chore: convert DHashMap to a structure

This PR implements model-based theory combination for grind linarith.
Example:
```lean
example [CommRing α] [LinearOrder α] [Ring.IsOrdered α] (f : α → α → α) (x y z : α)
    : z ≤ x → x ≤ 1 → z = 1 → f x y = 2 → f 1 y = 2 := by
  grind
```

.github/workflows/build-template.yml

@@ -105,11 +105,11 @@ jobs:
           path: |
             .ccache
             ${{ matrix.name == 'Linux Lake' && 'build/stage1/**/*.trace
-            build/stage1/**/*.olean
+            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
@@ -243,7 +243,7 @@ jobs:
           path: |
             .ccache
             ${{ matrix.name == 'Linux Lake' && 'build/stage1/**/*.trace
-            build/stage1/**/*.olean
+            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
@@ -357,7 +364,7 @@ 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 +408,7 @@ 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

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/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'")

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

@@ -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]
@@ -70,7 +70,7 @@ protected theorem seqLeft_eq {α β ε : Type u} {m : Type u → Type v} [Monad
     cases b <;> simp [comp, 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/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

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)
 
@@ -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} :
@@ -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

@@ -105,6 +105,7 @@ theorem boole_getElem_le_countP {xs : Array α} {i : Nat} (h : i < xs.size) :
 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} :

src/Init/Data/Array/DecidableEq.lean

@@ -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⟩
@@ -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⟩
@@ -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⟩
@@ -339,6 +356,7 @@ theorem getElem?_eraseIdx_of_ge {xs : Array α} {i : Nat} (h : i < xs.size) {j :
   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/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]
 
-@[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 [← 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]
 
@@ -270,7 +305,7 @@ theorem find?_flatten_eq_some_iff {xss : Array (Array α)} {p : α → Bool} {a
 @[deprecated find?_flatten_eq_some_iff (since := "2025-02-03")]
 abbrev find?_flatten_eq_some := @find?_flatten_eq_some_iff
 
-@[simp] theorem find?_flatMap {xs : Array α} {f : α → Array β} {p : β → Bool} :
+@[simp, 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]
@@ -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]
@@ -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
@@ -433,6 +482,7 @@ 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]
@@ -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⟩
@@ -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
@@ -728,26 +800,29 @@ 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]
 
-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

@@ -44,6 +44,7 @@ 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) :

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")]
@@ -133,7 +133,6 @@ 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
 
@@ -169,13 +168,14 @@ theorem getD_getElem? {xs : Array α} {i : Nat} {d : α} :
 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]
 
-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']
@@ -762,6 +762,7 @@ 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 +777,7 @@ 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]
@@ -951,6 +953,13 @@ 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 +992,11 @@ 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
@@ -1075,7 +1088,7 @@ theorem mem_or_eq_of_mem_setIfInBounds
   by_cases h : i < xs.size <;>
     simp [setIfInBounds, Nat.not_lt_of_le, h,  getD_getElem?]
 
-@[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
@@ -1257,7 +1270,8 @@ 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 +1498,19 @@ 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'
@@ -1858,7 +1885,7 @@ 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) :
@@ -2025,7 +2052,7 @@ 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 +2072,7 @@ 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) :
@@ -2993,6 +3020,10 @@ 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 +3634,8 @@ 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 +3645,8 @@ 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 +3761,7 @@ 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 +4104,11 @@ 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 +4116,7 @@ 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 +4131,7 @@ 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
@@ -4149,20 +4180,18 @@ 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 +4314,44 @@ 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 +4359,44 @@ 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
 
@@ -4432,7 +4465,7 @@ theorem getElem?_size_le {xs : Array α} {i : Nat} (h : xs.size ≤ i) : xs[i]?
   simp [getElem?_neg, h]
 
 theorem getElem_mem_toList {xs : Array α} {i : Nat} (h : i < xs.size) : xs[i] ∈ xs.toList := by
-  simp only [← getElem_toList, List.getElem_mem]
+  simp only [← getElem_toList, List.getElem_mem, ugetElem_eq_getElem]
 
 theorem back!_eq_back? [Inhabited α] {xs : Array α} : xs.back! = xs.back?.getD default := by
   simp [back!, back?, getElem!_def, Option.getD]; rfl
@@ -4500,12 +4533,13 @@ 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 +4606,7 @@ 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} :
@@ -4686,13 +4720,6 @@ 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")]
@@ -4745,17 +4772,6 @@ 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/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]
 
@@ -140,7 +140,7 @@ abbrev getElem_zipWithIndex := @getElem_zipIdx
 @[deprecated zipIdx_toArray (since := "2025-01-21")]
 abbrev zipWithIndex_toArray := @zipIdx_toArray
 
-@[simp] theorem toList_zipIdx {xs : Array α} {k : Nat} :
+@[simp, 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

@@ -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/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⟩⟩
@@ -116,6 +121,7 @@ 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
@@ -124,6 +130,7 @@ theorem erase_range' :
 
 /-! ### range -/
 
+@[grind _=_]
 theorem range_eq_range' {n : Nat} : range n = range' 0 n := by
   simp [range, range']
 
@@ -145,6 +152,7 @@ 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 +168,7 @@ 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]
 
@@ -168,7 +176,7 @@ 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} :
@@ -179,6 +187,7 @@ theorem self_mem_range_succ {n : Nat} : n ∈ range (n + 1) := by simp
     (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']
 

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/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`. -/
@@ -77,10 +77,10 @@ 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
 
 /-- Returns the `i`th least significant bit, or `none` if `i ≥ w`. -/
-@[inline] def getLsb? (x : BitVec w) (i : Nat) : Option Bool :=
+@[inline, expose] def getLsb? (x : BitVec w) (i : Nat) : Option Bool :=
   if h : i < w then some (getLsb' x ⟨i, h⟩) else none
 
 /--
@@ -95,7 +95,7 @@ This will be renamed `BitVec.getMsb` after the existing deprecated alias is remo
   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`. -/
@@ -134,6 +134,7 @@ 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 +148,7 @@ 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 +174,7 @@ 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 +183,7 @@ 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 +220,14 @@ 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 +236,7 @@ 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 +247,7 @@ 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 +259,7 @@ 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 +269,7 @@ 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 +281,7 @@ 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 +351,7 @@ 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 +369,7 @@ Unsigned less-than for bitvectors.
 
 SMT-LIB name: `bvult`.
 -/
+@[expose]
 protected def ult (x y : BitVec n) : Bool := x.toNat < y.toNat
 
 /--
@@ -366,6 +377,7 @@ 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 +389,7 @@ 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 +397,7 @@ 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 +411,7 @@ 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 +427,7 @@ 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 +438,7 @@ 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 +447,7 @@ 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 +456,7 @@ 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 +513,7 @@ 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 +526,7 @@ 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 +539,7 @@ 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 +552,7 @@ 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 +562,7 @@ 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 +574,7 @@ 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 +592,7 @@ 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 +606,12 @@ 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 +626,7 @@ 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 +634,7 @@ 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 +649,7 @@ 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 +661,7 @@ 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 +684,7 @@ 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 +692,7 @@ 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 +701,7 @@ 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 ..)
 
@@ -752,6 +786,7 @@ 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 +795,7 @@ 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 +806,7 @@ 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 +816,7 @@ 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))
 

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

@@ -631,6 +631,7 @@ 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
@@ -1022,7 +1023,7 @@ 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)]
@@ -1091,6 +1092,7 @@ 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
@@ -1750,6 +1752,116 @@ 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 [hdvd, reduceIte, toInt_add, hxnonneg, show ¬0 ≤ y.toInt by omega]
+  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 [reduceIte, 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 _, show 0 ≤ (-y).toNat by omega]
+
 /-! ### Lemmas that use bit blasting circuits -/
 
 theorem add_sub_comm {x y : BitVec w} : x + y - z = x - z + y := by

src/Init/Data/BitVec/Lemmas.lean

@@ -125,7 +125,7 @@ theorem getElem_of_getLsbD_eq_true {x : BitVec w} {i : Nat} (h : x.getLsbD i = t
 This normalized a bitvec using `ofFin` to `ofNat`.
 -/
 theorem ofFin_eq_ofNat : @BitVec.ofFin w (Fin.mk x lt) = BitVec.ofNat w x := by
-  simp only [BitVec.ofNat, Fin.ofNat', lt, Nat.mod_eq_of_lt]
+  simp only [BitVec.ofNat, Fin.ofNat, lt, Nat.mod_eq_of_lt]
 
 /-- 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
@@ -314,11 +314,12 @@ theorem length_pos_of_ne {x y : BitVec w} (h : x ≠ y) : 0 < w :=
 
 theorem ofFin_ofNat (n : Nat) :
     ofFin (no_index (OfNat.ofNat n : Fin (2^w))) = OfNat.ofNat n := by
-  simp only [OfNat.ofNat, Fin.ofNat', BitVec.ofNat, Nat.and_two_pow_sub_one_eq_mod]
+  simp only [OfNat.ofNat, Fin.ofNat, BitVec.ofNat, Nat.and_two_pow_sub_one_eq_mod]
 
 @[simp] theorem ofFin_neg {x : Fin (2 ^ w)} : ofFin (-x) = -(ofFin x) := by
   rfl
 
+open Fin.NatCast in
 @[simp, norm_cast] theorem ofFin_natCast (n : Nat) : ofFin (n : Fin (2^w)) = (n : BitVec w) := by
   rfl
 
@@ -337,6 +338,7 @@ theorem toFin_zero : toFin (0 : BitVec w) = 0 := rfl
 theorem toFin_one  : toFin (1 : BitVec w) = 1 := by
   rw [toFin_inj]; simp only [ofNat_eq_ofNat, ofFin_ofNat]
 
+open Fin.NatCast in
 @[simp, norm_cast] theorem toFin_natCast (n : Nat) : toFin (n : BitVec w) = (n : Fin (2^w)) := by
   rfl
 
@@ -346,11 +348,11 @@ theorem toFin_one  : toFin (1 : BitVec w) = 1 := by
 @[simp] theorem toInt_ofBool (b : Bool) : (ofBool b).toInt = -b.toInt := by
   cases b <;> simp
 
-@[simp] theorem toFin_ofBool (b : Bool) : (ofBool b).toFin = Fin.ofNat' 2 (b.toNat) := by
+@[simp] theorem toFin_ofBool (b : Bool) : (ofBool b).toFin = Fin.ofNat 2 (b.toNat) := by
   cases b <;> rfl
 
 theorem ofNat_one (n : Nat) : BitVec.ofNat 1 n = BitVec.ofBool (n % 2 = 1) :=  by
-  rcases (Nat.mod_two_eq_zero_or_one n) with h | h <;> simp [h, BitVec.ofNat, Fin.ofNat']
+  rcases (Nat.mod_two_eq_zero_or_one n) with h | h <;> simp [h, BitVec.ofNat, Fin.ofNat]
 
 theorem ofBool_eq_iff_eq : ∀ {b b' : Bool}, BitVec.ofBool b = BitVec.ofBool b' ↔ b = b' := by
   decide
@@ -390,12 +392,12 @@ theorem getMsbD_ofNatLt {n x i : Nat} (h : x < 2^n) :
     getMsbD (x#'h) i = (decide (i < n) && x.testBit (n - 1 - i)) := getMsbD_ofNatLT h
 
 @[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']
+  simp [BitVec.toNat, BitVec.ofNat, Fin.ofNat]
 
 theorem ofNatLT_eq_ofNat {w : Nat} {n : Nat} (hn) : BitVec.ofNatLT n hn = BitVec.ofNat w n :=
   eq_of_toNat_eq (by simp [Nat.mod_eq_of_lt hn])
 
-@[simp] theorem toFin_ofNat (x : Nat) : toFin (BitVec.ofNat w x) = Fin.ofNat' (2^w) x := rfl
+@[simp] theorem toFin_ofNat (x : Nat) : toFin (BitVec.ofNat w x) = Fin.ofNat (2^w) x := rfl
 
 @[simp] theorem finMk_toNat (x : BitVec w) : Fin.mk x.toNat x.isLt = x.toFin := rfl
 
@@ -415,7 +417,7 @@ theorem ofNatLT_eq_ofNat {w : Nat} {n : Nat} (hn) : BitVec.ofNatLT n hn = BitVec
 -- If `x` and `n` are not literals, applying this theorem eagerly may not be a good idea.
 theorem getLsbD_ofNat (n : Nat) (x : Nat) (i : Nat) :
   getLsbD (BitVec.ofNat n x) i = (i < n && x.testBit i) := by
-  simp [getLsbD, BitVec.ofNat, Fin.val_ofNat']
+  simp [getLsbD, BitVec.ofNat, Fin.val_ofNat]
 
 @[simp] theorem getLsbD_zero : (0#w).getLsbD i = false := by simp [getLsbD]
 
@@ -880,6 +882,19 @@ theorem slt_eq_sle_and_ne {x y : BitVec w} : x.slt y = (x.sle y && x != y) := by
   apply Bool.eq_iff_iff.2
   simp [BitVec.slt, BitVec.sle, Int.lt_iff_le_and_ne, BitVec.toInt_inj]
 
+/-- For all bitvectors `x, y`, either `x` is signed less than `y`,
+or is equal to `y`, or is signed greater than `y`. -/
+theorem slt_trichotomy (x y : BitVec w) : x.slt y ∨ x = y ∨ y.slt x := by
+  simpa [slt_iff_toInt_lt, ← toInt_inj]
+    using Int.lt_trichotomy x.toInt y.toInt
+
+/-- For all bitvectors `x, y`, either `x` is unsigned less than `y`,
+or is equal to `y`, or is unsigned greater than `y`. -/
+theorem lt_trichotomy (x y : BitVec w) :
+    x < y ∨ x = y ∨ y < x := by
+  simpa [← ult_iff_lt, ult_eq_decide, decide_eq_true_eq, ← toNat_inj]
+    using Nat.lt_trichotomy x.toNat y.toNat
+
 /-! ### setWidth, zeroExtend and truncate -/
 
 @[simp]
@@ -909,7 +924,7 @@ theorem zeroExtend_eq_setWidth {v : Nat} {x : BitVec w} :
   simp [toInt_eq_toNat_bmod, toNat_setWidth, Int.emod_bmod, -Int.natCast_pow]
 
 @[simp] theorem toFin_setWidth {x : BitVec w} :
-    (x.setWidth v).toFin = Fin.ofNat' (2^v) x.toNat := by
+    (x.setWidth v).toFin = Fin.ofNat (2^v) x.toNat := by
   ext; simp
 
 @[simp] theorem setWidth_eq (x : BitVec n) : setWidth n x = x := by
@@ -1105,7 +1120,7 @@ theorem toInt_setWidth' {m n : Nat} (p : m ≤ n) {x : BitVec m} :
 @[simp] theorem toFin_setWidth' {m n : Nat} (p : m ≤ n) (x : BitVec m) :
     (setWidth' p x).toFin = x.toFin.castLE (Nat.pow_le_pow_right (by omega) (by omega)) := by
   ext
-  rw [setWidth'_eq, toFin_setWidth, Fin.val_ofNat', Fin.coe_castLE, val_toFin,
+  rw [setWidth'_eq, toFin_setWidth, Fin.val_ofNat, Fin.coe_castLE, val_toFin,
     Nat.mod_eq_of_lt (by apply BitVec.toNat_lt_twoPow_of_le p)]
 
 /-! ## extractLsb -/
@@ -1135,11 +1150,11 @@ protected theorem extractLsb_ofNat (x n : Nat) (hi lo : Nat) :
   simp [extractLsb, toInt_ofNat]
 
 @[simp] theorem toFin_extractLsb' {s m : Nat} {x : BitVec n} :
-    (extractLsb' s m x).toFin = Fin.ofNat' (2 ^ m) (x.toNat >>> s) := by
+    (extractLsb' s m x).toFin = Fin.ofNat (2 ^ m) (x.toNat >>> s) := by
   simp [extractLsb', toInt_ofNat]
 
 @[simp] theorem toFin_extractLsb {hi lo : Nat} {x : BitVec n} :
-  (extractLsb hi lo x).toFin = Fin.ofNat' (2 ^ (hi - lo + 1)) (x.toNat >>> lo) := by
+  (extractLsb hi lo x).toFin = Fin.ofNat (2 ^ (hi - lo + 1)) (x.toNat >>> lo) := by
   simp [extractLsb, toInt_ofNat]
 
 @[simp] theorem getElem_extractLsb' {start len : Nat} {x : BitVec n} {i : Nat} (h : i < len) :
@@ -1310,7 +1325,7 @@ theorem extractLsb'_eq_zero {x : BitVec w} {start : Nat} :
     simp [BitVec.toInt, -Int.natCast_pow]
     omega
 
-@[simp] theorem toFin_allOnes : (allOnes w).toFin = Fin.ofNat' (2^w) (2^w - 1) := by
+@[simp] theorem toFin_allOnes : (allOnes w).toFin = Fin.ofNat (2^w) (2^w - 1) := by
   ext
   simp
 
@@ -1847,7 +1862,7 @@ theorem not_xor_right {x y : BitVec w} : ~~~ (x ^^^ y) = x ^^^ ~~~ y := by
   simp [-Int.natCast_pow]
 
 @[simp] theorem toFin_shiftLeft {n : Nat} (x : BitVec w) :
-    (x <<< n).toFin = Fin.ofNat' (2^w) (x.toNat <<< n) := rfl
+    (x <<< n).toFin = Fin.ofNat (2^w) (x.toNat <<< n) := rfl
 
 @[simp]
 theorem shiftLeft_zero (x : BitVec w) : x <<< 0 = x := by
@@ -2089,7 +2104,7 @@ theorem toInt_ushiftRight {x : BitVec w} {n : Nat} :
 
 @[simp]
 theorem toFin_ushiftRight {x : BitVec w} {n : Nat} :
-    (x >>> n).toFin = x.toFin / (Fin.ofNat' (2^w) (2^n)) := by
+    (x >>> n).toFin = x.toFin / (Fin.ofNat (2^w) (2^n)) := by
   apply Fin.eq_of_val_eq
   by_cases hn : n < w
   · simp [Nat.shiftRight_eq_div_pow, Nat.mod_eq_of_lt (Nat.pow_lt_pow_of_lt Nat.one_lt_two hn)]
@@ -2340,26 +2355,26 @@ theorem toNat_sshiftRight {x : BitVec w} {n : Nat} :
     simp [toNat_sshiftRight_of_msb_false, h]
 
 theorem toFin_sshiftRight_of_msb_true {x : BitVec w} {n : Nat} (h : x.msb = true) :
-    (x.sshiftRight n).toFin = Fin.ofNat' (2^w) (2 ^ w - 1 - (2 ^ w - 1 - x.toNat) >>> n) := by
+    (x.sshiftRight n).toFin = Fin.ofNat (2^w) (2 ^ w - 1 - (2 ^ w - 1 - x.toNat) >>> n) := by
   apply Fin.eq_of_val_eq
-  simp only [val_toFin, toNat_sshiftRight, h, ↓reduceIte, Fin.val_ofNat']
+  simp only [val_toFin, toNat_sshiftRight, h, ↓reduceIte, Fin.val_ofNat]
   rw [Nat.mod_eq_of_lt]
   have := x.isLt
   have ineq : ∀ y, 2 ^ w - 1 - y < 2 ^ w := by omega
   exact ineq ((2 ^ w - 1 - x.toNat) >>> n)
 
 theorem toFin_sshiftRight_of_msb_false {x : BitVec w} {n : Nat} (h : x.msb = false) :
-    (x.sshiftRight n).toFin = Fin.ofNat' (2^w) (x.toNat >>> n) := by
+    (x.sshiftRight n).toFin = Fin.ofNat (2^w) (x.toNat >>> n) := by
   apply Fin.eq_of_val_eq
-  simp only [val_toFin, toNat_sshiftRight, h, Bool.false_eq_true, ↓reduceIte, Fin.val_ofNat']
+  simp only [val_toFin, toNat_sshiftRight, h, Bool.false_eq_true, ↓reduceIte, Fin.val_ofNat]
   have := Nat.shiftRight_le x.toNat n
   rw [Nat.mod_eq_of_lt (by omega)]
 
 theorem toFin_sshiftRight {x : BitVec w} {n : Nat} :
     (x.sshiftRight n).toFin =
       if x.msb
-      then Fin.ofNat' (2^w) (2 ^ w - 1 - (2 ^ w - 1 - x.toNat) >>> n)
-      else Fin.ofNat' (2^w) (x.toNat >>> n) := by
+      then Fin.ofNat (2^w) (2 ^ w - 1 - (2 ^ w - 1 - x.toNat) >>> n)
+      else Fin.ofNat (2^w) (x.toNat >>> n) := by
   by_cases h : x.msb
   · simp [toFin_sshiftRight_of_msb_true, h]
   · simp [toFin_sshiftRight_of_msb_false, h]
@@ -2397,18 +2412,18 @@ theorem toNat_sshiftRight' {x y : BitVec w} :
   rw [sshiftRight_eq', toNat_sshiftRight]
 
 theorem toFin_sshiftRight'_of_msb_true {x y : BitVec w} (h : x.msb = true) :
-    (x.sshiftRight' y).toFin = Fin.ofNat' (2^w) (2 ^ w - 1 - (2 ^ w - 1 - x.toNat) >>> y.toNat) := by
+    (x.sshiftRight' y).toFin = Fin.ofNat (2^w) (2 ^ w - 1 - (2 ^ w - 1 - x.toNat) >>> y.toNat) := by
   rw [sshiftRight_eq', toFin_sshiftRight_of_msb_true h]
 
 theorem toFin_sshiftRight'_of_msb_false {x y : BitVec w} (h : x.msb = false) :
-    (x.sshiftRight' y).toFin = Fin.ofNat' (2^w) (x.toNat >>> y.toNat) := by
+    (x.sshiftRight' y).toFin = Fin.ofNat (2^w) (x.toNat >>> y.toNat) := by
   rw [sshiftRight_eq', toFin_sshiftRight_of_msb_false h]
 
 theorem toFin_sshiftRight' {x y : BitVec w} :
     (x.sshiftRight' y).toFin =
       if x.msb
-      then Fin.ofNat' (2^w) (2 ^ w - 1 - (2 ^ w - 1 - x.toNat) >>> y.toNat)
-      else Fin.ofNat' (2^w) (x.toNat >>> y.toNat) := by
+      then Fin.ofNat (2^w) (2 ^ w - 1 - (2 ^ w - 1 - x.toNat) >>> y.toNat)
+      else Fin.ofNat (2^w) (x.toNat >>> y.toNat) := by
   rw [sshiftRight_eq', toFin_sshiftRight]
 
 theorem toInt_sshiftRight' {x y : BitVec w} :
@@ -2614,16 +2629,16 @@ theorem toInt_signExtend_eq_toInt_bmod_of_le (x : BitVec w) (h : v ≤ w) :
   rw [BitVec.toInt_signExtend, Nat.min_eq_left h]
 
 theorem toFin_signExtend_of_le {x : BitVec w} (hv : v ≤ w):
-    (x.signExtend v).toFin = Fin.ofNat' (2 ^ v) x.toNat := by
+    (x.signExtend v).toFin = Fin.ofNat (2 ^ v) x.toNat := by
   simp [signExtend_eq_setWidth_of_le _ hv]
 
 theorem toFin_signExtend (x : BitVec w) :
-    (x.signExtend v).toFin = Fin.ofNat' (2 ^ v) (x.toNat + if x.msb = true then 2 ^ v - 2 ^ w else 0):= by
+    (x.signExtend v).toFin = Fin.ofNat (2 ^ v) (x.toNat + if x.msb = true then 2 ^ v - 2 ^ w else 0):= by
   by_cases hv : v ≤ w
   · simp [toFin_signExtend_of_le hv, show 2 ^ v - 2 ^ w = 0 by rw [@Nat.sub_eq_zero_iff_le]; apply Nat.pow_le_pow_of_le (by decide) (by omega)]
   · simp only [Nat.not_le] at hv
     apply Fin.eq_of_val_eq
-    simp only [val_toFin, Fin.val_ofNat']
+    simp only [val_toFin, Fin.val_ofNat]
     rw [toNat_signExtend_of_le _ (by omega)]
     have : 2 ^ w < 2 ^ v := by apply Nat.pow_lt_pow_of_lt <;> omega
     rw [Nat.mod_eq_of_lt]
@@ -2974,7 +2989,7 @@ theorem extractLsb'_append_eq_ite {v w} {xhi : BitVec v} {xlo : BitVec w} {start
     extractLsb' start len (xhi ++ xlo) =
     if hstart : start < w
     then
-      if hlen : start + len < w
+      if hlen : start + len ≤ w
       then extractLsb' start len xlo
       else
         (((extractLsb' (start - w) (len - (w - start)) xhi) ++
@@ -2983,7 +2998,7 @@ theorem extractLsb'_append_eq_ite {v w} {xhi : BitVec v} {xlo : BitVec w} {start
       extractLsb' (start - w) len xhi := by
   by_cases hstart : start < w
   · simp only [hstart, ↓reduceDIte]
-    by_cases hlen : start + len < w
+    by_cases hlen : start + len ≤ w
     · simp only [hlen, ↓reduceDIte]
       ext i hi
       simp only [getElem_extractLsb', getLsbD_append, ite_eq_left_iff, Nat.not_lt]
@@ -3006,11 +3021,14 @@ theorem extractLsb'_append_eq_ite {v w} {xhi : BitVec v} {xlo : BitVec w} {start
 /-- Extracting bits `[start..start+len)` from `(xhi ++ xlo)` equals extracting
 the bits from `xlo` when `start + len` is within `xlo`.
 -/
-theorem extractLsb'_append_eq_of_lt {v w} {xhi : BitVec v} {xlo : BitVec w}
-    {start len : Nat} (h : start + len < w) :
+theorem extractLsb'_append_eq_of_add_le {v w} {xhi : BitVec v} {xlo : BitVec w}
+    {start len : Nat} (h : start + len ≤ w) :
     extractLsb' start len (xhi ++ xlo) = extractLsb' start len xlo := by
-  simp [extractLsb'_append_eq_ite, h]
-  omega
+  simp only [extractLsb'_append_eq_ite, h, ↓reduceDIte, dite_eq_ite, ite_eq_left_iff, Nat.not_lt]
+  intro h'
+  have : len = 0 := by omega
+  subst this
+  simp
 
 /-- Extracting bits `[start..start+len)` from `(xhi ++ xlo)` equals extracting
 the bits from `xhi` when `start` is outside `xlo`.
@@ -3179,7 +3197,7 @@ theorem getElem_concat (x : BitVec w) (b : Bool) (i : Nat) (h : i < w + 1) :
   · simp [Nat.mod_eq_of_lt b.toNat_lt]
   · simp [Nat.div_eq_of_lt b.toNat_lt, Nat.testBit_add_one]
 
-@[simp] theorem getElem_concat_zero : (concat x b)[0] = b := by
+@[simp] theorem getElem_concat_zero {x : BitVec w} : (concat x b)[0] = b := by
   simp [getElem_concat]
 
 theorem getLsbD_concat_zero : (concat x b).getLsbD 0 = b := by
@@ -3323,11 +3341,19 @@ Definition of bitvector addition as a nat.
 
 theorem ofNat_add {n} (x y : Nat) : BitVec.ofNat n (x + y) = BitVec.ofNat n x + BitVec.ofNat n y := by
   apply eq_of_toNat_eq
-  simp [BitVec.ofNat, Fin.ofNat'_add]
+  simp [BitVec.ofNat, Fin.ofNat_add]
 
 theorem ofNat_add_ofNat {n} (x y : Nat) : BitVec.ofNat n x + BitVec.ofNat n y = BitVec.ofNat n (x + y) :=
   (ofNat_add x y).symm
 
+@[simp]
+theorem toNat_add_of_not_uaddOverflow {x y : BitVec w} (h : ¬ uaddOverflow x y) :
+    (x + y).toNat = x.toNat + y.toNat := by
+  rcases w with _|w
+  · simp [of_length_zero]
+  · simp only [uaddOverflow, ge_iff_le, decide_eq_true_eq, Nat.not_le] at h
+    rw [toNat_add, Nat.mod_eq_of_lt h]
+
 protected theorem add_assoc (x y z : BitVec n) : x + y + z = x + (y + z) := by
   apply eq_of_toNat_eq ; simp [Nat.add_assoc]
 instance : Std.Associative (α := BitVec n) (· + ·) := ⟨BitVec.add_assoc⟩
@@ -3357,6 +3383,15 @@ theorem ofInt_add {n} (x y : Int) : BitVec.ofInt n (x + y) =
   apply eq_of_toInt_eq
   simp
 
+@[simp]
+theorem toInt_add_of_not_saddOverflow {x y : BitVec w} (h : ¬ saddOverflow x y) :
+    (x + y).toInt = x.toInt + y.toInt := by
+  rcases w with _|w
+  · simp [of_length_zero]
+  · simp only [saddOverflow, Nat.add_one_sub_one, ge_iff_le, Bool.or_eq_true, decide_eq_true_eq,
+      _root_.not_or, Int.not_le, Int.not_lt] at h
+    rw [toInt_add, Int.bmod_eq_of_le (by push_cast; omega) (by push_cast; omega)]
+
 @[simp]
 theorem shiftLeft_add_distrib {x y : BitVec w} {n : Nat} :
     (x + y) <<< n = x <<< n + y <<< n := by
@@ -3382,6 +3417,24 @@ theorem sub_def {n} (x y : BitVec n) : x - y = .ofNat n ((2^n - y.toNat) + x.toN
     (x - y).toInt = (x.toInt - y.toInt).bmod (2 ^ w) := by
   simp [toInt_eq_toNat_bmod, @Int.ofNat_sub y.toNat (2 ^ w) (by omega), -Int.natCast_pow]
 
+@[simp]
+theorem toNat_sub_of_not_usubOverflow {x y : BitVec w} (h : ¬ usubOverflow x y) :
+    (x - y).toNat = x.toNat - y.toNat := by
+  rcases w with _|w
+  · simp [of_length_zero]
+  · simp only [usubOverflow, decide_eq_true_eq, Nat.not_lt] at h
+    rw [toNat_sub, ← Nat.sub_add_comm (by omega), Nat.add_sub_assoc h, Nat.add_mod_left,
+      Nat.mod_eq_of_lt (by omega)]
+
+@[simp]
+theorem toInt_sub_of_not_ssubOverflow {x y : BitVec w} (h : ¬ ssubOverflow x y) :
+    (x - y).toInt = x.toInt - y.toInt := by
+  rcases w with _|w
+  · simp [of_length_zero]
+  · simp only [ssubOverflow, Nat.add_one_sub_one, ge_iff_le, Bool.or_eq_true, decide_eq_true_eq,
+      _root_.not_or, Int.not_le, Int.not_lt] at h
+    rw [toInt_sub, Int.bmod_eq_of_le (by push_cast; omega) (by push_cast; omega)]
+
 theorem toInt_sub_toInt_lt_twoPow_iff {x y : BitVec w} :
     (x.toInt - y.toInt < - 2 ^ (w - 1))
     ↔ (x.toInt < 0 ∧ 0 ≤ y.toInt ∧ 0 ≤ (x.toInt - y.toInt).bmod (2 ^ w)) := by
@@ -3433,7 +3486,7 @@ theorem sub_ofFin (x : BitVec n) (y : Fin (2^n)) : x - .ofFin y = .ofFin (x.toFi
 -- If `x` and `n` are not literals, applying this theorem eagerly may not be a good idea.
 theorem ofNat_sub_ofNat {n} (x y : Nat) : BitVec.ofNat n x - BitVec.ofNat n y = .ofNat n ((2^n - y % 2^n) + x) := by
   apply eq_of_toNat_eq
-  simp [BitVec.ofNat, Fin.ofNat'_sub]
+  simp [BitVec.ofNat, Fin.ofNat_sub]
 
 @[simp] protected theorem sub_zero (x : BitVec n) : x - 0#n = x := by apply eq_of_toNat_eq ; simp
 
@@ -3460,11 +3513,21 @@ theorem toInt_neg {x : BitVec w} :
   rw [← BitVec.zero_sub, toInt_sub]
   simp [BitVec.toInt_ofNat]
 
+@[simp]
+theorem toInt_neg_of_not_negOverflow {x : BitVec w} (h : ¬ negOverflow x):
+    (-x).toInt = -x.toInt := by
+  rcases w with _|w
+  · simp [of_length_zero]
+  · have := toInt_lt (x := x); simp only [Nat.add_one_sub_one] at this
+    have := le_toInt (x := x); simp only [Nat.add_one_sub_one] at this
+    simp only [negOverflow, Nat.add_one_sub_one, beq_iff_eq] at h
+    rw [toInt_neg, Int.bmod_eq_of_le (by push_cast; omega) (by push_cast; omega)]
+
 theorem ofInt_neg {w : Nat} {n : Int} : BitVec.ofInt w (-n) = -BitVec.ofInt w n :=
   eq_of_toInt_eq (by simp [toInt_neg])
 
 @[simp] theorem toFin_neg (x : BitVec n) :
-    (-x).toFin = Fin.ofNat' (2^n) (2^n - x.toNat) :=
+    (-x).toFin = Fin.ofNat (2^n) (2^n - x.toNat) :=
   rfl
 
 theorem sub_eq_add_neg {n} (x y : BitVec n) : x - y = x + - y := by
@@ -3679,7 +3742,7 @@ theorem fill_false {w : Nat} : fill w false = 0#w := by
   by_cases h : v <;> simp [h]
 
 @[simp] theorem fill_toFin {w : Nat} {v : Bool} :
-    (fill w v).toFin = if v = true then (allOnes w).toFin else Fin.ofNat' (2 ^ w) 0 := by
+    (fill w v).toFin = if v = true then (allOnes w).toFin else Fin.ofNat (2 ^ w) 0 := by
   by_cases h : v <;> simp [h]
 
 /-! ### mul -/
@@ -3691,7 +3754,7 @@ theorem mul_def {n} {x y : BitVec n} : x * y = (ofFin <| x.toFin * y.toFin) := r
 
 theorem ofNat_mul {n} (x y : Nat) : BitVec.ofNat n (x * y) = BitVec.ofNat n x * BitVec.ofNat n y := by
   apply eq_of_toNat_eq
-  simp [BitVec.ofNat, Fin.ofNat'_mul]
+  simp [BitVec.ofNat, Fin.ofNat_mul]
 
 theorem ofNat_mul_ofNat {n} (x y : Nat) : BitVec.ofNat n x * BitVec.ofNat n y = BitVec.ofNat n (x * y) :=
   (ofNat_mul x y).symm
@@ -3749,6 +3812,23 @@ theorem two_mul {x : BitVec w} : 2#w * x = x + x := by rw [BitVec.mul_comm, mul_
   (x * y).toInt = (x.toInt * y.toInt).bmod (2^w) := by
   simp [toInt_eq_toNat_bmod, -Int.natCast_pow]
 
+@[simp]
+theorem toNat_mul_of_not_umulOverflow {x y : BitVec w} (h : ¬ umulOverflow x y) :
+    (x * y).toNat = x.toNat * y.toNat := by
+  rcases w with _|w
+  · simp [of_length_zero]
+  · simp only [umulOverflow, ge_iff_le, decide_eq_true_eq, Nat.not_le] at h
+    rw [toNat_mul, Nat.mod_eq_of_lt h]
+
+@[simp]
+theorem toInt_mul_of_not_smulOverflow {x y : BitVec w} (h : ¬ smulOverflow x y) :
+    (x * y).toInt = x.toInt * y.toInt := by
+  rcases w with _|w
+  · simp [of_length_zero]
+  · simp only [smulOverflow, Nat.add_one_sub_one, ge_iff_le, Bool.or_eq_true, decide_eq_true_eq,
+      _root_.not_or, Int.not_le, Int.not_lt] at h
+    rw [toInt_mul, Int.bmod_eq_of_le (by push_cast; omega) (by push_cast; omega)]
+
 theorem ofInt_mul {n} (x y : Int) : BitVec.ofInt n (x * y) =
     BitVec.ofInt n x * BitVec.ofInt n y := by
   apply eq_of_toInt_eq
@@ -3933,6 +4013,15 @@ theorem pos_of_msb {x : BitVec w} (hx : x.msb = true) : 0#w < x := by
   rw [BitVec.not_lt, le_zero_iff] at h
   simp [h] at hx
 
+@[simp]
+theorem lt_of_msb_false_of_msb_true {x y : BitVec w} (hx : x.msb = false) (hy : y.msb = true) :
+    x < y := by
+  simp only [LT.lt]
+  have := toNat_ge_of_msb_true hy
+  have := toNat_lt_of_msb_false hx
+  simp
+  omega
+
 /-! ### udiv -/
 
 theorem udiv_def {x y : BitVec n} : x / y = BitVec.ofNat n (x.toNat / y.toNat) := by
@@ -4114,6 +4203,14 @@ theorem toInt_umod_of_msb {x y : BitVec w} (h : x.msb = false) :
     (x % y).toInt = x.toInt % y.toNat := by
   simp [toInt_eq_msb_cond, h]
 
+@[simp]
+theorem msb_umod_of_msb_false_of_ne_zero {x y : BitVec w} (hmsb : y.msb = false) (h_ne_zero : y ≠ 0#w) :
+    (x % y).msb = false := by
+  simp only [msb_umod, Bool.and_eq_false_imp, Bool.or_eq_false_iff, beq_eq_false_iff_ne,
+    ne_eq, h_ne_zero]
+  intro h
+  simp [BitVec.le_of_lt, lt_of_msb_false_of_msb_true hmsb h]
+
 /-! ### smtUDiv -/
 
 theorem smtUDiv_eq (x y : BitVec w) : smtUDiv x y = if y = 0#w then allOnes w else x / y := by
@@ -4562,7 +4659,7 @@ theorem toInt_rotateLeft {x : BitVec w} {r : Nat} :
 
 theorem toFin_rotateLeft {x : BitVec w} {r : Nat} :
   (x.rotateLeft r).toFin =
-    Fin.ofNat' (2 ^ w) (x.toNat <<< (r % w)) ||| x.toFin / Fin.ofNat' (2 ^ w) (2 ^ (w - r % w)) := by
+    Fin.ofNat (2 ^ w) (x.toNat <<< (r % w)) ||| x.toFin / Fin.ofNat (2 ^ w) (2 ^ (w - r % w)) := by
   simp [rotateLeft_def, toFin_shiftLeft, toFin_ushiftRight, toFin_or]
 
 /-! ## Rotate Right -/
@@ -4724,7 +4821,7 @@ theorem toInt_rotateRight {x : BitVec w} {r : Nat} :
   simp [rotateRight_def, toInt_shiftLeft, toInt_ushiftRight, toInt_or]
 
 theorem toFin_rotateRight {x : BitVec w} {r : Nat} :
-    (x.rotateRight r).toFin = x.toFin / Fin.ofNat' (2 ^ w) (2 ^ (r % w)) ||| Fin.ofNat' (2 ^ w) (x.toNat <<< (w - r % w)) := by
+    (x.rotateRight r).toFin = x.toFin / Fin.ofNat (2 ^ w) (2 ^ (r % w)) ||| Fin.ofNat (2 ^ w) (x.toNat <<< (w - r % w)) := by
   simp [rotateRight_def, toFin_shiftLeft, toFin_ushiftRight, toFin_or]
 
 /- ## twoPow -/
@@ -4796,7 +4893,7 @@ theorem toInt_twoPow {w i : Nat} :
       · simp [h, h', show i < w + 1 by omega, Int.natCast_pow]
 
 theorem toFin_twoPow {w i : Nat} :
-    (BitVec.twoPow w i).toFin = Fin.ofNat' (2^w) (2^i) := by
+    (BitVec.twoPow w i).toFin = Fin.ofNat (2^w) (2^i) := by
   rcases w with rfl | w
   · simp [BitVec.twoPow, BitVec.toFin, toFin_shiftLeft, Fin.fin_one_eq_zero]
   · simp [BitVec.twoPow, BitVec.toFin, toFin_shiftLeft, Nat.shiftLeft_eq]
@@ -5348,6 +5445,27 @@ theorem neg_ofNat_eq_ofInt_neg {w : Nat} {x : Nat} :
   apply BitVec.eq_of_toInt_eq
   simp [BitVec.toInt_neg, BitVec.toInt_ofNat]
 
+@[simp]
+theorem neg_toInt_neg {x : BitVec w} (h : x.msb = false) :
+    -(-x).toInt = x.toNat := by
+  simp [toInt_neg_eq_of_msb h, toInt_eq_toNat_of_msb, h]
+
+theorem toNat_pos_of_ne_zero {x : BitVec w} (hx : x ≠ 0#w) :
+    0 < x.toNat := by
+  simp [toNat_eq] at hx; omega
+
+theorem toNat_neg_lt_of_msb (x : BitVec w) (hmsb : x.msb = true) :
+    (-x).toNat ≤ 2^(w-1) := by
+  rcases w with _|w
+  · simp [BitVec.eq_nil x]
+  · by_cases hx : x = 0#(w + 1)
+    · simp [hx]
+    · have := BitVec.le_toNat_of_msb_true hmsb
+      have := toNat_pos_of_ne_zero hx
+      rw [toNat_neg, Nat.mod_eq_of_lt (by omega), ← Nat.two_pow_pred_add_two_pow_pred (by omega),
+        ← Nat.two_mul]
+      omega
+
 /-! ### abs -/
 
 theorem abs_eq (x : BitVec w) : x.abs = if x.msb then -x else x := rfl
@@ -5440,7 +5558,7 @@ theorem toInt_abs_eq_natAbs_of_ne_intMin {x : BitVec w} (hx : x ≠ intMin w) :
   simp [toInt_abs_eq_natAbs, hx]
 
 theorem toFin_abs {x : BitVec w} :
-    x.abs.toFin = if x.msb then Fin.ofNat' (2 ^ w) (2 ^ w - x.toNat) else x.toFin := by
+    x.abs.toFin = if x.msb then Fin.ofNat (2 ^ w) (2 ^ w - x.toNat) else x.toFin := by
   by_cases h : x.msb <;> simp [BitVec.abs, h]
 
 /-! ### Reverse -/

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
 

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 ..

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 -/
 
@@ -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

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/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/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
@@ -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]
@@ -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
@@ -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

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

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")]

src/Init/Data/Int/Linear.lean

@@ -1665,7 +1665,7 @@ 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

src/Init/Data/Int/Order.lean

@@ -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/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) :
@@ -675,6 +676,7 @@ 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

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
@@ -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 -/
 
@@ -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? -/
@@ -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
 
@@ -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' -/
 

src/Init/Data/List/BasicAux.lean

@@ -27,7 +27,7 @@ Returns the `i`-th element in the list (zero-based).
 If the index is out of bounds (`i ≥ as.length`), this function returns `none`.
 Also see `get`, `getD` and `get!`.
 -/
-@[deprecated "Use `a[i]?` instead." (since := "2025-02-12")]
+@[deprecated "Use `a[i]?` instead." (since := "2025-02-12"), expose]
 def get? : (as : List α) → (i : Nat) → Option α
   | a::_,  0   => some a
   | _::as, n+1 => get? as n
@@ -61,7 +61,7 @@ Returns the `i`-th element in the list (zero-based).
 If the index is out of bounds (`i ≥ as.length`), this function panics when executed, and returns
 `default`. See `get?` and `getD` for safer alternatives.
 -/
-@[deprecated "Use `a[i]!` instead." (since := "2025-02-12")]
+@[deprecated "Use `a[i]!` instead." (since := "2025-02-12"), expose]
 def get! [Inhabited α] : (as : List α) → (i : Nat) → α
   | a::_,  0   => a
   | _::as, n+1 => get! as n
@@ -92,7 +92,7 @@ Examples:
  * `["spring", "summer", "fall", "winter"].getD 0 "never" = "spring"`
  * `["spring", "summer", "fall", "winter"].getD 4 "never" = "never"`
 -/
-def getD (as : List α) (i : Nat) (fallback : α) : α :=
+@[expose] def getD (as : List α) (i : Nat) (fallback : α) : α :=
   as[i]?.getD fallback
 
 @[simp] theorem getD_nil : getD [] n d = d := rfl
@@ -111,6 +111,7 @@ Examples:
  * `["circle", "rectangle"].getLast! = "rectangle"`
  * `["circle"].getLast! = "circle"`
 -/
+@[expose]
 def getLast! [Inhabited α] : List α → α
   | []    => panic! "empty list"
   | a::as => getLast (a::as) (fun h => List.noConfusion h)
@@ -146,7 +147,7 @@ Examples:
  * `["apple", "banana", "grape"].tail! = ["banana", "grape"]`
  * `["banana", "grape"].tail! = ["grape"]`
 -/
-def tail! : List α → List α
+@[expose] def tail! : List α → List α
   | []    => panic! "empty list"
   | _::as => as
 

src/Init/Data/List/Control.lean

@@ -54,7 +54,7 @@ This implementation is tail recursive. `List.mapM'` is a a non-tail-recursive va
 more convenient to reason about. `List.forM` is the variant that discards the results and
 `List.mapA` is the variant that works with `Applicative`.
 -/
-@[inline]
+@[inline, expose]
 def mapM {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f : α → m β) (as : List α) : m (List β) :=
   let rec @[specialize] loop
     | [],      bs => pure bs.reverse
@@ -83,7 +83,7 @@ Applies the monadic action `f` to every element in the list, in order.
 `List.mapM` is a variant that collects results. `List.forA` is a variant that works on any
 `Applicative`.
 -/
-@[specialize]
+@[specialize, expose]
 protected def forM {m : Type u → Type v} [Monad m] {α : Type w} (as : List α) (f : α → m PUnit) : m PUnit :=
   match as with
   | []      => pure ⟨⟩
@@ -191,7 +191,7 @@ Examining 7
 [10, 14, 14]
 ```
 -/
-@[inline]
+@[inline, expose]
 def filterMapM {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f : α → m (Option β)) (as : List α) : m (List β) :=
   let rec @[specialize] loop
     | [],     bs => pure bs.reverse
@@ -205,7 +205,7 @@ def filterMapM {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f
 Applies a monadic function that returns a list to each element of a list, from left to right, and
 concatenates the resulting lists.
 -/
-@[inline]
+@[inline, expose]
 def flatMapM {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f : α → m (List β)) (as : List α) : m (List β) :=
   let rec @[specialize] loop
     | [],     bs => pure bs.reverse.flatten
@@ -230,7 +230,7 @@ example [Monad m] (f : α → β → m α) :
   := by rfl
 ```
 -/
-@[specialize]
+@[specialize, expose]
 def foldlM {m : Type u → Type v} [Monad m] {s : Type u} {α : Type w} : (f : s → α → m s) → (init : s) → List α → m s
   | _, s, []      => pure s
   | f, s, a :: as => do
@@ -257,7 +257,7 @@ example [Monad m] (f : α → β → m β) :
   := by rfl
 ```
 -/
-@[inline]
+@[inline, expose]
 def foldrM {m : Type u → Type v} [Monad m] {s : Type u} {α : Type w} (f : α → s → m s) (init : s) (l : List α) : m s :=
   l.reverse.foldlM (fun s a => f a s) init
 
@@ -422,7 +422,7 @@ theorem findM?_eq_findSomeM? [Monad m] [LawfulMonad m] {p : α → m Bool} {as :
     intro b
     cases b <;> simp
 
-@[inline] protected def forIn' {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : List α) (init : β) (f : (a : α) → a ∈ as → β → m (ForInStep β)) : m β :=
+@[inline, expose] protected def forIn' {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : List α) (init : β) (f : (a : α) → a ∈ as → β → m (ForInStep β)) : m β :=
   let rec @[specialize] loop : (as' : List α) → (b : β) → Exists (fun bs => bs ++ as' = as) → m β
     | [], b, _    => pure b
     | a::as', b, h => do

src/Init/Data/List/Count.lean

@@ -10,6 +10,9 @@ import Init.Data.List.Sublist
 
 /-!
 # Lemmas about `List.countP` and `List.count`.
+
+Because we mark `countP_eq_length_filter` and `count_eq_countP` with `@[grind _=_]`,
+we don't need many other `@[grind]` annotations here.
 -/
 
 set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
@@ -61,6 +64,7 @@ theorem length_eq_countP_add_countP (p : α → Bool) {l : List α} : length l =
       · rfl
       · simp [h]
 
+@[grind =]
 theorem countP_eq_length_filter {l : List α} : countP p l = length (filter p l) := by
   induction l with
   | nil => rfl
@@ -69,6 +73,7 @@ theorem countP_eq_length_filter {l : List α} : countP p l = length (filter p l)
     then rw [countP_cons_of_pos h, ih, filter_cons_of_pos h, length]
     else rw [countP_cons_of_neg h, ih, filter_cons_of_neg h]
 
+@[grind =]
 theorem countP_eq_length_filter' : countP p = length ∘ filter p := by
   funext l
   apply countP_eq_length_filter
@@ -97,6 +102,7 @@ theorem countP_replicate {p : α → Bool} {a : α} {n : Nat} :
   simp only [countP_eq_length_filter, filter_replicate]
   split <;> simp
 
+@[grind]
 theorem boole_getElem_le_countP {p : α → Bool} {l : List α} {i : Nat} (h : i < l.length) :
     (if p l[i] then 1 else 0) ≤ l.countP p := by
   induction l generalizing i with
@@ -120,6 +126,7 @@ theorem IsInfix.countP_le (s : l₁ <:+: l₂) : countP p l₁ ≤ countP p l₂
 
 -- See `Init.Data.List.Nat.Count` for `Sublist.le_countP : countP p l₂ - (l₂.length - l₁.length) ≤ countP p l₁`.
 
+@[grind]
 theorem countP_tail_le (l) : countP p l.tail ≤ countP p l :=
   (tail_sublist l).countP_le
 
@@ -198,18 +205,21 @@ variable [BEq α]
 
 @[simp] theorem count_nil {a : α} : count a [] = 0 := rfl
 
+@[grind]
 theorem count_cons {a b : α} {l : List α} :
     count a (b :: l) = count a l + if b == a then 1 else 0 := by
   simp [count, countP_cons]
 
-theorem count_eq_countP {a : α} {l : List α} : count a l = countP (· == a) l := rfl
+@[grind =] theorem count_eq_countP {a : α} {l : List α} : count a l = countP (· == a) l := rfl
 theorem count_eq_countP' {a : α} : count a = countP (· == a) := by
   funext l
   apply count_eq_countP
 
-theorem count_tail : ∀ {l : List α} (h : l ≠ []) (a : α),
-      l.tail.count a = l.count a - if l.head h == a then 1 else 0
-  | _ :: _, a, _ => by simp [count_cons]
+@[grind]
+theorem count_tail : ∀ {l : List α} {a : α},
+      l.tail.count a = l.count a - if l.head? == some a then 1 else 0
+  | [], a => by simp
+  | _ :: _, a => by simp [count_cons]
 
 theorem count_le_length {a : α} {l : List α} : count a l ≤ l.length := countP_le_length
 
@@ -232,7 +242,7 @@ theorem count_le_count_cons {a b : α} {l : List α} : count a l ≤ count a (b
 theorem count_singleton {a b : α} : count a [b] = if b == a then 1 else 0 := by
   simp [count_cons]
 
-@[simp] theorem count_append {a : α} {l₁ l₂ : List α} : count a (l₁ ++ l₂) = count a l₁ + count a l₂ :=
+@[simp, grind =] theorem count_append {a : α} {l₁ l₂ : List α} : count a (l₁ ++ l₂) = count a l₁ + count a l₂ :=
   countP_append
 
 theorem count_flatten {a : α} {l : List (List α)} : count a l.flatten = (l.map (count a)).sum := by
@@ -241,6 +251,7 @@ theorem count_flatten {a : α} {l : List (List α)} : count a l.flatten = (l.map
 @[simp] theorem count_reverse {a : α} {l : List α} : count a l.reverse = count a l := by
   simp only [count_eq_countP, countP_eq_length_filter, filter_reverse, length_reverse]
 
+@[grind]
 theorem boole_getElem_le_count {a : α} {l : List α} {i : Nat} (h : i < l.length) :
     (if l[i] == a then 1 else 0) ≤ l.count a := by
   rw [count_eq_countP]
@@ -283,7 +294,7 @@ theorem count_eq_length {l : List α} : count a l = l.length ↔ ∀ b ∈ l, a
 @[simp] theorem count_replicate_self {a : α} {n : Nat} : count a (replicate n a) = n :=
   (count_eq_length.2 <| fun _ h => (eq_of_mem_replicate h).symm).trans (length_replicate ..)
 
-theorem count_replicate {a b : α} {n : Nat} : count a (replicate n b) = if b == a then n else 0 := by
+@[grind =] theorem count_replicate {a b : α} {n : Nat} : count a (replicate n b) = if b == a then n else 0 := by
   split <;> (rename_i h; simp only [beq_iff_eq] at h)
   · exact ‹b = a› ▸ count_replicate_self ..
   · exact count_eq_zero.2 <| mt eq_of_mem_replicate (Ne.symm h)
@@ -295,14 +306,18 @@ theorem filter_beq {l : List α} (a : α) : l.filter (· == a) = replicate (coun
 theorem filter_eq [DecidableEq α] {l : List α} (a : α) : l.filter (· = a) = replicate (count a l) a :=
   funext (Bool.beq_eq_decide_eq · a) ▸ filter_beq a
 
-theorem le_count_iff_replicate_sublist {l : List α} : n ≤ count a l ↔ replicate n a <+ l := by
+@[grind =] theorem replicate_sublist_iff {l : List α} : replicate n a <+ l ↔ n ≤ count a l := by
   refine ⟨fun h => ?_, fun h => ?_⟩
-  · exact ((replicate_sublist_replicate a).2 h).trans <| filter_beq a ▸ filter_sublist
   · simpa only [count_replicate_self] using h.count_le a
+  · exact ((replicate_sublist_replicate a).2 h).trans <| filter_beq a ▸ filter_sublist
+
+@[deprecated replicate_sublist_iff (since := "2025-05-26")]
+theorem le_count_iff_replicate_sublist {l : List α} : n ≤ count a l ↔ replicate n a <+ l :=
+  replicate_sublist_iff.symm
 
 theorem replicate_count_eq_of_count_eq_length {l : List α} (h : count a l = length l) :
     replicate (count a l) a = l :=
-  (le_count_iff_replicate_sublist.mp (Nat.le_refl _)).eq_of_length <| length_replicate.trans h
+  (replicate_sublist_iff.mpr (Nat.le_refl _)).eq_of_length <| length_replicate.trans h
 
 @[simp] theorem count_filter {l : List α} (h : p a) : count a (filter p l) = count a l := by
   rw [count, countP_filter]; congr; funext b
@@ -325,6 +340,7 @@ theorem count_filterMap {α} [BEq β] {b : β} {f : α → Option β} {l : List
 theorem count_flatMap {α} [BEq β] {l : List α} {f : α → List β} {x : β} :
     count x (l.flatMap f) = sum (map (count x ∘ f) l) := countP_flatMap
 
+@[grind]
 theorem count_erase {a b : α} :
     ∀ {l : List α}, count a (l.erase b) = count a l - if b == a then 1 else 0
   | [] => by simp

src/Init/Data/List/Erase.lean

@@ -23,9 +23,9 @@ open Nat
 
 /-! ### eraseP -/
 
-@[simp] theorem eraseP_nil : [].eraseP p = [] := rfl
+@[simp, grind =] theorem eraseP_nil : [].eraseP p = [] := rfl
 
-theorem eraseP_cons {a : α} {l : List α} :
+@[grind =] theorem eraseP_cons {a : α} {l : List α} :
     (a :: l).eraseP p = bif p a then l else a :: l.eraseP p := rfl
 
 @[simp] theorem eraseP_cons_of_pos {l : List α} {p} (h : p a) : (a :: l).eraseP p = l := by
@@ -92,7 +92,7 @@ theorem exists_or_eq_self_of_eraseP (p) (l : List α) :
   let ⟨_, l₁, l₂, _, _, e₁, e₂⟩ := exists_of_eraseP al pa
   rw [e₂]; simp [length_append, e₁]
 
-theorem length_eraseP {l : List α} : (l.eraseP p).length = if l.any p then l.length - 1 else l.length := by
+@[grind =] theorem length_eraseP {l : List α} : (l.eraseP p).length = if l.any p then l.length - 1 else l.length := by
   split <;> rename_i h
   · simp only [any_eq_true] at h
     obtain ⟨x, m, h⟩ := h
@@ -106,8 +106,13 @@ theorem eraseP_sublist {l : List α} : l.eraseP p <+ l := by
   | .inl h => rw [h]; apply Sublist.refl
   | .inr ⟨c, l₁, l₂, _, _, h₃, h₄⟩ => rw [h₄, h₃]; simp
 
+grind_pattern eraseP_sublist => l.eraseP p, List.Sublist
+
 theorem eraseP_subset {l : List α} : l.eraseP p ⊆ l := eraseP_sublist.subset
 
+grind_pattern eraseP_subset => l.eraseP p, List.Subset
+
+@[grind ←]
 protected theorem Sublist.eraseP : l₁ <+ l₂ → l₁.eraseP p <+ l₂.eraseP p
   | .slnil => Sublist.refl _
   | .cons a s => by
@@ -126,9 +131,10 @@ theorem le_length_eraseP {l : List α} : l.length - 1 ≤ (l.eraseP p).length :=
   rw [length_eraseP]
   split <;> simp
 
+@[grind →]
 theorem mem_of_mem_eraseP {l : List α} : a ∈ l.eraseP p → a ∈ l := (eraseP_subset ·)
 
-@[simp] theorem mem_eraseP_of_neg {l : List α} (pa : ¬p a) : a ∈ l.eraseP p ↔ a ∈ l := by
+@[simp, grind] theorem mem_eraseP_of_neg {l : List α} (pa : ¬p a) : a ∈ l.eraseP p ↔ a ∈ l := by
   refine ⟨mem_of_mem_eraseP, fun al => ?_⟩
   match exists_or_eq_self_of_eraseP p l with
   | .inl h => rw [h]; assumption
@@ -146,10 +152,12 @@ theorem mem_of_mem_eraseP {l : List α} : a ∈ l.eraseP p → a ∈ l := (erase
     · intro; obtain ⟨x, m, h⟩ := h; simp_all
   · simp_all
 
+@[grind _=_]
 theorem eraseP_map {f : β → α} : ∀ {l : List β}, (map f l).eraseP p = map f (l.eraseP (p ∘ f))
   | [] => rfl
   | b::l => by by_cases h : p (f b) <;> simp [h, eraseP_map, eraseP_cons_of_pos]
 
+@[grind =]
 theorem eraseP_filterMap {f : α → Option β} : ∀ {l : List α},
     (filterMap f l).eraseP p = filterMap f (l.eraseP (fun x => match f x with | some y => p y | none => false))
   | [] => rfl
@@ -164,6 +172,7 @@ theorem eraseP_filterMap {f : α → Option β} : ∀ {l : List α},
       · simp only [w, cond_false]
         rw [filterMap_cons_some h, eraseP_filterMap]
 
+@[grind =]
 theorem eraseP_filter {f : α → Bool} {l : List α} :
     (filter f l).eraseP p = filter f (l.eraseP (fun x => p x && f x)) := by
   rw [← filterMap_eq_filter, eraseP_filterMap]
@@ -173,18 +182,19 @@ theorem eraseP_filter {f : α → Bool} {l : List α} :
   split <;> split at * <;> simp_all
 
 theorem eraseP_append_left {a : α} (pa : p a) :
-    ∀ {l₁ : List α} l₂, a ∈ l₁ → (l₁++l₂).eraseP p = l₁.eraseP p ++ l₂
+    ∀ {l₁ : List α} l₂, a ∈ l₁ → (l₁ ++ l₂).eraseP p = l₁.eraseP p ++ l₂
   | x :: xs, l₂, h => by
     by_cases h' : p x <;> simp [h']
     rw [eraseP_append_left pa l₂ ((mem_cons.1 h).resolve_left (mt _ h'))]
     intro | rfl => exact pa
 
 theorem eraseP_append_right :
-    ∀ {l₁ : List α} l₂, (∀ b ∈ l₁, ¬p b) → eraseP p (l₁++l₂) = l₁ ++ l₂.eraseP p
+    ∀ {l₁ : List α} l₂, (∀ b ∈ l₁, ¬p b) → eraseP p (l₁ ++ l₂) = l₁ ++ l₂.eraseP p
   | [],     _, _ => rfl
   | _ :: _, _, h => by
     simp [(forall_mem_cons.1 h).1, eraseP_append_right _ (forall_mem_cons.1 h).2]
 
+@[grind =]
 theorem eraseP_append {l₁ l₂ : List α} :
     (l₁ ++ l₂).eraseP p = if l₁.any p then l₁.eraseP p ++ l₂ else l₁ ++ l₂.eraseP p := by
   split <;> rename_i h
@@ -195,6 +205,7 @@ theorem eraseP_append {l₁ l₂ : List α} :
     rw [eraseP_append_right _]
     simp_all
 
+@[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
   induction n with
@@ -211,6 +222,7 @@ theorem eraseP_replicate {n : Nat} {a : α} {p : α → Bool} :
     (replicate n a).eraseP p = replicate n a := by
   rw [eraseP_of_forall_not (by simp_all)]
 
+@[grind ←]
 protected theorem IsPrefix.eraseP (h : l₁ <+: l₂) : l₁.eraseP p <+: l₂.eraseP p := by
   rw [IsPrefix] at h
   obtain ⟨t, rfl⟩ := h
@@ -257,12 +269,15 @@ theorem eraseP_eq_iff {p} {l : List α} :
         subst p
         simp_all
 
+@[grind ←]
 theorem Pairwise.eraseP (q) : Pairwise p l → Pairwise p (l.eraseP q) :=
   Pairwise.sublist <| eraseP_sublist
 
+@[grind ←]
 theorem Nodup.eraseP (p) : Nodup l → Nodup (l.eraseP p) :=
   Pairwise.eraseP p
 
+@[grind =]
 theorem eraseP_comm {l : List α} (h : ∀ a ∈ l, ¬ p a ∨ ¬ q a) :
     (l.eraseP p).eraseP q = (l.eraseP q).eraseP p := by
   induction l with
@@ -355,6 +370,7 @@ theorem exists_erase_eq [LawfulBEq α] {a : α} {l : List α} (h : a ∈ l) :
     length (l.erase a) = length l - 1 := by
   rw [erase_eq_eraseP]; exact length_eraseP_of_mem h (beq_self_eq_true a)
 
+@[grind =]
 theorem length_erase [LawfulBEq α] {a : α} {l : List α} :
     length (l.erase a) = if a ∈ l then length l - 1 else length l := by
   rw [erase_eq_eraseP, length_eraseP]
@@ -363,11 +379,17 @@ theorem length_erase [LawfulBEq α] {a : α} {l : List α} :
 theorem erase_sublist {a : α} {l : List α} : l.erase a <+ l :=
   erase_eq_eraseP' a l ▸ eraseP_sublist ..
 
+grind_pattern length_erase => l.erase a, List.Sublist
+
 theorem erase_subset {a : α} {l : List α} : l.erase a ⊆ l := erase_sublist.subset
 
+grind_pattern erase_subset => l.erase a, List.Subset
+
+@[grind ←]
 theorem Sublist.erase (a : α) {l₁ l₂ : List α} (h : l₁ <+ l₂) : l₁.erase a <+ l₂.erase a := by
   simp only [erase_eq_eraseP']; exact h.eraseP
 
+@[grind ←]
 theorem IsPrefix.erase (a : α) {l₁ l₂ : List α} (h : l₁ <+: l₂) : l₁.erase a <+: l₂.erase a := by
   simp only [erase_eq_eraseP']; exact h.eraseP
 
@@ -378,9 +400,10 @@ theorem le_length_erase [LawfulBEq α] {a : α} {l : List α} : l.length - 1 ≤
   rw [length_erase]
   split <;> simp
 
+@[grind →]
 theorem mem_of_mem_erase {a b : α} {l : List α} (h : a ∈ l.erase b) : a ∈ l := erase_subset h
 
-@[simp] theorem mem_erase_of_ne [LawfulBEq α] {a b : α} {l : List α} (ab : a ≠ b) :
+@[simp, grind] theorem mem_erase_of_ne [LawfulBEq α] {a b : α} {l : List α} (ab : a ≠ b) :
     a ∈ l.erase b ↔ a ∈ l :=
   erase_eq_eraseP b l ▸ mem_eraseP_of_neg (mt eq_of_beq ab.symm)
 
@@ -388,6 +411,7 @@ theorem mem_of_mem_erase {a b : α} {l : List α} (h : a ∈ l.erase b) : a ∈
   rw [erase_eq_eraseP', eraseP_eq_self_iff]
   simp [forall_mem_ne']
 
+@[grind _=_]
 theorem erase_filter [LawfulBEq α] {f : α → Bool} {l : List α} :
     (filter f l).erase a = filter f (l.erase a) := by
   induction l with
@@ -415,10 +439,12 @@ theorem erase_append_right [LawfulBEq α] {a : α} {l₁ : List α} (l₂ : List
   rw [erase_eq_eraseP, erase_eq_eraseP, eraseP_append_right]
   intros b h' h''; rw [eq_of_beq h''] at h; exact h h'
 
+@[grind =]
 theorem erase_append [LawfulBEq α] {a : α} {l₁ l₂ : List α} :
     (l₁ ++ l₂).erase a = if a ∈ l₁ then l₁.erase a ++ l₂ else l₁ ++ l₂.erase a := by
   simp [erase_eq_eraseP, eraseP_append]
 
+@[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
   rw [erase_eq_eraseP]
@@ -426,6 +452,7 @@ theorem erase_replicate [LawfulBEq α] {n : Nat} {a b : α} :
 
 -- 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) {l : List α} :
     (l.erase a).erase b = (l.erase b).erase a := by
   if ab : a == b then rw [eq_of_beq ab] else ?_
@@ -465,6 +492,7 @@ theorem erase_eq_iff [LawfulBEq α] {a : α} {l : List α} :
   rw [erase_of_not_mem]
   simp_all
 
+@[grind ←]
 theorem Pairwise.erase [LawfulBEq α] {l : List α} (a) : Pairwise p l → Pairwise p (l.erase a) :=
   Pairwise.sublist <| erase_sublist
 
@@ -487,6 +515,10 @@ theorem Nodup.mem_erase_iff [LawfulBEq α] {a : α} (d : Nodup l) : a ∈ l.eras
 theorem Nodup.not_mem_erase [LawfulBEq α] {a : α} (h : Nodup l) : a ∉ l.erase a := fun H => by
   simpa using ((Nodup.mem_erase_iff h).mp H).left
 
+-- Only activate `not_mem_erase` when `l.Nodup` is already available.
+grind_pattern List.Nodup.not_mem_erase => a ∈ l.erase a, l.Nodup
+
+@[grind]
 theorem Nodup.erase [LawfulBEq α] (a : α) : Nodup l → Nodup (l.erase a) :=
   Pairwise.erase a
 
@@ -513,6 +545,7 @@ end erase
 
 /-! ### eraseIdx -/
 
+@[grind =]
 theorem length_eraseIdx {l : List α} {i : Nat} :
     (l.eraseIdx i).length = if i < l.length then l.length - 1 else l.length := by
   induction l generalizing i with
@@ -530,8 +563,9 @@ theorem length_eraseIdx_of_lt {l : List α} {i} (h : i < length l) :
     (l.eraseIdx i).length = length l - 1 := by
   simp [length_eraseIdx, h]
 
-@[simp] theorem eraseIdx_zero {l : List α} : eraseIdx l 0 = l.tail := by cases l <;> rfl
+@[simp, grind =] theorem eraseIdx_zero {l : List α} : eraseIdx l 0 = l.tail := by cases l <;> rfl
 
+@[grind =]
 theorem eraseIdx_eq_take_drop_succ :
     ∀ (l : List α) (i : Nat), l.eraseIdx i = l.take i ++ l.drop (i + 1)
   | nil, _ => by simp
@@ -558,6 +592,7 @@ theorem eraseIdx_ne_nil_iff {l : List α} {i : Nat} : eraseIdx l i ≠ [] ↔ 2
 @[deprecated eraseIdx_ne_nil_iff (since := "2025-01-30")]
 abbrev eraseIdx_ne_nil := @eraseIdx_ne_nil_iff
 
+@[grind]
 theorem eraseIdx_sublist : ∀ (l : List α) (k : Nat), eraseIdx l k <+ l
   | [], _ => by simp
   | a::l, 0 => by simp
@@ -566,6 +601,7 @@ theorem eraseIdx_sublist : ∀ (l : List α) (k : Nat), eraseIdx l k <+ l
 theorem mem_of_mem_eraseIdx {l : List α} {i : Nat} {a : α} (h : a ∈ l.eraseIdx i) : a ∈ l :=
   (eraseIdx_sublist _ _).mem h
 
+@[grind]
 theorem eraseIdx_subset {l : List α} {k : Nat} : eraseIdx l k ⊆ l :=
   (eraseIdx_sublist _ _).subset
 
@@ -605,6 +641,15 @@ theorem eraseIdx_append_of_length_le {l : List α} {k : Nat} (hk : length l ≤
     | zero => simp_all
     | succ k => simp_all [eraseIdx_cons_succ, Nat.succ_sub_succ]
 
+@[grind =]
+theorem eraseIdx_append :
+    eraseIdx (l ++ l') k = if k < length l then eraseIdx l k ++ l' else l ++ eraseIdx l' (k - length l) := by
+  split <;> rename_i h
+  · simp [eraseIdx_append_of_lt_length h]
+  · rw [eraseIdx_append_of_length_le]
+    omega
+
+@[grind =]
 theorem eraseIdx_replicate {n : Nat} {a : α} {k : Nat} :
     (replicate n a).eraseIdx k = if k < n then replicate (n - 1) a else replicate n a := by
   split <;> rename_i h
@@ -616,12 +661,15 @@ theorem eraseIdx_replicate {n : Nat} {a : α} {k : Nat} :
     exact m.2
   · rw [eraseIdx_of_length_le (by simpa using h)]
 
+@[grind ←]
 theorem Pairwise.eraseIdx {l : List α} (k) : Pairwise p l → Pairwise p (l.eraseIdx k) :=
   Pairwise.sublist <| eraseIdx_sublist _ _
 
+@[grind ←]
 theorem Nodup.eraseIdx {l : List α} (k) : Nodup l → Nodup (l.eraseIdx k) :=
   Pairwise.eraseIdx k
 
+@[grind ←]
 protected theorem IsPrefix.eraseIdx {l l' : List α} (h : l <+: l') (k : Nat) :
     eraseIdx l k <+: eraseIdx l' k := by
   rcases h with ⟨t, rfl⟩

src/Init/Data/List/FinRange.lean

@@ -23,14 +23,14 @@ Examples:
 -/
 def finRange (n : Nat) : List (Fin n) := ofFn fun i => i
 
-@[simp] theorem length_finRange {n : Nat} : (List.finRange n).length = n := by
+@[simp, grind =] theorem length_finRange {n : Nat} : (List.finRange n).length = n := by
   simp [List.finRange]
 
-@[simp] theorem getElem_finRange {i : Nat} (h : i < (List.finRange n).length) :
+@[simp, grind =] theorem getElem_finRange {i : Nat} (h : i < (List.finRange n).length) :
     (finRange n)[i] = Fin.cast length_finRange ⟨i, h⟩ := by
   simp [List.finRange]
 
-@[simp] theorem finRange_zero : finRange 0 = [] := by simp [finRange]
+@[simp, grind =] theorem finRange_zero : finRange 0 = [] := by simp [finRange]
 
 theorem finRange_succ {n} : finRange (n+1) = 0 :: (finRange n).map Fin.succ := by
   apply List.ext_getElem; simp; intro i; cases i <;> simp
@@ -46,6 +46,7 @@ theorem finRange_succ_last {n} :
     · rfl
     · next h => exact Fin.eq_last_of_not_lt h
 
+@[grind _=_]
 theorem finRange_reverse {n} : (finRange n).reverse = (finRange n).map Fin.rev := by
   induction n with
   | zero => simp

src/Init/Data/List/Find.lean

@@ -45,7 +45,7 @@ theorem exists_of_findSome?_eq_some {l : List α} {f : α → Option β} (w : l.
     simp_all only [findSome?_cons, mem_cons, exists_eq_or_imp]
     split at w <;> simp_all
 
-@[simp] theorem findSome?_eq_none_iff : findSome? p l = none ↔ ∀ x ∈ l, p x = none := by
+@[simp, grind =] theorem findSome?_eq_none_iff : findSome? p l = none ↔ ∀ x ∈ l, p x = none := by
   induction l <;> simp [findSome?_cons]; split <;> simp [*]
 
 @[simp] theorem findSome?_isSome_iff {f : α → Option β} {l : List α} :
@@ -91,7 +91,7 @@ theorem findSome?_eq_some_iff {f : α → Option β} {l : List α} {b : β} :
           obtain ⟨⟨rfl, rfl⟩, rfl⟩ := h₁
           exact ⟨l₁, a, l₂, rfl, h₂, fun a' w => h₃ a' (mem_cons_of_mem p w)⟩
 
-@[simp] theorem findSome?_guard {l : List α} : findSome? (Option.guard fun x => p x) l = find? p l := by
+@[simp, grind =] theorem findSome?_guard {l : List α} : findSome? (Option.guard p) l = find? p l := by
   induction l with
   | nil => simp
   | cons x xs ih =>
@@ -103,32 +103,33 @@ theorem findSome?_eq_some_iff {f : α → Option β} {l : List α} {b : β} :
     · simp only [Option.guard_eq_none_iff] at h
       simp [ih, h]
 
-theorem find?_eq_findSome?_guard {l : List α} : find? p l = findSome? (Option.guard fun x => p x) l :=
+theorem find?_eq_findSome?_guard {l : List α} : find? p l = findSome? (Option.guard p) l :=
   findSome?_guard.symm
 
-@[simp] theorem head?_filterMap {f : α → Option β} {l : List α} : (l.filterMap f).head? = l.findSome? f := by
+@[simp, grind =] theorem head?_filterMap {f : α → Option β} {l : List α} : (l.filterMap f).head? = l.findSome? f := by
   induction l with
   | nil => simp
   | cons x xs ih =>
     simp only [filterMap_cons, findSome?_cons]
     split <;> simp [*]
 
-@[simp] theorem head_filterMap {f : α → Option β} {l : List α} (h) :
+@[simp, grind =] theorem head_filterMap {f : α → Option β} {l : List α} (h) :
     (l.filterMap f).head h = (l.findSome? f).get (by simp_all [Option.isSome_iff_ne_none]) := by
   simp [head_eq_iff_head?_eq_some]
 
-@[simp] theorem getLast?_filterMap {f : α → Option β} {l : List α} : (l.filterMap f).getLast? = l.reverse.findSome? f := by
+@[simp, grind =] theorem getLast?_filterMap {f : α → Option β} {l : List α} : (l.filterMap f).getLast? = l.reverse.findSome? f := by
   rw [getLast?_eq_head?_reverse]
   simp [← filterMap_reverse]
 
-@[simp] theorem getLast_filterMap {f : α → Option β} {l : List α} (h) :
+@[simp, grind =] theorem getLast_filterMap {f : α → Option β} {l : List α} (h) :
     (l.filterMap f).getLast h = (l.reverse.findSome? f).get (by simp_all [Option.isSome_iff_ne_none]) := by
   simp [getLast_eq_iff_getLast?_eq_some]
 
-@[simp] theorem map_findSome? {f : α → Option β} {g : β → γ} {l : List α} :
+@[simp, grind _=_] theorem map_findSome? {f : α → Option β} {g : β → γ} {l : List α} :
     (l.findSome? f).map g = l.findSome? (Option.map g ∘ f) := by
   induction l <;> simp [findSome?_cons]; split <;> simp [*]
 
+@[grind _=_]
 theorem findSome?_map {f : β → γ} {l : List β} : findSome? p (l.map f) = l.findSome? (p ∘ f) := by
   induction l with
   | nil => simp
@@ -136,15 +137,18 @@ theorem findSome?_map {f : β → γ} {l : List β} : findSome? p (l.map f) = l.
     simp only [map_cons, findSome?]
     split <;> simp_all
 
+@[grind =]
 theorem head_flatten {L : List (List α)} (h : ∃ l, l ∈ L ∧ l ≠ []) :
-    (flatten L).head (by simpa using h) = (L.findSome? fun l => l.head?).get (by simpa using h) := by
+    (flatten L).head (by simpa using h) = (L.findSome? head?).get (by simpa using h) := by
   simp [head_eq_iff_head?_eq_some, head?_flatten]
 
+@[grind =]
 theorem getLast_flatten {L : List (List α)} (h : ∃ l, l ∈ L ∧ l ≠ []) :
     (flatten L).getLast (by simpa using h) =
-      (L.reverse.findSome? fun l => l.getLast?).get (by simpa using h) := by
+      (L.reverse.findSome? getLast?).get (by simpa using h) := by
   simp [getLast_eq_iff_getLast?_eq_some, getLast?_flatten]
 
+@[grind =]
 theorem findSome?_replicate : findSome? f (replicate n a) = if n = 0 then none else f a := by
   cases n with
   | zero => simp
@@ -174,6 +178,9 @@ theorem Sublist.findSome?_isSome {l₁ l₂ : List α} (h : l₁ <+ l₂) :
     · simp_all
     · exact ih
 
+grind_pattern Sublist.findSome?_isSome => l₁ <+ l₂, l₁.findSome? f
+grind_pattern Sublist.findSome?_isSome => l₁ <+ l₂, l₂.findSome? f
+
 theorem Sublist.findSome?_eq_none {l₁ l₂ : List α} (h : l₁ <+ l₂) :
     l₂.findSome? f = none → l₁.findSome? f = none := by
   simp only [List.findSome?_eq_none_iff, Bool.not_eq_true]
@@ -185,16 +192,30 @@ theorem IsPrefix.findSome?_eq_some {l₁ l₂ : List α} {f : α → Option β}
   obtain ⟨t, rfl⟩ := h
   simp +contextual [findSome?_append]
 
+grind_pattern IsPrefix.findSome?_eq_some => l₁ <+: l₂, l₁.findSome? f, some b
+grind_pattern IsPrefix.findSome?_eq_some => l₁ <+: l₂, l₂.findSome? f, some b
+
 theorem IsPrefix.findSome?_eq_none {l₁ l₂ : List α} {f : α → Option β} (h : l₁ <+: l₂) :
     List.findSome? f l₂ = none → List.findSome? f l₁ = none :=
   h.sublist.findSome?_eq_none
+
+grind_pattern IsPrefix.findSome?_eq_none => l₁ <+: l₂, l₂.findSome? f
+grind_pattern IsPrefix.findSome?_eq_none => l₁ <+: l₂, l₁.findSome? f
+
 theorem IsSuffix.findSome?_eq_none {l₁ l₂ : List α} {f : α → Option β} (h : l₁ <:+ l₂) :
     List.findSome? f l₂ = none → List.findSome? f l₁ = none :=
   h.sublist.findSome?_eq_none
+
+grind_pattern IsSuffix.findSome?_eq_none => l₁ <+: l₂, l₂.findSome? f
+grind_pattern IsSuffix.findSome?_eq_none => l₁ <+: l₂, l₁.findSome? f
+
 theorem IsInfix.findSome?_eq_none {l₁ l₂ : List α} {f : α → Option β} (h : l₁ <:+: l₂) :
     List.findSome? f l₂ = none → List.findSome? f l₁ = none :=
   h.sublist.findSome?_eq_none
 
+grind_pattern IsInfix.findSome?_eq_none => l₁ <+: l₂, l₂.findSome? f
+grind_pattern IsInfix.findSome?_eq_none => l₁ <+: l₂, l₁.findSome? f
+
 /-! ### find? -/
 
 @[simp] theorem find?_cons_of_pos {l} (h : p a) : find? p (a :: l) = some a := by
@@ -203,7 +224,7 @@ theorem IsInfix.findSome?_eq_none {l₁ l₂ : List α} {f : α → Option β} (
 @[simp] theorem find?_cons_of_neg {l} (h : ¬p a) : find? p (a :: l) = find? p l := by
   simp [find?, h]
 
-@[simp] theorem find?_eq_none : find? p l = none ↔ ∀ x ∈ l, ¬ p x := by
+@[simp, grind =] theorem find?_eq_none : find? p l = none ↔ ∀ x ∈ l, ¬ p x := by
   induction l <;> simp [find?_cons]; split <;> simp [*]
 
 theorem find?_eq_some_iff_append :
@@ -243,33 +264,33 @@ theorem find?_eq_some_iff_append :
           cases h₁
           simp
 
-@[deprecated find?_eq_some_iff_append (since := "2024-11-06")]
-abbrev find?_eq_some := @find?_eq_some_iff_append
-
 @[simp]
 theorem find?_cons_eq_some : (a :: xs).find? p = some b ↔ (p a ∧ a = b) ∨ (!p a ∧ xs.find? p = some b) := by
   rw [find?_cons]
   split <;> simp_all
 
-@[simp] theorem find?_isSome {xs : List α} {p : α → Bool} : (xs.find? p).isSome ↔ ∃ x, x ∈ xs ∧ p x := by
+@[simp, grind =] theorem find?_isSome {xs : List α} {p : α → Bool} : (xs.find? p).isSome ↔ ∃ x, x ∈ xs ∧ p x := by
   induction xs with
   | nil => simp
   | cons x xs ih =>
     simp only [find?_cons, mem_cons, exists_eq_or_imp]
     split <;> simp_all
 
+@[grind →]
 theorem find?_some : ∀ {l}, find? p l = some a → p a
   | b :: l, H => by
     by_cases h : p b <;> simp [find?, h] at H
     · exact H ▸ h
     · exact find?_some H
 
+@[grind →]
 theorem mem_of_find?_eq_some : ∀ {l}, find? p l = some a → a ∈ l
   | b :: l, H => by
     by_cases h : p b <;> simp [find?, h] at H
     · exact H ▸ .head _
     · exact .tail _ (mem_of_find?_eq_some H)
 
+@[grind]
 theorem get_find?_mem {xs : List α} {p : α → Bool} (h) : (xs.find? p).get h ∈ xs := by
   induction xs with
   | nil => simp at h
@@ -281,7 +302,7 @@ theorem get_find?_mem {xs : List α} {p : α → Bool} (h) : (xs.find? p).get h
       right
       apply ih
 
-@[simp] theorem find?_filter {xs : List α} {p : α → Bool} {q : α → Bool} :
+@[simp, grind =] theorem find?_filter {xs : List α} {p : α → Bool} {q : α → Bool} :
     (xs.filter p).find? q = xs.find? (fun a => p a ∧ q a) := by
   induction xs with
   | nil => simp
@@ -291,22 +312,22 @@ theorem get_find?_mem {xs : List α} {p : α → Bool} (h) : (xs.find? p).get h
     · simp only [find?_cons]
       split <;> simp_all
 
-@[simp] theorem head?_filter {p : α → Bool} {l : List α} : (l.filter p).head? = l.find? p := by
+@[simp, grind =] theorem head?_filter {p : α → Bool} {l : List α} : (l.filter p).head? = l.find? p := by
   rw [← filterMap_eq_filter, head?_filterMap, findSome?_guard]
 
-@[simp] theorem head_filter {p : α → Bool} {l : List α} (h) :
+@[simp, grind =] theorem head_filter {p : α → Bool} {l : List α} (h) :
     (l.filter p).head h = (l.find? p).get (by simp_all [Option.isSome_iff_ne_none]) := by
   simp [head_eq_iff_head?_eq_some]
 
-@[simp] theorem getLast?_filter {p : α → Bool} {l : List α} : (l.filter p).getLast? = l.reverse.find? p := by
+@[simp, grind =] theorem getLast?_filter {p : α → Bool} {l : List α} : (l.filter p).getLast? = l.reverse.find? p := by
   rw [getLast?_eq_head?_reverse]
   simp [← filter_reverse]
 
-@[simp] theorem getLast_filter {p : α → Bool} {l : List α} (h) :
+@[simp, grind =] theorem getLast_filter {p : α → Bool} {l : List α} (h) :
     (l.filter p).getLast h = (l.reverse.find? p).get (by simp_all [Option.isSome_iff_ne_none]) := by
   simp [getLast_eq_iff_getLast?_eq_some]
 
-@[simp] theorem find?_filterMap {xs : List α} {f : α → Option β} {p : β → Bool} :
+@[simp, grind =] theorem find?_filterMap {xs : List α} {f : α → Option β} {p : β → Bool} :
     (xs.filterMap f).find? p = (xs.find? (fun a => (f a).any p)).bind f := by
   induction xs with
   | nil => simp
@@ -316,15 +337,15 @@ theorem get_find?_mem {xs : List α} {p : α → Bool} (h) : (xs.find? p).get h
     · simp only [find?_cons]
       split <;> simp_all
 
-@[simp] theorem find?_map {f : β → α} {l : List β} : find? p (l.map f) = (l.find? (p ∘ f)).map f := by
+@[simp, grind =] theorem find?_map {f : β → α} {l : List β} : find? p (l.map f) = (l.find? (p ∘ f)).map f := by
   induction l with
   | nil => simp
   | cons x xs ih =>
     simp only [map_cons, find?]
     by_cases h : p (f x) <;> simp [h, ih]
 
-@[simp] theorem find?_flatten {xss : List (List α)} {p : α → Bool} :
-    xss.flatten.find? p = xss.findSome? (·.find? p) := by
+@[simp, grind _=_] theorem find?_flatten {xss : List (List α)} {p : α → Bool} :
+    xss.flatten.find? p = xss.findSome? (find? p) := by
   induction xss with
   | nil => simp
   | cons _ _ ih =>
@@ -381,7 +402,7 @@ theorem find?_flatten_eq_some_iff {xs : List (List α)} {p : α → Bool} {a :
 @[deprecated find?_flatten_eq_some_iff (since := "2025-02-03")]
 abbrev find?_flatten_eq_some := @find?_flatten_eq_some_iff
 
-@[simp] theorem find?_flatMap {xs : List α} {f : α → List β} {p : β → Bool} :
+@[simp, grind =] theorem find?_flatMap {xs : List α} {f : α → List β} {p : β → Bool} :
     (xs.flatMap f).find? p = xs.findSome? (fun x => (f x).find? p) := by
   simp [flatMap_def, findSome?_map]; rfl
 
@@ -389,6 +410,7 @@ theorem find?_flatMap_eq_none_iff {xs : List α} {f : α → List β} {p : β
     (xs.flatMap f).find? p = none ↔ ∀ x ∈ xs, ∀ y ∈ f x, !p y := by
   simp
 
+@[grind =]
 theorem find?_replicate : find? p (replicate n a) = if n = 0 then none else if p a then some a else none := by
   cases n
   · simp
@@ -433,6 +455,9 @@ theorem Sublist.find?_isSome {l₁ l₂ : List α} (h : l₁ <+ l₂) : (l₁.fi
     · simp
     · simpa using ih
 
+grind_pattern Sublist.find?_isSome => l₁ <+ l₂, l₁.find? p
+grind_pattern Sublist.find?_isSome => l₁ <+ l₂, l₂.find? p
+
 theorem Sublist.find?_eq_none {l₁ l₂ : List α} (h : l₁ <+ l₂) : l₂.find? p = none → l₁.find? p = none := by
   simp only [List.find?_eq_none, Bool.not_eq_true]
   exact fun w x m => w x (Sublist.mem m h)
@@ -443,16 +468,31 @@ theorem IsPrefix.find?_eq_some {l₁ l₂ : List α} {p : α → Bool} (h : l₁
   obtain ⟨t, rfl⟩ := h
   simp +contextual [find?_append]
 
+grind_pattern IsPrefix.find?_eq_some => l₁ <+: l₂, l₁.find? p, some b
+grind_pattern IsPrefix.find?_eq_some => l₁ <+: l₂, l₂.find? p, some b
+
 theorem IsPrefix.find?_eq_none {l₁ l₂ : List α} {p : α → Bool} (h : l₁ <+: l₂) :
     List.find? p l₂ = none → List.find? p l₁ = none :=
   h.sublist.find?_eq_none
+
+grind_pattern Sublist.find?_eq_none => l₁ <+ l₂, l₂.find? p
+grind_pattern Sublist.find?_eq_none => l₁ <+ l₂, l₁.find? p
+
 theorem IsSuffix.find?_eq_none {l₁ l₂ : List α} {p : α → Bool} (h : l₁ <:+ l₂) :
     List.find? p l₂ = none → List.find? p l₁ = none :=
   h.sublist.find?_eq_none
+
+grind_pattern IsPrefix.find?_eq_none => l₁ <+: l₂, l₂.find? p
+grind_pattern IsPrefix.find?_eq_none => l₁ <+: l₂, l₁.find? p
+
 theorem IsInfix.find?_eq_none {l₁ l₂ : List α} {p : α → Bool} (h : l₁ <:+: l₂) :
     List.find? p l₂ = none → List.find? p l₁ = none :=
   h.sublist.find?_eq_none
 
+grind_pattern IsSuffix.find?_eq_none => l₁ <:+ l₂, l₂.find? p
+grind_pattern IsSuffix.find?_eq_none => l₁ <:+ l₂, l₁.find? p
+
+@[grind =]
 theorem find?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
     (H : ∀ (a : α), a ∈ xs → P a) {p : β → Bool} :
     (xs.pmap f H).find? p = (xs.attach.find? (fun ⟨a, m⟩ => p (f a (H a m)))).map fun ⟨a, m⟩ => f a (H a m) := by
@@ -485,9 +525,9 @@ private theorem findIdx?_go_eq {p : α → Bool} {xs : List α} {i : Nat} :
       ext
       simp only [Nat.add_comm i, Function.comp_apply, Nat.add_assoc]
 
-@[simp] theorem findIdx?_nil : ([] : List α).findIdx? p = none := rfl
+@[simp, grind =] theorem findIdx?_nil : ([] : List α).findIdx? p = none := rfl
 
-theorem findIdx?_cons :
+@[grind =] theorem findIdx?_cons :
     (x :: xs).findIdx? p = if p x then some 0 else (xs.findIdx? p).map fun i => i + 1 := by
   simp [findIdx?, findIdx?_go_eq]
 
@@ -496,6 +536,7 @@ theorem findIdx?_cons :
 
 /-! ### findIdx -/
 
+@[grind =]
 theorem findIdx_cons {p : α → Bool} {b : α} {l : List α} :
     (b :: l).findIdx p = bif p b then 0 else (l.findIdx p) + 1 := by
   cases H : p b with
@@ -514,6 +555,7 @@ where
 @[simp] theorem findIdx_singleton {a : α} {p : α → Bool} : [a].findIdx p = if p a then 0 else 1 := by
   simp [findIdx_cons, findIdx_nil]
 
+@[grind →]
 theorem findIdx_of_getElem?_eq_some {xs : List α} (w : xs[xs.findIdx p]? = some y) : p y := by
   induction xs with
   | nil => simp_all
@@ -523,6 +565,8 @@ theorem findIdx_getElem {xs : List α} {w : xs.findIdx p < xs.length} :
     p xs[xs.findIdx p] :=
   xs.findIdx_of_getElem?_eq_some (getElem?_eq_getElem w)
 
+grind_pattern findIdx_getElem => xs[xs.findIdx p]
+
 theorem findIdx_lt_length_of_exists {xs : List α} (h : ∃ x ∈ xs, p x) :
     xs.findIdx p < xs.length := by
   induction xs with
@@ -561,6 +605,8 @@ theorem findIdx_le_length {p : α → Bool} {xs : List α} : xs.findIdx p ≤ xs
   · simp at e
     exact Nat.le_of_eq (findIdx_eq_length.mpr e)
 
+grind_pattern findIdx_le_length => xs.findIdx p, xs.length
+
 @[simp]
 theorem findIdx_lt_length {p : α → Bool} {xs : List α} :
     xs.findIdx p < xs.length ↔ ∃ x ∈ xs, p x := by
@@ -570,6 +616,8 @@ theorem findIdx_lt_length {p : α → Bool} {xs : List α} :
   rw [← this, findIdx_eq_length, not_exists]
   simp only [Bool.not_eq_true, not_and]
 
+grind_pattern findIdx_lt_length => xs.findIdx p, xs.length
+
 /-- `p` does not hold for elements with indices less than `xs.findIdx p`. -/
 theorem not_of_lt_findIdx {p : α → Bool} {xs : List α} {i : Nat} (h : i < xs.findIdx p) :
     p (xs[i]'(Nat.le_trans h findIdx_le_length)) = false := by
@@ -594,6 +642,8 @@ theorem not_of_lt_findIdx {p : α → Bool} {xs : List α} {i : Nat} (h : i < xs
       rw [← ipm, Nat.succ_lt_succ_iff] at h
       simpa using ih 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 : List α} {i : Nat} (h : i < xs.length)
     (h2 : ∀ j (hji : j < i), p (xs[j]'(Nat.lt_trans hji h)) = false) : i ≤ xs.findIdx p := by
@@ -621,6 +671,7 @@ theorem findIdx_eq {p : α → Bool} {xs : List α} {i : Nat} (h : i < xs.length
   simp at h3
   simp_all [not_of_lt_findIdx h3]
 
+@[grind =]
 theorem findIdx_append {p : α → Bool} {l₁ l₂ : List α} :
     (l₁ ++ l₂).findIdx p =
       if l₁.findIdx p < l₁.length then l₁.findIdx p else l₂.findIdx p + l₁.length := by
@@ -642,6 +693,9 @@ theorem IsPrefix.findIdx_le {l₁ l₂ : List α} {p : α → Bool} (h : l₁ <+
   · exact Nat.le_refl ..
   · simp_all [findIdx_eq_length_of_false]
 
+grind_pattern IsPrefix.findIdx_le => l₁ <:+ l₂, l₁.findIdx p
+grind_pattern IsPrefix.findIdx_le => l₁ <:+ l₂, l₂.findIdx p
+
 theorem IsPrefix.findIdx_eq_of_findIdx_lt_length {l₁ l₂ : List α} {p : α → Bool} (h : l₁ <+: l₂)
     (lt : l₁.findIdx p < l₁.length) : l₂.findIdx p = l₁.findIdx p := by
   rw [IsPrefix] at h
@@ -651,6 +705,8 @@ theorem IsPrefix.findIdx_eq_of_findIdx_lt_length {l₁ l₂ : List α} {p : α
   · rfl
   · simp_all
 
+grind_pattern IsPrefix.findIdx_eq_of_findIdx_lt_length => l₁ <:+ l₂, l₁.findIdx p, l₂.findIdx p
+
 theorem findIdx_le_findIdx {l : List α} {p q : α → Bool} (h : ∀ x ∈ l, p x → q x) : l.findIdx q ≤ l.findIdx p := by
   induction l with
   | nil => simp
@@ -674,7 +730,7 @@ theorem findIdx_le_findIdx {l : List α} {p q : α → Bool} (h : ∀ x ∈ l, p
 
 /-! ### findIdx? -/
 
-@[simp]
+@[simp, grind =]
 theorem findIdx?_eq_none_iff {xs : List α} {p : α → Bool} :
     xs.findIdx? p = none ↔ ∀ x, x ∈ xs → p x = false := by
   induction xs with
@@ -683,7 +739,7 @@ theorem findIdx?_eq_none_iff {xs : List α} {p : α → Bool} :
     simp only [findIdx?_cons]
     split <;> simp_all [cond_eq_if]
 
-@[simp]
+@[simp, grind =]
 theorem findIdx?_isSome {xs : List α} {p : α → Bool} :
     (xs.findIdx? p).isSome = xs.any p := by
   induction xs with
@@ -692,7 +748,7 @@ theorem findIdx?_isSome {xs : List α} {p : α → Bool} :
     simp only [findIdx?_cons]
     split <;> simp_all
 
-@[simp]
+@[simp, grind =]
 theorem findIdx?_isNone {xs : List α} {p : α → Bool} :
     (xs.findIdx? p).isNone = xs.all (¬p ·) := by
   induction xs with
@@ -798,14 +854,14 @@ theorem of_findIdx?_eq_none {xs : List α} {p : α → Bool} (w : xs.findIdx? p
 @[deprecated of_findIdx?_eq_none (since := "2025-02-02")]
 abbrev findIdx?_of_eq_none := @of_findIdx?_eq_none
 
-@[simp] theorem findIdx?_map {f : β → α} {l : List β} : findIdx? p (l.map f) = l.findIdx? (p ∘ f) := by
+@[simp, grind _=_] theorem findIdx?_map {f : β → α} {l : List β} : findIdx? p (l.map f) = l.findIdx? (p ∘ f) := by
   induction l with
   | nil => simp
   | cons x xs ih =>
     simp only [map_cons, findIdx?_cons]
     split <;> simp_all
 
-@[simp] theorem findIdx?_append :
+@[simp, grind =] theorem findIdx?_append :
     (xs ++ ys : List α).findIdx? p =
       (xs.findIdx? p).or ((ys.findIdx? p).map fun i => i + xs.length) := by
   induction xs with simp [findIdx?_cons]
@@ -827,7 +883,7 @@ theorem findIdx?_flatten {l : List (List α)} {p : α → Bool} :
     · rw [Option.or_of_isNone (by simp_all [findIdx?_isNone])]
       simp [Function.comp_def, Nat.add_comm, Nat.add_assoc]
 
-@[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
   cases n with
   | zero => simp
@@ -881,22 +937,38 @@ theorem Sublist.findIdx?_eq_none {l₁ l₂ : List α} (h : l₁ <+ l₂) :
   simp only [findIdx?_eq_none_iff]
   exact fun w x m => w x (h.mem m)
 
+grind_pattern Sublist.findIdx?_eq_none => l₁ <+ l₂, l₁.findIdx? p
+grind_pattern Sublist.findIdx?_eq_none => l₁ <+ l₂, l₂.findIdx? p
+
 theorem IsPrefix.findIdx?_eq_some {l₁ l₂ : List α} {p : α → Bool} (h : l₁ <+: l₂) :
     List.findIdx? p l₁ = some i → List.findIdx? p l₂ = some i := by
   rw [IsPrefix] at h
   obtain ⟨t, rfl⟩ := h
   intro h
   simp [findIdx?_append, h]
+
 theorem IsPrefix.findIdx?_eq_none {l₁ l₂ : List α} {p : α → Bool} (h : l₁ <+: l₂) :
     List.findIdx? p l₂ = none → List.findIdx? p l₁ = none :=
   h.sublist.findIdx?_eq_none
+
+grind_pattern IsPrefix.findIdx?_eq_none => l₁ <+: l₂, l₁.findIdx? p
+grind_pattern IsPrefix.findIdx?_eq_none => l₁ <+: l₂, l₂.findIdx? p
+
 theorem IsSuffix.findIdx?_eq_none {l₁ l₂ : List α} {p : α → Bool} (h : l₁ <:+ l₂) :
     List.findIdx? p l₂ = none → List.findIdx? p l₁ = none :=
   h.sublist.findIdx?_eq_none
+
+grind_pattern IsSuffix.findIdx?_eq_none => l₁ <:+ l₂, l₁.findIdx? p
+grind_pattern IsSuffix.findIdx?_eq_none => l₁ <:+ l₂, l₂.findIdx? p
+
 theorem IsInfix.findIdx?_eq_none {l₁ l₂ : List α} {p : α → Bool} (h : l₁ <:+: l₂) :
     List.findIdx? p l₂ = none → List.findIdx? p l₁ = none :=
   h.sublist.findIdx?_eq_none
 
+grind_pattern IsInfix.findIdx?_eq_none => l₁ <:+: l₂, l₁.findIdx? p
+grind_pattern IsInfix.findIdx?_eq_none => l₁ <:+: l₂, l₂.findIdx? p
+
+@[grind =]
 theorem findIdx_eq_getD_findIdx? {xs : List α} {p : α → Bool} :
     xs.findIdx p = (xs.findIdx? p).getD xs.length := by
   induction xs with
@@ -917,7 +989,7 @@ theorem findIdx_eq_getD_findIdx? {xs : List α} {p : α → Bool} :
 
 /-! ### findFinIdx? -/
 
-@[simp] theorem findFinIdx?_nil {p : α → Bool} : findFinIdx? p [] = none := rfl
+@[simp, grind =] theorem findFinIdx?_nil {p : α → Bool} : findFinIdx? p [] = none := rfl
 
 theorem findIdx?_go_eq_map_findFinIdx?_go_val {xs : List α} {p : α → Bool} {i : Nat} {h} :
     List.findIdx?.go p xs i =
@@ -943,6 +1015,7 @@ theorem findFinIdx?_eq_pmap_findIdx? {xs : List α} {p : α → Bool} :
         (fun i h => h) := by
   simp [findIdx?_eq_map_findFinIdx?_val, Option.pmap_map]
 
+@[grind =]
 theorem findFinIdx?_cons {p : α → Bool} {x : α} {xs : List α} :
     findFinIdx? p (x :: xs) = if p x then some 0 else (findFinIdx? p xs).map Fin.succ := by
   rw [← Option.map_inj_right (f := Fin.val) (fun a b => Fin.eq_of_val_eq)]
@@ -953,6 +1026,7 @@ theorem findFinIdx?_cons {p : α → Bool} {x : α} {xs : List α} :
   · rw [findIdx?_eq_map_findFinIdx?_val]
     simp [Function.comp_def]
 
+@[grind =]
 theorem findFinIdx?_append {xs ys : List α} {p : α → Bool} :
     (xs ++ ys).findFinIdx? p =
       ((xs.findFinIdx? p).map (Fin.castLE (by simp))).or
@@ -962,11 +1036,11 @@ theorem findFinIdx?_append {xs ys : List α} {p : α → Bool} :
   · simp [h, Option.pmap_map, Option.map_pmap, Nat.add_comm]
   · simp [h]
 
-@[simp] theorem findFinIdx?_singleton {a : α} {p : α → Bool} :
+@[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 [findFinIdx?_cons, findFinIdx?_nil]
 
-@[simp] theorem findFinIdx?_eq_none_iff {l : List α} {p : α → Bool} :
+@[simp, grind =] theorem findFinIdx?_eq_none_iff {l : List α} {p : α → Bool} :
     l.findFinIdx? p = none ↔ ∀ x ∈ l, ¬ p x := by
   simp [findFinIdx?_eq_pmap_findIdx?]
 
@@ -982,7 +1056,7 @@ theorem findFinIdx?_eq_some_iff {xs : List α} {p : α → Bool} {i : Fin xs.len
   · rintro ⟨h, w⟩
     exact ⟨i, ⟨i.2, h, fun j hji => w ⟨j, by omega⟩ hji⟩, rfl⟩
 
-@[simp]
+@[simp, grind =]
 theorem isSome_findFinIdx? {l : List α} {p : α → Bool} :
     (l.findFinIdx? p).isSome = l.any p := by
   induction l with
@@ -991,7 +1065,7 @@ theorem isSome_findFinIdx? {l : List α} {p : α → Bool} :
     simp only [findFinIdx?_cons]
     split <;> simp_all
 
-@[simp]
+@[simp, grind =]
 theorem isNone_findFinIdx? {l : List α} {p : α → Bool} :
     (l.findFinIdx? p).isNone = l.all (fun x => ¬ p x) := by
   induction l with
@@ -1016,6 +1090,7 @@ 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_cons [BEq α] :
     (x :: xs : List α).idxOf y = bif x == y then 0 else xs.idxOf y + 1 := by
   dsimp [idxOf]
@@ -1030,6 +1105,7 @@ abbrev indexOf_cons := @idxOf_cons
 @[deprecated idxOf_cons_self (since := "2025-01-29")]
 abbrev indexOf_cons_self := @idxOf_cons_self
 
+@[grind =]
 theorem idxOf_append [BEq α] [LawfulBEq α] {l₁ l₂ : List α} {a : α} :
     (l₁ ++ l₂).idxOf a = if a ∈ l₁ then l₁.idxOf a else l₂.idxOf a + l₁.length := by
   rw [idxOf, findIdx_append]
@@ -1053,7 +1129,7 @@ theorem idxOf_eq_length [BEq α] [LawfulBEq α] {l : List α} (h : a ∉ l) : l.
 @[deprecated idxOf_eq_length (since := "2025-01-29")]
 abbrev indexOf_eq_length := @idxOf_eq_length
 
-theorem idxOf_lt_length [BEq α] [EquivBEq α] {l : List α} (h : a ∈ l) : l.idxOf a < l.length := by
+theorem idxOf_lt_length_of_mem [BEq α] [EquivBEq α] {l : List α} (h : a ∈ l) : l.idxOf a < l.length := by
   induction l with
   | nil => simp at h
   | cons x xs ih =>
@@ -1066,8 +1142,23 @@ theorem idxOf_lt_length [BEq α] [EquivBEq α] {l : List α} (h : a ∈ l) : l.i
       · exact zero_lt_succ xs.length
       · exact Nat.add_lt_add_right ih 1
 
-@[deprecated idxOf_lt_length (since := "2025-01-29")]
-abbrev indexOf_lt_length := @idxOf_lt_length
+theorem idxOf_le_length [BEq α] [LawfulBEq α] {l : List α} {a : α} :
+    l.idxOf a ≤ l.length := by
+  simpa [idxOf] using findIdx_le_length
+
+grind_pattern idxOf_le_length => l.idxOf a, l.length
+
+theorem idxOf_lt_length_iff [BEq α] [LawfulBEq α] {l : List α} {a : α} :
+    l.idxOf a < l.length ↔ a ∈ l := by
+  constructor
+  · intro h
+    simpa [idxOf] using h
+  · exact idxOf_lt_length_of_mem
+
+grind_pattern idxOf_lt_length_iff => l.idxOf a, l.length
+
+@[deprecated idxOf_lt_length_of_mem (since := "2025-01-29")]
+abbrev indexOf_lt_length := @idxOf_lt_length_of_mem
 
 /-! ### finIdxOf?
 
@@ -1079,14 +1170,14 @@ theorem idxOf?_eq_map_finIdxOf?_val [BEq α] {xs : List α} {a : α} :
     xs.idxOf? a = (xs.finIdxOf? a).map (·.val) := by
   simp [idxOf?, finIdxOf?, findIdx?_eq_map_findFinIdx?_val]
 
-@[simp] theorem finIdxOf?_nil [BEq α] : ([] : List α).finIdxOf? a = none := rfl
+@[simp, grind =] theorem finIdxOf?_nil [BEq α] : ([] : List α).finIdxOf? a = none := rfl
 
-theorem finIdxOf?_cons [BEq α] {a : α} {xs : List α} :
+@[grind =] theorem finIdxOf?_cons [BEq α] {a : α} {xs : List α} :
     (a :: xs).finIdxOf? b =
       if a == b then some ⟨0, by simp⟩ else (xs.finIdxOf? b).map (·.succ) := by
   simp [finIdxOf?, findFinIdx?_cons]
 
-@[simp] theorem finIdxOf?_eq_none_iff [BEq α] [LawfulBEq α] {l : List α} {a : α} :
+@[simp, grind =] theorem finIdxOf?_eq_none_iff [BEq α] [LawfulBEq α] {l : List α} {a : α} :
     l.finIdxOf? a = none ↔ a ∉ l := by
   simp only [finIdxOf?, findFinIdx?_eq_none_iff, beq_iff_eq]
   constructor
@@ -1099,18 +1190,19 @@ theorem finIdxOf?_cons [BEq α] {a : α} {xs : List α} :
     l.finIdxOf? a = some i ↔ l[i] = a ∧ ∀ j (_ : j < i), ¬l[j] = a := by
   simp only [finIdxOf?, findFinIdx?_eq_some_iff, beq_iff_eq]
 
-@[simp]
-theorem isSome_finIdxOf? [BEq α] [LawfulBEq α] {l : List α} {a : α} :
-    (l.finIdxOf? a).isSome ↔ a ∈ l := by
+@[simp, grind =]
+theorem isSome_finIdxOf? [BEq α] [PartialEquivBEq α] {l : List α} {a : α} :
+    (l.finIdxOf? a).isSome = l.contains a := by
   induction l with
   | nil => simp
   | cons x xs ih =>
     simp only [finIdxOf?_cons]
-    split <;> simp_all [@eq_comm _ x a]
+    split <;> simp_all [BEq.comm]
 
-theorem isNone_finIdxOf? [BEq α] [LawfulBEq α] {l : List α} {a : α} :
-    (l.finIdxOf? a).isNone = ¬ a ∈ l := by
-  simp
+@[simp]
+theorem isNone_finIdxOf? [BEq α] [PartialEquivBEq α] {l : List α} {a : α} :
+    (l.finIdxOf? a).isNone = !l.contains a := by
+  rw [← isSome_finIdxOf?, Option.not_isSome]
 
 /-! ### idxOf?
 
@@ -1118,16 +1210,16 @@ The verification API for `idxOf?` is still incomplete.
 The lemmas below should be made consistent with those for `findIdx?` (and proved using them).
 -/
 
-@[simp] theorem idxOf?_nil [BEq α] : ([] : List α).idxOf? a = none := rfl
+@[simp, grind =] theorem idxOf?_nil [BEq α] : ([] : List α).idxOf? a = none := rfl
 
-theorem idxOf?_cons [BEq α] {a : α} {xs : List α} {b : α} :
+@[grind =] theorem idxOf?_cons [BEq α] {a : α} {xs : List α} {b : α} :
     (a :: xs).idxOf? b = if a == b then some 0 else (xs.idxOf? b).map (· + 1) := by
   simp [idxOf?, findIdx?_cons]
 
 @[simp] theorem idxOf?_singleton [BEq α] {a b : α} : [a].idxOf? b = if a == b then some 0 else none := by
   simp [idxOf?_cons, idxOf?_nil]
 
-@[simp] theorem idxOf?_eq_none_iff [BEq α] [LawfulBEq α] {l : List α} {a : α} :
+@[simp, grind =] theorem idxOf?_eq_none_iff [BEq α] [LawfulBEq α] {l : List α} {a : α} :
     l.idxOf? a = none ↔ a ∉ l := by
   simp only [idxOf?, findIdx?_eq_none_iff, beq_eq_false_iff_ne, ne_eq]
   constructor
@@ -1140,7 +1232,7 @@ theorem idxOf?_cons [BEq α] {a : α} {xs : List α} {b : α} :
 @[deprecated idxOf?_eq_none_iff (since := "2025-01-29")]
 abbrev indexOf?_eq_none_iff := @idxOf?_eq_none_iff
 
-@[simp]
+@[simp, grind =]
 theorem isSome_idxOf? [BEq α] [LawfulBEq α] {l : List α} {a : α} :
     (l.idxOf? a).isSome ↔ a ∈ l := by
   induction l with
@@ -1149,6 +1241,7 @@ theorem isSome_idxOf? [BEq α] [LawfulBEq α] {l : List α} {a : α} :
     simp only [idxOf?_cons]
     split <;> simp_all [@eq_comm _ x a]
 
+@[grind =]
 theorem isNone_idxOf? [BEq α] [LawfulBEq α] {l : List α} {a : α} :
     (l.idxOf? a).isNone = ¬ a ∈ l := by
   simp
@@ -1175,7 +1268,7 @@ theorem lookup_eq_findSome? {l : List (α × β)} {k : α} :
       simp only [lookup_cons, findSome?_cons]
       split <;> simp_all
 
-@[simp] theorem lookup_eq_none_iff {l : List (α × β)} {k : α} :
+@[simp, grind =] theorem lookup_eq_none_iff {l : List (α × β)} {k : α} :
     l.lookup k = none ↔ ∀ p ∈ l, k != p.1 := by
   simp [lookup_eq_findSome?]
 
@@ -1195,10 +1288,12 @@ theorem lookup_eq_some_iff {l : List (α × β)} {k : α} {b : β} :
   · rintro ⟨l₁, l₂, rfl, h⟩
     exact ⟨l₁, (k, b), l₂, rfl, by simp, by simpa using h⟩
 
+@[grind =]
 theorem lookup_append {l₁ l₂ : List (α × β)} {k : α} :
     (l₁ ++ l₂).lookup k = (l₁.lookup k).or (l₂.lookup k) := by
   simp [lookup_eq_findSome?, findSome?_append]
 
+@[grind =]
 theorem lookup_replicate {k : α} :
     (replicate n (a,b)).lookup k = if n = 0 then none else if k == a then some b else none := by
   induction n with
@@ -1233,6 +1328,9 @@ theorem Sublist.lookup_eq_none {l₁ l₂ : List (α × β)} (h : l₁ <+ l₂)
   simp only [lookup_eq_findSome?]
   exact h.findSome?_eq_none
 
+grind_pattern Sublist.lookup_isSome => l₁ <+ l₂, l₁.lookup k
+grind_pattern Sublist.lookup_isSome => l₁ <+ l₂, l₂.lookup k
+
 theorem IsPrefix.lookup_eq_some {l₁ l₂ : List (α × β)} (h : l₁ <+: l₂) :
     List.lookup k l₁ = some b → List.lookup k l₂ = some b := by
   simp only [lookup_eq_findSome?]
@@ -1241,13 +1339,24 @@ theorem IsPrefix.lookup_eq_some {l₁ l₂ : List (α × β)} (h : l₁ <+: l₂
 theorem IsPrefix.lookup_eq_none {l₁ l₂ : List (α × β)} (h : l₁ <+: l₂) :
     List.lookup k l₂ = none → List.lookup k l₁ = none :=
   h.sublist.lookup_eq_none
+
+grind_pattern IsPrefix.lookup_eq_none => l₁ <+: l₂, l₁.lookup k
+grind_pattern IsPrefix.lookup_eq_none => l₁ <+: l₂, l₂.lookup k
+
 theorem IsSuffix.lookup_eq_none {l₁ l₂ : List (α × β)} (h : l₁ <:+ l₂) :
     List.lookup k l₂ = none → List.lookup k l₁ = none :=
   h.sublist.lookup_eq_none
+
+grind_pattern IsSuffix.lookup_eq_none => l₁ <:+ l₂, l₁.lookup k
+grind_pattern IsSuffix.lookup_eq_none => l₁ <:+ l₂, l₂.lookup k
+
 theorem IsInfix.lookup_eq_none {l₁ l₂ : List (α × β)} (h : l₁ <:+: l₂) :
     List.lookup k l₂ = none → List.lookup k l₁ = none :=
   h.sublist.lookup_eq_none
 
+grind_pattern IsInfix.lookup_eq_none => l₁ <:+: l₂, l₁.lookup k
+grind_pattern IsInfix.lookup_eq_none => l₁ <:+: l₂, l₂.lookup k
+
 end lookup
 
 end List

src/Init/Data/List/Impl.lean

@@ -261,11 +261,11 @@ Examples:
 /-- Tail recursive implementation of `findRev?`. This is only used at runtime. -/
 def findRev?TR (p : α → Bool) (l : List α) : Option α := l.reverse.find? p
 
-@[simp] theorem find?_singleton {a : α} : [a].find? p = if p a then some a else none := by
+@[simp, grind =] theorem find?_singleton {a : α} : [a].find? p = if p a then some a else none := by
   simp only [find?]
   split <;> simp_all
 
-@[simp] theorem find?_append {xs ys : List α} : (xs ++ ys).find? p = (xs.find? p).or (ys.find? p) := by
+@[simp, grind =] theorem find?_append {xs ys : List α} : (xs ++ ys).find? p = (xs.find? p).or (ys.find? p) := by
   induction xs with
   | nil => simp [find?]
   | cons x xs ih =>
@@ -287,12 +287,12 @@ def findRev?TR (p : α → Bool) (l : List α) : Option α := l.reverse.find? p
 /-- Tail recursive implementation of `finSomedRev?`. This is only used at runtime. -/
 def findSomeRev?TR (f : α → Option β) (l : List α) : Option β := l.reverse.findSome? f
 
-@[simp] theorem findSome?_singleton {a : α} :
+@[simp, grind =] theorem findSome?_singleton {a : α} :
     [a].findSome? f = f a := by
   simp only [findSome?_cons, findSome?_nil]
   split <;> simp_all
 
-@[simp] theorem findSome?_append {xs ys : List α} : (xs ++ ys).findSome? f = (xs.findSome? f).or (ys.findSome? f) := by
+@[simp, grind =] theorem findSome?_append {xs ys : List α} : (xs ++ ys).findSome? f = (xs.findSome? f).or (ys.findSome? f) := by
   induction xs with
   | nil => simp [findSome?]
   | cons x xs ih =>
@@ -550,7 +550,7 @@ def zipIdxTR (l : List α) (n : Nat := 0) : List (α × Nat) :=
   (as.foldr (fun a (n, acc) => (n-1, (a, n-1) :: acc)) (n + as.size, [])).2
 
 @[csimp] theorem zipIdx_eq_zipIdxTR : @zipIdx = @zipIdxTR := by
-  funext α l n; simp only [zipIdxTR, size_toArray]
+  funext α l n; simp only [zipIdxTR]
   let f := fun (a : α) (n, acc) => (n-1, (a, n-1) :: acc)
   let rec go : ∀ l i, l.foldr f (i + l.length, []) = (i, zipIdx l i)
     | [], n => rfl
@@ -571,7 +571,7 @@ def enumFromTR (n : Nat) (l : List α) : List (Nat × α) :=
 set_option linter.deprecated false in
 @[deprecated zipIdx_eq_zipIdxTR (since := "2025-01-21"), csimp]
 theorem enumFrom_eq_enumFromTR : @enumFrom = @enumFromTR := by
-  funext α n l; simp only [enumFromTR, size_toArray]
+  funext α n l; simp only [enumFromTR]
   let f := fun (a : α) (n, acc) => (n-1, (n-1, a) :: acc)
   let rec go : ∀ l n, l.foldr f (n + l.length, []) = (n, enumFrom n l)
     | [], n => rfl

src/Init/Data/List/Lemmas.lean

@@ -575,9 +575,9 @@ theorem isEmpty_iff_length_eq_zero {l : List α} : l.isEmpty ↔ l.length = 0 :=
 
 /-! ### any / all -/
 
-theorem any_eq {l : List α} : l.any p = decide (∃ x, x ∈ l ∧ p x) := by induction l <;> simp [*]
+@[grind =] theorem any_eq {l : List α} : l.any p = decide (∃ x, x ∈ l ∧ p x) := by induction l <;> simp [*]
 
-theorem all_eq {l : List α} : l.all p = decide (∀ x, x ∈ l → p x) := by induction l <;> simp [*]
+@[grind =] theorem all_eq {l : List α} : l.all p = decide (∀ x, x ∈ l → p x) := by induction l <;> simp [*]
 
 theorem decide_exists_mem {l : List α} {p : α → Prop} [DecidablePred p] :
     decide (∃ x, x ∈ l ∧ p x) = l.any p := by
@@ -834,7 +834,7 @@ theorem getElem_length_sub_one_eq_getLast {l : List α} (h : l.length - 1 < l.le
   rw [← getLast_eq_getElem]
 
 @[simp, grind] theorem getLast_cons_cons {a : α} {l : List α} :
-    getLast (a :: b :: l) (by simp) = getLast (b :: l) (by simp) := by
+    getLast (a :: b :: l) (by simp) = getLast (b :: l) (by simp) :=
   rfl
 
 theorem getLast_cons {a : α} {l : List α} : ∀ (h : l ≠ nil),
@@ -1128,7 +1128,8 @@ theorem map_singleton {f : α → β} {a : α} : map f [a] = [f a] := rfl
 
 -- 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} : ∀ {l : List α}, b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b
+@[simp 500, grind =] theorem mem_map {f : α → β} :
+    ∀ {l : List α}, b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b
   | [] => by simp
   | _ :: l => by simp [mem_map (l := l), eq_comm (a := b)]
 
@@ -1252,7 +1253,7 @@ theorem tailD_map {f : α → β} {l l' : List α} :
 theorem getLastD_map {f : α → β} {l : List α} {a : α} : (map f l).getLastD (f a) = f (l.getLastD a) := by
   simp
 
-@[simp] theorem map_map {g : β → γ} {f : α → β} {l : List α} :
+@[simp, grind _=_] theorem map_map {g : β → γ} {f : α → β} {l : List α} :
     map g (map f l) = map (g ∘ f) l := by induction l <;> simp_all
 
 /-! ### filter -/
@@ -1317,6 +1318,19 @@ theorem forall_mem_filter {l : List α} {p : α → Bool} {P : α → Prop} :
     (∀ (i) (_ : i ∈ l.filter p), P i) ↔ ∀ (j) (_ : j ∈ l), p j → P j := by
   simp
 
+@[grind] theorem getElem_filter {xs : List α} {p : α → Bool} {i : Nat} (h : i < (xs.filter p).length) :
+    p (xs.filter p)[i] :=
+  (mem_filter.mp (getElem_mem h)).2
+
+theorem getElem?_filter {xs : List α} {p : α → Bool} {i : Nat} (h : i < (xs.filter p).length)
+    (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 : ∀ {l}, filter p (filter q l) = filter (fun a => p a && q a) l
   | [] => rfl
   | a :: l => by by_cases hp : p a <;> by_cases hq : q a <;> simp [hp, hq, filter_filter]
@@ -1337,7 +1351,7 @@ theorem foldr_filter {p : α → Bool} {f : α → β → β} {l : List α} {ini
     simp only [filter_cons, foldr_cons]
     split <;> simp [ih]
 
-theorem filter_map {f : β → α} {p : α → Bool} {l : List β} :
+@[grind _=_] theorem filter_map {f : β → α} {p : α → Bool} {l : List β} :
     filter p (map f l) = map f (filter (p ∘ f) l) := by
   induction l with
   | nil => rfl
@@ -1572,9 +1586,6 @@ theorem not_mem_append {a : α} {s t : List α} (h₁ : a ∉ s) (h₂ : a ∉ t
 theorem mem_append_eq {a : α} {s t : List α} : (a ∈ s ++ t) = (a ∈ s ∨ a ∈ t) :=
   propext mem_append
 
-@[deprecated mem_append_left (since := "2024-11-20")] abbrev mem_append_of_mem_left := @mem_append_left
-@[deprecated mem_append_right (since := "2024-11-20")] abbrev mem_append_of_mem_right := @mem_append_right
-
 /--
 See also `eq_append_cons_of_mem`, which proves a stronger version
 in which the initial list must not contain the element.
@@ -1882,7 +1893,7 @@ theorem eq_nil_or_concat : ∀ l : List α, l = [] ∨ ∃ l' b, l = concat l' b
 
 /-! ### flatten -/
 
-@[simp] theorem length_flatten {L : List (List α)} : L.flatten.length = (L.map length).sum := by
+@[simp, grind _=_] theorem length_flatten {L : List (List α)} : L.flatten.length = (L.map length).sum := by
   induction L with
   | nil => rfl
   | cons =>
@@ -2052,7 +2063,7 @@ theorem eq_iff_flatten_eq : ∀ {L L' : List (List α)},
 
 /-! ### flatMap -/
 
-theorem flatMap_def {l : List α} {f : α → List β} : l.flatMap f = flatten (map f l) := rfl
+@[grind _=_] theorem flatMap_def {l : List α} {f : α → List β} : l.flatMap f = flatten (map f l) := rfl
 
 @[simp] theorem flatMap_id {L : List (List α)} : L.flatMap id = L.flatten := by simp [flatMap_def]
 
@@ -2721,6 +2732,7 @@ example {xs : List Nat} : xs.foldl (· + ·) 1 > 0 := by
     intros; omega
 ```
 -/
+@[expose]
 def foldlRecOn {motive : β → Sort _} : ∀ (l : List α) (op : β → α → β) {b : β} (_ : motive b)
     (_ : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ l), motive (op b a)), motive (List.foldl op b l)
   | [], _, _, hb, _ => hb
@@ -2755,6 +2767,7 @@ example {xs : List Nat} : xs.foldr (· + ·) 1 > 0 := by
     intros; omega
 ```
 -/
+@[expose]
 def foldrRecOn {motive : β → Sort _} : ∀ (l : List α) (op : α → β → β) {b : β} (_ : motive b)
     (_ : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ l), motive (op a b)), motive (List.foldr op b l)
   | nil, _, _, hb, _ => hb
@@ -2778,8 +2791,8 @@ We can prove that two folds over the same list are related (by some arbitrary re
 if we know that the initial elements are related and the folding function, for each element of the list,
 preserves the relation.
 -/
-theorem foldl_rel {l : List α} {f g : β → α → β} {a b : β} {r : β → β → Prop}
-    (h : r a b) (h' : ∀ (a : α), a ∈ l → ∀ (c c' : β), r c c' → r (f c a) (g c' a)) :
+theorem foldl_rel {l : List 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 ∈ l → ∀ (c : β) (c' : γ), r c c' → r (f c a) (g c' a)) :
     r (l.foldl (fun acc a => f acc a) a) (l.foldl (fun acc a => g acc a) b) := by
   induction l generalizing a b with
   | nil => simp_all
@@ -2794,8 +2807,8 @@ We can prove that two folds over the same list are related (by some arbitrary re
 if we know that the initial elements are related and the folding function, for each element of the list,
 preserves the relation.
 -/
-theorem foldr_rel {l : List α} {f g : α → β → β} {a b : β} {r : β → β → Prop}
-    (h : r a b) (h' : ∀ (a : α), a ∈ l → ∀ (c c' : β), r c c' → r (f a c) (g a c')) :
+theorem foldr_rel {l : List 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 ∈ l → ∀ (c : β) (c' : γ), r c c' → r (f a c) (g a c')) :
     r (l.foldr (fun a acc => f a acc) a) (l.foldr (fun a acc => g a acc) b) := by
   induction l generalizing a b with
   | nil => simp_all
@@ -3704,17 +3717,6 @@ theorem mem_iff_get? {a} {l : List α} : a ∈ l ↔ ∃ n, l.get? n = some a :=
 
 /-! ### Deprecations -/
 
-@[deprecated get?_eq_none (since := "2024-11-29")] abbrev get?_len_le := @getElem?_eq_none
-@[deprecated getElem?_eq_some_iff (since := "2024-11-29")]
-abbrev getElem?_eq_some := @getElem?_eq_some_iff
-@[deprecated get?_eq_some_iff (since := "2024-11-29")]
-abbrev get?_eq_some := @getElem?_eq_some_iff
-@[deprecated LawfulGetElem.getElem?_def (since := "2024-11-29")]
-theorem getElem?_eq (l : List α) (i : Nat) :
-    l[i]? = if h : i < l.length then some l[i] else none :=
-  getElem?_def _ _
-@[deprecated getElem?_eq_none (since := "2024-11-29")] abbrev getElem?_len_le := @getElem?_eq_none
-
 @[deprecated _root_.isSome_getElem? (since := "2024-12-09")]
 theorem isSome_getElem? {l : List α} {i : Nat} : l[i]?.isSome ↔ i < l.length := by
   simp

src/Init/Data/List/MapIdx.lean

@@ -27,7 +27,7 @@ that the index is valid.
 
 `List.mapIdx` is a variant that does not provide the function with evidence that the index is valid.
 -/
-@[inline] def mapFinIdx (as : List α) (f : (i : Nat) → α → (h : i < as.length) → β) : List β :=
+@[inline, expose] def mapFinIdx (as : List α) (f : (i : Nat) → α → (h : i < as.length) → β) : List β :=
   go as #[] (by simp)
 where
   /-- Auxiliary for `mapFinIdx`:
@@ -44,7 +44,7 @@ returning the list of results.
 `List.mapFinIdx` is a variant that additionally provides the function with a proof that the index
 is valid.
 -/
-@[inline] def mapIdx (f : Nat → α → β) (as : List α) : List β := go as #[] where
+@[inline, expose] def mapIdx (f : Nat → α → β) (as : List α) : List β := go as #[] where
   /-- Auxiliary for `mapIdx`:
   `mapIdx.go [a₀, a₁, ...] acc = acc.toList ++ [f acc.size a₀, f (acc.size + 1) a₁, ...]` -/
   @[specialize] go : List α → Array β → List β
@@ -91,7 +91,7 @@ is valid.
   subst w
   rfl
 
-@[simp]
+@[simp, grind =]
 theorem mapFinIdx_nil {f : (i : Nat) → α → (h : i < 0) → β} : mapFinIdx [] f = [] :=
   rfl
 
@@ -101,7 +101,7 @@ theorem mapFinIdx_nil {f : (i : Nat) → α → (h : i < 0) → β} : mapFinIdx
   | nil => simpa using h
   | cons _ _ ih => simp [mapFinIdx.go, ih]
 
-@[simp] theorem length_mapFinIdx {as : List α} {f : (i : Nat) → α → (h : i < as.length) → β} :
+@[simp, grind =] theorem length_mapFinIdx {as : List α} {f : (i : Nat) → α → (h : i < as.length) → β} :
     (as.mapFinIdx f).length = as.length := by
   simp [mapFinIdx, length_mapFinIdx_go]
 
@@ -129,7 +129,7 @@ theorem getElem_mapFinIdx_go {as : List α} {f : (i : Nat) → α → (h : i < a
     · have h₃ : i - acc.size = (i - (acc.size + 1)) + 1 := by omega
       simp [h₃]
 
-@[simp] theorem getElem_mapFinIdx {as : List α} {f : (i : Nat) → α → (h : i < as.length) → β} {i : Nat} {h} :
+@[simp, grind =] theorem getElem_mapFinIdx {as : List α} {f : (i : Nat) → α → (h : i < as.length) → β} {i : Nat} {h} :
     (as.mapFinIdx f)[i] = f i (as[i]'(by simp at h; omega)) (by simp at h; omega) := by
   simp [mapFinIdx, getElem_mapFinIdx_go]
 
@@ -137,18 +137,19 @@ theorem mapFinIdx_eq_ofFn {as : List α} {f : (i : Nat) → α → (h : i < as.l
     as.mapFinIdx f = List.ofFn fun i : Fin as.length => f i as[i] i.2 := by
   apply ext_getElem <;> simp
 
-@[simp] theorem getElem?_mapFinIdx {l : List α} {f : (i : Nat) → α → (h : i < l.length) → β} {i : Nat} :
+@[simp, grind =] theorem getElem?_mapFinIdx {l : List α} {f : (i : Nat) → α → (h : i < l.length) → β} {i : Nat} :
     (l.mapFinIdx f)[i]? = l[i]?.pbind fun x m => some <| f i x (by simp [getElem?_eq_some_iff] at m; exact m.1) := by
   simp only [getElem?_def, length_mapFinIdx, getElem_mapFinIdx]
   split <;> simp
 
-@[simp]
+@[simp, grind =]
 theorem mapFinIdx_cons {l : List α} {a : α} {f : (i : Nat) → α → (h : i < l.length + 1) → β} :
     mapFinIdx (a :: l) f = f 0 a (by omega) :: mapFinIdx l (fun i a h => f (i + 1) a (by omega)) := by
   apply ext_getElem
   · simp
   · rintro (_|i) h₁ h₂ <;> simp
 
+@[grind =]
 theorem mapFinIdx_append {xs ys : List α} {f : (i : Nat) → α → (h : i < (xs ++ ys).length) → β} :
     (xs ++ ys).mapFinIdx f =
       xs.mapFinIdx (fun i a h => f i a (by simp; omega)) ++
@@ -165,7 +166,7 @@ theorem mapFinIdx_append {xs ys : List α} {f : (i : Nat) → α → (h : i < (x
       congr
       omega
 
-@[simp] theorem mapFinIdx_concat {l : List α} {e : α} {f : (i : Nat) → α → (h : i < (l ++ [e]).length) → β}:
+@[simp, grind =] theorem mapFinIdx_concat {l : List α} {e : α} {f : (i : Nat) → α → (h : i < (l ++ [e]).length) → β}:
     (l ++ [e]).mapFinIdx f = l.mapFinIdx (fun i a h => f i a (by simp; omega)) ++ [f l.length e (by simp)] := by
   simp [mapFinIdx_append]
 
@@ -201,7 +202,7 @@ theorem exists_of_mem_mapFinIdx {b : β} {l : List α} {f : (i : Nat) → α →
   obtain ⟨h', rfl⟩ := h
   exact ⟨i, h', rfl⟩
 
-@[simp] theorem mem_mapFinIdx {b : β} {l : List α} {f : (i : Nat) → α → (h : i < l.length) → β} :
+@[simp, grind =] theorem mem_mapFinIdx {b : β} {l : List α} {f : (i : Nat) → α → (h : i < l.length) → β} :
     b ∈ l.mapFinIdx f ↔ ∃ (i : Nat) (h : i < l.length), f i l[i] h = b := by
   constructor
   · intro h
@@ -287,7 +288,7 @@ theorem mapFinIdx_eq_mapFinIdx_iff {l : List α} {f g : (i : Nat) → α → (h
   rw [eq_comm, mapFinIdx_eq_iff]
   simp [Fin.forall_iff]
 
-@[simp] theorem mapFinIdx_mapFinIdx {l : List α}
+@[simp, grind =] theorem mapFinIdx_mapFinIdx {l : List α}
     {f : (i : Nat) → α → (h : i < l.length) → β}
     {g : (i : Nat) → β → (h : i < (l.mapFinIdx f).length) → γ} :
     (l.mapFinIdx f).mapFinIdx g = l.mapFinIdx (fun i a h => g i (f i a h) (by simpa)) := by
@@ -303,7 +304,7 @@ theorem mapFinIdx_eq_replicate_iff {l : List α} {f : (i : Nat) → α → (h :
   · rintro w b i h rfl
     exact w i h
 
-@[simp] theorem mapFinIdx_reverse {l : List α} {f : (i : Nat) → α → (h : i < l.reverse.length) → β} :
+@[simp, grind =] theorem mapFinIdx_reverse {l : List α} {f : (i : Nat) → α → (h : i < l.reverse.length) → β} :
     l.reverse.mapFinIdx f =
       (l.mapFinIdx (fun i a h => f (l.length - 1 - i) a (by simp; omega))).reverse := by
   simp [mapFinIdx_eq_iff]
@@ -313,14 +314,14 @@ theorem mapFinIdx_eq_replicate_iff {l : List α} {f : (i : Nat) → α → (h :
 
 /-! ### mapIdx -/
 
-@[simp]
+@[simp, grind =]
 theorem mapIdx_nil {f : Nat → α → β} : mapIdx f [] = [] :=
   rfl
 
 theorem mapIdx_go_length {acc : Array β} :
     length (mapIdx.go f l acc) = length l + acc.size := by
   induction l generalizing acc with
-  | nil => simp only [mapIdx.go, length_nil, Nat.zero_add]
+  | nil => simp [mapIdx.go]
   | cons _ _ ih =>
     simp only [mapIdx.go, ih, Array.size_push, Nat.add_succ, length_cons, Nat.add_comm]
 
@@ -333,7 +334,7 @@ theorem length_mapIdx_go : ∀ {l : List α} {acc : Array β},
     simp
     omega
 
-@[simp] theorem length_mapIdx {l : List α} : (l.mapIdx f).length = l.length := by
+@[simp, grind =] theorem length_mapIdx {l : List α} : (l.mapIdx f).length = l.length := by
   simp [mapIdx, length_mapIdx_go]
 
 theorem getElem?_mapIdx_go : ∀ {l : List α} {acc : Array β} {i : Nat},
@@ -356,11 +357,11 @@ theorem getElem?_mapIdx_go : ∀ {l : List α} {acc : Array β} {i : Nat},
     · have : i - acc.size = i - (acc.size + 1) + 1 := by omega
       simp_all
 
-@[simp] theorem getElem?_mapIdx {l : List α} {i : Nat} :
+@[simp, grind =] theorem getElem?_mapIdx {l : List α} {i : Nat} :
     (l.mapIdx f)[i]? = Option.map (f i) l[i]? := by
   simp [mapIdx, getElem?_mapIdx_go]
 
-@[simp] theorem getElem_mapIdx {l : List α} {f : Nat → α → β} {i : Nat} {h : i < (l.mapIdx f).length} :
+@[simp, grind =] theorem getElem_mapIdx {l : List α} {f : Nat → α → β} {i : Nat} {h : i < (l.mapIdx f).length} :
     (l.mapIdx f)[i] = f i (l[i]'(by simpa using h)) := by
   apply Option.some_inj.mp
   rw [← getElem?_eq_getElem, getElem?_mapIdx, getElem?_eq_getElem (by simpa using h)]
@@ -384,18 +385,19 @@ theorem mapIdx_eq_zipIdx_map {l : List α} {f : Nat → α → β} :
 @[deprecated mapIdx_eq_zipIdx_map (since := "2025-01-21")]
 abbrev mapIdx_eq_enum_map := @mapIdx_eq_zipIdx_map
 
-@[simp]
+@[simp, grind =]
 theorem mapIdx_cons {l : List α} {a : α} :
     mapIdx f (a :: l) = f 0 a :: mapIdx (fun i => f (i + 1)) l := by
   simp [mapIdx_eq_zipIdx_map, List.zipIdx_succ]
 
+@[grind =]
 theorem mapIdx_append {xs ys : List α} :
     (xs ++ ys).mapIdx f = xs.mapIdx f ++ ys.mapIdx fun i => f (i + xs.length) := by
   induction xs generalizing f with
   | nil => rfl
   | cons _ _ ih => simp [ih (f := fun i => f (i + 1)), Nat.add_assoc]
 
-@[simp] theorem mapIdx_concat {l : List α} {e : α} :
+@[simp, grind =] theorem mapIdx_concat {l : List α} {e : α} :
     mapIdx f (l ++ [e]) = mapIdx f l ++ [f l.length e] := by
   simp [mapIdx_append]
 
@@ -415,7 +417,7 @@ theorem exists_of_mem_mapIdx {b : β} {l : List α}
   rw [mapIdx_eq_mapFinIdx] at h
   simpa [Fin.exists_iff] using exists_of_mem_mapFinIdx h
 
-@[simp] theorem mem_mapIdx {b : β} {l : List α} :
+@[simp, grind =] theorem mem_mapIdx {b : β} {l : List α} :
     b ∈ mapIdx f l ↔ ∃ (i : Nat) (h : i < l.length), f i l[i] = b := by
   constructor
   · intro h
@@ -470,7 +472,7 @@ theorem mapIdx_eq_mapIdx_iff {l : List α} :
     · intro i h₁ h₂
       simp [w]
 
-@[simp] theorem mapIdx_set {l : List α} {i : Nat} {a : α} :
+@[simp, grind =] theorem mapIdx_set {l : List α} {i : Nat} {a : α} :
     (l.set i a).mapIdx f = (l.mapIdx f).set i (f i a) := by
   simp only [mapIdx_eq_iff, getElem?_set, length_mapIdx, getElem?_mapIdx]
   intro i
@@ -478,16 +480,16 @@ theorem mapIdx_eq_mapIdx_iff {l : List α} :
   · split <;> simp_all
   · rfl
 
-@[simp] theorem head_mapIdx {l : List α} {f : Nat → α → β} {w : mapIdx f l ≠ []} :
+@[simp, grind =] theorem head_mapIdx {l : List α} {f : Nat → α → β} {w : mapIdx f l ≠ []} :
     (mapIdx f l).head w = f 0 (l.head (by simpa using w)) := by
   cases l with
   | nil => simp at w
   | cons _ _ => simp
 
-@[simp] theorem head?_mapIdx {l : List α} {f : Nat → α → β} : (mapIdx f l).head? = l.head?.map (f 0) := by
+@[simp, grind =] theorem head?_mapIdx {l : List α} {f : Nat → α → β} : (mapIdx f l).head? = l.head?.map (f 0) := by
   cases l <;> simp
 
-@[simp] theorem getLast_mapIdx {l : List α} {f : Nat → α → β} {h} :
+@[simp, grind =] theorem getLast_mapIdx {l : List α} {f : Nat → α → β} {h} :
     (mapIdx f l).getLast h = f (l.length - 1) (l.getLast (by simpa using h)) := by
   cases l with
   | nil => simp at h
@@ -498,13 +500,13 @@ theorem mapIdx_eq_mapIdx_iff {l : List α} :
     simp only [← mapIdx_cons, getElem_mapIdx]
     simp
 
-@[simp] theorem getLast?_mapIdx {l : List α} {f : Nat → α → β} :
+@[simp, grind =] theorem getLast?_mapIdx {l : List α} {f : Nat → α → β} :
     (mapIdx f l).getLast? = (getLast? l).map (f (l.length - 1)) := by
   cases l
   · simp
   · rw [getLast?_eq_getLast, getLast?_eq_getLast, getLast_mapIdx] <;> simp
 
-@[simp] theorem mapIdx_mapIdx {l : List α} {f : Nat → α → β} {g : Nat → β → γ} :
+@[simp, grind =] theorem mapIdx_mapIdx {l : List α} {f : Nat → α → β} {g : Nat → β → γ} :
     (l.mapIdx f).mapIdx g = l.mapIdx (fun i => g i ∘ f i) := by
   simp [mapIdx_eq_iff]
 
@@ -517,7 +519,7 @@ theorem mapIdx_eq_replicate_iff {l : List α} {f : Nat → α → β} {b : β} :
   · rintro w _ i h rfl
     exact w i h
 
-@[simp] theorem mapIdx_reverse {l : List α} {f : Nat → α → β} :
+@[simp, grind =] theorem mapIdx_reverse {l : List α} {f : Nat → α → β} :
     l.reverse.mapIdx f = (mapIdx (fun i => f (l.length - 1 - i)) l).reverse := by
   simp [mapIdx_eq_iff]
   intro i

src/Init/Data/List/Monadic.lean

@@ -44,6 +44,7 @@ This is a non-tail-recursive variant of `List.mapM` that's easier to reason abou
 as the main definition and replaced by the tail-recursive version because they can only be proved
 equal when `m` is a `LawfulMonad`.
 -/
+@[expose]
 def mapM' [Monad m] (f : α → m β) : List α → m (List β)
   | [] => pure []
   | a :: l => return (← f a) :: (← l.mapM' f)

src/Init/Data/List/Nat/Erase.lean

@@ -14,6 +14,7 @@ set_option linter.indexVariables true -- Enforce naming conventions for index va
 
 namespace List
 
+@[grind =]
 theorem getElem?_eraseIdx {l : List α} {i : Nat} {j : Nat} :
     (l.eraseIdx i)[j]? = if j < i then l[j]? else l[j + 1]? := by
   rw [eraseIdx_eq_take_drop_succ, getElem?_append]
@@ -49,6 +50,7 @@ theorem getElem?_eraseIdx_of_ge {l : List α} {i : Nat} {j : Nat} (h : i ≤ j)
   intro h'
   omega
 
+@[grind =]
 theorem getElem_eraseIdx {l : List α} {i : Nat} {j : Nat} (h : j < (l.eraseIdx i).length) :
     (l.eraseIdx i)[j] = if h' : j < i then
         l[j]'(by have := length_eraseIdx_le l i; omega)
@@ -123,6 +125,48 @@ theorem eraseIdx_set_gt {l : List α} {i : Nat} {j : Nat} {a : α} (h : i < j) :
       · have t : i ≠ n := by omega
         simp [t]
 
+@[grind =]
+theorem eraseIdx_set {xs : List α} {i : Nat} {a : α} {j : Nat} :
+    (xs.set i a).eraseIdx j =
+      if j < i then
+        (xs.eraseIdx j).set (i - 1) a
+      else if j = i then
+        xs.eraseIdx i
+      else
+        (xs.eraseIdx j).set i a := 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 : List α} {i : Nat} {j : Nat} {a : α} (h : i ≤ j) :
+    (xs.eraseIdx i).set j a = (xs.set (j + 1) a).eraseIdx i := by
+  rw [eraseIdx_set_lt]
+  · simp
+  · omega
+
+theorem set_eraseIdx_gt {xs : List α} {i : Nat} {j : Nat} {a : α} (h : j < i) :
+    (xs.eraseIdx i).set j a = (xs.set j a).eraseIdx i := by
+  rw [eraseIdx_set_gt]
+  omega
+
+@[grind =]
+theorem set_eraseIdx {xs : List α} {i : Nat} {j : Nat} {a : α} :
+    (xs.eraseIdx i).set j a =
+      if i ≤ j then
+        (xs.set (j + 1) a).eraseIdx i
+      else
+        (xs.set j a).eraseIdx i := by
+  split <;> rename_i h'
+  · rw [set_eraseIdx_le]
+    omega
+  · rw [set_eraseIdx_gt]
+    omega
+
 @[simp] theorem set_getElem_succ_eraseIdx_succ
     {l : List α} {i : Nat} (h : i + 1 < l.length) :
     (l.eraseIdx (i + 1)).set i l[i + 1] = l.eraseIdx i := by

src/Init/Data/List/Nat/Modify.lean

@@ -156,7 +156,7 @@ theorem modifyHead_eq_modify_zero (f : α → α) (l : List α) :
 @[simp] theorem modify_eq_nil_iff {f : α → α} {i} {l : List α} :
     l.modify i f = [] ↔ l = [] := by cases l <;> cases i <;> simp
 
-theorem getElem?_modify (f : α → α) :
+@[grind =] theorem getElem?_modify (f : α → α) :
     ∀ i (l : List α) j, (l.modify i f)[j]? = (fun a => if i = j then f a else a) <$> l[j]?
   | n, l, 0 => by cases l <;> cases n <;> simp
   | n, [], _+1 => by cases n <;> rfl
@@ -167,7 +167,7 @@ theorem getElem?_modify (f : α → α) :
     cases h' : l[j]? <;> by_cases h : i = j <;>
       simp [h, if_pos, if_neg, Option.map, mt Nat.succ.inj, not_false_iff, h']
 
-@[simp] theorem length_modify (f : α → α) : ∀ (l : List α) i, (l.modify i f).length = l.length :=
+@[simp, grind =] theorem length_modify (f : α → α) : ∀ (l : List α) i, (l.modify i f).length = l.length :=
   length_modifyTailIdx _ fun l => by cases l <;> rfl
 
 @[simp] theorem getElem?_modify_eq (f : α → α) (i) (l : List α) :
@@ -178,7 +178,7 @@ theorem getElem?_modify (f : α → α) :
     (l.modify i f)[j]? = l[j]? := by
   simp only [getElem?_modify, if_neg h, id_map']
 
-theorem getElem_modify (f : α → α) (i) (l : List α) (j) (h : j < (l.modify i f).length) :
+@[grind =] theorem getElem_modify (f : α → α) (i) (l : List α) (j) (h : j < (l.modify i f).length) :
     (l.modify i f)[j] =
       if i = j then f (l[j]'(by simp at h; omega)) else l[j]'(by simp at h; omega) := by
   rw [getElem_eq_iff, getElem?_modify]
@@ -245,6 +245,7 @@ theorem exists_of_modify (f : α → α) {i} {l : List α} (h : i < l.length) :
 @[simp] theorem modify_id (i) (l : List α) : l.modify i id = l := by
   simp [modify]
 
+@[grind =]
 theorem take_modify (f : α → α) (i j) (l : List α) :
     (l.modify i f).take j = (l.take j).modify i f := by
   induction j generalizing l i with
@@ -257,6 +258,7 @@ theorem take_modify (f : α → α) (i j) (l : List α) :
       | zero => simp
       | succ i => simp [ih]
 
+@[grind =]
 theorem drop_modify_of_lt (f : α → α) (i j) (l : List α) (h : i < j) :
     (l.modify i f).drop j = l.drop j := by
   apply ext_getElem
@@ -266,6 +268,7 @@ theorem drop_modify_of_lt (f : α → α) (i j) (l : List α) (h : i < j) :
     intro h'
     omega
 
+@[grind =]
 theorem drop_modify_of_ge (f : α → α) (i j) (l : List α) (h : i ≥ j) :
     (l.modify i f).drop j = (l.drop j).modify (i - j) f  := by
   apply ext_getElem

src/Init/Data/List/Nat/Pairwise.lean

@@ -55,7 +55,7 @@ theorem sublist_eq_map_getElem {l l' : List α} (h : l' <+ l) : ∃ is : List (F
     simp [Function.comp_def, pairwise_map, IH, ← get_eq_getElem, get_cons_zero, get_cons_succ']
 
 set_option linter.listVariables false in
-theorem pairwise_iff_getElem : Pairwise R l ↔
+theorem pairwise_iff_getElem {l : List α} : Pairwise R l ↔
     ∀ (i j : Nat) (_hi : i < l.length) (_hj : j < l.length) (_hij : i < j), R l[i] l[j] := by
   rw [pairwise_iff_forall_sublist]
   constructor <;> intro h

src/Init/Data/List/Nat/Range.lean

@@ -617,9 +617,6 @@ set_option linter.deprecated false
 @[deprecated zipIdx_eq_nil_iff (since := "2025-01-21"), simp]
 theorem enum_eq_nil_iff {l : List α} : List.enum l = [] ↔ l = [] := enumFrom_eq_nil
 
-@[deprecated zipIdx_eq_nil_iff (since := "2024-11-04")]
-theorem enum_eq_nil {l : List α} : List.enum l = [] ↔ l = [] := enum_eq_nil_iff
-
 @[deprecated zipIdx_singleton (since := "2025-01-21"), simp]
 theorem enum_singleton (x : α) : enum [x] = [(0, x)] := rfl
 

src/Init/Data/List/Nat/Sublist.lean

@@ -30,7 +30,7 @@ theorem IsSuffix.getElem {xs ys : List α} (h : xs <:+ ys) {i} (hn : i < xs.leng
   have := h.length_le
   omega
 
-theorem isSuffix_iff : l₁ <:+ l₂ ↔
+theorem suffix_iff_getElem? {l₁ l₂ : List α} : l₁ <:+ l₂ ↔
     l₁.length ≤ l₂.length ∧ ∀ i (h : i < l₁.length), l₂[i + l₂.length - l₁.length]? = some l₁[i] := by
   suffices l₁.length ≤ l₂.length ∧ l₁ <:+ l₂ ↔
       l₁.length ≤ l₂.length ∧ ∀ i (h : i < l₁.length), l₂[i + l₂.length - l₁.length]? = some l₁[i] by
@@ -41,7 +41,7 @@ theorem isSuffix_iff : l₁ <:+ l₂ ↔
       exact (this.mpr h).2
   simp only [and_congr_right_iff]
   intro le
-  rw [← reverse_prefix, isPrefix_iff]
+  rw [← reverse_prefix, prefix_iff_getElem?]
   simp only [length_reverse]
   constructor
   · intro w i h
@@ -60,15 +60,33 @@ theorem isSuffix_iff : l₁ <:+ l₂ ↔
     rw [w, getElem_reverse]
     exact Nat.lt_of_lt_of_le h le
 
-theorem isInfix_iff : l₁ <:+: l₂ ↔
+@[deprecated suffix_iff_getElem? (since := "2025-05-27")]
+abbrev isSuffix_iff := @suffix_iff_getElem?
+
+theorem suffix_iff_getElem {l₁ l₂ : List α} :
+    l₁ <:+ l₂ ↔ ∃ (_ : l₁.length ≤ l₂.length), ∀ i (_ : i < l₁.length), l₂[i + l₂.length - l₁.length] = l₁[i] := by
+  rw [suffix_iff_getElem?]
+  constructor
+  · rintro ⟨h, w⟩
+    refine ⟨h, fun i h => ?_⟩
+    specialize w i h
+    rw [getElem?_eq_getElem] at w
+    simpa using w
+  · rintro ⟨h, w⟩
+    refine ⟨h, fun i h => ?_⟩
+    specialize w i h
+    rw [getElem?_eq_getElem]
+    simpa using w
+
+theorem infix_iff_getElem? {l₁ l₂ : List α} : l₁ <:+: l₂ ↔
     ∃ k, l₁.length + k ≤ l₂.length ∧ ∀ i (h : i < l₁.length), l₂[i + k]? = some l₁[i] := by
   constructor
   · intro h
     obtain ⟨t, p, s⟩ := infix_iff_suffix_prefix.mp h
     refine ⟨t.length - l₁.length, by have := p.length_le; have := s.length_le; omega, ?_⟩
-    rw [isSuffix_iff] at p
+    rw [suffix_iff_getElem?] at p
     obtain ⟨p', p⟩ := p
-    rw [isPrefix_iff] at s
+    rw [prefix_iff_getElem?] at s
     intro i h
     rw [s _ (by omega)]
     specialize p i (by omega)
@@ -93,6 +111,9 @@ theorem isInfix_iff : l₁ <:+: l₂ ↔
       simp_all
       omega
 
+@[deprecated infix_iff_getElem? (since := "2025-05-27")]
+abbrev isInfix_iff := @infix_iff_getElem?
+
 theorem suffix_iff_eq_append : l₁ <:+ l₂ ↔ take (length l₂ - length l₁) l₂ ++ l₁ = l₂ :=
   ⟨by rintro ⟨r, rfl⟩; simp only [length_append, Nat.add_sub_cancel_right, take_left], fun e =>
     ⟨_, e⟩⟩
@@ -115,7 +136,7 @@ theorem suffix_iff_eq_drop : l₁ <:+ l₂ ↔ l₁ = drop (length l₂ - length
   ⟨fun h => append_cancel_left <| (suffix_iff_eq_append.1 h).trans (take_append_drop _ _).symm,
     fun e => e.symm ▸ drop_suffix _ _⟩
 
-theorem prefix_take_le_iff {xs : List α} (hm : i < xs.length) :
+@[grind =] theorem prefix_take_le_iff {xs : List α} (hm : i < xs.length) :
     xs.take i <+: xs.take j ↔ i ≤ j := by
   simp only [prefix_iff_eq_take, length_take]
   induction i generalizing xs j with

src/Init/Data/List/Nat/TakeDrop.lean

@@ -199,7 +199,7 @@ theorem take_eq_dropLast {l : List α} {i : Nat} (h : i + 1 = l.length) :
         simpa using h
 
 theorem take_prefix_take_left {l : List α} {i j : Nat} (h : i ≤ j) : take i l <+: take j l := by
-  rw [isPrefix_iff]
+  rw [prefix_iff_getElem?]
   intro i w
   rw [getElem?_take_of_lt, getElem_take, getElem?_eq_getElem]
   simp only [length_take] at w
@@ -538,7 +538,7 @@ theorem dropWhile_eq_drop_findIdx_not {xs : List α} {p : α → Bool} :
 
 /-! ### zipWith -/
 
-@[simp] theorem length_zipWith {f : α → β → γ} {l₁ : List α} {l₂ : List β} :
+@[simp, grind =] theorem length_zipWith {f : α → β → γ} {l₁ : List α} {l₂ : List β} :
     length (zipWith f l₁ l₂) = min (length l₁) (length l₂) := by
   induction l₁ generalizing l₂ <;> cases l₂ <;>
     simp_all [succ_min_succ, Nat.zero_min, Nat.min_zero]
@@ -549,7 +549,7 @@ theorem lt_length_left_of_zipWith {f : α → β → γ} {i : Nat} {l : List α}
 theorem lt_length_right_of_zipWith {f : α → β → γ} {i : Nat} {l : List α} {l' : List β}
     (h : i < (zipWith f l l').length) : i < l'.length := by rw [length_zipWith] at h; omega
 
-@[simp]
+@[simp, grind =]
 theorem getElem_zipWith {f : α → β → γ} {l : List α} {l' : List β}
     {i : Nat} {h : i < (zipWith f l l').length} :
     (zipWith f l l')[i] =
@@ -566,6 +566,7 @@ theorem zipWith_eq_zipWith_take_min : ∀ {l₁ : List α} {l₂ : List β},
   | _, [] => by simp
   | a :: l₁, b :: l₂ => by simp [succ_min_succ, zipWith_eq_zipWith_take_min (l₁ := l₁) (l₂ := l₂)]
 
+@[grind =]
 theorem reverse_zipWith (h : l.length = l'.length) :
     (zipWith f l l').reverse = zipWith f l.reverse l'.reverse := by
   induction l generalizing l' with
@@ -578,14 +579,14 @@ theorem reverse_zipWith (h : l.length = l'.length) :
       have : tl.reverse.length = tl'.reverse.length := by simp [h]
       simp [hl h, zipWith_append this]
 
-@[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
   rw [zipWith_eq_zipWith_take_min]
   simp
 
 /-! ### zip -/
 
-@[simp] theorem length_zip {l₁ : List α} {l₂ : List β} :
+@[simp, grind =] theorem length_zip {l₁ : List α} {l₂ : List β} :
     length (zip l₁ l₂) = min (length l₁) (length l₂) := by
   simp [zip]
 
@@ -597,7 +598,7 @@ theorem lt_length_right_of_zip {i : Nat} {l : List α} {l' : List β} (h : i < (
     i < l'.length :=
   lt_length_right_of_zipWith h
 
-@[simp]
+@[simp, grind =]
 theorem getElem_zip {l : List α} {l' : List β} {i : Nat} {h : i < (zip l l').length} :
     (zip l l')[i] =
       (l[i]'(lt_length_left_of_zip h), l'[i]'(lt_length_right_of_zip h)) :=
@@ -609,7 +610,7 @@ theorem zip_eq_zip_take_min : ∀ {l₁ : List α} {l₂ : List β},
   | _, [] => by simp
   | a :: l₁, b :: l₂ => by simp [succ_min_succ, zip_eq_zip_take_min (l₁ := l₁) (l₂ := l₂)]
 
-@[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
   rw [zip_eq_zip_take_min]
   simp

src/Init/Data/List/Notation.lean

@@ -6,7 +6,7 @@ Author: Leonardo de Moura
 module
 
 prelude
-import Init.Data.Nat.Div.Basic
+meta import Init.Data.Nat.Div.Basic
 
 /-!
 # Notation for `List` literals.

src/Init/Data/List/OfFn.lean

@@ -34,14 +34,14 @@ to each potential index in order, starting at `0`.
 def ofFnM {n} [Monad m] (f : Fin n → m α) : m (List α) :=
   List.reverse <$> Fin.foldlM n (fun xs i => (· :: xs) <$> f i) []
 
-@[simp]
+@[simp, grind =]
 theorem length_ofFn {f : Fin n → α} : (ofFn f).length = n := by
   simp only [ofFn]
   induction n with
   | zero => simp
   | succ n ih => simp [Fin.foldr_succ, ih]
 
-@[simp]
+@[simp, grind =]
 protected theorem getElem_ofFn {f : Fin n → α} (h : i < (ofFn f).length) :
     (ofFn f)[i] = f ⟨i, by simp_all⟩ := by
   simp only [ofFn]
@@ -55,7 +55,7 @@ protected theorem getElem_ofFn {f : Fin n → α} (h : i < (ofFn f).length) :
       apply ih
       simp_all
 
-@[simp]
+@[simp, grind =]
 protected theorem getElem?_ofFn {f : Fin n → α} :
     (ofFn f)[i]? = if h : i < n then some (f ⟨i, h⟩) else none :=
   if h : i < (ofFn f).length
@@ -67,7 +67,7 @@ protected theorem getElem?_ofFn {f : Fin n → α} :
     simpa using h
 
 /-- `ofFn` on an empty domain is the empty list. -/
-@[simp]
+@[simp, grind =]
 theorem ofFn_zero {f : Fin 0 → α} : ofFn f = [] := by
   rw [ofFn, Fin.foldr_zero]
 
@@ -98,7 +98,7 @@ theorem ofFn_add {n m} {f : Fin (n + m) → α} :
 theorem ofFn_eq_nil_iff {f : Fin n → α} : ofFn f = [] ↔ n = 0 := by
   cases n <;> simp only [ofFn_zero, ofFn_succ, eq_self_iff_true, Nat.succ_ne_zero, reduceCtorEq]
 
-@[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
@@ -107,17 +107,17 @@ theorem mem_ofFn {n} {f : Fin n → α} {a : α} : a ∈ ofFn f ↔ ∃ i, f i =
   · rintro ⟨i, rfl⟩
     apply mem_of_getElem (i := i) <;> simp
 
-theorem head_ofFn {n} {f : Fin n → α} (h : ofFn f ≠ []) :
+@[grind =] theorem head_ofFn {n} {f : Fin n → α} (h : ofFn f ≠ []) :
     (ofFn f).head h = f ⟨0, Nat.pos_of_ne_zero (mt ofFn_eq_nil_iff.2 h)⟩ := by
   rw [← getElem_zero (length_ofFn ▸ Nat.pos_of_ne_zero (mt ofFn_eq_nil_iff.2 h)),
     List.getElem_ofFn]
 
-theorem getLast_ofFn {n} {f : Fin n → α} (h : ofFn f ≠ []) :
+@[grind =]theorem getLast_ofFn {n} {f : Fin n → α} (h : ofFn f ≠ []) :
     (ofFn f).getLast h = f ⟨n - 1, Nat.sub_one_lt (mt ofFn_eq_nil_iff.2 h)⟩ := by
   simp [getLast_eq_getElem, length_ofFn, List.getElem_ofFn]
 
 /-- `ofFnM` on an empty domain is the empty list. -/
-@[simp]
+@[simp, grind =]
 theorem ofFnM_zero [Monad m] [LawfulMonad m] {f : Fin 0 → m α} : ofFnM f = pure [] := by
   simp [ofFnM]
 

src/Init/Data/List/Pairwise.lean

@@ -159,7 +159,7 @@ theorem pairwise_append_comm {R : α → α → Prop} (s : ∀ {x y}, R x y →
 
 @[grind =] theorem pairwise_middle {R : α → α → Prop} (s : ∀ {x y}, R x y → R y x) {a : α} {l₁ l₂ : List α} :
     Pairwise R (l₁ ++ a :: l₂) ↔ Pairwise R (a :: (l₁ ++ l₂)) := by
-  show Pairwise R (l₁ ++ ([a] ++ l₂)) ↔ Pairwise R ([a] ++ l₁ ++ l₂)
+  change Pairwise R (l₁ ++ ([a] ++ l₂)) ↔ Pairwise R ([a] ++ l₁ ++ l₂)
   rw [← append_assoc, pairwise_append, @pairwise_append _ _ ([a] ++ l₁), pairwise_append_comm s]
   simp only [mem_append, or_comm]
 
@@ -211,6 +211,7 @@ theorem pairwise_append_comm {R : α → α → Prop} (s : ∀ {x y}, R x y →
 @[grind] theorem Pairwise.take {l : List α} {i : Nat} (h : List.Pairwise R l) : List.Pairwise R (l.take i) :=
   h.sublist (take_sublist _ _)
 
+@[grind =]
 theorem pairwise_iff_forall_sublist : l.Pairwise R ↔ (∀ {a b}, [a,b] <+ l → R a b) := by
   induction l with
   | nil => simp
@@ -268,6 +269,8 @@ theorem pairwise_of_forall_mem_list {l : List α} {r : α → α → Prop} (h :
 
 /-! ### Nodup -/
 
+@[grind =] theorem nodup_iff_pairwise_ne : List.Nodup l ↔ List.Pairwise (· ≠ ·) l := Iff.rfl
+
 @[simp, grind]
 theorem nodup_nil : @Nodup α [] :=
   Pairwise.nil
@@ -279,6 +282,9 @@ theorem nodup_cons {a : α} {l : List α} : Nodup (a :: l) ↔ a ∉ l ∧ Nodup
 @[grind →] theorem Nodup.sublist : l₁ <+ l₂ → Nodup l₂ → Nodup l₁ :=
   Pairwise.sublist
 
+grind_pattern Nodup.sublist => l₁ <+ l₂, Nodup l₁
+grind_pattern Nodup.sublist => l₁ <+ l₂, Nodup l₂
+
 theorem Sublist.nodup : l₁ <+ l₂ → Nodup l₂ → Nodup l₁ :=
   Nodup.sublist
 

src/Init/Data/List/Range.lean

@@ -142,6 +142,8 @@ theorem range'_eq_cons_iff : range' s n = a :: xs ↔ s = a ∧ 0 < n ∧ xs = r
 
 /-! ### range -/
 
+@[simp, grind =] theorem range_one : range 1 = [0] := rfl
+
 theorem range_loop_range' : ∀ s n, range.loop s (range' s n) = range' 0 (n + s)
   | 0, _ => rfl
   | s + 1, n => by rw [← Nat.add_assoc, Nat.add_right_comm n s 1]; exact range_loop_range' s (n + 1)
@@ -223,7 +225,7 @@ theorem zipIdx_eq_nil_iff {l : List α} {i : Nat} : List.zipIdx l i = [] ↔ l =
   | [], _ => rfl
   | _ :: _, _ => congrArg Nat.succ length_zipIdx
 
-@[simp]
+@[simp, grind =]
 theorem getElem?_zipIdx :
     ∀ {l : List α} {i j}, (zipIdx l i)[j]? = l[j]?.map fun a => (a, i + j)
   | [], _, _ => rfl
@@ -232,7 +234,7 @@ theorem getElem?_zipIdx :
     simp only [zipIdx_cons, getElem?_cons_succ]
     exact getElem?_zipIdx.trans <| by rw [Nat.add_right_comm]; rfl
 
-@[simp]
+@[simp, grind =]
 theorem getElem_zipIdx {l : List α} (h : i < (l.zipIdx j).length) :
     (l.zipIdx j)[i] = (l[i]'(by simpa [length_zipIdx] using h), j + i) := by
   simp only [length_zipIdx] at h
@@ -240,7 +242,7 @@ theorem getElem_zipIdx {l : List α} (h : i < (l.zipIdx j).length) :
   simp only [getElem?_zipIdx, getElem?_eq_getElem h]
   simp
 
-@[simp]
+@[simp, grind =]
 theorem tail_zipIdx {l : List α} {i : Nat} : (zipIdx l i).tail = zipIdx l.tail (i + 1) := by
   induction l generalizing i with
   | nil => simp

src/Init/Data/List/Sort/Impl.lean

@@ -153,12 +153,12 @@ where
     mergeTR (run' r) (run l) le
 
 theorem splitRevInTwo'_fst (l : { l : List α // l.length = n }) :
-    (splitRevInTwo' l).1 = ⟨(splitInTwo ⟨l.1.reverse, by simpa using l.2⟩).2.1, by simp; omega⟩ := by
+    (splitRevInTwo' l).1 = ⟨(splitInTwo (n := n) ⟨l.1.reverse, by simpa using l.2⟩).2.1, by simp; omega⟩ := by
   simp only [splitRevInTwo', splitRevAt_eq, reverse_take, splitInTwo_snd]
   congr
   omega
 theorem splitRevInTwo'_snd (l : { l : List α // l.length = n }) :
-    (splitRevInTwo' l).2 = ⟨(splitInTwo ⟨l.1.reverse, by simpa using l.2⟩).1.1.reverse, by simp; omega⟩ := by
+    (splitRevInTwo' l).2 = ⟨(splitInTwo (n := n) ⟨l.1.reverse, by simpa using l.2⟩).1.1.reverse, by simp; omega⟩ := by
   simp only [splitRevInTwo', splitRevAt_eq, reverse_take, splitInTwo_fst, reverse_reverse]
   congr 2
   simp

src/Init/Data/List/Sublist.lean

@@ -24,14 +24,14 @@ open Nat
 section isPrefixOf
 variable [BEq α]
 
-@[simp] theorem isPrefixOf_cons₂_self [LawfulBEq α] {a : α} :
+@[simp, grind =] theorem isPrefixOf_cons₂_self [LawfulBEq α] {a : α} :
     isPrefixOf (a::as) (a::bs) = isPrefixOf as bs := by simp [isPrefixOf_cons₂]
 
 @[simp] theorem isPrefixOf_length_pos_nil {l : List α} (h : 0 < l.length) : isPrefixOf l [] = false := by
   cases l <;> simp_all [isPrefixOf]
 
-@[simp] theorem isPrefixOf_replicate {a : α} :
-    isPrefixOf l (replicate n a) = (decide (l.length ≤ n) && l.all (· == a)) := by
+@[simp, grind =] theorem isPrefixOf_replicate {a : α} :
+    isPrefixOf l (replicate n a) = ((l.length ≤ n) && l.all (· == a)) := by
   induction l generalizing n with
   | nil => simp
   | cons _ _ ih =>
@@ -45,10 +45,10 @@ end isPrefixOf
 section isSuffixOf
 variable [BEq α]
 
-@[simp] theorem isSuffixOf_cons_nil : isSuffixOf (a::as) ([] : List α) = false := by
+@[simp, grind =] theorem isSuffixOf_cons_nil : isSuffixOf (a::as) ([] : List α) = false := by
   simp [isSuffixOf]
 
-@[simp] theorem isSuffixOf_replicate {a : α} :
+@[simp, grind =] theorem isSuffixOf_replicate {a : α} :
     isSuffixOf l (replicate n a) = (decide (l.length ≤ n) && l.all (· == a)) := by
   simp [isSuffixOf, all_eq]
 
@@ -58,7 +58,8 @@ end isSuffixOf
 
 /-! ### List subset -/
 
-theorem subset_def {l₁ l₂ : List α} : l₁ ⊆ l₂ ↔ ∀ {a : α}, a ∈ l₁ → a ∈ l₂ := .rfl
+-- For now we don't annotate lemmas about `Subset` for `grind`, but instead just unfold the definition.
+@[grind =] theorem subset_def {l₁ l₂ : List α} : l₁ ⊆ l₂ ↔ ∀ {a : α}, a ∈ l₁ → a ∈ l₂ := .rfl
 
 @[simp] theorem nil_subset (l : List α) : [] ⊆ l := nofun
 
@@ -95,9 +96,15 @@ theorem eq_nil_of_subset_nil {l : List α} : l ⊆ [] → l = [] := subset_nil.m
 theorem map_subset {l₁ l₂ : List α} (f : α → β) (h : l₁ ⊆ l₂) : map f l₁ ⊆ map f l₂ :=
   fun x => by simp only [mem_map]; exact .imp fun a => .imp_left (@h _)
 
+grind_pattern map_subset => l₁ ⊆ l₂, map f l₁
+grind_pattern map_subset => l₁ ⊆ l₂, map f l₂
+
 theorem filter_subset {l₁ l₂ : List α} (p : α → Bool) (H : l₁ ⊆ l₂) : filter p l₁ ⊆ filter p l₂ :=
   fun x => by simp_all [mem_filter, subset_def.1 H]
 
+grind_pattern filter_subset => l₁ ⊆ l₂, filter p l₁
+grind_pattern filter_subset => l₁ ⊆ l₂, filter p l₂
+
 theorem filterMap_subset {l₁ l₂ : List α} (f : α → Option β) (H : l₁ ⊆ l₂) :
     filterMap f l₁ ⊆ filterMap f l₂ := by
   intro x
@@ -105,6 +112,9 @@ theorem filterMap_subset {l₁ l₂ : List α} (f : α → Option β) (H : l₁
   rintro ⟨a, h, w⟩
   exact ⟨a, H h, w⟩
 
+grind_pattern filterMap_subset => l₁ ⊆ l₂, filterMap f l₁
+grind_pattern filterMap_subset => l₁ ⊆ l₂, filterMap f l₂
+
 theorem subset_append_left (l₁ l₂ : List α) : l₁ ⊆ l₁ ++ l₂ := fun _ => mem_append_left _
 
 theorem subset_append_right (l₁ l₂ : List α) : l₂ ⊆ l₁ ++ l₂ := fun _ => mem_append_right _
@@ -139,11 +149,11 @@ theorem subset_replicate {n : Nat} {a : α} {l : List α} (h : n ≠ 0) : l ⊆
 
 /-! ### Sublist and isSublist -/
 
-@[simp] theorem nil_sublist : ∀ l : List α, [] <+ l
+@[simp, grind] theorem nil_sublist : ∀ l : List α, [] <+ l
   | [] => .slnil
   | a :: l => (nil_sublist l).cons a
 
-@[simp] theorem Sublist.refl : ∀ l : List α, l <+ l
+@[simp, grind] theorem Sublist.refl : ∀ l : List α, l <+ l
   | [] => .slnil
   | a :: l => (Sublist.refl l).cons₂ a
 
@@ -160,14 +170,14 @@ theorem Sublist.trans {l₁ l₂ l₃ : List α} (h₁ : l₁ <+ l₂) (h₂ : l
 
 instance : Trans (@Sublist α) Sublist Sublist := ⟨Sublist.trans⟩
 
-attribute [simp] Sublist.cons
+attribute [simp, grind] Sublist.cons
 
 theorem sublist_cons_self (a : α) (l : List α) : l <+ a :: l := (Sublist.refl l).cons _
 
 theorem sublist_of_cons_sublist : a :: l₁ <+ l₂ → l₁ <+ l₂ :=
   (sublist_cons_self a l₁).trans
 
-@[simp]
+@[simp, grind =]
 theorem cons_sublist_cons : a :: l₁ <+ a :: l₂ ↔ l₁ <+ l₂ :=
   ⟨fun | .cons _ s => sublist_of_cons_sublist s | .cons₂ _ s => s, .cons₂ _⟩
 
@@ -181,7 +191,7 @@ theorem sublist_or_mem_of_sublist (h : l <+ l₁ ++ a :: l₂) : l <+ l₁ ++ l
     | .cons _ h => exact (IH h).imp_left (Sublist.cons _)
     | .cons₂ _ h => exact (IH h).imp (Sublist.cons₂ _) (.tail _)
 
-theorem Sublist.subset : l₁ <+ l₂ → l₁ ⊆ l₂
+@[grind →] theorem Sublist.subset : l₁ <+ l₂ → l₁ ⊆ l₂
   | .slnil, _, h => h
   | .cons _ s, _, h => .tail _ (s.subset h)
   | .cons₂ .., _, .head .. => .head ..
@@ -190,10 +200,10 @@ theorem Sublist.subset : l₁ <+ l₂ → l₁ ⊆ l₂
 protected theorem Sublist.mem (hx : a ∈ l₁) (hl : l₁ <+ l₂) : a ∈ l₂ :=
   hl.subset hx
 
-theorem Sublist.head_mem (s : ys <+ xs) (h) : ys.head h ∈ xs :=
+@[grind] theorem Sublist.head_mem (s : ys <+ xs) (h) : ys.head h ∈ xs :=
   s.mem (List.head_mem h)
 
-theorem Sublist.getLast_mem (s : ys <+ xs) (h) : ys.getLast h ∈ xs :=
+@[grind] theorem Sublist.getLast_mem (s : ys <+ xs) (h) : ys.getLast h ∈ xs :=
   s.mem (List.getLast_mem h)
 
 instance : Trans (@Sublist α) Subset Subset :=
@@ -208,7 +218,7 @@ instance : Trans (fun l₁ l₂ => Sublist l₂ l₁) (Membership.mem : List α
 theorem mem_of_cons_sublist {a : α} {l₁ l₂ : List α} (s : a :: l₁ <+ l₂) : a ∈ l₂ :=
   (cons_subset.1 s.subset).1
 
-@[simp] theorem sublist_nil {l : List α} : l <+ [] ↔ l = [] :=
+@[simp, grind =] theorem sublist_nil {l : List α} : l <+ [] ↔ l = [] :=
   ⟨fun s => subset_nil.1 s.subset, fun H => H ▸ Sublist.refl _⟩
 
 theorem eq_nil_of_sublist_nil {l : List α} (s : l <+ []) : l = [] :=
@@ -219,29 +229,39 @@ theorem Sublist.length_le : l₁ <+ l₂ → length l₁ ≤ length l₂
   | .cons _l s => le_succ_of_le (length_le s)
   | .cons₂ _ s => succ_le_succ (length_le s)
 
+grind_pattern Sublist.length_le => l₁ <+ l₂, length l₁
+grind_pattern Sublist.length_le => l₁ <+ l₂, length l₂
+
 theorem Sublist.eq_of_length : l₁ <+ l₂ → length l₁ = length l₂ → l₁ = l₂
   | .slnil, _ => rfl
   | .cons a s, h => nomatch Nat.not_lt.2 s.length_le (h ▸ lt_succ_self _)
   | .cons₂ a s, h => by rw [s.eq_of_length (succ.inj h)]
 
+-- Only activative `eq_of_length` if we're already thinking about lengths.
+grind_pattern Sublist.eq_of_length => l₁ <+ l₂, length l₁, length l₂
+
 theorem Sublist.eq_of_length_le (s : l₁ <+ l₂) (h : length l₂ ≤ length l₁) : l₁ = l₂ :=
   s.eq_of_length <| Nat.le_antisymm s.length_le h
 
 theorem Sublist.length_eq (s : l₁ <+ l₂) : length l₁ = length l₂ ↔ l₁ = l₂ :=
   ⟨s.eq_of_length, congrArg _⟩
 
+@[grind]
 theorem tail_sublist : ∀ l : List α, tail l <+ l
   | [] => .slnil
   | a::l => sublist_cons_self a l
 
+@[grind]
 protected theorem Sublist.tail : ∀ {l₁ l₂ : List α}, l₁ <+ l₂ → tail l₁ <+ tail l₂
   | _, _, slnil => .slnil
   | _, _, Sublist.cons _ h => (tail_sublist _).trans h
   | _, _, Sublist.cons₂ _ h => h
 
+@[grind →]
 theorem Sublist.of_cons_cons {l₁ l₂ : List α} {a b : α} (h : a :: l₁ <+ b :: l₂) : l₁ <+ l₂ :=
   h.tail
 
+@[grind]
 protected theorem Sublist.map (f : α → β) {l₁ l₂} (s : l₁ <+ l₂) : map f l₁ <+ map f l₂ := by
   induction s with
   | slnil => simp
@@ -250,19 +270,31 @@ protected theorem Sublist.map (f : α → β) {l₁ l₂} (s : l₁ <+ l₂) : m
   | cons₂ a s ih =>
     simpa using cons₂ (f a) ih
 
+grind_pattern Sublist.map => l₁ <+ l₂, map f l₁
+grind_pattern Sublist.map => l₁ <+ l₂, map f l₂
+
+@[grind]
 protected theorem Sublist.filterMap (f : α → Option β) (s : l₁ <+ l₂) :
     filterMap f l₁ <+ filterMap f l₂ := by
   induction s <;> simp [filterMap_cons] <;> split <;> simp [*, cons, cons₂]
 
+grind_pattern Sublist.filterMap => l₁ <+ l₂, filterMap f l₁
+grind_pattern Sublist.filterMap => l₁ <+ l₂, filterMap f l₂
+
+@[grind]
 protected theorem Sublist.filter (p : α → Bool) {l₁ l₂} (s : l₁ <+ l₂) : filter p l₁ <+ filter p l₂ := by
   rw [← filterMap_eq_filter]; apply s.filterMap
 
+grind_pattern Sublist.filter => l₁ <+ l₂, l₁.filter p
+grind_pattern Sublist.filter => l₁ <+ l₂, l₂.filter p
+
 theorem head_filter_mem (xs : List α) (p : α → Bool) (h) : (xs.filter p).head h ∈ xs :=
   filter_sublist.head_mem h
 
 theorem getLast_filter_mem (xs : List α) (p : α → Bool) (h) : (xs.filter p).getLast h ∈ xs :=
   filter_sublist.getLast_mem h
 
+@[grind =]
 theorem sublist_filterMap_iff {l₁ : List β} {f : α → Option β} :
     l₁ <+ l₂.filterMap f ↔ ∃ l', l' <+ l₂ ∧ l₁ = l'.filterMap f := by
   induction l₂ generalizing l₁ with
@@ -297,10 +329,12 @@ theorem sublist_filterMap_iff {l₁ : List β} {f : α → Option β} :
         rwa [filterMap_cons_some] at h
         assumption
 
+@[grind =]
 theorem sublist_map_iff {l₁ : List β} {f : α → β} :
     l₁ <+ l₂.map f ↔ ∃ l', l' <+ l₂ ∧ l₁ = l'.map f := by
   simp only [← filterMap_eq_map, sublist_filterMap_iff]
 
+@[grind =]
 theorem sublist_filter_iff {l₁ : List α} {p : α → Bool} :
     l₁ <+ l₂.filter p ↔ ∃ l', l' <+ l₂ ∧ l₁ = l'.filter p := by
   simp only [← filterMap_eq_filter, sublist_filterMap_iff]
@@ -309,11 +343,15 @@ theorem sublist_append_left : ∀ l₁ l₂ : List α, l₁ <+ l₁ ++ l₂
   | [], _ => nil_sublist _
   | _ :: l₁, l₂ => (sublist_append_left l₁ l₂).cons₂ _
 
+grind_pattern sublist_append_left => Sublist, l₁ ++ l₂
+
 theorem sublist_append_right : ∀ l₁ l₂ : List α, l₂ <+ l₁ ++ l₂
   | [], _ => Sublist.refl _
   | _ :: l₁, l₂ => (sublist_append_right l₁ l₂).cons _
 
-@[simp] theorem singleton_sublist {a : α} {l} : [a] <+ l ↔ a ∈ l := by
+grind_pattern sublist_append_right => Sublist, l₁ ++ l₂
+
+@[simp, grind =] theorem singleton_sublist {a : α} {l} : [a] <+ l ↔ a ∈ l := by
   refine ⟨fun h => h.subset (mem_singleton_self _), fun h => ?_⟩
   obtain ⟨_, _, rfl⟩ := append_of_mem h
   exact ((nil_sublist _).cons₂ _).trans (sublist_append_right ..)
@@ -321,10 +359,14 @@ theorem sublist_append_right : ∀ l₁ l₂ : List α, l₂ <+ l₁ ++ l₂
 @[simp] theorem sublist_append_of_sublist_left (s : l <+ l₁) : l <+ l₁ ++ l₂ :=
   s.trans <| sublist_append_left ..
 
+grind_pattern sublist_append_of_sublist_left => l <+ l₁, l₁ ++ l₂
+
 @[simp] theorem sublist_append_of_sublist_right (s : l <+ l₂) : l <+ l₁ ++ l₂ :=
   s.trans <| sublist_append_right ..
 
-@[simp] theorem append_sublist_append_left : ∀ l, l ++ l₁ <+ l ++ l₂ ↔ l₁ <+ l₂
+grind_pattern sublist_append_of_sublist_right => l <+ l₂, l₁ ++ l₂
+
+@[simp, grind =] theorem append_sublist_append_left : ∀ l, l ++ l₁ <+ l ++ l₂ ↔ l₁ <+ l₂
   | [] => Iff.rfl
   | _ :: l => cons_sublist_cons.trans (append_sublist_append_left l)
 
@@ -339,6 +381,9 @@ theorem Sublist.append_right : l₁ <+ l₂ → ∀ l, l₁ ++ l <+ l₂ ++ l
 theorem Sublist.append (hl : l₁ <+ l₂) (hr : r₁ <+ r₂) : l₁ ++ r₁ <+ l₂ ++ r₂ :=
   (hl.append_right _).trans ((append_sublist_append_left _).2 hr)
 
+grind_pattern Sublist.append => l₁ <+ l₂, r₁ <+ r₂, l₁ ++ r₁, l₂ ++ r₂
+
+@[grind =]
 theorem sublist_cons_iff {a : α} {l l'} :
     l <+ a :: l' ↔ l <+ l' ∨ ∃ r, l = a :: r ∧ r <+ l' := by
   constructor
@@ -350,6 +395,7 @@ theorem sublist_cons_iff {a : α} {l l'} :
     · exact h.cons _
     · exact h.cons₂ _
 
+@[grind =]
 theorem cons_sublist_iff {a : α} {l l'} :
     a :: l <+ l' ↔ ∃ r₁ r₂, l' = r₁ ++ r₂ ∧ a ∈ r₁ ∧ l <+ r₂ := by
   induction l' with
@@ -433,6 +479,7 @@ theorem Sublist.of_sublist_append_right (w : ∀ a, a ∈ l → a ∉ l₁) (h :
     exact fun x m => w x (mem_append_left l₂' m) (h₁.mem m)
   simp_all
 
+@[grind]
 theorem Sublist.middle {l : List α} (h : l <+ l₁ ++ l₂) (a : α) : l <+ l₁ ++ a :: l₂ := by
   rw [sublist_append_iff] at h
   obtain ⟨l₁', l₂', rfl, h₁, h₂⟩ := h
@@ -443,13 +490,14 @@ theorem Sublist.reverse : l₁ <+ l₂ → l₁.reverse <+ l₂.reverse
   | .cons _ h => by rw [reverse_cons]; exact sublist_append_of_sublist_left h.reverse
   | .cons₂ _ h => by rw [reverse_cons, reverse_cons]; exact h.reverse.append_right _
 
-@[simp] theorem reverse_sublist : l₁.reverse <+ l₂.reverse ↔ l₁ <+ l₂ :=
+@[simp, grind =] theorem reverse_sublist : l₁.reverse <+ l₂.reverse ↔ l₁ <+ l₂ :=
   ⟨fun h => l₁.reverse_reverse ▸ l₂.reverse_reverse ▸ h.reverse, Sublist.reverse⟩
 
+@[grind _=_]
 theorem sublist_reverse_iff : l₁ <+ l₂.reverse ↔ l₁.reverse <+ l₂ :=
   by rw [← reverse_sublist, reverse_reverse]
 
-@[simp] theorem append_sublist_append_right (l) : l₁ ++ l <+ l₂ ++ l ↔ l₁ <+ l₂ :=
+@[simp, grind =] theorem append_sublist_append_right (l) : l₁ ++ l <+ l₂ ++ l ↔ l₁ <+ l₂ :=
   ⟨fun h => by
     have := h.reverse
     simp only [reverse_append, append_sublist_append_left, reverse_sublist] at this
@@ -464,6 +512,7 @@ theorem sublist_reverse_iff : l₁ <+ l₂.reverse ↔ l₁.reverse <+ l₂ :=
     | refl => apply Sublist.refl
     | step => simp [*, replicate, Sublist.cons]
 
+@[grind =]
 theorem sublist_replicate_iff : l <+ replicate m a ↔ ∃ n, n ≤ m ∧ l = replicate n a := by
   induction l generalizing m with
   | nil =>
@@ -551,7 +600,7 @@ theorem flatten_sublist_iff {L : List (List α)} {l} :
         exact ⟨l₁, L'.flatten, by simp, by simpa using h 0 (by simp), L', rfl,
           fun i lt => by simpa using h (i+1) (Nat.add_lt_add_right lt 1)⟩
 
-@[simp] theorem isSublist_iff_sublist [BEq α] [LawfulBEq α] {l₁ l₂ : List α} :
+@[simp, grind =] theorem isSublist_iff_sublist [BEq α] [LawfulBEq α] {l₁ l₂ : List α} :
     l₁.isSublist l₂ ↔ l₁ <+ l₂ := by
   cases l₁ <;> cases l₂ <;> simp [isSublist]
   case cons.cons hd₁ tl₁ hd₂ tl₂ =>
@@ -573,41 +622,49 @@ theorem flatten_sublist_iff {L : List (List α)} {l} :
 instance [DecidableEq α] (l₁ l₂ : List α) : Decidable (l₁ <+ l₂) :=
   decidable_of_iff (l₁.isSublist l₂) isSublist_iff_sublist
 
+@[grind]
 protected theorem Sublist.drop : ∀ {l₁ l₂ : List α}, l₁ <+ l₂ → ∀ i, l₁.drop i <+ l₂.drop i
   | _, _, h, 0 => h
   | _, _, h, i + 1 => by rw [← drop_tail, ← drop_tail]; exact h.tail.drop i
 
 /-! ### IsPrefix / IsSuffix / IsInfix -/
 
-@[simp] theorem prefix_append (l₁ l₂ : List α) : l₁ <+: l₁ ++ l₂ := ⟨l₂, rfl⟩
+@[simp, grind] theorem prefix_append (l₁ l₂ : List α) : l₁ <+: l₁ ++ l₂ := ⟨l₂, rfl⟩
 
-@[simp] theorem suffix_append (l₁ l₂ : List α) : l₂ <:+ l₁ ++ l₂ := ⟨l₁, rfl⟩
+@[simp, grind] theorem suffix_append (l₁ l₂ : List α) : l₂ <:+ l₁ ++ l₂ := ⟨l₁, rfl⟩
 
 theorem infix_append (l₁ l₂ l₃ : List α) : l₂ <:+: l₁ ++ l₂ ++ l₃ := ⟨l₁, l₃, rfl⟩
 
-@[simp] theorem infix_append' (l₁ l₂ l₃ : List α) : l₂ <:+: l₁ ++ (l₂ ++ l₃) := by
+@[simp, grind] theorem infix_append' (l₁ l₂ l₃ : List α) : l₂ <:+: l₁ ++ (l₂ ++ l₃) := by
   rw [← List.append_assoc]; apply infix_append
 
+theorem infix_append_left : l₁ <:+: l₁ ++ l₂ := ⟨[], l₂, rfl⟩
+theorem infix_append_right : l₂ <:+: l₁ ++ l₂ := ⟨l₁, [], by simp⟩
+
 theorem IsPrefix.isInfix : l₁ <+: l₂ → l₁ <:+: l₂ := fun ⟨t, h⟩ => ⟨[], t, h⟩
 
+grind_pattern IsPrefix.isInfix => l₁ <+: l₂, IsInfix
+
 theorem IsSuffix.isInfix : l₁ <:+ l₂ → l₁ <:+: l₂ := fun ⟨t, h⟩ => ⟨t, [], by rw [h, append_nil]⟩
 
-@[simp] theorem nil_prefix {l : List α} : [] <+: l := ⟨l, rfl⟩
+grind_pattern IsSuffix.isInfix => l₁ <:+ l₂, IsInfix
 
-@[simp] theorem nil_suffix {l : List α} : [] <:+ l := ⟨l, append_nil _⟩
+@[simp, grind] theorem nil_prefix {l : List α} : [] <+: l := ⟨l, rfl⟩
 
-@[simp] theorem nil_infix {l : List α} : [] <:+: l := nil_prefix.isInfix
+@[simp, grind] theorem nil_suffix {l : List α} : [] <:+ l := ⟨l, append_nil _⟩
+
+@[simp, grind] theorem nil_infix {l : List α} : [] <:+: l := nil_prefix.isInfix
 
 theorem prefix_refl (l : List α) : l <+: l := ⟨[], append_nil _⟩
-@[simp] theorem prefix_rfl {l : List α} : l <+: l := prefix_refl l
+@[simp, grind] theorem prefix_rfl {l : List α} : l <+: l := prefix_refl l
 
 theorem suffix_refl (l : List α) : l <:+ l := ⟨[], rfl⟩
-@[simp] theorem suffix_rfl {l : List α} : l <:+ l := suffix_refl l
+@[simp, grind] theorem suffix_rfl {l : List α} : l <:+ l := suffix_refl l
 
 theorem infix_refl (l : List α) : l <:+: l := prefix_rfl.isInfix
-@[simp] theorem infix_rfl {l : List α} : l <:+: l := infix_refl l
+@[simp, grind] theorem infix_rfl {l : List α} : l <:+: l := infix_refl l
 
-@[simp] theorem suffix_cons (a : α) : ∀ l, l <:+ a :: l := suffix_append [a]
+@[simp, grind] theorem suffix_cons (a : α) : ∀ l, l <:+ a :: l := suffix_append [a]
 
 theorem infix_cons : l₁ <:+: l₂ → l₁ <:+: a :: l₂ := fun ⟨l₁', l₂', h⟩ => ⟨a :: l₁', l₂', h ▸ rfl⟩
 
@@ -617,12 +674,38 @@ theorem infix_concat : l₁ <:+: l₂ → l₁ <:+: concat l₂ a := fun ⟨l₁
 theorem IsPrefix.trans : ∀ {l₁ l₂ l₃ : List α}, l₁ <+: l₂ → l₂ <+: l₃ → l₁ <+: l₃
   | _, _, _, ⟨r₁, rfl⟩, ⟨r₂, rfl⟩ => ⟨r₁ ++ r₂, (append_assoc _ _ _).symm⟩
 
+grind_pattern IsPrefix.trans => l₁ <+: l₂, l₂ <+: l₃
+
 theorem IsSuffix.trans : ∀ {l₁ l₂ l₃ : List α}, l₁ <:+ l₂ → l₂ <:+ l₃ → l₁ <:+ l₃
   | _, _, _, ⟨l₁, rfl⟩, ⟨l₂, rfl⟩ => ⟨l₂ ++ l₁, append_assoc _ _ _⟩
 
+grind_pattern IsSuffix.trans => l₁ <:+ l₂, l₂ <:+ l₃
+
 theorem IsInfix.trans : ∀ {l₁ l₂ l₃ : List α}, l₁ <:+: l₂ → l₂ <:+: l₃ → l₁ <:+: l₃
   | l, _, _, ⟨l₁, r₁, rfl⟩, ⟨l₂, r₂, rfl⟩ => ⟨l₂ ++ l₁, r₁ ++ r₂, by simp only [append_assoc]⟩
 
+grind_pattern IsInfix.trans => l₁ <:+: l₂, l₂ <:+: l₃
+
+theorem prefix_append_of_prefix (h : l₁ <+: l₂) : l₁ <+: l₂ ++ l₃ :=
+  h.trans (prefix_append l₂ l₃)
+
+grind_pattern prefix_append_of_prefix => l₁ <+: l₂, l₂ ++ l₃
+
+theorem suffix_append_of_suffix (h : l₁ <:+ l₃) : l₁ <:+ l₂ ++ l₃ :=
+  h.trans (suffix_append l₂ l₃)
+
+grind_pattern suffix_append_of_suffix => l₁ <:+ l₃, l₂ ++ l₃
+
+theorem infix_append_of_infix_left (h : l₁ <:+: l₂) : l₁ <:+: l₂ ++ l₃ :=
+  h.trans infix_append_left
+
+grind_pattern infix_append_of_infix_left => l₁ <:+: l₂, l₂ ++ l₃
+
+theorem infix_append_of_infix_right (h : l₁ <:+: l₃) : l₁ <:+: l₂ ++ l₃ :=
+  h.trans infix_append_right
+
+grind_pattern infix_append_of_infix_right => l₁ <:+: l₃, l₂ ++ l₃
+
 protected theorem IsInfix.sublist : l₁ <:+: l₂ → l₁ <+ l₂
   | ⟨_, _, h⟩ => h ▸ (sublist_append_right ..).trans (sublist_append_left ..)
 
@@ -641,11 +724,11 @@ protected theorem IsSuffix.sublist (h : l₁ <:+ l₂) : l₁ <+ l₂ :=
 protected theorem IsSuffix.subset (hl : l₁ <:+ l₂) : l₁ ⊆ l₂ :=
   hl.sublist.subset
 
-@[simp] theorem infix_nil : l <:+: [] ↔ l = [] := ⟨(sublist_nil.1 ·.sublist), (· ▸ infix_rfl)⟩
+@[simp, grind =] theorem infix_nil : l <:+: [] ↔ l = [] := ⟨(sublist_nil.1 ·.sublist), (· ▸ infix_rfl)⟩
 
-@[simp] theorem prefix_nil : l <+: [] ↔ l = [] := ⟨(sublist_nil.1 ·.sublist), (· ▸ prefix_rfl)⟩
+@[simp, grind =] theorem prefix_nil : l <+: [] ↔ l = [] := ⟨(sublist_nil.1 ·.sublist), (· ▸ prefix_rfl)⟩
 
-@[simp] theorem suffix_nil : l <:+ [] ↔ l = [] := ⟨(sublist_nil.1 ·.sublist), (· ▸ suffix_rfl)⟩
+@[simp, grind =] theorem suffix_nil : l <:+ [] ↔ l = [] := ⟨(sublist_nil.1 ·.sublist), (· ▸ suffix_rfl)⟩
 
 theorem eq_nil_of_infix_nil (h : l <:+: []) : l = [] := infix_nil.mp h
 theorem eq_nil_of_prefix_nil (h : l <+: []) : l = [] := prefix_nil.mp h
@@ -663,12 +746,21 @@ theorem IsInfix.ne_nil {xs ys : List α} (h : xs <:+: ys) (hx : xs ≠ []) : ys
 theorem IsInfix.length_le (h : l₁ <:+: l₂) : l₁.length ≤ l₂.length :=
   h.sublist.length_le
 
+grind_pattern IsInfix.length_le => l₁ <:+: l₂, l₁.length
+grind_pattern IsInfix.length_le => l₁ <:+: l₂, l₂.length
+
 theorem IsPrefix.length_le (h : l₁ <+: l₂) : l₁.length ≤ l₂.length :=
   h.sublist.length_le
 
+grind_pattern IsPrefix.length_le => l₁ <+: l₂, l₁.length
+grind_pattern IsPrefix.length_le => l₁ <+: l₂, l₂.length
+
 theorem IsSuffix.length_le (h : l₁ <:+ l₂) : l₁.length ≤ l₂.length :=
   h.sublist.length_le
 
+grind_pattern IsSuffix.length_le => l₁ <:+ l₂, l₁.length
+grind_pattern IsSuffix.length_le => l₁ <:+ l₂, l₂.length
+
 theorem IsPrefix.getElem {xs ys : List α} (h : xs <+: ys) {i} (hi : i < xs.length) :
     xs[i] = ys[i]'(Nat.le_trans hi h.length_le) := by
   obtain ⟨_, rfl⟩ := h
@@ -676,23 +768,23 @@ theorem IsPrefix.getElem {xs ys : List α} (h : xs <+: ys) {i} (hi : i < xs.leng
 
 -- See `Init.Data.List.Nat.Sublist` for `IsSuffix.getElem`.
 
-theorem IsPrefix.mem (hx : a ∈ l₁) (hl : l₁ <+: l₂) : a ∈ l₂ :=
+@[grind →] theorem IsPrefix.mem (hx : a ∈ l₁) (hl : l₁ <+: l₂) : a ∈ l₂ :=
   hl.subset hx
 
-theorem IsSuffix.mem (hx : a ∈ l₁) (hl : l₁ <:+ l₂) : a ∈ l₂ :=
+@[grind →] theorem IsSuffix.mem (hx : a ∈ l₁) (hl : l₁ <:+ l₂) : a ∈ l₂ :=
   hl.subset hx
 
-theorem IsInfix.mem (hx : a ∈ l₁) (hl : l₁ <:+: l₂) : a ∈ l₂ :=
+@[grind →] theorem IsInfix.mem (hx : a ∈ l₁) (hl : l₁ <:+: l₂) : a ∈ l₂ :=
   hl.subset hx
 
-@[simp] theorem reverse_suffix : reverse l₁ <:+ reverse l₂ ↔ l₁ <+: l₂ :=
+@[simp, grind =] theorem reverse_suffix : reverse l₁ <:+ reverse l₂ ↔ l₁ <+: l₂ :=
   ⟨fun ⟨r, e⟩ => ⟨reverse r, by rw [← reverse_reverse l₁, ← reverse_append, e, reverse_reverse]⟩,
    fun ⟨r, e⟩ => ⟨reverse r, by rw [← reverse_append, e]⟩⟩
 
-@[simp] theorem reverse_prefix : reverse l₁ <+: reverse l₂ ↔ l₁ <:+ l₂ := by
+@[simp, grind =] theorem reverse_prefix : reverse l₁ <+: reverse l₂ ↔ l₁ <:+ l₂ := by
   rw [← reverse_suffix]; simp only [reverse_reverse]
 
-@[simp] theorem reverse_infix : reverse l₁ <:+: reverse l₂ ↔ l₁ <:+: l₂ := by
+@[simp, grind =] theorem reverse_infix : reverse l₁ <:+: reverse l₂ ↔ l₁ <:+: l₂ := by
   refine ⟨fun ⟨s, t, e⟩ => ⟨reverse t, reverse s, ?_⟩, fun ⟨s, t, e⟩ => ⟨reverse t, reverse s, ?_⟩⟩
   · rw [← reverse_reverse l₁, append_assoc, ← reverse_append, ← reverse_append, e,
       reverse_reverse]
@@ -701,12 +793,21 @@ theorem IsInfix.mem (hx : a ∈ l₁) (hl : l₁ <:+: l₂) : a ∈ l₂ :=
 theorem IsInfix.reverse : l₁ <:+: l₂ → reverse l₁ <:+: reverse l₂ :=
   reverse_infix.2
 
+grind_pattern IsInfix.reverse => l₁ <:+: l₂, l₁.reverse
+grind_pattern IsInfix.reverse => l₁ <:+: l₂, l₂.reverse
+
 theorem IsSuffix.reverse : l₁ <:+ l₂ → reverse l₁ <+: reverse l₂ :=
   reverse_prefix.2
 
+grind_pattern IsSuffix.reverse => l₁ <:+ l₂, l₁.reverse
+grind_pattern IsSuffix.reverse => l₁ <:+ l₂, l₂.reverse
+
 theorem IsPrefix.reverse : l₁ <+: l₂ → reverse l₁ <:+ reverse l₂ :=
   reverse_suffix.2
 
+grind_pattern IsPrefix.reverse => l₁ <+: l₂, l₁.reverse
+grind_pattern IsPrefix.reverse => l₁ <+: l₂, l₂.reverse
+
 theorem IsPrefix.head {l₁ l₂ : List α} (h : l₁ <+: l₂) (hx : l₁ ≠ []) :
     l₁.head hx = l₂.head (h.ne_nil hx) := by
   cases l₁ <;> cases l₂ <;> simp only [head_cons, ne_eq, not_true_eq_false] at hx ⊢
@@ -780,7 +881,7 @@ theorem prefix_cons_iff : l₁ <+: a :: l₂ ↔ l₁ = [] ∨ ∃ t, l₁ = a :
       · simp only [w]
         refine ⟨s, by simp [h']⟩
 
-@[simp] theorem cons_prefix_cons : a :: l₁ <+: b :: l₂ ↔ a = b ∧ l₁ <+: l₂ := by
+@[simp, grind =] theorem cons_prefix_cons : a :: l₁ <+: b :: l₂ ↔ a = b ∧ l₁ <+: l₂ := by
   simp only [prefix_cons_iff, cons.injEq, false_or, List.cons_ne_nil]
   constructor
   · rintro ⟨t, ⟨rfl, rfl⟩, h⟩
@@ -831,7 +932,8 @@ theorem infix_concat_iff {l₁ l₂ : List α} {a : α} :
   rw [← reverse_infix, reverse_concat, infix_cons_iff, reverse_infix,
     ← reverse_prefix, reverse_concat]
 
-theorem isPrefix_iff : l₁ <+: l₂ ↔ ∀ i (h : i < l₁.length), l₂[i]? = some l₁[i] := by
+theorem prefix_iff_getElem? {l₁ l₂ : List α} :
+    l₁ <+: l₂ ↔ ∀ i (h : i < l₁.length), l₂[i]? = some l₁[i] := by
   induction l₁ generalizing l₂ with
   | nil => simp
   | cons a l₁ ih =>
@@ -843,7 +945,12 @@ theorem isPrefix_iff : l₁ <+: l₂ ↔ ∀ i (h : i < l₁.length), l₂[i]? =
       rw (occs := [2]) [← Nat.and_forall_add_one]
       simp [Nat.succ_lt_succ_iff, eq_comm]
 
-theorem isPrefix_iff_getElem {l₁ l₂ : List α} :
+-- See `Init.Data.List.Nat.Sublist` for `isSuffix_iff` and `ifInfix_iff`.
+
+@[deprecated prefix_iff_getElem? (since := "2025-05-27")]
+abbrev isPrefix_iff := @prefix_iff_getElem?
+
+theorem prefix_iff_getElem {l₁ l₂ : List α} :
     l₁ <+: l₂ ↔ ∃ (h : l₁.length ≤ l₂.length), ∀ i (hx : i < l₁.length),
       l₁[i] = l₂[i]'(Nat.lt_of_lt_of_le hx h) where
   mp h := ⟨h.length_le, fun _ h' ↦ h.getElem h'⟩
@@ -861,9 +968,16 @@ theorem isPrefix_iff_getElem {l₁ l₂ : List α} :
         simp only [cons_prefix_cons]
         exact ⟨h 0 (zero_lt_succ _), tail_ih hl fun a ha ↦ h a.succ (succ_lt_succ ha)⟩
 
--- See `Init.Data.List.Nat.Sublist` for `isSuffix_iff` and `ifInfix_iff`.
+@[deprecated prefix_iff_getElem (since := "2025-05-27")]
+abbrev isPrefix_iff_getElem := @prefix_iff_getElem
 
-theorem isPrefix_filterMap_iff {β} {f : α → Option β} {l₁ : List α} {l₂ : List β} :
+theorem cons_prefix_iff {a : α} {l₁ l₂ : List α} :
+    a :: l₁ <+: l₂ ↔ ∃ l', l₂ = a :: l' ∧ l₁ <+: l' := by
+  match l₂ with
+  | nil => simp
+  | cons b l₂ => simp [and_assoc, eq_comm]
+
+theorem prefix_filterMap_iff {β} {f : α → Option β} {l₁ : List α} {l₂ : List β} :
     l₂ <+: filterMap f l₁ ↔ ∃ l, l <+: l₁ ∧ l₂ = filterMap f l := by
   simp only [IsPrefix, append_eq_filterMap_iff]
   constructor
@@ -872,7 +986,10 @@ theorem isPrefix_filterMap_iff {β} {f : α → Option β} {l₁ : List α} {l
   · rintro ⟨l₁, ⟨l₂, rfl⟩, rfl⟩
     exact ⟨_, l₁, l₂, rfl, rfl, rfl⟩
 
-theorem isSuffix_filterMap_iff {β} {f : α → Option β} {l₁ : List α} {l₂ : List β} :
+@[deprecated prefix_filterMap_iff (since := "2025-05-27")]
+abbrev isPrefix_filterMap_iff := @prefix_filterMap_iff
+
+theorem suffix_filterMap_iff {β} {f : α → Option β} {l₁ : List α} {l₂ : List β} :
     l₂ <:+ filterMap f l₁ ↔ ∃ l, l <:+ l₁ ∧ l₂ = filterMap f l := by
   simp only [IsSuffix, append_eq_filterMap_iff]
   constructor
@@ -881,7 +998,10 @@ theorem isSuffix_filterMap_iff {β} {f : α → Option β} {l₁ : List α} {l
   · rintro ⟨l₁, ⟨l₂, rfl⟩, rfl⟩
     exact ⟨_, l₂, l₁, rfl, rfl, rfl⟩
 
-theorem isInfix_filterMap_iff {β} {f : α → Option β} {l₁ : List α} {l₂ : List β} :
+@[deprecated suffix_filterMap_iff (since := "2025-05-27")]
+abbrev isSuffix_filterMap_iff := @suffix_filterMap_iff
+
+theorem infix_filterMap_iff {β} {f : α → Option β} {l₁ : List α} {l₂ : List β} :
     l₂ <:+: filterMap f l₁ ↔ ∃ l, l <:+: l₁ ∧ l₂ = filterMap f l := by
   simp only [IsInfix, append_eq_filterMap_iff, filterMap_eq_append_iff]
   constructor
@@ -890,31 +1010,52 @@ theorem isInfix_filterMap_iff {β} {f : α → Option β} {l₁ : List α} {l₂
   · rintro ⟨l₃, ⟨l₂, l₁, rfl⟩, rfl⟩
     exact ⟨_, _, _, l₁, rfl, ⟨⟨l₂, l₃, rfl, rfl, rfl⟩, rfl⟩⟩
 
-theorem isPrefix_filter_iff {p : α → Bool} {l₁ l₂ : List α} :
+@[deprecated infix_filterMap_iff (since := "2025-05-27")]
+abbrev isInfix_filterMap_iff := @infix_filterMap_iff
+
+theorem prefix_filter_iff {p : α → Bool} {l₁ l₂ : List α} :
     l₂ <+: l₁.filter p ↔ ∃ l, l <+: l₁ ∧ l₂ = l.filter p := by
-  rw [← filterMap_eq_filter, isPrefix_filterMap_iff]
+  rw [← filterMap_eq_filter, prefix_filterMap_iff]
 
-theorem isSuffix_filter_iff {p : α → Bool} {l₁ l₂ : List α} :
+@[deprecated prefix_filter_iff (since := "2025-05-27")]
+abbrev isPrefix_filter_iff := @prefix_filter_iff
+
+theorem suffix_filter_iff {p : α → Bool} {l₁ l₂ : List α} :
     l₂ <:+ l₁.filter p ↔ ∃ l, l <:+ l₁ ∧ l₂ = l.filter p := by
-  rw [← filterMap_eq_filter, isSuffix_filterMap_iff]
+  rw [← filterMap_eq_filter, suffix_filterMap_iff]
 
-theorem isInfix_filter_iff {p : α → Bool} {l₁ l₂ : List α} :
+@[deprecated suffix_filter_iff (since := "2025-05-27")]
+abbrev isSuffix_filter_iff := @suffix_filter_iff
+
+theorem infix_filter_iff {p : α → Bool} {l₁ l₂ : List α} :
     l₂ <:+: l₁.filter p ↔ ∃ l, l <:+: l₁ ∧ l₂ = l.filter p := by
-  rw [← filterMap_eq_filter, isInfix_filterMap_iff]
+  rw [← filterMap_eq_filter, infix_filterMap_iff]
 
-theorem isPrefix_map_iff {β} {f : α → β} {l₁ : List α} {l₂ : List β} :
+@[deprecated infix_filter_iff (since := "2025-05-27")]
+abbrev isInfix_filter_iff := @infix_filter_iff
+
+theorem prefix_map_iff {β} {f : α → β} {l₁ : List α} {l₂ : List β} :
     l₂ <+: l₁.map f ↔ ∃ l, l <+: l₁ ∧ l₂ = l.map f := by
-  rw [← filterMap_eq_map, isPrefix_filterMap_iff]
+  rw [← filterMap_eq_map, prefix_filterMap_iff]
 
-theorem isSuffix_map_iff {β} {f : α → β} {l₁ : List α} {l₂ : List β} :
+@[deprecated prefix_map_iff (since := "2025-05-27")]
+abbrev isPrefix_map_iff := @prefix_map_iff
+
+theorem suffix_map_iff {β} {f : α → β} {l₁ : List α} {l₂ : List β} :
     l₂ <:+ l₁.map f ↔ ∃ l, l <:+ l₁ ∧ l₂ = l.map f := by
-  rw [← filterMap_eq_map, isSuffix_filterMap_iff]
+  rw [← filterMap_eq_map, suffix_filterMap_iff]
 
-theorem isInfix_map_iff {β} {f : α → β} {l₁ : List α} {l₂ : List β} :
+@[deprecated suffix_map_iff (since := "2025-05-27")]
+abbrev isSuffix_map_iff := @suffix_map_iff
+
+theorem infix_map_iff {β} {f : α → β} {l₁ : List α} {l₂ : List β} :
     l₂ <:+: l₁.map f ↔ ∃ l, l <:+: l₁ ∧ l₂ = l.map f := by
-  rw [← filterMap_eq_map, isInfix_filterMap_iff]
+  rw [← filterMap_eq_map, infix_filterMap_iff]
 
-theorem isPrefix_replicate_iff {n} {a : α} {l : List α} :
+@[deprecated infix_map_iff (since := "2025-05-27")]
+abbrev isInfix_map_iff := @infix_map_iff
+
+@[grind =] theorem prefix_replicate_iff {n} {a : α} {l : List α} :
     l <+: List.replicate n a ↔ l.length ≤ n ∧ l = List.replicate l.length a := by
   rw [IsPrefix]
   simp only [append_eq_replicate_iff]
@@ -926,12 +1067,18 @@ theorem isPrefix_replicate_iff {n} {a : α} {l : List α} :
     · simpa using add_sub_of_le h
     · simpa using w
 
-theorem isSuffix_replicate_iff {n} {a : α} {l : List α} :
+@[deprecated prefix_replicate_iff (since := "2025-05-27")]
+abbrev isPrefix_replicate_iff := @prefix_replicate_iff
+
+@[grind =] theorem suffix_replicate_iff {n} {a : α} {l : List α} :
     l <:+ List.replicate n a ↔ l.length ≤ n ∧ l = List.replicate l.length a := by
-  rw [← reverse_prefix, reverse_replicate, isPrefix_replicate_iff]
+  rw [← reverse_prefix, reverse_replicate, prefix_replicate_iff]
   simp [reverse_eq_iff]
 
-theorem isInfix_replicate_iff {n} {a : α} {l : List α} :
+@[deprecated suffix_replicate_iff (since := "2025-05-27")]
+abbrev isSuffix_replicate_iff := @suffix_replicate_iff
+
+@[grind =] theorem infix_replicate_iff {n} {a : α} {l : List α} :
     l <:+: List.replicate n a ↔ l.length ≤ n ∧ l = List.replicate l.length a := by
   rw [IsInfix]
   simp only [append_eq_replicate_iff, length_append]
@@ -943,6 +1090,9 @@ theorem isInfix_replicate_iff {n} {a : α} {l : List α} :
     · simpa using Nat.sub_add_cancel h
     · simpa using w
 
+@[deprecated infix_replicate_iff (since := "2025-05-27")]
+abbrev isInfix_replicate_iff := @infix_replicate_iff
+
 theorem infix_of_mem_flatten : ∀ {L : List (List α)}, l ∈ L → l <:+: flatten L
   | l' :: _, h =>
     match h with
@@ -956,16 +1106,16 @@ theorem infix_of_mem_flatten : ∀ {L : List (List α)}, l ∈ L → l <:+: flat
 theorem prefix_cons_inj (a) : a :: l₁ <+: a :: l₂ ↔ l₁ <+: l₂ :=
   prefix_append_right_inj [a]
 
-theorem take_prefix (i) (l : List α) : take i l <+: l :=
+@[grind] theorem take_prefix (i) (l : List α) : take i l <+: l :=
   ⟨_, take_append_drop _ _⟩
 
-theorem drop_suffix (i) (l : List α) : drop i l <:+ l :=
+@[grind] theorem drop_suffix (i) (l : List α) : drop i l <:+ l :=
   ⟨_, take_append_drop _ _⟩
 
-theorem take_sublist (i) (l : List α) : take i l <+ l :=
+@[grind] theorem take_sublist (i) (l : List α) : take i l <+ l :=
   (take_prefix i l).sublist
 
-theorem drop_sublist (i) (l : List α) : drop i l <+ l :=
+@[grind] theorem drop_sublist (i) (l : List α) : drop i l <+ l :=
   (drop_suffix i l).sublist
 
 theorem take_subset (i) (l : List α) : take i l ⊆ l :=
@@ -986,22 +1136,22 @@ theorem drop_suffix_drop_left (l : List α) {i j : Nat} (h : i ≤ j) : drop j l
 
 -- See `Init.Data.List.Nat.TakeDrop` for `take_prefix_take_left`.
 
-theorem drop_sublist_drop_left (l : List α) {i j : Nat} (h : i ≤ j) : drop j l <+ drop i l :=
+@[grind] theorem drop_sublist_drop_left (l : List α) {i j : Nat} (h : i ≤ j) : drop j l <+ drop i l :=
   (drop_suffix_drop_left l h).sublist
 
-theorem drop_subset_drop_left (l : List α) {i j : Nat} (h : i ≤ j) : drop j l ⊆ drop i l :=
+@[grind] theorem drop_subset_drop_left (l : List α) {i j : Nat} (h : i ≤ j) : drop j l ⊆ drop i l :=
   (drop_sublist_drop_left l h).subset
 
-theorem takeWhile_prefix (p : α → Bool) : l.takeWhile p <+: l :=
+@[grind] theorem takeWhile_prefix (p : α → Bool) : l.takeWhile p <+: l :=
   ⟨l.dropWhile p, takeWhile_append_dropWhile⟩
 
-theorem dropWhile_suffix (p : α → Bool) : l.dropWhile p <:+ l :=
+@[grind] theorem dropWhile_suffix (p : α → Bool) : l.dropWhile p <:+ l :=
   ⟨l.takeWhile p, takeWhile_append_dropWhile⟩
 
-theorem takeWhile_sublist (p : α → Bool) : l.takeWhile p <+ l :=
+@[grind] theorem takeWhile_sublist (p : α → Bool) : l.takeWhile p <+ l :=
   (takeWhile_prefix p).sublist
 
-theorem dropWhile_sublist (p : α → Bool) : l.dropWhile p <+ l :=
+@[grind] theorem dropWhile_sublist (p : α → Bool) : l.dropWhile p <+ l :=
   (dropWhile_suffix p).sublist
 
 theorem takeWhile_subset {l : List α} (p : α → Bool) : l.takeWhile p ⊆ l :=
@@ -1010,61 +1160,88 @@ theorem takeWhile_subset {l : List α} (p : α → Bool) : l.takeWhile p ⊆ l :
 theorem dropWhile_subset {l : List α} (p : α → Bool) : l.dropWhile p ⊆ l :=
   (dropWhile_sublist p).subset
 
-theorem dropLast_prefix : ∀ l : List α, l.dropLast <+: l
+@[grind] theorem dropLast_prefix : ∀ l : List α, l.dropLast <+: l
   | [] => ⟨nil, by rw [dropLast, List.append_nil]⟩
   | a :: l => ⟨_, dropLast_concat_getLast (cons_ne_nil a l)⟩
 
-theorem dropLast_sublist (l : List α) : l.dropLast <+ l :=
+@[grind] theorem dropLast_sublist (l : List α) : l.dropLast <+ l :=
   (dropLast_prefix l).sublist
 
 theorem dropLast_subset (l : List α) : l.dropLast ⊆ l :=
   (dropLast_sublist l).subset
 
-theorem tail_suffix (l : List α) : tail l <:+ l := by rw [← drop_one]; apply drop_suffix
+@[grind] theorem tail_suffix (l : List α) : tail l <:+ l := by rw [← drop_one]; apply drop_suffix
 
-theorem IsPrefix.map {β} (f : α → β) ⦃l₁ l₂ : List α⦄ (h : l₁ <+: l₂) : l₁.map f <+: l₂.map f := by
+@[grind] theorem IsPrefix.map {β} (f : α → β) ⦃l₁ l₂ : List α⦄ (h : l₁ <+: l₂) : l₁.map f <+: l₂.map f := by
   obtain ⟨r, rfl⟩ := h
   rw [map_append]; apply prefix_append
 
-theorem IsSuffix.map {β} (f : α → β) ⦃l₁ l₂ : List α⦄ (h : l₁ <:+ l₂) : l₁.map f <:+ l₂.map f := by
+grind_pattern IsPrefix.map => l₁ <+: l₂, l₁.map f
+grind_pattern IsPrefix.map => l₁ <+: l₂, l₂.map f
+
+@[grind] theorem IsSuffix.map {β} (f : α → β) ⦃l₁ l₂ : List α⦄ (h : l₁ <:+ l₂) : l₁.map f <:+ l₂.map f := by
   obtain ⟨r, rfl⟩ := h
   rw [map_append]; apply suffix_append
 
-theorem IsInfix.map {β} (f : α → β) ⦃l₁ l₂ : List α⦄ (h : l₁ <:+: l₂) : l₁.map f <:+: l₂.map f := by
+grind_pattern IsSuffix.map => l₁ <:+ l₂, l₁.map f
+grind_pattern IsSuffix.map => l₁ <:+ l₂, l₂.map f
+
+@[grind] theorem IsInfix.map {β} (f : α → β) ⦃l₁ l₂ : List α⦄ (h : l₁ <:+: l₂) : l₁.map f <:+: l₂.map f := by
   obtain ⟨r₁, r₂, rfl⟩ := h
   rw [map_append, map_append]; apply infix_append
 
-theorem IsPrefix.filter (p : α → Bool) ⦃l₁ l₂ : List α⦄ (h : l₁ <+: l₂) :
+grind_pattern IsInfix.map => l₁ <:+: l₂, l₁.map f
+grind_pattern IsInfix.map => l₁ <:+: l₂, l₂.map f
+
+@[grind] theorem IsPrefix.filter (p : α → Bool) ⦃l₁ l₂ : List α⦄ (h : l₁ <+: l₂) :
     l₁.filter p <+: l₂.filter p := by
   obtain ⟨xs, rfl⟩ := h
   rw [filter_append]; apply prefix_append
 
-theorem IsSuffix.filter (p : α → Bool) ⦃l₁ l₂ : List α⦄ (h : l₁ <:+ l₂) :
+grind_pattern IsPrefix.filter => l₁ <+: l₂, l₁.filter p
+grind_pattern IsPrefix.filter => l₁ <+: l₂, l₂.filter p
+
+@[grind] theorem IsSuffix.filter (p : α → Bool) ⦃l₁ l₂ : List α⦄ (h : l₁ <:+ l₂) :
     l₁.filter p <:+ l₂.filter p := by
   obtain ⟨xs, rfl⟩ := h
   rw [filter_append]; apply suffix_append
 
-theorem IsInfix.filter (p : α → Bool) ⦃l₁ l₂ : List α⦄ (h : l₁ <:+: l₂) :
+grind_pattern IsSuffix.filter => l₁ <:+ l₂, l₁.filter p
+grind_pattern IsSuffix.filter => l₁ <:+ l₂, l₂.filter p
+
+@[grind] theorem IsInfix.filter (p : α → Bool) ⦃l₁ l₂ : List α⦄ (h : l₁ <:+: l₂) :
     l₁.filter p <:+: l₂.filter p := by
   obtain ⟨xs, ys, rfl⟩ := h
   rw [filter_append, filter_append]; apply infix_append _
 
-theorem IsPrefix.filterMap {β} (f : α → Option β) ⦃l₁ l₂ : List α⦄ (h : l₁ <+: l₂) :
+grind_pattern IsInfix.filter => l₁ <:+: l₂, l₁.filter p
+grind_pattern IsInfix.filter => l₁ <:+: l₂, l₂.filter p
+
+@[grind] theorem IsPrefix.filterMap {β} (f : α → Option β) ⦃l₁ l₂ : List α⦄ (h : l₁ <+: l₂) :
     filterMap f l₁ <+: filterMap f l₂ := by
   obtain ⟨xs, rfl⟩ := h
   rw [filterMap_append]; apply prefix_append
 
-theorem IsSuffix.filterMap {β} (f : α → Option β) ⦃l₁ l₂ : List α⦄ (h : l₁ <:+ l₂) :
+grind_pattern IsPrefix.filterMap => l₁ <+: l₂, filterMap f l₁
+grind_pattern IsPrefix.filterMap => l₁ <+: l₂, filterMap f l₂
+
+@[grind] theorem IsSuffix.filterMap {β} (f : α → Option β) ⦃l₁ l₂ : List α⦄ (h : l₁ <:+ l₂) :
     filterMap f l₁ <:+ filterMap f l₂ := by
   obtain ⟨xs, rfl⟩ := h
   rw [filterMap_append]; apply suffix_append
 
-theorem IsInfix.filterMap {β} (f : α → Option β) ⦃l₁ l₂ : List α⦄ (h : l₁ <:+: l₂) :
+grind_pattern IsSuffix.filterMap => l₁ <:+ l₂, filterMap f l₁
+grind_pattern IsSuffix.filterMap => l₁ <:+ l₂, filterMap f l₂
+
+@[grind] theorem IsInfix.filterMap {β} (f : α → Option β) ⦃l₁ l₂ : List α⦄ (h : l₁ <:+: l₂) :
     filterMap f l₁ <:+: filterMap f l₂ := by
   obtain ⟨xs, ys, rfl⟩ := h
   rw [filterMap_append, filterMap_append]; apply infix_append
 
-@[simp] theorem isPrefixOf_iff_prefix [BEq α] [LawfulBEq α] {l₁ l₂ : List α} :
+grind_pattern IsInfix.filterMap => l₁ <:+: l₂, filterMap f l₁
+grind_pattern IsInfix.filterMap => l₁ <:+: l₂, filterMap f l₂
+
+@[simp, grind =] theorem isPrefixOf_iff_prefix [BEq α] [LawfulBEq α] {l₁ l₂ : List α} :
     l₁.isPrefixOf l₂ ↔ l₁ <+: l₂ := by
   induction l₁ generalizing l₂ with
   | nil => simp
@@ -1076,7 +1253,7 @@ theorem IsInfix.filterMap {β} (f : α → Option β) ⦃l₁ l₂ : List α⦄
 instance [DecidableEq α] (l₁ l₂ : List α) : Decidable (l₁ <+: l₂) :=
   decidable_of_iff (l₁.isPrefixOf l₂) isPrefixOf_iff_prefix
 
-@[simp] theorem isSuffixOf_iff_suffix [BEq α] [LawfulBEq α] {l₁ l₂ : List α} :
+@[simp, grind =] theorem isSuffixOf_iff_suffix [BEq α] [LawfulBEq α] {l₁ l₂ : List α} :
     l₁.isSuffixOf l₂ ↔ l₁ <:+ l₂ := by
   simp [isSuffixOf]
 

src/Init/Data/List/TakeDrop.lean

@@ -257,6 +257,17 @@ theorem dropLast_eq_take {l : List α} : l.dropLast = l.take (l.length - 1) := b
     dsimp
     rw [map_drop]
 
+theorem drop_eq_extract {l : List α} {k : Nat} :
+    l.drop k = l.extract k := by
+  induction l generalizing k
+  case nil => simp
+  case cons _ _ ih =>
+    match k with
+    | 0 => simp
+    | _ + 1 =>
+      simp only [List.drop_succ_cons, List.length_cons, ih]
+      simp only [List.extract_eq_drop_take, List.drop_succ_cons, Nat.succ_sub_succ]
+
 /-! ### takeWhile and dropWhile -/
 
 theorem takeWhile_cons {p : α → Bool} {a : α} {l : List α} :

src/Init/Data/List/ToArray.lean

@@ -302,7 +302,7 @@ termination_by l.length - j
 @[simp, grind =] theorem findIdx?_toArray (p : α → Bool) (l : List α) :
     l.toArray.findIdx? p = l.findIdx? p := by
   rw [Array.findIdx?_eq_map_findFinIdx?_val, findIdx?_eq_map_findFinIdx?_val]
-  simp
+  simp [Array.size]
 
 private theorem idxAuxOf_toArray [BEq α] (a : α) (l : List α) (j : Nat) (w : l' = l.drop j) (h) :
     l.toArray.idxOfAux a j = findFinIdx?.go (fun x => x == a) l l' j h := by
@@ -339,11 +339,11 @@ termination_by l.length - j
 @[simp, grind =] theorem idxOf?_toArray [BEq α] (a : α) (l : List α) :
     l.toArray.idxOf? a = l.idxOf? a := by
   rw [Array.idxOf?, idxOf?]
-  simp [finIdxOf?, findIdx?_eq_map_findFinIdx?_val]
+  simp [finIdxOf?, findIdx?_eq_map_findFinIdx?_val, Array.size]
 
 @[simp, grind =] theorem findIdx_toArray {as : List α} {p : α → Bool} :
     as.toArray.findIdx p = as.findIdx p := by
-  rw [Array.findIdx, findIdx?_toArray, findIdx_eq_getD_findIdx?]
+  rw [Array.findIdx, findIdx?_toArray, findIdx_eq_getD_findIdx?, Array.size]
 
 @[simp, grind =] theorem idxOf_toArray [BEq α] {as : List α} {a : α} :
     as.toArray.idxOf a = as.idxOf a := by
@@ -670,9 +670,9 @@ theorem replace_toArray [BEq α] [LawfulBEq α] (l : List α) (a b : α) :
   split <;> rename_i i h
   · simp only [finIdxOf?_toArray, finIdxOf?_eq_none_iff] at h
     rw [replace_of_not_mem]
-    simpa
+    exact finIdxOf?_eq_none_iff.mp h
   · simp_all only [finIdxOf?_toArray, finIdxOf?_eq_some_iff, Fin.getElem_fin, set_toArray,
-      mk.injEq]
+      mk.injEq, Array.size]
     apply List.ext_getElem
     · simp
     · intro j h₁ h₂
@@ -685,7 +685,7 @@ theorem replace_toArray [BEq α] [LawfulBEq α] (l : List α) (a b : α) :
         · rw [if_pos (by omega), if_pos, if_neg]
           · simp only [mem_take_iff_getElem, not_exists]
             intro k hk
-            simpa using h.2 ⟨k, by omega⟩ (by show k < i.1; omega)
+            simpa using h.2 ⟨k, by omega⟩ (by change k < i.1; omega)
           · subst h₃
             simpa using h.1
         · rw [if_neg (by omega)]

src/Init/Data/List/Zip.lean

@@ -46,6 +46,7 @@ theorem zipWith_self {f : α → α → δ} : ∀ {l : List α}, zipWith f l l =
 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
@@ -83,33 +84,39 @@ theorem getElem?_zip_eq_some {l₁ : List α} {l₂ : List β} {z : α × β} {i
   · rintro ⟨h₀, h₁⟩
     exact ⟨_, _, h₀, h₁, rfl⟩
 
+@[grind =]
 theorem head?_zipWith {f : α → β → γ} :
     (List.zipWith f as bs).head? = match as.head?, bs.head? with
       | some a, some b => some (f a b) | _, _ => none := by
   simp [head?_eq_getElem?, getElem?_zipWith]
 
+@[grind =]
 theorem head_zipWith {f : α → β → γ} (h):
     (List.zipWith f as bs).head h = f (as.head (by rintro rfl; simp_all)) (bs.head (by rintro rfl; simp_all)) := by
   apply Option.some.inj
   rw [← head?_eq_head, head?_zipWith, head?_eq_head, head?_eq_head]
 
-@[simp]
+@[simp, grind =]
 theorem zipWith_map {μ} {f : γ → δ → μ} {g : α → γ} {h : β → δ} {l₁ : List α} {l₂ : List β} :
     zipWith f (l₁.map g) (l₂.map h) = zipWith (fun a b => f (g a) (h b)) l₁ l₂ := by
   induction l₁ generalizing l₂ <;> cases l₂ <;> simp_all
 
+@[grind =]
 theorem zipWith_map_left {l₁ : List α} {l₂ : List β} {f : α → α'} {g : α' → β → γ} :
     zipWith g (l₁.map f) l₂ = zipWith (fun a b => g (f a) b) l₁ l₂ := by
   induction l₁ generalizing l₂ <;> cases l₂ <;> simp_all
 
+@[grind =]
 theorem zipWith_map_right {l₁ : List α} {l₂ : List β} {f : β → β'} {g : α → β' → γ} :
     zipWith g l₁ (l₂.map f) = zipWith (fun a b => g a (f b)) l₁ l₂ := by
   induction l₁ generalizing l₂ <;> cases l₂ <;> simp_all
 
+@[grind =]
 theorem zipWith_foldr_eq_zip_foldr {f : α → β → γ} {i : δ} {g : γ → δ → δ} :
     (zipWith f l₁ l₂).foldr g i = (zip l₁ l₂).foldr (fun p r => g (f p.1 p.2) r) i := by
   induction l₁ generalizing l₂ <;> cases l₂ <;> simp_all
 
+@[grind =]
 theorem zipWith_foldl_eq_zip_foldl {f : α → β → γ} {i : δ} {g : δ → γ → δ} :
     (zipWith f l₁ l₂).foldl g i = (zip l₁ l₂).foldl (fun r p => g r (f p.1 p.2)) i := by
   induction l₁ generalizing i l₂ <;> cases l₂ <;> simp_all
@@ -118,6 +125,7 @@ theorem zipWith_foldl_eq_zip_foldl {f : α → β → γ} {i : δ} {g : δ →
 theorem zipWith_eq_nil_iff {f : α → β → γ} {l l'} : zipWith f l l' = [] ↔ l = [] ∨ l' = [] := by
   cases l <;> cases l' <;> simp
 
+@[grind =]
 theorem map_zipWith {δ : Type _} {f : α → β} {g : γ → δ → α} {l : List γ} {l' : List δ} :
     map f (zipWith g l l') = zipWith (fun x y => f (g x y)) l l' := by
   induction l generalizing l' with
@@ -127,6 +135,7 @@ theorem map_zipWith {δ : Type _} {f : α → β} {g : γ → δ → α} {l : Li
       · simp
       · simp [hl]
 
+@[grind =]
 theorem take_zipWith : (zipWith f l l').take i = zipWith f (l.take i) (l'.take i) := by
   induction l generalizing l' i with
   | nil => simp
@@ -137,6 +146,7 @@ theorem take_zipWith : (zipWith f l l').take i = zipWith f (l.take i) (l'.take i
       · simp
       · simp [hl]
 
+@[grind =]
 theorem drop_zipWith : (zipWith f l l').drop i = zipWith f (l.drop i) (l'.drop i) := by
   induction l generalizing l' i with
   | nil => simp
@@ -147,10 +157,11 @@ theorem drop_zipWith : (zipWith f l l').drop i = zipWith f (l.drop i) (l'.drop i
         · simp
         · simp [hl]
 
-@[simp]
+@[simp, grind =]
 theorem tail_zipWith : (zipWith f l l').tail = zipWith f l.tail l'.tail := by
   rw [← drop_one]; simp [drop_zipWith]
 
+@[grind =]
 theorem zipWith_append {f : α → β → γ} {l₁ l₁' : List α} {l₂ l₂' : List β}
     (h : l₁.length = l₂.length) :
     zipWith f (l₁ ++ l₁') (l₂ ++ l₂') = zipWith f l₁ l₂ ++ zipWith f l₁' l₂' := by
@@ -254,22 +265,26 @@ theorem zip_eq_zipWith : ∀ {l₁ : List α} {l₂ : List β}, zip l₁ l₂ =
   | _, [] => rfl
   | a :: l₁, b :: l₂ => by simp [zip_cons_cons, zip_eq_zipWith (l₁ := l₁)]
 
+@[grind _=_]
 theorem zip_map {f : α → γ} {g : β → δ} :
     ∀ {l₁ : List α} {l₂ : List β}, zip (l₁.map f) (l₂.map g) = (zip l₁ l₂).map (Prod.map f g)
   | [], _ => rfl
   | _, [] => by simp only [map, zip_nil_right]
   | _ :: _, _ :: _ => by simp only [map, zip_cons_cons, zip_map, Prod.map]
 
+@[grind _=_]
 theorem zip_map_left {f : α → γ} {l₁ : List α} {l₂ : List β} :
     zip (l₁.map f) l₂ = (zip l₁ l₂).map (Prod.map f id) := by rw [← zip_map, map_id]
 
+@[grind _=_]
 theorem zip_map_right {f : β → γ} {l₁ : List α} {l₂ : List β} :
     zip l₁ (l₂.map f) = (zip l₁ l₂).map (Prod.map id f) := by rw [← zip_map, map_id]
 
-@[simp] theorem tail_zip {l₁ : List α} {l₂ : List β} :
+@[simp, grind =] theorem tail_zip {l₁ : List α} {l₂ : List β} :
     (zip l₁ l₂).tail = zip l₁.tail l₂.tail := by
   cases l₁ <;> cases l₂ <;> simp
 
+@[grind =]
 theorem zip_append :
     ∀ {l₁ r₁ : List α} {l₂ r₂ : List β} (_h : length l₁ = length l₂),
       zip (l₁ ++ r₁) (l₂ ++ r₂) = zip l₁ l₂ ++ zip r₁ r₂
@@ -278,6 +293,7 @@ theorem zip_append :
   | _ :: _, _, _ :: _, _, h => by
     simp only [cons_append, zip_cons_cons, zip_append (Nat.succ.inj h)]
 
+@[grind =]
 theorem zip_map' {f : α → β} {g : α → γ} :
     ∀ {l : List α}, zip (l.map f) (l.map g) = l.map fun a => (f a, g a)
   | [] => rfl
@@ -296,7 +312,7 @@ theorem map_fst_zip :
   | [], _, _ => rfl
   | _ :: as, _ :: bs, h => by
     simp [Nat.succ_le_succ_iff] at h
-    show _ :: map Prod.fst (zip as bs) = _ :: as
+    change _ :: map Prod.fst (zip as bs) = _ :: as
     rw [map_fst_zip (l₁ := as) h]
   | _ :: _, [], h => by simp at h
 
@@ -308,7 +324,7 @@ theorem map_snd_zip :
   | [], b :: bs, h => by simp at h
   | a :: as, b :: bs, h => by
     simp [Nat.succ_le_succ_iff] at h
-    show _ :: map Prod.snd (zip as bs) = _ :: bs
+    change _ :: map Prod.snd (zip as bs) = _ :: bs
     rw [map_snd_zip (l₂ := bs) h]
 
 theorem map_prod_left_eq_zip {l : List α} {f : α → β} :
@@ -353,6 +369,7 @@ theorem zip_eq_append_iff {l₁ : List α} {l₂ : List 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
@@ -366,33 +383,38 @@ theorem getElem?_zipWithAll {f : Option α → Option β → γ} {i : Nat} :
       cases i <;> simp_all
     | cons b bs => cases i <;> simp_all
 
+@[grind =]
 theorem head?_zipWithAll {f : Option α → Option β → γ} :
     (zipWithAll f as bs).head? = match as.head?, bs.head? with
       | none, none => .none | a?, b? => some (f a? b?) := by
   simp [head?_eq_getElem?, getElem?_zipWithAll]
 
-@[simp] theorem head_zipWithAll {f : Option α → Option β → γ} (h) :
+@[simp, grind =] theorem head_zipWithAll {f : Option α → Option β → γ} (h) :
     (zipWithAll f as bs).head h = f as.head? bs.head? := by
   apply Option.some.inj
   rw [← head?_eq_head, head?_zipWithAll]
   split <;> simp_all
 
-@[simp] theorem tail_zipWithAll {f : Option α → Option β → γ} :
+@[simp, grind =] theorem tail_zipWithAll {f : Option α → Option β → γ} :
     (zipWithAll f as bs).tail = zipWithAll f as.tail bs.tail := by
   cases as <;> cases bs <;> simp
 
+@[grind =]
 theorem zipWithAll_map {μ} {f : Option γ → Option δ → μ} {g : α → γ} {h : β → δ} {l₁ : List α} {l₂ : List β} :
     zipWithAll f (l₁.map g) (l₂.map h) = zipWithAll (fun a b => f (g <$> a) (h <$> b)) l₁ l₂ := by
   induction l₁ generalizing l₂ <;> cases l₂ <;> simp_all
 
+@[grind =]
 theorem zipWithAll_map_left {l₁ : List α} {l₂ : List β} {f : α → α'} {g : Option α' → Option β → γ} :
     zipWithAll g (l₁.map f) l₂ = zipWithAll (fun a b => g (f <$> a) b) l₁ l₂ := by
   induction l₁ generalizing l₂ <;> cases l₂ <;> simp_all
 
+@[grind =]
 theorem zipWithAll_map_right {l₁ : List α} {l₂ : List β} {f : β → β'} {g : Option α → Option β' → γ} :
     zipWithAll g l₁ (l₂.map f) = zipWithAll (fun a b => g a (f <$> b)) l₁ l₂ := by
   induction l₁ generalizing l₂ <;> cases l₂ <;> simp_all
 
+@[grind =]
 theorem map_zipWithAll {δ : Type _} {f : α → β} {g : Option γ → Option δ → α} {l : List γ} {l' : List δ} :
     map f (zipWithAll g l l') = zipWithAll (fun x y => f (g x y)) l l' := by
   induction l generalizing l' with
@@ -400,7 +422,7 @@ theorem map_zipWithAll {δ : Type _} {f : α → β} {g : Option γ → Option
   | cons hd tl hl =>
     cases l' <;> simp_all
 
-@[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
   induction n with
   | zero => rfl
@@ -408,12 +430,13 @@ theorem map_zipWithAll {δ : Type _} {f : α → β} {g : Option γ → Option
 
 /-! ### unzip -/
 
-@[simp] theorem unzip_fst : (unzip l).fst = l.map Prod.fst := by
+@[simp, grind =] theorem unzip_fst : (unzip l).fst = l.map Prod.fst := by
   induction l <;> simp_all
 
-@[simp] theorem unzip_snd : (unzip l).snd = l.map Prod.snd := by
+@[simp, grind =] theorem unzip_snd : (unzip l).snd = l.map Prod.snd := by
   induction l <;> simp_all
 
+@[grind =]
 theorem unzip_eq_map : ∀ {l : List (α × β)}, unzip l = (l.map Prod.fst, l.map Prod.snd)
   | [] => rfl
   | (a, b) :: l => by simp only [unzip_cons, map_cons, unzip_eq_map (l := l)]
@@ -453,6 +476,6 @@ theorem tail_zip_fst {l : List (α × β)} : l.unzip.1.tail = l.tail.unzip.1 :=
 theorem tail_zip_snd {l : List (α × β)} : l.unzip.2.tail = l.tail.unzip.2 := by
   simp
 
-@[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

src/Init/Data/Nat/Basic.lean

@@ -1069,7 +1069,7 @@ protected theorem sub_lt_sub_right : ∀ {a b c : Nat}, c ≤ a → a < b → a
     exact Nat.sub_lt_sub_right (le_of_succ_le_succ hle) (lt_of_succ_lt_succ h)
 
 protected theorem sub_self_add (n m : Nat) : n - (n + m) = 0 := by
-  show (n + 0) - (n + m) = 0
+  change (n + 0) - (n + m) = 0
   rw [Nat.add_sub_add_left, Nat.zero_sub]
 
 @[simp] protected theorem sub_eq_zero_of_le {n m : Nat} (h : n ≤ m) : n - m = 0 := by

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

@@ -72,7 +72,7 @@ Examples:
  * `0 <<< 3 = 0`
  * `0xf1 <<< 4 = 0xf10`
 -/
-@[extern "lean_nat_shiftl"]
+@[extern "lean_nat_shiftl", expose]
 def shiftLeft : @& Nat → @& Nat → Nat
   | n, 0 => n
   | n, succ m => shiftLeft (2*n) m
@@ -88,7 +88,7 @@ Examples:
  * `0 >>> 3 = 0`
  * `0xf13a >>> 8 = 0xf1`
 -/
-@[extern "lean_nat_shiftr"]
+@[extern "lean_nat_shiftr", expose]
 def shiftRight : @& Nat → @& Nat → Nat
   | n, 0 => n
   | n, succ m => shiftRight n m / 2

src/Init/Data/Nat/Div/Basic.lean

@@ -9,6 +9,7 @@ prelude
 import Init.WF
 import Init.WFTactics
 import Init.Data.Nat.Basic
+meta import Init.MetaTypes
 
 @[expose] section
 
@@ -75,7 +76,7 @@ private theorem div.go.fuel_congr (x y fuel1 fuel2 : Nat) (hy : 0 < y) (h1 : x <
 termination_by structural fuel1
 
 theorem div_eq (x y : Nat) : x / y = if 0 < y ∧ y ≤ x then (x - y) / y + 1 else 0 := by
-  show Nat.div _ _ = ite _ (Nat.div _ _ + 1) _
+  change Nat.div _ _ = ite _ (Nat.div _ _ + 1) _
   unfold Nat.div
   split
   next =>
@@ -257,7 +258,7 @@ protected def mod : @& Nat → @& Nat → Nat
 instance instMod : Mod Nat := ⟨Nat.mod⟩
 
 protected theorem modCore_eq_mod (n m : Nat) : Nat.modCore n m = n % m := by
-  show Nat.modCore n m = Nat.mod n m
+  change Nat.modCore n m = Nat.mod n m
   match n, m with
   | 0, _ =>
     rw [Nat.modCore_eq]
@@ -521,7 +522,7 @@ theorem mul_sub_div (x n p : Nat) (h₁ : x < n*p) : (n * p - (x + 1)) / n = p -
     rw [Nat.mul_sub_right_distrib, Nat.mul_comm]
     exact Nat.sub_le_sub_left ((div_lt_iff_lt_mul npos).1 (lt_succ_self _)) _
   focus
-    show succ (pred (n * p - x)) ≤ (succ (pred (p - x / n))) * n
+    change succ (pred (n * p - x)) ≤ (succ (pred (p - x / n))) * n
     rw [succ_pred_eq_of_pos (Nat.sub_pos_of_lt h₁),
       fun h => succ_pred_eq_of_pos (Nat.sub_pos_of_lt h)] -- TODO: why is the function needed?
     focus

src/Init/Data/Nat/Lcm.lean

@@ -26,6 +26,7 @@ Examples:
  * `Nat.lcm 0 3 = 0`
  * `Nat.lcm 3 0 = 0`
 -/
+@[expose]
 def lcm (m n : Nat) : Nat := m * n / gcd m n
 
 theorem lcm_eq_mul_div (m n : Nat) : lcm m n = m * n / gcd m n := rfl

src/Init/Data/Nat/Lemmas.lean

@@ -1767,8 +1767,16 @@ instance decidableExistsLT' {p : (m : Nat) → m < k → Prop} [I : ∀ m h, Dec
 /-- Dependent version of `decidableExistsLE`. -/
 instance decidableExistsLE' {p : (m : Nat) → m ≤ k → Prop} [I : ∀ m h, Decidable (p m h)] :
     Decidable (∃ m : Nat, ∃ h : m ≤ k, p m h) :=
-  decidable_of_iff (∃ m, ∃ h : m < k + 1, p m (by omega)) (exists_congr fun _ =>
-    ⟨fun ⟨h, w⟩ => ⟨le_of_lt_succ h, w⟩, fun ⟨h, w⟩ => ⟨lt_add_one_of_le h, w⟩⟩)
+  decidable_of_iff (∃ m, ∃ h : m < k + 1, p m (by omega)) <| by
+    apply exists_congr
+    intro
+    exact ⟨fun ⟨h, w⟩ => ⟨le_of_lt_succ h, w⟩, fun ⟨h, w⟩ => ⟨lt_add_one_of_le h, w⟩⟩
+
+instance decidableExistsFin (P : Fin n → Prop) [DecidablePred P] : Decidable (∃ i, P i) :=
+  decidable_of_iff (∃ k, k < n ∧ ((h: k < n) → P ⟨k, h⟩))
+    ⟨fun ⟨k, a⟩ => Exists.intro ⟨k, a.left⟩ (a.right a.left),
+    fun ⟨i, e⟩ => Exists.intro i.val ⟨i.isLt, fun _ => e⟩⟩
+
 
 /-! ### Results about `List.sum` specialized to `Nat` -/
 

src/Init/Data/Nat/Linear.lean

@@ -149,7 +149,7 @@ instance : LawfulBEq PolyCnstr where
     rw [h₁, h₂, h₃]
   rfl {a} := by
     cases a; rename_i eq lhs rhs
-    show (eq == eq && (lhs == lhs && rhs == rhs)) = true
+    change (eq == eq && (lhs == lhs && rhs == rhs)) = true
     simp
 
 structure ExprCnstr where

src/Init/Data/Option/Array.lean

@@ -84,7 +84,7 @@ theorem toArray_eq_singleton_iff {o : Option α} : o.toArray = #[a] ↔ o = some
 
 theorem size_toArray_eq_zero_iff {o : Option α} :
     o.toArray.size = 0 ↔ o = none := by
-  simp
+  simp [Array.size]
 
 @[simp]
 theorem size_toArray_eq_one_iff {o : Option α} :

src/Init/Data/Option/Attach.lean

@@ -34,7 +34,7 @@ well-founded recursion that use iteration operators (such as `Option.map`) to pr
 value drawn from a parameter is smaller than the parameter. This allows the well-founded recursion
 mechanism to prove that the function terminates.
 -/
-@[implemented_by attachWithImpl] def attachWith
+@[implemented_by attachWithImpl, expose] def attachWith
     (xs : Option α) (P : α → Prop) (H : ∀ x, xs = some x → P x) : Option {x // P x} :=
   match xs with
   | none => none
@@ -49,7 +49,7 @@ operators (such as `Option.map`) to prove that an optional value drawn from a pa
 than the parameter. This allows the well-founded recursion mechanism to prove that the function
 terminates.
 -/
-@[inline] def attach (xs : Option α) : Option {x // xs = some x} := xs.attachWith _ fun _ => id
+@[inline, expose] def attach (xs : Option α) : Option {x // xs = some x} := xs.attachWith _ fun _ => id
 
 @[simp, grind =] theorem attach_none : (none : Option α).attach = none := rfl
 @[simp, grind =] theorem attachWith_none : (none : Option α).attachWith P H = none := rfl
@@ -325,6 +325,7 @@ If this function is encountered in a proof state, the right approach is usually
 
 It is a synonym for `Option.map Subtype.val`.
 -/
+@[expose]
 def unattach {α : Type _} {p : α → Prop} (o : Option { x // p x }) := o.map (·.val)
 
 @[simp] theorem unattach_none {p : α → Prop} : (none : Option { x // p x }).unattach = none := rfl

src/Init/Data/Option/Basic.lean

@@ -435,7 +435,7 @@ This is the monadic analogue of `Option.getD`.
 @[simp, grind] theorem getDM_some [Pure m] (a : α) (y : m α) : (some a).getDM y = pure a := rfl
 
 instance (α) [BEq α] [ReflBEq α] : ReflBEq (Option α) where
-  rfl {x} :=
+  rfl {x} := private
     match x with
     | some _ => BEq.rfl (α := α)
     | none => rfl

src/Init/Data/Option/BasicAux.lean

@@ -16,7 +16,7 @@ namespace Option
 /--
 Extracts the value from an `Option`, panicking on `none`.
 -/
-@[inline] def get! {α : Type u} [Inhabited α] : Option α → α
+@[inline, expose] def get! {α : Type u} [Inhabited α] : Option α → α
   | some x => x
   | none   => panic! "value is none"
 

src/Init/Data/Option/Instances.lean

@@ -87,7 +87,7 @@ some ⟨3, ⋯⟩
 none
 ```
 -/
-@[inline]
+@[inline, expose]
 def pbind : (o : Option α) → (f : (a : α) → o = some a → Option β) → Option β
   | none, _ => none
   | some a, f => f a rfl
@@ -114,7 +114,7 @@ some ⟨3, ⋯⟩
 none
 ```
 -/
-@[inline] def pmap {p : α → Prop}
+@[inline, expose] def pmap {p : α → Prop}
     (f : ∀ a : α, p a → β) :
     (o : Option α) → (∀ a, o = some a → p a) → Option β
   | none, _ => none
@@ -147,14 +147,14 @@ some ⟨3, ⋯⟩
 none
 ```
 -/
-@[inline] def pelim (o : Option α) (b : β) (f : (a : α) → o = some a → β) : β :=
+@[inline, expose] def pelim (o : Option α) (b : β) (f : (a : α) → o = some a → β) : β :=
   match o with
   | none => b
   | some a => f a rfl
 
 /-- Partial filter. If `o : Option α`, `p : (a : α) → o = some a → Bool`, then `o.pfilter p` is
 the same as `o.filter p` but `p` is passed the proof that `o = some a`. -/
-@[inline] def pfilter (o : Option α) (p : (a : α) → o = some a → Bool) : Option α :=
+@[inline, expose] def pfilter (o : Option α) (p : (a : α) → o = some a → Bool) : Option α :=
   match o with
   | none => none
   | some a => bif p a rfl then o else none
@@ -177,7 +177,7 @@ Examples:
 ((), 0)
 ```
 -/
-@[inline] protected def forM [Pure m] : Option α → (α → m PUnit) → m PUnit
+@[inline, expose] protected def forM [Pure m] : Option α → (α → m PUnit) → m PUnit
   | none  , _ => pure ⟨⟩
   | some a, f => f a
 

src/Init/Data/Option/Lemmas.lean

@@ -70,8 +70,6 @@ theorem some_get! [Inhabited α] : (o : Option α) → o.isSome → some (o.get!
 
 theorem get!_eq_getD [Inhabited α] (o : Option α) : o.get! = o.getD default := rfl
 
-@[deprecated get!_eq_getD (since := "2024-11-18")] abbrev get!_eq_getD_default := @get!_eq_getD
-
 theorem get_congr {o o' : Option α} {ho : o.isSome} (h : o = o') :
     o.get ho = o'.get (h ▸ ho) := by
   cases h; rfl
@@ -1165,8 +1163,11 @@ end ite
 
 /-! ### pbind -/
 
-@[simp, grind] theorem pbind_none : pbind none f = none := rfl
-@[simp, grind] theorem pbind_some : pbind (some a) f = f a rfl := rfl
+@[simp] theorem pbind_none : pbind none f = none := rfl
+@[simp] theorem pbind_some : pbind (some a) f = f a rfl := rfl
+
+@[grind = gen] theorem pbind_none' (h : x = none) : pbind x f = none := by subst h; rfl
+@[grind = gen] theorem pbind_some' (h : x = some a) : pbind x f = f a h := by subst h; rfl
 
 @[simp, grind] theorem map_pbind {o : Option α} {f : (a : α) → o = some a → Option β}
     {g : β → γ} : (o.pbind f).map g = o.pbind (fun a h => (f a h).map g) := by
@@ -1229,12 +1230,18 @@ theorem get_pbind {o : Option α} {f : (a : α) → o = some a → Option β} {h
 
 /-! ### pmap -/
 
-@[simp, grind] theorem pmap_none {p : α → Prop} {f : ∀ (a : α), p a → β} {h} :
+@[simp] theorem pmap_none {p : α → Prop} {f : ∀ (a : α), p a → β} {h} :
     pmap f none h = none := rfl
 
-@[simp, grind] theorem pmap_some {p : α → Prop} {f : ∀ (a : α), p a → β} {h} :
+@[simp] theorem pmap_some {p : α → Prop} {f : ∀ (a : α), p a → β} {h} :
     pmap f (some a) h = some (f a (h a rfl)) := rfl
 
+@[grind = gen] theorem pmap_none' {p : α → Prop} {f : ∀ (a : α), p a → β} (he : x = none) {h} :
+    pmap f x h = none := by subst he; rfl
+
+@[grind = gen] theorem pmap_some' {p : α → Prop} {f : ∀ (a : α), p a → β} (he : x = some a) {h} :
+    pmap f x h = some (f a (h a he)) := by subst he; rfl
+
 @[simp] theorem pmap_eq_none_iff {p : α → Prop} {f : ∀ (a : α), p a → β} {h} :
     pmap f o h = none ↔ o = none := by
   cases o <;> simp
@@ -1317,8 +1324,11 @@ theorem get_pmap {p : α → Bool} {f : (x : α) → p x → β} {o : Option α}
 
 /-! ### pelim -/
 
-@[simp, grind] theorem pelim_none : pelim none b f = b := rfl
-@[simp, grind] theorem pelim_some : pelim (some a) b f = f a rfl := rfl
+@[simp] theorem pelim_none : pelim none b f = b := rfl
+@[simp] theorem pelim_some : pelim (some a) b f = f a rfl := rfl
+
+@[grind = gen] theorem pelim_none' (h : x = none) : pelim x b f = b := by subst h; rfl
+@[grind = gen] theorem pelim_some' (h : x = some a) : pelim x b f = f a h := by subst h; rfl
 
 @[simp] theorem pelim_eq_elim : pelim o b (fun a _ => f a) = o.elim b f := by
   cases o <;> simp

src/Init/Data/Ord.lean

@@ -38,7 +38,7 @@ Examples:
  * `Ordering.eq.swap = Ordering.eq`
  * `Ordering.gt.swap = Ordering.lt`
 -/
-@[inline]
+@[inline, expose]
 def swap : Ordering → Ordering
   | .lt => .gt
   | .eq => .eq
@@ -96,7 +96,7 @@ Ordering.lt
 /--
 Checks whether the ordering is `eq`.
 -/
-@[inline]
+@[inline, expose]
 def isEq : Ordering → Bool
   | eq => true
   | _ => false
@@ -104,7 +104,7 @@ def isEq : Ordering → Bool
 /--
 Checks whether the ordering is not `eq`.
 -/
-@[inline]
+@[inline, expose]
 def isNe : Ordering → Bool
   | eq => false
   | _ => true
@@ -112,7 +112,7 @@ def isNe : Ordering → Bool
 /--
 Checks whether the ordering is `lt` or `eq`.
 -/
-@[inline]
+@[inline, expose]
 def isLE : Ordering → Bool
   | gt => false
   | _ => true
@@ -120,7 +120,7 @@ def isLE : Ordering → Bool
 /--
 Checks whether the ordering is `lt`.
 -/
-@[inline]
+@[inline, expose]
 def isLT : Ordering → Bool
   | lt => true
   | _ => false
@@ -128,7 +128,7 @@ def isLT : Ordering → Bool
 /--
 Checks whether the ordering is `gt`.
 -/
-@[inline]
+@[inline, expose]
 def isGT : Ordering → Bool
   | gt => true
   | _ => false
@@ -136,7 +136,7 @@ def isGT : Ordering → Bool
 /--
 Checks whether the ordering is `gt` or `eq`.
 -/
-@[inline]
+@[inline, expose]
 def isGE : Ordering → Bool
   | lt => false
   | _ => true
@@ -524,7 +524,7 @@ instance : Ord Ordering where
 
 namespace List
 
-@[specialize]
+@[specialize, expose]
 protected def compareLex {α} (cmp : α → α → Ordering) :
     List α → List α → Ordering
   | [], [] => .eq
@@ -696,6 +696,7 @@ end Array
 
 namespace Vector
 
+@[expose]
 protected def compareLex {α n} (cmp : α → α → Ordering) (a b : Vector α n) : Ordering :=
   Array.compareLex cmp a.toArray b.toArray
 

src/Init/Data/Prod.lean

@@ -54,7 +54,7 @@ Examples:
  * `(1, 2).swap = (2, 1)`
  * `("orange", -87).swap = (-87, "orange")`
 -/
-def swap : α × β → β × α := fun p => (p.2, p.1)
+@[expose] def swap : α × β → β × α := fun p => (p.2, p.1)
 
 @[simp]
 theorem swap_swap : ∀ x : α × β, swap (swap x) = x

src/Init/Data/Range/Basic.lean

@@ -25,7 +25,7 @@ namespace Range
 universe u v
 
 /-- The number of elements in the range. -/
-@[simp] def size (r : Range) : Nat := (r.stop - r.start + r.step - 1) / r.step
+@[simp, expose] def size (r : Range) : Nat := (r.stop - r.start + r.step - 1) / r.step
 
 @[inline] protected def forIn' [Monad m] (range : Range) (init : β)
     (f : (i : Nat) → i ∈ range → β → m (ForInStep β)) : m β :=
@@ -85,4 +85,4 @@ theorem Membership.get_elem_helper {i n : Nat} {r : Std.Range} (h₁ : i ∈ r)
     i < n := h₂ ▸ h₁.2.1
 
 macro_rules
-  | `(tactic| get_elem_tactic_trivial) => `(tactic| apply Membership.get_elem_helper; assumption; rfl)
+  | `(tactic| get_elem_tactic_extensible) => `(tactic| apply Membership.get_elem_helper; assumption; rfl)

src/Init/Data/Repr.lean

@@ -210,7 +210,7 @@ protected def _root_.USize.repr (n : @& USize) : String :=
 private def reprArray : Array String := Id.run do
   List.range 128 |>.map (·.toUSize.repr) |> Array.mk
 
-private def reprFast (n : Nat) : String :=
+def reprFast (n : Nat) : String :=
   if h : n < Nat.reprArray.size then Nat.reprArray.getInternal n h else
   if h : n < USize.size then (USize.ofNatLT n h).repr
   else (toDigits 10 n).asString