKER_FLAGS='-lgmp $(pkg-config --libs libuv) -lucrtbase'"
 # do not set `LEAN_CC` for tests
-echo -n " -DAUTO_THREAD_FINALIZATION=OFF -DSTAGE0_AUTO_THREAD_FINALIZATION=OFF"
 echo -n " -DLEAN_TEST_VARS=''"

script/release_checklist.py

@@ -53,6 +53,23 @@ def tag_exists(repo_url, tag_name, github_token):
     matching_tags = response.json()
     return any(tag["ref"] == f"refs/tags/{tag_name}" for tag in matching_tags)
 
+def commit_hash_for_tag(repo_url, tag_name, github_token):
+    # Use /git/matching-refs/tags/ to get all matching tags
+    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/git/matching-refs/tags/{tag_name}"
+    headers = {'Authorization': f'token {github_token}'} if github_token else {}
+    response = requests.get(api_url, headers=headers)
+
+    if response.status_code != 200:
+        return False
+
+    # Check if any of the returned refs exactly match our tag
+    matching_tags = response.json()
+    matching_commits = [tag["object"]["sha"] for tag in matching_tags if tag["ref"] == f"refs/tags/{tag_name}"]
+    if len(matching_commits) != 1:
+        return None
+    else:
+        return matching_commits[0]
+
 def release_page_exists(repo_url, tag_name, github_token):
     api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/releases/tags/{tag_name}"
     headers = {'Authorization': f'token {github_token}'} if github_token else {}
@@ -286,6 +303,14 @@ def main():
         lean4_success = False
     else:
         print(f"  ✅ Tag {toolchain} exists")
+        commit_hash = commit_hash_for_tag(lean_repo_url, toolchain, github_token)
+        SHORT_HASH_LENGTH = 7 # Lake abbreviates the Lean commit to 7 characters.
+        if commit_hash is None:
+            print(f"  ❌ Could not resolve tag {toolchain} to a commit.")
+            lean4_success = False
+        elif commit_hash[0] == '0' and commit_hash[:SHORT_HASH_LENGTH].isnumeric():
+            print(f"  ❌ Short commit hash {commit_hash[:SHORT_HASH_LENGTH]} is numeric and starts with 0, causing issues for version parsing. Try regenerating the last commit to get a new hash.")
+            lean4_success = False
 
     if not release_page_exists(lean_repo_url, toolchain, github_token):
         print(f"  ❌ Release page for {toolchain} does not exist")

script/release_steps.py

@@ -94,6 +94,7 @@ def generate_script(repo, version, config):
             "echo 'This repo has nightly-testing infrastructure'",
             f"git merge origin/bump/{version.split('-rc')[0]}",
             "echo 'Please resolve any conflicts.'",
+            "grep nightly-testing lakefile.* && echo 'Please ensure the lakefile does not include nightly-testing versions.'",
             ""
         ])
     if re.search(r'rc\d+$', version) and repo_name in ["verso", "reference-manual"]:

src/CMakeLists.txt

@@ -10,7 +10,7 @@ endif()
 include(ExternalProject)
 project(LEAN CXX C)
 set(LEAN_VERSION_MAJOR 4)
-set(LEAN_VERSION_MINOR 21)
+set(LEAN_VERSION_MINOR 22)
 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'")
@@ -58,9 +58,6 @@ option(USE_GITHASH        "GIT_HASH"           ON)
 option(INSTALL_LICENSE "INSTALL_LICENSE" ON)
 # When ON we install a copy of cadical
 option(INSTALL_CADICAL "Install a copy of cadical" ON)
-# When ON thread storage is automatically finalized, it assumes platform support pthreads.
-# This option is important when using Lean as library that is invoked from a different programming language (e.g., Haskell).
-option(AUTO_THREAD_FINALIZATION "AUTO_THREAD_FINALIZATION" ON)
 
 # FLAGS for disabling optimizations and debugging
 option(FREE_VAR_RANGE_OPT  "FREE_VAR_RANGE_OPT"   ON)
@@ -182,10 +179,6 @@ else()
   string(APPEND LEAN_EXTRA_CXX_FLAGS " -D LEAN_MULTI_THREAD")
 endif()
 
-if(AUTO_THREAD_FINALIZATION AND NOT MSVC)
-  string(APPEND LEAN_EXTRA_CXX_FLAGS " -D LEAN_AUTO_THREAD_FINALIZATION")
-endif()
-
 # Set Module Path
 set(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} "${CMAKE_SOURCE_DIR}/cmake/Modules")
 

src/Init.lean

@@ -37,6 +37,7 @@ import Init.Ext
 import Init.Omega
 import Init.MacroTrace
 import Init.Grind
+import Init.GrindInstances
 import Init.While
 import Init.Syntax
 import Init.Internal

src/Init/Classical.lean

@@ -45,7 +45,7 @@ theorem em (p : Prop) : p ∨ ¬p :=
     | Or.inr h, _ => Or.inr h
     | _, Or.inr h => Or.inr h
     | Or.inl hut, Or.inl hvf =>
-      have hne : u ≠ v := by simp [hvf, hut, true_ne_false]
+      have hne : u ≠ v := by simp [hvf, hut]
       Or.inl hne
   have p_implies_uv : p → u = v :=
     fun hp =>

src/Init/Coe.lean

@@ -7,6 +7,7 @@ module
 
 prelude
 import Init.Prelude
+meta import Init.Prelude
 set_option linter.missingDocs true -- keep it documented
 
 /-!

src/Init/Control/Basic.lean

@@ -49,7 +49,7 @@ abbrev forIn_eq_forin' := @forIn_eq_forIn'
 /--
 Extracts the value from a `ForInStep`, ignoring whether it is `ForInStep.done` or `ForInStep.yield`.
 -/
-def ForInStep.value (x : ForInStep α) : α :=
+@[expose] def ForInStep.value (x : ForInStep α) : α :=
   match x with
   | ForInStep.done b => b
   | ForInStep.yield b => b

src/Init/Control/Except.lean

@@ -136,7 +136,7 @@ may throw the corresponding exception.
 
 This is the inverse of `ExceptT.run`.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def ExceptT.mk {ε : Type u} {m : Type u → Type v} {α : Type u} (x : m (Except ε α)) : ExceptT ε m α := x
 
 /--
@@ -144,7 +144,7 @@ Use a monadic action that may throw an exception as an action that may return an
 
 This is the inverse of `ExceptT.mk`.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def ExceptT.run {ε : Type u} {m : Type u → Type v} {α : Type u} (x : ExceptT ε m α) : m (Except ε α) := x
 
 namespace ExceptT
@@ -154,14 +154,14 @@ variable {ε : Type u} {m : Type u → Type v} [Monad m]
 /--
 Returns the value `a` without throwing exceptions or having any other effect.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 protected def pure {α : Type u} (a : α) : ExceptT ε m α :=
   ExceptT.mk <| pure (Except.ok a)
 
 /--
 Handles exceptions thrown by an action that can have no effects _other_ than throwing exceptions.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 protected def bindCont {α β : Type u} (f : α → ExceptT ε m β) : Except ε α → m (Except ε β)
   | Except.ok a    => f a
   | Except.error e => pure (Except.error e)
@@ -170,14 +170,14 @@ protected def bindCont {α β : Type u} (f : α → ExceptT ε m β) : Except ε
 Sequences two actions that may throw exceptions. Typically used via `do`-notation or the `>>=`
 operator.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 protected def bind {α β : Type u} (ma : ExceptT ε m α) (f : α → ExceptT ε m β) : ExceptT ε m β :=
   ExceptT.mk <| ma >>= ExceptT.bindCont f
 
 /--
 Transforms a successful computation's value using `f`. Typically used via the `<$>` operator.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 protected def map {α β : Type u} (f : α → β) (x : ExceptT ε m α) : ExceptT ε m β :=
   ExceptT.mk <| x >>= fun a => match a with
     | (Except.ok a)    => pure <| Except.ok (f a)
@@ -186,7 +186,7 @@ protected def map {α β : Type u} (f : α → β) (x : ExceptT ε m α) : Excep
 /--
 Runs a computation from an underlying monad in the transformed monad with exceptions.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 protected def lift {α : Type u} (t : m α) : ExceptT ε m α :=
   ExceptT.mk <| Except.ok <$> t
 
@@ -197,7 +197,7 @@ instance : MonadLift m (ExceptT ε m) := ⟨ExceptT.lift⟩
 /--
 Handles exceptions produced in the `ExceptT ε` transformer.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 protected def tryCatch {α : Type u} (ma : ExceptT ε m α) (handle : ε → ExceptT ε m α) : ExceptT ε m α :=
   ExceptT.mk <| ma >>= fun res => match res with
    | Except.ok a    => pure (Except.ok a)

src/Init/Control/ExceptCps.lean

@@ -25,7 +25,7 @@ namespace ExceptCpsT
 /--
 Use a monadic action that may throw an exception as an action that may return an exception's value.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def run {ε α : Type u} [Monad m] (x : ExceptCpsT ε m α) : m (Except ε α) :=
   x _ (fun a => pure (Except.ok a)) (fun e => pure (Except.error e))
 
@@ -43,7 +43,7 @@ Returns the value of a computation, forgetting whether it was an exception or a
 
 This corresponds to early return.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def runCatch [Monad m] (x : ExceptCpsT α m α) : m α :=
   x α pure pure
 
@@ -63,7 +63,7 @@ instance : MonadExceptOf ε (ExceptCpsT ε m) where
 /--
 Run an action from the transformed monad in the exception monad.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def lift [Monad m] (x : m α) : ExceptCpsT ε m α :=
   fun _ k _ => x >>= k
 

src/Init/Control/Lawful.lean

@@ -9,3 +9,4 @@ prelude
 import Init.Control.Lawful.Basic
 import Init.Control.Lawful.Instances
 import Init.Control.Lawful.Lemmas
+import Init.Control.Lawful.MonadLift

src/Init/Control/Lawful/Basic.lean

@@ -50,7 +50,7 @@ attribute [simp] id_map
   (comp_map _ _ _).symm
 
 theorem Functor.map_unit [Functor f] [LawfulFunctor f] {a : f PUnit} : (fun _ => PUnit.unit) <$> a = a := by
-  simp [map]
+  simp
 
 /--
 An applicative functor satisfies the laws of an applicative functor.
@@ -148,7 +148,7 @@ attribute [simp] pure_bind bind_assoc bind_pure_comp
 attribute [grind] pure_bind
 
 @[simp] theorem bind_pure [Monad m] [LawfulMonad m] (x : m α) : x >>= pure = x := by
-  show x >>= (fun a => pure (id a)) = x
+  change x >>= (fun a => pure (id a)) = x
   rw [bind_pure_comp, id_map]
 
 /--

src/Init/Control/Lawful/Instances.lean

@@ -58,7 +58,7 @@ protected theorem bind_pure_comp [Monad m] (f : α → β) (x : ExceptT ε m α)
   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 <$> x <*> y := by
-  show (x >>= fun a => y >>= fun _ => pure a) = (const (α := α) β <$> x) >>= fun f => f <$> y
+  change (x >>= fun a => y >>= fun _ => pure a) = (const (α := α) β <$> x) >>= fun f => f <$> y
   rw [← ExceptT.bind_pure_comp]
   apply ext
   simp [run_bind]
@@ -67,10 +67,10 @@ protected theorem seqLeft_eq {α β ε : Type u} {m : Type u → Type v} [Monad
   | Except.error _ => simp
   | Except.ok _ =>
     simp [←bind_pure_comp]; apply bind_congr; intro b;
-    cases b <;> simp [comp, Except.map, const]
+    cases b <;> simp [Except.map, const]
 
 protected theorem seqRight_eq [Monad m] [LawfulMonad m] (x : ExceptT ε m α) (y : ExceptT ε m β) : x *> y = const α id <$> x <*> y := by
-  show (x >>= fun _ => y) = (const α id <$> x) >>= fun f => f <$> y
+  change (x >>= fun _ => y) = (const α id <$> x) >>= fun f => f <$> y
   rw [← ExceptT.bind_pure_comp]
   apply ext
   simp [run_bind]
@@ -206,15 +206,15 @@ theorem run_bind_lift {α σ : Type u} [Monad m] [LawfulMonad m] (x : m α) (f :
     (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 = _
+  change (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
-  show (x >>= fun _ => y).run s = _
+  change (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
-  show (x >>= fun a => y >>= fun _ => pure a).run s = _
+  change (x >>= fun a => y >>= fun _ => pure a).run s = _
   simp
 
 theorem seqRight_eq [Monad m] [LawfulMonad m] (x : StateT σ m α) (y : StateT σ m β) : x *> y = const α id <$> x <*> y := by

src/Init/Control/Lawful/MonadLift.lean

@@ -0,0 +1,11 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Control.Lawful.MonadLift.Basic
+import Init.Control.Lawful.MonadLift.Lemmas
+import Init.Control.Lawful.MonadLift.Instances

src/Init/Control/Lawful/MonadLift/Basic.lean

@@ -0,0 +1,52 @@
+/-
+Copyright (c) 2025 Quang Dao. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Quang Dao
+-/
+module
+
+prelude
+import Init.Control.Basic
+
+/-!
+# LawfulMonadLift and LawfulMonadLiftT
+
+This module provides classes asserting that `MonadLift` and `MonadLiftT` are lawful, which means
+that `monadLift` is compatible with `pure` and `bind`.
+-/
+
+section MonadLift
+
+/-- The `MonadLift` typeclass only contains the lifting operation. `LawfulMonadLift` further
+  asserts that lifting commutes with `pure` and `bind`:
+```
+monadLift (pure a) = pure a
+monadLift (ma >>= f) = monadLift ma >>= monadLift ∘ f
+```
+-/
+class LawfulMonadLift (m : semiOutParam (Type u → Type v)) (n : Type u → Type w)
+    [Monad m] [Monad n] [inst : MonadLift m n] : Prop where
+  /-- Lifting preserves `pure` -/
+  monadLift_pure {α : Type u} (a : α) : inst.monadLift (pure a) = pure a
+  /-- Lifting preserves `bind` -/
+  monadLift_bind {α β : Type u} (ma : m α) (f : α → m β) :
+    inst.monadLift (ma >>= f) = inst.monadLift ma >>= (fun x => inst.monadLift (f x))
+
+/-- The `MonadLiftT` typeclass only contains the transitive lifting operation.
+  `LawfulMonadLiftT` further asserts that lifting commutes with `pure` and `bind`:
+```
+monadLift (pure a) = pure a
+monadLift (ma >>= f) = monadLift ma >>= monadLift ∘ f
+```
+-/
+class LawfulMonadLiftT (m : Type u → Type v) (n : Type u → Type w) [Monad m] [Monad n]
+    [inst : MonadLiftT m n] : Prop where
+  /-- Lifting preserves `pure` -/
+  monadLift_pure {α : Type u} (a : α) : inst.monadLift (pure a) = pure a
+  /-- Lifting preserves `bind` -/
+  monadLift_bind {α β : Type u} (ma : m α) (f : α → m β) :
+    inst.monadLift (ma >>= f) = monadLift ma >>= (fun x => monadLift (f x))
+
+export LawfulMonadLiftT (monadLift_pure monadLift_bind)
+
+end MonadLift

src/Init/Control/Lawful/MonadLift/Instances.lean

@@ -0,0 +1,137 @@
+/-
+Copyright (c) 2025 Quang Dao. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Quang Dao, Paul Reichert
+-/
+module
+
+prelude
+import all Init.Control.Option
+import all Init.Control.Except
+import all Init.Control.ExceptCps
+import all Init.Control.StateRef
+import all Init.Control.StateCps
+import Init.Control.Lawful.MonadLift.Lemmas
+import Init.Control.Lawful.Instances
+
+universe u v w x
+
+variable {m : Type u → Type v} {n : Type u → Type w} {o : Type u → Type x}
+
+variable (m n o) in
+instance [Monad m] [Monad n] [Monad o] [MonadLift n o] [MonadLiftT m n]
+    [LawfulMonadLift n o] [LawfulMonadLiftT m n] : LawfulMonadLiftT m o where
+  monadLift_pure := fun a => by
+    simp only [monadLift, LawfulMonadLift.monadLift_pure, liftM_pure]
+  monadLift_bind := fun ma f => by
+    simp only [monadLift, LawfulMonadLift.monadLift_bind, liftM_bind]
+
+variable (m) in
+instance [Monad m] : LawfulMonadLiftT m m where
+  monadLift_pure _ := rfl
+  monadLift_bind _ _ := rfl
+
+namespace StateT
+
+variable [Monad m] [LawfulMonad m]
+
+instance {σ : Type u} : LawfulMonadLift m (StateT σ m) where
+  monadLift_pure _ := by ext; simp [MonadLift.monadLift]
+  monadLift_bind _ _ := by ext; simp [MonadLift.monadLift]
+
+end StateT
+
+namespace ReaderT
+
+variable [Monad m]
+
+instance {ρ : Type u} : LawfulMonadLift m (ReaderT ρ m) where
+  monadLift_pure _ := rfl
+  monadLift_bind _ _ := rfl
+
+end ReaderT
+
+namespace OptionT
+
+variable [Monad m] [LawfulMonad m]
+
+@[simp]
+theorem lift_pure {α : Type u} (a : α) : OptionT.lift (pure a : m α) = pure a := by
+  simp only [OptionT.lift, OptionT.mk, bind_pure_comp, map_pure, pure, OptionT.pure]
+
+@[simp]
+theorem lift_bind {α β : Type u} (ma : m α) (f : α → m β) :
+    OptionT.lift (ma >>= f) = OptionT.lift ma >>= (fun a => OptionT.lift (f a)) := by
+  simp only [instMonad, OptionT.bind, OptionT.mk, OptionT.lift, bind_pure_comp, bind_map_left,
+    map_bind]
+
+instance : LawfulMonadLift m (OptionT m) where
+  monadLift_pure := lift_pure
+  monadLift_bind := lift_bind
+
+end OptionT
+
+namespace ExceptT
+
+variable [Monad m] [LawfulMonad m]
+
+@[simp]
+theorem lift_bind {α β ε : Type u} (ma : m α) (f : α → m β) :
+    ExceptT.lift (ε := ε) (ma >>= f) = ExceptT.lift ma >>= (fun a => ExceptT.lift (f a)) := by
+  simp only [instMonad, ExceptT.bind, mk, ExceptT.lift, bind_map_left, ExceptT.bindCont, map_bind]
+
+instance : LawfulMonadLift m (ExceptT ε m) where
+  monadLift_pure := lift_pure
+  monadLift_bind := lift_bind
+
+instance : LawfulMonadLift (Except ε) (ExceptT ε m) where
+  monadLift_pure _ := by
+    simp only [MonadLift.monadLift, mk, pure, Except.pure, ExceptT.pure]
+  monadLift_bind ma _ := by
+    simp only [instMonad, ExceptT.bind, mk, MonadLift.monadLift, pure_bind, ExceptT.bindCont,
+      Except.instMonad, Except.bind]
+    rcases ma with _ | _ <;> simp
+
+end ExceptT
+
+namespace StateRefT'
+
+instance {ω σ : Type} {m : Type → Type} [Monad m] : LawfulMonadLift m (StateRefT' ω σ m) where
+  monadLift_pure _ := by
+    simp only [MonadLift.monadLift, pure]
+    unfold StateRefT'.lift ReaderT.pure
+    simp only
+  monadLift_bind _ _ := by
+    simp only [MonadLift.monadLift, bind]
+    unfold StateRefT'.lift ReaderT.bind
+    simp only
+
+end StateRefT'
+
+namespace StateCpsT
+
+instance {σ : Type u} [Monad m] [LawfulMonad m] : LawfulMonadLift m (StateCpsT σ m) where
+  monadLift_pure _ := by
+    simp only [MonadLift.monadLift, pure]
+    unfold StateCpsT.lift
+    simp only [pure_bind]
+  monadLift_bind _ _ := by
+    simp only [MonadLift.monadLift, bind]
+    unfold StateCpsT.lift
+    simp only [bind_assoc]
+
+end StateCpsT
+
+namespace ExceptCpsT
+
+instance {ε : Type u} [Monad m] [LawfulMonad m] : LawfulMonadLift m (ExceptCpsT ε m) where
+  monadLift_pure _ := by
+    simp only [MonadLift.monadLift, pure]
+    unfold ExceptCpsT.lift
+    simp only [pure_bind]
+  monadLift_bind _ _ := by
+    simp only [MonadLift.monadLift, bind]
+    unfold ExceptCpsT.lift
+    simp only [bind_assoc]
+
+end ExceptCpsT

src/Init/Control/Lawful/MonadLift/Lemmas.lean

@@ -0,0 +1,63 @@
+/-
+Copyright (c) 2025 Quang Dao. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Quang Dao
+-/
+module
+
+prelude
+import Init.Control.Lawful.Basic
+import Init.Control.Lawful.MonadLift.Basic
+
+universe u v w
+
+variable {m : Type u → Type v} {n : Type u → Type w} [Monad m] [Monad n] [MonadLiftT m n]
+  [LawfulMonadLiftT m n] {α β : Type u}
+
+theorem monadLift_map [LawfulMonad m] [LawfulMonad n] (f : α → β) (ma : m α) :
+    monadLift (f <$> ma) = f <$> (monadLift ma : n α) := by
+  rw [← bind_pure_comp, ← bind_pure_comp, monadLift_bind]
+  simp only [bind_pure_comp, monadLift_pure]
+
+theorem monadLift_seq [LawfulMonad m] [LawfulMonad n] (mf : m (α → β)) (ma : m α) :
+    monadLift (mf <*> ma) = monadLift mf <*> (monadLift ma : n α) := by
+  simp only [seq_eq_bind, monadLift_map, monadLift_bind]
+
+theorem monadLift_seqLeft [LawfulMonad m] [LawfulMonad n] (x : m α) (y : m β) :
+    monadLift (x <* y) = (monadLift x : n α) <* (monadLift y : n β) := by
+  simp only [seqLeft_eq, monadLift_map, monadLift_seq]
+
+theorem monadLift_seqRight [LawfulMonad m] [LawfulMonad n] (x : m α) (y : m β) :
+    monadLift (x *> y) = (monadLift x : n α) *> (monadLift y : n β) := by
+  simp only [seqRight_eq, monadLift_map, monadLift_seq]
+
+/-! We duplicate the theorems for `monadLift` to `liftM` since `rw` matches on syntax only. -/
+
+@[simp]
+theorem liftM_pure (a : α) : liftM (pure a : m α) = pure (f := n) a :=
+  monadLift_pure _
+
+@[simp]
+theorem liftM_bind (ma : m α) (f : α → m β) :
+    liftM (n := n) (ma >>= f) = liftM ma >>= (fun a => liftM (f a)) :=
+  monadLift_bind _ _
+
+@[simp]
+theorem liftM_map [LawfulMonad m] [LawfulMonad n] (f : α → β) (ma : m α) :
+    liftM (f <$> ma) = f <$> (liftM ma : n α) :=
+  monadLift_map _ _
+
+@[simp]
+theorem liftM_seq [LawfulMonad m] [LawfulMonad n] (mf : m (α → β)) (ma : m α) :
+    liftM (mf <*> ma) = liftM mf <*> (liftM ma : n α) :=
+  monadLift_seq _ _
+
+@[simp]
+theorem liftM_seqLeft [LawfulMonad m] [LawfulMonad n] (x : m α) (y : m β) :
+    liftM (x <* y) = (liftM x : n α) <* (liftM y : n β) :=
+  monadLift_seqLeft _ _
+
+@[simp]
+theorem liftM_seqRight [LawfulMonad m] [LawfulMonad n] (x : m α) (y : m β) :
+    liftM (x *> y) = (liftM x : n α) *> (liftM y : n β) :=
+  monadLift_seqRight _ _

src/Init/Control/State.lean

@@ -29,7 +29,7 @@ of a value and a state.
 Executes an action from a monad with added state in the underlying monad `m`. Given an initial
 state, it returns a value paired with the final state.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def StateT.run {σ : Type u} {m : Type u → Type v} {α : Type u} (x : StateT σ m α) (s : σ) : m (α × σ) :=
   x s
 
@@ -37,7 +37,7 @@ def StateT.run {σ : Type u} {m : Type u → Type v} {α : Type u} (x : StateT
 Executes an action from a monad with added state in the underlying monad `m`. Given an initial
 state, it returns a value, discarding the final state.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def StateT.run' {σ : Type u} {m : Type u → Type v} [Functor m] {α : Type u} (x : StateT σ m α) (s : σ) : m α :=
   (·.1) <$> x s
 
@@ -66,21 +66,21 @@ variable [Monad m] {α β : Type u}
 /--
 Returns the given value without modifying the state. Typically used via `Pure.pure`.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 protected def pure (a : α) : StateT σ m α :=
   fun s => pure (a, s)
 
 /--
 Sequences two actions. Typically used via the `>>=` operator.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 protected def bind (x : StateT σ m α) (f : α → StateT σ m β) : StateT σ m β :=
   fun s => do let (a, s) ← x s; f a s
 
 /--
 Modifies the value returned by a computation. Typically used via the `<$>` operator.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 protected def map (f : α → β) (x : StateT σ m α) : StateT σ m β :=
   fun s => do let (a, s) ← x s; pure (f a, s)
 
@@ -114,14 +114,14 @@ Retrieves the current value of the monad's mutable state.
 
 This increments the reference count of the state, which may inhibit in-place updates.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 protected def get : StateT σ m σ :=
   fun s => pure (s, s)
 
 /--
 Replaces the mutable state with a new value.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 protected def set : σ → StateT σ m PUnit :=
   fun s' _ => pure (⟨⟩, s')
 
@@ -133,7 +133,7 @@ It is equivalent to `do let (a, s) := f (← StateT.get); StateT.set s; pure a`.
 `StateT.modifyGet` may lead to better performance because it doesn't add a new reference to the
 state value, and additional references can inhibit in-place updates of data.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 protected def modifyGet (f : σ → α × σ) : StateT σ m α :=
   fun s => pure (f s)
 
@@ -143,7 +143,7 @@ Runs an action from the underlying monad in the monad with state. The state is n
 This function is typically implicitly accessed via a `MonadLiftT` instance as part of [automatic
 lifting](lean-manual://section/monad-lifting).
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 protected def lift {α : Type u} (t : m α) : StateT σ m α :=
   fun s => do let a ← t; pure (a, s)
 

src/Init/Control/StateCps.lean

@@ -28,7 +28,7 @@ variable {α σ : Type u} {m : Type u → Type v}
 Runs a stateful computation that's represented using continuation passing style by providing it with
 an initial state and a continuation.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def runK (x : StateCpsT σ m α) (s : σ) (k : α → σ → m β) : m β :=
   x _ s k
 
@@ -39,7 +39,7 @@ state, it returns a value paired with the final state.
 While the state is internally represented in continuation passing style, the resulting value is the
 same as for a non-CPS state monad.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def run [Monad m] (x : StateCpsT σ m α) (s : σ) : m (α × σ) :=
   runK x s (fun a s => pure (a, s))
 
@@ -47,7 +47,7 @@ def run [Monad m] (x : StateCpsT σ m α) (s : σ) : m (α × σ) :=
 Executes an action from a monad with added state in the underlying monad `m`. Given an initial
 state, it returns a value, discarding the final state.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def run' [Monad m] (x : StateCpsT σ m α) (s : σ) : m α :=
   runK x s (fun a _ => pure a)
 
@@ -72,7 +72,7 @@ Runs an action from the underlying monad in the monad with state. The state is n
 This function is typically implicitly accessed via a `MonadLiftT` instance as part of [automatic
 lifting](lean-manual://section/monad-lifting).
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 protected def lift [Monad m] (x : m α) : StateCpsT σ m α :=
   fun _ s k => x >>= (k . s)
 

src/Init/Conv.lean

@@ -9,7 +9,7 @@ module
 
 prelude
 import Init.Tactics
-import Init.Meta
+meta import Init.Meta
 
 namespace Lean.Parser.Tactic.Conv
 

src/Init/Core.lean

@@ -8,7 +8,7 @@ notation, basic datatypes and type classes
 module
 
 prelude
-import Init.Prelude
+meta import Init.Prelude
 import Init.SizeOf
 set_option linter.missingDocs true -- keep it documented
 
@@ -43,14 +43,14 @@ and `flip (·<·)` is the greater-than relation.
 theorem Function.comp_def {α β δ} (f : β → δ) (g : α → β) : f ∘ g = fun x => f (g x) := rfl
 
 @[simp] theorem Function.const_comp {f : α → β} {c : γ} :
-    (Function.const β c ∘ f) = Function.const α c := by
+    (Function.const β c ∘ f) = Function.const α c :=
   rfl
 @[simp] theorem Function.comp_const {f : β → γ} {b : β} :
-    (f ∘ Function.const α b) = Function.const α (f b) := by
+    (f ∘ Function.const α b) = Function.const α (f b) :=
   rfl
-@[simp] theorem Function.true_comp {f : α → β} : ((fun _ => true) ∘ f) = fun _ => true := by
+@[simp] theorem Function.true_comp {f : α → β} : ((fun _ => true) ∘ f) = fun _ => true :=
   rfl
-@[simp] theorem Function.false_comp {f : α → β} : ((fun _ => false) ∘ f) = fun _ => false := by
+@[simp] theorem Function.false_comp {f : α → β} : ((fun _ => false) ∘ f) = fun _ => false :=
   rfl
 
 @[simp] theorem Function.comp_id (f : α → β) : f ∘ id = f := rfl
@@ -95,7 +95,8 @@ structure Thunk (α : Type u) : Type u where
   -/
   mk ::
   /-- Extract the getter function out of a thunk. Use `Thunk.get` instead. -/
-  private fn : Unit → α
+  -- The field is public so as to allow computation through it.
+  fn : Unit → α
 
 attribute [extern "lean_mk_thunk"] Thunk.mk
 
@@ -117,6 +118,10 @@ Computed values are cached, so the value is not recomputed.
 @[extern "lean_thunk_get_own"] protected def Thunk.get (x : @& Thunk α) : α :=
   x.fn ()
 
+-- Ensure `Thunk.fn` is still computable even if it shouldn't be accessed directly.
+@[inline] private def Thunk.fnImpl (x : Thunk α) : Unit → α := fun _ => x.get
+@[csimp] private theorem Thunk.fn_eq_fnImpl : @Thunk.fn = @Thunk.fnImpl := rfl
+
 /--
 Constructs a new thunk that forces `x` and then applies `x` to the result. Upon forcing, the result
 of `f` is cached and the reference to the thunk `x` is dropped.
@@ -897,43 +902,43 @@ section
 variable {α β φ : Sort u} {a a' : α} {b b' : β} {c : φ}
 
 /-- Non-dependent recursor for `HEq` -/
-noncomputable def HEq.ndrec.{u1, u2} {α : Sort u2} {a : α} {motive : {β : Sort u2} → β → Sort u1} (m : motive a) {β : Sort u2} {b : β} (h : HEq a b) : motive b :=
+noncomputable def HEq.ndrec.{u1, u2} {α : Sort u2} {a : α} {motive : {β : Sort u2} → β → Sort u1} (m : motive a) {β : Sort u2} {b : β} (h : a ≍ b) : motive b :=
   h.rec m
 
 /-- `HEq.ndrec` variant -/
-noncomputable def HEq.ndrecOn.{u1, u2} {α : Sort u2} {a : α} {motive : {β : Sort u2} → β → Sort u1} {β : Sort u2} {b : β} (h : HEq a b) (m : motive a) : motive b :=
+noncomputable def HEq.ndrecOn.{u1, u2} {α : Sort u2} {a : α} {motive : {β : Sort u2} → β → Sort u1} {β : Sort u2} {b : β} (h : a ≍ b) (m : motive a) : motive b :=
   h.rec m
 
 /-- `HEq.ndrec` variant -/
-noncomputable def HEq.elim {α : Sort u} {a : α} {p : α → Sort v} {b : α} (h₁ : HEq a b) (h₂ : p a) : p b :=
+noncomputable def HEq.elim {α : Sort u} {a : α} {p : α → Sort v} {b : α} (h₁ : a ≍ b) (h₂ : p a) : p b :=
   eq_of_heq h₁ ▸ h₂
 
 /-- Substitution with heterogeneous equality. -/
-theorem HEq.subst {p : (T : Sort u) → T → Prop} (h₁ : HEq a b) (h₂ : p α a) : p β b :=
+theorem HEq.subst {p : (T : Sort u) → T → Prop} (h₁ : a ≍ b) (h₂ : p α a) : p β b :=
   HEq.ndrecOn h₁ h₂
 
 /-- Heterogeneous equality is symmetric. -/
-@[symm] theorem HEq.symm (h : HEq a b) : HEq b a :=
+@[symm] theorem HEq.symm (h : a ≍ b) : b ≍ a :=
   h.rec (HEq.refl a)
 
 /-- Propositionally equal terms are also heterogeneously equal. -/
-theorem heq_of_eq (h : a = a') : HEq a a' :=
+theorem heq_of_eq (h : a = a') : a ≍ a' :=
   Eq.subst h (HEq.refl a)
 
 /-- Heterogeneous equality is transitive. -/
-theorem HEq.trans (h₁ : HEq a b) (h₂ : HEq b c) : HEq a c :=
+theorem HEq.trans (h₁ : a ≍ b) (h₂ : b ≍ c) : a ≍ c :=
   HEq.subst h₂ h₁
 
 /-- Heterogeneous equality precomposes with propositional equality. -/
-theorem heq_of_heq_of_eq (h₁ : HEq a b) (h₂ : b = b') : HEq a b' :=
+theorem heq_of_heq_of_eq (h₁ : a ≍ b) (h₂ : b = b') : a ≍ b' :=
   HEq.trans h₁ (heq_of_eq h₂)
 
 /-- Heterogeneous equality postcomposes with propositional equality. -/
-theorem heq_of_eq_of_heq (h₁ : a = a') (h₂ : HEq a' b) : HEq a b :=
+theorem heq_of_eq_of_heq (h₁ : a = a') (h₂ : a' ≍ b) : a ≍ b :=
   HEq.trans (heq_of_eq h₁) h₂
 
 /-- If two terms are heterogeneously equal then their types are propositionally equal. -/
-theorem type_eq_of_heq (h : HEq a b) : α = β :=
+theorem type_eq_of_heq (h : a ≍ b) : α = β :=
   h.rec (Eq.refl α)
 
 end
@@ -942,7 +947,7 @@ end
 Rewriting inside `φ` using `Eq.recOn` yields a term that's heterogeneously equal to the original
 term.
 -/
-theorem eqRec_heq {α : Sort u} {φ : α → Sort v} {a a' : α} : (h : a = a') → (p : φ a) → HEq (Eq.recOn (motive := fun x _ => φ x) h p) p
+theorem eqRec_heq {α : Sort u} {φ : α → Sort v} {a a' : α} : (h : a = a') → (p : φ a) → Eq.recOn (motive := fun x _ => φ x) h p ≍ p
   | rfl, p => HEq.refl p
 
 /--
@@ -950,8 +955,8 @@ Heterogeneous equality with an `Eq.rec` application on the left is equivalent to
 equality on the original term.
 -/
 theorem eqRec_heq_iff {α : Sort u} {a : α} {motive : (b : α) → a = b → Sort v}
-    {b : α} {refl : motive a (Eq.refl a)} {h : a = b} {c : motive b h} :
-    HEq (@Eq.rec α a motive refl b h) c ↔ HEq refl c :=
+    {b : α} {refl : motive a (Eq.refl a)} {h : a = b} {c : motive b h}
+    : @Eq.rec α a motive refl b h ≍ c ↔ refl ≍ c :=
   h.rec (fun _ => ⟨id, id⟩) c
 
 /--
@@ -960,7 +965,7 @@ equality on the original term.
 -/
 theorem heq_eqRec_iff {α : Sort u} {a : α} {motive : (b : α) → a = b → Sort v}
     {b : α} {refl : motive a (Eq.refl a)} {h : a = b} {c : motive b h} :
-    HEq c (@Eq.rec α a motive refl b h) ↔ HEq c refl :=
+    c ≍ @Eq.rec α a motive refl b h ↔ c ≍ refl :=
   h.rec (fun _ => ⟨id, id⟩) c
 
 /--
@@ -977,7 +982,7 @@ theorem apply_eqRec {α : Sort u} {a : α} (motive : (b : α) → a = b → Sort
 If casting a term with `Eq.rec` to another type makes it equal to some other term, then the two
 terms are heterogeneously equal.
 -/
-theorem heq_of_eqRec_eq {α β : Sort u} {a : α} {b : β} (h₁ : α = β) (h₂ : Eq.rec (motive := fun α _ => α) a h₁ = b) : HEq a b := by
+theorem heq_of_eqRec_eq {α β : Sort u} {a : α} {b : β} (h₁ : α = β) (h₂ : Eq.rec (motive := fun α _ => α) a h₁ = b) : a ≍ b := by
   subst h₁
   apply heq_of_eq
   exact h₂
@@ -985,7 +990,7 @@ theorem heq_of_eqRec_eq {α β : Sort u} {a : α} {b : β} (h₁ : α = β) (h
 /--
 The result of casting a term with `cast` is heterogeneously equal to the original term.
 -/
-theorem cast_heq {α β : Sort u} : (h : α = β) → (a : α) → HEq (cast h a) a
+theorem cast_heq {α β : Sort u} : (h : α = β) → (a : α) → cast h a ≍ a
   | rfl, a => HEq.refl a
 
 variable {a b c d : Prop}
@@ -1014,8 +1019,8 @@ 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
 
-theorem HEq.comm {a : α} {b : β} : HEq a b ↔ HEq b a := Iff.intro HEq.symm HEq.symm
-theorem heq_comm {a : α} {b : β} : HEq a b ↔ HEq b a := HEq.comm
+theorem HEq.comm {a : α} {b : β} : a ≍ b ↔ b ≍ a := Iff.intro HEq.symm HEq.symm
+theorem heq_comm {a : α} {b : β} : a ≍ b ↔ b ≍ a := HEq.comm
 
 @[symm] 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
@@ -1048,11 +1053,6 @@ theorem Exists.elim {α : Sort u} {p : α → Prop} {b : Prop}
   | isFalse _ => rfl
   | isTrue h  => False.elim h
 
-set_option linter.missingDocs false in
-@[deprecated decide_true (since := "2024-11-05")] abbrev decide_true_eq_true := decide_true
-set_option linter.missingDocs false in
-@[deprecated decide_false (since := "2024-11-05")] abbrev decide_false_eq_false := decide_false
-
 /-- Similar to `decide`, but uses an explicit instance -/
 @[inline] def toBoolUsing {p : Prop} (d : Decidable p) : Bool :=
   decide (h := d)
@@ -1239,7 +1239,7 @@ protected theorem Subsingleton.elim {α : Sort u} [h : Subsingleton α] : (a b :
 If two types are equal and one of them is a subsingleton, then all of their elements are
 [heterogeneously equal](lean-manual://section/HEq).
 -/
-protected theorem Subsingleton.helim {α β : Sort u} [h₁ : Subsingleton α] (h₂ : α = β) (a : α) (b : β) : HEq a b := by
+protected theorem Subsingleton.helim {α β : Sort u} [h₁ : Subsingleton α] (h₂ : α = β) (a : α) (b : β) : a ≍ b := by
   subst h₂
   apply heq_of_eq
   apply Subsingleton.elim
@@ -1690,7 +1690,7 @@ theorem true_iff_false : (True ↔ False) ↔ False := iff_false_intro (·.mp  T
 theorem false_iff_true : (False ↔ True) ↔ False := iff_false_intro (·.mpr True.intro)
 
 theorem iff_not_self : ¬(a ↔ ¬a) | H => let f h := H.1 h h; f (H.2 f)
-theorem heq_self_iff_true (a : α) : HEq a a ↔ True := iff_true_intro HEq.rfl
+theorem heq_self_iff_true (a : α) : a ≍ a ↔ True := iff_true_intro HEq.rfl
 
 /-! ## implies -/
 
@@ -1890,7 +1890,7 @@ a structure.
 protected abbrev hrecOn
     (q : Quot r)
     (f : (a : α) → motive (Quot.mk r a))
-    (c : (a b : α) → (p : r a b) → HEq (f a) (f b))
+    (c : (a b : α) → (p : r a b) → f a ≍ f b)
     : motive q :=
   Quot.recOn q f fun a b p => eq_of_heq (eqRec_heq_iff.mpr (c a b p))
 
@@ -2088,7 +2088,7 @@ a structure.
 protected abbrev hrecOn
     (q : Quotient s)
     (f : (a : α) → motive (Quotient.mk s a))
-    (c : (a b : α) → (p : a ≈ b) → HEq (f a) (f b))
+    (c : (a b : α) → (p : a ≈ b) → f a ≍ f b)
     : motive q :=
   Quot.hrecOn q f c
 end
@@ -2252,7 +2252,7 @@ theorem funext {α : Sort u} {β : α → Sort v} {f g : (x : α) → β x}
     Quot.liftOn f
       (fun (f : ∀ (x : α), β x) => f x)
       (fun _ _ h => h x)
-  show extfunApp (Quot.mk eqv f) = extfunApp (Quot.mk eqv g)
+  change extfunApp (Quot.mk eqv f) = extfunApp (Quot.mk eqv g)
   exact congrArg extfunApp (Quot.sound h)
 
 /--

src/Init/Data.lean

@@ -46,3 +46,4 @@ import Init.Data.NeZero
 import Init.Data.Function
 import Init.Data.RArray
 import Init.Data.Vector
+import Init.Data.Iterators

src/Init/Data/AC.lean

@@ -209,7 +209,7 @@ theorem Context.evalList_sort_congr
   induction c generalizing a b with
   | nil => simp [sort.loop, h₂]
   | cons c _  ih =>
-    simp [sort.loop]; apply ih; simp [evalList_insert ctx h, evalList]
+    simp [sort.loop]; apply ih; simp [evalList_insert ctx h]
     cases a with
     | nil => apply absurd h₃; simp
     | cons a as =>
@@ -282,7 +282,7 @@ theorem Context.toList_nonEmpty (e : Expr) : e.toList ≠ [] := by
     simp [Expr.toList]
     cases h : l.toList with
     | nil => contradiction
-    | cons => simp [List.append]
+    | cons => simp
 
 theorem Context.unwrap_isNeutral
   {ctx : Context α}
@@ -328,13 +328,13 @@ theorem Context.eval_toList (ctx : Context α) (e : Expr) : evalList α ctx e.to
   induction e with
   | var x => rfl
   | op l r ih₁ ih₂ =>
-    simp [evalList, Expr.toList, eval, ←ih₁, ←ih₂]
+    simp [Expr.toList, eval, ←ih₁, ←ih₂]
     apply evalList_append <;> apply toList_nonEmpty
 
 theorem Context.eval_norm (ctx : Context α) (e : Expr) : evalList α ctx (norm ctx e) = eval α ctx e := by
   simp [norm]
   cases h₁ : ContextInformation.isIdem ctx <;> cases h₂ : ContextInformation.isComm ctx <;>
-  simp_all [evalList_removeNeutrals, eval_toList, toList_nonEmpty, evalList_mergeIdem, evalList_sort]
+  simp_all [evalList_removeNeutrals, eval_toList, evalList_mergeIdem, evalList_sort]
 
 theorem Context.eq_of_norm (ctx : Context α) (a b : Expr) (h : norm ctx a == norm ctx b) : eval α ctx a = eval α ctx b := by
   have h := congrArg (evalList α ctx) (eq_of_beq h)

src/Init/Data/Array/Attach.lean

@@ -22,7 +22,7 @@ an array `xs : Array α`, given a proof that every element of `xs` in fact satis
 
 `Array.pmap`, named for “partial map,” is the equivalent of `Array.map` for such partial functions.
 -/
-
+@[expose]
 def pmap {P : α → Prop} (f : ∀ a, P a → β) (xs : Array α) (H : ∀ a ∈ xs, P a) : Array β :=
   (xs.toList.pmap f (fun a m => H a (mem_def.mpr m))).toArray
 
@@ -39,7 +39,7 @@ of elements in the corresponding subtype `{ x // P x }`.
 
 `O(1)`.
 -/
-@[implemented_by attachWithImpl] def attachWith
+@[implemented_by attachWithImpl, expose] def attachWith
     (xs : Array α) (P : α → Prop) (H : ∀ x ∈ xs, P x) : Array {x // P x} :=
   ⟨xs.toList.attachWith P fun x h => H x (Array.Mem.mk h)⟩
 
@@ -54,7 +54,7 @@ recursion](lean-manual://section/well-founded-recursion) that use higher-order f
 `Array.map`) to prove that an value taken from a list is smaller than the list. This allows the
 well-founded recursion mechanism to prove that the function terminates.
 -/
-@[inline] def attach (xs : Array α) : Array {x // x ∈ xs} := xs.attachWith _ fun _ => id
+@[inline, expose] def attach (xs : Array α) : Array {x // x ∈ xs} := xs.attachWith _ fun _ => id
 
 @[simp, grind =] theorem _root_.List.attachWith_toArray {l : List α} {P : α → Prop} {H : ∀ x ∈ l.toArray, P x} :
     l.toArray.attachWith P H = (l.attachWith P (by simpa using H)).toArray := by
@@ -68,15 +68,15 @@ well-founded recursion mechanism to prove that the function terminates.
     l.toArray.pmap f H = (l.pmap f (by simpa using H)).toArray := by
   simp [pmap]
 
-@[simp] theorem toList_attachWith {xs : Array α} {P : α → Prop} {H : ∀ x ∈ xs, P x} :
+@[simp, grind =] theorem toList_attachWith {xs : Array α} {P : α → Prop} {H : ∀ x ∈ xs, P x} :
    (xs.attachWith P H).toList = xs.toList.attachWith P (by simpa [mem_toList_iff] using H) := by
   simp [attachWith]
 
-@[simp] theorem toList_attach {xs : Array α} :
+@[simp, grind =] theorem toList_attach {xs : Array α} :
     xs.attach.toList = xs.toList.attachWith (· ∈ xs) (by simp [mem_toList_iff]) := by
   simp [attach]
 
-@[simp] theorem toList_pmap {xs : Array α} {P : α → Prop} {f : ∀ a, P a → β} {H : ∀ a ∈ xs, P a} :
+@[simp, grind =] theorem toList_pmap {xs : Array α} {P : α → Prop} {f : ∀ a, P a → β} {H : ∀ a ∈ xs, P a} :
     (xs.pmap f H).toList = xs.toList.pmap f (fun a m => H a (mem_def.mpr m)) := by
   simp [pmap]
 
@@ -92,16 +92,16 @@ well-founded recursion mechanism to prove that the function terminates.
   intro a m h₁ h₂
   congr
 
-@[simp] theorem pmap_empty {P : α → Prop} (f : ∀ a, P a → β) : pmap f #[] (by simp) = #[] := rfl
+@[simp, grind =] theorem pmap_empty {P : α → Prop} (f : ∀ a, P a → β) : pmap f #[] (by simp) = #[] := rfl
 
-@[simp] theorem pmap_push {P : α → Prop} (f : ∀ a, P a → β) (a : α) (xs : Array α) (h : ∀ b ∈ xs.push a, P b) :
+@[simp, grind =] theorem pmap_push {P : α → Prop} (f : ∀ a, P a → β) (a : α) (xs : Array α) (h : ∀ b ∈ xs.push a, P b) :
     pmap f (xs.push a) h =
       (pmap f xs (fun a m => by simp at h; exact h a (.inl m))).push (f a (h a (by simp))) := by
   simp [pmap]
 
-@[simp] theorem attach_empty : (#[] : Array α).attach = #[] := rfl
+@[simp, grind =] theorem attach_empty : (#[] : Array α).attach = #[] := rfl
 
-@[simp] theorem attachWith_empty {P : α → Prop} (H : ∀ x ∈ #[], P x) : (#[] : Array α).attachWith P H = #[] := rfl
+@[simp, grind =] theorem attachWith_empty {P : α → Prop} (H : ∀ x ∈ #[], P x) : (#[] : Array α).attachWith P H = #[] := rfl
 
 @[simp] theorem _root_.List.attachWith_mem_toArray {l : List α} :
     l.attachWith (fun x => x ∈ l.toArray) (fun x h => by simpa using h) =
@@ -122,11 +122,13 @@ theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a,
   simp only [List.pmap_toArray, mk.injEq]
   rw [List.pmap_congr_left _ h]
 
+@[grind =]
 theorem map_pmap {p : α → Prop} {g : β → γ} {f : ∀ a, p a → β} {xs : Array α} (H) :
     map g (pmap f xs H) = pmap (fun a h => g (f a h)) xs H := by
   cases xs
   simp [List.map_pmap]
 
+@[grind =]
 theorem pmap_map {p : β → Prop} {g : ∀ b, p b → γ} {f : α → β} {xs : Array α} (H) :
     pmap g (map f xs) H = pmap (fun a h => g (f a) h) xs fun _ h => H _ (mem_map_of_mem h) := by
   cases xs
@@ -142,18 +144,18 @@ theorem attachWith_congr {xs ys : Array α} (w : xs = ys) {P : α → Prop} {H :
   subst w
   simp
 
-@[simp] theorem attach_push {a : α} {xs : Array α} :
+@[simp, grind =] theorem attach_push {a : α} {xs : Array α} :
     (xs.push a).attach =
       (xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_push_of_mem a h⟩)).push ⟨a, by simp⟩ := by
   cases xs
   rw [attach_congr (List.push_toArray _ _)]
   simp [Function.comp_def]
 
-@[simp] theorem attachWith_push {a : α} {xs : Array α} {P : α → Prop} {H : ∀ x ∈ xs.push a, P x} :
+@[simp, grind =] theorem attachWith_push {a : α} {xs : Array α} {P : α → Prop} {H : ∀ x ∈ xs.push a, P x} :
     (xs.push a).attachWith P H =
       (xs.attachWith P (fun x h => by simp at H; exact H x (.inl h))).push ⟨a, H a (by simp)⟩ := by
   cases xs
-  simp [attachWith_congr (List.push_toArray _ _)]
+  simp
 
 theorem pmap_eq_map_attach {p : α → Prop} {f : ∀ a, p a → β} {xs : Array α} (H) :
     pmap f xs H = xs.attach.map fun x => f x.1 (H _ x.2) := by
@@ -189,38 +191,39 @@ theorem attachWith_map_subtype_val {p : α → Prop} {xs : Array α} (H : ∀ a
     (xs.attachWith p H).map Subtype.val = xs := by
   cases xs; simp
 
-@[simp]
+@[simp, grind]
 theorem mem_attach (xs : Array α) : ∀ x, x ∈ xs.attach
   | ⟨a, h⟩ => by
     have := mem_map.1 (by rw [attach_map_subtype_val] <;> exact h)
     rcases this with ⟨⟨_, _⟩, m, rfl⟩
     exact m
 
-@[simp]
+@[simp, grind]
 theorem mem_attachWith {xs : Array α} {q : α → Prop} (H) (x : {x // q x}) :
     x ∈ xs.attachWith q H ↔ x.1 ∈ xs := by
   cases xs
   simp
 
-@[simp]
+@[simp, grind =]
 theorem mem_pmap {p : α → Prop} {f : ∀ a, p a → β} {xs H b} :
     b ∈ pmap f xs H ↔ ∃ (a : _) (h : a ∈ xs), f a (H a h) = b := by
   simp only [pmap_eq_map_attach, mem_map, mem_attach, true_and, Subtype.exists, eq_comm]
 
+@[grind]
 theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {xs H} {a} (h : a ∈ xs) :
     f a (H a h) ∈ pmap f xs H := by
   rw [mem_pmap]
   exact ⟨a, h, rfl⟩
 
-@[simp]
+@[simp, grind =]
 theorem size_pmap {p : α → Prop} {f : ∀ a, p a → β} {xs H} : (pmap f xs H).size = xs.size := by
   cases xs; simp
 
-@[simp]
+@[simp, grind =]
 theorem size_attach {xs : Array α} : xs.attach.size = xs.size := by
   cases xs; simp
 
-@[simp]
+@[simp, grind =]
 theorem size_attachWith {p : α → Prop} {xs : Array α} {H} : (xs.attachWith p H).size = xs.size := by
   cases xs; simp
 
@@ -252,13 +255,13 @@ theorem attachWith_ne_empty_iff {xs : Array α} {P : α → Prop} {H : ∀ a ∈
     xs.attachWith P H ≠ #[] ↔ xs ≠ #[] := by
   cases xs; simp
 
-@[simp]
+@[simp, grind =]
 theorem getElem?_pmap {p : α → Prop} {f : ∀ a, p a → β} {xs : Array α} (h : ∀ a ∈ xs, p a) (i : Nat) :
     (pmap f xs h)[i]? = Option.pmap f xs[i]? fun x H => h x (mem_of_getElem? H) := by
   cases xs; simp
 
 -- The argument `f` is explicit to allow rewriting from right to left.
-@[simp]
+@[simp, grind =]
 theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {xs : Array α} (h : ∀ a ∈ xs, p a) {i : Nat}
     (hi : i < (pmap f xs h).size) :
     (pmap f xs h)[i] =
@@ -266,57 +269,59 @@ theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {xs : Array α} (
         (h _ (getElem_mem (@size_pmap _ _ p f xs h ▸ hi))) := by
   cases xs; simp
 
-@[simp]
+@[simp, grind =]
 theorem getElem?_attachWith {xs : Array α} {i : Nat} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
     (xs.attachWith P H)[i]? = xs[i]?.pmap Subtype.mk (fun _ a => H _ (mem_of_getElem? a)) :=
   getElem?_pmap ..
 
-@[simp]
+@[simp, grind =]
 theorem getElem?_attach {xs : Array α} {i : Nat} :
     xs.attach[i]? = xs[i]?.pmap Subtype.mk (fun _ a => mem_of_getElem? a) :=
   getElem?_attachWith
 
-@[simp]
+@[simp, grind =]
 theorem getElem_attachWith {xs : Array α} {P : α → Prop} {H : ∀ a ∈ xs, P a}
     {i : Nat} (h : i < (xs.attachWith P H).size) :
     (xs.attachWith P H)[i] = ⟨xs[i]'(by simpa using h), H _ (getElem_mem (by simpa using h))⟩ :=
   getElem_pmap _ _ h
 
-@[simp]
+@[simp, grind =]
 theorem getElem_attach {xs : Array α} {i : Nat} (h : i < xs.attach.size) :
     xs.attach[i] = ⟨xs[i]'(by simpa using h), getElem_mem (by simpa using h)⟩ :=
   getElem_attachWith h
 
-@[simp] theorem pmap_attach {xs : Array α} {p : {x // x ∈ xs} → Prop} {f : ∀ a, p a → β} (H) :
+@[simp, grind =] theorem pmap_attach {xs : Array α} {p : {x // x ∈ xs} → Prop} {f : ∀ a, p a → β} (H) :
     pmap f xs.attach H =
       xs.pmap (P := fun a => ∃ h : a ∈ xs, p ⟨a, h⟩)
         (fun a h => f ⟨a, h.1⟩ h.2) (fun a h => ⟨h, H ⟨a, h⟩ (by simp)⟩) := by
   ext <;> simp
 
-@[simp] theorem pmap_attachWith {xs : Array α} {p : {x // q x} → Prop} {f : ∀ a, p a → β} (H₁ H₂) :
+@[simp, grind =] theorem pmap_attachWith {xs : Array α} {p : {x // q x} → Prop} {f : ∀ a, p a → β} (H₁ H₂) :
     pmap f (xs.attachWith q H₁) H₂ =
       xs.pmap (P := fun a => ∃ h : q a, p ⟨a, h⟩)
         (fun a h => f ⟨a, h.1⟩ h.2) (fun a h => ⟨H₁ _ h, H₂ ⟨a, H₁ _ h⟩ (by simpa)⟩) := by
   ext <;> simp
 
+@[grind =]
 theorem foldl_pmap {xs : Array α} {P : α → Prop} {f : (a : α) → P a → β}
     (H : ∀ (a : α), a ∈ xs → P a) (g : γ → β → γ) (x : γ) :
     (xs.pmap f H).foldl g x = xs.attach.foldl (fun acc a => g acc (f a.1 (H _ a.2))) x := by
   rw [pmap_eq_map_attach, foldl_map]
 
+@[grind =]
 theorem foldr_pmap {xs : Array α} {P : α → Prop} {f : (a : α) → P a → β}
     (H : ∀ (a : α), a ∈ xs → P a) (g : β → γ → γ) (x : γ) :
     (xs.pmap f H).foldr g x = xs.attach.foldr (fun a acc => g (f a.1 (H _ a.2)) acc) x := by
   rw [pmap_eq_map_attach, foldr_map]
 
-@[simp] theorem foldl_attachWith
+@[simp, grind =] theorem foldl_attachWith
     {xs : Array α} {q : α → Prop} (H : ∀ a, a ∈ xs → q a) {f : β → { x // q x} → β} {b} (w : stop = xs.size) :
     (xs.attachWith q H).foldl f b 0 stop = xs.attach.foldl (fun b ⟨a, h⟩ => f b ⟨a, H _ h⟩) b := by
   subst w
   rcases xs with ⟨xs⟩
   simp [List.foldl_attachWith, List.foldl_map]
 
-@[simp] theorem foldr_attachWith
+@[simp, grind =] theorem foldr_attachWith
     {xs : Array α} {q : α → Prop} (H : ∀ a, a ∈ xs → q a) {f : { x // q x} → β → β} {b} (w : start = xs.size) :
     (xs.attachWith q H).foldr f b start 0 = xs.attach.foldr (fun a acc => f ⟨a.1, H _ a.2⟩ acc) b := by
   subst w
@@ -337,7 +342,7 @@ theorem foldl_attach {xs : Array α} {f : β → α → β} {b : β} :
     xs.attach.foldl (fun acc t => f acc t.1) b = xs.foldl f b := by
   rcases xs with ⟨xs⟩
   simp only [List.attach_toArray, List.attachWith_mem_toArray, List.size_toArray,
-    List.length_pmap, List.foldl_toArray', mem_toArray, List.foldl_subtype]
+    List.foldl_toArray', mem_toArray, List.foldl_subtype]
   congr
   ext
   simpa using fun a => List.mem_of_getElem? a
@@ -356,23 +361,25 @@ theorem foldr_attach {xs : Array α} {f : α → β → β} {b : β} :
     xs.attach.foldr (fun t acc => f t.1 acc) b = xs.foldr f b := by
   rcases xs with ⟨xs⟩
   simp only [List.attach_toArray, List.attachWith_mem_toArray, List.size_toArray,
-    List.length_pmap, List.foldr_toArray', mem_toArray, List.foldr_subtype]
+    List.foldr_toArray', mem_toArray, List.foldr_subtype]
   congr
   ext
   simpa using fun a => List.mem_of_getElem? a
 
+@[grind =]
 theorem attach_map {xs : Array α} {f : α → β} :
     (xs.map f).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨f x, mem_map_of_mem h⟩) := by
   cases xs
   ext <;> simp
 
+@[grind =]
 theorem attachWith_map {xs : Array α} {f : α → β} {P : β → Prop} (H : ∀ (b : β), b ∈ xs.map f → P b) :
     (xs.map f).attachWith P H = (xs.attachWith (P ∘ f) (fun _ h => H _ (mem_map_of_mem h))).map
       fun ⟨x, h⟩ => ⟨f x, h⟩ := by
   cases xs
   simp [List.attachWith_map]
 
-@[simp] theorem map_attachWith {xs : Array α} {P : α → Prop} {H : ∀ (a : α), a ∈ xs → P a}
+@[simp, grind =] theorem map_attachWith {xs : Array α} {P : α → Prop} {H : ∀ (a : α), a ∈ xs → P a}
     {f : { x // P x } → β} :
     (xs.attachWith P H).map f = xs.attach.map fun ⟨x, h⟩ => f ⟨x, H _ h⟩ := by
   cases xs <;> simp_all
@@ -393,6 +400,7 @@ theorem map_attach_eq_pmap {xs : Array α} {f : { x // x ∈ xs } → β} :
 @[deprecated map_attach_eq_pmap (since := "2025-02-09")]
 abbrev map_attach := @map_attach_eq_pmap
 
+@[grind =]
 theorem attach_filterMap {xs : Array α} {f : α → Option β} :
     (xs.filterMap f).attach = xs.attach.filterMap
       fun ⟨x, h⟩ => (f x).pbind (fun b m => some ⟨b, mem_filterMap.mpr ⟨x, h, m⟩⟩) := by
@@ -400,6 +408,7 @@ theorem attach_filterMap {xs : Array α} {f : α → Option β} :
   rw [attach_congr List.filterMap_toArray]
   simp [List.attach_filterMap, List.map_filterMap, Function.comp_def]
 
+@[grind =]
 theorem attach_filter {xs : Array α} (p : α → Bool) :
     (xs.filter p).attach = xs.attach.filterMap
       fun x => if w : p x.1 then some ⟨x.1, mem_filter.mpr ⟨x.2, w⟩⟩ else none := by
@@ -409,7 +418,7 @@ theorem attach_filter {xs : Array α} (p : α → Bool) :
 
 -- We are still missing here `attachWith_filterMap` and `attachWith_filter`.
 
-@[simp]
+@[simp, grind =]
 theorem filterMap_attachWith {q : α → Prop} {xs : Array α} {f : {x // q x} → Option β} (H)
     (w : stop = (xs.attachWith q H).size) :
     (xs.attachWith q H).filterMap f 0 stop = xs.attach.filterMap (fun ⟨x, h⟩ => f ⟨x, H _ h⟩) := by
@@ -417,7 +426,7 @@ theorem filterMap_attachWith {q : α → Prop} {xs : Array α} {f : {x // q x}
   cases xs
   simp [Function.comp_def]
 
-@[simp]
+@[simp, grind =]
 theorem filter_attachWith {q : α → Prop} {xs : Array α} {p : {x // q x} → Bool} (H)
     (w : stop = (xs.attachWith q H).size) :
     (xs.attachWith q H).filter p 0 stop =
@@ -426,6 +435,7 @@ theorem filter_attachWith {q : α → Prop} {xs : Array α} {p : {x // q x} →
   cases xs
   simp [Function.comp_def, List.filter_map]
 
+@[grind =]
 theorem pmap_pmap {p : α → Prop} {q : β → Prop} {g : ∀ a, p a → β} {f : ∀ b, q b → γ} {xs} (H₁ H₂) :
     pmap f (pmap g xs H₁) H₂ =
       pmap (α := { x // x ∈ xs }) (fun a h => f (g a h) (H₂ (g a h) (mem_pmap_of_mem a.2))) xs.attach
@@ -433,7 +443,7 @@ theorem pmap_pmap {p : α → Prop} {q : β → Prop} {g : ∀ a, p a → β} {f
   cases xs
   simp [List.pmap_pmap, List.pmap_map]
 
-@[simp] theorem pmap_append {p : ι → Prop} {f : ∀ a : ι, p a → α} {xs ys : Array ι}
+@[simp, grind =] theorem pmap_append {p : ι → Prop} {f : ∀ a : ι, p a → α} {xs ys : Array ι}
     (h : ∀ a ∈ xs ++ ys, p a) :
     (xs ++ ys).pmap f h =
       (xs.pmap f fun a ha => h a (mem_append_left ys ha)) ++
@@ -448,7 +458,7 @@ theorem pmap_append' {p : α → Prop} {f : ∀ a : α, p a → β} {xs ys : Arr
       xs.pmap f h₁ ++ ys.pmap f h₂ :=
   pmap_append _
 
-@[simp] theorem attach_append {xs ys : Array α} :
+@[simp, grind =] theorem attach_append {xs ys : Array α} :
     (xs ++ ys).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_append_left ys h⟩) ++
       ys.attach.map fun ⟨x, h⟩ => ⟨x, mem_append_right xs h⟩ := by
   cases xs
@@ -456,59 +466,62 @@ theorem pmap_append' {p : α → Prop} {f : ∀ a : α, p a → β} {xs ys : Arr
   rw [attach_congr (List.append_toArray _ _)]
   simp [List.attach_append, Function.comp_def]
 
-@[simp] theorem attachWith_append {P : α → Prop} {xs ys : Array α}
+@[simp, grind =] theorem attachWith_append {P : α → Prop} {xs ys : Array α}
     {H : ∀ (a : α), a ∈ xs ++ ys → P a} :
     (xs ++ ys).attachWith P H = xs.attachWith P (fun a h => H a (mem_append_left ys h)) ++
       ys.attachWith P (fun a h => H a (mem_append_right xs h)) := by
-  simp [attachWith, attach_append, map_pmap, pmap_append]
+  simp [attachWith]
 
-@[simp] theorem pmap_reverse {P : α → Prop} {f : (a : α) → P a → β} {xs : Array α}
+@[simp, grind =] theorem pmap_reverse {P : α → Prop} {f : (a : α) → P a → β} {xs : Array α}
     (H : ∀ (a : α), a ∈ xs.reverse → P a) :
     xs.reverse.pmap f H = (xs.pmap f (fun a h => H a (by simpa using h))).reverse := by
   induction xs <;> simp_all
 
+@[grind =]
 theorem reverse_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : Array α}
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.pmap f H).reverse = xs.reverse.pmap f (fun a h => H a (by simpa using h)) := by
   rw [pmap_reverse]
 
-@[simp] theorem attachWith_reverse {P : α → Prop} {xs : Array α}
+@[simp, grind =] theorem attachWith_reverse {P : α → Prop} {xs : Array α}
     {H : ∀ (a : α), a ∈ xs.reverse → P a} :
     xs.reverse.attachWith P H =
       (xs.attachWith P (fun a h => H a (by simpa using h))).reverse := by
   cases xs
   simp
 
+@[grind =]
 theorem reverse_attachWith {P : α → Prop} {xs : Array α}
     {H : ∀ (a : α), a ∈ xs → P a} :
     (xs.attachWith P H).reverse = (xs.reverse.attachWith P (fun a h => H a (by simpa using h))) := by
   cases xs
   simp
 
-@[simp] theorem attach_reverse {xs : Array α} :
+@[simp, grind =] theorem attach_reverse {xs : Array α} :
     xs.reverse.attach = xs.attach.reverse.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
   cases xs
   rw [attach_congr List.reverse_toArray]
   simp
 
+@[grind =]
 theorem reverse_attach {xs : Array α} :
     xs.attach.reverse = xs.reverse.attach.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
   cases xs
   simp
 
-@[simp] theorem back?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : Array α}
+@[simp, grind =] theorem back?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : Array α}
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.pmap f H).back? = xs.attach.back?.map fun ⟨a, m⟩ => f a (H a m) := by
   cases xs
   simp
 
-@[simp] theorem back?_attachWith {P : α → Prop} {xs : Array α}
+@[simp, grind =] theorem back?_attachWith {P : α → Prop} {xs : Array α}
     {H : ∀ (a : α), a ∈ xs → P a} :
     (xs.attachWith P H).back? = xs.back?.pbind (fun a h => some ⟨a, H _ (mem_of_back? h)⟩) := by
   cases xs
   simp
 
-@[simp]
+@[simp, grind =]
 theorem back?_attach {xs : Array α} :
     xs.attach.back? = xs.back?.pbind fun a h => some ⟨a, mem_of_back? h⟩ := by
   cases xs
@@ -526,7 +539,7 @@ theorem countP_attachWith {p : α → Prop} {q : α → Bool} {xs : Array α} {H
   cases xs
   simp
 
-@[simp]
+@[simp, grind =]
 theorem count_attach [BEq α] {xs : Array α} {a : {x // x ∈ xs}} :
     xs.attach.count a = xs.count ↑a := by
   rcases xs with ⟨xs⟩
@@ -535,13 +548,13 @@ theorem count_attach [BEq α] {xs : Array α} {a : {x // x ∈ xs}} :
   simp only [Subtype.beq_iff]
   rw [List.countP_pmap, List.countP_attach (p := (fun x => x == a.1)), List.count]
 
-@[simp]
+@[simp, grind =]
 theorem count_attachWith [BEq α] {p : α → Prop} {xs : Array α} (H : ∀ a ∈ xs, p a) {a : {x // p x}} :
     (xs.attachWith p H).count a = xs.count ↑a := by
   cases xs
   simp
 
-@[simp] theorem countP_pmap {p : α → Prop} {g : ∀ a, p a → β} {f : β → Bool} {xs : Array α} (H₁) :
+@[simp, grind =] theorem countP_pmap {p : α → Prop} {g : ∀ a, p a → β} {f : β → Bool} {xs : Array α} (H₁) :
     (xs.pmap g H₁).countP f =
       xs.attach.countP (fun ⟨a, m⟩ => f (g a (H₁ a m))) := by
   simp [pmap_eq_map_attach, countP_map, Function.comp_def]
@@ -690,7 +703,7 @@ and simplifies these to the function directly taking the value.
     {f : { x // p x } → Array β} {g : α → Array β} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
     (xs.flatMap f) = xs.unattach.flatMap g := by
   cases xs
-  simp only [List.size_toArray, List.flatMap_toArray, List.unattach_toArray, List.length_unattach,
+  simp only [List.flatMap_toArray, List.unattach_toArray, 
     mk.injEq]
   rw [List.flatMap_subtype]
   simp [hf]

src/Init/Data/Array/Basic.lean

@@ -91,7 +91,8 @@ theorem ext' {xs ys : Array α} (h : xs.toList = ys.toList) : xs = ys := by
 @[simp, grind =] theorem getElem_toList {xs : Array α} {i : Nat} (h : i < xs.size) : xs.toList[i] = xs[i] := rfl
 
 @[simp, grind =] theorem getElem?_toList {xs : Array α} {i : Nat} : xs.toList[i]? = xs[i]? := by
-  simp [getElem?_def]
+  simp only [getElem?_def, getElem_toList]
+  simp only [Array.size]
 
 /-- `a ∈ as` is a predicate which asserts that `a` is in the array `as`. -/
 -- NB: This is defined as a structure rather than a plain def so that a lemma
@@ -167,7 +168,7 @@ Low-level indexing operator which is as fast as a C array read.
 
 This avoids overhead due to unboxing a `Nat` used as an index.
 -/
-@[extern "lean_array_uget", simp]
+@[extern "lean_array_uget", simp, expose]
 def uget (a : @& Array α) (i : USize) (h : i.toNat < a.size) : α :=
   a[i.toNat]
 
@@ -190,7 +191,7 @@ Examples:
 * `#["orange", "yellow"].pop = #["orange"]`
 * `(#[] : Array String).pop = #[]`
 -/
-@[extern "lean_array_pop"]
+@[extern "lean_array_pop", expose]
 def pop (xs : Array α) : Array α where
   toList := xs.toList.dropLast
 
@@ -209,7 +210,7 @@ Examples:
  * `Array.replicate 3 () = #[(), (), ()]`
  * `Array.replicate 0 "anything" = #[]`
 -/
-@[extern "lean_mk_array"]
+@[extern "lean_mk_array", expose]
 def replicate {α : Type u} (n : Nat) (v : α) : Array α where
   toList := List.replicate n v
 
@@ -237,7 +238,7 @@ Examples:
 * `#["red", "green", "blue", "brown"].swap 1 2 = #["red", "blue", "green", "brown"]`
 * `#["red", "green", "blue", "brown"].swap 3 0 = #["brown", "green", "blue", "red"]`
 -/
-@[extern "lean_array_fswap"]
+@[extern "lean_array_fswap", expose]
 def swap (xs : Array α) (i j : @& Nat) (hi : i < xs.size := by get_elem_tactic) (hj : j < xs.size := by get_elem_tactic) : Array α :=
   let v₁ := xs[i]
   let v₂ := xs[j]
@@ -245,7 +246,7 @@ def swap (xs : Array α) (i j : @& Nat) (hi : i < xs.size := by get_elem_tactic)
   xs'.set j v₁ (Nat.lt_of_lt_of_eq hj (size_set _).symm)
 
 @[simp] theorem size_swap {xs : Array α} {i j : Nat} {hi hj} : (xs.swap i j hi hj).size = xs.size := by
-  show ((xs.set i xs[j]).set j xs[i]
+  change ((xs.set i xs[j]).set j xs[i]
     (Nat.lt_of_lt_of_eq hj (size_set _).symm)).size = xs.size
   rw [size_set, size_set]
 
@@ -267,8 +268,6 @@ def swapIfInBounds (xs : Array α) (i j : @& Nat) : Array α :=
   else xs
   else xs
 
-@[deprecated swapIfInBounds (since := "2024-11-24")] abbrev swap! := @swapIfInBounds
-
 /-! ### GetElem instance for `USize`, backed by `uget` -/
 
 instance : GetElem (Array α) USize α fun xs i => i.toNat < xs.size where
@@ -290,6 +289,7 @@ Examples:
  * `#[1, 2].isEmpty = false`
  * `#[()].isEmpty = false`
 -/
+@[expose]
 def isEmpty (xs : Array α) : Bool :=
   xs.size = 0
 
@@ -331,12 +331,14 @@ Examples:
  * `Array.ofFn (n := 3) toString = #["0", "1", "2"]`
  * `Array.ofFn (fun i => #["red", "green", "blue"].get i.val i.isLt) = #["red", "green", "blue"]`
 -/
-def ofFn {n} (f : Fin n → α) : Array α := go 0 (emptyWithCapacity n) where
-  /-- Auxiliary for `ofFn`. `ofFn.go f i acc = acc ++ #[f i, ..., f(n - 1)]` -/
-  @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
-  go (i : Nat) (acc : Array α) : Array α :=
-    if h : i < n then go (i+1) (acc.push (f ⟨i, h⟩)) else acc
-  decreasing_by simp_wf; decreasing_trivial_pre_omega
+def ofFn {n} (f : Fin n → α) : Array α := go (emptyWithCapacity n) n (Nat.le_refl n) where
+  /-- Auxiliary for `ofFn`. `ofFn.go f acc i h = acc ++ #[f (n - i), ..., f(n - 1)]` -/
+  go (acc : Array α) : (i : Nat) → i ≤ n → Array α
+  | i + 1, h =>
+     have w : n - i - 1 < n :=
+       Nat.lt_of_lt_of_le (Nat.sub_one_lt (Nat.sub_ne_zero_iff_lt.mpr h)) (Nat.sub_le n i)
+     go (acc.push (f ⟨n - i - 1, w⟩)) i (Nat.le_of_succ_le h)
+  | 0, _ => acc
 
 -- See also `Array.ofFnM` defined in `Init.Data.Array.OfFn`.
 
@@ -373,7 +375,7 @@ Examples:
  * `Array.singleton 5 = #[5]`
  * `Array.singleton "one" = #["one"]`
 -/
-@[inline] protected def singleton (v : α) : Array α := #[v]
+@[inline, expose] protected def singleton (v : α) : Array α := #[v]
 
 /--
 Returns the last element of an array, or panics if the array is empty.
@@ -402,7 +404,7 @@ that requires a proof the array is non-empty.
 def back? (xs : Array α) : Option α :=
   xs[xs.size - 1]?
 
-@[deprecated "Use `a[i]?` instead." (since := "2025-02-12")]
+@[deprecated "Use `a[i]?` instead." (since := "2025-02-12"), expose]
 def get? (xs : Array α) (i : Nat) : Option α :=
   if h : i < xs.size then some xs[i] else none
 
@@ -416,7 +418,7 @@ Examples:
 * `#["spinach", "broccoli", "carrot"].swapAt 1 "pepper" = ("broccoli", #["spinach", "pepper", "carrot"])`
 * `#["spinach", "broccoli", "carrot"].swapAt 2 "pepper" = ("carrot", #["spinach", "broccoli", "pepper"])`
 -/
-@[inline] def swapAt (xs : Array α) (i : Nat) (v : α) (hi : i < xs.size := by get_elem_tactic) : α × Array α :=
+@[inline, expose] def swapAt (xs : Array α) (i : Nat) (v : α) (hi : i < xs.size := by get_elem_tactic) : α × Array α :=
   let e := xs[i]
   let xs' := xs.set i v
   (e, xs')
@@ -431,7 +433,7 @@ Examples:
 * `#["spinach", "broccoli", "carrot"].swapAt! 1 "pepper" = (#["spinach", "pepper", "carrot"], "broccoli")`
 * `#["spinach", "broccoli", "carrot"].swapAt! 2 "pepper" = (#["spinach", "broccoli", "pepper"], "carrot")`
 -/
-@[inline]
+@[inline, expose]
 def swapAt! (xs : Array α) (i : Nat) (v : α) : α × Array α :=
   if h : i < xs.size then
     swapAt xs i v
@@ -577,7 +579,7 @@ def modifyOp (xs : Array α) (idx : Nat) (f : α → α) : Array α :=
   loop 0 b
 
 /-- Reference implementation for `forIn'` -/
-@[implemented_by Array.forIn'Unsafe]
+@[implemented_by Array.forIn'Unsafe, expose]
 protected def forIn' {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (b : β) (f : (a : α) → a ∈ as → β → m (ForInStep β)) : m β :=
   let rec loop (i : Nat) (h : i ≤ as.size) (b : β) : m β := do
     match i, h with
@@ -644,7 +646,7 @@ example [Monad m] (f : α → β → m α) :
 ```
 -/
 -- Reference implementation for `foldlM`
-@[implemented_by foldlMUnsafe]
+@[implemented_by foldlMUnsafe, expose]
 def foldlM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : β → α → m β) (init : β) (as : Array α) (start := 0) (stop := as.size) : m β :=
   let fold (stop : Nat) (h : stop ≤ as.size) :=
     let rec loop (i : Nat) (j : Nat) (b : β) : m β := do
@@ -709,7 +711,7 @@ example [Monad m] (f : α → β → m β) :
 ```
 -/
 -- Reference implementation for `foldrM`
-@[implemented_by foldrMUnsafe]
+@[implemented_by foldrMUnsafe, expose]
 def foldrM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → β → m β) (init : β) (as : Array α) (start := as.size) (stop := 0) : m β :=
   let rec fold (i : Nat) (h : i ≤ as.size) (b : β) : m β := do
     if i == stop then
@@ -764,13 +766,11 @@ def mapM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α
   decreasing_by simp_wf; decreasing_trivial_pre_omega
   map 0 (emptyWithCapacity as.size)
 
-@[deprecated mapM (since := "2024-11-11")] abbrev sequenceMap := @mapM
-
 /--
 Applies the monadic action `f` to every element in the array, along with the element's index and a
 proof that the index is in bounds, from left to right. Returns the array of results.
 -/
-@[inline]
+@[inline, expose]
 def mapFinIdxM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m]
     (as : Array α) (f : (i : Nat) → α → (h : i < as.size) → m β) : m (Array β) :=
   let rec @[specialize] map (i : Nat) (j : Nat) (inv : i + j = as.size) (bs : Array β) : m (Array β) := do
@@ -788,7 +788,7 @@ def mapFinIdxM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m]
 Applies the monadic action `f` to every element in the array, along with the element's index, from
 left to right. Returns the array of results.
 -/
-@[inline]
+@[inline, expose]
 def mapIdxM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : Nat → α → m β) (as : Array α) : m (Array β) :=
   as.mapFinIdxM fun i a _ => f i a
 
@@ -834,7 +834,7 @@ Almost! 5
 some 10
 ```
 -/
-@[inline]
+@[inline, expose]
 def findSomeM? {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m (Option β)) (as : Array α) : m (Option β) := do
   for a in as do
     match (← f a) with
@@ -915,7 +915,7 @@ The optional parameters `start` and `stop` control the region of the array to be
 elements with indices from `start` (inclusive) to `stop` (exclusive) are checked. By default, the
 entire array is checked.
 -/
-@[implemented_by anyMUnsafe]
+@[implemented_by anyMUnsafe, expose]
 def anyM {α : Type u} {m : Type → Type w} [Monad m] (p : α → m Bool) (as : Array α) (start := 0) (stop := as.size) : m Bool :=
   let any (stop : Nat) (h : stop ≤ as.size) :=
     let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
@@ -1057,7 +1057,7 @@ Examples:
  * `#[1, 2, 3].foldl (· ++ toString ·) "" = "123"`
  * `#[1, 2, 3].foldl (s!"({·} {·})") "" = "((( 1) 2) 3)"`
 -/
-@[inline]
+@[inline, expose]
 def foldl {α : Type u} {β : Type v} (f : β → α → β) (init : β) (as : Array α) (start := 0) (stop := as.size) : β :=
   Id.run <| as.foldlM (pure <| f · ·) init start stop
 
@@ -1074,7 +1074,7 @@ Examples:
  * `#[1, 2, 3].foldr (toString · ++ ·) "" = "123"`
  * `#[1, 2, 3].foldr (s!"({·} {·})") "!" = "(1 (2 (3 !)))"`
 -/
-@[inline]
+@[inline, expose]
 def foldr {α : Type u} {β : Type v} (f : α → β → β) (init : β) (as : Array α) (start := as.size) (stop := 0) : β :=
   Id.run <| as.foldrM (pure <| f · ·) init start stop
 
@@ -1085,7 +1085,7 @@ Examples:
  * `#[a, b, c].sum = a + (b + (c + 0))`
  * `#[1, 2, 5].sum = 8`
 -/
-@[inline]
+@[inline, expose]
 def sum {α} [Add α] [Zero α] : Array α → α :=
   foldr (· + ·) 0
 
@@ -1097,7 +1097,7 @@ Examples:
  * `#[1, 2, 3, 4, 5].countP (· < 5) = 4`
  * `#[1, 2, 3, 4, 5].countP (· > 5) = 0`
 -/
-@[inline]
+@[inline, expose]
 def countP {α : Type u} (p : α → Bool) (as : Array α) : Nat :=
   as.foldr (init := 0) fun a acc => bif p a then acc + 1 else acc
 
@@ -1109,7 +1109,7 @@ Examples:
  * `#[1, 1, 2, 3, 5].count 5 = 1`
  * `#[1, 1, 2, 3, 5].count 4 = 0`
 -/
-@[inline]
+@[inline, expose]
 def count {α : Type u} [BEq α] (a : α) (as : Array α) : Nat :=
   countP (· == a) as
 
@@ -1122,7 +1122,7 @@ Examples:
 * `#["one", "two", "three"].map (·.length) = #[3, 3, 5]`
 * `#["one", "two", "three"].map (·.reverse) = #["eno", "owt", "eerht"]`
 -/
-@[inline]
+@[inline, expose]
 def map {α : Type u} {β : Type v} (f : α → β) (as : Array α) : Array β :=
   Id.run <| as.mapM (pure <| f ·)
 
@@ -1137,7 +1137,7 @@ that the index is valid.
 `Array.mapIdx` is a variant that does not provide the function with evidence that the index is
 valid.
 -/
-@[inline]
+@[inline, expose]
 def mapFinIdx {α : Type u} {β : Type v} (as : Array α) (f : (i : Nat) → α → (h : i < as.size) → β) : Array β :=
   Id.run <| as.mapFinIdxM (pure <| f · · ·)
 
@@ -1148,7 +1148,7 @@ returning the array of results.
 `Array.mapFinIdx` is a variant that additionally provides the function with a proof that the index
 is valid.
 -/
-@[inline]
+@[inline, expose]
 def mapIdx {α : Type u} {β : Type v} (f : Nat → α → β) (as : Array α) : Array β :=
   Id.run <| as.mapIdxM (pure <| f · ·)
 
@@ -1159,6 +1159,7 @@ Examples:
 * `#[a, b, c].zipIdx = #[(a, 0), (b, 1), (c, 2)]`
 * `#[a, b, c].zipIdx 5 = #[(a, 5), (b, 6), (c, 7)]`
 -/
+@[expose]
 def zipIdx (xs : Array α) (start := 0) : Array (α × Nat) :=
   xs.mapIdx fun i a => (a, start + i)
 
@@ -1172,7 +1173,7 @@ Examples:
 * `#[7, 6, 5, 8, 1, 2, 6].find? (· < 5) = some 1`
 * `#[7, 6, 5, 8, 1, 2, 6].find? (· < 1) = none`
 -/
-@[inline]
+@[inline, expose]
 def find? {α : Type u} (p : α → Bool) (as : Array α) : Option α :=
   Id.run do
     for a in as do
@@ -1196,7 +1197,7 @@ Example:
 some 10
 ```
 -/
-@[inline]
+@[inline, expose]
 def findSome? {α : Type u} {β : Type v} (f : α → Option β) (as : Array α) : Option β :=
   Id.run <| as.findSomeM? (pure <| f ·)
 
@@ -1254,7 +1255,7 @@ Examples:
 * `#[7, 6, 5, 8, 1, 2, 6].findIdx (· < 5) = some 4`
 * `#[7, 6, 5, 8, 1, 2, 6].findIdx (· < 1) = none`
 -/
-@[inline]
+@[inline, expose]
 def findIdx? {α : Type u} (p : α → Bool) (as : Array α) : Option Nat :=
   let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
   loop (j : Nat) :=
@@ -1308,7 +1309,7 @@ Examples:
 * `#[7, 6, 5, 8, 1, 2, 6].findIdx (· < 5) = 4`
 * `#[7, 6, 5, 8, 1, 2, 6].findIdx (· < 1) = 7`
 -/
-@[inline]
+@[inline, expose]
 def findIdx (p : α → Bool) (as : Array α) : Nat := (as.findIdx? p).getD as.size
 
 @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
@@ -1362,10 +1363,6 @@ Examples:
 def idxOf? [BEq α] (xs : Array α) (v : α) : Option Nat :=
   (xs.finIdxOf? v).map (·.val)
 
-@[deprecated idxOf? (since := "2024-11-20")]
-def getIdx? [BEq α] (xs : Array α) (v : α) : Option Nat :=
-  xs.findIdx? fun a => a == v
-
 /--
 Returns `true` if `p` returns `true` for any element of `as`.
 
@@ -1381,7 +1378,7 @@ Examples:
 * `#[2, 4, 5, 6].any (· % 2 = 0) = true`
 * `#[2, 4, 5, 6].any (· % 2 = 1) = true`
 -/
-@[inline]
+@[inline, expose]
 def any (as : Array α) (p : α → Bool) (start := 0) (stop := as.size) : Bool :=
   Id.run <| as.anyM (pure <| p ·) start stop
 
@@ -1412,6 +1409,7 @@ Examples:
 * `#[1, 4, 2, 3, 3, 7].contains 3 = true`
 * `Array.contains #[1, 4, 2, 3, 3, 7] 5 = false`
 -/
+@[expose]
 def contains [BEq α] (as : Array α) (a : α) : Bool :=
   as.any (a == ·)
 
@@ -1460,6 +1458,7 @@ Examples:
   * `#[] ++ #[4, 5] = #[4, 5]`.
   * `#[1, 2, 3] ++ #[] = #[1, 2, 3]`.
 -/
+@[expose]
 protected def append (as : Array α) (bs : Array α) : Array α :=
   bs.foldl (init := as) fun xs v => xs.push v
 
@@ -1497,7 +1496,7 @@ Examples:
 * `#[2, 3, 2].flatMap Array.range = #[0, 1, 0, 1, 2, 0, 1]`
 * `#[['a', 'b'], ['c', 'd', 'e']].flatMap List.toArray = #['a', 'b', 'c', 'd', 'e']`
 -/
-@[inline]
+@[inline, expose]
 def flatMap (f : α → Array β) (as : Array α) : Array β :=
   as.foldl (init := empty) fun bs a => bs ++ f a
 
@@ -1510,7 +1509,7 @@ Examples:
  * `#[#[0, 1], #[], #[2], #[1, 0, 1]].flatten = #[0, 1, 2, 1, 0, 1]`
  * `(#[] : Array Nat).flatten = #[]`
 -/
-@[inline] def flatten (xss : Array (Array α)) : Array α :=
+@[inline, expose] def flatten (xss : Array (Array α)) : Array α :=
   xss.foldl (init := empty) fun acc xs => acc ++ xs
 
 /--
@@ -1523,6 +1522,7 @@ Examples:
 * `#[0, 1].reverse = #[1, 0]`
 * `#[0, 1, 2].reverse = #[2, 1, 0]`
 -/
+@[expose]
 def reverse (as : Array α) : Array α :=
   if h : as.size ≤ 1 then
     as
@@ -1555,7 +1555,7 @@ Examples:
 * `#[1, 2, 5, 2, 7, 7].filter (fun _ => true) (start := 3) = #[2, 7, 7]`
 * `#[1, 2, 5, 2, 7, 7].filter (fun _ => true) (stop := 3) = #[1, 2, 5]`
 -/
-@[inline]
+@[inline, expose]
 def filter (p : α → Bool) (as : Array α) (start := 0) (stop := as.size) : Array α :=
   as.foldl (init := #[]) (start := start) (stop := stop) fun acc a =>
     if p a then acc.push a else acc
@@ -1648,7 +1648,7 @@ Examining 7
 #[10, 14, 14]
 ```
 -/
-@[specialize]
+@[specialize, expose]
 def filterMapM [Monad m] (f : α → m (Option β)) (as : Array α) (start := 0) (stop := as.size) : m (Array β) :=
   as.foldlM (init := #[]) (start := start) (stop := stop) fun bs a => do
     match (← f a) with
@@ -1668,7 +1668,7 @@ Example:
 #[10, 14, 14]
 ```
 -/
-@[inline]
+@[inline, expose]
 def filterMap (f : α → Option β) (as : Array α) (start := 0) (stop := as.size) : Array β :=
   Id.run <| as.filterMapM (pure <| f ·) (start := start) (stop := stop)
 
@@ -1788,7 +1788,7 @@ decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ h
   induction xs, i, h using Array.eraseIdx.induct with
   | @case1 xs i h h' xs' ih =>
     unfold eraseIdx
-    simp +zetaDelta [h', xs', ih]
+    simp +zetaDelta [h', ih]
   | case2 xs i h h' =>
     unfold eraseIdx
     simp [h']
@@ -1881,8 +1881,6 @@ Examples:
   let as := as.push a
   loop as ⟨j, size_push .. ▸ j.lt_succ_self⟩
 
-@[deprecated insertIdx (since := "2024-11-20")] abbrev insertAt := @insertIdx
-
 /--
 Inserts an element into an array at the specified index. Panics if the index is greater than the
 size of the array.
@@ -1903,8 +1901,6 @@ def insertIdx! (as : Array α) (i : Nat) (a : α) : Array α :=
     insertIdx as i a
   else panic! "invalid index"
 
-@[deprecated insertIdx! (since := "2024-11-20")] abbrev insertAt! := @insertIdx!
-
 /--
 Inserts an element into an array at the specified index. The array is returned unmodified if the
 index is greater than the size of the array.
@@ -2027,11 +2023,6 @@ Examples:
 def unzip (as : Array (α × β)) : Array α × Array β :=
   as.foldl (init := (#[], #[])) fun (as, bs) (a, b) => (as.push a, bs.push b)
 
-@[deprecated partition (since := "2024-11-06")]
-def split (as : Array α) (p : α → Bool) : Array α × Array α :=
-  as.foldl (init := (#[], #[])) fun (as, bs) a =>
-    if p a then (as.push a, bs) else (as, bs.push a)
-
 /--
 Replaces the first occurrence of `a` with `b` in an array. The modification is performed in-place
 when the reference to the array is unique. Returns the array unmodified when `a` is not present.

src/Init/Data/Array/Bootstrap.lean

@@ -40,7 +40,7 @@ Use the indexing notation `a[i]!` instead.
 
 Access an element from an array, or panic if the index is out of bounds.
 -/
-@[deprecated "Use indexing notation `as[i]!` instead" (since := "2025-02-17")]
+@[deprecated "Use indexing notation `as[i]!` instead" (since := "2025-02-17"), expose]
 def get! {α : Type u} [Inhabited α] (a : @& Array α) (i : @& Nat) : α :=
   Array.getD a i default
 
@@ -78,7 +78,8 @@ theorem foldrM_eq_reverse_foldlM_toList [Monad m] {f : α → β → m β} {init
   have : xs = #[] ∨ 0 < xs.size :=
     match xs with | ⟨[]⟩ => .inl rfl | ⟨a::l⟩ => .inr (Nat.zero_lt_succ _)
   match xs, this with | _, .inl rfl => simp [foldrM] | xs, .inr h => ?_
-  simp [foldrM, h, ← foldrM_eq_reverse_foldlM_toList.aux, List.take_length]
+  simp only [foldrM, h, ← foldrM_eq_reverse_foldlM_toList.aux]
+  simp [Array.size]
 
 @[simp, grind =] theorem foldrM_toList [Monad m]
     {f : α → β → m β} {init : β} {xs : Array α} :
@@ -118,13 +119,13 @@ abbrev pop_toList := @Array.toList_pop
 @[simp] theorem toList_empty : (#[] : Array α).toList = [] := rfl
 
 @[simp, grind =] theorem append_empty {xs : Array α} : xs ++ #[] = xs := by
-  apply ext'; simp only [toList_append, toList_empty, List.append_nil]
+  apply ext'; simp only [toList_append, List.append_nil]
 
 @[deprecated append_empty (since := "2025-01-13")]
 abbrev append_nil := @append_empty
 
 @[simp, grind =] theorem empty_append {xs : Array α} : #[] ++ xs = xs := by
-  apply ext'; simp only [toList_append, toList_empty, List.nil_append]
+  apply ext'; simp only [toList_append, List.nil_append]
 
 @[deprecated empty_append (since := "2025-01-13")]
 abbrev nil_append := @empty_append
@@ -142,26 +143,4 @@ abbrev nil_append := @empty_append
 @[deprecated toList_appendList (since := "2024-12-11")]
 abbrev appendList_toList := @toList_appendList
 
-@[deprecated "Use the reverse direction of `foldrM_toList`." (since := "2024-11-13")]
-theorem foldrM_eq_foldrM_toList [Monad m]
-    {f : α → β → m β} {init : β} {xs : Array α} :
-    xs.foldrM f init = xs.toList.foldrM f init := by
-  simp
-
-@[deprecated "Use the reverse direction of `foldlM_toList`." (since := "2024-11-13")]
-theorem foldlM_eq_foldlM_toList [Monad m]
-    {f : β → α → m β} {init : β} {xs : Array α} :
-    xs.foldlM f init = xs.toList.foldlM f init:= by
-  simp
-
-@[deprecated "Use the reverse direction of `foldr_toList`." (since := "2024-11-13")]
-theorem foldr_eq_foldr_toList {f : α → β → β} {init : β} {xs : Array α} :
-    xs.foldr f init = xs.toList.foldr f init := by
-  simp
-
-@[deprecated "Use the reverse direction of `foldl_toList`." (since := "2024-11-13")]
-theorem foldl_eq_foldl_toList {f : β → α → β} {init : β} {xs : Array α} :
-    xs.foldl f init = xs.toList.foldl f init:= by
-  simp
-
 end Array

src/Init/Data/Array/Count.lean

@@ -52,6 +52,7 @@ theorem countP_push {a : α} {xs : Array α} : countP p (xs.push a) = countP p x
   rcases xs with ⟨xs⟩
   simp_all
 
+@[grind =]
 theorem countP_singleton {a : α} : countP p #[a] = if p a then 1 else 0 := by
   simp
 
@@ -59,10 +60,12 @@ theorem size_eq_countP_add_countP {xs : Array α} : xs.size = countP p xs + coun
   rcases xs with ⟨xs⟩
   simp [List.length_eq_countP_add_countP (p := p)]
 
+@[grind _=_]
 theorem countP_eq_size_filter {xs : Array α} : countP p xs = (filter p xs).size := by
   rcases xs with ⟨xs⟩
   simp [List.countP_eq_length_filter]
 
+@[grind =]
 theorem countP_eq_size_filter' : countP p = size ∘ filter p := by
   funext xs
   apply countP_eq_size_filter
@@ -71,7 +74,7 @@ theorem countP_le_size : countP p xs ≤ xs.size := by
   simp only [countP_eq_size_filter]
   apply size_filter_le
 
-@[simp] theorem countP_append {xs ys : Array α} : countP p (xs ++ ys) = countP p xs + countP p ys := by
+@[simp, grind =] theorem countP_append {xs ys : Array α} : countP p (xs ++ ys) = countP p xs + countP p ys := by
   rcases xs with ⟨xs⟩
   rcases ys with ⟨ys⟩
   simp
@@ -102,9 +105,11 @@ theorem boole_getElem_le_countP {xs : Array α} {i : Nat} (h : i < xs.size) :
   rcases xs with ⟨xs⟩
   simp [List.boole_getElem_le_countP]
 
+@[grind =]
 theorem countP_set {xs : Array α} {i : Nat} {a : α} (h : i < xs.size) :
     (xs.set i a).countP p = xs.countP p - (if p xs[i] then 1 else 0) + (if p a then 1 else 0) := by
   rcases xs with ⟨xs⟩
+  simp at h
   simp [List.countP_set, h]
 
 theorem countP_filter {xs : Array α} :
@@ -145,7 +150,7 @@ theorem countP_flatMap {p : β → Bool} {xs : Array α} {f : α → Array β} :
   rcases xs with ⟨xs⟩
   simp [List.countP_flatMap, Function.comp_def]
 
-@[simp] theorem countP_reverse {xs : Array α} : countP p xs.reverse = countP p xs := by
+@[simp, grind =] theorem countP_reverse {xs : Array α} : countP p xs.reverse = countP p xs := by
   rcases xs with ⟨xs⟩
   simp [List.countP_reverse]
 
@@ -172,7 +177,7 @@ variable [BEq α]
   cases xs
   simp
 
-@[simp] theorem count_empty {a : α} : count a #[] = 0 := rfl
+@[simp, grind =] theorem count_empty {a : α} : count a #[] = 0 := rfl
 
 theorem count_push {a b : α} {xs : Array α} :
     count a (xs.push b) = count a xs + if b == a then 1 else 0 := by
@@ -185,21 +190,28 @@ theorem count_eq_countP' {a : α} : count a = countP (· == a) := by
 
 theorem count_le_size {a : α} {xs : Array α} : count a xs ≤ xs.size := countP_le_size
 
+grind_pattern count_le_size => count a xs
+
+@[grind =]
+theorem count_eq_size_filter {a : α} {xs : Array α} : count a xs = (filter (· == a) xs).size := by
+  simp [count, countP_eq_size_filter]
+
 theorem count_le_count_push {a b : α} {xs : Array α} : count a xs ≤ count a (xs.push b) := by
   simp [count_push]
 
+@[grind =]
 theorem count_singleton {a b : α} : count a #[b] = if b == a then 1 else 0 := by
   simp [count_eq_countP]
 
-@[simp] theorem count_append {a : α} {xs ys : Array α} : count a (xs ++ ys) = count a xs + count a ys :=
+@[simp, grind =] theorem count_append {a : α} {xs ys : Array α} : count a (xs ++ ys) = count a xs + count a ys :=
   countP_append
 
-@[simp] theorem count_flatten {a : α} {xss : Array (Array α)} :
+@[simp, grind =] theorem count_flatten {a : α} {xss : Array (Array α)} :
     count a xss.flatten = (xss.map (count a)).sum := by
   cases xss using array₂_induction
   simp [List.count_flatten, Function.comp_def]
 
-@[simp] theorem count_reverse {a : α} {xs : Array α} : count a xs.reverse = count a xs := by
+@[simp, grind =] theorem count_reverse {a : α} {xs : Array α} : count a xs.reverse = count a xs := by
   rcases xs with ⟨xs⟩
   simp
 
@@ -208,9 +220,10 @@ theorem boole_getElem_le_count {xs : Array α} {i : Nat} {a : α} (h : i < xs.si
   rw [count_eq_countP]
   apply boole_getElem_le_countP (p := (· == a))
 
+@[grind =]
 theorem count_set {xs : Array α} {i : Nat} {a b : α} (h : i < xs.size) :
     (xs.set i a).count b = xs.count b - (if xs[i] == b then 1 else 0) + (if a == b then 1 else 0) := by
-  simp [count_eq_countP, countP_set, h]
+  simp [count_eq_countP, countP_set]
 
 variable [LawfulBEq α]
 
@@ -218,7 +231,7 @@ variable [LawfulBEq α]
   simp [count_push]
 
 @[simp] theorem count_push_of_ne {xs : Array α} (h : b ≠ a) : count a (xs.push b) = count a xs := by
-  simp_all [count_push, h]
+  simp_all [count_push]
 
 theorem count_singleton_self {a : α} : count a #[a] = 1 := by simp
 
@@ -279,17 +292,17 @@ abbrev mkArray_count_eq_of_count_eq_size := @replicate_count_eq_of_count_eq_size
 theorem count_le_count_map [BEq β] [LawfulBEq β] {xs : Array α} {f : α → β} {x : α} :
     count x xs ≤ count (f x) (map f xs) := by
   rcases xs with ⟨xs⟩
-  simp [List.count_le_count_map, countP_map]
+  simp [List.count_le_count_map]
 
 theorem count_filterMap {α} [BEq β] {b : β} {f : α → Option β} {xs : Array α} :
     count b (filterMap f xs) = countP (fun a => f a == some b) xs := by
   rcases xs with ⟨xs⟩
-  simp [List.count_filterMap, countP_filterMap]
+  simp [List.count_filterMap]
 
 theorem count_flatMap {α} [BEq β] {xs : Array α} {f : α → Array β} {x : β} :
     count x (xs.flatMap f) = sum (map (count x ∘ f) xs) := by
   rcases xs with ⟨xs⟩
-  simp [List.count_flatMap, countP_flatMap, Function.comp_def]
+  simp [List.count_flatMap, Function.comp_def]
 
 theorem countP_replace {a b : α} {xs : Array α} {p : α → Bool} :
     (xs.replace a b).countP p =

src/Init/Data/Array/DecidableEq.lean

@@ -23,7 +23,7 @@ private theorem rel_of_isEqvAux
   induction i with
   | zero => contradiction
   | succ i ih =>
-    simp only [Array.isEqvAux, Bool.and_eq_true, decide_eq_true_eq] at heqv
+    simp only [Array.isEqvAux, Bool.and_eq_true] at heqv
     by_cases hj' : j < i
     next =>
       exact ih _ heqv.right hj'
@@ -69,7 +69,7 @@ theorem isEqv_eq_decide (xs ys : Array α) (r) :
     simpa [isEqv_iff_rel] using h'
 
 @[simp, grind =] theorem isEqv_toList [BEq α] (xs ys : Array α) : (xs.toList.isEqv ys.toList r) = (xs.isEqv ys r) := by
-  simp [isEqv_eq_decide, List.isEqv_eq_decide]
+  simp [isEqv_eq_decide, List.isEqv_eq_decide, Array.size]
 
 theorem eq_of_isEqv [DecidableEq α] (xs ys : Array α) (h : Array.isEqv xs ys (fun x y => x = y)) : xs = ys := by
   have ⟨h, h'⟩ := rel_of_isEqv h
@@ -100,7 +100,7 @@ theorem beq_eq_decide [BEq α] (xs ys : Array α) :
   simp [BEq.beq, isEqv_eq_decide]
 
 @[simp, grind =] theorem beq_toList [BEq α] (xs ys : Array α) : (xs.toList == ys.toList) = (xs == ys) := by
-  simp [beq_eq_decide, List.beq_eq_decide]
+  simp [beq_eq_decide, List.beq_eq_decide, Array.size]
 
 end Array
 

src/Init/Data/Array/Erase.lean

@@ -24,6 +24,7 @@ open Nat
 
 /-! ### eraseP -/
 
+@[grind =]
 theorem eraseP_empty : #[].eraseP p = #[] := by simp
 
 theorem eraseP_of_forall_mem_not {xs : Array α} (h : ∀ a, a ∈ xs → ¬p a) : xs.eraseP p = xs := by
@@ -64,6 +65,7 @@ theorem exists_or_eq_self_of_eraseP (p) (xs : Array α) :
   let ⟨_, ys, zs, _, _, e₁, e₂⟩ := exists_of_eraseP al pa
   rw [e₂]; simp [size_append, e₁]
 
+@[grind =]
 theorem size_eraseP {xs : Array α} : (xs.eraseP p).size = if xs.any p then xs.size - 1 else xs.size := by
   split <;> rename_i h
   · simp only [any_eq_true] at h
@@ -81,11 +83,12 @@ theorem le_size_eraseP {xs : Array α} : xs.size - 1 ≤ (xs.eraseP p).size := b
   rcases xs with ⟨xs⟩
   simpa using List.le_length_eraseP
 
+@[grind →]
 theorem mem_of_mem_eraseP {xs : Array α} : a ∈ xs.eraseP p → a ∈ xs := by
   rcases xs with ⟨xs⟩
   simpa using List.mem_of_mem_eraseP
 
-@[simp] theorem mem_eraseP_of_neg {xs : Array α} (pa : ¬p a) : a ∈ xs.eraseP p ↔ a ∈ xs := by
+@[simp, grind] theorem mem_eraseP_of_neg {xs : Array α} (pa : ¬p a) : a ∈ xs.eraseP p ↔ a ∈ xs := by
   rcases xs with ⟨xs⟩
   simpa using List.mem_eraseP_of_neg pa
 
@@ -93,15 +96,18 @@ theorem mem_of_mem_eraseP {xs : Array α} : a ∈ xs.eraseP p → a ∈ xs := by
   rcases xs with ⟨xs⟩
   simp
 
+@[grind _=_]
 theorem eraseP_map {f : β → α} {xs : Array β} : (xs.map f).eraseP p = (xs.eraseP (p ∘ f)).map f := by
   rcases xs with ⟨xs⟩
   simpa using List.eraseP_map
 
+@[grind =]
 theorem eraseP_filterMap {f : α → Option β} {xs : Array α} :
     (filterMap f xs).eraseP p = filterMap f (xs.eraseP (fun x => match f x with | some y => p y | none => false)) := by
   rcases xs with ⟨xs⟩
   simpa using List.eraseP_filterMap
 
+@[grind =]
 theorem eraseP_filter {f : α → Bool} {xs : Array α} :
     (filter f xs).eraseP p = filter f (xs.eraseP (fun x => p x && f x)) := by
   rcases xs with ⟨xs⟩
@@ -119,6 +125,7 @@ theorem eraseP_append_right {xs : Array α} ys (h : ∀ b ∈ xs, ¬p b) :
   rcases ys with ⟨ys⟩
   simpa using List.eraseP_append_right ys (by simpa using h)
 
+@[grind =]
 theorem eraseP_append {xs : Array α} {ys : Array α} :
     (xs ++ ys).eraseP p = if xs.any p then xs.eraseP p ++ ys else xs ++ ys.eraseP p := by
   rcases xs with ⟨xs⟩
@@ -126,6 +133,7 @@ theorem eraseP_append {xs : Array α} {ys : Array α} :
   simp only [List.append_toArray, List.eraseP_toArray, List.eraseP_append, List.any_toArray]
   split <;> simp
 
+@[grind =]
 theorem eraseP_replicate {n : Nat} {a : α} {p : α → Bool} :
     (replicate n a).eraseP p = if p a then replicate (n - 1) a else replicate n a := by
   simp only [← List.toArray_replicate, List.eraseP_toArray, List.eraseP_replicate]
@@ -165,6 +173,7 @@ theorem eraseP_eq_iff {p} {xs : Array α} :
     · exact Or.inl h
     · exact Or.inr ⟨a, l₁, by simpa using h₁, h₂, ⟨l, by simp⟩⟩
 
+@[grind =]
 theorem eraseP_comm {xs : Array α} (h : ∀ a ∈ xs, ¬ p a ∨ ¬ q a) :
     (xs.eraseP p).eraseP q = (xs.eraseP q).eraseP p := by
   rcases xs with ⟨xs⟩
@@ -197,7 +206,7 @@ theorem erase_eq_eraseP [LawfulBEq α] (a : α) (xs : Array α) : xs.erase a = x
 theorem erase_ne_empty_iff [LawfulBEq α] {xs : Array α} {a : α} :
     xs.erase a ≠ #[] ↔ xs ≠ #[] ∧ xs ≠ #[a] := by
   rcases xs with ⟨xs⟩
-  simp [List.erase_ne_nil_iff]
+  simp
 
 theorem exists_erase_eq [LawfulBEq α] {a : α} {xs : Array α} (h : a ∈ xs) :
     ∃ ys zs, a ∉ ys ∧ xs = ys.push a ++ zs ∧ xs.erase a = ys ++ zs := by
@@ -208,6 +217,7 @@ theorem exists_erase_eq [LawfulBEq α] {a : α} {xs : Array α} (h : a ∈ xs) :
     (xs.erase a).size = xs.size - 1 := by
   rw [erase_eq_eraseP]; exact size_eraseP_of_mem h (beq_self_eq_true a)
 
+@[grind =]
 theorem size_erase [LawfulBEq α] {a : α} {xs : Array α} :
     (xs.erase a).size = if a ∈ xs then xs.size - 1 else xs.size := by
   rw [erase_eq_eraseP, size_eraseP]
@@ -222,11 +232,12 @@ theorem le_size_erase [LawfulBEq α] {a : α} {xs : Array α} : xs.size - 1 ≤
   rcases xs with ⟨xs⟩
   simpa using List.le_length_erase
 
+@[grind →]
 theorem mem_of_mem_erase {a b : α} {xs : Array α} (h : a ∈ xs.erase b) : a ∈ xs := by
   rcases xs with ⟨xs⟩
   simpa using List.mem_of_mem_erase (by simpa using h)
 
-@[simp] theorem mem_erase_of_ne [LawfulBEq α] {a b : α} {xs : Array α} (ab : a ≠ b) :
+@[simp, grind] theorem mem_erase_of_ne [LawfulBEq α] {a b : α} {xs : Array α} (ab : a ≠ b) :
     a ∈ xs.erase b ↔ a ∈ xs :=
   erase_eq_eraseP b xs ▸ mem_eraseP_of_neg (mt eq_of_beq ab.symm)
 
@@ -234,6 +245,7 @@ theorem mem_of_mem_erase {a b : α} {xs : Array α} (h : a ∈ xs.erase b) : a
   rw [erase_eq_eraseP', eraseP_eq_self_iff]
   simp [forall_mem_ne']
 
+@[grind _=_]
 theorem erase_filter [LawfulBEq α] {f : α → Bool} {xs : Array α} :
     (filter f xs).erase a = filter f (xs.erase a) := by
   rcases xs with ⟨xs⟩
@@ -251,6 +263,7 @@ theorem erase_append_right [LawfulBEq α] {a : α} {xs : Array α} (ys : Array
   rcases ys with ⟨ys⟩
   simpa using List.erase_append_right ys (by simpa using h)
 
+@[grind =]
 theorem erase_append [LawfulBEq α] {a : α} {xs ys : Array α} :
     (xs ++ ys).erase a = if a ∈ xs then xs.erase a ++ ys else xs ++ ys.erase a := by
   rcases xs with ⟨xs⟩
@@ -258,6 +271,7 @@ theorem erase_append [LawfulBEq α] {a : α} {xs ys : Array α} :
   simp only [List.append_toArray, List.erase_toArray, List.erase_append, mem_toArray]
   split <;> simp
 
+@[grind =]
 theorem erase_replicate [LawfulBEq α] {n : Nat} {a b : α} :
     (replicate n a).erase b = if b == a then replicate (n - 1) a else replicate n a := by
   simp only [← List.toArray_replicate, List.erase_toArray]
@@ -269,6 +283,7 @@ abbrev erase_mkArray := @erase_replicate
 
 -- The arguments `a b` are explicit,
 -- so they can be specified to prevent `simp` repeatedly applying the lemma.
+@[grind =]
 theorem erase_comm [LawfulBEq α] (a b : α) {xs : Array α} :
     (xs.erase a).erase b = (xs.erase b).erase a := by
   rcases xs with ⟨xs⟩
@@ -291,7 +306,7 @@ theorem erase_eq_iff [LawfulBEq α] {a : α} {xs : Array α} :
 @[simp] theorem erase_replicate_self [LawfulBEq α] {a : α} :
     (replicate n a).erase a = replicate (n - 1) a := by
   simp only [← List.toArray_replicate, List.erase_toArray]
-  simp [List.erase_replicate]
+  simp
 
 @[deprecated erase_replicate_self (since := "2025-03-18")]
 abbrev erase_mkArray_self := @erase_replicate_self
@@ -312,6 +327,7 @@ theorem eraseIdx_eq_eraseIdxIfInBounds {xs : Array α} {i : Nat} (h : i < xs.siz
     xs.eraseIdx i h = xs.eraseIdxIfInBounds i := by
   simp [eraseIdxIfInBounds, h]
 
+@[grind =]
 theorem eraseIdx_eq_take_drop_succ {xs : Array α} {i : Nat} (h) :
     xs.eraseIdx i h = xs.take i ++ xs.drop (i + 1) := by
   rcases xs with ⟨xs⟩
@@ -322,6 +338,7 @@ theorem eraseIdx_eq_take_drop_succ {xs : Array α} {i : Nat} (h) :
   rw [List.take_of_length_le]
   simp
 
+@[grind =]
 theorem getElem?_eraseIdx {xs : Array α} {i : Nat} (h : i < xs.size) {j : Nat} :
     (xs.eraseIdx i)[j]? = if j < i then xs[j]? else xs[j + 1]? := by
   rcases xs with ⟨xs⟩
@@ -335,10 +352,11 @@ theorem getElem?_eraseIdx_of_lt {xs : Array α} {i : Nat} (h : i < xs.size) {j :
 theorem getElem?_eraseIdx_of_ge {xs : Array α} {i : Nat} (h : i < xs.size) {j : Nat} (h' : i ≤ j) :
     (xs.eraseIdx i)[j]? = xs[j + 1]? := by
   rw [getElem?_eraseIdx]
-  simp only [dite_eq_ite, ite_eq_right_iff]
+  simp only [ite_eq_right_iff]
   intro h'
   omega
 
+@[grind =]
 theorem getElem_eraseIdx {xs : Array α} {i : Nat} (h : i < xs.size) {j : Nat} (h' : j < (xs.eraseIdx i).size) :
     (xs.eraseIdx i)[j] = if h'' : j < i then
         xs[j]
@@ -362,6 +380,7 @@ theorem eraseIdx_ne_empty_iff {xs : Array α} {i : Nat} {h} : xs.eraseIdx i ≠
     simp [h]
   · simp
 
+@[grind →]
 theorem mem_of_mem_eraseIdx {xs : Array α} {i : Nat} {h} {a : α} (h : a ∈ xs.eraseIdx i) : a ∈ xs := by
   rcases xs with ⟨xs⟩
   simpa using List.mem_of_mem_eraseIdx (by simpa using h)
@@ -373,13 +392,29 @@ theorem eraseIdx_append_of_lt_size {xs : Array α} {k : Nat} (hk : k < xs.size)
   simp at hk
   simp [List.eraseIdx_append_of_lt_length, *]
 
-theorem eraseIdx_append_of_length_le {xs : Array α} {k : Nat} (hk : xs.size ≤ k) (ys : Array α) (h) :
+theorem eraseIdx_append_of_size_le {xs : Array α} {k : Nat} (hk : xs.size ≤ k) (ys : Array α) (h) :
     eraseIdx (xs ++ ys) k = xs ++ eraseIdx ys (k - xs.size) (by simp at h; omega) := by
   rcases xs with ⟨l⟩
   rcases ys with ⟨l'⟩
   simp at hk
   simp [List.eraseIdx_append_of_length_le, *]
 
+@[deprecated eraseIdx_append_of_size_le (since := "2025-06-11")]
+abbrev eraseIdx_append_of_length_le := @eraseIdx_append_of_size_le
+
+@[grind =]
+theorem eraseIdx_append {xs ys : Array α} (h : k < (xs ++ ys).size) :
+    eraseIdx (xs ++ ys) k =
+      if h' : k < xs.size then
+        eraseIdx xs k ++ ys
+      else
+        xs ++ eraseIdx ys (k - xs.size) (by simp at h; omega) := by
+  split <;> rename_i h
+  · simp [eraseIdx_append_of_lt_size h]
+  · rw [eraseIdx_append_of_size_le]
+    omega
+
+@[grind =]
 theorem eraseIdx_replicate {n : Nat} {a : α} {k : Nat} {h} :
     (replicate n a).eraseIdx k = replicate (n - 1) a := by
   simp at h
@@ -428,6 +463,48 @@ theorem eraseIdx_set_gt {xs : Array α} {i : Nat} {j : Nat} {a : α} (h : i < j)
   rcases xs with ⟨xs⟩
   simp [List.eraseIdx_set_gt, *]
 
+@[grind =]
+theorem eraseIdx_set {xs : Array α} {i : Nat} {a : α} {hi : i < xs.size} {j : Nat} {hj : j < (xs.set i a).size} :
+    (xs.set i a).eraseIdx j =
+      if h' : j < i then
+        (xs.eraseIdx j).set (i - 1) a (by simp; omega)
+      else if h'' : j = i then
+        xs.eraseIdx i
+      else
+        (xs.eraseIdx j (by simp at hj; omega)).set i a (by simp at hj ⊢; omega) := by
+  split <;> rename_i h'
+  · rw [eraseIdx_set_lt]
+    omega
+  · split <;> rename_i h''
+    · subst h''
+      rw [eraseIdx_set_eq]
+    · rw [eraseIdx_set_gt]
+      omega
+
+theorem set_eraseIdx_le {xs : Array α} {i : Nat} {w : i < xs.size} {j : Nat} {a : α} (h : i ≤ j) (hj : j < (xs.eraseIdx i).size) :
+    (xs.eraseIdx i).set j a = (xs.set (j + 1) a (by simp at hj; omega)).eraseIdx i (by simp at ⊢; omega) := by
+  rw [eraseIdx_set_lt]
+  · simp
+  · omega
+
+theorem set_eraseIdx_gt {xs : Array α} {i : Nat} {w : i < xs.size} {j : Nat} {a : α} (h : j < i) (hj : j < (xs.eraseIdx i).size) :
+    (xs.eraseIdx i).set j a = (xs.set j a).eraseIdx i (by simp at ⊢; omega) := by
+  rw [eraseIdx_set_gt]
+  omega
+
+@[grind =]
+theorem set_eraseIdx {xs : Array α} {i : Nat} {w : i < xs.size} {j : Nat} {a : α} (hj : j < (xs.eraseIdx i).size) :
+    (xs.eraseIdx i).set j a =
+      if h' : i ≤ j then
+        (xs.set (j + 1) a (by simp at hj; omega)).eraseIdx i (by simp at ⊢; omega)
+      else
+        (xs.set j a).eraseIdx i (by simp at ⊢; omega) := by
+  split <;> rename_i h'
+  · rw [set_eraseIdx_le]
+    omega
+  · rw [set_eraseIdx_gt]
+    omega
+
 @[simp] theorem set_getElem_succ_eraseIdx_succ
     {xs : Array α} {i : Nat} (h : i + 1 < xs.size) :
     (xs.eraseIdx (i + 1)).set i xs[i + 1] (by simp; omega) = xs.eraseIdx i := by

src/Init/Data/Array/Extract.lean

@@ -29,7 +29,7 @@ namespace Array
   · simp
     omega
   · simp only [size_extract] at h₁ h₂
-    simp [h]
+    simp
 
 theorem size_extract_le {as : Array α} {i j : Nat} :
     (as.extract i j).size ≤ j - i := by
@@ -46,7 +46,7 @@ theorem size_extract_of_le {as : Array α} {i j : Nat} (h : j ≤ as.size) :
   simp
   omega
 
-@[simp]
+@[simp, grind =]
 theorem extract_push {as : Array α} {b : α} {start stop : Nat} (h : stop ≤ as.size) :
     (as.push b).extract start stop = as.extract start stop := by
   ext i h₁ h₂
@@ -56,7 +56,7 @@ theorem extract_push {as : Array α} {b : α} {start stop : Nat} (h : stop ≤ a
     simp only [getElem_extract, getElem_push]
     rw [dif_pos (by omega)]
 
-@[simp]
+@[simp, grind =]
 theorem extract_eq_pop {as : Array α} {stop : Nat} (h : stop = as.size - 1) :
     as.extract 0 stop = as.pop := by
   ext i h₁ h₂
@@ -65,7 +65,7 @@ theorem extract_eq_pop {as : Array α} {stop : Nat} (h : stop = as.size - 1) :
   · simp only [size_extract, size_pop] at h₁ h₂
     simp [getElem_extract, getElem_pop]
 
-@[simp]
+@[simp, grind _=_]
 theorem extract_append_extract {as : Array α} {i j k : Nat} :
     as.extract i j ++ as.extract j k = as.extract (min i j) (max j k) := by
   ext l h₁ h₂
@@ -162,14 +162,14 @@ theorem extract_sub_one {as : Array α} {i j : Nat} (h : j < as.size) :
 @[simp]
 theorem getElem?_extract_of_lt {as : Array α} {i j k : Nat} (h : k < min j as.size - i) :
     (as.extract i j)[k]? = some (as[i + k]'(by omega)) := by
-  simp [getElem?_extract, h]
+  simp [h]
 
 theorem getElem?_extract_of_succ {as : Array α} {j : Nat} :
     (as.extract 0 (j + 1))[j]? = as[j]? := by
   simp [getElem?_extract]
   omega
 
-@[simp] theorem extract_extract {as : Array α} {i j k l : Nat} :
+@[simp, grind =] theorem extract_extract {as : Array α} {i j k l : Nat} :
     (as.extract i j).extract k l = as.extract (i + k) (min (i + l) j) := by
   ext m h₁ h₂
   · simp
@@ -185,6 +185,7 @@ theorem ne_empty_of_extract_ne_empty {as : Array α} {i j : Nat} (h : as.extract
     as ≠ #[] :=
   mt extract_eq_empty_of_eq_empty h
 
+@[grind =]
 theorem extract_set {as : Array α} {i j k : Nat} (h : k < as.size) {a : α} :
     (as.set k a).extract i j =
       if _ : k < i then
@@ -211,13 +212,14 @@ theorem extract_set {as : Array α} {i j k : Nat} (h : k < as.size) {a : α} :
         simp [getElem_set]
         omega
 
+@[grind =]
 theorem set_extract {as : Array α} {i j k : Nat} (h : k < (as.extract i j).size) {a : α} :
     (as.extract i j).set k a = (as.set (i + k) a (by simp at h; omega)).extract i j := by
   ext l h₁ h₂
   · simp
   · simp_all [getElem_set]
 
-@[simp]
+@[simp, grind =]
 theorem extract_append {as bs : Array α} {i j : Nat} :
     (as ++ bs).extract i j = as.extract i j ++ bs.extract (i - as.size) (j - as.size) := by
   ext l h₁ h₂
@@ -242,14 +244,14 @@ theorem extract_append_right {as bs : Array α} :
     (as ++ bs).extract as.size (as.size + i) = bs.extract 0 i := by
   simp
 
-@[simp] theorem map_extract {as : Array α} {i j : Nat} :
+@[simp, grind =] theorem map_extract {as : Array α} {i j : Nat} :
     (as.extract i j).map f = (as.map f).extract i j := by
   ext l h₁ h₂
   · simp
   · simp only [size_map, size_extract] at h₁ h₂
     simp only [getElem_map, getElem_extract]
 
-@[simp] theorem extract_replicate {a : α} {n i j : Nat} :
+@[simp, grind =] theorem extract_replicate {a : α} {n i j : Nat} :
     (replicate n a).extract i j = replicate (min j n - i) a := by
   ext l h₁ h₂
   · simp
@@ -297,6 +299,7 @@ theorem set_eq_push_extract_append_extract {as : Array α} {i : Nat} (h : i < as
   simp at h
   simp [List.set_eq_take_append_cons_drop, h, List.take_of_length_le]
 
+@[grind =]
 theorem extract_reverse {as : Array α} {i j : Nat} :
     as.reverse.extract i j = (as.extract (as.size - j) (as.size - i)).reverse := by
   ext l h₁ h₂
@@ -307,6 +310,7 @@ theorem extract_reverse {as : Array α} {i j : Nat} :
     congr 1
     omega
 
+@[grind =]
 theorem reverse_extract {as : Array α} {i j : Nat} :
     (as.extract i j).reverse = as.reverse.extract (as.size - j) (as.size - i) := by
   rw [extract_reverse]

src/Init/Data/Array/FinRange.lean

@@ -23,10 +23,10 @@ Examples:
 -/
 protected def finRange (n : Nat) : Array (Fin n) := ofFn fun i => i
 
-@[simp] theorem size_finRange {n} : (Array.finRange n).size = n := by
+@[simp, grind =] theorem size_finRange {n} : (Array.finRange n).size = n := by
   simp [Array.finRange]
 
-@[simp] theorem getElem_finRange {i : Nat} (h : i < (Array.finRange n).size) :
+@[simp, grind =] theorem getElem_finRange {i : Nat} (h : i < (Array.finRange n).size) :
     (Array.finRange n)[i] = Fin.cast size_finRange ⟨i, h⟩ := by
   simp [Array.finRange]
 
@@ -49,6 +49,7 @@ theorem finRange_succ_last {n} :
     · simp_all
       omega
 
+@[grind _=_]
 theorem finRange_reverse {n} : (Array.finRange n).reverse = (Array.finRange n).map Fin.rev := by
   ext i h
   · simp

src/Init/Data/Array/Find.lean

@@ -38,11 +38,22 @@ theorem findSome?_singleton {a : α} {f : α → Option β} : #[a].findSome? f =
 @[simp] theorem findSomeRev?_push_of_isNone {xs : Array α} (h : (f a).isNone) : (xs.push a).findSomeRev? f = xs.findSomeRev? f := by
   cases xs; simp_all
 
+@[grind =]
+theorem findSomeRev?_push {xs : Array α} {a : α} {f : α → Option β} :
+    (xs.push a).findSomeRev? f = (f a).or (xs.findSomeRev? f) := by
+  match h : f a with
+  | some b =>
+    rw [findSomeRev?_push_of_isSome]
+    all_goals simp_all
+  | none =>
+    rw [findSomeRev?_push_of_isNone]
+    all_goals simp_all
+
 theorem exists_of_findSome?_eq_some {f : α → Option β} {xs : Array α} (w : xs.findSome? f = some b) :
     ∃ a, a ∈ xs ∧ f a = some b := by
   cases xs; simp_all [List.exists_of_findSome?_eq_some]
 
-@[simp] theorem findSome?_eq_none_iff : findSome? p xs = none ↔ ∀ x ∈ xs, p x = none := by
+@[simp, grind =] theorem findSome?_eq_none_iff : findSome? p xs = none ↔ ∀ x ∈ xs, p x = none := by
   cases xs; simp
 
 @[simp] theorem findSome?_isSome_iff {f : α → Option β} {xs : Array α} :
@@ -59,36 +70,39 @@ theorem findSome?_eq_some_iff {f : α → Option β} {xs : Array α} {b : β} :
   · rintro ⟨xs, a, ys, h₀, h₁, h₂⟩
     exact ⟨xs.toList, a, ys.toList, by simpa using congrArg toList h₀, h₁, by simpa⟩
 
-@[simp] theorem findSome?_guard {xs : Array α} : findSome? (Option.guard fun x => p x) xs = find? p xs := by
+@[simp, grind =] theorem findSome?_guard {xs : Array α} : findSome? (Option.guard p) xs = find? p xs := by
   cases xs; simp
 
-theorem find?_eq_findSome?_guard {xs : Array α} : find? p xs = findSome? (Option.guard fun x => p x) xs :=
+theorem find?_eq_findSome?_guard {xs : Array α} : find? p xs = findSome? (Option.guard p) xs :=
   findSome?_guard.symm
 
-@[simp] theorem getElem?_zero_filterMap {f : α → Option β} {xs : Array α} : (xs.filterMap f)[0]? = xs.findSome? f := by
+@[simp, grind =] theorem getElem?_zero_filterMap {f : α → Option β} {xs : Array α} : (xs.filterMap f)[0]? = xs.findSome? f := by
   cases xs; simp [← List.head?_eq_getElem?]
 
-@[simp] theorem getElem_zero_filterMap {f : α → Option β} {xs : Array α} (h) :
+@[simp, grind =] theorem getElem_zero_filterMap {f : α → Option β} {xs : Array α} (h) :
     (xs.filterMap f)[0] = (xs.findSome? f).get (by cases xs; simpa [List.length_filterMap_eq_countP] using h) := by
-  cases xs; simp [← List.head_eq_getElem, ← getElem?_zero_filterMap]
+  cases xs; simp [← getElem?_zero_filterMap]
 
-@[simp] theorem back?_filterMap {f : α → Option β} {xs : Array α} : (xs.filterMap f).back? = xs.findSomeRev? f := by
+@[simp, grind =] theorem back?_filterMap {f : α → Option β} {xs : Array α} : (xs.filterMap f).back? = xs.findSomeRev? f := by
   cases xs; simp
 
-@[simp] theorem back!_filterMap [Inhabited β] {f : α → Option β} {xs : Array α} :
+@[simp, grind =] theorem back!_filterMap [Inhabited β] {f : α → Option β} {xs : Array α} :
     (xs.filterMap f).back! = (xs.findSomeRev? f).getD default := by
   cases xs; simp
 
-@[simp] theorem map_findSome? {f : α → Option β} {g : β → γ} {xs : Array α} :
+@[simp, grind _=_] theorem map_findSome? {f : α → Option β} {g : β → γ} {xs : Array α} :
     (xs.findSome? f).map g = xs.findSome? (Option.map g ∘ f) := by
   cases xs; simp
 
+@[grind _=_]
 theorem findSome?_map {f : β → γ} {xs : Array β} : findSome? p (xs.map f) = xs.findSome? (p ∘ f) := by
   cases xs; simp [List.findSome?_map]
 
+@[grind =]
 theorem findSome?_append {xs ys : Array α} : (xs ++ ys).findSome? f = (xs.findSome? f).or (ys.findSome? f) := by
   cases xs; cases ys; simp [List.findSome?_append]
 
+@[grind =]
 theorem getElem?_zero_flatten (xss : Array (Array α)) :
     (flatten xss)[0]? = xss.findSome? fun xs => xs[0]? := by
   cases xss using array₂_induction
@@ -104,12 +118,14 @@ theorem getElem_zero_flatten.proof {xss : Array (Array α)} (h : 0 < xss.flatten
   obtain ⟨_, ⟨xs, m, rfl⟩, h⟩ := h
   exact ⟨xs, m, by simpa using h⟩
 
+@[grind =]
 theorem getElem_zero_flatten {xss : Array (Array α)} (h) :
     (flatten xss)[0] = (xss.findSome? fun xs => xs[0]?).get (getElem_zero_flatten.proof h) := by
   have t := getElem?_zero_flatten xss
-  simp [getElem?_eq_getElem, h] at t
+  simp at t
   simp [← t]
 
+@[grind =]
 theorem findSome?_replicate : findSome? f (replicate n a) = if n = 0 then none else f a := by
   simp [← List.toArray_replicate, List.findSome?_replicate]
 
@@ -140,8 +156,9 @@ abbrev findSome?_mkArray_of_isNone := @findSome?_replicate_of_isNone
 
 /-! ### find? -/
 
-@[simp] theorem find?_empty : find? p #[] = none := rfl
+@[simp, grind =] theorem find?_empty : find? p #[] = none := rfl
 
+@[grind =]
 theorem find?_singleton {a : α} {p : α → Bool} :
     #[a].find? p = if p a then some a else none := by
   simp
@@ -150,11 +167,26 @@ theorem find?_singleton {a : α} {p : α → Bool} :
     findRev? p (xs.push a) = some a := by
   cases xs; simp [h]
 
-@[simp] theorem findRev?_cons_of_neg {xs : Array α} (h : ¬p a) :
+@[simp] theorem findRev?_push_of_neg {xs : Array α} (h : ¬p a) :
     findRev? p (xs.push a) = findRev? p xs := by
   cases xs; simp [h]
 
-@[simp] theorem find?_eq_none : find? p xs = none ↔ ∀ x ∈ xs, ¬ p x := by
+@[deprecated findRev?_push_of_neg (since := "2025-06-12")]
+abbrev findRev?_cons_of_neg := @findRev?_push_of_neg
+
+@[grind =]
+theorem finRev?_push {xs : Array α} :
+    findRev? p (xs.push a) = (Option.guard p a).or (xs.findRev? p) := by
+  cases h : p a
+  · rw [findRev?_push_of_neg, Option.guard_eq_none_iff.mpr h]
+    all_goals simp [h]
+  · rw [findRev?_push_of_pos, Option.guard_eq_some_iff.mpr ⟨rfl, h⟩]
+    all_goals simp [h]
+
+@[deprecated finRev?_push (since := "2025-06-12")]
+abbrev findRev?_cons := @finRev?_push
+
+@[simp, grind =] theorem find?_eq_none : find? p xs = none ↔ ∀ x ∈ xs, ¬ p x := by
   cases xs; simp
 
 theorem find?_eq_some_iff_append {xs : Array α} :
@@ -178,60 +210,63 @@ theorem find?_push_eq_some {xs : Array α} :
     (xs.push a).find? p = some b ↔ xs.find? p = some b ∨ (xs.find? p = none ∧ (p a ∧ a = b)) := by
   cases xs; simp
 
-@[simp] theorem find?_isSome {xs : Array α} {p : α → Bool} : (xs.find? p).isSome ↔ ∃ x, x ∈ xs ∧ p x := by
+@[simp, grind =] theorem find?_isSome {xs : Array α} {p : α → Bool} : (xs.find? p).isSome ↔ ∃ x, x ∈ xs ∧ p x := by
   cases xs; simp
 
+@[grind →]
 theorem find?_some {xs : Array α} (h : find? p xs = some a) : p a := by
   cases xs
   simp at h
   exact List.find?_some h
 
+@[grind →]
 theorem mem_of_find?_eq_some {xs : Array α} (h : find? p xs = some a) : a ∈ xs := by
   cases xs
   simp at h
   simpa using List.mem_of_find?_eq_some h
 
+@[grind]
 theorem get_find?_mem {xs : Array α} (h) : (xs.find? p).get h ∈ xs := by
   cases xs
   simp [List.get_find?_mem]
 
-@[simp] theorem find?_filter {xs : Array α} (p q : α → Bool) :
+@[simp, grind =] theorem find?_filter {xs : Array α} (p q : α → Bool) :
     (xs.filter p).find? q = xs.find? (fun a => p a ∧ q a) := by
   cases xs; simp
 
-@[simp] theorem getElem?_zero_filter {p : α → Bool} {xs : Array α} :
+@[simp, grind =] theorem getElem?_zero_filter {p : α → Bool} {xs : Array α} :
     (xs.filter p)[0]? = xs.find? p := by
   cases xs; simp [← List.head?_eq_getElem?]
 
-@[simp] theorem getElem_zero_filter {p : α → Bool} {xs : Array α} (h) :
+@[simp, grind =] theorem getElem_zero_filter {p : α → Bool} {xs : Array α} (h) :
     (xs.filter p)[0] =
       (xs.find? p).get (by cases xs; simpa [← List.countP_eq_length_filter] using h) := by
   cases xs
   simp [List.getElem_zero_eq_head]
 
-@[simp] theorem back?_filter {p : α → Bool} {xs : Array α} : (xs.filter p).back? = xs.findRev? p := by
+@[simp, grind =] theorem back?_filter {p : α → Bool} {xs : Array α} : (xs.filter p).back? = xs.findRev? p := by
   cases xs; simp
 
-@[simp] theorem back!_filter [Inhabited α] {p : α → Bool} {xs : Array α} :
+@[simp, grind =] theorem back!_filter [Inhabited α] {p : α → Bool} {xs : Array α} :
     (xs.filter p).back! = (xs.findRev? p).get! := by
   cases xs; simp [Option.get!_eq_getD]
 
-@[simp] theorem find?_filterMap {xs : Array α} {f : α → Option β} {p : β → Bool} :
+@[simp, grind =] theorem find?_filterMap {xs : Array α} {f : α → Option β} {p : β → Bool} :
     (xs.filterMap f).find? p = (xs.find? (fun a => (f a).any p)).bind f := by
   cases xs; simp
 
-@[simp] theorem find?_map {f : β → α} {xs : Array β} :
+@[simp, grind =] theorem find?_map {f : β → α} {xs : Array β} :
     find? p (xs.map f) = (xs.find? (p ∘ f)).map f := by
   cases xs; simp
 
-@[simp] theorem find?_append {xs ys : Array α} :
+@[simp, grind =] theorem find?_append {xs ys : Array α} :
     (xs ++ ys).find? p = (xs.find? p).or (ys.find? p) := by
   cases xs
   cases ys
   simp
 
-@[simp] theorem find?_flatten {xss : Array (Array α)} {p : α → Bool} :
-    xss.flatten.find? p = xss.findSome? (·.find? p) := by
+@[simp, grind _=_] theorem find?_flatten {xss : Array (Array α)} {p : α → Bool} :
+    xss.flatten.find? p = xss.findSome? (find? p) := by
   cases xss using array₂_induction
   simp [List.findSome?_map, Function.comp_def]
 
@@ -270,10 +305,10 @@ theorem find?_flatten_eq_some_iff {xss : Array (Array α)} {p : α → Bool} {a
 @[deprecated find?_flatten_eq_some_iff (since := "2025-02-03")]
 abbrev find?_flatten_eq_some := @find?_flatten_eq_some_iff
 
-@[simp] theorem find?_flatMap {xs : Array α} {f : α → Array β} {p : β → Bool} :
+@[simp, grind =] theorem find?_flatMap {xs : Array α} {f : α → Array β} {p : β → Bool} :
     (xs.flatMap f).find? p = xs.findSome? (fun x => (f x).find? p) := by
   cases xs
-  simp [List.find?_flatMap, Array.flatMap_toArray]
+  simp [List.find?_flatMap]
 
 theorem find?_flatMap_eq_none_iff {xs : Array α} {f : α → Array β} {p : β → Bool} :
     (xs.flatMap f).find? p = none ↔ ∀ x ∈ xs, ∀ y ∈ f x, !p y := by
@@ -282,6 +317,7 @@ theorem find?_flatMap_eq_none_iff {xs : Array α} {f : α → Array β} {p : β
 @[deprecated find?_flatMap_eq_none_iff (since := "2025-02-03")]
 abbrev find?_flatMap_eq_none := @find?_flatMap_eq_none_iff
 
+@[grind =]
 theorem find?_replicate :
     find? p (replicate n a) = if n = 0 then none else if p a then some a else none := by
   simp [← List.toArray_replicate, List.find?_replicate]
@@ -312,7 +348,7 @@ abbrev find?_mkArray_of_neg := @find?_replicate_of_neg
 -- This isn't a `@[simp]` lemma since there is already a lemma for `l.find? p = none` for any `l`.
 theorem find?_replicate_eq_none_iff {n : Nat} {a : α} {p : α → Bool} :
     (replicate n a).find? p = none ↔ n = 0 ∨ !p a := by
-  simp [← List.toArray_replicate, List.find?_replicate_eq_none_iff, Classical.or_iff_not_imp_left]
+  simp [← List.toArray_replicate, Classical.or_iff_not_imp_left]
 
 @[deprecated find?_replicate_eq_none_iff (since := "2025-03-18")]
 abbrev find?_mkArray_eq_none_iff := @find?_replicate_eq_none_iff
@@ -334,6 +370,7 @@ abbrev find?_mkArray_eq_some := @find?_replicate_eq_some_iff
 @[deprecated get_find?_replicate (since := "2025-03-18")]
 abbrev get_find?_mkArray := @get_find?_replicate
 
+@[grind =]
 theorem find?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : Array α}
     (H : ∀ (a : α), a ∈ xs → P a) {p : β → Bool} :
     (xs.pmap f H).find? p = (xs.attach.find? (fun ⟨a, m⟩ => p (f a (H a m)))).map fun ⟨a, m⟩ => f a (H a m) := by
@@ -347,12 +384,15 @@ theorem find?_eq_some_iff_getElem {xs : Array α} {p : α → Bool} {b : α} :
 
 /-! ### findIdx -/
 
+@[grind =]
 theorem findIdx_empty : findIdx p #[] = 0 := rfl
 
+@[grind =]
 theorem findIdx_singleton {a : α} {p : α → Bool} :
     #[a].findIdx p = if p a then 0 else 1 := by
   simp
 
+@[grind →]
 theorem findIdx_of_getElem?_eq_some {xs : Array α} (w : xs[xs.findIdx p]? = some y) : p y := by
   rcases xs with ⟨xs⟩
   exact List.findIdx_of_getElem?_eq_some (by simpa using w)
@@ -361,6 +401,8 @@ theorem findIdx_getElem {xs : Array α} {w : xs.findIdx p < xs.size} :
     p xs[xs.findIdx p] :=
   xs.findIdx_of_getElem?_eq_some (getElem?_eq_getElem w)
 
+grind_pattern findIdx_getElem => xs[xs.findIdx p]
+
 theorem findIdx_lt_size_of_exists {xs : Array α} (h : ∃ x ∈ xs, p x) :
     xs.findIdx p < xs.size := by
   rcases xs with ⟨xs⟩
@@ -387,18 +429,24 @@ theorem findIdx_le_size {p : α → Bool} {xs : Array α} : xs.findIdx p ≤ xs.
   · simp at e
     exact Nat.le_of_eq (findIdx_eq_size.mpr e)
 
+grind_pattern findIdx_le_size => xs.findIdx p, xs.size
+
 @[simp]
 theorem findIdx_lt_size {p : α → Bool} {xs : Array α} :
     xs.findIdx p < xs.size ↔ ∃ x ∈ xs, p x := by
   rcases xs with ⟨xs⟩
   simp
 
+grind_pattern findIdx_lt_size => xs.findIdx p, xs.size
+
 /-- `p` does not hold for elements with indices less than `xs.findIdx p`. -/
 theorem not_of_lt_findIdx {p : α → Bool} {xs : Array α} {i : Nat} (h : i < xs.findIdx p) :
     p (xs[i]'(Nat.le_trans h findIdx_le_size)) = false := by
   rcases xs with ⟨xs⟩
   simpa using List.not_of_lt_findIdx (by simpa using h)
 
+grind_pattern not_of_lt_findIdx => xs.findIdx p, xs[i]
+
 /-- If `¬ p xs[j]` for all `j < i`, then `i ≤ xs.findIdx p`. -/
 theorem le_findIdx_of_not {p : α → Bool} {xs : Array α} {i : Nat} (h : i < xs.size)
     (h2 : ∀ j (hji : j < i), p (xs[j]'(Nat.lt_trans hji h)) = false) : i ≤ xs.findIdx p := by
@@ -426,6 +474,7 @@ theorem findIdx_eq {p : α → Bool} {xs : Array α} {i : Nat} (h : i < xs.size)
   simp at h3
   simp_all [not_of_lt_findIdx h3]
 
+@[grind =]
 theorem findIdx_append {p : α → Bool} {xs ys : Array α} :
     (xs ++ ys).findIdx p =
       if xs.findIdx p < xs.size then xs.findIdx p else ys.findIdx p + xs.size := by
@@ -433,12 +482,13 @@ theorem findIdx_append {p : α → Bool} {xs ys : Array α} :
   rcases ys with ⟨ys⟩
   simp [List.findIdx_append]
 
+@[grind =]
 theorem findIdx_push {xs : Array α} {a : α} {p : α → Bool} :
     (xs.push a).findIdx p = if xs.findIdx p < xs.size then xs.findIdx p else xs.size + if p a then 0 else 1 := by
   simp only [push_eq_append, findIdx_append]
   split <;> rename_i h
   · rfl
-  · simp [findIdx_singleton, Nat.add_comm]
+  · simp [Nat.add_comm]
 
 theorem findIdx_le_findIdx {xs : Array α} {p q : α → Bool} (h : ∀ x ∈ xs, p x → q x) : xs.findIdx q ≤ xs.findIdx p := by
   rcases xs with ⟨xs⟩
@@ -455,7 +505,7 @@ theorem false_of_mem_extract_findIdx {xs : Array α} {p : α → Bool} (h : x
   rcases xs with ⟨xs⟩
   exact List.false_of_mem_take_findIdx (by simpa using h)
 
-@[simp] theorem findIdx_extract {xs : Array α} {i : Nat} {p : α → Bool} :
+@[simp, grind =] theorem findIdx_extract {xs : Array α} {i : Nat} {p : α → Bool} :
     (xs.extract 0 i).findIdx p = min i (xs.findIdx p) := by
   cases xs
   simp
@@ -467,24 +517,24 @@ theorem false_of_mem_extract_findIdx {xs : Array α} {p : α → Bool} (h : x
 
 /-! ### findIdx? -/
 
-@[simp] theorem findIdx?_empty : (#[] : Array α).findIdx? p = none := by simp
-theorem findIdx?_singleton {a : α} {p : α → Bool} :
+@[simp, grind =] theorem findIdx?_empty : (#[] : Array α).findIdx? p = none := by simp
+@[grind =] theorem findIdx?_singleton {a : α} {p : α → Bool} :
     #[a].findIdx? p = if p a then some 0 else none := by
   simp
 
-@[simp]
+@[simp, grind =]
 theorem findIdx?_eq_none_iff {xs : Array α} {p : α → Bool} :
     xs.findIdx? p = none ↔ ∀ x, x ∈ xs → p x = false := by
   rcases xs with ⟨xs⟩
   simp
 
-@[simp]
+@[simp, grind =]
 theorem findIdx?_isSome {xs : Array α} {p : α → Bool} :
     (xs.findIdx? p).isSome = xs.any p := by
   rcases xs with ⟨xs⟩
   simp [List.findIdx?_isSome]
 
-@[simp]
+@[simp, grind =]
 theorem findIdx?_isNone {xs : Array α} {p : α → Bool} :
     (xs.findIdx? p).isNone = xs.all (¬p ·) := by
   rcases xs with ⟨xs⟩
@@ -503,7 +553,7 @@ theorem findIdx?_eq_some_of_exists {xs : Array α} {p : α → Bool} (h : ∃ x,
 theorem findIdx?_eq_none_iff_findIdx_eq {xs : Array α} {p : α → Bool} :
     xs.findIdx? p = none ↔ xs.findIdx p = xs.size := by
   rcases xs with ⟨xs⟩
-  simp [List.findIdx?_eq_none_iff_findIdx_eq]
+  simp
 
 theorem findIdx?_eq_guard_findIdx_lt {xs : Array α} {p : α → Bool} :
     xs.findIdx? p = Option.guard (fun i => i < xs.size) (xs.findIdx p) := by
@@ -526,18 +576,19 @@ theorem of_findIdx?_eq_none {xs : Array α} {p : α → Bool} (w : xs.findIdx? p
   rcases xs with ⟨xs⟩
   simpa using List.of_findIdx?_eq_none (by simpa using w)
 
-@[simp] theorem findIdx?_map {f : β → α} {xs : Array β} {p : α → Bool} :
+@[simp, grind =] theorem findIdx?_map {f : β → α} {xs : Array β} {p : α → Bool} :
     findIdx? p (xs.map f) = xs.findIdx? (p ∘ f) := by
   rcases xs with ⟨xs⟩
   simp [List.findIdx?_map]
 
-@[simp] theorem findIdx?_append :
+@[simp, grind =] theorem findIdx?_append :
     (xs ++ ys : Array α).findIdx? p =
       (xs.findIdx? p).or ((ys.findIdx? p).map fun i => i + xs.size) := by
   rcases xs with ⟨xs⟩
   rcases ys with ⟨ys⟩
   simp [List.findIdx?_append]
 
+@[grind =]
 theorem findIdx?_push {xs : Array α} {a : α} {p : α → Bool} :
     (xs.push a).findIdx? p = (xs.findIdx? p).or (if p a then some xs.size else none) := by
   simp only [push_eq_append, findIdx?_append]
@@ -553,7 +604,7 @@ theorem findIdx?_flatten {xss : Array (Array α)} {p : α → Bool} :
   cases xss using array₂_induction
   simp [List.findIdx?_flatten, Function.comp_def]
 
-@[simp] theorem findIdx?_replicate :
+@[simp, grind =] theorem findIdx?_replicate :
     (replicate n a).findIdx? p = if 0 < n ∧ p a then some 0 else none := by
   rw [← List.toArray_replicate]
   simp only [List.findIdx?_toArray]
@@ -578,6 +629,7 @@ theorem findIdx?_eq_none_of_findIdx?_eq_none {xs : Array α} {p q : α → Bool}
   rcases xs with ⟨xs⟩
   simpa using List.findIdx?_eq_none_of_findIdx?_eq_none (by simpa using w)
 
+@[grind =]
 theorem findIdx_eq_getD_findIdx? {xs : Array α} {p : α → Bool} :
     xs.findIdx p = (xs.findIdx? p).getD xs.size := by
   rcases xs with ⟨xs⟩
@@ -594,15 +646,17 @@ theorem findIdx?_eq_some_le_of_findIdx?_eq_some {xs : Array α} {p q : α → Bo
   cases xs
   simp [hf]
 
-@[simp] theorem findIdx?_take {xs : Array α} {i : Nat} {p : α → Bool} :
+@[simp, grind =] theorem findIdx?_take {xs : Array α} {i : Nat} {p : α → Bool} :
     (xs.take i).findIdx? p = (xs.findIdx? p).bind (Option.guard (fun j => j < i)) := by
   cases xs
   simp
 
 /-! ### findFinIdx? -/
 
+@[grind =]
 theorem findFinIdx?_empty {p : α → Bool} : findFinIdx? p #[] = none := by simp
 
+@[grind =]
 theorem findFinIdx?_singleton {a : α} {p : α → Bool} :
     #[a].findFinIdx? p = if p a then some ⟨0, by simp⟩ else none := by
   simp
@@ -620,7 +674,7 @@ theorem findFinIdx?_eq_pmap_findIdx? {xs : Array α} {p : α → Bool} :
         (fun i h => h) := by
   simp [findIdx?_eq_map_findFinIdx?_val, Option.pmap_map]
 
-@[simp] theorem findFinIdx?_eq_none_iff {xs : Array α} {p : α → Bool} :
+@[simp, grind =] theorem findFinIdx?_eq_none_iff {xs : Array α} {p : α → Bool} :
     xs.findFinIdx? p = none ↔ ∀ x, x ∈ xs → ¬ p x := by
   simp [findFinIdx?_eq_pmap_findIdx?]
 
@@ -636,12 +690,14 @@ theorem findFinIdx?_eq_some_iff {xs : Array α} {p : α → Bool} {i : Fin xs.si
   · rintro ⟨h, w⟩
     exact ⟨i, ⟨i.2, h, fun j hji => w ⟨j, by omega⟩ hji⟩, rfl⟩
 
+@[grind =]
 theorem findFinIdx?_push {xs : Array α} {a : α} {p : α → Bool} :
     (xs.push a).findFinIdx? p =
       ((xs.findFinIdx? p).map (Fin.castLE (by simp))).or (if p a then some ⟨xs.size, by simp⟩ else none) := by
   simp only [findFinIdx?_eq_pmap_findIdx?, findIdx?_push, Option.pmap_or]
   split <;> rename_i h _ <;> split <;> simp [h]
 
+@[grind =]
 theorem findFinIdx?_append {xs ys : Array α} {p : α → Bool} :
     (xs ++ ys).findFinIdx? p =
       ((xs.findFinIdx? p).map (Fin.castLE (by simp))).or
@@ -651,17 +707,17 @@ theorem findFinIdx?_append {xs ys : Array α} {p : α → Bool} :
   · simp [h, Option.pmap_map, Option.map_pmap, Nat.add_comm]
   · simp [h]
 
-@[simp]
+@[simp, grind =]
 theorem isSome_findFinIdx? {xs : Array α} {p : α → Bool} :
     (xs.findFinIdx? p).isSome = xs.any p := by
   rcases xs with ⟨xs⟩
-  simp
+  simp [Array.size]
 
-@[simp]
+@[simp, grind =]
 theorem isNone_findFinIdx? {xs : Array α} {p : α → Bool} :
     (xs.findFinIdx? p).isNone = xs.all (fun x => ¬ p x) := by
   rcases xs with ⟨xs⟩
-  simp
+  simp [Array.size]
 
 @[simp] theorem findFinIdx?_subtype {p : α → Prop} {xs : Array { x // p x }}
     {f : { x // p x } → Bool} {g : α → Bool} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
@@ -669,7 +725,8 @@ theorem isNone_findFinIdx? {xs : Array α} {p : α → Bool} :
   cases xs
   simp only [List.findFinIdx?_toArray, hf, List.findFinIdx?_subtype]
   rw [findFinIdx?_congr List.unattach_toArray]
-  simp [Function.comp_def]
+  simp only [Option.map_map, Function.comp_def, Fin.cast_trans]
+  simp [Array.size]
 
 /-! ### idxOf
 
@@ -677,6 +734,7 @@ The verification API for `idxOf` is still incomplete.
 The lemmas below should be made consistent with those for `findIdx` (and proved using them).
 -/
 
+@[grind =]
 theorem idxOf_append [BEq α] [LawfulBEq α] {xs ys : Array α} {a : α} :
     (xs ++ ys).idxOf a = if a ∈ xs then xs.idxOf a else ys.idxOf a + xs.size := by
   rw [idxOf, findIdx_append]
@@ -690,10 +748,23 @@ theorem idxOf_eq_size [BEq α] [LawfulBEq α] {xs : Array α} (h : a ∉ xs) : x
   rcases xs with ⟨xs⟩
   simp [List.idxOf_eq_length (by simpa using h)]
 
-theorem idxOf_lt_length [BEq α] [LawfulBEq α] {xs : Array α} (h : a ∈ xs) : xs.idxOf a < xs.size := by
+theorem idxOf_lt_length_of_mem [BEq α] [LawfulBEq α] {xs : Array α} (h : a ∈ xs) : xs.idxOf a < xs.size := by
   rcases xs with ⟨xs⟩
-  simp [List.idxOf_lt_length (by simpa using h)]
+  simp [List.idxOf_lt_length_of_mem (by simpa using h)]
 
+theorem idxOf_le_size [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
+    xs.idxOf a ≤ xs.size := by
+  rcases xs with ⟨xs⟩
+  simp [List.idxOf_le_length]
+
+grind_pattern idxOf_le_size => xs.idxOf a, xs.size
+
+theorem idxOf_lt_size_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
+    xs.idxOf a < xs.size ↔ a ∈ xs := by
+  rcases xs with ⟨xs⟩
+  simp [List.idxOf_lt_length_iff]
+
+grind_pattern idxOf_lt_size_iff => xs.idxOf a, xs.size
 
 /-! ### idxOf?
 
@@ -701,19 +772,20 @@ The verification API for `idxOf?` is still incomplete.
 The lemmas below should be made consistent with those for `findIdx?` (and proved using them).
 -/
 
-theorem idxOf?_empty [BEq α] : (#[] : Array α).idxOf? a = none := by simp
+@[grind =] theorem idxOf?_empty [BEq α] : (#[] : Array α).idxOf? a = none := by simp
 
-@[simp] theorem idxOf?_eq_none_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
+@[simp, grind =] theorem idxOf?_eq_none_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
     xs.idxOf? a = none ↔ a ∉ xs := by
   rcases xs with ⟨xs⟩
   simp [List.idxOf?_eq_none_iff]
 
-@[simp]
+@[simp, grind =]
 theorem isSome_idxOf? [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
     (xs.idxOf? a).isSome ↔ a ∈ xs := by
   rcases xs with ⟨xs⟩
   simp
 
+@[grind =]
 theorem isNone_idxOf? [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
     (xs.idxOf? a).isNone = ¬ a ∈ xs := by
   simp
@@ -726,28 +798,31 @@ The lemmas below should be made consistent with those for `findFinIdx?` (and pro
 
 theorem idxOf?_eq_map_finIdxOf?_val [BEq α] {xs : Array α} {a : α} :
     xs.idxOf? a = (xs.finIdxOf? a).map (·.val) := by
-  simp [idxOf?, finIdxOf?, findIdx?_eq_map_findFinIdx?_val]
+  simp [idxOf?, finIdxOf?]
 
-theorem finIdxOf?_empty [BEq α] : (#[] : Array α).finIdxOf? a = none := by simp
+@[grind =] theorem finIdxOf?_empty [BEq α] : (#[] : Array α).finIdxOf? a = none := by simp
 
-@[simp] theorem finIdxOf?_eq_none_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
+@[simp, grind =] theorem finIdxOf?_eq_none_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
     xs.finIdxOf? a = none ↔ a ∉ xs := by
   rcases xs with ⟨xs⟩
-  simp [List.finIdxOf?_eq_none_iff]
+  simp [List.finIdxOf?_eq_none_iff, Array.size]
 
 @[simp] theorem finIdxOf?_eq_some_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} {i : Fin xs.size} :
     xs.finIdxOf? a = some i ↔ xs[i] = a ∧ ∀ j (_ : j < i), ¬xs[j] = a := by
   rcases xs with ⟨xs⟩
+  unfold Array.size at i ⊢
   simp [List.finIdxOf?_eq_some_iff]
 
-@[simp]
-theorem isSome_finIdxOf? [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
-    (xs.finIdxOf? a).isSome ↔ a ∈ xs := by
+@[simp, grind =]
+theorem isSome_finIdxOf? [BEq α] [PartialEquivBEq α] {xs : Array α} {a : α} :
+    (xs.finIdxOf? a).isSome = xs.contains a := by
   rcases xs with ⟨xs⟩
-  simp
+  simp [Array.size]
 
-theorem isNone_finIdxOf? [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
-    (xs.finIdxOf? a).isNone = ¬ a ∈ xs := by
-  simp
+@[simp, grind =]
+theorem isNone_finIdxOf? [BEq α] [PartialEquivBEq α] {xs : Array α} {a : α} :
+    (xs.finIdxOf? a).isNone = !xs.contains a := by
+  rcases xs with ⟨xs⟩
+  simp [Array.size]
 
 end Array

src/Init/Data/Array/InsertIdx.lean

@@ -44,13 +44,19 @@ theorem insertIdx_zero {xs : Array α} {x : α} : xs.insertIdx 0 x = #[x] ++ xs
 
 @[simp] theorem size_insertIdx {xs : Array α} (h : i ≤ xs.size) : (xs.insertIdx i a).size = xs.size + 1 := by
   rcases xs with ⟨xs⟩
+  simp at h
   simp [List.length_insertIdx, h]
 
-theorem eraseIdx_insertIdx {i : Nat} {xs : Array α} (h : i ≤ xs.size) :
+theorem eraseIdx_insertIdx_self {i : Nat} {xs : Array α} (h : i ≤ xs.size) :
     (xs.insertIdx i a).eraseIdx i (by simp; omega) = xs := by
   rcases xs with ⟨xs⟩
   simp_all
 
+@[deprecated eraseIdx_insertIdx_self (since := "2025-06-15")]
+theorem eraseIdx_insertIdx {i : Nat} {xs : Array α} (h : i ≤ xs.size) :
+    (xs.insertIdx i a).eraseIdx i (by simp; omega) = xs := by
+  simp [eraseIdx_insertIdx_self]
+
 theorem insertIdx_eraseIdx_of_ge {as : Array α}
     (w₁ : i < as.size) (w₂ : j ≤ (as.eraseIdx i).size) (h : i ≤ j) :
     (as.eraseIdx i).insertIdx j a =
@@ -65,6 +71,18 @@ theorem insertIdx_eraseIdx_of_le {as : Array α}
   cases as
   simpa using List.insertIdx_eraseIdx_of_le (by simpa) (by simpa)
 
+@[grind =]
+theorem insertIdx_eraseIdx {as : Array α} (h₁ : i < as.size) (h₂ : j ≤ (as.eraseIdx i).size) :
+    (as.eraseIdx i).insertIdx j a =
+      if h : i ≤ j then
+        (as.insertIdx (j + 1) a (by simp_all; omega)).eraseIdx i (by simp_all; omega)
+      else
+        (as.insertIdx j a).eraseIdx (i + 1) (by simp_all) := by
+  split <;> rename_i h'
+  · rw [insertIdx_eraseIdx_of_ge] <;> omega
+  · rw [insertIdx_eraseIdx_of_le] <;> omega
+
+@[grind =]
 theorem insertIdx_comm (a b : α) {i j : Nat} {xs : Array α} (_ : i ≤ j) (_ : j ≤ xs.size) :
     (xs.insertIdx i a).insertIdx (j + 1) b (by simpa) =
       (xs.insertIdx j b).insertIdx i a (by simp; omega) := by
@@ -80,6 +98,7 @@ theorem insertIdx_size_self {xs : Array α} {x : α} : xs.insertIdx xs.size x =
   rcases xs with ⟨xs⟩
   simp
 
+@[grind =]
 theorem getElem_insertIdx {xs : Array α} {x : α} {i k : Nat} (w : i ≤ xs.size) (h : k < (xs.insertIdx i x).size) :
     (xs.insertIdx i x)[k] =
       if h₁ : k < i then
@@ -90,21 +109,22 @@ theorem getElem_insertIdx {xs : Array α} {x : α} {i k : Nat} (w : i ≤ xs.siz
         else
           xs[k-1]'(by simp [size_insertIdx] at h; omega) := by
   cases xs
-  simp [List.getElem_insertIdx, w]
+  simp [List.getElem_insertIdx]
 
 theorem getElem_insertIdx_of_lt {xs : Array α} {x : α} {i k : Nat} (w : i ≤ xs.size) (h : k < i) :
     (xs.insertIdx i x)[k]'(by simp; omega) = xs[k] := by
-  simp [getElem_insertIdx, w, h]
+  simp [getElem_insertIdx, h]
 
 theorem getElem_insertIdx_self {xs : Array α} {x : α} {i : Nat} (w : i ≤ xs.size) :
     (xs.insertIdx i x)[i]'(by simp; omega) = x := by
-  simp [getElem_insertIdx, w]
+  simp [getElem_insertIdx]
 
 theorem getElem_insertIdx_of_gt {xs : Array α} {x : α} {i k : Nat} (w : k ≤ xs.size) (h : k > i) :
     (xs.insertIdx i x)[k]'(by simp; omega) = xs[k - 1]'(by omega) := by
-  simp [getElem_insertIdx, w, h]
+  simp [getElem_insertIdx]
   rw [dif_neg (by omega), dif_neg (by omega)]
 
+@[grind =]
 theorem getElem?_insertIdx {xs : Array α} {x : α} {i k : Nat} (h : i ≤ xs.size) :
     (xs.insertIdx i x)[k]? =
       if k < i then
@@ -115,7 +135,7 @@ theorem getElem?_insertIdx {xs : Array α} {x : α} {i k : Nat} (h : i ≤ xs.si
         else
           xs[k-1]? := by
   cases xs
-  simp [List.getElem?_insertIdx, h]
+  simp [List.getElem?_insertIdx]
 
 theorem getElem?_insertIdx_of_lt {xs : Array α} {x : α} {i k : Nat} (w : i ≤ xs.size) (h : k < i) :
     (xs.insertIdx i x)[k]? = xs[k]? := by

src/Init/Data/Array/Lemmas.lean

@@ -75,7 +75,7 @@ theorem ne_empty_of_size_pos (h : 0 < xs.size) : xs ≠ #[] := by
   cases xs
   simpa using List.ne_nil_of_length_pos h
 
-theorem size_eq_zero_iff : xs.size = 0 ↔ xs = #[] :=
+@[simp] theorem size_eq_zero_iff : xs.size = 0 ↔ xs = #[] :=
   ⟨eq_empty_of_size_eq_zero, fun h => h ▸ rfl⟩
 
 @[deprecated size_eq_zero_iff (since := "2025-02-24")]
@@ -89,6 +89,8 @@ theorem size_pos_of_mem {a : α} {xs : Array α} (h : a ∈ xs) : 0 < xs.size :=
   simp only [mem_toArray] at h
   simpa using List.length_pos_of_mem h
 
+grind_pattern size_pos_of_mem => a ∈ xs, xs.size
+
 theorem exists_mem_of_size_pos {xs : Array α} (h : 0 < xs.size) : ∃ a, a ∈ xs := by
   cases xs
   simpa using List.exists_mem_of_length_pos h
@@ -123,7 +125,7 @@ theorem none_eq_getElem?_iff {xs : Array α} {i : Nat} : none = xs[i]? ↔ xs.si
   simp
 
 theorem getElem?_eq_none {xs : Array α} (h : xs.size ≤ i) : xs[i]? = none := by
-  simp [getElem?_eq_none_iff, h]
+  simp [h]
 
 grind_pattern Array.getElem?_eq_none => xs.size ≤ i, xs[i]?
 
@@ -133,7 +135,6 @@ grind_pattern Array.getElem?_eq_none => xs.size ≤ i, xs[i]?
 theorem getElem?_eq_some_iff {xs : Array α} : xs[i]? = some b ↔ ∃ h : i < xs.size, xs[i] = b :=
   _root_.getElem?_eq_some_iff
 
-@[grind →]
 theorem getElem_of_getElem? {xs : Array α} : xs[i]? = some a → ∃ h : i < xs.size, xs[i] = a :=
   getElem?_eq_some_iff.mp
 
@@ -153,34 +154,35 @@ theorem getElem_eq_iff {xs : Array α} {i : Nat} {h : i < xs.size} : xs[i] = x
   exact ⟨fun w => ⟨h, w⟩, fun h => h.2⟩
 
 theorem getElem_eq_getElem?_get {xs : Array α} {i : Nat} (h : i < xs.size) :
-    xs[i] = xs[i]?.get (by simp [getElem?_eq_getElem, h]) := by
-  simp [getElem_eq_iff]
+    xs[i] = xs[i]?.get (by simp [h]) := by
+  simp
 
 theorem getD_getElem? {xs : Array α} {i : Nat} {d : α} :
     xs[i]?.getD d = if p : i < xs.size then xs[i]'p else d := by
   if h : i < xs.size then
-    simp [h, getElem?_def]
+    simp [h]
   else
     have p : i ≥ xs.size := Nat.le_of_not_gt h
-    simp [getElem?_eq_none p, h]
+    simp [h]
 
 @[simp] theorem getElem?_empty {i : Nat} : (#[] : Array α)[i]? = none := rfl
 
 theorem getElem_push_lt {xs : Array α} {x : α} {i : Nat} (h : i < xs.size) :
     have : i < (xs.push x).size := by simp [*, Nat.lt_succ_of_le, Nat.le_of_lt]
     (xs.push x)[i] = xs[i] := by
+  rw [Array.size] at h
   simp only [push, ← getElem_toList, List.concat_eq_append, List.getElem_append_left, h]
 
 @[simp] theorem getElem_push_eq {xs : Array α} {x : α} : (xs.push x)[xs.size] = x := by
   simp only [push, ← getElem_toList, List.concat_eq_append]
-  rw [List.getElem_append_right] <;> simp [← getElem_toList, Nat.zero_lt_one]
+  rw [List.getElem_append_right] <;> simp
 
-theorem getElem_push {xs : Array α} {x : α} {i : Nat} (h : i < (xs.push x).size) :
+@[grind =] theorem getElem_push {xs : Array α} {x : α} {i : Nat} (h : i < (xs.push x).size) :
     (xs.push x)[i] = if h : i < xs.size then xs[i] else x := by
   by_cases h' : i < xs.size
   · simp [getElem_push_lt, h']
   · simp at h
-    simp [getElem_push_lt, Nat.le_antisymm (Nat.le_of_lt_succ h) (Nat.ge_of_not_lt h')]
+    simp [Nat.le_antisymm (Nat.le_of_lt_succ h) (Nat.ge_of_not_lt h')]
 
 @[grind =] theorem getElem?_push {xs : Array α} {x} : (xs.push x)[i]? = if i = xs.size then some x else xs[i]? := by
   simp [getElem?_def, getElem_push]
@@ -762,6 +764,7 @@ theorem all_eq_false' {p : α → Bool} {as : Array α} :
   rw [Bool.eq_false_iff, Ne, all_eq_true']
   simp
 
+@[grind =]
 theorem any_eq {xs : Array α} {p : α → Bool} : xs.any p = decide (∃ i : Nat, ∃ h, p (xs[i]'h)) := by
   by_cases h : xs.any p
   · simp_all [any_eq_true]
@@ -776,6 +779,7 @@ theorem any_eq' {xs : Array α} {p : α → Bool} : xs.any p = decide (∃ x, x
     simp only [any_eq_false'] at h
     simpa using h
 
+@[grind =]
 theorem all_eq {xs : Array α} {p : α → Bool} : xs.all p = decide (∀ i, (_ : i < xs.size) → p xs[i]) := by
   by_cases h : xs.all p
   · simp_all [all_eq_true]
@@ -902,7 +906,7 @@ theorem all_push [BEq α] {xs : Array α} {a : α} {p : α → Bool} :
 abbrev getElem_set_eq := @getElem_set_self
 
 @[simp] theorem getElem?_set_self {xs : Array α} {i : Nat} (h : i < xs.size) {v : α} :
-    (xs.set i v)[i]? = some v := by simp [getElem?_eq_getElem, h]
+    (xs.set i v)[i]? = some v := by simp [h]
 
 @[deprecated getElem?_set_self (since := "2024-12-11")]
 abbrev getElem?_set_eq := @getElem?_set_self
@@ -914,7 +918,7 @@ abbrev getElem?_set_eq := @getElem?_set_self
 
 @[simp] theorem getElem?_set_ne {xs : Array α} {i : Nat} (h : i < xs.size) {v : α} {j : Nat}
     (ne : i ≠ j) : (xs.set i v)[j]? = xs[j]? := by
-  by_cases h : j < xs.size <;> simp [getElem?_eq_getElem, getElem?_eq_none, Nat.ge_of_not_lt, ne, h]
+  by_cases h : j < xs.size <;> simp [ne, h]
 
 @[grind] theorem getElem_set {xs : Array α} {i : Nat} (h' : i < xs.size) {v : α} {j : Nat}
     (h : j < (xs.set i v).size) :
@@ -951,6 +955,13 @@ theorem set_push {xs : Array α} {x y : α} {h} :
         · simp at h
           omega
 
+@[grind _=_]
+theorem set_pop {xs : Array α} {x : α} {i : Nat} (h : i < xs.pop.size) :
+    xs.pop.set i x h = (xs.set i x (by simp at h; omega)).pop := by
+  ext i h₁ h₂
+  · simp
+  · simp [getElem_set]
+
 @[simp] theorem set_eq_empty_iff {xs : Array α} {i : Nat} {a : α} {h : i < xs.size} :
     xs.set i a = #[] ↔ xs = #[] := by
   cases xs <;> cases i <;> simp [set]
@@ -983,7 +994,11 @@ theorem mem_or_eq_of_mem_set
 @[simp, grind] theorem setIfInBounds_empty {i : Nat} {a : α} :
     #[].setIfInBounds i a = #[] := rfl
 
-@[simp] theorem set!_eq_setIfInBounds : @set! = @setIfInBounds := rfl
+@[simp, grind =] theorem set!_eq_setIfInBounds : set! xs i v = setIfInBounds xs i v := rfl
+
+@[grind]
+theorem setIfInBounds_def (xs : Array α) (i : Nat) (a : α) :
+    xs.setIfInBounds i a = if h : i < xs.size then xs.set i a else xs := rfl
 
 @[deprecated set!_eq_setIfInBounds (since := "2024-12-12")]
 abbrev set!_is_setIfInBounds := @set!_eq_setIfInBounds
@@ -1029,7 +1044,7 @@ theorem getElem?_setIfInBounds_self {xs : Array α} {i : Nat} {a : α} :
 @[simp]
 theorem getElem?_setIfInBounds_self_of_lt {xs : Array α} {i : Nat} {a : α} (h : i < xs.size) :
     (xs.setIfInBounds i a)[i]? = some a := by
-  simp [getElem?_setIfInBounds, h]
+  simp [h]
 
 @[deprecated getElem?_setIfInBounds_self (since := "2024-12-11")]
 abbrev getElem?_setIfInBounds_eq := @getElem?_setIfInBounds_self
@@ -1073,9 +1088,9 @@ theorem mem_or_eq_of_mem_setIfInBounds
 @[simp] theorem getD_getElem?_setIfInBounds {xs : Array α} {i : Nat} {v d : α} :
     (xs.setIfInBounds i v)[i]?.getD d = if i < xs.size then v else d := by
   by_cases h : i < xs.size <;>
-    simp [setIfInBounds, Nat.not_lt_of_le, h,  getD_getElem?]
+    simp [setIfInBounds, h,  ]
 
-@[simp] theorem toList_setIfInBounds {xs : Array α} {i : Nat} {x : α} :
+@[simp, grind =] theorem toList_setIfInBounds {xs : Array α} {i : Nat} {x : α} :
     (xs.setIfInBounds i x).toList = xs.toList.set i x := by
   simp only [setIfInBounds]
   split <;> rename_i h
@@ -1185,7 +1200,7 @@ where
       mapM.map f xs i bs = (xs.toList.drop i).foldlM (fun bs a => bs.push <$> f a) bs := by
     unfold mapM.map; split
     · rw [← List.getElem_cons_drop_succ_eq_drop ‹_›]
-      simp only [aux (i + 1), map_eq_pure_bind, length_toList, List.foldlM_cons, bind_assoc,
+      simp only [aux (i + 1), map_eq_pure_bind, List.foldlM_cons, bind_assoc,
         pure_bind]
       rfl
     · rw [List.drop_of_length_le (Nat.ge_of_not_lt ‹_›)]; rfl
@@ -1257,7 +1272,8 @@ theorem map_singleton {f : α → β} {a : α} : map f #[a] = #[f a] := by simp
 
 -- We use a lower priority here as there are more specific lemmas in downstream libraries
 -- which should be able to fire first.
-@[simp 500] theorem mem_map {f : α → β} {xs : Array α} : b ∈ xs.map f ↔ ∃ a, a ∈ xs ∧ f a = b := by
+@[simp 500, grind =] theorem mem_map {f : α → β} {xs : Array α} :
+    b ∈ xs.map f ↔ ∃ a, a ∈ xs ∧ f a = b := by
   simp only [mem_def, toList_map, List.mem_map]
 
 theorem exists_of_mem_map (h : b ∈ map f l) : ∃ a, a ∈ l ∧ f a = b := mem_map.1 h
@@ -1484,6 +1500,19 @@ theorem forall_mem_filter {p : α → Bool} {xs : Array α} {P : α → Prop} :
     (∀ (i) (_ : i ∈ xs.filter p), P i) ↔ ∀ (j) (_ : j ∈ xs), p j → P j := by
   simp
 
+@[grind] theorem getElem_filter {xs : Array α} {p : α → Bool} {i : Nat} (h : i < (xs.filter p).size) :
+    p (xs.filter p)[i] :=
+  (mem_filter.mp (getElem_mem h)).2
+
+theorem getElem?_filter {xs : Array α} {p : α → Bool} {i : Nat} (h : i < (xs.filter p).size)
+    (w : (xs.filter p)[i]? = some a) : p a := by
+  rw [getElem?_eq_getElem] at w
+  simp only [Option.some.injEq] at w
+  rw [← w]
+  apply getElem_filter h
+
+grind_pattern getElem?_filter => (xs.filter p)[i]?, some a
+
 @[simp] theorem filter_filter {p q : α → Bool} {xs : Array α} :
     filter p (filter q xs) = filter (fun a => p a && q a) xs := by
   apply ext'
@@ -1726,7 +1755,7 @@ theorem forall_mem_filterMap {f : α → Option β} {xs : Array α} {P : β →
 
 theorem map_filterMap_of_inv {f : α → Option β} {g : β → α} (H : ∀ x : α, (f x).map g = some x) {xs : Array α} :
     map g (filterMap f xs) = xs := by
-  simp only [map_filterMap, H, filterMap_some, id]
+  simp only [map_filterMap, H, filterMap_some]
 
 @[grind →]
 theorem forall_none_of_filterMap_eq_empty (h : filterMap f xs = #[]) : ∀ x ∈ xs, f x = none := by
@@ -1858,14 +1887,14 @@ theorem getElem_append_right {xs ys : Array α} {h : i < (xs ++ ys).size} (hle :
     (xs ++ ys)[i] = ys[i - xs.size]'(Nat.sub_lt_left_of_lt_add hle (size_append .. ▸ h)) := by
   simp only [← getElem_toList]
   have h' : i < (xs.toList ++ ys.toList).length := by rwa [← length_toList, toList_append] at h
-  conv => rhs; rw [← List.getElem_append_right (h₁ := hle) (h₂ := h')]
+  conv => rhs; unfold Array.size; rw [← List.getElem_append_right (h₁ := hle) (h₂ := h')]
   apply List.get_of_eq; rw [toList_append]
 
 theorem getElem?_append_left {xs ys : Array α} {i : Nat} (hn : i < xs.size) :
     (xs ++ ys)[i]? = xs[i]? := by
   have hn' : i < (xs ++ ys).size := Nat.lt_of_lt_of_le hn <|
     size_append .. ▸ Nat.le_add_right ..
-  simp_all [getElem?_eq_getElem, getElem_append]
+  simp_all
 
 theorem getElem?_append_right {xs ys : Array α} {i : Nat} (h : xs.size ≤ i) :
     (xs ++ ys)[i]? = ys[i - xs.size]? := by
@@ -1996,7 +2025,7 @@ theorem append_eq_singleton_iff {xs ys : Array α} {x : α} :
     xs ++ ys = #[x] ↔ (xs = #[] ∧ ys = #[x]) ∨ (xs = #[x] ∧ ys = #[]) := by
   rcases xs with ⟨xs⟩
   rcases ys with ⟨ys⟩
-  simp only [List.append_toArray, mk.injEq, List.append_eq_singleton_iff, toArray_eq_append_iff]
+  simp only [List.append_toArray, mk.injEq, List.append_eq_singleton_iff]
 
 theorem singleton_eq_append_iff {xs ys : Array α} {x : α} :
     #[x] = xs ++ ys ↔ (xs = #[] ∧ ys = #[x]) ∨ (xs = #[x] ∧ ys = #[]) := by
@@ -2025,7 +2054,7 @@ theorem append_eq_append_iff {ws xs ys zs : Array α} :
         xs ++ ys.set (i - xs.size) x (by simp at h; omega) := by
   rcases xs with ⟨s⟩
   rcases ys with ⟨t⟩
-  simp only [List.append_toArray, List.set_toArray, List.set_append]
+  simp only [List.append_toArray, List.set_toArray, List.set_append, Array.size]
   split <;> simp
 
 @[simp] theorem set_append_left {xs ys : Array α} {i : Nat} {x : α} (h : i < xs.size)  :
@@ -2045,7 +2074,7 @@ theorem append_eq_append_iff {ws xs ys zs : Array α} :
         xs ++ ys.setIfInBounds (i - xs.size) x := by
   rcases xs with ⟨s⟩
   rcases ys with ⟨t⟩
-  simp only [List.append_toArray, List.setIfInBounds_toArray, List.set_append]
+  simp only [List.append_toArray, List.setIfInBounds_toArray, List.set_append, Array.size]
   split <;> simp
 
 @[simp] theorem setIfInBounds_append_left {xs ys : Array α} {i : Nat} {x : α} (h : i < xs.size) :
@@ -2322,7 +2351,7 @@ theorem flatMap_toArray {β} {f : α → Array β} {as : List α} :
 theorem size_flatMap {xs : Array α} {f : α → Array β} :
     (xs.flatMap f).size = sum (map (fun a => (f a).size) xs) := by
   rcases xs with ⟨l⟩
-  simp [Function.comp_def]
+  simp
 
 @[simp, grind] theorem mem_flatMap {f : α → Array β} {b} {xs : Array α} : b ∈ xs.flatMap f ↔ ∃ a, a ∈ xs ∧ b ∈ f a := by
   simp [flatMap_def, mem_flatten]
@@ -2540,7 +2569,7 @@ abbrev map_mkArray := @map_replicate
 @[grind] theorem filter_replicate (w : stop = n) :
     (replicate n a).filter p 0 stop = if p a then replicate n a else #[] := by
   apply Array.ext'
-  simp only [w, toList_filter', toList_replicate, List.filter_replicate]
+  simp only [w]
   split <;> simp_all
 
 @[deprecated filter_replicate (since := "2025-03-18")]
@@ -2580,7 +2609,7 @@ abbrev filterMap_mkArray_of_some := @filterMap_replicate_of_some
 @[simp] theorem filterMap_replicate_of_isSome {f : α → Option β} (h : (f a).isSome) :
     (replicate n a).filterMap f = replicate n (Option.get _ h) := by
   match w : f a, h with
-  | some b, _ => simp [filterMap_replicate, h, w]
+  | some b, _ => simp [filterMap_replicate, w]
 
 @[deprecated filterMap_replicate_of_isSome (since := "2025-03-18")]
 abbrev filterMap_mkArray_of_isSome := @filterMap_replicate_of_isSome
@@ -2615,7 +2644,7 @@ abbrev flatten_mkArray_replicate := @flatten_replicate_replicate
 
 theorem flatMap_replicate {f : α → Array β} : (replicate n a).flatMap f = (replicate n (f a)).flatten := by
   rw [← toList_inj]
-  simp [flatMap_toList, List.flatMap_replicate]
+  simp [List.flatMap_replicate]
 
 @[deprecated flatMap_replicate (since := "2025-03-18")]
 abbrev flatMap_mkArray := @flatMap_replicate
@@ -2993,6 +3022,10 @@ theorem extract_empty_of_size_le_start {xs : Array α} {start stop : Nat} (h : x
   apply ext'
   simp
 
+theorem _root_.List.toArray_drop {l : List α} {k : Nat} :
+    (l.drop k).toArray = l.toArray.extract k := by
+  rw [List.drop_eq_extract, List.extract_toArray, List.size_toArray]
+
 @[deprecated extract_size (since := "2025-02-27")]
 theorem take_size {xs : Array α} : xs.take xs.size = xs := by
   cases xs
@@ -3603,8 +3636,8 @@ We can prove that two folds over the same array are related (by some arbitrary r
 if we know that the initial elements are related and the folding function, for each element of the array,
 preserves the relation.
 -/
-theorem foldl_rel {xs : Array α} {f g : β → α → β} {a b : β} {r : β → β → Prop}
-    (h : r a b) (h' : ∀ (a : α), a ∈ xs → ∀ (c c' : β), r c c' → r (f c a) (g c' a)) :
+theorem foldl_rel {xs : Array α} {f : β → α → β} {g : γ → α → γ} {a : β} {b : γ} {r : β → γ → Prop}
+    (h : r a b) (h' : ∀ (a : α), a ∈ xs → ∀ (c : β) (c' : γ), r c c' → r (f c a) (g c' a)) :
     r (xs.foldl (fun acc a => f acc a) a) (xs.foldl (fun acc a => g acc a) b) := by
   rcases xs with ⟨xs⟩
   simpa using List.foldl_rel h (by simpa using h')
@@ -3614,8 +3647,8 @@ We can prove that two folds over the same array are related (by some arbitrary r
 if we know that the initial elements are related and the folding function, for each element of the array,
 preserves the relation.
 -/
-theorem foldr_rel {xs : Array α} {f g : α → β → β} {a b : β} {r : β → β → Prop}
-    (h : r a b) (h' : ∀ (a : α), a ∈ xs → ∀ (c c' : β), r c c' → r (f a c) (g a c')) :
+theorem foldr_rel {xs : Array α} {f : α → β → β} {g : α → γ → γ} {a : β} {b : γ} {r : β → γ → Prop}
+    (h : r a b) (h' : ∀ (a : α), a ∈ xs → ∀ (c : β) (c' : γ), r c c' → r (f a c) (g a c')) :
     r (xs.foldr (fun a acc => f a acc) a) (xs.foldr (fun a acc => g a acc) b) := by
   rcases xs with ⟨xs⟩
   simpa using List.foldr_rel h (by simpa using h')
@@ -3730,7 +3763,7 @@ theorem back?_replicate {a : α} {n : Nat} :
 @[deprecated back?_replicate (since := "2025-03-18")]
 abbrev back?_mkArray := @back?_replicate
 
-@[simp] theorem back_replicate (w : 0 < n) : (replicate n a).back (by simpa using w) = a := by
+@[simp] theorem back_replicate {xs : Array α} (w : 0 < n) : (replicate n xs).back (by simpa using w) = xs := by
   simp [back_eq_getElem]
 
 @[deprecated back_replicate (since := "2025-03-18")]
@@ -4073,11 +4106,11 @@ abbrev all_mkArray := @all_replicate
 
 /-! ### modify -/
 
-@[simp] theorem size_modify {xs : Array α} {i : Nat} {f : α → α} : (xs.modify i f).size = xs.size := by
+@[simp, grind =] theorem size_modify {xs : Array α} {i : Nat} {f : α → α} : (xs.modify i f).size = xs.size := by
   unfold modify modifyM
   split <;> simp
 
-theorem getElem_modify {xs : Array α} {j i} (h : i < (xs.modify j f).size) :
+@[grind =] theorem getElem_modify {xs : Array α} {j i} (h : i < (xs.modify j f).size) :
     (xs.modify j f)[i] = if j = i then f (xs[i]'(by simpa using h)) else xs[i]'(by simpa using h) := by
   simp only [modify, modifyM]
   split
@@ -4085,7 +4118,7 @@ theorem getElem_modify {xs : Array α} {j i} (h : i < (xs.modify j f).size) :
   · simp only [Id.run_pure]
     rw [if_neg (mt (by rintro rfl; exact h) (by simp_all))]
 
-@[simp] theorem toList_modify {xs : Array α} {f : α → α} {i : Nat} :
+@[simp, grind =] theorem toList_modify {xs : Array α} {f : α → α} {i : Nat} :
     (xs.modify i f).toList = xs.toList.modify i f := by
   apply List.ext_getElem
   · simp
@@ -4100,7 +4133,7 @@ theorem getElem_modify_of_ne {xs : Array α} {i : Nat} (h : i ≠ j)
     (xs.modify i f)[j] = xs[j]'(by simpa using hj) := by
   simp [getElem_modify hj, h]
 
-theorem getElem?_modify {xs : Array α} {i : Nat} {f : α → α} {j : Nat} :
+@[grind =] theorem getElem?_modify {xs : Array α} {i : Nat} {f : α → α} {j : Nat} :
     (xs.modify i f)[j]? = if i = j then xs[j]?.map f else xs[j]? := by
   simp only [getElem?_def, size_modify, getElem_modify, Option.map_dif]
   split <;> split <;> rfl
@@ -4109,7 +4142,7 @@ theorem getElem?_modify {xs : Array α} {i : Nat} {f : α → α} {j : Nat} :
 
 @[simp] theorem getElem_swap_right {xs : Array α} {i j : Nat} {hi hj} :
     (xs.swap i j hi hj)[j]'(by simpa using hj) = xs[i] := by
-  simp [swap_def, getElem_set]
+  simp [swap_def]
 
 @[simp] theorem getElem_swap_left {xs : Array α} {i j : Nat} {hi hj} :
     (xs.swap i j hi hj)[i]'(by simpa using hi) = xs[j] := by
@@ -4149,20 +4182,18 @@ theorem swap_comm {xs : Array α} {i j : Nat} (hi hj) : xs.swap i j hi hj = xs.s
     · split <;> simp_all
     · split <;> simp_all
 
-@[simp] theorem size_swapIfInBounds {xs : Array α} {i j : Nat} :
+@[simp, grind =] theorem size_swapIfInBounds {xs : Array α} {i j : Nat} :
     (xs.swapIfInBounds i j).size = xs.size := by unfold swapIfInBounds; split <;> (try split) <;> simp [size_swap]
 
-@[deprecated size_swapIfInBounds (since := "2024-11-24")] abbrev size_swap! := @size_swapIfInBounds
-
 /-! ### swapAt -/
 
-@[simp] theorem swapAt_def {xs : Array α} {i : Nat} {v : α} (hi) :
+@[simp, grind =] theorem swapAt_def {xs : Array α} {i : Nat} {v : α} (hi) :
     xs.swapAt i v hi = (xs[i], xs.set i v) := rfl
 
 theorem size_swapAt {xs : Array α} {i : Nat} {v : α} (hi) :
     (xs.swapAt i v hi).2.size = xs.size := by simp
 
-@[simp]
+@[simp, grind =]
 theorem swapAt!_def {xs : Array α} {i : Nat} {v : α} (h : i < xs.size) :
     xs.swapAt! i v = (xs[i], xs.set i v) := by simp [swapAt!, h]
 
@@ -4285,42 +4316,44 @@ Examples:
 
 /-! ### Preliminaries about `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, 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_go {n} {f : Fin n → α} {i acc h} :
+    (ofFn.go f acc i h).size = acc.size + i := by
+  induction i generalizing acc with
+  | zero => simp [ofFn.go]
+  | succ i ih =>
+    simpa [ofFn.go, ih] using Nat.succ_add_eq_add_succ acc.size i
 
 @[simp] theorem size_ofFn {n : Nat} {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 _ 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 [getElem_push, hj, hacc j hj]
-    | inr hj => simp [getElem_push, *]
-  else
-    simp [hin, hacc k (Nat.lt_of_lt_of_le hki (Nat.le_of_not_lt (hi ▸ hin)))]
-termination_by n - i
+-- Recall `ofFn.go f acc i h = acc ++ #[f (n - i), ..., f(n - 1)]`
+theorem getElem_ofFn_go {f : Fin n → α} {acc i k} (h : i ≤ n) (w₁ : k < acc.size + i) :
+    (ofFn.go f acc i h)[k]'(by simpa using w₁) =
+      if w₂ : k < acc.size then acc[k] else f ⟨n - i + k - acc.size, by omega⟩ := by
+  induction i generalizing acc k with
+  | zero =>
+    simp at w₁
+    simp_all [ofFn.go]
+  | succ i ih =>
+    unfold ofFn.go
+    rw [ih]
+    · simp only [size_push]
+      split <;> rename_i h'
+      · rw [Array.getElem_push]
+        split
+        · rfl
+        · congr 2
+          omega
+      · split
+        · omega
+        · congr 2
+          omega
+    · simp
+      omega
 
 @[simp] theorem getElem_ofFn {f : Fin n → α} {i : Nat} (h : i < (ofFn f).size) :
-    (ofFn f)[i] = f ⟨i, size_ofFn (f := f) ▸ h⟩ :=
-  getElem_ofFn_go _ (by simp) (by simp) nofun
+    (ofFn f)[i] = f ⟨i, size_ofFn (f := f) ▸ h⟩ := by
+  unfold ofFn
+  rw [getElem_ofFn_go] <;> simp_all
 
 theorem getElem?_ofFn {f : Fin n → α} {i : Nat} :
     (ofFn f)[i]? = if h : i < n then some (f ⟨i, h⟩) else none := by
@@ -4328,42 +4361,44 @@ theorem getElem?_ofFn {f : Fin n → α} {i : Nat} :
 
 /-! ### Preliminaries about `range` and `range'` -/
 
-@[simp] theorem size_range' {start size step} : (range' start size step).size = size := by
+@[simp, grind =] theorem size_range' {start size step} : (range' start size step).size = size := by
   simp [range']
 
-@[simp] theorem toList_range' {start size step} :
+@[simp, grind =] theorem toList_range' {start size step} :
      (range' start size step).toList = List.range' start size step := by
   apply List.ext_getElem <;> simp [range']
 
-@[simp]
+@[simp, grind =]
 theorem getElem_range' {start size step : Nat} {i : Nat}
     (h : i < (Array.range' start size step).size) :
     (Array.range' start size step)[i] = start + step * i := by
   simp [← getElem_toList]
 
+@[grind =]
 theorem getElem?_range' {start size step : Nat} {i : Nat} :
     (Array.range' start size step)[i]? = if i < size then some (start + step * i) else none := by
   simp [getElem?_def, getElem_range']
 
-@[simp] theorem _root_.List.toArray_range' {start size step : Nat} :
+@[simp, grind =] theorem _root_.List.toArray_range' {start size step : Nat} :
     (List.range' start size step).toArray = Array.range' start size step := by
   apply ext'
   simp
 
-@[simp] theorem size_range {n : Nat} : (range n).size = n := by
+@[simp, grind =] theorem size_range {n : Nat} : (range n).size = n := by
   simp [range]
 
-@[simp] theorem toList_range {n : Nat} : (range n).toList = List.range n := by
+@[simp, grind =] theorem toList_range {n : Nat} : (range n).toList = List.range n := by
   apply List.ext_getElem <;> simp [range]
 
-@[simp]
+@[simp, grind =]
 theorem getElem_range {n : Nat} {i : Nat} (h : i < (Array.range n).size) : (Array.range n)[i] = i := by
   simp [← getElem_toList]
 
+@[grind =]
 theorem getElem?_range {n : Nat} {i : Nat} : (Array.range n)[i]? = if i < n then some i else none := by
   simp [getElem?_def, getElem_range]
 
-@[simp] theorem _root_.List.toArray_range {n : Nat} : (List.range n).toArray = Array.range n := by
+@[simp, grind =] theorem _root_.List.toArray_range {n : Nat} : (List.range n).toArray = Array.range n := by
   apply ext'
   simp
 
@@ -4404,7 +4439,7 @@ theorem size_uset {xs : Array α} {v : α} {i : USize} (h : i.toNat < xs.size) :
 
 @[simp] theorem getD_eq_getD_getElem? {xs : Array α} {i : Nat} {d : α} :
     xs.getD i d = xs[i]?.getD d := by
-  simp only [getD]; split <;> simp [getD_getElem?, *]
+  simp only [getD]; split <;> simp [*]
 
 theorem getElem!_eq_getD [Inhabited α] {xs : Array α} {i} : xs[i]! = xs.getD i default := by
   rfl
@@ -4438,7 +4473,7 @@ theorem back!_eq_back? [Inhabited α] {xs : Array α} : xs.back! = xs.back?.getD
   simp [back!, back?, getElem!_def, Option.getD]; rfl
 
 @[simp, grind] theorem back?_push {xs : Array α} {x : α} : (xs.push x).back? = some x := by
-  simp [back?, ← getElem?_toList]
+  simp [back?]
 
 @[simp] theorem back!_push [Inhabited α] {xs : Array α} {x : α} : (xs.push x).back! = x := by
   simp [back!_eq_back?]
@@ -4500,12 +4535,13 @@ abbrev contains_def [DecidableEq α] {a : α} {xs : Array α} : xs.contains a
 @[simp] theorem size_zipWith {xs : Array α} {ys : Array β} {f : α → β → γ} :
     (zipWith f xs ys).size = min xs.size ys.size := by
   rw [size_eq_length_toList, toList_zipWith, List.length_zipWith]
+  simp only [Array.size]
 
 @[simp] theorem size_zip {xs : Array α} {ys : Array β} :
     (zip xs ys).size = min xs.size ys.size :=
   size_zipWith
 
-@[simp] theorem getElem_zipWith {xs : Array α} {ys : Array β} {f : α → β → γ} {i : Nat}
+@[simp, grind =] theorem getElem_zipWith {xs : Array α} {ys : Array β} {f : α → β → γ} {i : Nat}
     (hi : i < (zipWith f xs ys).size) :
     (zipWith f xs ys)[i] = f (xs[i]'(by simp at hi; omega)) (ys[i]'(by simp at hi; omega)) := by
   cases xs
@@ -4572,7 +4608,7 @@ theorem toListRev_toArray {l : List α} : l.toArray.toListRev = l.reverse := by
   | nil => simp
   | cons a l ih =>
     simp only [foldlM_toArray] at ih
-    rw [size_toArray, mapM'_cons, foldlM_toArray]
+    rw [size_toArray, mapM'_cons]
     simp [ih]
 
 theorem uset_toArray {l : List α} {i : USize} {a : α} {h : i.toNat < l.toArray.size} :
@@ -4586,7 +4622,7 @@ theorem uset_toArray {l : List α} {i : USize} {a : α} {h : i.toNat < l.toArray
 @[simp, grind =] theorem flatten_toArray {L : List (List α)} :
     (L.toArray.map List.toArray).flatten = L.flatten.toArray := by
   apply ext'
-  simp [Function.comp_def]
+  simp
 
 end List
 
@@ -4678,7 +4714,7 @@ namespace List
       intro h'
       specialize ih (by omega)
       have : as.length - (i + 1) + 1 = as.length - i := by omega
-      simp_all [ih]
+      simp_all
     · simp only [size_toArray, Nat.not_lt] at h
       have : as.length = 0 := by omega
       simp_all
@@ -4686,17 +4722,10 @@ namespace List
 end List
 
 /-! ### Deprecations -/
-
-namespace List
-
-@[deprecated setIfInBounds_toArray (since := "2024-11-24")] abbrev setD_toArray := @setIfInBounds_toArray
-
-end List
-
 namespace Array
 
 @[deprecated size_toArray (since := "2024-12-11")]
-theorem size_mk (as : List α) : (Array.mk as).size = as.length := by simp [size]
+theorem size_mk (as : List α) : (Array.mk as).size = as.length := by simp
 
 @[deprecated getElem?_eq_getElem (since := "2024-12-11")]
 theorem getElem?_lt
@@ -4712,7 +4741,7 @@ theorem get?_eq_getElem? (xs : Array α) (i : Nat) : xs.get? i = xs[i]? := rfl
 
 @[deprecated getElem?_eq_none (since := "2024-12-11")]
 theorem getElem?_len_le (xs : Array α) {i : Nat} (h : xs.size ≤ i) : xs[i]? = none := by
-  simp [getElem?_eq_none, h]
+  simp [h]
 
 @[deprecated getD_getElem? (since := "2024-12-11")] abbrev getD_get? := @getD_getElem?
 
@@ -4727,7 +4756,7 @@ set_option linter.deprecated false in
 theorem get!_eq_getD_getElem? [Inhabited α] (xs : Array α) (i : Nat) :
     xs.get! i = xs[i]?.getD default := by
   by_cases p : i < xs.size <;>
-  simp [get!, getElem!_eq_getD, getD_eq_getD_getElem?, getD_getElem?, p]
+  simp [get!, getD_eq_getD_getElem?, p]
 
 set_option linter.deprecated false in
 @[deprecated get!_eq_getD_getElem? (since := "2025-02-12")] abbrev get!_eq_getElem? := @get!_eq_getD_getElem?
@@ -4745,17 +4774,6 @@ theorem get_set_eq (xs : Array α) (i : Nat) (v : α) (h : i < xs.size) :
     (xs.set i v h)[i]'(by simp [h]) = v := by
   simp only [set, ← getElem_toList, List.getElem_set_self]
 
-@[deprecated set!_is_setIfInBounds (since := "2024-11-24")] abbrev set_is_setIfInBounds := @set!_eq_setIfInBounds
-@[deprecated size_setIfInBounds (since := "2024-11-24")] abbrev size_setD := @size_setIfInBounds
-@[deprecated getElem_setIfInBounds_eq (since := "2024-11-24")] abbrev getElem_setD_eq := @getElem_setIfInBounds_self
-@[deprecated getElem?_setIfInBounds_eq (since := "2024-11-24")] abbrev get?_setD_eq := @getElem?_setIfInBounds_self
-@[deprecated getD_getElem?_setIfInBounds (since := "2025-04-04")] abbrev getD_get?_setIfInBounds := @getD_getElem?_setIfInBounds
-@[deprecated getD_getElem?_setIfInBounds (since := "2024-11-24")] abbrev getD_setD := @getD_getElem?_setIfInBounds
-@[deprecated getElem_setIfInBounds (since := "2024-11-24")] abbrev getElem_setD := @getElem_setIfInBounds
-
-@[deprecated List.getElem_toArray (since := "2024-11-29")]
-theorem getElem_mk {xs : List α} {i : Nat} (h : i < xs.length) : (Array.mk xs)[i] = xs[i] := rfl
-
 @[deprecated Array.getElem_toList (since := "2024-12-08")]
 theorem getElem_eq_getElem_toList {xs : Array α} (h : i < xs.size) : xs[i] = xs.toList[i] := rfl
 

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

@@ -162,7 +162,7 @@ instance [DecidableEq α] [LT α] [DecidableLT α]
     {xs ys : Array α} : lex xs ys = false ↔ ys ≤ xs := by
   cases xs
   cases ys
-  simp [List.not_lt_iff_ge]
+  simp
 
 instance [DecidableEq α] [LT α] [DecidableLT α] : DecidableLT (Array α) :=
   fun xs ys => decidable_of_iff (lex xs ys = true) lex_eq_true_iff_lt

src/Init/Data/Array/MapIdx.lean

@@ -51,27 +51,27 @@ theorem mapFinIdx_spec {xs : Array α} {f : (i : Nat) → α → (h : i < xs.siz
       ∀ i h, p i ((Array.mapFinIdx xs f)[i]) h :=
   (mapFinIdx_induction _ _ (fun _ => True) trivial p fun _ _ _ => ⟨hs .., trivial⟩).2
 
-@[simp] theorem size_mapFinIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
+@[simp, grind =] theorem size_mapFinIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
     (xs.mapFinIdx f).size = xs.size :=
   (mapFinIdx_spec (p := fun _ _ _ => True) (hs := fun _ _ => trivial)).1
 
-@[simp] theorem size_zipIdx {xs : Array α} {k : Nat} : (xs.zipIdx k).size = xs.size :=
+@[simp, grind =] theorem size_zipIdx {xs : Array α} {k : Nat} : (xs.zipIdx k).size = xs.size :=
   Array.size_mapFinIdx
 
 @[deprecated size_zipIdx (since := "2025-01-21")] abbrev size_zipWithIndex := @size_zipIdx
 
-@[simp] theorem getElem_mapFinIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {i : Nat}
+@[simp, grind =] theorem getElem_mapFinIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {i : Nat}
     (h : i < (xs.mapFinIdx f).size) :
     (xs.mapFinIdx f)[i] = f i (xs[i]'(by simp_all)) (by simp_all) :=
   (mapFinIdx_spec (p := fun i b h => b = f i xs[i] h) fun _ _ => rfl).2 i _
 
-@[simp] theorem getElem?_mapFinIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {i : Nat} :
+@[simp, grind =] theorem getElem?_mapFinIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {i : Nat} :
     (xs.mapFinIdx f)[i]? =
       xs[i]?.pbind fun b h => some <| f i b (getElem?_eq_some_iff.1 h).1 := by
   simp only [getElem?_def, size_mapFinIdx, getElem_mapFinIdx]
   split <;> simp_all
 
-@[simp] theorem toList_mapFinIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
+@[simp, grind =] theorem toList_mapFinIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
     (xs.mapFinIdx f).toList = xs.toList.mapFinIdx (fun i a h => f i a (by simpa)) := by
   apply List.ext_getElem <;> simp
 
@@ -91,20 +91,20 @@ theorem mapIdx_spec {f : Nat → α → β} {xs : Array α}
       ∀ i h, p i ((xs.mapIdx f)[i]) h :=
   (mapIdx_induction (motive := fun _ => True) trivial fun _ _ _ => ⟨hs .., trivial⟩).2
 
-@[simp] theorem size_mapIdx {f : Nat → α → β} {xs : Array α} : (xs.mapIdx f).size = xs.size :=
+@[simp, grind =] theorem size_mapIdx {f : Nat → α → β} {xs : Array α} : (xs.mapIdx f).size = xs.size :=
   (mapIdx_spec (p := fun _ _ _ => True) (hs := fun _ _ => trivial)).1
 
-@[simp] theorem getElem_mapIdx {f : Nat → α → β} {xs : Array α} {i : Nat}
+@[simp, grind =] theorem getElem_mapIdx {f : Nat → α → β} {xs : Array α} {i : Nat}
     (h : i < (xs.mapIdx f).size) :
     (xs.mapIdx f)[i] = f i (xs[i]'(by simp_all)) :=
   (mapIdx_spec (p := fun i b h => b = f i xs[i]) fun _ _ => rfl).2 i (by simp_all)
 
-@[simp] theorem getElem?_mapIdx {f : Nat → α → β} {xs : Array α} {i : Nat} :
+@[simp, grind =] theorem getElem?_mapIdx {f : Nat → α → β} {xs : Array α} {i : Nat} :
     (xs.mapIdx f)[i]? =
       xs[i]?.map (f i) := by
   simp [getElem?_def, size_mapIdx, getElem_mapIdx]
 
-@[simp] theorem toList_mapIdx {f : Nat → α → β} {xs : Array α} :
+@[simp, grind =] theorem toList_mapIdx {f : Nat → α → β} {xs : Array α} :
     (xs.mapIdx f).toList = xs.toList.mapIdx (fun i a => f i a) := by
   apply List.ext_getElem <;> simp
 
@@ -126,7 +126,7 @@ namespace Array
 
 /-! ### zipIdx -/
 
-@[simp] theorem getElem_zipIdx {xs : Array α} {k : Nat} {i : Nat} (h : i < (xs.zipIdx k).size) :
+@[simp, grind =] theorem getElem_zipIdx {xs : Array α} {k : Nat} {i : Nat} (h : i < (xs.zipIdx k).size) :
     (xs.zipIdx k)[i] = (xs[i]'(by simp_all), k + i) := by
   simp [zipIdx]
 
@@ -135,12 +135,12 @@ abbrev getElem_zipWithIndex := @getElem_zipIdx
 
 @[simp, grind =] theorem zipIdx_toArray {l : List α} {k : Nat} :
     l.toArray.zipIdx k = (l.zipIdx k).toArray := by
-  ext i hi₁ hi₂ <;> simp [Nat.add_comm]
+  ext i hi₁ hi₂ <;> simp
 
 @[deprecated zipIdx_toArray (since := "2025-01-21")]
 abbrev zipWithIndex_toArray := @zipIdx_toArray
 
-@[simp] theorem toList_zipIdx {xs : Array α} {k : Nat} :
+@[simp, grind =] theorem toList_zipIdx {xs : Array α} {k : Nat} :
     (xs.zipIdx k).toList = xs.toList.zipIdx k := by
   rcases xs with ⟨xs⟩
   simp
@@ -185,24 +185,26 @@ abbrev mem_zipWithIndex_iff_getElem? := @mem_zipIdx_iff_getElem?
   subst w
   rfl
 
-@[simp]
+@[simp, grind =]
 theorem mapFinIdx_empty {f : (i : Nat) → α → (h : i < 0) → β} : mapFinIdx #[] f = #[] :=
   rfl
 
 theorem mapFinIdx_eq_ofFn {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
     xs.mapFinIdx f = Array.ofFn fun i : Fin xs.size => f i xs[i] i.2 := by
   cases xs
-  simp [List.mapFinIdx_eq_ofFn]
+  simp only [List.mapFinIdx_toArray, List.mapFinIdx_eq_ofFn, Fin.getElem_fin, List.getElem_toArray]
+  simp [Array.size]
 
+@[grind =]
 theorem mapFinIdx_append {xs ys : Array α} {f : (i : Nat) → α → (h : i < (xs ++ ys).size) → β} :
     (xs ++ ys).mapFinIdx f =
       xs.mapFinIdx (fun i a h => f i a (by simp; omega)) ++
         ys.mapFinIdx (fun i a h => f (i + xs.size) a (by simp; omega)) := by
   cases xs
   cases ys
-  simp [List.mapFinIdx_append]
+  simp [List.mapFinIdx_append, Array.size]
 
-@[simp]
+@[simp, grind =]
 theorem mapFinIdx_push {xs : Array α} {a : α} {f : (i : Nat) → α → (h : i < (xs.push a).size) → β} :
     mapFinIdx (xs.push a) f =
       (mapFinIdx xs (fun i a h => f i a (by simp; omega))).push (f xs.size a (by simp)) := by
@@ -236,7 +238,7 @@ theorem exists_of_mem_mapFinIdx {b : β} {xs : Array α} {f : (i : Nat) → α
   rcases xs with ⟨xs⟩
   exact List.exists_of_mem_mapFinIdx (by simpa using h)
 
-@[simp] theorem mem_mapFinIdx {b : β} {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
+@[simp, grind =] theorem mem_mapFinIdx {b : β} {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
     b ∈ xs.mapFinIdx f ↔ ∃ (i : Nat) (h : i < xs.size), f i xs[i] h = b := by
   rcases xs with ⟨xs⟩
   simp
@@ -264,12 +266,12 @@ theorem mapFinIdx_eq_append_iff {xs : Array α} {f : (i : Nat) → α → (h : i
     toArray_eq_append_iff]
   constructor
   · rintro ⟨l₁, l₂, rfl, rfl, rfl⟩
-    refine ⟨l₁.toArray, l₂.toArray, by simp_all⟩
+    refine ⟨l₁.toArray, l₂.toArray, by simp_all [Array.size]⟩
   · rintro ⟨⟨l₁⟩, ⟨l₂⟩, rfl, h₁, h₂⟩
     simp [← toList_inj] at h₁ h₂
     obtain rfl := h₁
     obtain rfl := h₂
-    refine ⟨l₁, l₂, by simp_all⟩
+    refine ⟨l₁, l₂, by simp_all [Array.size]⟩
 
 theorem mapFinIdx_eq_push_iff {xs : Array α} {b : β} {f : (i : Nat) → α → (h : i < xs.size) → β} :
     xs.mapFinIdx f = ys.push b ↔
@@ -289,7 +291,7 @@ theorem mapFinIdx_eq_mapFinIdx_iff {xs : Array α} {f g : (i : Nat) → α → (
   rw [eq_comm, mapFinIdx_eq_iff]
   simp
 
-@[simp] theorem mapFinIdx_mapFinIdx {xs : Array α}
+@[simp, grind =] theorem mapFinIdx_mapFinIdx {xs : Array α}
     {f : (i : Nat) → α → (h : i < xs.size) → β}
     {g : (i : Nat) → β → (h : i < (xs.mapFinIdx f).size) → γ} :
     (xs.mapFinIdx f).mapFinIdx g = xs.mapFinIdx (fun i a h => g i (f i a h) (by simpa using h)) := by
@@ -304,14 +306,14 @@ theorem mapFinIdx_eq_replicate_iff {xs : Array α} {f : (i : Nat) → α → (h
 @[deprecated mapFinIdx_eq_replicate_iff (since := "2025-03-18")]
 abbrev mapFinIdx_eq_mkArray_iff := @mapFinIdx_eq_replicate_iff
 
-@[simp] theorem mapFinIdx_reverse {xs : Array α} {f : (i : Nat) → α → (h : i < xs.reverse.size) → β} :
+@[simp, grind =] theorem mapFinIdx_reverse {xs : Array α} {f : (i : Nat) → α → (h : i < xs.reverse.size) → β} :
     xs.reverse.mapFinIdx f = (xs.mapFinIdx (fun i a h => f (xs.size - 1 - i) a (by simp; omega))).reverse := by
   rcases xs with ⟨l⟩
-  simp [List.mapFinIdx_reverse]
+  simp [List.mapFinIdx_reverse, Array.size]
 
 /-! ### mapIdx -/
 
-@[simp]
+@[simp, grind =]
 theorem mapIdx_empty {f : Nat → α → β} : mapIdx f #[] = #[] :=
   rfl
 
@@ -331,13 +333,14 @@ theorem mapIdx_eq_zipIdx_map {xs : Array α} {f : Nat → α → β} :
 @[deprecated mapIdx_eq_zipIdx_map (since := "2025-01-21")]
 abbrev mapIdx_eq_zipWithIndex_map := @mapIdx_eq_zipIdx_map
 
+@[grind =]
 theorem mapIdx_append {xs ys : Array α} :
     (xs ++ ys).mapIdx f = xs.mapIdx f ++ ys.mapIdx (fun i => f (i + xs.size)) := by
   rcases xs with ⟨xs⟩
   rcases ys with ⟨ys⟩
   simp [List.mapIdx_append]
 
-@[simp]
+@[simp, grind =]
 theorem mapIdx_push {xs : Array α} {a : α} :
     mapIdx f (xs.push a) = (mapIdx f xs).push (f xs.size a) := by
   simp [← append_singleton, mapIdx_append]
@@ -359,7 +362,7 @@ theorem exists_of_mem_mapIdx {b : β} {xs : Array α}
   rw [mapIdx_eq_mapFinIdx] at h
   simpa [Fin.exists_iff] using exists_of_mem_mapFinIdx h
 
-@[simp] theorem mem_mapIdx {b : β} {xs : Array α} :
+@[simp, grind =] theorem mem_mapIdx {b : β} {xs : Array α} :
     b ∈ mapIdx f xs ↔ ∃ (i : Nat) (h : i < xs.size), f i xs[i] = b := by
   constructor
   · intro h
@@ -413,7 +416,7 @@ theorem mapIdx_eq_mapIdx_iff {xs : Array α} :
   rcases xs with ⟨xs⟩
   simp [List.mapIdx_eq_mapIdx_iff]
 
-@[simp] theorem mapIdx_set {xs : Array α} {i : Nat} {h : i < xs.size} {a : α} :
+@[simp, grind =] theorem mapIdx_set {f : Nat → α → β} {xs : Array α} {i : Nat} {h : i < xs.size} {a : α} :
     (xs.set i a).mapIdx f = (xs.mapIdx f).set i (f i a) (by simpa) := by
   rcases xs with ⟨xs⟩
   simp [List.mapIdx_set]
@@ -423,17 +426,17 @@ theorem mapIdx_eq_mapIdx_iff {xs : Array α} :
   rcases xs with ⟨xs⟩
   simp [List.mapIdx_set]
 
-@[simp] theorem back?_mapIdx {xs : Array α} {f : Nat → α → β} :
+@[simp, grind =] theorem back?_mapIdx {xs : Array α} {f : Nat → α → β} :
     (mapIdx f xs).back? = (xs.back?).map (f (xs.size - 1)) := by
   rcases xs with ⟨xs⟩
   simp [List.getLast?_mapIdx]
 
-@[simp] theorem back_mapIdx {xs : Array α} {f : Nat → α → β} (h) :
+@[simp, grind =] theorem back_mapIdx {xs : Array α} {f : Nat → α → β} (h) :
     (xs.mapIdx f).back h = f (xs.size - 1) (xs.back (by simpa using h)) := by
   rcases xs with ⟨xs⟩
   simp [List.getLast_mapIdx]
 
-@[simp] theorem mapIdx_mapIdx {xs : Array α} {f : Nat → α → β} {g : Nat → β → γ} :
+@[simp, grind =] theorem mapIdx_mapIdx {xs : Array α} {f : Nat → α → β} {g : Nat → β → γ} :
     (xs.mapIdx f).mapIdx g = xs.mapIdx (fun i => g i ∘ f i) := by
   simp [mapIdx_eq_iff]
 
@@ -446,7 +449,7 @@ theorem mapIdx_eq_replicate_iff {xs : Array α} {f : Nat → α → β} {b : β}
 @[deprecated mapIdx_eq_replicate_iff (since := "2025-03-18")]
 abbrev mapIdx_eq_mkArray_iff := @mapIdx_eq_replicate_iff
 
-@[simp] theorem mapIdx_reverse {xs : Array α} {f : Nat → α → β} :
+@[simp, grind =] theorem mapIdx_reverse {xs : Array α} {f : Nat → α → β} :
     xs.reverse.mapIdx f = (mapIdx (fun i => f (xs.size - 1 - i)) xs).reverse := by
   rcases xs with ⟨xs⟩
   simp [List.mapIdx_reverse]
@@ -455,7 +458,7 @@ end Array
 
 namespace List
 
-@[grind] theorem mapFinIdxM_toArray [Monad m] [LawfulMonad m] {l : List α}
+@[grind =] theorem mapFinIdxM_toArray [Monad m] [LawfulMonad m] {l : List α}
     {f : (i : Nat) → α → (h : i < l.length) → m β} :
     l.toArray.mapFinIdxM f = toArray <$> l.mapFinIdxM f := by
   let rec go (i : Nat) (acc : Array β) (inv : i + acc.size = l.length) :
@@ -476,7 +479,7 @@ namespace List
   simp only [Array.mapFinIdxM, mapFinIdxM]
   exact go _ #[] _
 
-@[grind] theorem mapIdxM_toArray [Monad m] [LawfulMonad m] {l : List α}
+@[grind =] theorem mapIdxM_toArray [Monad m] [LawfulMonad m] {l : List α}
     {f : Nat → α → m β} :
     l.toArray.mapIdxM f = toArray <$> l.mapIdxM f := by
   let rec go (bs : List α) (acc : Array β) (inv : bs.length + acc.size = l.length) :
@@ -486,7 +489,7 @@ namespace List
     | x :: xs => simp only [mapFinIdxM.go, mapIdxM.go, go]
   unfold Array.mapIdxM
   rw [mapFinIdxM_toArray]
-  simp only [mapFinIdxM, mapIdxM]
+  simp only [mapFinIdxM, mapIdxM, Array.size]
   rw [go]
 
 end List

src/Init/Data/Array/Monadic.lean

@@ -36,19 +36,19 @@ theorem map_toList_inj [Monad m] [LawfulMonad m]
     xs.mapM (m := m) (pure <| f ·) = pure (xs.map f) := by
   induction xs; simp_all
 
-@[simp] theorem idRun_mapM {xs : Array α} {f : α → Id β} : (xs.mapM f).run = xs.map (f · |>.run) :=
+@[simp, grind =] theorem idRun_mapM {xs : Array α} {f : α → Id β} : (xs.mapM f).run = xs.map (f · |>.run) :=
   mapM_pure
 
 @[deprecated idRun_mapM (since := "2025-05-21")]
 theorem mapM_id {xs : Array α} {f : α → Id β} : xs.mapM f = xs.map f :=
   mapM_pure
 
-@[simp] theorem mapM_map [Monad m] [LawfulMonad m] {f : α → β} {g : β → m γ} {xs : Array α} :
+@[simp, grind =] theorem mapM_map [Monad m] [LawfulMonad m] {f : α → β} {g : β → m γ} {xs : Array α} :
     (xs.map f).mapM g = xs.mapM (g ∘ f) := by
   rcases xs with ⟨xs⟩
   simp
 
-@[simp] theorem mapM_append [Monad m] [LawfulMonad m] {f : α → m β} {xs ys : Array α} :
+@[simp, grind =] theorem mapM_append [Monad m] [LawfulMonad m] {f : α → m β} {xs ys : Array α} :
     (xs ++ ys).mapM f = (return (← xs.mapM f) ++ (← ys.mapM f)) := by
   rcases xs with ⟨xs⟩
   rcases ys with ⟨ys⟩
@@ -59,7 +59,7 @@ theorem mapM_eq_foldlM_push [Monad m] [LawfulMonad m] {f : α → m β} {xs : Ar
   rcases xs with ⟨xs⟩
   simp only [List.mapM_toArray, bind_pure_comp, List.size_toArray, List.foldlM_toArray']
   rw [List.mapM_eq_reverse_foldlM_cons]
-  simp only [bind_pure_comp, Functor.map_map]
+  simp only [Functor.map_map]
   suffices ∀ (l), (fun l' => l'.reverse.toArray) <$> List.foldlM (fun acc a => (fun a => a :: acc) <$> f a) l xs =
       List.foldlM (fun acc a => acc.push <$> f a) l.reverse.toArray xs by
     exact this []
@@ -143,13 +143,13 @@ theorem foldrM_filter [Monad m] [LawfulMonad m] {p : α → Bool} {g : α → β
   cases as <;> cases bs
   simp_all
 
-@[simp] theorem forM_append [Monad m] [LawfulMonad m] {xs ys : Array α} {f : α → m PUnit} :
+@[simp, grind =] theorem forM_append [Monad m] [LawfulMonad m] {xs ys : Array α} {f : α → m PUnit} :
     forM (xs ++ ys) f = (do forM xs f; forM ys f) := by
   rcases xs with ⟨xs⟩
   rcases ys with ⟨ys⟩
   simp
 
-@[simp] theorem forM_map [Monad m] [LawfulMonad m] {xs : Array α} {g : α → β} {f : β → m PUnit} :
+@[simp, grind =] theorem forM_map [Monad m] [LawfulMonad m] {xs : Array α} {g : α → β} {f : β → m PUnit} :
     forM (xs.map g) f = forM xs (fun a => f (g a)) := by
   rcases xs with ⟨xs⟩
   simp
@@ -208,7 +208,7 @@ theorem forIn'_yield_eq_foldl
       xs.attach.foldl (fun b ⟨a, h⟩ => f a h b) init :=
   forIn'_pure_yield_eq_foldl _ _
 
-@[simp] theorem forIn'_map [Monad m] [LawfulMonad m]
+@[simp, grind =] theorem forIn'_map [Monad m] [LawfulMonad m]
     {xs : Array α} (g : α → β) (f : (b : β) → b ∈ xs.map g → γ → m (ForInStep γ)) :
     forIn' (xs.map g) init f = forIn' xs init fun a h y => f (g a) (mem_map_of_mem h) y := by
   rcases xs with ⟨xs⟩
@@ -234,14 +234,14 @@ theorem forIn_eq_foldlM [Monad m] [LawfulMonad m]
     forIn xs init (fun a b => (fun c => .yield (g a b c)) <$> f a b) =
       xs.foldlM (fun b a => g a b <$> f a b) init := by
   rcases xs with ⟨xs⟩
-  simp [List.foldlM_map]
+  simp
 
 @[simp] theorem forIn_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
     {xs : Array α} (f : α → β → β) (init : β) :
     forIn xs init (fun a b => pure (.yield (f a b))) =
       pure (f := m) (xs.foldl (fun b a => f a b) init) := by
   rcases xs with ⟨xs⟩
-  simp [List.forIn_pure_yield_eq_foldl, List.foldl_map]
+  simp [List.forIn_pure_yield_eq_foldl]
 
 theorem idRun_forIn_yield_eq_foldl
     {xs : Array α} (f : α → β → Id β) (init : β) :
@@ -256,7 +256,7 @@ theorem forIn_yield_eq_foldl
       xs.foldl (fun b a => f a b) init :=
   forIn_pure_yield_eq_foldl _ _
 
-@[simp] theorem forIn_map [Monad m] [LawfulMonad m]
+@[simp, grind =] theorem forIn_map [Monad m] [LawfulMonad m]
     {xs : Array α} {g : α → β} {f : β → γ → m (ForInStep γ)} :
     forIn (xs.map g) init f = forIn xs init fun a y => f (g a) y := by
   rcases xs with ⟨xs⟩
@@ -310,7 +310,7 @@ namespace List
 @[simp] theorem filterM_toArray' [Monad m] [LawfulMonad m] {l : List α} {p : α → m Bool} (w : stop = l.length) :
     l.toArray.filterM p 0 stop = toArray <$> l.filterM p := by
   subst w
-  rw [filterM_toArray]
+  simp [← filterM_toArray]
 
 @[grind =] theorem filterRevM_toArray [Monad m] [LawfulMonad m] {l : List α} {p : α → m Bool} :
     l.toArray.filterRevM p = toArray <$> l.filterRevM p := by
@@ -322,7 +322,7 @@ namespace List
 @[simp] theorem filterRevM_toArray' [Monad m] [LawfulMonad m] {l : List α} {p : α → m Bool} (w : start = l.length) :
     l.toArray.filterRevM p start 0 = toArray <$> l.filterRevM p := by
   subst w
-  rw [filterRevM_toArray]
+  simp [← filterRevM_toArray]
 
 @[grind =] theorem filterMapM_toArray [Monad m] [LawfulMonad m] {l : List α} {f : α → m (Option β)} :
     l.toArray.filterMapM f = toArray <$> l.filterMapM f := by
@@ -340,7 +340,7 @@ namespace List
 @[simp] theorem filterMapM_toArray' [Monad m] [LawfulMonad m] {l : List α} {f : α → m (Option β)} (w : stop = l.length) :
     l.toArray.filterMapM f 0 stop = toArray <$> l.filterMapM f := by
   subst w
-  rw [filterMapM_toArray]
+  simp [← filterMapM_toArray]
 
 @[simp, grind =] theorem flatMapM_toArray [Monad m] [LawfulMonad m] {l : List α} {f : α → m (Array β)} :
     l.toArray.flatMapM f = toArray <$> l.flatMapM (fun a => Array.toList <$> f a) := by

src/Init/Data/Array/OfFn.lean

@@ -23,7 +23,7 @@ namespace Array
 
 /-! ### ofFn -/
 
-@[simp] theorem ofFn_zero {f : Fin 0 → α} : ofFn f = #[] := by
+@[simp, grind =] theorem ofFn_zero {f : Fin 0 → α} : ofFn f = #[] := by
   simp [ofFn, ofFn.go]
 
 theorem ofFn_succ {f : Fin (n+1) → α} :
@@ -42,10 +42,10 @@ theorem ofFn_add {n m} {f : Fin (n + m) → α} :
   | zero => simp
   | succ m ih => simp [ofFn_succ, ih]
 
-@[simp] theorem _root_.List.toArray_ofFn {f : Fin n → α} : (List.ofFn f).toArray = Array.ofFn f := by
+@[simp, grind =] theorem _root_.List.toArray_ofFn {f : Fin n → α} : (List.ofFn f).toArray = Array.ofFn f := by
   ext <;> simp
 
-@[simp] theorem toList_ofFn {f : Fin n → α} : (Array.ofFn f).toList = List.ofFn f := by
+@[simp, grind =] theorem toList_ofFn {f : Fin n → α} : (Array.ofFn f).toList = List.ofFn f := by
   apply List.ext_getElem <;> simp
 
 theorem ofFn_succ' {f : Fin (n+1) → α} :
@@ -58,7 +58,7 @@ theorem ofFn_eq_empty_iff {f : Fin n → α} : ofFn f = #[] ↔ n = 0 := by
   rw [← Array.toList_inj]
   simp
 
-@[simp 500]
+@[simp 500, grind =]
 theorem mem_ofFn {n} {f : Fin n → α} {a : α} : a ∈ ofFn f ↔ ∃ i, f i = a := by
   constructor
   · intro w
@@ -73,7 +73,7 @@ theorem mem_ofFn {n} {f : Fin n → α} {a : α} : a ∈ ofFn f ↔ ∃ i, f i =
 def ofFnM {n} [Monad m] (f : Fin n → m α) : m (Array α) :=
   Fin.foldlM n (fun xs i => xs.push <$> f i) (Array.emptyWithCapacity n)
 
-@[simp]
+@[simp, grind =]
 theorem ofFnM_zero [Monad m] {f : Fin 0 → m α} : ofFnM f = pure #[] := by
   simp [ofFnM]
 
@@ -109,7 +109,7 @@ theorem ofFnM_add {n m} [Monad m] [LawfulMonad m] {f : Fin (n + k) → m α} :
     funext x
     simp
 
-@[simp] theorem toList_ofFnM [Monad m] [LawfulMonad m] {f : Fin n → m α} :
+@[simp, grind =] theorem toList_ofFnM [Monad m] [LawfulMonad m] {f : Fin n → m α} :
     toList <$> ofFnM f = List.ofFnM f := by
   induction n with
   | zero => simp

src/Init/Data/Array/Perm.lean

@@ -91,17 +91,26 @@ theorem Perm.mem_iff {a : α} {xs ys : Array α} (p : xs ~ ys) : a ∈ xs ↔ a
   simp only [perm_iff_toList_perm] at p
   simpa using p.mem_iff
 
+grind_pattern Perm.mem_iff => xs ~ ys, a ∈ xs
+grind_pattern Perm.mem_iff => xs ~ ys, a ∈ ys
+
 theorem Perm.append {xs ys as bs : Array α} (p₁ : xs ~ ys) (p₂ : as ~ bs) :
     xs ++ as ~ ys ++ bs := by
   cases xs; cases ys; cases as; cases bs
   simp only [append_toArray, perm_iff_toList_perm] at p₁ p₂ ⊢
   exact p₁.append p₂
 
+grind_pattern Perm.append => xs ~ ys, as ~ bs, xs ++ as
+grind_pattern Perm.append => xs ~ ys, as ~ bs, ys ++ bs
+
 theorem Perm.push (x : α) {xs ys : Array α} (p : xs ~ ys) :
     xs.push x ~ ys.push x := by
   rw [push_eq_append_singleton]
   exact p.append .rfl
 
+grind_pattern Perm.push => xs ~ ys, xs.push x
+grind_pattern Perm.push => xs ~ ys, ys.push x
+
 theorem Perm.push_comm (x y : α) {xs ys : Array α} (p : xs ~ ys) :
     (xs.push x).push y ~ (ys.push y).push x := by
   cases xs; cases ys

src/Init/Data/Array/Range.lean

@@ -29,6 +29,7 @@ open Nat
 
 /-! ### range' -/
 
+@[grind _=_]
 theorem range'_succ {s n step} : range' s (n + 1) step = #[s] ++ range' (s + step) n step := by
   rw [← toList_inj]
   simp [List.range'_succ]
@@ -39,16 +40,17 @@ theorem range'_succ {s n step} : range' s (n + 1) step = #[s] ++ range' (s + ste
 theorem range'_ne_empty_iff : range' s n step ≠ #[] ↔ n ≠ 0 := by
   cases n <;> simp
 
-@[simp] theorem range'_zero : range' s 0 step = #[] := by
+@[simp, grind =] theorem range'_zero : range' s 0 step = #[] := by
   simp
 
-@[simp] theorem range'_one {s step : Nat} : range' s 1 step = #[s] := by
+@[simp, grind =] theorem range'_one {s step : Nat} : range' s 1 step = #[s] := by
   simp [range', ofFn, ofFn.go]
 
 @[simp] theorem range'_inj : range' s n = range' s' n' ↔ n = n' ∧ (n = 0 ∨ s = s') := by
   rw [← toList_inj]
   simp [List.range'_inj]
 
+@[grind =]
 theorem mem_range' {n} : m ∈ range' s n step ↔ ∃ i < n, m = s + step * i := by
   simp [range']
   constructor
@@ -57,6 +59,7 @@ theorem mem_range' {n} : m ∈ range' s n step ↔ ∃ i < n, m = s + step * i :
   · rintro ⟨i, w, h'⟩
     exact ⟨⟨i, w⟩, by simp_all⟩
 
+@[simp, grind =]
 theorem pop_range' : (range' s n step).pop = range' s (n - 1) step := by
   ext <;> simp
 
@@ -66,6 +69,7 @@ theorem map_add_range' {a} (s n step) : map (a + ·) (range' s n step) = range'
 theorem range'_succ_left : range' (s + 1) n step = (range' s n step).map (· + 1) := by
   ext <;> simp <;> omega
 
+@[grind _=_]
 theorem range'_append {s m n step : Nat} :
     range' s m step ++ range' (s + step * m) n step = range' s (m + n) step := by
   ext i h₁ h₂
@@ -77,7 +81,8 @@ theorem range'_append {s m n step : Nat} :
     have : step * m ≤ step * i := by exact mul_le_mul_left step h
     omega
 
-@[simp] theorem range'_append_1 {s m n : Nat} :
+@[simp, grind _=_]
+theorem range'_append_1 {s m n : Nat} :
     range' s m ++ range' (s + m) n = range' s (m + n) := by simpa using range'_append (step := 1)
 
 theorem range'_concat {s n : Nat} : range' s (n + 1) step = range' s n step ++ #[s + step * n] := by
@@ -86,7 +91,7 @@ theorem range'_concat {s n : Nat} : range' s (n + 1) step = range' s n step ++ #
 theorem range'_1_concat {s n : Nat} : range' s (n + 1) = range' s n ++ #[s + n] := by
   simp [range'_concat]
 
-@[simp] theorem mem_range'_1 : m ∈ range' s n ↔ s ≤ m ∧ m < s + n := by
+@[simp, grind =] theorem mem_range'_1 : m ∈ range' s n ↔ s ≤ m ∧ m < s + n := by
   simp [mem_range']; exact ⟨
     fun ⟨i, h, e⟩ => e ▸ ⟨Nat.le_add_right .., Nat.add_lt_add_left h _⟩,
     fun ⟨h₁, h₂⟩ => ⟨m - s, Nat.sub_lt_left_of_lt_add h₁ h₂, (Nat.add_sub_cancel' h₁).symm⟩⟩
@@ -116,14 +121,26 @@ theorem range'_eq_append_iff : range' s n = xs ++ ys ↔ ∃ k, k ≤ n ∧ xs =
   simp only [List.find?_toArray]
   simp
 
+@[grind =]
 theorem erase_range' :
     (range' s n).erase i =
       range' s (min n (i - s)) ++ range' (max s (i + 1)) (min s (i + 1) + n - (i + 1)) := by
   simp only [← List.toArray_range', List.erase_toArray]
   simp [List.erase_range']
 
+@[simp, grind =]
+theorem count_range' {a s n step} (h : 0 < step := by simp) :
+    count a (range' s n step) = if ∃ i, i < n ∧ a = s + step * i then 1 else 0 := by
+  rw [← List.toArray_range', List.count_toArray, ← List.count_range' h]
+
+@[simp, grind =]
+theorem count_range_1' {a s n} :
+    count a (range' s n) = if s ≤ a ∧ a < s + n then 1 else 0 := by
+  rw [← List.toArray_range', List.count_toArray, ← List.count_range_1']
+
 /-! ### range -/
 
+@[grind _=_]
 theorem range_eq_range' {n : Nat} : range n = range' 0 n := by
   simp [range, range']
 
@@ -145,6 +162,7 @@ theorem range'_eq_map_range {s n : Nat} : range' s n = map (s + ·) (range n) :=
 theorem range_ne_empty_iff {n : Nat} : range n ≠ #[] ↔ n ≠ 0 := by
   cases n <;> simp
 
+@[grind _=_]
 theorem range_succ {n : Nat} : range (succ n) = range n ++ #[n] := by
   ext i h₁ h₂
   · simp
@@ -160,7 +178,7 @@ theorem range_add {n m : Nat} : range (n + m) = range n ++ (range m).map (n + ·
 theorem reverse_range' {s n : Nat} : reverse (range' s n) = map (s + n - 1 - ·) (range n) := by
   simp [← toList_inj, List.reverse_range']
 
-@[simp]
+@[simp, grind =]
 theorem mem_range {m n : Nat} : m ∈ range n ↔ m < n := by
   simp only [range_eq_range', mem_range'_1, Nat.zero_le, true_and, Nat.zero_add]
 
@@ -168,20 +186,25 @@ theorem not_mem_range_self {n : Nat} : n ∉ range n := by simp
 
 theorem self_mem_range_succ {n : Nat} : n ∈ range (n + 1) := by simp
 
-@[simp] theorem take_range {i n : Nat} : take (range n) i = range (min i n) := by
+@[simp, grind =] theorem take_range {i n : Nat} : take (range n) i = range (min i n) := by
   ext <;> simp
 
-@[simp] theorem find?_range_eq_some {n : Nat} {i : Nat} {p : Nat → Bool} :
+@[simp, grind =] theorem find?_range_eq_some {n : Nat} {i : Nat} {p : Nat → Bool} :
     (range n).find? p = some i ↔ p i ∧ i ∈ range n ∧ ∀ j, j < i → !p j := by
   simp [range_eq_range']
 
-@[simp] theorem find?_range_eq_none {n : Nat} {p : Nat → Bool} :
+@[simp, grind =] theorem find?_range_eq_none {n : Nat} {p : Nat → Bool} :
     (range n).find? p = none ↔ ∀ i, i < n → !p i := by
   simp only [← List.toArray_range, List.find?_toArray, List.find?_range_eq_none]
 
+@[grind =]
 theorem erase_range : (range n).erase i = range (min n i) ++ range' (i + 1) (n - (i + 1)) := by
   simp [range_eq_range', erase_range']
 
+@[simp, grind =]
+theorem count_range {a n} :
+    count a (range n) = if a < n then 1 else 0 := by
+  rw [← List.toArray_range, List.count_toArray, ← List.count_range]
 
 /-! ### zipIdx -/
 
@@ -190,13 +213,13 @@ theorem zipIdx_eq_empty_iff {xs : Array α} {i : Nat} : xs.zipIdx i = #[] ↔ xs
   cases xs
   simp
 
-@[simp]
+@[simp, grind =]
 theorem getElem?_zipIdx {xs : Array α} {i j} : (zipIdx xs i)[j]? = xs[j]?.map fun a => (a, i + j) := by
   simp [getElem?_def]
 
 theorem map_snd_add_zipIdx_eq_zipIdx {xs : Array α} {n k : Nat} :
     map (Prod.map id (· + n)) (zipIdx xs k) = zipIdx xs (n + k) :=
-  ext_getElem? fun i ↦ by simp [(· ∘ ·), Nat.add_comm, Nat.add_left_comm]; rfl
+  ext_getElem? fun i ↦ by simp [Nat.add_comm, Nat.add_left_comm]; rfl
 
 -- Arguments are explicit for parity with `zipIdx_map_fst`.
 @[simp]
@@ -233,7 +256,7 @@ theorem zipIdx_eq_map_add {xs : Array α} {i : Nat} :
   simp only [zipIdx_toArray, List.map_toArray, mk.injEq]
   rw [List.zipIdx_eq_map_add]
 
-@[simp]
+@[simp, grind =]
 theorem zipIdx_singleton {x : α} {k : Nat} : zipIdx #[x] k = #[(x, k)] :=
   rfl
 
@@ -281,6 +304,7 @@ theorem zipIdx_map {xs : Array α} {k : Nat} {f : α → β} :
   cases xs
   simp [List.zipIdx_map]
 
+@[grind =]
 theorem zipIdx_append {xs ys : Array α} {k : Nat} :
     zipIdx (xs ++ ys) k = zipIdx xs k ++ zipIdx ys (k + xs.size) := by
   cases xs

src/Init/Data/Array/Set.lean

@@ -24,7 +24,7 @@ Examples:
 * `#[0, 1, 2].set 1 5 = #[0, 5, 2]`
 * `#["orange", "apple"].set 1 "grape" = #["orange", "grape"]`
 -/
-@[extern "lean_array_fset"]
+@[extern "lean_array_fset", expose]
 def Array.set (xs : Array α) (i : @& Nat) (v : α) (h : i < xs.size := by get_elem_tactic) :
     Array α where
   toList := xs.toList.set i v
@@ -40,17 +40,15 @@ Examples:
 * `#["orange", "apple"].setIfInBounds 1 "grape" = #["orange", "grape"]`
 * `#["orange", "apple"].setIfInBounds 5 "grape" = #["orange", "apple"]`
 -/
-@[inline] def Array.setIfInBounds (xs : Array α) (i : Nat) (v : α) : Array α :=
+@[inline, expose] def Array.setIfInBounds (xs : Array α) (i : Nat) (v : α) : Array α :=
   dite (LT.lt i xs.size) (fun h => xs.set i v h) (fun _ => xs)
 
-@[deprecated Array.setIfInBounds (since := "2024-11-24")] abbrev Array.setD := @Array.setIfInBounds
-
 /--
 Set an element in an array, or panic if the index is out of bounds.
 
 This will perform the update destructively provided that `a` has a reference
 count of 1 when called.
 -/
-@[extern "lean_array_set"]
+@[extern "lean_array_set", expose]
 def Array.set! (xs : Array α) (i : @& Nat) (v : α) : Array α :=
   Array.setIfInBounds xs i v

src/Init/Data/Array/Zip.lean

@@ -45,6 +45,7 @@ theorem zipWith_self {f : α → α → δ} {xs : Array α} : zipWith f xs xs =
 See also `getElem?_zipWith'` for a variant
 using `Option.map` and `Option.bind` rather than a `match`.
 -/
+@[grind =]
 theorem getElem?_zipWith {f : α → β → γ} {i : Nat} :
     (zipWith f as bs)[i]? = match as[i]?, bs[i]? with
       | some a, some b => some (f a b) | _, _ => none := by
@@ -76,31 +77,35 @@ theorem getElem?_zip_eq_some {as : Array α} {bs : Array β} {z : α × β} {i :
   · rintro ⟨h₀, h₁⟩
     exact ⟨_, _, h₀, h₁, rfl⟩
 
-@[simp]
+@[simp, grind =]
 theorem zipWith_map {μ} {f : γ → δ → μ} {g : α → γ} {h : β → δ} {as : Array α} {bs : Array β} :
     zipWith f (as.map g) (bs.map h) = zipWith (fun a b => f (g a) (h b)) as bs := by
   cases as
   cases bs
   simp [List.zipWith_map]
 
+@[grind =]
 theorem zipWith_map_left {as : Array α} {bs : Array β} {f : α → α'} {g : α' → β → γ} :
     zipWith g (as.map f) bs = zipWith (fun a b => g (f a) b) as bs := by
   cases as
   cases bs
   simp [List.zipWith_map_left]
 
+@[grind =]
 theorem zipWith_map_right {as : Array α} {bs : Array β} {f : β → β'} {g : α → β' → γ} :
     zipWith g as (bs.map f) = zipWith (fun a b => g a (f b)) as bs := by
   cases as
   cases bs
   simp [List.zipWith_map_right]
 
+@[grind =]
 theorem zipWith_foldr_eq_zip_foldr {f : α → β → γ} {i : δ} :
     (zipWith f as bs).foldr g i = (zip as bs).foldr (fun p r => g (f p.1 p.2) r) i := by
   cases as
   cases bs
   simp [List.zipWith_foldr_eq_zip_foldr]
 
+@[grind =]
 theorem zipWith_foldl_eq_zip_foldl {f : α → β → γ} {i : δ} :
     (zipWith f as bs).foldl g i = (zip as bs).foldl (fun r p => g r (f p.1 p.2)) i := by
   cases as
@@ -111,22 +116,26 @@ theorem zipWith_foldl_eq_zip_foldl {f : α → β → γ} {i : δ} :
 theorem zipWith_eq_empty_iff {f : α → β → γ} {as : Array α} {bs : Array β} : zipWith f as bs = #[] ↔ as = #[] ∨ bs = #[] := by
   cases as <;> cases bs <;> simp
 
+@[grind =]
 theorem map_zipWith {δ : Type _} {f : α → β} {g : γ → δ → α} {cs : Array γ} {ds : Array δ} :
     map f (zipWith g cs ds) = zipWith (fun x y => f (g x y)) cs ds := by
   cases cs
   cases ds
   simp [List.map_zipWith]
 
+@[grind =]
 theorem take_zipWith : (zipWith f as bs).take i = zipWith f (as.take i) (bs.take i) := by
   cases as
   cases bs
   simp [List.take_zipWith]
 
+@[grind =]
 theorem extract_zipWith : (zipWith f as bs).extract i j = zipWith f (as.extract i j) (bs.extract i j) := by
   cases as
   cases bs
   simp [List.drop_zipWith, List.take_zipWith]
 
+@[grind =]
 theorem zipWith_append {f : α → β → γ} {as as' : Array α} {bs bs' : Array β}
     (h : as.size = bs.size) :
     zipWith f (as ++ as') (bs ++ bs') = zipWith f as bs ++ zipWith f as' bs' := by
@@ -152,7 +161,7 @@ theorem zipWith_eq_append_iff {f : α → β → γ} {as : Array α} {bs : Array
   · rintro ⟨⟨ws⟩, ⟨xs⟩, ⟨ys⟩, ⟨zs⟩, h, rfl, rfl, h₁, h₂⟩
     exact ⟨ws, xs, ys, zs, by simp_all⟩
 
-@[simp] theorem zipWith_replicate {a : α} {b : β} {m n : Nat} :
+@[simp, grind =] theorem zipWith_replicate {a : α} {b : β} {m n : Nat} :
     zipWith f (replicate m a) (replicate n b) = replicate (min m n) (f a b) := by
   simp [← List.toArray_replicate]
 
@@ -184,6 +193,7 @@ theorem zipWith_eq_zipWith_take_min (as : Array α) (bs : Array β) :
   simp
   rw [List.zipWith_eq_zipWith_take_min]
 
+@[grind =]
 theorem reverse_zipWith (h : as.size = bs.size) :
     (zipWith f as bs).reverse = zipWith f as.reverse bs.reverse := by
   cases as
@@ -200,7 +210,7 @@ theorem lt_size_right_of_zip {i : Nat} {as : Array α} {bs : Array β} (h : i <
     i < bs.size :=
   lt_size_right_of_zipWith h
 
-@[simp]
+@[simp, grind =]
 theorem getElem_zip {as : Array α} {bs : Array β} {i : Nat} {h : i < (zip as bs).size} :
     (zip as bs)[i] =
       (as[i]'(lt_size_left_of_zip h), bs[i]'(lt_size_right_of_zip h)) :=
@@ -211,18 +221,22 @@ theorem zip_eq_zipWith {as : Array α} {bs : Array β} : zip as bs = zipWith Pro
   cases bs
   simp [List.zip_eq_zipWith]
 
+@[grind _=_]
 theorem zip_map {f : α → γ} {g : β → δ} {as : Array α} {bs : Array β} :
     zip (as.map f) (bs.map g) = (zip as bs).map (Prod.map f g) := by
   cases as
   cases bs
   simp [List.zip_map]
 
+@[grind _=_]
 theorem zip_map_left {f : α → γ} {as : Array α} {bs : Array β} :
     zip (as.map f) bs = (zip as bs).map (Prod.map f id) := by rw [← zip_map, map_id]
 
+@[grind _=_]
 theorem zip_map_right {f : β → γ} {as : Array α} {bs : Array β} :
     zip as (bs.map f) = (zip as bs).map (Prod.map id f) := by rw [← zip_map, map_id]
 
+@[grind =]
 theorem zip_append {as bs : Array α} {cs ds : Array β} (_h : as.size = cs.size) :
     zip (as ++ bs) (cs ++ ds) = zip as cs ++ zip bs ds := by
   cases as
@@ -231,6 +245,7 @@ theorem zip_append {as bs : Array α} {cs ds : Array β} (_h : as.size = cs.size
   cases ds
   simp_all [List.zip_append]
 
+@[grind =]
 theorem zip_map' {f : α → β} {g : α → γ} {xs : Array α} :
     zip (xs.map f) (xs.map g) = xs.map fun a => (f a, g a) := by
   cases xs
@@ -276,7 +291,7 @@ theorem zip_eq_append_iff {as : Array α} {bs : Array β} :
       ∃ as₁ as₂ bs₁ bs₂, as₁.size = bs₁.size ∧ as = as₁ ++ as₂ ∧ bs = bs₁ ++ bs₂ ∧ xs = zip as₁ bs₁ ∧ ys = zip as₂ bs₂ := by
   simp [zip_eq_zipWith, zipWith_eq_append_iff]
 
-@[simp] theorem zip_replicate {a : α} {b : β} {m n : Nat} :
+@[simp, grind =] theorem zip_replicate {a : α} {b : β} {m n : Nat} :
     zip (replicate m a) (replicate n b) = replicate (min m n) (a, b) := by
   simp [← List.toArray_replicate]
 
@@ -293,6 +308,7 @@ theorem zip_eq_zip_take_min {as : Array α} {bs : Array β} :
 
 /-! ### zipWithAll -/
 
+@[grind =]
 theorem getElem?_zipWithAll {f : Option α → Option β → γ} {i : Nat} :
     (zipWithAll f as bs)[i]? = match as[i]?, bs[i]? with
       | none, none => .none | a?, b? => some (f a? b?) := by
@@ -301,31 +317,35 @@ theorem getElem?_zipWithAll {f : Option α → Option β → γ} {i : Nat} :
   simp [List.getElem?_zipWithAll]
   rfl
 
+@[grind =]
 theorem zipWithAll_map {μ} {f : Option γ → Option δ → μ} {g : α → γ} {h : β → δ} {as : Array α} {bs : Array β} :
     zipWithAll f (as.map g) (bs.map h) = zipWithAll (fun a b => f (g <$> a) (h <$> b)) as bs := by
   cases as
   cases bs
   simp [List.zipWithAll_map]
 
+@[grind =]
 theorem zipWithAll_map_left {as : Array α} {bs : Array β} {f : α → α'} {g : Option α' → Option β → γ} :
     zipWithAll g (as.map f) bs = zipWithAll (fun a b => g (f <$> a) b) as bs := by
   cases as
   cases bs
   simp [List.zipWithAll_map_left]
 
+@[grind =]
 theorem zipWithAll_map_right {as : Array α} {bs : Array β} {f : β → β'} {g : Option α → Option β' → γ} :
     zipWithAll g as (bs.map f) = zipWithAll (fun a b => g a (f <$> b)) as bs := by
   cases as
   cases bs
   simp [List.zipWithAll_map_right]
 
+@[grind =]
 theorem map_zipWithAll {δ : Type _} {f : α → β} {g : Option γ → Option δ → α} {cs : Array γ} {ds : Array δ} :
     map f (zipWithAll g cs ds) = zipWithAll (fun x y => f (g x y)) cs ds := by
   cases cs
   cases ds
   simp [List.map_zipWithAll]
 
-@[simp] theorem zipWithAll_replicate {a : α} {b : β} {n : Nat} :
+@[simp, grind =] theorem zipWithAll_replicate {a : α} {b : β} {n : Nat} :
     zipWithAll f (replicate n a) (replicate n b) = replicate n (f (some a) (some b)) := by
   simp [← List.toArray_replicate]
 
@@ -342,6 +362,7 @@ theorem unzip_fst : (unzip l).fst = l.map Prod.fst := by
 theorem unzip_snd : (unzip l).snd = l.map Prod.snd := by
   simp
 
+@[grind =]
 theorem unzip_eq_map {xs : Array (α × β)} : unzip xs = (xs.map Prod.fst, xs.map Prod.snd) := by
   cases xs
   simp [List.unzip_eq_map]
@@ -375,9 +396,11 @@ theorem zip_of_prod {as : Array α} {bs : Array β} {xs : Array (α × β)} (hl
     (hr : xs.map Prod.snd = bs) : xs = as.zip bs := by
   rw [← hl, ← hr, ← zip_unzip xs, ← fst_unzip, ← snd_unzip, zip_unzip, zip_unzip]
 
-@[simp] theorem unzip_replicate {n : Nat} {a : α} {b : β} :
+@[simp, grind =] theorem unzip_replicate {n : Nat} {a : α} {b : β} :
     unzip (replicate n (a, b)) = (replicate n a, replicate n b) := by
   ext1 <;> simp
 
 @[deprecated unzip_replicate (since := "2025-03-18")]
 abbrev unzip_mkArray := @unzip_replicate
+
+end Array

src/Init/Data/BEq.lean

@@ -27,7 +27,7 @@ class EquivBEq (α) [BEq α] : Prop extends PartialEquivBEq α, ReflBEq α
 theorem BEq.symm [BEq α] [PartialEquivBEq α] {a b : α} : a == b → b == a :=
   PartialEquivBEq.symm
 
-@[grind] theorem BEq.comm [BEq α] [PartialEquivBEq α] {a b : α} : (a == b) = (b == a) :=
+theorem BEq.comm [BEq α] [PartialEquivBEq α] {a b : α} : (a == b) = (b == a) :=
   Bool.eq_iff_iff.2 ⟨BEq.symm, BEq.symm⟩
 
 theorem bne_comm [BEq α] [PartialEquivBEq α] {a b : α} : (a != b) = (b != a) := by

src/Init/Data/BitVec.lean

@@ -6,7 +6,10 @@ Authors: Kim Morrison
 module
 
 prelude
+import Init.Data.BitVec.BasicAux
 import Init.Data.BitVec.Basic
+import Init.Data.BitVec.Bootstrap
 import Init.Data.BitVec.Bitblast
-import Init.Data.BitVec.Folds
+import Init.Data.BitVec.Decidable
 import Init.Data.BitVec.Lemmas
+import Init.Data.BitVec.Folds

src/Init/Data/BitVec/Basic.lean

@@ -61,7 +61,7 @@ end subsingleton
 section zero_allOnes
 
 /-- Returns a bitvector of size `n` where all bits are `0`. -/
-protected def zero (n : Nat) : BitVec n := .ofNatLT 0 (Nat.two_pow_pos n)
+@[expose] protected def zero (n : Nat) : BitVec n := .ofNatLT 0 (Nat.two_pow_pos n)
 instance : Inhabited (BitVec n) where default := .zero n
 
 /-- Returns a bitvector of size `n` where all bits are `1`. -/
@@ -74,28 +74,30 @@ section getXsb
 
 /--
 Returns the `i`th least significant bit.
-
-This will be renamed `getLsb` after the existing deprecated alias is removed.
 -/
-@[inline] def getLsb' (x : BitVec w) (i : Fin w) : Bool := x.toNat.testBit i
+@[inline, expose] def getLsb (x : BitVec w) (i : Fin w) : Bool := x.toNat.testBit i
+
+@[deprecated getLsb (since := "2025-06-17"), inherit_doc getLsb]
+abbrev getLsb' := @getLsb
 
 /-- Returns the `i`th least significant bit, or `none` if `i ≥ w`. -/
-@[inline] def getLsb? (x : BitVec w) (i : Nat) : Option Bool :=
-  if h : i < w then some (getLsb' x ⟨i, h⟩) else none
+@[inline, expose] def getLsb? (x : BitVec w) (i : Nat) : Option Bool :=
+  if h : i < w then some (getLsb x ⟨i, h⟩) else none
 
 /--
 Returns the `i`th most significant bit.
-
-This will be renamed `BitVec.getMsb` after the existing deprecated alias is removed.
 -/
-@[inline] def getMsb' (x : BitVec w) (i : Fin w) : Bool := x.getLsb' ⟨w-1-i, by omega⟩
+@[inline] def getMsb (x : BitVec w) (i : Fin w) : Bool := x.getLsb ⟨w-1-i, by omega⟩
+
+@[deprecated getMsb (since := "2025-06-17"), inherit_doc getMsb]
+abbrev getMsb' := @getMsb
 
 /-- Returns the `i`th most significant bit or `none` if `i ≥ w`. -/
 @[inline] def getMsb? (x : BitVec w) (i : Nat) : Option Bool :=
-  if h : i < w then some (getMsb' x ⟨i, h⟩) else none
+  if h : i < w then some (getMsb x ⟨i, h⟩) else none
 
 /-- Returns the `i`th least significant bit or `false` if `i ≥ w`. -/
-@[inline] def getLsbD (x : BitVec w) (i : Nat) : Bool :=
+@[inline, expose] def getLsbD (x : BitVec w) (i : Nat) : Bool :=
   x.toNat.testBit i
 
 /-- Returns the `i`th most significant bit, or `false` if `i ≥ w`. -/
@@ -110,11 +112,11 @@ end getXsb
 section getElem
 
 instance : GetElem (BitVec w) Nat Bool fun _ i => i < w where
-  getElem xs i h := xs.getLsb' ⟨i, h⟩
+  getElem xs i h := xs.getLsb ⟨i, h⟩
 
 /-- We prefer `x[i]` as the simp normal form for `getLsb'` -/
-@[simp] theorem getLsb'_eq_getElem (x : BitVec w) (i : Fin w) :
-    x.getLsb' i = x[i] := rfl
+@[simp] theorem getLsb_eq_getElem (x : BitVec w) (i : Fin w) :
+    x.getLsb i = x[i] := rfl
 
 /-- We prefer `x[i]?` as the simp normal form for `getLsb?` -/
 @[simp] theorem getLsb?_eq_getElem? (x : BitVec w) (i : Nat) :
@@ -134,6 +136,7 @@ section Int
 /--
 Interprets the bitvector as an integer stored in two's complement form.
 -/
+@[expose]
 protected def toInt (x : BitVec n) : Int :=
   if 2 * x.toNat < 2^n then
     x.toNat
@@ -147,6 +150,7 @@ over- and underflowing as needed.
 The underlying `Nat` is `(2^n + (i mod 2^n)) mod 2^n`. Converting the bitvector back to an `Int`
 with `BitVec.toInt` results in the value `i.bmod (2^n)`.
 -/
+@[expose]
 protected def ofInt (n : Nat) (i : Int) : BitVec n := .ofNatLT (i % (Int.ofNat (2^n))).toNat (by
   apply (Int.toNat_lt _).mpr
   · apply Int.emod_lt_of_pos
@@ -172,7 +176,7 @@ recommended_spelling "zero" for "0#n" in [BitVec.ofNat, «term__#__»]
 recommended_spelling "one" for "1#n" in [BitVec.ofNat, «term__#__»]
 
 /-- Unexpander for bitvector literals. -/
-@[app_unexpander BitVec.ofNat] def unexpandBitVecOfNat : Lean.PrettyPrinter.Unexpander
+@[app_unexpander BitVec.ofNat] meta def unexpandBitVecOfNat : Lean.PrettyPrinter.Unexpander
   | `($(_) $n $i:num) => `($i:num#$n)
   | _ => throw ()
 
@@ -181,7 +185,7 @@ scoped syntax:max term:max noWs "#'" noWs term:max : term
 macro_rules | `($i#'$p) => `(BitVec.ofNatLT $i $p)
 
 /-- Unexpander for bitvector literals without truncation. -/
-@[app_unexpander BitVec.ofNatLT] def unexpandBitVecOfNatLt : Lean.PrettyPrinter.Unexpander
+@[app_unexpander BitVec.ofNatLT] meta def unexpandBitVecOfNatLt : Lean.PrettyPrinter.Unexpander
   | `($(_) $i $p) => `($i#'$p)
   | _ => throw ()
 
@@ -218,12 +222,14 @@ Usually accessed via the `-` prefix operator.
 
 SMT-LIB name: `bvneg`.
 -/
+@[expose]
 protected def neg (x : BitVec n) : BitVec n := .ofNat n (2^n - x.toNat)
 instance : Neg (BitVec n) := ⟨.neg⟩
 
 /--
 Returns the absolute value of a signed bitvector.
 -/
+@[expose]
 protected def abs (x : BitVec n) : BitVec n := if x.msb then .neg x else x
 
 /--
@@ -232,6 +238,7 @@ modulo `2^n`. Usually accessed via the `*` operator.
 
 SMT-LIB name: `bvmul`.
 -/
+@[expose]
 protected def mul (x y : BitVec n) : BitVec n := BitVec.ofNat n (x.toNat * y.toNat)
 instance : Mul (BitVec n) := ⟨.mul⟩
 
@@ -242,6 +249,7 @@ Note that this is currently an inefficient implementation,
 and should be replaced via an `@[extern]` with a native implementation.
 See https://github.com/leanprover/lean4/issues/7887.
 -/
+@[expose]
 protected def pow (x : BitVec n) (y : Nat) : BitVec n :=
   match y with
   | 0 => 1
@@ -253,6 +261,7 @@ instance : Pow (BitVec n) Nat where
 Unsigned division of bitvectors using the Lean convention where division by zero returns zero.
 Usually accessed via the `/` operator.
 -/
+@[expose]
 def udiv (x y : BitVec n) : BitVec n :=
   (x.toNat / y.toNat)#'(Nat.lt_of_le_of_lt (Nat.div_le_self _ _) x.isLt)
 instance : Div (BitVec n) := ⟨.udiv⟩
@@ -262,6 +271,7 @@ Unsigned modulo for bitvectors. Usually accessed via the `%` operator.
 
 SMT-LIB name: `bvurem`.
 -/
+@[expose]
 def umod (x y : BitVec n) : BitVec n :=
   (x.toNat % y.toNat)#'(Nat.lt_of_le_of_lt (Nat.mod_le _ _) x.isLt)
 instance : Mod (BitVec n) := ⟨.umod⟩
@@ -273,6 +283,7 @@ where division by zero returns `BitVector.allOnes n`.
 
 SMT-LIB name: `bvudiv`.
 -/
+@[expose]
 def smtUDiv (x y : BitVec n) : BitVec n := if y = 0 then allOnes n else udiv x y
 
 /--
@@ -342,6 +353,7 @@ end arithmetic
 section bool
 
 /-- Turns a `Bool` into a bitvector of length `1`. -/
+@[expose]
 def ofBool (b : Bool) : BitVec 1 := cond b 1 0
 
 @[simp] theorem ofBool_false : ofBool false = 0 := by trivial
@@ -359,6 +371,7 @@ Unsigned less-than for bitvectors.
 
 SMT-LIB name: `bvult`.
 -/
+@[expose]
 protected def ult (x y : BitVec n) : Bool := x.toNat < y.toNat
 
 /--
@@ -366,6 +379,7 @@ Unsigned less-than-or-equal-to for bitvectors.
 
 SMT-LIB name: `bvule`.
 -/
+@[expose]
 protected def ule (x y : BitVec n) : Bool := x.toNat ≤ y.toNat
 
 /--
@@ -377,6 +391,7 @@ Examples:
  * `BitVec.slt 6#4 7 = true`
  * `BitVec.slt 7#4 8 = false`
 -/
+@[expose]
 protected def slt (x y : BitVec n) : Bool := x.toInt < y.toInt
 
 /--
@@ -384,6 +399,7 @@ Signed less-than-or-equal-to for bitvectors.
 
 SMT-LIB name: `bvsle`.
 -/
+@[expose]
 protected def sle (x y : BitVec n) : Bool := x.toInt ≤ y.toInt
 
 end relations
@@ -397,7 +413,7 @@ width `m`.
 Using `x.cast eq` should be preferred over `eq ▸ x` because there are special-purpose `simp` lemmas
 that can more consistently simplify `BitVec.cast` away.
 -/
-@[inline] protected def cast (eq : n = m) (x : BitVec n) : BitVec m := .ofNatLT x.toNat (eq ▸ x.isLt)
+@[inline, expose] protected def cast (eq : n = m) (x : BitVec n) : BitVec m := .ofNatLT x.toNat (eq ▸ x.isLt)
 
 @[simp] theorem cast_ofNat {n m : Nat} (h : n = m) (x : Nat) :
     (BitVec.ofNat n x).cast h = BitVec.ofNat m x := by
@@ -413,6 +429,7 @@ that can more consistently simplify `BitVec.cast` away.
 Extracts the bits `start` to `start + len - 1` from a bitvector of size `n` to yield a
 new bitvector of size `len`. If `start + len > n`, then the bitvector is zero-extended.
 -/
+@[expose]
 def extractLsb' (start len : Nat) (x : BitVec n) : BitVec len := .ofNat _ (x.toNat >>> start)
 
 /--
@@ -423,6 +440,7 @@ The resulting bitvector has size `hi - lo + 1`.
 
 SMT-LIB name: `extract`.
 -/
+@[expose]
 def extractLsb (hi lo : Nat) (x : BitVec n) : BitVec (hi - lo + 1) := extractLsb' lo _ x
 
 /--
@@ -431,6 +449,7 @@ Increases the width of a bitvector to one that is at least as large by zero-exte
 This is a constant-time operation because the underlying `Nat` is unmodified; because the new width
 is at least as large as the old one, no overflow is possible.
 -/
+@[expose]
 def setWidth' {n w : Nat} (le : n ≤ w) (x : BitVec n) : BitVec w :=
   x.toNat#'(by
     apply Nat.lt_of_lt_of_le x.isLt
@@ -439,6 +458,7 @@ def setWidth' {n w : Nat} (le : n ≤ w) (x : BitVec n) : BitVec w :=
 /--
 Returns `zeroExtend (w+n) x <<< n` without needing to compute `x % 2^(2+n)`.
 -/
+@[expose]
 def shiftLeftZeroExtend (msbs : BitVec w) (m : Nat) : BitVec (w + m) :=
   let shiftLeftLt {x : Nat} (p : x < 2^w) (m : Nat) : x <<< m < 2^(w + m) := by
         simp [Nat.shiftLeft_eq, Nat.pow_add]
@@ -495,6 +515,7 @@ SMT-LIB name: `bvand`.
 Example:
  * `0b1010#4 &&& 0b0110#4 = 0b0010#4`
 -/
+@[expose]
 protected def and (x y : BitVec n) : BitVec n :=
   (x.toNat &&& y.toNat)#'(Nat.and_lt_two_pow x.toNat y.isLt)
 instance : AndOp (BitVec w) := ⟨.and⟩
@@ -507,6 +528,7 @@ SMT-LIB name: `bvor`.
 Example:
  * `0b1010#4 ||| 0b0110#4 = 0b1110#4`
 -/
+@[expose]
 protected def or (x y : BitVec n) : BitVec n :=
   (x.toNat ||| y.toNat)#'(Nat.or_lt_two_pow x.isLt y.isLt)
 instance : OrOp (BitVec w) := ⟨.or⟩
@@ -519,6 +541,7 @@ SMT-LIB name: `bvxor`.
 Example:
  * `0b1010#4 ^^^ 0b0110#4 = 0b1100#4`
 -/
+@[expose]
 protected def xor (x y : BitVec n) : BitVec n :=
   (x.toNat ^^^ y.toNat)#'(Nat.xor_lt_two_pow x.isLt y.isLt)
 instance : Xor (BitVec w) := ⟨.xor⟩
@@ -531,6 +554,7 @@ SMT-LIB name: `bvnot`.
 Example:
  * `~~~(0b0101#4) == 0b1010`
 -/
+@[expose]
 protected def not (x : BitVec n) : BitVec n := allOnes n ^^^ x
 instance : Complement (BitVec w) := ⟨.not⟩
 
@@ -540,6 +564,7 @@ equivalent to `x * 2^s`, modulo `2^n`.
 
 SMT-LIB name: `bvshl` except this operator uses a `Nat` shift value.
 -/
+@[expose]
 protected def shiftLeft (x : BitVec n) (s : Nat) : BitVec n := BitVec.ofNat n (x.toNat <<< s)
 instance : HShiftLeft (BitVec w) Nat (BitVec w) := ⟨.shiftLeft⟩
 
@@ -551,6 +576,7 @@ As a numeric operation, this is equivalent to `x / 2^s`, rounding down.
 
 SMT-LIB name: `bvlshr` except this operator uses a `Nat` shift value.
 -/
+@[expose]
 def ushiftRight (x : BitVec n) (s : Nat) : BitVec n :=
   (x.toNat >>> s)#'(by
   let ⟨x, lt⟩ := x
@@ -568,6 +594,7 @@ As a numeric operation, this is equivalent to `x.toInt >>> s`.
 
 SMT-LIB name: `bvashr` except this operator uses a `Nat` shift value.
 -/
+@[expose]
 def sshiftRight (x : BitVec n) (s : Nat) : BitVec n := .ofInt n (x.toInt >>> s)
 
 instance {n} : HShiftLeft  (BitVec m) (BitVec n) (BitVec m) := ⟨fun x y => x <<< y.toNat⟩
@@ -581,10 +608,12 @@ As a numeric operation, this is equivalent to `a.toInt >>> s.toNat`.
 
 SMT-LIB name: `bvashr`.
 -/
+@[expose]
 def sshiftRight' (a : BitVec n) (s : BitVec m) : BitVec n := a.sshiftRight s.toNat
 
 /-- Auxiliary function for `rotateLeft`, which does not take into account the case where
 the rotation amount is greater than the bitvector width. -/
+@[expose]
 def rotateLeftAux (x : BitVec w) (n : Nat) : BitVec w :=
   x <<< n ||| x >>> (w - n)
 
@@ -599,6 +628,7 @@ SMT-LIB name: `rotate_left`, except this operator uses a `Nat` shift amount.
 Example:
  * `(0b0011#4).rotateLeft 3 = 0b1001`
 -/
+@[expose]
 def rotateLeft (x : BitVec w) (n : Nat) : BitVec w := rotateLeftAux x (n % w)
 
 
@@ -606,6 +636,7 @@ 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.
 -/
+@[expose]
 def rotateRightAux (x : BitVec w) (n : Nat) : BitVec w :=
   x >>> n ||| x <<< (w - n)
 
@@ -620,6 +651,7 @@ SMT-LIB name: `rotate_right`, except this operator uses a `Nat` shift amount.
 Example:
  * `rotateRight 0b01001#5 1 = 0b10100`
 -/
+@[expose]
 def rotateRight (x : BitVec w) (n : Nat) : BitVec w := rotateRightAux x (n % w)
 
 /--
@@ -631,6 +663,7 @@ SMT-LIB name: `concat`.
 Example:
  * `0xAB#8 ++ 0xCD#8 = 0xABCD#16`.
 -/
+@[expose]
 def append (msbs : BitVec n) (lsbs : BitVec m) : BitVec (n+m) :=
   shiftLeftZeroExtend msbs m ||| setWidth' (Nat.le_add_left m n) lsbs
 
@@ -653,6 +686,7 @@ result of appending a single bit to the front in the naive implementation).
 
 /-- Append a single bit to the end of a bitvector, using big endian order (see `append`).
     That is, the new bit is the least significant bit. -/
+@[expose]
 def concat {n} (msbs : BitVec n) (lsb : Bool) : BitVec (n+1) := msbs ++ (ofBool lsb)
 
 /--
@@ -660,6 +694,7 @@ Shifts all bits of `x` to the left by `1` and sets the least significant bit to
 
 This is a non-dependent version of `BitVec.concat` that does not change the total bitwidth.
 -/
+@[expose]
 def shiftConcat (x : BitVec n) (b : Bool) : BitVec n :=
   (x.concat b).truncate n
 
@@ -668,6 +703,7 @@ Prepends a single bit to the front of a bitvector, using big-endian order (see `
 
 The new bit is the most significant bit.
 -/
+@[expose]
 def cons {n} (msb : Bool) (lsbs : BitVec n) : BitVec (n+1) :=
   ((ofBool msb) ++ lsbs).cast (Nat.add_comm ..)
 
@@ -689,6 +725,12 @@ def twoPow (w : Nat) (i : Nat) : BitVec w := 1#w <<< i
 
 end bitwise
 
+/-- The bitvector of width `w` that has the smallest value when interpreted as an integer. -/
+def intMin (w : Nat) := twoPow w (w - 1)
+
+/-- The bitvector of width `w` that has the largest value when interpreted as an integer. -/
+def intMax (w : Nat) := (twoPow w (w - 1)) - 1
+
 /--
 Computes a hash of a bitvector, combining 64-bit words using `mixHash`.
 -/
@@ -752,6 +794,7 @@ Checks whether subtraction of `x` and `y` results in *unsigned* overflow.
 
 SMT-Lib name: `bvusubo`.
 -/
+@[expose]
 def usubOverflow {w : Nat} (x y : BitVec w) : Bool := x.toNat < y.toNat
 
 /--
@@ -760,6 +803,7 @@ Checks whether the subtraction of `x` and `y` results in *signed* overflow, trea
 
 SMT-Lib name: `bvssubo`.
 -/
+@[expose]
 def ssubOverflow {w : Nat} (x y : BitVec w) : Bool :=
   (x.toInt - y.toInt ≥ 2 ^ (w - 1)) || (x.toInt - y.toInt < - 2 ^ (w - 1))
 
@@ -770,6 +814,7 @@ For a bitvector `x` with nonzero width, this only happens if `x = intMin`.
 
 SMT-Lib name: `bvnego`.
 -/
+@[expose]
 def negOverflow {w : Nat} (x : BitVec w) : Bool :=
   x.toInt == - 2 ^ (w - 1)
 
@@ -779,6 +824,7 @@ For BitVecs `x` and `y` with nonzero width, this only happens if `x = intMin` an
 
 SMT-LIB name: `bvsdivo`.
 -/
+@[expose]
 def sdivOverflow {w : Nat} (x y : BitVec w) : Bool :=
   (2 ^ (w - 1) ≤ x.toInt / y.toInt) || (x.toInt / y.toInt <  - 2 ^ (w - 1))
 
@@ -804,4 +850,15 @@ treating `x` and `y` as 2's complement signed bitvectors.
 def smulOverflow {w : Nat} (x y : BitVec w) : Bool :=
   (x.toInt * y.toInt ≥ 2 ^ (w - 1)) || (x.toInt * y.toInt < - 2 ^ (w - 1))
 
+/-- Count the number of leading zeros downward from the `n`-th bit to the `0`-th bit for the bitblaster.
+  This builds a tree of `if-then-else` lookups whose length is linear in the bitwidth,
+  and an efficient circuit for bitblasting `clz`. -/
+def clzAuxRec {w : Nat} (x : BitVec w) (n : Nat) : BitVec w :=
+  match n with
+  | 0 => if x.getLsbD 0 then BitVec.ofNat w (w - 1) else BitVec.ofNat w w
+  | n' + 1 => if x.getLsbD n then BitVec.ofNat w (w - 1 - n) else clzAuxRec x n'
+
+/-- Count the number of leading zeros. -/
+def clz (x : BitVec w) : BitVec w := clzAuxRec x (w - 1)
+
 end BitVec

src/Init/Data/BitVec/BasicAux.lean

@@ -24,7 +24,7 @@ The bitvector with value `i mod 2^n`.
 -/
 @[expose, match_pattern]
 protected def ofNat (n : Nat) (i : Nat) : BitVec n where
-  toFin := Fin.ofNat' (2^n) i
+  toFin := Fin.ofNat (2^n) i
 
 instance instOfNat : OfNat (BitVec n) i where ofNat := .ofNat n i
 
@@ -41,6 +41,7 @@ Usually accessed via the `+` operator.
 
 SMT-LIB name: `bvadd`.
 -/
+@[expose]
 protected def add (x y : BitVec n) : BitVec n := .ofNat n (x.toNat + y.toNat)
 instance : Add (BitVec n) := ⟨BitVec.add⟩
 
@@ -49,6 +50,7 @@ Subtracts one bitvector from another. This can be interpreted as either signed o
 modulo `2^n`. Usually accessed via the `-` operator.
 
 -/
+@[expose]
 protected def sub (x y : BitVec n) : BitVec n := .ofNat n ((2^n - y.toNat) + x.toNat)
 instance : Sub (BitVec n) := ⟨BitVec.sub⟩
 

src/Init/Data/BitVec/Bitblast.lean

@@ -6,12 +6,14 @@ Authors: Harun Khan, Abdalrhman M Mohamed, Joe Hendrix, Siddharth Bhat
 module
 
 prelude
-import Init.Data.BitVec.Folds
 import all Init.Data.Nat.Bitwise.Basic
 import Init.Data.Nat.Mod
 import all Init.Data.Int.DivMod
 import Init.Data.Int.LemmasAux
-import all Init.Data.BitVec.Lemmas
+import all Init.Data.BitVec.Basic
+import Init.Data.BitVec.Decidable
+import Init.Data.BitVec.Lemmas
+import Init.Data.BitVec.Folds
 
 /-!
 # Bit blasting of bitvectors
@@ -238,7 +240,7 @@ theorem toNat_add_of_and_eq_zero {x y : BitVec w} (h : x &&& y = 0#w) :
     simp only [decide_eq_true_eq] at this
     omega
   rw [← carry_width]
-  simp [not_eq_true, carry_of_and_eq_zero h]
+  simp [carry_of_and_eq_zero h]
 
 /-- Carry function for bitwise addition. -/
 def adcb (x y c : Bool) : Bool × Bool := (atLeastTwo x y c, x ^^ (y ^^ c))
@@ -252,7 +254,7 @@ theorem getLsbD_add_add_bool {i : Nat} (i_lt : i < w) (x y : BitVec w) (c : Bool
       (getLsbD x i ^^ (getLsbD y i ^^ carry i x y c)) := by
   let ⟨x, x_lt⟩ := x
   let ⟨y, y_lt⟩ := y
-  simp only [getLsbD, toNat_add, toNat_setWidth, i_lt, toNat_ofFin, toNat_ofBool,
+  simp only [getLsbD, toNat_add, toNat_setWidth, toNat_ofFin, toNat_ofBool,
     Nat.mod_add_mod, Nat.add_mod_mod]
   apply Eq.trans
   rw [← Nat.div_add_mod x (2^i), ← Nat.div_add_mod y (2^i)]
@@ -295,7 +297,7 @@ theorem adc_spec (x y : BitVec w) (c : Bool) :
     simp [carry, Nat.mod_one]
     cases c <;> rfl
   case step =>
-    simp [adcb, Prod.mk.injEq, carry_succ, getElem_add_add_bool]
+    simp [adcb, carry_succ, getElem_add_add_bool]
 
 theorem add_eq_adc (w : Nat) (x y : BitVec w) : x + y = (adc x y false).snd := by
   simp [adc_spec]
@@ -312,7 +314,7 @@ theorem msb_add {w : Nat} {x y: BitVec w} :
       Bool.xor x.msb (Bool.xor y.msb (carry (w - 1) x y false)) := by
   simp only [BitVec.msb, BitVec.getMsbD]
   by_cases h : w ≤ 0
-  · simp [h, show w = 0 by omega]
+  · simp [show w = 0 by omega]
   · rw [getLsbD_add (x := x)]
     simp [show w > 0 by omega]
     omega
@@ -332,15 +334,15 @@ 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, getLsbD_or,
+  · simp only [adcb, atLeastTwo, Bool.and_false, Bool.or_false, bne_false, 
     Prod.mk.injEq, and_eq_false_imp]
     intros i
     replace h : (x &&& y).getLsbD i = (0#w).getLsbD i := by rw [h]
     simp only [getLsbD_and, getLsbD_zero, and_eq_false_imp] at h
     constructor
     · intros hx
-      simp_all [hx]
-    · by_cases hx : x.getLsbD i <;> simp_all [hx]
+      simp_all
+    · by_cases hx : x.getLsbD i <;> simp_all
 
 /-! ### Sub-/
 
@@ -377,7 +379,7 @@ theorem bit_not_add_self (x : BitVec w) :
   simp only [add_eq_adc]
   apply iunfoldr_replace_snd (fun _ => false) (-1) false rfl
   intro i; simp only [adcb, Fin.is_lt, getLsbD_eq_getElem, atLeastTwo_false_right, bne_false,
-    ofNat_eq_ofNat, Fin.getElem_fin, Prod.mk.injEq, and_eq_false_imp]
+    ofNat_eq_ofNat, Prod.mk.injEq, and_eq_false_imp]
   rw [iunfoldr_replace_snd (fun _ => ()) (((iunfoldr (fun i c => (c, !(x[i.val])))) ()).snd)]
   <;> simp [bit_not_testBit, neg_one_eq_allOnes, getElem_allOnes]
 
@@ -409,7 +411,7 @@ theorem getLsbD_neg {i : Nat} {x : BitVec w} :
   · rw [getLsbD_add hi]
     have : 0 < w := by omega
     simp only [getLsbD_not, hi, decide_true, Bool.true_and, getLsbD_one, this, not_bne,
-      _root_.true_and, not_eq_eq_eq_not]
+      not_eq_eq_eq_not]
     cases i with
     | zero =>
       have carry_zero : carry 0 ?x ?y false = false := by
@@ -424,7 +426,7 @@ theorem getLsbD_neg {i : Nat} {x : BitVec w} :
       · rintro h j hj; exact And.right <| h j (by omega)
       · rintro h j hj; exact ⟨by omega, h j (by omega)⟩
   · have h_ge : w ≤ i := by omega
-    simp [getLsbD_of_ge _ _ h_ge, h_ge, hi]
+    simp [h_ge, hi]
 
 theorem getElem_neg {i : Nat} {x : BitVec w} (h : i < w) :
     (-x)[i] = (x[i] ^^ decide (∃ j < i, x.getLsbD j = true)) := by
@@ -433,7 +435,7 @@ theorem getElem_neg {i : Nat} {x : BitVec w} (h : i < w) :
 theorem getMsbD_neg {i : Nat} {x : BitVec w} :
     getMsbD (-x) i =
       (getMsbD x i ^^ decide (∃ j < w, i < j ∧ getMsbD x j = true)) := by
-  simp only [getMsbD, getLsbD_neg, Bool.decide_and, Bool.and_eq_true, decide_eq_true_eq]
+  simp only [getMsbD, getLsbD_neg, Bool.and_eq_true, decide_eq_true_eq]
   by_cases hi : i < w
   case neg =>
     simp [hi]; omega
@@ -518,14 +520,11 @@ theorem msb_neg {w : Nat} {x : BitVec w} :
   rw [(show w = w - 1 + 1 by omega), Int.pow_succ] at this
   omega
 
-@[simp] theorem setWidth_neg_of_le {x : BitVec v} (h : w ≤ v) : BitVec.setWidth w (-x) = -BitVec.setWidth w x := by
-  simp [← BitVec.signExtend_eq_setWidth_of_le _ h, BitVec.signExtend_neg_of_le h]
-
 /-! ### abs -/
 
 theorem msb_abs {w : Nat} {x : BitVec w} :
     x.abs.msb = (decide (x = intMin w) && decide (0 < w)) := by
-  simp only [BitVec.abs, getMsbD_neg, ne_eq, decide_not, Bool.not_bne]
+  simp only [BitVec.abs]
   by_cases h₀ : 0 < w
   · by_cases h₁ : x = intMin w
     · simp [h₁, msb_intMin]
@@ -548,54 +547,14 @@ theorem ult_eq_not_carry (x y : BitVec w) : x.ult y = !carry w x (~~~y) true :=
   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 [-Int.natCast_pow]; 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 zero_sle_eq_not_msb {w : Nat} {x : BitVec w} : BitVec.sle 0#w x = !x.msb := by
-  rw [sle_eq_not_slt, BitVec.slt_zero_eq_msb]
-
-theorem zero_sle_iff_msb_eq_false {w : Nat} {x : BitVec w} : BitVec.sle 0#w x ↔ x.msb = false := by
-  simp [zero_sle_eq_not_msb]
-
-theorem toNat_toInt_of_sle {w : Nat} {x : BitVec w} (hx : BitVec.sle 0#w x) : x.toInt.toNat = x.toNat :=
-  toNat_toInt_of_msb x (zero_sle_iff_msb_eq_false.1 hx)
-
 theorem sle_eq_carry {x y : BitVec w} :
     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]
@@ -618,12 +577,6 @@ theorem neg_sle_zero (h : 0 < w) {x : BitVec w} :
   rw [sle_eq_slt_or_eq, neg_slt_zero h, sle_eq_slt_or_eq]
   simp [Bool.beq_eq_decide_eq (-x), Bool.beq_eq_decide_eq _ x, Eq.comm (a := x), Bool.or_assoc]
 
-theorem sle_eq_ule {x y : BitVec w} : x.sle y = (x.msb != y.msb ^^ x.ule y) := by
-  rw [sle_eq_not_slt, slt_eq_ult, ← Bool.xor_not, ← ule_eq_not_ult, bne_comm]
-
-theorem sle_eq_ule_of_msb_eq {x y : BitVec w} (h : x.msb = y.msb) : x.sle y = x.ule y := by
-  simp [BitVec.sle_eq_ule, h]
-
 /-! ### mul recurrence for bit blasting -/
 
 /--
@@ -631,6 +584,7 @@ A recurrence that describes multiplication as repeated addition.
 
 This function is useful for bit blasting multiplication.
 -/
+@[expose]
 def mulRec (x y : BitVec w) (s : Nat) : BitVec w :=
   let cur := if y.getLsbD s then (x <<< s) else 0
   match s with
@@ -657,7 +611,7 @@ theorem setWidth_setWidth_succ_eq_setWidth_setWidth_add_twoPow (x : BitVec w) (i
       getElem_twoPow]
     by_cases hik : i = k
     · subst hik
-      simp [h]
+      simp
     · by_cases hik' : k < (i + 1)
       · have hik'' : k < i := by omega
         simp [hik', hik'']
@@ -666,8 +620,8 @@ theorem setWidth_setWidth_succ_eq_setWidth_setWidth_add_twoPow (x : BitVec w) (i
         simp [hik', hik'']
         omega
   · ext k
-    simp only [and_twoPow, getLsbD_and, getLsbD_setWidth, Fin.is_lt, decide_true, Bool.true_and,
-      getLsbD_zero, and_eq_false_imp, and_eq_true, decide_eq_true_eq, and_imp]
+    simp only [and_twoPow, 
+      ]
     by_cases hi : x.getLsbD i <;> simp [hi] <;> omega
 
 /--
@@ -824,7 +778,7 @@ private theorem Nat.div_add_eq_left_of_lt {x y z : Nat} (hx : z ∣ x) (hy : y <
   · apply Nat.le_trans
     · exact div_mul_le_self x z
     · omega
-  · simp only [succ_eq_add_one, Nat.add_mul, Nat.one_mul]
+  · simp only [Nat.add_mul, Nat.one_mul]
     apply Nat.add_lt_add_of_le_of_lt
     · apply Nat.le_of_eq
       exact (Nat.div_eq_iff_eq_mul_left hz hx).mp rfl
@@ -937,10 +891,10 @@ def DivModState.lawful_init {w : Nat} (args : DivModArgs w) (hd : 0#w < args.d)
     hwrn := by simp only; omega,
     hdPos := by assumption
     hrLtDivisor := by simp [BitVec.lt_def] at hd ⊢; assumption
-    hrWidth := by simp [DivModState.init],
-    hqWidth := by simp [DivModState.init],
+    hrWidth := by simp,
+    hqWidth := by simp,
     hdiv := by
-      simp only [DivModState.init, toNat_ofNat, zero_mod, Nat.mul_zero, Nat.add_zero];
+      simp only [toNat_ofNat, zero_mod, Nat.mul_zero, Nat.add_zero];
       rw [Nat.shiftRight_eq_div_pow]
       apply Nat.div_eq_of_lt args.n.isLt
   }
@@ -968,7 +922,7 @@ theorem DivModState.umod_eq_of_lawful {qr : DivModState w}
     n % d = qr.r := by
   apply umod_eq_of_mul_add_toNat h.hrLtDivisor
   have hdiv := h.hdiv
-  simp only [shiftRight_zero] at hdiv
+  simp only at hdiv
   simp only [h_final] at *
   exact hdiv.symm
 
@@ -1022,7 +976,7 @@ theorem DivModState.toNat_shiftRight_sub_one_eq
     {args : DivModArgs w} {qr : DivModState w} (h : qr.Poised args) :
     args.n.toNat >>> (qr.wn - 1)
     = (args.n.toNat >>> qr.wn) * 2 + (args.n.getLsbD (qr.wn - 1)).toNat := by
-  show BitVec.toNat (args.n >>> (qr.wn - 1)) = _
+  change BitVec.toNat (args.n >>> (qr.wn - 1)) = _
   have {..} := h -- break the structure down for `omega`
   rw [shiftRight_sub_one_eq_shiftConcat args.n h.hwn_lt]
   rw [toNat_shiftConcat_eq_of_lt (k := w - qr.wn)]
@@ -1046,7 +1000,7 @@ obeys the division equation. -/
 theorem lawful_divSubtractShift (qr : DivModState w) (h : qr.Poised args) :
     DivModState.Lawful args (divSubtractShift args qr) := by
   rcases args with ⟨n, d⟩
-  simp only [divSubtractShift, decide_eq_true_eq]
+  simp only [divSubtractShift]
   -- We add these hypotheses for `omega` to find them later.
   have ⟨⟨hrwn, hd, hrd, hr, hn, hrnd⟩, hwn_lt⟩ := h
   have : d.toNat * (qr.q.toNat * 2) = d.toNat * qr.q.toNat * 2 := by rw [Nat.mul_assoc]
@@ -1091,6 +1045,7 @@ theorem lawful_divSubtractShift (qr : DivModState w) (h : qr.Poised args) :
 /-! ### Core division algorithm circuit -/
 
 /-- A recursive definition of division for bit blasting, in terms of a shift-subtraction circuit. -/
+@[expose]
 def divRec {w : Nat} (m : Nat) (args : DivModArgs w) (qr : DivModState w) :
     DivModState w :=
   match m with
@@ -1182,7 +1137,7 @@ theorem getLsbD_udiv (n d : BitVec w) (hy : 0#w < d)  (i : Nat) :
 
 theorem getMsbD_udiv (n d : BitVec w) (hd : 0#w < d)  (i : Nat) :
     (n / d).getMsbD i = (decide (i < w) && (divRec w {n, d} (DivModState.init w)).q.getMsbD i) := by
-  simp [getMsbD_eq_getLsbD, getLsbD_udiv, udiv_eq_divRec (by assumption)]
+  simp [getMsbD_eq_getLsbD, udiv_eq_divRec (by assumption)]
 
 /- ### Arithmetic shift right (sshiftRight) recurrence -/
 
@@ -1349,7 +1304,7 @@ theorem negOverflow_eq {w : Nat} (x : BitVec w) :
     (negOverflow x) = (decide (0 < w) && (x == intMin w)) := by
   simp only [negOverflow]
   rcases w with _|w
-  · simp [toInt_of_zero_length, Int.min_eq_right]
+  · simp [toInt_of_zero_length]
   · suffices - 2 ^ w = (intMin (w + 1)).toInt by simp [beq_eq_decide_eq, ← toInt_inj, this]
     simp only [toInt_intMin, Nat.add_one_sub_one, Int.natCast_emod, Int.neg_inj]
     rw_mod_cast [Nat.mod_eq_of_lt (by simp [Nat.pow_lt_pow_succ])]
@@ -1391,7 +1346,7 @@ theorem umulOverflow_eq {w : Nat} (x y : BitVec w) :
       (0 < w && BitVec.twoPow (w * 2) w ≤ x.zeroExtend (w * 2) * y.zeroExtend (w * 2)) := by
   simp only [umulOverflow, toNat_twoPow, le_def, toNat_mul, toNat_setWidth, mod_mul_mod]
   rcases w with _|w
-  · simp [of_length_zero, toInt_zero, mul_mod_mod]
+  · simp [of_length_zero]
   · simp only [ge_iff_le, show 0 < w + 1 by omega, decide_true, mul_mod_mod, Bool.true_and,
       decide_eq_decide]
     rw [Nat.mod_eq_of_lt BitVec.toNat_mul_toNat_lt, Nat.mod_eq_of_lt]
@@ -1627,11 +1582,11 @@ theorem toInt_sdiv_of_ne_or_ne (a b : BitVec w) (h : a ≠ intMin w ∨ b ≠ -1
   have := Nat.two_pow_pos (w - 1)
 
   by_cases hbintMin : b = intMin w
-  · simp only [ne_eq, Decidable.not_not] at hbintMin
+  · simp only at hbintMin
     subst hbintMin
     have toIntA_lt := @BitVec.toInt_lt w a; norm_cast at toIntA_lt
     have le_toIntA := @BitVec.le_toInt w a; norm_cast at le_toIntA
-    simp only [sdiv_intMin, h, ↓reduceIte, toInt_zero, toInt_intMin, wpos,
+    simp only [sdiv_intMin, toInt_intMin, wpos,
       Nat.two_pow_pred_mod_two_pow, Int.tdiv_neg]
     · by_cases ha_intMin : a = intMin w
       · simp only [ha_intMin, ↓reduceIte, show 1 < w by omega, toInt_one, toInt_intMin, wpos,
@@ -1707,6 +1662,88 @@ theorem toInt_sdiv (a b : BitVec w) : (a.sdiv b).toInt = (a.toInt.tdiv b.toInt).
   · rw [← toInt_bmod_cancel]
     rw [BitVec.toInt_sdiv_of_ne_or_ne _ _ (by simpa only [Decidable.not_and_iff_not_or_not] using h)]
 
+private theorem neg_udiv_eq_intMin_iff_eq_intMin_eq_one_of_msb_eq_true
+    {x y : BitVec w} (hx : x.msb = true) (hy : y.msb = false) :
+    -x / y = intMin w ↔ (x = intMin w ∧ y = 1#w) := by
+  constructor
+  · intros h
+    rcases w with _ | w; decide +revert
+    have : (-x / y).msb = true := by simp [h, msb_intMin]
+    rw [msb_udiv] at this
+    simp only [bool_to_prop] at this
+    obtain ⟨hx, hy⟩ := this
+    simp only [beq_iff_eq] at hy
+    subst hy
+    simp only [udiv_one, zero_lt_succ, neg_eq_intMin] at h
+    simp [h]
+  · rintro ⟨hx, hy⟩
+    subst hx hy
+    simp
+
+/--
+the most significant bit of the signed division `x.sdiv y` can be computed
+by the following cases:
+(1) x nonneg, y nonneg: never neg.
+(2) x nonneg, y neg: neg when result nonzero.
+   We know that y is nonzero since it is negative, so we only check `|x| ≥ |y|`.
+(3) x neg, y nonneg: neg when result nonzero.
+  We check that `y ≠ 0` and `|x| ≥ |y|`.
+(4) x neg, y neg: neg when `x = intMin, `y = -1`, since `intMin / -1 = intMin`.
+
+The proof strategy is to perform a case analysis on the sign of `x` and `y`,
+followed by unfolding the `sdiv` into `udiv`.
+-/
+theorem msb_sdiv_eq_decide {x y : BitVec w} :
+    (x.sdiv y).msb = (decide (0 < w) &&
+      (!x.msb && y.msb && decide (-y ≤ x)) ||
+      (x.msb && !y.msb && decide (y ≤ -x) && !decide (y = 0#w)) ||
+      (x.msb && y.msb && decide (x = intMin w) && decide (y = -1#w)))
+     := by
+  rcases w; decide +revert
+  case succ w =>
+    simp only [decide_true, ne_eq, decide_and, decide_not, Bool.true_and,
+      sdiv_eq, udiv_eq]
+    rcases hxmsb : x.msb <;> rcases hymsb : y.msb
+    · simp [hxmsb, hymsb, msb_udiv_eq_false_of, Bool.not_false, Bool.and_false, Bool.false_and,
+        Bool.and_true, Bool.or_self, Bool.and_self]
+    · simp only [hxmsb, hymsb, msb_neg, msb_udiv_eq_false_of, bne_false, Bool.not_false,
+        Bool.and_self, ne_zero_of_msb_true, decide_false, Bool.and_true, Bool.true_and, Bool.not_true,
+        Bool.false_and, Bool.or_false, bool_to_prop]
+      have : x / -y ≠ intMin (w + 1) := by
+        intros h
+        have : (x / -y).msb = (intMin (w + 1)).msb := by simp only [h]
+        simp only [msb_udiv, msb_intMin, show 0 < w + 1 by omega, decide_true, and_eq_true, beq_iff_eq] at this
+        obtain ⟨hcontra, _⟩ := this
+        simp only [hcontra, true_eq_false] at hxmsb
+      simp [this, hymsb, udiv_ne_zero_iff_ne_zero_and_le]
+    · simp only [hxmsb, hymsb, Bool.not_true, Bool.and_self, Bool.false_and, Bool.not_false,
+        Bool.true_and, Bool.false_or, Bool.and_false, Bool.or_false]
+      by_cases hx₁ : x = 0#(w + 1)
+      · simp [hx₁, neg_zero, zero_udiv, msb_zero, le_zero_iff, Bool.and_not_self]
+      · by_cases hy₁ : y = 0#(w + 1)
+        · simp [hy₁, udiv_zero, neg_zero, msb_zero, decide_true, Bool.not_true, Bool.and_false]
+        · simp only [hy₁, decide_false, Bool.not_false, Bool.and_true]
+          by_cases hxy₁ : (- x / y) = 0#(w + 1)
+          · simp only [hxy₁, neg_zero, msb_zero, false_eq_decide_iff, BitVec.not_le,
+              decide_eq_true_eq, BitVec.not_le]
+            simp only [udiv_eq_zero_iff_eq_zero_or_lt, hy₁, _root_.false_or] at hxy₁
+            bv_omega
+          · simp only [udiv_eq_zero_iff_eq_zero_or_lt, _root_.not_or, BitVec.not_lt,
+              hy₁, not_false_eq_true, _root_.true_and] at hxy₁
+            simp only [hxy₁, decide_true, msb_neg, bne_iff_ne, ne_eq,
+              bool_to_prop,
+              bne_iff_ne, ne_eq, udiv_eq_zero_iff_eq_zero_or_lt, hy₁, _root_.false_or,
+              BitVec.not_lt, hxy₁, _root_.true_and, decide_not, not_eq_eq_eq_not, not_eq_not,
+              msb_udiv, msb_neg]
+            simp only [hx₁, not_false_eq_true, _root_.true_and, decide_not, hxmsb, not_eq_eq_eq_not,
+              Bool.not_true, decide_eq_false_iff_not, Decidable.not_not, beq_iff_eq]
+            rw [neg_udiv_eq_intMin_iff_eq_intMin_eq_one_of_msb_eq_true hxmsb hymsb]
+    · simp only [msb_udiv, msb_neg, hxmsb, bne_true, Bool.not_and, Bool.not_true, Bool.and_true,
+        Bool.false_and, Bool.and_false, hymsb, ne_zero_of_msb_true, decide_false, Bool.not_false,
+        Bool.or_self, Bool.and_self, Bool.true_and, Bool.false_or]
+      simp only [bool_to_prop]
+      simp [BitVec.ne_zero_of_msb_true (x := x) hxmsb, neg_eq_iff_eq_neg]
+
 theorem msb_umod_eq_false_of_left {x : BitVec w} (hx : x.msb = false) (y : BitVec w) : (x % y).msb = false := by
   rw [msb_eq_false_iff_two_mul_lt] at hx ⊢
   rw [toNat_umod]
@@ -1726,7 +1763,7 @@ theorem msb_umod_of_le_of_ne_zero_of_le {x y : BitVec w}
 theorem toInt_srem (x y : BitVec w) : (x.srem y).toInt = x.toInt.tmod y.toInt := by
   rw [srem_eq]
   by_cases hyz : y = 0#w
-  · simp only [hyz, ofNat_eq_ofNat, msb_zero, umod_zero, neg_zero, neg_neg, toInt_zero, Int.tmod_zero]
+  · simp only [hyz, msb_zero, umod_zero, neg_zero, neg_neg, toInt_zero, Int.tmod_zero]
     cases x.msb <;> rfl
   cases h : x.msb
   · cases h' : y.msb
@@ -1750,6 +1787,116 @@ theorem toInt_srem (x y : BitVec w) : (x.srem y).toInt = x.toInt.tmod y.toInt :=
         ((not_congr neg_eq_zero_iff).mpr hyz)]
       exact neg_le_intMin_of_msb_eq_true h'
 
+@[simp]
+theorem msb_intMin_umod_neg_of_msb_true {y : BitVec w} (hy : y.msb = true) :
+    (intMin w % -y).msb = false := by
+  by_cases hyintmin : y = intMin w
+  · simp [hyintmin]
+  · rw [msb_umod_of_msb_false_of_ne_zero (by simp [hyintmin, hy])]
+    simp [hy]
+
+@[simp]
+theorem msb_neg_umod_neg_of_msb_true_of_msb_true {x y : BitVec w} (hx : x.msb = true) (hy : y.msb = true) :
+      (-x % -y).msb = false := by
+  by_cases hx' : x = intMin w
+  · simp only [hx', neg_intMin, msb_intMin_umod_neg_of_msb_true hy]
+  · simp [show (-x).msb = false by simp [hx, hx']]
+
+theorem toInt_dvd_toInt_iff {x y : BitVec w} :
+    y.toInt ∣ x.toInt ↔ (if x.msb then -x else x) % (if y.msb then -y else y) = 0#w := by
+  constructor
+  <;> by_cases hxmsb : x.msb <;> by_cases hymsb: y.msb
+  <;> intros h
+  <;> simp only [hxmsb, hymsb, reduceIte, false_eq_true, toNat_eq, toNat_umod, toNat_ofNat,
+        zero_mod, toInt_eq_neg_toNat_neg_of_msb_true, Int.dvd_neg, Int.neg_dvd,
+        toInt_eq_toNat_of_msb] at h
+  <;> simp only [hxmsb, hymsb, toInt_eq_neg_toNat_neg_of_msb_true, toInt_eq_toNat_of_msb,
+        Int.dvd_neg, Int.neg_dvd, toNat_eq, toNat_umod, reduceIte, toNat_ofNat, zero_mod]
+  <;> norm_cast
+  <;> norm_cast at h
+  <;> simp only [dvd_of_mod_eq_zero, h, dvd_iff_mod_eq_zero.mp, reduceIte]
+
+theorem toInt_dvd_toInt_iff_of_msb_true_msb_false {x y : BitVec w} (hx : x.msb = true) (hy : y.msb = false) :
+    y.toInt ∣ x.toInt ↔ (-x) % y = 0#w := by
+  simpa [hx, hy] using toInt_dvd_toInt_iff (x := x) (y := y)
+
+theorem toInt_dvd_toInt_iff_of_msb_false_msb_true {x y : BitVec w} (hx : x.msb = false) (hy : y.msb = true) :
+    y.toInt ∣ x.toInt ↔ x % (-y) = 0#w := by
+  simpa [hx, hy] using toInt_dvd_toInt_iff (x := x) (y := y)
+
+@[simp]
+theorem neg_toInt_neg_umod_eq_of_msb_true_msb_true {x y : BitVec w} (hx : x.msb = true) (hy : y.msb = true) :
+    -(-(-x % -y)).toInt = (-x % -y).toNat := by
+  rw [neg_toInt_neg]
+  by_cases h : -x % -y = 0#w
+  · simp [h]
+  · rw [msb_neg_umod_neg_of_msb_true_of_msb_true hx hy]
+
+@[simp]
+theorem toInt_umod_neg_add {x y : BitVec w} (hymsb : y.msb = true) (hxmsb : x.msb = false) (hdvd : ¬y.toInt ∣ x.toInt) :
+    (x % -y + y).toInt = x.toInt % y.toInt + y.toInt := by
+  rcases w with _|w ; simp [of_length_zero]
+  have hypos : 0 < y.toNat := toNat_pos_of_ne_zero (by simp [hymsb])
+  have hxnonneg := toInt_nonneg_of_msb_false hxmsb
+  have hynonpos := toInt_neg_of_msb_true hymsb
+  have hylt : (-y).toNat ≤ 2 ^ (w) := toNat_neg_lt_of_msb y hymsb
+  have hmodlt := Nat.mod_lt x.toNat (y := (-y).toNat)
+      (by rw [toNat_neg, Nat.mod_eq_of_lt (by omega)]; omega)
+  simp only [toInt_add]
+  rw [toInt_umod, toInt_eq_neg_toNat_neg_of_msb_true hymsb, Int.bmod_add_bmod,
+    Int.bmod_eq_of_le (by omega) (by omega),
+    toInt_eq_toNat_of_msb hxmsb, Int.emod_neg]
+
+@[simp]
+theorem toInt_sub_neg_umod {x y : BitVec w} (hxmsb : x.msb = true) (hymsb : y.msb = false) (hdvd : ¬y.toInt ∣ x.toInt) :
+    (y - -x % y).toInt = x.toInt % y.toInt := by
+  rcases w with _|w
+  · simp [of_length_zero]
+  · have : y.toNat < 2 ^ w := toNat_lt_of_msb_false hymsb
+    by_cases hyzero : y = 0#(w+1)
+    · subst hyzero; simp
+    · simp only [toNat_eq, toNat_ofNat, zero_mod] at hyzero
+      have hypos : 0 < y.toNat := by omega
+      simp only [toInt_sub, toInt_eq_toNat_of_msb hymsb, toInt_umod,
+        Int.sub_bmod_bmod, toInt_eq_neg_toNat_neg_of_msb_true hxmsb, Int.neg_emod]
+      have hmodlt := Nat.mod_lt (x := (-x).toNat) (y := y.toNat) hypos
+      rw [Int.bmod_eq_of_le (by omega) (by omega)]
+      simp only [toInt_eq_toNat_of_msb hymsb, BitVec.toInt_eq_neg_toNat_neg_of_msb_true hxmsb,
+        Int.dvd_neg] at hdvd
+      simp only [hdvd, ↓reduceIte, Int.natAbs_cast]
+
+theorem toInt_smod {x y : BitVec w} :
+    (x.smod y).toInt = x.toInt.fmod y.toInt := by
+  rcases w with _|w
+  · decide +revert
+  · by_cases hyzero : y = 0#(w + 1)
+    · simp [hyzero]
+    · rw [smod_eq]
+      cases hxmsb : x.msb <;> cases hymsb : y.msb
+      <;> simp only [umod_eq]
+      · have : 0 < y.toNat := by simp [toNat_eq] at hyzero; omega
+        have : y.toNat < 2 ^ w := toNat_lt_of_msb_false hymsb
+        have : x.toNat % y.toNat < y.toNat := Nat.mod_lt x.toNat (by omega)
+        rw [toInt_umod, Int.fmod_eq_emod_of_nonneg x.toInt (toInt_nonneg_of_msb_false hymsb),
+          toInt_eq_toNat_of_msb hxmsb, toInt_eq_toNat_of_msb hymsb,
+          Int.bmod_eq_of_le_mul_two (by omega) (by omega)]
+      · have := toInt_dvd_toInt_iff_of_msb_false_msb_true hxmsb hymsb
+        by_cases hx_dvd_y : y.toInt ∣ x.toInt
+        · simp [show x % -y = 0#(w + 1) by simp_all, hx_dvd_y, Int.fmod_eq_zero_of_dvd]
+        · have hynonpos := toInt_neg_of_msb_true hymsb
+          simp only [show ¬x % -y = 0#(w + 1) by simp_all, ↓reduceIte,
+            toInt_umod_neg_add hymsb hxmsb hx_dvd_y, Int.fmod_eq_emod, show ¬0 ≤ y.toInt by omega,
+            hx_dvd_y, _root_.or_self]
+      · have hynonneg := toInt_nonneg_of_msb_false hymsb
+        rw [Int.fmod_eq_emod_of_nonneg x.toInt (b := y.toInt) (by omega)]
+        have hdvd := toInt_dvd_toInt_iff_of_msb_true_msb_false hxmsb hymsb
+        by_cases hx_dvd_y : y.toInt ∣ x.toInt
+        · simp [show -x % y = 0#(w + 1) by simp_all, hx_dvd_y, Int.emod_eq_zero_of_dvd]
+        · simp [show ¬-x % y = 0#(w + 1) by simp_all, toInt_sub_neg_umod hxmsb hymsb hx_dvd_y]
+      · rw [←Int.neg_inj, neg_toInt_neg_umod_eq_of_msb_true_msb_true hxmsb hymsb]
+        simp [BitVec.toInt_eq_neg_toNat_neg_of_msb_true, hxmsb, hymsb,
+          Int.fmod_eq_emod_of_nonneg _]
+
 /-! ### Lemmas that use bit blasting circuits -/
 
 theorem add_sub_comm {x y : BitVec w} : x + y - z = x - z + y := by
@@ -1782,7 +1929,7 @@ theorem carry_extractLsb'_eq_carry {w i len : Nat} (hi : i < len)
     {x y : BitVec w} {b : Bool}:
     (carry i (extractLsb' 0 len x) (extractLsb' 0 len y) b)
     = (carry i x y b) := by
-  simp only [carry, extractLsb'_toNat, shiftRight_zero, toNat_false, Nat.add_zero, ge_iff_le,
+  simp only [carry, extractLsb'_toNat, shiftRight_zero, ge_iff_le,
     decide_eq_decide]
   have : 2 ^ i ∣ 2^len := by
     apply Nat.pow_dvd_pow

src/Init/Data/BitVec/Bootstrap.lean

@@ -0,0 +1,146 @@
+/-
+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, Siddharth Bhat
+-/
+module
+
+prelude
+import all Init.Data.BitVec.Basic
+
+namespace BitVec
+
+theorem testBit_toNat (x : BitVec w) : x.toNat.testBit i = x.getLsbD i := rfl
+
+@[simp] theorem getLsbD_ofFin (x : Fin (2^n)) (i : Nat) :
+    getLsbD (BitVec.ofFin x) i = x.val.testBit i := rfl
+
+@[simp] theorem getLsbD_of_ge (x : BitVec w) (i : Nat) (ge : w ≤ i) : getLsbD x i = false := by
+  let ⟨x, x_lt⟩ := x
+  simp only [getLsbD_ofFin]
+  apply Nat.testBit_lt_two_pow
+  have p : 2^w ≤ 2^i := Nat.pow_le_pow_right (by omega) ge
+  omega
+
+/-- Prove equality of bitvectors in terms of nat operations. -/
+theorem eq_of_toNat_eq {n} : ∀ {x y : BitVec n}, x.toNat = y.toNat → x = y
+  | ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
+
+theorem eq_of_getLsbD_eq {x y : BitVec w}
+    (pred : ∀ i, i < w → x.getLsbD i = y.getLsbD i) : x = y := by
+  apply eq_of_toNat_eq
+  apply Nat.eq_of_testBit_eq
+  intro i
+  if i_lt : i < w then
+    exact pred i i_lt
+  else
+    have p : i ≥ w := Nat.le_of_not_gt i_lt
+    simp [testBit_toNat, getLsbD_of_ge _ _ p]
+
+@[simp, bitvec_to_nat] theorem toNat_ofNat (x w : Nat) : (BitVec.ofNat w x).toNat = x % 2^w := by
+  simp [BitVec.toNat, BitVec.ofNat, Fin.ofNat]
+
+@[ext] theorem eq_of_getElem_eq {x y : BitVec n} :
+        (∀ i (hi : i < n), x[i] = y[i]) → x = y :=
+  fun h => BitVec.eq_of_getLsbD_eq (h ↑·)
+
+@[simp] theorem toNat_append (x : BitVec m) (y : BitVec n) :
+    (x ++ y).toNat = x.toNat <<< n ||| y.toNat :=
+  rfl
+
+@[simp] theorem toNat_ofBool (b : Bool) : (ofBool b).toNat = b.toNat := by
+  cases b <;> rfl
+
+@[simp, bitvec_to_nat] theorem toNat_cast (h : w = v) (x : BitVec w) : (x.cast h).toNat = x.toNat := rfl
+
+@[simp, bitvec_to_nat] theorem toNat_ofFin (x : Fin (2^n)) : (BitVec.ofFin x).toNat = x.val := rfl
+
+@[simp] theorem toNat_ofNatLT (x : Nat) (p : x < 2^w) : (x#'p).toNat = x := rfl
+
+@[simp] theorem toNat_cons (b : Bool) (x : BitVec w) :
+    (cons b x).toNat = (b.toNat <<< w) ||| x.toNat := by
+  let ⟨x, _⟩ := x
+  simp only [cons, toNat_cast, toNat_append, toNat_ofBool, toNat_ofFin]
+
+theorem getElem_cons {b : Bool} {n} {x : BitVec n} {i : Nat} (h : i < n + 1) :
+    (cons b x)[i] = if h : i = n then b else x[i] := by
+  simp only [getElem_eq_testBit_toNat, toNat_cons, Nat.testBit_or]
+  rw [Nat.testBit_shiftLeft]
+  rcases Nat.lt_trichotomy i n with i_lt_n | i_eq_n | n_lt_i
+  · have p1 : ¬(n ≤ i) := by omega
+    have p2 : i ≠ n := by omega
+    simp [p1, p2]
+  · simp only [i_eq_n, ge_iff_le, Nat.le_refl, decide_true, Nat.sub_self, Nat.testBit_zero,
+    Bool.true_and, testBit_toNat, getLsbD_of_ge, Bool.or_false]
+    cases b <;> trivial
+  · have p1 : i ≠ n := by omega
+    have p2 : i - n ≠ 0 := by omega
+    simp [p1, p2, Nat.testBit_bool_to_nat]
+
+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_right (by trivial : 0 < 2) le)
+
+@[simp, bitvec_to_nat] theorem toNat_setWidth' {m n : Nat} (p : m ≤ n) (x : BitVec m) :
+    (setWidth' p x).toNat = x.toNat := by
+  simp only [setWidth', toNat_ofNatLT]
+
+@[simp, bitvec_to_nat] theorem toNat_setWidth (i : Nat) (x : BitVec n) :
+    BitVec.toNat (setWidth i x) = x.toNat % 2^i := by
+  let ⟨x, lt_n⟩ := x
+  simp only [setWidth]
+  if n_le_i : n ≤ i then
+    have x_lt_two_i : x < 2 ^ i := lt_two_pow_of_le lt_n n_le_i
+    simp [n_le_i, Nat.mod_eq_of_lt, x_lt_two_i]
+  else
+    simp [n_le_i, toNat_ofNat]
+
+@[simp] theorem ofNat_toNat (m : Nat) (x : BitVec n) : BitVec.ofNat m x.toNat = setWidth m x := by
+  apply eq_of_toNat_eq
+  simp only [toNat_ofNat, toNat_setWidth]
+
+theorem getElem_setWidth' (x : BitVec w) (i : Nat) (h : w ≤ v) (hi : i < v) :
+    (setWidth' h x)[i] = x.getLsbD i := by
+  rw [getElem_eq_testBit_toNat, toNat_setWidth', getLsbD]
+
+@[simp]
+theorem getElem_setWidth (m : Nat) (x : BitVec n) (i : Nat) (h : i < m) :
+    (setWidth m x)[i] = x.getLsbD i := by
+  rw [setWidth]
+  split
+  · rw [getElem_setWidth']
+  · simp only [ofNat_toNat, getElem_eq_testBit_toNat, toNat_setWidth, Nat.testBit_mod_two_pow,
+      getLsbD, Bool.and_eq_right_iff_imp, decide_eq_true_eq]
+    omega
+
+@[simp] theorem cons_msb_setWidth (x : BitVec (w+1)) : (cons x.msb (x.setWidth w)) = x := by
+  ext i
+  simp only [getElem_cons]
+  split <;> rename_i h
+  · simp [BitVec.msb, getMsbD, h]
+  · by_cases h' : i < w
+    · simp_all only [getElem_setWidth, getLsbD_eq_getElem]
+    · omega
+
+@[simp, bitvec_to_nat] theorem toNat_neg (x : BitVec n) : (- x).toNat = (2^n - x.toNat) % 2^n := by
+  simp [Neg.neg, BitVec.neg]
+
+@[simp] theorem setWidth_neg_of_le {x : BitVec v} (h : w ≤ v) : BitVec.setWidth w (-x) = -BitVec.setWidth w x := by
+  apply BitVec.eq_of_toNat_eq
+  simp only [toNat_setWidth, toNat_neg]
+  rw [Nat.mod_mod_of_dvd _ (Nat.pow_dvd_pow 2 h)]
+  rw [Nat.mod_eq_mod_iff]
+  rw [Nat.mod_def]
+  refine ⟨1 + x.toNat / 2^w, 2^(v-w), ?_⟩
+  rw [← Nat.pow_add]
+  have : v - w + w = v := by omega
+  rw [this]
+  rw [Nat.add_mul, Nat.one_mul, Nat.mul_comm (2^w)]
+  have sub_sub : ∀ (a : Nat) {b c : Nat} (h : c ≤ b), a - (b - c) = a + c - b := by omega
+  rw [sub_sub _ (Nat.div_mul_le_self x.toNat (2 ^ w))]
+  have : x.toNat / 2 ^ w * 2 ^ w ≤ x.toNat := Nat.div_mul_le_self x.toNat (2 ^ w)
+  have : x.toNat < 2 ^w ∨ x.toNat - 2 ^ w < x.toNat / 2 ^ w * 2 ^ w := by
+    have := Nat.lt_div_mul_add (a := x.toNat) (b := 2 ^ w) (Nat.two_pow_pos w)
+    omega
+  omega
+
+end BitVec

src/Init/Data/BitVec/Decidable.lean

@@ -0,0 +1,79 @@
+/-
+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, Siddharth Bhat
+
+-/
+module
+
+prelude
+import Init.Data.BitVec.Bootstrap
+
+set_option linter.missingDocs true
+
+namespace BitVec
+
+/-! ### Decidable quantifiers -/
+
+theorem forall_zero_iff {P : BitVec 0 → Prop} :
+    (∀ v, P v) ↔ P 0#0 := by
+  constructor
+  · intro h
+    apply h
+  · intro h v
+    obtain (rfl : v = 0#0) := (by ext i ⟨⟩)
+    apply h
+
+theorem forall_cons_iff {P : BitVec (n + 1) → Prop} :
+    (∀ v : BitVec (n + 1), P v) ↔ (∀ (x : Bool) (v : BitVec n), P (v.cons x)) := by
+  constructor
+  · intro h _ _
+    apply h
+  · intro h v
+    have w : v = (v.setWidth n).cons v.msb := by simp only [cons_msb_setWidth]
+    rw [w]
+    apply h
+
+instance instDecidableForallBitVecZero (P : BitVec 0 → Prop) :
+    ∀ [Decidable (P 0#0)], Decidable (∀ v, P v)
+  | .isTrue h => .isTrue fun v => by
+    obtain (rfl : v = 0#0) := (by ext i ⟨⟩)
+    exact h
+  | .isFalse h => .isFalse (fun w => h (w _))
+
+instance instDecidableForallBitVecSucc (P : BitVec (n+1) → Prop) [DecidablePred P]
+    [Decidable (∀ (x : Bool) (v : BitVec n), P (v.cons x))] : Decidable (∀ v, P v) :=
+  decidable_of_iff' (∀ x (v : BitVec n), P (v.cons x)) forall_cons_iff
+
+instance instDecidableExistsBitVecZero (P : BitVec 0 → Prop) [Decidable (P 0#0)] :
+    Decidable (∃ v, P v) :=
+  decidable_of_iff (¬ ∀ v, ¬ P v) Classical.not_forall_not
+
+instance instDecidableExistsBitVecSucc (P : BitVec (n+1) → Prop) [DecidablePred P]
+    [Decidable (∀ (x : Bool) (v : BitVec n), ¬ P (v.cons x))] : Decidable (∃ v, P v) :=
+  decidable_of_iff (¬ ∀ v, ¬ P v) Classical.not_forall_not
+
+/--
+For small numerals this isn't necessary (as typeclass search can use the above two instances),
+but for large numerals this provides a shortcut.
+Note, however, that for large numerals the decision procedure may be very slow,
+and you should use `bv_decide` if possible.
+-/
+instance instDecidableForallBitVec :
+    ∀ (n : Nat) (P : BitVec n → Prop) [DecidablePred P], Decidable (∀ v, P v)
+  | 0, _, _ => inferInstance
+  | n + 1, _, _ =>
+    have := instDecidableForallBitVec n
+    inferInstance
+
+/--
+For small numerals this isn't necessary (as typeclass search can use the above two instances),
+but for large numerals this provides a shortcut.
+Note, however, that for large numerals the decision procedure may be very slow.
+-/
+instance instDecidableExistsBitVec :
+    ∀ (n : Nat) (P : BitVec n → Prop) [DecidablePred P], Decidable (∃ v, P v)
+  | 0, _, _ => inferInstance
+  | _ + 1, _, _ => inferInstance
+
+end BitVec

src/Init/Data/BitVec/Folds.lean

@@ -82,9 +82,9 @@ theorem iunfoldr_getLsbD' {f : Fin w → α → α × Bool} (state : Nat → α)
       simp only [getLsbD_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)]
+      | inl h3 => simp [(Nat.ne_of_lt h3)]
                   exact (ih hj2).1 ⟨i.val, h3⟩
-      | inr h3 => simp [h3, if_pos]
+      | inr h3 => simp [h3]
                   cases (Nat.eq_zero_or_pos j.val) with
                   | inl hj3 => congr
                                rw [← (ih hj2).2]

src/Init/Data/Bool.lean

@@ -455,7 +455,7 @@ theorem toNat_lt (b : Bool) : b.toNat < 2 :=
 /--
 Converts `true` to `1` and `false` to `0`.
 -/
-def toInt (b : Bool) : Int := cond b 1 0
+@[expose] def toInt (b : Bool) : Int := cond b 1 0
 
 @[simp] theorem toInt_false : false.toInt = 0 := rfl
 
@@ -488,7 +488,7 @@ def toInt (b : Bool) : Int := cond b 1 0
 
 @[simp] theorem ite_eq_true_else_eq_false {q : Prop} :
     (if b = true then q else b = false) ↔ (b = true → q) := by
-  cases b <;> simp [not_eq_self]
+  cases b <;> simp
 
 /-
 `not_ite_eq_true_eq_true` and related theorems below are added for

src/Init/Data/Fin/Basic.lean

@@ -46,15 +46,12 @@ Returns `a` modulo `n` as a `Fin n`.
 
 The assumption `NeZero n` ensures that `Fin n` is nonempty.
 -/
-@[expose] protected def ofNat' (n : Nat) [NeZero n] (a : Nat) : Fin n :=
+@[expose] protected def ofNat (n : Nat) [NeZero n] (a : Nat) : Fin n :=
   ⟨a % n, Nat.mod_lt _ (pos_of_neZero n)⟩
 
-/--
-Returns `a` modulo `n + 1` as a `Fin n.succ`.
--/
-@[deprecated Fin.ofNat' (since := "2024-11-27")]
-protected def ofNat {n : Nat} (a : Nat) : Fin (n + 1) :=
-  ⟨a % (n+1), Nat.mod_lt _ (Nat.zero_lt_succ _)⟩
+@[deprecated Fin.ofNat (since := "2025-05-28")]
+protected def ofNat' (n : Nat) [NeZero n] (a : Nat) : Fin n :=
+  Fin.ofNat n a
 
 -- We provide this because other similar types have a `toNat` function, but `simp` rewrites
 -- `i.toNat` to `i.val`.
@@ -84,7 +81,7 @@ Examples:
  * `(2 : Fin 3) + (2 : Fin 3) = (1 : Fin 3)`
 -/
 protected def add : Fin n → Fin n → Fin n
-  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a + b) % n, mlt h⟩
+  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a + b) % n, by exact mlt h⟩
 
 /--
 Multiplication modulo `n`, usually invoked via the `*` operator.
@@ -95,7 +92,7 @@ Examples:
  * `(3 : Fin 10) * (7 : Fin 10) = (1 : Fin 10)`
 -/
 protected def mul : Fin n → Fin n → Fin n
-  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a * b) % n, mlt h⟩
+  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a * b) % n, by exact mlt h⟩
 
 /--
 Subtraction modulo `n`, usually invoked via the `-` operator.
@@ -122,7 +119,7 @@ protected def sub : Fin n → Fin n → Fin n
   using recursion on the second argument.
   See issue #4413.
   -/
-  | ⟨a, h⟩, ⟨b, _⟩ => ⟨((n - b) + a) % n, mlt h⟩
+  | ⟨a, h⟩, ⟨b, _⟩ => ⟨((n - b) + a) % n, by exact mlt h⟩
 
 /-!
 Remark: land/lor can be defined without using (% n), but
@@ -164,19 +161,19 @@ def modn : Fin n → Nat → Fin n
 Bitwise and.
 -/
 def land : Fin n → Fin n → Fin n
-  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(Nat.land a b) % n, mlt h⟩
+  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(Nat.land a b) % n, by exact mlt h⟩
 
 /--
 Bitwise or.
 -/
 def lor : Fin n → Fin n → Fin n
-  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(Nat.lor a b) % n, mlt h⟩
+  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(Nat.lor a b) % n, by exact mlt h⟩
 
 /--
 Bitwise xor (“exclusive or”).
 -/
 def xor : Fin n → Fin n → Fin n
-  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(Nat.xor a b) % n, mlt h⟩
+  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(Nat.xor a b) % n, by exact mlt h⟩
 
 /--
 Bitwise left shift of bounded numbers, with wraparound on overflow.
@@ -187,7 +184,7 @@ Examples:
  * `(1 : Fin 10) <<< (4 : Fin 10) = (6 : Fin 10)`
 -/
 def shiftLeft : Fin n → Fin n → Fin n
-  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a <<< b) % n, mlt h⟩
+  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a <<< b) % n, by exact mlt h⟩
 
 /--
 Bitwise right shift of bounded numbers.
@@ -201,7 +198,7 @@ Examples:
  * `(15 : Fin 17) >>> (2 : Fin 17) = (3 : Fin 17)`
 -/
 def shiftRight : Fin n → Fin n → Fin n
-  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a >>> b) % n, mlt h⟩
+  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a >>> b) % n, by exact mlt h⟩
 
 instance : Add (Fin n) where
   add := Fin.add
@@ -230,7 +227,7 @@ instance : ShiftRight (Fin n) where
   shiftRight := Fin.shiftRight
 
 instance instOfNat {n : Nat} [NeZero n] {i : Nat} : OfNat (Fin n) i where
-  ofNat := Fin.ofNat' n i
+  ofNat := Fin.ofNat n i
 
 /-- If you actually have an element of `Fin n`, then the `n` is always positive -/
 protected theorem pos (i : Fin n) : 0 < n :=

src/Init/Data/Fin/Fold.lean

@@ -183,9 +183,7 @@ theorem foldrM_loop [Monad m] [LawfulMonad m] (f : Fin (n+1) → α → m α) (x
   | zero =>
     rw [foldrM_loop_zero, foldrM_loop_succ, pure_bind]
     conv => rhs; rw [←bind_pure (f 0 x)]
-    congr
-    funext
-    simp [foldrM_loop_zero]
+    rfl
   | succ i ih =>
     rw [foldrM_loop_succ, foldrM_loop_succ, bind_assoc]
     congr; funext; exact ih ..
@@ -254,7 +252,7 @@ theorem foldl_succ_last (f : α → Fin (n+1) → α) (x) :
     foldl (n+1) f x = f (foldl n (f · ·.castSucc) x) (last n) := by
   rw [foldl_succ]
   induction n generalizing x with
-  | zero => simp [foldl_succ, Fin.last]
+  | zero => simp [Fin.last]
   | succ n ih => rw [foldl_succ, ih (f · ·.succ), foldl_succ]; simp
 
 theorem foldl_add (f : α → Fin (n + m) → α) (x) :

src/Init/Data/Fin/Lemmas.lean

@@ -15,10 +15,9 @@ import Init.Omega
 
 namespace Fin
 
-@[simp] theorem ofNat'_zero (n : Nat) [NeZero n] : Fin.ofNat' n 0 = 0 := rfl
+@[simp] theorem ofNat_zero (n : Nat) [NeZero n] : Fin.ofNat n 0 = 0 := rfl
 
-@[deprecated Fin.pos (since := "2024-11-11")]
-theorem size_pos (i : Fin n) : 0 < n := i.pos
+@[deprecated ofNat_zero (since := "2025-05-28")] abbrev ofNat'_zero := @ofNat_zero
 
 theorem mod_def (a m : Fin n) : a % m = Fin.mk (a % m) (Nat.lt_of_le_of_lt (Nat.mod_le _ _) a.2) :=
   rfl
@@ -29,8 +28,6 @@ theorem sub_def (a b : Fin n) : a - b = Fin.mk (((n - b) + a) % n) (Nat.mod_lt _
 
 theorem pos' : ∀ [Nonempty (Fin n)], 0 < n | ⟨i⟩ => i.pos
 
-@[deprecated pos' (since := "2024-11-11")] abbrev size_pos' := @pos'
-
 @[simp] theorem is_lt (a : Fin n) : (a : Nat) < n := a.2
 
 theorem pos_iff_nonempty {n : Nat} : 0 < n ↔ Nonempty (Fin n) :=
@@ -66,19 +63,25 @@ theorem mk_val (i : Fin n) : (⟨i, i.isLt⟩ : Fin n) = i := Fin.eta ..
     0 = (⟨a, ha⟩ : Fin n) ↔ a = 0 := by
   simp [eq_comm]
 
-@[simp] theorem val_ofNat' (n : Nat) [NeZero n] (a : Nat) :
-  (Fin.ofNat' n a).val = a % n := rfl
+@[simp] theorem val_ofNat (n : Nat) [NeZero n] (a : Nat) :
+  (Fin.ofNat n a).val = a % n := rfl
 
-@[simp] theorem ofNat'_self {n : Nat} [NeZero n] : Fin.ofNat' n n = 0 := by
+@[deprecated val_ofNat (since := "2025-05-28")] abbrev val_ofNat' := @val_ofNat
+
+@[simp] theorem ofNat_self {n : Nat} [NeZero n] : Fin.ofNat n n = 0 := by
   ext
   simp
   congr
 
-@[simp] theorem ofNat'_val_eq_self [NeZero n] (x : Fin n) : (Fin.ofNat' n x) = x := by
+@[deprecated ofNat_self (since := "2025-05-28")] abbrev ofNat'_self := @ofNat_self
+
+@[simp] theorem ofNat_val_eq_self [NeZero n] (x : Fin n) : (Fin.ofNat n x) = x := by
   ext
-  rw [val_ofNat', Nat.mod_eq_of_lt]
+  rw [val_ofNat, Nat.mod_eq_of_lt]
   exact x.2
 
+@[deprecated ofNat_val_eq_self (since := "2025-05-28")] abbrev ofNat'_val_eq_self := @ofNat_val_eq_self
+
 @[simp] theorem mod_val (a b : Fin n) : (a % b).val = a.val % b.val :=
   rfl
 
@@ -99,20 +102,55 @@ theorem dite_val {n : Nat} {c : Prop} [Decidable c] {x y : Fin n} :
     (if c then x else y).val = if c then x.val else y.val := by
   by_cases c <;> simp [*]
 
-instance (n : Nat) [NeZero n] : NatCast (Fin n) where
-  natCast a := Fin.ofNat' n a
+namespace NatCast
 
+/--
+This is not a global instance, but may be activated locally via `open Fin.NatCast in ...`.
+
+This is not an instance because the `binop%` elaborator assumes that
+there are no non-trivial coercion loops,
+but this introduces a coercion from `Nat` to `Fin n` and back.
+
+Non-trivial loops lead to undesirable and counterintuitive elaboration behavior.
+For example, for `x : Fin k` and `n : Nat`,
+it causes `x < n` to be elaborated as `x < ↑n` rather than `↑x < n`,
+silently introducing wraparound arithmetic.
+
+Note: as of 2025-06-03, Mathlib has such a coercion for `Fin n` anyway!
+-/
+@[expose]
+def instNatCast (n : Nat) [NeZero n] : NatCast (Fin n) where
+  natCast a := Fin.ofNat n a
+
+attribute [scoped instance] instNatCast
+
+end NatCast
+
+@[expose]
 def intCast [NeZero n] (a : Int) : Fin n :=
   if 0 ≤ a then
-    Fin.ofNat' n a.natAbs
+    Fin.ofNat n a.natAbs
   else
-    - Fin.ofNat' n a.natAbs
+    - Fin.ofNat n a.natAbs
 
-instance (n : Nat) [NeZero n] : IntCast (Fin n) where
+namespace IntCast
+
+/--
+This is not a global instance, but may be activated locally via `open Fin.IntCast in ...`.
+
+See the doc-string for `Fin.NatCast.instNatCast` for more details.
+-/
+@[expose]
+def instIntCast (n : Nat) [NeZero n] : IntCast (Fin n) where
   intCast := Fin.intCast
 
+attribute [scoped instance] instIntCast
+
+end IntCast
+
+open IntCast in
 theorem intCast_def {n : Nat} [NeZero n] (x : Int) :
-    (x : Fin n) = if 0 ≤ x then Fin.ofNat' n x.natAbs else -Fin.ofNat' n x.natAbs := rfl
+    (x : Fin n) = if 0 ≤ x then Fin.ofNat n x.natAbs else -Fin.ofNat n x.natAbs := rfl
 
 /-! ### order -/
 
@@ -343,7 +381,7 @@ theorem zero_ne_one : (0 : Fin (n + 2)) ≠ 1 := Fin.ne_of_lt one_pos
 @[simp] theorem val_succ (j : Fin n) : (j.succ : Nat) = j + 1 := rfl
 
 @[simp] theorem succ_pos (a : Fin n) : (0 : Fin (n + 1)) < a.succ := by
-  simp [Fin.lt_def, Nat.succ_pos]
+  simp [Fin.lt_def]
 
 @[simp] theorem succ_le_succ_iff {a b : Fin n} : a.succ ≤ b.succ ↔ a ≤ b := Nat.succ_le_succ_iff
 
@@ -376,7 +414,7 @@ theorem one_lt_succ_succ (a : Fin n) : (1 : Fin (n + 2)) < a.succ.succ := by
   simp only [lt_def, val_add, val_last, Fin.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]
+  | .inl h => cases h; simp
   | .inr hk' => simp [Nat.ne_of_lt hk', Nat.mod_eq_of_lt (Nat.succ_lt_succ hk'), Nat.le_succ]
 
 @[simp] theorem add_one_le_iff {n : Nat} : ∀ {k : Fin (n + 1)}, k + 1 ≤ k ↔ k = last _ := by
@@ -388,7 +426,7 @@ theorem one_lt_succ_succ (a : Fin n) : (1 : Fin (n + 2)) < a.succ.succ := by
     intro (k : Fin (n+2))
     rw [← add_one_lt_iff, lt_def, le_def, Nat.lt_iff_le_and_ne, and_iff_left]
     rw [val_add_one]
-    split <;> simp [*, (Nat.succ_ne_zero _).symm, Nat.ne_of_gt (Nat.lt_succ_self _)]
+    split <;> simp [*, 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)]
@@ -700,7 +738,7 @@ 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 [Fin.ext_iff]
 
 @[simp] theorem pred_one {n : Nat} :
     Fin.pred (1 : Fin (n + 2)) (Ne.symm (Fin.ne_of_lt one_pos)) = 0 := rfl
@@ -797,7 +835,7 @@ parameter, `Fin.cases` is the corresponding case analysis operator, and `Fin.rev
 version that starts at the greatest value instead of `0`.
 -/
 -- FIXME: Performance review
-@[elab_as_elim] def induction {motive : Fin (n + 1) → Sort _} (zero : motive 0)
+@[elab_as_elim, expose] 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
@@ -839,7 +877,7 @@ The two cases are:
 
 The corresponding induction principle is `Fin.induction`.
 -/
-@[elab_as_elim] def cases {motive : Fin (n + 1) → Sort _}
+@[elab_as_elim, expose] def cases {motive : Fin (n + 1) → Sort _}
     (zero : motive 0) (succ : ∀ i : Fin n, motive i.succ) :
     ∀ i : Fin (n + 1), motive i := induction zero fun i _ => succ i
 
@@ -965,30 +1003,38 @@ theorem val_ne_zero_iff [NeZero n] {a : Fin n} : a.val ≠ 0 ↔ a ≠ 0 :=
 
 /-! ### add -/
 
-theorem ofNat'_add [NeZero n] (x : Nat) (y : Fin n) :
-    Fin.ofNat' n x + y = Fin.ofNat' n (x + y.val) := by
+theorem ofNat_add [NeZero n] (x : Nat) (y : Fin n) :
+    Fin.ofNat n x + y = Fin.ofNat n (x + y.val) := by
   apply Fin.eq_of_val_eq
-  simp [Fin.ofNat', Fin.add_def]
+  simp [Fin.ofNat, Fin.add_def]
 
-theorem add_ofNat' [NeZero n] (x : Fin n) (y : Nat) :
-    x + Fin.ofNat' n y = Fin.ofNat' n (x.val + y) := by
+@[deprecated ofNat_add (since := "2025-05-28")] abbrev ofNat_add' := @ofNat_add
+
+theorem add_ofNat [NeZero n] (x : Fin n) (y : Nat) :
+    x + Fin.ofNat n y = Fin.ofNat n (x.val + y) := by
   apply Fin.eq_of_val_eq
-  simp [Fin.ofNat', Fin.add_def]
+  simp [Fin.ofNat, Fin.add_def]
+
+@[deprecated add_ofNat (since := "2025-05-28")] abbrev add_ofNat' := @add_ofNat
 
 /-! ### sub -/
 
 protected theorem coe_sub (a b : Fin n) : ((a - b : Fin n) : Nat) = ((n - b) + a) % n := by
   cases a; cases b; rfl
 
-theorem ofNat'_sub [NeZero n] (x : Nat) (y : Fin n) :
-    Fin.ofNat' n x - y = Fin.ofNat' n ((n - y.val) + x) := by
+theorem ofNat_sub [NeZero n] (x : Nat) (y : Fin n) :
+    Fin.ofNat n x - y = Fin.ofNat n ((n - y.val) + x) := by
   apply Fin.eq_of_val_eq
-  simp [Fin.ofNat', Fin.sub_def]
+  simp [Fin.ofNat, Fin.sub_def]
 
-theorem sub_ofNat' [NeZero n] (x : Fin n) (y : Nat) :
-    x - Fin.ofNat' n y = Fin.ofNat' n ((n - y % n) + x.val) := by
+@[deprecated ofNat_sub (since := "2025-05-28")] abbrev ofNat_sub' := @ofNat_sub
+
+theorem sub_ofNat [NeZero n] (x : Fin n) (y : Nat) :
+    x - Fin.ofNat n y = Fin.ofNat n ((n - y % n) + x.val) := by
   apply Fin.eq_of_val_eq
-  simp [Fin.ofNat', Fin.sub_def]
+  simp [Fin.ofNat, Fin.sub_def]
+
+@[deprecated sub_ofNat (since := "2025-05-28")] abbrev sub_ofNat' := @sub_ofNat
 
 @[simp] protected theorem sub_self [NeZero n] {x : Fin n} : x - x = 0 := by
   ext
@@ -1033,17 +1079,32 @@ theorem val_neg {n : Nat} [NeZero n] (x : Fin n) :
     have := Fin.val_ne_zero_iff.mpr h
     omega
 
+protected theorem sub_eq_add_neg {n : Nat} (x y : Fin n) : x - y = x + -y := by
+  by_cases h : n = 0
+  · subst h
+    apply elim0 x
+  · replace h : NeZero n := ⟨h⟩
+    ext
+    rw [Fin.coe_sub, Fin.val_add, val_neg]
+    split
+    · simp_all
+    · simp [Nat.add_comm]
+
 /-! ### mul -/
 
-theorem ofNat'_mul [NeZero n] (x : Nat) (y : Fin n) :
-    Fin.ofNat' n x * y = Fin.ofNat' n (x * y.val) := by
+theorem ofNat_mul [NeZero n] (x : Nat) (y : Fin n) :
+    Fin.ofNat n x * y = Fin.ofNat n (x * y.val) := by
   apply Fin.eq_of_val_eq
-  simp [Fin.ofNat', Fin.mul_def]
+  simp [Fin.ofNat, Fin.mul_def]
 
-theorem mul_ofNat' [NeZero n] (x : Fin n) (y : Nat) :
-    x * Fin.ofNat' n y = Fin.ofNat' n (x.val * y) := by
+@[deprecated ofNat_mul (since := "2025-05-28")] abbrev ofNat_mul' := @ofNat_mul
+
+theorem mul_ofNat [NeZero n] (x : Fin n) (y : Nat) :
+    x * Fin.ofNat n y = Fin.ofNat n (x.val * y) := by
   apply Fin.eq_of_val_eq
-  simp [Fin.ofNat', Fin.mul_def]
+  simp [Fin.ofNat, Fin.mul_def]
+
+@[deprecated mul_ofNat (since := "2025-05-28")] abbrev mul_ofNat' := @mul_ofNat
 
 theorem val_mul {n : Nat} : ∀ a b : Fin n, (a * b).val = a.val * b.val % n
   | ⟨_, _⟩, ⟨_, _⟩ => rfl
@@ -1056,7 +1117,7 @@ protected theorem mul_one [i : NeZero n] (k : Fin n) : k * 1 = k := by
   | n + 1, _ =>
     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 [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]

src/Init/Data/Format/Basic.lean

@@ -142,17 +142,36 @@ private structure WorkItem where
   indent : Int
   activeTags : Nat
 
+/--
+A directive indicating whether a given work group is able to be flattened.
+
+- `allow` indicates that the group is allowed to be flattened; its argument is `true` if
+  there is sufficient space for it to be flattened (and so it should be), or `false` if not.
+- `disallow` means that this group should not be flattened irrespective of space concerns.
+  This is used at levels of a `Format` outside of any flattening groups. It is necessary to track
+  this so that, after a hard line break, we know whether to try to flatten the next line.
+-/
+inductive FlattenAllowability where
+  | allow (fits : Bool)
+  | disallow
+  deriving BEq
+
+/-- Whether the given directive indicates that flattening should occur. -/
+def FlattenAllowability.shouldFlatten : FlattenAllowability → Bool
+  | allow true => true
+  | _ => false
+
 private structure WorkGroup where
-  flatten : Bool
-  flb     : FlattenBehavior
-  items   : List WorkItem
+  fla   : FlattenAllowability
+  flb   : FlattenBehavior
+  items : List WorkItem
 
 private partial def spaceUptoLine' : List WorkGroup → Nat → Nat → SpaceResult
   |   [],                         _,   _ => {}
   |   { items := [],    .. }::gs, col, w => spaceUptoLine' gs col w
   | g@{ items := i::is, .. }::gs, col, w =>
     merge w
-      (spaceUptoLine i.f g.flatten (w + col - i.indent) w)
+      (spaceUptoLine i.f g.fla.shouldFlatten (w + col - i.indent) w)
       (spaceUptoLine' ({ g with items := is }::gs) col)
 
 /-- A monad in which we can pretty-print `Format` objects. -/
@@ -169,11 +188,11 @@ open MonadPrettyFormat
 private def pushGroup (flb : FlattenBehavior) (items : List WorkItem) (gs : List WorkGroup) (w : Nat) [Monad m] [MonadPrettyFormat m] : m (List WorkGroup) := do
   let k  ← currColumn
   -- Flatten group if it + the remainder (gs) fits in the remaining space. For `fill`, measure only up to the next (ungrouped) line break.
-  let g  := { flatten := flb == FlattenBehavior.allOrNone, flb := flb, items := items : WorkGroup }
+  let g  := { fla := .allow (flb == FlattenBehavior.allOrNone), flb := flb, items := items : WorkGroup }
   let r  := spaceUptoLine' [g] k (w-k)
   let r' := merge (w-k) r (spaceUptoLine' gs k)
   -- Prevent flattening if any item contains a hard line break, except within `fill` if it is ungrouped (=> unflattened)
-  return { g with flatten := !r.foundFlattenedHardLine && r'.space <= w-k }::gs
+  return { g with fla := .allow (!r.foundFlattenedHardLine && r'.space <= w-k) }::gs
 
 private partial def be (w : Nat) [Monad m] [MonadPrettyFormat m] : List WorkGroup → m Unit
   | []                           => pure ()
@@ -200,11 +219,15 @@ private partial def be (w : Nat) [Monad m] [MonadPrettyFormat m] : List WorkGrou
         pushNewline i.indent.toNat
         let is := { i with f := text (s.extract (s.next p) s.endPos) }::is
         -- after a hard line break, re-evaluate whether to flatten the remaining group
-        pushGroup g.flb is gs w >>= be w
+        -- note that we shouldn't start flattening after a hard break outside a group
+        if g.fla == .disallow then
+          be w (gs' is)
+        else
+          pushGroup g.flb is gs w >>= be w
     | line =>
       match g.flb with
       | FlattenBehavior.allOrNone =>
-        if g.flatten then
+        if g.fla.shouldFlatten then
           -- flatten line = text " "
           pushOutput " "
           endTags i.activeTags
@@ -220,10 +243,10 @@ private partial def be (w : Nat) [Monad m] [MonadPrettyFormat m] : List WorkGrou
           endTags i.activeTags
           pushGroup FlattenBehavior.fill is gs w >>= be w
         -- if preceding fill item fit in a single line, try to fit next one too
-        if g.flatten then
+        if g.fla.shouldFlatten then
           let gs'@(g'::_) ← pushGroup FlattenBehavior.fill is gs (w - " ".length)
             | panic "unreachable"
-          if g'.flatten then
+          if g'.fla.shouldFlatten then
             pushOutput " "
             endTags i.activeTags
             be w gs'  -- TODO: use `return`
@@ -232,7 +255,7 @@ private partial def be (w : Nat) [Monad m] [MonadPrettyFormat m] : List WorkGrou
         else
           breakHere
     | align force =>
-      if g.flatten && !force then
+      if g.fla.shouldFlatten && !force then
         -- flatten (align false) = nil
         endTags i.activeTags
         be w (gs' is)
@@ -247,7 +270,7 @@ private partial def be (w : Nat) [Monad m] [MonadPrettyFormat m] : List WorkGrou
           endTags i.activeTags
           be w (gs' is)
     | group f flb =>
-      if g.flatten then
+      if g.fla.shouldFlatten then
         -- flatten (group f) = flatten f
         be w (gs' ({ i with f }::is))
       else
@@ -256,7 +279,7 @@ private partial def be (w : Nat) [Monad m] [MonadPrettyFormat m] : List WorkGrou
 /-- Render the given `f : Format` with a line width of `w`.
 `indent` is the starting amount to indent each line by. -/
 def prettyM (f : Format) (w : Nat) (indent : Nat := 0) [Monad m] [MonadPrettyFormat m] : m Unit :=
-  be w [{ flb := FlattenBehavior.allOrNone, flatten := false, items := [{ f := f, indent, activeTags := 0 }]}]
+  be w [{ flb := FlattenBehavior.allOrNone, fla := .disallow, items := [{ f := f, indent, activeTags := 0 }]}]
 
 /-- Create a format `l ++ f ++ r` with a flatten group.
 FlattenBehaviour is `allOrNone`; for `fill` use `bracketFill`. -/
@@ -294,7 +317,7 @@ private structure State where
   out    : String := ""
   column : Nat    := 0
 
-instance : MonadPrettyFormat (StateM State) where
+private instance : MonadPrettyFormat (StateM State) where
   -- We avoid a structure instance update, and write these functions using pattern matching because of issue #316
   pushOutput s       := modify fun ⟨out, col⟩ => ⟨out ++ s, col + s.length⟩
   pushNewline indent := modify fun ⟨out, _⟩ => ⟨out ++ "\n".pushn ' ' indent, indent⟩

src/Init/Data/Function.lean

@@ -31,19 +31,19 @@ Examples:
 @[inline, expose]
 def uncurry : (α → β → φ) → α × β → φ := fun f a => f a.1 a.2
 
-@[simp]
+@[simp, grind]
 theorem curry_uncurry (f : α → β → φ) : curry (uncurry f) = f :=
   rfl
 
-@[simp]
+@[simp, grind]
 theorem uncurry_curry (f : α × β → φ) : uncurry (curry f) = f :=
   funext fun ⟨_a, _b⟩ => rfl
 
-@[simp]
+@[simp, grind]
 theorem uncurry_apply_pair {α β γ} (f : α → β → γ) (x : α) (y : β) : uncurry f (x, y) = f x y :=
   rfl
 
-@[simp]
+@[simp, grind]
 theorem curry_apply {α β γ} (f : α × β → γ) (x : α) (y : β) : curry f x y = f (x, y) :=
   rfl
 

src/Init/Data/Int/Basic.lean

@@ -269,7 +269,7 @@ set_option bootstrap.genMatcherCode false in
 
   Implemented by efficient native code. -/
 @[extern "lean_int_dec_nonneg"]
-private def decNonneg (m : @& Int) : Decidable (NonNeg m) :=
+def decNonneg (m : @& Int) : Decidable (NonNeg m) :=
   match m with
   | ofNat m => isTrue <| NonNeg.mk m
   | -[_ +1] => isFalse <| fun h => nomatch h

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

@@ -41,6 +41,7 @@ Examples:
 * `(-0b1000 : Int) >>> 1 = -0b0100`
 * `(-0b0111 : Int) >>> 1 = -0b0100`
 -/
+@[expose]
 protected def shiftRight : Int → Nat → Int
   | Int.ofNat n, s => Int.ofNat (n >>> s)
   | Int.negSucc n, s => Int.negSucc (n >>> s)

src/Init/Data/Int/Compare.lean

@@ -37,7 +37,7 @@ theorem compare_eq_ite_le (a b : Int) :
   · next hlt => simp [Int.le_of_lt hlt, Int.not_le.2 hlt]
   · next hge =>
     split
-    · next hgt => simp [Int.le_of_lt hgt, Int.not_le.2 hgt]
+    · next hgt => simp [Int.not_le.2 hgt]
     · next hle => simp [Int.not_lt.1 hge, Int.not_lt.1 hle]
 
 protected theorem compare_swap (a b : Int) : (compare a b).swap = compare b a := by

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

@@ -3,7 +3,6 @@ Copyright (c) 2016 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Mario Carneiro
 -/
-
 module
 
 prelude
@@ -57,7 +56,7 @@ protected theorem dvd_trans : ∀ {a b c : Int}, a ∣ b → b ∣ c → a ∣ c
 
 @[simp] protected theorem dvd_neg {a b : Int} : a ∣ -b ↔ a ∣ b := by
   constructor <;> exact fun ⟨k, e⟩ =>
-    ⟨-k, by simp [← e, Int.neg_mul, Int.mul_neg, Int.neg_neg]⟩
+    ⟨-k, by simp [← e, Int.mul_neg, Int.neg_neg]⟩
 
 @[simp] theorem natAbs_dvd_natAbs {a b : Int} : natAbs a ∣ natAbs b ↔ a ∣ b := by
   refine ⟨fun ⟨k, hk⟩ => ?_, fun ⟨k, hk⟩ => ⟨natAbs k, hk.symm ▸ natAbs_mul a k⟩⟩
@@ -99,7 +98,7 @@ theorem ofNat_emod (m n : Nat) : (↑(m % n) : Int) = m % n := natCast_emod m n
 theorem emod_add_ediv : ∀ a b : Int, a % b + b * (a / b) = a
   | ofNat _, ofNat _ => congrArg ofNat <| Nat.mod_add_div ..
   | ofNat m, -[n+1] => by
-    show (m % succ n + -↑(succ n) * -↑(m / succ n) : Int) = m
+    change (m % succ n + -↑(succ n) * -↑(m / succ n) : Int) = m
     rw [Int.neg_mul_neg]; exact congrArg ofNat <| Nat.mod_add_div ..
   | -[_+1], 0 => by rw [emod_zero]; rfl
   | -[m+1], succ n => aux m n.succ
@@ -149,7 +148,7 @@ theorem add_mul_ediv_right (a b : Int) {c : Int} (H : c ≠ 0) : (a + b * c) / c
   fun {k n} => @fun
   | ofNat _ => congrArg ofNat <| Nat.add_mul_div_right _ _ k.succ_pos
   | -[m+1] => by
-    show ((n * k.succ : Nat) - m.succ : Int).ediv k.succ = n - (m / k.succ + 1 : Nat)
+    change ((n * k.succ : Nat) - m.succ : Int).ediv k.succ = n - (m / k.succ + 1 : Nat)
     by_cases h : m < n * k.succ
     · rw [← Int.ofNat_sub h, ← Int.ofNat_sub ((Nat.div_lt_iff_lt_mul k.succ_pos).2 h)]
       apply congrArg ofNat
@@ -158,7 +157,7 @@ theorem add_mul_ediv_right (a b : Int) {c : Int} (H : c ≠ 0) : (a + b * c) / c
       have H {a b : Nat} (h : a ≤ b) : (a : Int) + -((b : Int) + 1) = -[b - a +1] := by
         rw [negSucc_eq, Int.ofNat_sub h]
         simp only [Int.sub_eq_add_neg, Int.neg_add, Int.neg_neg, Int.add_left_comm, Int.add_assoc]
-      show ediv (↑(n * succ k) + -((m : Int) + 1)) (succ k) = n + -(↑(m / succ k) + 1 : Int)
+      change ediv (↑(n * succ k) + -((m : Int) + 1)) (succ k) = n + -(↑(m / succ k) + 1 : Int)
       rw [H h, H ((Nat.le_div_iff_mul_le k.succ_pos).2 h)]
       apply congrArg negSucc
       rw [Nat.mul_comm, Nat.sub_mul_div_of_le]; rwa [Nat.mul_comm]

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

@@ -3,7 +3,6 @@ Copyright (c) 2016 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Mario Carneiro, Kim Morrison, Markus Himmel
 -/
-
 module
 
 prelude
@@ -203,6 +202,9 @@ theorem tdiv_eq_ediv_of_nonneg : ∀ {a b : Int}, 0 ≤ a → a.tdiv b = a / b
   | succ _, succ _, _ => rfl
   | succ _, -[_+1], _ => rfl
 
+@[simp] theorem natCast_tdiv_eq_ediv {a : Nat} {b : Int} : (a : Int).tdiv b = a / b :=
+    tdiv_eq_ediv_of_nonneg (by simp)
+
 theorem tdiv_eq_ediv {a b : Int} :
     a.tdiv b = a / b + if 0 ≤ a ∨ b ∣ a then 0 else sign b := by
   simp only [dvd_iff_emod_eq_zero]
@@ -215,7 +217,7 @@ theorem tdiv_eq_ediv {a b : Int} :
       negSucc_not_nonneg, sign_of_add_one]
     simp only [negSucc_emod_ofNat_succ_eq_zero_iff]
     norm_cast
-    simp only [subNat_eq_zero_iff, Nat.succ_eq_add_one, sign_negSucc, Int.sub_neg, false_or]
+    simp only [Nat.succ_eq_add_one, false_or]
     split <;> rename_i h
     · rw [Int.add_zero, neg_ofNat_eq_negSucc_iff]
       exact Nat.succ_div_of_mod_eq_zero h
@@ -329,17 +331,17 @@ theorem fdiv_eq_ediv_of_dvd {a b : Int} (h : b ∣ a) : a.fdiv b = a / b := by
 theorem tmod_add_tdiv : ∀ a b : Int, tmod a b + b * (a.tdiv b) = a
   | ofNat _, ofNat _ => congrArg ofNat (Nat.mod_add_div ..)
   | ofNat m, -[n+1] => by
-    show (m % succ n + -↑(succ n) * -↑(m / succ n) : Int) = m
+    change (m % succ n + -↑(succ n) * -↑(m / succ n) : Int) = m
     rw [Int.neg_mul_neg]; exact congrArg ofNat (Nat.mod_add_div ..)
   | -[m+1], 0 => by
-    show -(↑((succ m) % 0) : Int) + 0 * -↑(succ m / 0) = -↑(succ m)
+    change -(↑((succ m) % 0) : Int) + 0 * -↑(succ m / 0) = -↑(succ m)
     rw [Nat.mod_zero, Int.zero_mul, Int.add_zero]
   | -[m+1], ofNat n => by
-    show -(↑((succ m) % n) : Int) + ↑n * -↑(succ m / n) = -↑(succ m)
+    change -(↑((succ m) % n) : Int) + ↑n * -↑(succ m / n) = -↑(succ m)
     rw [Int.mul_neg, ← Int.neg_add]
     exact congrArg (-ofNat ·) (Nat.mod_add_div ..)
   | -[m+1], -[n+1] => by
-    show -(↑(succ m % succ n) : Int) + -↑(succ n) * ↑(succ m / succ n) = -↑(succ m)
+    change -(↑(succ m % succ n) : Int) + -↑(succ n) * ↑(succ m / succ n) = -↑(succ m)
     rw [Int.neg_mul, ← Int.neg_add]
     exact congrArg (-ofNat ·) (Nat.mod_add_div ..)
 
@@ -361,17 +363,17 @@ theorem fmod_add_fdiv : ∀ a b : Int, a.fmod b + b * a.fdiv b = a
   | 0, ofNat _ | 0, -[_+1] => congrArg ofNat <| by simp
   | succ _, ofNat _ => congrArg ofNat <| Nat.mod_add_div ..
   | succ m, -[n+1] => by
-    show subNatNat (m % succ n) n + (↑(succ n * (m / succ n)) + n + 1) = (m + 1)
+    change subNatNat (m % succ n) n + (↑(succ n * (m / succ n)) + n + 1) = (m + 1)
     rw [Int.add_comm _ n, ← Int.add_assoc, ← Int.add_assoc,
       Int.subNatNat_eq_coe, Int.sub_add_cancel]
     exact congrArg (ofNat · + 1) <| Nat.mod_add_div ..
   | -[_+1], 0 => by rw [fmod_zero]; rfl
   | -[m+1], succ n => by
-    show subNatNat .. - (↑(succ n * (m / succ n)) + ↑(succ n)) = -↑(succ m)
+    change subNatNat .. - (↑(succ n * (m / succ n)) + ↑(succ n)) = -↑(succ m)
     rw [Int.subNatNat_eq_coe, ← Int.sub_sub, ← Int.neg_sub, Int.sub_sub, Int.sub_sub_self]
     exact congrArg (-ofNat ·) <| Nat.succ_add .. ▸ Nat.mod_add_div .. ▸ rfl
   | -[m+1], -[n+1] => by
-    show -(↑(succ m % succ n) : Int) + -↑(succ n * (succ m / succ n)) = -↑(succ m)
+    change -(↑(succ m % succ n) : Int) + -↑(succ n * (succ m / succ n)) = -↑(succ m)
     rw [← Int.neg_add]; exact congrArg (-ofNat ·) <| Nat.mod_add_div ..
 
 /-- Variant of `fmod_add_fdiv` with the multiplication written the other way around. -/
@@ -572,7 +574,7 @@ theorem neg_one_ediv (b : Int) : -1 / b = -b.sign :=
       · refine Nat.le_trans ?_ (Nat.le_add_right _ _)
         rw [← Nat.mul_div_mul_left _ _ m.succ_pos]
         apply Nat.div_mul_le_self
-      · show m.succ * n.succ ≤ _
+      · change m.succ * n.succ ≤ _
         rw [Nat.mul_left_comm]
         apply Nat.mul_le_mul_left
         apply (Nat.div_lt_iff_lt_mul k.succ_pos).1
@@ -1315,7 +1317,7 @@ protected theorem eq_tdiv_of_mul_eq_left {a b c : Int}
   | 0, n => by simp [Int.neg_zero]
   | succ _, (n:Nat) => by simp [tdiv, ← Int.negSucc_eq]
   | -[_+1], 0 | -[_+1], -[_+1] => by
-    simp only [tdiv, neg_negSucc, ← Int.natCast_succ, Int.neg_neg]
+    simp only [tdiv, neg_negSucc, Int.neg_neg]
   | succ _, -[_+1] | -[_+1], succ _ => (Int.neg_neg _).symm
 
 protected theorem neg_tdiv_neg (a b : Int) : (-a).tdiv (-b) = a.tdiv b := by
@@ -1406,7 +1408,7 @@ theorem mul_tmod (a b n : Int) : (a * b).tmod n = (a.tmod n * b.tmod n).tmod n :
   case inv => simp [Int.dvd_neg]
   induction m using wlog_sign
   case inv => simp
-  simp only [← Int.natCast_mul, ← ofNat_tmod]
+  simp only [← ofNat_tmod]
   norm_cast at h
   rw [Nat.mod_mod_of_dvd _ h]
 
@@ -1574,7 +1576,7 @@ theorem neg_mul_tmod_left (a b : Int) : (-(a * b)).tmod b = 0 := by
 
 @[simp] protected theorem tdiv_one : ∀ a : Int, a.tdiv 1 = a
   | (n:Nat) => congrArg ofNat (Nat.div_one _)
-  | -[n+1] => by simp [Int.tdiv, neg_ofNat_succ]; rfl
+  | -[n+1] => by simp [Int.tdiv]; rfl
 
 @[simp] theorem tmod_one (a : Int) : tmod a 1 = 0 := by
   simp [tmod_def, Int.tdiv_one, Int.one_mul, Int.sub_self]
@@ -1696,7 +1698,7 @@ theorem lt_ediv_iff_of_dvd_of_neg {a b c : Int} (hc : c < 0) (hcb : c ∣ b) :
 theorem ediv_le_ediv_iff_of_dvd_of_pos_of_pos {a b c d : Int} (hb : 0 < b) (hd : 0 < d)
     (hba : b ∣ a) (hdc : d ∣ c) : a / b ≤ c / d ↔ d * a ≤ c * b := by
   obtain ⟨⟨x, rfl⟩, y, rfl⟩ := hba, hdc
-  simp [*, Int.ne_of_lt, Int.ne_of_gt, d.mul_assoc, b.mul_comm]
+  simp [*, Int.ne_of_gt, d.mul_assoc, b.mul_comm]
 
 theorem ediv_le_ediv_iff_of_dvd_of_pos_of_neg {a b c d : Int} (hb : 0 < b) (hd : d < 0)
     (hba : b ∣ a) (hdc : d ∣ c) : a / b ≤ c / d ↔ c * b ≤ d * a := by
@@ -1711,12 +1713,12 @@ theorem ediv_le_ediv_iff_of_dvd_of_neg_of_pos {a b c d : Int} (hb : b < 0) (hd :
 theorem ediv_le_ediv_iff_of_dvd_of_neg_of_neg {a b c d : Int} (hb : b < 0) (hd : d < 0)
     (hba : b ∣ a) (hdc : d ∣ c) : a / b ≤ c / d ↔ d * a ≤ c * b := by
   obtain ⟨⟨x, rfl⟩, y, rfl⟩ := hba, hdc
-  simp [*, Int.ne_of_lt, Int.ne_of_gt, d.mul_assoc, b.mul_comm]
+  simp [*, Int.ne_of_lt, d.mul_assoc, b.mul_comm]
 
 theorem ediv_lt_ediv_iff_of_dvd_of_pos {a b c d : Int} (hb : 0 < b) (hd : 0 < d) (hba : b ∣ a)
     (hdc : d ∣ c) : a / b < c / d ↔ d * a < c * b := by
   obtain ⟨⟨x, rfl⟩, y, rfl⟩ := hba, hdc
-  simp [*, Int.ne_of_lt, Int.ne_of_gt, d.mul_assoc, b.mul_comm]
+  simp [*, Int.ne_of_gt, d.mul_assoc, b.mul_comm]
 
 theorem ediv_lt_ediv_iff_of_dvd_of_pos_of_neg {a b c d : Int} (hb : 0 < b) (hd : d < 0)
     (hba : b ∣ a) (hdc : d ∣ c) : a / b < c / d ↔ c * b < d * a := by
@@ -1731,7 +1733,7 @@ theorem ediv_lt_ediv_iff_of_dvd_of_neg_of_pos {a b c d : Int} (hb : b < 0) (hd :
 theorem ediv_lt_ediv_iff_of_dvd_of_neg_of_neg {a b c d : Int} (hb : b < 0) (hd : d < 0)
     (hba : b ∣ a) (hdc : d ∣ c) : a / b < c / d ↔ d * a < c * b := by
   obtain ⟨⟨x, rfl⟩, y, rfl⟩ := hba, hdc
-  simp [*, Int.ne_of_lt, Int.ne_of_gt, d.mul_assoc, b.mul_comm]
+  simp [*, Int.ne_of_lt, d.mul_assoc, b.mul_comm]
 
 /-! ### `tdiv` and ordering -/
 
@@ -2444,7 +2446,7 @@ theorem lt_mul_fdiv_self_add {x k : Int} (h : 0 < k) : x < k * (x.fdiv k) + k :=
 
 @[simp]
 theorem emod_bmod (x : Int) (n : Nat) : Int.bmod (x%n) n = Int.bmod x n := by
-  simp [bmod, Int.emod_emod]
+  simp [bmod]
 
 @[deprecated emod_bmod (since := "2025-04-11")]
 theorem emod_bmod_congr (x : Int) (n : Nat) : Int.bmod (x%n) n = Int.bmod x n :=
@@ -2745,7 +2747,7 @@ theorem bmod_lt {x : Int} {m : Nat} (h : 0 < m) : bmod x m < (m + 1) / 2 := by
   split
   · assumption
   · apply Int.lt_of_lt_of_le
-    · show _ < 0
+    · change _ < 0
       have : x % m < m := emod_lt_of_pos x (natCast_pos.mpr h)
       exact Int.sub_neg_of_lt this
     · exact Int.le.intro_sub _ rfl
@@ -2985,7 +2987,7 @@ theorem self_le_ediv_of_nonpos_of_nonneg {x y : Int} (hx : x ≤ 0) (hy : 0 ≤
   · simp [hx', zero_ediv]
   · by_cases hy : y = 0
     · simp [hy]; omega
-    · simp only [ge_iff_le, Int.le_ediv_iff_mul_le (c := y) (a := x) (b := x) (by omega),
+    · simp only [Int.le_ediv_iff_mul_le (c := y) (a := x) (b := x) (by omega),
         show (x * y ≤ x) = (x * y ≤ x * 1) by rw [Int.mul_one], Int.mul_one]
       apply Int.mul_le_mul_of_nonpos_left (a := x) (b := y) (c  := (1 : Int)) (by omega) (by omega)
 

src/Init/Data/Int/Gcd.lean

@@ -35,6 +35,7 @@ Examples:
 * `Int.gcd 0 5 = 5`
 * `Int.gcd (-7) 0 = 7`
 -/
+@[expose]
 def gcd (m n : Int) : Nat := m.natAbs.gcd n.natAbs
 
 theorem gcd_eq_natAbs_gcd_natAbs (m n : Int) : gcd m n = Nat.gcd m.natAbs n.natAbs := rfl
@@ -428,6 +429,7 @@ Examples:
  * `Int.lcm 0 3 = 0`
  * `Int.lcm (-3) 0 = 0`
 -/
+@[expose]
 def lcm (m n : Int) : Nat := m.natAbs.lcm n.natAbs
 
 theorem lcm_eq_natAbs_lcm_natAbs (m n : Int) : lcm m n = Nat.lcm m.natAbs n.natAbs := rfl
@@ -629,7 +631,7 @@ theorem lcm_mul_left_dvd_mul_lcm (k m n : Nat) : lcm (m * n) k ∣ lcm m k * lcm
   simpa [lcm_comm, Nat.mul_comm] using lcm_mul_right_dvd_mul_lcm _ _ _
 
 theorem lcm_dvd_mul_self_left_iff_dvd_mul {k n m : Nat} : lcm k n ∣ k * m ↔ n ∣ k * m := by
-  simp [← natAbs_dvd_natAbs, natAbs_mul, Nat.lcm_dvd_mul_self_left_iff_dvd_mul,
+  simp [Nat.lcm_dvd_mul_self_left_iff_dvd_mul,
     lcm_eq_natAbs_lcm_natAbs]
 
 theorem lcm_dvd_mul_self_right_iff_dvd_mul {k m n : Nat} : lcm n k ∣ m * k ↔ n ∣ m * k := by

src/Init/Data/Int/Lemmas.lean

@@ -339,7 +339,7 @@ protected theorem add_sub_assoc (a b c : Int) : a + b - c = a + (b - c) := by
   match m with
   | 0 => rfl
   | succ m =>
-    show ofNat (n - succ m) = subNatNat n (succ m)
+    change ofNat (n - succ m) = subNatNat n (succ m)
     rw [subNatNat, Nat.sub_eq_zero_of_le h]
 
 @[deprecated negSucc_eq (since := "2025-03-11")]
@@ -454,7 +454,7 @@ theorem negOfNat_eq_subNatNat_zero (n) : negOfNat n = subNatNat 0 n := by cases
 theorem ofNat_mul_subNatNat (m n k : Nat) :
     m * subNatNat n k = subNatNat (m * n) (m * k) := by
   cases m with
-  | zero => simp [ofNat_zero, Int.zero_mul, Nat.zero_mul, subNatNat_self]
+  | zero => simp [Int.zero_mul, Nat.zero_mul, subNatNat_self]
   | succ m => cases n.lt_or_ge k with
     | inl h =>
       have h' : succ m * n < succ m * k := Nat.mul_lt_mul_of_pos_left h (Nat.succ_pos m)

src/Init/Data/Int/Linear.lean

@@ -23,6 +23,7 @@ namespace Int.Linear
 abbrev Var := Nat
 abbrev Context := Lean.RArray Int
 
+@[expose]
 def Var.denote (ctx : Context) (v : Var) : Int :=
   ctx.get v
 
@@ -36,6 +37,7 @@ inductive Expr where
   | mulR (a : Expr) (k : Int)
   deriving Inhabited, BEq
 
+@[expose]
 def Expr.denote (ctx : Context) : Expr → Int
   | .add a b  => Int.add (denote ctx a) (denote ctx b)
   | .sub a b  => Int.sub (denote ctx a) (denote ctx b)
@@ -50,6 +52,7 @@ inductive Poly where
   | add (k : Int) (v : Var) (p : Poly)
   deriving BEq
 
+@[expose]
 def Poly.denote (ctx : Context) (p : Poly) : Int :=
   match p with
   | .num k => k
@@ -59,6 +62,7 @@ def Poly.denote (ctx : Context) (p : Poly) : Int :=
 Similar to `Poly.denote`, but produces a denotation better for `simp +arith`.
 Remark: we used to convert `Poly` back into `Expr` to achieve that.
 -/
+@[expose]
 def Poly.denote' (ctx : Context) (p : Poly) : Int :=
   match p with
   | .num k => k
@@ -75,8 +79,8 @@ where
 theorem Poly.denote'_go_eq_denote (ctx : Context) (p : Poly) (r : Int) : denote'.go ctx r p = p.denote ctx + r := by
   induction r, p using denote'.go.induct ctx <;> simp [denote'.go, denote]
   next => rw [Int.add_comm]
-  next ih => simp [denote'.go] at ih; rw [ih]; ac_rfl
-  next ih => simp [denote'.go] at ih; rw [ih]; ac_rfl
+  next ih => simp at ih; rw [ih]; ac_rfl
+  next ih => simp at ih; rw [ih]; ac_rfl
 
 theorem Poly.denote'_eq_denote (ctx : Context) (p : Poly) : p.denote' ctx = p.denote ctx := by
   unfold denote' <;> split <;> simp [denote, denote'_go_eq_denote] <;> ac_rfl
@@ -84,11 +88,13 @@ theorem Poly.denote'_eq_denote (ctx : Context) (p : Poly) : p.denote' ctx = p.de
 theorem Poly.denote'_add (ctx : Context) (a : Int) (x : Var) (p : Poly) : (Poly.add a x p).denote' ctx = a * x.denote ctx + p.denote ctx := by
   simp [Poly.denote'_eq_denote, denote]
 
+@[expose]
 def Poly.addConst (p : Poly) (k : Int) : Poly :=
   match p with
   | .num k' => .num (k+k')
   | .add k' v' p => .add k' v' (addConst p k)
 
+@[expose]
 def Poly.insert (k : Int) (v : Var) (p : Poly) : Poly :=
   match p with
   | .num k' => .add k v (.num k')
@@ -104,16 +110,19 @@ def Poly.insert (k : Int) (v : Var) (p : Poly) : Poly :=
       .add k' v' (insert k v p)
 
 /-- Normalizes the given polynomial by fusing monomial and constants. -/
+@[expose]
 def Poly.norm (p : Poly) : Poly :=
   match p with
   | .num k => .num k
   | .add k v p => (norm p).insert k v
 
+@[expose]
 def Poly.append (p₁ p₂ : Poly) : Poly :=
   match p₁ with
   | .num k₁ => p₂.addConst k₁
   | .add k x p₁ => .add k x (append p₁ p₂)
 
+@[expose]
 def Poly.combine' (fuel : Nat) (p₁ p₂ : Poly) : Poly :=
   match fuel with
   | 0 => p₁.append p₂
@@ -133,10 +142,12 @@ def Poly.combine' (fuel : Nat) (p₁ p₂ : Poly) : Poly :=
     else
       .add a₂ x₂ (combine' fuel (.add a₁ x₁ p₁) p₂)
 
+@[expose]
 def Poly.combine (p₁ p₂ : Poly) : Poly :=
   combine' 100000000 p₁ p₂
 
 /-- Converts the given expression into a polynomial. -/
+@[expose]
 def Expr.toPoly' (e : Expr) : Poly :=
   go 1 e (.num 0)
 where
@@ -150,6 +161,7 @@ where
     | .neg a    => go (-coeff) a
 
 /-- Converts the given expression into a polynomial, and then normalizes it. -/
+@[expose]
 def Expr.norm (e : Expr) : Poly :=
   e.toPoly'.norm
 
@@ -159,6 +171,7 @@ Examples:
 - `cdiv 7 3` returns `3`
 - `cdiv (-7) 3` returns `-2`.
 -/
+@[expose]
 def cdiv (a b : Int) : Int :=
   -((-a)/b)
 
@@ -173,6 +186,7 @@ See theorem `cdiv_add_cmod`. We also have
 -b < cmod a b ≤ 0
 ```
 -/
+@[expose]
 def cmod (a b : Int) : Int :=
   -((-a)%b)
 
@@ -219,6 +233,7 @@ theorem cdiv_eq_div_of_divides {a b : Int} (h : a % b = 0) : a/b = cdiv a b := b
   next => rw [Int.mul_eq_mul_right_iff h] at this; assumption
 
 /-- Returns the constant of the given linear polynomial. -/
+@[expose]
 def Poly.getConst : Poly → Int
   | .num k => k
   | .add _ _ p => getConst p
@@ -230,6 +245,7 @@ Notes:
 - We only use this function with `k`s that divides all coefficients.
 - We use `cdiv` for the constant to implement the inequality tightening rule.
 -/
+@[expose]
 def Poly.div (k : Int) : Poly → Poly
   | .num k' => .num (cdiv k' k)
   | .add k' x p => .add (k'/k) x (div k p)
@@ -238,6 +254,7 @@ def Poly.div (k : Int) : Poly → Poly
 Returns `true` if `k` divides all coefficients and the constant of the given
 linear polynomial.
 -/
+@[expose]
 def Poly.divAll (k : Int) : Poly → Bool
   | .num k' => k' % k == 0
   | .add k' _ p => k' % k == 0 && divAll k p
@@ -245,6 +262,7 @@ def Poly.divAll (k : Int) : Poly → Bool
 /--
 Returns `true` if `k` divides all coefficients of the given linear polynomial.
 -/
+@[expose]
 def Poly.divCoeffs (k : Int) : Poly → Bool
   | .num _ => true
   | .add k' _ p => k' % k == 0 && divCoeffs k p
@@ -252,11 +270,13 @@ def Poly.divCoeffs (k : Int) : Poly → Bool
 /--
 `p.mul k` multiplies all coefficients and constant of the polynomial `p` by `k`.
 -/
+@[expose]
 def Poly.mul' (p : Poly) (k : Int) : Poly :=
   match p with
   | .num k' => .num (k*k')
   | .add k' v p => .add (k*k') v (mul' p k)
 
+@[expose]
 def Poly.mul (p : Poly) (k : Int) : Poly :=
   if k == 0 then
     .num 0
@@ -343,7 +363,7 @@ theorem Expr.denote_toPoly'_go (ctx : Context) (e : Expr) :
     simp [eq_of_beq h]
   | case2 k k' h =>
     simp only [toPoly'.go, h, cond_false]
-    simp [Var.denote]
+    simp
   | case3 k i => simp [toPoly'.go]
   | case4 k a b iha ihb => simp [toPoly'.go, iha, ihb]
   | case5 k a b iha ihb =>
@@ -351,7 +371,7 @@ theorem Expr.denote_toPoly'_go (ctx : Context) (e : Expr) :
     rw [Int.sub_eq_add_neg, ←Int.neg_mul, Int.add_assoc]
   | case6 k k' a h
   | case8 k a k' h =>
-    simp only [toPoly'.go, h, cond_false]
+    simp only [toPoly'.go, h]
     simp [eq_of_beq h]
   | case7 k a k' h ih =>
     simp only [toPoly'.go, h, cond_false]
@@ -383,9 +403,10 @@ attribute [local simp] Poly.denote'_eq_denote
 
 theorem Expr.eq_of_norm_eq (ctx : Context) (e : Expr) (p : Poly) (h : e.norm == p) : e.denote ctx = p.denote' ctx := by
   have h := congrArg (Poly.denote ctx) (eq_of_beq h)
-  simp [Poly.norm] at h
+  simp at h
   simp [*]
 
+@[expose]
 def norm_eq_cert (lhs rhs : Expr) (p : Poly) : Bool :=
   p == (lhs.sub rhs).norm
 
@@ -401,6 +422,7 @@ theorem norm_le (ctx : Context) (lhs rhs : Expr) (p : Poly) (h : norm_eq_cert lh
   · exact Int.sub_nonpos_of_le
   · exact Int.le_of_sub_nonpos
 
+@[expose]
 def norm_eq_var_cert (lhs rhs : Expr) (x y : Var) : Bool :=
   (lhs.sub rhs).norm == .add 1 x (.add (-1) y (.num 0))
 
@@ -411,6 +433,7 @@ theorem norm_eq_var (ctx : Context) (lhs rhs : Expr) (x y : Var) (h : norm_eq_va
   simp at h
   rw [←Int.sub_eq_zero, h, ← @Int.sub_eq_zero (Var.denote ctx x), Int.sub_eq_add_neg]
 
+@[expose]
 def norm_eq_var_const_cert (lhs rhs : Expr) (x : Var) (k : Int) : Bool :=
   (lhs.sub rhs).norm == .add 1 x (.num (-k))
 
@@ -429,6 +452,7 @@ private theorem mul_eq_zero_iff (a k : Int) (h₁ : k > 0) : k * a = 0 ↔ a = 0
 theorem norm_eq_coeff' (ctx : Context) (p p' : Poly) (k : Int) : p = p'.mul k → k > 0 → (p.denote ctx = 0 ↔ p'.denote ctx = 0) := by
   intro; subst p; intro h; simp [mul_eq_zero_iff, *]
 
+@[expose]
 def norm_eq_coeff_cert (lhs rhs : Expr) (p : Poly) (k : Int) : Bool :=
   (lhs.sub rhs).norm == p.mul k && k > 0
 
@@ -448,7 +472,7 @@ private theorem mul_le_zero_iff (a k : Int) (h₁ : k > 0) : k * a ≤ 0 ↔ a
     simp at h; assumption
 
 private theorem norm_le_coeff' (ctx : Context) (p p' : Poly) (k : Int) : p = p'.mul k → k > 0 → (p.denote ctx ≤ 0 ↔ p'.denote ctx ≤ 0) := by
-  simp [norm_eq_coeff_cert]
+  simp
   intro; subst p; intro h; simp [mul_le_zero_iff, *]
 
 theorem norm_le_coeff (ctx : Context) (lhs rhs : Expr) (p : Poly) (k : Int)
@@ -492,6 +516,7 @@ private theorem eq_of_norm_eq_of_divCoeffs {ctx : Context} {p₁ p₂ : Poly} {k
   apply mul_add_cmod_le_iff
   assumption
 
+@[expose]
 def norm_le_coeff_tight_cert (lhs rhs : Expr) (p : Poly) (k : Int) : Bool :=
   let p' := lhs.sub rhs |>.norm
   k > 0 && (p'.divCoeffs k && p == p'.div k)
@@ -502,11 +527,13 @@ theorem norm_le_coeff_tight (ctx : Context) (lhs rhs : Expr) (p : Poly) (k : Int
   rw [norm_le ctx lhs rhs (lhs.sub rhs).norm BEq.rfl, Poly.denote'_eq_denote]
   apply eq_of_norm_eq_of_divCoeffs
 
+@[expose]
 def Poly.isUnsatEq (p : Poly) : Bool :=
   match p with
   | .num k => k != 0
   | _ => false
 
+@[expose]
 def Poly.isValidEq (p : Poly) : Bool :=
   match p with
   | .num k => k == 0
@@ -530,11 +557,13 @@ theorem eq_eq_true (ctx : Context) (lhs rhs : Expr) : (lhs.sub rhs).norm.isValid
     rw [← Int.sub_eq_zero, h]
     assumption
 
+@[expose]
 def Poly.isUnsatLe (p : Poly) : Bool :=
   match p with
   | .num k => k > 0
   | _ => false
 
+@[expose]
 def Poly.isValidLe (p : Poly) : Bool :=
   match p with
   | .num k => k ≤ 0
@@ -595,6 +624,7 @@ private theorem poly_eq_zero_eq_false (ctx : Context) {p : Poly} {k : Int} : p.d
   have high := h₃
   exact contra h₂ low high this
 
+@[expose]
 def unsatEqDivCoeffCert (lhs rhs : Expr) (k : Int) : Bool :=
   let p := (lhs.sub rhs).norm
   p.divCoeffs k && k > 0 && cmod p.getConst k < 0
@@ -621,6 +651,7 @@ private theorem gcd_dvd_step {k a b x : Int} (h : k ∣ a*x + b) : gcd a k ∣ b
   have h₂ : gcd a k ∣ a*x := Int.dvd_trans (gcd_dvd_left a k) (Int.dvd_mul_right a x)
   exact Int.dvd_iff_dvd_of_dvd_add h₁ |>.mp h₂
 
+@[expose]
 def Poly.gcdCoeffs : Poly → Int → Int
   | .num _, k => k
   | .add k' _ p, k => gcdCoeffs p (gcd k' k)
@@ -631,6 +662,7 @@ theorem Poly.gcd_dvd_const {ctx : Context} {p : Poly} {k : Int} (h : k ∣ p.den
     rw [Int.add_comm] at h
     exact ih (gcd_dvd_step h)
 
+@[expose]
 def Poly.isUnsatDvd (k : Int) (p : Poly) : Bool :=
   p.getConst % p.gcdCoeffs k != 0
 
@@ -668,9 +700,11 @@ theorem dvd_eq_false (ctx : Context) (k : Int) (e : Expr) (h : e.norm.isUnsatDvd
   rw [norm_dvd ctx k e e.norm BEq.rfl]
   apply dvd_eq_false' ctx k e.norm h
 
+@[expose]
 def dvd_coeff_cert (k₁ : Int) (p₁ : Poly) (k₂ : Int) (p₂ : Poly) (k : Int) : Bool :=
   k != 0 && (k₁ == k*k₂ && p₁ == p₂.mul k)
 
+@[expose]
 def norm_dvd_gcd_cert (k₁ : Int) (e₁ : Expr) (k₂ : Int) (p₂ : Poly) (k : Int) : Bool :=
   dvd_coeff_cert k₁ e₁.norm k₂ p₂ k
 
@@ -702,6 +736,7 @@ private theorem dvd_gcd_of_dvd (d a x p : Int) (h : d ∣ a * x + p) : gcd d a
   rw [Int.mul_assoc, Int.mul_assoc, ← Int.mul_sub] at h
   exists k₁ * k - k₂ * x
 
+@[expose]
 def dvd_elim_cert (k₁ : Int) (p₁ : Poly) (k₂ : Int) (p₂ : Poly) : Bool :=
   match p₁ with
   | .add a _ p => k₂ == gcd k₁ a && p₂ == p
@@ -764,6 +799,7 @@ private theorem dvd_solve_elim' {x : Int} {d₁ a₁ p₁ : Int} {d₂ a₂ p₂
  rw [h₃, h₄, Int.mul_assoc, Int.mul_assoc, ←Int.mul_sub] at this
  exact ⟨k₄ * k₁ - k₃ * k₂, this⟩
 
+@[expose]
 def dvd_solve_combine_cert (d₁ : Int) (p₁ : Poly) (d₂ : Int) (p₂ : Poly) (d : Int) (p : Poly) (g α β : Int) : Bool :=
   match p₁, p₂ with
   | .add a₁ x₁ p₁, .add a₂ x₂ p₂ =>
@@ -779,12 +815,13 @@ theorem dvd_solve_combine (ctx : Context) (d₁ : Int) (p₁ : Poly) (d₂ : Int
   split <;> simp
   next a₁ x₁ p₁ a₂ x₂ p₂ =>
   intro _ hg hd hp; subst x₁ p
-  simp [Poly.denote'_add]
+  simp
   intro h₁ h₂
   rw [Int.add_comm] at h₁ h₂
   rw [Int.add_comm _ (g * x₂.denote ctx), Int.add_left_comm, ← Int.add_assoc, hd]
   exact dvd_solve_combine' hg.symm h₁ h₂
 
+@[expose]
 def dvd_solve_elim_cert (d₁ : Int) (p₁ : Poly) (d₂ : Int) (p₂ : Poly) (d : Int) (p : Poly) : Bool :=
   match p₁, p₂ with
   | .add a₁ x₁ p₁, .add a₂ x₂ p₂ =>
@@ -816,6 +853,7 @@ theorem le_norm (ctx : Context) (p₁ p₂ : Poly) (h : p₁.norm == p₂) : p
   simp at h
   simp [*]
 
+@[expose]
 def le_coeff_cert (p₁ p₂ : Poly) (k : Int) : Bool :=
   k > 0 && (p₁.divCoeffs k && p₂ == p₁.div k)
 
@@ -824,6 +862,7 @@ theorem le_coeff (ctx : Context) (p₁ p₂ : Poly) (k : Int) : le_coeff_cert p
   intro h₁ h₂ h₃
   exact eq_of_norm_eq_of_divCoeffs h₁ h₂ h₃ |>.mp
 
+@[expose]
 def le_neg_cert (p₁ p₂ : Poly) : Bool :=
   p₂ == (p₁.mul (-1) |>.addConst 1)
 
@@ -834,11 +873,13 @@ theorem le_neg (ctx : Context) (p₁ p₂ : Poly) : le_neg_cert p₁ p₂ → ¬
   simp at h
   exact h
 
+@[expose]
 def Poly.leadCoeff (p : Poly) : Int :=
   match p with
   | .add a _ _ => a
   | _ => 1
 
+@[expose]
 def le_combine_cert (p₁ p₂ p₃ : Poly) : Bool :=
   let a₁ := p₁.leadCoeff.natAbs
   let a₂ := p₂.leadCoeff.natAbs
@@ -854,6 +895,7 @@ theorem le_combine (ctx : Context) (p₁ p₂ p₃ : Poly)
   · rw [← Int.zero_mul (Poly.denote ctx p₂)]; apply Int.mul_le_mul_of_nonpos_right <;> simp [*]
   · rw [← Int.zero_mul (Poly.denote ctx p₁)]; apply Int.mul_le_mul_of_nonpos_right <;> simp [*]
 
+@[expose]
 def le_combine_coeff_cert (p₁ p₂ p₃ : Poly) (k : Int) : Bool :=
   let a₁ := p₁.leadCoeff.natAbs
   let a₂ := p₂.leadCoeff.natAbs
@@ -883,6 +925,7 @@ theorem eq_norm (ctx : Context) (p₁ p₂ : Poly) (h : p₁.norm == p₂) : p
   simp at h
   simp [*]
 
+@[expose]
 def eq_coeff_cert (p p' : Poly) (k : Int) : Bool :=
   p == p'.mul k && k > 0
 
@@ -893,6 +936,7 @@ theorem eq_coeff (ctx : Context) (p p' : Poly) (k : Int) : eq_coeff_cert p p' k
 theorem eq_unsat (ctx : Context) (p : Poly) : p.isUnsatEq → p.denote' ctx = 0 → False := by
   simp [Poly.isUnsatEq] <;> split <;> simp
 
+@[expose]
 def eq_unsat_coeff_cert (p : Poly) (k : Int) : Bool :=
   p.divCoeffs k && k > 0 && cmod p.getConst k < 0
 
@@ -902,6 +946,7 @@ theorem eq_unsat_coeff (ctx : Context) (p : Poly) (k : Int) : eq_unsat_coeff_cer
   have h := poly_eq_zero_eq_false ctx h₁ h₂ h₃; clear h₁ h₂ h₃
   simp [h]
 
+@[expose]
 def Poly.coeff (p : Poly) (x : Var) : Int :=
   match p with
   | .add a y p => bif x == y then a else coeff p x
@@ -916,7 +961,8 @@ private theorem dvd_of_eq' {a x p : Int} : a*x + p = 0 → a ∣ p := by
   rw [Int.mul_comm, ← Int.neg_mul, Eq.comm, Int.mul_comm] at h
   exact ⟨-x, h⟩
 
-private def abs (x : Int) : Int :=
+@[expose]
+def abs (x : Int) : Int :=
   Int.ofNat x.natAbs
 
 private theorem abs_dvd {a p : Int} (h : a ∣ p) : abs a ∣ p := by
@@ -924,6 +970,7 @@ private theorem abs_dvd {a p : Int} (h : a ∣ p) : abs a ∣ p := by
   · simp at h; assumption
   · simp [Int.negSucc_eq] at h; assumption
 
+@[expose]
 def dvd_of_eq_cert (x : Var) (p₁ : Poly) (d₂ : Int) (p₂ : Poly) : Bool :=
   let a := p₁.coeff x
   d₂ == abs a && p₂ == p₁.insert (-a) x
@@ -950,6 +997,7 @@ private theorem eq_dvd_subst' {a x p d b q : Int} : a*x + p = 0 → d ∣ b*x +
   rw [← Int.mul_assoc] at h
   exact ⟨z, h⟩
 
+@[expose]
 def eq_dvd_subst_cert (x : Var) (p₁ : Poly) (d₂ : Int) (p₂ : Poly) (d₃ : Int) (p₃ : Poly) : Bool :=
   let a := p₁.coeff x
   let b := p₂.coeff x
@@ -979,6 +1027,7 @@ theorem eq_dvd_subst (ctx : Context) (x : Var) (p₁ : Poly) (d₂ : Int) (p₂
   apply abs_dvd
   simp [this, Int.neg_mul]
 
+@[expose]
 def eq_eq_subst_cert (x : Var) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly) : Bool :=
   let a := p₁.coeff x
   let b := p₂.coeff x
@@ -991,6 +1040,7 @@ theorem eq_eq_subst (ctx : Context) (x : Var) (p₁ : Poly) (p₂ : Poly) (p₃
   intro h₁ h₂
   simp [*]
 
+@[expose]
 def eq_le_subst_nonneg_cert (x : Var) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly) : Bool :=
   let a := p₁.coeff x
   let b := p₂.coeff x
@@ -1006,6 +1056,7 @@ theorem eq_le_subst_nonneg (ctx : Context) (x : Var) (p₁ : Poly) (p₂ : Poly)
   simp at h₂
   simp [*]
 
+@[expose]
 def eq_le_subst_nonpos_cert (x : Var) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly) : Bool :=
   let a := p₁.coeff x
   let b := p₂.coeff x
@@ -1022,6 +1073,7 @@ theorem eq_le_subst_nonpos (ctx : Context) (x : Var) (p₁ : Poly) (p₂ : Poly)
   rw [Int.mul_comm]
   assumption
 
+@[expose]
 def eq_of_core_cert (p₁ : Poly) (p₂ : Poly) (p₃ : Poly) : Bool :=
   p₃ == p₁.combine (p₂.mul (-1))
 
@@ -1031,6 +1083,7 @@ theorem eq_of_core (ctx : Context) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly)
   intro; subst p₃; simp
   intro h; rw [h, Int.add_neg_eq_sub, Int.sub_self]
 
+@[expose]
 def Poly.isUnsatDiseq (p : Poly) : Bool :=
   match p with
   | .num 0 => true
@@ -1047,11 +1100,12 @@ theorem diseq_coeff (ctx : Context) (p p' : Poly) (k : Int) : eq_coeff_cert p p'
   intro _ _; simp [mul_eq_zero_iff, *]
 
 theorem diseq_neg (ctx : Context) (p p' : Poly) : p' == p.mul (-1) → p.denote' ctx ≠ 0 → p'.denote' ctx ≠ 0 := by
-  simp; intro _ _; simp [mul_eq_zero_iff, *]
+  simp; intro _ _; simp [*]
 
 theorem diseq_unsat (ctx : Context) (p : Poly) : p.isUnsatDiseq → p.denote' ctx ≠ 0 → False := by
   simp [Poly.isUnsatDiseq] <;> split <;> simp
 
+@[expose]
 def diseq_eq_subst_cert (x : Var) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly) : Bool :=
   let a := p₁.coeff x
   let b := p₂.coeff x
@@ -1071,6 +1125,7 @@ theorem diseq_of_core (ctx : Context) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly)
   intro h; rw [← Int.sub_eq_zero] at h
   rw [Int.add_neg_eq_sub]; assumption
 
+@[expose]
 def eq_of_le_ge_cert (p₁ p₂ : Poly) : Bool :=
   p₂ == p₁.mul (-1)
 
@@ -1081,6 +1136,7 @@ theorem eq_of_le_ge (ctx : Context) (p₁ : Poly) (p₂ : Poly)
   intro h₁ h₂
   simp [Int.eq_iff_le_and_ge, *]
 
+@[expose]
 def le_of_le_diseq_cert (p₁ : Poly) (p₂ : Poly) (p₃ : Poly) : Bool :=
   -- Remark: we can generate two different certificates in the future, and avoid the `||` in the certificate.
   (p₂ == p₁ || p₂ == p₁.mul (-1)) &&
@@ -1095,6 +1151,7 @@ theorem le_of_le_diseq (ctx : Context) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly)
     next h => have := Int.lt_of_le_of_lt h₁ h; simp at this
   intro h; cases h <;> intro <;> subst p₂ p₃ <;> simp <;> apply this
 
+@[expose]
 def diseq_split_cert (p₁ p₂ p₃ : Poly) : Bool :=
   p₂ == p₁.addConst 1 &&
   p₃ == (p₁.mul (-1)).addConst 1
@@ -1113,6 +1170,7 @@ theorem diseq_split_resolve (ctx : Context) (p₁ p₂ p₃ : Poly)
   intro h₁ h₂ h₃
   exact (diseq_split ctx p₁ p₂ p₃ h₁ h₂).resolve_left h₃
 
+@[expose]
 def OrOver (n : Nat) (p : Nat → Prop) : Prop :=
   match n with
   | 0 => False
@@ -1127,6 +1185,7 @@ theorem orOver_resolve {n p} : OrOver (n+1) p → ¬ p n → OrOver n p := by
   · contradiction
   · assumption
 
+@[expose]
 def OrOver_cases_type (n : Nat) (p : Nat → Prop) : Prop :=
   match n with
   | 0 => p 0
@@ -1186,6 +1245,7 @@ private theorem cooper_dvd_left_core
   rw [this] at h₃
   exists k.toNat
 
+@[expose]
 def cooper_dvd_left_cert (p₁ p₂ p₃ : Poly) (d : Int) (n : Nat) : Bool :=
   p₁.casesOn (fun _ => false) fun a x _ =>
   p₂.casesOn (fun _ => false) fun b y _ =>
@@ -1194,11 +1254,13 @@ def cooper_dvd_left_cert (p₁ p₂ p₃ : Poly) (d : Int) (n : Nat) : Bool :=
    .and (a < 0)  <| .and (b > 0)  <|
    .and (d > 0)  <| n == Int.lcm a (a * d / Int.gcd (a * d) c)
 
+@[expose]
 def Poly.tail (p : Poly) : Poly :=
   match p with
   | .add _ _ p => p
   | _ => p
 
+@[expose]
 def cooper_dvd_left_split (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (k : Nat) : Prop :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1238,6 +1300,7 @@ theorem cooper_dvd_left (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (n : N
  simp only [denote'_addConst_eq]
  exact cooper_dvd_left_core ha hb hd h₁ h₂ h₃
 
+@[expose]
 def cooper_dvd_left_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (b : Int) (p' : Poly) : Bool :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1248,8 +1311,9 @@ def cooper_dvd_left_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (b : Int) (p' :
 theorem cooper_dvd_left_split_ineq (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (k : Nat) (b : Int) (p' : Poly)
     : cooper_dvd_left_split ctx p₁ p₂ p₃ d k → cooper_dvd_left_split_ineq_cert p₁ p₂ k b p' → p'.denote' ctx ≤ 0 := by
   simp [cooper_dvd_left_split_ineq_cert, cooper_dvd_left_split]
-  intros; subst p' b; simp [denote'_mul_combine_mul_addConst_eq]; assumption
+  intros; subst p' b; simp; assumption
 
+@[expose]
 def cooper_dvd_left_split_dvd1_cert (p₁ p' : Poly) (a : Int) (k : Int) : Bool :=
   a == p₁.leadCoeff && p' == p₁.tail.addConst k
 
@@ -1258,6 +1322,7 @@ theorem cooper_dvd_left_split_dvd1 (ctx : Context) (p₁ p₂ p₃ : Poly) (d :
   simp [cooper_dvd_left_split_dvd1_cert, cooper_dvd_left_split]
   intros; subst a p'; simp; assumption
 
+@[expose]
 def cooper_dvd_left_split_dvd2_cert (p₁ p₃ : Poly) (d : Int) (k : Nat) (d' : Int) (p' : Poly): Bool :=
   let p  := p₁.tail
   let s  := p₃.tail
@@ -1283,16 +1348,18 @@ private theorem cooper_left_core
   have h := cooper_dvd_left_core a_neg b_pos d_pos h₁ h₂ h₃
   simp only [Int.mul_one, gcd_zero, ofNat_natAbs_of_nonpos (Int.le_of_lt a_neg), Int.ediv_neg,
     Int.ediv_self (Int.ne_of_lt a_neg), Int.reduceNeg, lcm_neg_right, lcm_one,
-    Int.add_left_comm, Int.zero_mul, Int.mul_zero, Int.add_zero, Int.dvd_zero,
+    Int.zero_mul, Int.mul_zero, Int.add_zero, Int.dvd_zero,
     and_true] at h
   assumption
 
+@[expose]
 def cooper_left_cert (p₁ p₂ : Poly) (n : Nat) : Bool :=
   p₁.casesOn (fun _ => false) fun a x _ =>
   p₂.casesOn (fun _ => false) fun b y _ =>
    .and (x == y) <| .and (a < 0)  <| .and (b > 0)  <|
    n == a.natAbs
 
+@[expose]
 def cooper_left_split (ctx : Context) (p₁ p₂ : Poly) (k : Nat) : Prop :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1320,6 +1387,7 @@ theorem cooper_left (ctx : Context) (p₁ p₂ : Poly) (n : Nat)
  simp only [denote'_addConst_eq]
  assumption
 
+@[expose]
 def cooper_left_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (b : Int) (p' : Poly) : Bool :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1330,8 +1398,9 @@ def cooper_left_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (b : Int) (p' : Pol
 theorem cooper_left_split_ineq (ctx : Context) (p₁ p₂ : Poly) (k : Nat) (b : Int) (p' : Poly)
     : cooper_left_split ctx p₁ p₂ k → cooper_left_split_ineq_cert p₁ p₂ k b p' → p'.denote' ctx ≤ 0 := by
   simp [cooper_left_split_ineq_cert, cooper_left_split]
-  intros; subst p' b; simp [denote'_mul_combine_mul_addConst_eq]; assumption
+  intros; subst p' b; simp; assumption
 
+@[expose]
 def cooper_left_split_dvd_cert (p₁ p' : Poly) (a : Int) (k : Int) : Bool :=
   a == p₁.leadCoeff && p' == p₁.tail.addConst k
 
@@ -1353,7 +1422,7 @@ private theorem cooper_dvd_right_core
   have h₁'    : p ≤ (-a)*x := by rw [Int.neg_mul, ← Lean.Omega.Int.add_le_zero_iff_le_neg']; assumption
   have h₂'    : b * x ≤ -q := by rw [← Lean.Omega.Int.add_le_zero_iff_le_neg', Int.add_comm]; assumption
   have ⟨k, h₁, h₂, h₃, h₄, h₅⟩ := Int.cooper_resolution_dvd_right a_pos' b_pos d_pos |>.mp ⟨x, h₁', h₂', h₃⟩
-  simp only [Int.neg_mul, neg_gcd, lcm_neg_left, Int.mul_neg, Int.neg_neg, Int.neg_dvd] at *
+  simp only [Int.neg_mul, Int.mul_neg, Int.neg_neg] at *
   apply orOver_of_exists
   have hlt := ofNat_lt h₁ h₂
   replace h₃ := Int.add_le_add_right h₃ (-(a*q)); rw [Int.add_right_neg] at h₃
@@ -1363,8 +1432,9 @@ private theorem cooper_dvd_right_core
   have : -(c * k) + -(c * q) + b * s = -(c * q) + b * s + -(c * k) := by ac_rfl
   rw [this] at h₅; clear this
   exists k.toNat
-  simp only [hlt, true_and, and_true, cast_toNat h₁, h₃, h₄, h₅]
+  simp only [hlt, and_true, cast_toNat h₁, h₃, h₄, h₅]
 
+@[expose]
 def cooper_dvd_right_cert (p₁ p₂ p₃ : Poly) (d : Int) (n : Nat) : Bool :=
   p₁.casesOn (fun _ => false) fun a x _ =>
   p₂.casesOn (fun _ => false) fun b y _ =>
@@ -1373,6 +1443,7 @@ def cooper_dvd_right_cert (p₁ p₂ p₃ : Poly) (d : Int) (n : Nat) : Bool :=
    .and (a < 0)  <| .and (b > 0)  <|
    .and (d > 0)  <| n == Int.lcm b (b * d / Int.gcd (b * d) c)
 
+@[expose]
 def cooper_dvd_right_split (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (k : Nat) : Prop :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1402,9 +1473,10 @@ theorem cooper_dvd_right (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (n :
  intro h₁ h₂ h₃
  have := cooper_dvd_right_core ha hb hd h₁ h₂ h₃
  simp only [denote'_mul_combine_mul_addConst_eq]
- simp only [denote'_addConst_eq, ←Int.neg_mul]
+ simp only [denote'_addConst_eq]
  exact cooper_dvd_right_core ha hb hd h₁ h₂ h₃
 
+@[expose]
 def cooper_dvd_right_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (a : Int) (p' : Poly) : Bool :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1415,8 +1487,9 @@ def cooper_dvd_right_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (a : Int) (p'
 theorem cooper_dvd_right_split_ineq (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (k : Nat) (a : Int) (p' : Poly)
     : cooper_dvd_right_split ctx p₁ p₂ p₃ d k → cooper_dvd_right_split_ineq_cert p₁ p₂ k a p' → p'.denote' ctx ≤ 0 := by
   simp [cooper_dvd_right_split_ineq_cert, cooper_dvd_right_split]
-  intros; subst a p'; simp [denote'_mul_combine_mul_addConst_eq]; assumption
+  intros; subst a p'; simp; assumption
 
+@[expose]
 def cooper_dvd_right_split_dvd1_cert (p₂ p' : Poly) (b : Int) (k : Int) : Bool :=
   b == p₂.leadCoeff && p' == p₂.tail.addConst k
 
@@ -1425,6 +1498,7 @@ theorem cooper_dvd_right_split_dvd1 (ctx : Context) (p₁ p₂ p₃ : Poly) (d :
   simp [cooper_dvd_right_split_dvd1_cert, cooper_dvd_right_split]
   intros; subst b p'; simp; assumption
 
+@[expose]
 def cooper_dvd_right_split_dvd2_cert (p₂ p₃ : Poly) (d : Int) (k : Nat) (d' : Int) (p' : Poly): Bool :=
   let q  := p₂.tail
   let s  := p₃.tail
@@ -1448,17 +1522,19 @@ private theorem cooper_right_core
   have d_pos : (0 : Int) < 1 := by decide
   have h₃ : 1 ∣ 0*x + 0 := Int.one_dvd _
   have h := cooper_dvd_right_core a_neg b_pos d_pos h₁ h₂ h₃
-  simp only [Int.mul_one, gcd_zero, Int.natAbs_of_nonneg (Int.le_of_lt b_pos), Int.ediv_neg,
-    Int.ediv_self (Int.ne_of_gt b_pos), Int.reduceNeg, lcm_neg_right, lcm_one,
-    Int.add_left_comm, Int.zero_mul, Int.mul_zero, Int.add_zero, Int.dvd_zero,
+  simp only [Int.mul_one, gcd_zero, Int.natAbs_of_nonneg (Int.le_of_lt b_pos), 
+    Int.ediv_self (Int.ne_of_gt b_pos), lcm_one,
+    Int.zero_mul, Int.mul_zero, Int.add_zero, Int.dvd_zero,
     and_true, Int.neg_zero] at h
   assumption
 
+@[expose]
 def cooper_right_cert (p₁ p₂ : Poly) (n : Nat) : Bool :=
   p₁.casesOn (fun _ => false) fun a x _ =>
   p₂.casesOn (fun _ => false) fun b y _ =>
   .and (x == y) <| .and (a < 0)  <| .and (b > 0) <| n == b.natAbs
 
+@[expose]
 def cooper_right_split (ctx : Context) (p₁ p₂ : Poly) (k : Nat) : Prop :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1483,9 +1559,10 @@ theorem cooper_right (ctx : Context) (p₁ p₂ : Poly) (n : Nat)
  intro h₁ h₂
  have := cooper_right_core ha hb h₁ h₂
  simp only [denote'_mul_combine_mul_addConst_eq]
- simp only [denote'_addConst_eq, ←Int.neg_mul]
+ simp only [denote'_addConst_eq]
  assumption
 
+@[expose]
 def cooper_right_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (a : Int) (p' : Poly) : Bool :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1496,8 +1573,9 @@ def cooper_right_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (a : Int) (p' : Po
 theorem cooper_right_split_ineq (ctx : Context) (p₁ p₂ : Poly) (k : Nat) (a : Int) (p' : Poly)
     : cooper_right_split ctx p₁ p₂ k → cooper_right_split_ineq_cert p₁ p₂ k a p' → p'.denote' ctx ≤ 0 := by
   simp [cooper_right_split_ineq_cert, cooper_right_split]
-  intros; subst a p'; simp [denote'_mul_combine_mul_addConst_eq]; assumption
+  intros; subst a p'; simp; assumption
 
+@[expose]
 def cooper_right_split_dvd_cert (p₂ p' : Poly) (b : Int) (k : Int) : Bool :=
   b == p₂.leadCoeff && p' == p₂.tail.addConst k
 
@@ -1587,6 +1665,7 @@ abbrev Poly.casesOnAdd (p : Poly) (k : Int → Var → Poly → Bool) : Bool :=
 abbrev Poly.casesOnNum (p : Poly) (k : Int → Bool) : Bool :=
   p.casesOn k (fun _ _ _ => false)
 
+@[expose]
 def cooper_unsat_cert (p₁ p₂ p₃ : Poly) (d : Int) (α β : Int) : Bool :=
   p₁.casesOnAdd fun k₁ x p₁ =>
   p₂.casesOnAdd fun k₂ y p₂ =>
@@ -1603,7 +1682,7 @@ theorem cooper_unsat (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (α β :
    : cooper_unsat_cert p₁ p₂ p₃ d α β →
      p₁.denote' ctx ≤ 0 → p₂.denote' ctx ≤ 0 → d ∣ p₃.denote' ctx → False := by
   unfold cooper_unsat_cert <;> cases p₁ <;> cases p₂ <;> cases p₃ <;> simp only [Poly.casesOnAdd,
-    Bool.false_eq_true, Poly.denote'_add, mul_def, add_def, false_implies]
+    Bool.false_eq_true, Poly.denote'_add, false_implies]
   next k₁ x p₁ k₂ y p₂ c z p₃ =>
   cases p₁ <;> cases p₂ <;> cases p₃ <;> simp only [Poly.casesOnNum, Int.reduceNeg,
     Bool.and_eq_true, beq_iff_eq, decide_eq_true_eq, and_imp, Bool.false_eq_true,
@@ -1626,6 +1705,7 @@ theorem emod_nonneg (x y : Int) : y != 0 → -1 * (x % y) ≤ 0 := by
   simp at this
   assumption
 
+@[expose]
 def emod_le_cert (y n : Int) : Bool :=
   y != 0 && n == 1 - y.natAbs
 
@@ -1665,7 +1745,7 @@ theorem natCast_sub (x y : Nat)
         (NatCast.natCast x : Int) + -1*NatCast.natCast y
       else
         (0 : Int) := by
-  show (↑(x - y) : Int) = if (↑y : Int) + (-1)*↑x ≤ 0 then ↑x + (-1)*↑y else 0
+  change (↑(x - y) : Int) = if (↑y : Int) + (-1)*↑x ≤ 0 then (↑x : Int) + (-1)*↑y else 0
   rw [Int.neg_mul, ← Int.sub_eq_add_neg, Int.one_mul]
   rw [Int.neg_mul, ← Int.sub_eq_add_neg, Int.one_mul]
   split
@@ -1708,6 +1788,7 @@ private theorem eq_neg_addConst_add (ctx : Context) (p : Poly)
   rw [Int.add_right_neg]
   simp
 
+@[expose]
 def dvd_le_tight_cert (d : Int) (p₁ p₂ p₃ : Poly) : Bool :=
   let b₁ := p₁.getConst
   let b₂ := p₂.getConst
@@ -1728,6 +1809,7 @@ theorem dvd_le_tight (ctx : Context) (d : Int) (p₁ p₂ p₃ : Poly)
   simp only [Poly.denote'_eq_denote]
   exact dvd_le_tight' hd
 
+@[expose]
 def dvd_neg_le_tight_cert (d : Int) (p₁ p₂ p₃ : Poly) : Bool :=
   let b₁ := p₁.getConst
   let b₂ := p₂.getConst
@@ -1737,7 +1819,7 @@ def dvd_neg_le_tight_cert (d : Int) (p₁ p₂ p₃ : Poly) : Bool :=
   d > 0 && (p₂ == p.addConst b₂ && p₃ == p.addConst (b₁ - d*((b₁ - b₂)/d)))
 
 theorem Poly.mul_minus_one_getConst_eq (p : Poly) : (p.mul (-1)).getConst = -p.getConst := by
-  simp [Poly.mul, Poly.getConst]
+  simp [Poly.mul]
   induction p <;> simp [Poly.mul', Poly.getConst, *]
 
 theorem dvd_neg_le_tight (ctx : Context) (d : Int) (p₁ p₂ p₃ : Poly)
@@ -1764,6 +1846,7 @@ theorem le_norm_expr (ctx : Context) (lhs rhs : Expr) (p : Poly)
     : norm_eq_cert lhs rhs p → lhs.denote ctx ≤ rhs.denote ctx → p.denote' ctx ≤ 0 := by
   intro h₁ h₂; rwa [norm_le ctx lhs rhs p h₁] at h₂
 
+@[expose]
 def not_le_norm_expr_cert (lhs rhs : Expr) (p : Poly) : Bool :=
   p == (((lhs.sub rhs).norm).mul (-1)).addConst 1
 
@@ -1796,6 +1879,7 @@ theorem of_not_dvd (a b : Int) : a != 0 → ¬ (a ∣ b) → b % a > 0 := by
   simp [h₁] at h₂
   assumption
 
+@[expose]
 def le_of_le_cert (p q : Poly) (k : Nat) : Bool :=
   q == p.addConst (- k)
 
@@ -1806,6 +1890,7 @@ theorem le_of_le (ctx : Context) (p q : Poly) (k : Nat)
   simp [Lean.Omega.Int.add_le_zero_iff_le_neg']
   exact Int.le_trans h (Int.ofNat_zero_le _)
 
+@[expose]
 def not_le_of_le_cert (p q : Poly) (k : Nat) : Bool :=
   q == (p.mul (-1)).addConst (1 + k)
 
@@ -1815,10 +1900,11 @@ theorem not_le_of_le (ctx : Context) (p q : Poly) (k : Nat)
   intro h
   apply Int.pos_of_neg_neg
   apply Int.lt_of_add_one_le
-  simp [Int.neg_add, Int.neg_sub]
+  simp [Int.neg_add]
   rw [← Int.add_assoc, ← Int.add_assoc, Int.add_neg_cancel_right, Lean.Omega.Int.add_le_zero_iff_le_neg']
   simp; exact Int.le_trans h (Int.ofNat_zero_le _)
 
+@[expose]
 def eq_def_cert (x : Var) (xPoly : Poly) (p : Poly) : Bool :=
   p == .add (-1) x xPoly
 
@@ -1827,6 +1913,7 @@ theorem eq_def (ctx : Context) (x : Var) (xPoly : Poly) (p : Poly)
   simp [eq_def_cert]; intro _ h; subst p; simp [h]
   rw [← Int.sub_eq_add_neg, Int.sub_self]
 
+@[expose]
 def eq_def'_cert (x : Var) (e : Expr) (p : Poly) : Bool :=
   p == .add (-1) x e.norm
 

src/Init/Data/Int/OfNat.lean

@@ -19,6 +19,7 @@ We use them to implement the arithmetic theories in `grind`
 
 abbrev Var := Nat
 abbrev Context := Lean.RArray Nat
+@[expose]
 def Var.denote (ctx : Context) (v : Var) : Nat :=
   ctx.get v
 
@@ -31,6 +32,7 @@ inductive Expr where
   | mod  (a b : Expr)
   deriving BEq
 
+@[expose]
 def Expr.denote (ctx : Context) : Expr → Nat
   | .num k    => k
   | .var v    => v.denote ctx
@@ -39,6 +41,7 @@ def Expr.denote (ctx : Context) : Expr → Nat
   | .div a b  => Nat.div (denote ctx a) (denote ctx b)
   | .mod a b  => Nat.mod (denote ctx a) (denote ctx b)
 
+@[expose]
 def Expr.denoteAsInt (ctx : Context) : Expr → Int
   | .num k    => Int.ofNat k
   | .var v    => Int.ofNat (v.denote ctx)
@@ -48,7 +51,7 @@ def Expr.denoteAsInt (ctx : Context) : Expr → Int
   | .mod a b  => Int.emod (denoteAsInt ctx a) (denoteAsInt ctx b)
 
 theorem Expr.denoteAsInt_eq (ctx : Context) (e : Expr) : e.denoteAsInt ctx = e.denote ctx := by
-  induction e <;> simp [denote, denoteAsInt, Int.natCast_ediv, *] <;> rfl
+  induction e <;> simp [denote, denoteAsInt, *] <;> rfl
 
 theorem Expr.eq_denoteAsInt (ctx : Context) (e : Expr) : e.denote ctx = e.denoteAsInt ctx := by
   apply Eq.symm; apply denoteAsInt_eq

src/Init/Data/Int/Order.lean

@@ -448,7 +448,7 @@ protected theorem le_max_left (a b : Int) : a ≤ max a b := by rw [Int.max_def]
 protected theorem le_max_right (a b : Int) : b ≤ max a b := Int.max_comm .. ▸ Int.le_max_left ..
 
 protected theorem max_eq_right {a b : Int} (h : a ≤ b) : max a b = b := by
-  simp [Int.max_def, h, Int.not_lt.2 h]
+  simp [Int.max_def, h]
 
 protected theorem max_eq_left {a b : Int} (h : b ≤ a) : max a b = a := by
   rw [← Int.max_comm b a]; exact Int.max_eq_right h
@@ -638,7 +638,7 @@ theorem toNat_of_nonneg {a : Int} (h : 0 ≤ a) : (toNat a : Int) = a := by
 @[simp] theorem toNat_natCast (n : Nat) : toNat ↑n = n := rfl
 
 @[deprecated toNat_natCast (since := "2025-04-16")]
-theorem toNat_ofNat (n : Nat) : toNat ↑n = n := toNat_natCast n
+theorem toNat_ofNat (n : Nat) : toNat ↑n = n := rfl
 
 @[simp] theorem toNat_negSucc (n : Nat) : (Int.negSucc n).toNat = 0 := by
   simp [toNat]

src/Init/Data/Int/Pow.lean

@@ -19,6 +19,13 @@ protected theorem pow_succ (b : Int) (e : Nat) : b ^ (e+1) = (b ^ e) * b := rfl
 protected theorem pow_succ' (b : Int) (e : Nat) : b ^ (e+1) = b * (b ^ e) := by
   rw [Int.mul_comm, Int.pow_succ]
 
+protected theorem zero_pow {n : Nat} (h : n ≠ 0) : (0 : Int) ^ n = 0 := by
+  match n, h with
+  | n + 1, _ => simp [Int.pow_succ]
+
+protected theorem one_pow {n : Nat} : (1 : Int) ^ n = 1 := by
+  induction n with simp_all [Int.pow_succ]
+
 protected theorem pow_pos {n : Int} {m : Nat} : 0 < n → 0 < n ^ m := by
   induction m with
   | zero => simp

src/Init/Data/Iterators.lean

@@ -0,0 +1,19 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Basic
+import Init.Data.Iterators.PostconditionMonad
+import Init.Data.Iterators.Consumers
+import Init.Data.Iterators.Lemmas
+import Init.Data.Iterators.Internal
+
+/-!
+# Iterators
+
+See `Std.Data.Iterators` for an overview over the iterator API.
+-/

src/Init/Data/Iterators/Basic.lean

@@ -3,9 +3,12 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
 import Init.Core
 import Init.Classical
+import Init.Ext
 import Init.NotationExtra
 import Init.TacticsExtra
 
@@ -30,7 +33,7 @@ See `Std.Data.Iterators.Producers` for ways to iterate over common data structur
 By convention, the monadic iterator associated with an object can be obtained via dot notation.
 For example, `List.iterM IO` creates an iterator over a list in the monad `IO`.
 
-See `Std.Data.Iterators.Consumers` for ways to use an iterator. For example, `it.toList` will
+See `Init.Data.Iterators.Consumers` for ways to use an iterator. For example, `it.toList` will
 convert a provably finite iterator `it` into a list and `it.allowNontermination.toList` will
 do so even if finiteness cannot be proved. It is also always possible to manually iterate using
 `it.step`, relying on the termination measures `it.finitelyManySteps` and `it.finitelyManySkips`.
@@ -58,6 +61,7 @@ def x := [1, 2, 3].iterM IO
 def x := ([1, 2, 3].iterM IO : IterM IO Nat)
 ```
 -/
+@[ext]
 structure IterM {α : Type w} (m : Type w → Type w') (β : Type w) where
   /-- Internal implementation detail of the iterator. -/
   internalState : α
@@ -73,7 +77,7 @@ See `Std.Data.Iterators.Producers` for ways to iterate over common data structur
 By convention, the monadic iterator associated with an object can be obtained via dot notation.
 For example, `List.iterM IO` creates an iterator over a list in the monad `IO`.
 
-See `Std.Data.Iterators.Consumers` for ways to use an iterator. For example, `it.toList` will
+See `Init.Data.Iterators.Consumers` for ways to use an iterator. For example, `it.toList` will
 convert a provably finite iterator `it` into a list and `it.allowNontermination.toList` will
 do so even if finiteness cannot be proved. It is also always possible to manually iterate using
 `it.step`, relying on the termination measures `it.finitelyManySteps` and `it.finitelyManySkips`.
@@ -109,12 +113,14 @@ structure Iter {α : Type w} (β : Type w) where
 Converts a pure iterator (`Iter β`) into a monadic iterator (`IterM Id β`) in the
 identity monad `Id`.
 -/
+@[expose]
 def Iter.toIterM {α : Type w} {β : Type w} (it : Iter (α := α) β) : IterM (α := α) Id β :=
   ⟨it.internalState⟩
 
 /--
 Converts a monadic iterator (`IterM Id β`) over `Id` into a pure iterator (`Iter β`).
 -/
+@[expose]
 def IterM.toIter {α : Type w} {β : Type w} (it : IterM (α := α) Id β) : Iter (α := α) β :=
   ⟨it.internalState⟩
 
@@ -168,6 +174,7 @@ inductive IterStep (α β) where
 Returns the succeeding iterator stored in an iterator step or `none` if the step is `.done`
 and the iterator has finished.
 -/
+@[expose]
 def IterStep.successor : IterStep α β → Option α
   | .yield it _ => some it
   | .skip it => some it
@@ -177,7 +184,7 @@ def IterStep.successor : IterStep α β → Option α
 If present, applies `f` to the iterator of an `IterStep` and replaces the iterator
 with the result of the application of `f`.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def IterStep.mapIterator {α' : Type u'} (f : α → α') : IterStep α β → IterStep α' β
   | .yield it out => .yield (f it) out
   | .skip it => .skip (f it)
@@ -204,6 +211,12 @@ theorem IterStep.mapIterator_mapIterator {α' : Type u'} {α'' : Type u''}
     (step.mapIterator f).mapIterator g = step.mapIterator (g ∘ f) := by
   cases step <;> rfl
 
+theorem IterStep.mapIterator_comp {α' : Type u'} {α'' : Type u''}
+    {f : α → α'} {g : α' → α''} :
+    IterStep.mapIterator (β := β) (g ∘ f) = mapIterator g ∘ mapIterator f := by
+  apply funext
+  exact fun _ => mapIterator_mapIterator.symm
+
 @[simp]
 theorem IterStep.mapIterator_id {step : IterStep α β} :
     step.mapIterator id = step := by
@@ -216,12 +229,13 @@ of another state. Having this proof bundled up with the step is important for te
 
 See `IterM.Step` and `Iter.Step` for the concrete choice of the plausibility predicate.
 -/
+@[expose]
 def PlausibleIterStep (IsPlausibleStep : IterStep α β → Prop) := Subtype IsPlausibleStep
 
 /--
 Match pattern for the `yield` case. See also `IterStep.yield`.
 -/
-@[match_pattern]
+@[match_pattern, simp, expose]
 def PlausibleIterStep.yield {IsPlausibleStep : IterStep α β → Prop}
     (it' : α) (out : β) (h : IsPlausibleStep (.yield it' out)) :
     PlausibleIterStep IsPlausibleStep :=
@@ -230,7 +244,7 @@ def PlausibleIterStep.yield {IsPlausibleStep : IterStep α β → Prop}
 /--
 Match pattern for the `skip` case. See also `IterStep.skip`.
 -/
-@[match_pattern]
+@[match_pattern, simp, expose]
 def PlausibleIterStep.skip {IsPlausibleStep : IterStep α β → Prop}
     (it' : α) (h : IsPlausibleStep (.skip it')) : PlausibleIterStep IsPlausibleStep :=
   ⟨.skip it', h⟩
@@ -238,7 +252,7 @@ def PlausibleIterStep.skip {IsPlausibleStep : IterStep α β → Prop}
 /--
 Match pattern for the `done` case. See also `IterStep.done`.
 -/
-@[match_pattern]
+@[match_pattern, simp, expose]
 def PlausibleIterStep.done {IsPlausibleStep : IterStep α β → Prop}
     (h : IsPlausibleStep .done) : PlausibleIterStep IsPlausibleStep :=
   ⟨.done, h⟩
@@ -275,7 +289,7 @@ section Monadic
 /--
 Converts wraps the state of an iterator into an `IterM` object.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def toIterM {α : Type w} (it : α) (m : Type w → Type w') (β : Type w) :
     IterM (α := α) m β :=
   ⟨it⟩
@@ -294,6 +308,7 @@ theorem internalState_toIterM {α m β} (it : α) :
 Asserts that certain step is plausibly the successor of a given iterator. What "plausible" means
 is up to the `Iterator` instance but it should be strong enough to allow termination proofs.
 -/
+@[expose]
 abbrev IterM.IsPlausibleStep {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β] :
     IterM (α := α) m β → IterStep (IterM (α := α) m β) β → Prop :=
   Iterator.IsPlausibleStep (α := α) (m := m)
@@ -302,6 +317,7 @@ abbrev IterM.IsPlausibleStep {α : Type w} {m : Type w → Type w'} {β : Type w
 The type of the step object returned by `IterM.step`, containing an `IterStep`
 and a proof that this is a plausible step for the given iterator.
 -/
+@[expose]
 abbrev IterM.Step {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     (it : IterM (α := α) m β) :=
   PlausibleIterStep it.IsPlausibleStep
@@ -310,6 +326,7 @@ abbrev IterM.Step {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator
 Asserts that a certain output value could plausibly be emitted by the given iterator in its next
 step.
 -/
+@[expose]
 def IterM.IsPlausibleOutput {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     (it : IterM (α := α) m β) (out : β) : Prop :=
   ∃ it', it.IsPlausibleStep (.yield it' out)
@@ -318,6 +335,7 @@ def IterM.IsPlausibleOutput {α : Type w} {m : Type w → Type w'} {β : Type w}
 Asserts that a certain iterator `it'` could plausibly be the directly succeeding iterator of another
 given iterator `it`.
 -/
+@[expose]
 def IterM.IsPlausibleSuccessorOf {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     (it' it : IterM (α := α) m β) : Prop :=
   ∃ step, step.successor = some it' ∧ it.IsPlausibleStep step
@@ -326,6 +344,7 @@ def IterM.IsPlausibleSuccessorOf {α : Type w} {m : Type w → Type w'} {β : Ty
 Asserts that a certain iterator `it'` could plausibly be the directly succeeding iterator of another
 given iterator `it` while no value is emitted (see `IterStep.skip`).
 -/
+@[expose]
 def IterM.IsPlausibleSkipSuccessorOf {α : Type w} {m : Type w → Type w'} {β : Type w}
     [Iterator α m β] (it' it : IterM (α := α) m β) : Prop :=
   it.IsPlausibleStep (.skip it')
@@ -348,14 +367,27 @@ section Pure
 Asserts that certain step is plausibly the successor of a given iterator. What "plausible" means
 is up to the `Iterator` instance but it should be strong enough to allow termination proofs.
 -/
+@[expose]
 def Iter.IsPlausibleStep {α : Type w} {β : Type w} [Iterator α Id β]
     (it : Iter (α := α) β) (step : IterStep (Iter (α := α) β) β) : Prop :=
   it.toIterM.IsPlausibleStep (step.mapIterator Iter.toIterM)
 
+/--
+Asserts that a certain iterator `it` could plausibly yield the value `out` after an arbitrary
+number of steps.
+-/
+inductive IterM.IsPlausibleIndirectOutput {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    : IterM (α := α) m β → β → Prop where
+  | direct {it : IterM (α := α) m β} {out : β} : it.IsPlausibleOutput out →
+      it.IsPlausibleIndirectOutput out
+  | indirect {it it' : IterM (α := α) m β} {out : β} : it'.IsPlausibleSuccessorOf it →
+      it'.IsPlausibleIndirectOutput out → it.IsPlausibleIndirectOutput out
+
 /--
 The type of the step object returned by `Iter.step`, containing an `IterStep`
 and a proof that this is a plausible step for the given iterator.
 -/
+@[expose]
 def Iter.Step {α : Type w} {β : Type w} [Iterator α Id β] (it : Iter (α := α) β) :=
   PlausibleIterStep (Iter.IsPlausibleStep it)
 
@@ -370,7 +402,7 @@ def Iter.Step.toMonadic {α : Type w} {β : Type w} [Iterator α Id β] {it : It
 /--
 Converts an `IterM.Step` into an `Iter.Step`.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def IterM.Step.toPure {α : Type w} {β : Type w} [Iterator α Id β] {it : IterM (α := α) Id β}
     (step : it.Step) : it.toIter.Step :=
   ⟨step.val.mapIterator IterM.toIter, (by simp [Iter.IsPlausibleStep, step.property])⟩
@@ -394,6 +426,7 @@ theorem IterM.Step.toPure_done {α β : Type w} [Iterator α Id β] {it : IterM
 Asserts that a certain output value could plausibly be emitted by the given iterator in its next
 step.
 -/
+@[expose]
 def Iter.IsPlausibleOutput {α : Type w} {β : Type w} [Iterator α Id β]
     (it : Iter (α := α) β) (out : β) : Prop :=
   it.toIterM.IsPlausibleOutput out
@@ -402,10 +435,43 @@ def Iter.IsPlausibleOutput {α : Type w} {β : Type w} [Iterator α Id β]
 Asserts that a certain iterator `it'` could plausibly be the directly succeeding iterator of another
 given iterator `it`.
 -/
+@[expose]
 def Iter.IsPlausibleSuccessorOf {α : Type w} {β : Type w} [Iterator α Id β]
     (it' it : Iter (α := α) β) : Prop :=
   it'.toIterM.IsPlausibleSuccessorOf it.toIterM
 
+/--
+Asserts that a certain iterator `it` could plausibly yield the value `out` after an arbitrary
+number of steps.
+-/
+inductive Iter.IsPlausibleIndirectOutput {α β : Type w} [Iterator α Id β] :
+    Iter (α := α) β → β → Prop where
+  | direct {it : Iter (α := α) β} {out : β} : it.IsPlausibleOutput out →
+      it.IsPlausibleIndirectOutput out
+  | indirect {it it' : Iter (α := α) β} {out : β} : it'.IsPlausibleSuccessorOf it →
+      it'.IsPlausibleIndirectOutput out → it.IsPlausibleIndirectOutput out
+
+theorem Iter.isPlausibleIndirectOutput_iff_isPlausibleIndirectOutput_toIterM {α β : Type w}
+    [Iterator α Id β] {it : Iter (α := α) β} {out : β} :
+    it.IsPlausibleIndirectOutput out ↔ it.toIterM.IsPlausibleIndirectOutput out := by
+  constructor
+  · intro h
+    induction h with
+    | direct h =>
+      exact .direct h
+    | indirect h _ ih =>
+      exact .indirect h ih
+  · intro h
+    rw [← Iter.toIter_toIterM (it := it)]
+    generalize it.toIterM = it at ⊢ h
+    induction h with
+    | direct h =>
+      exact .direct h
+    | indirect h h' ih =>
+      rename_i it it' out
+      replace h : it'.toIter.IsPlausibleSuccessorOf it.toIter := h
+      exact .indirect (α := α) h ih
+
 /--
 Asserts that a certain iterator `it'` could plausibly be the directly succeeding iterator of another
 given iterator `it` while no value is emitted (see `IterStep.skip`).
@@ -419,7 +485,7 @@ Makes a single step with the given iterator `it`, potentially emitting a value a
 succeeding iterator. If this function is used recursively, termination can sometimes be proved with
 the termination measures `it.finitelyManySteps` and `it.finitelyManySkips`.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def Iter.step {α β : Type w} [Iterator α Id β] (it : Iter (α := α) β) : it.Step :=
   it.toIterM.step.run.toPure
 
@@ -448,6 +514,7 @@ structure IterM.TerminationMeasures.Finite
 The relation of plausible successors on `IterM.TerminationMeasures.Finite`. It is well-founded
 if there is a `Finite` instance.
 -/
+@[expose]
 def IterM.TerminationMeasures.Finite.Rel
     {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β] :
     TerminationMeasures.Finite α m → TerminationMeasures.Finite α m → Prop :=
@@ -456,12 +523,13 @@ def IterM.TerminationMeasures.Finite.Rel
 instance {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     [Finite α m] : WellFoundedRelation (IterM.TerminationMeasures.Finite α m) where
   rel := IterM.TerminationMeasures.Finite.Rel
-  wf := (InvImage.wf _ Finite.wf).transGen
+  wf := by exact (InvImage.wf _ Finite.wf).transGen
 
 /--
 Termination measure to be used in well-founded recursive functions recursing over a finite iterator
 (see also `Finite`).
 -/
+@[expose]
 def IterM.finitelyManySteps {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     [Finite α m] (it : IterM (α := α) m β) : IterM.TerminationMeasures.Finite α m :=
   ⟨it⟩
@@ -486,9 +554,10 @@ theorem IterM.TerminationMeasures.Finite.rel_of_skip
 macro_rules | `(tactic| decreasing_trivial) => `(tactic|
   first
   | exact IterM.TerminationMeasures.Finite.rel_of_yield ‹_›
-  | exact IterM.TerminationMeasures.Finite.rel_of_skip ‹_›)
+  | exact IterM.TerminationMeasures.Finite.rel_of_skip ‹_›
+  | fail)
 
-@[inherit_doc IterM.finitelyManySteps]
+@[inherit_doc IterM.finitelyManySteps, expose]
 def Iter.finitelyManySteps {α : Type w} {β : Type w} [Iterator α Id β] [Finite α Id]
     (it : Iter (α := α) β) : IterM.TerminationMeasures.Finite α Id :=
   it.toIterM.finitelyManySteps
@@ -513,7 +582,8 @@ theorem Iter.TerminationMeasures.Finite.rel_of_skip
 macro_rules | `(tactic| decreasing_trivial) => `(tactic|
   first
   | exact Iter.TerminationMeasures.Finite.rel_of_yield ‹_›
-  | exact Iter.TerminationMeasures.Finite.rel_of_skip ‹_›)
+  | exact Iter.TerminationMeasures.Finite.rel_of_skip ‹_›
+  | fail)
 
 theorem IterM.isPlausibleSuccessorOf_of_yield
     {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
@@ -553,6 +623,7 @@ structure IterM.TerminationMeasures.Productive
 The relation of plausible successors while skipping on `IterM.TerminationMeasures.Productive`.
 It is well-founded if there is a `Productive` instance.
 -/
+@[expose]
 def IterM.TerminationMeasures.Productive.Rel
     {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β] :
     TerminationMeasures.Productive α m → TerminationMeasures.Productive α m → Prop :=
@@ -561,12 +632,13 @@ def IterM.TerminationMeasures.Productive.Rel
 instance {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     [Productive α m] : WellFoundedRelation (IterM.TerminationMeasures.Productive α m) where
   rel := IterM.TerminationMeasures.Productive.Rel
-  wf := (InvImage.wf _ Productive.wf).transGen
+  wf := by exact (InvImage.wf _ Productive.wf).transGen
 
 /--
 Termination measure to be used in well-founded recursive functions recursing over a productive
 iterator (see also `Productive`).
 -/
+@[expose]
 def IterM.finitelyManySkips {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     [Productive α m] (it : IterM (α := α) m β) : IterM.TerminationMeasures.Productive α m :=
   ⟨it⟩
@@ -582,9 +654,11 @@ theorem IterM.TerminationMeasures.Productive.rel_of_skip
   .single h
 
 macro_rules | `(tactic| decreasing_trivial) => `(tactic|
-  exact IterM.TerminationMeasures.Productive.rel_of_skip ‹_›)
+  first
+    | exact IterM.TerminationMeasures.Productive.rel_of_skip ‹_›
+    | fail)
 
-@[inherit_doc IterM.finitelyManySkips]
+@[inherit_doc IterM.finitelyManySkips, expose]
 def Iter.finitelyManySkips {α : Type w} {β : Type w} [Iterator α Id β] [Productive α Id]
     (it : Iter (α := α) β) : IterM.TerminationMeasures.Productive α Id :=
   it.toIterM.finitelyManySkips
@@ -600,7 +674,9 @@ theorem Iter.TerminationMeasures.Productive.rel_of_skip
   IterM.TerminationMeasures.Productive.rel_of_skip h
 
 macro_rules | `(tactic| decreasing_trivial) => `(tactic|
-  exact Iter.TerminationMeasures.Productive.rel_of_skip ‹_›)
+  first
+    | exact Iter.TerminationMeasures.Productive.rel_of_skip ‹_›
+    | fail)
 
 instance [Iterator α m β] [Finite α m] : Productive α m where
   wf := by

src/Init/Data/Iterators/Consumers.lean

@@ -0,0 +1,13 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Consumers.Monadic
+import Init.Data.Iterators.Consumers.Access
+import Init.Data.Iterators.Consumers.Collect
+import Init.Data.Iterators.Consumers.Loop
+import Init.Data.Iterators.Consumers.Partial

src/Init/Data/Iterators/Consumers/Access.lean

@@ -3,8 +3,10 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Consumers.Partial
+import Init.Data.Iterators.Consumers.Partial
 
 namespace Std.Iterators
 

src/Init/Data/Iterators/Consumers/Collect.lean

@@ -3,10 +3,12 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Basic
-import Std.Data.Iterators.Consumers.Partial
-import Std.Data.Iterators.Consumers.Monadic.Collect
+import Init.Data.Iterators.Basic
+import Init.Data.Iterators.Consumers.Partial
+import Init.Data.Iterators.Consumers.Monadic.Collect
 
 /-!
 # Collectors
@@ -26,12 +28,12 @@ namespace Std.Iterators
 
 @[always_inline, inline, inherit_doc IterM.toArray]
 def Iter.toArray {α : Type w} {β : Type w}
-    [Iterator α Id β] [Finite α Id] [IteratorCollect α Id] (it : Iter (α := α) β) : Array β :=
+    [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id] (it : Iter (α := α) β) : Array β :=
   it.toIterM.toArray.run
 
 @[always_inline, inline, inherit_doc IterM.Partial.toArray]
 def Iter.Partial.toArray {α : Type w} {β : Type w}
-    [Iterator α Id β] [IteratorCollectPartial α Id] (it : Iter.Partial (α := α) β) : Array β :=
+    [Iterator α Id β] [IteratorCollectPartial α Id Id] (it : Iter.Partial (α := α) β) : Array β :=
   it.it.toIterM.allowNontermination.toArray.run
 
 @[always_inline, inline, inherit_doc IterM.toListRev]
@@ -46,12 +48,26 @@ def Iter.Partial.toListRev {α : Type w} {β : Type w}
 
 @[always_inline, inline, inherit_doc IterM.toList]
 def Iter.toList {α : Type w} {β : Type w}
-    [Iterator α Id β] [Finite α Id] [IteratorCollect α Id] (it : Iter (α := α) β) : List β :=
+    [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id] (it : Iter (α := α) β) : List β :=
   it.toIterM.toList.run
 
 @[always_inline, inline, inherit_doc IterM.Partial.toList]
 def Iter.Partial.toList {α : Type w} {β : Type w}
-    [Iterator α Id β] [IteratorCollectPartial α Id] (it : Iter.Partial (α := α) β) : List β :=
+    [Iterator α Id β] [IteratorCollectPartial α Id Id] (it : Iter.Partial (α := α) β) : List β :=
   it.it.toIterM.allowNontermination.toList.run
 
+/--
+This class charaterizes how the plausibility behavior (`IsPlausibleStep`) and the actual iteration
+behavior (`it.step`) should relate to each other for pure iterators. Intuitively, a step should
+only be plausible if it is possible. For simplicity's sake, the actual definition is weaker but
+presupposes that the iterator is finite.
+
+This is an experimental instance and it should not be explicitly used downstream of the standard
+library.
+-/
+class LawfulPureIterator (α : Type w) [Iterator α Id β]
+    [Finite α Id] [IteratorCollect α Id Id] where
+  mem_toList_iff_isPlausibleIndirectOutput {it : Iter (α := α) β} {out : β} :
+    out ∈ it.toList ↔ it.IsPlausibleIndirectOutput out
+
 end Std.Iterators

src/Init/Data/Iterators/Consumers/Loop.lean

@@ -3,9 +3,11 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Consumers.Monadic.Loop
-import Std.Data.Iterators.Consumers.Partial
+import Init.Data.Iterators.Consumers.Monadic.Loop
+import Init.Data.Iterators.Consumers.Partial
 
 /-!
 # Loop consumers
@@ -22,11 +24,24 @@ These operations are implemented using the `IteratorLoop` and `IteratorLoopParti
 
 namespace Std.Iterators
 
+/--
+A `ForIn'` instance for iterators. Its generic membership relation is not easy to use,
+so this is not marked as `instance`. This way, more convenient instances can be built on top of it
+or future library improvements will make it more comfortable.
+-/
+def Iter.instForIn' {α : Type w} {β : Type w} {n : Type w → Type w'} [Monad n]
+    [Iterator α Id β] [Finite α Id] [IteratorLoop α Id n] :
+    ForIn' n (Iter (α := α) β) β ⟨fun it out => it.IsPlausibleIndirectOutput out⟩ where
+  forIn' it init f :=
+    IteratorLoop.finiteForIn' (fun δ (c : Id δ) => pure c.run) |>.forIn' it.toIterM init
+        fun out h acc =>
+          f out (Iter.isPlausibleIndirectOutput_iff_isPlausibleIndirectOutput_toIterM.mpr h) acc
+
 instance (α : Type w) (β : Type w) (n : Type w → Type w') [Monad n]
     [Iterator α Id β] [Finite α Id] [IteratorLoop α Id n] :
-    ForIn n (Iter (α := α) β) β where
-  forIn it init f :=
-    IteratorLoop.finiteForIn (fun δ (c : Id δ) => pure c.run) |>.forIn it.toIterM init f
+    ForIn n (Iter (α := α) β) β :=
+  haveI : ForIn' n (Iter (α := α) β) β _ := Iter.instForIn'
+  instForInOfForIn'
 
 instance (α : Type w) (β : Type w) (n : Type w → Type w') [Monad n]
     [Iterator α Id β] [IteratorLoopPartial α Id n] :
@@ -35,6 +50,16 @@ instance (α : Type w) (β : Type w) (n : Type w → Type w') [Monad n]
     letI : MonadLift Id n := ⟨pure⟩
     ForIn.forIn it.it.toIterM.allowNontermination init f
 
+instance {m : Type w → Type w'}
+    {α : Type w} {β : Type w} [Iterator α Id β] [Finite α Id] [IteratorLoop α Id m] :
+    ForM m (Iter (α := α) β) β where
+  forM it f := forIn it PUnit.unit (fun out _ => do f out; return .yield .unit)
+
+instance {m : Type w → Type w'}
+    {α : Type w} {β : Type w} [Iterator α Id β] [Finite α Id] [IteratorLoopPartial α Id m] :
+    ForM m (Iter.Partial (α := α) β) β where
+  forM it f := forIn it PUnit.unit (fun out _ => do f out; return .yield .unit)
+
 /--
 Folds a monadic function over an iterator from the left, accumulating a value starting with `init`.
 The accumulated value is combined with the each element of the list in order, using `f`.
@@ -47,10 +72,10 @@ number of steps. If the iterator is not finite or such an instance is not availa
 verify the behavior of the partial variant.
 -/
 @[always_inline, inline]
-def Iter.foldM {n : Type w → Type w} [Monad n]
+def Iter.foldM {m : Type w → Type w'} [Monad m]
     {α : Type w} {β : Type w} {γ : Type w} [Iterator α Id β] [Finite α Id]
-    [IteratorLoop α Id n] (f : γ → β → n γ)
-    (init : γ) (it : Iter (α := α) β) : n γ :=
+    [IteratorLoop α Id m] (f : γ → β → m γ)
+    (init : γ) (it : Iter (α := α) β) : m γ :=
   ForIn.forIn it init (fun x acc => ForInStep.yield <$> f acc x)
 
 /--
@@ -63,10 +88,10 @@ This is a partial, potentially nonterminating, function. It is not possible to f
 its behavior. If the iterator has a `Finite` instance, consider using `IterM.foldM` instead.
 -/
 @[always_inline, inline]
-def Iter.Partial.foldM {n : Type w → Type w} [Monad n]
+def Iter.Partial.foldM {m : Type w → Type w'} [Monad m]
     {α : Type w} {β : Type w} {γ : Type w} [Iterator α Id β]
-    [IteratorLoopPartial α Id n] (f : γ → β → n γ)
-    (init : γ) (it : Iter.Partial (α := α) β) : n γ :=
+    [IteratorLoopPartial α Id m] (f : γ → β → m γ)
+    (init : γ) (it : Iter.Partial (α := α) β) : m γ :=
   ForIn.forIn it init (fun x acc => ForInStep.yield <$> f acc x)
 
 /--
@@ -101,4 +126,14 @@ def Iter.Partial.fold {α : Type w} {β : Type w} {γ : Type w} [Iterator α Id
     (init : γ) (it : Iter.Partial (α := α) β) : γ :=
   ForIn.forIn (m := Id) it init (fun x acc => ForInStep.yield (f acc x))
 
+@[always_inline, inline, inherit_doc IterM.size]
+def Iter.size {α : Type w} {β : Type w} [Iterator α Id β] [IteratorSize α Id]
+    (it : Iter (α := α) β) : Nat :=
+  (IteratorSize.size it.toIterM).run.down
+
+@[always_inline, inline, inherit_doc IterM.Partial.size]
+def Iter.Partial.size {α : Type w} {β : Type w} [Iterator α Id β] [IteratorSizePartial α Id]
+    (it : Iter (α := α) β) : Nat :=
+  (IteratorSizePartial.size it.toIterM).run.down
+
 end Std.Iterators

src/Init/Data/Iterators/Consumers/Monadic.lean

@@ -0,0 +1,11 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Consumers.Monadic.Collect
+import Init.Data.Iterators.Consumers.Monadic.Loop
+import Init.Data.Iterators.Consumers.Monadic.Partial

src/Init/Data/Iterators/Consumers/Monadic/Collect.lean

@@ -3,8 +3,11 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Consumers.Monadic.Partial
+import Init.Data.Iterators.Consumers.Monadic.Partial
+import Init.Data.Iterators.Internal.LawfulMonadLiftFunction
 
 /-!
 # Collectors
@@ -23,6 +26,7 @@ asserts that an `IteratorCollect` instance equals the default implementation.
 -/
 
 namespace Std.Iterators
+open Std.Internal
 
 section Typeclasses
 
@@ -33,13 +37,20 @@ iterators. Right now, it is limited to a potentially optimized `toArray` impleme
 This class is experimental and users of the iterator API should not explicitly depend on it.
 They can, however, assume that consumers that require an instance will work for all iterators
 provided by the standard library.
+
+Note: For this to be compositional enough to be useful, `toArrayMapped` would need to accept a
+termination proof for the specific mapping function used instead of the blanket `Finite α m`
+instance. Otherwise, most combinators like `map` cannot implement their own instance relying on
+the instance of their base iterators. However, fixing this is currently low priority.
 -/
-class IteratorCollect (α : Type w) (m : Type w → Type w') {β : Type w} [Iterator α m β] where
+class IteratorCollect (α : Type w) (m : Type w → Type w') (n : Type w → Type w'')
+    {β : Type w} [Iterator α m β] where
   /--
   Maps the emitted values of an iterator using the given function and collects the results in an
   `Array`. This is an internal implementation detail. Consider using `it.map f |>.toArray` instead.
   -/
-  toArrayMapped [Finite α m] : ∀ {γ : Type w}, (β → m γ) → IterM (α := α) m β → m (Array γ)
+  toArrayMapped [Finite α m] :
+    (lift : ⦃δ : Type w⦄ → m δ → n δ) → {γ : Type w} → (β → n γ) → IterM (α := α) m β → n (Array γ)
 
 /--
 `IteratorCollectPartial α m` provides efficient implementations of collectors for `α`-based
@@ -49,14 +60,15 @@ This class is experimental and users of the iterator API should not explicitly d
 They can, however, assume that consumers that require an instance will work for all iterators
 provided by the standard library.
 -/
-class IteratorCollectPartial
-    (α : Type w) (m : Type w → Type w') {β : Type w} [Iterator α m β] where
+class IteratorCollectPartial (α : Type w) (m : Type w → Type w') (n : Type w → Type w'')
+    {β : Type w} [Iterator α m β] where
   /--
   Maps the emitted values of an iterator using the given function and collects the results in an
   `Array`. This is an internal implementation detail.
   Consider using `it.map f |>.allowNontermination.toArray` instead.
   -/
-  toArrayMappedPartial : ∀ {γ : Type w}, (β → m γ) → IterM (α := α) m β → m (Array γ)
+  toArrayMappedPartial :
+    (lift : ⦃δ : Type w⦄ → m δ → n δ) → {γ : Type w} → (β → n γ) → IterM (α := α) m β → n (Array γ)
 
 end Typeclasses
 
@@ -69,12 +81,14 @@ It iterates over an iterator and applies `f` whenever a value is emitted before
 of `f` into an array.
 -/
 @[always_inline, inline]
-def IterM.DefaultConsumers.toArrayMapped {α : Type w} {m : Type w → Type w'} [Monad m] {β : Type w}
-    [Iterator α m β] [Finite α m] {γ : Type w} (f : β → m γ) (it : IterM (α := α) m β) : m (Array γ) :=
+def IterM.DefaultConsumers.toArrayMapped {α β : Type w} {m : Type w → Type w'}
+    {n : Type w → Type w''} [Monad n] [Iterator α m β] [Finite α m]
+    (lift : ⦃α : Type w⦄ → m α → n α) {γ : Type w} (f : β → n γ)
+    (it : IterM (α := α) m β) : n (Array γ) :=
   go it #[]
 where
   @[specialize]
-  go [Monad m] [Finite α m] (it : IterM (α := α) m β) a := do
+  go [Monad n] [Finite α m] (it : IterM (α := α) m β) a := letI : MonadLift m n := ⟨lift (α := _)⟩; do
     match ← it.step with
     | .yield it' b _ => go it' (a.push (← f b))
     | .skip it' _ => go it' a
@@ -88,30 +102,36 @@ data structure. For certain iterators, more efficient implementations are possib
 used instead.
 -/
 @[always_inline, inline]
-def IteratorCollect.defaultImplementation {α : Type w} {m : Type w → Type w'}
-    [Monad m] [Iterator α m β] : IteratorCollect α m where
+def IteratorCollect.defaultImplementation {α β : Type w} {m : Type w → Type w'}
+    {n : Type w → Type w''} [Monad n] [Iterator α m β] :
+    IteratorCollect α m n where
   toArrayMapped := IterM.DefaultConsumers.toArrayMapped
 
 /--
 Asserts that a given `IteratorCollect` instance is equal to `IteratorCollect.defaultImplementation`.
 (Even though equal, the given instance might be vastly more efficient.)
 -/
-class LawfulIteratorCollect (α : Type w) (m : Type w → Type w') [Monad m] [Iterator α m β]
-    [i : IteratorCollect α m] where
-  lawful : i = .defaultImplementation
+class LawfulIteratorCollect (α : Type w) (m : Type w → Type w') (n : Type w → Type w'')
+    {β : Type w} [Monad m] [Monad n] [Iterator α m β] [i : IteratorCollect α m n] where
+  lawful_toArrayMapped : ∀ lift [LawfulMonadLiftFunction lift] [Finite α m],
+    i.toArrayMapped lift (α := α) (γ := γ)
+      = IteratorCollect.defaultImplementation.toArrayMapped lift
 
-theorem LawfulIteratorCollect.toArrayMapped_eq {α β γ : Type w} {m : Type w → Type w'} [Monad m]
-    [Iterator α m β] [Finite α m] [IteratorCollect α m] [hl : LawfulIteratorCollect α m]
-    {f : β → m γ} {it : IterM (α := α) m β} :
-    IteratorCollect.toArrayMapped f it = IterM.DefaultConsumers.toArrayMapped f it := by
-  cases hl.lawful; rfl
+theorem LawfulIteratorCollect.toArrayMapped_eq {α β γ : Type w} {m : Type w → Type w'}
+    {n : Type w → Type w''} [Monad m] [Monad n] [Iterator α m β] [Finite α m] [IteratorCollect α m n]
+    [hl : LawfulIteratorCollect α m n] {lift : ⦃δ : Type w⦄ → m δ → n δ}
+    [LawfulMonadLiftFunction lift]
+    {f : β → n γ} {it : IterM (α := α) m β} :
+    IteratorCollect.toArrayMapped lift f it (m := m) =
+      IterM.DefaultConsumers.toArrayMapped lift f it (m := m) := by
+  rw [lawful_toArrayMapped]; rfl
 
-instance (α : Type w) (m : Type w → Type w') [Monad m] [Iterator α m β]
-    [Monad m] [Iterator α m β] [Finite α m] :
-    haveI : IteratorCollect α m := .defaultImplementation
-    LawfulIteratorCollect α m :=
-  letI : IteratorCollect α m := .defaultImplementation
-  ⟨rfl⟩
+instance (α β : Type w) (m : Type w → Type w') (n : Type w → Type w'') [Monad n]
+    [Iterator α m β] [Monad m] [Iterator α m β] [Finite α m] :
+    haveI : IteratorCollect α m n := .defaultImplementation
+    LawfulIteratorCollect α m n :=
+  letI : IteratorCollect α m n := .defaultImplementation
+  ⟨fun _ => rfl⟩
 
 /--
 This is an internal function used in `IteratorCollectPartial.defaultImplementation`.
@@ -120,12 +140,14 @@ It iterates over an iterator and applies `f` whenever a value is emitted before
 of `f` into an array.
 -/
 @[always_inline, inline]
-partial def IterM.DefaultConsumers.toArrayMappedPartial {α : Type w} {m : Type w → Type w'} [Monad m] {β : Type w}
-    [Iterator α m β] {γ : Type w} (f : β → m γ) (it : IterM (α := α) m β) : m (Array γ) :=
+partial def IterM.DefaultConsumers.toArrayMappedPartial {α β : Type w} {m : Type w → Type w'}
+    {n : Type w → Type w''} [Monad n] [Iterator α m β]
+    (lift : {α : Type w} → m α → n α) {γ : Type w} (f : β → n γ)
+    (it : IterM (α := α) m β) : n (Array γ) :=
   go it #[]
 where
   @[specialize]
-  go [Monad m] (it : IterM (α := α) m β) a := do
+  go [Monad n] (it : IterM (α := α) m β) a := letI : MonadLift m n := ⟨lift⟩; do
     match ← it.step with
     | .yield it' b _ => go it' (a.push (← f b))
     | .skip it' _ => go it' a
@@ -138,8 +160,9 @@ data structure. For certain iterators, more efficient implementations are possib
 used instead.
 -/
 @[always_inline, inline]
-def IteratorCollectPartial.defaultImplementation {α : Type w} {m : Type w → Type w'}
-    [Monad m] [Iterator α m β] : IteratorCollectPartial α m where
+def IteratorCollectPartial.defaultImplementation {α β : Type w} {m : Type w → Type w'}
+    {n : Type w → Type w''} [Monad n] [Iterator α m β] :
+    IteratorCollectPartial α m n where
   toArrayMappedPartial := IterM.DefaultConsumers.toArrayMappedPartial
 
 /--
@@ -151,9 +174,10 @@ number of steps. If the iterator is not finite or such an instance is not availa
 verify the behavior of the partial variant.
 -/
 @[always_inline, inline]
-def IterM.toArray {α : Type w} {m : Type w → Type w'} {β : Type w} [Monad m]
-    [Iterator α m β] [Finite α m] [IteratorCollect α m] (it : IterM (α := α) m β) : m (Array β) :=
-  IteratorCollect.toArrayMapped pure it
+def IterM.toArray {α β : Type w} {m : Type w → Type w'} [Monad m]
+    [Iterator α m β] [Finite α m] [IteratorCollect α m m]
+    (it : IterM (α := α) m β) : m (Array β) :=
+  IteratorCollect.toArrayMapped (fun ⦃_⦄ => id) pure it
 
 /--
 Traverses the given iterator and stores the emitted values in an array.
@@ -163,8 +187,8 @@ its behavior. If the iterator has a `Finite` instance, consider using `IterM.toA
 -/
 @[always_inline, inline]
 def IterM.Partial.toArray {α : Type w} {m : Type w → Type w'} {β : Type w} [Monad m]
-    [Iterator α m β] (it : IterM.Partial (α := α) m β) [IteratorCollectPartial α m] : m (Array β) :=
-  IteratorCollectPartial.toArrayMappedPartial pure it.it
+    [Iterator α m β] (it : IterM.Partial (α := α) m β) [IteratorCollectPartial α m m] : m (Array β) :=
+  IteratorCollectPartial.toArrayMappedPartial (fun ⦃_⦄ => id) pure it.it
 
 end ToArray
 
@@ -219,7 +243,7 @@ formally verify the behavior of the partial variant.
 -/
 @[always_inline, inline]
 def IterM.toList {α : Type w} {m : Type w → Type w'} [Monad m] {β : Type w}
-    [Iterator α m β] [Finite α m] [IteratorCollect α m] (it : IterM (α := α) m β) : m (List β) :=
+    [Iterator α m β] [Finite α m] [IteratorCollect α m m] (it : IterM (α := α) m β) : m (List β) :=
   Array.toList <$> IterM.toArray it
 
 /--
@@ -231,7 +255,8 @@ its behavior. If the iterator has a `Finite` instance, consider using `IterM.toL
 -/
 @[always_inline, inline]
 def IterM.Partial.toList {α : Type w} {m : Type w → Type w'} [Monad m] {β : Type w}
-    [Iterator α m β] (it : IterM.Partial (α := α) m β) [IteratorCollectPartial α m] : m (List β) :=
+    [Iterator α m β] (it : IterM.Partial (α := α) m β) [IteratorCollectPartial α m m] :
+    m (List β) :=
   Array.toList <$> it.toArray
 
 end Std.Iterators

src/Init/Data/Iterators/Consumers/Monadic/Loop.lean

@@ -3,10 +3,12 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
 import Init.RCases
-import Std.Data.Iterators.Basic
-import Std.Data.Iterators.Consumers.Monadic.Partial
+import Init.Data.Iterators.Basic
+import Init.Data.Iterators.Consumers.Monadic.Partial
 
 /-!
 # Loop-based consumers
@@ -62,8 +64,9 @@ class IteratorLoop (α : Type w) (m : Type w → Type w') {β : Type w} [Iterato
   forIn : ∀ (_lift : (γ : Type w) → m γ → n γ) (γ : Type w),
       (plausible_forInStep : β → γ → ForInStep γ → Prop) →
       IteratorLoop.WellFounded α m plausible_forInStep →
-      IterM (α := α) m β → γ →
-      ((b : β) → (c : γ) → n (Subtype (plausible_forInStep b c))) → n γ
+      (it : IterM (α := α) m β) → γ →
+      ((b : β) → it.IsPlausibleIndirectOutput b → (c : γ) → n (Subtype (plausible_forInStep b c))) →
+      n γ
 
 /--
 `IteratorLoopPartial α m` provides efficient implementations of loop-based consumers for `α`-based
@@ -76,7 +79,29 @@ provided by the standard library.
 class IteratorLoopPartial (α : Type w) (m : Type w → Type w') {β : Type w} [Iterator α m β]
     (n : Type w → Type w'') where
   forInPartial : ∀ (_lift : (γ : Type w) → m γ → n γ) {γ : Type w},
-      IterM (α := α) m β → γ → ((b : β) → (c : γ) → n (ForInStep γ)) → n γ
+      (it : IterM (α := α) m β) → γ →
+      ((b : β) → it.IsPlausibleIndirectOutput b → (c : γ) → n (ForInStep γ)) → n γ
+
+/--
+`IteratorSize α m` provides an implementation of the `IterM.size` function.
+
+This class is experimental and users of the iterator API should not explicitly depend on it.
+They can, however, assume that consumers that require an instance will work for all iterators
+provided by the standard library.
+-/
+class IteratorSize (α : Type w) (m : Type w → Type w') {β : Type w} [Iterator α m β] where
+  size : IterM (α := α) m β → m (ULift Nat)
+
+/--
+`IteratorSizePartial α m` provides an implementation of the `IterM.Partial.size` function that
+can be used as `it.allowTermination.size`.
+
+This class is experimental and users of the iterator API should not explicitly depend on it.
+They can, however, assume that consumers that require an instance will work for all iterators
+provided by the standard library.
+-/
+class IteratorSizePartial (α : Type w) (m : Type w → Type w') {β : Type w} [Iterator α m β] where
+  size : IterM (α := α) m β → m (ULift Nat)
 
 end Typeclasses
 
@@ -91,7 +116,7 @@ private def IteratorLoop.WFRel.mk {α : Type w} {m : Type w → Type w'} {β : T
     IteratorLoop.WFRel wf :=
   (it, c)
 
-instance {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
+private instance {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     {γ : Type x} {plausible_forInStep : β → γ → ForInStep γ → Prop}
     (wf : IteratorLoop.WellFounded α m plausible_forInStep) :
     WellFoundedRelation (IteratorLoop.WFRel wf) where
@@ -102,23 +127,27 @@ instance {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
 This is the loop implementation of the default instance `IteratorLoop.defaultImplementation`.
 -/
 @[specialize]
-def IterM.DefaultConsumers.forIn {m : Type w → Type w'} {α : Type w} {β : Type w}
+def IterM.DefaultConsumers.forIn' {m : Type w → Type w'} {α : Type w} {β : Type w}
     [Iterator α m β]
     {n : Type w → Type w''} [Monad n]
     (lift : ∀ γ, m γ → n γ) (γ : Type w)
     (plausible_forInStep : β → γ → ForInStep γ → Prop)
     (wf : IteratorLoop.WellFounded α m plausible_forInStep)
     (it : IterM (α := α) m β) (init : γ)
-    (f : (b : β) → (c : γ) → n (Subtype (plausible_forInStep b c))) : n γ :=
+    (f : (b : β) → it.IsPlausibleIndirectOutput b → (c : γ) → n (Subtype (plausible_forInStep b c))) : n γ :=
   haveI : WellFounded _ := wf
   letI : MonadLift m n := ⟨fun {γ} => lift γ⟩
   do
     match ← it.step with
-    | .yield it' out _ =>
-      match ← f out init with
-      | ⟨.yield c, _⟩ => IterM.DefaultConsumers.forIn lift _ plausible_forInStep wf it' c f
+    | .yield it' out h =>
+      match ← f out (.direct ⟨_, h⟩) init with
+      | ⟨.yield c, _⟩ =>
+        IterM.DefaultConsumers.forIn' lift _ plausible_forInStep wf it' c
+          (fun out h' acc => f out (.indirect ⟨_, rfl, h⟩ h') acc)
       | ⟨.done c, _⟩ => return c
-    | .skip it' _ => IterM.DefaultConsumers.forIn lift _ plausible_forInStep wf it' init f
+    | .skip it' h =>
+      IterM.DefaultConsumers.forIn' lift _ plausible_forInStep wf it' init
+        (fun out h' acc => f out (.indirect ⟨_, rfl, h⟩ h') acc)
     | .done _ => return init
 termination_by IteratorLoop.WFRel.mk wf it init
 decreasing_by
@@ -134,7 +163,7 @@ implementations are possible and should be used instead.
 def IteratorLoop.defaultImplementation {α : Type w} {m : Type w → Type w'} {n : Type w → Type w''}
     [Monad n] [Iterator α m β] :
     IteratorLoop α m n where
-  forIn lift := IterM.DefaultConsumers.forIn lift
+  forIn lift := IterM.DefaultConsumers.forIn' lift
 
 /--
 Asserts that a given `IteratorLoop` instance is equal to `IteratorLoop.defaultImplementation`.
@@ -153,15 +182,19 @@ partial def IterM.DefaultConsumers.forInPartial {m : Type w → Type w'} {α : T
     {n : Type w → Type w''} [Monad n]
     (lift : ∀ γ, m γ → n γ) (γ : Type w)
     (it : IterM (α := α) m β) (init : γ)
-    (f : (b : β) → (c : γ) → n (ForInStep γ)) : n γ :=
+    (f : (b : β) → it.IsPlausibleIndirectOutput b → (c : γ) → n (ForInStep γ)) : n γ :=
   letI : MonadLift m n := ⟨fun {γ} => lift γ⟩
   do
     match ← it.step with
-    | .yield it' out _ =>
-      match ← f out init with
-      | .yield c => IterM.DefaultConsumers.forInPartial lift _ it' c f
+    | .yield it' out h =>
+      match ← f out (.direct ⟨_, h⟩) init with
+      | .yield c =>
+        IterM.DefaultConsumers.forInPartial lift _ it' c
+          fun out h' acc => f out (.indirect ⟨_, rfl, h⟩ h') acc
       | .done c => return c
-    | .skip it' _ => IterM.DefaultConsumers.forInPartial lift _ it' init f
+    | .skip it' h =>
+      IterM.DefaultConsumers.forInPartial lift _ it' init
+        fun out h' acc => f out (.indirect ⟨_, rfl, h⟩ h') acc
     | .done _ => return init
 
 /--
@@ -170,49 +203,79 @@ It simply iterates through the iterator using `IterM.step`. For certain iterator
 implementations are possible and should be used instead.
 -/
 @[always_inline, inline]
-def IteratorLoopPartial.defaultImplementation {α : Type w} {m : Type w → Type w'} {n : Type w → Type w'}
-    [Monad m] [Monad n] [Iterator α m β] :
+def IteratorLoopPartial.defaultImplementation {α : Type w} {m : Type w → Type w'}
+    {n : Type w → Type w''} [Monad m] [Monad n] [Iterator α m β] :
     IteratorLoopPartial α m n where
   forInPartial lift := IterM.DefaultConsumers.forInPartial lift _
 
-instance (α : Type w) (m : Type w → Type w') (n : Type w → Type w')
+instance (α : Type w) (m : Type w → Type w') (n : Type w → Type w'')
     [Monad m] [Monad n] [Iterator α m β] [Finite α m] :
     letI : IteratorLoop α m n := .defaultImplementation
     LawfulIteratorLoop α m n :=
   letI : IteratorLoop α m n := .defaultImplementation
   ⟨rfl⟩
 
+theorem IteratorLoop.wellFounded_of_finite {m : Type w → Type w'}
+    {α β γ : Type w} [Iterator α m β] [Finite α m] :
+    WellFounded α m (γ := γ) fun _ _ _ => True := by
+  apply Subrelation.wf
+    (r := InvImage IterM.TerminationMeasures.Finite.Rel (fun p => p.1.finitelyManySteps))
+  · intro p' p h
+    apply Relation.TransGen.single
+    obtain ⟨b, h, _⟩ | ⟨h, _⟩ := h
+    · exact ⟨.yield p'.fst b, rfl, h⟩
+    · exact ⟨.skip p'.fst, rfl, h⟩
+  · apply InvImage.wf
+    exact WellFoundedRelation.wf
+
 /--
-This `ForIn`-style loop construct traverses a finite iterator using an `IteratorLoop` instance.
+This `ForIn'`-style loop construct traverses a finite iterator using an `IteratorLoop` instance.
 -/
 @[always_inline, inline]
-def IteratorLoop.finiteForIn {m : Type w → Type w'} {n : Type w → Type w''}
+def IteratorLoop.finiteForIn' {m : Type w → Type w'} {n : Type w → Type w''}
     {α : Type w} {β : Type w} [Iterator α m β] [Finite α m] [IteratorLoop α m n]
     (lift : ∀ γ, m γ → n γ) :
-    ForIn n (IterM (α := α) m β) β where
-  forIn {γ} [Monad n] it init f :=
+    ForIn' n (IterM (α := α) m β) β ⟨fun it out => it.IsPlausibleIndirectOutput out⟩ where
+  forIn' {γ} [Monad n] it init f :=
     IteratorLoop.forIn (α := α) (m := m) lift γ (fun _ _ _ => True)
-      (by
-        apply Subrelation.wf
-          (r := InvImage IterM.TerminationMeasures.Finite.Rel (fun p => p.1.finitelyManySteps))
-        · intro p' p h
-          apply Relation.TransGen.single
-          obtain ⟨b, h, _⟩ | ⟨h, _⟩ := h
-          · exact ⟨.yield p'.fst b, rfl, h⟩
-          · exact ⟨.skip p'.fst, rfl, h⟩
-        · apply InvImage.wf
-          exact WellFoundedRelation.wf)
-      it init ((⟨·, .intro⟩) <$> f · ·)
+      wellFounded_of_finite
+      it init (fun out h acc => (⟨·, .intro⟩) <$> f out h acc)
+
+/--
+A `ForIn'` instance for iterators. Its generic membership relation is not easy to use,
+so this is not marked as `instance`. This way, more convenient instances can be built on top of it
+or future library improvements will make it more comfortable.
+-/
+def IterM.instForIn' {m : Type w → Type w'} {n : Type w → Type w''}
+    {α : Type w} {β : Type w} [Iterator α m β] [Finite α m] [IteratorLoop α m n]
+    [MonadLiftT m n] :
+    ForIn' n (IterM (α := α) m β) β ⟨fun it out => it.IsPlausibleIndirectOutput out⟩ :=
+  IteratorLoop.finiteForIn' (fun _ => monadLift)
 
 instance {m : Type w → Type w'} {n : Type w → Type w''}
     {α : Type w} {β : Type w} [Iterator α m β] [Finite α m] [IteratorLoop α m n]
     [MonadLiftT m n] :
-    ForIn n (IterM (α := α) m β) β := IteratorLoop.finiteForIn (fun _ => monadLift)
+    ForIn n (IterM (α := α) m β) β :=
+  haveI : ForIn' n (IterM (α := α) m β) β _ := IterM.instForIn'
+  instForInOfForIn'
 
 instance {m : Type w → Type w'} {n : Type w → Type w''}
     {α : Type w} {β : Type w} [Iterator α m β] [IteratorLoopPartial α m n] [MonadLiftT m n] :
-    ForIn n (IterM.Partial (α := α) m β) β where
-  forIn it init f := IteratorLoopPartial.forInPartial (α := α) (m := m) (fun _ => monadLift) it.it init f
+    ForIn' n (IterM.Partial (α := α) m β) β ⟨fun it out => it.it.IsPlausibleIndirectOutput out⟩ where
+  forIn' it init f :=
+    IteratorLoopPartial.forInPartial (α := α) (m := m) (fun _ => monadLift) it.it init f
+
+instance {m : Type w → Type w'} {n : Type w → Type w''}
+    {α : Type w} {β : Type w} [Iterator α m β] [Finite α m] [IteratorLoop α m n]
+    [MonadLiftT m n] :
+    ForM n (IterM (α := α) m β) β where
+  forM it f := forIn it PUnit.unit (fun out _ => do f out; return .yield .unit)
+
+instance {m : Type w → Type w'} {n : Type w → Type w''}
+    {α : Type w} {β : Type w} [Iterator α m β] [Finite α m] [IteratorLoopPartial α m n]
+    [MonadLiftT m n] :
+    ForM n (IterM.Partial (α := α) m β) β where
+  forM it f := forIn it PUnit.unit (fun out _ => do f out; return .yield .unit)
 
 /--
 Folds a monadic function over an iterator from the left, accumulating a value starting with `init`.
@@ -227,7 +290,7 @@ number of steps. If the iterator is not finite or such an instance is not availa
 verify the behavior of the partial variant.
 -/
 @[always_inline, inline]
-def IterM.foldM {m : Type w → Type w'} {n : Type w → Type w'} [Monad n]
+def IterM.foldM {m : Type w → Type w'} {n : Type w → Type w''} [Monad n]
     {α : Type w} {β : Type w} {γ : Type w} [Iterator α m β] [Finite α m] [IteratorLoop α m n]
     [MonadLiftT m n]
     (f : γ → β → n γ) (init : γ) (it : IterM (α := α) m β) : n γ :=
@@ -295,7 +358,7 @@ verify the behavior of the partial variant.
 def IterM.drain {α : Type w} {m : Type w → Type w'} [Monad m] {β : Type w}
     [Iterator α m β] [Finite α m] (it : IterM (α := α) m β) [IteratorLoop α m m] :
     m PUnit :=
-  it.foldM (γ := PUnit) (fun _ _ => pure .unit) .unit
+  it.fold (γ := PUnit) (fun _ _ => .unit) .unit
 
 /--
 Iterates over the whole iterator, applying the monadic effects of each step, discarding all
@@ -308,6 +371,88 @@ its behavior. If the iterator has a `Finite` instance, consider using `IterM.dra
 def IterM.Partial.drain {α : Type w} {m : Type w → Type w'} [Monad m] {β : Type w}
     [Iterator α m β] (it : IterM.Partial (α := α) m β) [IteratorLoopPartial α m m] :
     m PUnit :=
-  it.foldM (γ := PUnit) (fun _ _ => pure .unit) .unit
+  it.fold (γ := PUnit) (fun _ _ => .unit) .unit
+
+section Size
+
+/--
+This is the implementation of the default instance `IteratorSize.defaultImplementation`.
+-/
+@[always_inline, inline]
+def IterM.DefaultConsumers.size {α : Type w} {m : Type w → Type w'} [Monad m] {β : Type w}
+    [Iterator α m β] [IteratorLoop α m m] [Finite α m] (it : IterM (α := α) m β) :
+    m (ULift Nat) :=
+  it.fold (init := .up 0) fun acc _ => .up (acc.down + 1)
+
+/--
+This is the implementation of the default instance `IteratorSizePartial.defaultImplementation`.
+-/
+@[always_inline, inline]
+def IterM.DefaultConsumers.sizePartial {α : Type w} {m : Type w → Type w'} [Monad m] {β : Type w}
+    [Iterator α m β] [IteratorLoopPartial α m m] (it : IterM (α := α) m β) :
+    m (ULift Nat) :=
+  it.allowNontermination.fold (init := .up 0) fun acc _ => .up (acc.down + 1)
+
+/--
+This is the default implementation of the `IteratorSize` class.
+It simply iterates using `IteratorLoop` and counts the elements.
+For certain iterators, more efficient implementations are possible and should be used instead.
+-/
+@[always_inline, inline]
+def IteratorSize.defaultImplementation {α β : Type w} {m : Type w → Type w'} [Monad m]
+    [Iterator α m β] [Finite α m] [IteratorLoop α m m] :
+    IteratorSize α m where
+  size := IterM.DefaultConsumers.size
+
+
+/--
+This is the default implementation of the `IteratorSizePartial` class.
+It simply iterates using `IteratorLoopPartial` and counts the elements.
+For certain iterators, more efficient implementations are possible and should be used instead.
+-/
+@[always_inline, inline]
+instance IteratorSizePartial.defaultImplementation {α β : Type w} {m : Type w → Type w'} [Monad m]
+    [Iterator α m β] [IteratorLoopPartial α m m] :
+    IteratorSizePartial α m where
+  size := IterM.DefaultConsumers.sizePartial
+
+/--
+Computes how many elements the iterator returns. In monadic situations, it is unclear which effects
+are caused by calling `size`, and if the monad is nondeterministic, it is also unclear what the
+returned value should be. The reference implementation, `IteratorSize.defaultImplementation`,
+simply iterates over the whole iterator monadically, counting the number of emitted values.
+An `IteratorSize` instance is considered lawful if it is equal to the reference implementation.
+
+**Performance**:
+
+Default performance is linear in the number of steps taken by the iterator.
+-/
+@[always_inline, inline]
+def IterM.size {α : Type} {m : Type → Type w'} {β : Type} [Iterator α m β] [Monad m]
+    (it : IterM (α := α) m β) [IteratorSize α m] : m Nat :=
+  ULift.down <$> IteratorSize.size it
+
+/--
+Computes how many elements the iterator emits.
+
+With monadic iterators (`IterM`), it is unclear which effects
+are caused by calling `size`, and if the monad is nondeterministic, it is also unclear what the
+returned value should be. The reference implementation, `IteratorSize.defaultImplementation`,
+simply iterates over the whole iterator monadically, counting the number of emitted values.
+An `IteratorSize` instance is considered lawful if it is equal to the reference implementation.
+
+This is the partial version of `size`. It does not require a proof of finiteness and might loop
+forever. It is not possible to verify the behavior in Lean because it uses `partial`.
+
+**Performance**:
+
+Default performance is linear in the number of steps taken by the iterator.
+-/
+@[always_inline, inline]
+def IterM.Partial.size {α : Type} {m : Type → Type w'} {β : Type} [Iterator α m β] [Monad m]
+    (it : IterM.Partial (α := α) m β) [IteratorSizePartial α m] : m Nat :=
+  ULift.down <$> IteratorSizePartial.size it.it
+
+end Size
 
 end Std.Iterators

src/Init/Data/Iterators/Consumers/Monadic/Partial.lean

@@ -3,8 +3,10 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Basic
+import Init.Data.Iterators.Basic
 
 namespace Std.Iterators
 

src/Init/Data/Iterators/Consumers/Partial.lean

@@ -3,8 +3,10 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Basic
+import Init.Data.Iterators.Basic
 
 namespace Std.Iterators
 

src/Init/Data/Iterators/Internal.lean

@@ -0,0 +1,10 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Internal.LawfulMonadLiftFunction
+import Init.Data.Iterators.Internal.Termination

src/Init/Data/Iterators/Internal/LawfulMonadLiftFunction.lean

@@ -0,0 +1,80 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Control.Basic
+import Init.Control.Lawful.Basic
+import Init.NotationExtra
+import Init.Control.Lawful.MonadLift
+
+/-!
+# Typeclass for lawful monad lifting functions
+
+This module provides a typeclass `LawfulMonadLiftFunction f` that asserts that a function `f`
+mapping values from one monad to another monad commutes with `pure` and `bind`. This equivalent to
+the requirement that the `MonadLift(T)` instance induced by `f` admits a
+`LawfulMonadLift(T)` instance.
+-/
+
+namespace Std.Internal
+
+class LawfulMonadLiftFunction {m : Type u → Type v} {n : Type u → Type w}
+    [Monad m] [Monad n] (lift : ⦃α : Type u⦄ → m α → n α) where
+  lift_pure {α : Type u} (a : α) : lift (pure a) = pure a
+  lift_bind {α β : Type u} (ma : m α) (f : α → m β) :
+    lift (ma >>= f) = lift ma >>= (fun x => lift (f x))
+
+instance {m : Type u → Type v} [Monad m] : LawfulMonadLiftFunction (fun ⦃α⦄ => (id : m α → m α)) where
+  lift_pure := by simp
+  lift_bind := by simp
+
+instance {m : Type u → Type v} [Monad m] {n : Type u → Type w} [Monad n] [MonadLiftT m n]
+    [LawfulMonadLiftT m n] :
+    LawfulMonadLiftFunction (fun ⦃α⦄ => (monadLift : m α → n α)) where
+  lift_pure := monadLift_pure
+  lift_bind := monadLift_bind
+
+variable {m : Type u → Type v} {n : Type u → Type w} [Monad m] [Monad n]
+    {lift : ⦃α : Type u⦄ → m α → n α}
+
+theorem LawfulMonadLiftFunction.lift_map [LawfulMonad m] [LawfulMonad n]
+    [LawfulMonadLiftFunction lift] (f : α → β) (ma : m α) :
+    lift (f <$> ma) = f <$> (lift ma : n α) := by
+  rw [← bind_pure_comp, ← bind_pure_comp, lift_bind (lift := lift)]
+  simp only [bind_pure_comp, lift_pure]
+
+theorem LawfulMonadLiftFunction.lift_seq [LawfulMonad m] [LawfulMonad n]
+    [LawfulMonadLiftFunction lift] (mf : m (α → β)) (ma : m α) :
+    lift (mf <*> ma) = lift mf <*> (lift ma : n α) := by
+  simp only [seq_eq_bind, lift_map, lift_bind]
+
+theorem LawfulMonadLiftFunction.lift_seqLeft [LawfulMonad m] [LawfulMonad n]
+    [LawfulMonadLiftFunction lift] (x : m α) (y : m β) :
+    lift (x <* y) = (lift x : n α) <* (lift y : n β) := by
+  simp only [seqLeft_eq, lift_map, lift_seq]
+
+theorem LawfulMonadLiftFunction.lift_seqRight [LawfulMonad m] [LawfulMonad n]
+    [LawfulMonadLiftFunction lift] (x : m α) (y : m β) :
+    lift (x *> y) = (lift x : n α) *> (lift y : n β) := by
+  simp only [seqRight_eq, lift_map, lift_seq]
+
+abbrev idToMonad [Monad m] ⦃α : Type u⦄ (x : Id α) : m α :=
+    pure x.run
+
+def LawfulMonadLiftFunction.idToMonad [Monad m] [LawfulMonad m] :
+    LawfulMonadLiftFunction (m := Id) (n := m) idToMonad where
+  lift_pure := by simp [Internal.idToMonad]
+  lift_bind := by simp [Internal.idToMonad]
+
+instance [LawfulMonadLiftFunction lift] :
+    letI : MonadLift m n := ⟨lift (α := _)⟩
+    LawfulMonadLift m n :=
+  letI : MonadLift m n := ⟨lift (α := _)⟩
+  { monadLift_pure := LawfulMonadLiftFunction.lift_pure
+    monadLift_bind := LawfulMonadLiftFunction.lift_bind }
+
+end Std.Internal

src/Init/Data/Iterators/Internal/Termination.lean

@@ -3,8 +3,10 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Basic
+import Init.Data.Iterators.Basic
 
 /-!
 This is an internal module used by iterator implementations.

src/Init/Data/Iterators/Lemmas.lean

@@ -3,5 +3,7 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Internal.Termination
+import Init.Data.Iterators.Lemmas.Consumers

src/Init/Data/Iterators/Lemmas/Basic.lean

@@ -3,8 +3,10 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Basic
+import Init.Data.Iterators.Basic
 
 namespace Std.Iterators
 

src/Init/Data/Iterators/Lemmas/Consumers.lean

@@ -0,0 +1,11 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Lemmas.Consumers.Monadic
+import Init.Data.Iterators.Lemmas.Consumers.Collect
+import Init.Data.Iterators.Lemmas.Consumers.Loop

src/Init/Data/Iterators/Lemmas/Consumers/Collect.lean

@@ -0,0 +1,114 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Lemmas.Basic
+import Init.Data.Iterators.Lemmas.Consumers.Monadic.Collect
+import all Init.Data.Iterators.Consumers.Access
+import all Init.Data.Iterators.Consumers.Collect
+
+namespace Std.Iterators
+
+theorem Iter.toArray_eq_toArray_toIterM {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
+    it.toArray = it.toIterM.toArray.run :=
+  (rfl)
+
+theorem Iter.toList_eq_toList_toIterM {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
+    it.toList = it.toIterM.toList.run :=
+  (rfl)
+
+theorem Iter.toListRev_eq_toListRev_toIterM {α β} [Iterator α Id β] [Finite α Id]
+    {it : Iter (α := α) β} :
+    it.toListRev = it.toIterM.toListRev.run :=
+  (rfl)
+
+@[simp]
+theorem IterM.toList_toIter {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    {it : IterM (α := α) Id β} :
+    it.toIter.toList = it.toList.run :=
+  (rfl)
+
+@[simp]
+theorem IterM.toListRev_toIter {α β} [Iterator α Id β] [Finite α Id]
+    {it : IterM (α := α) Id β} :
+    it.toIter.toListRev = it.toListRev.run :=
+  (rfl)
+
+theorem Iter.toList_toArray {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
+    it.toArray.toList = it.toList := by
+  simp [toArray_eq_toArray_toIterM, toList_eq_toList_toIterM, ← IterM.toList_toArray]
+
+theorem Iter.toArray_toList {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
+    it.toList.toArray = it.toArray := by
+  simp [toArray_eq_toArray_toIterM, toList_eq_toList_toIterM, ← IterM.toArray_toList]
+
+@[simp]
+theorem Iter.reverse_toListRev [Iterator α Id β] [Finite α Id]
+    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    {it : Iter (α := α) β} :
+    it.toListRev.reverse = it.toList := by
+  simp [toListRev_eq_toListRev_toIterM, toList_eq_toList_toIterM, ← IterM.reverse_toListRev]
+
+theorem Iter.toListRev_eq {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
+    it.toListRev = it.toList.reverse := by
+  simp [Iter.toListRev_eq_toListRev_toIterM, Iter.toList_eq_toList_toIterM, IterM.toListRev_eq]
+
+theorem Iter.toArray_eq_match_step {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
+    it.toArray = match it.step with
+      | .yield it' out _ => #[out] ++ it'.toArray
+      | .skip it' _ => it'.toArray
+      | .done _ => #[] := by
+  simp only [Iter.toArray_eq_toArray_toIterM, Iter.step]
+  rw [IterM.toArray_eq_match_step, Id.run_bind]
+  generalize it.toIterM.step.run = step
+  cases step using PlausibleIterStep.casesOn <;> simp
+
+theorem Iter.toList_eq_match_step {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
+    it.toList = match it.step with
+      | .yield it' out _ => out :: it'.toList
+      | .skip it' _ => it'.toList
+      | .done _ => [] := by
+  rw [← Iter.toList_toArray, Iter.toArray_eq_match_step]
+  split <;> simp [Iter.toList_toArray]
+
+theorem Iter.toListRev_eq_match_step {α β} [Iterator α Id β] [Finite α Id] {it : Iter (α := α) β} :
+    it.toListRev = match it.step with
+      | .yield it' out _ => it'.toListRev ++ [out]
+      | .skip it' _ => it'.toListRev
+      | .done _ => [] := by
+  rw [Iter.toListRev_eq_toListRev_toIterM, IterM.toListRev_eq_match_step, Iter.step, Id.run_bind]
+  generalize it.toIterM.step.run = step
+  cases step using PlausibleIterStep.casesOn <;> simp
+
+theorem Iter.getElem?_toList_eq_atIdxSlow? {α β}
+    [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    {it : Iter (α := α) β} {k : Nat} :
+    it.toList[k]? = it.atIdxSlow? k := by
+  induction it using Iter.inductSteps generalizing k with | step it ihy ihs =>
+  rw [toList_eq_match_step, atIdxSlow?]
+  obtain ⟨step, h⟩ := it.step
+  cases step
+  · cases k <;> simp [ihy h]
+  · simp [ihs h]
+  · simp
+
+theorem Iter.toList_eq_of_atIdxSlow?_eq {α₁ α₂ β}
+    [Iterator α₁ Id β] [Finite α₁ Id] [IteratorCollect α₁ Id Id] [LawfulIteratorCollect α₁ Id Id]
+    [Iterator α₂ Id β] [Finite α₂ Id] [IteratorCollect α₂ Id Id] [LawfulIteratorCollect α₂ Id Id]
+    {it₁ : Iter (α := α₁) β} {it₂ : Iter (α := α₂) β}
+    (h : ∀ k, it₁.atIdxSlow? k = it₂.atIdxSlow? k) :
+    it₁.toList = it₂.toList := by
+  ext; simp [getElem?_toList_eq_atIdxSlow?, h]
+
+end Std.Iterators

src/Init/Data/Iterators/Lemmas/Consumers/Loop.lean

@@ -0,0 +1,285 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Lemmas.Consumers.Collect
+import all Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop
+import all Init.Data.Iterators.Consumers.Loop
+
+namespace Std.Iterators
+
+theorem Iter.forIn'_eq {α β : Type w} [Iterator α Id β] [Finite α Id]
+    {m : Type w → Type w''} [Monad m] [IteratorLoop α Id m] [hl : LawfulIteratorLoop α Id m]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : (b : β) → it.IsPlausibleIndirectOutput b → γ → m (ForInStep γ)} :
+    letI : ForIn' m (Iter (α := α) β) β _ := Iter.instForIn'
+    ForIn'.forIn' it init f =
+      IterM.DefaultConsumers.forIn' (fun _ c => pure c.run) γ (fun _ _ _ => True)
+        IteratorLoop.wellFounded_of_finite it.toIterM init
+          (fun out h acc => (⟨·, .intro⟩) <$>
+            f out (Iter.isPlausibleIndirectOutput_iff_isPlausibleIndirectOutput_toIterM.mpr h) acc) := by
+  cases hl.lawful; rfl
+
+theorem Iter.forIn_eq {α β : Type w} [Iterator α Id β] [Finite α Id]
+    {m : Type w → Type w''} [Monad m] [IteratorLoop α Id m] [hl : LawfulIteratorLoop α Id m]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : (b : β) → γ → m (ForInStep γ)} :
+    ForIn.forIn it init f =
+      IterM.DefaultConsumers.forIn' (fun _ c => pure c.run) γ (fun _ _ _ => True)
+        IteratorLoop.wellFounded_of_finite it.toIterM init
+          (fun out _ acc => (⟨·, .intro⟩) <$>
+            f out acc) := by
+  cases hl.lawful; rfl
+
+theorem Iter.forIn'_eq_forIn'_toIterM {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : (out : β) → _ → γ → m (ForInStep γ)} :
+    letI : ForIn' m (Iter (α := α) β) β _ := Iter.instForIn'
+    ForIn'.forIn' it init f =
+      letI : MonadLift Id m := ⟨Std.Internal.idToMonad (α := _)⟩
+      letI : ForIn' m (IterM (α := α) Id β) β _ := IterM.instForIn'
+      ForIn'.forIn' it.toIterM init
+        (fun out h acc => f out (isPlausibleIndirectOutput_iff_isPlausibleIndirectOutput_toIterM.mpr h) acc) := by
+  rfl
+
+theorem Iter.forIn_eq_forIn_toIterM {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : β → γ → m (ForInStep γ)} :
+    ForIn.forIn it init f =
+      letI : MonadLift Id m := ⟨Std.Internal.idToMonad (α := _)⟩
+      ForIn.forIn it.toIterM init f := by
+  rfl
+
+theorem Iter.forIn'_eq_match_step {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : (out : β) → _ → γ → m (ForInStep γ)} :
+    letI : ForIn' m (Iter (α := α) β) β _ := Iter.instForIn'
+    ForIn'.forIn' it init f = (do
+      match it.step with
+      | .yield it' out h =>
+        match ← f out (.direct ⟨_, h⟩) init with
+        | .yield c =>
+          ForIn'.forIn' it' c
+            fun out h'' acc => f out (.indirect ⟨_, rfl, h⟩ h'') acc
+        | .done c => return c
+      | .skip it' h =>
+          ForIn'.forIn' it' init
+            fun out h' acc => f out (.indirect ⟨_, rfl, h⟩ h') acc
+      | .done _ => return init) := by
+  rw [Iter.forIn'_eq_forIn'_toIterM, @IterM.forIn'_eq_match_step, Iter.step]
+  simp only [liftM, monadLift, pure_bind]
+  generalize it.toIterM.step = step
+  cases step using PlausibleIterStep.casesOn
+  · apply bind_congr
+    intro forInStep
+    rfl
+  · rfl
+  · rfl
+
+theorem Iter.forIn_eq_match_step {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : β → γ → m (ForInStep γ)} :
+    ForIn.forIn it init f = (do
+      match it.step with
+      | .yield it' out _ =>
+        match ← f out init with
+        | .yield c => ForIn.forIn it' c f
+        | .done c => return c
+      | .skip it' _ => ForIn.forIn it' init f
+      | .done _ => return init) := by
+  rw [Iter.forIn_eq_forIn_toIterM, @IterM.forIn_eq_match_step, Iter.step]
+  simp only [liftM, monadLift, pure_bind]
+  generalize it.toIterM.step = step
+  cases step using PlausibleIterStep.casesOn
+  · apply bind_congr
+    intro forInStep
+    rfl
+  · rfl
+  · rfl
+
+private theorem Iter.forIn'_toList.aux {ρ : Type u} {α : Type v} {γ : Type w} {m : Type w → Type w'}
+    [Monad m] {_ : Membership α ρ} [ForIn' m ρ α inferInstance]
+    {r s : ρ} {init : γ} {f : (a : α) → _ → γ → m (ForInStep γ)} (h : r = s) :
+    forIn' r init f = forIn' s init (fun a h' acc => f a (h ▸ h') acc) := by
+  cases h; rfl
+
+theorem Iter.forIn'_toList {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    [LawfulPureIterator α]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : (out : β) → _ → γ → m (ForInStep γ)} :
+    letI : ForIn' m (Iter (α := α) β) β _ := Iter.instForIn'
+    ForIn'.forIn' it.toList init f = ForIn'.forIn' it init (fun out h acc => f out (LawfulPureIterator.mem_toList_iff_isPlausibleIndirectOutput.mpr h) acc) := by
+  induction it using Iter.inductSteps generalizing init with case step it ihy ihs =>
+  have := it.toList_eq_match_step
+  generalize hs : it.step = step at this
+  rw [forIn'_toList.aux this]
+  rw [forIn'_eq_match_step]
+  rw [List.forIn'_eq_foldlM] at *
+  simp only [map_eq_pure_bind, List.foldlM_map, hs]
+  cases step using PlausibleIterStep.casesOn
+  · rename_i it' out h
+    simp only [List.attach_cons, List.foldlM_cons, bind_pure_comp, map_bind]
+    apply bind_congr
+    intro forInStep
+    cases forInStep
+    · induction it'.toList.attach <;> simp [*]
+    · simp only [List.foldlM_map]
+      simp only [List.forIn'_eq_foldlM] at ihy
+      simp only at this
+      simp only [ihy h (f := fun out h acc => f out (by rw [this]; exact List.mem_cons_of_mem _ h) acc)]
+  · rename_i it' h
+    simp only [bind_pure_comp]
+    simp only [List.forIn'_eq_foldlM] at ihs
+    simp only at this
+    simp only [ihs h (f := fun out h acc => f out (this ▸ h) acc)]
+  · simp
+
+theorem Iter.forIn'_eq_forIn'_toList {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    [LawfulPureIterator α]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : (out : β) → _ → γ → m (ForInStep γ)} :
+    letI : ForIn' m (Iter (α := α) β) β _ := Iter.instForIn'
+    ForIn'.forIn' it init f = ForIn'.forIn' it.toList init (fun out h acc => f out (LawfulPureIterator.mem_toList_iff_isPlausibleIndirectOutput.mp h) acc) := by
+  simp only [forIn'_toList]
+  congr
+
+theorem Iter.forIn_toList {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : β → γ → m (ForInStep γ)} :
+    ForIn.forIn it.toList init f = ForIn.forIn it init f := by
+  rw [List.forIn_eq_foldlM]
+  induction it using Iter.inductSteps generalizing init with case step it ihy ihs =>
+  rw [forIn_eq_match_step, Iter.toList_eq_match_step]
+  simp only [map_eq_pure_bind]
+  generalize it.step = step
+  cases step using PlausibleIterStep.casesOn
+  · rename_i it' out h
+    simp only [List.foldlM_cons, bind_pure_comp, map_bind]
+    apply bind_congr
+    intro forInStep
+    cases forInStep
+    · induction it'.toList <;> simp [*]
+    · simp only [ForIn.forIn, forIn', List.forIn'] at ihy
+      simp [ihy h, forIn_eq_forIn_toIterM]
+  · rename_i it' h
+    simp only [bind_pure_comp]
+    rw [ihs h]
+  · simp
+
+theorem Iter.foldM_eq_forIn {α β γ : Type w} [Iterator α Id β] [Finite α Id] {m : Type w → Type w'}
+    [Monad m] [IteratorLoop α Id m] {f : γ → β → m γ}
+    {init : γ} {it : Iter (α := α) β} :
+    it.foldM (init := init) f = ForIn.forIn it init (fun x acc => ForInStep.yield <$> f acc x) :=
+  (rfl)
+
+theorem Iter.foldM_eq_foldM_toIterM {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ} {f : γ → β → m γ} :
+    it.foldM (init := init) f = letI : MonadLift Id m := ⟨pure⟩; it.toIterM.foldM (init := init) f :=
+  (rfl)
+
+theorem Iter.forIn_yield_eq_foldM {α β γ δ : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m] [IteratorLoop α Id m]
+    [LawfulIteratorLoop α Id m] {f : β → γ → m δ} {g : β → γ → δ → γ} {init : γ}
+    {it : Iter (α := α) β} :
+    ForIn.forIn it init (fun c b => (fun d => .yield (g c b d)) <$> f c b) =
+      it.foldM (fun b c => g c b <$> f c b) init := by
+  simp [Iter.foldM_eq_forIn]
+
+theorem Iter.foldM_eq_match_step {α β γ : Type w} [Iterator α Id β] [Finite α Id]
+    {m : Type w → Type w'} [Monad m] [LawfulMonad m] [IteratorLoop α Id m]
+    [LawfulIteratorLoop α Id m] {f : γ → β → m γ} {init : γ} {it : Iter (α := α) β} :
+    it.foldM (init := init) f = (do
+      match it.step with
+      | .yield it' out _ => it'.foldM (init := ← f init out) f
+      | .skip it' _ => it'.foldM (init := init) f
+      | .done _ => return init) := by
+  rw [Iter.foldM_eq_forIn, Iter.forIn_eq_match_step]
+  generalize it.step = step
+  cases step using PlausibleIterStep.casesOn <;> simp [foldM_eq_forIn]
+
+theorem Iter.foldlM_toList {α β γ : Type w} [Iterator α Id β] [Finite α Id] {m : Type w → Type w'}
+    [Monad m] [LawfulMonad m] [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    {f : γ → β → m γ}
+    {init : γ} {it : Iter (α := α) β} :
+    it.toList.foldlM (init := init) f = it.foldM (init := init) f := by
+  rw [Iter.foldM_eq_forIn, ← Iter.forIn_toList]
+  simp only [List.forIn_yield_eq_foldlM, id_map']
+
+theorem IterM.forIn_eq_foldM {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : β → γ → m (ForInStep γ)} :
+    forIn it init f = ForInStep.value <$>
+      it.foldM (fun c b => match c with
+        | .yield c => f b c
+        | .done c => pure (.done c)) (ForInStep.yield init) := by
+  simp only [← Iter.forIn_toList, List.forIn_eq_foldlM, ← Iter.foldlM_toList]; rfl
+
+theorem Iter.fold_eq_forIn {α β γ : Type w} [Iterator α Id β]
+    [Finite α Id] [IteratorLoop α Id Id] {f : γ → β → γ} {init : γ} {it : Iter (α := α) β} :
+    it.fold (init := init) f =
+      (ForIn.forIn (m := Id) it init (fun x acc => pure (ForInStep.yield (f acc x)))).run := by
+  rfl
+
+theorem Iter.fold_eq_foldM {α β γ : Type w} [Iterator α Id β]
+    [Finite α Id] [IteratorLoop α Id Id] {f : γ → β → γ} {init : γ}
+    {it : Iter (α := α) β} :
+    it.fold (init := init) f = (it.foldM (m := Id) (init := init) (pure <| f · ·)).run := by
+  simp [foldM_eq_forIn, fold_eq_forIn]
+
+@[simp]
+theorem Iter.forIn_pure_yield_eq_fold {α β γ : Type w} [Iterator α Id β]
+    [Finite α Id] [IteratorLoop α Id Id]
+    [LawfulIteratorLoop α Id Id] {f : β → γ → γ} {init : γ}
+    {it : Iter (α := α) β} :
+    ForIn.forIn (m := Id) it init (fun c b => pure (.yield (f c b))) =
+      pure (it.fold (fun b c => f c b) init) := by
+  simp only [fold_eq_forIn]
+  rfl
+
+theorem Iter.fold_eq_match_step {α β γ : Type w} [Iterator α Id β] [Finite α Id]
+    [IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
+    {f : γ → β → γ} {init : γ} {it : Iter (α := α) β} :
+    it.fold (init := init) f = (match it.step with
+      | .yield it' out _ => it'.fold (init := f init out) f
+      | .skip it' _ => it'.fold (init := init) f
+      | .done _ => init) := by
+  rw [fold_eq_foldM, foldM_eq_match_step]
+  simp only [fold_eq_foldM]
+  generalize it.step = step
+  cases step using PlausibleIterStep.casesOn <;> simp
+
+theorem Iter.foldl_toList {α β γ : Type w} [Iterator α Id β] [Finite α Id]
+    [IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
+    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    {f : γ → β → γ} {init : γ} {it : Iter (α := α) β} :
+    it.toList.foldl (init := init) f = it.fold (init := init) f := by
+  rw [fold_eq_foldM, List.foldl_eq_foldlM, ← Iter.foldlM_toList]
+
+end Std.Iterators

src/Init/Data/Iterators/Lemmas/Consumers/Monadic.lean

@@ -3,7 +3,8 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Consumers.Monadic.Collect
-import Std.Data.Iterators.Consumers.Monadic.Loop
-import Std.Data.Iterators.Consumers.Monadic.Partial
+import Init.Data.Iterators.Lemmas.Consumers.Monadic.Collect
+import Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop

src/Init/Data/Iterators/Lemmas/Consumers/Monadic/Collect.lean

@@ -0,0 +1,157 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Array.Lemmas
+import Init.Data.Iterators.Lemmas.Monadic.Basic
+import all Init.Data.Iterators.Consumers.Monadic.Collect
+
+namespace Std.Iterators
+
+variable {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''}
+  {lift : ⦃δ : Type w⦄ → m δ → n δ} {f : β → n γ} {it : IterM (α := α) m β}
+
+theorem IterM.DefaultConsumers.toArrayMapped.go.aux₁ [Monad n] [LawfulMonad n] [Iterator α m β]
+    [Finite α m] {b : γ} {bs : Array γ} :
+    IterM.DefaultConsumers.toArrayMapped.go lift f it (#[b] ++ bs) (m := m) =
+      (#[b] ++ ·) <$> IterM.DefaultConsumers.toArrayMapped.go lift f it bs (m := m) := by
+  induction it, bs using IterM.DefaultConsumers.toArrayMapped.go.induct
+  next it bs ih₁ ih₂ =>
+  rw [go, map_eq_pure_bind, go, bind_assoc]
+  apply bind_congr
+  intro step
+  split
+  · simp [ih₁ _ _ ‹_›]
+  · simp [ih₂ _ ‹_›]
+  · simp
+
+theorem IterM.DefaultConsumers.toArrayMapped.go.aux₂ [Monad n] [LawfulMonad n] [Iterator α m β]
+    [Finite α m] {acc : Array γ} :
+    IterM.DefaultConsumers.toArrayMapped.go lift f it acc (m := m) =
+      (acc ++ ·) <$> IterM.DefaultConsumers.toArrayMapped lift f it (m := m) := by
+  rw [← Array.toArray_toList (xs := acc)]
+  generalize acc.toList = acc
+  induction acc with
+  | nil => simp [toArrayMapped]
+  | cons x xs ih =>
+    rw [List.toArray_cons, IterM.DefaultConsumers.toArrayMapped.go.aux₁, ih]
+    simp only [Functor.map_map, Array.append_assoc]
+
+theorem IterM.DefaultConsumers.toArrayMapped_eq_match_step [Monad n] [LawfulMonad n]
+    [Iterator α m β] [Finite α m] :
+    IterM.DefaultConsumers.toArrayMapped lift f it (m := m) = letI : MonadLift m n := ⟨lift (δ := _)⟩; (do
+      match ← it.step with
+      | .yield it' out _ =>
+        return #[← f out] ++ (← IterM.DefaultConsumers.toArrayMapped lift f it' (m := m))
+      | .skip it' _ => IterM.DefaultConsumers.toArrayMapped lift f it' (m := m)
+      | .done _ => return #[]) := by
+  rw [IterM.DefaultConsumers.toArrayMapped, IterM.DefaultConsumers.toArrayMapped.go]
+  apply bind_congr
+  intro step
+  split <;> simp [IterM.DefaultConsumers.toArrayMapped.go.aux₂]
+
+theorem IterM.toArray_eq_match_step [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m] :
+    it.toArray = (do
+      match ← it.step with
+      | .yield it' out _ => return #[out] ++ (← it'.toArray)
+      | .skip it' _ => it'.toArray
+      | .done _ => return #[]) := by
+  simp only [IterM.toArray, LawfulIteratorCollect.toArrayMapped_eq]
+  rw [IterM.DefaultConsumers.toArrayMapped_eq_match_step]
+  simp [bind_pure_comp, pure_bind, toArray]
+
+theorem IterM.toList_toArray [Monad m] [Iterator α m β] [Finite α m] [IteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    Array.toList <$> it.toArray = it.toList := by
+  simp [IterM.toList]
+
+theorem IterM.toArray_toList [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    [IteratorCollect α m m] {it : IterM (α := α) m β} :
+    List.toArray <$> it.toList = it.toArray := by
+  simp [IterM.toList]
+
+theorem IterM.toList_eq_match_step [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m] {it : IterM (α := α) m β} :
+    it.toList = (do
+      match ← it.step with
+      | .yield it' out _ => return out :: (← it'.toList)
+      | .skip it' _ => it'.toList
+      | .done _ => return []) := by
+  simp [← IterM.toList_toArray]
+  rw [IterM.toArray_eq_match_step, map_eq_pure_bind, bind_assoc]
+  apply bind_congr
+  intro step
+  split <;> simp
+
+theorem IterM.toListRev.go.aux₁ [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    {it : IterM (α := α) m β} {b : β} {bs : List β} :
+    IterM.toListRev.go it (bs ++ [b]) = (· ++ [b]) <$> IterM.toListRev.go it bs:= by
+  induction it, bs using IterM.toListRev.go.induct
+  next it bs ih₁ ih₂ =>
+  rw [go, go, map_eq_pure_bind, bind_assoc]
+  apply bind_congr
+  intro step
+  simp only [List.cons_append] at ih₁
+  split <;> simp [*]
+
+theorem IterM.toListRev.go.aux₂ [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    {it : IterM (α := α) m β} {acc : List β} :
+    IterM.toListRev.go it acc = (· ++ acc) <$> it.toListRev := by
+  rw [← List.reverse_reverse (as := acc)]
+  generalize acc.reverse = acc
+  induction acc with
+  | nil => simp [toListRev]
+  | cons x xs ih => simp [IterM.toListRev.go.aux₁, ih]
+
+theorem IterM.toListRev_eq_match_step [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    {it : IterM (α := α) m β} :
+    it.toListRev = (do
+      match ← it.step with
+      | .yield it' out _ => return (← it'.toListRev) ++ [out]
+      | .skip it' _ => it'.toListRev
+      | .done _ => return []) := by
+  simp [IterM.toListRev]
+  rw [toListRev.go]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn <;> simp [IterM.toListRev.go.aux₂]
+
+theorem IterM.reverse_toListRev [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    List.reverse <$> it.toListRev = it.toList := by
+  apply Eq.symm
+  induction it using IterM.inductSteps
+  rename_i it ihy ihs
+  rw [toListRev_eq_match_step, toList_eq_match_step, map_eq_pure_bind, bind_assoc]
+  apply bind_congr
+  intro step
+  split <;> simp (discharger := assumption) [ihy, ihs]
+
+theorem IterM.toListRev_eq [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    it.toListRev = List.reverse <$> it.toList := by
+  rw [← IterM.reverse_toListRev]
+  simp
+
+theorem LawfulIteratorCollect.toArray_eq {α β : Type w} {m : Type w → Type w'}
+    [Monad m] [Iterator α m β] [Finite α m] [IteratorCollect α m m]
+    [hl : LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    it.toArray = (letI : IteratorCollect α m m := .defaultImplementation; it.toArray) := by
+  simp only [IterM.toArray, toArrayMapped_eq]
+
+theorem LawfulIteratorCollect.toList_eq {α β : Type w} {m : Type w → Type w'}
+    [Monad m] [Iterator α m β] [Finite α m] [IteratorCollect α m m]
+    [hl : LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    it.toList = (letI : IteratorCollect α m m := .defaultImplementation; it.toList) := by
+  simp [IterM.toList, toArray_eq]
+
+end Std.Iterators

src/Init/Data/Iterators/Lemmas/Consumers/Monadic/Loop.lean

@@ -0,0 +1,277 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Lemmas.Consumers.Monadic.Collect
+import all Init.Data.Iterators.Consumers.Monadic.Loop
+
+namespace Std.Iterators
+
+theorem IterM.DefaultConsumers.forIn'_eq_match_step {α β : Type w} {m : Type w → Type w'}
+    [Iterator α m β]
+    {n : Type w → Type w''} [Monad n]
+    {lift : ∀ γ, m γ → n γ} {γ : Type w}
+    {plausible_forInStep : β → γ → ForInStep γ → Prop}
+    {wf : IteratorLoop.WellFounded α m plausible_forInStep}
+    {it : IterM (α := α) m β} {init : γ}
+    {f : (b : β) → it.IsPlausibleIndirectOutput b → (c : γ) → n (Subtype (plausible_forInStep b c))} :
+    IterM.DefaultConsumers.forIn' lift γ plausible_forInStep wf it init f = (do
+      match ← lift _ it.step with
+      | .yield it' out h =>
+        match ← f out (.direct ⟨_, h⟩) init with
+        | ⟨.yield c, _⟩ =>
+          IterM.DefaultConsumers.forIn' lift _ plausible_forInStep wf it' c
+            fun out h'' acc => f out (.indirect ⟨_, rfl, h⟩ h'') acc
+        | ⟨.done c, _⟩ => return c
+      | .skip it' h =>
+        IterM.DefaultConsumers.forIn' lift _ plausible_forInStep wf it' init
+          fun out h' acc => f out (.indirect ⟨_, rfl, h⟩ h') acc
+      | .done _ => return init) := by
+  rw [forIn']
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn <;> rfl
+
+theorem IterM.forIn'_eq {α β : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    {n : Type w → Type w''} [Monad n] [IteratorLoop α m n] [hl : LawfulIteratorLoop α m n]
+    [MonadLiftT m n] {γ : Type w} {it : IterM (α := α) m β} {init : γ}
+    {f : (b : β) → it.IsPlausibleIndirectOutput b → γ → n (ForInStep γ)} :
+    letI : ForIn' n (IterM (α := α) m β) β _ := IterM.instForIn'
+    ForIn'.forIn' it init f = IterM.DefaultConsumers.forIn' (fun _ => monadLift) γ (fun _ _ _ => True)
+        IteratorLoop.wellFounded_of_finite it init ((⟨·, .intro⟩) <$> f · · ·) := by
+  cases hl.lawful; rfl
+
+theorem IterM.forIn_eq {α β : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    {n : Type w → Type w''} [Monad n] [IteratorLoop α m n] [hl : LawfulIteratorLoop α m n]
+    [MonadLiftT m n] {γ : Type w} {it : IterM (α := α) m β} {init : γ}
+    {f : β → γ → n (ForInStep γ)} :
+    ForIn.forIn it init f = IterM.DefaultConsumers.forIn' (fun _ => monadLift) γ (fun _ _ _ => True)
+        IteratorLoop.wellFounded_of_finite it init (fun out _ acc => (⟨·, .intro⟩) <$> f out acc) := by
+  cases hl.lawful; rfl
+
+theorem IterM.forIn'_eq_match_step {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] {n : Type w → Type w''} [Monad n] [LawfulMonad n]
+    [IteratorLoop α m n] [LawfulIteratorLoop α m n]
+    [MonadLiftT m n] {γ : Type w} {it : IterM (α := α) m β} {init : γ}
+    {f : (out : β) → _ → γ → n (ForInStep γ)} :
+    letI : ForIn' n (IterM (α := α) m β) β _ := IterM.instForIn'
+    ForIn'.forIn' it init f = (do
+      match ← it.step with
+      | .yield it' out h =>
+        match ← f out (.direct ⟨_, h⟩) init with
+        | .yield c =>
+          ForIn'.forIn' it' c
+            fun out h'' acc => f out (.indirect ⟨_, rfl, h⟩ h'') acc
+        | .done c => return c
+      | .skip it' h =>
+        ForIn'.forIn' it' init
+          fun out h' acc => f out (.indirect ⟨_, rfl, h⟩ h') acc
+      | .done _ => return init) := by
+  rw [IterM.forIn'_eq, DefaultConsumers.forIn'_eq_match_step]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn
+  · simp only [map_eq_pure_bind, bind_assoc]
+    apply bind_congr
+    intro forInStep
+    cases forInStep <;> simp [IterM.forIn'_eq]
+  · simp [IterM.forIn'_eq]
+  · simp
+
+theorem IterM.forIn_eq_match_step {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] {n : Type w → Type w''} [Monad n] [LawfulMonad n]
+    [IteratorLoop α m n] [LawfulIteratorLoop α m n]
+    [MonadLiftT m n] {γ : Type w} {it : IterM (α := α) m β} {init : γ}
+    {f : β → γ → n (ForInStep γ)} :
+    ForIn.forIn it init f = (do
+      match ← it.step with
+      | .yield it' out _ =>
+        match ← f out init with
+        | .yield c => ForIn.forIn it' c f
+        | .done c => return c
+      | .skip it' _ => ForIn.forIn it' init f
+      | .done _ => return init) := by
+  rw [IterM.forIn_eq, DefaultConsumers.forIn'_eq_match_step]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn
+  · simp only [map_eq_pure_bind, bind_assoc]
+    apply bind_congr
+    intro forInStep
+    cases forInStep <;> simp [IterM.forIn_eq]
+  · simp [IterM.forIn_eq]
+  · simp
+
+theorem IterM.forM_eq_forIn {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] {n : Type w → Type w''} [Monad n] [LawfulMonad n]
+    [IteratorLoop α m n] [LawfulIteratorLoop α m n]
+    [MonadLiftT m n] {it : IterM (α := α) m β}
+    {f : β → n PUnit} :
+    ForM.forM it f = ForIn.forIn it PUnit.unit (fun out _ => do f out; return .yield .unit) :=
+  rfl
+
+theorem IterM.forM_eq_match_step {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] {n : Type w → Type w''} [Monad n] [LawfulMonad n]
+    [IteratorLoop α m n] [LawfulIteratorLoop α m n]
+    [MonadLiftT m n] {it : IterM (α := α) m β}
+    {f : β → n PUnit} :
+    ForM.forM it f = (do
+      match ← it.step with
+      | .yield it' out _ =>
+        f out
+        ForM.forM it' f
+      | .skip it' _ => ForM.forM it' f
+      | .done _ => return) := by
+  rw [forM_eq_forIn, forIn_eq_match_step]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn <;> simp [forM_eq_forIn]
+
+theorem IterM.foldM_eq_forIn {α β γ : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    {n : Type w → Type w''} [Monad n] [IteratorLoop α m n] [MonadLiftT m n] {f : γ → β → n γ}
+    {init : γ} {it : IterM (α := α) m β} :
+    it.foldM (init := init) f = ForIn.forIn it init (fun x acc => ForInStep.yield <$> f acc x) :=
+  (rfl)
+
+theorem IterM.forIn_yield_eq_foldM {α β γ δ : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] {n : Type w → Type w''} [Monad n] [LawfulMonad n] [IteratorLoop α m n]
+    [LawfulIteratorLoop α m n] [MonadLiftT m n] {f : β → γ → n δ} {g : β → γ → δ → γ} {init : γ}
+    {it : IterM (α := α) m β} :
+    ForIn.forIn it init (fun c b => (fun d => .yield (g c b d)) <$> f c b) =
+      it.foldM (fun b c => g c b <$> f c b) init := by
+  simp [IterM.foldM_eq_forIn]
+
+theorem IterM.foldM_eq_match_step {α β γ : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    {n : Type w → Type w''} [Monad n] [LawfulMonad n] [IteratorLoop α m n] [LawfulIteratorLoop α m n]
+    [MonadLiftT m n] {f : γ → β → n γ} {init : γ} {it : IterM (α := α) m β} :
+    it.foldM (init := init) f = (do
+      match ← it.step with
+      | .yield it' out _ => it'.foldM (init := ← f init out) f
+      | .skip it' _ => it'.foldM (init := init) f
+      | .done _ => return init) := by
+  rw [IterM.foldM_eq_forIn, IterM.forIn_eq_match_step]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn <;> simp [foldM_eq_forIn]
+
+theorem IterM.fold_eq_forIn {α β γ : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] [Monad m]
+    [IteratorLoop α m m] {f : γ → β → γ} {init : γ} {it : IterM (α := α) m β} :
+    it.fold (init := init) f =
+      ForIn.forIn (m := m) it init (fun x acc => pure (ForInStep.yield (f acc x))) := by
+  rfl
+
+theorem IterM.fold_eq_foldM {α β γ : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] [Monad m] [LawfulMonad m] [IteratorLoop α m m] {f : γ → β → γ} {init : γ}
+    {it : IterM (α := α) m β} :
+    it.fold (init := init) f = it.foldM (init := init) (pure <| f · ·) := by
+  simp [foldM_eq_forIn, fold_eq_forIn]
+
+@[simp]
+theorem IterM.forIn_pure_yield_eq_fold {α β γ : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] [Monad m] [LawfulMonad m] [IteratorLoop α m m]
+    [LawfulIteratorLoop α m m] {f : β → γ → γ} {init : γ}
+    {it : IterM (α := α) m β} :
+    ForIn.forIn it init (fun c b => pure (.yield (f c b))) =
+      it.fold (fun b c => f c b) init := by
+  simp [IterM.fold_eq_forIn]
+
+theorem IterM.fold_eq_match_step {α β γ : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    [Monad m] [LawfulMonad m] [IteratorLoop α m m] [LawfulIteratorLoop α m m]
+    {f : γ → β → γ} {init : γ} {it : IterM (α := α) m β} :
+    it.fold (init := init) f = (do
+      match ← it.step with
+      | .yield it' out _ => it'.fold (init := f init out) f
+      | .skip it' _ => it'.fold (init := init) f
+      | .done _ => return init) := by
+  rw [fold_eq_foldM, foldM_eq_match_step]
+  simp only [fold_eq_foldM]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn <;> simp
+
+theorem IterM.toList_eq_fold {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] [Monad m] [LawfulMonad m] [IteratorLoop α m m] [LawfulIteratorLoop α m m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    it.toList = it.fold (init := []) (fun l out => l ++ [out]) := by
+  suffices h : ∀ l' : List β, (l' ++ ·) <$> it.toList =
+      it.fold (init := l') (fun l out => l ++ [out]) by
+    specialize h []
+    simpa using h
+  induction it using IterM.inductSteps with | step it ihy ihs =>
+  intro l'
+  rw [IterM.toList_eq_match_step, IterM.fold_eq_match_step]
+  simp only [map_eq_pure_bind, bind_assoc]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn
+  · rename_i it' out h
+    specialize ihy h (l' ++ [out])
+    simpa using ihy
+  · rename_i it' h
+    simp [ihs h]
+  · simp
+
+theorem IterM.drain_eq_fold {α β : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    [Monad m] [IteratorLoop α m m] {it : IterM (α := α) m β} :
+    it.drain = it.fold (init := PUnit.unit) (fun _ _ => .unit) :=
+  (rfl)
+
+theorem IterM.drain_eq_foldM {α β : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    [Monad m] [LawfulMonad m] [IteratorLoop α m m] {it : IterM (α := α) m β} :
+    it.drain = it.foldM (init := PUnit.unit) (fun _ _ => pure .unit) := by
+  simp [IterM.drain_eq_fold, IterM.fold_eq_foldM]
+
+theorem IterM.drain_eq_forIn {α β : Type w} {m : Type w → Type w'}  [Iterator α m β] [Finite α m]
+    [Monad m] [IteratorLoop α m m] {it : IterM (α := α) m β} :
+    it.drain = ForIn.forIn (m := m) it PUnit.unit (fun _ _ => pure (ForInStep.yield .unit)) := by
+  simp [IterM.drain_eq_fold, IterM.fold_eq_forIn]
+
+theorem IterM.drain_eq_match_step {α β : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    [Monad m] [LawfulMonad m] [IteratorLoop α m m] [LawfulIteratorLoop α m m]
+    {it : IterM (α := α) m β} :
+    it.drain = (do
+      match ← it.step with
+      | .yield it' _ _ => it'.drain
+      | .skip it' _ => it'.drain
+      | .done _ => return .unit) := by
+  rw [IterM.drain_eq_fold, IterM.fold_eq_match_step]
+  simp [IterM.drain_eq_fold]
+
+theorem IterM.drain_eq_map_toList {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] [Monad m] [LawfulMonad m] [IteratorLoop α m m] [LawfulIteratorLoop α m m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    it.drain = (fun _ => .unit) <$> it.toList := by
+  induction it using IterM.inductSteps with | step it ihy ihs =>
+  rw [IterM.drain_eq_match_step, IterM.toList_eq_match_step]
+  simp only [map_eq_pure_bind, bind_assoc]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn
+  · rename_i it' out h
+    simp [ihy h]
+  · rename_i it' h
+    simp [ihs h]
+  · simp
+
+theorem IterM.drain_eq_map_toListRev {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] [Monad m] [LawfulMonad m] [IteratorLoop α m m] [LawfulIteratorLoop α m m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    it.drain = (fun _ => .unit) <$> it.toListRev := by
+  simp [IterM.drain_eq_map_toList, IterM.toListRev_eq]
+
+theorem IterM.drain_eq_map_toArray {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] [Monad m] [LawfulMonad m] [IteratorLoop α m m] [LawfulIteratorLoop α m m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    it.drain = (fun _ => .unit) <$> it.toList := by
+  simp [IterM.drain_eq_map_toList]
+
+end Std.Iterators

src/Init/Data/Iterators/Lemmas/Monadic/Basic.lean

@@ -3,8 +3,10 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Basic
+import Init.Data.Iterators.Basic
 
 namespace Std.Iterators
 

src/Init/Data/Iterators/PostconditionMonad.lean

@@ -0,0 +1,234 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Control.Lawful.Basic
+import Init.Data.Subtype
+import Init.PropLemmas
+
+namespace Std.Iterators
+
+/--
+`PostconditionT m α` represents an operation in the monad `m` together with a
+intrinsic proof that some postcondition holds for the `α` valued monadic result.
+It consists of a predicate `P` about `α` and an element of `m ({ a // P a })` and is a helpful tool
+for intrinsic verification, notably termination proofs, in the context of iterators.
+
+`PostconditionT m` is a monad if `m` is. However, note that `PostconditionT m α` is a structure,
+so that the compiler will generate inefficient code from recursive functions returning
+`PostconditionT m α`. Optimizations for `ReaderT`, `StateT` etc. aren't applicable for structures.
+
+Moreover, `PostconditionT m α` is not a well-behaved monad transformer because `PostconditionT.lift`
+neither commutes with `pure` nor with `bind`.
+-/
+@[unbox]
+structure PostconditionT (m : Type w → Type w') (α : Type w) where
+  /--
+  A predicate that holds for the return value(s) of the `m`-monadic operation.
+  -/
+  Property : α → Prop
+
+  /--
+  The actual monadic operation. Its return value is bundled together with a proof that
+  it satisfies `Property`.
+  -/
+  operation : m (Subtype Property)
+
+/--
+Lifts an operation from `m` to `PostconditionT m` without asserting any nontrivial postcondition.
+
+Caution: `lift` is not a lawful lift function.
+For example, `pure a : PostconditionT m α` is not the same as
+`PostconditionT.lift (pure a : m α)`.
+-/
+@[always_inline, inline]
+def PostconditionT.lift {α : Type w} {m : Type w → Type w'} [Functor m] (x : m α) :
+    PostconditionT m α :=
+  ⟨fun _ => True, (⟨·, .intro⟩) <$> x⟩
+
+@[always_inline, inline]
+protected def PostconditionT.pure {m : Type w → Type w'} [Pure m] {α : Type w}
+    (a : α) : PostconditionT m α :=
+  ⟨fun y => a = y, pure <| ⟨a, rfl⟩⟩
+
+/--
+Lifts a monadic value from `m { a : α // P a }` to a value `PostconditionT m α`.
+-/
+@[always_inline, inline]
+def PostconditionT.liftWithProperty {α : Type w} {m : Type w → Type w'} {P : α → Prop}
+    (x : m { α // P α }) : PostconditionT m α :=
+  ⟨P, x⟩
+
+/--
+Given a function `f : α → β`, returns a a function `PostconditionT m α → PostconditionT m β`,
+turning `PostconditionT m` into a functor.
+
+The postcondition of the `x.map f` states that the return value is the image under `f` of some
+`a : α` satisfying the `x.Property`.
+-/
+@[always_inline, inline]
+protected def PostconditionT.map {m : Type w → Type w'} [Functor m] {α : Type w} {β : Type w}
+    (f : α → β) (x : PostconditionT m α) : PostconditionT m β :=
+  ⟨fun b => ∃ a : Subtype x.Property, f a.1 = b,
+    (fun a => ⟨f a.val, _, rfl⟩) <$> x.operation⟩
+
+/--
+Given a function `α → PostconditionT m β`, returns a a function
+`PostconditionT m α → PostconditionT m β`, turning `PostconditionT m` into a monad.
+-/
+@[always_inline, inline]
+protected def PostconditionT.bind {m : Type w → Type w'} [Monad m] {α : Type w} {β : Type w}
+    (x : PostconditionT m α) (f : α → PostconditionT m β) : PostconditionT m β :=
+  ⟨fun b => ∃ a, x.Property a ∧ (f a).Property b,
+    x.operation >>= fun a =>
+      (fun b =>
+        ⟨b.val, a.val, a.property, b.property⟩) <$> (f a).operation⟩
+
+/--
+A version of `bind` that provides a proof of the previous postcondition to the mapping function.
+-/
+@[always_inline, inline]
+protected def PostconditionT.pbind {m : Type w → Type w'} [Monad m] {α : Type w} {β : Type w}
+    (x : PostconditionT m α) (f : Subtype x.Property → PostconditionT m β) : PostconditionT m β :=
+  ⟨fun b => ∃ a, (f a).Property b,
+    x.operation >>= fun a => (fun b => ⟨b.val, a, b.property⟩) <$> (f a).operation⟩
+
+/--
+Lifts an operation from `m` to `PostConditionT m` and then applies `PostconditionT.map`.
+-/
+@[always_inline, inline]
+protected def PostconditionT.liftMap {m : Type w → Type w'} [Monad m] {α : Type w} {β : Type w}
+    (f : α → β) (x : m α) : PostconditionT m β :=
+  ⟨fun b => ∃ a, f a = b, (fun a => ⟨f a, a, rfl⟩) <$> x⟩
+
+/--
+Converts an operation from `PostConditionT m` to `m`, discarding the postcondition.
+-/
+@[always_inline, inline]
+def PostconditionT.run {m : Type w → Type w'} [Monad m] {α : Type w} (x : PostconditionT m α) :
+    m α :=
+  (fun a => a.val) <$> x.operation
+
+instance {m : Type w → Type w'} [Functor m] : Functor (PostconditionT m) where
+  map := PostconditionT.map
+
+instance {m : Type w → Type w'} [Monad m] : Monad (PostconditionT m) where
+  pure := PostconditionT.pure
+  bind := PostconditionT.bind
+
+theorem PostconditionT.pure_eq_pure {m : Type w → Type w'} [Monad m] {α} {a : α} :
+    pure a = PostconditionT.pure (m := m) a :=
+  rfl
+
+@[simp]
+theorem PostconditionT.property_pure {m : Type w → Type w'} [Monad m] {α : Type w}
+    {x : α} :
+    (pure x : PostconditionT m α).Property = (x = ·) := by
+  rfl
+
+@[simp]
+theorem PostconditionT.operation_pure {m : Type w → Type w'} [Monad m] {α : Type w}
+    {x : α} :
+    (pure x : PostconditionT m α).operation = pure ⟨x, property_pure (m := m) ▸ rfl⟩ := by
+  rfl
+
+theorem PostconditionT.ext {m : Type w → Type w'} [Monad m] [LawfulMonad m]
+    {α : Type w} {x y : PostconditionT m α}
+    (h : x.Property = y.Property) (h' : (fun p => ⟨p.1, h ▸ p.2⟩) <$> x.operation = y.operation) :
+    x = y := by
+  cases x; cases y; cases h
+  simpa using h'
+
+theorem PostconditionT.ext_iff {m : Type w → Type w'} [Monad m] [LawfulMonad m]
+    {α : Type w} {x y : PostconditionT m α} :
+    x = y ↔ ∃ h : x.Property = y.Property, (fun p => ⟨p.1, h ▸ p.2⟩) <$> x.operation = y.operation := by
+  constructor
+  · rintro rfl
+    exact ⟨rfl, by simp⟩
+  · rintro ⟨h, h'⟩
+    exact PostconditionT.ext h h'
+
+@[simp]
+protected theorem PostconditionT.map_eq_pure_bind {m : Type w → Type w'} [Monad m] [LawfulMonad m]
+    {α : Type w} {β : Type w} {f : α → β} {x : PostconditionT m α} :
+    x.map f = x.bind (pure ∘ f) := by
+  apply PostconditionT.ext <;> simp [PostconditionT.map, PostconditionT.bind]
+
+@[simp]
+protected theorem PostconditionT.pure_bind {m : Type w → Type w'} [Monad m] [LawfulMonad m]
+    {α : Type w} {β : Type w} {f : α → PostconditionT m β} {a : α} :
+    (pure a : PostconditionT m α).bind f = f a := by
+  apply PostconditionT.ext <;> simp [pure, PostconditionT.pure, PostconditionT.bind]
+
+@[simp]
+protected theorem PostconditionT.bind_pure {m : Type w → Type w'} [Monad m] [LawfulMonad m]
+    {α : Type w} {x : PostconditionT m α} :
+    x.bind pure = x := by
+  apply PostconditionT.ext <;> simp [pure, PostconditionT.pure, PostconditionT.bind]
+
+@[simp]
+protected theorem PostconditionT.bind_assoc {m : Type w → Type w'} [Monad m] [LawfulMonad m]
+    {α β γ: Type w} {x : PostconditionT m α} {f : α → PostconditionT m β} {g : β → PostconditionT m γ} :
+    (x.bind f).bind g = x.bind (fun a => (f a).bind g) := by
+  apply PostconditionT.ext
+  · simp [PostconditionT.bind]
+  · simp only [PostconditionT.bind, bind_assoc, bind_map_left, map_bind, Functor.map_map]
+    ext c
+    constructor
+    · rintro ⟨b, ⟨a, ha, hb⟩, h⟩
+      exact ⟨a, ha, b, hb, h⟩
+    · rintro ⟨a, ha, b, hb, h⟩
+      exact ⟨b, ⟨a, ha, hb⟩, h⟩
+
+@[simp]
+protected theorem PostconditionT.map_pure {m : Type w → Type w'} [Monad m] [LawfulMonad m]
+    {α : Type w} {β : Type w} {f : α → β} {a : α} :
+    (pure a : PostconditionT m α).map f = pure (f a) := by
+  apply PostconditionT.ext <;> simp [pure, PostconditionT.map, PostconditionT.pure]
+
+instance [Monad m] [LawfulMonad m] : LawfulMonad (PostconditionT m) where
+  map_const {α β} := by ext a x; simp [Functor.mapConst, Functor.map]
+  id_map {α} x := by simp [Functor.map]
+  comp_map {α β γ} g h := by intro x; simp [Functor.map]; rfl
+  seqLeft_eq {α β} x y := by simp [SeqLeft.seqLeft, Functor.map, Seq.seq]; rfl
+  seqRight_eq {α β} x y := by simp [Seq.seq, SeqRight.seqRight, Functor.map]
+  pure_seq g x := by simp [Seq.seq, Functor.map]
+  bind_pure_comp f x := by simp [Functor.map, Bind.bind]; rfl
+  bind_map f x := by simp [Seq.seq, Functor.map]; rfl
+  pure_bind x f := PostconditionT.pure_bind
+  bind_assoc x f g := PostconditionT.bind_assoc
+
+@[simp]
+theorem PostconditionT.property_map {m : Type w → Type w'} [Functor m] {α : Type w} {β : Type w}
+    {x : PostconditionT m α} {f : α → β} {b : β} :
+    (x.map f).Property b ↔ (∃ a, f a = b ∧ x.Property a) := by
+  simp only [PostconditionT.map]
+  apply Iff.intro
+  · rintro ⟨⟨a, ha⟩, h⟩
+    exact ⟨a, h, ha⟩
+  · rintro ⟨a, h, ha⟩
+    exact ⟨⟨a, ha⟩, h⟩
+
+@[simp]
+theorem PostconditionT.operation_map {m : Type w → Type w'} [Functor m] {α : Type w} {β : Type w}
+    {x : PostconditionT m α} {f : α → β} :
+    (x.map f).operation =
+      (fun a => ⟨_, (property_map (m := m)).mpr ⟨a.1, rfl, a.2⟩⟩) <$> x.operation := by
+  rfl
+
+@[simp]
+theorem PostconditionT.property_lift {m : Type w → Type w'} [Functor m] {α : Type w}
+    {x : m α} : (lift x : PostconditionT m α).Property = (fun _ => True) := by
+  rfl
+
+@[simp]
+theorem PostconditionT.operation_lift {m : Type w → Type w'} [Functor m] {α : Type w}
+    {x : m α} : (lift x : PostconditionT m α).operation =
+      (⟨·, property_lift (m := m) ▸ True.intro⟩) <$> x := by
+  rfl
+
+end Std.Iterators

src/Init/Data/List/Attach.lean

@@ -23,6 +23,7 @@ a list `l : List α`, given a proof that every element of `l` in fact satisfies
 `O(|l|)`. `List.pmap`, named for “partial map,” is the equivalent of `List.map` for such partial
 functions.
 -/
+@[expose]
 def pmap {P : α → Prop} (f : ∀ a, P a → β) : ∀ l : List α, (H : ∀ a ∈ l, P a) → List β
   | [], _ => []
   | a :: l, H => f a (forall_mem_cons.1 H).1 :: pmap f l (forall_mem_cons.1 H).2
@@ -40,7 +41,7 @@ elements in the corresponding subtype `{ x // P x }`.
 
 `O(1)`.
 -/
-@[implemented_by attachWithImpl] def attachWith
+@[implemented_by attachWithImpl, expose] def attachWith
     (l : List α) (P : α → Prop) (H : ∀ x ∈ l, P x) : List {x // P x} := pmap Subtype.mk l H
 
 /--
@@ -54,7 +55,7 @@ recursion](lean-manual://section/well-founded-recursion) that use higher-order f
 `List.map`) to prove that an value taken from a list is smaller than the list. This allows the
 well-founded recursion mechanism to prove that the function terminates.
 -/
-@[inline] def attach (l : List α) : List {x // x ∈ l} := attachWith l _ fun _ => id
+@[inline, expose] def attach (l : List α) : List {x // x ∈ l} := attachWith l _ fun _ => id
 
 /-- Implementation of `pmap` using the zero-copy version of `attach`. -/
 @[inline] private def pmapImpl {P : α → Prop} (f : ∀ a, P a → β) (l : List α) (H : ∀ a ∈ l, P a) :
@@ -68,14 +69,14 @@ well-founded recursion mechanism to prove that the function terminates.
   | cons _ l', hL' => congrArg _ <| go l' fun _ hx => hL' (.tail _ hx)
   exact go l h'
 
-@[simp] theorem pmap_nil {P : α → Prop} {f : ∀ a, P a → β} : pmap f [] (by simp) = [] := rfl
+@[simp, grind =] theorem pmap_nil {P : α → Prop} {f : ∀ a, P a → β} : pmap f [] (by simp) = [] := rfl
 
-@[simp] theorem pmap_cons {P : α → Prop} {f : ∀ a, P a → β} {a : α} {l : List α} (h : ∀ b ∈ a :: l, P b) :
+@[simp, grind =] theorem pmap_cons {P : α → Prop} {f : ∀ a, P a → β} {a : α} {l : List α} (h : ∀ b ∈ a :: l, P b) :
     pmap f (a :: l) h = f a (forall_mem_cons.1 h).1 :: pmap f l (forall_mem_cons.1 h).2 := rfl
 
-@[simp] theorem attach_nil : ([] : List α).attach = [] := rfl
+@[simp, grind =] theorem attach_nil : ([] : List α).attach = [] := rfl
 
-@[simp] theorem attachWith_nil : ([] : List α).attachWith P H = [] := rfl
+@[simp, grind =] theorem attachWith_nil : ([] : List α).attachWith P H = [] := rfl
 
 @[simp]
 theorem pmap_eq_map {p : α → Prop} {f : α → β} {l : List α} (H) :
@@ -91,12 +92,14 @@ theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a,
   | cons x l ih =>
     rw [pmap, pmap, h _ mem_cons_self, ih fun a ha => h a (mem_cons_of_mem _ ha)]
 
+@[grind =]
 theorem map_pmap {p : α → Prop} {g : β → γ} {f : ∀ a, p a → β} {l : List α} (H) :
     map g (pmap f l H) = pmap (fun a h => g (f a h)) l H := by
   induction l
   · rfl
   · simp only [*, pmap, map]
 
+@[grind =]
 theorem pmap_map {p : β → Prop} {g : ∀ b, p b → γ} {f : α → β} {l : List α} (H) :
     pmap g (map f l) H = pmap (fun a h => g (f a) h) l fun _ h => H _ (mem_map_of_mem h) := by
   induction l
@@ -113,7 +116,7 @@ theorem attachWith_congr {l₁ l₂ : List α} (w : l₁ = l₂) {P : α → Pro
   subst w
   simp
 
-@[simp] theorem attach_cons {x : α} {xs : List α} :
+@[simp, grind =] theorem attach_cons {x : α} {xs : List α} :
     (x :: xs).attach =
       ⟨x, mem_cons_self⟩ :: xs.attach.map fun ⟨y, h⟩ => ⟨y, mem_cons_of_mem x h⟩ := by
   simp only [attach, attachWith, pmap, map_pmap, cons.injEq, true_and]
@@ -121,7 +124,7 @@ theorem attachWith_congr {l₁ l₂ : List α} (w : l₁ = l₂) {P : α → Pro
   intros a _ m' _
   rfl
 
-@[simp]
+@[simp, grind =]
 theorem attachWith_cons {x : α} {xs : List α} {p : α → Prop} (h : ∀ a ∈ x :: xs, p a) :
     (x :: xs).attachWith p h = ⟨x, h x (mem_cons_self)⟩ ::
       xs.attachWith p (fun a ha ↦ h a (mem_cons_of_mem x ha)) :=
@@ -161,14 +164,14 @@ theorem attachWith_map_subtype_val {p : α → Prop} {l : List α} (H : ∀ a
     (l.attachWith p H).map Subtype.val = l :=
   (attachWith_map_val _).trans (List.map_id _)
 
-@[simp]
+@[simp, grind]
 theorem mem_attach (l : List α) : ∀ x, x ∈ l.attach
   | ⟨a, h⟩ => by
     have := mem_map.1 (by rw [attach_map_subtype_val]; exact h)
     rcases this with ⟨⟨_, _⟩, m, rfl⟩
     exact m
 
-@[simp]
+@[simp, grind]
 theorem mem_attachWith {l : List α} {q : α → Prop} (H) (x : {x // q x}) :
     x ∈ l.attachWith q H ↔ x.1 ∈ l := by
   induction l with
@@ -181,27 +184,28 @@ theorem mem_attachWith {l : List α} {q : α → Prop} (H) (x : {x // q x}) :
       · simp [← h]
       · simp_all
 
-@[simp]
+@[simp, grind =]
 theorem mem_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H b} :
     b ∈ pmap f l H ↔ ∃ (a : _) (h : a ∈ l), f a (H a h) = b := by
   simp only [pmap_eq_map_attach, mem_map, mem_attach, true_and, Subtype.exists, eq_comm]
 
+@[grind]
 theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {l H} {a} (h : a ∈ l) :
     f a (H a h) ∈ pmap f l H := by
   rw [mem_pmap]
   exact ⟨a, h, rfl⟩
 
-@[simp]
+@[simp, grind =]
 theorem length_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H} : (pmap f l H).length = l.length := by
   induction l
   · rfl
   · simp only [*, pmap, length]
 
-@[simp]
+@[simp, grind =]
 theorem length_attach {l : List α} : l.attach.length = l.length :=
   length_pmap
 
-@[simp]
+@[simp, grind =]
 theorem length_attachWith {p : α → Prop} {l H} : length (l.attachWith p H) = length l :=
   length_pmap
 
@@ -236,7 +240,7 @@ theorem attachWith_ne_nil_iff {l : List α} {P : α → Prop} {H : ∀ a ∈ l,
     l.attachWith P H ≠ [] ↔ l ≠ [] :=
   pmap_ne_nil_iff _ _
 
-@[simp]
+@[simp, grind =]
 theorem getElem?_pmap {p : α → Prop} {f : ∀ a, p a → β} {l : List α} (h : ∀ a ∈ l, p a) (i : Nat) :
     (pmap f l h)[i]? = Option.pmap f l[i]? fun x H => h x (mem_of_getElem? H) := by
   induction l generalizing i with
@@ -251,10 +255,10 @@ set_option linter.deprecated false in
 theorem get?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h : ∀ a ∈ l, p a) (n : Nat) :
     get? (pmap f l h) n = Option.pmap f (get? l n) fun x H => h x (mem_of_get? H) := by
   simp only [get?_eq_getElem?]
-  simp [getElem?_pmap, h]
+  simp [getElem?_pmap]
 
 -- The argument `f` is explicit to allow rewriting from right to left.
-@[simp]
+@[simp, grind =]
 theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h : ∀ a ∈ l, p a) {i : Nat}
     (hn : i < (pmap f l h).length) :
     (pmap f l h)[i] =
@@ -278,109 +282,111 @@ theorem get_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h :
   simp only [get_eq_getElem]
   simp [getElem_pmap]
 
-@[simp]
+@[simp, grind =]
 theorem getElem?_attachWith {xs : List α} {i : Nat} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
     (xs.attachWith P H)[i]? = xs[i]?.pmap Subtype.mk (fun _ a => H _ (mem_of_getElem? a)) :=
   getElem?_pmap ..
 
-@[simp]
+@[simp, grind =]
 theorem getElem?_attach {xs : List α} {i : Nat} :
     xs.attach[i]? = xs[i]?.pmap Subtype.mk (fun _ a => mem_of_getElem? a) :=
   getElem?_attachWith
 
-@[simp]
+@[simp, grind =]
 theorem getElem_attachWith {xs : List α} {P : α → Prop} {H : ∀ a ∈ xs, P a}
     {i : Nat} (h : i < (xs.attachWith P H).length) :
     (xs.attachWith P H)[i] = ⟨xs[i]'(by simpa using h), H _ (getElem_mem (by simpa using h))⟩ :=
   getElem_pmap ..
 
-@[simp]
+@[simp, grind =]
 theorem getElem_attach {xs : List α} {i : Nat} (h : i < xs.attach.length) :
     xs.attach[i] = ⟨xs[i]'(by simpa using h), getElem_mem (by simpa using h)⟩ :=
   getElem_attachWith h
 
-@[simp] theorem pmap_attach {l : List α} {p : {x // x ∈ l} → Prop} {f : ∀ a, p a → β} (H) :
+@[simp, grind =] theorem pmap_attach {l : List α} {p : {x // x ∈ l} → Prop} {f : ∀ a, p a → β} (H) :
     pmap f l.attach H =
       l.pmap (P := fun a => ∃ h : a ∈ l, p ⟨a, h⟩)
         (fun a h => f ⟨a, h.1⟩ h.2) (fun a h => ⟨h, H ⟨a, h⟩ (by simp)⟩) := by
   apply ext_getElem <;> simp
 
-@[simp] theorem pmap_attachWith {l : List α} {p : {x // q x} → Prop} {f : ∀ a, p a → β} (H₁ H₂) :
+@[simp, grind =] theorem pmap_attachWith {l : List α} {p : {x // q x} → Prop} {f : ∀ a, p a → β} (H₁ H₂) :
     pmap f (l.attachWith q H₁) H₂ =
       l.pmap (P := fun a => ∃ h : q a, p ⟨a, h⟩)
         (fun a h => f ⟨a, h.1⟩ h.2) (fun a h => ⟨H₁ _ h, H₂ ⟨a, H₁ _ h⟩ (by simpa)⟩) := by
   apply ext_getElem <;> simp
 
-@[simp] theorem head?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp, grind =] theorem head?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.pmap f H).head? = xs.attach.head?.map fun ⟨a, m⟩ => f a (H a m) := by
   induction xs with
   | nil => simp
   | cons x xs ih =>
     simp at ih
-    simp [head?_pmap, ih]
+    simp
 
-@[simp] theorem head_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp, grind =] theorem head_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
     (H : ∀ (a : α), a ∈ xs → P a) (h : xs.pmap f H ≠ []) :
     (xs.pmap f H).head h = f (xs.head (by simpa using h)) (H _ (head_mem _)) := by
   induction xs with
   | nil => simp at h
-  | cons x xs ih => simp [head_pmap, ih]
+  | cons x xs ih => simp
 
-@[simp] theorem head?_attachWith {P : α → Prop} {xs : List α}
+@[simp, grind =] theorem head?_attachWith {P : α → Prop} {xs : List α}
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.attachWith P H).head? = xs.head?.pbind (fun a h => some ⟨a, H _ (mem_of_head? h)⟩) := by
   cases xs <;> simp_all
 
-@[simp] theorem head_attachWith {P : α → Prop} {xs : List α}
+@[simp, grind =] theorem head_attachWith {P : α → Prop} {xs : List α}
     {H : ∀ (a : α), a ∈ xs → P a} (h : xs.attachWith P H ≠ []) :
     (xs.attachWith P H).head h = ⟨xs.head (by simpa using h), H _ (head_mem _)⟩ := by
   cases xs with
   | nil => simp at h
-  | cons x xs => simp [head_attachWith, h]
+  | cons x xs => simp
 
-@[simp] theorem head?_attach {xs : List α} :
+@[simp, grind =] theorem head?_attach {xs : List α} :
     xs.attach.head? = xs.head?.pbind (fun a h => some ⟨a, mem_of_head? h⟩) := by
   cases xs <;> simp_all
 
-@[simp] theorem head_attach {xs : List α} (h) :
+@[simp, grind =] theorem head_attach {xs : List α} (h) :
     xs.attach.head h = ⟨xs.head (by simpa using h), head_mem (by simpa using h)⟩ := by
   cases xs with
   | nil => simp at h
-  | cons x xs => simp [head_attach, h]
+  | cons x xs => simp
 
-@[simp] theorem tail_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp, grind =] theorem tail_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.pmap f H).tail = xs.tail.pmap f (fun a h => H a (mem_of_mem_tail h)) := by
   cases xs <;> simp
 
-@[simp] theorem tail_attachWith {P : α → Prop} {xs : List α}
+@[simp, grind =] theorem tail_attachWith {P : α → Prop} {xs : List α}
     {H : ∀ (a : α), a ∈ xs → P a} :
     (xs.attachWith P H).tail = xs.tail.attachWith P (fun a h => H a (mem_of_mem_tail h)) := by
   cases xs <;> simp
 
-@[simp] theorem tail_attach {xs : List α} :
+@[simp, grind =] theorem tail_attach {xs : List α} :
     xs.attach.tail = xs.tail.attach.map (fun ⟨x, h⟩ => ⟨x, mem_of_mem_tail h⟩) := by
   cases xs <;> simp
 
+@[grind]
 theorem foldl_pmap {l : List α} {P : α → Prop} {f : (a : α) → P a → β}
     (H : ∀ (a : α), a ∈ l → P a) (g : γ → β → γ) (x : γ) :
     (l.pmap f H).foldl g x = l.attach.foldl (fun acc a => g acc (f a.1 (H _ a.2))) x := by
   rw [pmap_eq_map_attach, foldl_map]
 
+@[grind]
 theorem foldr_pmap {l : List α} {P : α → Prop} {f : (a : α) → P a → β}
     (H : ∀ (a : α), a ∈ l → P a) (g : β → γ → γ) (x : γ) :
     (l.pmap f H).foldr g x = l.attach.foldr (fun a acc => g (f a.1 (H _ a.2)) acc) x := by
   rw [pmap_eq_map_attach, foldr_map]
 
-@[simp] theorem foldl_attachWith
+@[simp, grind =] theorem foldl_attachWith
     {l : List α} {q : α → Prop} (H : ∀ a, a ∈ l → q a) {f : β → { x // q x } → β} {b} :
     (l.attachWith q H).foldl f b = l.attach.foldl (fun b ⟨a, h⟩ => f b ⟨a, H _ h⟩) b := by
   induction l generalizing b with
   | nil => simp
   | cons a l ih => simp [ih, foldl_map]
 
-@[simp] theorem foldr_attachWith
+@[simp, grind =] theorem foldr_attachWith
     {l : List α} {q : α → Prop} (H : ∀ a, a ∈ l → q a) {f : { x // q x } → β → β} {b} :
     (l.attachWith q H).foldr f b = l.attach.foldr (fun a acc => f ⟨a.1, H _ a.2⟩ acc) b := by
   induction l generalizing b with
@@ -419,16 +425,18 @@ theorem foldr_attach {l : List α} {f : α → β → β} {b : β} :
   | nil => simp
   | cons a l ih => rw [foldr_cons, attach_cons, foldr_cons, foldr_map, ih]
 
+@[grind =]
 theorem attach_map {l : List α} {f : α → β} :
     (l.map f).attach = l.attach.map (fun ⟨x, h⟩ => ⟨f x, mem_map_of_mem h⟩) := by
   induction l <;> simp [*]
 
+@[grind =]
 theorem attachWith_map {l : List α} {f : α → β} {P : β → Prop} (H : ∀ (b : β), b ∈ l.map f → P b) :
     (l.map f).attachWith P H = (l.attachWith (P ∘ f) (fun _ h => H _ (mem_map_of_mem h))).map
       fun ⟨x, h⟩ => ⟨f x, h⟩ := by
   induction l <;> simp [*]
 
-@[simp] theorem map_attachWith {l : List α} {P : α → Prop} {H : ∀ (a : α), a ∈ l → P a}
+@[simp, grind =] theorem map_attachWith {l : List α} {P : α → Prop} {H : ∀ (a : α), a ∈ l → P a}
     {f : { x // P x } → β} :
     (l.attachWith P H).map f = l.attach.map fun ⟨x, h⟩ => f ⟨x, H _ h⟩ := by
   induction l <;> simp_all
@@ -457,13 +465,14 @@ theorem map_attach_eq_pmap {l : List α} {f : { x // x ∈ l } → β} :
 @[deprecated map_attach_eq_pmap (since := "2025-02-09")]
 abbrev map_attach := @map_attach_eq_pmap
 
+@[grind =]
 theorem attach_filterMap {l : List α} {f : α → Option β} :
     (l.filterMap f).attach = l.attach.filterMap
       fun ⟨x, h⟩ => (f x).pbind (fun b m => some ⟨b, mem_filterMap.mpr ⟨x, h, m⟩⟩) := by
   induction l with
   | nil => rfl
   | cons x xs ih =>
-    simp only [filterMap_cons, attach_cons, ih, filterMap_map]
+    simp only [filterMap_cons, attach_cons, filterMap_map]
     split <;> rename_i h
     · simp only [Option.pbind_eq_none_iff, reduceCtorEq, exists_false,
         or_false] at h
@@ -487,6 +496,7 @@ theorem attach_filterMap {l : List α} {f : α → Option β} :
       ext
       simp
 
+@[grind =]
 theorem attach_filter {l : List α} (p : α → Bool) :
     (l.filter p).attach = l.attach.filterMap
       fun x => if w : p x.1 then some ⟨x.1, mem_filter.mpr ⟨x.2, w⟩⟩ else none := by
@@ -498,7 +508,7 @@ theorem attach_filter {l : List α} (p : α → Bool) :
 
 -- We are still missing here `attachWith_filterMap` and `attachWith_filter`.
 
-@[simp]
+@[simp, grind =]
 theorem filterMap_attachWith {q : α → Prop} {l : List α} {f : {x // q x} → Option β} (H) :
     (l.attachWith q H).filterMap f = l.attach.filterMap (fun ⟨x, h⟩ => f ⟨x, H _ h⟩) := by
   induction l with
@@ -507,7 +517,7 @@ theorem filterMap_attachWith {q : α → Prop} {l : List α} {f : {x // q x} →
     simp only [attachWith_cons, filterMap_cons]
     split <;> simp_all [Function.comp_def]
 
-@[simp]
+@[simp, grind =]
 theorem filter_attachWith {q : α → Prop} {l : List α} {p : {x // q x} → Bool} (H) :
     (l.attachWith q H).filter p =
       (l.attach.filter (fun ⟨x, h⟩ => p ⟨x, H _ h⟩)).map (fun ⟨x, h⟩ => ⟨x, H _ h⟩) := by
@@ -517,13 +527,14 @@ theorem filter_attachWith {q : α → Prop} {l : List α} {p : {x // q x} → Bo
     simp only [attachWith_cons, filter_cons]
     split <;> simp_all [Function.comp_def, filter_map]
 
+@[grind =]
 theorem pmap_pmap {p : α → Prop} {q : β → Prop} {g : ∀ a, p a → β} {f : ∀ b, q b → γ} {l} (H₁ H₂) :
     pmap f (pmap g l H₁) H₂ =
       pmap (α := { x // x ∈ l }) (fun a h => f (g a h) (H₂ (g a h) (mem_pmap_of_mem a.2))) l.attach
         (fun a _ => H₁ a a.2) := by
   simp [pmap_eq_map_attach, attach_map]
 
-@[simp] theorem pmap_append {p : ι → Prop} {f : ∀ a : ι, p a → α} {l₁ l₂ : List ι}
+@[simp, grind =] theorem pmap_append {p : ι → Prop} {f : ∀ a : ι, p a → α} {l₁ l₂ : List ι}
     (h : ∀ a ∈ l₁ ++ l₂, p a) :
     (l₁ ++ l₂).pmap f h =
       (l₁.pmap f fun a ha => h a (mem_append_left l₂ ha)) ++
@@ -540,47 +551,50 @@ theorem pmap_append' {p : α → Prop} {f : ∀ a : α, p a → β} {l₁ l₂ :
       l₁.pmap f h₁ ++ l₂.pmap f h₂ :=
   pmap_append _
 
-@[simp] theorem attach_append {xs ys : List α} :
+@[simp, grind =] theorem attach_append {xs ys : List α} :
     (xs ++ ys).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_append_left ys h⟩) ++
       ys.attach.map fun ⟨x, h⟩ => ⟨x, mem_append_right xs h⟩ := by
-  simp only [attach, attachWith, pmap, map_pmap, pmap_append]
+  simp only [attach, attachWith, map_pmap, pmap_append]
   congr 1 <;>
   exact pmap_congr_left _ fun _ _ _ _ => rfl
 
-@[simp] theorem attachWith_append {P : α → Prop} {xs ys : List α}
+@[simp, grind =] theorem attachWith_append {P : α → Prop} {xs ys : List α}
     {H : ∀ (a : α), a ∈ xs ++ ys → P a} :
     (xs ++ ys).attachWith P H = xs.attachWith P (fun a h => H a (mem_append_left ys h)) ++
       ys.attachWith P (fun a h => H a (mem_append_right xs h)) := by
-  simp only [attachWith, attach_append, map_pmap, pmap_append]
+  simp only [attachWith, pmap_append]
 
-@[simp] theorem pmap_reverse {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp, grind =] theorem pmap_reverse {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
     (H : ∀ (a : α), a ∈ xs.reverse → P a) :
     xs.reverse.pmap f H = (xs.pmap f (fun a h => H a (by simpa using h))).reverse := by
   induction xs <;> simp_all
 
+@[grind =]
 theorem reverse_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.pmap f H).reverse = xs.reverse.pmap f (fun a h => H a (by simpa using h)) := by
   rw [pmap_reverse]
 
-@[simp] theorem attachWith_reverse {P : α → Prop} {xs : List α}
+@[simp, grind =] theorem attachWith_reverse {P : α → Prop} {xs : List α}
     {H : ∀ (a : α), a ∈ xs.reverse → P a} :
     xs.reverse.attachWith P H =
       (xs.attachWith P (fun a h => H a (by simpa using h))).reverse :=
   pmap_reverse ..
 
+@[grind =]
 theorem reverse_attachWith {P : α → Prop} {xs : List α}
     {H : ∀ (a : α), a ∈ xs → P a} :
     (xs.attachWith P H).reverse = (xs.reverse.attachWith P (fun a h => H a (by simpa using h))) :=
   reverse_pmap ..
 
-@[simp] theorem attach_reverse {xs : List α} :
+@[simp, grind =] theorem attach_reverse {xs : List α} :
     xs.reverse.attach = xs.attach.reverse.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
   simp only [attach, attachWith, reverse_pmap, map_pmap]
   apply pmap_congr_left
   intros
   rfl
 
+@[grind =]
 theorem reverse_attach {xs : List α} :
     xs.attach.reverse = xs.reverse.attach.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
   simp only [attach, attachWith, reverse_pmap, map_pmap]
@@ -588,7 +602,7 @@ theorem reverse_attach {xs : List α} :
   intros
   rfl
 
-@[simp] theorem getLast?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp, grind =] theorem getLast?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.pmap f H).getLast? = xs.attach.getLast?.map fun ⟨a, m⟩ => f a (H a m) := by
   simp only [getLast?_eq_head?_reverse]
@@ -596,30 +610,30 @@ theorem reverse_attach {xs : List α} :
   simp only [Option.map_map]
   congr
 
-@[simp] theorem getLast_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp, grind =] theorem getLast_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
     (H : ∀ (a : α), a ∈ xs → P a) (h : xs.pmap f H ≠ []) :
     (xs.pmap f H).getLast h = f (xs.getLast (by simpa using h)) (H _ (getLast_mem _)) := by
   simp only [getLast_eq_head_reverse]
   simp only [reverse_pmap, head_pmap, head_reverse]
 
-@[simp] theorem getLast?_attachWith {P : α → Prop} {xs : List α}
+@[simp, grind =] theorem getLast?_attachWith {P : α → Prop} {xs : List α}
     {H : ∀ (a : α), a ∈ xs → P a} :
     (xs.attachWith P H).getLast? = xs.getLast?.pbind (fun a h => some ⟨a, H _ (mem_of_getLast? h)⟩) := by
   rw [getLast?_eq_head?_reverse, reverse_attachWith, head?_attachWith]
   simp
 
-@[simp] theorem getLast_attachWith {P : α → Prop} {xs : List α}
+@[simp, grind =] theorem getLast_attachWith {P : α → Prop} {xs : List α}
     {H : ∀ (a : α), a ∈ xs → P a} (h : xs.attachWith P H ≠ []) :
     (xs.attachWith P H).getLast h = ⟨xs.getLast (by simpa using h), H _ (getLast_mem _)⟩ := by
-  simp only [getLast_eq_head_reverse, reverse_attachWith, head_attachWith, head_map]
+  simp only [getLast_eq_head_reverse, reverse_attachWith, head_attachWith]
 
-@[simp]
+@[simp, grind =]
 theorem getLast?_attach {xs : List α} :
     xs.attach.getLast? = xs.getLast?.pbind fun a h => some ⟨a, mem_of_getLast? h⟩ := by
   rw [getLast?_eq_head?_reverse, reverse_attach, head?_map, head?_attach]
   simp
 
-@[simp]
+@[simp, grind =]
 theorem getLast_attach {xs : List α} (h : xs.attach ≠ []) :
     xs.attach.getLast h = ⟨xs.getLast (by simpa using h), getLast_mem (by simpa using h)⟩ := by
   simp only [getLast_eq_head_reverse, reverse_attach, head_map, head_attach]
@@ -637,14 +651,14 @@ theorem countP_attachWith {p : α → Prop} {q : α → Bool} {l : List α} (H :
 @[simp]
 theorem count_attach [BEq α] {l : List α} {a : {x // x ∈ l}} :
     l.attach.count a = l.count ↑a :=
-  Eq.trans (countP_congr fun _ _ => by simp [Subtype.ext_iff]) <| countP_attach
+  Eq.trans (countP_congr fun _ _ => by simp) <| countP_attach
 
-@[simp]
+@[simp, grind =]
 theorem count_attachWith [BEq α] {p : α → Prop} {l : List α} (H : ∀ a ∈ l, p a) {a : {x // p x}} :
     (l.attachWith p H).count a = l.count ↑a :=
-  Eq.trans (countP_congr fun _ _ => by simp [Subtype.ext_iff]) <| countP_attachWith _
+  Eq.trans (countP_congr fun _ _ => by simp) <| countP_attachWith _
 
-@[simp] theorem countP_pmap {p : α → Prop} {g : ∀ a, p a → β} {f : β → Bool} {l : List α} (H₁) :
+@[simp, grind =] theorem countP_pmap {p : α → Prop} {g : ∀ a, p a → β} {f : β → Bool} {l : List α} (H₁) :
     (l.pmap g H₁).countP f =
       l.attach.countP (fun ⟨a, m⟩ => f (g a (H₁ a m))) := by
   simp [pmap_eq_map_attach, countP_map, Function.comp_def]
@@ -675,6 +689,7 @@ the elaboration of definitions by [well-founded
 recursion](lean-manual://section/well-founded-recursion). If this function is encountered in a proof
 state, the right approach is usually the tactic `simp [List.unattach, -List.map_subtype]`.
 -/
+@[expose]
 def unattach {α : Type _} {p : α → Prop} (l : List { x // p x }) : List α := l.map (·.val)
 
 @[simp] theorem unattach_nil {p : α → Prop} : ([] : List { x // p x }).unattach = [] := rfl
@@ -702,7 +717,7 @@ def unattach {α : Type _} {p : α → Prop} (l : List { x // p x }) : List α :
   unfold unattach
   induction l with
   | nil => simp
-  | cons a l ih => simp [ih, Function.comp_def]
+  | cons a l ih => simp [ih]
 
 @[simp] theorem getElem?_unattach {p : α → Prop} {l : List { x // p x }} (i : Nat) :
     l.unattach[i]? = l[i]?.map Subtype.val := by

src/Init/Data/List/Basic.lean

@@ -9,6 +9,7 @@ prelude
 import Init.SimpLemmas
 import Init.Data.Nat.Basic
 import Init.Data.List.Notation
+import Init.Data.Nat.Div.Basic
 
 @[expose] section
 
@@ -586,7 +587,7 @@ Examples:
 * `[1, 2, 3, 4].reverse = [4, 3, 2, 1]`
 * `[].reverse = []`
 -/
-def reverse (as : List α) : List α :=
+@[expose] def reverse (as : List α) : List α :=
   reverseAux as []
 
 @[simp, grind] theorem reverse_nil : reverse ([] : List α) = [] := rfl
@@ -672,7 +673,7 @@ instance : Std.Associative (α := List α) (· ++ ·) := ⟨append_assoc⟩
 theorem append_cons (as : List α) (b : α) (bs : List α) : as ++ b :: bs = as ++ [b] ++ bs := by
   simp
 
-@[simp] theorem concat_eq_append {as : List α} {a : α} : as.concat a = as ++ [a] := by
+@[simp, grind =] theorem concat_eq_append {as : List α} {a : α} : as.concat a = as ++ [a] := by
   induction as <;> simp [concat, *]
 
 theorem reverseAux_eq_append {as bs : List α} : reverseAux as bs = reverseAux as [] ++ bs := by
@@ -715,7 +716,7 @@ Examples:
  * `List.singleton "green" = ["green"]`.
  * `List.singleton [1, 2, 3] = [[1, 2, 3]]`
 -/
-@[inline] protected def singleton {α : Type u} (a : α) : List α := [a]
+@[inline, expose] protected def singleton {α : Type u} (a : α) : List α := [a]
 
 /-! ### flatMap -/
 
@@ -729,9 +730,9 @@ Examples:
 -/
 @[inline] def flatMap {α : Type u} {β : Type v} (b : α → List β) (as : List α) : List β := flatten (map b as)
 
-@[simp, grind] theorem flatMap_nil {f : α → List β} : List.flatMap f [] = [] := by simp [flatten, List.flatMap]
+@[simp, grind] theorem flatMap_nil {f : α → List β} : List.flatMap f [] = [] := by simp [List.flatMap]
 @[simp, grind] theorem flatMap_cons {x : α} {xs : List α} {f : α → List β} :
-  List.flatMap f (x :: xs) = f x ++ List.flatMap f xs := by simp [flatten, List.flatMap]
+  List.flatMap f (x :: xs) = f x ++ List.flatMap f xs := by simp [List.flatMap]
 
 /-! ### replicate -/
 
@@ -752,7 +753,7 @@ def replicate : (n : Nat) → (a : α) → List α
 @[simp, grind] theorem length_replicate {n : Nat} {a : α} : (replicate n a).length = n := by
   induction n with
   | zero => simp
-  | succ n ih => simp only [ih, replicate_succ, length_cons, Nat.succ_eq_add_one]
+  | succ n ih => simp only [ih, replicate_succ, length_cons]
 
 /-! ## Additional functions -/
 
@@ -891,7 +892,7 @@ theorem mem_of_elem_eq_true [BEq α] [LawfulBEq α] {a : α} {as : List α} : el
   | a'::as =>
     simp [elem]
     split
-    next h => intros; simp [BEq.beq] at h; subst h; apply Mem.head
+    next h => intros; simp at h; subst h; apply Mem.head
     next _ => intro h; exact Mem.tail _ (mem_of_elem_eq_true h)
 
 theorem elem_eq_true_of_mem [BEq α] [ReflBEq α] {a : α} {as : List α} (h : a ∈ as) : elem a as = true := by
@@ -1190,10 +1191,10 @@ def isPrefixOf [BEq α] : List α → List α → Bool
   | _,     []    => false
   | a::as, b::bs => a == b && isPrefixOf as bs
 
-@[simp] theorem isPrefixOf_nil_left [BEq α] : isPrefixOf ([] : List α) l = true := by
+@[simp, grind =] theorem isPrefixOf_nil_left [BEq α] : isPrefixOf ([] : List α) l = true := by
   simp [isPrefixOf]
-@[simp] theorem isPrefixOf_cons_nil [BEq α] : isPrefixOf (a::as) ([] : List α) = false := rfl
-theorem isPrefixOf_cons₂ [BEq α] {a : α} :
+@[simp, grind =] theorem isPrefixOf_cons_nil [BEq α] : isPrefixOf (a::as) ([] : List α) = false := rfl
+@[grind =] theorem isPrefixOf_cons₂ [BEq α] {a : α} :
     isPrefixOf (a::as) (b::bs) = (a == b && isPrefixOf as bs) := rfl
 
 /--
@@ -1229,7 +1230,7 @@ Examples:
 def isSuffixOf [BEq α] (l₁ l₂ : List α) : Bool :=
   isPrefixOf l₁.reverse l₂.reverse
 
-@[simp] theorem isSuffixOf_nil_left [BEq α] : isSuffixOf ([] : List α) l = true := by
+@[simp, grind =] theorem isSuffixOf_nil_left [BEq α] : isSuffixOf ([] : List α) l = true := by
   simp [isSuffixOf]
 
 /--
@@ -1564,8 +1565,8 @@ protected def erase {α} [BEq α] : List α → α → List α
     | true  => as
     | false => a :: List.erase as b
 
-@[simp] theorem erase_nil [BEq α] (a : α) : [].erase a = [] := rfl
-theorem erase_cons [BEq α] {a b : α} {l : List α} :
+@[simp, grind =] theorem erase_nil [BEq α] (a : α) : [].erase a = [] := rfl
+@[grind =] theorem erase_cons [BEq α] {a b : α} {l : List α} :
     (b :: l).erase a = if b == a then l else b :: l.erase a := by
   simp only [List.erase]; split <;> simp_all
 
@@ -1624,8 +1625,8 @@ def find? (p : α → Bool) : List α → Option α
     | true  => some a
     | false => find? p as
 
-@[simp] theorem find?_nil : ([] : List α).find? p = none := rfl
-theorem find?_cons : (a::as).find? p = match p a with | true => some a | false => as.find? p :=
+@[simp, grind =] theorem find?_nil : ([] : List α).find? p = none := rfl
+@[grind =]theorem find?_cons : (a::as).find? p = match p a with | true => some a | false => as.find? p :=
   rfl
 
 /-! ### findSome? -/
@@ -1779,7 +1780,7 @@ where
   | a :: l, i, h =>
     if p a then
       some ⟨i, by
-        simp only [Nat.add_comm _ i, ← Nat.add_assoc] at h
+        simp only [Nat.add_comm _ i] at h
         exact Nat.lt_of_add_right_lt (Nat.lt_of_succ_le (Nat.le_of_eq h))⟩
     else
       go l (i + 1) (by simp at h; simpa [← Nat.add_assoc, Nat.add_right_comm] using h)
@@ -1845,8 +1846,8 @@ def lookup [BEq α] : α → List (α × β) → Option β
     | true  => some b
     | false => lookup a as
 
-@[simp] theorem lookup_nil [BEq α] : ([] : List (α × β)).lookup a = none := rfl
-theorem lookup_cons [BEq α] {k : α} :
+@[simp, grind =] theorem lookup_nil [BEq α] : ([] : List (α × β)).lookup a = none := rfl
+@[grind =] theorem lookup_cons [BEq α] {k : α} :
     ((k, b)::as).lookup a = match a == k with | true => some b | false => as.lookup a :=
   rfl
 
@@ -2014,7 +2015,7 @@ def zip : List α → List β → List (Prod α β) :=
   zipWith Prod.mk
 
 @[simp] theorem zip_nil_left : zip ([] : List α) (l : List β)  = [] := rfl
-@[simp] theorem zip_nil_right : zip (l : List α) ([] : List β)  = [] := by simp [zip, zipWith]
+@[simp] theorem zip_nil_right : zip (l : List α) ([] : List β)  = [] := by simp [zip]
 @[simp] theorem zip_cons_cons : zip (a :: as) (b :: bs) = (a, b) :: zip as bs := rfl
 
 /-! ### zipWithAll -/
@@ -2096,7 +2097,7 @@ where
   | 0,   acc => acc
   | n+1, acc => loop n (n::acc)
 
-@[simp] theorem range_zero : range 0 = [] := rfl
+@[simp, grind =] theorem range_zero : range 0 = [] := rfl
 
 /-! ### range' -/