feat: lemmas about rounding dyadics

.gitattributes

@@ -4,9 +4,3 @@ RELEASES.md merge=union
 stage0/** binary linguist-generated
 # The following file is often manually edited, so do show it in diffs
 stage0/src/stdlib_flags.h -binary -linguist-generated
-# These files should not have line endings translated on Windows, because
-# it throws off parser tests. Later lines override earlier ones, so the
-# runner code is still treated as ordinary text.
-tests/lean/docparse/* eol=lf
-tests/lean/docparse/*.lean eol=auto
-tests/lean/docparse/*.sh eol=auto

.github/workflows/actionlint.yml

@@ -15,7 +15,7 @@ jobs:
     runs-on: ubuntu-latest
     steps:
     - name: Checkout
-      uses: actions/checkout@v5
+      uses: actions/checkout@v4
     - name: actionlint
       uses: raven-actions/actionlint@v2
       with:

.github/workflows/build-template.yml

@@ -70,7 +70,7 @@ jobs:
         if: runner.os == 'macOS'
       - name: Checkout
         if: (!endsWith(matrix.os, '-with-cache'))
-        uses: actions/checkout@v5
+        uses: actions/checkout@v4
         with:
           # the default is to use a virtual merge commit between the PR and master: just use the PR
           ref: ${{ github.event.pull_request.head.sha }}
@@ -175,9 +175,7 @@ jobs:
       # Should be done as early as possible and in particular *before* "Check rebootstrap" which
       # changes the state of stage1/
       - name: Save Cache
-        # Caching on cancellation created some mysterious issues perhaps related to improper build
-        # shutdown
-        if: steps.restore-cache.outputs.cache-hit != 'true' && !cancelled()
+        if: steps.restore-cache.outputs.cache-hit != 'true'
         uses: actions/cache/save@v4
         with:
           # NOTE: must be in sync with `restore` above
@@ -229,7 +227,7 @@ jobs:
         id: test
         run: |
           ulimit -c unlimited  # coredumps
-          time ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/$TARGET_STAGE -j$NPROC --output-junit test-results.xml ${{ matrix.CTEST_OPTIONS }}
+          time ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/$TARGET_STAGE -j$NPROC --output-junit test-results.xml
         if: (matrix.wasm || !matrix.cross) && (inputs.check-level >= 1 || matrix.test)
       - name: Test Summary
         uses: test-summary/action@v2

.github/workflows/check-prelude.yml

@@ -7,7 +7,7 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - name: Checkout
-        uses: actions/checkout@v5
+        uses: actions/checkout@v4
         with:
           # the default is to use a virtual merge commit between the PR and master: just use the PR
           ref: ${{ github.event.pull_request.head.sha }}

.github/workflows/check-stage0.yml

@@ -8,7 +8,7 @@ jobs:
   check-stage0-on-queue:
     runs-on: ubuntu-latest
     steps:
-    - uses: actions/checkout@v5
+    - uses: actions/checkout@v4
       with:
         ref: ${{ github.event.pull_request.head.sha }}
         filter: blob:none

.github/workflows/ci.yml

@@ -54,7 +54,7 @@ jobs:
 
     steps:
       - name: Checkout
-        uses: actions/checkout@v5
+        uses: actions/checkout@v4
         # don't schedule nightlies on forks
         if: github.event_name == 'schedule' && github.repository == 'leanprover/lean4' || inputs.action == 'release nightly'
       - name: Set Nightly
@@ -200,6 +200,8 @@ jobs:
                 "os": "ubuntu-latest",
                 "check-level": 2,
                 "CMAKE_PRESET": "reldebug",
+                // exclude seriously slow/stackoverflowing tests
+                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest|bv_bitblast_stress|3807'"
               },
               // TODO: suddenly started failing in CI
               /*{
@@ -221,7 +223,6 @@ jobs:
                 "prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm*",
                 "binary-check": "otool -L",
                 "tar": "gtar", // https://github.com/actions/runner-images/issues/2619
-                "CTEST_OPTIONS": "-E 'leanlaketest_hello'", // started failing from unpack
               },
               {
                 "name": "macOS aarch64",
@@ -245,6 +246,8 @@ jobs:
                 "check-level": 2,
                 "shell": "msys2 {0}",
                 "CMAKE_OPTIONS": "-G \"Unix Makefiles\"",
+                // for reasons unknown, interactivetests are flaky on Windows
+                "CTEST_OPTIONS": "--repeat until-pass:2",
                 "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-w64-windows-gnu.tar.zst",
                 "prepare-llvm": "../script/prepare-llvm-mingw.sh lean-llvm*",
                 "binary-check": "ldd",
@@ -363,7 +366,7 @@ jobs:
     runs-on: ubuntu-latest
     needs: build
     steps:
-      - uses: actions/download-artifact@v5
+      - uses: actions/download-artifact@v4
         with:
           path: artifacts
       - name: Release
@@ -388,12 +391,12 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - name: Checkout
-        uses: actions/checkout@v5
+        uses: actions/checkout@v4
         with:
           # needed for tagging
           fetch-depth: 0
           token: ${{ secrets.PUSH_NIGHTLY_TOKEN }}
-      - uses: actions/download-artifact@v5
+      - uses: actions/download-artifact@v4
         with:
           path: artifacts
       - name: Prepare Nightly Release

.github/workflows/copyright-header.yml

@@ -6,7 +6,7 @@ jobs:
   check-lean-files:
     runs-on: ubuntu-latest
     steps:
-    - uses: actions/checkout@v5
+    - uses: actions/checkout@v4
 
     - name: Verify .lean files start with a copyright header.
       run: |

.github/workflows/pr-release.yml

@@ -395,7 +395,7 @@ jobs:
       # Checkout the Batteries repository with all branches
       - name: Checkout Batteries repository
         if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
-        uses: actions/checkout@v5
+        uses: actions/checkout@v4
         with:
           repository: leanprover-community/batteries
           token: ${{ secrets.MATHLIB4_BOT }}
@@ -454,7 +454,7 @@ jobs:
       # Checkout the mathlib4 repository with all branches
       - name: Checkout mathlib4 repository
         if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
-        uses: actions/checkout@v5
+        uses: actions/checkout@v4
         with:
           repository: leanprover-community/mathlib4-nightly-testing
           token: ${{ secrets.MATHLIB4_BOT }}
@@ -524,7 +524,7 @@ jobs:
       # Checkout the reference manual repository with all branches
       - name: Checkout mathlib4 repository
         if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.reference-manual-ready.outputs.manual_ready == 'true'
-        uses: actions/checkout@v5
+        uses: actions/checkout@v4
         with:
           repository: leanprover/reference-manual
           token: ${{ secrets.MANUAL_PR_BOT }}

.github/workflows/update-stage0.yml

@@ -19,15 +19,11 @@ concurrency:
 jobs:
   update-stage0:
     runs-on: nscloud-ubuntu-22.04-amd64-8x16
-    env:
-      CCACHE_DIR: ${{ github.workspace }}/.ccache
-      CCACHE_COMPRESS: true
-      CCACHE_MAXSIZE: 400M
     steps:
     # This action should push to an otherwise protected branch, so it
     # uses a deploy key with write permissions, as suggested at
     # https://stackoverflow.com/a/76135647/946226
-    - uses: actions/checkout@v5
+    - uses: actions/checkout@v4
       with:
         ssh-key: ${{secrets.STAGE0_SSH_KEY}}
     - run: echo "should_update_stage0=yes" >> "$GITHUB_ENV"
@@ -74,14 +70,10 @@ jobs:
         restore-keys: |
           Linux Lake-build-v3
     - if: env.should_update_stage0 == 'yes'
-      # sync options with `Linux Lake` to ensure cache reuse
-      run: |
-        mkdir -p build
-        cmake --preset release -B build -DLEAN_EXTRA_MAKE_OPTS=-DwarningAsError=true
+      run: cmake --preset release
       shell: 'nix develop -c bash -euxo pipefail {0}'
     - if: env.should_update_stage0 == 'yes'
-      run: |
-        make -j$NPROC -C build update-stage0-commit
+      run: make -j$NPROC -C build/release  update-stage0-commit
       shell: 'nix develop -c bash -euxo pipefail {0}'
     - if: env.should_update_stage0 == 'yes'
       run: git show --stat

README.md

@@ -2,19 +2,19 @@ This is the repository for **Lean 4**.
 
 # About
 
-- [Quickstart](https://lean-lang.org/install/)
+- [Quickstart](https://lean-lang.org/documentation/setup/)
 - [Homepage](https://lean-lang.org)
 - [Theorem Proving Tutorial](https://lean-lang.org/theorem_proving_in_lean4/)
 - [Functional Programming in Lean](https://lean-lang.org/functional_programming_in_lean/)
-- [Documentation Overview](https://lean-lang.org/learn/)
+- [Documentation Overview](https://lean-lang.org/documentation/)
 - [Language Reference](https://lean-lang.org/doc/reference/latest/)
 - [Release notes](RELEASES.md) starting at v4.0.0-m3
-- [Examples](https://lean-lang.org/examples/)
+- [Examples](https://lean-lang.org/lean4/doc/examples.html)
 - [External Contribution Guidelines](CONTRIBUTING.md)
 
 # Installation
 
-See [Install Lean](https://lean-lang.org/install/).
+See [Setting Up Lean](https://lean-lang.org/documentation/setup/).
 
 # Contributing
 

doc/dev/index.md

@@ -8,7 +8,7 @@ You should not edit the `stage0` directory except using the commands described i
 
 ## Development Setup
 
-You can use any of the [supported editors](https://lean-lang.org/install/manual/) for editing the Lean source code.
+You can use any of the [supported editors](../setup.md) for editing the Lean source code.
 Please see below for specific instructions for VS Code.
 
 ### Dev setup using elan
@@ -99,19 +99,3 @@ on to `nightly-with-manual` branch. (It is fine to force push after rebasing.)
 CI will generate a branch of the reference manual called `lean-pr-testing-NNNN`
 in `leanprover/reference-manual`. This branch uses the toolchain for your PR,
 and will report back to the Lean PR with results from Mathlib CI.
-
-### Avoiding rebuilds for downstream projects
-
-If you want to test changes to Lean on downstream projects and would like to avoid rebuilding modules you have already built/fetched using the project's configured Lean toolchain, you can often do so as long as your build of Lean is close enough to that Lean toolchain (compatible .olean format including structure of all relevant environment extensions).
-
-To override the toolchain without rebuilding for a single command, for example `lake build` or `lake lean`, you can use the prefix
-```
-LEAN_GITHASH=$(lean --githash) lake +lean4 ...
-```
-Alternatively, use
-```
-export LEAN_GITHASH=$(lean --githash)
-export ELAN_TOOLCHAIN=lean4
-```
-to persist these changes for the lifetime of the current shell, which will affect any processes spawned from it such as VS Code started via `code .`.
-If you use a setup where you cannot directly start your editor from the command line, such as VS Code Remote, you might want to consider using [direnv](https://direnv.net/) together with an editor extension for it instead so that you can put the lines above into `.envrc`.

doc/make/index.md

@@ -1,6 +1,6 @@
 These are instructions to set up a working development environment for those who wish to make changes to Lean itself. It is part of the [Development Guide](../dev/index.md).
 
-We strongly suggest that new users instead follow the [Installation Instructions](https://lean-lang.org/install/) to get started using Lean, since this sets up an environment that can automatically manage multiple Lean toolchain versions, which is necessary when working within the Lean ecosystem.
+We strongly suggest that new users instead follow the [Quickstart](../quickstart.md) to get started using Lean, since this sets up an environment that can automatically manage multiple Lean toolchain versions, which is necessary when working within the Lean ecosystem.
 
 Requirements
 ------------

lean.code-workspace

@@ -37,15 +37,6 @@
 					"isDefault": true
 				}
 			},
-			{
-				"label": "build-old",
-				"type": "shell",
-				"command": "make -C build/release -j$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4) LAKE_EXTRA_ARGS=--old",
-				"problemMatcher": [],
-				"group": {
-					"kind": "build"
-				}
-			},
 			{
 				"label": "test",
 				"type": "shell",

script/AnalyzeGrindAnnotations.lean

@@ -97,36 +97,5 @@ macro "#analyzeEMatchTheorems" : command => `(
 #analyzeEMatchTheorems
 
 -- -- We can analyze specific theorems using commands such as
-set_option trace.grind.ematch.instance true
-
--- 1. grind immediately sees `(#[] : Array α) = ([] : List α).toArray` but probably this should be hidden.
--- 2. `Vector.toArray_empty` keys on `Array.mk []` rather than `#v[].toArray`
--- I guess we could add `(#[].extract _ _).extract _ _` as a stop pattern.
-run_meta analyzeEMatchTheorem ``Array.extract_empty {}
-
--- Neither `Option.bind_some` nor `Option.bind_fun_some` fire, because the terms appear inside
--- lambdas. So we get crazy things like:
--- `fun x => ((some x).bind some).bind fun x => (some x).bind fun x => (some x).bind some`
--- We could consider replacing `filterMap_some` with
--- `filterMap g (filterMap f xs) = filterMap (f >=> g) xs`
--- to avoid the lambda that `grind` struggles with, but this would require more API around the fish.
-run_meta analyzeEMatchTheorem ``Array.filterMap_some {}
-
--- Not entirely certain what is wrong here, but certainly
--- `eq_empty_of_append_eq_empty` is firing too often.
--- Ideally we could instantiate this is we fine `xs ++ ys` in the same equivalence class,
--- note just as soon as we see `xs ++ ys`.
--- I've tried removing this in https://github.com/leanprover/lean4/pull/10162
-run_meta analyzeEMatchTheorem ``Array.range'_succ {}
-
--- Perhaps the same story here.
-run_meta analyzeEMatchTheorem ``Array.range_succ {}
-
--- `zip_map_left` and `zip_map_right` are bad grind lemmas,
--- checking if they can be removed in https://github.com/leanprover/lean4/pull/10163
-run_meta analyzeEMatchTheorem ``Array.zip_map {}
-
--- It seems crazy to me that as soon as we have `0 >>> n = 0`, we instantiate based on the
--- pattern `0 >>> n >>> m` by substituting `0` into `0 >>> n` to produce the `0 >>> n >>> n`.
--- I don't think any forbidden subterms can help us here. I don't know what to do. :-(
-run_meta analyzeEMatchTheorem ``Int.zero_shiftRight {}
+set_option trace.grind.ematch.instance true in
+run_meta analyzeEMatchTheorem ``List.filterMap_some {}

script/merge_remote.py

@@ -5,7 +5,6 @@ Merge a tag into a branch on a GitHub repository.
 
 This script checks if a specified tag can be merged cleanly into a branch and performs
 the merge if possible. If the merge cannot be done cleanly, it prints a helpful message.
-Merge conflicts in the lean-toolchain file are automatically resolved by accepting the incoming changes.
 
 Usage:
     python3 merge_remote.py <org/repo> <branch> <tag>
@@ -59,32 +58,6 @@ def clone_repo(repo, temp_dir):
     return True
 
 
-def get_conflicted_files():
-    """Get list of files with merge conflicts."""
-    result = run_command("git diff --name-only --diff-filter=U", check=False)
-    if result.returncode == 0:
-        return result.stdout.strip().split('\n') if result.stdout.strip() else []
-    return []
-
-
-def resolve_lean_toolchain_conflict(tag):
-    """Resolve lean-toolchain conflict by accepting incoming (tag) changes."""
-    print("Resolving lean-toolchain conflict by accepting incoming changes...")
-    # Accept theirs (incoming) version for lean-toolchain
-    result = run_command(f"git checkout --theirs lean-toolchain", check=False)
-    if result.returncode != 0:
-        print("Failed to resolve lean-toolchain conflict")
-        return False
-
-    # Add the resolved file
-    add_result = run_command("git add lean-toolchain", check=False)
-    if add_result.returncode != 0:
-        print("Failed to stage resolved lean-toolchain")
-        return False
-
-    return True
-
-
 def check_and_merge(repo, branch, tag, temp_dir):
     """Check if tag can be merged into branch and perform the merge if possible."""
     # Change to the temporary directory
@@ -125,37 +98,12 @@ def check_and_merge(repo, branch, tag, temp_dir):
     # Try merging the tag directly
     print(f"Merging {tag} into {branch}...")
     merge_result = run_command(f"git merge {tag} --no-edit", check=False)
-
+    
     if merge_result.returncode != 0:
-        # Check which files have conflicts
-        conflicted_files = get_conflicted_files()
-
-        if conflicted_files == ['lean-toolchain']:
-            # Only lean-toolchain has conflicts, resolve it
-            print("Merge conflict detected only in lean-toolchain.")
-            if resolve_lean_toolchain_conflict(tag):
-                # Continue the merge with the resolved conflict
-                print("Continuing merge with resolved lean-toolchain...")
-                continue_result = run_command(f"git commit --no-edit", check=False)
-                if continue_result.returncode != 0:
-                    print("Failed to complete merge after resolving lean-toolchain")
-                    run_command("git merge --abort")
-                    return False
-            else:
-                print("Failed to resolve lean-toolchain conflict")
-                run_command("git merge --abort")
-                return False
-        else:
-            # Other files have conflicts, or unable to determine
-            if conflicted_files:
-                print(f"Cannot merge {tag} cleanly into {branch}.")
-                print(f"Merge conflicts in: {', '.join(conflicted_files)}")
-            else:
-                print(f"Cannot merge {tag} cleanly into {branch}.")
-                print("Merge conflicts would occur.")
-            print("Aborting merge.")
-            run_command("git merge --abort")
-            return False
+        print(f"Cannot merge {tag} cleanly into {branch}.")
+        print("Merge conflicts would occur. Aborting merge.")
+        run_command("git merge --abort")
+        return False
     
     print(f"Pushing changes to remote...")
     push_result = run_command(f"git push origin {branch}")

script/release_notes.py

@@ -52,7 +52,6 @@ def sort_sections_order():
     return [
         "Language",
         "Library",
-        "Tactics",
         "Compiler",
         "Pretty Printing",
         "Documentation",

script/release_repos.yml

@@ -1,11 +1,4 @@
 repositories:
-  - name: lean4-cli
-    url: https://github.com/leanprover/lean4-cli
-    toolchain-tag: true
-    stable-branch: false
-    branch: main
-    dependencies: []
-
   - name: batteries
     url: https://github.com/leanprover-community/batteries
     toolchain-tag: true
@@ -14,13 +7,6 @@ repositories:
     bump-branch: true
     dependencies: []
 
-  - name: verso
-    url: https://github.com/leanprover/verso
-    toolchain-tag: true
-    stable-branch: false
-    branch: main
-    dependencies: []
-
   - name: lean4checker
     url: https://github.com/leanprover/lean4checker
     toolchain-tag: true
@@ -35,6 +21,20 @@ repositories:
     branch: master
     dependencies: []
 
+  - name: lean4-cli
+    url: https://github.com/leanprover/lean4-cli
+    toolchain-tag: true
+    stable-branch: false
+    branch: main
+    dependencies: []
+
+  - name: verso
+    url: https://github.com/leanprover/verso
+    toolchain-tag: true
+    stable-branch: false
+    branch: main
+    dependencies: []
+
   - name: plausible
     url: https://github.com/leanprover-community/plausible
     toolchain-tag: true
@@ -96,15 +96,6 @@ repositories:
       - import-graph
       - plausible
 
-  - name: cslib
-    url: https://github.com/leanprover/cslib
-    toolchain-tag: true
-    stable-branch: true
-    branch: main
-    bump-branch: true
-    dependencies:
-      - mathlib4
-
   - name: repl
     url: https://github.com/leanprover-community/repl
     toolchain-tag: true
@@ -112,11 +103,3 @@ repositories:
     branch: master
     dependencies:
       - mathlib4
-
-  - name: lean-fro.org
-    url: https://github.com/leanprover/lean-fro.org
-    toolchain-tag: false
-    stable-branch: false
-    branch: master
-    dependencies:
-      - verso

script/release_steps.py

@@ -377,33 +377,6 @@ def execute_release_steps(repo, version, config):
         except subprocess.CalledProcessError as e:
             print(red("Tests failed, but continuing with PR creation..."))
             print(red(f"Test error: {e}"))
-    elif repo_name == "lean-fro.org":
-        # Update lean-toolchain in examples/hero
-        print(blue("Updating examples/hero/lean-toolchain..."))
-        docs_toolchain = repo_path / "examples" / "hero" / "lean-toolchain"
-        with open(docs_toolchain, "w") as f:
-            f.write(f"leanprover/lean4:{version}\n")
-        print(green(f"Updated examples/hero/lean-toolchain to leanprover/lean4:{version}"))
-
-        print(blue("Running `lake update`..."))
-        run_command("lake update", cwd=repo_path, stream_output=True)
-        print(blue("Running `lake update` in examples/hero..."))
-        run_command("lake update", cwd=repo_path / "examples" / "hero", stream_output=True)
-    elif repo_name == "cslib":
-        print(blue("Updating lakefile.toml..."))
-        run_command(f'perl -pi -e \'s/"v4\\.[0-9]+(\\.[0-9]+)?(-rc[0-9]+)?"/"' + version + '"/g\' lakefile.*', cwd=repo_path)
-        
-        print(blue("Updating docs/lakefile.toml..."))
-        run_command(f'perl -pi -e \'s/"v4\\.[0-9]+(\\.[0-9]+)?(-rc[0-9]+)?"/"' + version + '"/g\' lakefile.*', cwd=repo_path / "docs")
-
-        # Update lean-toolchain in docs
-        print(blue("Updating docs/lean-toolchain..."))
-        docs_toolchain = repo_path / "docs" / "lean-toolchain"
-        with open(docs_toolchain, "w") as f:
-            f.write(f"leanprover/lean4:{version}\n")
-        print(green(f"Updated docs/lean-toolchain to leanprover/lean4:{version}"))
-
-        run_command("lake update", cwd=repo_path, stream_output=True)
     elif dependencies:
         run_command(f'perl -pi -e \'s/"v4\\.[0-9]+(\\.[0-9]+)?(-rc[0-9]+)?"/"' + version + '"/g\' lakefile.*', cwd=repo_path)
         run_command("lake update", cwd=repo_path, stream_output=True)

src/CMakeLists.txt

@@ -10,7 +10,7 @@ endif()
 include(ExternalProject)
 project(LEAN CXX C)
 set(LEAN_VERSION_MAJOR 4)
-set(LEAN_VERSION_MINOR 25)
+set(LEAN_VERSION_MINOR 24)
 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'")
@@ -469,7 +469,6 @@ elseif(${CMAKE_SYSTEM_NAME} MATCHES "Darwin")
   string(APPEND CMAKE_CXX_FLAGS " -ftls-model=initial-exec")
   string(APPEND INIT_SHARED_LINKER_FLAGS " -install_name @rpath/libInit_shared.dylib")
   string(APPEND LEANSHARED_1_LINKER_FLAGS " -install_name @rpath/libleanshared_1.dylib")
-  string(APPEND LEANSHARED_2_LINKER_FLAGS " -install_name @rpath/libleanshared_2.dylib")
   string(APPEND LEANSHARED_LINKER_FLAGS " -install_name @rpath/libleanshared.dylib")
   string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libLake.a.export -install_name @rpath/libLake_shared.dylib")
   string(APPEND CMAKE_EXE_LINKER_FLAGS " -Wl,-rpath,@executable_path/../lib -Wl,-rpath,@executable_path/../lib/lean")
@@ -503,7 +502,7 @@ endif()
 # are already loaded) and probably fail unless we set up LD_LIBRARY_PATH.
 if(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
   # import libraries created by the stdlib.make targets
-  string(APPEND LEANC_SHARED_LINKER_FLAGS " -lInit_shared -lleanshared_2 -lleanshared_1 -lleanshared")
+  string(APPEND LEANC_SHARED_LINKER_FLAGS " -lInit_shared -lleanshared_1 -lleanshared")
 elseif("${CMAKE_SYSTEM_NAME}" MATCHES "Darwin")
   # The second flag is necessary to even *load* dylibs without resolved symbols, as can happen
   # if a Lake `extern_lib` depends on a symbols defined by the Lean library but is loaded even
@@ -590,7 +589,7 @@ endif()
 
 add_subdirectory(initialize)
 add_subdirectory(shell)
-# to be included in `leanshared` but not the smaller `leanshared_*` (as it would pull
+# to be included in `leanshared` but not the smaller `leanshared_1` (as it would pull
 # in the world)
 add_library(leaninitialize STATIC $<TARGET_OBJECTS:initialize>)
 set_target_properties(leaninitialize PROPERTIES
@@ -715,7 +714,6 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
   )
   add_custom_target(leanshared ALL
     DEPENDS Init_shared leancpp
-    COMMAND touch ${CMAKE_LIBRARY_OUTPUT_DIRECTORY}/libleanshared_2${CMAKE_SHARED_LIBRARY_SUFFIX}
     COMMAND touch ${CMAKE_LIBRARY_OUTPUT_DIRECTORY}/libleanshared_1${CMAKE_SHARED_LIBRARY_SUFFIX}
     COMMAND touch ${CMAKE_LIBRARY_OUTPUT_DIRECTORY}/libleanshared${CMAKE_SHARED_LIBRARY_SUFFIX}
   )
@@ -736,7 +734,7 @@ else()
     COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make leanshared
     VERBATIM)
 
-  string(APPEND CMAKE_EXE_LINKER_FLAGS " -lInit_shared -lleanshared_2 -lleanshared_1 -lleanshared")
+  string(APPEND CMAKE_EXE_LINKER_FLAGS " -lInit_shared -lleanshared_1 -lleanshared")
 endif()
 
 if(NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")

src/Init.lean

@@ -42,8 +42,5 @@ public import Init.While
 public import Init.Syntax
 public import Init.Internal
 public import Init.Try
-public meta import Init.Try  -- make sure `Try.Config` can be evaluated anywhere
 public import Init.BinderNameHint
 public import Init.Task
-public import Init.MethodSpecsSimp
-public import Init.LawfulBEqTactics

src/Init/Control/EState.lean

@@ -19,8 +19,8 @@ variable {ε σ α : Type u}
 
 instance [ToString ε] [ToString α] : ToString (Result ε σ α) where
   toString
-    | Result.ok a _    => String.Internal.append "ok: " (toString a)
-    | Result.error e _ => String.Internal.append "error: " (toString e)
+    | Result.ok a _    => "ok: " ++ toString a
+    | Result.error e _ => "error: " ++ toString e
 
 instance [Repr ε] [Repr α] : Repr (Result ε σ α) where
   reprPrec

src/Init/Control/Lawful/Basic.lean

@@ -147,7 +147,7 @@ class LawfulMonad (m : Type u → Type v) [Monad m] : Prop extends LawfulApplica
 
 export LawfulMonad (bind_pure_comp bind_map pure_bind bind_assoc)
 attribute [simp] pure_bind bind_assoc bind_pure_comp
-attribute [grind <=] pure_bind
+attribute [grind] pure_bind
 
 @[simp] theorem bind_pure [Monad m] [LawfulMonad m] (x : m α) : x >>= pure = x := by
   change x >>= (fun a => pure (id a)) = x

src/Init/Control/Lawful/Instances.lean

@@ -22,24 +22,23 @@ open Function
 
 namespace ExceptT
 
-@[ext, grind ext] theorem ext {x y : ExceptT ε m α} (h : x.run = y.run) : x = y := by
+@[ext] theorem ext {x y : ExceptT ε m α} (h : x.run = y.run) : x = y := by
   simp [run] at h
   assumption
 
-@[simp, grind =] theorem run_pure [Monad m] (x : α) : run (pure x : ExceptT ε m α) = pure (Except.ok x) := rfl
+@[simp] theorem run_pure [Monad m] (x : α) : run (pure x : ExceptT ε m α) = pure (Except.ok x) := rfl
 
-@[simp, grind =] theorem run_lift  [Monad.{u, v} m] (x : m α) : run (ExceptT.lift x : ExceptT ε m α) = (Except.ok <$> x : m (Except ε α)) := rfl
+@[simp] theorem run_lift  [Monad.{u, v} m] (x : m α) : run (ExceptT.lift x : ExceptT ε m α) = (Except.ok <$> x : m (Except ε α)) := rfl
 
-@[simp, grind =] theorem run_throw [Monad m] : run (throw e : ExceptT ε m β) = pure (Except.error e) := rfl
+@[simp] theorem run_throw [Monad m] : run (throw e : ExceptT ε m β) = pure (Except.error e) := rfl
 
-@[simp, grind =] theorem run_bind_lift [Monad m] [LawfulMonad m] (x : m α) (f : α → ExceptT ε m β) : run (ExceptT.lift x >>= f : ExceptT ε m β) = x >>= fun a => run (f a) := by
+@[simp] theorem run_bind_lift [Monad m] [LawfulMonad m] (x : m α) (f : α → ExceptT ε m β) : run (ExceptT.lift x >>= f : ExceptT ε m β) = x >>= fun a => run (f a) := by
   simp [ExceptT.run, ExceptT.lift, bind, ExceptT.bind, ExceptT.mk, ExceptT.bindCont]
 
-@[simp, grind =] theorem bind_throw [Monad m] [LawfulMonad m] (f : α → ExceptT ε m β) : (throw e >>= f) = throw e := by
+@[simp] theorem bind_throw [Monad m] [LawfulMonad m] (f : α → ExceptT ε m β) : (throw e >>= f) = throw e := by
   simp [throw, throwThe, MonadExceptOf.throw, bind, ExceptT.bind, ExceptT.bindCont, ExceptT.mk]
 
-@[grind =]
-theorem run_bind [Monad m] (x : ExceptT ε m α) (f : α → ExceptT ε m β)
+theorem run_bind [Monad m] (x : ExceptT ε m α)
         : run (x >>= f : ExceptT ε m β)
           =
           run x >>= fun
@@ -47,10 +46,10 @@ theorem run_bind [Monad m] (x : ExceptT ε m α) (f : α → ExceptT ε m β)
                      | Except.error e => pure (Except.error e) :=
   rfl
 
-@[simp, grind =] theorem lift_pure [Monad m] [LawfulMonad m] (a : α) : ExceptT.lift (pure a) = (pure a : ExceptT ε m α) := by
+@[simp] theorem lift_pure [Monad m] [LawfulMonad m] (a : α) : ExceptT.lift (pure a) = (pure a : ExceptT ε m α) := by
   simp [ExceptT.lift, pure, ExceptT.pure]
 
-@[simp, grind =] theorem run_map [Monad m] [LawfulMonad m] (f : α → β) (x : ExceptT ε m α)
+@[simp] theorem run_map [Monad m] [LawfulMonad m] (f : α → β) (x : ExceptT ε m α)
     : (f <$> x).run = Except.map f <$> x.run := by
   simp [Functor.map, ExceptT.map, ←bind_pure_comp]
   apply bind_congr
@@ -114,28 +113,28 @@ instance : LawfulFunctor (Except ε) := inferInstance
 
 namespace ReaderT
 
-@[ext, grind ext] theorem ext {x y : ReaderT ρ m α} (h : ∀ ctx, x.run ctx = y.run ctx) : x = y := by
+@[ext] theorem ext {x y : ReaderT ρ m α} (h : ∀ ctx, x.run ctx = y.run ctx) : x = y := by
   simp [run] at h
   exact funext h
 
-@[simp, grind =] theorem run_pure [Monad m] (a : α) (ctx : ρ) : (pure a : ReaderT ρ m α).run ctx = pure a := rfl
+@[simp] theorem run_pure [Monad m] (a : α) (ctx : ρ) : (pure a : ReaderT ρ m α).run ctx = pure a := rfl
 
-@[simp, grind =] theorem run_bind [Monad m] (x : ReaderT ρ m α) (f : α → ReaderT ρ m β) (ctx : ρ)
+@[simp] theorem run_bind [Monad m] (x : ReaderT ρ m α) (f : α → ReaderT ρ m β) (ctx : ρ)
     : (x >>= f).run ctx = x.run ctx >>= λ a => (f a).run ctx := rfl
 
-@[simp, grind =] theorem run_mapConst [Monad m] (a : α) (x : ReaderT ρ m β) (ctx : ρ)
+@[simp] theorem run_mapConst [Monad m] (a : α) (x : ReaderT ρ m β) (ctx : ρ)
     : (Functor.mapConst a x).run ctx = Functor.mapConst a (x.run ctx) := rfl
 
-@[simp, grind =] theorem run_map [Monad m] (f : α → β) (x : ReaderT ρ m α) (ctx : ρ)
+@[simp] theorem run_map [Monad m] (f : α → β) (x : ReaderT ρ m α) (ctx : ρ)
     : (f <$> x).run ctx = f <$> x.run ctx := rfl
 
-@[simp, grind =] theorem run_monadLift [MonadLiftT n m] (x : n α) (ctx : ρ)
+@[simp] theorem run_monadLift [MonadLiftT n m] (x : n α) (ctx : ρ)
     : (monadLift x : ReaderT ρ m α).run ctx = (monadLift x : m α) := rfl
 
-@[simp, grind =] theorem run_monadMap [MonadFunctorT n m] (f : {β : Type u} → n β → n β) (x : ReaderT ρ m α) (ctx : ρ)
+@[simp] theorem run_monadMap [MonadFunctorT n m] (f : {β : Type u} → n β → n β) (x : ReaderT ρ m α) (ctx : ρ)
     : (monadMap @f x : ReaderT ρ m α).run ctx = monadMap @f (x.run ctx) := rfl
 
-@[simp, grind =] theorem run_read [Monad m] (ctx : ρ) : (ReaderT.read : ReaderT ρ m ρ).run ctx = pure ctx := rfl
+@[simp] theorem run_read [Monad m] (ctx : ρ) : (ReaderT.read : ReaderT ρ m ρ).run ctx = pure ctx := rfl
 
 @[simp] theorem run_seq {α β : Type u} [Monad m] (f : ReaderT ρ m (α → β)) (x : ReaderT ρ m α) (ctx : ρ)
     : (f <*> x).run ctx = (f.run ctx <*> x.run ctx) := rfl
@@ -176,39 +175,38 @@ instance [Monad m] [LawfulMonad m] : LawfulMonad (StateRefT' ω σ m) :=
 
 namespace StateT
 
-@[ext, grind ext] theorem ext {x y : StateT σ m α} (h : ∀ s, x.run s = y.run s) : x = y :=
+@[ext] theorem ext {x y : StateT σ m α} (h : ∀ s, x.run s = y.run s) : x = y :=
   funext h
 
-@[simp, grind =] theorem run'_eq [Monad m] (x : StateT σ m α) (s : σ) : run' x s = (·.1) <$> run x s :=
+@[simp] theorem run'_eq [Monad m] (x : StateT σ m α) (s : σ) : run' x s = (·.1) <$> run x s :=
   rfl
 
-@[simp, grind =] theorem run_pure [Monad m] (a : α) (s : σ) : (pure a : StateT σ m α).run s = pure (a, s) := rfl
+@[simp] theorem run_pure [Monad m] (a : α) (s : σ) : (pure a : StateT σ m α).run s = pure (a, s) := rfl
 
-@[simp, grind =] theorem run_bind [Monad m] (x : StateT σ m α) (f : α → StateT σ m β) (s : σ)
+@[simp] theorem run_bind [Monad m] (x : StateT σ m α) (f : α → StateT σ m β) (s : σ)
     : (x >>= f).run s = x.run s >>= λ p => (f p.1).run p.2 := by
   simp [bind, StateT.bind, run]
 
-@[simp, grind =] theorem run_map {α β σ : Type u} [Monad m] [LawfulMonad m] (f : α → β) (x : StateT σ m α) (s : σ) : (f <$> x).run s = (fun (p : α × σ) => (f p.1, p.2)) <$> x.run s := by
+@[simp] theorem run_map {α β σ : Type u} [Monad m] [LawfulMonad m] (f : α → β) (x : StateT σ m α) (s : σ) : (f <$> x).run s = (fun (p : α × σ) => (f p.1, p.2)) <$> x.run s := by
   simp [Functor.map, StateT.map, run, ←bind_pure_comp]
 
-@[simp, grind =] theorem run_get [Monad m] (s : σ)    : (get : StateT σ m σ).run s = pure (s, s) := rfl
+@[simp] theorem run_get [Monad m] (s : σ)    : (get : StateT σ m σ).run s = pure (s, s) := rfl
 
-@[simp, grind =] theorem run_set [Monad m] (s s' : σ) : (set s' : StateT σ m PUnit).run s = pure (⟨⟩, s') := rfl
+@[simp] theorem run_set [Monad m] (s s' : σ) : (set s' : StateT σ m PUnit).run s = pure (⟨⟩, s') := rfl
 
-@[simp, grind =] theorem run_modify [Monad m] (f : σ → σ) (s : σ) : (modify f : StateT σ m PUnit).run s = pure (⟨⟩, f s) := rfl
+@[simp] theorem run_modify [Monad m] (f : σ → σ) (s : σ) : (modify f : StateT σ m PUnit).run s = pure (⟨⟩, f s) := rfl
 
-@[simp, grind =] theorem run_modifyGet [Monad m] (f : σ → α × σ) (s : σ) : (modifyGet f : StateT σ m α).run s = pure ((f s).1, (f s).2) := by
+@[simp] theorem run_modifyGet [Monad m] (f : σ → α × σ) (s : σ) : (modifyGet f : StateT σ m α).run s = pure ((f s).1, (f s).2) := by
   simp [modifyGet, MonadStateOf.modifyGet, StateT.modifyGet, run]
 
-@[simp, grind =] theorem run_lift {α σ : Type u} [Monad m] (x : m α) (s : σ) : (StateT.lift x : StateT σ m α).run s = x >>= fun a => pure (a, s) := rfl
+@[simp] theorem run_lift {α σ : Type u} [Monad m] (x : m α) (s : σ) : (StateT.lift x : StateT σ m α).run s = x >>= fun a => pure (a, s) := rfl
 
-@[grind =]
 theorem run_bind_lift {α σ : Type u} [Monad m] [LawfulMonad m] (x : m α) (f : α → StateT σ m β) (s : σ) : (StateT.lift x >>= f).run s = x >>= fun a => (f a).run s := by
   simp [StateT.lift, StateT.run, bind, StateT.bind]
 
-@[simp, grind =] theorem run_monadLift {α σ : Type u} [Monad m] [MonadLiftT n m] (x : n α) (s : σ) : (monadLift x : StateT σ m α).run s = (monadLift x : m α) >>= fun a => pure (a, s) := rfl
+@[simp] theorem run_monadLift {α σ : Type u} [Monad m] [MonadLiftT n m] (x : n α) (s : σ) : (monadLift x : StateT σ m α).run s = (monadLift x : m α) >>= fun a => pure (a, s) := rfl
 
-@[simp, grind =] theorem run_monadMap [MonadFunctorT n m] (f : {β : Type u} → n β → n β) (x : StateT σ m α) (s : σ) :
+@[simp] theorem run_monadMap [MonadFunctorT n m] (f : {β : Type u} → n β → n β) (x : StateT σ m α) (s : σ) :
     (monadMap @f x : StateT σ m α).run s = monadMap @f (x.run s) := rfl
 
 @[simp] theorem run_seq {α β σ : Type u} [Monad m] [LawfulMonad m] (f : StateT σ m (α → β)) (x : StateT σ m α) (s : σ) : (f <*> x).run s = (f.run s >>= fun fs => (fun (p : α × σ) => (fs.1 p.1, p.2)) <$> x.run fs.2) := by

src/Init/Core.lean

@@ -101,6 +101,7 @@ instance : DecidableEq Empty := fun a => a.elim
 /-- Decidable equality for PEmpty -/
 instance : DecidableEq PEmpty := fun a => a.elim
 
+set_option genInjectivity false in
 /--
 Delays evaluation. The delayed code is evaluated at most once.
 
@@ -616,6 +617,7 @@ class Sep (α : outParam <| Type u) (γ : Type v) where
   /-- Computes `{ a ∈ c | p a }`. -/
   sep : (α → Prop) → γ → γ
 
+set_option genInjectivity false in
 /--
 `Task α` is a primitive for asynchronous computation.
 It represents a computation that will resolve to a value of type `α`,
@@ -1580,7 +1582,6 @@ instance {p q : Prop} [d : Decidable (p ↔ q)] : Decidable (p = q) :=
 
 gen_injective_theorems% Array
 gen_injective_theorems% BitVec
-gen_injective_theorems% ByteArray
 gen_injective_theorems% Char
 gen_injective_theorems% DoResultBC
 gen_injective_theorems% DoResultPR
@@ -2547,3 +2548,7 @@ class Irrefl (r : α → α → Prop) : Prop where
   irrefl : ∀ a, ¬r a a
 
 end Std
+
+/-- Deprecated alias for `XorOp`. -/
+@[deprecated XorOp (since := "2025-07-30")]
+abbrev Xor := XorOp

src/Init/Data/Array/Attach.lean

@@ -121,7 +121,7 @@ theorem pmap_eq_map {p : α → Prop} {f : α → β} {xs : Array α} (H) :
 theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a, q a → β} (xs : Array α) {H₁ H₂}
     (h : ∀ a ∈ xs, ∀ (h₁ h₂), f a h₁ = g a h₂) : pmap f xs H₁ = pmap g xs H₂ := by
   cases xs
-  simp only [List.mem_toArray] at h
+  simp only [mem_toArray] at h
   simp only [List.pmap_toArray, mk.injEq]
   rw [List.pmap_congr_left _ h]
 
@@ -194,14 +194,14 @@ theorem attachWith_map_subtype_val {p : α → Prop} {xs : Array α} (H : ∀ a
     (xs.attachWith p H).map Subtype.val = xs := by
   cases xs; simp
 
-@[simp, grind ←]
+@[simp, grind]
 theorem mem_attach (xs : Array α) : ∀ x, x ∈ xs.attach
   | ⟨a, h⟩ => by
     have := mem_map.1 (by rw [attach_map_subtype_val] <;> exact h)
     rcases this with ⟨⟨_, _⟩, m, rfl⟩
     exact m
 
-@[simp, grind =]
+@[simp, grind]
 theorem mem_attachWith {xs : Array α} {q : α → Prop} (H) (x : {x // q x}) :
     x ∈ xs.attachWith q H ↔ x.1 ∈ xs := by
   cases xs
@@ -212,13 +212,12 @@ theorem mem_pmap {p : α → Prop} {f : ∀ a, p a → β} {xs H b} :
     b ∈ pmap f xs H ↔ ∃ (a : _) (h : a ∈ xs), f a (H a h) = b := by
   simp only [pmap_eq_map_attach, mem_map, mem_attach, true_and, Subtype.exists, eq_comm]
 
+@[grind]
 theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {xs H} {a} (h : a ∈ xs) :
     f a (H a h) ∈ pmap f xs H := by
   rw [mem_pmap]
   exact ⟨a, h, rfl⟩
 
-grind_pattern mem_pmap_of_mem => _ ∈ pmap f xs H, a ∈ xs
-
 @[simp, grind =]
 theorem size_pmap {p : α → Prop} {f : ∀ a, p a → β} {xs H} : (pmap f xs H).size = xs.size := by
   cases xs; simp
@@ -346,7 +345,7 @@ theorem foldl_attach {xs : Array α} {f : β → α → β} {b : β} :
     xs.attach.foldl (fun acc t => f acc t.1) b = xs.foldl f b := by
   rcases xs with ⟨xs⟩
   simp only [List.attach_toArray, List.attachWith_mem_toArray, List.size_toArray,
-    List.foldl_toArray', List.mem_toArray, List.foldl_subtype]
+    List.foldl_toArray', mem_toArray, List.foldl_subtype]
   congr
   ext
   simpa using fun a => List.mem_of_getElem? a
@@ -365,7 +364,7 @@ theorem foldr_attach {xs : Array α} {f : α → β → β} {b : β} :
     xs.attach.foldr (fun t acc => f t.1 acc) b = xs.foldr f b := by
   rcases xs with ⟨xs⟩
   simp only [List.attach_toArray, List.attachWith_mem_toArray, List.size_toArray,
-    List.foldr_toArray', List.mem_toArray, List.foldr_subtype]
+    List.foldr_toArray', mem_toArray, List.foldr_subtype]
   congr
   ext
   simpa using fun a => List.mem_of_getElem? a
@@ -707,7 +706,7 @@ and simplifies these to the function directly taking the value.
     {f : { x // p x } → Array β} {g : α → Array β} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
     (xs.flatMap f) = xs.unattach.flatMap g := by
   cases xs
-  simp only [List.flatMap_toArray, List.unattach_toArray,
+  simp only [List.flatMap_toArray, List.unattach_toArray, 
     mk.injEq]
   rw [List.flatMap_subtype]
   simp [hf]

src/Init/Data/Array/Basic.lean

@@ -10,6 +10,8 @@ public import Init.WFTactics
 public import Init.Data.Nat.Basic
 public import Init.Data.Fin.Basic
 public import Init.Data.UInt.BasicAux
+public import Init.Data.Repr
+public import Init.Data.ToString.Basic
 public import Init.GetElem
 public import Init.Data.List.ToArrayImpl
 import all Init.Data.List.ToArrayImpl
@@ -40,11 +42,11 @@ namespace Array
 
 /-! ### Preliminary theorems -/
 
-@[simp, grind =] theorem size_set {xs : Array α} {i : Nat} {v : α} (h : i < xs.size) :
+@[simp, grind] theorem size_set {xs : Array α} {i : Nat} {v : α} (h : i < xs.size) :
     (set xs i v h).size = xs.size :=
   List.length_set ..
 
-@[simp, grind =] theorem size_push {xs : Array α} (v : α) : (push xs v).size = xs.size + 1 :=
+@[simp, grind] theorem size_push {xs : Array α} (v : α) : (push xs v).size = xs.size + 1 :=
   List.length_concat ..
 
 theorem ext {xs ys : Array α}
@@ -108,19 +110,13 @@ instance : Membership α (Array α) where
 theorem mem_def {a : α} {as : Array α} : a ∈ as ↔ a ∈ as.toList :=
   ⟨fun | .mk h => h, Array.Mem.mk⟩
 
-@[simp, grind =] theorem _root_.List.mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l := by
+@[simp, grind =] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l := by
   simp [mem_def]
 
-@[deprecated List.mem_toArray (since := "2025-09-04")]
-theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l :=
-  List.mem_toArray
-
-@[simp] theorem getElem_mem {xs : Array α} {i : Nat} (h : i < xs.size) : xs[i] ∈ xs := by
+@[simp, grind] theorem getElem_mem {xs : Array α} {i : Nat} (h : i < xs.size) : xs[i] ∈ xs := by
   rw [Array.mem_def, ← getElem_toList]
   apply List.getElem_mem
 
-grind_pattern getElem_mem => xs[i] ∈ xs
-
 @[simp, grind =] theorem emptyWithCapacity_eq {α n} : @emptyWithCapacity α n = #[] := rfl
 
 @[simp] theorem mkEmpty_eq {α n} : @mkEmpty α n = #[] := rfl
@@ -138,7 +134,7 @@ theorem toList_toArray {as : List α} : as.toArray.toList = as := rfl
 @[deprecated toList_toArray (since := "2025-02-17")]
 abbrev _root_.Array.toList_toArray := @List.toList_toArray
 
-@[simp, grind =] theorem size_toArray {as : List α} : as.toArray.size = as.length := by simp [Array.size]
+@[simp, grind] theorem size_toArray {as : List α} : as.toArray.size = as.length := by simp [Array.size]
 
 @[deprecated size_toArray (since := "2025-02-17")]
 abbrev _root_.Array.size_toArray := @List.size_toArray
@@ -168,7 +164,7 @@ This is a low-level version of `Array.size` that directly queries the runtime sy
 representation of arrays. While this is not provable, `Array.usize` always returns the exact size of
 the array since the implementation only supports arrays of size less than `USize.size`.
 -/
-@[extern "lean_array_size", simp, expose]
+@[extern "lean_array_size", simp]
 def usize (xs : @& Array α) : USize := xs.size.toUSize
 
 /--
@@ -203,7 +199,7 @@ Examples:
 def pop (xs : Array α) : Array α where
   toList := xs.toList.dropLast
 
-@[simp, grind =] theorem size_pop {xs : Array α} : xs.pop.size = xs.size - 1 := by
+@[simp, grind] theorem size_pop {xs : Array α} : xs.pop.size = xs.size - 1 := by
   match xs with
   | ⟨[]⟩ => rfl
   | ⟨a::as⟩ => simp [pop, Nat.succ_sub_succ_eq_sub, size]
@@ -447,7 +443,7 @@ def swapAt! (xs : Array α) (i : Nat) (v : α) : α × Array α :=
     swapAt xs i v
   else
     have : Inhabited (α × Array α) := ⟨(v, xs)⟩
-    panic! String.Internal.append (String.Internal.append "index " (toString i)) " out of bounds"
+    panic! ("index " ++ toString i ++ " out of bounds")
 
 /--
 Returns the first `n` elements of an array. The resulting array is produced by repeatedly calling
@@ -2173,7 +2169,7 @@ instance {α : Type u} [Repr α] : Repr (Array α) where
   reprPrec xs _ := Array.repr xs
 
 instance [ToString α] : ToString (Array α) where
-  toString xs := String.Internal.append "#" (toString xs.toList)
+  toString xs := "#" ++ toString xs.toList
 
 end Array
 

src/Init/Data/Array/Erase.lean

@@ -91,7 +91,7 @@ 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, grind =] 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
 
@@ -240,7 +240,7 @@ theorem mem_of_mem_erase {a b : α} {xs : Array α} (h : a ∈ xs.erase b) : a
   rcases xs with ⟨xs⟩
   simpa using List.mem_of_mem_erase (by simpa using h)
 
-@[simp, grind =] 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)
 
@@ -271,7 +271,7 @@ theorem erase_append [LawfulBEq α] {a : α} {xs ys : Array α} :
     (xs ++ ys).erase a = if a ∈ xs then xs.erase a ++ ys else xs ++ ys.erase a := by
   rcases xs with ⟨xs⟩
   rcases ys with ⟨ys⟩
-  simp only [List.append_toArray, List.erase_toArray, List.erase_append, List.mem_toArray]
+  simp only [List.append_toArray, List.erase_toArray, List.erase_append, mem_toArray]
   split <;> simp
 
 @[grind =]

src/Init/Data/Array/Find.lean

@@ -27,11 +27,11 @@ open Nat
 
 /-! ### findSome? -/
 
-@[simp, grind =] theorem findSome?_empty : (#[] : Array α).findSome? f = none := rfl
-@[simp, grind =] theorem findSome?_push {xs : Array α} : (xs.push a).findSome? f = (xs.findSome? f).or (f a) := by
+@[simp, grind] theorem findSome?_empty : (#[] : Array α).findSome? f = none := rfl
+@[simp, grind] theorem findSome?_push {xs : Array α} : (xs.push a).findSome? f = (xs.findSome? f).or (f a) := by
   cases xs; simp [List.findSome?_append]
 
-@[grind =]
+@[grind]
 theorem findSome?_singleton {a : α} {f : α → Option β} : #[a].findSome? f = f a := by
   simp
 
@@ -228,12 +228,11 @@ theorem mem_of_find?_eq_some {xs : Array α} (h : find? p xs = some a) : a ∈ x
   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]
 
-grind_pattern get_find?_mem => (xs.find? p).get h
-
 @[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
@@ -396,6 +395,7 @@ 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)
@@ -728,7 +728,7 @@ 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 only [Option.map_map, Function.comp_def, Fin.cast_cast]
+  simp only [Option.map_map, Function.comp_def, Fin.cast_trans]
   simp [Array.size]
 
 /-! ### idxOf

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

@@ -70,8 +70,8 @@ private theorem cons_lex_cons [BEq α] {lt : α → α → Bool} {a b : α} {xs
     rw [cons_lex_cons.forIn'_congr_aux Std.PRange.toList_eq_match rfl (fun _ _ _ => rfl)]
     simp only [Std.PRange.SupportsUpperBound.IsSatisfied, bind_pure_comp, map_pure]
     rw [cons_lex_cons.forIn'_congr_aux (if_pos (by omega)) rfl (fun _ _ _ => rfl)]
-  simp only [Std.PRange.toList_Rox_eq_toList_Rcx_of_isSome_succ? (lo := 0) (h := rfl),
-    Std.PRange.UpwardEnumerable.succ?, Nat.add_comm 1, Std.PRange.Nat.toList_Rco_succ_succ,
+  simp only [Std.PRange.toList_open_eq_toList_closed_of_isSome_succ? (lo := 0) (h := rfl),
+    Std.PRange.UpwardEnumerable.succ?, Nat.add_comm 1, Std.PRange.Nat.ClosedOpen.toList_succ_succ,
     Option.get_some, List.forIn'_cons, List.size_toArray, List.length_cons, List.length_nil,
     Nat.lt_add_one, getElem_append_left, List.getElem_toArray, List.getElem_cons_zero]
   cases lt a b

src/Init/Data/Array/Monadic.lean

@@ -167,7 +167,7 @@ theorem foldrM_filter [Monad m] [LawfulMonad m] {p : α → Bool} {g : α → β
     (h : ∀ a m b, f a (by simpa [w] using m) b = g a m b) :
     forIn' as b f = forIn' bs b' g := by
   cases as <;> cases bs
-  simp only [mk.injEq, List.mem_toArray, List.forIn'_toArray] at w h ⊢
+  simp only [mk.injEq, mem_toArray, List.forIn'_toArray] at w h ⊢
   exact List.forIn'_congr w hb h
 
 /--

src/Init/Data/Array/Range.lean

@@ -116,7 +116,7 @@ theorem range'_eq_append_iff : range' s n = xs ++ ys ↔ ∃ k, k ≤ n ∧ xs =
 @[simp] theorem find?_range'_eq_some {s n : Nat} {i : Nat} {p : Nat → Bool} :
     (range' s n).find? p = some i ↔ p i ∧ i ∈ range' s n ∧ ∀ j, s ≤ j → j < i → !p j := by
   rw [← List.toArray_range']
-  simp only [List.find?_toArray, List.mem_toArray]
+  simp only [List.find?_toArray, mem_toArray]
   simp [List.find?_range'_eq_some]
 
 @[simp] theorem find?_range'_eq_none {s n : Nat} {p : Nat → Bool} :

src/Init/Data/Array/Zip.lean

@@ -231,9 +231,11 @@ theorem zip_map {f : α → γ} {g : β → δ} {as : Array α} {bs : Array β}
   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]
 

src/Init/Data/BitVec/Basic.lean

@@ -206,13 +206,10 @@ Converts a bitvector into a fixed-width hexadecimal number with enough digits to
 
 If `n` is `0`, then one digit is returned. Otherwise, `⌊(n + 3) / 4⌋` digits are returned.
 -/
--- If we ever want to prove something about this, we can avoid having to use the opaque
--- `Internal` string functions by moving this definition out to a separate file that can live
--- downstream of `Init.Data.String.Basic`.
 protected def toHex {n : Nat} (x : BitVec n) : String :=
   let s := (Nat.toDigits 16 x.toNat).asString
-  let t := (List.replicate ((n+3) / 4 - String.Internal.length s) '0').asString
-  String.Internal.append t s
+  let t := (List.replicate ((n+3) / 4 - s.length) '0').asString
+  t ++ s
 
 /-- `BitVec` representation. -/
 protected def BitVec.repr (a : BitVec n) : Std.Format :=
@@ -874,7 +871,4 @@ def clzAuxRec {w : Nat} (x : BitVec w) (n : Nat) : BitVec w :=
 /-- Count the number of leading zeros. -/
 def clz (x : BitVec w) : BitVec w := clzAuxRec x (w - 1)
 
-/-- Count the number of trailing zeros. -/
-def ctz (x : BitVec w) : BitVec w := (x.reverse).clz
-
 end BitVec

src/Init/Data/BitVec/BasicAux.lean

@@ -21,6 +21,13 @@ namespace BitVec
 
 section Nat
 
+/--
+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
+
 instance instOfNat : OfNat (BitVec n) i where ofNat := .ofNat n i
 
 /-- Return the bound in terms of toNat. -/

src/Init/Data/BitVec/Bitblast.lean

@@ -2155,238 +2155,4 @@ theorem shiftLeft_add_eq_shiftLeft_or {x y : BitVec w} :
     (y <<< x) + x =  (y <<< x) ||| x := by
   rw [BitVec.add_comm, add_shiftLeft_eq_or_shiftLeft, or_comm]
 
-/- ### Fast Circuit For Unsigned Overflow Detection -/
-
-/-!
-# Note [Fast Unsigned Multiplication Overflow Detection]
-
-The fast unsigned multiplication overflow detection circuit is described in
-`Efficient integer multiplication overflow detection circuits` (https://ieeexplore.ieee.org/abstract/document/987767).
-With this circuit, the computation of the overflow flag for the unsigned multiplication of
-two bitvectors `x` and `y` with bitwidth `w` requires:
-· extending the operands by `1` bit and performing the multiplication with the extended operands,
-· computing the preliminary overflow flag, which describes whether `x` and `y` together have at most
-  `w - 2` leading zeros.
-If the most significant bit of the extended operands' multiplication is `true` or if the
-preliminary overflow flag is `true`, overflow happens.
-In particular, the conditions check two different cases:
-· if the most significant bit of the extended operands' multiplication is `true`, the result of the
-  multiplication 2 ^ w ≤ x.toNat * y.toNat < 2 ^ (w + 1),
-· if the preliminary flag is true, then 2 ^ (w + 1) ≤ x.toNat * y.toNat.
-
-The computation of the preliminary overflow flag `resRec` relies on two quantities:
-· `uppcRec`: the unsigned parallel prefix circuit for the bits until a certain `i`,
-· `aandRec`: the conjunction between the parallel prefix circuit at of the first operand until a certain `i`
-  and the `i`-th bit in the second operand.
--/
-
-/--
-  `uppcRec` is the unsigned parallel prefix, `x.uppcRec s = true` iff `x.toNat` is greater or equal
-  than `2 ^ (w - 1 - (s - 1))`.
--/
-def uppcRec {w} (x : BitVec w) (s : Nat) (hs : s < w) : Bool :=
-  match s with
-  | 0 => x.msb
-  | i + 1 =>  x[w - 1 - i] || uppcRec x i (by omega)
-
-/-- The unsigned parallel prefix of `x` at `s` is `true` if and only if x interpreted
-  as a natural number is greater or equal than `2 ^ (w - 1 - (s - 1))`. -/
-@[simp]
-theorem uppcRec_true_iff (x : BitVec w) (s : Nat) (h : s < w) :
-    uppcRec x s h ↔ 2 ^ (w - 1 - (s - 1)) ≤ x.toNat := by
-  rcases w with _|w
-  · omega
-  · induction s
-    · case succ.zero =>
-      simp only [uppcRec, msb_eq_true_iff_two_mul_ge, Nat.pow_add, Nat.pow_one,
-        Nat.mul_comm (2 ^ w) 2, ge_iff_le, Nat.add_one_sub_one, zero_le, Nat.sub_eq_zero_of_le,
-        Nat.sub_zero]
-      apply Nat.mul_le_mul_left_iff (by omega)
-    · case succ.succ s ihs =>
-      simp only [uppcRec, or_eq_true, ihs, Nat.add_one_sub_one]
-      have := Nat.pow_le_pow_of_le (a := 2) ( n := (w - s)) (m := (w - (s - 1))) (by omega) (by omega)
-      constructor
-      · intro h'
-        rcases h' with h'|h'
-        · apply ge_two_pow_of_testBit h'
-        · omega
-      · intro h'
-        by_cases hbit: x[w - s]
-        · simp [hbit]
-        · have := BitVec.le_toNat_iff_getLsbD_eq_true (x := x) (i := w - s) (by omega)
-          simp only [h', true_iff] at this
-          obtain ⟨k, hk⟩ := this
-          by_cases hwk : w - s + k < w + 1
-          · by_cases hk' : 0 < k
-            · have hle := ge_two_pow_of_testBit hk
-              have hpowle := Nat.pow_le_pow_of_le (a := 2) ( n := (w - (s - 1))) (m := (w - s + k)) (by omega) (by omega)
-              omega
-            · rw [getLsbD_eq_getElem (by omega)] at hk
-              simp [hbit, show k = 0 by omega] at hk
-          · simp_all
-
-/--
-  Conjunction for fast umulOverflow circuit
--/
-def aandRec (x y : BitVec w) (s : Nat) (hs : s < w) : Bool :=
-  y[s] && uppcRec x s (by omega)
-
-
-/--
-  Preliminary overflow flag for fast umulOverflow circuit as introduced in
-  `Efficient integer multiplication overflow detection circuits` (https://ieeexplore.ieee.org/abstract/document/987767).
--/
-def resRec (x y : BitVec w) (s : Nat) (hs : s < w) (hslt : 0 < s) : Bool :=
-  match hs0 : s with
-  | 0 => by omega
-  | s' + 1 =>
-    match hs' : s' with
-    | 0 => aandRec x y 1 (by omega)
-    | s'' + 1 =>
-      (resRec x y s' (by omega) (by omega)) || (aandRec x y s (by omega))
-
-/-- The preliminary overflow flag is true for a certain `s` if and only if the conjunction returns true at
-  any `k` smaller than or equal to `s`. -/
-theorem resRec_true_iff (x y : BitVec w) (s : Nat) (hs : s < w) (hs' : 0 < s) :
-    resRec x y s hs hs' = true ↔ ∃ (k : Nat), ∃ (h : k ≤ s), ∃ (_ : 0 < k), aandRec x y k (by omega) := by
-  unfold resRec
-  rcases s with _|s
-  · omega
-  · rcases s
-    · case zero =>
-      constructor
-      · intro ha
-        exists 1, by omega, by omega
-      · intro hr
-        obtain ⟨k, hk, hk', hk''⟩ := hr
-        simp only [show k = 1 by omega] at hk''
-        exact hk''
-    · case succ s =>
-      induction s
-      · case zero =>
-        unfold resRec
-        simp only [Nat.zero_add, Nat.reduceAdd, or_eq_true]
-        constructor
-        · intro h
-          rcases h with h|h
-          · exists 1, by omega, by omega
-          · exists 2, by omega, by omega
-        · intro h
-          obtain ⟨k, hk, hk', hk''⟩ := h
-          have h : k = 1 ∨ k = 2 := by omega
-          rcases h with h|h
-          <;> simp only [h] at hk''
-          <;> simp [hk'']
-      · case succ s ihs =>
-        specialize ihs (by omega) (by omega)
-        unfold resRec
-        simp only [or_eq_true, ihs]
-        constructor
-        · intro h
-          rcases h with h|h
-          · obtain ⟨k, hk, hk', hk''⟩ := h
-            exists k, by omega, by omega
-          · exists s + 1 + 1 + 1, by omega, by omega
-        · intro h
-          obtain ⟨k, hk, hk', hk''⟩ := h
-          by_cases h' : x.aandRec y (s + 1 + 1 + 1) (by omega) = true
-          · simp [h']
-          · simp only [h', false_eq_true, _root_.or_false]
-            by_cases h'' : k ≤ s + 1 + 1
-            · exists k, h'', by omega
-            · have : k = s + 1 + 1 + 1 := by omega
-              simp_all
-
-/-- If the sum of the leading zeroes of two bitvecs with bitwidth `w` is less than or equal to
-  (`w - 2`), then the preliminary overflow flag is true and their unsigned multiplication overflows.
-  The explanation is in `Efficient integer multiplication overflow detection circuits`
-  https://ieeexplore.ieee.org/abstract/document/987767
-  -/
-theorem resRec_of_clz_le {x y : BitVec w} (hw : 1 < w) (hx : x ≠ 0#w) (hy : y ≠ 0#w):
-    (clz x).toNat + (clz y).toNat ≤ w - 2 → resRec x y (w - 1) (by omega) (by omega) := by
-  intro h
-  rw [resRec_true_iff]
-  exists (w - 1 - y.clz.toNat), by omega, by omega
-  simp only [aandRec]
-  by_cases hw0 : w - 1 - y.clz.toNat = 0
-  · have := clz_lt_iff_ne_zero.mpr (by omega)
-    omega
-  · simp only [and_eq_true, getLsbD_true_clz_of_ne_zero (x := y) (by omega) (by omega),
-    getElem_of_getLsbD_eq_true, uppcRec_true_iff,
-    show w - 1 - (w - 1 - y.clz.toNat - 1) = y.clz.toNat + 1 by omega, _root_.true_and]
-    exact Nat.le_trans (Nat.pow_le_pow_of_le (a := 2) (n := y.clz.toNat + 1)
-          (m := w - 1 - x.clz.toNat) (by omega) (by omega))
-          (BitVec.two_pow_sub_clz_le_toNat_of_ne_zero (x := x) (by omega) (by omega))
-
-/--
-  Complete fast overflow detection circuit for unsigned multiplication.
--/
-theorem fastUmulOverflow (x y : BitVec w) :
-    umulOverflow x y = if hw : w ≤ 1 then false
-      else (setWidth (w + 1) x * setWidth (w + 1) y)[w] || x.resRec y (w - 1) (by omega) (by omega) := by
-  rcases w with _|_|w
-  · simp [of_length_zero, umulOverflow]
-  · have hx : x.toNat ≤ 1 := by omega
-    have hy : y.toNat ≤ 1 := by omega
-    have := Nat.mul_le_mul (n₁ := x.toNat) (m₁ := y.toNat) (n₂ := 1) (m₂ := 1) hx hy
-    simp [umulOverflow]
-    omega
-  · by_cases h : umulOverflow x y
-    · simp only [h, Nat.reduceLeDiff, reduceDIte, Nat.add_one_sub_one, true_eq, or_eq_true]
-      simp only [umulOverflow, ge_iff_le, decide_eq_true_eq] at h
-      by_cases h' : x.toNat * y.toNat < 2 ^ (w + 1 + 1 + 1)
-      · have hlt := BitVec.getElem_eq_true_of_lt_of_le
-          (x := (setWidth (w + 1 + 1 + 1) x * setWidth (w + 1 + 1 + 1) y))
-          (k := w + 1 + 1)  (by omega)
-        simp only [toNat_mul, toNat_setWidth, Nat.lt_add_one, toNat_mod_cancel_of_lt,
-          Nat.mod_eq_of_lt (a := x.toNat * y.toNat) (b := 2 ^ (w + 1 + 1 + 1)) (by omega), h', h,
-          forall_const] at hlt
-        simp [hlt]
-      · by_cases hsw : (setWidth (w + 1 + 1 + 1) x * setWidth (w + 1 + 1 + 1) y)[w + 1 + 1] = true
-        · simp [hsw]
-        · simp only [hsw, false_eq_true, _root_.false_or]
-          have := Nat.two_pow_pos (w := w + 1 + 1)
-          have hltx := BitVec.toNat_lt_two_pow_sub_clz (x := x)
-          have hlty := BitVec.toNat_lt_two_pow_sub_clz (x := y)
-          have := Nat.mul_ne_zero_iff (m := y.toNat) (n := x.toNat)
-          simp only [ne_eq, show ¬x.toNat * y.toNat = 0 by omega, not_false_eq_true,
-            true_iff] at this
-          obtain ⟨hxz,hyz⟩ := this
-          apply resRec_of_clz_le (x := x) (y := y) (by omega) (by simp [toNat_eq]; exact hxz) (by simp [toNat_eq]; exact hyz)
-          by_cases hzxy : x.clz.toNat + y.clz.toNat ≤ w
-          · omega
-          · by_cases heq : w + 1 - y.clz.toNat = 0
-            · by_cases heq' : w + 1 + 1 - y.clz.toNat = 0
-              · simp [heq', hyz] at hlty
-              · simp only [show y.clz.toNat = w + 1 by omega, Nat.add_sub_cancel_left,
-                  Nat.pow_one] at hlty
-                simp only [show y.toNat = 1 by omega, Nat.mul_one, Nat.not_lt] at h'
-                omega
-            · by_cases w + 1 < y.clz.toNat
-              · omega
-              · simp only [Nat.not_lt] at h'
-                have := Nat.mul_lt_mul'' (a := x.toNat) (b := y.toNat) (c := 2 ^ (w + 1 + 1 - x.clz.toNat)) (d := 2 ^ (w + 1 + 1 - y.clz.toNat)) hltx hlty
-                simp only [← Nat.pow_add] at this
-                have := Nat.pow_le_pow_of_le (a := 2) (n := w + 1 + 1 - x.clz.toNat + (w + 1 + 1 - y.clz.toNat)) (m := w + 1 + 1 + 1)
-                 (by omega) (by omega)
-                omega
-    · simp only [h, Nat.reduceLeDiff, reduceDIte, Nat.add_one_sub_one, false_eq, or_eq_false_iff]
-      simp only [umulOverflow, ge_iff_le, decide_eq_true_eq, Nat.not_le] at h
-      and_intros
-      · simp only [← getLsbD_eq_getElem, getLsbD_eq_getMsbD, Nat.lt_add_one, decide_true,
-          Nat.add_one_sub_one, Nat.sub_self, ← msb_eq_getMsbD_zero, Bool.true_and,
-          msb_eq_false_iff_two_mul_lt, toNat_mul, toNat_setWidth, toNat_mod_cancel_of_lt]
-        rw [Nat.mod_eq_of_lt (by omega),Nat.pow_add (m := w + 1 + 1) (n := 1)]
-        simp [Nat.mul_comm 2 (x.toNat * y.toNat), h]
-      · apply Classical.byContradiction
-        intro hcontra
-        simp only [not_eq_false, resRec_true_iff, exists_prop, exists_and_left] at hcontra
-        obtain ⟨k,hk,hk',hk''⟩ := hcontra
-        simp only [aandRec, and_eq_true, uppcRec_true_iff, Nat.add_one_sub_one] at hk''
-        obtain ⟨hky, hkx⟩ := hk''
-        have hyle := two_pow_le_toNat_of_getElem_eq_true (x := y) (i := k) (by omega) hky
-        have := Nat.mul_le_mul (n₁ := 2 ^ (w + 1 - (k - 1))) (m₁ := 2 ^ k) (n₂ := x.toNat) (m₂ := y.toNat) hkx hyle
-        simp [← Nat.pow_add, show w + 1 - (k - 1) + k = w + 1 + 1 by omega] at this
-        omega
-
 end BitVec

src/Init/Data/BitVec/Bootstrap.lean

@@ -19,7 +19,7 @@ theorem testBit_toNat (x : BitVec w) : x.toNat.testBit i = x.getLsbD i := rfl
 @[simp, grind =] theorem getLsbD_ofFin (x : Fin (2^n)) (i : Nat) :
     getLsbD (BitVec.ofFin x) i = x.val.testBit i := rfl
 
-@[simp, grind =] theorem getLsbD_of_ge (x : BitVec w) (i : Nat) (ge : w ≤ i) : getLsbD x i = false := by
+@[simp, grind] theorem getLsbD_of_ge (x : BitVec w) (i : Nat) (ge : w ≤ i) : getLsbD x i = false := by
   let ⟨x, x_lt⟩ := x
   simp only [getLsbD_ofFin]
   apply Nat.testBit_lt_two_pow

src/Init/Data/BitVec/Lemmas.lean

@@ -37,7 +37,7 @@ namespace BitVec
 @[simp] theorem getElem_ofFin (x : Fin (2^n)) (i : Nat) (h : i < n) :
     (BitVec.ofFin x)[i] = x.val.testBit i := rfl
 
-@[simp, grind =] theorem getMsbD_of_ge (x : BitVec w) (i : Nat) (ge : w ≤ i) : getMsbD x i = false := by
+@[simp, grind] theorem getMsbD_of_ge (x : BitVec w) (i : Nat) (ge : w ≤ i) : getMsbD x i = false := by
   rw [getMsbD]
   simp only [Bool.and_eq_false_imp, decide_eq_true_eq]
   omega
@@ -122,7 +122,7 @@ 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.Internal.ofNat_eq_ofNat, Fin.ofNat, lt, Nat.mod_eq_of_lt]
+  simp only [BitVec.ofNat, Fin.ofNat, lt, Nat.mod_eq_of_lt]
 
 /-- Prove nonequality of bitvectors in terms of nat operations. -/
 theorem toNat_ne_iff_ne {n} {x y : BitVec n} : x.toNat ≠ y.toNat ↔ x ≠ y := by
@@ -299,7 +299,7 @@ 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.Internal.ofNat_eq_ofNat, Fin.ofNat, BitVec.ofNat]
+  simp only [OfNat.ofNat, Fin.ofNat, BitVec.ofNat]
 
 -- We use a `grind_pattern` as `@[grind]` will not use the `no_index` term.
 grind_pattern ofFin_ofNat => ofFin (OfNat.ofNat n : Fin (2^w))
@@ -510,18 +510,6 @@ theorem getElem_ofBool {b : Bool} {h : i < 1}: (ofBool b)[i] = b := by
 @[simp] theorem zero_eq_one_iff (w : Nat) : (0#w = 1#w) ↔ (w = 0) := by
   rw [← one_eq_zero_iff, eq_comm]
 
-/-- A bitvector is equal to 0#w if and only if all bits are `false` -/
-theorem zero_iff_eq_false {x: BitVec w} :
-    x = 0#w ↔ ∀ i, x.getLsbD i = false := by
-  rcases w with _|w
-  · simp [of_length_zero]
-  · constructor
-    · intro hzero
-      simp [hzero]
-    · intro hfalse
-      ext j hj
-      simp [← getLsbD_eq_getElem, hfalse]
-
 /-! ### msb -/
 
 @[simp] theorem msb_zero : (0#w).msb = false := by simp [BitVec.msb, getMsbD]
@@ -1100,10 +1088,6 @@ theorem toInt_setWidth' {m n : Nat} (p : m ≤ n) {x : BitVec m} :
   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)]
 
-theorem toNat_setWidth_of_le {w w' : Nat} {b : BitVec w} (h : w ≤ w') : (b.setWidth w').toNat = b.toNat := by
-  rw [BitVec.toNat_setWidth, Nat.mod_eq_of_lt]
-  exact BitVec.toNat_lt_twoPow_of_le h
-
 /-! ## extractLsb -/
 
 @[simp, grind =]
@@ -1291,17 +1275,6 @@ theorem extractLsb'_eq_zero {x : BitVec w} {start : Nat} :
   ext i hi
   omega
 
-theorem extractLsb'_setWidth_of_le {b : BitVec w} {start len w' : Nat} (h : start + len ≤ w') :
-    (b.setWidth w').extractLsb' start len = b.extractLsb' start len := by
-  ext i h_i
-  simp
-  omega
-
-theorem setWidth_extractLsb'_of_le {c : BitVec w} (h : len₁ ≤ len₂) :
-    (c.extractLsb' start len₂).setWidth len₁ = c.extractLsb' start len₁ := by
-  ext i hi
-  simp [show i < len₂ by omega]
-
 /-! ### allOnes -/
 
 @[simp, grind =] theorem toNat_allOnes : (allOnes v).toNat = 2^v - 1 := by
@@ -1545,12 +1518,6 @@ theorem extractLsb_and {x : BitVec w} {hi lo : Nat} :
 @[simp, grind =] theorem ofNat_and {x y : Nat} : BitVec.ofNat w (x &&& y) = BitVec.ofNat w x &&& BitVec.ofNat w y :=
   eq_of_toNat_eq (by simp [Nat.and_mod_two_pow])
 
-theorem and_or_distrib_left {x y z : BitVec w} : x &&& (y ||| z) = (x &&& y) ||| (x &&& z) :=
-  BitVec.eq_of_getElem_eq (by simp [Bool.and_or_distrib_left])
-
-theorem and_or_distrib_right {x y z : BitVec w} : (x ||| y) &&& z = (x &&& z) ||| (y &&& z) :=
-  BitVec.eq_of_getElem_eq (by simp [Bool.and_or_distrib_right])
-
 /-! ### xor -/
 
 @[simp, grind =] theorem toNat_xor (x y : BitVec v) :
@@ -2201,10 +2168,6 @@ theorem msb_ushiftRight {x : BitVec w} {n : Nat} :
   have := lt_of_getLsbD ha
   omega
 
-theorem setWidth_ushiftRight_eq_extractLsb {b : BitVec w} : (b >>> w').setWidth w'' = b.extractLsb' w' w'' := by
-  ext i hi
-  simp
-
 /-! ### ushiftRight reductions from BitVec to Nat -/
 
 @[simp, grind =]
@@ -2995,9 +2958,10 @@ theorem shiftLeft_eq_concat_of_lt {x : BitVec w} {n : Nat} (hn : n < w) :
 /-- Combine adjacent `extractLsb'` operations into a single `extractLsb'`. -/
 theorem extractLsb'_append_extractLsb'_eq_extractLsb' {x : BitVec w} (h : start₂ = start₁ + len₁) :
     ((x.extractLsb' start₂ len₂) ++ (x.extractLsb' start₁ len₁)) =
-      x.extractLsb' start₁ (len₂ + len₁) := by
+    (x.extractLsb' start₁ (len₁ + len₂)).cast (by omega) := by
   ext i h
-  simp only [getElem_append, getElem_extractLsb', dite_eq_ite, ite_eq_left_iff, Nat.not_lt]
+  simp only [getElem_append, getElem_extractLsb', dite_eq_ite, getElem_cast, ite_eq_left_iff,
+    Nat.not_lt]
   intro hi
   congr 1
   omega
@@ -3109,51 +3073,6 @@ theorem extractLsb'_append_eq_of_le {v w} {xhi : BitVec v} {xlo : BitVec w}
     extractLsb' start len (xhi ++ xlo) = extractLsb' (start - w) len xhi := by
   simp [extractLsb'_append_eq_ite, show ¬ start < w by omega]
 
-theorem extractLsb'_append_eq_left {a : BitVec w} {b : BitVec w'} : (a ++ b).extractLsb' w' w = a := by
-  simp [BitVec.extractLsb'_append_eq_of_le]
-
-theorem extractLsb'_append_eq_right {a : BitVec w} {b : BitVec w'} : (a ++ b).extractLsb' 0 w' = b := by
-  simp [BitVec.extractLsb'_append_eq_of_add_le]
-
-theorem setWidth_append_eq_right {a : BitVec w} {b : BitVec w'} : (a ++ b).setWidth w' = b := by
-  ext i hi
-  simp [getLsbD_append, hi]
-
-theorem append_left_inj {s₁ s₂ : BitVec w} (t : BitVec w') : s₁ ++ t = s₂ ++ t ↔ s₁ = s₂ := by
-  refine ⟨fun h => ?_, fun h => h ▸ rfl⟩
-  ext i hi
-  simpa [getElem_append, dif_neg] using congrArg (·[i + w']'(by omega)) h
-
-theorem append_right_inj (s : BitVec w) {t₁ t₂ : BitVec w'} : s ++ t₁ = s ++ t₂ ↔ t₁ = t₂ := by
-  refine ⟨fun h => ?_, fun h => h ▸ rfl⟩
-  ext i hi
-  simpa [getElem_append, hi] using congrArg (·[i]) h
-
-theorem setWidth_append_eq_shiftLeft_setWidth_or {b : BitVec w} {b' : BitVec w'} :
-    (b ++ b').setWidth w'' = (b.setWidth w'' <<< w') ||| b'.setWidth w'' := by
-  ext i hi
-  simp only [getElem_setWidth, getElem_or, getElem_shiftLeft]
-  rw [getLsbD_append]
-  split <;> simp_all
-
-theorem setWidth_append_append_eq_shiftLeft_setWidth_or {b : BitVec w} {b' : BitVec w'} {b'' : BitVec w''} :
-    (b ++ b' ++ b'').setWidth w''' = (b.setWidth w''' <<< (w' + w'')) ||| (b'.setWidth w''' <<< w'') ||| b''.setWidth w''' := by
-  rw [BitVec.setWidth_append_eq_shiftLeft_setWidth_or,
-    BitVec.setWidth_append_eq_shiftLeft_setWidth_or,
-    BitVec.shiftLeft_or_distrib, BitVec.shiftLeft_add]
-
-theorem setWidth_append_append_append_eq_shiftLeft_setWidth_or {b : BitVec w} {b' : BitVec w'} {b'' : BitVec w''} {b''' : BitVec w'''} :
-    (b ++ b' ++ b'' ++ b''').setWidth w'''' = (b.setWidth w'''' <<< (w' + w'' + w''')) ||| (b'.setWidth w'''' <<< (w'' + w''')) |||
-      (b''.setWidth w'''' <<< w''') ||| b'''.setWidth w'''' := by
-  simp only [BitVec.setWidth_append_eq_shiftLeft_setWidth_or, BitVec.shiftLeft_or_distrib, BitVec.shiftLeft_add]
-
-theorem and_setWidth_allOnes (w' w : Nat) (b : BitVec (w' + w)) :
-    b &&& (BitVec.allOnes w).setWidth (w' + w) = 0#w' ++ b.setWidth w := by
-  ext i hi
-  simp only [getElem_and, getElem_setWidth, getLsbD_allOnes]
-  rw [BitVec.getElem_append]
-  split <;> simp_all
-
 /-! ### rev -/
 
 @[grind =]
@@ -4110,9 +4029,6 @@ instance instLawfulOrderLT : LawfulOrderLT (BitVec n) := by
   apply LawfulOrderLT.of_le
   simpa using fun _ _ => BitVec.lt_asymm
 
-theorem length_pos_of_lt {b b' : BitVec w} (h : b < b') : 0 < w :=
-  length_pos_of_ne (BitVec.ne_of_lt h)
-
 protected theorem umod_lt (x : BitVec n) {y : BitVec n} : 0 < y → x % y < y := by
   simp only [ofNat_eq_ofNat, lt_def, toNat_ofNat, Nat.zero_mod]
   apply Nat.mod_lt
@@ -4184,14 +4100,6 @@ theorem lt_of_msb_false_of_msb_true {x y : BitVec w} (hx : x.msb = false) (hy :
   simp
   omega
 
-theorem lt_add_one {b : BitVec w} (h : b ≠ allOnes w) : b < b + 1 := by
-  simp only [ne_eq, ← toNat_inj, toNat_allOnes] at h
-  simp only [BitVec.lt_def, ofNat_eq_ofNat, toNat_add, toNat_ofNat, Nat.add_mod_mod]
-  rw [Nat.mod_eq_of_lt]
-  · exact Nat.lt_add_one _
-  · have := b.toNat_lt_twoPow_of_le (Nat.le_refl _)
-    omega
-
 /-! ### udiv -/
 
 theorem udiv_def {x y : BitVec n} : x / y = BitVec.ofNat n (x.toNat / y.toNat) := by
@@ -5337,7 +5245,7 @@ theorem replicate_succ' {x : BitVec w} :
     (replicate n x ++ x).cast (by rw [Nat.mul_succ]) := by
   simp [replicate_append_self]
 
-theorem setWidth_add_eq_mod {x y : BitVec w} : BitVec.setWidth i (x + y) = (BitVec.setWidth i x + BitVec.setWidth i y) % (BitVec.twoPow i w) := by
+theorem BitVec.setWidth_add_eq_mod {x y : BitVec w} : BitVec.setWidth i (x + y) = (BitVec.setWidth i x + BitVec.setWidth i y) % (BitVec.twoPow i w) := by
   apply BitVec.eq_of_toNat_eq
   rw [toNat_setWidth]
   simp only [toNat_setWidth, toNat_add, toNat_umod, Nat.add_mod_mod, Nat.mod_add_mod, toNat_twoPow]
@@ -5346,14 +5254,6 @@ theorem setWidth_add_eq_mod {x y : BitVec w} : BitVec.setWidth i (x + y) = (BitV
   · have hk : 2 ^ w < 2 ^ i := Nat.pow_lt_pow_of_lt (by decide) (Nat.lt_of_not_le h)
     rw [Nat.mod_eq_of_lt hk, Nat.mod_mod_eq_mod_mod_of_dvd (Nat.pow_dvd_pow _ (Nat.le_of_not_le h))]
 
-theorem setWidth_setWidth_eq_self {a : BitVec w} {w' : Nat} (h : a < BitVec.twoPow w w') : (a.setWidth w').setWidth w = a := by
-  by_cases hw : w' < w
-  · simp only [toNat_eq, toNat_setWidth]
-    rw [Nat.mod_mod_of_dvd' (Nat.pow_dvd_pow _ (Nat.le_of_lt hw)), Nat.mod_eq_of_lt]
-    rwa [BitVec.lt_def, BitVec.toNat_twoPow_of_lt hw] at h
-  · rw [BitVec.lt_def, BitVec.toNat_twoPow_of_le (by omega)] at h
-    simp at h
-
 /-! ### intMin -/
 
 @[grind =]
@@ -5867,24 +5767,39 @@ theorem msb_replicate {n w : Nat} {x : BitVec w} :
   simp only [BitVec.msb, getMsbD_replicate, Nat.zero_mod]
   cases n <;> cases w <;> simp
 
-@[simp]
-theorem reverse_eq_zero_iff {x : BitVec w} :
-    x.reverse = 0#w ↔ x = 0#w := by
-  constructor
-  · intro hrev
-    ext i hi
-    rw [← getLsbD_eq_getElem, getLsbD_eq_getMsbD, ← getLsbD_reverse]
-    simp [hrev]
-  · intro hzero
-    ext i hi
-    rw [← getLsbD_eq_getElem, getLsbD_eq_getMsbD, getMsbD_reverse]
-    simp [hi, hzero]
+/-! ### Count leading zeros -/
+
+theorem clzAuxRec_zero (x : BitVec w) :
+    x.clzAuxRec 0 = if x.getLsbD 0 then BitVec.ofNat w (w - 1) else BitVec.ofNat w w := by rfl
+
+theorem clzAuxRec_succ (x : BitVec w) :
+    x.clzAuxRec (n + 1) = if x.getLsbD (n + 1) then BitVec.ofNat w (w - 1 - (n + 1)) else BitVec.clzAuxRec x n := by rfl
+
+theorem clzAuxRec_eq_clzAuxRec_of_le (x : BitVec w) (h : w - 1 ≤ n) :
+    x.clzAuxRec n = x.clzAuxRec (w - 1) := by
+  let k := n - (w - 1)
+  rw [show n = (w - 1) + k by omega]
+  induction k
+  case zero => simp
+  case succ k ihk =>
+    simp [show w - 1 + (k + 1) = (w - 1 + k) + 1 by omega, clzAuxRec_succ, ihk,
+      show x.getLsbD (w - 1 + k + 1) = false by simp only [show w ≤ w - 1 + k + 1 by omega, getLsbD_of_ge]]
+
+theorem clzAuxRec_eq_clzAuxRec_of_getLsbD_false {x : BitVec w} (h : ∀ i, n < i → x.getLsbD i = false) :
+    x.clzAuxRec n = x.clzAuxRec (n + k) := by
+  induction k
+  case zero => simp
+  case succ k ihk =>
+    simp only [show n + (k + 1) = (n + k) + 1 by omega, clzAuxRec_succ]
+    by_cases hxn : x.getLsbD (n + k + 1)
+    · have : ¬ ∀ (i : Nat), n < i → x.getLsbD i = false := by
+        simp only [Classical.not_forall, Bool.not_eq_false]
+        exists n + k + 1
+        simp [show n < n + k + 1 by omega, hxn]
+      contradiction
+    · simp only [hxn, Bool.false_eq_true, ↓reduceIte]
+      exact ihk
 
-@[simp]
-theorem reverse_reverse_eq {x : BitVec w} :
-    x.reverse.reverse = x := by
-  ext k hk
-  rw [getElem_reverse, getMsbD_reverse, getLsbD_eq_getElem]
 
 /-! ### Inequalities (le / lt) -/
 
@@ -5934,433 +5849,6 @@ theorem sle_eq_ule {x y : BitVec w} : x.sle y = (x.msb != y.msb ^^ x.ule y) := b
 theorem sle_eq_ule_of_msb_eq {x y : BitVec w} (h : x.msb = y.msb) : x.sle y = x.ule y := by
   simp [BitVec.sle_eq_ule, h]
 
-/-- A bitvector interpreted as a natural number is greater than or equal to `2 ^ i` if and only if
-  there exists at least one bit with `true` value at position `i` or higher. -/
-theorem le_toNat_iff_getLsbD_eq_true {x : BitVec w} (hi : i < w ) :
-    (2 ^ i ≤ x.toNat) ↔ (∃ k, x.getLsbD (i + k) = true) := by
-  rcases w with _|w
-  · simp [of_length_zero]
-  · constructor
-    · intro hle
-      apply Classical.byContradiction
-      intros hcontra
-      let x' := setWidth (i + 1) x
-      have hx' : setWidth (i + 1) x = x' := by rfl
-      have hcast : w - i + (i + 1) = w + 1 := by omega
-      simp only [not_exists, Bool.not_eq_true] at hcontra
-      have hx'' : x = BitVec.cast hcast (0#(w - i) ++ x') := by
-        ext j
-        by_cases hj : j < i + 1
-        · simp only [← hx', getElem_cast, getElem_append, hj, reduceDIte, getElem_setWidth]
-          rw [getLsbD_eq_getElem]
-        · simp only [getElem_cast, getElem_append, hj, reduceDIte, getElem_zero]
-          let j' := j - i
-          simp only [show j = i + j' by omega]
-          apply hcontra
-      have : x'.toNat < 2 ^ i := by
-        apply Nat.lt_pow_two_of_testBit (n := i) x'.toNat
-        intro j hj
-        let j' := j - i
-        specialize hcontra j'
-        have : x'.getLsbD (i + j') = x.getLsbD (i + j') := by
-          subst x'
-          simp [hcontra]
-        simp [show j = i + j' by omega, testBit_toNat, this, hcontra]
-      have : x'.toNat = x.toNat := by
-        have := BitVec.setWidth_eq_append (w := (w + 1)) (v := i + 1) (x := x')
-        specialize this (by omega)
-        rw [toNat_eq, toNat_setWidth, Nat.mod_eq_of_lt (by omega)] at this
-        simp [hx'']
-      omega
-    · intro h
-      obtain ⟨k, hk⟩ := h
-      by_cases hk' : i + k < w + 1
-      · have := Nat.ge_two_pow_of_testBit hk
-        have := Nat.pow_le_pow_of_le (a := 2) (n := i) (m := i + k) (by omega) (by omega)
-        omega
-      · simp [show w + 1 ≤ i + k by omega] at hk
-
-/-- A bitvector interpreted as a natural number is strictly smaller than `2 ^ i` if and only if
-  all bits at position `i` or higher are false. -/
-theorem toNat_lt_iff_getLsbD_eq_false {x : BitVec w} (i : Nat) (hi : i < w) :
-    x.toNat < 2 ^ i ↔ (∀ k, x.getLsbD (i + k) = false) := by
-  constructor
-  · intro h
-    apply Classical.byContradiction
-    intro hcontra
-    simp only [Classical.not_forall, Bool.not_eq_false] at hcontra
-    obtain ⟨k, hk⟩ := hcontra
-    have hle := Nat.ge_two_pow_of_testBit hk
-    by_cases hlt : i + k < w
-    · have := Nat.pow_le_pow_of_le (a := 2) (n := i) (m := i + k) (by omega) (by omega)
-      omega
-    · simp [show w ≤ i + k by omega] at hk
-  · intro h
-    apply Classical.byContradiction
-    intro hcontra
-    simp [BitVec.le_toNat_iff_getLsbD_eq_true (x := x) (i := i) hi, h] at hcontra
-
-/-- If a bitvector interpreted as a natural number is strictly smaller than `2 ^ (k + 1)` and greater than or
-  equal to 2 ^ k, then the bit at position `k` must be `true` -/
-theorem getElem_eq_true_of_lt_of_le {x : BitVec w} (hk' : k < w) (hlt: x.toNat < 2 ^ (k + 1)) (hle : 2 ^ k ≤ x.toNat) :
-    x[k] = true := by
-  have := le_toNat_iff_getLsbD_eq_true (x := x) (i := k) hk'
-  simp only [hle, true_iff] at this
-  obtain ⟨k',hk'⟩ := this
-  by_cases hkk' : k + k' < w
-  · have := Nat.ge_two_pow_of_testBit hk'
-    by_cases hzk' : k' = 0
-    · simp [hzk'] at hk'; exact hk'
-    · have := Nat.pow_lt_pow_of_lt (a := 2) (n := k) (m := k + k') (by omega) (by omega)
-      have := Nat.pow_le_pow_of_le (a := 2) (n := k + 1) (m := k + k') (by omega) (by omega)
-      omega
-  · simp [show w ≤ k + k' by omega] at hk'
-
-theorem not_lt_iff {b : BitVec w} : ~~~b < b ↔ 0 < w ∧ b.msb = true := by
-  refine ⟨fun h => ?_, fun ⟨hw, hb⟩ => ?_⟩
-  · have := length_pos_of_lt h
-    exact ⟨this, by rwa [← ult_iff_lt, ult_eq_msb_of_msb_neq (by simp_all)] at h⟩
-  · rwa [← ult_iff_lt, ult_eq_msb_of_msb_neq (by simp_all)]
-
-/-! ### Count leading zeros -/
-
-theorem clzAuxRec_zero (x : BitVec w) :
-    x.clzAuxRec 0 = if x.getLsbD 0 then BitVec.ofNat w (w - 1) else BitVec.ofNat w w := by rfl
-
-theorem clzAuxRec_succ (x : BitVec w) :
-    x.clzAuxRec (n + 1) = if x.getLsbD (n + 1) then BitVec.ofNat w (w - 1 - (n + 1)) else BitVec.clzAuxRec x n := by rfl
-
-theorem clzAuxRec_eq_clzAuxRec_of_le {x : BitVec w} (h : w - 1 ≤ n) :
-    x.clzAuxRec n = x.clzAuxRec (w - 1) := by
-  let k := n - (w - 1)
-  rw [show n = (w - 1) + k by omega]
-  induction k
-  · case zero => simp
-  · case succ k ihk =>
-    simp [show w - 1 + (k + 1) = (w - 1 + k) + 1 by omega, clzAuxRec_succ, ihk,
-      show x.getLsbD (w - 1 + k + 1) = false by simp only [show w ≤ w - 1 + k + 1 by omega, getLsbD_of_ge]]
-
-theorem clzAuxRec_eq_clzAuxRec_of_getLsbD_false {x : BitVec w} (h : ∀ i, n < i → x.getLsbD i = false) :
-    x.clzAuxRec n = x.clzAuxRec (n + k) := by
-  induction k
-  · case zero => simp
-  · case succ k ihk =>
-    simp only [show n + (k + 1) = (n + k) + 1 by omega, clzAuxRec_succ]
-    by_cases hxn : x.getLsbD (n + k + 1)
-    · have : ¬ ∀ (i : Nat), n < i → x.getLsbD i = false := by
-        simp only [Classical.not_forall, Bool.not_eq_false]
-        exists n + k + 1
-        simp [show n < n + k + 1 by omega, hxn]
-      contradiction
-    · simp only [hxn, Bool.false_eq_true, ↓reduceIte]
-      exact ihk
-
-theorem clzAuxRec_le {x : BitVec w} (n : Nat) :
-    clzAuxRec x n ≤ w := by
-  have := Nat.lt_pow_self (a := 2) (n := w) (by omega)
-  rcases w with _|w
-  · simp [of_length_zero]
-  · induction n
-    · case zero =>
-      simp only  [clzAuxRec_zero]
-      by_cases hx0 : x.getLsbD 0
-      · simp only [hx0, Nat.add_one_sub_one, reduceIte, natCast_eq_ofNat, ofNat_le_ofNat,
-          Nat.mod_two_pow_self, ge_iff_le, Nat.mod_eq_of_lt (a := w) (b := 2 ^ (w + 1)) (by omega)]
-        omega
-      · simp only [hx0, Bool.false_eq_true, reduceIte, natCast_eq_ofNat, BitVec.le_refl]
-    · case succ n ihn =>
-      simp only [clzAuxRec_succ, Nat.add_one_sub_one, natCast_eq_ofNat, ge_iff_le]
-      by_cases hxn : x.getLsbD (n + 1)
-      · simp [hxn, Nat.mod_eq_of_lt (a := w - (n + 1)) (b := 2 ^(w + 1)) (by omega)]
-        omega
-      · simp only [hxn, Bool.false_eq_true, reduceIte]
-        exact ihn
-
-theorem clzAuxRec_eq_iff_of_getLsbD_false {x : BitVec w} (h : ∀ i, n < i → x.getLsbD i = false) :
-    x.clzAuxRec n = BitVec.ofNat w w ↔ ∀ j, j ≤ n → x.getLsbD j = false := by
-  rcases w with _|w
-  · simp [of_length_zero]
-  · have := Nat.lt_pow_self (a := 2) (n := w + 1)
-    induction n
-    · case zero =>
-      simp only [clzAuxRec_zero, Nat.zero_lt_succ, getLsbD_eq_getElem, Nat.add_one_sub_one,
-        ite_eq_right_iff, Nat.le_zero_eq, forall_eq]
-      by_cases hx0 : x.getLsbD 0
-      · simp [hx0, toNat_eq, toNat_ofNat, Nat.mod_eq_of_lt (a := w) (b := 2 ^ (w + 1)) (by omega)]
-      · simp only [Nat.zero_lt_succ, getLsbD_eq_getElem, Bool.not_eq_true] at hx0
-        simp [hx0]
-    · case succ n ihn =>
-      simp only [clzAuxRec_succ, Nat.add_one_sub_one]
-      by_cases hxn : x.getLsbD (n + 1)
-      · simp only [hxn, reduceIte, toNat_eq, toNat_ofNat,
-          Nat.mod_eq_of_lt (a := w - (n + 1)) (b := 2 ^ (w + 1)) (by omega), Nat.mod_two_pow_self,
-          show ¬w - (n + 1) = w + 1 by omega, false_iff, Classical.not_forall,
-          Bool.not_eq_false]
-        exists n + 1, by omega
-      · have : ∀ (i : Nat), n < i → x.getLsbD i = false := by
-          intro i hi
-          by_cases hi' : i = n + 1
-          · simp [hi', hxn]
-          · apply h; omega
-        specialize ihn this
-        simp only [Bool.not_eq_true] at ihn hxn
-        simp only [hxn, Bool.false_eq_true, reduceIte, ihn]
-        constructor
-        <;> intro h' j hj
-        <;> (by_cases hj' : j = n + 1; simp [hj', hxn]; (apply h'; omega))
-
-theorem clz_le {x : BitVec w} :
-    clz x ≤ w := by
-  unfold clz
-  rcases w with _|w
-  · simp [of_length_zero]
-  · exact clzAuxRec_le (n := w)
-
-@[simp]
-theorem clz_eq_iff_eq_zero {x : BitVec w} :
-    clz x = w ↔ x = 0#w := by
-  rcases w with _|w
-  · simp [clz, of_length_zero]
-  · simp only [clz, Nat.add_one_sub_one, natCast_eq_ofNat, zero_iff_eq_false]
-    rw [clzAuxRec_eq_iff_of_getLsbD_false (x := x) (n := w) (w := w + 1) (by intros i hi; simp [show w + 1 ≤ i by omega])]
-    constructor
-    · intro h i
-      by_cases i ≤ w
-      · apply h; omega
-      · simp [show w + 1 ≤ i by omega]
-    · intro h j hj
-      apply h
-
-theorem clzAuxRec_eq_zero_iff {x : BitVec w} (h : ∀ i, n < i → x.getLsbD i = false) (hw : 0 < w) :
-    (x.clzAuxRec n).toNat = 0 ↔ x[w - 1] = true := by
-  have := Nat.lt_pow_self (a := 2) (n := w)
-  induction n
-  · case zero =>
-    simp only [clzAuxRec_zero]
-    by_cases hw1 : w - 1 = 0
-    · by_cases hx0 : x.getLsbD 0
-      · simp [hw1, hx0]
-      · simp [hw1, show ¬ w = 0 by omega, hx0, ← getLsbD_eq_getElem]
-    · by_cases hx0 : x.getLsbD 0
-      · simp only [hx0, ↓reduceIte, toNat_ofNat,
-          Nat.mod_eq_of_lt (a := w - 1) (b := 2 ^ w) (by omega), show ¬w - 1 = 0 by omega, false_iff,
-          Bool.not_eq_true]
-        specialize h (w - 1) (by omega)
-        exact h
-      · simp [hx0, show ¬ w = 0 by omega]
-        specialize h (w - 1) (by omega)
-        exact h
-  · case succ n ihn =>
-    by_cases hxn : x.getLsbD (n + 1)
-    · simp only [clzAuxRec_succ, hxn, reduceIte, toNat_ofNat]
-      rw [Nat.mod_eq_of_lt (by omega)]
-      by_cases hwn : w - 1 - (n + 1) = 0
-      · have := lt_of_getLsbD hxn
-        simp only [show w - 1 = n + 1 by omega, Nat.sub_self, true_iff]
-        exact hxn
-      · simp only [hwn, false_iff, Bool.not_eq_true]
-        specialize h (w - 1) (by omega)
-        exact h
-    · simp only [clzAuxRec_succ, hxn, Bool.false_eq_true, reduceIte]
-      apply ihn
-      intro i hi
-      by_cases hi : i = n + 1
-      · simp [hi, hxn]
-      · apply h; omega
-
-theorem clz_eq_zero_iff {x : BitVec w} (hw : 0 < w) :
-    (clz x).toNat = 0 ↔ 2 ^ (w - 1) ≤ x.toNat := by
-  simp only [clz, clzAuxRec_eq_zero_iff (x := x) (n := w - 1) (by intro i hi; simp [show w ≤ i by omega]) hw]
-  by_cases hxw : x[w - 1]
-  · simp [hxw, two_pow_le_toNat_of_getElem_eq_true (x := x) (i := w - 1) (by omega) hxw]
-  · simp only [hxw, Bool.false_eq_true, false_iff, Nat.not_le]
-    simp only [← getLsbD_eq_getElem, ← msb_eq_getLsbD_last, Bool.not_eq_true] at hxw
-    exact toNat_lt_of_msb_false hxw
-
-/-- The number of leading zeroes is strictly less than the bitwidth iff the bitvector is nonzero. -/
-theorem clz_lt_iff_ne_zero {x : BitVec w} :
-    clz x < w ↔ x ≠ 0#w := by
-  have hle := clz_le (x := x)
-  have heq := clz_eq_iff_eq_zero (x := x)
-  constructor
-  · intro h
-    simp only [natCast_eq_ofNat, BitVec.ne_of_lt (x := x.clz) (y := BitVec.ofNat w w) h,
-      false_iff] at heq
-    simp only [ne_eq, heq, not_false_eq_true]
-  · intro h
-    simp only [natCast_eq_ofNat, h, iff_false] at heq
-    apply BitVec.lt_of_le_ne (x := x.clz) (y := BitVec.ofNat w w) hle heq
-
-theorem getLsbD_false_of_clzAuxRec {x : BitVec w} (h : ∀ i, n < i → x.getLsbD i = false) :
-    ∀ j, x.getLsbD (w - (x.clzAuxRec n).toNat + j) = false := by
-  rcases w with _|w
-  · simp
-  · have := Nat.lt_pow_self (a := 2) (n := w + 1)
-    induction n
-    · case zero =>
-      intro j
-      simp only [clzAuxRec_zero, Nat.zero_lt_succ, getLsbD_eq_getElem, Nat.add_one_sub_one]
-      by_cases hx0 : x[0]
-      · specialize h (1 + j) (by omega)
-        simp [h, hx0, Nat.mod_eq_of_lt (a := w) (b := 2 ^ (w + 1)) (by omega)]
-      · simp only [hx0, Bool.false_eq_true, ↓reduceIte, toNat_ofNat, Nat.mod_two_pow_self,
-          Nat.sub_self, Nat.zero_add]
-        by_cases hj0 : j = 0
-        · simp [hj0, hx0]
-        · specialize h j (by omega)
-          exact h
-    · case succ n ihn =>
-      intro j
-      by_cases hxn : x.getLsbD (n + 1)
-      · have := lt_of_getLsbD hxn
-        specialize h (n + j + 1 + 1) (by omega)
-        simp [h, clzAuxRec_succ, hxn, Nat.mod_eq_of_lt (a := w - (n + 1)) (b := 2 ^ (w + 1)) (by omega),
-          show (w + 1 - (w - (n + 1)) + j) = n + j + 1 + 1 by omega]
-      · simp only [clzAuxRec_succ, hxn, Bool.false_eq_true, reduceIte]
-        apply ihn
-        intro i hi
-        by_cases hin : i = n + 1
-        · simp [hin, hxn]
-        · specialize h i (by omega)
-          exact h
-
-theorem getLsbD_true_of_eq_clzAuxRec_of_ne_zero {x : BitVec w} (hx : ¬ x = 0#w) (hn : ∀ i, n < i → x.getLsbD i = false) :
-    x.getLsbD (w - 1 - (x.clzAuxRec n).toNat) = true := by
-  rcases w with _|w
-  · simp [of_length_zero] at hx
-  · have := Nat.lt_pow_self (a := 2) (n := w + 1)
-    induction n
-    · case zero =>
-      by_cases hx0 : x[0]
-      · simp only [Nat.add_one_sub_one, clzAuxRec_zero, Nat.zero_lt_succ, getLsbD_eq_getElem, hx0,
-          reduceIte, toNat_ofNat, Nat.mod_eq_of_lt (a := w) (b := 2 ^(w + 1)) (by omega), show w - w = 0 by omega]
-      · simp only [zero_iff_eq_false, Classical.not_forall, Bool.not_eq_false] at hx
-        obtain ⟨m,hm⟩ := hx
-        specialize hn m
-        by_cases hm0 : m = 0
-        · simp [hm0, hx0] at hm
-        · simp [show 0 < m by omega, hm] at hn
-    · case succ n ihn =>
-      by_cases hxn : x.getLsbD (n + 1)
-      · have := lt_of_getLsbD hxn
-        simp [clzAuxRec_succ, hxn, toNat_ofNat, Nat.mod_eq_of_lt (a := w - (n + 1)) (b := 2 ^ (w + 1)) (by omega),
-          show w - (w - (n + 1)) = n + 1 by omega]
-      · simp only [Nat.add_one_sub_one, clzAuxRec_succ, hxn, Bool.false_eq_true, reduceIte]
-        simp only [Nat.add_one_sub_one] at ihn
-        apply ihn
-        intro j hj
-        by_cases hjn : j = n + 1
-        · simp [hjn, hxn]
-        · specialize hn j (by omega)
-          exact hn
-
-theorem getLsbD_true_clz_of_ne_zero {x : BitVec w} (hw : 0 < w) (hx : x ≠ 0#w) :
-    x.getLsbD (w - 1 - (clz x).toNat) = true := by
-  unfold clz
-  apply getLsbD_true_of_eq_clzAuxRec_of_ne_zero (x := x) (n := w - 1) (by omega)
-  intro i hi
-  simp [show w ≤ i by omega]
-
-/-- A nonzero bitvector is lower-bounded by its leading zeroes. -/
-theorem two_pow_sub_clz_le_toNat_of_ne_zero {x : BitVec w} (hw : 0 < w) (hx : x ≠ 0#w) :
-    2 ^ (w - 1 - (clz x).toNat) ≤ x.toNat := by
-  by_cases hc0 : x.clz.toNat  = 0
-  · simp [hc0, ← clz_eq_zero_iff (x := x) hw]
-  · have hclz := getLsbD_true_clz_of_ne_zero (x := x) hw hx
-    rw [getLsbD_eq_getElem (by omega)] at hclz
-    have hge := Nat.ge_two_pow_of_testBit hclz
-    push_cast at hge
-    exact hge
-
-/-- A bitvector is upper bounded by the number of leading zeroes. -/
-theorem toNat_lt_two_pow_sub_clz {x : BitVec w} :
-    x.toNat < 2 ^ (w - (clz x).toNat) := by
-  rcases w with _|w
-  · simp [of_length_zero]
-  · unfold clz
-    have hlt := toNat_lt_iff_getLsbD_eq_false (x := x)
-    have hzero := clzAuxRec_eq_zero_iff (x := x) (n := w) (by intro i hi; simp [show w + 1 ≤ i by omega]) (by omega)
-    simp only [Nat.add_one_sub_one] at hzero
-    by_cases hxw : x[w]
-    · simp only [hxw, iff_true] at hzero
-      simp only [Nat.add_one_sub_one, hzero, Nat.sub_zero, gt_iff_lt]
-      omega
-    · simp only [hxw, Bool.false_eq_true, iff_false] at hzero
-      rw [hlt]
-      · intro k
-        apply getLsbD_false_of_clzAuxRec (x := x) (n := w)
-        intro i hi
-        by_cases hiw : i = w
-        · simp [hiw, hxw]
-        · simp [show w + 1 ≤ i by omega]
-      · simp; omega
-
-theorem clz_eq_reverse_ctz {x : BitVec w} :
-    x.clz = (x.reverse).ctz := by
-  simp [ctz]
-
-/-! ### Count trailing zeros -/
-
-theorem ctz_eq_reverse_clz {x : BitVec w} :
-    x.ctz = (x.reverse).clz := by
-  simp [ctz]
-
-/-- The number of trailing zeroes is strictly less than the bitwidth iff the bitvector is nonzero. -/
-@[simp]
-theorem ctz_lt_iff_ne_zero {x : BitVec w} :
-    ctz x < w ↔ x ≠ 0#w := by
-  simp only [ctz_eq_reverse_clz, natCast_eq_ofNat, ne_eq]
-  rw [show BitVec.ofNat w w = w by simp, ← reverse_eq_zero_iff (x := x)]
-  apply clz_lt_iff_ne_zero (x := x.reverse)
-
-/-- If a bitvec is different than zero the bits at indexes lower than `ctz x` are false. -/
-theorem getLsbD_false_of_lt_ctz {x : BitVec w} (hi : i < x.ctz.toNat) :
-    x.getLsbD i = false := by
-  rw [getLsbD_eq_getMsbD, ← getLsbD_reverse]
-  have hiff := ctz_lt_iff_ne_zero (x := x)
-  by_cases hzero : x = 0#w
-  · simp [hzero, getLsbD_reverse]
-  · simp only [ctz_eq_reverse_clz, natCast_eq_ofNat, ne_eq, hzero, not_false_eq_true,
-      iff_true] at hiff
-    simp only [ctz] at hi
-    have hi' : i < w := by simp [BitVec.lt_def] at hiff; omega
-    simp only [hi', decide_true, Bool.true_and]
-    have : (x.reverse.clzAuxRec (w - 1)).toNat ≤ w := by
-      rw [show ((x.reverse.clzAuxRec (w - 1)).toNat ≤ w) =
-            ((x.reverse.clzAuxRec (w - 1)).toNat ≤ (BitVec.ofNat w w).toNat) by simp, ← le_def]
-      apply clzAuxRec_le (x := x.reverse) (n := w - 1)
-    let j := (x.reverse.clzAuxRec (w - 1)).toNat - 1 - i
-    rw [show w - 1 - i = w - (x.reverse.clzAuxRec (w - 1)).toNat + j by
-      subst j
-      rw [Nat.sub_sub (n := (x.reverse.clzAuxRec (w - 1)).toNat),
-        ← Nat.add_sub_assoc (by exact Nat.one_add_le_iff.mpr hi)]
-      omega]
-    have hfalse : ∀ (i : Nat), w - 1 < i → x.reverse.getLsbD i = false := by
-      intros i hj
-      simp [show w ≤ i by omega]
-    exact getLsbD_false_of_clzAuxRec (x := x.reverse) (n := w - 1) hfalse (j := j)
-
-/-- If a bitvec is different than zero, the bit at index `ctz x`, i.e., the first bit after the
-  trailing zeros, is true. -/
-theorem getLsbD_true_ctz_of_ne_zero {x : BitVec w} (hx : x ≠ 0#w) :
-    x.getLsbD (ctz x).toNat = true := by
-  simp only [ctz_eq_reverse_clz, clz]
-  rw [getLsbD_eq_getMsbD, ← getLsbD_reverse]
-  have := ctz_lt_iff_ne_zero (x := x)
-  simp only [ctz_eq_reverse_clz, clz, natCast_eq_ofNat, lt_def, toNat_ofNat, Nat.mod_two_pow_self,
-    ne_eq] at this
-  simp only [this, hx, not_false_eq_true, decide_true, Bool.true_and]
-  have hnotrev : ¬x.reverse = 0#w := by simp [reverse_eq_zero_iff, hx]
-  apply getLsbD_true_of_eq_clzAuxRec_of_ne_zero (x := x.reverse) (n := w - 1) hnotrev
-  intro i hi
-  simp [show w ≤ i by omega]
-
-/-- A nonzero bitvector is lower-bounded by its trailing zeroes. -/
-theorem two_pow_ctz_le_toNat_of_ne_zero {x : BitVec w} (hx : x ≠ 0#w) :
-    2 ^ (ctz x).toNat ≤ x.toNat := by
-  have hclz := getLsbD_true_ctz_of_ne_zero (x := x) hx
-  exact Nat.ge_two_pow_of_testBit hclz
-
 /-! ### Deprecations -/
 
 set_option linter.missingDocs false

src/Init/Data/Bool.lean

@@ -10,6 +10,7 @@ public import Init.NotationExtra
 
 public section
 
+
 namespace Bool
 
 /--

src/Init/Data/ByteArray.lean

@@ -7,8 +7,5 @@ module
 
 prelude
 public import Init.Data.ByteArray.Basic
-public import Init.Data.ByteArray.Bootstrap
-public import Init.Data.ByteArray.Extra
-public import Init.Data.ByteArray.Lemmas
 
 public section

src/Init/Data/ByteArray/Basic.lean

@@ -6,16 +6,25 @@ Author: Leonardo de Moura
 module
 
 prelude
+public import Init.Data.Array.Basic
 public import Init.Data.Array.DecidableEq
 public import Init.Data.UInt.Basic
 public import Init.Data.UInt.BasicAux
 import all Init.Data.UInt.BasicAux
 public import Init.Data.Option.Basic
-public import Init.Data.Array.Extract
 
 @[expose] public section
 universe u
 
+set_option genInjectivity false in
+structure ByteArray where
+  data : Array UInt8
+
+attribute [extern "lean_byte_array_mk"] ByteArray.mk
+attribute [extern "lean_byte_array_data"] ByteArray.data
+
+gen_injective_theorems% ByteArray
+
 namespace ByteArray
 
 deriving instance BEq for ByteArray
@@ -25,15 +34,29 @@ attribute [ext] ByteArray
 instance : DecidableEq ByteArray :=
   fun _ _ => decidable_of_decidable_of_iff ByteArray.ext_iff.symm
 
+@[extern "lean_mk_empty_byte_array"]
+def emptyWithCapacity (c : @& Nat) : ByteArray :=
+  { data := #[] }
+
 @[deprecated emptyWithCapacity (since := "2025-03-12")]
 abbrev mkEmpty := emptyWithCapacity
 
+def empty : ByteArray := emptyWithCapacity 0
+
 instance : Inhabited ByteArray where
   default := empty
 
 instance : EmptyCollection ByteArray where
   emptyCollection := ByteArray.empty
 
+@[extern "lean_byte_array_push"]
+def push : ByteArray → UInt8 → ByteArray
+  | ⟨bs⟩, b => ⟨bs.push b⟩
+
+@[extern "lean_byte_array_size"]
+def size : (@& ByteArray) → Nat
+  | ⟨bs⟩ => bs.size
+
 @[extern "lean_sarray_size", simp]
 def usize (a : @& ByteArray) : USize :=
   a.size.toUSize
@@ -87,31 +110,11 @@ def copySlice (src : @& ByteArray) (srcOff : Nat) (dest : ByteArray) (destOff le
 def extract (a : ByteArray) (b e : Nat) : ByteArray :=
   a.copySlice b empty 0 (e - b)
 
-protected def fastAppend (a : ByteArray) (b : ByteArray) : ByteArray :=
+protected def append (a : ByteArray) (b : ByteArray) : ByteArray :=
   -- we assume that `append`s may be repeated, so use asymptotic growing; use `copySlice` directly to customize
   b.copySlice 0 a a.size b.size false
 
-@[simp]
-theorem size_data {a : ByteArray} :
-  a.data.size = a.size := rfl
-
-@[csimp]
-theorem append_eq_fastAppend : @ByteArray.append = @ByteArray.fastAppend := by
-  funext a b
-  ext1
-  apply Array.ext'
-  simp [ByteArray.fastAppend, copySlice, ← size_data, - Array.append_assoc]
-
--- Needs to come after the `csimp` lemma
-instance : Append ByteArray where
-  append := ByteArray.append
-
-@[simp]
-theorem append_eq {a b : ByteArray} : a.append b = a ++ b := rfl
-
-@[simp]
-theorem fastAppend_eq {a b : ByteArray} : a.fastAppend b = a ++ b := by
-  simp [← append_eq_fastAppend]
+instance : Append ByteArray := ⟨ByteArray.append⟩
 
 def toList (bs : ByteArray) : List UInt8 :=
   let rec loop (i : Nat) (r : List UInt8) :=
@@ -351,4 +354,37 @@ def prevn : Iterator → Nat → Iterator
 end Iterator
 end ByteArray
 
+/--
+Converts a list of bytes into a `ByteArray`.
+-/
+def List.toByteArray (bs : List UInt8) : ByteArray :=
+  let rec loop
+    | [],    r => r
+    | b::bs, r => loop bs (r.push b)
+  loop bs ByteArray.empty
+
 instance : ToString ByteArray := ⟨fun bs => bs.toList.toString⟩
+
+/-- Interpret a `ByteArray` of size 8 as a little-endian `UInt64`. -/
+def ByteArray.toUInt64LE! (bs : ByteArray) : UInt64 :=
+  assert! bs.size == 8
+  (bs.get! 7).toUInt64 <<< 0x38 |||
+  (bs.get! 6).toUInt64 <<< 0x30 |||
+  (bs.get! 5).toUInt64 <<< 0x28 |||
+  (bs.get! 4).toUInt64 <<< 0x20 |||
+  (bs.get! 3).toUInt64 <<< 0x18 |||
+  (bs.get! 2).toUInt64 <<< 0x10 |||
+  (bs.get! 1).toUInt64 <<< 0x8  |||
+  (bs.get! 0).toUInt64
+
+/-- Interpret a `ByteArray` of size 8 as a big-endian `UInt64`. -/
+def ByteArray.toUInt64BE! (bs : ByteArray) : UInt64 :=
+  assert! bs.size == 8
+  (bs.get! 0).toUInt64 <<< 0x38 |||
+  (bs.get! 1).toUInt64 <<< 0x30 |||
+  (bs.get! 2).toUInt64 <<< 0x28 |||
+  (bs.get! 3).toUInt64 <<< 0x20 |||
+  (bs.get! 4).toUInt64 <<< 0x18 |||
+  (bs.get! 5).toUInt64 <<< 0x10 |||
+  (bs.get! 6).toUInt64 <<< 0x8  |||
+  (bs.get! 7).toUInt64

src/Init/Data/ByteArray/Bootstrap.lean

@@ -1,53 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Author: Markus Himmel
--/
-module
-
-prelude
-public import Init.Prelude
-public import Init.Data.List.Basic
-
-public section
-
-namespace ByteArray
-
-@[simp]
-theorem data_push {a : ByteArray} {b : UInt8} : (a.push b).data = a.data.push b := rfl
-
-@[expose]
-protected def append (a b : ByteArray) : ByteArray :=
-  ⟨⟨a.data.toList ++ b.data.toList⟩⟩
-
-@[simp]
-theorem toList_data_append' {a b : ByteArray} :
-    (a.append b).data.toList = a.data.toList ++ b.data.toList := by
-  have ⟨⟨a⟩⟩ := a
-  have ⟨⟨b⟩⟩ := b
-  rfl
-
-theorem ext : {x y : ByteArray} → x.data = y.data → x = y
-  | ⟨_⟩, ⟨_⟩, rfl => rfl
-
-end ByteArray
-
-@[simp]
-theorem List.toList_data_toByteArray {l : List UInt8} :
-    l.toByteArray.data.toList = l := by
-  rw [List.toByteArray]
-  suffices ∀ a b, (List.toByteArray.loop a b).data.toList = b.data.toList ++ a by
-    simpa using this l ByteArray.empty
-  intro a b
-  fun_induction List.toByteArray.loop a b with simp_all [toList_push]
-where
-  toList_push {xs : Array UInt8} {x : UInt8} : (xs.push x).toList = xs.toList ++ [x] := by
-    have ⟨xs⟩ := xs
-    simp [Array.push, List.concat_eq_append]
-
-theorem List.toByteArray_append' {l l' : List UInt8} :
-    (l ++ l').toByteArray = l.toByteArray.append l'.toByteArray :=
-  ByteArray.ext (ext (by simp))
-where
-  ext : {x y : Array UInt8} → x.toList = y.toList → x = y
-  | ⟨_⟩, ⟨_⟩, rfl => rfl

src/Init/Data/ByteArray/Extra.lean

@@ -1,34 +0,0 @@
-/-
-Copyright (c) 2019 Microsoft Corporation. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Author: Leonardo de Moura
--/
-module
-
-prelude
-public import Init.Data.ByteArray.Basic
-import Init.Data.String.Basic
-
-/-- Interpret a `ByteArray` of size 8 as a little-endian `UInt64`. -/
-public def ByteArray.toUInt64LE! (bs : ByteArray) : UInt64 :=
-  assert! bs.size == 8
-  (bs.get! 7).toUInt64 <<< 0x38 |||
-  (bs.get! 6).toUInt64 <<< 0x30 |||
-  (bs.get! 5).toUInt64 <<< 0x28 |||
-  (bs.get! 4).toUInt64 <<< 0x20 |||
-  (bs.get! 3).toUInt64 <<< 0x18 |||
-  (bs.get! 2).toUInt64 <<< 0x10 |||
-  (bs.get! 1).toUInt64 <<< 0x8  |||
-  (bs.get! 0).toUInt64
-
-/-- Interpret a `ByteArray` of size 8 as a big-endian `UInt64`. -/
-public def ByteArray.toUInt64BE! (bs : ByteArray) : UInt64 :=
-  assert! bs.size == 8
-  (bs.get! 0).toUInt64 <<< 0x38 |||
-  (bs.get! 1).toUInt64 <<< 0x30 |||
-  (bs.get! 2).toUInt64 <<< 0x28 |||
-  (bs.get! 3).toUInt64 <<< 0x20 |||
-  (bs.get! 4).toUInt64 <<< 0x18 |||
-  (bs.get! 5).toUInt64 <<< 0x10 |||
-  (bs.get! 6).toUInt64 <<< 0x8  |||
-  (bs.get! 7).toUInt64

src/Init/Data/ByteArray/Lemmas.lean

@@ -1,252 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Author: Markus Himmel
--/
-module
-
-prelude
-public import Init.Data.ByteArray.Basic
-public import Init.Data.Array.Extract
-
-public section
-
-@[simp]
-theorem ByteArray.data_empty : ByteArray.empty.data = #[] := rfl
-
-@[simp]
-theorem ByteArray.data_extract {a : ByteArray} {b e : Nat} :
-    (a.extract b e).data = a.data.extract b e := by
-  simp [extract, copySlice]
-  by_cases b ≤ e
-  · rw [(by omega : b + (e - b) = e)]
-  · rw [Array.extract_eq_empty_of_le (by omega), Array.extract_eq_empty_of_le (by omega)]
-
-@[simp]
-theorem ByteArray.extract_zero_size {b : ByteArray} : b.extract 0 b.size = b := by
-  ext1
-  simp
-
-@[simp]
-theorem ByteArray.extract_same {b : ByteArray} {i : Nat} : b.extract i i = ByteArray.empty := by
-  ext1
-  simp [Nat.min_le_left]
-
-theorem ByteArray.fastAppend_eq_copySlice {a b : ByteArray} :
-  a.fastAppend b = b.copySlice 0 a a.size b.size false := rfl
-
-@[simp]
-theorem List.toByteArray_append {l l' : List UInt8} :
-    (l ++ l').toByteArray = l.toByteArray ++ l'.toByteArray := by
-  simp [List.toByteArray_append']
-
-@[simp]
-theorem ByteArray.toList_data_append {l l' : ByteArray} :
-    (l ++ l').data.toList = l.data.toList ++ l'.data.toList := by
-  simp [← append_eq]
-
-@[simp]
-theorem ByteArray.data_append {l l' : ByteArray} :
-    (l ++ l').data = l.data ++ l'.data := by
-  simp [← Array.toList_inj]
-
-@[simp]
-theorem ByteArray.size_empty : ByteArray.empty.size = 0 := by
-  simp [← ByteArray.size_data]
-
-@[simp]
-theorem List.data_toByteArray {l : List UInt8} :
-    l.toByteArray.data = l.toArray := by
-  rw [List.toByteArray]
-  suffices ∀ a b, (List.toByteArray.loop a b).data = b.data ++ a.toArray by
-    simpa using this l ByteArray.empty
-  intro a b
-  fun_induction List.toByteArray.loop a b with simp_all
-
-@[simp]
-theorem List.size_toByteArray {l : List UInt8} :
-    l.toByteArray.size = l.length := by
-  simp [← ByteArray.size_data]
-
-@[simp]
-theorem List.toByteArray_nil : List.toByteArray [] = ByteArray.empty := rfl
-
-@[simp]
-theorem ByteArray.empty_append {b : ByteArray} : ByteArray.empty ++ b = b := by
-  ext1
-  simp
-
-@[simp]
-theorem ByteArray.append_empty {b : ByteArray} : b ++ ByteArray.empty = b := by
-  ext1
-  simp
-
-@[simp, grind =]
-theorem ByteArray.size_append {a b : ByteArray} : (a ++ b).size = a.size + b.size := by
-  simp [← size_data]
-
-@[simp]
-theorem ByteArray.size_eq_zero_iff {a : ByteArray} : a.size = 0 ↔ a = ByteArray.empty := by
-  refine ⟨fun h => ?_, fun h => h ▸ ByteArray.size_empty⟩
-  ext1
-  simp [← Array.size_eq_zero_iff, h]
-
-theorem ByteArray.getElem_eq_getElem_data {a : ByteArray} {i : Nat} {h : i < a.size} :
-    a[i] = a.data[i]'(by simpa [← size_data]) := rfl
-
-@[simp]
-theorem ByteArray.getElem_append_left {i : Nat} {a b : ByteArray} {h : i < (a ++ b).size}
-    (hlt : i < a.size) : (a ++ b)[i] = a[i] := by
-  simp only [getElem_eq_getElem_data, data_append]
-  rw [Array.getElem_append_left (by simpa)]
-
-theorem ByteArray.getElem_append_right {i : Nat} {a b : ByteArray} {h : i < (a ++ b).size}
-    (hle : a.size ≤ i) : (a ++ b)[i] = b[i - a.size]'(by simp_all; omega) := by
-  simp only [getElem_eq_getElem_data, data_append]
-  rw [Array.getElem_append_right (by simpa)]
-  simp
-
-@[simp]
-theorem List.getElem_toByteArray {l : List UInt8} {i : Nat} {h : i < l.toByteArray.size} :
-    l.toByteArray[i]'h = l[i]'(by simp_all) := by
-  simp [ByteArray.getElem_eq_getElem_data]
-
-theorem List.getElem_eq_getElem_toByteArray {l : List UInt8} {i : Nat} {h : i < l.length} :
-    l[i]'h = l.toByteArray[i]'(by simp_all) := by
-  simp
-
-@[simp]
-theorem ByteArray.size_extract {a : ByteArray} {b e : Nat} :
-    (a.extract b e).size = min e a.size - b := by
-  simp [← size_data]
-
-@[simp]
-theorem ByteArray.extract_eq_empty_iff {b : ByteArray} {i j : Nat} : b.extract i j = ByteArray.empty ↔ min j b.size ≤ i := by
-  rw [← size_eq_zero_iff, size_extract]
-  omega
-
-@[simp]
-theorem ByteArray.extract_add_left {b : ByteArray} {i j : Nat} : b.extract (i + j) i = ByteArray.empty := by
-  simp only [extract_eq_empty_iff]
-  exact Nat.le_trans (Nat.min_le_left _ _) (by simp)
-
-@[simp]
-theorem ByteArray.append_eq_empty_iff {a b : ByteArray} :
-    a ++ b = ByteArray.empty ↔ a = ByteArray.empty ∧ b = ByteArray.empty := by
-  simp [← size_eq_zero_iff, size_append]
-
-@[simp]
-theorem List.toByteArray_eq_empty {l : List UInt8} :
-    l.toByteArray = ByteArray.empty ↔ l = [] := by
-  simp [← ByteArray.size_eq_zero_iff]
-
-theorem ByteArray.append_right_inj {ys₁ ys₂ : ByteArray} (xs : ByteArray) :
-    xs ++ ys₁ = xs ++ ys₂ ↔ ys₁ = ys₂ := by
-  simp [ByteArray.ext_iff, Array.append_right_inj]
-
-@[simp]
-theorem ByteArray.extract_append_extract {a : ByteArray} {i j k : Nat} :
-    a.extract i j ++ a.extract j k = a.extract (min i j) (max j k) := by
-  ext1
-  simp
-
-theorem ByteArray.extract_eq_extract_append_extract {a : ByteArray} {i k : Nat} (j : Nat)
-    (hi : i ≤ j) (hk : j ≤ k) :
-    a.extract i k = a.extract i j ++ a.extract j k := by
-  simp
-  rw [Nat.min_eq_left hi, Nat.max_eq_right hk]
-
-theorem ByteArray.append_inj_left {xs₁ xs₂ ys₁ ys₂ : ByteArray} (h : xs₁ ++ ys₁ = xs₂ ++ ys₂) (hl : xs₁.size = xs₂.size) : xs₁ = xs₂ := by
-  simp only [ByteArray.ext_iff, ← ByteArray.size_data, ByteArray.data_append] at *
-  exact Array.append_inj_left h hl
-
-theorem ByteArray.extract_append_eq_right {a b : ByteArray} {i : Nat} (hi : i = a.size) :
-    (a ++ b).extract i (a ++ b).size = b := by
-  subst hi
-  ext1
-  simp [← size_data]
-
-theorem ByteArray.extract_append_eq_left {a b : ByteArray} {i : Nat} (hi : i = a.size) :
-    (a ++ b).extract 0 i = a := by
-  subst hi
-  ext1
-  simp
-
-theorem ByteArray.extract_append_size_left {a b : ByteArray} {i : Nat} :
-    (a ++ b).extract i a.size = a.extract i a.size := by
-  ext1
-  simp
-
-theorem ByteArray.extract_append_size_add {a b : ByteArray} {i j : Nat} :
-    (a ++ b).extract (a.size + i) (a.size + j) = b.extract i j := by
-  ext1
-  simp
-
-theorem ByteArray.extract_append  {as bs : ByteArray} {i j : Nat} :
-    (as ++ bs).extract i j = as.extract i j ++ bs.extract (i - as.size) (j - as.size) := by
-  ext1
-  simp
-
-theorem ByteArray.extract_append_size_add' {a b : ByteArray} {i j k : Nat} (h : k = a.size) :
-    (a ++ b).extract (k + i) (k + j) = b.extract i j := by
-  cases h
-  rw [extract_append_size_add]
-
-theorem ByteArray.extract_extract {a : ByteArray} {i j k l : Nat} :
-    (a.extract i j).extract k l = a.extract (i + k) (min (i + l) j) := by
-  ext1
-  simp
-
-theorem ByteArray.getElem_extract_aux {xs : ByteArray} {start stop : Nat} (h : i < (xs.extract start stop).size) :
-    start + i < xs.size := by
-  rw [size_extract] at h; apply Nat.add_lt_of_lt_sub'; apply Nat.lt_of_lt_of_le h
-  apply Nat.sub_le_sub_right; apply Nat.min_le_right
-
-theorem ByteArray.getElem_extract {i : Nat} {b : ByteArray} {start stop : Nat}
-    (h) : (b.extract start stop)[i]'h = b[start + i]'(getElem_extract_aux h) := by
-  simp [getElem_eq_getElem_data]
-
-theorem ByteArray.extract_eq_extract_left {a : ByteArray} {i i' j : Nat} :
-    a.extract i j = a.extract i' j ↔ min j a.size - i = min j a.size - i' := by
-  simp [ByteArray.ext_iff, Array.extract_eq_extract_left]
-
-theorem ByteArray.extract_add_one {a : ByteArray} {i : Nat} (ha : i + 1 ≤ a.size) :
-    a.extract i (i + 1) = [a[i]].toByteArray := by
-  ext
-  · simp
-    omega
-  · rename_i j hj hj'
-    obtain rfl : j = 0 := by simpa using hj'
-    simp [ByteArray.getElem_eq_getElem_data]
-
-theorem ByteArray.extract_add_two {a : ByteArray} {i : Nat} (ha : i + 2 ≤ a.size) :
-    a.extract i (i + 2) = [a[i], a[i + 1]].toByteArray := by
-  rw [extract_eq_extract_append_extract (i + 1) (by simp) (by omega),
-    extract_add_one (by omega), extract_add_one (by omega)]
-  simp [← List.toByteArray_append]
-
-theorem ByteArray.extract_add_three {a : ByteArray} {i : Nat} (ha : i + 3 ≤ a.size) :
-    a.extract i (i + 3) = [a[i], a[i + 1], a[i + 2]].toByteArray := by
-  rw [extract_eq_extract_append_extract (i + 1) (by simp) (by omega),
-    extract_add_one (by omega), extract_add_two (by omega)]
-  simp [← List.toByteArray_append]
-
-theorem ByteArray.extract_add_four {a : ByteArray} {i : Nat} (ha : i + 4 ≤ a.size) :
-    a.extract i (i + 4) = [a[i], a[i + 1], a[i + 2], a[i + 3]].toByteArray := by
-  rw [extract_eq_extract_append_extract (i + 1) (by simp) (by omega),
-    extract_add_one (by omega), extract_add_three (by omega)]
-  simp [← List.toByteArray_append]
-
-theorem ByteArray.append_assoc {a b c : ByteArray} : a ++ b ++ c = a ++ (b ++ c) := by
-  ext1
-  simp
-
-@[simp]
-theorem ByteArray.toList_empty : ByteArray.empty.toList = [] := by
-  simp [ByteArray.toList, ByteArray.toList.loop]
-
-theorem ByteArray.copySlice_eq_append {src : ByteArray} {srcOff : Nat} {dest : ByteArray} {destOff len : Nat} {exact : Bool} :
-    ByteArray.copySlice src srcOff dest destOff len exact =
-      dest.extract 0 destOff ++ src.extract srcOff (srcOff +len) ++ dest.extract (destOff + min len (src.data.size - srcOff)) dest.data.size := by
-  ext1
-  simp [copySlice]

src/Init/Data/Char/Lemmas.lean

@@ -66,6 +66,11 @@ instance leTotal : Std.Total (· ≤ · : Char → Char → Prop) where
 def notLTTotal : Std.Total (¬ · < · : Char → Char → Prop) where
   total := fun x y => by simpa using Char.le_total y x
 
+theorem utf8Size_eq (c : Char) : c.utf8Size = 1 ∨ c.utf8Size = 2 ∨ c.utf8Size = 3 ∨ c.utf8Size = 4 := by
+  have := c.utf8Size_pos
+  have := c.utf8Size_le_four
+  omega
+
 @[simp] theorem ofNat_toNat (c : Char) : Char.ofNat c.toNat = c := by
   rw [Char.ofNat, dif_pos]
   rfl

src/Init/Data/Dyadic.lean

@@ -9,4 +9,3 @@ prelude
 public import Init.Data.Dyadic.Basic
 public import Init.Data.Dyadic.Instances
 public import Init.Data.Dyadic.Round
-public import Init.Data.Dyadic.Inv

src/Init/Data/Dyadic/Basic.lean

@@ -75,7 +75,7 @@ theorem trailingZeros_two_mul {i : Int} (h : i ≠ 0) :
 
 theorem shiftRight_trailingZeros_mod_two {i : Int} (h : i ≠ 0) :
     (i >>> i.trailingZeros) % 2 = 1 := by
-  rw (occs := .pos [2]) [← Int.emod_add_mul_ediv i 2]
+  rw (occs := .pos [2]) [← Int.emod_add_ediv i 2]
   rcases i.emod_two_eq with h' | h' <;> rw [h']
   · rcases Int.dvd_of_emod_eq_zero h' with ⟨a, rfl⟩
     simp only [ne_eq, Int.mul_eq_zero, Int.reduceEq, false_or] at h
@@ -92,7 +92,7 @@ theorem two_pow_trailingZeros_dvd {i : Int} (h : i ≠ 0) :
     simp only [ne_eq, Int.mul_eq_zero, Int.reduceEq, false_or] at h
     rw [trailingZeros_two_mul h, Int.pow_succ']
     exact Int.mul_dvd_mul_left _ (two_pow_trailingZeros_dvd h)
-  · rw (occs := .pos [1]) [← Int.emod_add_mul_ediv i 2, h', Int.add_comm, trailingZeros_two_mul_add_one]
+  · rw (occs := .pos [1]) [← Int.emod_add_ediv i 2, h', Int.add_comm, trailingZeros_two_mul_add_one]
     exact Int.one_dvd _
 termination_by i.natAbs
 
@@ -415,22 +415,16 @@ theorem precision_ofIntWithPrec_le {i : Int} (h : i ≠ 0) (prec : Int) :
   | .zero => rfl
   | .ofOdd _ _ _ => rfl
 
-end Dyadic
-
-namespace Rat
-
-open Dyadic
-
 /--
 Convert a rational number `x` to the greatest dyadic number with precision at most `prec`
 which is less than or equal to `x`.
 -/
-def toDyadic (x : Rat) (prec : Int) : Dyadic :=
+def _root_.Rat.toDyadic (x : Rat) (prec : Int) : Dyadic :=
   match prec with
   | (n : Nat) => .ofIntWithPrec ((x.num <<< n) / x.den) prec
   | -(n + 1 : Nat) => .ofIntWithPrec (x.num / (x.den <<< (n + 1))) prec
 
-theorem toDyadic_mkRat (a : Int) (b : Nat) (prec : Int) :
+theorem _root_.Rat.toDyadic_mkRat (a : Int) (b : Nat) (prec : Int) :
     Rat.toDyadic (mkRat a b) prec =
       .ofIntWithPrec ((a <<< prec.toNat) / (b <<< (-prec).toNat)) prec := by
   by_cases hb : b = 0
@@ -438,96 +432,15 @@ theorem toDyadic_mkRat (a : Int) (b : Nat) (prec : Int) :
   rcases h : mkRat a b with ⟨n, d, hnz, hr⟩
   obtain ⟨m, hm, rfl, rfl⟩ := Rat.mkRat_num_den hb h
   cases prec
-  · simp only [Rat.toDyadic, Int.ofNat_eq_coe, Int.toNat_natCast, Int.toNat_neg_natCast,
+  · simp only [Rat.toDyadic, Int.ofNat_eq_coe, Int.toNat_natCast, Int.toNat_neg_nat,
       shiftLeft_zero, Int.natCast_mul]
     rw [Int.mul_comm d, ← Int.ediv_ediv (by simp), ← Int.shiftLeft_mul,
       Int.mul_ediv_cancel _ (by simpa using hm)]
   · simp only [Rat.toDyadic, Int.natCast_shiftLeft, Int.negSucc_eq, ← Int.natCast_add_one,
-      Int.toNat_neg_natCast, Int.shiftLeft_zero, Int.neg_neg, Int.toNat_natCast, Int.natCast_mul]
+      Int.toNat_neg_nat, Int.shiftLeft_zero, Int.neg_neg, Int.toNat_natCast, Int.natCast_mul]
     rw [Int.mul_comm d, ← Int.mul_shiftLeft, ← Int.ediv_ediv (by simp),
       Int.mul_ediv_cancel _ (by simpa using hm)]
 
-theorem toDyadic_eq_ofIntWithPrec (x : Rat) (prec : Int) :
-    x.toDyadic prec = .ofIntWithPrec ((x.num <<< prec.toNat) / (x.den <<< (-prec).toNat)) prec := by
-  conv => lhs; rw [← Rat.mkRat_self x]
-  rw [Rat.toDyadic_mkRat]
-
-/--
-Converting a rational to a dyadic at a given precision and then back to a rational
-gives the same result as taking the floor of the rational at precision `2 ^ prec`.
--/
-theorem toRat_toDyadic (x : Rat) (prec : Int) :
-    (x.toDyadic prec).toRat = (x * 2 ^ prec).floor / 2 ^ prec := by
-  rw [Rat.toDyadic_eq_ofIntWithPrec, toRat_ofIntWithPrec_eq_mul_two_pow, Rat.zpow_neg, Rat.div_def]
-  congr 2
-  rw [Rat.floor_def, Int.shiftLeft_eq, Nat.shiftLeft_eq]
-  match prec with
-  | .ofNat prec =>
-    simp only [Int.ofNat_eq_coe, Int.toNat_natCast, Int.toNat_neg_natCast, Nat.pow_zero,
-      Nat.mul_one]
-    have : (2 ^ prec : Rat) = ((2 ^ prec : Nat) : Rat) := by simp
-    rw [Rat.zpow_natCast, this, Rat.mul_def']
-    simp only [Rat.num_mkRat, Rat.den_mkRat]
-    simp only [Rat.natCast_pow, Rat.natCast_ofNat, Rat.num_pow, Rat.num_ofNat, Rat.den_pow,
-      Rat.den_ofNat, Nat.one_pow, Nat.mul_one]
-    split
-    · simp_all
-    · rw [Int.ediv_ediv (Int.ofNat_zero_le _)]
-      congr 1
-      rw [Int.natCast_ediv, Int.mul_ediv_cancel']
-      rw [Int.natCast_dvd_natCast]
-      apply gcd_dvd_left
-  | .negSucc prec =>
-    simp only [Int.toNat_negSucc, Int.pow_zero, Int.mul_one, Int.neg_negSucc, Int.natCast_mul,
-      Int.natCast_pow, Int.cast_ofNat_Int]
-    have : (2 ^ ((prec : Int) + 1)) = ((2 ^ (prec + 1) : Nat) : Rat) := by simp; rfl
-    rw [Int.negSucc_eq, Rat.zpow_neg, this, Rat.mul_def']
-    simp only [Rat.num_mkRat, Rat.den_mkRat]
-    simp only [natCast_pow, natCast_ofNat, den_inv, num_pow, num_ofNat, Int.natAbs_pow,
-      Int.reduceAbs, num_inv, den_pow, den_ofNat, Nat.one_pow, Int.cast_ofNat_Int, Int.mul_one]
-    have : ¬ (2 ^ (prec + 1) : Int) = 0 := NeZero.out
-    simp only [if_neg this]
-    have : (2 ^ (prec + 1) : Int).sign = 1 := by simpa using Int.pow_pos (by decide)
-    simp only [this]
-    have : x.den * 2 ^ (prec + 1) = 0 ↔ x.den = 0 := by
-      rw [Nat.mul_eq_zero]
-      simp_all
-    simp only [this, Int.mul_one]
-    split
-    · simp_all
-    · rw [Int.ediv_ediv (Int.ofNat_zero_le _)]
-      congr 1
-      rw [Int.natCast_ediv, Int.mul_ediv_cancel']
-      · simp
-      · rw [Int.natCast_dvd_natCast]
-        apply gcd_dvd_left
-
-theorem toRat_toDyadic_le {x : Rat} {prec : Int} : (x.toDyadic prec).toRat ≤ x := by
-  rw [toRat_toDyadic]
-  have : (x * 2 ^ prec).floor ≤ x * 2 ^ prec := Rat.floor_le _
-  apply Rat.le_of_mul_le_mul_right (c := 2 ^ prec)
-  rw [Rat.div_mul_cancel]
-  exact this
-  · apply Rat.ne_of_gt (Rat.zpow_pos (by decide))
-  · exact Rat.zpow_pos (by decide)
-
-theorem lt_toRat_toDyadic_add {x : Rat} {prec : Int} :
-    x < (x.toDyadic prec + ofIntWithPrec 1 prec).toRat := by
-  rw [toRat_add, toRat_toDyadic, toRat_ofIntWithPrec_eq_mul_two_pow]
-  have := Rat.lt_floor_add_one (x * 2 ^ prec)
-  rw [Rat.zpow_neg, Rat.div_def, ← Rat.add_mul]
-  apply Rat.lt_of_mul_lt_mul_right (c := 2 ^ prec)
-  rw [Rat.mul_assoc, Rat.inv_mul_cancel, Rat.mul_one]
-  exact mod_cast this
-  · apply Rat.ne_of_gt (Rat.zpow_pos (by decide))
-  · exact Rat.zpow_nonneg (by decide)
-
--- TODO: `x.toDyadic prec` is the unique dyadic with the given precision satisfying the two inequalities above.
-
-end Rat
-
-namespace Dyadic
-
 /--
 Rounds a dyadic rational `x` down to the greatest dyadic number with precision at most `prec`
 which is less than or equal to `x`.
@@ -566,11 +479,10 @@ theorem toDyadic_toRat (x : Dyadic) (prec : Int) :
     rw [this]
     cases h : k - prec
     · simp
-    · simp only [Int.neg_negSucc, Int.natCast_add, Int.cast_ofNat_Int, Int.toNat_natCast_add_one,
-        Int.toNat_negSucc, Int.shiftRight_zero]
+    · simp
       rw [Int.negSucc_eq, Int.eq_neg_comm, Int.neg_sub, eq_comm, Int.sub_eq_iff_eq_add] at h
-      simp only [h, ← Int.natCast_add_one, Int.add_comm _ k, ofIntWithPrec_shiftLeft_add,
-        ofOdd_eq_ofIntWithPrec]
+      simp only [Int.neg_negSucc, h, ← Int.natCast_add_one, Int.add_comm _ k,
+        Nat.succ_eq_add_one, Int.toNat_natCast, ofIntWithPrec_shiftLeft_add, ofOdd_eq_ofIntWithPrec]
 
 theorem toRat_inj {x y : Dyadic} : x.toRat = y.toRat ↔ x = y := by
   refine ⟨fun h => ?_, fun h => h ▸ rfl⟩
@@ -666,7 +578,7 @@ theorem blt_eq_false_iff : blt x y = false ↔ ble y x = true := by
     rcases k₁ - k₂ with (_ | _) | _
     · simp
     · simp [← Int.negSucc_eq]
-    · simp only [Int.neg_negSucc, decide_eq_false_iff_not, Int.not_lt,
+    · simp only [Int.neg_negSucc, succ_eq_add_one, decide_eq_false_iff_not, Int.not_lt,
         decide_eq_true_eq]
 
 theorem ble_iff_toRat : ble x y ↔ x.toRat ≤ y.toRat := by

src/Init/Data/Dyadic/Instances.lean

@@ -32,9 +32,7 @@ instance : CommRing Dyadic where
   pow_succ := Dyadic.pow_succ
   sub_eq_add_neg _ _ := rfl
   neg_add_cancel := Dyadic.neg_add_cancel
-  neg_zsmul i a := by
-    change ((-i : Int) : Dyadic) * a = -(i * a)
-    simp [← toRat_inj, Rat.neg_mul]
+  neg_zsmul _ _ := by simp [← toRat_inj, Rat.neg_mul]
   left_distrib := Dyadic.mul_add
   right_distrib := Dyadic.add_mul
   intCast_neg _ := by simp [← toRat_inj]
@@ -51,6 +49,13 @@ instance : NoNatZeroDivisors Dyadic where
     simp only [← toRat_inj, toRat_mul, toRat_natCast] at h₂ ⊢
     simpa [← Rat.mul_assoc, Rat.inv_mul_cancel, h₁] using congrArg ((k : Rat)⁻¹ * ·) h₂
 
+instance : LinearOrder Dyadic where
+  le_refl := Dyadic.le_refl
+  le_trans := Dyadic.le_trans
+  le_antisymm := Dyadic.le_antisymm
+  le_total := Dyadic.le_total
+  lt_iff_le_not_le := Std.LawfulOrderLT.lt_iff _ _
+
 instance : OrderedRing Dyadic where
   zero_lt_one := by decide
   add_le_left_iff _ := by simp [le_iff_toRat, Rat.add_le_add_right]

src/Init/Data/Dyadic/Inv.lean

@@ -1,80 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison
--/
-module
-prelude
-import Init.Data.Dyadic.Basic
-import Init.Data.Dyadic.Round
-import Init.Grind.Ordered.Ring
-
-/-!
-# Inversion for dyadic numbers
--/
-
-namespace Dyadic
-
-/--
-Inverts a dyadic number at a given (maximum) precision.
-Returns the greatest dyadic number with precision at most `prec` which is less than or equal to `1/x`.
-For `x = 0`, returns `0`.
--/
-def invAtPrec (x : Dyadic) (prec : Int) : Dyadic :=
-  match x with
-  | .zero => .zero
-  | _ => x.toRat.inv.toDyadic prec
-
-/-- For a positive dyadic `x`, `invAtPrec x prec * x ≤ 1`. -/
-theorem invAtPrec_mul_le_one {x : Dyadic} (hx : 0 < x) (prec : Int) :
-    invAtPrec x prec * x ≤ 1 := by
-  rw [le_iff_toRat]
-  rw [toRat_mul]
-  rw [show (1 : Dyadic).toRat = (1 : Rat) from rfl]
-  unfold invAtPrec
-  cases x with
-  | zero =>
-    exfalso
-    contradiction
-  | ofOdd n k hn =>
-    simp only
-    have h_le : ((ofOdd n k hn).toRat.inv.toDyadic prec).toRat ≤ (ofOdd n k hn).toRat.inv := Rat.toRat_toDyadic_le
-    have h_pos : 0 ≤ (ofOdd n k hn).toRat := by
-      rw [lt_iff_toRat, toRat_zero] at hx
-      exact Rat.le_of_lt hx
-    calc ((ofOdd n k hn).toRat.inv.toDyadic prec).toRat * (ofOdd n k hn).toRat
-        ≤ (ofOdd n k hn).toRat.inv * (ofOdd n k hn).toRat := Rat.mul_le_mul_of_nonneg_right h_le h_pos
-      _ = 1 := by
-        apply Rat.inv_mul_cancel
-        rw [lt_iff_toRat, toRat_zero] at hx
-        exact Rat.ne_of_gt hx
-
-/-- For a positive dyadic `x`, `1 < (invAtPrec x prec + 2^(-prec)) * x`. -/
-theorem one_lt_invAtPrec_add_inc_mul {x : Dyadic} (hx : 0 < x) (prec : Int) :
-    1 < (invAtPrec x prec + ofIntWithPrec 1 prec) * x := by
-  rw [lt_iff_toRat]
-  rw [toRat_mul]
-  rw [show (1 : Dyadic).toRat = (1 : Rat) from rfl]
-  unfold invAtPrec
-  cases x with
-  | zero =>
-    exfalso
-    contradiction
-  | ofOdd n k hn =>
-    simp only
-    have h_le : (ofOdd n k hn).toRat.inv < ((ofOdd n k hn).toRat.inv.toDyadic prec + ofIntWithPrec 1 prec).toRat :=
-      Rat.lt_toRat_toDyadic_add
-    have h_pos : 0 < (ofOdd n k hn).toRat := by
-      rwa [lt_iff_toRat, toRat_zero] at hx
-    calc
-      1 = (ofOdd n k hn).toRat.inv * (ofOdd n k hn).toRat := by
-        symm
-        apply Rat.inv_mul_cancel
-        rw [lt_iff_toRat, toRat_zero] at hx
-        exact Rat.ne_of_gt hx
-      _ < ((ofOdd n k hn).toRat.inv.toDyadic prec + ofIntWithPrec 1 prec).toRat * (ofOdd n k hn).toRat :=
-           Rat.mul_lt_mul_of_pos_right h_le h_pos
-
--- TODO: `invAtPrec` is the unique dyadic with the given precision satisfying the two inequalities above.
-
-end Dyadic

src/Init/Data/Fin/Basic.lean

@@ -51,11 +51,6 @@ The assumption `NeZero n` ensures that `Fin n` is nonempty.
 @[expose] protected def ofNat (n : Nat) [NeZero n] (a : Nat) : Fin n :=
   ⟨a % n, Nat.mod_lt _ (pos_of_neZero n)⟩
 
-@[simp]
-theorem Internal.ofNat_eq_ofNat {n : Nat} {hn} {a : Nat} :
-  letI : NeZero n := ⟨Nat.pos_iff_ne_zero.1 hn⟩
-  Fin.Internal.ofNat n hn a = Fin.ofNat n a := rfl
-
 @[deprecated Fin.ofNat (since := "2025-05-28")]
 protected def ofNat' (n : Nat) [NeZero n] (a : Nat) : Fin n :=
   Fin.ofNat n a

src/Init/Data/Fin/Fold.lean

@@ -122,7 +122,7 @@ private theorem foldlM_loop [Monad m] (f : α → Fin (n+1) → m α) (x) (h : i
     rw [foldlM_loop_lt _ _ h', foldlM_loop]; rfl
   else
     cases Nat.le_antisymm (Nat.le_of_lt_succ h) (Nat.not_lt.1 h')
-    rw [foldlM_loop_lt _ _ h]
+    rw [foldlM_loop_lt]
     congr; funext
     rw [foldlM_loop_eq, foldlM_loop_eq]
 termination_by n - i

src/Init/Data/Fin/Lemmas.lean

@@ -25,12 +25,12 @@ namespace Fin
 
 @[deprecated ofNat_zero (since := "2025-05-28")] abbrev ofNat'_zero := @ofNat_zero
 
-theorem mod_def (a m : Fin n) : a % m = Fin.mk (a.val % m.val) (Nat.lt_of_le_of_lt (Nat.mod_le _ _) a.2) :=
+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
 
-theorem mul_def (a b : Fin n) : a * b = Fin.mk ((a.val * b.val) % n) (Nat.mod_lt _ a.pos) := rfl
+theorem mul_def (a b : Fin n) : a * b = Fin.mk ((a * b) % n) (Nat.mod_lt _ a.pos) := rfl
 
-theorem sub_def (a b : Fin n) : a - b = Fin.mk (((n - b.val) + a.val) % n) (Nat.mod_lt _ a.pos) := rfl
+theorem sub_def (a b : Fin n) : a - b = Fin.mk (((n - b) + a) % n) (Nat.mod_lt _ a.pos) := rfl
 
 theorem pos' : ∀ [Nonempty (Fin n)], 0 < n | ⟨i⟩ => i.pos
 
@@ -81,7 +81,7 @@ theorem mk_val (i : Fin n) : (⟨i, i.isLt⟩ : Fin n) = i := Fin.eta ..
 
 @[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.val) = x := by
+@[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]
   exact x.2
@@ -121,6 +121,8 @@ 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
@@ -263,7 +265,7 @@ instance : LawfulOrderLT (Fin n) where
   lt_iff := by
     simp [← Fin.not_le, Decidable.imp_iff_not_or, Std.Total.total]
 
-@[simp, grind =] theorem val_rev (i : Fin n) : (rev i).val = n - (i + 1) := rfl
+@[simp, grind =] theorem val_rev (i : Fin n) : rev i = n - (i + 1) := rfl
 
 @[simp] theorem rev_rev (i : Fin n) : rev (rev i) = i := Fin.ext <| by
   rw [val_rev, val_rev, ← Nat.sub_sub, Nat.sub_sub_self (by exact i.2), Nat.add_sub_cancel]
@@ -498,11 +500,9 @@ theorem succ_succ_ne_one (a : Fin n) : Fin.succ (Fin.succ a) ≠ 1 :=
   ext
   simp
 
-@[simp, grind =] theorem cast_cast {k : Nat} (h : n = m) (h' : m = k) {i : Fin n} :
+@[simp] theorem cast_trans {k : Nat} (h : n = m) (h' : m = k) {i : Fin n} :
     (i.cast h).cast h' = i.cast (Eq.trans h h') := rfl
 
-@[deprecated cast_cast (since := "2025-09-03")] abbrev cast_trans := @cast_cast
-
 theorem castLE_of_eq {m n : Nat} (h : m = n) {h' : m ≤ n} : castLE h' = Fin.cast h := rfl
 
 @[simp] theorem coe_castAdd (m : Nat) (i : Fin n) : (castAdd m i : Nat) = i := rfl
@@ -531,7 +531,7 @@ theorem cast_castAdd_left {n n' m : Nat} (i : Fin n') (h : n' + m = n + m) :
     (i.castAdd m').cast h = i.castAdd m := rfl
 
 theorem castAdd_castAdd {m n p : Nat} (i : Fin m) :
-    (i.castAdd n).castAdd p = (i.castAdd (n + p)).cast (Nat.add_assoc ..).symm := rfl
+    (i.castAdd n).castAdd p = (i.castAdd (n + p)).cast (Nat.add_assoc ..).symm  := rfl
 
 /-- The cast of the successor is the successor of the cast. See `Fin.succ_cast_eq` for rewriting in
 the reverse direction. -/

src/Init/Data/Float.lean

@@ -30,6 +30,7 @@ opaque floatSpec : FloatSpec := {
   decLe := fun _ _ => inferInstanceAs (Decidable True)
 }
 
+set_option genInjectivity false in
 /--
 64-bit floating-point numbers.
 
@@ -500,3 +501,5 @@ This function does not reduce in the kernel.
 -/
 @[extern "lean_float_scaleb"]
 opaque Float.scaleB (x : Float) (i : @& Int) : Float
+
+gen_injective_theorems% Float

src/Init/Data/Float32.lean

@@ -23,6 +23,7 @@ opaque float32Spec : FloatSpec := {
   decLe := fun _ _ => inferInstanceAs (Decidable True)
 }
 
+set_option genInjectivity false in
 /--
 32-bit floating-point numbers.
 
@@ -513,3 +514,5 @@ This may lose precision.
 This function does not reduce in the kernel.
 -/
 @[extern "lean_float_to_float32"] opaque Float.toFloat32 : Float → Float32
+
+gen_injective_theorems% Float32

src/Init/Data/FloatArray/Basic.lean

@@ -15,12 +15,15 @@ public import Init.Data.Array.DecidableEq
 public section
 universe u
 
+set_option genInjectivity false in
 structure FloatArray where
   data : Array Float
 
 attribute [extern "lean_float_array_mk"] FloatArray.mk
 attribute [extern "lean_float_array_data"] FloatArray.data
 
+gen_injective_theorems% FloatArray
+
 namespace FloatArray
 
 deriving instance BEq for FloatArray

src/Init/Data/Format/Basic.lean

@@ -8,7 +8,7 @@ module
 prelude
 public import Init.Control.State
 public import Init.Data.Int.Basic
-public import Init.Data.String.Bootstrap
+public import Init.Data.String.Basic
 
 public section
 
@@ -168,8 +168,8 @@ private def spaceUptoLine : Format → Bool → Int → Nat → SpaceResult
     else
       { foundLine := true }
   | text s,       flatten, _, _ =>
-    let p := String.Internal.posOf s '\n'
-    let off := String.Internal.offsetOfPos s p
+    let p := s.posOf '\n'
+    let off := s.offsetOfPos p
     { foundLine := p != s.endPos, foundFlattenedHardLine := flatten && p != s.endPos, space := off }
   | append f₁ f₂, flatten, m, w => merge w (spaceUptoLine f₁ flatten m w) (spaceUptoLine f₂ flatten m)
   | nest n f,     flatten, m, w => spaceUptoLine f flatten (m - n) w
@@ -263,15 +263,15 @@ private partial def be (w : Nat) [Monad m] [MonadPrettyFormat m] : List WorkGrou
     | append f₁ f₂ => be w (gs' ({ i with f := f₁, activeTags := 0 }::{ i with f := f₂ }::is))
     | nest n f => be w (gs' ({ i with f, indent := i.indent + n }::is))
     | text s =>
-      let p := String.Internal.posOf s '\n'
+      let p := s.posOf '\n'
       if p == s.endPos then
         pushOutput s
         endTags i.activeTags
         be w (gs' is)
       else
-        pushOutput (String.Internal.extract s {} p)
+        pushOutput (s.extract {} p)
         pushNewline i.indent.toNat
-        let is := { i with f := text (String.Internal.extract s (String.Internal.next s p) s.endPos) }::is
+        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
         -- note that we shouldn't start flattening after a hard break outside a group
         if g.fla == .disallow then
@@ -298,7 +298,7 @@ private partial def be (w : Nat) [Monad m] [MonadPrettyFormat m] : List WorkGrou
           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.fla.shouldFlatten then
-          let gs'@(g'::_) ← pushGroup FlattenBehavior.fill is gs (w - String.Internal.length " ")
+          let gs'@(g'::_) ← pushGroup FlattenBehavior.fill is gs (w - " ".length)
             | panic "unreachable"
           if g'.fla.shouldFlatten then
             pushOutput " "
@@ -316,7 +316,7 @@ private partial def be (w : Nat) [Monad m] [MonadPrettyFormat m] : List WorkGrou
       else
         let k ← currColumn
         if k < i.indent then
-          pushOutput (String.Internal.pushn "" ' ' (i.indent - k).toNat)
+          pushOutput ("".pushn ' ' (i.indent - k).toNat)
           endTags i.activeTags
           be w (gs' is)
         else
@@ -350,7 +350,7 @@ Creates a format `l ++ f ++ r` with a flattening group, nesting the contents by
 The group's `FlattenBehavior` is `allOrNone`; for `fill` use `Std.Format.bracketFill`.
 -/
 @[inline] def bracket (l : String) (f : Format) (r : String) : Format :=
-  group (nest (String.Internal.length l) $ l ++ f ++ r)
+  group (nest l.length $ l ++ f ++ r)
 
 /--
 Creates the format `"(" ++ f ++ ")"` with a flattening group, nesting by one space.
@@ -372,7 +372,7 @@ Creates a format `l ++ f ++ r` with a flattening group, nesting the contents by
 The group's `FlattenBehavior` is `fill`; for `allOrNone` use `Std.Format.bracketFill`.
 -/
 @[inline] def bracketFill (l : String) (f : Format) (r : String) : Format :=
-  fill (nest (String.Internal.length l) $ l ++ f ++ r)
+  fill (nest l.length $ l ++ f ++ r)
 
 /-- The default indentation level, which is two spaces. -/
 def defIndent  := 2
@@ -397,8 +397,8 @@ private structure 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⟩ => ⟨String.Internal.append out s, col + (String.Internal.length s)⟩
-  pushNewline indent := modify fun ⟨out, _⟩ => ⟨String.Internal.append out (String.Internal.pushn "\n" ' ' indent), indent⟩
+  pushOutput s       := modify fun ⟨out, col⟩ => ⟨out ++ s, col + s.length⟩
+  pushNewline indent := modify fun ⟨out, _⟩ => ⟨out ++ "\n".pushn ' ' indent, indent⟩
   currColumn         := return (← get).column
   startTag _         := return ()
   endTags _          := return ()

src/Init/Data/Format/Instances.lean

@@ -9,7 +9,6 @@ prelude
 public import Init.Data.Format.Basic
 public import Init.Data.Array.Basic
 public import Init.Data.ToString.Basic
-import Init.Data.String.Basic
 
 public section
 

src/Init/Data/Format/Syntax.lean

@@ -9,8 +9,6 @@ prelude
 public import Init.Data.Format.Macro
 public import Init.Data.Format.Instances
 public import Init.Meta
-import Init.Data.String.Basic
-import Init.Data.ToString.Name
 
 public section
 

src/Init/Data/Function.lean

@@ -3,11 +3,15 @@ Copyright (c) 2024 Lean FRO. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kim Morrison
 -/
+
 module
+
 prelude
 public import Init.Core
 public import Init.Grind.Tactics
+
 public section
+
 namespace Function
 
 /--
@@ -30,108 +34,20 @@ Examples:
 @[inline, expose]
 def uncurry : (α → β → φ) → α × β → φ := fun f a => f a.1 a.2
 
-@[simp, grind =]
+@[simp, grind]
 theorem curry_uncurry (f : α → β → φ) : curry (uncurry f) = f :=
   rfl
 
-@[simp, grind =]
+@[simp, grind]
 theorem uncurry_curry (f : α × β → φ) : uncurry (curry f) = f :=
   funext fun ⟨_a, _b⟩ => rfl
 
-@[simp, grind =]
+@[simp, grind]
 theorem uncurry_apply_pair {α β γ} (f : α → β → γ) (x : α) (y : β) : uncurry f (x, y) = f x y :=
   rfl
 
-@[simp, grind =]
+@[simp, grind]
 theorem curry_apply {α β γ} (f : α × β → γ) (x : α) (y : β) : curry f x y = f (x, y) :=
   rfl
 
-/-- A function `f : α → β` is called injective if `f x = f y` implies `x = y`. -/
-@[expose]
-def Injective (f : α → β) : Prop :=
-  ∀ ⦃a₁ a₂⦄, f a₁ = f a₂ → a₁ = a₂
-
-theorem Injective.comp {α β γ} {g : β → γ} {f : α → β} (hg : Injective g) (hf : Injective f) :
-    Injective (g ∘ f) := fun _a₁ _a₂ => fun h => hf (hg h)
-
-/-- A function `f : α → β` is called surjective if every `b : β` is equal to `f a`
-for some `a : α`. -/
-@[expose]
-def Surjective (f : α → β) : Prop :=
-  ∀ b, Exists fun a => f a = b
-
-theorem Surjective.comp {α β γ} {g : β → γ} {f : α → β} (hg : Surjective g) (hf : Surjective f) :
-    Surjective (g ∘ f) := fun c : γ =>
-  Exists.elim (hg c) fun b hb =>
-    Exists.elim (hf b) fun a ha =>
-      Exists.intro a (show g (f a) = c from Eq.trans (congrArg g ha) hb)
-
-/-- `LeftInverse g f` means that `g` is a left inverse to `f`. That is, `g ∘ f = id`. -/
-@[expose, grind]
-def LeftInverse {α β} (g : β → α) (f : α → β) : Prop :=
-  ∀ x, g (f x) = x
-
-/-- `HasLeftInverse f` means that `f` has an unspecified left inverse. -/
-@[expose]
-def HasLeftInverse {α β} (f : α → β) : Prop :=
-  Exists fun finv : β → α => LeftInverse finv f
-
-/-- `RightInverse g f` means that `g` is a right inverse to `f`. That is, `f ∘ g = id`. -/
-@[expose, grind]
-def RightInverse {α β} (g : β → α) (f : α → β) : Prop :=
-  LeftInverse f g
-
-/-- `HasRightInverse f` means that `f` has an unspecified right inverse. -/
-@[expose]
-def HasRightInverse {α β} (f : α → β) : Prop :=
-  Exists fun finv : β → α => RightInverse finv f
-
-theorem LeftInverse.injective {α β} {g : β → α} {f : α → β} : LeftInverse g f → Injective f :=
-  fun h a b faeqfb => ((h a).symm.trans (congrArg g faeqfb)).trans (h b)
-
-theorem HasLeftInverse.injective {α β} {f : α → β} : HasLeftInverse f → Injective f := fun h =>
-  Exists.elim h fun _finv inv => inv.injective
-
-theorem rightInverse_of_injective_of_leftInverse {α β} {f : α → β} {g : β → α} (injf : Injective f)
-    (lfg : LeftInverse f g) : RightInverse f g := fun x =>
-  have h : f (g (f x)) = f x := lfg (f x)
-  injf h
-
-theorem RightInverse.surjective {α β} {f : α → β} {g : β → α} (h : RightInverse g f) : Surjective f :=
-  fun y => ⟨g y, h y⟩
-
-theorem HasRightInverse.surjective {α β} {f : α → β} : HasRightInverse f → Surjective f
-  | ⟨_finv, inv⟩ => inv.surjective
-
-theorem leftInverse_of_surjective_of_rightInverse {α β} {f : α → β} {g : β → α} (surjf : Surjective f)
-    (rfg : RightInverse f g) : LeftInverse f g := fun y =>
-  Exists.elim (surjf y) fun x hx => ((hx ▸ rfl : f (g y) = f (g (f x))).trans (Eq.symm (rfg x) ▸ rfl)).trans hx
-
-theorem injective_id : Injective (@id α) := fun _a₁ _a₂ h => h
-
-theorem surjective_id : Surjective (@id α) := fun a => ⟨a, rfl⟩
-
-variable {f : α → β}
-
-theorem Injective.eq_iff (I : Injective f) {a b : α} : f a = f b ↔ a = b :=
-  ⟨@I _ _, congrArg f⟩
-
-theorem Injective.eq_iff' (I : Injective f) {a b : α} {c : β} (h : f b = c) : f a = c ↔ a = b :=
-  h ▸ I.eq_iff
-
-theorem Injective.ne (hf : Injective f) {a₁ a₂ : α} : a₁ ≠ a₂ → f a₁ ≠ f a₂ :=
-  mt fun h ↦ hf h
-
-theorem Injective.ne_iff (hf : Injective f) {x y : α} : f x ≠ f y ↔ x ≠ y :=
-  ⟨mt <| congrArg f, hf.ne⟩
-
-theorem Injective.ne_iff' (hf : Injective f) {x y : α} {z : β} (h : f y = z) : f x ≠ z ↔ x ≠ y :=
-  h ▸ hf.ne_iff
-
-protected theorem LeftInverse.id {α β} {g : β → α} {f : α → β} (h : LeftInverse g f) : g ∘ f = id :=
-  funext h
-
-protected theorem RightInverse.id {α β} {g : β → α} {f : α → β} (h : RightInverse g f) : f ∘ g = id :=
-  funext h
-
 end Function

src/Init/Data/Int/Basic.lean

@@ -31,7 +31,7 @@ This file defines the `Int` type as well as
 Division and modulus operations are defined in `Init.Data.Int.DivMod.Basic`.
 -/
 
-set_option genCtorIdx false in
+set_option genInjectivity false in
 /--
 The integers.
 
@@ -321,7 +321,7 @@ def natAbs (m : @& Int) : Nat :=
   | ofNat m => m
   | -[m +1] => m.succ
 
-attribute [gen_constructor_elims] Int
+gen_injective_theorems% Int
 
 /-! ## sign -/
 

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

@@ -97,7 +97,7 @@ theorem ofNat_emod (m n : Nat) : (↑(m % n) : Int) = m % n := natCast_emod m n
 
 /-! ### mod definitions -/
 
-theorem emod_add_mul_ediv : ∀ a b : Int, a % b + b * (a / b) = a
+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
     change (m % succ n + -↑(succ n) * -↑(m / succ n) : Int) = m
@@ -111,35 +111,19 @@ where
       ← Int.neg_neg (_-_), Int.neg_sub, Int.sub_sub_self, Int.add_right_comm]
     exact congrArg (fun x => -(ofNat x + 1)) (Nat.mod_add_div ..)
 
-@[deprecated emod_add_mul_ediv (since := "2025-09-01")]
-def emod_add_ediv := @emod_add_mul_ediv
+/-- Variant of `emod_add_ediv` with the multiplication written the other way around. -/
+theorem emod_add_ediv' (a b : Int) : a % b + a / b * b = a := by
+  rw [Int.mul_comm]; exact emod_add_ediv ..
 
-theorem emod_add_ediv_mul (a b : Int) : a % b + a / b * b = a := by
-  rw [Int.mul_comm]; exact emod_add_mul_ediv ..
+theorem ediv_add_emod (a b : Int) : b * (a / b) + a % b = a := by
+  rw [Int.add_comm]; exact emod_add_ediv ..
 
-@[deprecated emod_add_ediv_mul (since := "2025-09-01")]
-def emod_add_ediv' := @emod_add_ediv_mul
-
-theorem mul_ediv_add_emod (a b : Int) : b * (a / b) + a % b = a := by
-  rw [Int.add_comm]; exact emod_add_mul_ediv ..
-
-@[deprecated mul_ediv_add_emod (since := "2025-09-01")]
-def ediv_add_emod := @mul_ediv_add_emod
-
-theorem ediv_mul_add_emod (a b : Int) : a / b * b + a % b = a := by
-  rw [Int.mul_comm]; exact mul_ediv_add_emod ..
-
-@[deprecated ediv_mul_add_emod (since := "2025-09-01")]
-def ediv_add_emod' := @ediv_mul_add_emod
+/-- Variant of `ediv_add_emod` with the multiplication written the other way around. -/
+theorem ediv_add_emod' (a b : Int) : a / b * b + a % b = a := by
+  rw [Int.mul_comm]; exact ediv_add_emod ..
 
 theorem emod_def (a b : Int) : a % b = a - b * (a / b) := by
-  rw [← Int.add_sub_cancel (a % b), emod_add_mul_ediv]
-
-theorem mul_ediv_self (a b : Int) : b * (a / b) = a - a % b := by
-  rw [emod_def, Int.sub_sub_self]
-
-theorem ediv_mul_self (a b : Int) : a / b * b = a - a % b := by
-  rw [Int.mul_comm, emod_def, Int.sub_sub_self]
+  rw [← Int.add_sub_cancel (a % b), emod_add_ediv]
 
 /-! ### `/` ediv -/
 
@@ -242,7 +226,7 @@ theorem add_mul_emod_self {a b c : Int} : (a + b * c) % c = a % c :=
 
 @[simp] theorem emod_add_emod (m n k : Int) : (m % n + k) % n = (m + k) % n := by
   have := (add_mul_emod_self_left (m % n + k) n (m / n)).symm
-  rwa [Int.add_right_comm, emod_add_mul_ediv] at this
+  rwa [Int.add_right_comm, emod_add_ediv] at this
 
 @[simp] theorem add_emod_emod (m n k : Int) : (m + n % k) % k = (m + n) % k := by
   rw [Int.add_comm, emod_add_emod, Int.add_comm]
@@ -268,7 +252,7 @@ theorem emod_add_cancel_right {m n k : Int} (i) : (m + i) % n = (k + i) % n ↔
 
 theorem mul_emod (a b n : Int) : (a * b) % n = (a % n) * (b % n) % n := by
   conv => lhs; rw [
-    ← emod_add_mul_ediv a n, ← emod_add_ediv_mul b n, Int.add_mul, Int.mul_add, Int.mul_add,
+    ← emod_add_ediv a n, ← emod_add_ediv' b n, Int.add_mul, Int.mul_add, Int.mul_add,
     Int.mul_assoc, Int.mul_assoc, ← Int.mul_add n _ _, add_mul_emod_self_left,
     ← Int.mul_assoc, add_mul_emod_self_right]
 
@@ -277,7 +261,7 @@ theorem mul_emod (a b n : Int) : (a * b) % n = (a % n) * (b % n) % n := by
 
 @[simp] theorem emod_emod_of_dvd (n : Int) {m k : Int}
     (h : m ∣ k) : (n % k) % m = n % m := by
-  conv => rhs; rw [← emod_add_mul_ediv n k]
+  conv => rhs; rw [← emod_add_ediv n k]
   match k, h with
   | _, ⟨t, rfl⟩ => rw [Int.mul_assoc, add_mul_emod_self_left]
 
@@ -291,7 +275,7 @@ theorem sub_emod (a b n : Int) : (a - b) % n = (a % n - b % n) % n := by
 /-! ### properties of `/` and `%` -/
 
 theorem mul_ediv_cancel_of_emod_eq_zero {a b : Int} (H : a % b = 0) : b * (a / b) = a := by
-  have := emod_add_mul_ediv a b; rwa [H, Int.zero_add] at this
+  have := emod_add_ediv a b; rwa [H, Int.zero_add] at this
 
 theorem ediv_mul_cancel_of_emod_eq_zero {a b : Int} (H : a % b = 0) : a / b * b = a := by
   rw [Int.mul_comm, mul_ediv_cancel_of_emod_eq_zero H]
@@ -342,11 +326,11 @@ theorem emod_pos_of_not_dvd {a b : Int} (h : ¬ a ∣ b) : a = 0 ∨ 0 < b % a :
 theorem mul_ediv_self_le {x k : Int} (h : k ≠ 0) : k * (x / k) ≤ x :=
   calc k * (x / k)
     _ ≤ k * (x / k) + x % k := Int.le_add_of_nonneg_right (emod_nonneg x h)
-    _ = x                   := mul_ediv_add_emod _ _
+    _ = x                   := ediv_add_emod _ _
 
 theorem lt_mul_ediv_self_add {x k : Int} (h : 0 < k) : x < k * (x / k) + k :=
   calc x
-    _ = k * (x / k) + x % k := (mul_ediv_add_emod _ _).symm
+    _ = k * (x / k) + x % k := (ediv_add_emod _ _).symm
     _ < k * (x / k) + k     := Int.add_lt_add_left (emod_lt_of_pos x h) _
 
 /-! ### bmod -/

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

@@ -334,7 +334,7 @@ theorem fdiv_eq_ediv_of_dvd {a b : Int} (h : b ∣ a) : a.fdiv b = a / b := by
 
 /-! ### mod definitions -/
 
-theorem tmod_add_mul_tdiv : ∀ a b : Int, tmod a b + b * (a.tdiv b) = a
+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
     change (m % succ n + -↑(succ n) * -↑(m / succ n) : Int) = m
@@ -351,37 +351,21 @@ theorem tmod_add_mul_tdiv : ∀ a b : Int, tmod a b + b * (a.tdiv b) = a
     rw [Int.neg_mul, ← Int.neg_add]
     exact congrArg (-ofNat ·) (Nat.mod_add_div ..)
 
-@[deprecated tmod_add_mul_tdiv (since := "2025-09-01")]
-def tmod_add_tdiv := @tmod_add_mul_tdiv
+theorem tdiv_add_tmod (a b : Int) : b * a.tdiv b + tmod a b = a := by
+  rw [Int.add_comm]; apply tmod_add_tdiv ..
 
-theorem mul_tdiv_add_tmod (a b : Int) : b * a.tdiv b + tmod a b = a := by
-  rw [Int.add_comm]; apply tmod_add_mul_tdiv ..
+/-- Variant of `tmod_add_tdiv` with the multiplication written the other way around. -/
+theorem tmod_add_tdiv' (m k : Int) : tmod m k + m.tdiv k * k = m := by
+  rw [Int.mul_comm]; apply tmod_add_tdiv
 
-@[deprecated mul_tdiv_add_tmod (since := "2025-09-01")]
-def tdiv_add_tmod := @mul_tdiv_add_tmod
-
-theorem tmod_add_tdiv_mul (m k : Int) : tmod m k + m.tdiv k * k = m := by
-  rw [Int.mul_comm]; apply tmod_add_mul_tdiv
-
-@[deprecated tmod_add_tdiv_mul (since := "2025-09-01")]
-def tmod_add_tdiv' := @tmod_add_mul_tdiv
-
-theorem tdiv_mul_add_tmod (m k : Int) : m.tdiv k * k + tmod m k = m := by
-  rw [Int.mul_comm]; apply mul_tdiv_add_tmod
-
-@[deprecated tdiv_mul_add_tmod (since := "2025-09-01")]
-def tdiv_add_tmod' := @tdiv_mul_add_tmod
+/-- Variant of `tdiv_add_tmod` with the multiplication written the other way around. -/
+theorem tdiv_add_tmod' (m k : Int) : m.tdiv k * k + tmod m k = m := by
+  rw [Int.mul_comm]; apply tdiv_add_tmod
 
 theorem tmod_def (a b : Int) : tmod a b = a - b * a.tdiv b := by
-  rw [← Int.add_sub_cancel (tmod a b), tmod_add_mul_tdiv]
+  rw [← Int.add_sub_cancel (tmod a b), tmod_add_tdiv]
 
-theorem mul_tdiv_self (a b : Int) : b * (a.tdiv b) = a - a.tmod b := by
-  rw [tmod_def, Int.sub_sub_self]
-
-theorem tdiv_mul_self (a b : Int) : a.tdiv b * b = a - a.tmod b := by
-  rw [Int.mul_comm, tmod_def, Int.sub_sub_self]
-
-theorem fmod_add_mul_fdiv : ∀ a b : Int, a.fmod b + b * a.fdiv b = a
+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
@@ -398,35 +382,19 @@ theorem fmod_add_mul_fdiv : ∀ a b : Int, a.fmod b + b * a.fdiv b = a
     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 ..
 
-@[deprecated fmod_add_mul_fdiv (since := "2025-09-01")]
-def fmod_add_fdiv := @fmod_add_mul_fdiv
+/-- Variant of `fmod_add_fdiv` with the multiplication written the other way around. -/
+theorem fmod_add_fdiv' (a b : Int) : a.fmod b + (a.fdiv b) * b = a := by
+  rw [Int.mul_comm]; exact fmod_add_fdiv ..
 
-theorem fmod_add_fdiv_mul (a b : Int) : a.fmod b + (a.fdiv b) * b = a := by
-  rw [Int.mul_comm]; exact fmod_add_mul_fdiv ..
+theorem fdiv_add_fmod (a b : Int) : b * a.fdiv b + a.fmod b = a := by
+  rw [Int.add_comm]; exact fmod_add_fdiv ..
 
-@[deprecated fmod_add_fdiv_mul (since := "2025-09-01")]
-def fmod_add_fdiv' := @fmod_add_fdiv_mul
-
-theorem mul_fdiv_add_fmod (a b : Int) : b * a.fdiv b + a.fmod b = a := by
-  rw [Int.add_comm]; exact fmod_add_mul_fdiv ..
-
-@[deprecated mul_fdiv_add_fmod (since := "2025-09-01")]
-def fdiv_add_fmod := @mul_fdiv_add_fmod
-
-theorem fdiv_mul_add_fmod (a b : Int) : (a.fdiv b) * b + a.fmod b = a := by
-  rw [Int.mul_comm]; exact mul_fdiv_add_fmod ..
-
-@[deprecated mul_fdiv_add_fmod (since := "2025-09-01")]
-def fdiv_add_fmod' := @mul_fdiv_add_fmod
+/-- Variant of `fdiv_add_fmod` with the multiplication written the other way around. -/
+theorem fdiv_add_fmod' (a b : Int) : (a.fdiv b) * b + a.fmod b = a := by
+  rw [Int.mul_comm]; exact fdiv_add_fmod ..
 
 theorem fmod_def (a b : Int) : a.fmod b = a - b * a.fdiv b := by
-  rw [← Int.add_sub_cancel (a.fmod b), fmod_add_mul_fdiv]
-
-theorem mul_fdiv_self (a b : Int) : b * (a.fdiv b) = a - a.fmod b := by
-  rw [fmod_def, Int.sub_sub_self]
-
-theorem fdiv_mul_self (a b : Int) : a.fdiv b * b = a - a.fmod b := by
-  rw [Int.mul_comm, fmod_def, Int.sub_sub_self]
+  rw [← Int.add_sub_cancel (a.fmod b), fmod_add_fdiv]
 
 /-! ### mod equivalences  -/
 
@@ -805,7 +773,7 @@ protected theorem ediv_emod_unique {a b r q : Int} (h : 0 < b) :
     a / b = q ∧ a % b = r ↔ r + b * q = a ∧ 0 ≤ r ∧ r < b := by
   constructor
   · intro ⟨rfl, rfl⟩
-    exact ⟨emod_add_mul_ediv a b, emod_nonneg _ (Int.ne_of_gt h), emod_lt_of_pos _ h⟩
+    exact ⟨emod_add_ediv a b, emod_nonneg _ (Int.ne_of_gt h), emod_lt_of_pos _ h⟩
   · intro ⟨rfl, hz, hb⟩
     constructor
     · rw [Int.add_mul_ediv_left r q (Int.ne_of_gt h), ediv_eq_zero_of_lt hz hb]
@@ -829,7 +797,7 @@ theorem neg_ediv {a b : Int} : (-a) / b = -(a / b) - if b ∣ a then 0 else b.si
   if hb : b = 0 then
     simp [hb]
   else
-    conv => lhs; rw [← mul_ediv_add_emod a b]
+    conv => lhs; rw [← ediv_add_emod a b]
     rw [Int.neg_add, ← Int.mul_neg, mul_add_ediv_left _ _ hb, Int.add_comm]
     split <;> rename_i h
     · rw [emod_eq_zero_of_dvd h]
@@ -1119,10 +1087,6 @@ theorem emod_natAbs_of_neg {x : Int} (h : x < 0) {n : Nat} (w : n ≠ 0) :
 protected theorem ediv_mul_le (a : Int) {b : Int} (H : b ≠ 0) : a / b * b ≤ a :=
   Int.le_of_sub_nonneg <| by rw [Int.mul_comm, ← emod_def]; apply emod_nonneg _ H
 
-protected theorem lt_ediv_mul (a : Int) {b : Int} (H : 0 < b) : a - b < a / b * b := by
-  rw [ediv_mul_self, Int.sub_lt_sub_left_iff]
-  exact emod_lt_of_pos a H
-
 theorem le_of_mul_le_mul_left {a b c : Int} (w : a * b ≤ a * c) (h : 0 < a) : b ≤ c := by
   have w := Int.sub_nonneg_of_le w
   rw [← Int.mul_sub] at w
@@ -1213,9 +1177,9 @@ theorem ediv_eq_iff_of_pos {k x y : Int} (h : 0 < k) : x / k = y ↔ y * k ≤ x
 theorem add_ediv_of_pos {a b c : Int} (h : 0 < c) :
     (a + b) / c = a / c + b / c + if c ≤ a % c + b % c then 1 else 0 := by
   have h' : c ≠ 0 := by omega
-  conv => lhs; rw [← Int.mul_ediv_add_emod a c]
+  conv => lhs; rw [← Int.ediv_add_emod a c]
   rw [Int.add_assoc, Int.mul_add_ediv_left _ _ h']
-  conv => lhs; rw [← Int.mul_ediv_add_emod b c]
+  conv => lhs; rw [← Int.ediv_add_emod b c]
   rw [Int.add_comm (a % c), Int.add_assoc, Int.mul_add_ediv_left _ _ h',
     ← Int.add_assoc, Int.add_comm (b % c)]
   congr
@@ -1246,7 +1210,7 @@ theorem not_dvd_iff_lt_mul_succ (m : Int) (hn : 0 < n) :
     ¬n ∣ m ↔ (∃ k, n * k < m ∧ m < n * (k + 1)) := by
   refine ⟨fun h ↦ ?_, ?_⟩
   · rw [dvd_iff_emod_eq_zero, ← Ne] at h
-    rw [← emod_add_mul_ediv m n]
+    rw [← emod_add_ediv m n]
     refine ⟨m / n, Int.lt_add_of_pos_left _ ?_, ?_⟩
     · have := emod_nonneg m (Int.ne_of_gt hn)
       omega
@@ -1521,7 +1485,7 @@ theorem sign_tmod (a b : Int) : sign (tmod a b) = if b ∣ a then 0 else sign a
 -- Analogues of statements about `ediv` and `emod` from `Bootstrap.lean`
 
 theorem mul_tdiv_cancel_of_tmod_eq_zero {a b : Int} (H : a.tmod b = 0) : b * (a.tdiv b) = a := by
-  have := tmod_add_mul_tdiv a b; rwa [H, Int.zero_add] at this
+  have := tmod_add_tdiv a b; rwa [H, Int.zero_add] at this
 
 theorem tdiv_mul_cancel_of_tmod_eq_zero {a b : Int} (H : a.tmod b = 0) : a.tdiv b * b = a := by
   rw [Int.mul_comm, mul_tdiv_cancel_of_tmod_eq_zero H]
@@ -2246,7 +2210,7 @@ theorem fmod_add_cancel_right {m n k : Int} (i) : (m + i).fmod n = (k + i).fmod
 
 theorem mul_fmod (a b n : Int) : (a * b).fmod n = (a.fmod n * b.fmod n).fmod n := by
   conv => lhs; rw [
-    ← fmod_add_mul_fdiv a n, ← fmod_add_fdiv_mul b n, Int.add_mul, Int.mul_add, Int.mul_add,
+    ← fmod_add_fdiv a n, ← fmod_add_fdiv' b n, Int.add_mul, Int.mul_add, Int.mul_add,
     Int.mul_assoc, Int.mul_assoc, ← Int.mul_add n _ _, add_mul_fmod_self_left,
     ← Int.mul_assoc, add_mul_fmod_self_right]
 
@@ -2255,7 +2219,7 @@ theorem mul_fmod (a b n : Int) : (a * b).fmod n = (a.fmod n * b.fmod n).fmod n :
 
 @[simp] theorem fmod_fmod_of_dvd (n : Int) {m k : Int}
     (h : m ∣ k) : (n.fmod k).fmod m = n.fmod m := by
-  conv => rhs; rw [← fmod_add_mul_fdiv n k]
+  conv => rhs; rw [← fmod_add_fdiv n k]
   match k, h with
   | _, ⟨t, rfl⟩ => rw [Int.mul_assoc, add_mul_fmod_self_left]
 
@@ -2285,7 +2249,7 @@ theorem fmod_eq_of_lt {a b : Int} (H1 : 0 ≤ a) (H2 : a < b) : a.fmod b = a :=
 -- Analogues of properties of `ediv` and `emod` from `Bootstrap.lean`
 
 theorem mul_fdiv_cancel_of_fmod_eq_zero {a b : Int} (H : a.fmod b = 0) : b * (a.fdiv b) = a := by
-  have := fmod_add_mul_fdiv a b; rwa [H, Int.zero_add] at this
+  have := fmod_add_fdiv a b; rwa [H, Int.zero_add] at this
 
 theorem fdiv_mul_cancel_of_fmod_eq_zero {a b : Int} (H : a.fmod b = 0) : (a.fdiv b) * b= a := by
   rw [Int.mul_comm, mul_fdiv_cancel_of_fmod_eq_zero H]
@@ -2527,9 +2491,9 @@ theorem bdiv_add_bmod (x : Int) (m : Nat) : m * bdiv x m + bmod x m = x := by
       ite_self]
   · dsimp only
     split
-    · exact mul_ediv_add_emod x m
+    · exact ediv_add_emod x m
     · rw [Int.mul_add, Int.mul_one, Int.add_assoc, Int.add_comm m, Int.sub_add_cancel]
-      exact mul_ediv_add_emod x m
+      exact ediv_add_emod x m
 
 theorem bmod_add_bdiv (x : Int) (m : Nat) : bmod x m + m * bdiv x m = x := by
   rw [Int.add_comm]; exact bdiv_add_bmod x m
@@ -2786,7 +2750,7 @@ theorem le_bmod {x : Int} {m : Nat} (h : 0 < m) : - (m/2) ≤ Int.bmod x m := by
     · exact Int.ne_of_gt (natCast_pos.mpr h)
   · simp [Int.not_lt] at w
     refine Int.le_trans ?_ (Int.sub_le_sub_right w _)
-    rw [← mul_ediv_add_emod m 2]
+    rw [← ediv_add_emod m 2]
     generalize (m : Int) / 2 = q
     generalize h : (m : Int) % 2 = r at *
     rcases v with rfl | rfl
@@ -2947,7 +2911,7 @@ theorem neg_bmod {a : Int} {b : Nat} :
           simp only [gt_iff_lt, Nat.zero_lt_succ, Nat.mul_pos_iff_of_pos_left, Int.natCast_mul,
             cast_ofNat_Int, Int.not_lt] at *
           rw [Int.mul_dvd_mul_iff_left (by omega)]
-          have := mul_ediv_add_emod a (2 * c)
+          have := ediv_add_emod a (2 * c)
           rw [(by omega : a % (2 * c) = c)] at this
           rw [← this]
           apply Int.dvd_add _ (by simp)

src/Init/Data/Int/Lemmas.lean

@@ -40,7 +40,7 @@ theorem ofNat_succ (n : Nat) : (succ n : Int) = n + 1 := rfl
 
 theorem neg_ofNat_zero : -((0 : Nat) : Int) = 0 := rfl
 theorem neg_ofNat_succ (n : Nat) : -(succ n : Int) = -[n+1] := rfl
-@[simp] theorem neg_negSucc (n : Nat) : -(-[n+1]) = ((n + 1 : Nat) : Int) := rfl
+theorem neg_negSucc (n : Nat) : -(-[n+1]) = succ n := rfl
 
 theorem negOfNat_eq : negOfNat n = -ofNat n := rfl
 

src/Init/Data/Int/Linear.lean

@@ -17,7 +17,6 @@ import all Init.Data.Int.Gcd
 public import Init.Data.RArray
 public import Init.Data.AC
 import all Init.Data.AC
-import Init.LawfulBEqTactics
 
 public section
 
@@ -55,7 +54,7 @@ def Expr.denote (ctx : Context) : Expr → Int
 inductive Poly where
   | num (k : Int)
   | add (k : Int) (v : Var) (p : Poly)
-  deriving @[expose] BEq, ReflBEq, LawfulBEq
+  deriving @[expose] BEq
 
 @[expose]
 protected noncomputable def Poly.beq' (p₁ : Poly) : Poly → Bool :=
@@ -248,7 +247,7 @@ def cmod (a b : Int) : Int :=
 
 theorem cdiv_add_cmod (a b : Int) : b*(cdiv a b) + cmod a b = a := by
   unfold cdiv cmod
-  have := Int.mul_ediv_add_emod (-a) b
+  have := Int.ediv_add_emod (-a) b
   have := congrArg (Neg.neg) this
   simp at this
   conv => rhs; rw[← this]
@@ -273,7 +272,7 @@ private abbrev div_mul_cancel_of_mod_zero :=
 theorem cdiv_eq_div_of_divides {a b : Int} (h : a % b = 0) : a/b = cdiv a b := by
   replace h := div_mul_cancel_of_mod_zero h
   have hz : a % b = 0 := by
-    have := Int.mul_ediv_add_emod a b
+    have := Int.ediv_add_emod a b
     conv at this => rhs; rw [← Int.add_zero a]
     rw [Int.mul_comm, h] at this
     exact Int.add_left_cancel this
@@ -380,11 +379,8 @@ def Poly.mul (p : Poly) (k : Int) : Poly :=
       p₁)
     fuel
 
-@[expose] noncomputable def Poly.combine_mul_k (a b : Int) (p₁ p₂ : Poly) : Poly :=
-  Bool.rec
-    (Bool.rec (combine_mul_k' hugeFuel a b p₁ p₂) (p₁.mul_k a) (Int.beq' b 0))
-    (p₂.mul_k b)
-    (Int.beq' a 0)
+@[expose] noncomputable def Poly.combine_mul_k (a b : Int) : Poly → Poly → Poly :=
+  combine_mul_k' hugeFuel a b
 
 @[simp] theorem Poly.denote_mul (ctx : Context) (p : Poly) (k : Int) : (p.mul k).denote ctx = k * p.denote ctx := by
   simp [mul]
@@ -428,36 +424,34 @@ theorem Poly.denote_combine (ctx : Context) (p₁ p₂ : Poly) : (p₁.combine p
 
 theorem Poly.denote_combine_mul_k (ctx : Context) (a b : Int) (p₁ p₂ : Poly) : (p₁.combine_mul_k a b p₂).denote ctx = a * p₁.denote ctx + b * p₂.denote ctx := by
   unfold combine_mul_k
-  cases h₁ : Int.beq' a 0 <;> simp at h₁ <;> simp [*]
-  cases h₂ : Int.beq' b 0 <;> simp at h₂ <;> simp [*]
   generalize hugeFuel = fuel
   induction fuel generalizing p₁ p₂
   next => show ((p₁.mul a).append (p₂.mul b)).denote ctx = _; simp
   next fuel ih =>
-  cases p₁ <;> cases p₂ <;> simp [combine_mul_k']
-  next k₁ k₂ v₂ p₂ =>
-    show _ + (combine_mul_k' fuel a b (.num k₁) p₂).denote ctx = _
-    simp [ih, Int.mul_assoc]
-  next k₁ v₁ p₁ k₂ =>
-    show _ + (combine_mul_k' fuel a b p₁ (.num k₂)).denote ctx = _
-    simp [ih, Int.mul_assoc]
-  next k₁ v₁ p₁ k₂ v₂ p₂ =>
-    cases h₁ : Nat.beq v₁ v₂ <;> simp
-    next =>
-      cases h₂ : Nat.blt v₂ v₁ <;> simp
-      next =>
-        show _ + (combine_mul_k' fuel a b (add k₁ v₁ p₁) p₂).denote ctx = _
-        simp [ih, Int.mul_assoc]
-      next =>
-        show _ + (combine_mul_k' fuel a b p₁ (add k₂ v₂ p₂)).denote ctx = _
-        simp [ih, Int.mul_assoc]
-    next =>
-      simp at h₁; subst v₂
-      cases h₂ : (a * k₁ + b * k₂).beq' 0 <;> simp
-      next =>
+   cases p₁ <;> cases p₂ <;> simp [combine_mul_k']
+   next k₁ k₂ v₂ p₂ =>
+     show _ + (combine_mul_k' fuel a b (.num k₁) p₂).denote ctx = _
+     simp [ih, Int.mul_assoc]
+   next k₁ v₁ p₁ k₂ =>
+     show _ + (combine_mul_k' fuel a b p₁ (.num k₂)).denote ctx = _
+     simp [ih, Int.mul_assoc]
+   next k₁ v₁ p₁ k₂ v₂ p₂ =>
+     cases h₁ : Nat.beq v₁ v₂ <;> simp
+     next =>
+       cases h₂ : Nat.blt v₂ v₁ <;> simp
+       next =>
+         show _ + (combine_mul_k' fuel a b (add k₁ v₁ p₁) p₂).denote ctx = _
+         simp [ih, Int.mul_assoc]
+       next =>
+         show _ + (combine_mul_k' fuel a b p₁ (add k₂ v₂ p₂)).denote ctx = _
+         simp [ih, Int.mul_assoc]
+     next =>
+       simp at h₁; subst v₂
+       cases h₂ : (a * k₁ + b * k₂).beq' 0 <;> simp
+       next =>
         show a * k₁ * v₁.denote ctx + (b * k₂ * v₁.denote ctx + (combine_mul_k' fuel a b p₁ p₂).denote ctx) = _
         simp [ih, Int.mul_assoc]
-      next =>
+       next =>
         simp at h₂
         show (combine_mul_k' fuel a b p₁ p₂).denote ctx = _
         simp [ih, ← Int.mul_assoc, ← Int.add_mul, h₂]
@@ -526,6 +520,18 @@ theorem Expr.denote_norm (ctx : Context) (e : Expr) : e.norm.denote ctx = e.deno
   simp [norm, toPoly', Expr.denote_toPoly'_go]
 
 attribute [local simp] Expr.denote_norm
+
+instance : LawfulBEq Poly where
+  eq_of_beq {a} := by
+    induction a <;> intro b <;> cases b <;> simp_all! [BEq.beq]
+    next ih =>
+      intro _ _ h
+      exact ih h
+  rfl := by
+    intro a
+    induction a <;> simp! [BEq.beq]
+    assumption
+
 attribute [local simp] Poly.denote'_eq_denote
 
 theorem Expr.eq_of_norm_eq (ctx : Context) (e : Expr) (p : Poly) (h : e.norm.beq' p) : e.denote ctx = p.denote' ctx := by
@@ -1747,7 +1753,7 @@ theorem cooper_right_split_dvd (ctx : Context) (p₁ p₂ : Poly) (k : Nat) (b :
   intros; subst b p'; simp; assumption
 
 private theorem one_emod_eq_one {a : Int} (h : a > 1) : 1 % a = 1 := by
-  have aux₁ := Int.mul_ediv_add_emod 1 a
+  have aux₁ := Int.ediv_add_emod 1 a
   have : 1 / a = 0 := Int.ediv_eq_zero_of_lt (by decide) h
   simp [this] at aux₁
   assumption
@@ -1774,7 +1780,7 @@ private theorem ex_of_dvd {α β a b d x : Int}
     rw [Int.mul_emod, aux₁, Int.one_mul, Int.emod_emod] at this
     assumption
   have : x = (x / d)*d + (- α * b) % d := by
-    conv => lhs; rw [← Int.mul_ediv_add_emod x d]
+    conv => lhs; rw [← Int.ediv_add_emod x d]
     rw [Int.mul_comm, this]
   exists x / d
 
@@ -1857,7 +1863,7 @@ theorem cooper_unsat (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (α β :
   exact cooper_unsat' h₁ h₂ h₃ h₄ h₅ h₆
 
 theorem ediv_emod (x y : Int) : -1 * x + y * (x / y) + x % y = 0 := by
-  rw [Int.add_assoc, Int.mul_ediv_add_emod x y, Int.add_comm]
+  rw [Int.add_assoc, Int.ediv_add_emod x y, Int.add_comm]
   simp
   rw [Int.add_neg_eq_sub, Int.sub_self]
 

src/Init/Data/Int/Order.lean

@@ -701,13 +701,10 @@ theorem toNat_sub_toNat_neg : ∀ n : Int, ↑n.toNat - ↑(-n).toNat = n
   | (_+1:Nat) => Nat.add_zero _
   | -[_+1] => Nat.zero_add _
 
-@[simp] theorem toNat_neg_natCast : ∀ n : Nat, (-(n : Int)).toNat = 0
+@[simp] theorem toNat_neg_nat : ∀ n : Nat, (-(n : Int)).toNat = 0
   | 0 => rfl
   | _+1 => rfl
 
-@[deprecated toNat_neg_natCast (since := "2025-08-29")]
-theorem toNat_neg_nat : ∀ n : Nat, (-(n : Int)).toNat = 0 := toNat_neg_natCast
-
 /-! ### toNat? -/
 
 theorem mem_toNat? : ∀ {a : Int} {n : Nat}, toNat? a = some n ↔ a = n

src/Init/Data/Iterators/Combinators/Monadic/ULift.lean

@@ -19,7 +19,6 @@ universe v u v' u'
 section ULiftT
 
 /-- `ULiftT.{v, u}` shrinks a monad on `Type max u v` to a monad on `Type u`. -/
-@[expose]  -- for codegen
 def ULiftT (n : Type max u v → Type v') (α : Type u) := n (ULift.{v} α)
 
 /-- Returns the underlying `n`-monadic representation of a `ULiftT n α` value. -/

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

@@ -139,7 +139,7 @@ def Iter.Partial.fold {α : Type w} {β : Type w} {γ : Type x} [Iterator α Id
     (init : γ) (it : Iter.Partial (α := α) β) : γ :=
   ForIn.forIn (m := Id) it init (fun x acc => ForInStep.yield (f acc x))
 
-@[always_inline, inline, expose, inherit_doc IterM.size]
+@[always_inline, inline, inherit_doc IterM.size]
 def Iter.size {α : Type w} {β : Type w} [Iterator α Id β] [IteratorSize α Id]
     (it : Iter (α := α) β) : Nat :=
   (IteratorSize.size it.toIterM).run.down

src/Init/Data/Iterators/Lemmas/Combinators/Monadic/Attach.lean

@@ -57,6 +57,6 @@ theorem IterM.map_unattach_toArray_attachWith [Iterator α m β] [Monad m] [Mona
     [LawfulMonad m] [LawfulIteratorCollect α m m] :
     (·.map Subtype.val) <$> (it.attachWith P hP).toArray = it.toArray := by
   rw [← toArray_toList, ← toArray_toList, ← map_unattach_toList_attachWith (it := it) (hP := hP)]
-  simp [-map_unattach_toList_attachWith, -IterM.toArray_toList]
+  simp [-map_unattach_toList_attachWith]
 
 end Std.Iterators

src/Init/Data/Iterators/Lemmas/Combinators/ULift.lean

@@ -53,6 +53,6 @@ theorem Iter.toArray_uLift [Iterator α Id β] {it : Iter (α := α) β}
     [LawfulIteratorCollect α Id Id] :
     it.uLift.toArray = it.toArray.map ULift.up := by
   rw [← toArray_toList, ← toArray_toList, toList_uLift]
-  simp [-toArray_toList]
+  simp
 
 end Std.Iterators

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

@@ -44,13 +44,11 @@ theorem IterM.toListRev_toIter {α β} [Iterator α Id β] [Finite α Id]
     it.toIter.toListRev = it.toListRev.run :=
   (rfl)
 
-@[simp]
 theorem Iter.toList_toArray {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
     [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
     it.toArray.toList = it.toList := by
   simp [toArray_eq_toArray_toIterM, toList_eq_toList_toIterM, ← IterM.toList_toArray]
 
-@[simp]
 theorem Iter.toArray_toList {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
     [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
     it.toList.toArray = it.toArray := by

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

@@ -14,7 +14,6 @@ public import Init.Data.Iterators.Consumers.Loop
 import all Init.Data.Iterators.Consumers.Loop
 public import Init.Data.Iterators.Consumers.Monadic.Collect
 import all Init.Data.Iterators.Consumers.Monadic.Collect
-import Init.Data.Array.Monadic
 
 public section
 
@@ -44,20 +43,6 @@ theorem Iter.forIn_eq {α β : Type w} [Iterator α Id β] [Finite α Id]
             f out acc) := by
   simp [ForIn.forIn, forIn'_eq, -forIn'_eq_forIn]
 
-@[congr] theorem Iter.forIn'_congr {α β : Type w}
-    [Iterator α Id β] [Finite α Id] [IteratorLoop α Id Id]
-    {ita itb : Iter (α := α) β} (w : ita = itb)
-    {b b' : γ} (hb : b = b')
-    {f : (a' : β) → _ → γ → Id (ForInStep γ)}
-    {g : (a' : β) → _ → γ → Id (ForInStep γ)}
-    (h : ∀ a m b, f a (by simpa [w] using m) b = g a m b) :
-    letI : ForIn' Id (Iter (α := α) β) β _ := Iter.instForIn'
-    forIn' ita b f = forIn' itb b' g := by
-  subst_eqs
-  simp only [← funext_iff] at h
-  rw [← h]
-  rfl
-
 theorem Iter.forIn'_eq_forIn'_toIterM {α β : Type w} [Iterator α Id β]
     [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
     [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
@@ -203,13 +188,6 @@ theorem Iter.mem_toList_iff_isPlausibleIndirectOutput {α β} [Iterator α Id β
         obtain ⟨step, h₁, rfl⟩ := h₁
         simp [heq, IterStep.successor] at h₁
 
-theorem Iter.mem_toArray_iff_isPlausibleIndirectOutput {α β} [Iterator α Id β]
-    [IteratorCollect α Id Id] [Finite α Id]
-    [LawfulIteratorCollect α Id Id] [LawfulDeterministicIterator α Id]
-    {it : Iter (α := α) β} {out : β} :
-    out ∈ it.toArray ↔ it.IsPlausibleIndirectOutput out := by
-  rw [← Iter.toArray_toList, List.mem_toArray, mem_toList_iff_isPlausibleIndirectOutput]
-
 theorem Iter.forIn'_toList {α β : Type w} [Iterator α Id β]
     [Finite α Id] {m : Type x → Type x'} [Monad m] [LawfulMonad m]
     [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
@@ -244,17 +222,6 @@ theorem Iter.forIn'_toList {α β : Type w} [Iterator α Id β]
     simp only [ihs h (f := fun out h acc => f out (this ▸ h) acc)]
   · simp
 
-theorem Iter.forIn'_toArray {α β : Type w} [Iterator α Id β]
-    [Finite α Id] {m : Type x → Type x'} [Monad m] [LawfulMonad m]
-    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
-    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
-    [LawfulDeterministicIterator α Id]
-    {γ : Type x} {it : Iter (α := α) β} {init : γ}
-    {f : (out : β) → _ → γ → m (ForInStep γ)} :
-    letI : ForIn' m (Iter (α := α) β) β _ := Iter.instForIn'
-    ForIn'.forIn' it.toArray init f = ForIn'.forIn' it init (fun out h acc => f out (Iter.mem_toArray_iff_isPlausibleIndirectOutput.mpr h) acc) := by
-  simp only [← Iter.toArray_toList (it := it), List.forIn'_toArray, Iter.forIn'_toList]
-
 theorem Iter.forIn'_eq_forIn'_toList {α β : Type w} [Iterator α Id β]
     [Finite α Id] {m : Type x → Type x'} [Monad m] [LawfulMonad m]
     [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
@@ -267,18 +234,6 @@ theorem Iter.forIn'_eq_forIn'_toList {α β : Type w} [Iterator α Id β]
   simp only [forIn'_toList]
   congr
 
-theorem Iter.forIn'_eq_forIn'_toArray {α β : Type w} [Iterator α Id β]
-    [Finite α Id] {m : Type x → Type x'} [Monad m] [LawfulMonad m]
-    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
-    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
-    [LawfulDeterministicIterator α Id]
-    {γ : Type x} {it : Iter (α := α) β} {init : γ}
-    {f : (out : β) → _ → γ → m (ForInStep γ)} :
-    letI : ForIn' m (Iter (α := α) β) β _ := Iter.instForIn'
-    ForIn'.forIn' it init f = ForIn'.forIn' it.toArray init (fun out h acc => f out (Iter.mem_toArray_iff_isPlausibleIndirectOutput.mp h) acc) := by
-  simp only [forIn'_toArray]
-  congr
-
 theorem Iter.forIn_toList {α β : Type w} [Iterator α Id β]
     [Finite α Id] {m : Type x → Type x'} [Monad m] [LawfulMonad m]
     [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
@@ -305,15 +260,6 @@ theorem Iter.forIn_toList {α β : Type w} [Iterator α Id β]
     rw [ihs h]
   · simp
 
-theorem Iter.forIn_toArray {α β : Type w} [Iterator α Id β]
-    [Finite α Id] {m : Type x → Type x'} [Monad m] [LawfulMonad m]
-    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
-    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
-    {γ : Type x} {it : Iter (α := α) β} {init : γ}
-    {f : β → γ → m (ForInStep γ)} :
-    ForIn.forIn it.toArray init f = ForIn.forIn it init f := by
-  simp only [← Iter.toArray_toList, List.forIn_toArray, forIn_toList]
-
 theorem Iter.foldM_eq_forIn {α β : Type w} {γ : Type x} [Iterator α Id β] [Finite α Id]
     {m : Type x → Type x'} [Monad m] [IteratorLoop α Id m] {f : γ → β → m γ}
     {init : γ} {it : Iter (α := α) β} :
@@ -355,14 +301,6 @@ theorem Iter.foldlM_toList {α β : Type w} {γ : Type x} [Iterator α Id β] [F
   rw [Iter.foldM_eq_forIn, ← Iter.forIn_toList]
   simp only [List.forIn_yield_eq_foldlM, id_map']
 
-theorem Iter.foldlM_toArray {α β : Type w} {γ : Type x} [Iterator α Id β] [Finite α Id]
-    {m : Type x → Type x'} [Monad m] [LawfulMonad m] [IteratorLoop α Id m]
-    [LawfulIteratorLoop α Id m] [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
-    {f : γ → β → m γ} {init : γ} {it : Iter (α := α) β} :
-    it.toArray.foldlM (init := init) f = it.foldM (init := init) f := by
-  rw [Iter.foldM_eq_forIn, ← Iter.forIn_toArray]
-  simp only [Array.forIn_yield_eq_foldlM, id_map']
-
 theorem IterM.forIn_eq_foldM {α β : Type w} [Iterator α Id β]
     [Finite α Id] {m : Type x → Type x'} [Monad m] [LawfulMonad m]
     [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
@@ -386,12 +324,6 @@ theorem Iter.fold_eq_foldM {α β : Type w} {γ : Type x} [Iterator α Id β]
     it.fold (init := init) f = (it.foldM (m := Id) (init := init) (pure <| f · ·)).run := by
   simp [foldM_eq_forIn, fold_eq_forIn]
 
-theorem Iter.fold_eq_fold_toIterM {α β : Type w} {γ : Type w} [Iterator α Id β]
-    [Finite α Id] [IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
-    {f : γ → β → γ} {init : γ} {it : Iter (α := α) β} :
-    it.fold (init := init) f = (it.toIterM.fold (init := init) f).run := by
-  rw [fold_eq_foldM, foldM_eq_foldM_toIterM, IterM.fold_eq_foldM]
-
 @[simp]
 theorem Iter.forIn_pure_yield_eq_fold {α β : Type w} {γ : Type x} [Iterator α Id β]
     [Finite α Id] [IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id] {f : β → γ → γ} {init : γ}
@@ -412,38 +344,6 @@ theorem Iter.fold_eq_match_step {α β : Type w} {γ : Type x} [Iterator α Id
   generalize it.step = step
   cases step using PlausibleIterStep.casesOn <;> simp
 
--- The argument `f : γ₁ → γ₂` is intentionally explicit, as it is sometimes not found by unification.
-theorem Iter.fold_hom [Iterator α Id β] [Finite α Id]
-    [IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
-    {it : Iter (α := α) β}
-    (f : γ₁ → γ₂) {g₁ : γ₁ → β → γ₁} {g₂ : γ₂ → β → γ₂} {init : γ₁}
-    (H : ∀ x y, g₂ (f x) y = f (g₁ x y)) :
-    it.fold g₂ (f init) = f (it.fold g₁ init) := by
-  -- We cannot reduce to `IterM.fold_hom` because `IterM.fold` is necessarily more restrictive
-  -- w.r.t. the universe of the output.
-  induction it using Iter.inductSteps generalizing init with | step it ihy ihs =>
-  rw [fold_eq_match_step, fold_eq_match_step]
-  split
-  · rw [H, ihy ‹_›]
-  · rw [ihs ‹_›]
-  · simp
-
-theorem Iter.toList_eq_fold {α β : Type w} [Iterator α Id β]
-    [Finite α Id] [IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
-    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
-    {it : Iter (α := α) β} :
-    it.toList = it.fold (init := []) (fun l out => l ++ [out]) := by
-  rw [Iter.toList_eq_toList_toIterM, IterM.toList_eq_fold, Iter.fold_eq_fold_toIterM]
-
-theorem Iter.toArray_eq_fold {α β : Type w} [Iterator α Id β]
-    [Finite α Id] [IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
-    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
-    {it : Iter (α := α) β} :
-    it.toArray = it.fold (init := #[]) (fun xs out => xs.push out) := by
-  simp only [← toArray_toList, toList_eq_fold]
-  rw [← fold_hom (List.toArray)]
-  simp
-
 @[simp]
 theorem Iter.foldl_toList {α β : Type w} {γ : Type x} [Iterator α Id β] [Finite α Id]
     [IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
@@ -452,14 +352,6 @@ theorem Iter.foldl_toList {α β : Type w} {γ : Type x} [Iterator α Id β] [Fi
     it.toList.foldl (init := init) f = it.fold (init := init) f := by
   rw [fold_eq_foldM, List.foldl_eq_foldlM, ← Iter.foldlM_toList]
 
-@[simp]
-theorem Iter.foldl_toArray {α β : Type w} {γ : Type x} [Iterator α Id β] [Finite α Id]
-    [IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
-    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
-    {f : γ → β → γ} {init : γ} {it : Iter (α := α) β} :
-    it.toArray.foldl (init := init) f = it.fold (init := init) f := by
-  rw [fold_eq_foldM, Array.foldl_eq_foldlM, ← Iter.foldlM_toArray]
-
 @[simp]
 theorem Iter.size_toArray_eq_size {α β : Type w} [Iterator α Id β] [Finite α Id]
     [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]

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

@@ -67,17 +67,15 @@ theorem IterM.toArray_eq_match_step [Monad m] [LawfulMonad m] [Iterator α m β]
   rw [IterM.DefaultConsumers.toArrayMapped_eq_match_step]
   simp [bind_pure_comp, pure_bind]
 
-@[simp]
 theorem IterM.toList_toArray [Monad m] [Iterator α m β] [Finite α m] [IteratorCollect α m m]
     {it : IterM (α := α) m β} :
     Array.toList <$> it.toArray = it.toList := by
   simp [IterM.toList]
 
-@[simp]
 theorem IterM.toArray_toList [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
     [IteratorCollect α m m] {it : IterM (α := α) m β} :
     List.toArray <$> it.toList = it.toArray := by
-  simp [IterM.toList, -toList_toArray]
+  simp [IterM.toList]
 
 theorem IterM.toList_eq_match_step [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
     [IteratorCollect α m m] [LawfulIteratorCollect α m m] {it : IterM (α := α) m β} :
@@ -155,6 +153,6 @@ theorem LawfulIteratorCollect.toList_eq {α β : Type w} {m : Type w → Type w'
     [hl : LawfulIteratorCollect α m m]
     {it : IterM (α := α) m β} :
     it.toList = (letI : IteratorCollect α m m := .defaultImplementation; it.toList) := by
-  simp [IterM.toList, toArray_eq, -IterM.toList_toArray]
+  simp [IterM.toList, toArray_eq]
 
 end Std.Iterators

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

@@ -60,20 +60,6 @@ theorem IterM.forIn_eq {α β : Type w} {m : Type w → Type w'} [Iterator α m
         IteratorLoop.wellFounded_of_finite it init _ (fun _ => id) (fun out _ acc => (⟨·, .intro⟩) <$> f out acc) := by
   simp only [ForIn.forIn, forIn'_eq]
 
-@[congr] theorem IterM.forIn'_congr {α β : Type w} {m : Type w → Type w'} [Monad m]
-    [Iterator α m β] [Finite α m] [IteratorLoop α m m]
-    {ita itb : IterM (α := α) m β} (w : ita = itb)
-    {b b' : γ} (hb : b = b')
-    {f : (a' : β) → _ → γ → m (ForInStep γ)}
-    {g : (a' : β) → _ → γ → m (ForInStep γ)}
-    (h : ∀ a m b, f a (by simpa [w] using m) b = g a m b) :
-    letI : ForIn' m (IterM (α := α) m β) β _ := IterM.instForIn'
-    forIn' ita b f = forIn' itb b' g := by
-  subst_eqs
-  simp only [← funext_iff] at h
-  rw [← h]
-  rfl
-
 theorem IterM.forIn'_eq_match_step {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
     [Finite α m] {n : Type w → Type w''} [Monad m] [Monad n] [LawfulMonad n]
     [IteratorLoop α m n] [LawfulIteratorLoop α m n]
@@ -214,23 +200,6 @@ theorem IterM.fold_eq_match_step {α β γ : Type w} {m : Type w → Type w'} [I
   intro step
   cases step using PlausibleIterStep.casesOn <;> simp
 
--- The argument `f : γ₁ → γ₂` is intentionally explicit, as it is sometimes not found by unification.
-theorem IterM.fold_hom {m : Type w → Type w'} [Iterator α m β] [Finite α m]
-    [Monad m] [LawfulMonad m] [IteratorLoop α m m] [LawfulIteratorLoop α m m]
-    {it : IterM (α := α) m β}
-    (f : γ₁ → γ₂) {g₁ : γ₁ → β → γ₁} {g₂ : γ₂ → β → γ₂} {init : γ₁}
-    (H : ∀ x y, g₂ (f x) y = f (g₁ x y)) :
-    it.fold g₂ (f init) = f <$> (it.fold g₁ init) := by
-  induction it using IterM.inductSteps generalizing init with | step it ihy ihs =>
-  rw [fold_eq_match_step, fold_eq_match_step, map_eq_pure_bind, bind_assoc]
-  apply bind_congr
-  intro step
-  rw [bind_pure_comp]
-  split
-  · rw [H, ihy ‹_›]
-  · rw [ihs ‹_›]
-  · simp
-
 theorem IterM.toList_eq_fold {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
     [Finite α m] [Monad m] [LawfulMonad m] [IteratorLoop α m m] [LawfulIteratorLoop α m m]
     [IteratorCollect α m m] [LawfulIteratorCollect α m m]
@@ -254,15 +223,6 @@ theorem IterM.toList_eq_fold {α β : Type w} {m : Type w → Type w'} [Iterator
     simp [ihs h]
   · simp
 
-theorem IterM.toArray_eq_fold {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
-    [Finite α m] [Monad m] [LawfulMonad m] [IteratorLoop α m m] [LawfulIteratorLoop α m m]
-    [IteratorCollect α m m] [LawfulIteratorCollect α m m]
-    {it : IterM (α := α) m β} :
-    it.toArray = it.fold (init := #[]) (fun xs out => xs.push out) := by
-  simp only [← toArray_toList, toList_eq_fold]
-  rw [← fold_hom]
-  simp
-
 theorem IterM.drain_eq_fold {α β : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
     [Monad m] [IteratorLoop α m m] {it : IterM (α := α) m β} :
     it.drain = it.fold (init := PUnit.unit) (fun _ _ => .unit) :=

src/Init/Data/List/Attach.lean

@@ -167,14 +167,14 @@ theorem attachWith_map_subtype_val {p : α → Prop} {l : List α} (H : ∀ a
     (l.attachWith p H).map Subtype.val = l :=
   (attachWith_map_val _).trans (List.map_id _)
 
-@[simp, grind ←]
+@[simp, grind]
 theorem mem_attach (l : List α) : ∀ x, x ∈ l.attach
   | ⟨a, h⟩ => by
     have := mem_map.1 (by rw [attach_map_subtype_val]; exact h)
     rcases this with ⟨⟨_, _⟩, m, rfl⟩
     exact m
 
-@[simp, grind =]
+@[simp, grind]
 theorem mem_attachWith {l : List α} {q : α → Prop} (H) (x : {x // q x}) :
     x ∈ l.attachWith q H ↔ x.1 ∈ l := by
   induction l with
@@ -192,13 +192,12 @@ theorem mem_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H b} :
     b ∈ pmap f l H ↔ ∃ (a : _) (h : a ∈ l), f a (H a h) = b := by
   simp only [pmap_eq_map_attach, mem_map, mem_attach, true_and, Subtype.exists, eq_comm]
 
+@[grind]
 theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {l H} {a} (h : a ∈ l) :
     f a (H a h) ∈ pmap f l H := by
   rw [mem_pmap]
   exact ⟨a, h, rfl⟩
 
-grind_pattern mem_pmap_of_mem => _ ∈ pmap f l H, a ∈ l
-
 @[simp, grind =]
 theorem length_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H} : (pmap f l H).length = l.length := by
   induction l
@@ -371,13 +370,13 @@ theorem getElem_attach {xs : List α} {i : Nat} (h : i < xs.attach.length) :
     xs.attach.tail = xs.tail.attach.map (fun ⟨x, h⟩ => ⟨x, mem_of_mem_tail h⟩) := by
   cases xs <;> simp
 
-@[grind =]
+@[grind]
 theorem foldl_pmap {l : List α} {P : α → Prop} {f : (a : α) → P a → β}
     (H : ∀ (a : α), a ∈ l → P a) (g : γ → β → γ) (x : γ) :
     (l.pmap f H).foldl g x = l.attach.foldl (fun acc a => g acc (f a.1 (H _ a.2))) x := by
   rw [pmap_eq_map_attach, foldl_map]
 
-@[grind =]
+@[grind]
 theorem foldr_pmap {l : List α} {P : α → Prop} {f : (a : α) → P a → β}
     (H : ∀ (a : α), a ∈ l → P a) (g : β → γ → γ) (x : γ) :
     (l.pmap f H).foldr g x = l.attach.foldr (fun a acc => g (f a.1 (H _ a.2)) acc) x := by

src/Init/Data/List/Basic.lean

@@ -80,17 +80,17 @@ namespace List
 
 /-! ### length -/
 
-@[simp, grind =] theorem length_nil : length ([] : List α) = 0 :=
+@[simp, grind] theorem length_nil : length ([] : List α) = 0 :=
   rfl
 
 @[simp] theorem length_singleton {a : α} : length [a] = 1 := rfl
 
-@[simp, grind =] theorem length_cons {a : α} {as : List α} : (cons a as).length = as.length + 1 :=
+@[simp, grind] theorem length_cons {a : α} {as : List α} : (cons a as).length = as.length + 1 :=
   rfl
 
 /-! ### set -/
 
-@[simp, grind =] theorem length_set {as : List α} {i : Nat} {a : α} : (as.set i a).length = as.length := by
+@[simp, grind] theorem length_set {as : List α} {i : Nat} {a : α} : (as.set i a).length = as.length := by
   induction as generalizing i with
   | nil => rfl
   | cons x xs ih =>
@@ -101,8 +101,8 @@ namespace List
 /-! ### foldl -/
 
 -- As `List.foldl` is defined in `Init.Prelude`, we write the basic simplification lemmas here.
-@[simp, grind =] theorem foldl_nil : [].foldl f b = b := rfl
-@[simp, grind =] theorem foldl_cons {l : List α} {f : β → α → β} {b : β} : (a :: l).foldl f b = l.foldl f (f b a) := rfl
+@[simp, grind] theorem foldl_nil : [].foldl f b = b := rfl
+@[simp, grind] theorem foldl_cons {l : List α} {f : β → α → β} {b : β} : (a :: l).foldl f b = l.foldl f (f b a) := rfl
 
 /-! ### concat -/
 
@@ -332,7 +332,7 @@ def getLast? : List α → Option α
   | []    => none
   | a::as => some (getLast (a::as) (fun h => List.noConfusion h))
 
-@[simp, grind =] theorem getLast?_nil : @getLast? α [] = none := rfl
+@[simp, grind] theorem getLast?_nil : @getLast? α [] = none := rfl
 
 /-! ### getLastD -/
 
@@ -365,7 +365,7 @@ Returns the first element of a non-empty list.
 def head : (as : List α) → as ≠ [] → α
   | a::_, _ => a
 
-@[simp, grind =] theorem head_cons {a : α} {l : List α} {h} : head (a::l) h = a := rfl
+@[simp, grind] theorem head_cons {a : α} {l : List α} {h} : head (a::l) h = a := rfl
 
 /-! ### head? -/
 
@@ -383,8 +383,8 @@ def head? : List α → Option α
   | []   => none
   | a::_ => some a
 
-@[simp, grind =] theorem head?_nil : head? ([] : List α) = none := rfl
-@[simp, grind =] theorem head?_cons {a : α} {l : List α} : head? (a::l) = some a := rfl
+@[simp, grind] theorem head?_nil : head? ([] : List α) = none := rfl
+@[simp, grind] theorem head?_cons {a : α} {l : List α} : head? (a::l) = some a := rfl
 
 /-! ### headD -/
 
@@ -420,8 +420,8 @@ def tail : List α → List α
   | []    => []
   | _::as => as
 
-@[simp, grind =] theorem tail_nil : tail ([] : List α) = [] := rfl
-@[simp, grind =] theorem tail_cons {a : α} {as : List α} : tail (a::as) = as := rfl
+@[simp, grind] theorem tail_nil : tail ([] : List α) = [] := rfl
+@[simp, grind] theorem tail_cons {a : α} {as : List α} : tail (a::as) = as := rfl
 
 /-! ### tail? -/
 
@@ -441,8 +441,8 @@ def tail? : List α → Option (List α)
   | []    => none
   | _::as => some as
 
-@[simp, grind =] theorem tail?_nil : tail? ([] : List α) = none := rfl
-@[simp, grind =] theorem tail?_cons {a : α} {l : List α} : tail? (a::l) = some l := rfl
+@[simp, grind] theorem tail?_nil : tail? ([] : List α) = none := rfl
+@[simp, grind] theorem tail?_cons {a : α} {l : List α} : tail? (a::l) = some l := rfl
 
 /-! ### tailD -/
 
@@ -475,8 +475,23 @@ We define the basic functional programming operations on `List`:
 
 /-! ### map -/
 
-@[simp, grind =] theorem map_nil {f : α → β} : map f [] = [] := rfl
-@[simp, grind =] theorem map_cons {f : α → β} {a : α} {l : List α} : map f (a :: l) = f a :: map f l := rfl
+/--
+Applies a function to each element of the list, returning the resulting list of values.
+
+`O(|l|)`.
+
+Examples:
+* `[a, b, c].map f = [f a, f b, f c]`
+* `[].map Nat.succ = []`
+* `["one", "two", "three"].map (·.length) = [3, 3, 5]`
+* `["one", "two", "three"].map (·.reverse) = ["eno", "owt", "eerht"]`
+-/
+@[specialize] def map (f : α → β) : (l : List α) → List β
+  | []    => []
+  | a::as => f a :: map f as
+
+@[simp, grind] theorem map_nil {f : α → β} : map f [] = [] := rfl
+@[simp, grind] theorem map_cons {f : α → β} {a : α} {l : List α} : map f (a :: l) = f a :: map f l := rfl
 
 /-! ### filter -/
 
@@ -496,7 +511,7 @@ def filter (p : α → Bool) : (l : List α) → List α
     | true => a :: filter p as
     | false => filter p as
 
-@[simp, grind =] theorem filter_nil {p : α → Bool} : filter p [] = [] := rfl
+@[simp, grind] theorem filter_nil {p : α → Bool} : filter p [] = [] := rfl
 
 /-! ### filterMap -/
 
@@ -522,8 +537,8 @@ Example:
     | none   => filterMap f as
     | some b => b :: filterMap f as
 
-@[simp, grind =] theorem filterMap_nil {f : α → Option β} : filterMap f [] = [] := rfl
-@[grind =] theorem filterMap_cons {f : α → Option β} {a : α} {l : List α} :
+@[simp, grind] theorem filterMap_nil {f : α → Option β} : filterMap f [] = [] := rfl
+@[grind] theorem filterMap_cons {f : α → Option β} {a : α} {l : List α} :
     filterMap f (a :: l) =
       match f a with
       | none => filterMap f l
@@ -546,8 +561,8 @@ Examples:
   | []     => init
   | a :: l => f a (foldr f init l)
 
-@[simp, grind =] theorem foldr_nil : [].foldr f b = b := rfl
-@[simp, grind =] theorem foldr_cons {a} {l : List α} {f : α → β → β} {b} :
+@[simp, grind] theorem foldr_nil : [].foldr f b = b := rfl
+@[simp, grind] theorem foldr_cons {a} {l : List α} {f : α → β → β} {b} :
     (a :: l).foldr f b = f a (l.foldr f b) := rfl
 
 /-! ### reverse -/
@@ -576,7 +591,7 @@ Examples:
 @[expose] def reverse (as : List α) : List α :=
   reverseAux as []
 
-@[simp, grind =] theorem reverse_nil : reverse ([] : List α) = [] := rfl
+@[simp, grind] theorem reverse_nil : reverse ([] : List α) = [] := rfl
 
 theorem reverseAux_reverseAux {as bs cs : List α} :
     reverseAux (reverseAux as bs) cs = reverseAux bs (reverseAux (reverseAux as []) cs) := by
@@ -591,6 +606,20 @@ Appends two lists. Normally used via the `++` operator.
 
 Appending lists takes time proportional to the length of the first list: `O(|xs|)`.
 
+Examples:
+  * `[1, 2, 3] ++ [4, 5] = [1, 2, 3, 4, 5]`.
+  * `[] ++ [4, 5] = [4, 5]`.
+  * `[1, 2, 3] ++ [] = [1, 2, 3]`.
+-/
+protected def append : (xs ys : List α) → List α
+  | [],    bs => bs
+  | a::as, bs => a :: List.append as bs
+
+/--
+Appends two lists. Normally used via the `++` operator.
+
+Appending lists takes time proportional to the length of the first list: `O(|xs|)`.
+
 This is a tail-recursive version of `List.append`.
 
 Examples:
@@ -616,10 +645,10 @@ instance : Append (List α) := ⟨List.append⟩
 
 @[simp] theorem append_eq {as bs : List α} : List.append as bs = as ++ bs := rfl
 
-@[simp, grind =] theorem nil_append (as : List α) : [] ++ as = as := rfl
+@[simp, grind] theorem nil_append (as : List α) : [] ++ as = as := rfl
 @[simp, grind _=_] theorem cons_append {a : α} {as bs : List α} : (a::as) ++ bs = a::(as ++ bs) := rfl
 
-@[simp, grind =] theorem append_nil (as : List α) : as ++ [] = as := by
+@[simp, grind] theorem append_nil (as : List α) : as ++ [] = as := by
   induction as with
   | nil => rfl
   | cons a as ih =>
@@ -629,7 +658,7 @@ instance : Std.LawfulIdentity (α := List α) (· ++ ·) [] where
   left_id := nil_append
   right_id := append_nil
 
-@[simp, grind =] theorem length_append {as bs : List α} : (as ++ bs).length = as.length + bs.length := by
+@[simp, grind] theorem length_append {as bs : List α} : (as ++ bs).length = as.length + bs.length := by
   induction as with
   | nil => simp
   | cons _ as ih => simp [ih, Nat.succ_add]
@@ -656,15 +685,27 @@ theorem reverseAux_eq_append {as bs : List α} : reverseAux as bs = reverseAux a
     rw [ih (bs := a :: bs), ih (bs := [a]), append_assoc]
     rfl
 
-@[simp, grind =] theorem reverse_cons {a : α} {as : List α} : reverse (a :: as) = reverse as ++ [a] := by
+@[simp, grind] theorem reverse_cons {a : α} {as : List α} : reverse (a :: as) = reverse as ++ [a] := by
   simp [reverse, reverseAux]
   rw [← reverseAux_eq_append]
 
 /-! ### flatten -/
 
+/--
+Concatenates a list of lists into a single list, preserving the order of the elements.
 
-@[simp, grind =] theorem flatten_nil : List.flatten ([] : List (List α)) = [] := rfl
-@[simp, grind =] theorem flatten_cons : (l :: L).flatten = l ++ L.flatten := rfl
+`O(|flatten L|)`.
+
+Examples:
+* `[["a"], ["b", "c"]].flatten = ["a", "b", "c"]`
+* `[["a"], [], ["b", "c"], ["d", "e", "f"]].flatten = ["a", "b", "c", "d", "e", "f"]`
+-/
+def flatten : List (List α) → List α
+  | []      => []
+  | l :: L => l ++ flatten L
+
+@[simp, grind] theorem flatten_nil : List.flatten ([] : List (List α)) = [] := rfl
+@[simp, grind] theorem flatten_cons : (l :: L).flatten = l ++ L.flatten := rfl
 
 /-! ### singleton -/
 
@@ -680,13 +721,19 @@ Examples:
 
 /-! ### flatMap -/
 
-@[simp, grind =] theorem flatMap_nil {f : α → List β} : List.flatMap f [] = [] := by simp [List.flatMap]
-@[simp, grind =] theorem flatMap_cons {x : α} {xs : List α} {f : α → List β} :
-  List.flatMap f (x :: xs) = f x ++ List.flatMap f xs := by simp [List.flatMap]
+/--
+Applies a function that returns a list to each element of a list, and concatenates the resulting
+lists.
 
-@[simp, grind _=_] theorem flatMap_append {xs ys : List α} {f : α → List β} :
-    (xs ++ ys).flatMap f = xs.flatMap f ++ ys.flatMap f := by
-  induction xs; {rfl}; simp_all [flatMap_cons, append_assoc]
+Examples:
+* `[2, 3, 2].flatMap List.range = [0, 1, 0, 1, 2, 0, 1]`
+* `["red", "blue"].flatMap String.toList = ['r', 'e', 'd', 'b', 'l', 'u', 'e']`
+-/
+@[inline] def flatMap {α : Type u} {β : Type v} (b : α → List β) (as : List α) : List β := flatten (map b as)
+
+@[simp, grind] theorem flatMap_nil {f : α → List β} : List.flatMap f [] = [] := by simp [List.flatMap]
+@[simp, grind] theorem flatMap_cons {x : α} {xs : List α} {f : α → List β} :
+  List.flatMap f (x :: xs) = f x ++ List.flatMap f xs := by simp [List.flatMap]
 
 /-! ### replicate -/
 
@@ -701,10 +748,10 @@ def replicate : (n : Nat) → (a : α) → List α
   | 0,   _ => []
   | n+1, a => a :: replicate n a
 
-@[simp, grind =] theorem replicate_zero {a : α} : replicate 0 a = [] := rfl
-@[grind =] theorem replicate_succ {a : α} {n : Nat} : replicate (n+1) a = a :: replicate n a := rfl
+@[simp, grind] theorem replicate_zero {a : α} : replicate 0 a = [] := rfl
+@[grind] theorem replicate_succ {a : α} {n : Nat} : replicate (n+1) a = a :: replicate n a := rfl
 
-@[simp, grind =] theorem length_replicate {n : Nat} {a : α} : (replicate n a).length = n := by
+@[simp, grind] theorem length_replicate {n : Nat} {a : α} : (replicate n a).length = n := by
   induction n with
   | zero => simp
   | succ n ih => simp only [ih, replicate_succ, length_cons]
@@ -772,8 +819,8 @@ def isEmpty : List α → Bool
   | []     => true
   | _ :: _ => false
 
-@[simp, grind =] theorem isEmpty_nil : ([] : List α).isEmpty = true := rfl
-@[simp, grind =] theorem isEmpty_cons : (x :: xs : List α).isEmpty = false := rfl
+@[simp, grind] theorem isEmpty_nil : ([] : List α).isEmpty = true := rfl
+@[simp, grind] theorem isEmpty_cons : (x :: xs : List α).isEmpty = false := rfl
 
 /-! ### elem -/
 
@@ -795,7 +842,7 @@ def elem [BEq α] (a : α) : (l : List α) → Bool
     | true  => true
     | false => elem a bs
 
-@[simp, grind =] theorem elem_nil [BEq α] : ([] : List α).elem a = false := rfl
+@[simp, grind] theorem elem_nil [BEq α] : ([] : List α).elem a = false := rfl
 theorem elem_cons [BEq α] {a : α} :
     (b::bs).elem a = match a == b with | true => true | false => bs.elem a := rfl
 
@@ -911,9 +958,9 @@ def take : (n : Nat) → (xs : List α) → List α
   | _+1, []    => []
   | n+1, a::as => a :: take n as
 
-@[simp, grind =] theorem take_nil {i : Nat} : ([] : List α).take i = [] := by cases i <;> rfl
-@[simp, grind =] theorem take_zero {l : List α} : l.take 0 = [] := rfl
-@[simp, grind =] theorem take_succ_cons {a : α} {as : List α} {i : Nat} : (a::as).take (i+1) = a :: as.take i := rfl
+@[simp, grind] theorem take_nil {i : Nat} : ([] : List α).take i = [] := by cases i <;> rfl
+@[simp, grind] theorem take_zero {l : List α} : l.take 0 = [] := rfl
+@[simp, grind] theorem take_succ_cons {a : α} {as : List α} {i : Nat} : (a::as).take (i+1) = a :: as.take i := rfl
 
 /-! ### drop -/
 
@@ -933,10 +980,10 @@ def drop : (n : Nat) → (xs : List α) → List α
   | _+1, []    => []
   | n+1, _::as => drop n as
 
-@[simp, grind =] theorem drop_nil : ([] : List α).drop i = [] := by
+@[simp, grind] theorem drop_nil : ([] : List α).drop i = [] := by
   cases i <;> rfl
-@[simp, grind =] theorem drop_zero {l : List α} : l.drop 0 = l := rfl
-@[simp, grind =] theorem drop_succ_cons {a : α} {l : List α} {i : Nat} : (a :: l).drop (i + 1) = l.drop i := rfl
+@[simp, grind] theorem drop_zero {l : List α} : l.drop 0 = l := rfl
+@[simp, grind] theorem drop_succ_cons {a : α} {l : List α} {i : Nat} : (a :: l).drop (i + 1) = l.drop i := rfl
 
 theorem drop_eq_nil_of_le {as : List α} {i : Nat} (h : as.length ≤ i) : as.drop i = [] := by
   match as, i with
@@ -1047,13 +1094,13 @@ def dropLast {α} : List α → List α
   | [_]   => []
   | a::as => a :: dropLast as
 
-@[simp, grind =] theorem dropLast_nil : ([] : List α).dropLast = [] := rfl
-@[simp, grind =] theorem dropLast_singleton : [x].dropLast = [] := rfl
+@[simp, grind] theorem dropLast_nil : ([] : List α).dropLast = [] := rfl
+@[simp, grind] theorem dropLast_singleton : [x].dropLast = [] := rfl
 
 @[deprecated dropLast_singleton (since := "2025-04-16")]
 theorem dropLast_single : [x].dropLast = [] := dropLast_singleton
 
-@[simp, grind =] theorem dropLast_cons₂ :
+@[simp, grind] theorem dropLast_cons₂ :
     (x::y::zs).dropLast = x :: (y::zs).dropLast := rfl
 
 -- Later this can be proved by `simp` via `[List.length_dropLast, List.length_cons, Nat.add_sub_cancel]`,
@@ -1392,8 +1439,8 @@ def replace [BEq α] : (l : List α) → (a : α) → (b : α) → List α
     | true  => c::as
     | false => a :: replace as b c
 
-@[simp, grind =] theorem replace_nil [BEq α] : ([] : List α).replace a b = [] := rfl
-@[grind =] theorem replace_cons [BEq α] {a : α} :
+@[simp, grind] theorem replace_nil [BEq α] : ([] : List α).replace a b = [] := rfl
+@[grind] theorem replace_cons [BEq α] {a : α} :
     (a::as).replace b c = match b == a with | true => c::as | false => a :: replace as b c :=
   rfl
 
@@ -1601,8 +1648,8 @@ def findSome? (f : α → Option β) : List α → Option β
     | some b => some b
     | none   => findSome? f as
 
-@[simp, grind =] theorem findSome?_nil : ([] : List α).findSome? f = none := rfl
-@[grind =] theorem findSome?_cons {f : α → Option β} :
+@[simp, grind] theorem findSome?_nil : ([] : List α).findSome? f = none := rfl
+@[grind] theorem findSome?_cons {f : α → Option β} :
     (a::as).findSome? f = match f a with | some b => some b | none => as.findSome? f :=
   rfl
 
@@ -1859,8 +1906,8 @@ def any : (l : List α) → (p : α → Bool) → Bool
   | [], _ => false
   | h :: t, p => p h || any t p
 
-@[simp, grind =] theorem any_nil : [].any f = false := rfl
-@[simp, grind =] theorem any_cons : (a::l).any f = (f a || l.any f) := rfl
+@[simp, grind] theorem any_nil : [].any f = false := rfl
+@[simp, grind] theorem any_cons : (a::l).any f = (f a || l.any f) := rfl
 
 /-! ### all -/
 
@@ -1878,8 +1925,8 @@ def all : List α → (α → Bool) → Bool
   | [], _ => true
   | h :: t, p => p h && all t p
 
-@[simp, grind =] theorem all_nil : [].all f = true := rfl
-@[simp, grind =] theorem all_cons : (a::l).all f = (f a && l.all f) := rfl
+@[simp, grind] theorem all_nil : [].all f = true := rfl
+@[simp, grind] theorem all_cons : (a::l).all f = (f a && l.all f) := rfl
 
 /-! ### or -/
 
@@ -2019,8 +2066,8 @@ Examples:
 def sum {α} [Add α] [Zero α] : List α → α :=
   foldr (· + ·) 0
 
-@[simp, grind =] theorem sum_nil [Add α] [Zero α] : ([] : List α).sum = 0 := rfl
-@[simp, grind =] theorem sum_cons [Add α] [Zero α] {a : α} {l : List α} : (a::l).sum = a + l.sum := rfl
+@[simp, grind] theorem sum_nil [Add α] [Zero α] : ([] : List α).sum = 0 := rfl
+@[simp, grind] theorem sum_cons [Add α] [Zero α] {a : α} {l : List α} : (a::l).sum = a + l.sum := rfl
 
 /-! ### range -/
 

src/Init/Data/List/Count.lean

@@ -223,7 +223,7 @@ variable [BEq α]
 
 @[simp, grind =] theorem count_nil {a : α} : count a [] = 0 := rfl
 
-@[grind =]
+@[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]
@@ -237,7 +237,7 @@ theorem count_eq_countP' {a : α} : count a = countP (· == a) := by
 theorem count_eq_length_filter {a : α} {l : List α} : count a l = (filter (· == a) l).length := by
   simp [count, countP_eq_length_filter]
 
-@[grind =]
+@[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
@@ -380,7 +380,7 @@ 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 =]
+@[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

@@ -130,7 +130,7 @@ theorem le_length_eraseP {l : List α} : l.length - 1 ≤ (l.eraseP p).length :=
 @[grind →]
 theorem mem_of_mem_eraseP {l : List α} : a ∈ l.eraseP p → a ∈ l := (eraseP_subset ·)
 
-@[simp, grind =] 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
@@ -265,18 +265,14 @@ 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_pattern Pairwise.eraseP => Pairwise p (l.eraseP q)
-grind_pattern Pairwise.eraseP => Pairwise p l, l.eraseP q
-
+@[grind ←]
 theorem Nodup.eraseP (p) : Nodup l → Nodup (l.eraseP p) :=
   Pairwise.eraseP p
 
-grind_pattern Nodup.eraseP => Nodup (l.eraseP p)
-grind_pattern Nodup.eraseP => Nodup l, l.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
@@ -397,7 +393,7 @@ theorem le_length_erase [LawfulBEq α] {a : α} {l : List α} : l.length - 1 ≤
 @[grind →]
 theorem mem_of_mem_erase {a b : α} {l : List α} (h : a ∈ l.erase b) : a ∈ l := erase_subset h
 
-@[simp, grind =] 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)
 
@@ -512,12 +508,10 @@ theorem Nodup.not_mem_erase [LawfulBEq α] {a : α} (h : Nodup l) : a ∉ l.eras
 -- 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
 
-grind_pattern Nodup.erase => Nodup (l.erase a)
-grind_pattern Nodup.erase => Nodup l, l.erase a
-
 theorem head_erase_mem (xs : List α) (a : α) (h) : (xs.erase a).head h ∈ xs :=
   erase_sublist.head_mem h
 
@@ -584,21 +578,21 @@ theorem eraseIdx_ne_nil_iff {l : List α} {i : Nat} : eraseIdx l i ≠ [] ↔ 2
   | [a]
   | a::b::l => simp
 
+
+
+@[grind]
 theorem eraseIdx_sublist : ∀ (l : List α) (k : Nat), eraseIdx l k <+ l
   | [], _ => by simp
   | a::l, 0 => by simp
   | a::l, k + 1 => by simp [eraseIdx_sublist]
 
-grind_pattern eraseIdx_sublist => l.eraseIdx 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
 
-grind_pattern eraseIdx_sublist => l.eraseIdx k, _ ⊆ l
-
 @[simp]
 theorem eraseIdx_eq_self : ∀ {l : List α} {k : Nat}, eraseIdx l k = l ↔ length l ≤ k
   | [], _ => by simp
@@ -655,18 +649,15 @@ 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_pattern Pairwise.eraseIdx => Pairwise p (l.eraseIdx k)
-grind_pattern Pairwise.eraseIdx => Pairwise p l, l.eraseIdx k
-
+@[grind ←]
 theorem Nodup.eraseIdx {l : List α} (k) : Nodup l → Nodup (l.eraseIdx k) :=
   Pairwise.eraseIdx k
 
-grind_pattern Nodup.eraseIdx => Nodup (l.eraseIdx k)
-grind_pattern Nodup.eraseIdx => Nodup l, l.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⟩
@@ -676,10 +667,6 @@ protected theorem IsPrefix.eraseIdx {l l' : List α} (h : l <+: l') (k : Nat) :
     rw [Nat.not_lt] at hkl
     simp [eraseIdx_append_of_length_le hkl, eraseIdx_of_length_le hkl]
 
-grind_pattern IsPrefix.eraseIdx => eraseIdx l k <+: eraseIdx l' k
-grind_pattern IsPrefix.eraseIdx => eraseIdx l k, l <+: l'
-grind_pattern IsPrefix.eraseIdx => eraseIdx l' k, l <+: l'
-
 -- See also `mem_eraseIdx_iff_getElem` and `mem_eraseIdx_iff_getElem?` in
 -- `Init/Data/List/Nat/Basic.lean`.
 
@@ -699,4 +686,6 @@ theorem erase_eq_eraseIdx_of_idxOf [BEq α] [LawfulBEq α]
     rw [eq_comm, eraseIdx_eq_self]
     exact Nat.le_of_eq (idxOf_eq_length h).symm
 
+
+
 end List

src/Init/Data/List/Find.lean

@@ -293,6 +293,7 @@ theorem mem_of_find?_eq_some : ∀ {l}, find? p l = some a → a ∈ l
     · exact H ▸ .head _
     · exact .tail _ (mem_of_find?_eq_some H)
 
+@[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
@@ -304,8 +305,6 @@ theorem get_find?_mem {xs : List α} {p : α → Bool} (h) : (xs.find? p).get h
       right
       apply ih
 
-grind_pattern get_find?_mem => (xs.find? p).get h
-
 @[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
@@ -559,6 +558,7 @@ 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

src/Init/Data/List/Lemmas.lean

@@ -28,14 +28,14 @@ For each `List` operation, we would like theorems describing the following, when
 * the length of the result `(f L).length`
 * the `i`-th element, described via `(f L)[i]` and/or `(f L)[i]?` (these should typically be `@[simp]`)
 * consequences for `f L` of the fact `x ∈ L` or `x ∉ L`
-* conditions characterizing `x ∈ f L` (often but not always `@[simp]`)
+* conditions characterising `x ∈ f L` (often but not always `@[simp]`)
 * injectivity statements, or congruence statements of the form `p L M → f L = f M`.
-* conditions characterizing the result, i.e. of the form `f L = M ↔ p M` for some predicate `p`,
+* conditions characterising the result, i.e. of the form `f L = M ↔ p M` for some predicate `p`,
   along with special cases of `M` (e.g. `List.append_eq_nil : L ++ M = [] ↔ L = [] ∧ M = []`)
-* negative characterizations are also useful, e.g. `List.cons_ne_nil`
+* negative characterisations are also useful, e.g. `List.cons_ne_nil`
 * interactions with all previously described `List` operations where possible
   (some of these should be `@[simp]`, particularly if the result can be described by a single operation)
-* characterizing `(∀ (i) (_ : i ∈ f L), P i)`, for some predicate `P`
+* characterising `(∀ (i) (_ : i ∈ f L), P i)`, for some predicate `P`
 
 Of course for any individual operation, not all of these will be relevant or helpful, so some judgement is required.
 
@@ -306,7 +306,7 @@ theorem getD_getElem? {l : List α} {i : Nat} {d : α} :
   match i, h with
   | 0, _ => rfl
 
-@[grind =]
+@[grind]
 theorem getElem?_singleton {a : α} {i : Nat} : [a][i]? = if i = 0 then some a else none := by
   simp [getElem?_cons]
 
@@ -348,18 +348,6 @@ theorem ext_getElem {l₁ l₂ : List α} (hl : length l₁ = length l₂)
 theorem getElem?_concat_length {l : List α} {a : α} : (l ++ [a])[l.length]? = some a := by
   simp
 
-theorem eq_getElem_of_length_eq_one : (l : List α) → (hl : l.length = 1) → l = [l[0]'(hl ▸ by decide)]
-  | [_], _ => rfl
-
-theorem eq_getElem_of_length_eq_two : (l : List α) → (hl : l.length = 2) → l = [l[0]'(hl ▸ by decide), l[1]'(hl ▸ by decide)]
-  | [_, _], _ => rfl
-
-theorem eq_getElem_of_length_eq_three : (l : List α) → (hl : l.length = 3) → l = [l[0]'(hl ▸ by decide), l[1]'(hl ▸ by decide), l[2]'(hl ▸ by decide)]
-  | [_, _, _], _ => rfl
-
-theorem eq_getElem_of_length_eq_four : (l : List α) → (hl : l.length = 4) → l = [l[0]'(hl ▸ by decide), l[1]'(hl ▸ by decide), l[2]'(hl ▸ by decide), l[3]'(hl ▸ by decide)]
-  | [_, _, _, _], _ => rfl
-
 /-! ### getD
 
 We simplify away `getD`, replacing `getD l n a` with `(l[n]?).getD a`.
@@ -394,20 +382,14 @@ theorem get!_eq_getElem! [Inhabited α] (l : List α) (i) : l.get! i = l[i]! :=
 
 @[simp] theorem not_mem_nil {a : α} : ¬ a ∈ [] := nofun
 
-@[simp, grind =] theorem mem_cons : a ∈ b :: l ↔ a = b ∨ a ∈ l :=
+@[simp] theorem mem_cons : a ∈ b :: l ↔ a = b ∨ a ∈ l :=
   ⟨fun h => by cases h <;> simp [Membership.mem, *],
    fun | Or.inl rfl => by constructor | Or.inr h => by constructor; assumption⟩
 
-theorem eq_or_mem_of_mem_cons {a b : α} {l : List α} :
+@[grind] theorem eq_or_mem_of_mem_cons {a b : α} {l : List α} :
     a ∈ b :: l → a = b ∨ a ∈ l := List.mem_cons.mp
 
--- This pattern may be excessively general:
--- it fires anytime we ae thinking about membership of lists,
--- and constructing a list via `cons`, even if the elements are unrelated.
--- Nevertheless in practice it is quite helpful!
-grind_pattern eq_or_mem_of_mem_cons => b :: l, a ∈ l
-
-theorem mem_cons_self {a : α} {l : List α} : a ∈ a :: l := .head ..
+@[grind] theorem mem_cons_self {a : α} {l : List α} : a ∈ a :: l := .head ..
 
 theorem mem_concat_self {xs : List α} {a : α} : a ∈ xs ++ [a] :=
   mem_append_right xs mem_cons_self
@@ -429,7 +411,7 @@ theorem eq_append_cons_of_mem {a : α} {xs : List α} (h : a ∈ xs) :
       · obtain ⟨as, bs, rfl, h⟩ := ih h
         exact ⟨x :: as, bs, rfl, by simp_all⟩
 
-theorem mem_cons_of_mem (y : α) {a : α} {l : List α} : a ∈ l → a ∈ y :: l := .tail _
+@[grind] theorem mem_cons_of_mem (y : α) {a : α} {l : List α} : a ∈ l → a ∈ y :: l := .tail _
 
 -- The argument `l : List α` is intentionally explicit,
 -- as a tactic may generate `h` without determining `l`.
@@ -565,10 +547,10 @@ theorem contains_iff [BEq α] [LawfulBEq α] {a : α} {as : List α} :
 theorem elem_eq_mem [BEq α] [LawfulBEq α] (a : α) (as : List α) :
     elem a as = decide (a ∈ as) := by rw [Bool.eq_iff_iff, elem_iff, decide_eq_true_iff]
 
-@[simp, grind =] theorem contains_eq_mem [BEq α] [LawfulBEq α] (a : α) (as : List α) :
+@[simp, grind] theorem contains_eq_mem [BEq α] [LawfulBEq α] (a : α) (as : List α) :
     as.contains a = decide (a ∈ as) := by rw [Bool.eq_iff_iff, elem_iff, decide_eq_true_iff]
 
-@[simp, grind =] theorem contains_cons [BEq α] {a : α} {b : α} {l : List α} :
+@[simp, grind] theorem contains_cons [BEq α] {a : α} {b : α} {l : List α} :
     (a :: l).contains b = (b == a || l.contains b) := by
   simp only [contains, elem_cons]
   split <;> simp_all
@@ -623,7 +605,7 @@ theorem decide_forall_mem {l : List α} {p : α → Prop} [DecidablePred p] :
 @[simp] theorem all_eq_false {l : List α} : l.all p = false ↔ ∃ x, x ∈ l ∧ ¬p x := by
   simp [all_eq]
 
-theorem any_beq [BEq α] {l : List α} {a : α} : (l.any fun x => a == x) = l.contains a := by
+@[grind] theorem any_beq [BEq α] {l : List α} {a : α} : (l.any fun x => a == x) = l.contains a := by
   induction l <;> simp_all [contains_cons]
 
 /-- Variant of `any_beq` with `==` reversed. -/
@@ -631,7 +613,7 @@ theorem any_beq' [BEq α] [PartialEquivBEq α] {l : List α} :
     (l.any fun x => x == a) = l.contains a := by
   simp only [BEq.comm, any_beq]
 
-theorem all_bne [BEq α] {l : List α} : (l.all fun x => a != x) = !l.contains a := by
+@[grind] theorem all_bne [BEq α] {l : List α} : (l.all fun x => a != x) = !l.contains a := by
   induction l <;> simp_all [bne]
 
 /-- Variant of `all_bne` with `!=` reversed. -/
@@ -642,10 +624,10 @@ theorem all_bne' [BEq α] [PartialEquivBEq α] {l : List α} :
 /-! ### set -/
 
 -- As `List.set` is defined in `Init.Prelude`, we write the basic simplification lemmas here.
-@[simp, grind =] theorem set_nil {i : Nat} {a : α} : [].set i a = [] := rfl
-@[simp, grind =] theorem set_cons_zero {x : α} {xs : List α} {a : α} :
+@[simp, grind] theorem set_nil {i : Nat} {a : α} : [].set i a = [] := rfl
+@[simp, grind] theorem set_cons_zero {x : α} {xs : List α} {a : α} :
   (x :: xs).set 0 a = a :: xs := rfl
-@[simp, grind =] theorem set_cons_succ {x : α} {xs : List α} {i : Nat} {a : α} :
+@[simp, grind] theorem set_cons_succ {x : α} {xs : List α} {i : Nat} {a : α} :
   (x :: xs).set (i + 1) a = x :: xs.set i a := rfl
 
 @[simp] theorem getElem_set_self {l : List α} {i : Nat} {a : α} (h : i < (l.set i a).length) :
@@ -688,14 +670,14 @@ theorem getElem?_set_self' {l : List α} {i : Nat} {a : α} :
     simp_all
   · rw [getElem?_eq_none (by simp_all), getElem?_eq_none (by simp_all)]
 
-@[grind =] theorem getElem_set {l : List α} {i j} {a} (h) :
+@[grind] theorem getElem_set {l : List α} {i j} {a} (h) :
     (set l i a)[j]'h = if i = j then a else l[j]'(length_set .. ▸ h) := by
   if h : i = j then
     subst h; simp only [getElem_set_self, ↓reduceIte]
   else
     simp [h]
 
-@[grind =] theorem getElem?_set {l : List α} {i j : Nat} {a : α} :
+@[grind] theorem getElem?_set {l : List α} {i j : Nat} {a : α} :
     (l.set i a)[j]? = if i = j then if i < l.length then some a else none else l[j]? := by
   if h : i = j then
     subst h
@@ -765,10 +747,10 @@ theorem mem_or_eq_of_mem_set : ∀ {l : List α} {i : Nat} {a b : α}, a ∈ l.s
 
 /-! ### BEq -/
 
-@[simp, grind =] theorem beq_nil_eq [BEq α] {l : List α} : (l == []) = l.isEmpty := by
+@[simp, grind] theorem beq_nil_eq [BEq α] {l : List α} : (l == []) = l.isEmpty := by
   cases l <;> rfl
 
-@[simp, grind =] theorem nil_beq_eq [BEq α] {l : List α} : ([] == l) = l.isEmpty := by
+@[simp, grind] theorem nil_beq_eq [BEq α] {l : List α} : ([] == l) = l.isEmpty := by
   cases l <;> rfl
 
 @[deprecated beq_nil_eq (since := "2025-04-04")]
@@ -777,7 +759,7 @@ abbrev beq_nil_iff := @beq_nil_eq
 @[deprecated nil_beq_eq (since := "2025-04-04")]
 abbrev nil_beq_iff := @nil_beq_eq
 
-@[simp, grind =] theorem cons_beq_cons [BEq α] {a b : α} {l₁ l₂ : List α} :
+@[simp, grind] theorem cons_beq_cons [BEq α] {a b : α} {l₁ l₂ : List α} :
     (a :: l₁ == b :: l₂) = (a == b && l₁ == l₂) := rfl
 
 @[simp] theorem concat_beq_concat [BEq α] {a b : α} {l₁ l₂ : List α} :
@@ -843,7 +825,7 @@ theorem length_eq_of_beq [BEq α] {l₁ l₂ : List α} (h : l₁ == l₂) : l
 
 /-! ### getLast -/
 
-@[grind =]
+@[grind]
 theorem getLast_eq_getElem : ∀ {l : List α} (h : l ≠ []),
     getLast l h = l[l.length - 1]'(by
       match l with
@@ -857,7 +839,7 @@ theorem getElem_length_sub_one_eq_getLast {l : List α} (h : l.length - 1 < l.le
     l[l.length - 1] = getLast l (by cases l; simp at h; simp) := by
   rw [← getLast_eq_getElem]
 
-@[simp, grind =] theorem getLast_cons_cons {a : α} {l : List α} :
+@[simp, grind] theorem getLast_cons_cons {a : α} {l : List α} :
     getLast (a :: b :: l) (by simp) = getLast (b :: l) (by simp) :=
   rfl
 
@@ -870,10 +852,10 @@ theorem getLast_cons {a : α} {l : List α} : ∀ (h : l ≠ nil),
 theorem getLast_eq_getLastD {a l} (h) : @getLast α (a::l) h = getLastD l a := by
   cases l <;> rfl
 
-@[simp, grind =] theorem getLastD_eq_getLast? {a l} : @getLastD α l a = (getLast? l).getD a := by
+@[simp, grind] theorem getLastD_eq_getLast? {a l} : @getLastD α l a = (getLast? l).getD a := by
   cases l <;> rfl
 
-@[simp, grind =] theorem getLast_singleton {a} (h) : @getLast α [a] h = a := rfl
+@[simp, grind] theorem getLast_singleton {a} (h) : @getLast α [a] h = a := rfl
 
 theorem getLast!_cons_eq_getLastD [Inhabited α] : @getLast! α _ (a::l) = getLastD l a := by
   simp [getLast!, getLast_eq_getLastD]
@@ -906,7 +888,7 @@ theorem getLast?_eq_getLast : ∀ {l : List α} h, l.getLast? = some (l.getLast
   | [], h => nomatch h rfl
   | _ :: _, _ => rfl
 
-@[grind =] theorem getLast?_eq_getElem? : ∀ {l : List α}, l.getLast? = l[l.length - 1]?
+@[grind] theorem getLast?_eq_getElem? : ∀ {l : List α}, l.getLast? = l[l.length - 1]?
   | [] => rfl
   | a::l => by
     rw [getLast?_eq_getLast (l := a :: l) nofun, getLast_eq_getElem, getElem?_eq_getElem]
@@ -919,14 +901,14 @@ theorem getLast_eq_iff_getLast?_eq_some {xs : List α} (h) :
 -- `getLast?_eq_none_iff`, `getLast?_eq_some_iff`, `getLast?_isSome`, and `getLast_mem`
 -- are proved later once more `reverse` theorems are available.
 
-@[grind =]
+@[grind]
 theorem getLast?_cons {a : α} : (a::l).getLast? = some (l.getLast?.getD a) := by
   cases l <;> simp [getLast?, getLast]
 
 @[simp] theorem getLast?_cons_cons : (a :: b :: l).getLast? = (b :: l).getLast? := by
   simp [getLast?_cons]
 
-@[grind =]
+@[grind]
 theorem getLast?_concat {l : List α} {a : α} : (l ++ [a]).getLast? = some a := by
   simp [getLast?_eq_getElem?, Nat.succ_sub_succ]
 
@@ -945,14 +927,14 @@ theorem getLast!_nil [Inhabited α] : ([] : List α).getLast! = default := rfl
 theorem getLast!_of_getLast? [Inhabited α] : ∀ {l : List α}, getLast? l = some a → getLast! l = a
   | _ :: _, rfl => rfl
 
-@[grind =]
+@[grind]
 theorem getLast!_eq_getElem! [Inhabited α] {l : List α} : l.getLast! = l[l.length - 1]! := by
   cases l with
   | nil => simp
   | cons _ _ =>
     apply getLast!_of_getLast?
-    rw [getLast?_eq_getElem?]
-    simp
+    rw [getElem!_pos, getElem_cons_length (h := by simp)]
+    rfl
 
 /-! ## Head and tail -/
 
@@ -973,7 +955,7 @@ theorem head?_eq_getElem? : ∀ {l : List α}, l.head? = l[0]?
 
 theorem head_singleton {a : α} : head [a] (by simp) = a := by simp
 
-@[grind =]
+@[grind]
 theorem head_eq_getElem {l : List α} (h : l ≠ []) : head l h = l[0]'(length_pos_iff.mpr h) := by
   cases l with
   | nil => simp at h
@@ -1035,18 +1017,18 @@ theorem head_of_mem_head? {l : List α} {x} (hx : x ∈ l.head?) :
 /-! ### headD -/
 
 /-- `simp` unfolds `headD` in terms of `head?` and `Option.getD`. -/
-@[simp, grind =] theorem headD_eq_head?_getD {l : List α} : headD l a = (head? l).getD a := by
+@[simp, grind] theorem headD_eq_head?_getD {l : List α} : headD l a = (head? l).getD a := by
   cases l <;> simp [headD]
 
 /-! ### tailD -/
 
 /-- `simp` unfolds `tailD` in terms of `tail?` and `Option.getD`. -/
-@[simp, grind =] theorem tailD_eq_tail? {l l' : List α} : tailD l l' = (tail? l).getD l' := by
+@[simp, grind] theorem tailD_eq_tail? {l l' : List α} : tailD l l' = (tail? l).getD l' := by
   cases l <;> rfl
 
 /-! ### tail -/
 
-@[simp, grind =] theorem length_tail {l : List α} : l.tail.length = l.length - 1 := by cases l <;> rfl
+@[simp, grind] theorem length_tail {l : List α} : l.tail.length = l.length - 1 := by cases l <;> rfl
 
 theorem tail_eq_tailD {l : List α} : l.tail = tailD l [] := by cases l <;> rfl
 
@@ -1058,13 +1040,13 @@ theorem mem_of_mem_tail {a : α} {l : List α} (h : a ∈ tail l) : a ∈ l := b
 theorem ne_nil_of_tail_ne_nil {l : List α} : l.tail ≠ [] → l ≠ [] := by
   cases l <;> simp
 
-@[simp, grind =] theorem getElem_tail {l : List α} {i : Nat} (h : i < l.tail.length) :
+@[simp, grind] theorem getElem_tail {l : List α} {i : Nat} (h : i < l.tail.length) :
     (tail l)[i] = l[i + 1]'(add_lt_of_lt_sub (by simpa using h)) := by
   cases l with
   | nil => simp at h
   | cons _ l => simp
 
-@[simp, grind =] theorem getElem?_tail {l : List α} {i : Nat} :
+@[simp, grind] theorem getElem?_tail {l : List α} {i : Nat} :
     (tail l)[i]? = l[i + 1]? := by
   cases l <;> simp
 
@@ -1088,7 +1070,7 @@ theorem one_lt_length_of_tail_ne_nil {l : List α} (h : l.tail ≠ []) : 1 < l.l
 @[simp] theorem head?_tail {l : List α} : (tail l).head? = l[1]? := by
   simp [head?_eq_getElem?]
 
-@[simp, grind =] theorem getLast_tail {l : List α} (h : l.tail ≠ []) :
+@[simp, grind] theorem getLast_tail {l : List α} (h : l.tail ≠ []) :
     (tail l).getLast h = l.getLast (ne_nil_of_tail_ne_nil h) := by
   simp only [getLast_eq_getElem, length_tail, getElem_tail]
   congr
@@ -1114,7 +1096,7 @@ theorem cons_head_tail (h : l ≠ []) : l.head h :: l.tail = l := by
 
 /-! ### map -/
 
-@[simp, grind =] theorem length_map {as : List α} (f : α → β) : (as.map f).length = as.length := by
+@[simp, grind] theorem length_map {as : List α} (f : α → β) : (as.map f).length = as.length := by
   induction as with
   | nil => simp [List.map]
   | cons _ as ih => simp [List.map, ih]
@@ -1122,13 +1104,13 @@ theorem cons_head_tail (h : l ≠ []) : l.head h :: l.tail = l := by
 @[simp] theorem isEmpty_map {l : List α} {f : α → β} : (l.map f).isEmpty = l.isEmpty := by
   cases l <;> simp
 
-@[simp, grind =] theorem getElem?_map {f : α → β} : ∀ {l : List α} {i : Nat}, (map f l)[i]? = Option.map f l[i]?
+@[simp, grind] theorem getElem?_map {f : α → β} : ∀ {l : List α} {i : Nat}, (map f l)[i]? = Option.map f l[i]?
   | [], _ => rfl
   | _ :: _, 0 => by simp
   | _ :: l, i+1 => by simp [getElem?_map]
 
 -- The argument `f : α → β` is explicit, to facilitate rewriting from right to left.
-@[simp, grind =] theorem getElem_map (f : α → β) {l} {i : Nat} {h : i < (map f l).length} :
+@[simp, grind] theorem getElem_map (f : α → β) {l} {i : Nat} {h : i < (map f l).length} :
     (map f l)[i] = f (l[i]'(length_map f ▸ h)) :=
   Option.some.inj <| by rw [← getElem?_eq_getElem, getElem?_map, getElem?_eq_getElem]; rfl
 
@@ -1174,9 +1156,7 @@ theorem forall_mem_map {f : α → β} {l : List α} {P : β → Prop} :
 @[simp] theorem map_eq_nil_iff {f : α → β} {l : List α} : map f l = [] ↔ l = [] := by
   constructor <;> exact fun _ => match l with | [] => rfl
 
--- This would be helpful as a `grind` lemma if
--- we could have it fire only once `map f l` and `[]` are the same equivalence class.
--- Otherwise it is too aggressive.
+@[grind →]
 theorem eq_nil_of_map_eq_nil {f : α → β} {l : List α} (h : map f l = []) : l = [] :=
   map_eq_nil_iff.mp h
 
@@ -1296,7 +1276,7 @@ theorem getLastD_map {f : α → β} {l : List α} {a : α} : (map f l).getLastD
 @[simp] theorem filter_cons_of_neg {p : α → Bool} {a : α} {l} (pa : ¬ p a) :
     filter p (a :: l) = filter p l := by rw [filter, eq_false_of_ne_true pa]
 
-@[grind =] theorem filter_cons :
+@[grind] theorem filter_cons :
     (x :: xs : List α).filter p = if p x then x :: (xs.filter p) else xs.filter p := by
   split <;> simp [*]
 
@@ -1335,7 +1315,7 @@ theorem length_filter_eq_length_iff {l} : (filter p l).length = l.length ↔ ∀
 @[deprecated length_filter_eq_length_iff (since := "2025-04-04")]
 abbrev filter_length_eq_length := @length_filter_eq_length_iff
 
-@[simp, grind =] theorem mem_filter : x ∈ filter p as ↔ x ∈ as ∧ p x := by
+@[simp, grind] theorem mem_filter : x ∈ filter p as ↔ x ∈ as ∧ p x := by
   induction as with
   | nil => simp
   | cons a as ih =>
@@ -1350,15 +1330,13 @@ 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
 
-theorem getElem_filter {xs : List α} {p : α → Bool} {i : Nat} (h : i < (xs.filter p).length) :
+@[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
 
-grind_pattern getElem_filter => (xs.filter p)[i]
-
 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 h] at w
+  rw [getElem?_eq_getElem] at w
   simp only [Option.some.injEq] at w
   rw [← w]
   apply getElem_filter h
@@ -1399,7 +1377,7 @@ theorem map_filter_eq_foldr {f : α → β} {p : α → Bool} {as : List α} :
     simp only [foldr]
     cases hp : p head <;> simp [filter, *]
 
-@[simp, grind =] theorem filter_append {p : α → Bool} :
+@[simp, grind] theorem filter_append {p : α → Bool} :
     ∀ (l₁ l₂ : List α), filter p (l₁ ++ l₂) = filter p l₁ ++ filter p l₂
   | [], _ => rfl
   | a :: l₁, l₂ => by simp only [cons_append, filter]; split <;> simp [filter_append l₁]
@@ -1464,7 +1442,7 @@ theorem filterMap_some_fun : filterMap (some : α → Option α) = id := by
   erw [filterMap_eq_map]
   simp
 
-@[simp, grind =] theorem filterMap_some {l : List α} : filterMap some l = l := by
+@[simp, grind] theorem filterMap_some {l : List α} : filterMap some l = l := by
   rw [filterMap_some_fun, id]
 
 theorem map_filterMap_some_eq_filter_map_isSome {f : α → Option β} {l : List α} :
@@ -1499,19 +1477,19 @@ theorem filterMap_eq_filter {p : α → Bool} :
   | nil => rfl
   | cons a l IH => by_cases pa : p a <;> simp [Option.guard, pa, ← IH]
 
-@[grind =]
+@[grind]
 theorem filterMap_filterMap {f : α → Option β} {g : β → Option γ} {l : List α} :
     filterMap g (filterMap f l) = filterMap (fun x => (f x).bind g) l := by
   induction l with
   | nil => rfl
   | cons a l IH => cases h : f a <;> simp [filterMap_cons, *]
 
-@[grind =]
+@[grind]
 theorem map_filterMap {f : α → Option β} {g : β → γ} {l : List α} :
     map g (filterMap f l) = filterMap (fun x => (f x).map g) l := by
   simp only [← filterMap_eq_map, filterMap_filterMap, Option.map_eq_bind]
 
-@[simp, grind =]
+@[simp, grind]
 theorem filterMap_map {f : α → β} {g : β → Option γ} {l : List α} :
     filterMap g (map f l) = filterMap (g ∘ f) l := by
   rw [← filterMap_eq_map, filterMap_filterMap]; rfl
@@ -1526,7 +1504,7 @@ theorem filterMap_filter {p : α → Bool} {f : α → Option β} {l : List α}
   rw [← filterMap_eq_filter, filterMap_filterMap]
   congr; funext x; by_cases h : p x <;> simp [Option.guard, h]
 
-@[simp, grind =] theorem mem_filterMap {f : α → Option β} {l : List α} {b : β} :
+@[simp, grind] theorem mem_filterMap {f : α → Option β} {l : List α} {b : β} :
     b ∈ filterMap f l ↔ ∃ a, a ∈ l ∧ f a = some b := by
   induction l <;> simp [filterMap_cons]; split <;> simp [*, eq_comm]
 
@@ -1538,7 +1516,7 @@ theorem forall_mem_filterMap {f : α → Option β} {l : List α} {P : β → Pr
   intro a
   rw [forall_comm]
 
-@[simp, grind =] theorem filterMap_append {l l' : List α} {f : α → Option β} :
+@[simp, grind] theorem filterMap_append {l l' : List α} {f : α → Option β} :
     filterMap f (l ++ l') = filterMap f l ++ filterMap f l' := by
   induction l <;> simp [filterMap_cons]; split <;> simp [*]
 
@@ -1610,7 +1588,7 @@ theorem filterMap_eq_cons_iff {l} {b} {bs} :
 @[simp] theorem cons_append_fun {a : α} {as : List α} :
     (fun bs => ((a :: as) ++ bs)) = fun bs => a :: (as ++ bs) := rfl
 
-@[simp, grind =] theorem mem_append {a : α} {s t : List α} : a ∈ s ++ t ↔ a ∈ s ∨ a ∈ t := by
+@[simp, grind] theorem mem_append {a : α} {s t : List α} : a ∈ s ++ t ↔ a ∈ s ∨ a ∈ t := by
   induction s <;> simp_all [or_assoc]
 
 theorem not_mem_append {a : α} {s t : List α} (h₁ : a ∉ s) (h₂ : a ∉ t) : a ∉ s ++ t :=
@@ -1633,7 +1611,7 @@ theorem forall_mem_append {p : α → Prop} {l₁ l₂ : List α} :
     (∀ (x) (_ : x ∈ l₁ ++ l₂), p x) ↔ (∀ (x) (_ : x ∈ l₁), p x) ∧ (∀ (x) (_ : x ∈ l₂), p x) := by
   simp only [mem_append, or_imp, forall_and]
 
-@[grind =] theorem getElem_append {l₁ l₂ : List α} {i : Nat} (h : i < (l₁ ++ l₂).length) :
+@[grind] theorem getElem_append {l₁ l₂ : List α} {i : Nat} (h : i < (l₁ ++ l₂).length) :
     (l₁ ++ l₂)[i] = if h' : i < l₁.length then l₁[i] else l₂[i - l₁.length]'(by simp at h h'; exact Nat.sub_lt_left_of_lt_add h' h) := by
   split <;> rename_i h'
   · rw [getElem_append_left h']
@@ -1652,7 +1630,7 @@ theorem getElem?_append_right : ∀ {l₁ l₂ : List α} {i : Nat}, l₁.length
   rw [cons_append]
   simp [Nat.succ_sub_succ_eq_sub, getElem?_append_right (Nat.lt_succ.1 h₁)]
 
-@[grind =] theorem getElem?_append {l₁ l₂ : List α} {i : Nat} :
+@[grind] theorem getElem?_append {l₁ l₂ : List α} {i : Nat} :
     (l₁ ++ l₂)[i]? = if i < l₁.length then l₁[i]? else l₂[i - l₁.length]? := by
   split <;> rename_i h
   · exact getElem?_append_left h
@@ -1731,6 +1709,7 @@ theorem getLast_concat {a : α} : ∀ {l : List α}, getLast (l ++ [a]) (by simp
 theorem nil_eq_append_iff : [] = a ++ b ↔ a = [] ∧ b = [] := by
   simp
 
+@[grind →]
 theorem eq_nil_of_append_eq_nil {l₁ l₂ : List α} (h : l₁ ++ l₂ = []) : l₁ = [] ∧ l₂ = [] :=
   append_eq_nil_iff.mp h
 
@@ -1760,12 +1739,12 @@ theorem append_eq_append_iff {ws xs ys zs : List α} :
   | nil => simp_all
   | cons a as ih => cases ys <;> simp [eq_comm, and_assoc, ih, and_or_left]
 
-@[simp, grind =] theorem head_append_of_ne_nil {l : List α} {w₁} (w₂) :
+@[simp, grind] theorem head_append_of_ne_nil {l : List α} {w₁} (w₂) :
     head (l ++ l') w₁ = head l w₂ := by
   match l, w₂ with
   | a :: l, _ => rfl
 
-@[grind =] theorem head_append {l₁ l₂ : List α} (w : l₁ ++ l₂ ≠ []) :
+@[grind] theorem head_append {l₁ l₂ : List α} (w : l₁ ++ l₂ ≠ []) :
     head (l₁ ++ l₂) w =
       if h : l₁.isEmpty then
         head l₂ (by simp_all [isEmpty_iff])
@@ -1786,28 +1765,28 @@ theorem head_append_right {l₁ l₂ : List α} (w : l₁ ++ l₂ ≠ []) (h : l
     head (l₁ ++ l₂) w = head l₂ (by simp_all) := by
   rw [head_append, dif_pos (by simp_all)]
 
-@[simp, grind =] theorem head?_append {l : List α} : (l ++ l').head? = l.head?.or l'.head? := by
+@[simp, grind] theorem head?_append {l : List α} : (l ++ l').head? = l.head?.or l'.head? := by
   cases l <;> simp
 
 -- Note:
 -- `getLast_append_of_ne_nil`, `getLast_append` and `getLast?_append`
 -- are stated and proved later in the `reverse` section.
 
-@[grind =] theorem tail?_append {l l' : List α} : (l ++ l').tail? = (l.tail?.map (· ++ l')).or l'.tail? := by
+@[grind] theorem tail?_append {l l' : List α} : (l ++ l').tail? = (l.tail?.map (· ++ l')).or l'.tail? := by
   cases l <;> simp
 
 theorem tail?_append_of_ne_nil {l l' : List α} (_ : l ≠ []) : (l ++ l').tail? = some (l.tail ++ l') :=
   match l with
   | _ :: _ => by simp
 
-@[grind =] theorem tail_append {l l' : List α} : (l ++ l').tail = if l.isEmpty then l'.tail else l.tail ++ l' := by
+@[grind] theorem tail_append {l l' : List α} : (l ++ l').tail = if l.isEmpty then l'.tail else l.tail ++ l' := by
   cases l <;> simp
 
 @[simp] theorem tail_append_of_ne_nil {xs ys : List α} (h : xs ≠ []) :
     (xs ++ ys).tail = xs.tail ++ ys := by
   simp_all [tail_append]
 
-@[grind =] theorem set_append {s t : List α} :
+@[grind] theorem set_append {s t : List α} :
     (s ++ t).set i x = if i < s.length then s.set i x ++ t else s ++ t.set (i - s.length) x := by
   induction s generalizing i with
   | nil => simp
@@ -1865,7 +1844,7 @@ theorem append_eq_filter_iff {p : α → Bool} :
     L₁ ++ L₂ = filter p l ↔ ∃ l₁ l₂, l = l₁ ++ l₂ ∧ filter p l₁ = L₁ ∧ filter p l₂ = L₂ := by
   rw [eq_comm, filter_eq_append_iff]
 
-@[simp, grind =] theorem map_append {f : α → β} : ∀ {l₁ l₂}, map f (l₁ ++ l₂) = map f l₁ ++ map f l₂ := by
+@[simp, grind] theorem map_append {f : α → β} : ∀ {l₁ l₂}, map f (l₁ ++ l₂) = map f l₁ ++ map f l₂ := by
   intro l₁; induction l₁ <;> intros <;> simp_all
 
 theorem map_eq_append_iff {f : α → β} :
@@ -1938,7 +1917,7 @@ theorem eq_nil_or_concat : ∀ l : List α, l = [] ∨ ∃ l' b, l = concat l' b
   | cons =>
     simp [flatten, length_append, *]
 
-@[grind =] theorem flatten_singleton {l : List α} : [l].flatten = l := by simp
+@[grind] theorem flatten_singleton {l : List α} : [l].flatten = l := by simp
 
 @[simp] theorem mem_flatten : ∀ {L : List (List α)}, a ∈ L.flatten ↔ ∃ l, l ∈ L ∧ a ∈ l
   | [] => by simp
@@ -2113,7 +2092,7 @@ theorem length_flatMap {l : List α} {f : α → List β} :
     length (l.flatMap f) = sum (map (fun a => (f a).length) l) := by
   rw [List.flatMap, length_flatten, map_map, Function.comp_def]
 
-@[simp, grind =] theorem mem_flatMap {f : α → List β} {b} {l : List α} : b ∈ l.flatMap f ↔ ∃ a, a ∈ l ∧ b ∈ f a := by
+@[simp, grind] theorem mem_flatMap {f : α → List β} {b} {l : List α} : b ∈ l.flatMap f ↔ ∃ a, a ∈ l ∧ b ∈ f a := by
   simp [flatMap_def, mem_flatten]
   exact ⟨fun ⟨_, ⟨a, h₁, rfl⟩, h₂⟩ => ⟨a, h₁, h₂⟩, fun ⟨a, h₁, h₂⟩ => ⟨_, ⟨a, h₁, rfl⟩, h₂⟩⟩
 
@@ -2140,7 +2119,7 @@ theorem flatMap_singleton (f : α → List β) (x : α) : [x].flatMap f = f x :=
 @[simp] theorem flatMap_singleton' (l : List α) : (l.flatMap fun x => [x]) = l := by
   induction l <;> simp [*]
 
-@[grind =] theorem head?_flatMap {l : List α} {f : α → List β} :
+@[grind] theorem head?_flatMap {l : List α} {f : α → List β} :
     (l.flatMap f).head? = l.findSome? fun a => (f a).head? := by
   induction l with
   | nil => rfl
@@ -2148,6 +2127,10 @@ theorem flatMap_singleton (f : α → List β) (x : α) : [x].flatMap f = f x :=
     simp only [findSome?_cons]
     split <;> simp_all
 
+@[simp, grind _=_] theorem flatMap_append {xs ys : List α} {f : α → List β} :
+    (xs ++ ys).flatMap f = xs.flatMap f ++ ys.flatMap f := by
+  induction xs; {rfl}; simp_all [flatMap_cons, append_assoc]
+
 theorem flatMap_assoc {l : List α} {f : α → List β} {g : β → List γ} :
     (l.flatMap f).flatMap g = l.flatMap fun x => (f x).flatMap g := by
   induction l <;> simp [*]
@@ -2189,7 +2172,7 @@ theorem flatMap_eq_foldl {f : α → List β} {l : List α} :
 theorem replicate_succ' : replicate (n + 1) a = replicate n a ++ [a] := by
   induction n <;> simp_all [replicate_succ, ← cons_append]
 
-@[simp, grind =] theorem mem_replicate {a b : α} : ∀ {n}, b ∈ replicate n a ↔ n ≠ 0 ∧ b = a
+@[simp, grind] theorem mem_replicate {a b : α} : ∀ {n}, b ∈ replicate n a ↔ n ≠ 0 ∧ b = a
   | 0 => by simp
   | n+1 => by simp [replicate_succ, mem_replicate, Nat.succ_ne_zero]
 
@@ -2214,11 +2197,11 @@ theorem forall_mem_replicate {p : α → Prop} {a : α} {n} :
 @[simp] theorem replicate_eq_nil_iff {n : Nat} (a : α) : replicate n a = [] ↔ n = 0 := by
   cases n <;> simp
 
-@[simp, grind =] theorem getElem_replicate {a : α} {n : Nat} {i : Nat} (h : i < (replicate n a).length) :
+@[simp, grind] theorem getElem_replicate {a : α} {n : Nat} {i : Nat} (h : i < (replicate n a).length) :
     (replicate n a)[i] = a :=
   eq_of_mem_replicate (getElem_mem _)
 
-@[grind =] theorem getElem?_replicate : (replicate n a)[i]? = if i < n then some a else none := by
+@[grind] theorem getElem?_replicate : (replicate n a)[i]? = if i < n then some a else none := by
   by_cases h : i < n
   · rw [getElem?_eq_getElem (by simpa), getElem_replicate, if_pos h]
   · rw [getElem?_eq_none (by simpa using h), if_neg h]
@@ -2226,7 +2209,7 @@ theorem forall_mem_replicate {p : α → Prop} {a : α} {n} :
 @[simp] theorem getElem?_replicate_of_lt {n : Nat} {i : Nat} (h : i < n) : (replicate n a)[i]? = some a := by
   simp [h]
 
-@[grind =] theorem head?_replicate {a : α} {n : Nat} : (replicate n a).head? = if n = 0 then none else some a := by
+@[grind] theorem head?_replicate {a : α} {n : Nat} : (replicate n a).head? = if n = 0 then none else some a := by
   cases n <;> simp [replicate_succ]
 
 @[simp] theorem head_replicate (w : replicate n a ≠ []) : (replicate n a).head w = a := by
@@ -2315,7 +2298,7 @@ theorem replicate_eq_append_iff {l₁ l₂ : List α} {a : α} :
   simp only [getElem?_map, getElem?_replicate]
   split <;> simp
 
- @[grind =] theorem filter_replicate : (replicate n a).filter p = if p a then replicate n a else [] := by
+@[grind] theorem filter_replicate : (replicate n a).filter p = if p a then replicate n a else [] := by
   cases n with
   | zero => simp
   | succ n =>
@@ -2418,7 +2401,7 @@ termination_by l.length
 
 /-! ### reverse -/
 
-@[simp, grind =] theorem length_reverse {as : List α} : (as.reverse).length = as.length := by
+@[simp, grind] theorem length_reverse {as : List α} : (as.reverse).length = as.length := by
   induction as with
   | nil => rfl
   | cons a as ih => simp [ih]
@@ -2427,7 +2410,7 @@ theorem mem_reverseAux {x : α} : ∀ {as bs}, x ∈ reverseAux as bs ↔ x ∈
   | [], _ => ⟨.inr, fun | .inr h => h⟩
   | a :: _, _ => by rw [reverseAux, mem_cons, or_assoc, or_left_comm, mem_reverseAux, mem_cons]
 
-@[simp, grind =] theorem mem_reverse {x : α} {as : List α} : x ∈ reverse as ↔ x ∈ as := by
+@[simp, grind] theorem mem_reverse {x : α} {as : List α} : x ∈ reverse as ↔ x ∈ as := by
   simp [reverse, mem_reverseAux]
 
 @[simp] theorem reverse_eq_nil_iff {xs : List α} : xs.reverse = [] ↔ xs = [] := by
@@ -2451,14 +2434,14 @@ theorem getElem?_reverse' : ∀ {l : List α} {i j}, i + j + 1 = length l →
     rw [getElem?_append_left, getElem?_reverse' this]
     rw [length_reverse, ← this]; apply Nat.lt_add_of_pos_right (Nat.succ_pos _)
 
-@[simp, grind =]
+@[simp, grind]
 theorem getElem?_reverse {l : List α} {i} (h : i < length l) :
     l.reverse[i]? = l[l.length - 1 - i]? :=
   getElem?_reverse' <| by
     rw [Nat.add_sub_of_le (Nat.le_sub_one_of_lt h),
       Nat.sub_add_cancel (Nat.lt_of_le_of_lt (Nat.zero_le _) h)]
 
-@[simp, grind =]
+@[simp, grind]
 theorem getElem_reverse {l : List α} {i} (h : i < l.reverse.length) :
     l.reverse[i] = l[l.length - 1 - i]'(Nat.sub_one_sub_lt_of_lt (by simpa using h)) := by
   apply Option.some.inj
@@ -2471,7 +2454,7 @@ theorem reverseAux_reverseAux_nil {as bs : List α} : reverseAux (reverseAux as
   | cons a as ih => simp [reverseAux, ih]
 
 -- The argument `as : List α` is explicit to allow rewriting from right to left.
-@[simp, grind =] theorem reverse_reverse (as : List α) : as.reverse.reverse = as := by
+@[simp, grind] theorem reverse_reverse (as : List α) : as.reverse.reverse = as := by
   simp only [reverse]; rw [reverseAux_reverseAux_nil]; rfl
 
 theorem reverse_eq_iff {as bs : List α} : as.reverse = bs ↔ as = bs.reverse := by
@@ -2484,10 +2467,10 @@ theorem reverse_eq_iff {as bs : List α} : as.reverse = bs ↔ as = bs.reverse :
     xs.reverse = a :: ys ↔ xs = ys.reverse ++ [a] := by
   rw [reverse_eq_iff, reverse_cons]
 
-@[simp, grind =] theorem getLast?_reverse {l : List α} : l.reverse.getLast? = l.head? := by
+@[simp, grind] theorem getLast?_reverse {l : List α} : l.reverse.getLast? = l.head? := by
   cases l <;> simp [getLast?_concat]
 
-@[simp, grind =] theorem head?_reverse {l : List α} : l.reverse.head? = l.getLast? := by
+@[simp, grind] theorem head?_reverse {l : List α} : l.reverse.head? = l.getLast? := by
   rw [← getLast?_reverse, reverse_reverse]
 
 theorem getLast?_eq_head?_reverse {xs : List α} : xs.getLast? = xs.reverse.head? := by
@@ -2551,16 +2534,16 @@ theorem flatten_reverse {L : List (List α)} :
     L.reverse.flatten = (L.map reverse).flatten.reverse := by
   induction L <;> simp_all
 
-@[grind =] theorem reverse_flatMap {β} {l : List α} {f : α → List β} : (l.flatMap f).reverse = l.reverse.flatMap (reverse ∘ f) := by
+@[grind] theorem reverse_flatMap {β} {l : List α} {f : α → List β} : (l.flatMap f).reverse = l.reverse.flatMap (reverse ∘ f) := by
   induction l <;> simp_all
 
-@[grind =] theorem flatMap_reverse {β} {l : List α} {f : α → List β} : (l.reverse.flatMap f) = (l.flatMap (reverse ∘ f)).reverse := by
+@[grind] theorem flatMap_reverse {β} {l : List α} {f : α → List β} : (l.reverse.flatMap f) = (l.flatMap (reverse ∘ f)).reverse := by
   induction l <;> simp_all
 
 @[simp] theorem reverseAux_eq {as bs : List α} : reverseAux as bs = reverse as ++ bs :=
   reverseAux_eq_append ..
 
-@[simp, grind =] theorem reverse_replicate {n : Nat} {a : α} : (replicate n a).reverse = replicate n a :=
+@[simp, grind] theorem reverse_replicate {n : Nat} {a : α} : (replicate n a).reverse = replicate n a :=
   eq_replicate_iff.2
     ⟨by rw [length_reverse, length_replicate],
      fun _ h => eq_of_mem_replicate (mem_reverse.1 h)⟩
@@ -2572,7 +2555,7 @@ theorem flatten_reverse {L : List (List α)} :
     (l ++ l').foldlM f b = l.foldlM f b >>= l'.foldlM f := by
   induction l generalizing b <;> simp [*]
 
-@[simp, grind =] theorem foldrM_cons [Monad m] [LawfulMonad m] {a : α} {l : List α} {f : α → β → m β} {b : β} :
+@[simp, grind] theorem foldrM_cons [Monad m] [LawfulMonad m] {a : α} {l : List α} {f : α → β → m β} {b : β} :
     (a :: l).foldrM f b = l.foldrM f b >>= f a := by
   simp only [foldrM]
   induction l <;> simp_all
@@ -2616,37 +2599,37 @@ theorem id_run_foldrM {f : α → β → Id β} {b : β} {l : List α} :
 
 /-! ### foldl and foldr -/
 
-@[simp] theorem foldr_cons_eq_append {l : List α} {f : α → β} {l' : List β} :
+@[simp, grind] theorem foldr_cons_eq_append {l : List α} {f : α → β} {l' : List β} :
     l.foldr (fun x ys => f x :: ys) l' = l.map f ++ l' := by
   induction l <;> simp [*]
 
 /-- Variant of `foldr_cons_eq_append` specalized to `f = id`. -/
-@[simp, grind =] theorem foldr_cons_eq_append' {l l' : List β} :
+@[simp, grind] theorem foldr_cons_eq_append' {l l' : List β} :
     l.foldr cons l' = l ++ l' := by
   induction l <;> simp [*]
 
-@[simp] theorem foldl_flip_cons_eq_append {l : List α} {f : α → β} {l' : List β} :
+@[simp, grind] theorem foldl_flip_cons_eq_append {l : List α} {f : α → β} {l' : List β} :
     l.foldl (fun xs y => f y :: xs) l' = (l.map f).reverse ++ l' := by
   induction l generalizing l' <;> simp [*]
 
 /-- Variant of `foldl_flip_cons_eq_append` specalized to `f = id`. -/
-theorem foldl_flip_cons_eq_append' {l l' : List α} :
+@[grind] theorem foldl_flip_cons_eq_append' {l l' : List α} :
     l.foldl (fun xs y => y :: xs) l' = l.reverse ++ l' := by
   simp
 
-@[simp] theorem foldr_append_eq_append {l : List α} {f : α → List β} {l' : List β} :
+@[simp, grind] theorem foldr_append_eq_append {l : List α} {f : α → List β} {l' : List β} :
     l.foldr (f · ++ ·) l' = (l.map f).flatten ++ l' := by
   induction l <;> simp [*]
 
-@[simp] theorem foldl_append_eq_append {l : List α} {f : α → List β} {l' : List β} :
+@[simp, grind] theorem foldl_append_eq_append {l : List α} {f : α → List β} {l' : List β} :
     l.foldl (· ++ f ·) l' = l' ++ (l.map f).flatten := by
   induction l generalizing l'<;> simp [*]
 
-@[simp] theorem foldr_flip_append_eq_append {l : List α} {f : α → List β} {l' : List β} :
+@[simp, grind] theorem foldr_flip_append_eq_append {l : List α} {f : α → List β} {l' : List β} :
     l.foldr (fun x ys => ys ++ f x) l' = l' ++ (l.map f).reverse.flatten := by
   induction l generalizing l' <;> simp [*]
 
-@[simp] theorem foldl_flip_append_eq_append {l : List α} {f : α → List β} {l' : List β} :
+@[simp, grind] theorem foldl_flip_append_eq_append {l : List α} {f : α → List β} {l' : List β} :
     l.foldl (fun xs y => f y ++ xs) l' = (l.map f).reverse.flatten ++ l' := by
   induction l generalizing l' <;> simp [*]
 
@@ -2700,19 +2683,19 @@ theorem foldr_map_hom {g : α → β} {f : α → α → α} {f' : β → β →
 @[simp, grind _=_] theorem foldr_append {f : α → β → β} {b : β} {l l' : List α} :
     (l ++ l').foldr f b = l.foldr f (l'.foldr f b) := by simp [foldr_eq_foldrM, -foldrM_pure]
 
-@[grind =] theorem foldl_flatten {f : β → α → β} {b : β} {L : List (List α)} :
+@[grind] theorem foldl_flatten {f : β → α → β} {b : β} {L : List (List α)} :
     (flatten L).foldl f b = L.foldl (fun b l => l.foldl f b) b := by
   induction L generalizing b <;> simp_all
 
-@[grind =] theorem foldr_flatten {f : α → β → β} {b : β} {L : List (List α)} :
+@[grind] theorem foldr_flatten {f : α → β → β} {b : β} {L : List (List α)} :
     (flatten L).foldr f b = L.foldr (fun l b => l.foldr f b) b := by
   induction L <;> simp_all
 
-@[simp, grind =] theorem foldl_reverse {l : List α} {f : β → α → β} {b : β} :
+@[simp, grind] theorem foldl_reverse {l : List α} {f : β → α → β} {b : β} :
     l.reverse.foldl f b = l.foldr (fun x y => f y x) b := by
   simp [foldl_eq_foldlM, foldr_eq_foldrM, -foldrM_pure]
 
-@[simp, grind =] theorem foldr_reverse {l : List α} {f : α → β → β} {b : β} :
+@[simp, grind] theorem foldr_reverse {l : List α} {f : α → β → β} {b : β} :
     l.reverse.foldr f b = l.foldl (fun x y => f y x) b :=
   (foldl_reverse ..).symm.trans <| by simp
 
@@ -2866,7 +2849,7 @@ theorem foldr_rel {l : List α} {f : α → β → β} {g : α → γ → γ} {a
 
 /-! #### Further results about `getLast` and `getLast?` -/
 
-@[simp, grind =] theorem head_reverse {l : List α} (h : l.reverse ≠ []) :
+@[simp, grind] theorem head_reverse {l : List α} (h : l.reverse ≠ []) :
     l.reverse.head h = getLast l (by simp_all) := by
   induction l with
   | nil => contradiction
@@ -2896,7 +2879,7 @@ theorem getLast?_eq_some_iff {xs : List α} {a : α} : xs.getLast? = some a ↔
   rw [getLast?_eq_head?_reverse, isSome_head?]
   simp
 
-@[simp, grind =] theorem getLast_reverse {l : List α} (h : l.reverse ≠ []) :
+@[simp, grind] theorem getLast_reverse {l : List α} (h : l.reverse ≠ []) :
     l.reverse.getLast h = l.head (by simp_all) := by
   simp [getLast_eq_head_reverse]
 
@@ -2909,7 +2892,7 @@ theorem head_eq_getLast_reverse {l : List α} (h : l ≠ []) :
   simp only [getLast_eq_head_reverse, reverse_append]
   rw [head_append_of_ne_nil]
 
-@[grind =] theorem getLast_append {l : List α} (h : l ++ l' ≠ []) :
+@[grind] theorem getLast_append {l : List α} (h : l ++ l' ≠ []) :
     (l ++ l').getLast h =
       if h' : l'.isEmpty then
         l.getLast (by simp_all [isEmpty_iff])
@@ -2930,7 +2913,7 @@ theorem getLast_append_left {l : List α} (w : l ++ l' ≠ []) (h : l' = []) :
     (l ++ l').getLast w = l.getLast (by simp_all) := by
   rw [getLast_append, dif_pos (by simp_all)]
 
-@[simp, grind =] theorem getLast?_append {l l' : List α} : (l ++ l').getLast? = l'.getLast?.or l.getLast? := by
+@[simp, grind] theorem getLast?_append {l l' : List α} : (l ++ l').getLast? = l'.getLast?.or l.getLast? := by
   simp [← head?_reverse]
 
 theorem getLast_filter_of_pos {p : α → Bool} {l : List α} (w : l ≠ []) (h : p (getLast l w) = true) :
@@ -2966,7 +2949,7 @@ theorem getLast?_replicate {a : α} {n : Nat} : (replicate n a).getLast? = if n
 /-! ### leftpad -/
 
 -- We unfold `leftpad` and `rightpad` for verification purposes.
-attribute [simp, grind =] leftpad rightpad
+attribute [simp, grind] leftpad rightpad
 
 -- `length_leftpad` and `length_rightpad` are in `Init.Data.List.Nat.Basic`.
 
@@ -2995,21 +2978,17 @@ theorem contains_iff_exists_mem_beq [BEq α] {l : List α} {a : α} :
     l.contains a ↔ ∃ a' ∈ l, a == a' := by
   induction l <;> simp_all
 
--- We add this as a `grind` lemma because it is useful without `LawfulBEq α`.
--- With `LawfulBEq α`, it would be better to use `contains_iff_mem` directly.
-grind_pattern contains_iff_exists_mem_beq => l.contains a
-
 @[grind _=_]
 theorem contains_iff_mem [BEq α] [LawfulBEq α] {l : List α} {a : α} :
     l.contains a ↔ a ∈ l := by
   simp
 
-@[simp, grind =]
+@[simp, grind]
 theorem contains_map [BEq β] {l : List α} {x : β} {f : α → β} :
     (l.map f).contains x = l.any (fun a => x == f a) := by
   induction l with simp_all
 
-@[simp, grind =]
+@[simp, grind]
 theorem contains_filter [BEq α] {l : List α} {x : α} {p : α → Bool} :
     (l.filter p).contains x = l.any (fun a => x == a && p a) := by
   induction l with
@@ -3018,7 +2997,7 @@ theorem contains_filter [BEq α] {l : List α} {x : α} {p : α → Bool} :
     simp only [filter_cons, any_cons]
     split <;> simp_all
 
-@[simp, grind =]
+@[simp, grind]
 theorem contains_filterMap [BEq β] {l : List α} {x : β} {f : α → Option β} :
     (l.filterMap f).contains x = l.any (fun a => (f a).any fun b => x == b) := by
   induction l with
@@ -3034,21 +3013,21 @@ theorem contains_append [BEq α] {l₁ l₂ : List α} {x : α} :
   | nil => simp
   | cons a l ih => simp [ih, Bool.or_assoc]
 
-@[simp, grind =]
+@[simp, grind]
 theorem contains_flatten [BEq α] {l : List (List α)} {x : α} :
     l.flatten.contains x = l.any fun l => l.contains x := by
   induction l with
   | nil => simp
   | cons _ l ih => simp [ih]
 
-@[simp, grind =]
+@[simp, grind]
 theorem contains_reverse [BEq α] {l : List α} {x : α} :
     (l.reverse).contains x = l.contains x := by
   induction l with
   | nil => simp
   | cons a l ih => simp [ih, Bool.or_comm]
 
-@[simp, grind =]
+@[simp, grind]
 theorem contains_flatMap [BEq β] {l : List α} {f : α → List β} {x : β} :
     (l.flatMap f).contains x = l.any fun a => (f a).contains x := by
   induction l with
@@ -3063,7 +3042,7 @@ Because we immediately simplify `partition` into two `filter`s for verification
 we do not separately develop much theory about it.
 -/
 
-@[simp, grind =] theorem partition_eq_filter_filter {p : α → Bool} {l : List α} :
+@[simp, grind] theorem partition_eq_filter_filter {p : α → Bool} {l : List α} :
     partition p l = (filter p l, filter (not ∘ p) l) := by simp [partition, aux]
   where
     aux : ∀ l {as bs}, partition.loop p l (as, bs) =
@@ -3083,16 +3062,16 @@ grind_pattern mem_partition => a ∈ (partition p l).2
 are often used for theorems about `Array.pop`.
 -/
 
-@[simp, grind =] theorem length_dropLast : ∀ {xs : List α}, xs.dropLast.length = xs.length - 1
+@[simp, grind] theorem length_dropLast : ∀ {xs : List α}, xs.dropLast.length = xs.length - 1
   | [] => rfl
   | x::xs => by simp
 
-@[simp, grind =] theorem getElem_dropLast : ∀ {xs : List α} {i : Nat} (h : i < xs.dropLast.length),
+@[simp, grind] theorem getElem_dropLast : ∀ {xs : List α} {i : Nat} (h : i < xs.dropLast.length),
     xs.dropLast[i] = xs[i]'(Nat.lt_of_lt_of_le h (length_dropLast .. ▸ Nat.pred_le _))
   | _ :: _ :: _, 0, _ => rfl
   | _ :: _ :: _, _ + 1, h => getElem_dropLast (Nat.add_one_lt_add_one_iff.mp h)
 
-@[grind =] theorem getElem?_dropLast {xs : List α} {i : Nat} :
+@[grind] theorem getElem?_dropLast {xs : List α} {i : Nat} :
     xs.dropLast[i]? = if i < xs.length - 1 then xs[i]? else none := by
   split
   · rw [getElem?_eq_getElem, getElem?_eq_getElem, getElem_dropLast]
@@ -3290,24 +3269,24 @@ theorem all_eq_not_any_not {l : List α} {p : α → Bool} : l.all p = !l.any (!
   | nil => rfl
   | cons h t ih => simp_all [Bool.and_assoc]
 
-@[simp, grind =] theorem any_flatten {l : List (List α)} : l.flatten.any f = l.any (any · f) := by
+@[simp, grind] theorem any_flatten {l : List (List α)} : l.flatten.any f = l.any (any · f) := by
   induction l <;> simp_all
 
-@[simp, grind =] theorem all_flatten {l : List (List α)} : l.flatten.all f = l.all (all · f) := by
+@[simp, grind] theorem all_flatten {l : List (List α)} : l.flatten.all f = l.all (all · f) := by
   induction l <;> simp_all
 
-@[simp, grind =] theorem any_flatMap {l : List α} {f : α → List β} :
+@[simp, grind] theorem any_flatMap {l : List α} {f : α → List β} :
     (l.flatMap f).any p = l.any fun a => (f a).any p := by
   induction l <;> simp_all
 
-@[simp, grind =] theorem all_flatMap {l : List α} {f : α → List β} :
+@[simp, grind] theorem all_flatMap {l : List α} {f : α → List β} :
     (l.flatMap f).all p = l.all fun a => (f a).all p := by
   induction l <;> simp_all
 
-@[simp, grind =] theorem any_reverse {l : List α} : l.reverse.any f = l.any f := by
+@[simp, grind] theorem any_reverse {l : List α} : l.reverse.any f = l.any f := by
   induction l <;> simp_all [Bool.or_comm]
 
-@[simp, grind =] theorem all_reverse {l : List α} : l.reverse.all f = l.all f := by
+@[simp, grind] theorem all_reverse {l : List α} : l.reverse.all f = l.all f := by
   induction l <;> simp_all [Bool.and_comm]
 
 @[simp] theorem any_replicate {n : Nat} {a : α} :
@@ -3357,14 +3336,14 @@ variable [BEq α]
     simp only [replace_cons]
     split <;> simp_all
 
-@[simp, grind =] theorem length_replace {l : List α} : (l.replace a b).length = l.length := by
+@[simp, grind] theorem length_replace {l : List α} : (l.replace a b).length = l.length := by
   induction l with
   | nil => simp
   | cons x l ih =>
     simp only [replace_cons]
     split <;> simp_all
 
-@[grind =] theorem getElem?_replace [LawfulBEq α] {l : List α} {i : Nat} :
+@[grind] theorem getElem?_replace [LawfulBEq α] {l : List α} {i : Nat} :
     (l.replace a b)[i]? = if l[i]? == some a then if a ∈ l.take i then some a else some b else l[i]? := by
   induction l generalizing i with
   | nil => cases i <;> simp
@@ -3377,7 +3356,7 @@ theorem getElem?_replace_of_ne [LawfulBEq α] {l : List α} {i : Nat} (h : l[i]?
     (l.replace a b)[i]? = l[i]? := by
   simp_all [getElem?_replace]
 
-@[grind =] theorem getElem_replace [LawfulBEq α] {l : List α} {i : Nat} (h : i < l.length) :
+@[grind] theorem getElem_replace [LawfulBEq α] {l : List α} {i : Nat} (h : i < l.length) :
     (l.replace a b)[i]'(by simpa) = if l[i] == a then if a ∈ l.take i then a else b else l[i] := by
   apply Option.some.inj
   rw [← getElem?_eq_getElem, getElem?_replace]
@@ -3407,7 +3386,7 @@ theorem head_replace {l : List α} {a b : α} (w) :
   apply Option.some.inj
   rw [← head?_eq_head, head?_replace, head?_eq_head]
 
-@[grind =] theorem replace_append [LawfulBEq α] {l₁ l₂ : List α} :
+@[grind] theorem replace_append [LawfulBEq α] {l₁ l₂ : List α} :
     (l₁ ++ l₂).replace a b = if a ∈ l₁ then l₁.replace a b ++ l₂ else l₁ ++ l₂.replace a b := by
   induction l₁ with
   | nil => simp
@@ -3451,9 +3430,9 @@ end replace
 section insert
 variable [BEq α]
 
-@[simp, grind =] theorem insert_nil (a : α) : [].insert a = [a] := rfl
+@[simp, grind] theorem insert_nil (a : α) : [].insert a = [a] := rfl
 
-@[simp, grind =] theorem contains_insert [PartialEquivBEq α] {l : List α} {a : α} {x : α} :
+@[simp, grind] theorem contains_insert [PartialEquivBEq α] {l : List α} {a : α} {x : α} :
     (l.insert a).contains x = (x == a || l.contains x) := by
   simp only [List.insert]
   split <;> rename_i h
@@ -3470,7 +3449,7 @@ variable [LawfulBEq α]
 @[simp] theorem insert_of_not_mem {l : List α} (h : a ∉ l) : l.insert a = a :: l := by
   simp [List.insert, h]
 
-@[simp, grind =] theorem mem_insert_iff {l : List α} : a ∈ l.insert b ↔ a = b ∨ a ∈ l := by
+@[simp, grind] theorem mem_insert_iff {l : List α} : a ∈ l.insert b ↔ a = b ∨ a ∈ l := by
   if h : b ∈ l then
     rw [insert_of_mem h]
     constructor; {apply Or.inr}
@@ -3494,7 +3473,7 @@ theorem eq_or_mem_of_mem_insert {l : List α} (h : a ∈ l.insert b) : a = b ∨
 @[simp] theorem length_insert_of_not_mem {l : List α} (h : a ∉ l) :
     length (l.insert a) = length l + 1 := by rw [insert_of_not_mem h]; rfl
 
-@[grind =] theorem length_insert {l : List α} :
+@[grind] theorem length_insert {l : List α} :
     (l.insert a).length = l.length + if a ∈ l then 0 else 1 := by
   split <;> simp_all
 
@@ -3529,13 +3508,13 @@ theorem getElem?_insert_succ {l : List α} {a : α} {i : Nat} :
   simp only [insert_eq]
   split <;> simp
 
-@[grind =] theorem getElem?_insert {l : List α} {a : α} {i : Nat} :
+@[grind] theorem getElem?_insert {l : List α} {a : α} {i : Nat} :
     (l.insert a)[i]? = if a ∈ l then l[i]? else if i = 0 then some a else l[i-1]? := by
   cases i
   · simp [getElem?_insert_zero]
   · simp [getElem?_insert_succ]
 
-@[grind =] theorem getElem_insert {l : List α} {a : α} {i : Nat} (h : i < l.length) :
+@[grind] theorem getElem_insert {l : List α} {a : α} {i : Nat} (h : i < l.length) :
     (l.insert a)[i]'(Nat.lt_of_lt_of_le h length_le_length_insert) =
       if a ∈ l then l[i] else if i = 0 then a else l[i-1]'(Nat.lt_of_le_of_lt (Nat.pred_le _) h) := by
   apply Option.some.inj
@@ -3559,7 +3538,7 @@ theorem head_insert {l : List α} {a : α} (w) :
   apply Option.some.inj
   rw [← head?_eq_head, head?_insert]
 
-@[grind =] theorem insert_append {l₁ l₂ : List α} {a : α} :
+@[grind] theorem insert_append {l₁ l₂ : List α} {a : α} :
     (l₁ ++ l₂).insert a = if a ∈ l₂ then l₁ ++ l₂ else l₁.insert a ++ l₂ := by
   simp only [insert_eq, mem_append]
   (repeat split) <;> simp_all
@@ -3572,7 +3551,7 @@ theorem insert_append_of_not_mem_left {l₁ l₂ : List α} (h : ¬ a ∈ l₂)
     (l₁ ++ l₂).insert a = l₁.insert a ++ l₂ := by
   simp [insert_append, h]
 
-@[simp, grind =] theorem insert_replicate_self {a : α} (h : 0 < n) : (replicate n a).insert a = replicate n a := by
+@[simp, grind] theorem insert_replicate_self {a : α} (h : 0 < n) : (replicate n a).insert a = replicate n a := by
   cases n <;> simp_all
 
 @[simp] theorem insert_replicate_ne {a b : α} (h : !b == a) :

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

@@ -248,10 +248,11 @@ theorem pairwise_le_range {n : Nat} : Pairwise (· ≤ ·) (range n) :=
 theorem nodup_range {n : Nat} : Nodup (range n) := by
   simp +decide only [range_eq_range', nodup_range']
 
-@[simp] theorem find?_range_eq_some {n : Nat} {i : Nat} {p : Nat → Bool} :
+@[simp, grind] theorem find?_range_eq_some {n : Nat} {i : Nat} {p : Nat → Bool} :
     (range n).find? p = some i ↔ p i ∧ i ∈ range n ∧ ∀ j, j < i → !p j := by
   simp [range_eq_range']
 
+@[grind]
 theorem find?_range_eq_none {n : Nat} {p : Nat → Bool} :
     (range n).find? p = none ↔ ∀ i, i < n → !p i := by
   simp

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

@@ -567,10 +567,9 @@ theorem getElem_zipWith {f : α → β → γ} {l : List α} {l' : List β}
       f (l[i]'(lt_length_left_of_zipWith h))
         (l'[i]'(lt_length_right_of_zipWith h)) := by
   rw [← Option.some_inj, ← getElem?_eq_getElem, getElem?_zipWith_eq_some]
-  have := lt_length_right_of_zipWith h
   exact
-    ⟨l[i]'(lt_length_left_of_zipWith h), l'[i],
-      by rw [getElem?_eq_getElem], by rw [getElem?_eq_getElem this]; exact ⟨rfl, rfl⟩⟩
+    ⟨l[i]'(lt_length_left_of_zipWith h), l'[i]'(lt_length_right_of_zipWith h),
+      by rw [getElem?_eq_getElem], by rw [getElem?_eq_getElem]; exact ⟨rfl, rfl⟩⟩
 
 theorem zipWith_eq_zipWith_take_min : ∀ {l₁ : List α} {l₂ : List β},
     zipWith f l₁ l₂ = zipWith f (l₁.take (min l₁.length l₂.length)) (l₂.take (min l₁.length l₂.length))

src/Init/Data/List/Pairwise.lean

@@ -43,7 +43,7 @@ theorem rel_of_pairwise_cons (p : (a :: l).Pairwise R) : ∀ {a'}, a' ∈ l →
   (pairwise_cons.1 p).2
 
 set_option linter.unusedVariables false in
-@[grind ←] theorem Pairwise.tail : ∀ {l : List α} (h : Pairwise R l), Pairwise R l.tail
+@[grind] theorem Pairwise.tail : ∀ {l : List α} (h : Pairwise R l), Pairwise R l.tail
   | [], h => h
   | _ :: _, h => h.of_cons
 
@@ -103,7 +103,7 @@ theorem Pairwise.forall_of_forall_of_flip (h₁ : ∀ x ∈ l, R x x) (h₂ : Pa
     · exact h₃.1 _ hx
     · exact ih (fun x hx => h₁ _ <| mem_cons_of_mem _ hx) h₂.2 h₃.2 hx hy
 
-@[grind ←] theorem pairwise_singleton (R) (a : α) : Pairwise R [a] := by simp
+@[grind] theorem pairwise_singleton (R) (a : α) : Pairwise R [a] := by simp
 
 @[grind =] theorem pairwise_pair {a b : α} : Pairwise R [a, b] ↔ R a b := by simp
 
@@ -117,7 +117,7 @@ theorem Pairwise.of_map {S : β → β → Prop} (f : α → β) (H : ∀ a b :
     (p : Pairwise S (map f l)) : Pairwise R l :=
   (pairwise_map.1 p).imp (H _ _)
 
-@[grind <=] theorem Pairwise.map {S : β → β → Prop} (f : α → β) (H : ∀ a b : α, R a b → S (f a) (f b))
+@[grind] theorem Pairwise.map {S : β → β → Prop} (f : α → β) (H : ∀ a b : α, R a b → S (f a) (f b))
     (p : Pairwise R l) : Pairwise S (map f l) :=
   pairwise_map.2 <| p.imp (H _ _)
 
@@ -136,7 +136,7 @@ theorem Pairwise.of_map {S : β → β → Prop} (f : α → β) (H : ∀ a b :
     simpa [IH, e] using fun _ =>
       ⟨fun h a ha b hab => h _ _ ha hab, fun h a b ha hab => h _ ha _ hab⟩
 
-@[grind <=] theorem Pairwise.filterMap {S : β → β → Prop} (f : α → Option β)
+@[grind] theorem Pairwise.filterMap {S : β → β → Prop} (f : α → Option β)
     (H : ∀ a a' : α, R a a' → ∀ b, f a = some b → ∀ b', f a' = some b' → S b b') {l : List α} (p : Pairwise R l) :
     Pairwise S (filterMap f l) :=
   pairwise_filterMap.2 <| p.imp (H _ _)
@@ -146,7 +146,7 @@ theorem Pairwise.of_map {S : β → β → Prop} (f : α → β) (H : ∀ a b :
   rw [← filterMap_eq_filter, pairwise_filterMap]
   simp
 
-@[grind ←] theorem Pairwise.filter (p : α → Bool) : Pairwise R l → Pairwise R (filter p l) :=
+@[grind] theorem Pairwise.filter (p : α → Bool) : Pairwise R l → Pairwise R (filter p l) :=
   Pairwise.sublist filter_sublist
 
 @[grind =] theorem pairwise_append {l₁ l₂ : List α} :
@@ -171,7 +171,7 @@ theorem pairwise_append_comm {R : α → α → Prop} (s : ∀ {x y}, R x y →
   induction L with
   | nil => simp
   | cons l L IH =>
-    simp only [flatten_cons, pairwise_append, IH, mem_flatten, exists_imp, and_imp, forall_mem_cons,
+    simp only [flatten, pairwise_append, IH, mem_flatten, exists_imp, and_imp, forall_mem_cons,
       pairwise_cons, and_assoc, and_congr_right_iff]
     rw [and_comm, and_congr_left_iff]
     intros; exact ⟨fun h l' b c d e => h c d e l' b, fun h c d e l' b => h l' b c d e⟩
@@ -207,10 +207,10 @@ theorem pairwise_append_comm {R : α → α → Prop} (s : ∀ {x y}, R x y →
         simp
       · exact ⟨fun _ => h, Or.inr h⟩
 
-@[grind ←] theorem Pairwise.drop {l : List α} {i : Nat} (h : List.Pairwise R l) : List.Pairwise R (l.drop i) :=
+@[grind] theorem Pairwise.drop {l : List α} {i : Nat} (h : List.Pairwise R l) : List.Pairwise R (l.drop i) :=
   h.sublist (drop_sublist _ _)
 
-@[grind ←] theorem Pairwise.take {l : List α} {i : Nat} (h : List.Pairwise R l) : List.Pairwise R (l.take i) :=
+@[grind] theorem Pairwise.take {l : List α} {i : Nat} (h : List.Pairwise R l) : List.Pairwise R (l.take i) :=
   h.sublist (take_sublist _ _)
 
 -- This theorem is not annotated with `grind` because it leads to a loop of instantiations with `Pairwise.sublist`.
@@ -266,7 +266,7 @@ theorem pairwise_of_forall_mem_list {l : List α} {r : α → α → Prop} (h :
     rintro H _ b hb rfl
     exact H b hb _ _
 
-@[grind <=] theorem Pairwise.pmap {l : List α} (hl : Pairwise R l) {p : α → Prop} {f : ∀ a, p a → β}
+@[grind] theorem Pairwise.pmap {l : List α} (hl : Pairwise R l) {p : α → Prop} {f : ∀ a, p a → β}
     (h : ∀ x ∈ l, p x) {S : β → β → Prop}
     (hS : ∀ ⦃x⦄ (hx : p x) ⦃y⦄ (hy : p y), R x y → S (f x hx) (f y hy)) :
     Pairwise S (l.pmap f h) := by
@@ -277,12 +277,10 @@ theorem pairwise_of_forall_mem_list {l : List α} {r : α → α → Prop} (h :
 
 @[grind =] theorem nodup_iff_pairwise_ne : List.Nodup l ↔ List.Pairwise (· ≠ ·) l := Iff.rfl
 
-@[simp]
+@[simp, grind]
 theorem nodup_nil : @Nodup α [] :=
   Pairwise.nil
 
-grind_pattern nodup_nil => @Nodup α []
-
 @[simp, grind =]
 theorem nodup_cons {a : α} {l : List α} : Nodup (a :: l) ↔ a ∉ l ∧ Nodup l := by
   simp only [Nodup, pairwise_cons, forall_mem_ne]

src/Init/Data/List/Sublist.lean

@@ -151,11 +151,11 @@ theorem subset_replicate {n : Nat} {a : α} {l : List α} (h : n ≠ 0) : l ⊆
 
 /-! ### Sublist and isSublist -/
 
-@[simp, grind ←] 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, grind ←] 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
 
@@ -172,7 +172,7 @@ theorem Sublist.trans {l₁ l₂ l₃ : List α} (h₁ : l₁ <+ l₂) (h₂ : l
 
 instance : Trans (@Sublist α) Sublist Sublist := ⟨Sublist.trans⟩
 
-attribute [simp, grind ←] Sublist.cons
+attribute [simp, grind] Sublist.cons
 
 theorem sublist_cons_self (a : α) (l : List α) : l <+ a :: l := (Sublist.refl l).cons _
 
@@ -202,18 +202,12 @@ theorem sublist_or_mem_of_sublist (h : l <+ l₁ ++ a :: l₂) : l <+ l₁ ++ l
 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)
 
-grind_pattern Sublist.head_mem => ys <+ xs, ys.head h
-grind_pattern Sublist.head_mem => ys.head h ∈ xs -- This is somewhat aggressive, as it initiates sublist based reasoning.
-
-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)
 
-grind_pattern Sublist.getLast_mem => ys <+ xs, ys.getLast h
-grind_pattern Sublist.getLast_mem => ys.getLast h ∈ xs -- This is somewhat aggressive, as it initiates sublist based reasoning.
-
 instance : Trans (@Sublist α) Subset Subset :=
   ⟨fun h₁ h₂ => trans h₁.subset h₂⟩
 
@@ -254,13 +248,12 @@ theorem Sublist.eq_of_length_le (s : l₁ <+ l₂) (h : length l₂ ≤ length l
 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_pattern tail_sublist => tail l <+ _
-
-@[grind ←]
+@[grind]
 protected theorem Sublist.tail : ∀ {l₁ l₂ : List α}, l₁ <+ l₂ → tail l₁ <+ tail l₂
   | _, _, slnil => .slnil
   | _, _, Sublist.cons _ h => (tail_sublist _).trans h
@@ -270,7 +263,7 @@ protected theorem Sublist.tail : ∀ {l₁ l₂ : List α}, l₁ <+ l₂ → tai
 theorem Sublist.of_cons_cons {l₁ l₂ : List α} {a b : α} (h : a :: l₁ <+ b :: l₂) : l₁ <+ l₂ :=
   h.tail
 
-@[grind ←]
+@[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
@@ -282,7 +275,7 @@ protected theorem Sublist.map (f : α → β) {l₁ l₂} (s : l₁ <+ l₂) : m
 grind_pattern Sublist.map => l₁ <+ l₂, map f l₁
 grind_pattern Sublist.map => l₁ <+ l₂, map f l₂
 
-@[grind ←]
+@[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]
@@ -290,7 +283,7 @@ protected theorem Sublist.filterMap (f : α → Option β) (s : l₁ <+ l₂) :
 grind_pattern Sublist.filterMap => l₁ <+ l₂, filterMap f l₁
 grind_pattern Sublist.filterMap => l₁ <+ l₂, filterMap f l₂
 
-@[grind ←]
+@[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
 
@@ -488,7 +481,7 @@ 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 ←]
+@[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
@@ -631,28 +624,22 @@ 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 ←]
+@[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⟩
 
-grind_pattern prefix_append => l₁ <+: l₁ ++ l₂
-
-@[simp] theorem suffix_append (l₁ l₂ : List α) : l₂ <:+ l₁ ++ l₂ := ⟨l₁, rfl⟩
-
-grind_pattern suffix_append => l₂ <:+ l₁ ++ l₂
+@[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
 
-grind_pattern infix_append' => l₂ <:+: l₁ ++ (l₂ ++ l₃)
-
 theorem infix_append_left : l₁ <:+: l₁ ++ l₂ := ⟨[], l₂, rfl⟩
 theorem infix_append_right : l₂ <:+: l₁ ++ l₂ := ⟨l₁, [], by simp⟩
 
@@ -664,24 +651,22 @@ theorem IsSuffix.isInfix : l₁ <:+ l₂ → l₁ <:+: l₂ := fun ⟨t, h⟩ =>
 
 grind_pattern IsSuffix.isInfix => l₁ <:+ l₂, IsInfix
 
-@[simp, grind ←] theorem nil_prefix {l : List α} : [] <+: l := ⟨l, rfl⟩
+@[simp, grind] theorem nil_prefix {l : List α} : [] <+: l := ⟨l, rfl⟩
 
-@[simp, grind ←] theorem nil_suffix {l : List α} : [] <:+ l := ⟨l, append_nil _⟩
+@[simp, grind] theorem nil_suffix {l : List α} : [] <:+ l := ⟨l, append_nil _⟩
 
-@[simp, grind ←] theorem nil_infix {l : List α} : [] <:+: l := nil_prefix.isInfix
+@[simp, grind] theorem nil_infix {l : List α} : [] <:+: l := nil_prefix.isInfix
 
 theorem prefix_refl (l : List α) : l <+: l := ⟨[], append_nil _⟩
-@[simp, grind ←] 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, grind ←] 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, grind ←] 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]
-
-grind_pattern suffix_cons => _ <:+ a :: l
+@[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⟩
 
@@ -1123,36 +1108,24 @@ 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 _ _⟩
 
-grind_pattern take_prefix => take i l <+: _
-
-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 _ _⟩
 
-grind_pattern drop_suffix => drop i l <+: _
-
-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
 
-grind_pattern take_sublist => take i l <+ l
-
-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
 
-grind_pattern drop_sublist => drop i l <+ l
-
 theorem take_subset (i) (l : List α) : take i l ⊆ l :=
   (take_sublist i l).subset
 
-grind_pattern take_subset => take i l ⊆ l
-
 theorem drop_subset (i) (l : List α) : drop i l ⊆ l :=
   (drop_sublist i l).subset
 
-grind_pattern drop_subset => drop i l ⊆ l
-
 theorem mem_of_mem_take {l : List α} (h : a ∈ l.take i) : a ∈ l :=
   take_subset _ _ h
 
@@ -1165,84 +1138,64 @@ 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`.
 
-@[grind ←] 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
 
-@[grind ←] 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⟩
 
-grind_pattern takeWhile_prefix => l.takeWhile p <+: _
-
-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⟩
 
-grind_pattern dropWhile_suffix => l.dropWhile p <+: _
-
-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
 
-grind_pattern takeWhile_sublist => l.takeWhile p <+ _
-
-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
 
-grind_pattern dropWhile_sublist => l.dropWhile p <+ _
-
 theorem takeWhile_subset {l : List α} (p : α → Bool) : l.takeWhile p ⊆ l :=
   (takeWhile_sublist p).subset
 
-grind_pattern takeWhile_subset => l.takeWhile p ⊆ _
-
 theorem dropWhile_subset {l : List α} (p : α → Bool) : l.dropWhile p ⊆ l :=
   (dropWhile_sublist p).subset
 
-grind_pattern dropWhile_subset => l.dropWhile p ⊆ _
-
-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)⟩
 
-grind_pattern dropLast_prefix => l.dropLast <+: _
-
-theorem dropLast_sublist (l : List α) : l.dropLast <+ l :=
+@[grind] theorem dropLast_sublist (l : List α) : l.dropLast <+ l :=
   (dropLast_prefix l).sublist
 
-grind_pattern dropLast_sublist => l.dropLast <+ _
-
 theorem dropLast_subset (l : List α) : l.dropLast ⊆ l :=
   (dropLast_sublist l).subset
 
-grind_pattern dropLast_subset => l.dropLast ⊆ _
+@[grind] theorem tail_suffix (l : List α) : tail l <:+ l := by rw [← drop_one]; apply drop_suffix
 
-theorem tail_suffix (l : List α) : tail l <:+ l := by rw [← drop_one]; apply drop_suffix
-
-grind_pattern tail_suffix => tail l <+: _
-
-@[grind ←] 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
 
 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
+@[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
 
 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
+@[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
 
 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) :
+@[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
@@ -1250,7 +1203,7 @@ grind_pattern IsInfix.map => l₁ <:+: l₂, l₂.map f
 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) :
+@[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
@@ -1258,7 +1211,7 @@ grind_pattern IsPrefix.filter => l₁ <+: l₂, l₂.filter p
 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) :
+@[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 _
@@ -1266,7 +1219,7 @@ grind_pattern IsSuffix.filter => l₁ <:+ l₂, l₂.filter p
 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) :
+@[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
@@ -1274,7 +1227,7 @@ grind_pattern IsInfix.filter => l₁ <:+: l₂, l₂.filter p
 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) :
+@[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
@@ -1282,7 +1235,7 @@ grind_pattern IsPrefix.filterMap => l₁ <+: l₂, filterMap f 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) :
+@[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

src/Init/Data/List/ToArray.lean

@@ -12,6 +12,7 @@ public import Init.Data.List.Impl
 public import Init.Data.List.Nat.Erase
 public import Init.Data.List.Monadic
 public import Init.Data.List.Nat.InsertIdx
+public import Init.Data.Array.Lex.Basic
 public import Init.Data.Array.Basic
 import all Init.Data.Array.Basic
 public import Init.Data.Array.Set

src/Init/Data/List/Zip.lean

@@ -274,9 +274,11 @@ theorem zip_map {f : α → γ} {g : β → δ} :
   | _, [] => 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]
 

src/Init/Data/Nat/Basic.lean

@@ -257,6 +257,8 @@ attribute [simp] Nat.le_refl
 
 theorem succ_lt_succ {n m : Nat} : n < m → succ n < succ m := succ_le_succ
 
+theorem lt_succ_of_le {n m : Nat} : n ≤ m → n < succ m := succ_le_succ
+
 theorem le_of_lt_add_one {n m : Nat} : n < m + 1 → n ≤ m := le_of_succ_le_succ
 
 theorem lt_add_one_of_le {n m : Nat} : n ≤ m → n < m + 1 := succ_le_succ
@@ -269,15 +271,37 @@ theorem not_add_one_le_self : (n : Nat) → ¬ n + 1 ≤ n := Nat.not_succ_le_se
 
 theorem add_one_pos (n : Nat) : 0 < n + 1 := Nat.zero_lt_succ n
 
+theorem succ_sub_succ_eq_sub (n m : Nat) : succ n - succ m = n - m := by
+  induction m with
+  | zero      => exact rfl
+  | succ m ih => apply congrArg pred ih
+
+theorem pred_le : ∀ (n : Nat), pred n ≤ n
+  | zero   => Nat.le.refl
+  | succ _ => le_succ _
+
 theorem pred_lt : ∀ {n : Nat}, n ≠ 0 → pred n < n
   | zero,   h => absurd rfl h
   | succ _, _ => lt_succ_of_le (Nat.le_refl _)
 
 theorem sub_one_lt : ∀ {n : Nat}, n ≠ 0 → n - 1 < n := pred_lt
 
+@[simp] theorem sub_le (n m : Nat) : n - m ≤ n := by
+  induction m with
+  | zero      => exact Nat.le_refl (n - 0)
+  | succ m ih => apply Nat.le_trans (pred_le (n - m)) ih
+
 theorem sub_lt_of_lt {a b c : Nat} (h : a < c) : a - b < c :=
   Nat.lt_of_le_of_lt (Nat.sub_le _ _) h
 
+theorem sub_lt : ∀ {n m : Nat}, 0 < n → 0 < m → n - m < n
+  | 0,   _,   h1, _  => absurd h1 (Nat.lt_irrefl 0)
+  | _+1, 0,   _, h2  => absurd h2 (Nat.lt_irrefl 0)
+  | n+1, m+1, _,  _  =>
+    Eq.symm (succ_sub_succ_eq_sub n m) ▸
+      show n - m < succ n from
+      lt_succ_of_le (sub_le n m)
+
 theorem sub_succ (n m : Nat) : n - succ m = pred (n - m) := rfl
 
 theorem succ_sub_succ (n m : Nat) : succ n - succ m = n - m :=
@@ -292,6 +316,9 @@ theorem sub_add_eq (a b c : Nat) : a - (b + c) = a - b - c := by
   | zero => simp
   | succ c ih => simp only [Nat.add_succ, Nat.sub_succ, ih]
 
+protected theorem lt_of_lt_of_le {n m k : Nat} : n < m → m ≤ k → n < k :=
+  Nat.le_trans
+
 protected theorem lt_of_lt_of_eq {n m k : Nat} : n < m → m = k → n < k :=
   fun h₁ h₂ => h₂ ▸ h₁
 
@@ -329,10 +356,12 @@ protected theorem pos_of_ne_zero {n : Nat} : n ≠ 0 → 0 < n := (eq_zero_or_po
 
 theorem pos_of_neZero (n : Nat) [NeZero n] : 0 < n := Nat.pos_of_ne_zero (NeZero.ne _)
 
-attribute [simp] Nat.lt_add_one
-
 theorem lt.base (n : Nat) : n < succ n := Nat.le_refl (succ n)
 
+theorem lt_succ_self (n : Nat) : n < succ n := lt.base n
+
+@[simp] protected theorem lt_add_one (n : Nat) : n < n + 1 := lt.base n
+
 protected theorem le_total (m n : Nat) : m ≤ n ∨ n ≤ m :=
   match Nat.lt_or_ge m n with
   | Or.inl h => Or.inl (Nat.le_of_lt h)
@@ -428,6 +457,7 @@ protected theorem le_lt_asymm : ∀{a b : Nat}, a ≤ b → ¬(b < a) := flip Na
 
 theorem gt_of_not_le {n m : Nat} (h : ¬ n ≤ m) : n > m := (Nat.lt_or_ge m n).resolve_right h
 protected theorem lt_of_not_ge : ∀{a b : Nat}, ¬(b ≥ a) → b < a := Nat.gt_of_not_le
+protected theorem lt_of_not_le : ∀{a b : Nat}, ¬(a ≤ b) → b < a := Nat.gt_of_not_le
 
 theorem ge_of_not_lt {n m : Nat} (h : ¬ n < m) : n ≥ m := (Nat.lt_or_ge n m).resolve_left h
 protected theorem le_of_not_gt : ∀{a b : Nat}, ¬(b > a) → b ≤ a := Nat.ge_of_not_lt
@@ -740,6 +770,10 @@ protected theorem mul_lt_mul_of_pos_left {n m k : Nat} (h : n < m) (hk : k > 0)
 protected theorem mul_lt_mul_of_pos_right {n m k : Nat} (h : n < m) (hk : k > 0) : n * k < m * k :=
   Nat.mul_comm k m ▸ Nat.mul_comm k n ▸ Nat.mul_lt_mul_of_pos_left h hk
 
+protected theorem mul_pos {n m : Nat} (ha : n > 0) (hb : m > 0) : n * m > 0 :=
+  have h : 0 * m < n * m := Nat.mul_lt_mul_of_pos_right ha hb
+  Nat.zero_mul m ▸ h
+
 protected theorem le_of_mul_le_mul_left {a b c : Nat} (h : c * a ≤ c * b) (hc : 0 < c) : a ≤ b :=
   Nat.ge_of_not_lt fun hlt : b < a =>
     have h' : c * b < c * a := Nat.mul_lt_mul_of_pos_left hlt hc
@@ -799,6 +833,11 @@ set_option linter.missingDocs false in
 @[deprecated Nat.pow_le_pow_right (since := "2025-02-17")]
 abbrev pow_le_pow_of_le_right := @Nat.pow_le_pow_right
 
+protected theorem pow_pos (h : 0 < a) : 0 < a^n :=
+  match n with
+  | 0 => Nat.zero_lt_one
+  | _ + 1 => Nat.mul_pos (Nat.pow_pos h) h
+
 set_option linter.missingDocs false in
 @[deprecated Nat.pow_pos (since := "2025-02-17")]
 abbrev pos_pow_of_pos := @Nat.pow_pos
@@ -1160,8 +1199,6 @@ protected theorem sub_eq_iff_eq_add {c : Nat} (h : b ≤ a) : a - b = c ↔ a =
 protected theorem sub_eq_iff_eq_add' {c : Nat} (h : b ≤ a) : a - b = c ↔ a = b + c := by
   rw [Nat.add_comm, Nat.sub_eq_iff_eq_add h]
 
-attribute [simp] sub_le
-
 protected theorem sub_one_sub_lt_of_lt (h : a < b) : b - 1 - a < b := by
   rw [← Nat.sub_add_eq]
   exact sub_lt (zero_lt_of_lt h) (Nat.lt_add_right a Nat.one_pos)

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

@@ -24,6 +24,47 @@ there is some `c` such that `b = a * c`.
 instance : Dvd Nat where
   dvd a b := Exists (fun c => b = a * c)
 
+theorem div_rec_lemma {x y : Nat} : 0 < y ∧ y ≤ x → x - y < x :=
+  fun ⟨ypos, ylex⟩ => sub_lt (Nat.lt_of_lt_of_le ypos ylex) ypos
+
+theorem div_rec_fuel_lemma {x y fuel : Nat} (hy : 0 < y) (hle : y ≤ x) (hfuel : x < fuel + 1) :
+    x - y < fuel :=
+  Nat.lt_of_lt_of_le (div_rec_lemma ⟨hy, hle⟩) (Nat.le_of_lt_succ hfuel)
+
+/--
+Division of natural numbers, discarding the remainder. Division by `0` returns `0`. Usually accessed
+via the `/` operator.
+
+This operation is sometimes called “floor division.”
+
+This function is overridden at runtime with an efficient implementation. This definition is
+the logical model.
+
+Examples:
+ * `21 / 3 = 7`
+ * `21 / 5 = 4`
+ * `0 / 22 = 0`
+ * `5 / 0 = 0`
+-/
+@[extern "lean_nat_div", irreducible]
+protected def div (x y : @& Nat) : Nat :=
+  if hy : 0 < y then
+    let rec
+      go (fuel : Nat) (x : Nat) (hfuel : x < fuel) : Nat :=
+      match fuel with
+      | 0 => by contradiction
+      | succ fuel =>
+        if h : y ≤ x then
+          go fuel (x - y) (div_rec_fuel_lemma hy h hfuel) + 1
+        else
+          0
+      termination_by structural fuel
+    go (x + 1) x (Nat.lt_succ_self _)
+  else
+    0
+
+instance instDiv : Div Nat := ⟨Nat.div⟩
+
 private theorem div.go.fuel_congr (x y fuel1 fuel2 : Nat) (hy : 0 < y) (h1 : x < fuel1) (h2 : x < fuel2) :
     Nat.div.go y hy fuel1 x h1 = Nat.div.go y hy fuel2 x h2 := by
   match fuel1, fuel2 with
@@ -113,6 +154,36 @@ protected def divExact (x y : @& Nat) (h : y ∣ x) : Nat :=
 @[simp]
 theorem divExact_eq_div {x y : Nat} (h : y ∣ x) : x.divExact y h = x / y := rfl
 
+/--
+The modulo operator, which computes the remainder when dividing one natural number by another.
+Usually accessed via the `%` operator. When the divisor is `0`, the result is the dividend rather
+than an error.
+
+This is the core implementation of `Nat.mod`. It computes the correct result for any two closed
+natural numbers, but it does not have some convenient [definitional
+reductions](lean-manual://section/type-system) when the `Nat`s contain free variables. The wrapper
+`Nat.mod` handles those cases specially and then calls `Nat.modCore`.
+
+This function is overridden at runtime with an efficient implementation. This definition is the
+logical model.
+-/
+@[extern "lean_nat_mod", irreducible]
+protected noncomputable def modCore (x y : Nat) : Nat :=
+  if hy : 0 < y then
+    let rec
+      go (fuel : Nat) (x : Nat) (hfuel : x < fuel) : Nat :=
+      match fuel with
+      | 0 => by contradiction
+      | succ fuel =>
+        if h : y ≤ x then
+          go fuel (x - y) (div_rec_fuel_lemma hy h hfuel)
+        else
+          x
+      termination_by structural fuel
+    go (x + 1) x (Nat.lt_succ_self _)
+  else
+    x
+
 private theorem modCore.go.fuel_congr (x y fuel1 fuel2 : Nat) (hy : 0 < y) (h1 : x < fuel1) (h2 : x < fuel2) :
     Nat.modCore.go y hy fuel1 x h1 = Nat.modCore.go y hy fuel2 x h2 := by
   match fuel1, fuel2 with
@@ -143,6 +214,51 @@ protected theorem modCore_eq (x y : Nat) : Nat.modCore x y =
   next =>
     simp only [false_and, ↓reduceIte, *]
 
+
+/--
+The modulo operator, which computes the remainder when dividing one natural number by another.
+Usually accessed via the `%` operator. When the divisor is `0`, the result is the dividend rather
+than an error.
+
+`Nat.mod` is a wrapper around `Nat.modCore` that special-cases two situations, giving better
+definitional reductions:
+ * `Nat.mod 0 m` should reduce to `m`, for all terms `m : Nat`.
+ * `Nat.mod n (m + n + 1)` should reduce to `n` for concrete `Nat` literals `n`.
+
+These reductions help `Fin n` literals work well, because the `OfNat` instance for `Fin` uses
+`Nat.mod`. In particular, `(0 : Fin (n + 1)).val` should reduce definitionally to `0`. `Nat.modCore`
+can handle all numbers, but its definitional reductions are not as convenient.
+
+This function is overridden at runtime with an efficient implementation. This definition is the
+logical model.
+
+Examples:
+ * `7 % 2 = 1`
+ * `9 % 3 = 0`
+ * `5 % 7 = 5`
+ * `5 % 0 = 5`
+ * `show ∀ (n : Nat), 0 % n = 0 from fun _ => rfl`
+ * `show ∀ (m : Nat), 5 % (m + 6) = 5 from fun _ => rfl`
+-/
+@[extern "lean_nat_mod"]
+protected def mod : @& Nat → @& Nat → Nat
+  /-
+  Nat.modCore is defined with fuel and thus does not reduce with open terms very well.
+  Nevertheless it is desirable for trivial `Nat.mod` calculations, namely
+  * `Nat.mod 0 m` for all `m`
+  * `Nat.mod n (m + n + 1)` for concrete literals `n`,
+  to reduce definitionally.
+  This property is desirable for `Fin n` literals, as it means `(ofNat 0 : Fin n).val = 0` by
+  definition.
+   -/
+  | 0, _ => 0
+  | n@(_ + 1), m =>
+    if m ≤ n -- NB: if n < m does not reduce as well as `m ≤ n`!
+    then Nat.modCore n m
+    else n
+
+instance instMod : Mod Nat := ⟨Nat.mod⟩
+
 protected theorem modCore_eq_mod (n m : Nat) : Nat.modCore n m = n % m := by
   change Nat.modCore n m = Nat.mod n m
   match n, m with
@@ -199,6 +315,24 @@ theorem mod_eq_sub_mod {a b : Nat} (h : a ≥ b) : a % b = (a - b) % b :=
   | Or.inl h₁ => h₁.symm ▸ (Nat.sub_zero a).symm ▸ rfl
   | Or.inr h₁ => (mod_eq a b).symm ▸ if_pos ⟨h₁, h⟩
 
+theorem mod_lt (x : Nat) {y : Nat} : y > 0 → x % y < y := by
+  induction x, y using mod.inductionOn with
+  | base x y h₁ =>
+    intro h₂
+    have h₁ : ¬ 0 < y ∨ ¬ y ≤ x := Decidable.not_and_iff_or_not.mp h₁
+    match h₁ with
+    | Or.inl h₁ => exact absurd h₂ h₁
+    | Or.inr h₁ =>
+      have hgt : y > x := gt_of_not_le h₁
+      have heq : x % y = x := mod_eq_of_lt hgt
+      rw [← heq] at hgt
+      exact hgt
+  | ind x y h h₂ =>
+    intro h₃
+    have ⟨_, h₁⟩ := h
+    rw [mod_eq_sub_mod h₁]
+    exact h₂ h₃
+
 @[simp] protected theorem sub_mod_add_mod_cancel (a b : Nat) [NeZero a] : a - b % a + b % a = a := by
   rw [Nat.sub_add_cancel]
   cases a with

src/Init/Data/Nat/Fold.lean

@@ -128,12 +128,6 @@ theorem fold_congr {α : Type u} {n m : Nat} (w : n = m)
   subst m
   rfl
 
-theorem foldRev_congr {α : Type u} {n m : Nat} (w : n = m)
-     (f : (i : Nat) → i < n → α → α) (init : α) :
-     foldRev n f init = foldRev m (fun i h => f i (by omega)) init := by
-  subst m
-  rfl
-
 private theorem foldTR_loop_congr {α : Type u} {n m : Nat} (w : n = m)
      (f : (i : Nat) → i < n → α → α) (j : Nat) (h : j ≤ n) (init : α) :
      foldTR.loop n f j h init = foldTR.loop m (fun i h => f i (by omega)) j (by omega) init := by
@@ -276,16 +270,6 @@ def dfoldRev (n : Nat) {α : (i : Nat) → (h : i ≤ n := by omega) → Type u}
   | succ n ih =>
     simp [ih, List.finRange_succ_last, List.foldl_map]
 
-theorem fold_add
-    {α n m} (f : (i : Nat) → i < n + m → α → α) (init : α) :
-    fold (n + m) f init =
-      fold m (fun i h => f (n + i) (by omega))
-        (fold n (fun i h => f i (by omega)) init) := by
-  induction m with
-  | zero => simp; rfl
-  | succ m ih =>
-    simp [fold_congr (Nat.add_assoc n m 1).symm, ih]
-
 /-! ### `foldRev` -/
 
 @[simp] theorem foldRev_zero {α : Type u} (f : (i : Nat) → i < 0 → α → α) (init : α) :
@@ -301,17 +285,6 @@ theorem fold_add
   | zero => simp
   | succ n ih => simp [ih, List.finRange_succ_last, List.foldr_map]
 
-theorem foldRev_add
-    {α n m} (f : (i : Nat) → i < n + m → α → α) (init : α) :
-    foldRev (n + m) f init =
-      foldRev n (fun i h => f i (by omega))
-        (foldRev m (fun i h => f (n + i) (by omega)) init) := by
-  induction m generalizing init with
-  | zero => simp; rfl
-  | succ m ih =>
-    rw [foldRev_congr (Nat.add_assoc n m 1).symm]
-    simp [ih]
-
 /-! ### `any` -/
 
 @[simp] theorem any_zero {f : (i : Nat) → i < 0 → Bool} : any 0 f = false := by simp [any]

src/Init/Data/Nat/Lemmas.lean

@@ -264,6 +264,9 @@ protected theorem pos_of_lt_add_left : n < k + n → 0 < k := by
 protected theorem add_pos_left (h : 0 < m) (n) : 0 < m + n :=
   Nat.lt_of_lt_of_le h (Nat.le_add_right ..)
 
+protected theorem add_pos_right (m) (h : 0 < n) : 0 < m + n :=
+  Nat.lt_of_lt_of_le h (Nat.le_add_left ..)
+
 protected theorem add_self_ne_one : ∀ n, n + n ≠ 1
   | n+1, h => by rw [Nat.succ_add, Nat.succ.injEq] at h; contradiction
 

src/Init/Data/Nat/Linear.lean

@@ -9,7 +9,6 @@ prelude
 public import Init.ByCases
 public import Init.Data.Prod
 public import Init.Data.RArray
-import Init.LawfulBEqTactics
 
 public section
 
@@ -139,7 +138,21 @@ structure PolyCnstr  where
   eq  : Bool
   lhs : Poly
   rhs : Poly
-  deriving BEq, ReflBEq, LawfulBEq
+  deriving BEq
+
+-- TODO: implement LawfulBEq generator companion for BEq
+instance : LawfulBEq PolyCnstr where
+  eq_of_beq {a b} h := by
+    cases a; rename_i eq₁ lhs₁ rhs₁
+    cases b; rename_i eq₂ lhs₂ rhs₂
+    have h : eq₁ == eq₂ && (lhs₁ == lhs₂ && rhs₁ == rhs₂) := h
+    simp at h
+    have ⟨h₁, h₂, h₃⟩ := h
+    rw [h₁, h₂, h₃]
+  rfl {a} := by
+    cases a; rename_i eq lhs rhs
+    change (eq == eq && (lhs == lhs && rhs == rhs)) = true
+    simp
 
 structure ExprCnstr where
   eq  : Bool

src/Init/Data/Option/Array.lean

@@ -15,30 +15,30 @@ public section
 
 namespace Option
 
-@[simp, grind =] theorem mem_toArray {a : α} {o : Option α} : a ∈ o.toArray ↔ o = some a := by
+@[simp, grind] theorem mem_toArray {a : α} {o : Option α} : a ∈ o.toArray ↔ o = some a := by
   cases o <;> simp [eq_comm]
 
-@[simp, grind =] theorem forIn'_toArray [Monad m] (o : Option α) (b : β) (f : (a : α) → a ∈ o.toArray → β → m (ForInStep β)) :
+@[simp, grind] theorem forIn'_toArray [Monad m] (o : Option α) (b : β) (f : (a : α) → a ∈ o.toArray → β → m (ForInStep β)) :
     forIn' o.toArray b f = forIn' o b fun a m b => f a (by simpa using m) b := by
   cases o <;> simp <;> rfl
 
-@[simp, grind =] theorem forIn_toArray [Monad m] (o : Option α) (b : β) (f : α → β → m (ForInStep β)) :
+@[simp, grind] theorem forIn_toArray [Monad m] (o : Option α) (b : β) (f : α → β → m (ForInStep β)) :
     forIn o.toArray b f = forIn o b f := by
   cases o <;> simp <;> rfl
 
-@[simp, grind =] theorem foldlM_toArray [Monad m] [LawfulMonad m] (o : Option β) (a : α) (f : α → β → m α) :
+@[simp, grind] theorem foldlM_toArray [Monad m] [LawfulMonad m] (o : Option β) (a : α) (f : α → β → m α) :
     o.toArray.foldlM f a = o.elim (pure a) (fun b => f a b) := by
   cases o <;> simp
 
-@[simp, grind =] theorem foldrM_toArray [Monad m] [LawfulMonad m] (o : Option β) (a : α) (f : β → α → m α) :
+@[simp, grind] theorem foldrM_toArray [Monad m] [LawfulMonad m] (o : Option β) (a : α) (f : β → α → m α) :
     o.toArray.foldrM f a = o.elim (pure a) (fun b => f b a) := by
   cases o <;> simp
 
-@[simp, grind =] theorem foldl_toArray (o : Option β) (a : α) (f : α → β → α) :
+@[simp, grind] theorem foldl_toArray (o : Option β) (a : α) (f : α → β → α) :
     o.toArray.foldl f a = o.elim a (fun b => f a b) := by
   cases o <;> simp
 
-@[simp, grind =] theorem foldr_toArray (o : Option β) (a : α) (f : β → α → α) :
+@[simp, grind] theorem foldr_toArray (o : Option β) (a : α) (f : β → α → α) :
     o.toArray.foldr f a = o.elim a (fun b => f b a) := by
   cases o <;> simp
 

src/Init/Data/Option/Attach.lean

@@ -97,7 +97,7 @@ theorem attach_eq_some : ∀ (o : Option α) (x : {x // o = some x}), o.attach =
   | none, ⟨x, h⟩ => by simp at h
   | some a, ⟨x, h⟩ => by simpa using h
 
-@[grind ←]
+@[grind]
 theorem mem_attach : ∀ (o : Option α) (x : {x // o = some x}), x ∈ o.attach :=
   attach_eq_some
 

src/Init/Data/Option/Basic.lean

@@ -18,27 +18,27 @@ namespace Option
 deriving instance DecidableEq for Option
 deriving instance BEq for Option
 
-@[simp, grind =] theorem getD_none : getD none a = a := rfl
-@[simp, grind =] theorem getD_some : getD (some a) b = a := rfl
+@[simp, grind] theorem getD_none : getD none a = a := rfl
+@[simp, grind] theorem getD_some : getD (some a) b = a := rfl
 
-@[simp, grind =] theorem map_none (f : α → β) : none.map f = none := rfl
-@[simp, grind =] theorem map_some (a) (f : α → β) : (some a).map f = some (f a) := rfl
+@[simp, grind] theorem map_none (f : α → β) : none.map f = none := rfl
+@[simp, grind] theorem map_some (a) (f : α → β) : (some a).map f = some (f a) := rfl
 
 /-- Lifts an optional value to any `Alternative`, sending `none` to `failure`. -/
 def getM [Alternative m] : Option α → m α
   | none     => failure
   | some a   => pure a
 
-@[simp, grind =] theorem getM_none [Alternative m] : getM none = (failure : m α) := rfl
-@[simp, grind =] theorem getM_some [Alternative m] {a : α} : getM (some a) = (pure a : m α) := rfl
+@[simp, grind] theorem getM_none [Alternative m] : getM none = (failure : m α) := rfl
+@[simp, grind] theorem getM_some [Alternative m] {a : α} : getM (some a) = (pure a : m α) := rfl
 
 /-- Returns `true` on `some x` and `false` on `none`. -/
 @[inline] def isSome : Option α → Bool
   | some _ => true
   | none   => false
 
-@[simp, grind =] theorem isSome_none : @isSome α none = false := rfl
-@[simp, grind =] theorem isSome_some : isSome (some a) = true := rfl
+@[simp, grind] theorem isSome_none : @isSome α none = false := rfl
+@[simp, grind] theorem isSome_some : isSome (some a) = true := rfl
 
 /--
 Returns `true` on `none` and `false` on `some x`.
@@ -53,8 +53,8 @@ Examples:
   | some _ => false
   | none   => true
 
-@[simp, grind =] theorem isNone_none : @isNone α none = true := rfl
-@[simp, grind =] theorem isNone_some : isNone (some a) = false := rfl
+@[simp, grind] theorem isNone_none : @isNone α none = true := rfl
+@[simp, grind] theorem isNone_some : isNone (some a) = false := rfl
 
 /--
 Checks whether an optional value is both present and equal to some other value.
@@ -89,8 +89,8 @@ Examples:
   | none,   _ => none
   | some a, f => f a
 
-@[simp, grind =] theorem bind_none (f : α → Option β) : none.bind f = none := rfl
-@[simp, grind =] theorem bind_some (a) (f : α → Option β) : (some a).bind f = f a := rfl
+@[simp, grind] theorem bind_none (f : α → Option β) : none.bind f = none := rfl
+@[simp, grind] theorem bind_some (a) (f : α → Option β) : (some a).bind f = f a := rfl
 
 @[deprecated bind_none (since := "2025-05-03")]
 abbrev none_bind := @bind_none
@@ -125,8 +125,8 @@ This function only requires `m` to be an applicative functor. An alias `Option.m
   | none => pure none
   | some x => some <$> f x
 
-@[simp, grind =] theorem mapM_none [Applicative m] (f : α → m β) : none.mapM f = pure none := rfl
-@[simp, grind =] theorem mapM_some [Applicative m] (x) (f : α → m β) : (some x).mapM f = some <$> f x := rfl
+@[simp, grind] theorem mapM_none [Applicative m] (f : α → m β) : none.mapM f = pure none := rfl
+@[simp, grind] theorem mapM_some [Applicative m] (x) (f : α → m β) : (some x).mapM f = some <$> f x := rfl
 
 /--
 Applies a function in some applicative functor to an optional value, returning `none` with no
@@ -138,9 +138,9 @@ This is an alias for `Option.mapM`, which already works for applicative functors
   Option.mapM f
 
 /-- For verification purposes, we replace `mapA` with `mapM`. -/
-@[simp, grind =] theorem mapA_eq_mapM [Applicative m] {f : α → m β} : Option.mapA f o = Option.mapM f o := rfl
+@[simp, grind] theorem mapA_eq_mapM [Applicative m] {f : α → m β} : Option.mapA f o = Option.mapM f o := rfl
 
-@[simp, grind =]
+@[simp, grind]
 theorem map_id : (Option.map id : Option α → Option α) = id :=
   funext (fun o => match o with | none => rfl | some _ => rfl)
 
@@ -182,8 +182,8 @@ Examples:
   | some a => p a
   | none   => true
 
-@[simp, grind =] theorem all_none : Option.all p none = true := rfl
-@[simp, grind =] theorem all_some : Option.all p (some x) = p x := rfl
+@[simp, grind] theorem all_none : Option.all p none = true := rfl
+@[simp, grind] theorem all_some : Option.all p (some x) = p x := rfl
 
 /--
 Checks whether an optional value is not `none` and satisfies a Boolean predicate.
@@ -197,8 +197,8 @@ Examples:
   | some a => p a
   | none   => false
 
-@[simp, grind =] theorem any_none : Option.any p none = false := rfl
-@[simp, grind =] theorem any_some : Option.any p (some x) = p x := rfl
+@[simp, grind] theorem any_none : Option.any p none = false := rfl
+@[simp, grind] theorem any_some : Option.any p (some x) = p x := rfl
 
 /--
 Implementation of `OrElse`'s `<|>` syntax for `Option`. If the first argument is `some a`, returns
@@ -210,8 +210,8 @@ See also `or` for a version that is strict in the second argument.
   | some a, _ => some a
   | none,   b => b ()
 
-@[simp, grind =] theorem orElse_some : (some a).orElse b = some a := rfl
-@[simp, grind =] theorem orElse_none : none.orElse b = b () := rfl
+@[simp, grind] theorem orElse_some : (some a).orElse b = some a := rfl
+@[simp, grind] theorem orElse_none : none.orElse b = b () := rfl
 
 instance : OrElse (Option α) where
   orElse := Option.orElse
@@ -351,9 +351,9 @@ Extracts the value from an option that can be proven to be `some`.
 @[inline] def get {α : Type u} : (o : Option α) → isSome o → α
   | some x, _ => x
 
-@[simp, grind =] theorem some_get : ∀ {x : Option α} (h : isSome x), some (x.get h) = x
+@[simp, grind] theorem some_get : ∀ {x : Option α} (h : isSome x), some (x.get h) = x
 | some _, _ => rfl
-@[simp, grind =] theorem get_some (x : α) (h : isSome (some x)) : (some x).get h = x := rfl
+@[simp, grind] theorem get_some (x : α) (h : isSome (some x)) : (some x).get h = x := rfl
 
 /--
 Returns `none` if a value doesn't satisfy a Boolean predicate, or the value itself otherwise.
@@ -431,8 +431,8 @@ Examples:
 -/
 @[inline] def join (x : Option (Option α)) : Option α := x.bind id
 
-@[simp, grind =] theorem join_none : (none : Option (Option α)).join = none := rfl
-@[simp, grind =] theorem join_some : (some o).join = o := rfl
+@[simp, grind] theorem join_none : (none : Option (Option α)).join = none := rfl
+@[simp, grind] theorem join_some : (some o).join = o := rfl
 
 /--
 Converts an optional monadic computation into a monadic computation of an optional value.
@@ -457,8 +457,8 @@ some "world"
   | none => pure none
   | some f => some <$> f
 
-@[simp, grind =] theorem sequence_none [Applicative m] : (none : Option (m α)).sequence = pure none := rfl
-@[simp, grind =] theorem sequence_some [Applicative m] (f : m α) : (some f).sequence = some <$> f := rfl
+@[simp, grind] theorem sequence_none [Applicative m] : (none : Option (m α)).sequence = pure none := rfl
+@[simp, grind] theorem sequence_some [Applicative m] (f : m α) : (some f).sequence = some <$> f := rfl
 
 /--
 A monadic case analysis function for `Option`.
@@ -483,8 +483,8 @@ This is the monadic analogue of `Option.getD`.
   | some a => pure a
   | none => y
 
-@[simp, grind =] theorem getDM_none [Pure m] (y : m α) : (none : Option α).getDM y = y := rfl
-@[simp, grind =] theorem getDM_some [Pure m] (a : α) (y : m α) : (some a).getDM y = pure a := rfl
+@[simp, grind] theorem getDM_none [Pure m] (y : m α) : (none : Option α).getDM y = y := rfl
+@[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} := private
@@ -520,10 +520,10 @@ protected def min [Min α] : Option α → Option α → Option α
 
 instance [Min α] : Min (Option α) where min := Option.min
 
-@[simp, grind =] theorem min_some_some [Min α] {a b : α} : min (some a) (some b) = some (min a b) := rfl
-@[simp, grind =] theorem min_none_left [Min α] {o : Option α} : min none o = none := by
+@[simp, grind] theorem min_some_some [Min α] {a b : α} : min (some a) (some b) = some (min a b) := rfl
+@[simp, grind] theorem min_none_left [Min α] {o : Option α} : min none o = none := by
   cases o <;> rfl
-@[simp, grind =] theorem min_none_right [Min α] {o : Option α} : min o none = none := by
+@[simp, grind] theorem min_none_right [Min α] {o : Option α} : min o none = none := by
   cases o <;> rfl
 
 @[deprecated min_none_right (since := "2025-05-12")]
@@ -553,10 +553,10 @@ protected def max [Max α] : Option α → Option α → Option α
 
 instance [Max α] : Max (Option α) where max := Option.max
 
-@[simp, grind =] theorem max_some_some [Max α] {a b : α} : max (some a) (some b) = some (max a b) := rfl
-@[simp, grind =] theorem max_none_left [Max α] {o : Option α} : max none o = o := by
+@[simp, grind] theorem max_some_some [Max α] {a b : α} : max (some a) (some b) = some (max a b) := rfl
+@[simp, grind] theorem max_none_left [Max α] {o : Option α} : max none o = o := by
   cases o <;> rfl
-@[simp, grind =] theorem max_none_right [Max α] {o : Option α} : max o none = o := by
+@[simp, grind] theorem max_none_right [Max α] {o : Option α} : max o none = o := by
   cases o <;> rfl
 
 @[deprecated max_none_right (since := "2025-05-12")]

src/Init/Data/Option/Lemmas.lean

@@ -24,7 +24,7 @@ namespace Option
 @[deprecated mem_def (since := "2025-04-07")]
 theorem mem_iff {a : α} {b : Option α} : a ∈ b ↔ b = some a := .rfl
 
-@[grind =] theorem mem_some {a b : α} : a ∈ some b ↔ b = a := by simp
+@[grind] theorem mem_some {a b : α} : a ∈ some b ↔ b = a := by simp
 
 theorem mem_some_iff {a b : α} : a ∈ some b ↔ b = a := mem_some
 
@@ -52,7 +52,7 @@ theorem get_of_mem : ∀ {o : Option α} (h : isSome o), a ∈ o → o.get h = a
 theorem get_of_eq_some : ∀ {o : Option α} (h : isSome o), o = some a → o.get h = a
   | _, _, rfl => rfl
 
-@[simp, grind ←] theorem not_mem_none (a : α) : a ∉ (none : Option α) := nofun
+@[simp, grind] theorem not_mem_none (a : α) : a ∉ (none : Option α) := nofun
 
 theorem getD_of_ne_none {x : Option α} (hx : x ≠ none) (y : α) : some (x.getD y) = x := by
   cases x; {contradiction}; rw [getD_some]
@@ -797,7 +797,7 @@ theorem get_merge {o o' : Option α} {f : α → α → α} {i : α} [Std.Lawful
     (o.merge f o').get h = f (o.getD i) (o'.getD i) := by
   cases o <;> cases o' <;> simp [Std.LawfulLeftIdentity.left_id, Std.LawfulRightIdentity.right_id]
 
-@[simp, grind =] theorem elim_none (x : β) (f : α → β) : Option.elim none x f = x := rfl
+@[simp, grind =] theorem elim_none (x : β) (f : α → β) : none.elim x f = x := rfl
 
 @[simp, grind =] theorem elim_some (x : β) (f : α → β) (a : α) : (some a).elim x f = f a := rfl
 

src/Init/Data/Option/List.lean

@@ -16,38 +16,38 @@ public section
 
 namespace Option
 
-@[simp, grind =] theorem mem_toList {a : α} {o : Option α} : a ∈ o.toList ↔ o = some a := by
+@[simp, grind] theorem mem_toList {a : α} {o : Option α} : a ∈ o.toList ↔ o = some a := by
   cases o <;> simp [eq_comm]
 
-@[simp, grind =] theorem forIn'_toList [Monad m] (o : Option α) (b : β) (f : (a : α) → a ∈ o.toList → β → m (ForInStep β)) :
+@[simp, grind] theorem forIn'_toList [Monad m] (o : Option α) (b : β) (f : (a : α) → a ∈ o.toList → β → m (ForInStep β)) :
     forIn' o.toList b f = forIn' o b fun a m b => f a (by simpa using m) b := by
   cases o <;> rfl
 
-@[simp, grind =] theorem forIn_toList [Monad m] (o : Option α) (b : β) (f : α → β → m (ForInStep β)) :
+@[simp, grind] theorem forIn_toList [Monad m] (o : Option α) (b : β) (f : α → β → m (ForInStep β)) :
     forIn o.toList b f = forIn o b f := by
   cases o <;> rfl
 
-@[simp, grind =] theorem foldlM_toList [Monad m] [LawfulMonad m] (o : Option β) (a : α) (f : α → β → m α) :
+@[simp, grind] theorem foldlM_toList [Monad m] [LawfulMonad m] (o : Option β) (a : α) (f : α → β → m α) :
     o.toList.foldlM f a = o.elim (pure a) (fun b => f a b) := by
   cases o <;> simp
 
-@[simp, grind =] theorem foldrM_toList [Monad m] [LawfulMonad m] (o : Option β) (a : α) (f : β → α → m α) :
+@[simp, grind] theorem foldrM_toList [Monad m] [LawfulMonad m] (o : Option β) (a : α) (f : β → α → m α) :
     o.toList.foldrM f a = o.elim (pure a) (fun b => f b a) := by
   cases o <;> simp
 
-@[simp, grind =] theorem foldl_toList (o : Option β) (a : α) (f : α → β → α) :
+@[simp, grind] theorem foldl_toList (o : Option β) (a : α) (f : α → β → α) :
     o.toList.foldl f a = o.elim a (fun b => f a b) := by
   cases o <;> simp
 
-@[simp, grind =] theorem foldr_toList (o : Option β) (a : α) (f : β → α → α) :
+@[simp, grind] theorem foldr_toList (o : Option β) (a : α) (f : β → α → α) :
     o.toList.foldr f a = o.elim a (fun b => f b a) := by
   cases o <;> simp
 
-@[simp, grind ←]
+@[simp, grind]
 theorem pairwise_toList {P : α → α → Prop} {o : Option α} : o.toList.Pairwise P := by
   cases o <;> simp
 
-@[simp, grind =]
+@[simp, grind]
 theorem head?_toList {o : Option α} : o.toList.head? = o := by
   cases o <;> simp
 

src/Init/Data/Option/Monadic.lean

@@ -16,20 +16,20 @@ public section
 
 namespace Option
 
-@[simp, grind =] theorem bindM_none [Pure m] (f : α → m (Option β)) : none.bindM f = pure none := rfl
-@[simp, grind =] theorem bindM_some [Pure m] (a) (f : α → m (Option β)) : (some a).bindM f = f a := by
+@[simp, grind] theorem bindM_none [Pure m] (f : α → m (Option β)) : none.bindM f = pure none := rfl
+@[simp, grind] theorem bindM_some [Pure m] (a) (f : α → m (Option β)) : (some a).bindM f = f a := by
   simp [Option.bindM]
 
 -- We simplify `Option.forM` to `forM`.
 @[simp] theorem forM_eq_forM [Monad m] : @Option.forM m α _ = forM := rfl
 
-@[simp, grind =] theorem forM_none [Monad m] (f : α → m PUnit) :
+@[simp, grind] theorem forM_none [Monad m] (f : α → m PUnit) :
     forM none f = pure .unit := rfl
 
-@[simp, grind =] theorem forM_some [Monad m] (f : α → m PUnit) (a : α) :
+@[simp, grind] theorem forM_some [Monad m] (f : α → m PUnit) (a : α) :
     forM (some a) f = f a := rfl
 
-@[simp, grind =] theorem forM_map [Monad m] [LawfulMonad m] (o : Option α) (g : α → β) (f : β → m PUnit) :
+@[simp, grind] theorem forM_map [Monad m] [LawfulMonad m] (o : Option α) (g : α → β) (f : β → m PUnit) :
     forM (o.map g) f = forM o (fun a => f (g a)) := by
   cases o <;> simp
 
@@ -37,11 +37,11 @@ theorem forM_join [Monad m] [LawfulMonad m] (o : Option (Option α)) (f : α →
     forM o.join f = forM o (forM · f) := by
   cases o <;> simp
 
-@[simp, grind =] theorem forIn'_none [Monad m] (b : β) (f : (a : α) → a ∈ none → β → m (ForInStep β)) :
+@[simp, grind] theorem forIn'_none [Monad m] (b : β) (f : (a : α) → a ∈ none → β → m (ForInStep β)) :
     forIn' none b f = pure b := by
   rfl
 
-@[simp, grind =] theorem forIn'_some [Monad m] [LawfulMonad m] (a : α) (b : β) (f : (a' : α) → a' ∈ some a → β → m (ForInStep β)) :
+@[simp, grind] theorem forIn'_some [Monad m] [LawfulMonad m] (a : α) (b : β) (f : (a' : α) → a' ∈ some a → β → m (ForInStep β)) :
     forIn' (some a) b f = bind (f a rfl b) (fun r => pure (ForInStep.value r)) := by
   simp only [forIn', bind_pure_comp]
   rw [map_eq_pure_bind]
@@ -49,11 +49,11 @@ theorem forM_join [Monad m] [LawfulMonad m] (o : Option (Option α)) (f : α →
   funext x
   split <;> simp
 
-@[simp, grind =] theorem forIn_none [Monad m] (b : β) (f : α → β → m (ForInStep β)) :
+@[simp, grind] theorem forIn_none [Monad m] (b : β) (f : α → β → m (ForInStep β)) :
     forIn none b f = pure b := by
   rfl
 
-@[simp, grind =] theorem forIn_some [Monad m] [LawfulMonad m] (a : α) (b : β) (f : α → β → m (ForInStep β)) :
+@[simp, grind] theorem forIn_some [Monad m] [LawfulMonad m] (a : α) (b : β) (f : α → β → m (ForInStep β)) :
     forIn (some a) b f = bind (f a b) (fun r => pure (ForInStep.value r)) := by
   simp only [forIn, forIn', bind_pure_comp]
   rw [map_eq_pure_bind]
@@ -106,7 +106,7 @@ theorem forIn'_id_yield_eq_pelim
       o.pelim b (fun a h => f a h b) :=
   forIn'_pure_yield_eq_pelim _ _ _
 
-@[simp, grind =] theorem forIn'_map [Monad m] [LawfulMonad m]
+@[simp, grind] theorem forIn'_map [Monad m] [LawfulMonad m]
     (o : Option α) (g : α → β) (f : (b : β) → b ∈ o.map g → γ → m (ForInStep γ)) :
     forIn' (o.map g) init f = forIn' o init fun a h y => f (g a) (mem_map_of_mem g h) y := by
   cases o <;> simp
@@ -149,7 +149,7 @@ theorem forIn_id_yield_eq_elim
       o.elim b (fun a => f a b) :=
   forIn_pure_yield_eq_elim _ _ _
 
-@[simp, grind =] theorem forIn_map [Monad m] [LawfulMonad m]
+@[simp, grind] theorem forIn_map [Monad m] [LawfulMonad m]
     (o : Option α) (g : α → β) (f : β → γ → m (ForInStep γ)) :
     forIn (o.map g) init f = forIn o init fun a y => f (g a) y := by
   cases o <;> simp

src/Init/Data/Order/Ord.lean

@@ -37,10 +37,6 @@ namespace ReflCmp
 theorem cmp_eq_of_eq {α : Type u} {cmp : α → α → Ordering} [Std.ReflCmp cmp] {a b : α} : a = b → cmp a b = .eq := by
   intro h; subst a; apply compare_self
 
-theorem ne_of_cmp_ne_eq {α : Type u} {cmp : α → α → Ordering} [Std.ReflCmp cmp] {a b : α} :
-    cmp a b ≠ .eq → a ≠ b :=
-  mt cmp_eq_of_eq
-
 end ReflCmp
 
 /-- A typeclasses for ordered types for which `compare a a = .eq` for all `a`. -/
@@ -349,13 +345,13 @@ theorem LawfulEqCmp.compare_beq_iff_eq {a b : α} : cmp a b == .eq ↔ a = b :=
   beq_iff_eq.trans compare_eq_iff_eq
 
 /-- The corresponding lemma for `LawfulEqCmp` is `LawfulEqCmp.compare_eq_iff_eq` -/
-@[simp, grind =]
+@[simp, grind]
 theorem LawfulEqOrd.compare_eq_iff_eq [Ord α] [LawfulEqOrd α] {a b : α} :
     compare a b = .eq ↔ a = b :=
   LawfulEqCmp.compare_eq_iff_eq
 
 /-- The corresponding lemma for `LawfulEqCmp` is `LawfulEqCmp.compare_beq_iff_eq` -/
-@[grind =]
+@[grind]
 theorem LawfulEqOrd.compare_beq_iff_eq [Ord α] [LawfulEqOrd α] {a b : α} :
     compare a b == .eq ↔ a = b :=
   LawfulEqCmp.compare_beq_iff_eq

src/Init/Data/Order/PackageFactories.lean

@@ -67,20 +67,20 @@ public structure Packages.PreorderOfLEArgs (α : Type u) where
     extract_lets
     first
     | infer_instance
-    | exact _root_.Classical.Order.instLT
+    | exact Classical.Order.instLT
   beq :
     let := le; let := decidableLE
     BEq α := by
     extract_lets
     first
     | infer_instance
-    | exact _root_.Std.FactoryInstances.beqOfDecidableLE
+    | exact FactoryInstances.beqOfDecidableLE
   lt_iff :
       let := le; let := lt
       ∀ a b : α, a < b ↔ a ≤ b ∧ ¬ b ≤ a := by
     extract_lets
     first
-    | exact _root_.Std.LawfulOrderLT.lt_iff
+    | exact LawfulOrderLT.lt_iff
     | fail "Failed to automatically prove that the `LE` and `LT` instances are compatible. \
             Please ensure that a `LawfulOrderLT` instance can be synthesized or \
             manually provide the field `lt_iff`."
@@ -89,10 +89,10 @@ public structure Packages.PreorderOfLEArgs (α : Type u) where
       have := lt_iff
       DecidableLT α := by
     extract_lets
-    haveI := @_root_.Std.LawfulOrderLT.mk (lt_iff := by assumption) ..
+    haveI := @LawfulOrderLT.mk (lt_iff := by assumption) ..
     first
     | infer_instance
-    | exact _root_.Std.FactoryInstances.decidableLTOfLE
+    | exact FactoryInstances.decidableLTOfLE
     | fail "Failed to automatically derive that `LT` is decidable. \
             Please ensure that a `DecidableLT` instance can be synthesized or \
             manually provide the field `decidableLT`."
@@ -101,7 +101,7 @@ public structure Packages.PreorderOfLEArgs (α : Type u) where
       ∀ a b : α, a == b ↔ a ≤ b ∧ b ≤ a := by
     extract_lets
     first
-      | exact _root_.Std.LawfulOrderBEq.beq_iff_le_and_ge
+      | exact LawfulOrderBEq.beq_iff_le_and_ge
       | fail "Failed to automatically prove that the `LE` and `BEq` instances are compatible. \
               Please ensure that a `LawfulOrderBEq` instance can be synthesized or \
               manually provide the field `beq_iff_le_and_ge`."
@@ -110,7 +110,7 @@ public structure Packages.PreorderOfLEArgs (α : Type u) where
       ∀ a : α, a ≤ a := by
     extract_lets
     first
-    | exact _root_.Std.Refl.refl (r := (· ≤ ·))
+    | exact Std.Refl.refl (r := (· ≤ ·))
     | fail "Failed to automatically prove that the `LE` instance is reflexive. \
             Please ensure that a `Refl` instance can be synthesized or \
             manually provide the field `le_refl`."
@@ -119,7 +119,7 @@ public structure Packages.PreorderOfLEArgs (α : Type u) where
       ∀ a b c : α, a ≤ b → b ≤ c → a ≤ c := by
     extract_lets
     first
-    | exact fun _ _ _ hab hbc => _root_.Trans.trans (r := (· ≤ ·)) (s := (· ≤ ·)) (t := (· ≤ ·)) hab hbc
+    | exact fun _ _ _ hab hbc => Trans.trans (r := (· ≤ ·)) (s := (· ≤ ·)) (t := (· ≤ ·)) hab hbc
     | fail "Failed to automatically prove that the `LE` instance is transitive. \
             Please ensure that a `Trans` instance can be synthesized or \
             manually provide the field `le_trans`."
@@ -202,7 +202,7 @@ public structure Packages.PartialOrderOfLEArgs (α : Type u) extends Packages.Pr
       ∀ a b : α, a ≤ b → b ≤ a → a = b := by
     extract_lets
     first
-    | exact _root_.Std.Antisymm.antisymm
+    | exact Antisymm.antisymm
     | fail "Failed to automatically prove that the `LE` instance is antisymmetric. \
             Please ensure that a `Antisymm` instance can be synthesized or \
             manually provide the field `le_antisymm`."
@@ -310,11 +310,11 @@ public structure Packages.LinearPreorderOfLEArgs (α : Type u) extends
     extract_lets
     first
     | infer_instance
-    | exact _root_.Std.FactoryInstances.instOrdOfDecidableLE
+    | exact FactoryInstances.instOrdOfDecidableLE
   le_total :
       ∀ a b : α, a ≤ b ∨ b ≤ a := by
     first
-    | exact _root_.Std.Total.total
+    | exact Total.total
     | fail "Failed to automatically prove that the `LE` instance is total. \
             Please ensure that a `Total` instance can be synthesized or \
             manually provide the field `le_total`."
@@ -324,7 +324,7 @@ public structure Packages.LinearPreorderOfLEArgs (α : Type u) extends
       ∀ a b : α, (compare a b).isLE ↔ a ≤ b := by
     extract_lets
     first
-    | exact _root_.Std.LawfulOrderOrd.isLE_compare
+    | exact LawfulOrderOrd.isLE_compare
     | fail "Failed to automatically prove that `(compare a b).isLE` is equivalent to `a ≤ b`. \
             Please ensure that a `LawfulOrderOrd` instance can be synthesized or \
             manually provide the field `isLE_compare`."
@@ -333,7 +333,7 @@ public structure Packages.LinearPreorderOfLEArgs (α : Type u) extends
       ∀ a b : α, (compare a b).isGE ↔ b ≤ a := by
     extract_lets
     first
-    | exact _root_.Std.LawfulOrderOrd.isGE_compare
+    | exact LawfulOrderOrd.isGE_compare
     | fail "Failed to automatically prove that `(compare a b).isGE` is equivalent to `b ≤ a`. \
             Please ensure that a `LawfulOrderOrd` instance can be synthesized or \
             manually provide the field `isGE_compare`."
@@ -411,20 +411,20 @@ public structure Packages.LinearOrderOfLEArgs (α : Type u) extends
     extract_lets
     first
     | infer_instance
-    | exact _root_.Min.leftLeaningOfLE _
+    | exact Min.leftLeaningOfLE _
   max :
       let := le; let := decidableLE
       Max α := by
     extract_lets
     first
     | infer_instance
-    | exact _root_.Max.leftLeaningOfLE _
+    | exact Max.leftLeaningOfLE _
   min_eq :
       let := le; let := decidableLE; let := min
       ∀ a b : α, Min.min a b = if a ≤ b then a else b := by
     extract_lets
     first
-    | exact fun a b => _root_.Std.min_eq_if (a := a) (b := b)
+    | exact fun a b => Std.min_eq_if (a := a) (b := b)
     | fail "Failed to automatically prove that `min` is left-leaning. \
             Please ensure that a `LawfulOrderLeftLeaningMin` instance can be synthesized or \
             manually provide the field `min_eq`."
@@ -433,7 +433,7 @@ public structure Packages.LinearOrderOfLEArgs (α : Type u) extends
       ∀ a b : α, Max.max a b = if b ≤ a then a else b := by
     extract_lets
     first
-    | exact fun a b => _root_.Std.max_eq_if (a := a) (b := b)
+    | exact fun a b => Std.max_eq_if (a := a) (b := b)
     | fail "Failed to automatically prove that `max` is left-leaning. \
             Please ensure that a `LawfulOrderLeftLeaningMax` instance can be synthesized or \
             manually provide the field `max_eq`."
@@ -538,7 +538,7 @@ public structure Packages.LinearPreorderOfOrdArgs (α : Type u) where
     extract_lets
     first
     | infer_instance
-    | exact _root_.LE.ofOrd _
+    | exact LE.ofOrd _
   lawfulOrderOrd :
       let := ord; let := transOrd; let := le
       LawfulOrderOrd α := by
@@ -554,7 +554,7 @@ public structure Packages.LinearPreorderOfOrdArgs (α : Type u) where
     extract_lets
     first
     | infer_instance
-    | exact _root_.DecidableLE.ofOrd _
+    | exact DecidableLE.ofOrd _
     | fail "Failed to automatically derive that `LE` is decidable.\
             Please ensure that a `DecidableLE` instance can be synthesized or \
             manually provide the field `decidableLE`."
@@ -570,7 +570,7 @@ public structure Packages.LinearPreorderOfOrdArgs (α : Type u) where
       ∀ a b : α, a < b ↔ compare a b = .lt := by
     extract_lets
     first
-    | exact fun _ _ => _root_.Std.compare_eq_lt.symm
+    | exact fun _ _ => Std.compare_eq_lt.symm
     | fail "Failed to automatically derive that `LT` and `Ord` are compatible. \
             Please ensure that a `LawfulOrderLT` instance can be synthesized or \
             manually provide the field `lt_iff`."
@@ -580,7 +580,7 @@ public structure Packages.LinearPreorderOfOrdArgs (α : Type u) where
     extract_lets
     first
     | infer_instance
-    | exact _root_DecidableLT.ofOrd _
+    | exact DecidableLT.ofOrd _
     | fail "Failed to automatically derive that `LT` is decidable. \
             Please ensure that a `DecidableLT` instance can be synthesized or \
             manually provide the field `decidableLT`."
@@ -589,7 +589,7 @@ public structure Packages.LinearPreorderOfOrdArgs (α : Type u) where
     extract_lets
     first
     | infer_instance
-    | exact _root_.BEq.ofOrd _
+    | exact BEq.ofOrd _
   beq_iff :
       let := ord; let := le; have := lawfulOrderOrd; let := beq
       ∀ a b : α, a == b ↔ compare a b = .eq := by
@@ -708,7 +708,7 @@ public structure Packages.LinearOrderOfOrdArgs (α : Type u) extends
       ∀ a b : α, compare a b = .eq → a = b := by
     extract_lets
     first
-    | exact fun _ _ => _root_.Std.LawfulEqOrd.eq_of_compare
+    | exact LawfulEqOrd.eq_of_compare
     | fail "Failed to derive a `LawfulEqOrd` instance. \
             Please make sure that it can be synthesized or \
             manually provide the field `eq_of_compare`."
@@ -718,20 +718,20 @@ public structure Packages.LinearOrderOfOrdArgs (α : Type u) extends
     extract_lets
     first
     | infer_instance
-    | exact _root_.Std.FactoryInstances.instMinOfOrd
+    | exact FactoryInstances.instMinOfOrd
   max :
       let := ord
       Max α := by
     extract_lets
     first
     | infer_instance
-    | exact _root_.Std.FactoryInstances.instMaxOfOrd
+    | exact FactoryInstances.instMaxOfOrd
   min_eq :
       let := ord; let := le; let := min; have := lawfulOrderOrd
       ∀ a b : α, Min.min a b = if (compare a b).isLE then a else b := by
     extract_lets
     first
-    | exact fun a b => _root_.Std.min_eq_if_isLE_compare (a := a) (b := b)
+    | exact fun a b => Std.min_eq_if_isLE_compare (a := a) (b := b)
     | fail "Failed to automatically prove that `min` is left-leaning. \
             Please ensure that a `LawfulOrderLeftLeaningMin` instance can be synthesized or \
             manually provide the field `min_eq`."
@@ -740,7 +740,7 @@ public structure Packages.LinearOrderOfOrdArgs (α : Type u) extends
       ∀ a b : α, Max.max a b = if (compare a b).isGE then a else b := by
     extract_lets
     first
-    | exact fun a b => _root_.Std.max_eq_if_isGE_compare (a := a) (b := b)
+    | exact fun a b => Std.max_eq_if_isGE_compare (a := a) (b := b)
     | fail "Failed to automatically prove that `max` is left-leaning. \
             Please ensure that a `LawfulOrderLeftLeaningMax` instance can be synthesized or \
             manually provide the field `max_eq`."

src/Init/Data/Random.lean

@@ -7,7 +7,6 @@ module
 
 prelude
 public import Init.System.IO
-import Init.Data.ByteArray.Extra
 
 public section
 universe u

src/Init/Data/Range/Polymorphic.lean

@@ -12,8 +12,6 @@ public import Init.Data.Range.Polymorphic.Stream
 public import Init.Data.Range.Polymorphic.Lemmas
 public import Init.Data.Range.Polymorphic.Nat
 public import Init.Data.Range.Polymorphic.Int
-public import Init.Data.Range.Polymorphic.BitVec
-public import Init.Data.Range.Polymorphic.UInt
 public import Init.Data.Range.Polymorphic.NatLemmas
 public import Init.Data.Range.Polymorphic.GetElemTactic