feat: add user-defined fallback procedure for the grind tactic

This PR introduces support for user-defined fallback code in the
`grind` tactic. The fallback code can be utilized to inspect the state
of failing `grind` subgoals and/or invoke user-defined
automation. Users can now write `grind on_failure <code>`, where
`<code>` should have the type `GoalM Unit`. See the modified tests in
this PR for examples.

.github/workflows/ci.yml

@@ -238,7 +238,7 @@ jobs:
                 "name": "Linux 32bit",
                 "os": "ubuntu-latest",
                 // Use 32bit on stage0 and stage1 to keep oleans compatible
-                "CMAKE_OPTIONS": "-DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_MMAP=OFF -DUSE_GMP=OFF -DLEAN_EXTRA_CXX_FLAGS='-m32' -DLEANC_OPTS='-m32' -DMMAP=OFF -DLEAN_INSTALL_SUFFIX=-linux_x86 -DCMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -DSTAGE0_CMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -DPKG_CONFIG_EXECUTABLE=/usr/bin/i386-linux-gnu-pkg-config",
+                "CMAKE_OPTIONS": "-DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_MMAP=OFF -DUSE_GMP=OFF -DLEAN_EXTRA_CXX_FLAGS='-m32' -DLEANC_OPTS='-m32' -DMMAP=OFF -DLEAN_INSTALL_SUFFIX=-linux_x86 -DCMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -DSTAGE0_CMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/",
                 "cmultilib": true,
                 "release": true,
                 "check-level": 2,
@@ -327,7 +327,7 @@ jobs:
         run: |
           sudo dpkg --add-architecture i386
           sudo apt-get update
-          sudo apt-get install -y gcc-multilib g++-multilib ccache libuv1-dev:i386 pkgconf:i386
+          sudo apt-get install -y gcc-multilib g++-multilib ccache libuv1-dev:i386
         if: matrix.cmultilib
       - name: Cache
         uses: actions/cache@v4

CMakeLists.txt

@@ -18,9 +18,6 @@ foreach(var ${vars})
     if("${var}" MATCHES "LLVM*")
       list(APPEND STAGE0_ARGS "-D${var}=${${var}}")
     endif()
-    if("${var}" MATCHES "PKG_CONFIG*")
-      list(APPEND STAGE0_ARGS "-D${var}=${${var}}")
-    endif()
   elseif(("${var}" MATCHES "CMAKE_.*") AND NOT ("${var}" MATCHES "CMAKE_BUILD_TYPE") AND NOT ("${var}" MATCHES "CMAKE_HOME_DIRECTORY"))
     list(APPEND PLATFORM_ARGS "-D${var}=${${var}}")
   endif()

doc/dev/commit_convention.md

@@ -33,9 +33,6 @@ Format of the commit message
  - chore (maintain, ex: travis-ci)
  - perf (performance improvement, optimization, ...)
 
-Every `feat` or `fix` commit must have a `changelog-*` label, and a commit message
-beginning with "This PR " that will be included in the changelog.
-
 ``<subject>`` has the following constraints:
 
  - use imperative, present tense: "change" not "changed" nor "changes"
@@ -47,7 +44,6 @@ beginning with "This PR " that will be included in the changelog.
  - just as in ``<subject>``, use imperative, present tense
  - includes motivation for the change and contrasts with previous
    behavior
- - If a `changelog-*` label is present, the body must begin with "This PR ".
 
 ``<footer>`` is optional and may contain two items:
 
@@ -64,21 +60,17 @@ Examples
 
 fix: add declarations for operator<<(std::ostream&, expr const&) and operator<<(std::ostream&, context const&) in the kernel
 
-This PR adds declarations `operator<<` for raw printing.
 The actual implementation of these two operators is outside of the
-kernel. They are implemented in the file 'library/printer.cpp'.
-
-We declare them in the kernel to prevent the following problem.
-Suppose there is a file 'foo.cpp' that does not include 'library/printer.h',
+kernel. They are implemented in the file 'library/printer.cpp'. We
+declare them in the kernel to prevent the following problem. Suppose
+there is a file 'foo.cpp' that does not include 'library/printer.h',
 but contains
-```cpp
-expr a;
-...
-std::cout << a << "\n";
-...
-```
+
+    expr a;
+    ...
+    std::cout << a << "\n";
+    ...
 
 The compiler does not generate an error message. It silently uses the
 operator bool() to coerce the expression into a Boolean. This produces
 counter-intuitive behavior, and may confuse developers.
-

doc/dev/ffi.md

@@ -49,9 +49,8 @@ In the case of `@[extern]` all *irrelevant* types are removed first; see next se
   is represented by the representation of that parameter's type.
 
   For example, `{ x : α // p }`, the `Subtype` structure of a value of type `α` and an irrelevant proof, is represented by the representation of `α`.
-  Similarly, the signed integer types `Int8`, ..., `Int64`, `ISize` are also represented by the unsigned C types `uint8_t`, ..., `uint64_t`, `size_t`, respectively, because they have a trivial structure.
-* `Nat` and `Int` are represented by `lean_object *`.
-  Their runtime values is either a pointer to an opaque bignum object or, if the lowest bit of the "pointer" is 1 (`lean_is_scalar`), an encoded unboxed natural number or integer (`lean_box`/`lean_unbox`).
+* `Nat` is represented by `lean_object *`.
+  Its runtime value is either a pointer to an opaque bignum object or, if the lowest bit of the "pointer" is 1 (`lean_is_scalar`), an encoded unboxed natural number (`lean_box`/`lean_unbox`).
 * A universe `Sort u`, type constructor `... → Sort u`, or proposition `p : Prop` is *irrelevant* and is either statically erased (see above) or represented as a `lean_object *` with the runtime value `lean_box(0)`
 * Any other type is represented by `lean_object *`.
   Its runtime value is a pointer to an object of a subtype of `lean_object` (see the "Inductive types" section below) or the unboxed value `lean_box(cidx)` for the `cidx`th constructor of an inductive type if this constructor does not have any relevant parameters.

doc/dev/index.md

@@ -80,10 +80,3 @@ Unlike most Lean projects, all submodules of the `Lean` module begin with the
 `prelude` keyword. This disables the automated import of `Init`, meaning that
 developers need to figure out their own subset of `Init` to import. This is done
 such that changing files in `Init` doesn't force a full rebuild of `Lean`.
-
-### Testing against Mathlib/Batteries
-You can test a Lean PR against Mathlib and Batteries by rebasing your PR
-on to `nightly-with-mathlib` branch. (It is fine to force push after rebasing.)
-CI will generate a branch of Mathlib and Batteries called `lean-pr-testing-NNNN`
-that uses the toolchain for your PR, and will report back to the Lean PR with results from Mathlib CI.
-See https://leanprover-community.github.io/contribute/tags_and_branches.html for more details.

doc/dev/release_checklist.md

@@ -5,6 +5,11 @@ See below for the checklist for release candidates.
 
 We'll use `v4.6.0` as the intended release version as a running example.
 
+- One week before the planned release, ensure that
+  (1) someone has written the release notes and
+  (2) someone has written the first draft of the release blog post.
+  If there is any material in `./releases_drafts/` on the `releases/v4.6.0` branch, then the release notes are not done.
+  (See the section "Writing the release notes".)
 - `git checkout releases/v4.6.0`
   (This branch should already exist, from the release candidates.)
 - `git pull`
@@ -37,32 +42,16 @@ We'll use `v4.6.0` as the intended release version as a running example.
     - Create the tag `v4.6.0` from `master`/`main` and push it.
     - Merge the tag `v4.6.0` into the `stable` branch and push it.
   - We do this for the repositories:
-    - [Batteries](https://github.com/leanprover-community/batteries)
-      - No dependencies
-      - Toolchain bump PR
-      - Create and push the tag
-      - Merge the tag into `stable`
     - [lean4checker](https://github.com/leanprover/lean4checker)
       - No dependencies
       - Toolchain bump PR
       - Create and push the tag
       - Merge the tag into `stable`
-    - [doc-gen4](https://github.com/leanprover/doc-gen4)
-      - Dependencies: exist, but they're not part of the release workflow
-      - Toolchain bump PR including updated Lake manifest
-      - Create and push the tag
-      - There is no `stable` branch; skip this step
-    - [Verso](https://github.com/leanprover/verso)
-      - Dependencies: exist, but they're not part of the release workflow
-      - The `SubVerso` dependency should be compatible with _every_ Lean release simultaneously, rather than following this workflow
-      - Toolchain bump PR including updated Lake manifest
-      - Create and push the tag
-      - There is no `stable` branch; skip this step
-    - [Cli](https://github.com/leanprover/lean4-cli)
+    - [Batteries](https://github.com/leanprover-community/batteries)
       - No dependencies
       - Toolchain bump PR
       - Create and push the tag
-      - There is no `stable` branch; skip this step
+      - Merge the tag into `stable`
     - [ProofWidgets4](https://github.com/leanprover-community/ProofWidgets4)
       - Dependencies: `Batteries`
       - Note on versions and branches:
@@ -77,11 +66,18 @@ We'll use `v4.6.0` as the intended release version as a running example.
       - Toolchain bump PR including updated Lake manifest
       - Create and push the tag
       - Merge the tag into `stable`
-    - [import-graph](https://github.com/leanprover-community/import-graph)
+    - [doc-gen4](https://github.com/leanprover/doc-gen4)
+      - Dependencies: exist, but they're not part of the release workflow
       - Toolchain bump PR including updated Lake manifest
       - Create and push the tag
       - There is no `stable` branch; skip this step
-    - [plausible](https://github.com/leanprover-community/plausible)
+    - [Verso](https://github.com/leanprover/verso)
+      - Dependencies: exist, but they're not part of the release workflow
+      - The `SubVerso` dependency should be compatible with _every_ Lean release simultaneously, rather than following this workflow
+      - Toolchain bump PR including updated Lake manifest
+      - Create and push the tag
+      - There is no `stable` branch; skip this step
+    - [import-graph](https://github.com/leanprover-community/import-graph)
       - Toolchain bump PR including updated Lake manifest
       - Create and push the tag
       - There is no `stable` branch; skip this step
@@ -90,7 +86,7 @@ We'll use `v4.6.0` as the intended release version as a running example.
       - Toolchain bump PR notes:
         - In addition to updating the `lean-toolchain` and `lakefile.lean`,
           in `.github/workflows/lean4checker.yml` update the line
-          `git checkout v4.6.0` to the appropriate tag.
+          `git checkout v4.6.0` to the appropriate tag. 
         - Push the PR branch to the main Mathlib repository rather than a fork, or CI may not work reliably
         - Create and push the tag
         - Create a new branch from the tag, push it, and open a pull request against `stable`.
@@ -102,7 +98,6 @@ We'll use `v4.6.0` as the intended release version as a running example.
       - Toolchain bump PR including updated Lake manifest
       - Create and push the tag
       - Merge the tag into `stable`
-- Run `scripts/release_checklist.py v4.6.0` to check that everything is in order.
 - The `v4.6.0` section of `RELEASES.md` is out of sync between
   `releases/v4.6.0` and `master`. This should be reconciled:
   - Replace the `v4.6.0` section on `master` with the `v4.6.0` section on `releases/v4.6.0`
@@ -144,13 +139,16 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
     git checkout -b releases/v4.7.0
     ```
 - In `RELEASES.md` replace `Development in progress` in the `v4.7.0` section with `Release notes to be written.`
-- It is essential to choose the nightly that will become the release candidate as early as possible, to avoid confusion.
+- We will rely on automatically generated release notes for release candidates,
+  and the written release notes will be used for stable versions only.
+  It is essential to choose the nightly that will become the release candidate as early as possible, to avoid confusion.
 - In `src/CMakeLists.txt`,
   - verify that you see `set(LEAN_VERSION_MINOR 7)` (for whichever `7` is appropriate); this should already have been updated when the development cycle began.
   - `set(LEAN_VERSION_IS_RELEASE 1)` (this should be a change; on `master` and nightly releases it is always `0`).
   - Commit your changes to `src/CMakeLists.txt`, and push.
 - `git tag v4.7.0-rc1`
 - `git push origin v4.7.0-rc1`
+- Ping the FRO Zulip that release notes need to be written. The release notes do not block completing the rest of this checklist.
 - Now wait, while CI runs.
   - You can monitor this at `https://github.com/leanprover/lean4/actions/workflows/ci.yml`, looking for the `v4.7.0-rc1` tag.
   - This step can take up to an hour.
@@ -250,12 +248,15 @@ Please read https://leanprover-community.github.io/contribute/tags_and_branches.
 
 # Writing the release notes
 
-Release notes are automatically generated from the commit history, using `script/release_notes.py`.
+We are currently trying a system where release notes are compiled all at once from someone looking through the commit history.
+The exact steps are a work in progress.
+Here is the general idea:
 
-Run this as `script/release_notes.py v4.6.0`, where `v4.6.0` is the *previous* release version. This will generate output
-for all commits since that tag. Note that there is output on both stderr, which should be manually reviewed,
-and on stdout, which should be manually copied to `RELEASES.md`.
-
-There can also be pre-written entries in `./releases_drafts`, which should be all incorporated in the release notes and then deleted from the branch.
+* The work is done right on the `releases/v4.6.0` branch sometime after it is created but before the stable release is made.
+  The release notes for `v4.6.0` will later be copied to `master` when we begin a new development cycle.
+* There can be material for release notes entries in commit messages.
+* There can also be pre-written entries in `./releases_drafts`, which should be all incorporated in the release notes and then deleted from the branch.
   See `./releases_drafts/README.md` for more information.
+* The release notes should be written from a downstream expert user's point of view.
 
+This section will be updated when the next release notes are written (for `v4.10.0`).

doc/make/osx-10.9.md

@@ -32,13 +32,12 @@ following to use `g++`.
 cmake -DCMAKE_CXX_COMPILER=g++ ...
 ```
 
-## Required Packages: CMake, GMP, libuv, pkgconf
+## Required Packages: CMake, GMP, libuv
 
 ```bash
 brew install cmake
 brew install gmp
 brew install libuv
-brew install pkgconf
 ```
 
 ## Recommended Packages: CCache

doc/make/ubuntu.md

@@ -8,5 +8,5 @@ follow the [generic build instructions](index.md).
 ## Basic packages
 
 ```bash
-sudo apt-get install git libgmp-dev libuv1-dev cmake ccache clang pkgconf
+sudo apt-get install git libgmp-dev libuv1-dev cmake ccache clang
 ```

flake.nix

@@ -28,7 +28,7 @@
           stdenv = pkgs.overrideCC pkgs.stdenv lean-packages.llvmPackages.clang;
         } ({
           buildInputs = with pkgs; [
-            cmake gmp libuv ccache cadical pkg-config
+            cmake gmp libuv ccache cadical
             lean-packages.llvmPackages.llvm  # llvm-symbolizer for asan/lsan
             gdb
             tree  # for CI

nix/bootstrap.nix

@@ -1,12 +1,12 @@
 { src, debug ? false, stage0debug ? false, extraCMakeFlags ? [],
-  stdenv, lib, cmake, pkg-config, gmp, libuv, cadical, git, gnumake, bash, buildLeanPackage, writeShellScriptBin, runCommand, symlinkJoin, lndir, perl, gnused, darwin, llvmPackages, linkFarmFromDrvs,
+  stdenv, lib, cmake, gmp, libuv, cadical, git, gnumake, bash, buildLeanPackage, writeShellScriptBin, runCommand, symlinkJoin, lndir, perl, gnused, darwin, llvmPackages, linkFarmFromDrvs,
   ... } @ args:
 with builtins;
 lib.warn "The Nix-based build is deprecated" rec {
   inherit stdenv;
   sourceByRegex = p: rs: lib.sourceByRegex p (map (r: "(/src/)?${r}") rs);
   buildCMake = args: stdenv.mkDerivation ({
-    nativeBuildInputs = [ cmake pkg-config ];
+    nativeBuildInputs = [ cmake ];
     buildInputs = [ gmp libuv llvmPackages.llvm ];
     # https://github.com/NixOS/nixpkgs/issues/60919
     hardeningDisable = [ "all" ];

releases_drafts/list_lex.md

@@ -0,0 +1,16 @@
+We replace the inductive predicate `List.lt` with an upstreamed version of `List.Lex` from Mathlib.
+(Previously `Lex.lt` was defined in terms of `<`; now it is generalized to take an arbitrary relation.)
+This subtely changes the notion of ordering on `List α`.
+
+`List.lt` was a weaker relation: in particular if `l₁ < l₂`, then
+`a :: l₁ < b :: l₂` may hold according to `List.lt` even if `a` and `b` are merely incomparable
+(either neither `a < b` nor `b < a`), whereas according to `List.Lex` this would require `a = b`.
+
+When `<` is total, in the sense that `¬ · < ·` is antisymmetric, then the two relations coincide.
+
+Mathlib was already overriding the order instances for `List α`,
+so this change should not be noticed by anyone already using Mathlib.
+
+We simultaneously add the boolean valued `List.lex` function, parameterised by a `BEq` typeclass
+and an arbitrary `lt` function. This will support the flexibility previously provided for `List.lt`,
+via a `==` function which is weaker than strict equality.

script/prepare-llvm-linux.sh

@@ -63,8 +63,8 @@ else
 fi
 # use `-nostdinc` to make sure headers are not visible by default (in particular, not to `#include_next` in the clang headers),
 # but do not change sysroot so users can still link against system libs
-echo -n " -DLEANC_INTERNAL_FLAGS='--sysroot ROOT -nostdinc -isystem ROOT/include/clang' -DLEANC_CC=ROOT/bin/clang"
-echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='--sysroot ROOT -L ROOT/lib -L ROOT/lib/glibc ROOT/lib/glibc/libc_nonshared.a ROOT/lib/glibc/libpthread_nonshared.a -Wl,--as-needed -Wl,-Bstatic -lgmp -lunwind -luv -Wl,-Bdynamic -Wl,--no-as-needed -fuse-ld=lld'"
+echo -n " -DLEANC_INTERNAL_FLAGS='-nostdinc -isystem ROOT/include/clang' -DLEANC_CC=ROOT/bin/clang"
+echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='-L ROOT/lib -L ROOT/lib/glibc ROOT/lib/glibc/libc_nonshared.a ROOT/lib/glibc/libpthread_nonshared.a -Wl,--as-needed -Wl,-Bstatic -lgmp -lunwind -luv -Wl,-Bdynamic -Wl,--no-as-needed -fuse-ld=lld'"
 # when not using the above flags, link GMP dynamically/as usual
 echo -n " -DLEAN_EXTRA_LINKER_FLAGS='-Wl,--as-needed -lgmp -luv -lpthread -ldl -lrt -Wl,--no-as-needed'"
 # do not set `LEAN_CC` for tests

script/prepare-llvm-macos.sh

@@ -48,11 +48,12 @@ if [[ -L llvm-host ]]; then
   echo -n " -DCMAKE_C_COMPILER=$PWD/stage1/bin/clang"
   gcp $GMP/lib/libgmp.a stage1/lib/
   gcp $LIBUV/lib/libuv.a stage1/lib/
+  echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='-L ROOT/lib -L ROOT/lib/libc -fuse-ld=lld'"
   echo -n " -DLEAN_EXTRA_LINKER_FLAGS='-lgmp -luv'"
 else
   echo -n " -DCMAKE_C_COMPILER=$PWD/llvm-host/bin/clang -DLEANC_OPTS='--sysroot $PWD/stage1 -resource-dir $PWD/stage1/lib/clang/15.0.1 ${EXTRA_FLAGS:-}'"
+  echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='-L ROOT/lib -L ROOT/lib/libc -fuse-ld=lld'"
 fi
-echo -n " -DLEANC_INTERNAL_FLAGS='--sysroot ROOT -nostdinc -isystem ROOT/include/clang' -DLEANC_CC=ROOT/bin/clang"
-echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='--sysroot ROOT -L ROOT/lib -L ROOT/lib/libc -fuse-ld=lld'"
+echo -n " -DLEANC_INTERNAL_FLAGS='-nostdinc -isystem ROOT/include/clang' -DLEANC_CC=ROOT/bin/clang"
 # do not set `LEAN_CC` for tests
 echo -n " -DLEAN_TEST_VARS=''"

script/prepare-llvm-mingw.sh

@@ -43,7 +43,7 @@ echo -n " -DCMAKE_C_COMPILER=$PWD/stage1/bin/clang.exe -DCMAKE_C_COMPILER_WORKS=
 echo -n " -DSTAGE0_CMAKE_C_COMPILER=clang -DSTAGE0_CMAKE_CXX_COMPILER=clang++"
 echo -n " -DLEAN_EXTRA_CXX_FLAGS='--sysroot $PWD/llvm -idirafter /clang64/include/'"
 echo -n " -DLEANC_INTERNAL_FLAGS='--sysroot ROOT -nostdinc -isystem ROOT/include/clang' -DLEANC_CC=ROOT/bin/clang.exe"
-echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='--sysroot ROOT -L ROOT/lib -Wl,-Bstatic -lgmp $(pkg-config --static --libs libuv) -lunwind -Wl,-Bdynamic -fuse-ld=lld'"
+echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='-L ROOT/lib -static-libgcc -Wl,-Bstatic -lgmp $(pkg-config --static --libs libuv) -lunwind -Wl,-Bdynamic -fuse-ld=lld'"
 # when not using the above flags, link GMP dynamically/as usual. Always link ICU dynamically.
 echo -n " -DLEAN_EXTRA_LINKER_FLAGS='-lgmp $(pkg-config --libs libuv) -lucrtbase'"
 # do not set `LEAN_CC` for tests

script/push_repo_release_tag.py

@@ -1,69 +0,0 @@
-#!/usr/bin/env python3
-import sys
-import subprocess
-import requests
-
-def main():
-    if len(sys.argv) != 4:
-        print("Usage: ./push_repo_release_tag.py <repo> <branch> <version_tag>")
-        sys.exit(1)
-
-    repo, branch, version_tag = sys.argv[1], sys.argv[2], sys.argv[3]
-
-    if branch not in {"master", "main"}:
-        print(f"Error: Branch '{branch}' is not 'master' or 'main'.")
-        sys.exit(1)
-
-    # Get the `lean-toolchain` file content
-    lean_toolchain_url = f"https://raw.githubusercontent.com/{repo}/{branch}/lean-toolchain"
-    try:
-        response = requests.get(lean_toolchain_url)
-        response.raise_for_status()
-    except requests.exceptions.RequestException as e:
-        print(f"Error fetching 'lean-toolchain' file: {e}")
-        sys.exit(1)
-
-    lean_toolchain_content = response.text.strip()
-    expected_prefix = "leanprover/lean4:"
-    if not lean_toolchain_content.startswith(expected_prefix) or lean_toolchain_content != f"{expected_prefix}{version_tag}":
-        print(f"Error: 'lean-toolchain' content does not match '{expected_prefix}{version_tag}'.")
-        sys.exit(1)
-
-    # Create and push the tag using `gh`
-    try:
-        # Check if the tag already exists
-        list_tags_cmd = ["gh", "api", f"repos/{repo}/git/matching-refs/tags/v4", "--jq", ".[].ref"]
-        list_tags_output = subprocess.run(list_tags_cmd, capture_output=True, text=True)
-
-        if list_tags_output.returncode == 0:
-            existing_tags = list_tags_output.stdout.strip().splitlines()
-            if f"refs/tags/{version_tag}" in existing_tags:
-                print(f"Error: Tag '{version_tag}' already exists.")
-                print("Existing tags starting with 'v4':")
-                for tag in existing_tags:
-                    print(tag.replace("refs/tags/", ""))
-                sys.exit(1)
-
-        # Get the SHA of the branch
-        get_sha_cmd = [
-            "gh", "api", f"repos/{repo}/git/ref/heads/{branch}", "--jq", ".object.sha"
-        ]
-        sha_result = subprocess.run(get_sha_cmd, capture_output=True, text=True, check=True)
-        sha = sha_result.stdout.strip()
-
-        # Create the tag
-        create_tag_cmd = [
-            "gh", "api", f"repos/{repo}/git/refs",
-            "-X", "POST",
-            "-F", f"ref=refs/tags/{version_tag}",
-            "-F", f"sha={sha}"
-        ]
-        subprocess.run(create_tag_cmd, capture_output=True, text=True, check=True)
-
-        print(f"Successfully created and pushed tag '{version_tag}' to {repo}.")
-    except subprocess.CalledProcessError as e:
-        print(f"Error while creating/pushing tag: {e.stderr.strip() if e.stderr else e}")
-        sys.exit(1)
-
-if __name__ == "__main__":
-    main()

script/release_checklist.py

@@ -1,227 +0,0 @@
-#!/usr/bin/env python3
-
-import argparse
-import yaml
-import requests
-import base64
-import subprocess
-import sys
-import os
-
-def parse_repos_config(file_path):
-    with open(file_path, "r") as f:
-        return yaml.safe_load(f)["repositories"]
-
-def get_github_token():
-    try:
-        import subprocess
-        result = subprocess.run(['gh', 'auth', 'token'], capture_output=True, text=True)
-        if result.returncode == 0:
-            return result.stdout.strip()
-    except FileNotFoundError:
-        print("Warning: 'gh' CLI not found. Some API calls may be rate-limited.")
-    return None
-
-def strip_rc_suffix(toolchain):
-    """Remove -rcX suffix from the toolchain."""
-    return toolchain.split("-")[0]
-
-def branch_exists(repo_url, branch, github_token):
-    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/branches/{branch}"
-    headers = {'Authorization': f'token {github_token}'} if github_token else {}
-    response = requests.get(api_url, headers=headers)
-    return response.status_code == 200
-
-def tag_exists(repo_url, tag_name, github_token):
-    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/git/refs/tags/{tag_name}"
-    headers = {'Authorization': f'token {github_token}'} if github_token else {}
-    response = requests.get(api_url, headers=headers)
-    return response.status_code == 200
-
-def release_page_exists(repo_url, tag_name, github_token):
-    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/releases/tags/{tag_name}"
-    headers = {'Authorization': f'token {github_token}'} if github_token else {}
-    response = requests.get(api_url, headers=headers)
-    return response.status_code == 200
-
-def get_release_notes(repo_url, tag_name, github_token):
-    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/releases/tags/{tag_name}"
-    headers = {'Authorization': f'token {github_token}'} if github_token else {}
-    response = requests.get(api_url, headers=headers)
-    if response.status_code == 200:
-        return response.json().get("body", "").strip()
-    return None
-
-def get_branch_content(repo_url, branch, file_path, github_token):
-    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/contents/{file_path}?ref={branch}"
-    headers = {'Authorization': f'token {github_token}'} if github_token else {}
-    response = requests.get(api_url, headers=headers)
-    if response.status_code == 200:
-        content = response.json().get("content", "")
-        content = content.replace("\n", "")
-        try:
-            return base64.b64decode(content).decode('utf-8').strip()
-        except Exception:
-            return None
-    return None
-
-def parse_version(version_str):
-    # Remove 'v' prefix and extract version and release candidate suffix
-    if ':' in version_str:
-        version_str = version_str.split(':')[1]
-    version = version_str.lstrip('v')
-    parts = version.split('-')
-    base_version = tuple(map(int, parts[0].split('.')))
-    rc_part = parts[1] if len(parts) > 1 and parts[1].startswith('rc') else None
-    rc_number = int(rc_part[2:]) if rc_part else float('inf')  # Treat non-rc as higher than rc
-    return base_version + (rc_number,)
-
-def is_version_gte(version1, version2):
-    """Check if version1 >= version2, including proper handling of release candidates."""
-    return parse_version(version1) >= parse_version(version2)
-
-def is_merged_into_stable(repo_url, tag_name, stable_branch, github_token):
-    # First get the commit SHA for the tag
-    api_base = repo_url.replace("https://github.com/", "https://api.github.com/repos/")
-    headers = {'Authorization': f'token {github_token}'} if github_token else {}
-
-    # Get tag's commit SHA
-    tag_response = requests.get(f"{api_base}/git/refs/tags/{tag_name}", headers=headers)
-    if tag_response.status_code != 200:
-        return False
-    tag_sha = tag_response.json()['object']['sha']
-
-    # Get commits on stable branch containing this SHA
-    commits_response = requests.get(
-        f"{api_base}/commits?sha={stable_branch}&per_page=100",
-        headers=headers
-    )
-    if commits_response.status_code != 200:
-        return False
-
-    # Check if any commit in stable's history matches our tag's SHA
-    stable_commits = [commit['sha'] for commit in commits_response.json()]
-    return tag_sha in stable_commits
-
-def is_release_candidate(version):
-    return "-rc" in version
-
-def check_cmake_version(repo_url, branch, version_major, version_minor, github_token):
-    """Verify the CMake version settings in src/CMakeLists.txt."""
-    cmake_file_path = "src/CMakeLists.txt"
-    content = get_branch_content(repo_url, branch, cmake_file_path, github_token)
-    if content is None:
-        print(f"  ❌ Could not retrieve {cmake_file_path} from {branch}")
-        return False
-
-    expected_lines = [
-        f"set(LEAN_VERSION_MAJOR {version_major})",
-        f"set(LEAN_VERSION_MINOR {version_minor})",
-        f"set(LEAN_VERSION_PATCH 0)",
-        f"set(LEAN_VERSION_IS_RELEASE 1)"
-    ]
-
-    for line in expected_lines:
-        if not any(l.strip().startswith(line) for l in content.splitlines()):
-            print(f"  ❌ Missing or incorrect line in {cmake_file_path}: {line}")
-            return False
-
-    print(f"  ✅ CMake version settings are correct in {cmake_file_path}")
-    return True
-
-def extract_org_repo_from_url(repo_url):
-    """Extract the 'org/repo' part from a GitHub URL."""
-    if repo_url.startswith("https://github.com/"):
-        return repo_url.replace("https://github.com/", "").rstrip("/")
-    return repo_url
-
-def main():
-    github_token = get_github_token()
-
-    if len(sys.argv) != 2:
-        print("Usage: python3 release_checklist.py <toolchain>")
-        sys.exit(1)
-
-    toolchain = sys.argv[1]
-    stripped_toolchain = strip_rc_suffix(toolchain)
-    lean_repo_url = "https://github.com/leanprover/lean4"
-
-    # Preliminary checks
-    print("\nPerforming preliminary checks...")
-
-    # Check for branch releases/v4.Y.0
-    version_major, version_minor, _ = map(int, stripped_toolchain.lstrip('v').split('.'))
-    branch_name = f"releases/v{version_major}.{version_minor}.0"
-    if branch_exists(lean_repo_url, branch_name, github_token):
-        print(f"  ✅ Branch {branch_name} exists")
-
-        # Check CMake version settings
-        check_cmake_version(lean_repo_url, branch_name, version_major, version_minor, github_token)
-    else:
-        print(f"  ❌ Branch {branch_name} does not exist")
-
-    # Check for tag v4.X.Y(-rcZ)
-    if tag_exists(lean_repo_url, toolchain, github_token):
-        print(f"  ✅ Tag {toolchain} exists")
-    else:
-        print(f"  ❌ Tag {toolchain} does not exist.")
-
-    # Check for release page
-    if release_page_exists(lean_repo_url, toolchain, github_token):
-        print(f"  ✅ Release page for {toolchain} exists")
-
-        # Check the first line of the release notes
-        release_notes = get_release_notes(lean_repo_url, toolchain, github_token)
-        if release_notes and release_notes.splitlines()[0].strip() == toolchain:
-            print(f"  ✅ Release notes look good.")
-        else:
-            previous_minor_version = version_minor - 1
-            previous_stable_branch = f"releases/v{version_major}.{previous_minor_version}.0"
-            previous_release = f"v{version_major}.{previous_minor_version}.0"
-            print(f"  ❌ Release notes not published. Please run `script/release_notes.py {previous_release}` on branch `{previous_stable_branch}`.")
-    else:
-        print(f"  ❌ Release page for {toolchain} does not exist")
-
-    # Load repositories and perform further checks
-    print("\nChecking repositories...")
-
-    with open(os.path.join(os.path.dirname(__file__), "release_repos.yml")) as f:
-        repos = yaml.safe_load(f)["repositories"]
-
-    for repo in repos:
-        name = repo["name"]
-        url = repo["url"]
-        branch = repo["branch"]
-        check_stable = repo["stable-branch"]
-        check_tag = repo.get("toolchain-tag", True)
-
-        print(f"\nRepository: {name}")
-
-        # Check if branch is on at least the target toolchain
-        lean_toolchain_content = get_branch_content(url, branch, "lean-toolchain", github_token)
-        if lean_toolchain_content is None:
-            print(f"  ❌ No lean-toolchain file found in {branch} branch")
-            continue
-
-        on_target_toolchain = is_version_gte(lean_toolchain_content.strip(), toolchain)
-        if not on_target_toolchain:
-            print(f"  ❌ Not on target toolchain (needs ≥ {toolchain}, but {branch} is on {lean_toolchain_content.strip()})")
-            continue
-        print(f"  ✅ On compatible toolchain (>= {toolchain})")
-
-        # Only check for tag if toolchain-tag is true
-        if check_tag:
-            if not tag_exists(url, toolchain, github_token):
-                print(f"  ❌ Tag {toolchain} does not exist. Run `script/push_repo_release_tag.py {extract_org_repo_from_url(url)} {branch} {toolchain}`.")
-                continue
-            print(f"  ✅ Tag {toolchain} exists")
-
-        # Only check merging into stable if stable-branch is true and not a release candidate
-        if check_stable and not is_release_candidate(toolchain):
-            if not is_merged_into_stable(url, toolchain, "stable", github_token):
-                print(f"  ❌ Tag {toolchain} is not merged into stable")
-                continue
-            print(f"  ✅ Tag {toolchain} is merged into stable")
-
-if __name__ == "__main__":
-    main()

script/release_notes.py

@@ -1,145 +0,0 @@
-#!/usr/bin/env python3
-
-import sys
-import re
-import json
-import requests
-import subprocess
-from collections import defaultdict
-from git import Repo
-
-def get_commits_since_tag(repo, tag):
-    try:
-        tag_commit = repo.commit(tag)
-        commits = list(repo.iter_commits(f"{tag_commit.hexsha}..HEAD"))
-        return [
-            (commit.hexsha, commit.message.splitlines()[0], commit.message)
-            for commit in commits
-        ]
-    except Exception as e:
-        sys.stderr.write(f"Error retrieving commits: {e}\n")
-        sys.exit(1)
-
-def check_pr_number(first_line):
-    match = re.search(r"\(\#(\d+)\)$", first_line)
-    if match:
-        return int(match.group(1))
-    return None
-
-def fetch_pr_labels(pr_number):
-    try:
-        # Use gh CLI to fetch PR details
-        result = subprocess.run([
-            "gh", "api", f"repos/leanprover/lean4/pulls/{pr_number}"
-        ], capture_output=True, text=True, check=True)
-        pr_data = result.stdout
-        pr_json = json.loads(pr_data)
-        return [label["name"] for label in pr_json.get("labels", [])]
-    except subprocess.CalledProcessError as e:
-        sys.stderr.write(f"Failed to fetch PR #{pr_number} using gh: {e.stderr}\n")
-        return []
-
-def format_section_title(label):
-    title = label.replace("changelog-", "").capitalize()
-    if title == "Doc":
-        return "Documentation"
-    elif title == "Pp":
-        return "Pretty Printing"
-    return title
-
-def sort_sections_order():
-    return [
-        "Language",
-        "Library",
-        "Compiler",
-        "Pretty Printing",
-        "Documentation",
-        "Server",
-        "Lake",
-        "Other",
-        "Uncategorised"
-    ]
-
-def format_markdown_description(pr_number, description):
-    link = f"[#{pr_number}](https://github.com/leanprover/lean4/pull/{pr_number})"
-    return f"{link} {description}"
-
-def main():
-    if len(sys.argv) != 2:
-        sys.stderr.write("Usage: script.py <git-tag>\n")
-        sys.exit(1)
-
-    tag = sys.argv[1]
-    try:
-        repo = Repo(".")
-    except Exception as e:
-        sys.stderr.write(f"Error opening Git repository: {e}\n")
-        sys.exit(1)
-
-    commits = get_commits_since_tag(repo, tag)
-
-    sys.stderr.write(f"Found {len(commits)} commits since tag {tag}:\n")
-    for commit_hash, first_line, _ in commits:
-        sys.stderr.write(f"- {commit_hash}: {first_line}\n")
-
-    changelog = defaultdict(list)
-
-    for commit_hash, first_line, full_message in commits:
-        # Skip commits with the specific first lines
-        if first_line == "chore: update stage0" or first_line.startswith("chore: CI: bump "):
-            continue
-
-        pr_number = check_pr_number(first_line)
-
-        if not pr_number:
-            sys.stderr.write(f"No PR number found in {first_line}\n")
-            continue
-
-        # Remove the first line from the full_message for further processing
-        body = full_message[len(first_line):].strip()
-
-        paragraphs = body.split('\n\n')
-        second_paragraph = paragraphs[0] if len(paragraphs) > 0 else ""
-
-        labels = fetch_pr_labels(pr_number)
-
-        # Skip entries with the "changelog-no" label
-        if "changelog-no" in labels:
-            continue
-
-        report_errors = first_line.startswith("feat:") or first_line.startswith("fix:")
-
-        if not second_paragraph.startswith("This PR "):
-            if report_errors:
-                sys.stderr.write(f"No PR description found in commit:\n{commit_hash}\n{first_line}\n{body}\n\n")
-                fallback_description = re.sub(r":$", "", first_line.split(" ", 1)[1]).rsplit(" (#", 1)[0]
-                markdown_description = format_markdown_description(pr_number, fallback_description)
-            else:
-                continue
-        else:
-            markdown_description = format_markdown_description(pr_number, second_paragraph.replace("This PR ", ""))
-
-        changelog_labels = [label for label in labels if label.startswith("changelog-")]
-        if len(changelog_labels) > 1:
-            sys.stderr.write(f"Warning: Multiple changelog-* labels found for PR #{pr_number}: {changelog_labels}\n")
-
-        if not changelog_labels:
-            if report_errors:
-                sys.stderr.write(f"Warning: No changelog-* label found for PR #{pr_number}\n")
-            else:
-                continue
-
-        for label in changelog_labels:
-            changelog[label].append((pr_number, markdown_description))
-
-    section_order = sort_sections_order()
-    sorted_changelog = sorted(changelog.items(), key=lambda item: section_order.index(format_section_title(item[0])) if format_section_title(item[0]) in section_order else len(section_order))
-
-    for label, entries in sorted_changelog:
-        section_title = format_section_title(label) if label != "Uncategorised" else "Uncategorised"
-        print(f"## {section_title}\n")
-        for _, entry in sorted(entries, key=lambda x: x[0]):
-            print(f"* {entry}\n")
-
-if __name__ == "__main__":
-    main()

script/release_repos.yml

@@ -1,86 +0,0 @@
-repositories:
-  - name: Batteries
-    url: https://github.com/leanprover-community/batteries
-    toolchain-tag: true
-    stable-branch: true
-    branch: main
-    dependencies: []
-
-  - name: lean4checker
-    url: https://github.com/leanprover/lean4checker
-    toolchain-tag: true
-    stable-branch: true
-    branch: master
-    dependencies: []
-
-  - name: doc-gen4
-    url: https://github.com/leanprover/doc-gen4
-    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: Cli
-    url: https://github.com/leanprover/lean4-cli
-    toolchain-tag: true
-    stable-branch: false
-    branch: main
-    dependencies: []
-
-  - name: ProofWidgets4
-    url: https://github.com/leanprover-community/ProofWidgets4
-    toolchain-tag: false
-    stable-branch: false
-    branch: main
-    dependencies:
-      - Batteries
-
-  - name: Aesop
-    url: https://github.com/leanprover-community/aesop
-    toolchain-tag: true
-    stable-branch: true
-    branch: master
-    dependencies:
-      - Batteries
-
-  - name: import-graph
-    url: https://github.com/leanprover-community/import-graph
-    toolchain-tag: true
-    stable-branch: false
-    branch: main
-    dependencies: []
-
-  - name: plausible
-    url: https://github.com/leanprover-community/plausible
-    toolchain-tag: true
-    stable-branch: false
-    branch: main
-    dependencies: []
-
-  - name: Mathlib
-    url: https://github.com/leanprover-community/mathlib4
-    toolchain-tag: true
-    stable-branch: true
-    branch: master
-    dependencies:
-      - Aesop
-      - ProofWidgets4
-      - lean4checker
-      - Batteries
-      - doc-gen4
-      - import-graph
-
-  - name: REPL
-    url: https://github.com/leanprover-community/repl
-    toolchain-tag: true
-    stable-branch: true
-    branch: master
-    dependencies:
-      - Mathlib

src/CMakeLists.txt

@@ -295,15 +295,14 @@ index 5e8e0166..f3b29134 100644
 	  PATCH_COMMAND git reset --hard HEAD && printf "${LIBUV_PATCH}" > patch.diff && git apply patch.diff
     BUILD_IN_SOURCE ON
     INSTALL_COMMAND "")
-  set(LIBUV_INCLUDE_DIRS "${CMAKE_BINARY_DIR}/libuv/src/libuv/include")
-  set(LIBUV_LDFLAGS "${CMAKE_BINARY_DIR}/libuv/src/libuv/libuv.a")
+  set(LIBUV_INCLUDE_DIR "${CMAKE_BINARY_DIR}/libuv/src/libuv/include")
+  set(LIBUV_LIBRARIES "${CMAKE_BINARY_DIR}/libuv/src/libuv/libuv.a")
 else()
   find_package(LibUV 1.0.0 REQUIRED)
 endif()
-include_directories(${LIBUV_INCLUDE_DIRS})
+include_directories(${LIBUV_INCLUDE_DIR})
 if(NOT LEAN_STANDALONE)
-  string(JOIN " " LIBUV_LDFLAGS ${LIBUV_LDFLAGS})
-  string(APPEND LEAN_EXTRA_LINKER_FLAGS " ${LIBUV_LDFLAGS}")
+  string(APPEND LEAN_EXTRA_LINKER_FLAGS " ${LIBUV_LIBRARIES}")
 endif()
 
 # Windows SDK (for ICU)

src/Init/Conv.lean

@@ -150,10 +150,6 @@ See the `simp` tactic for more information. -/
 syntax (name := simp) "simp" optConfig (discharger)? (&" only")?
   (" [" withoutPosition((simpStar <|> simpErase <|> simpLemma),*) "]")? : conv
 
-/-- `simp?` takes the same arguments as `simp`, but reports an equivalent call to `simp only`
-that would be sufficient to close the goal. See the `simp?` tactic for more information. -/
-syntax (name := simpTrace) "simp?" optConfig (discharger)? (&" only")? (simpArgs)? : conv
-
 /--
 `dsimp` is the definitional simplifier in `conv`-mode. It differs from `simp` in that it only
 applies theorems that hold by reflexivity.
@@ -171,9 +167,6 @@ example (a : Nat): (0 + 0) = a - a := by
 syntax (name := dsimp) "dsimp" optConfig (discharger)? (&" only")?
   (" [" withoutPosition((simpErase <|> simpLemma),*) "]")? : conv
 
-@[inherit_doc simpTrace]
-syntax (name := dsimpTrace) "dsimp?" optConfig (&" only")? (dsimpArgs)? : conv
-
 /-- `simp_match` simplifies match expressions. For example,
 ```
 match [a, b] with

src/Init/Data/Array/Basic.lean

@@ -244,7 +244,8 @@ def ofFn {n} (f : Fin n → α) : Array α := go 0 (mkEmpty n) where
 def range (n : Nat) : Array Nat :=
   ofFn fun (i : Fin n) => i
 
-@[inline] protected def singleton (v : α) : Array α := #[v]
+def singleton (v : α) : Array α :=
+  mkArray 1 v
 
 def back! [Inhabited α] (a : Array α) : α :=
   a[a.size - 1]!
@@ -576,12 +577,6 @@ def foldl {α : Type u} {β : Type v} (f : β → α → β) (init : β) (as : A
 def foldr {α : Type u} {β : Type v} (f : α → β → β) (init : β) (as : Array α) (start := as.size) (stop := 0) : β :=
   Id.run <| as.foldrM f init start stop
 
-/-- Sum of an array.
-
-`Array.sum #[a, b, c] = a + (b + (c + 0))` -/
-def sum {α} [Add α] [Zero α] : Array α → α :=
-  foldr (· + ·) 0
-
 @[inline]
 def map {α : Type u} {β : Type v} (f : α → β) (as : Array α) : Array β :=
   Id.run <| as.mapM f

src/Init/Data/Array/Bootstrap.lean

@@ -81,18 +81,12 @@ theorem foldrM_eq_reverse_foldlM_toList [Monad m] (f : α → β → m β) (init
 
 @[simp] theorem toList_empty : (#[] : Array α).toList = [] := rfl
 
-@[simp] theorem append_empty (as : Array α) : as ++ #[] = as := by
+@[simp] theorem append_nil (as : Array α) : as ++ #[] = as := by
   apply ext'; simp only [toList_append, toList_empty, List.append_nil]
 
-@[deprecated append_empty (since := "2025-01-13")]
-abbrev append_nil := @append_empty
-
-@[simp] theorem empty_append (as : Array α) : #[] ++ as = as := by
+@[simp] theorem nil_append (as : Array α) : #[] ++ as = as := by
   apply ext'; simp only [toList_append, toList_empty, List.nil_append]
 
-@[deprecated empty_append (since := "2025-01-13")]
-abbrev nil_append := @empty_append
-
 @[simp] theorem append_assoc (as bs cs : Array α) : as ++ bs ++ cs = as ++ (bs ++ cs) := by
   apply ext'; simp only [toList_append, List.append_assoc]
 

src/Init/Data/Array/Find.lean

@@ -74,12 +74,12 @@ theorem findSome?_append {l₁ l₂ : Array α} : (l₁ ++ l₂).findSome? f = (
 
 theorem getElem?_zero_flatten (L : Array (Array α)) :
     (flatten L)[0]? = L.findSome? fun l => l[0]? := by
-  cases L using array₂_induction
+  cases L using array_array_induction
   simp [← List.head?_eq_getElem?, List.head?_flatten, List.findSome?_map, Function.comp_def]
 
 theorem getElem_zero_flatten.proof {L : Array (Array α)} (h : 0 < L.flatten.size) :
     (L.findSome? fun l => l[0]?).isSome := by
-  cases L using array₂_induction
+  cases L using array_array_induction
   simp only [List.findSome?_toArray, List.findSome?_map, Function.comp_def, List.getElem?_toArray,
     List.findSome?_isSome_iff, isSome_getElem?]
   simp only [flatten_toArray_map_toArray, size_toArray, List.length_flatten,
@@ -95,7 +95,7 @@ theorem getElem_zero_flatten {L : Array (Array α)} (h) :
 
 theorem back?_flatten {L : Array (Array α)} :
     (flatten L).back? = (L.findSomeRev? fun l => l.back?) := by
-  cases L using array₂_induction
+  cases L using array_array_induction
   simp [List.getLast?_flatten, ← List.map_reverse, List.findSome?_map, Function.comp_def]
 
 theorem findSome?_mkArray : findSome? f (mkArray n a) = if n = 0 then none else f a := by
@@ -203,7 +203,7 @@ theorem get_find?_mem {xs : Array α} (h) : (xs.find? p).get h ∈ xs := by
 
 @[simp] theorem find?_flatten (xs : Array (Array α)) (p : α → Bool) :
     xs.flatten.find? p = xs.findSome? (·.find? p) := by
-  cases xs using array₂_induction
+  cases xs using array_array_induction
   simp [List.findSome?_map, Function.comp_def]
 
 theorem find?_flatten_eq_none {xs : Array (Array α)} {p : α → Bool} :
@@ -220,7 +220,7 @@ theorem find?_flatten_eq_some {xs : Array (Array α)} {p : α → Bool} {a : α}
       p a ∧ ∃ (as : Array (Array α)) (ys zs : Array α) (bs : Array (Array α)),
         xs = as.push (ys.push a ++ zs) ++ bs ∧
         (∀ a ∈ as, ∀ x ∈ a, !p x) ∧ (∀ x ∈ ys, !p x) := by
-  cases xs using array₂_induction
+  cases xs using array_array_induction
   simp only [flatten_toArray_map_toArray, List.find?_toArray, List.find?_flatten_eq_some]
   simp only [Bool.not_eq_eq_eq_not, Bool.not_true, exists_and_right, and_congr_right_iff]
   intro w

src/Init/Data/BitVec/Lemmas.lean

@@ -9,9 +9,7 @@ import Init.Data.Bool
 import Init.Data.BitVec.Basic
 import Init.Data.Fin.Lemmas
 import Init.Data.Nat.Lemmas
-import Init.Data.Nat.Div.Lemmas
 import Init.Data.Nat.Mod
-import Init.Data.Nat.Div.Lemmas
 import Init.Data.Int.Bitwise.Lemmas
 import Init.Data.Int.Pow
 
@@ -100,12 +98,6 @@ theorem ofFin_eq_ofNat : @BitVec.ofFin w (Fin.mk x lt) = BitVec.ofNat w x := by
 theorem eq_of_toNat_eq {n} : ∀ {x y : BitVec n}, x.toNat = y.toNat → x = y
   | ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
 
-/-- 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
-  constructor
-  · rintro h rfl; apply h rfl
-  · intro h h_eq; apply h <| eq_of_toNat_eq h_eq
-
 @[simp] theorem val_toFin (x : BitVec w) : x.toFin.val = x.toNat := rfl
 
 @[bv_toNat] theorem toNat_eq {x y : BitVec n} : x = y ↔ x.toNat = y.toNat :=
@@ -450,10 +442,6 @@ theorem toInt_eq_toNat_cond (x : BitVec n) :
         (x.toNat : Int) - (2^n : Nat) :=
   rfl
 
-theorem toInt_eq_toNat_of_lt {x : BitVec n} (h : 2 * x.toNat < 2^n) :
-    x.toInt = x.toNat := by
-  simp [toInt_eq_toNat_cond, h]
-
 theorem msb_eq_false_iff_two_mul_lt {x : BitVec w} : x.msb = false ↔ 2 * x.toNat < 2^w := by
   cases w <;> simp [Nat.pow_succ, Nat.mul_comm _ 2, msb_eq_decide, toNat_of_zero_length]
 
@@ -466,9 +454,6 @@ theorem toInt_eq_msb_cond (x : BitVec w) :
   simp only [BitVec.toInt, ← msb_eq_false_iff_two_mul_lt]
   cases x.msb <;> rfl
 
-theorem toInt_eq_toNat_of_msb {x : BitVec w} (h : x.msb = false) :
-    x.toInt = x.toNat := by
-  simp [toInt_eq_msb_cond, h]
 
 theorem toInt_eq_toNat_bmod (x : BitVec n) : x.toInt = Int.bmod x.toNat (2^n) := by
   simp only [toInt_eq_toNat_cond]
@@ -800,19 +785,6 @@ theorem extractLsb'_eq_extractLsb {w : Nat} (x : BitVec w) (start len : Nat) (h
   unfold allOnes
   simp
 
-@[simp] theorem toInt_allOnes : (allOnes w).toInt = if 0 < w then -1 else 0 := by
-  norm_cast
-  by_cases h : w = 0
-  · subst h
-    simp
-  · have : 1 < 2 ^ w := by simp [h]
-    simp [BitVec.toInt]
-    omega
-
-@[simp] theorem toFin_allOnes : (allOnes w).toFin = Fin.ofNat' (2^w) (2^w - 1) := by
-  ext
-  simp
-
 @[simp] theorem getLsbD_allOnes : (allOnes v).getLsbD i = decide (i < v) := by
   simp [allOnes]
 
@@ -1170,16 +1142,11 @@ theorem getMsb_not {x : BitVec w} :
 /-! ### shiftLeft -/
 
 @[simp, bv_toNat] theorem toNat_shiftLeft {x : BitVec v} :
-    (x <<< n).toNat = x.toNat <<< n % 2^v :=
+    BitVec.toNat (x <<< n) = BitVec.toNat x <<< n % 2^v :=
   BitVec.toNat_ofNat _ _
 
-@[simp] theorem toInt_shiftLeft {x : BitVec w} :
-    (x <<< n).toInt = (x.toNat <<< n : Int).bmod (2^w) := by
-  rw [toInt_eq_toNat_bmod, toNat_shiftLeft, Nat.shiftLeft_eq]
-  simp
-
 @[simp] theorem toFin_shiftLeft {n : Nat} (x : BitVec w) :
-    (x <<< n).toFin = Fin.ofNat' (2^w) (x.toNat <<< n) := rfl
+    BitVec.toFin (x <<< n) = Fin.ofNat' (2^w) (x.toNat <<< n) := rfl
 
 @[simp]
 theorem shiftLeft_zero (x : BitVec w) : x <<< 0 = x := by
@@ -2315,12 +2282,6 @@ theorem ofNat_sub_ofNat {n} (x y : Nat) : BitVec.ofNat n x - BitVec.ofNat n y =
 @[simp, bv_toNat] theorem toNat_neg (x : BitVec n) : (- x).toNat = (2^n - x.toNat) % 2^n := by
   simp [Neg.neg, BitVec.neg]
 
-theorem toNat_neg_of_pos {x : BitVec n} (h : 0#n < x) :
-    (- x).toNat = 2^n - x.toNat := by
-  change 0 < x.toNat at h
-  rw [toNat_neg, Nat.mod_eq_of_lt]
-  omega
-
 theorem toInt_neg {x : BitVec w} :
     (-x).toInt = (-x.toInt).bmod (2 ^ w) := by
   rw [← BitVec.zero_sub, toInt_sub]
@@ -2416,54 +2377,6 @@ theorem not_neg (x : BitVec w) : ~~~(-x) = x + -1#w := by
         show (_ - x.toNat) % _ = _ by rw [Nat.mod_eq_of_lt (by omega)]]
       omega
 
-/-! ### fill -/
-
-@[simp]
-theorem getLsbD_fill {w i : Nat} {v : Bool} :
-    (fill w v).getLsbD i = (v && decide (i < w)) := by
-  by_cases h : v
-  <;> simp [h, BitVec.fill, BitVec.negOne_eq_allOnes]
-
-@[simp]
-theorem getMsbD_fill {w i : Nat} {v : Bool} :
-    (fill w v).getMsbD i = (v && decide (i < w)) := by
-  by_cases h : v
-  <;> simp [h, BitVec.fill, BitVec.negOne_eq_allOnes]
-
-@[simp]
-theorem getElem_fill {w i : Nat} {v : Bool} (h : i < w) :
-    (fill w v)[i] = v := by
-  by_cases h : v
-  <;> simp [h, BitVec.fill, BitVec.negOne_eq_allOnes]
-
-@[simp]
-theorem msb_fill {w : Nat} {v : Bool} :
-    (fill w v).msb = (v && decide (0 < w)) := by
-  simp [BitVec.msb]
-
-theorem fill_eq {w : Nat} {v : Bool} : fill w v = if v = true then allOnes w else 0#w := by
-  by_cases h : v <;> (simp only [h] ; ext ; simp)
-
-@[simp]
-theorem fill_true {w : Nat} : fill w true = allOnes w := by
-  simp [fill_eq]
-
-@[simp]
-theorem fill_false {w : Nat} : fill w false = 0#w := by
-  simp [fill_eq]
-
-@[simp] theorem fill_toNat {w : Nat} {v : Bool} :
-    (fill w v).toNat = if v = true then 2^w - 1 else 0 := by
-  by_cases h : v <;> simp [h]
-
-@[simp] theorem fill_toInt {w : Nat} {v : Bool} :
-    (fill w v).toInt = if v = true && 0 < w then -1 else 0 := by
-  by_cases h : v <;> simp [h]
-
-@[simp] theorem fill_toFin {w : Nat} {v : Bool} :
-    (fill w v).toFin = if v = true then (allOnes w).toFin else Fin.ofNat' (2 ^ w) 0 := by
-  by_cases h : v <;> simp [h]
-
 /-! ### mul -/
 
 theorem mul_def {n} {x y : BitVec n} : x * y = (ofFin <| x.toFin * y.toFin) := by rfl
@@ -2607,13 +2520,13 @@ theorem udiv_def {x y : BitVec n} : x / y = BitVec.ofNat n (x.toNat / y.toNat) :
   rw [← udiv_eq]
   simp [udiv, bv_toNat, h, Nat.mod_eq_of_lt]
 
-@[simp]
-theorem toFin_udiv {x y : BitVec n} : (x / y).toFin = x.toFin / y.toFin := by
-  rfl
-
 @[simp, bv_toNat]
 theorem toNat_udiv {x y : BitVec n} : (x / y).toNat = x.toNat / y.toNat := by
-  rfl
+  rw [udiv_def]
+  by_cases h : y = 0
+  · simp [h]
+  · rw [toNat_ofNat, Nat.mod_eq_of_lt]
+    exact Nat.lt_of_le_of_lt (Nat.div_le_self ..) (by omega)
 
 @[simp]
 theorem zero_udiv {x : BitVec w} : (0#w) / x = 0#w := by
@@ -2649,45 +2562,6 @@ theorem udiv_self {x : BitVec w} :
       ↓reduceIte, toNat_udiv]
     rw [Nat.div_self (by omega), Nat.mod_eq_of_lt (by omega)]
 
-theorem msb_udiv (x y : BitVec w) :
-    (x / y).msb = (x.msb && y == 1#w) := by
-  cases msb_x : x.msb
-  · suffices x.toNat / y.toNat < 2 ^ (w - 1) by simpa [msb_eq_decide]
-    calc
-      x.toNat / y.toNat ≤ x.toNat     := by apply Nat.div_le_self
-                      _ < 2 ^ (w - 1) := by simpa [msb_eq_decide] using msb_x
-  . rcases w with _|w
-    · contradiction
-    · have : (y == 1#_) = decide (y.toNat = 1) := by
-        simp [(· == ·), toNat_eq]
-      simp only [this, Bool.true_and]
-      match hy : y.toNat with
-      | 0 =>
-        obtain rfl : y = 0#_ := eq_of_toNat_eq hy
-        simp
-      | 1 =>
-        obtain rfl : y = 1#_ := eq_of_toNat_eq (by simp [hy])
-        simpa using msb_x
-      | y + 2 =>
-        suffices x.toNat / (y + 2) < 2 ^ w by
-          simp_all [msb_eq_decide, hy]
-        calc
-          x.toNat / (y + 2)
-            ≤ x.toNat / 2 := by apply Nat.div_add_le_right (by omega)
-          _ < 2 ^ w       := by omega
-
-theorem msb_udiv_eq_false_of {x : BitVec w} (h : x.msb = false) (y : BitVec w) :
-    (x / y).msb = false := by
-  simp [msb_udiv, h]
-
-/--
-If `x` is nonnegative (i.e., does not have its msb set),
-then `x / y` is nonnegative, thus `toInt` and `toNat` coincide.
--/
-theorem toInt_udiv_of_msb {x : BitVec w} (h : x.msb = false) (y : BitVec w) :
-    (x / y).toInt = x.toNat / y.toNat := by
-  simp [toInt_eq_msb_cond, msb_udiv_eq_false_of h]
-
 /-! ### umod -/
 
 theorem umod_def {x y : BitVec n} :
@@ -2700,10 +2574,6 @@ theorem umod_def {x y : BitVec n} :
 theorem toNat_umod {x y : BitVec n} :
     (x % y).toNat = x.toNat % y.toNat := rfl
 
-@[simp]
-theorem toFin_umod {x y : BitVec w} :
-    (x % y).toFin = x.toFin % y.toFin := rfl
-
 @[simp]
 theorem umod_zero {x : BitVec n} : x % 0#n = x := by
   simp [umod_def]
@@ -2731,55 +2601,6 @@ theorem umod_eq_and {x y : BitVec 1} : x % y = x &&& (~~~y) := by
     rcases hy with rfl | rfl <;>
       rfl
 
-theorem umod_eq_of_lt {x y : BitVec w} (h : x < y) :
-    x % y = x := by
-  apply eq_of_toNat_eq
-  simp [Nat.mod_eq_of_lt h]
-
-@[simp]
-theorem msb_umod {x y : BitVec w} :
-    (x % y).msb = (x.msb && (x < y || y == 0#w)) := by
-  rw [msb_eq_decide, toNat_umod]
-  cases msb_x : x.msb
-  · suffices x.toNat % y.toNat < 2 ^ (w - 1) by simpa
-    calc
-      x.toNat % y.toNat ≤ x.toNat     := by apply Nat.mod_le
-                      _ < 2 ^ (w - 1) := by simpa [msb_eq_decide] using msb_x
-  . by_cases hy : y = 0
-    · simp_all [msb_eq_decide]
-    · suffices 2 ^ (w - 1) ≤ x.toNat % y.toNat ↔ x < y by simp_all
-      by_cases x_lt_y : x < y
-      . simp_all [Nat.mod_eq_of_lt x_lt_y, msb_eq_decide]
-      · suffices x.toNat % y.toNat < 2 ^ (w - 1) by
-          simpa [x_lt_y]
-        have y_le_x : y.toNat ≤ x.toNat := by
-          simpa using x_lt_y
-        replace hy : y.toNat ≠ 0 :=
-          toNat_ne_iff_ne.mpr hy
-        by_cases msb_y : y.toNat < 2 ^ (w - 1)
-        · have : x.toNat % y.toNat < y.toNat := Nat.mod_lt _ (by omega)
-          omega
-        · rcases w with _|w
-          · contradiction
-          simp only [Nat.add_one_sub_one]
-          replace msb_y : 2 ^ w ≤ y.toNat := by
-            simpa using msb_y
-          have : y.toNat ≤ y.toNat * (x.toNat / y.toNat) := by
-              apply Nat.le_mul_of_pos_right
-              apply Nat.div_pos y_le_x
-              omega
-          have : x.toNat % y.toNat ≤ x.toNat - y.toNat := by
-            rw [Nat.mod_eq_sub]; omega
-          omega
-
-theorem toInt_umod {x y : BitVec w} :
-    (x % y).toInt = (x.toNat % y.toNat : Int).bmod (2 ^ w) := by
-  simp [toInt_eq_toNat_bmod]
-
-theorem toInt_umod_of_msb {x y : BitVec w} (h : x.msb = false) :
-    (x % y).toInt = x.toInt % y.toNat := by
-  simp [toInt_eq_msb_cond, h]
-
 /-! ### smtUDiv -/
 
 theorem smtUDiv_eq (x y : BitVec w) : smtUDiv x y = if y = 0#w then allOnes w else x / y := by
@@ -2936,12 +2757,7 @@ theorem smod_zero {x : BitVec n} : x.smod 0#n = x := by
 
 /-! # Rotate Left -/
 
-/--`rotateLeft` is defined in terms of left and right shifts. -/
-theorem rotateLeft_def {x : BitVec w} {r : Nat} :
-    x.rotateLeft r = (x <<< (r % w)) ||| (x >>> (w - r % w)) := by
-  simp only [rotateLeft, rotateLeftAux]
-
-/-- `rotateLeft` is invariant under `mod` by the bitwidth. -/
+/-- rotateLeft is invariant under `mod` by the bitwidth. -/
 @[simp]
 theorem rotateLeft_mod_eq_rotateLeft {x : BitVec w} {r : Nat} :
     x.rotateLeft (r % w) = x.rotateLeft r := by
@@ -3085,18 +2901,8 @@ theorem msb_rotateLeft {m w : Nat} {x : BitVec w} :
   · simp
     omega
 
-@[simp]
-theorem toNat_rotateLeft {x : BitVec w} {r : Nat} :
-    (x.rotateLeft r).toNat = (x.toNat <<< (r % w)) % (2^w) ||| x.toNat >>> (w - r % w) := by
-  simp only [rotateLeft_def, toNat_shiftLeft, toNat_ushiftRight, toNat_or]
-
 /-! ## Rotate Right -/
 
-/-- `rotateRight` is defined in terms of left and right shifts. -/
-theorem rotateRight_def {x : BitVec w} {r : Nat} :
-    x.rotateRight r = (x >>> (r % w)) ||| (x <<< (w - r % w)) := by
-  simp only [rotateRight, rotateRightAux]
-
 /--
 Accessing bits in `x.rotateRight r` the range `[0, w-r)` is equal to
 accessing bits `x` in the range `[r, w)`.
@@ -3232,11 +3038,6 @@ theorem msb_rotateRight {r w : Nat} {x : BitVec w} :
     simp [h₁]
   · simp [show w = 0 by omega]
 
-@[simp]
-theorem toNat_rotateRight {x : BitVec w} {r : Nat} :
-    (x.rotateRight r).toNat = (x.toNat >>> (r % w)) ||| x.toNat <<< (w - r % w) % (2^w) := by
-  simp only [rotateRight_def, toNat_shiftLeft, toNat_ushiftRight, toNat_or]
-
 /- ## twoPow -/
 
 theorem twoPow_eq (w : Nat) (i : Nat) : twoPow w i = 1#w <<< i := by
@@ -3539,7 +3340,7 @@ theorem getLsbD_intMax (w : Nat) : (intMax w).getLsbD i = decide (i + 1 < w) :=
 
 /-! ### Non-overflow theorems -/
 
-/-- If `x.toNat + y.toNat < 2^w`, then the addition `(x + y)` does not overflow. -/
+/-- If `x.toNat * y.toNat < 2^w`, then the multiplication `(x * y)` does not overflow. -/
 theorem toNat_add_of_lt {w} {x y : BitVec w} (h : x.toNat + y.toNat < 2^w) :
     (x + y).toNat = x.toNat + y.toNat := by
   rw [BitVec.toNat_add, Nat.mod_eq_of_lt h]

src/Init/Data/Int/DivModLemmas.lean

@@ -534,13 +534,6 @@ theorem mul_emod (a b n : Int) : (a * b) % n = (a % n) * (b % n) % n := by
 @[simp] theorem emod_emod (a b : Int) : (a % b) % b = a % b := by
   conv => rhs; rw [← emod_add_ediv a b, add_mul_emod_self_left]
 
-@[simp] theorem emod_sub_emod (m n k : Int) : (m % n - k) % n = (m - k) % n :=
-  Int.emod_add_emod m n (-k)
-
-@[simp] theorem sub_emod_emod (m n k : Int) : (m - n % k) % k = (m - n) % k := by
-  apply (emod_add_cancel_right (n % k)).mp
-  rw [Int.sub_add_cancel, Int.add_emod_emod, Int.sub_add_cancel]
-
 theorem sub_emod (a b n : Int) : (a - b) % n = (a % n - b % n) % n := by
   apply (emod_add_cancel_right b).mp
   rw [Int.sub_add_cancel, ← Int.add_emod_emod, Int.sub_add_cancel, emod_emod]
@@ -1105,32 +1098,6 @@ theorem bmod_def (x : Int) (m : Nat) : bmod x m =
     (x % m) - m :=
   rfl
 
-theorem bdiv_add_bmod (x : Int) (m : Nat) : m * bdiv x m + bmod x m = x := by
-  unfold bdiv bmod
-  split
-  · simp_all only [Nat.cast_ofNat_Int, Int.mul_zero, emod_zero, Int.zero_add, Int.sub_zero,
-      ite_self]
-  · dsimp only
-    split
-    · 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 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
-
-theorem bdiv_add_bmod' (x : Int) (m : Nat) : bdiv x m * m + bmod x m = x := by
-  rw [Int.mul_comm]; exact bdiv_add_bmod x m
-
-theorem bmod_add_bdiv' (x : Int) (m : Nat) : bmod x m + bdiv x m * m = x := by
-  rw [Int.add_comm]; exact bdiv_add_bmod' x m
-
-theorem bmod_eq_self_sub_mul_bdiv (x : Int) (m : Nat) : bmod x m = x - m * bdiv x m := by
-  rw [← Int.add_sub_cancel (bmod x m), bmod_add_bdiv]
-
-theorem bmod_eq_self_sub_bdiv_mul (x : Int) (m : Nat) : bmod x m = x - bdiv x m * m := by
-  rw [← Int.add_sub_cancel (bmod x m), bmod_add_bdiv']
-
 theorem bmod_pos (x : Int) (m : Nat) (p : x % m < (m + 1) / 2) : bmod x m = x % m := by
   simp [bmod_def, p]
 

src/Init/Data/List/Basic.lean

@@ -606,11 +606,11 @@ set_option linter.missingDocs false in
 to get a list of lists, and then concatenates them all together.
 * `[2, 3, 2].bind range = [0, 1, 0, 1, 2, 0, 1]`
 -/
-@[inline] def flatMap {α : Type u} {β : Type v} (b : α → List β) (a : List α) : List β := flatten (map b a)
+@[inline] def flatMap {α : Type u} {β : Type v} (a : List α) (b : α → List β) : List β := flatten (map b a)
 
-@[simp] theorem flatMap_nil (f : α → List β) : List.flatMap f [] = [] := by simp [flatten, List.flatMap]
+@[simp] theorem flatMap_nil (f : α → List β) : List.flatMap [] f = [] := by simp [flatten, List.flatMap]
 @[simp] theorem flatMap_cons x xs (f : α → List β) :
-  List.flatMap f (x :: xs) = f x ++ List.flatMap f xs := by simp [flatten, List.flatMap]
+  List.flatMap (x :: xs) f = f x ++ List.flatMap xs f := by simp [flatten, List.flatMap]
 
 set_option linter.missingDocs false in
 @[deprecated flatMap (since := "2024-10-16")] abbrev bind := @flatMap

src/Init/Data/List/Impl.lean

@@ -96,14 +96,14 @@ The following operations are given `@[csimp]` replacements below:
 /-! ### flatMap  -/
 
 /-- Tail recursive version of `List.flatMap`. -/
-@[inline] def flatMapTR (f : α → List β) (as : List α) : List β := go as #[] where
+@[inline] def flatMapTR (as : List α) (f : α → List β) : List β := go as #[] where
   /-- Auxiliary for `flatMap`: `flatMap.go f as = acc.toList ++ bind f as` -/
   @[specialize] go : List α → Array β → List β
   | [], acc => acc.toList
   | x::xs, acc => go xs (acc ++ f x)
 
 @[csimp] theorem flatMap_eq_flatMapTR : @List.flatMap = @flatMapTR := by
-  funext α β f as
+  funext α β as f
   let rec go : ∀ as acc, flatMapTR.go f as acc = acc.toList ++ as.flatMap f
     | [], acc => by simp [flatMapTR.go, flatMap]
     | x::xs, acc => by simp [flatMapTR.go, flatMap, go xs]
@@ -112,7 +112,7 @@ The following operations are given `@[csimp]` replacements below:
 /-! ### flatten -/
 
 /-- Tail recursive version of `List.flatten`. -/
-@[inline] def flattenTR (l : List (List α)) : List α := l.flatMapTR id
+@[inline] def flattenTR (l : List (List α)) : List α := flatMapTR l id
 
 @[csimp] theorem flatten_eq_flattenTR : @flatten = @flattenTR := by
   funext α l; rw [← List.flatMap_id, List.flatMap_eq_flatMapTR]; rfl

src/Init/Data/List/Lemmas.lean

@@ -1,8 +1,7 @@
 /-
 Copyright (c) 2014 Parikshit Khanna. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro,
-  Kim Morrison
+Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
 -/
 prelude
 import Init.Data.Bool
@@ -758,6 +757,207 @@ theorem length_eq_of_beq [BEq α] {l₁ l₂ : List α} (h : l₁ == l₂) : l
     | nil => simp
     | cons b l₂ => simp [isEqv, ih]
 
+/-! ### foldlM and foldrM -/
+
+@[simp] theorem foldlM_reverse [Monad m] (l : List α) (f : β → α → m β) (b) :
+    l.reverse.foldlM f b = l.foldrM (fun x y => f y x) b := rfl
+
+@[simp] theorem foldlM_append [Monad m] [LawfulMonad m] (f : β → α → m β) (b) (l l' : List α) :
+    (l ++ l').foldlM f b = l.foldlM f b >>= l'.foldlM f := by
+  induction l generalizing b <;> simp [*]
+
+@[simp] theorem foldrM_cons [Monad m] [LawfulMonad m] (a : α) (l) (f : α → β → m β) (b) :
+    (a :: l).foldrM f b = l.foldrM f b >>= f a := by
+  simp only [foldrM]
+  induction l <;> simp_all
+
+theorem foldl_eq_foldlM (f : β → α → β) (b) (l : List α) :
+    l.foldl f b = l.foldlM (m := Id) f b := by
+  induction l generalizing b <;> simp [*, foldl]
+
+theorem foldr_eq_foldrM (f : α → β → β) (b) (l : List α) :
+    l.foldr f b = l.foldrM (m := Id) f b := by
+  induction l <;> simp [*, foldr]
+
+@[simp] theorem id_run_foldlM (f : β → α → Id β) (b) (l : List α) :
+    Id.run (l.foldlM f b) = l.foldl f b := (foldl_eq_foldlM f b l).symm
+
+@[simp] theorem id_run_foldrM (f : α → β → Id β) (b) (l : List α) :
+    Id.run (l.foldrM f b) = l.foldr f b := (foldr_eq_foldrM f b l).symm
+
+/-! ### foldl and foldr -/
+
+@[simp] theorem foldr_cons_eq_append (l : List α) : l.foldr cons l' = l ++ l' := by
+  induction l <;> simp [*]
+
+@[deprecated foldr_cons_eq_append (since := "2024-08-22")] abbrev foldr_self_append := @foldr_cons_eq_append
+
+@[simp] theorem foldl_flip_cons_eq_append (l : List α) : l.foldl (fun x y => y :: x) l' = l.reverse ++ l' := by
+  induction l generalizing l' <;> simp [*]
+
+theorem foldr_cons_nil (l : List α) : l.foldr cons [] = l := by simp
+
+@[deprecated foldr_cons_nil (since := "2024-09-04")] abbrev foldr_self := @foldr_cons_nil
+
+theorem foldl_map (f : β₁ → β₂) (g : α → β₂ → α) (l : List β₁) (init : α) :
+    (l.map f).foldl g init = l.foldl (fun x y => g x (f y)) init := by
+  induction l generalizing init <;> simp [*]
+
+theorem foldr_map (f : α₁ → α₂) (g : α₂ → β → β) (l : List α₁) (init : β) :
+    (l.map f).foldr g init = l.foldr (fun x y => g (f x) y) init := by
+  induction l generalizing init <;> simp [*]
+
+theorem foldl_filterMap (f : α → Option β) (g : γ → β → γ) (l : List α) (init : γ) :
+    (l.filterMap f).foldl g init = l.foldl (fun x y => match f y with | some b => g x b | none => x) init := by
+  induction l generalizing init with
+  | nil => rfl
+  | cons a l ih =>
+    simp only [filterMap_cons, foldl_cons]
+    cases f a <;> simp [ih]
+
+theorem foldr_filterMap (f : α → Option β) (g : β → γ → γ) (l : List α) (init : γ) :
+    (l.filterMap f).foldr g init = l.foldr (fun x y => match f x with | some b => g b y | none => y) init := by
+  induction l generalizing init with
+  | nil => rfl
+  | cons a l ih =>
+    simp only [filterMap_cons, foldr_cons]
+    cases f a <;> simp [ih]
+
+theorem foldl_map' (g : α → β) (f : α → α → α) (f' : β → β → β) (a : α) (l : List α)
+    (h : ∀ x y, f' (g x) (g y) = g (f x y)) :
+    (l.map g).foldl f' (g a) = g (l.foldl f a) := by
+  induction l generalizing a
+  · simp
+  · simp [*, h]
+
+theorem foldr_map' (g : α → β) (f : α → α → α) (f' : β → β → β) (a : α) (l : List α)
+    (h : ∀ x y, f' (g x) (g y) = g (f x y)) :
+    (l.map g).foldr f' (g a) = g (l.foldr f a) := by
+  induction l generalizing a
+  · simp
+  · simp [*, h]
+
+theorem foldl_assoc {op : α → α → α} [ha : Std.Associative op] :
+    ∀ {l : List α} {a₁ a₂}, l.foldl op (op a₁ a₂) = op a₁ (l.foldl op a₂)
+  | [], a₁, a₂ => rfl
+  | a :: l, a₁, a₂ => by
+    simp only [foldl_cons, ha.assoc]
+    rw [foldl_assoc]
+
+theorem foldr_assoc {op : α → α → α} [ha : Std.Associative op] :
+    ∀ {l : List α} {a₁ a₂}, l.foldr op (op a₁ a₂) = op (l.foldr op a₁) a₂
+  | [], a₁, a₂ => rfl
+  | a :: l, a₁, a₂ => by
+    simp only [foldr_cons, ha.assoc]
+    rw [foldr_assoc]
+
+theorem foldl_hom (f : α₁ → α₂) (g₁ : α₁ → β → α₁) (g₂ : α₂ → β → α₂) (l : List β) (init : α₁)
+    (H : ∀ x y, g₂ (f x) y = f (g₁ x y)) : l.foldl g₂ (f init) = f (l.foldl g₁ init) := by
+  induction l generalizing init <;> simp [*, H]
+
+theorem foldr_hom (f : β₁ → β₂) (g₁ : α → β₁ → β₁) (g₂ : α → β₂ → β₂) (l : List α) (init : β₁)
+    (H : ∀ x y, g₂ x (f y) = f (g₁ x y)) : l.foldr g₂ (f init) = f (l.foldr g₁ init) := by
+  induction l <;> simp [*, H]
+
+/--
+Prove a proposition about the result of `List.foldl`,
+by proving it for the initial data,
+and the implication that the operation applied to any element of the list preserves the property.
+
+The motive can take values in `Sort _`, so this may be used to construct data,
+as well as to prove propositions.
+-/
+def foldlRecOn {motive : β → Sort _} : ∀ (l : List α) (op : β → α → β) (b : β) (_ : motive b)
+    (_ : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ l), motive (op b a)), motive (List.foldl op b l)
+  | [], _, _, hb, _ => hb
+  | hd :: tl, op, b, hb, hl =>
+    foldlRecOn tl op (op b hd) (hl b hb hd (mem_cons_self hd tl))
+      fun y hy x hx => hl y hy x (mem_cons_of_mem hd hx)
+
+@[simp] theorem foldlRecOn_nil {motive : β → Sort _} (hb : motive b)
+    (hl : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ []), motive (op b a)) :
+    foldlRecOn [] op b hb hl = hb := rfl
+
+@[simp] theorem foldlRecOn_cons {motive : β → Sort _} (hb : motive b)
+    (hl : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ x :: l), motive (op b a)) :
+    foldlRecOn (x :: l) op b hb hl =
+      foldlRecOn l op (op b x) (hl b hb x (mem_cons_self x l))
+        (fun b c a m => hl b c a (mem_cons_of_mem x m)) :=
+  rfl
+
+/--
+Prove a proposition about the result of `List.foldr`,
+by proving it for the initial data,
+and the implication that the operation applied to any element of the list preserves the property.
+
+The motive can take values in `Sort _`, so this may be used to construct data,
+as well as to prove propositions.
+-/
+def foldrRecOn {motive : β → Sort _} : ∀ (l : List α) (op : α → β → β) (b : β) (_ : motive b)
+    (_ : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ l), motive (op a b)), motive (List.foldr op b l)
+  | nil, _, _, hb, _ => hb
+  | x :: l, op, b, hb, hl =>
+    hl (foldr op b l)
+      (foldrRecOn l op b hb fun b c a m => hl b c a (mem_cons_of_mem x m)) x (mem_cons_self x l)
+
+@[simp] theorem foldrRecOn_nil {motive : β → Sort _} (hb : motive b)
+    (hl : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ []), motive (op a b)) :
+    foldrRecOn [] op b hb hl = hb := rfl
+
+@[simp] theorem foldrRecOn_cons {motive : β → Sort _} (hb : motive b)
+    (hl : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ x :: l), motive (op a b)) :
+    foldrRecOn (x :: l) op b hb hl =
+      hl _ (foldrRecOn l op b hb fun b c a m => hl b c a (mem_cons_of_mem x m))
+        x (mem_cons_self x l) :=
+  rfl
+
+/--
+We can prove that two folds over the same list are related (by some arbitrary relation)
+if we know that the initial elements are related and the folding function, for each element of the list,
+preserves the relation.
+-/
+theorem foldl_rel {l : List α} {f g : β → α → β} {a b : β} (r : β → β → Prop)
+    (h : r a b) (h' : ∀ (a : α), a ∈ l → ∀ (c c' : β), r c c' → r (f c a) (g c' a)) :
+    r (l.foldl (fun acc a => f acc a) a) (l.foldl (fun acc a => g acc a) b) := by
+  induction l generalizing a b with
+  | nil => simp_all
+  | cons a l ih =>
+    simp only [foldl_cons]
+    apply ih
+    · simp_all
+    · exact fun a m c c' h => h' _ (by simp_all) _ _ h
+
+/--
+We can prove that two folds over the same list are related (by some arbitrary relation)
+if we know that the initial elements are related and the folding function, for each element of the list,
+preserves the relation.
+-/
+theorem foldr_rel {l : List α} {f g : α → β → β} {a b : β} (r : β → β → Prop)
+    (h : r a b) (h' : ∀ (a : α), a ∈ l → ∀ (c c' : β), r c c' → r (f a c) (g a c')) :
+    r (l.foldr (fun a acc => f a acc) a) (l.foldr (fun a acc => g a acc) b) := by
+  induction l generalizing a b with
+  | nil => simp_all
+  | cons a l ih =>
+    simp only [foldr_cons]
+    apply h'
+    · simp
+    · exact ih h fun a m c c' h => h' _ (by simp_all) _ _ h
+
+@[simp] theorem foldl_add_const (l : List α) (a b : Nat) :
+    l.foldl (fun x _ => x + a) b = b + a * l.length := by
+  induction l generalizing b with
+  | nil => simp
+  | cons y l ih =>
+    simp only [foldl_cons, ih, length_cons, Nat.mul_add, Nat.mul_one, Nat.add_assoc,
+      Nat.add_comm a]
+
+@[simp] theorem foldr_add_const (l : List α) (a b : Nat) :
+    l.foldr (fun _ x => x + a) b = b + a * l.length := by
+  induction l generalizing b with
+  | nil => simp
+  | cons y l ih =>
+    simp only [foldr_cons, ih, length_cons, Nat.mul_add, Nat.mul_one, Nat.add_assoc]
+
 /-! ### getLast -/
 
 theorem getLast_eq_getElem : ∀ (l : List α) (h : l ≠ []),
@@ -1016,6 +1216,27 @@ theorem getLast?_tail (l : List α) : (tail l).getLast? = if l.length = 1 then n
 
 /-! ### map -/
 
+@[simp] theorem map_id_fun : map (id : α → α) = id := by
+  funext l
+  induction l <;> simp_all
+
+/-- `map_id_fun'` differs from `map_id_fun` by representing the identity function as a lambda, rather than `id`. -/
+@[simp] theorem map_id_fun' : map (fun (a : α) => a) = id := map_id_fun
+
+-- This is not a `@[simp]` lemma because `map_id_fun` will apply.
+theorem map_id (l : List α) : map (id : α → α) l = l := by
+  induction l <;> simp_all
+
+/-- `map_id'` differs from `map_id` by representing the identity function as a lambda, rather than `id`. -/
+-- This is not a `@[simp]` lemma because `map_id_fun'` will apply.
+theorem map_id' (l : List α) : map (fun (a : α) => a) l = l := map_id l
+
+/-- Variant of `map_id`, with a side condition that the function is pointwise the identity. -/
+theorem map_id'' {f : α → α} (h : ∀ x, f x = x) (l : List α) : map f l = l := by
+  simp [show f = id from funext h]
+
+theorem map_singleton (f : α → β) (a : α) : map f [a] = [f a] := rfl
+
 @[simp] theorem length_map (as : List α) (f : α → β) : (as.map f).length = as.length := by
   induction as with
   | nil => simp [List.map]
@@ -1041,27 +1262,6 @@ theorem get_map (f : α → β) {l i} :
     get (map f l) i = f (get l ⟨i, length_map l f ▸ i.2⟩) := by
   simp
 
-@[simp] theorem map_id_fun : map (id : α → α) = id := by
-  funext l
-  induction l <;> simp_all
-
-/-- `map_id_fun'` differs from `map_id_fun` by representing the identity function as a lambda, rather than `id`. -/
-@[simp] theorem map_id_fun' : map (fun (a : α) => a) = id := map_id_fun
-
--- This is not a `@[simp]` lemma because `map_id_fun` will apply.
-theorem map_id (l : List α) : map (id : α → α) l = l := by
-  induction l <;> simp_all
-
-/-- `map_id'` differs from `map_id` by representing the identity function as a lambda, rather than `id`. -/
--- This is not a `@[simp]` lemma because `map_id_fun'` will apply.
-theorem map_id' (l : List α) : map (fun (a : α) => a) l = l := map_id l
-
-/-- Variant of `map_id`, with a side condition that the function is pointwise the identity. -/
-theorem map_id'' {f : α → α} (h : ∀ x, f x = x) (l : List α) : map f l = l := by
-  simp [show f = id from funext h]
-
-theorem map_singleton (f : α → β) (a : α) : map f [a] = [f a] := rfl
-
 @[simp] theorem mem_map {f : α → β} : ∀ {l : List α}, b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b
   | [] => by simp
   | _ :: l => by simp [mem_map (l := l), eq_comm (a := b)]
@@ -1076,31 +1276,9 @@ theorem forall_mem_map {f : α → β} {l : List α} {P : β → Prop} :
 
 @[deprecated forall_mem_map (since := "2024-07-25")] abbrev forall_mem_map_iff := @forall_mem_map
 
-@[simp] theorem map_eq_nil_iff {f : α → β} {l : List α} : map f l = [] ↔ l = [] := by
-  constructor <;> exact fun _ => match l with | [] => rfl
-
-@[deprecated map_eq_nil_iff (since := "2024-09-05")] abbrev map_eq_nil := @map_eq_nil_iff
-
-theorem eq_nil_of_map_eq_nil {f : α → β} {l : List α} (h : map f l = []) : l = [] :=
-  map_eq_nil_iff.mp h
-
 @[simp] theorem map_inj_left {f g : α → β} : map f l = map g l ↔ ∀ a ∈ l, f a = g a := by
   induction l <;> simp_all
 
-theorem map_inj_right {f : α → β} (w : ∀ x y, f x = f y → x = y) : map f l = map f l' ↔ l = l' := by
-  induction l generalizing l' with
-  | nil => simp
-  | cons a l ih =>
-    simp only [map_cons]
-    cases l' with
-    | nil => simp
-    | cons a' l' =>
-      simp only [map_cons, cons.injEq, ih, and_congr_left_iff]
-      intro h
-      constructor
-      · apply w
-      · simp +contextual
-
 theorem map_congr_left (h : ∀ a ∈ l, f a = g a) : map f l = map g l :=
   map_inj_left.2 h
 
@@ -1109,6 +1287,14 @@ theorem map_inj : map f = map g ↔ f = g := by
   · intro h; ext a; replace h := congrFun h [a]; simpa using h
   · intro h; subst h; rfl
 
+@[simp] theorem map_eq_nil_iff {f : α → β} {l : List α} : map f l = [] ↔ l = [] := by
+  constructor <;> exact fun _ => match l with | [] => rfl
+
+@[deprecated map_eq_nil_iff (since := "2024-09-05")] abbrev map_eq_nil := @map_eq_nil_iff
+
+theorem eq_nil_of_map_eq_nil {f : α → β} {l : List α} (h : map f l = []) : l = [] :=
+  map_eq_nil_iff.mp h
+
 theorem map_eq_cons_iff {f : α → β} {l : List α} :
     map f l = b :: l₂ ↔ ∃ a l₁, l = a :: l₁ ∧ f a = b ∧ map f l₁ = l₂ := by
   cases l
@@ -1129,10 +1315,6 @@ theorem map_eq_cons_iff' {f : α → β} {l : List α} :
 
 @[deprecated map_eq_cons' (since := "2024-09-05")] abbrev map_eq_cons' := @map_eq_cons_iff'
 
-@[simp] theorem map_eq_singleton_iff {f : α → β} {l : List α} {b : β} :
-    map f l = [b] ↔ ∃ a, l = [a] ∧ f a = b := by
-  simp [map_eq_cons_iff]
-
 theorem map_eq_map_iff : map f l = map g l ↔ ∀ a ∈ l, f a = g a := by
   induction l <;> simp
 
@@ -1299,7 +1481,7 @@ theorem map_filter_eq_foldr (f : α → β) (p : α → Bool) (as : List α) :
 @[simp] 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]
+  | a :: l₁, l₂ => by simp [filter]; split <;> simp [filter_append l₁]
 
 theorem filter_eq_cons_iff {l} {a} {as} :
     filter p l = a :: as ↔
@@ -1508,34 +1690,6 @@ 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] 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 :=
-  mt mem_append.1 $ not_or.mpr ⟨h₁, h₂⟩
-
-@[deprecated mem_append (since := "2025-01-13")]
-theorem mem_append_eq (a : α) (s t : List α) : (a ∈ s ++ t) = (a ∈ s ∨ a ∈ t) :=
-  propext mem_append
-
-@[deprecated mem_append_left (since := "2024-11-20")] abbrev mem_append_of_mem_left := @mem_append_left
-@[deprecated mem_append_right (since := "2024-11-20")] abbrev mem_append_of_mem_right := @mem_append_right
-
-/--
-See also `eq_append_cons_of_mem`, which proves a stronger version
-in which the initial list must not contain the element.
--/
-theorem append_of_mem {a : α} {l : List α} : a ∈ l → ∃ s t : List α, l = s ++ a :: t
-  | .head l => ⟨[], l, rfl⟩
-  | .tail b h => let ⟨s, t, h'⟩ := append_of_mem h; ⟨b::s, t, by rw [h', cons_append]⟩
-
-theorem mem_iff_append {a : α} {l : List α} : a ∈ l ↔ ∃ s t : List α, l = s ++ a :: t :=
-  ⟨append_of_mem, fun ⟨s, t, e⟩ => e ▸ by simp⟩
-
-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]
-
 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'
@@ -1603,6 +1757,14 @@ theorem get_of_append {l : List α} (eq : l = l₁ ++ a :: l₂) (h : l₁.lengt
     l.get ⟨i, get_of_append_proof eq h⟩ = a := Option.some.inj <| by
   rw [← get?_eq_get, eq, get?_append_right (h ▸ Nat.le_refl _), h, Nat.sub_self]; rfl
 
+/--
+See also `eq_append_cons_of_mem`, which proves a stronger version
+in which the initial list must not contain the element.
+-/
+theorem append_of_mem {a : α} {l : List α} : a ∈ l → ∃ s t : List α, l = s ++ a :: t
+  | .head l => ⟨[], l, rfl⟩
+  | .tail b h => let ⟨s, t, h'⟩ := append_of_mem h; ⟨b::s, t, by rw [h', cons_append]⟩
+
 @[simp 1100] theorem singleton_append : [x] ++ l = x :: l := rfl
 
 theorem append_inj :
@@ -1619,8 +1781,8 @@ theorem append_inj_left (h : s₁ ++ t₁ = s₂ ++ t₂) (hl : length s₁ = le
 
 /-- Variant of `append_inj` instead requiring equality of the lengths of the second lists. -/
 theorem append_inj' (h : s₁ ++ t₁ = s₂ ++ t₂) (hl : length t₁ = length t₂) : s₁ = s₂ ∧ t₁ = t₂ :=
-  append_inj h <| @Nat.add_right_cancel _ t₁.length _ <| by
-    let hap := congrArg length h; simp only [length_append, ← hl] at hap; exact hap
+  append_inj h <| @Nat.add_right_cancel _ (length t₁) _ <| by
+  let hap := congrArg length h; simp only [length_append, ← hl] at hap; exact hap
 
 /-- Variant of `append_inj_right` instead requiring equality of the lengths of the second lists. -/
 theorem append_inj_right' (h : s₁ ++ t₁ = s₂ ++ t₂) (hl : length t₁ = length t₂) : t₁ = t₂ :=
@@ -1648,6 +1810,9 @@ theorem append_left_inj {s₁ s₂ : List α} (t) : s₁ ++ t = s₂ ++ t ↔ s
 @[simp] theorem self_eq_append_right {x y : List α} : x = x ++ y ↔ y = [] := by
   rw [eq_comm, append_right_eq_self]
 
+@[simp] theorem append_eq_nil : p ++ q = [] ↔ p = [] ∧ q = [] := by
+  cases p <;> simp
+
 theorem getLast_concat {a : α} : ∀ (l : List α), getLast (l ++ [a]) (by simp) = a
   | [] => rfl
   | a::t => by
@@ -1673,54 +1838,6 @@ theorem get?_append {l₁ l₂ : List α} {n : Nat} (hn : n < l₁.length) :
     (l₁ ++ l₂).get? n = l₁.get? n := by
   simp [getElem?_append_left hn]
 
-@[simp] theorem append_eq_nil_iff : p ++ q = [] ↔ p = [] ∧ q = [] := by
-  cases p <;> simp
-
-@[deprecated append_eq_nil_iff (since := "2025-01-13")] abbrev append_eq_nil := @append_eq_nil_iff
-
-@[simp] theorem nil_eq_append_iff : [] = a ++ b ↔ a = [] ∧ b = [] := by
-  rw [eq_comm, append_eq_nil_iff]
-
-@[deprecated nil_eq_append_iff (since := "2024-07-24")] abbrev nil_eq_append := @nil_eq_append_iff
-
-theorem append_ne_nil_of_left_ne_nil {s : List α} (h : s ≠ []) (t : List α) : s ++ t ≠ [] := by simp_all
-theorem append_ne_nil_of_right_ne_nil (s : List α) : t ≠ [] → s ++ t ≠ [] := by simp_all
-
-@[deprecated append_ne_nil_of_left_ne_nil (since := "2024-07-24")]
-theorem append_ne_nil_of_ne_nil_left {s : List α} (h : s ≠ []) (t : List α) : s ++ t ≠ [] := by simp_all
-@[deprecated append_ne_nil_of_right_ne_nil (since := "2024-07-24")]
-theorem append_ne_nil_of_ne_nil_right (s : List α) : t ≠ [] → s ++ t ≠ [] := by simp_all
-
-theorem append_eq_cons_iff :
-    a ++ b = x :: c ↔ (a = [] ∧ b = x :: c) ∨ (∃ a', a = x :: a' ∧ c = a' ++ b) := by
-  cases a with simp | cons a as => ?_
-  exact ⟨fun h => ⟨as, by simp [h]⟩, fun ⟨a', ⟨aeq, aseq⟩, h⟩ => ⟨aeq, by rw [aseq, h]⟩⟩
-
-@[deprecated append_eq_cons_iff (since := "2024-07-24")] abbrev append_eq_cons := @append_eq_cons_iff
-
-theorem cons_eq_append_iff :
-    x :: c = a ++ b ↔ (a = [] ∧ b = x :: c) ∨ (∃ a', a = x :: a' ∧ c = a' ++ b) := by
-  rw [eq_comm, append_eq_cons_iff]
-
-@[deprecated cons_eq_append_iff (since := "2024-07-24")] abbrev cons_eq_append := @cons_eq_append_iff
-
-theorem append_eq_singleton_iff :
-    a ++ b = [x] ↔ (a = [] ∧ b = [x]) ∨ (a = [x] ∧ b = []) := by
-  cases a <;> cases b <;> simp
-
-theorem singleton_eq_append_iff :
-    [x] = a ++ b ↔ (a = [] ∧ b = [x]) ∨ (a = [x] ∧ b = []) := by
-  cases a <;> cases b <;> simp [eq_comm]
-
-theorem append_eq_append_iff {a b c d : List α} :
-    a ++ b = c ++ d ↔ (∃ a', c = a ++ a' ∧ b = a' ++ d) ∨ ∃ c', a = c ++ c' ∧ d = c' ++ b := by
-  induction a generalizing c with
-  | nil => simp_all
-  | cons a as ih => cases c <;> simp [eq_comm, and_assoc, ih, and_or_left]
-
-@[deprecated append_inj (since := "2024-07-24")] abbrev append_inj_of_length_left := @append_inj
-@[deprecated append_inj' (since := "2024-07-24")] abbrev append_inj_of_length_right := @append_inj'
-
 @[simp] theorem head_append_of_ne_nil {l : List α} {w₁} (w₂) :
     head (l ++ l') w₁ = head l w₂ := by
   match l, w₂ with
@@ -1770,6 +1887,60 @@ theorem tail_append {l l' : List α} : (l ++ l').tail = if l.isEmpty then l'.tai
 
 @[deprecated tail_append_of_ne_nil (since := "2024-07-24")] abbrev tail_append_left := @tail_append_of_ne_nil
 
+theorem nil_eq_append_iff : [] = a ++ b ↔ a = [] ∧ b = [] := by
+  rw [eq_comm, append_eq_nil]
+
+@[deprecated nil_eq_append_iff (since := "2024-07-24")] abbrev nil_eq_append := @nil_eq_append_iff
+
+theorem append_ne_nil_of_left_ne_nil {s : List α} (h : s ≠ []) (t : List α) : s ++ t ≠ [] := by simp_all
+theorem append_ne_nil_of_right_ne_nil (s : List α) : t ≠ [] → s ++ t ≠ [] := by simp_all
+
+@[deprecated append_ne_nil_of_left_ne_nil (since := "2024-07-24")]
+theorem append_ne_nil_of_ne_nil_left {s : List α} (h : s ≠ []) (t : List α) : s ++ t ≠ [] := by simp_all
+@[deprecated append_ne_nil_of_right_ne_nil (since := "2024-07-24")]
+theorem append_ne_nil_of_ne_nil_right (s : List α) : t ≠ [] → s ++ t ≠ [] := by simp_all
+
+theorem append_eq_cons_iff :
+    a ++ b = x :: c ↔ (a = [] ∧ b = x :: c) ∨ (∃ a', a = x :: a' ∧ c = a' ++ b) := by
+  cases a with simp | cons a as => ?_
+  exact ⟨fun h => ⟨as, by simp [h]⟩, fun ⟨a', ⟨aeq, aseq⟩, h⟩ => ⟨aeq, by rw [aseq, h]⟩⟩
+
+@[deprecated append_eq_cons_iff (since := "2024-07-24")] abbrev append_eq_cons := @append_eq_cons_iff
+
+theorem cons_eq_append_iff :
+    x :: c = a ++ b ↔ (a = [] ∧ b = x :: c) ∨ (∃ a', a = x :: a' ∧ c = a' ++ b) := by
+  rw [eq_comm, append_eq_cons_iff]
+
+@[deprecated cons_eq_append_iff (since := "2024-07-24")] abbrev cons_eq_append := @cons_eq_append_iff
+
+theorem append_eq_append_iff {a b c d : List α} :
+    a ++ b = c ++ d ↔ (∃ a', c = a ++ a' ∧ b = a' ++ d) ∨ ∃ c', a = c ++ c' ∧ d = c' ++ b := by
+  induction a generalizing c with
+  | nil => simp_all
+  | cons a as ih => cases c <;> simp [eq_comm, and_assoc, ih, and_or_left]
+
+@[deprecated append_inj (since := "2024-07-24")] abbrev append_inj_of_length_left := @append_inj
+@[deprecated append_inj' (since := "2024-07-24")] abbrev append_inj_of_length_right := @append_inj'
+
+@[simp] 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 :=
+  mt mem_append.1 $ not_or.mpr ⟨h₁, h₂⟩
+
+theorem mem_append_eq (a : α) (s t : List α) : (a ∈ s ++ t) = (a ∈ s ∨ a ∈ t) :=
+  propext mem_append
+
+@[deprecated mem_append_left (since := "2024-11-20")] abbrev mem_append_of_mem_left := @mem_append_left
+@[deprecated mem_append_right (since := "2024-11-20")] abbrev mem_append_of_mem_right := @mem_append_right
+
+theorem mem_iff_append {a : α} {l : List α} : a ∈ l ↔ ∃ s t : List α, l = s ++ a :: t :=
+  ⟨append_of_mem, fun ⟨s, t, e⟩ => e ▸ by simp⟩
+
+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]
+
 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
@@ -1790,6 +1961,16 @@ theorem set_append {s t : List α} :
     (s ++ t).set i x = s ++ t.set (i - s.length) x := by
   rw [set_append, if_neg (by simp_all)]
 
+@[simp] theorem foldrM_append [Monad m] [LawfulMonad m] (f : α → β → m β) (b) (l l' : List α) :
+    (l ++ l').foldrM f b = l'.foldrM f b >>= l.foldrM f := by
+  induction l <;> simp [*]
+
+@[simp] theorem foldl_append {β : Type _} (f : β → α → β) (b) (l l' : List α) :
+    (l ++ l').foldl f b = l'.foldl f (l.foldl f b) := by simp [foldl_eq_foldlM]
+
+@[simp] theorem foldr_append (f : α → β → β) (b) (l l' : List α) :
+    (l ++ l').foldr f b = l.foldr f (l'.foldr f b) := by simp [foldr_eq_foldrM]
+
 theorem filterMap_eq_append_iff {f : α → Option β} :
     filterMap f l = L₁ ++ L₂ ↔ ∃ l₁ l₂, l = l₁ ++ l₂ ∧ filterMap f l₁ = L₁ ∧ filterMap f l₂ = L₂ := by
   constructor
@@ -1898,7 +2079,7 @@ theorem eq_nil_or_concat : ∀ l : List α, l = [] ∨ ∃ L b, l = concat L b
 
 /-! ### flatten -/
 
-@[simp] theorem length_flatten (L : List (List α)) : L.flatten.length = (L.map length).sum := by
+@[simp] theorem length_flatten (L : List (List α)) : (flatten L).length = (L.map length).sum := by
   induction L with
   | nil => rfl
   | cons =>
@@ -1913,9 +2094,6 @@ theorem flatten_singleton (l : List α) : [l].flatten = l := by simp
 @[simp] theorem flatten_eq_nil_iff {L : List (List α)} : L.flatten = [] ↔ ∀ l ∈ L, l = [] := by
   induction L <;> simp_all
 
-@[simp] theorem nil_eq_flatten_iff {L : List (List α)} : [] = L.flatten ↔ ∀ l ∈ L, l = [] := by
-  rw [eq_comm, flatten_eq_nil_iff]
-
 theorem flatten_ne_nil_iff {xs : List (List α)} : xs.flatten ≠ [] ↔ ∃ x, x ∈ xs ∧ x ≠ [] := by
   simp
 
@@ -1941,8 +2119,15 @@ theorem head?_flatten {L : List (List α)} : (flatten L).head? = L.findSome? fun
 -- `getLast?_flatten` is proved later, after the `reverse` section.
 -- `head_flatten` and `getLast_flatten` are proved in `Init.Data.List.Find`.
 
-@[simp] theorem map_flatten (f : α → β) (L : List (List α)) :
-    (flatten L).map f = (map (map f) L).flatten := by
+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
+
+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] theorem map_flatten (f : α → β) (L : List (List α)) : map f (flatten L) = flatten (map (map f) L) := by
   induction L <;> simp_all
 
 @[simp] theorem filterMap_flatten (f : α → Option β) (L : List (List α)) :
@@ -1995,26 +2180,6 @@ theorem flatten_eq_cons_iff {xs : List (List α)} {y : α} {ys : List α} :
   · rintro ⟨as, bs, cs, rfl, h₁, rfl⟩
     simp [flatten_eq_nil_iff.mpr h₁]
 
-theorem cons_eq_flatten_iff {xs : List (List α)} {y : α} {ys : List α} :
-    y :: ys = xs.flatten ↔
-      ∃ as bs cs, xs = as ++ (y :: bs) :: cs ∧ (∀ l, l ∈ as → l = []) ∧ ys = bs ++ cs.flatten := by
-  rw [eq_comm, flatten_eq_cons_iff]
-
-theorem flatten_eq_singleton_iff {xs : List (List α)} {y : α} :
-    xs.flatten = [y] ↔ ∃ as bs, xs = as ++ [y] :: bs ∧ (∀ l, l ∈ as → l = []) ∧ (∀ l, l ∈ bs → l = []) := by
-  rw [flatten_eq_cons_iff]
-  constructor
-  · rintro ⟨as, bs, cs, rfl, h₁, h₂⟩
-    simp at h₂
-    obtain ⟨rfl, h₂⟩ := h₂
-    exact ⟨as, cs, by simp, h₁, h₂⟩
-  · rintro ⟨as, bs, rfl, h₁, h₂⟩
-    exact ⟨as, [], bs, rfl, h₁, by simpa⟩
-
-theorem singleton_eq_flatten_iff {xs : List (List α)} {y : α} :
-    [y] = xs.flatten ↔ ∃ as bs, xs = as ++ [y] :: bs ∧ (∀ l, l ∈ as → l = []) ∧ (∀ l, l ∈ bs → l = []) := by
-  rw [eq_comm, flatten_eq_singleton_iff]
-
 theorem flatten_eq_append_iff {xs : List (List α)} {ys zs : List α} :
     xs.flatten = ys ++ zs ↔
       (∃ as bs, xs = as ++ bs ∧ ys = as.flatten ∧ zs = bs.flatten) ∨
@@ -2023,8 +2188,8 @@ theorem flatten_eq_append_iff {xs : List (List α)} {ys zs : List α} :
   constructor
   · induction xs generalizing ys with
     | nil =>
-      simp only [flatten_nil, nil_eq, append_eq_nil_iff, and_false, cons_append, false_and,
-        exists_const, exists_false, or_false, and_imp, List.cons_ne_nil]
+      simp only [flatten_nil, nil_eq, append_eq_nil, and_false, cons_append, false_and, exists_const,
+        exists_false, or_false, and_imp, List.cons_ne_nil]
       rintro rfl rfl
       exact ⟨[], [], by simp⟩
     | cons x xs ih =>
@@ -2043,13 +2208,6 @@ theorem flatten_eq_append_iff {xs : List (List α)} {ys zs : List α} :
     · simp
     · simp
 
-theorem append_eq_flatten_iff {xs : List (List α)} {ys zs : List α} :
-    ys ++ zs = xs.flatten ↔
-      (∃ as bs, xs = as ++ bs ∧ ys = as.flatten ∧ zs = bs.flatten) ∨
-        ∃ as bs c cs ds, xs = as ++ (bs ++ c :: cs) :: ds ∧ ys = as.flatten ++ bs ∧
-          zs = c :: cs ++ ds.flatten := by
-  rw [eq_comm, flatten_eq_append_iff]
-
 /-- Two lists of sublists are equal iff their flattens coincide, as well as the lengths of the
 sublists. -/
 theorem eq_iff_flatten_eq : ∀ {L L' : List (List α)},
@@ -2070,14 +2228,12 @@ theorem eq_iff_flatten_eq : ∀ {L L' : List (List α)},
 
 theorem flatMap_def (l : List α) (f : α → List β) : l.flatMap f = flatten (map f l) := by rfl
 
-@[simp] theorem flatMap_id (l : List (List α)) : l.flatMap id = l.flatten := by simp [flatMap_def]
-
-@[simp] theorem flatMap_id' (l : List (List α)) : l.flatMap (fun a => a) = l.flatten := by simp [flatMap_def]
+@[simp] theorem flatMap_id (l : List (List α)) : List.flatMap l id = l.flatten := by simp [flatMap_def]
 
 @[simp]
 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]
+    length (l.flatMap f) = sum (map (length ∘ f) l) := by
+  rw [List.flatMap, length_flatten, map_map]
 
 @[simp] 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]
@@ -2090,7 +2246,7 @@ theorem mem_flatMap_of_mem {b : β} {l : List α} {f : α → List β} {a} (al :
     b ∈ l.flatMap f := mem_flatMap.2 ⟨a, al, h⟩
 
 @[simp]
-theorem flatMap_eq_nil_iff {l : List α} {f : α → List β} : l.flatMap f = [] ↔ ∀ x ∈ l, f x = [] :=
+theorem flatMap_eq_nil_iff {l : List α} {f : α → List β} : List.flatMap l f = [] ↔ ∀ x ∈ l, f x = [] :=
   flatten_eq_nil_iff.trans <| by
     simp only [mem_map, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂]
 
@@ -2395,9 +2551,6 @@ theorem replicateRecOn {α : Type _} {p : List α → Prop} (m : List α)
     exact hi _ _ _ _ h hn (replicateRecOn (b :: l') h0 hr hi)
 termination_by m.length
 
-@[simp] theorem sum_replicate_nat (n : Nat) (a : Nat) : (replicate n a).sum = n * a := by
-  induction n <;> simp_all [replicate_succ, Nat.add_mul, Nat.add_comm]
-
 /-! ### reverse -/
 
 @[simp] theorem length_reverse (as : List α) : (as.reverse).length = as.length := by
@@ -2546,114 +2699,10 @@ theorem flatMap_reverse {β} (l : List α) (f : α → List β) : (l.reverse.fla
 @[simp] theorem reverseAux_eq (as bs : List α) : reverseAux as bs = reverse as ++ bs :=
   reverseAux_eq_append ..
 
-@[simp] theorem reverse_replicate (n) (a : α) : reverse (replicate n a) = replicate n a :=
-  eq_replicate_iff.2
-    ⟨by rw [length_reverse, length_replicate],
-     fun _ h => eq_of_mem_replicate (mem_reverse.1 h)⟩
-
-
-/-! ### foldlM and foldrM -/
-
-@[simp] theorem foldlM_append [Monad m] [LawfulMonad m] (f : β → α → m β) (b) (l l' : List α) :
-    (l ++ l').foldlM f b = l.foldlM f b >>= l'.foldlM f := by
-  induction l generalizing b <;> simp [*]
-
-@[simp] theorem foldrM_cons [Monad m] [LawfulMonad m] (a : α) (l) (f : α → β → m β) (b) :
-    (a :: l).foldrM f b = l.foldrM f b >>= f a := by
-  simp only [foldrM]
-  induction l <;> simp_all
-
-theorem foldl_eq_foldlM (f : β → α → β) (b) (l : List α) :
-    l.foldl f b = l.foldlM (m := Id) f b := by
-  induction l generalizing b <;> simp [*, foldl]
-
-theorem foldr_eq_foldrM (f : α → β → β) (b) (l : List α) :
-    l.foldr f b = l.foldrM (m := Id) f b := by
-  induction l <;> simp [*, foldr]
-
-@[simp] theorem id_run_foldlM (f : β → α → Id β) (b) (l : List α) :
-    Id.run (l.foldlM f b) = l.foldl f b := (foldl_eq_foldlM f b l).symm
-
-@[simp] theorem id_run_foldrM (f : α → β → Id β) (b) (l : List α) :
-    Id.run (l.foldrM f b) = l.foldr f b := (foldr_eq_foldrM f b l).symm
-
-@[simp] theorem foldlM_reverse [Monad m] (l : List α) (f : β → α → m β) (b) :
-    l.reverse.foldlM f b = l.foldrM (fun x y => f y x) b := rfl
-
 @[simp] theorem foldrM_reverse [Monad m] (l : List α) (f : α → β → m β) (b) :
     l.reverse.foldrM f b = l.foldlM (fun x y => f y x) b :=
   (foldlM_reverse ..).symm.trans <| by simp
 
-/-! ### foldl and foldr -/
-
-@[simp] theorem foldr_cons_eq_append (l : List α) : l.foldr cons l' = l ++ l' := by
-  induction l <;> simp [*]
-
-@[deprecated foldr_cons_eq_append (since := "2024-08-22")] abbrev foldr_self_append := @foldr_cons_eq_append
-
-@[simp] theorem foldl_flip_cons_eq_append (l : List α) : l.foldl (fun x y => y :: x) l' = l.reverse ++ l' := by
-  induction l generalizing l' <;> simp [*]
-
-theorem foldr_cons_nil (l : List α) : l.foldr cons [] = l := by simp
-
-@[deprecated foldr_cons_nil (since := "2024-09-04")] abbrev foldr_self := @foldr_cons_nil
-
-theorem foldl_map (f : β₁ → β₂) (g : α → β₂ → α) (l : List β₁) (init : α) :
-    (l.map f).foldl g init = l.foldl (fun x y => g x (f y)) init := by
-  induction l generalizing init <;> simp [*]
-
-theorem foldr_map (f : α₁ → α₂) (g : α₂ → β → β) (l : List α₁) (init : β) :
-    (l.map f).foldr g init = l.foldr (fun x y => g (f x) y) init := by
-  induction l generalizing init <;> simp [*]
-
-theorem foldl_filterMap (f : α → Option β) (g : γ → β → γ) (l : List α) (init : γ) :
-    (l.filterMap f).foldl g init = l.foldl (fun x y => match f y with | some b => g x b | none => x) init := by
-  induction l generalizing init with
-  | nil => rfl
-  | cons a l ih =>
-    simp only [filterMap_cons, foldl_cons]
-    cases f a <;> simp [ih]
-
-theorem foldr_filterMap (f : α → Option β) (g : β → γ → γ) (l : List α) (init : γ) :
-    (l.filterMap f).foldr g init = l.foldr (fun x y => match f x with | some b => g b y | none => y) init := by
-  induction l generalizing init with
-  | nil => rfl
-  | cons a l ih =>
-    simp only [filterMap_cons, foldr_cons]
-    cases f a <;> simp [ih]
-
-theorem foldl_map' (g : α → β) (f : α → α → α) (f' : β → β → β) (a : α) (l : List α)
-    (h : ∀ x y, f' (g x) (g y) = g (f x y)) :
-    (l.map g).foldl f' (g a) = g (l.foldl f a) := by
-  induction l generalizing a
-  · simp
-  · simp [*, h]
-
-theorem foldr_map' (g : α → β) (f : α → α → α) (f' : β → β → β) (a : α) (l : List α)
-    (h : ∀ x y, f' (g x) (g y) = g (f x y)) :
-    (l.map g).foldr f' (g a) = g (l.foldr f a) := by
-  induction l generalizing a
-  · simp
-  · simp [*, h]
-
-@[simp] theorem foldrM_append [Monad m] [LawfulMonad m] (f : α → β → m β) (b) (l l' : List α) :
-    (l ++ l').foldrM f b = l'.foldrM f b >>= l.foldrM f := by
-  induction l <;> simp [*]
-
-@[simp] theorem foldl_append {β : Type _} (f : β → α → β) (b) (l l' : List α) :
-    (l ++ l').foldl f b = l'.foldl f (l.foldl f b) := by simp [foldl_eq_foldlM]
-
-@[simp] theorem foldr_append (f : α → β → β) (b) (l l' : List α) :
-    (l ++ l').foldr f b = l.foldr f (l'.foldr f b) := by simp [foldr_eq_foldrM]
-
-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
-
-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] theorem foldl_reverse (l : List α) (f : β → α → β) (b) :
     l.reverse.foldl f b = l.foldr (fun x y => f y x) b := by simp [foldl_eq_foldlM, foldr_eq_foldrM]
 
@@ -2667,127 +2716,10 @@ theorem foldl_eq_foldr_reverse (l : List α) (f : β → α → β) (b) :
 theorem foldr_eq_foldl_reverse (l : List α) (f : α → β → β) (b) :
     l.foldr f b = l.reverse.foldl (fun x y => f y x) b := by simp
 
-theorem foldl_assoc {op : α → α → α} [ha : Std.Associative op] :
-    ∀ {l : List α} {a₁ a₂}, l.foldl op (op a₁ a₂) = op a₁ (l.foldl op a₂)
-  | [], a₁, a₂ => rfl
-  | a :: l, a₁, a₂ => by
-    simp only [foldl_cons, ha.assoc]
-    rw [foldl_assoc]
-
-theorem foldr_assoc {op : α → α → α} [ha : Std.Associative op] :
-    ∀ {l : List α} {a₁ a₂}, l.foldr op (op a₁ a₂) = op (l.foldr op a₁) a₂
-  | [], a₁, a₂ => rfl
-  | a :: l, a₁, a₂ => by
-    simp only [foldr_cons, ha.assoc]
-    rw [foldr_assoc]
-
-theorem foldl_hom (f : α₁ → α₂) (g₁ : α₁ → β → α₁) (g₂ : α₂ → β → α₂) (l : List β) (init : α₁)
-    (H : ∀ x y, g₂ (f x) y = f (g₁ x y)) : l.foldl g₂ (f init) = f (l.foldl g₁ init) := by
-  induction l generalizing init <;> simp [*, H]
-
-theorem foldr_hom (f : β₁ → β₂) (g₁ : α → β₁ → β₁) (g₂ : α → β₂ → β₂) (l : List α) (init : β₁)
-    (H : ∀ x y, g₂ x (f y) = f (g₁ x y)) : l.foldr g₂ (f init) = f (l.foldr g₁ init) := by
-  induction l <;> simp [*, H]
-
-/--
-Prove a proposition about the result of `List.foldl`,
-by proving it for the initial data,
-and the implication that the operation applied to any element of the list preserves the property.
-
-The motive can take values in `Sort _`, so this may be used to construct data,
-as well as to prove propositions.
--/
-def foldlRecOn {motive : β → Sort _} : ∀ (l : List α) (op : β → α → β) (b : β) (_ : motive b)
-    (_ : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ l), motive (op b a)), motive (List.foldl op b l)
-  | [], _, _, hb, _ => hb
-  | hd :: tl, op, b, hb, hl =>
-    foldlRecOn tl op (op b hd) (hl b hb hd (mem_cons_self hd tl))
-      fun y hy x hx => hl y hy x (mem_cons_of_mem hd hx)
-
-@[simp] theorem foldlRecOn_nil {motive : β → Sort _} (hb : motive b)
-    (hl : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ []), motive (op b a)) :
-    foldlRecOn [] op b hb hl = hb := rfl
-
-@[simp] theorem foldlRecOn_cons {motive : β → Sort _} (hb : motive b)
-    (hl : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ x :: l), motive (op b a)) :
-    foldlRecOn (x :: l) op b hb hl =
-      foldlRecOn l op (op b x) (hl b hb x (mem_cons_self x l))
-        (fun b c a m => hl b c a (mem_cons_of_mem x m)) :=
-  rfl
-
-/--
-Prove a proposition about the result of `List.foldr`,
-by proving it for the initial data,
-and the implication that the operation applied to any element of the list preserves the property.
-
-The motive can take values in `Sort _`, so this may be used to construct data,
-as well as to prove propositions.
--/
-def foldrRecOn {motive : β → Sort _} : ∀ (l : List α) (op : α → β → β) (b : β) (_ : motive b)
-    (_ : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ l), motive (op a b)), motive (List.foldr op b l)
-  | nil, _, _, hb, _ => hb
-  | x :: l, op, b, hb, hl =>
-    hl (foldr op b l)
-      (foldrRecOn l op b hb fun b c a m => hl b c a (mem_cons_of_mem x m)) x (mem_cons_self x l)
-
-@[simp] theorem foldrRecOn_nil {motive : β → Sort _} (hb : motive b)
-    (hl : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ []), motive (op a b)) :
-    foldrRecOn [] op b hb hl = hb := rfl
-
-@[simp] theorem foldrRecOn_cons {motive : β → Sort _} (hb : motive b)
-    (hl : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ x :: l), motive (op a b)) :
-    foldrRecOn (x :: l) op b hb hl =
-      hl _ (foldrRecOn l op b hb fun b c a m => hl b c a (mem_cons_of_mem x m))
-        x (mem_cons_self x l) :=
-  rfl
-
-/--
-We can prove that two folds over the same list are related (by some arbitrary relation)
-if we know that the initial elements are related and the folding function, for each element of the list,
-preserves the relation.
--/
-theorem foldl_rel {l : List α} {f g : β → α → β} {a b : β} (r : β → β → Prop)
-    (h : r a b) (h' : ∀ (a : α), a ∈ l → ∀ (c c' : β), r c c' → r (f c a) (g c' a)) :
-    r (l.foldl (fun acc a => f acc a) a) (l.foldl (fun acc a => g acc a) b) := by
-  induction l generalizing a b with
-  | nil => simp_all
-  | cons a l ih =>
-    simp only [foldl_cons]
-    apply ih
-    · simp_all
-    · exact fun a m c c' h => h' _ (by simp_all) _ _ h
-
-/--
-We can prove that two folds over the same list are related (by some arbitrary relation)
-if we know that the initial elements are related and the folding function, for each element of the list,
-preserves the relation.
--/
-theorem foldr_rel {l : List α} {f g : α → β → β} {a b : β} (r : β → β → Prop)
-    (h : r a b) (h' : ∀ (a : α), a ∈ l → ∀ (c c' : β), r c c' → r (f a c) (g a c')) :
-    r (l.foldr (fun a acc => f a acc) a) (l.foldr (fun a acc => g a acc) b) := by
-  induction l generalizing a b with
-  | nil => simp_all
-  | cons a l ih =>
-    simp only [foldr_cons]
-    apply h'
-    · simp
-    · exact ih h fun a m c c' h => h' _ (by simp_all) _ _ h
-
-@[simp] theorem foldl_add_const (l : List α) (a b : Nat) :
-    l.foldl (fun x _ => x + a) b = b + a * l.length := by
-  induction l generalizing b with
-  | nil => simp
-  | cons y l ih =>
-    simp only [foldl_cons, ih, length_cons, Nat.mul_add, Nat.mul_one, Nat.add_assoc,
-      Nat.add_comm a]
-
-@[simp] theorem foldr_add_const (l : List α) (a b : Nat) :
-    l.foldr (fun _ x => x + a) b = b + a * l.length := by
-  induction l generalizing b with
-  | nil => simp
-  | cons y l ih =>
-    simp only [foldr_cons, ih, length_cons, Nat.mul_add, Nat.mul_one, Nat.add_assoc]
-
+@[simp] theorem reverse_replicate (n) (a : α) : reverse (replicate n a) = replicate n a :=
+  eq_replicate_iff.2
+    ⟨by rw [length_reverse, length_replicate],
+     fun _ h => eq_of_mem_replicate (mem_reverse.1 h)⟩
 
 /-! #### Further results about `getLast` and `getLast?` -/
 

src/Init/Data/List/Perm.lean

@@ -510,18 +510,4 @@ theorem Perm.eraseP (f : α → Bool) {l₁ l₂ : List α}
     refine (IH₁ H).trans (IH₂ ((p₁.pairwise_iff ?_).1 H))
     exact fun h h₁ h₂ => h h₂ h₁
 
-theorem perm_insertIdx {α} (x : α) (l : List α) {n} (h : n ≤ l.length) :
-    insertIdx n x l ~ x :: l := by
-  induction l generalizing n with
-  | nil =>
-    cases n with
-    | zero => rfl
-    | succ => cases h
-  | cons _ _ ih =>
-    cases n with
-    | zero => simp [insertIdx]
-    | succ =>
-      simp only [insertIdx, modifyTailIdx]
-      refine .trans (.cons _ (ih (Nat.le_of_succ_le_succ h))) (.swap ..)
-
 end List

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

@@ -253,10 +253,6 @@ theorem merge_perm_append : ∀ {xs ys : List α}, merge xs ys le ~ xs ++ ys
     · exact (merge_perm_append.cons y).trans
         ((Perm.swap x y _).trans (perm_middle.symm.cons x))
 
-theorem Perm.merge (s₁ s₂ : α → α → Bool) (hl : l₁ ~ l₂) (hr : r₁ ~ r₂) :
-    merge l₁ r₁ s₁ ~ merge l₂ r₂ s₂ :=
-  Perm.trans (merge_perm_append ..) <| Perm.trans (Perm.append hl hr) <| Perm.symm (merge_perm_append ..)
-
 /-! ### mergeSort -/
 
 @[simp] theorem mergeSort_nil : [].mergeSort r = [] := by rw [List.mergeSort]

src/Init/Data/List/ToArray.lean

@@ -46,7 +46,7 @@ theorem toArray_cons (a : α) (l : List α) : (a :: l).toArray = #[a] ++ l.toArr
 @[simp] theorem isEmpty_toArray (l : List α) : l.toArray.isEmpty = l.isEmpty := by
   cases l <;> simp [Array.isEmpty]
 
-@[simp] theorem toArray_singleton (a : α) : (List.singleton a).toArray = Array.singleton a := rfl
+@[simp] theorem toArray_singleton (a : α) : (List.singleton a).toArray = singleton a := rfl
 
 @[simp] theorem back!_toArray [Inhabited α] (l : List α) : l.toArray.back! = l.getLast! := by
   simp only [back!, size_toArray, Array.get!_eq_getElem!, getElem!_toArray, getLast!_eq_getElem!]
@@ -143,9 +143,6 @@ theorem forM_toArray [Monad m] (l : List α) (f : α → m PUnit) :
   subst h
   rw [foldl_toList]
 
-@[simp] theorem sum_toArray [Add α] [Zero α] (l : List α) : l.toArray.sum = l.sum := by
-  simp [Array.sum, List.sum]
-
 @[simp] theorem append_toArray (l₁ l₂ : List α) :
     l₁.toArray ++ l₂.toArray = (l₁ ++ l₂).toArray := by
   apply ext'
@@ -397,24 +394,4 @@ theorem takeWhile_go_toArray (p : α → Bool) (l : List α) (i : Nat) :
 @[deprecated toArray_replicate (since := "2024-12-13")]
 abbrev _root_.Array.mkArray_eq_toArray_replicate := @toArray_replicate
 
-@[simp] theorem flatMap_empty {β} (f : α → Array β) : (#[] : Array α).flatMap f = #[] := rfl
-
-theorem flatMap_toArray_cons {β} (f : α → Array β) (a : α) (as : List α) :
-    (a :: as).toArray.flatMap f = f a ++ as.toArray.flatMap f := by
-  simp [Array.flatMap]
-  suffices ∀ cs, List.foldl (fun bs a => bs ++ f a) (f a ++ cs) as =
-      f a ++ List.foldl (fun bs a => bs ++ f a) cs as by
-    erw [empty_append] -- Why doesn't this work via `simp`?
-    simpa using this #[]
-  intro cs
-  induction as generalizing cs <;> simp_all
-
-@[simp] theorem flatMap_toArray {β} (f : α → Array β) (as : List α) :
-    as.toArray.flatMap f = (as.flatMap (fun a => (f a).toList)).toArray := by
-  induction as with
-  | nil => simp
-  | cons a as ih =>
-    apply ext'
-    simp [ih, flatMap_toArray_cons]
-
 end List

src/Init/Data/List/Zip.lean

@@ -203,11 +203,11 @@ theorem zipWith_eq_append_iff {f : α → β → γ} {l₁ : List α} {l₂ : Li
     cases l₂ with
     | nil =>
       constructor
-      · simp only [zipWith_nil_right, nil_eq, append_eq_nil_iff, exists_and_left, and_imp]
+      · simp only [zipWith_nil_right, nil_eq, append_eq_nil, exists_and_left, and_imp]
         rintro rfl  rfl
         exact ⟨[], x₁ :: l₁, [], by simp⟩
       · rintro ⟨w, x, y, z, h₁, _, h₃, rfl, rfl⟩
-        simp only [nil_eq, append_eq_nil_iff] at h₃
+        simp only [nil_eq, append_eq_nil] at h₃
         obtain ⟨rfl, rfl⟩ := h₃
         simp
     | cons x₂ l₂ =>

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

@@ -49,17 +49,4 @@ theorem lt_div_mul_self (h : 0 < k) (w : k ≤ x) : x - k < x / k * k := by
   have : x % k < k := mod_lt x h
   omega
 
-theorem div_pos (hba : b ≤ a) (hb : 0 < b) : 0 < a / b := by
-  cases b
-  · contradiction
-  · simp [Nat.pos_iff_ne_zero, div_eq_zero_iff_lt, hba]
-
-theorem div_le_div_left (hcb : c ≤ b) (hc : 0 < c) : a / b ≤ a / c :=
-  (Nat.le_div_iff_mul_le hc).2 <|
-    Nat.le_trans (Nat.mul_le_mul_left _ hcb) (Nat.div_mul_le_self a b)
-
-theorem div_add_le_right {z : Nat} (h : 0 < z) (x y : Nat) :
-    x / (y + z) ≤ x / z :=
-  div_le_div_left (Nat.le_add_left z y) h
-
 end Nat

src/Init/Data/Nat/Lemmas.lean

@@ -622,14 +622,6 @@ protected theorem pos_of_mul_pos_right {a b : Nat} (h : 0 < a * b) : 0 < a := by
     0 < a * b ↔ 0 < a :=
   ⟨Nat.pos_of_mul_pos_right, fun w => Nat.mul_pos w h⟩
 
-protected theorem pos_of_lt_mul_left {a b c : Nat} (h : a < b * c) : 0 < c := by
-  replace h : 0 < b * c := by omega
-  exact Nat.pos_of_mul_pos_left h
-
-protected theorem pos_of_lt_mul_right {a b c : Nat} (h : a < b * c) : 0 < b := by
-  replace h : 0 < b * c := by omega
-  exact Nat.pos_of_mul_pos_right h
-
 /-! ### div/mod -/
 
 theorem mod_two_eq_zero_or_one (n : Nat) : n % 2 = 0 ∨ n % 2 = 1 :=

src/Init/Data/Option/Lemmas.lean

@@ -208,15 +208,6 @@ theorem comp_map (h : β → γ) (g : α → β) (x : Option α) : x.map (h ∘
 
 theorem mem_map_of_mem (g : α → β) (h : a ∈ x) : g a ∈ Option.map g x := h.symm ▸ map_some' ..
 
-theorem map_inj_right {f : α → β} {o o' : Option α} (w : ∀ x y, f x = f y → x = y) :
-    o.map f = o'.map f ↔ o = o' := by
-  cases o with
-  | none => cases o' <;> simp
-  | some a =>
-    cases o' with
-    | none => simp
-    | some a' => simpa using ⟨fun h => w _ _ h, fun h => congrArg f h⟩
-
 @[simp] theorem map_if {f : α → β} [Decidable c] :
      (if c then some a else none).map f = if c then some (f a) else none := by
   split <;> rfl
@@ -638,15 +629,6 @@ theorem pbind_eq_some_iff {o : Option α} {f : (a : α) → a ∈ o → Option
     · rintro ⟨h, rfl⟩
       rfl
 
-@[simp]
-theorem pmap_eq_map (p : α → Prop) (f : α → β) (o : Option α) (H) :
-    @pmap _ _ p (fun a _ => f a) o H = Option.map f o := by
-  cases o <;> simp
-
-theorem map_pmap {p : α → Prop} (g : β → γ) (f : ∀ a, p a → β) (o H) :
-    Option.map g (pmap f o H) = pmap (fun a h => g (f a h)) o H := by
-  cases o <;> simp
-
 /-! ### pelim -/
 
 @[simp] theorem pelim_none : pelim none b f = b := rfl

src/Init/Data/UInt/Basic.lean

@@ -159,8 +159,6 @@ def UInt32.xor (a b : UInt32) : UInt32 := ⟨a.toBitVec ^^^ b.toBitVec⟩
 def UInt32.shiftLeft (a b : UInt32) : UInt32 := ⟨a.toBitVec <<< (mod b 32).toBitVec⟩
 @[extern "lean_uint32_shift_right"]
 def UInt32.shiftRight (a b : UInt32) : UInt32 := ⟨a.toBitVec >>> (mod b 32).toBitVec⟩
-def UInt32.lt (a b : UInt32) : Prop := a.toBitVec < b.toBitVec
-def UInt32.le (a b : UInt32) : Prop := a.toBitVec ≤ b.toBitVec
 
 instance : Add UInt32       := ⟨UInt32.add⟩
 instance : Sub UInt32       := ⟨UInt32.sub⟩
@@ -171,8 +169,6 @@ set_option linter.deprecated false in
 instance : HMod UInt32 Nat UInt32 := ⟨UInt32.modn⟩
 
 instance : Div UInt32       := ⟨UInt32.div⟩
-instance : LT UInt32        := ⟨UInt32.lt⟩
-instance : LE UInt32        := ⟨UInt32.le⟩
 
 @[extern "lean_uint32_complement"]
 def UInt32.complement (a : UInt32) : UInt32 := ⟨~~~a.toBitVec⟩

src/Init/Data/UInt/Bitwise.lean

@@ -13,17 +13,11 @@ macro "declare_bitwise_uint_theorems" typeName:ident bits:term:arg : command =>
 `(
 namespace $typeName
 
-@[simp, int_toBitVec] protected theorem toBitVec_add {a b : $typeName} : (a + b).toBitVec = a.toBitVec + b.toBitVec := rfl
-@[simp, int_toBitVec] protected theorem toBitVec_sub {a b : $typeName} : (a - b).toBitVec = a.toBitVec - b.toBitVec := rfl
-@[simp, int_toBitVec] protected theorem toBitVec_mul {a b : $typeName} : (a * b).toBitVec = a.toBitVec * b.toBitVec := rfl
-@[simp, int_toBitVec] protected theorem toBitVec_div {a b : $typeName} : (a / b).toBitVec = a.toBitVec / b.toBitVec := rfl
-@[simp, int_toBitVec] protected theorem toBitVec_mod {a b : $typeName} : (a % b).toBitVec = a.toBitVec % b.toBitVec := rfl
-@[simp, int_toBitVec] protected theorem toBitVec_not {a : $typeName} : (~~~a).toBitVec = ~~~a.toBitVec := rfl
-@[simp, int_toBitVec] protected theorem toBitVec_and (a b : $typeName) : (a &&& b).toBitVec = a.toBitVec &&& b.toBitVec := rfl
-@[simp, int_toBitVec] protected theorem toBitVec_or (a b : $typeName) : (a ||| b).toBitVec = a.toBitVec ||| b.toBitVec := rfl
-@[simp, int_toBitVec] protected theorem toBitVec_xor (a b : $typeName) : (a ^^^ b).toBitVec = a.toBitVec ^^^ b.toBitVec := rfl
-@[simp, int_toBitVec] protected theorem toBitVec_shiftLeft (a b : $typeName) : (a <<< b).toBitVec = a.toBitVec <<< (b.toBitVec % $bits) := rfl
-@[simp, int_toBitVec] protected theorem toBitVec_shiftRight (a b : $typeName) : (a >>> b).toBitVec = a.toBitVec >>> (b.toBitVec % $bits) := rfl
+@[simp] protected theorem toBitVec_and (a b : $typeName) : (a &&& b).toBitVec = a.toBitVec &&& b.toBitVec := rfl
+@[simp] protected theorem toBitVec_or (a b : $typeName) : (a ||| b).toBitVec = a.toBitVec ||| b.toBitVec := rfl
+@[simp] protected theorem toBitVec_xor (a b : $typeName) : (a ^^^ b).toBitVec = a.toBitVec ^^^ b.toBitVec := rfl
+@[simp] protected theorem toBitVec_shiftLeft (a b : $typeName) : (a <<< b).toBitVec = a.toBitVec <<< (b.toBitVec % $bits) := rfl
+@[simp] protected theorem toBitVec_shiftRight (a b : $typeName) : (a >>> b).toBitVec = a.toBitVec >>> (b.toBitVec % $bits) := rfl
 
 @[simp] protected theorem toNat_and (a b : $typeName) : (a &&& b).toNat = a.toNat &&& b.toNat := by simp [toNat]
 @[simp] protected theorem toNat_or (a b : $typeName) : (a ||| b).toNat = a.toNat ||| b.toNat := by simp [toNat]
@@ -43,31 +37,3 @@ declare_bitwise_uint_theorems UInt16 16
 declare_bitwise_uint_theorems UInt32 32
 declare_bitwise_uint_theorems UInt64 64
 declare_bitwise_uint_theorems USize System.Platform.numBits
-
-@[simp, int_toBitVec]
-theorem Bool.toBitVec_toUInt8 {b : Bool} :
-    b.toUInt8.toBitVec = (BitVec.ofBool b).setWidth 8 := by
-  cases b <;> simp [toUInt8]
-
-@[simp, int_toBitVec]
-theorem Bool.toBitVec_toUInt16 {b : Bool} :
-    b.toUInt16.toBitVec = (BitVec.ofBool b).setWidth 16 := by
-  cases b <;> simp [toUInt16]
-
-@[simp, int_toBitVec]
-theorem Bool.toBitVec_toUInt32 {b : Bool} :
-    b.toUInt32.toBitVec = (BitVec.ofBool b).setWidth 32 := by
-  cases b <;> simp [toUInt32]
-
-@[simp, int_toBitVec]
-theorem Bool.toBitVec_toUInt64 {b : Bool} :
-    b.toUInt64.toBitVec = (BitVec.ofBool b).setWidth 64 := by
-  cases b <;> simp [toUInt64]
-
-@[simp, int_toBitVec]
-theorem Bool.toBitVec_toUSize {b : Bool} :
-    b.toUSize.toBitVec = (BitVec.ofBool b).setWidth System.Platform.numBits := by
-  cases b
-  · simp [toUSize]
-  · apply BitVec.eq_of_toNat_eq
-    simp [toUSize]

src/Init/Data/UInt/Lemmas.lean

@@ -41,9 +41,9 @@ macro "declare_uint_theorems" typeName:ident bits:term:arg : command => do
   theorem toNat_ofNat_of_lt {n : Nat} (h : n < size) : (ofNat n).toNat = n := by
     rw [toNat, toBitVec_eq_of_lt h]
 
-  @[int_toBitVec] theorem le_def {a b : $typeName} : a ≤ b ↔ a.toBitVec ≤ b.toBitVec := .rfl
+  theorem le_def {a b : $typeName} : a ≤ b ↔ a.toBitVec ≤ b.toBitVec := .rfl
 
-  @[int_toBitVec] theorem lt_def {a b : $typeName} : a < b ↔ a.toBitVec < b.toBitVec := .rfl
+  theorem lt_def {a b : $typeName} : a < b ↔ a.toBitVec < b.toBitVec := .rfl
 
   theorem le_iff_toNat_le {a b : $typeName} : a ≤ b ↔ a.toNat ≤ b.toNat := .rfl
 
@@ -74,11 +74,6 @@ macro "declare_uint_theorems" typeName:ident bits:term:arg : command => do
   protected theorem toBitVec_inj {a b : $typeName} : a.toBitVec = b.toBitVec ↔ a = b :=
     Iff.intro eq_of_toBitVec_eq toBitVec_eq_of_eq
 
-  open $typeName (eq_of_toBitVec_eq toBitVec_eq_of_eq) in
-  @[int_toBitVec]
-  protected theorem eq_iff_toBitVec_eq {a b : $typeName} : a = b ↔ a.toBitVec = b.toBitVec :=
-    Iff.intro toBitVec_eq_of_eq eq_of_toBitVec_eq
-
   open $typeName (eq_of_toBitVec_eq) in
   protected theorem eq_of_val_eq {a b : $typeName} (h : a.val = b.val) : a = b := by
     rcases a with ⟨⟨_⟩⟩; rcases b with ⟨⟨_⟩⟩; simp_all [val]
@@ -87,19 +82,10 @@ macro "declare_uint_theorems" typeName:ident bits:term:arg : command => do
   protected theorem val_inj {a b : $typeName} : a.val = b.val ↔ a = b :=
     Iff.intro eq_of_val_eq (congrArg val)
 
-  open $typeName (eq_of_toBitVec_eq) in
-  protected theorem toBitVec_ne_of_ne {a b : $typeName} (h : a ≠ b) : a.toBitVec ≠ b.toBitVec :=
-    fun h' => h (eq_of_toBitVec_eq h')
-
   open $typeName (toBitVec_eq_of_eq) in
   protected theorem ne_of_toBitVec_ne {a b : $typeName} (h : a.toBitVec ≠ b.toBitVec) : a ≠ b :=
     fun h' => absurd (toBitVec_eq_of_eq h') h
 
-  open $typeName (ne_of_toBitVec_ne toBitVec_ne_of_ne) in
-  @[int_toBitVec]
-  protected theorem ne_iff_toBitVec_ne {a b : $typeName} : a ≠ b ↔ a.toBitVec ≠ b.toBitVec :=
-    Iff.intro toBitVec_ne_of_ne ne_of_toBitVec_ne
-
   open $typeName (ne_of_toBitVec_ne) in
   protected theorem ne_of_lt {a b : $typeName} (h : a < b) : a ≠ b := by
     apply ne_of_toBitVec_ne
@@ -173,7 +159,7 @@ macro "declare_uint_theorems" typeName:ident bits:term:arg : command => do
   @[simp]
   theorem val_ofNat (n : Nat) : val (no_index (OfNat.ofNat n)) = OfNat.ofNat n := rfl
 
-  @[simp, int_toBitVec]
+  @[simp]
   theorem toBitVec_ofNat (n : Nat) : toBitVec (no_index (OfNat.ofNat n)) = BitVec.ofNat _ n := rfl
 
   @[simp]

src/Init/Data/Vector/Basic.lean

@@ -103,7 +103,7 @@ of bounds.
 @[inline] def head [NeZero n] (v : Vector α n) := v[0]'(Nat.pos_of_neZero n)
 
 /-- Push an element `x` to the end of a vector. -/
-@[inline] def push (v : Vector α n) (x : α) : Vector α (n + 1) :=
+@[inline] def push (x : α) (v : Vector α n)  : Vector α (n + 1) :=
   ⟨v.toArray.push x, by simp⟩
 
 /-- Remove the last element of a vector. -/
@@ -136,18 +136,6 @@ This will perform the update destructively provided that the vector has a refere
 @[inline] def set! (v : Vector α n) (i : Nat) (x : α) : Vector α n :=
   ⟨v.toArray.set! i x, by simp⟩
 
-@[inline] def foldlM [Monad m] (f : β → α → m β) (b : β) (v : Vector α n) : m β :=
-  v.toArray.foldlM f b
-
-@[inline] def foldrM [Monad m] (f : α → β → m β) (b : β) (v : Vector α n) : m β :=
-  v.toArray.foldrM f b
-
-@[inline] def foldl (f : β → α → β) (b : β) (v : Vector α n) : β :=
-  v.toArray.foldl f b
-
-@[inline] def foldr (f : α → β → β) (b : β) (v : Vector α n) : β :=
-  v.toArray.foldr f b
-
 /-- Append two vectors. -/
 @[inline] def append (v : Vector α n) (w : Vector α m) : Vector α (n + m) :=
   ⟨v.toArray ++ w.toArray, by simp⟩
@@ -170,13 +158,6 @@ result is empty. If `stop` is greater than the size of the vector, the size is u
 @[inline] def map (f : α → β) (v : Vector α n) : Vector β n :=
   ⟨v.toArray.map f, by simp⟩
 
-@[inline] def flatten (v : Vector (Vector α n) m) : Vector α (m * n) :=
-  ⟨(v.toArray.map Vector.toArray).flatten,
-    by rcases v; simp_all [Function.comp_def, Array.map_const']⟩
-
-@[inline] def flatMap (v : Vector α n) (f : α → Vector β m) : Vector β (n * m) :=
-  ⟨v.toArray.flatMap fun a => (f a).toArray, by simp [Array.map_const']⟩
-
 /-- Maps corresponding elements of two vectors of equal size using the function `f`. -/
 @[inline] def zipWith (a : Vector α n) (b : Vector β n) (f : α → β → φ) : Vector φ n :=
   ⟨Array.zipWith a.toArray b.toArray f, by simp⟩

src/Init/Data/Vector/Lemmas.lean

@@ -1,11 +1,10 @@
 /-
 Copyright (c) 2024 Shreyas Srinivas. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Shreyas Srinivas, Francois Dorais, Kim Morrison
+Authors: Shreyas Srinivas, Francois Dorais
 -/
 prelude
 import Init.Data.Vector.Basic
-import Init.Data.Array.Attach
 
 /-!
 ## Vectors
@@ -28,9 +27,6 @@ namespace Vector
 
 theorem toArray_mk (a : Array α) (h : a.size = n) : (Vector.mk a h).toArray = a := rfl
 
-@[simp] theorem mk_toArray (v : Vector α n) : mk v.toArray v.2 = v := by
-  rfl
-
 @[simp] theorem getElem_mk {data : Array α} {size : data.size = n} {i : Nat} (h : i < n) :
     (Vector.mk data size)[i] = data[i] := rfl
 
@@ -70,18 +66,6 @@ theorem toArray_mk (a : Array α) (h : a.size = n) : (Vector.mk a h).toArray = a
 @[simp] theorem back?_mk (a : Array α) (h : a.size = n) :
     (Vector.mk a h).back? = a.back? := rfl
 
-@[simp] theorem foldlM_mk [Monad m] (f : β → α → m β) (b : β) (a : Array α) (h : a.size = n) :
-    (Vector.mk a h).foldlM f b = a.foldlM f b := rfl
-
-@[simp] theorem foldrM_mk [Monad m] (f : α → β → m β) (b : β) (a : Array α) (h : a.size = n) :
-    (Vector.mk a h).foldrM f b = a.foldrM f b := rfl
-
-@[simp] theorem foldl_mk (f : β → α → β) (b : β) (a : Array α) (h : a.size = n) :
-    (Vector.mk a h).foldl f b = a.foldl f b := rfl
-
-@[simp] theorem foldr_mk (f : α → β → β) (b : β) (a : Array α) (h : a.size = n) :
-    (Vector.mk a h).foldr f b = a.foldr f b := rfl
-
 @[simp] theorem drop_mk (a : Array α) (h : a.size = n) (m) :
     (Vector.mk a h).drop m = Vector.mk (a.extract m a.size) (by simp [h]) := rfl
 
@@ -157,14 +141,6 @@ theorem toArray_mk (a : Array α) (h : a.size = n) : (Vector.mk a h).toArray = a
 @[simp] theorem all_mk (p : α → Bool) (a : Array α) (h : a.size = n) :
     (Vector.mk a h).all p = a.all p := rfl
 
-@[simp] theorem eq_mk : v = Vector.mk a h ↔ v.toArray = a := by
-  cases v
-  simp
-
-@[simp] theorem mk_eq : Vector.mk a h = v ↔ a = v.toArray := by
-  cases v
-  simp
-
 /-! ### toArray lemmas -/
 
 @[simp] theorem getElem_toArray {α n} (xs : Vector α n) (i : Nat) (h : i < xs.toArray.size) :
@@ -697,24 +673,6 @@ theorem forall_getElem {l : Vector α n} {p : α → Prop} :
   rcases l with ⟨l, rfl⟩
   simp [Array.forall_getElem]
 
-
-/-! ### cast -/
-
-@[simp] theorem getElem_cast (a : Vector α n) (h : n = m) (i : Nat) (hi : i < m) :
-    (a.cast h)[i] = a[i] := by
-  cases a
-  simp
-
-@[simp] theorem getElem?_cast {l : Vector α n} {m : Nat} {w : n = m} {i : Nat} :
-    (l.cast w)[i]? = l[i]? := by
-  rcases l with ⟨l, rfl⟩
-  simp
-
-@[simp] theorem mem_cast {a : α} {l : Vector α n} {m : Nat} {w : n = m} :
-    a ∈ l.cast w ↔ a ∈ l := by
-  rcases l with ⟨l, rfl⟩
-  simp
-
 /-! ### Decidability of bounded quantifiers -/
 
 instance {xs : Vector α n} {p : α → Prop} [DecidablePred p] :
@@ -1065,12 +1023,11 @@ theorem mem_setIfInBounds (v : Vector α n) (i : Nat) (hi : i < n) (a : α) :
   cases l₂
   simp
 
-/-! ### map -/
+/-! Content below this point has not yet been aligned with `List` and `Array`. -/
 
-@[simp] theorem getElem_map (f : α → β) (a : Vector α n) (i : Nat) (hi : i < n) :
-    (a.map f)[i] = f a[i] := by
-  cases a
-  simp
+@[simp] theorem getElem_ofFn {α n} (f : Fin n → α) (i : Nat) (h : i < n) :
+    (Vector.ofFn f)[i] = f ⟨i, by simpa using h⟩ := by
+  simp [ofFn]
 
 /-- The empty vector maps to the empty vector. -/
 @[simp]
@@ -1078,583 +1035,6 @@ theorem map_empty (f : α → β) : map f #v[] = #v[] := by
   rw [map, mk.injEq]
   exact Array.map_empty f
 
-@[simp] theorem map_push {f : α → β} {as : Vector α n} {x : α} :
-    (as.push x).map f = (as.map f).push (f x) := by
-  cases as
-  simp
-
-@[simp] theorem map_id_fun : map (n := n) (id : α → α) = id := by
-  funext l
-  induction l <;> simp_all
-
-/-- `map_id_fun'` differs from `map_id_fun` by representing the identity function as a lambda, rather than `id`. -/
-@[simp] theorem map_id_fun' : map (n := n) (fun (a : α) => a) = id := map_id_fun
-
--- This is not a `@[simp]` lemma because `map_id_fun` will apply.
-theorem map_id (l : Vector α n) : map (id : α → α) l = l := by
-  cases l <;> simp_all
-
-/-- `map_id'` differs from `map_id` by representing the identity function as a lambda, rather than `id`. -/
--- This is not a `@[simp]` lemma because `map_id_fun'` will apply.
-theorem map_id' (l : Vector α n) : map (fun (a : α) => a) l = l := map_id l
-
-/-- Variant of `map_id`, with a side condition that the function is pointwise the identity. -/
-theorem map_id'' {f : α → α} (h : ∀ x, f x = x) (l : Vector α n) : map f l = l := by
-  simp [show f = id from funext h]
-
-theorem map_singleton (f : α → β) (a : α) : map f #v[a] = #v[f a] := rfl
-
-@[simp] theorem mem_map {f : α → β} {l : Vector α n} : b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b := by
-  cases l
-  simp
-
-theorem exists_of_mem_map (h : b ∈ map f l) : ∃ a, a ∈ l ∧ f a = b := mem_map.1 h
-
-theorem mem_map_of_mem (f : α → β) (h : a ∈ l) : f a ∈ map f l := mem_map.2 ⟨_, h, rfl⟩
-
-theorem forall_mem_map {f : α → β} {l : Vector α n} {P : β → Prop} :
-    (∀ (i) (_ : i ∈ l.map f), P i) ↔ ∀ (j) (_ : j ∈ l), P (f j) := by
-  simp
-
-@[simp] theorem map_inj_left {f g : α → β} : map f l = map g l ↔ ∀ a ∈ l, f a = g a := by
-  cases l <;> simp_all
-
-theorem map_inj_right {f : α → β} (w : ∀ x y, f x = f y → x = y) : map f l = map f l' ↔ l = l' := by
-  cases l
-  cases l'
-  simp [Array.map_inj_right w]
-
-theorem map_congr_left (h : ∀ a ∈ l, f a = g a) : map f l = map g l :=
-  map_inj_left.2 h
-
-theorem map_inj [NeZero n] : map (n := n) f = map g ↔ f = g := by
-  constructor
-  · intro h
-    ext a
-    replace h := congrFun h (mkVector n a)
-    simp only [mkVector, map_mk, mk.injEq, Array.map_inj_left, Array.mem_mkArray,  and_imp,
-      forall_eq_apply_imp_iff] at h
-    exact h (NeZero.ne n)
-  · intro h; subst h; rfl
-
-theorem map_eq_push_iff {f : α → β} {l : Vector α (n + 1)} {l₂ : Vector β n} {b : β} :
-    map f l = l₂.push b ↔ ∃ l₁ a, l = l₁.push a ∧ map f l₁ = l₂ ∧ f a = b := by
-  rcases l with ⟨l, h⟩
-  rcases l₂ with ⟨l₂, rfl⟩
-  simp only [map_mk, push_mk, mk.injEq, Array.map_eq_push_iff]
-  constructor
-  · rintro ⟨l₁, a, rfl, rfl, rfl⟩
-    refine ⟨⟨l₁, by simp⟩, a, by simp⟩
-  · rintro ⟨l₁, a, h₁, h₂, rfl⟩
-    refine ⟨l₁.toArray, a, by simp_all⟩
-
-@[simp] theorem map_eq_singleton_iff {f : α → β} {l : Vector α 1} {b : β} :
-    map f l = #v[b] ↔ ∃ a, l = #v[a] ∧ f a = b := by
-  cases l
-  simp
-
-theorem map_eq_map_iff {f g : α → β} {l : Vector α n} :
-    map f l = map g l ↔ ∀ a ∈ l, f a = g a := by
-  cases l <;> simp_all
-
-theorem map_eq_iff {f : α → β} {l : Vector α n} {l' : Vector β n} :
-    map f l = l' ↔ ∀ i (h : i < n), l'[i] = f l[i] := by
-  rcases l with ⟨l, rfl⟩
-  rcases l' with ⟨l', h'⟩
-  simp only [map_mk, eq_mk, Array.map_eq_iff, getElem_mk]
-  constructor
-  · intro w i h
-    simpa [h, h'] using w i
-  · intro w i
-    if h : i < l.size then
-      simpa [h, h'] using w i h
-    else
-      rw [getElem?_neg, getElem?_neg, Option.map_none'] <;> omega
-
-@[simp] theorem map_set {f : α → β} {l : Vector α n} {i : Nat} {h : i < n} {a : α} :
-    (l.set i a).map f = (l.map f).set i (f a) (by simpa using h) := by
-  cases l
-  simp
-
-@[simp] theorem map_setIfInBounds {f : α → β} {l : Vector α n} {i : Nat} {a : α} :
-    (l.setIfInBounds i a).map f = (l.map f).setIfInBounds i (f a) := by
-  cases l
-  simp
-
-@[simp] theorem map_pop {f : α → β} {l : Vector α n} : l.pop.map f = (l.map f).pop := by
-  cases l
-  simp
-
-@[simp] theorem back?_map {f : α → β} {l : Vector α n} : (l.map f).back? = l.back?.map f := by
-  cases l
-  simp
-
-@[simp] theorem map_map {f : α → β} {g : β → γ} {as : Vector α n} :
-    (as.map f).map g = as.map (g ∘ f) := by
-  cases as
-  simp
-
-/--
-Use this as `induction ass using vector₂_induction` on a hypothesis of the form `ass : Vector (Vector α n) m`.
-The hypothesis `ass` will be replaced with a hypothesis `ass : Array (Array α)`
-along with additional hypotheses `h₁ : ass.size = m` and `h₂ : ∀ xs ∈ ass, xs.size = n`.
-Appearances of the original `ass` in the goal will be replaced with
-`Vector.mk (xss.attach.map (fun ⟨xs, m⟩ => Vector.mk xs ⋯)) ⋯`.
--/
--- We can't use `@[cases_eliminator]` here as
--- `Lean.Meta.getCustomEliminator?` only looks at the top-level constant.
-theorem vector₂_induction (P : Vector (Vector α n) m → Prop)
-    (of : ∀ (xss : Array (Array α)) (h₁ : xss.size = m) (h₂ : ∀ xs ∈ xss, xs.size = n),
-      P (mk (xss.attach.map (fun ⟨xs, m⟩ => mk xs (h₂ xs m))) (by simpa using h₁)))
-    (ass : Vector (Vector α n) m) : P ass := by
-  specialize of (ass.map toArray).toArray (by simp) (by simp)
-  simpa [Array.map_attach, Array.pmap_map] using of
-
-/--
-Use this as `induction ass using vector₃_induction` on a hypothesis of the form `ass : Vector (Vector (Vector α n) m) k`.
-The hypothesis `ass` will be replaced with a hypothesis `ass : Array (Array (Array α))`
-along with additional hypotheses `h₁ : ass.size = k`, `h₂ : ∀ xs ∈ ass, xs.size = m`,
-and `h₃ : ∀ xs ∈ ass, ∀ x ∈ xs, x.size = n`.
-Appearances of the original `ass` in the goal will be replaced with
-`Vector.mk (xss.attach.map (fun ⟨xs, m⟩ => Vector.mk (xs.attach.map (fun ⟨x, m'⟩ => Vector.mk x ⋯)) ⋯)) ⋯`.
--/
-theorem vector₃_induction (P : Vector (Vector (Vector α n) m) k → Prop)
-    (of : ∀ (xss : Array (Array (Array α))) (h₁ : xss.size = k) (h₂ : ∀ xs ∈ xss, xs.size = m)
-      (h₃ : ∀ xs ∈ xss, ∀ x ∈ xs, x.size = n),
-      P (mk (xss.attach.map (fun ⟨xs, m⟩ =>
-        mk (xs.attach.map (fun ⟨x, m'⟩ =>
-          mk x (h₃ xs m x m'))) (by simpa using h₂ xs m))) (by simpa using h₁)))
-    (ass : Vector (Vector (Vector α n) m) k) : P ass := by
-  specialize of (ass.map (fun as => (as.map toArray).toArray)).toArray (by simp) (by simp) (by simp)
-  simpa [Array.map_attach, Array.pmap_map] using of
-
-/-! ### singleton -/
-
-@[simp] theorem singleton_def (v : α) : Vector.singleton v = #v[v] := rfl
-
-/-! ### append -/
-
-@[simp] theorem append_push {as : Vector α n} {bs : Vector α m} {a : α} :
-    as ++ bs.push a = (as ++ bs).push a := by
-  cases as
-  cases bs
-  simp
-
-theorem singleton_eq_toVector_singleton (a : α) : #v[a] = #[a].toVector := rfl
-
-@[simp] theorem mem_append {a : α} {s : Vector α n} {t : Vector α m} :
-    a ∈ s ++ t ↔ a ∈ s ∨ a ∈ t := by
-  cases s
-  cases t
-  simp
-
-theorem mem_append_left {a : α} {s : Vector α n} {t : Vector α m} (h : a ∈ s) : a ∈ s ++ t :=
-  mem_append.2 (Or.inl h)
-
-theorem mem_append_right {a : α} {s : Vector α n} {t : Vector α m} (h : a ∈ t) : a ∈ s ++ t :=
-  mem_append.2 (Or.inr h)
-
-theorem not_mem_append {a : α} {s : Vector α n} {t : Vector α m} (h₁ : a ∉ s) (h₂ : a ∉ t) :
-    a ∉ s ++ t :=
-  mt mem_append.1 $ not_or.mpr ⟨h₁, h₂⟩
-
-/--
-See also `eq_push_append_of_mem`, which proves a stronger version
-in which the initial array must not contain the element.
--/
-theorem append_of_mem {a : α} {l : Vector α n} (h : a ∈ l) :
-    ∃ (m k : Nat) (w : m + 1 + k = n) (s : Vector α m) (t : Vector α k),
-      l = (s.push a ++ t).cast w := by
-  rcases l with ⟨l, rfl⟩
-  obtain ⟨s, t, rfl⟩ := Array.append_of_mem (by simpa using h)
-  refine ⟨_, _, by simp, s.toVector, t.toVector, by simp_all⟩
-
-theorem mem_iff_append {a : α} {l : Vector α n} :
-    a ∈ l ↔ ∃ (m k : Nat) (w : m + 1 + k = n) (s : Vector α m) (t : Vector α k),
-      l = (s.push a ++ t).cast w :=
-  ⟨append_of_mem, by rintro ⟨m, k, rfl, s, t, rfl⟩; simp⟩
-
-theorem forall_mem_append {p : α → Prop} {l₁ : Vector α n} {l₂ : Vector α m} :
-    (∀ (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]
-
-theorem empty_append (as : Vector α n) : (#v[] : Vector α 0) ++ as = as.cast (by omega) := by
-  rcases as with ⟨as, rfl⟩
-  simp
-
-theorem append_empty (as : Vector α n) : as ++ (#v[] : Vector α 0) = as := by
-  rw [← toArray_inj, toArray_append, Array.append_empty]
-
-theorem getElem_append (a : Vector α n) (b : Vector α m) (i : Nat) (hi : i < n + m) :
-    (a ++ b)[i] = if h : i < n then a[i] else b[i - n] := by
-  rcases a with ⟨a, rfl⟩
-  rcases b with ⟨b, rfl⟩
-  simp [Array.getElem_append, hi]
-
-theorem getElem_append_left {a : Vector α n} {b : Vector α m} {i : Nat} (hi : i < n) :
-    (a ++ b)[i] = a[i] := by simp [getElem_append, hi]
-
-theorem getElem_append_right {a : Vector α n} {b : Vector α m} {i : Nat} (h : i < n + m) (hi : n ≤ i) :
-    (a ++ b)[i] = b[i - n] := by
-  rw [getElem_append, dif_neg (by omega)]
-
-theorem getElem?_append_left {as : Vector α n} {bs : Vector α m} {i : Nat} (hn : i < n) :
-    (as ++ bs)[i]? = as[i]? := by
-  have hn' : i < n + m := by omega
-  simp_all [getElem?_eq_getElem, getElem_append]
-
-theorem getElem?_append_right {as : Vector α n} {bs : Vector α m} {i : Nat} (h : n ≤ i) :
-    (as ++ bs)[i]? = bs[i - n]? := by
-  rcases as with ⟨as, rfl⟩
-  rcases bs with ⟨bs, rfl⟩
-  simp [Array.getElem?_append_right, h]
-
-theorem getElem?_append {as : Vector α n} {bs : Vector α m} {i : Nat} :
-    (as ++ bs)[i]? = if i < n then as[i]? else bs[i - n]? := by
-  split <;> rename_i h
-  · exact getElem?_append_left h
-  · exact getElem?_append_right (by simpa using h)
-
-/-- Variant of `getElem_append_left` useful for rewriting from the small array to the big array. -/
-theorem getElem_append_left' (l₁ : Vector α m) {l₂ : Vector α n} {i : Nat} (hi : i < m) :
-    l₁[i] = (l₁ ++ l₂)[i] := by
-  rw [getElem_append_left] <;> simp
-
-/-- Variant of `getElem_append_right` useful for rewriting from the small array to the big array. -/
-theorem getElem_append_right' (l₁ : Vector α m) {l₂ : Vector α n} {i : Nat} (hi : i < n) :
-    l₂[i] = (l₁ ++ l₂)[i + m] := by
-  rw [getElem_append_right] <;> simp [*, Nat.le_add_left]
-
-theorem getElem_of_append {l : Vector α n} {l₁ : Vector α m} {l₂ : Vector α k}
-    (w : m + 1 + k = n) (eq : l = (l₁.push a ++ l₂).cast w) :
-    l[m] = a := Option.some.inj <| by
-  rw [← getElem?_eq_getElem, eq, getElem?_cast, getElem?_append_left (by simp)]
-  simp
-
-@[simp 1100] theorem append_singleton {a : α} {as : Vector α n} : as ++ #v[a] = as.push a := by
-  cases as
-  simp
-
-theorem append_inj {s₁ s₂ : Vector α n} {t₁ t₂ : Vector α m} (h : s₁ ++ t₁ = s₂ ++ t₂) :
-    s₁ = s₂ ∧ t₁ = t₂ := by
-  rcases s₁ with ⟨s₁, rfl⟩
-  rcases s₂ with ⟨s₂, hs⟩
-  rcases t₁ with ⟨t₁, rfl⟩
-  rcases t₂ with ⟨t₂, ht⟩
-  simpa using Array.append_inj (by simpa using h) (by omega)
-
-theorem append_inj_right {s₁ s₂ : Vector α n} {t₁ t₂ : Vector α m}
-    (h : s₁ ++ t₁ = s₂ ++ t₂) : t₁ = t₂ :=
-  (append_inj h).right
-
-theorem append_inj_left {s₁ s₂ : Vector α n} {t₁ t₂ : Vector α m}
-    (h : s₁ ++ t₁ = s₂ ++ t₂) : s₁ = s₂ :=
-  (append_inj h).left
-
-theorem append_right_inj {t₁ t₂ : Vector α m} (s : Vector α n) : s ++ t₁ = s ++ t₂ ↔ t₁ = t₂ :=
-  ⟨fun h => append_inj_right h, congrArg _⟩
-
-theorem append_left_inj {s₁ s₂ : Vector α n} (t : Vector α m) : s₁ ++ t = s₂ ++ t ↔ s₁ = s₂ :=
-  ⟨fun h => append_inj_left h, congrArg (· ++ _)⟩
-
-theorem append_eq_append_iff {a : Vector α n} {b : Vector α m} {c : Vector α k} {d : Vector α l}
-    (w : k + l = n + m) :
-    a ++ b = (c ++ d).cast w ↔
-      if h : n ≤ k then
-        ∃ a' : Vector α (k - n), c = (a ++ a').cast (by omega) ∧ b = (a' ++ d).cast (by omega)
-      else
-        ∃ c' : Vector α (n - k), a = (c ++ c').cast (by omega) ∧ d = (c' ++ b).cast (by omega) := by
-  rcases a with ⟨a, rfl⟩
-  rcases b with ⟨b, rfl⟩
-  rcases c with ⟨c, rfl⟩
-  rcases d with ⟨d, rfl⟩
-  simp only [mk_append_mk, Array.append_eq_append_iff, mk_eq, toArray_cast]
-  constructor
-  · rintro (⟨a', rfl, rfl⟩ | ⟨c', rfl, rfl⟩)
-    · rw [dif_pos (by simp)]
-      exact ⟨a'.toVector.cast (by simp; omega), by simp⟩
-    · split <;> rename_i h
-      · have hc : c'.size = 0 := by simp at h; omega
-        simp at hc
-        exact ⟨#v[].cast (by simp; omega), by simp_all⟩
-      · exact ⟨c'.toVector.cast (by simp; omega), by simp⟩
-  · split <;> rename_i h
-    · rintro ⟨a', hc, rfl⟩
-      left
-      refine ⟨a'.toArray, hc, rfl⟩
-    · rintro ⟨c', ha, rfl⟩
-      right
-      refine ⟨c'.toArray, ha, rfl⟩
-
-theorem set_append {s : Vector α n} {t : Vector α m} {i : Nat} {x : α} (h : i < n + m) :
-    (s ++ t).set i x =
-      if h' : i < n then
-        s.set i x ++ t
-      else
-        s ++ t.set (i - n) x := by
-  rcases s with ⟨s, rfl⟩
-  rcases t with ⟨t, rfl⟩
-  simp only [mk_append_mk, set_mk, Array.set_append]
-  split <;> simp
-
-@[simp] theorem set_append_left {s : Vector α n} {t : Vector α m} {i : Nat} {x : α} (h : i < n) :
-    (s ++ t).set i x = s.set i x ++ t := by
-  simp [set_append, h]
-
-@[simp] theorem set_append_right {s : Vector α n} {t : Vector α m} {i : Nat} {x : α}
-    (h' : i < n + m) (h : n ≤ i) :
-    (s ++ t).set i x = s ++ t.set (i - n) x := by
-  rw [set_append, dif_neg (by omega)]
-
-theorem setIfInBounds_append {s : Vector α n} {t : Vector α m} {i : Nat} {x : α} :
-    (s ++ t).setIfInBounds i x =
-      if i < n then
-        s.setIfInBounds i x ++ t
-      else
-        s ++ t.setIfInBounds (i - n) x := by
-  rcases s with ⟨s, rfl⟩
-  rcases t with ⟨t, rfl⟩
-  simp only [mk_append_mk, setIfInBounds_mk, Array.setIfInBounds_append]
-  split <;> simp
-
-@[simp] theorem setIfInBounds_append_left {s : Vector α n} {t : Vector α m} {i : Nat} {x : α} (h : i < n) :
-    (s ++ t).setIfInBounds i x = s.setIfInBounds i x ++ t := by
-  simp [setIfInBounds_append, h]
-
-@[simp] theorem setIfInBounds_append_right {s : Vector α n} {t : Vector α m} {i : Nat} {x : α}
-    (h : n ≤ i) :
-    (s ++ t).setIfInBounds i x = s ++ t.setIfInBounds (i - n) x := by
-  rw [setIfInBounds_append, if_neg (by omega)]
-
-@[simp] theorem map_append (f : α → β) (l₁ : Vector α n) (l₂ : Vector α m) :
-    map f (l₁ ++ l₂) = map f l₁ ++ map f l₂ := by
-  rcases l₁ with ⟨l₁, rfl⟩
-  rcases l₂ with ⟨l₂, rfl⟩
-  simp
-
-theorem map_eq_append_iff {f : α → β} :
-    map f l = L₁ ++ L₂ ↔ ∃ l₁ l₂, l = l₁ ++ l₂ ∧ map f l₁ = L₁ ∧ map f l₂ = L₂ := by
-  rcases l with ⟨l, h⟩
-  rcases L₁ with ⟨L₁, rfl⟩
-  rcases L₂ with ⟨L₂, rfl⟩
-  simp only [map_mk, mk_append_mk, eq_mk, Array.map_eq_append_iff, mk_eq, toArray_append,
-    toArray_map]
-  constructor
-  · rintro ⟨l₁, l₂, rfl, rfl, rfl⟩
-    exact ⟨l₁.toVector.cast (by simp), l₂.toVector.cast (by simp), by simp⟩
-  · rintro ⟨⟨l₁⟩, ⟨l₂⟩, rfl, h₁, h₂⟩
-    exact ⟨l₁, l₂, by simp_all⟩
-
-theorem append_eq_map_iff {f : α → β} :
-    L₁ ++ L₂ = map f l ↔ ∃ l₁ l₂, l = l₁ ++ l₂ ∧ map f l₁ = L₁ ∧ map f l₂ = L₂ := by
-  rw [eq_comm, map_eq_append_iff]
-
-/-! ### flatten -/
-
-@[simp] theorem flatten_mk (L : Array (Vector α n)) (h : L.size = m) :
-    (mk L h).flatten =
-      mk (L.map toArray).flatten (by simp [Function.comp_def, Array.map_const', h]) := by
-  simp [flatten]
-
-@[simp] theorem getElem_flatten (l : Vector (Vector β m) n) (i : Nat) (hi : i < n * m) :
-    l.flatten[i] =
-      haveI : i / m < n := by rwa [Nat.div_lt_iff_lt_mul (Nat.pos_of_lt_mul_left hi)]
-      haveI : i % m < m := Nat.mod_lt _ (Nat.pos_of_lt_mul_left hi)
-      l[i / m][i % m] := by
-  rcases l with ⟨⟨l⟩, rfl⟩
-  simp only [flatten_mk, List.map_toArray, getElem_mk, List.getElem_toArray, Array.flatten_toArray]
-  induction l generalizing i with
-  | nil => simp at hi
-  | cons a l ih =>
-    simp only [List.map_cons, List.map_map, List.flatten_cons]
-    by_cases h : i < m
-    · rw [List.getElem_append_left (by simpa)]
-      have h₁ : i / m = 0 := Nat.div_eq_of_lt h
-      have h₂ : i % m = i := Nat.mod_eq_of_lt h
-      simp [h₁, h₂]
-    · have h₁ : a.toList.length ≤ i := by simp; omega
-      rw [List.getElem_append_right h₁]
-      simp only [Array.length_toList, size_toArray]
-      specialize ih (i - m) (by simp_all [Nat.add_one_mul]; omega)
-      have h₂ : i / m = (i - m) / m + 1 := by
-        conv => lhs; rw [show i = i - m + m by omega]
-        rw [Nat.add_div_right]
-        exact Nat.pos_of_lt_mul_left hi
-      simp only [Array.length_toList, size_toArray] at h₁
-      have h₃ : (i - m) % m = i % m := (Nat.mod_eq_sub_mod h₁).symm
-      simp_all
-
-theorem getElem?_flatten (l : Vector (Vector β m) n) (i : Nat) :
-    l.flatten[i]? =
-      if hi : i < n * m then
-        haveI : i / m < n := by rwa [Nat.div_lt_iff_lt_mul (Nat.pos_of_lt_mul_left hi)]
-        haveI : i % m < m := Nat.mod_lt _ (Nat.pos_of_lt_mul_left hi)
-        some l[i / m][i % m]
-      else
-        none := by
-  simp [getElem?_def]
-
-@[simp] theorem flatten_singleton (l : Vector α n) : #v[l].flatten = l.cast (by simp) := by
-  simp [flatten]
-
-theorem mem_flatten {L : Vector (Vector α n) m} : a ∈ L.flatten ↔ ∃ l, l ∈ L ∧ a ∈ l := by
-  rcases L with ⟨L, rfl⟩
-  simp [Array.mem_flatten]
-  constructor
-  · rintro ⟨_, ⟨l, h₁, rfl⟩, h₂⟩
-    exact ⟨l, h₁, by simpa using h₂⟩
-  · rintro ⟨l, h₁, h₂⟩
-    exact ⟨l.toArray, ⟨l, h₁, rfl⟩, by simpa using h₂⟩
-
-theorem exists_of_mem_flatten : a ∈ flatten L → ∃ l, l ∈ L ∧ a ∈ l := mem_flatten.1
-
-theorem mem_flatten_of_mem (lL : l ∈ L) (al : a ∈ l) : a ∈ flatten L := mem_flatten.2 ⟨l, lL, al⟩
-
-theorem forall_mem_flatten {p : α → Prop} {L : Vector (Vector α n) m} :
-    (∀ (x) (_ : x ∈ flatten L), p x) ↔ ∀ (l) (_ : l ∈ L) (x) (_ : x ∈ l), p x := by
-  simp only [mem_flatten, forall_exists_index, and_imp]
-  constructor <;> (intros; solve_by_elim)
-
-@[simp] theorem map_flatten (f : α → β) (L : Vector (Vector α n) m) :
-    (flatten L).map f = (map (map f) L).flatten := by
-  induction L using vector₂_induction with
-  | of xss h₁ h₂ => simp
-
-@[simp] theorem flatten_append (L₁ : Vector (Vector α n) m₁) (L₂ : Vector (Vector α n) m₂) :
-    flatten (L₁ ++ L₂) = (flatten L₁ ++ flatten L₂).cast (by simp [Nat.add_mul]) := by
-  induction L₁ using vector₂_induction
-  induction L₂ using vector₂_induction
-  simp
-
-theorem flatten_push (L : Vector (Vector α n) m) (l : Vector α n) :
-    flatten (L.push l) = (flatten L ++ l).cast (by simp [Nat.add_mul]) := by
-  induction L using vector₂_induction
-  rcases l with ⟨l⟩
-  simp [Array.flatten_push]
-
-theorem flatten_flatten {L : Vector (Vector (Vector α n) m) k} :
-    flatten (flatten L) = (flatten (map flatten L)).cast (by simp [Nat.mul_assoc]) := by
-  induction L using vector₃_induction with
-  | of xss h₁ h₂ h₃ =>
-    -- simp [Array.flatten_flatten] -- FIXME: `simp` produces a bad proof here!
-    simp [Array.map_attach, Array.flatten_flatten, Array.map_pmap]
-
-/-- Two vectors of constant length vectors are equal iff their flattens coincide. -/
-theorem eq_iff_flatten_eq {L L' : Vector (Vector α n) m} :
-    L = L' ↔ L.flatten = L'.flatten := by
-  induction L using vector₂_induction with | of L h₁ h₂ =>
-  induction L' using vector₂_induction with | of L' h₁' h₂' =>
-  simp only [eq_mk, flatten_mk, Array.map_map, Function.comp_apply, Array.map_subtype,
-    Array.unattach_attach, Array.map_id_fun', id_eq]
-  constructor
-  · intro h
-    suffices L = L' by simp_all
-    apply Array.ext_getElem?
-    intro i
-    replace h := congrArg (fun x => x[i]?.map (fun x => x.toArray)) h
-    simpa [Option.map_pmap] using h
-  · intro h
-    have w : L.map Array.size = L'.map Array.size := by
-      ext i h h'
-      · simp_all
-      · simp only [Array.getElem_map]
-        rw [h₂ _ (by simp), h₂' _ (by simp)]
-    have := Array.eq_iff_flatten_eq.mpr ⟨h, w⟩
-    subst this
-    rfl
-
-
-/-! ### flatMap -/
-
-@[simp] theorem flatMap_mk (l : Array α) (h : l.size = m) (f : α → Vector β n) :
-    (mk l h).flatMap f =
-      mk (l.flatMap (fun a => (f a).toArray)) (by simp [Array.map_const', h]) := by
-  simp [flatMap]
-
-@[simp] theorem flatMap_toArray (l : Vector α n) (f : α → Vector β m) :
-    l.toArray.flatMap (fun a => (f a).toArray) = (l.flatMap f).toArray := by
-  rcases l with ⟨l, rfl⟩
-  simp
-
-theorem flatMap_def (l : Vector α n) (f : α → Vector β m) : l.flatMap f = flatten (map f l) := by
-  rcases l with ⟨l, rfl⟩
-  simp [Array.flatMap_def, Function.comp_def]
-
-@[simp] theorem getElem_flatMap (l : Vector α n) (f : α → Vector β m) (i : Nat) (hi : i < n * m) :
-    (l.flatMap f)[i] =
-      haveI : i / m < n := by rwa [Nat.div_lt_iff_lt_mul (Nat.pos_of_lt_mul_left hi)]
-      haveI : i % m < m := Nat.mod_lt _ (Nat.pos_of_lt_mul_left hi)
-      (f (l[i / m]))[i % m] := by
-  rw [flatMap_def, getElem_flatten, getElem_map]
-
-theorem getElem?_flatMap (l : Vector α n) (f : α → Vector β m) (i : Nat) :
-    (l.flatMap f)[i]? =
-      if hi : i < n * m then
-        haveI : i / m < n := by rwa [Nat.div_lt_iff_lt_mul (Nat.pos_of_lt_mul_left hi)]
-        haveI : i % m < m := Nat.mod_lt _ (Nat.pos_of_lt_mul_left hi)
-        some ((f (l[i / m]))[i % m])
-      else
-        none := by
-  simp [getElem?_def]
-
-@[simp] theorem flatMap_id (l : Vector (Vector α m) n) : l.flatMap id = l.flatten := by simp [flatMap_def]
-
-@[simp] theorem flatMap_id' (l : Vector (Vector α m) n) : l.flatMap (fun a => a) = l.flatten := by simp [flatMap_def]
-
-@[simp] theorem mem_flatMap {f : α → Vector β m} {b} {l : Vector α n} : 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⟩⟩
-
-theorem exists_of_mem_flatMap {b : β} {l : Vector α n} {f : α → Vector β m} :
-    b ∈ l.flatMap f → ∃ a, a ∈ l ∧ b ∈ f a := mem_flatMap.1
-
-theorem mem_flatMap_of_mem {b : β} {l : Vector α n} {f : α → Vector β m} {a} (al : a ∈ l) (h : b ∈ f a) :
-    b ∈ l.flatMap f := mem_flatMap.2 ⟨a, al, h⟩
-
-theorem forall_mem_flatMap {p : β → Prop} {l : Vector α n} {f : α → Vector β m} :
-    (∀ (x) (_ : x ∈ l.flatMap f), p x) ↔ ∀ (a) (_ : a ∈ l) (b) (_ : b ∈ f a), p b := by
-  simp only [mem_flatMap, forall_exists_index, and_imp]
-  constructor <;> (intros; solve_by_elim)
-
-theorem flatMap_singleton (f : α → Vector β m) (x : α) : #v[x].flatMap f = (f x).cast (by simp) := by
-  simp [flatMap_def]
-
-@[simp] theorem flatMap_singleton' (l : Vector α n) : (l.flatMap fun x => #v[x]) = l.cast (by simp) := by
-  rcases l with ⟨l, rfl⟩
-  simp
-
-@[simp] theorem flatMap_append (xs ys : Vector α n) (f : α → Vector β m) :
-    (xs ++ ys).flatMap f = (xs.flatMap f ++ ys.flatMap f).cast (by simp [Nat.add_mul]) := by
-  rcases xs with ⟨xs⟩
-  rcases ys with ⟨ys⟩
-  simp [flatMap_def, flatten_append]
-
-theorem flatMap_assoc {α β} (l : Vector α n) (f : α → Vector β m) (g : β → Vector γ k) :
-    (l.flatMap f).flatMap g = (l.flatMap fun x => (f x).flatMap g).cast (by simp [Nat.mul_assoc]) := by
-  rcases l with ⟨l, rfl⟩
-  simp [Array.flatMap_assoc]
-
-theorem map_flatMap (f : β → γ) (g : α → Vector β m) (l : Vector α n) :
-     (l.flatMap g).map f = l.flatMap fun a => (g a).map f := by
-  rcases l with ⟨l, rfl⟩
-  simp [Array.map_flatMap]
-
-theorem flatMap_map (f : α → β) (g : β → Vector γ k) (l : Vector α n) :
-     (map f l).flatMap g = l.flatMap (fun a => g (f a)) := by
-  rcases l with ⟨l, rfl⟩
-  simp [Array.flatMap_map]
-
-theorem map_eq_flatMap {α β} (f : α → β) (l : Vector α n) :
-    map f l = (l.flatMap fun x => #v[f x]).cast (by simp) := by
-  rcases l with ⟨l, rfl⟩
-  simp [Array.map_eq_flatMap]
-
-/-! Content below this point has not yet been aligned with `List` and `Array`. -/
-
-@[simp] theorem getElem_ofFn {α n} (f : Fin n → α) (i : Nat) (h : i < n) :
-    (Vector.ofFn f)[i] = f ⟨i, by simpa using h⟩ := by
-  simp [ofFn]
-
 @[simp] theorem getElem_push_last {v : Vector α n} {x : α} : (v.push x)[n] = x := by
   rcases v with ⟨data, rfl⟩
   simp
@@ -1679,6 +1059,28 @@ defeq issues in the implicit size argument.
     subst h
     simp [pop, back, back!, ← Array.eq_push_pop_back!_of_size_ne_zero]
 
+/-! ### append -/
+
+theorem getElem_append (a : Vector α n) (b : Vector α m) (i : Nat) (hi : i < n + m) :
+    (a ++ b)[i] = if h : i < n then a[i] else b[i - n] := by
+  rcases a with ⟨a, rfl⟩
+  rcases b with ⟨b, rfl⟩
+  simp [Array.getElem_append, hi]
+
+theorem getElem_append_left {a : Vector α n} {b : Vector α m} {i : Nat} (hi : i < n) :
+    (a ++ b)[i] = a[i] := by simp [getElem_append, hi]
+
+theorem getElem_append_right {a : Vector α n} {b : Vector α m} {i : Nat} (h : i < n + m) (hi : n ≤ i) :
+    (a ++ b)[i] = b[i - n] := by
+  rw [getElem_append, dif_neg (by omega)]
+
+/-! ### cast -/
+
+@[simp] theorem getElem_cast (a : Vector α n) (h : n = m) (i : Nat) (hi : i < m) :
+    (a.cast h)[i] = a[i] := by
+  cases a
+  simp
+
 /-! ### extract -/
 
 @[simp] theorem getElem_extract (a : Vector α n) (start stop) (i : Nat) (hi : i < min stop n - start) :
@@ -1686,6 +1088,13 @@ defeq issues in the implicit size argument.
   cases a
   simp
 
+/-! ### map -/
+
+@[simp] theorem getElem_map (f : α → β) (a : Vector α n) (i : Nat) (hi : i < n) :
+    (a.map f)[i] = f a[i] := by
+  cases a
+  simp
+
 /-! ### zipWith -/
 
 @[simp] theorem getElem_zipWith (f : α → β → γ) (a : Vector α n) (b : Vector β n) (i : Nat)
@@ -1694,37 +1103,6 @@ defeq issues in the implicit size argument.
   cases b
   simp
 
-/-! ### foldlM and foldrM -/
-
-@[simp] theorem foldlM_append [Monad m] [LawfulMonad m] (f : β → α → m β) (b) (l : Vector α n) (l' : Vector α n') :
-    (l ++ l').foldlM f b = l.foldlM f b >>= l'.foldlM f := by
-  cases l
-  cases l'
-  simp
-
-@[simp] theorem foldrM_push [Monad m] (f : α → β → m β) (init : β) (l : Vector α n) (a : α) :
-    (l.push a).foldrM f init = f a init >>= l.foldrM f := by
-  cases l
-  simp
-
-theorem foldl_eq_foldlM (f : β → α → β) (b) (l : Vector α n) :
-    l.foldl f b = l.foldlM (m := Id) f b := by
-  cases l
-  simp [Array.foldl_eq_foldlM]
-
-theorem foldr_eq_foldrM (f : α → β → β) (b) (l : Vector α n) :
-    l.foldr f b = l.foldrM (m := Id) f b := by
-  cases l
-  simp [Array.foldr_eq_foldrM]
-
-@[simp] theorem id_run_foldlM (f : β → α → Id β) (b) (l : Vector α n) :
-    Id.run (l.foldlM f b) = l.foldl f b := (foldl_eq_foldlM f b l).symm
-
-@[simp] theorem id_run_foldrM (f : α → β → Id β) (b) (l : Vector α n) :
-    Id.run (l.foldrM f b) = l.foldr f b := (foldr_eq_foldrM f b l).symm
-
-/-! ### foldl and foldr -/
-
 /-! ### take -/
 
 @[simp] theorem take_size (a : Vector α n) : a.take n = a.cast (by simp) := by

src/Init/Grind.lean

@@ -10,5 +10,3 @@ import Init.Grind.Lemmas
 import Init.Grind.Cases
 import Init.Grind.Propagator
 import Init.Grind.Util
-import Init.Grind.Offset
-import Init.Grind.PP

src/Init/Grind/Lemmas.lean

@@ -12,9 +12,6 @@ import Init.Grind.Util
 
 namespace Lean.Grind
 
-theorem rfl_true : true = true :=
-  rfl
-
 theorem intro_with_eq (p p' q : Prop) (he : p = p') (h : p' → q) : p → q :=
   fun hp => h (he.mp hp)
 
@@ -28,9 +25,6 @@ theorem and_eq_of_eq_false_right {a b : Prop} (h : b = False) : (a ∧ b) = Fals
 theorem eq_true_of_and_eq_true_left {a b : Prop} (h : (a ∧ b) = True) : a = True := by simp_all
 theorem eq_true_of_and_eq_true_right {a b : Prop} (h : (a ∧ b) = True) : b = True := by simp_all
 
-theorem or_of_and_eq_false {a b : Prop} (h : (a ∧ b) = False) : (¬a ∨ ¬b) := by
-  by_cases a <;> by_cases b <;> simp_all
-
 /-! Or -/
 
 theorem or_eq_of_eq_true_left {a b : Prop} (h : a = True) : (a ∨ b) = True := by simp [h]
@@ -41,15 +35,6 @@ theorem or_eq_of_eq_false_right {a b : Prop} (h : b = False) : (a ∨ b) = a :=
 theorem eq_false_of_or_eq_false_left {a b : Prop} (h : (a ∨ b) = False) : a = False := by simp_all
 theorem eq_false_of_or_eq_false_right {a b : Prop} (h : (a ∨ b) = False) : b = False := by simp_all
 
-/-! Implies -/
-
-theorem imp_eq_of_eq_false_left {a b : Prop} (h : a = False) : (a → b) = True := by simp [h]
-theorem imp_eq_of_eq_true_right {a b : Prop} (h : b = True) : (a → b) = True := by simp [h]
-theorem imp_eq_of_eq_true_left {a b : Prop} (h : a = True) : (a → b) = b := by simp [h]
-
-theorem eq_true_of_imp_eq_false {a b : Prop} (h : (a → b) = False) : a = True := by simp_all
-theorem eq_false_of_imp_eq_false {a b : Prop} (h : (a → b) = False) : b = False := by simp_all
-
 /-! Not -/
 
 theorem not_eq_of_eq_true {a : Prop} (h : a = True) : (Not a) = False := by simp [h]
@@ -69,12 +54,6 @@ theorem eq_eq_of_eq_true_right {a b : Prop} (h : b = True) : (a = b) = a := by s
 theorem eq_congr  {α : Sort u} {a₁ b₁ a₂ b₂ : α} (h₁ : a₁ = a₂) (h₂ : b₁ = b₂) : (a₁ = b₁) = (a₂ = b₂) := by simp [*]
 theorem eq_congr' {α : Sort u} {a₁ b₁ a₂ b₂ : α} (h₁ : a₁ = b₂) (h₂ : b₁ = a₂) : (a₁ = b₁) = (a₂ = b₂) := by rw [h₁, h₂, Eq.comm (a := a₂)]
 
-/- The following two helper theorems are used to case-split `a = b` representing `iff`. -/
-theorem of_eq_eq_true {a b : Prop} (h : (a = b) = True) : (¬a ∨ b) ∧ (¬b ∨ a) := by
-  by_cases a <;> by_cases b <;> simp_all
-theorem of_eq_eq_false {a b : Prop} (h : (a = b) = False) : (¬a ∨ ¬b) ∧ (b ∨ a) := by
-  by_cases a <;> by_cases b <;> simp_all
-
 /-! Forall -/
 
 theorem forall_propagator (p : Prop) (q : p → Prop) (q' : Prop) (h₁ : p = True) (h₂ : q (of_eq_true h₁) = q') : (∀ hp : p, q hp) = q' := by
@@ -82,28 +61,4 @@ theorem forall_propagator (p : Prop) (q : p → Prop) (q' : Prop) (h₁ : p = Tr
   · intro h'; exact Eq.mp h₂ (h' (of_eq_true h₁))
   · intro h'; intros; exact Eq.mpr h₂ h'
 
-theorem of_forall_eq_false (α : Sort u) (p : α → Prop) (h : (∀ x : α, p x) = False) : ∃ x : α, ¬ p x := by simp_all
-
-/-! dite -/
-
-theorem dite_cond_eq_true' {α : Sort u} {c : Prop} {_ : Decidable c} {a : c → α} {b : ¬ c → α} {r : α} (h₁ : c = True) (h₂ : a (of_eq_true h₁) = r) : (dite c a b) = r := by simp [h₁, h₂]
-theorem dite_cond_eq_false' {α : Sort u} {c : Prop} {_ : Decidable c} {a : c → α} {b : ¬ c → α} {r : α} (h₁ : c = False) (h₂ : b (of_eq_false h₁) = r) : (dite c a b) = r := by simp [h₁, h₂]
-
-/-! Casts -/
-
-theorem eqRec_heq.{u_1, u_2} {α : Sort u_2} {a : α}
-        {motive : (x : α) → a = x → Sort u_1} (v : motive a (Eq.refl a)) {b : α} (h : a = b)
-        : HEq (@Eq.rec α a motive v b h) v := by
- subst h; rfl
-
-theorem eqRecOn_heq.{u_1, u_2} {α : Sort u_2} {a : α}
-        {motive : (x : α) → a = x → Sort u_1} {b : α} (h : a = b) (v : motive a (Eq.refl a))
-        : HEq (@Eq.recOn α a motive b h v) v := by
- subst h; rfl
-
-theorem eqNDRec_heq.{u_1, u_2} {α : Sort u_2} {a : α}
-        {motive : α → Sort u_1} (v : motive a) {b : α} (h : a = b)
-        : HEq (@Eq.ndrec α a motive v b h) v := by
- subst h; rfl
-
 end Lean.Grind

src/Init/Grind/Norm.lean

@@ -5,7 +5,6 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Init.SimpLemmas
-import Init.PropLemmas
 import Init.Classical
 import Init.ByCases
 
@@ -41,17 +40,10 @@ attribute [grind_norm] not_true
 -- False
 attribute [grind_norm] not_false_eq_true
 
--- Remark: we disabled the following normalization rule because we want this information when implementing splitting heuristics
 -- Implication as a clause
-theorem imp_eq (p q : Prop) : (p → q) = (¬ p ∨ q) := by
+@[grind_norm↓] theorem imp_eq (p q : Prop) : (p → q) = (¬ p ∨ q) := by
   by_cases p <;> by_cases q <;> simp [*]
 
-@[grind_norm] theorem true_imp_eq (p : Prop) : (True → p) = p := by simp
-@[grind_norm] theorem false_imp_eq (p : Prop) : (False → p) = True := by simp
-@[grind_norm] theorem imp_true_eq (p : Prop) : (p → True) = True := by simp
-@[grind_norm] theorem imp_false_eq (p : Prop) : (p → False) = ¬p := by simp
-@[grind_norm] theorem imp_self_eq (p : Prop) : (p → p) = True := by simp
-
 -- And
 @[grind_norm↓] theorem not_and (p q : Prop) : (¬(p ∧ q)) = (¬p ∨ ¬q) := by
   by_cases p <;> by_cases q <;> simp [*]
@@ -66,19 +58,13 @@ attribute [grind_norm] ite_true ite_false
 @[grind_norm↓] theorem not_ite {_ : Decidable p} (q r : Prop) : (¬ite p q r) = ite p (¬q) (¬r) := by
   by_cases p <;> simp [*]
 
-@[grind_norm] theorem ite_true_false {_ : Decidable p} : (ite p True False) = p := by
-  by_cases p <;> simp
-
-@[grind_norm] theorem ite_false_true {_ : Decidable p} : (ite p False True) = ¬p := by
-  by_cases p <;> simp
-
 -- Forall
 @[grind_norm↓] theorem not_forall (p : α → Prop) : (¬∀ x, p x) = ∃ x, ¬p x := by simp
 attribute [grind_norm] forall_and
 
 -- Exists
 @[grind_norm↓] theorem not_exists (p : α → Prop) : (¬∃ x, p x) = ∀ x, ¬p x := by simp
-attribute [grind_norm] exists_const exists_or exists_prop exists_and_left exists_and_right
+attribute [grind_norm] exists_const exists_or
 
 -- Bool cond
 @[grind_norm] theorem cond_eq_ite (c : Bool) (a b : α) : cond c a b = ite c a b := by
@@ -121,7 +107,4 @@ attribute [grind_norm] Nat.le_zero_eq
 -- GT GE
 attribute [grind_norm] GT.gt GE.ge
 
--- Succ
-attribute [grind_norm] Nat.succ_eq_add_one
-
 end Lean.Grind

src/Init/Grind/Offset.lean

@@ -1,92 +0,0 @@
-/-
-Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Init.Core
-import Init.Omega
-
-namespace Lean.Grind
-abbrev isLt (x y : Nat) : Bool := x < y
-abbrev isLE (x y : Nat) : Bool := x ≤ y
-
-/-! Theorems for transitivity. -/
-theorem Nat.le_ro (u w v k : Nat) : u ≤ w → w ≤ v + k → u ≤ v + k := by
-  omega
-theorem Nat.le_lo (u w v k : Nat) : u ≤ w → w + k ≤ v → u + k ≤ v := by
-  omega
-theorem Nat.lo_le (u w v k : Nat) : u + k ≤ w → w ≤ v → u + k ≤ v := by
-  omega
-theorem Nat.lo_lo (u w v k₁ k₂ : Nat) : u + k₁ ≤ w → w + k₂ ≤ v → u + (k₁ + k₂) ≤ v := by
-  omega
-theorem Nat.lo_ro_1 (u w v k₁ k₂ : Nat) : isLt k₂ k₁ = true → u + k₁ ≤ w → w ≤ v + k₂ → u + (k₁ - k₂) ≤ v := by
-  simp [isLt]; omega
-theorem Nat.lo_ro_2 (u w v k₁ k₂ : Nat) : u + k₁ ≤ w → w ≤ v + k₂ → u ≤ v + (k₂ - k₁) := by
-  omega
-theorem Nat.ro_le (u w v k : Nat) : u ≤ w + k → w ≤ v → u ≤ v + k := by
-  omega
-theorem Nat.ro_lo_1 (u w v k₁ k₂ : Nat) : u ≤ w + k₁ → w + k₂ ≤ v → u ≤ v + (k₁ - k₂) := by
-  omega
-theorem Nat.ro_lo_2 (u w v k₁ k₂ : Nat) : isLt k₁ k₂ = true → u ≤ w + k₁ → w + k₂ ≤ v → u + (k₂ - k₁) ≤ v := by
-  simp [isLt]; omega
-theorem Nat.ro_ro (u w v k₁ k₂ : Nat) : u ≤ w + k₁ → w ≤ v + k₂ → u ≤ v + (k₁ + k₂) := by
-  omega
-
-/-! Theorems for negating constraints. -/
-theorem Nat.of_le_eq_false (u v : Nat) : ((u ≤ v) = False) → v + 1 ≤ u := by
-  simp; omega
-theorem Nat.of_lo_eq_false_1 (u v : Nat) : ((u + 1 ≤ v) = False) → v ≤ u := by
-  simp; omega
-theorem Nat.of_lo_eq_false (u v k : Nat) : ((u + k ≤ v) = False) → v ≤ u + (k-1) := by
-  simp; omega
-theorem Nat.of_ro_eq_false (u v k : Nat) : ((u ≤ v + k) = False) → v + (k+1) ≤ u := by
-  simp; omega
-
-/-! Theorems for closing a goal. -/
-theorem Nat.unsat_le_lo (u v k : Nat) : isLt 0 k = true → u ≤ v → v + k ≤ u → False := by
-  simp [isLt]; omega
-theorem Nat.unsat_lo_lo (u v k₁ k₂ : Nat) : isLt 0 (k₁+k₂) = true → u + k₁ ≤ v → v + k₂ ≤ u → False := by
-  simp [isLt]; omega
-theorem Nat.unsat_lo_ro (u v k₁ k₂ : Nat) : isLt k₂ k₁ = true → u + k₁ ≤ v → v ≤ u + k₂ → False := by
-  simp [isLt]; omega
-
-/-! Theorems for propagating constraints to `True` -/
-theorem Nat.lo_eq_true_of_lo (u v k₁ k₂ : Nat) : isLE k₂ k₁ = true → u + k₁ ≤ v → (u + k₂ ≤ v) = True :=
-  by simp [isLt]; omega
-theorem Nat.le_eq_true_of_lo (u v k : Nat) : u + k ≤ v → (u ≤ v) = True :=
-  by simp; omega
-theorem Nat.le_eq_true_of_le (u v : Nat) : u ≤ v → (u ≤ v) = True :=
-  by simp
-theorem Nat.ro_eq_true_of_lo (u v k₁ k₂ : Nat) : u + k₁ ≤ v → (u ≤ v + k₂) = True :=
-  by simp; omega
-theorem Nat.ro_eq_true_of_le (u v k : Nat) : u ≤ v → (u ≤ v + k) = True :=
-  by simp; omega
-theorem Nat.ro_eq_true_of_ro (u v k₁ k₂ : Nat) : isLE k₁ k₂ = true → u ≤ v + k₁ → (u ≤ v + k₂) = True :=
-  by simp [isLE]; omega
-
-/-!
-Theorems for propagating constraints to `False`.
-They are variants of the theorems for closing a goal.
--/
-theorem Nat.lo_eq_false_of_le (u v k : Nat) : isLt 0 k = true → u ≤ v → (v + k ≤ u) = False := by
- simp [isLt]; omega
-theorem Nat.le_eq_false_of_lo (u v k : Nat) : isLt 0 k = true → u + k ≤ v → (v ≤ u) = False := by
- simp [isLt]; omega
-theorem Nat.lo_eq_false_of_lo (u v k₁ k₂ : Nat) : isLt 0 (k₁+k₂) = true → u + k₁ ≤ v → (v + k₂ ≤ u) = False := by
-  simp [isLt]; omega
-theorem Nat.ro_eq_false_of_lo (u v k₁ k₂ : Nat) : isLt k₂ k₁ = true → u + k₁ ≤ v → (v ≤ u + k₂) = False := by
-  simp [isLt]; omega
-theorem Nat.lo_eq_false_of_ro (u v k₁ k₂ : Nat) : isLt k₁ k₂ = true → u ≤ v + k₁ → (v + k₂ ≤ u) = False := by
-  simp [isLt]; omega
-
-/-!
-Helper theorems for equality propagation
--/
-
-theorem Nat.le_of_eq_1 (u v : Nat) : u = v → u ≤ v := by omega
-theorem Nat.le_of_eq_2 (u v : Nat) : u = v → v ≤ u := by omega
-theorem Nat.eq_of_le_of_le (u v : Nat) : u ≤ v → v ≤ u → u = v := by omega
-theorem Nat.le_offset (a k : Nat) : k ≤ a + k := by omega
-
-end Lean.Grind

src/Init/Grind/PP.lean

@@ -1,30 +0,0 @@
-/-
-Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Init.NotationExtra
-
-namespace Lean.Grind
-/-!
-This is a hackish module for hovering node information in the `grind` tactic state.
--/
-
-inductive NodeDef where
-  | unit
-
-set_option linter.unusedVariables false in
-def node_def (_ : Nat) {α : Sort u} {a : α} : NodeDef := .unit
-
-@[app_unexpander node_def]
-def nodeDefUnexpander : PrettyPrinter.Unexpander := fun stx => do
-  match stx with
-  | `($_ $id:num) => return mkIdent <| Name.mkSimple $ "#" ++ toString id.getNat
-  | _ => throw ()
-
-@[app_unexpander NodeDef]
-def NodeDefUnexpander : PrettyPrinter.Unexpander := fun _ => do
-  return mkIdent <| Name.mkSimple "NodeDef"
-
-end Lean.Grind

src/Init/Grind/Tactics.lean

@@ -6,27 +6,20 @@ Authors: Leonardo de Moura
 prelude
 import Init.Tactics
 
-namespace Lean.Parser.Attr
-
-syntax grindEq     := "="
-syntax grindEqBoth := atomic("_" "=" "_")
-syntax grindEqRhs  := atomic("=" "_")
-syntax grindBwd    := "←"
-syntax grindFwd    := "→"
-
-syntax (name := grind) "grind" (grindEqBoth <|> grindEqRhs <|> grindEq <|> grindBwd <|> grindFwd)? : attr
-
-end Lean.Parser.Attr
-
 namespace Lean.Grind
 /--
 The configuration for `grind`.
-Passed to `grind` using, for example, the `grind (config := { matchEqs := true })` syntax.
+Passed to `grind` using, for example, the `grind (config := { eager := true })` syntax.
 -/
 structure Config where
-  /-- Maximum number of case-splits in a proof search branch. It does not include splits performed during normalization. -/
-  splits : Nat := 8
-  /-- Maximum number of E-matching (aka heuristic theorem instantiation) rounds before each case split. -/
+  /-- When `eager` is true (default: `false`), `grind` eagerly splits `if-then-else` and `match` expressions during internalization. -/
+  eager : Bool := false
+  /-- Maximum number of branches (i.e., case-splits) in the proof search tree. -/
+  splits : Nat := 100
+  /--
+  Maximum number of E-matching (aka heuristic theorem instantiation)
+  in a proof search tree branch.
+  -/
   ematch : Nat := 5
   /--
   Maximum term generation.
@@ -35,20 +28,6 @@ structure Config where
   gen : Nat := 5
   /-- Maximum number of theorem instances generated using E-matching in a proof search tree branch. -/
   instances : Nat := 1000
-  /-- If `matchEqs` is `true`, `grind` uses `match`-equations as E-matching theorems. -/
-  matchEqs : Bool := true
-  /-- If `splitMatch` is `true`, `grind` performs case-splitting on `match`-expressions during the search. -/
-  splitMatch : Bool := true
-  /-- If `splitIte` is `true`, `grind` performs case-splitting on `if-then-else` expressions during the search. -/
-  splitIte : Bool := true
-  /--
-  If `splitIndPred` is `true`, `grind` performs case-splitting on inductive predicates.
-  Otherwise, it performs case-splitting only on types marked with `[grind_split]` attribute. -/
-  splitIndPred : Bool := true
-  /-- By default, `grind` halts as soon as it encounters a sub-goal where no further progress can be made. -/
-  failures : Nat := 1
-  /-- Maximum number of heartbeats (in thousands) the canonicalizer can spend per definitional equality test. -/
-  canonHeartbeats : Nat := 1000
   deriving Inhabited, BEq
 
 end Lean.Grind

src/Init/Grind/Util.lean

@@ -9,26 +9,11 @@ import Init.Core
 namespace Lean.Grind
 
 /-- A helper gadget for annotating nested proofs in goals. -/
-def nestedProof (p : Prop) {h : p} : p := h
+def nestedProof (p : Prop) (h : p) : p := h
 
-/--
-Gadget for marking terms that should not be normalized by `grind`s simplifier.
-`grind` uses a simproc to implement this feature.
-We use it when adding instances of `match`-equations to prevent them from being simplified to true.
--/
-def doNotSimp {α : Sort u} (a : α) : α := a
+set_option pp.proofs true
 
-/-- Gadget for representing offsets `t+k` in patterns. -/
-def offset (a b : Nat) : Nat := a + b
-
-/--
-Gadget for annotating the equalities in `match`-equations conclusions.
-`_origin` is the term used to instantiate the `match`-equation using E-matching.
-When `EqMatch a b origin` is `True`, we mark `origin` as a resolved case-split.
--/
-def EqMatch (a b : α) {_origin : α} : Prop := a = b
-
-theorem nestedProof_congr (p q : Prop) (h : p = q) (hp : p) (hq : q) : HEq (@nestedProof p hp) (@nestedProof q hq) := by
+theorem nestedProof_congr (p q : Prop) (h : p = q) (hp : p) (hq : q) : HEq (nestedProof p hp) (nestedProof q hq) := by
   subst h; apply HEq.refl
 
 end Lean.Grind

src/Init/Prelude.lean

@@ -4170,16 +4170,6 @@ def withRef [Monad m] [MonadRef m] {α} (ref : Syntax) (x : m α) : m α :=
   let ref := replaceRef ref oldRef
   MonadRef.withRef ref x
 
-/--
-If `ref? = some ref`, run `x : m α` with a modified value for the `ref` by calling `withRef`.
-Otherwise, run `x` directly.
--/
-@[always_inline, inline]
-def withRef? [Monad m] [MonadRef m] {α} (ref? : Option Syntax) (x : m α) : m α :=
-  match ref? with
-  | some ref => withRef ref x
-  | _        => x
-
 /-- A monad that supports syntax quotations. Syntax quotations (in term
     position) are monadic values that when executed retrieve the current "macro
     scope" from the monad and apply it to every identifier they introduce

src/Init/Tactics.lean

@@ -818,7 +818,7 @@ syntax inductionAlt  := ppDedent(ppLine) inductionAltLHS+ " => " (hole <|> synth
 After `with`, there is an optional tactic that runs on all branches, and
 then a list of alternatives.
 -/
-syntax inductionAlts := " with" (ppSpace colGt tactic)? withPosition((colGe inductionAlt)*)
+syntax inductionAlts := " with" (ppSpace colGt tactic)? withPosition((colGe inductionAlt)+)
 
 /--
 Assuming `x` is a variable in the local context with an inductive type,

src/Lean/AddDecl.lean

@@ -21,6 +21,11 @@ def Environment.addDecl (env : Environment) (opts : Options) (decl : Declaration
   else
     addDeclCore env (Core.getMaxHeartbeats opts).toUSize decl cancelTk?
 
+def Environment.addAndCompile (env : Environment) (opts : Options) (decl : Declaration)
+    (cancelTk? : Option IO.CancelToken := none) : Except KernelException Environment := do
+  let env ← addDecl env opts decl cancelTk?
+  compileDecl env opts decl
+
 def addDecl (decl : Declaration) : CoreM Unit := do
   profileitM Exception "type checking" (← getOptions) do
     withTraceNode `Kernel (fun _ => return m!"typechecking declaration") do

src/Lean/Compiler/InitAttr.lean

@@ -144,7 +144,11 @@ def declareBuiltin (forDecl : Name) (value : Expr) : CoreM Unit := do
   let type := mkApp (mkConst `IO) (mkConst `Unit)
   let decl := Declaration.defnDecl { name, levelParams := [], type, value, hints := ReducibilityHints.opaque,
                                      safety := DefinitionSafety.safe }
-  addAndCompile decl
-  IO.ofExcept (setBuiltinInitAttr (← getEnv) name) >>= setEnv
+  match (← getEnv).addAndCompile {} decl with
+  -- TODO: pretty print error
+  | Except.error e => do
+    let msg ← (e.toMessageData {}).toString
+    throwError "failed to emit registration code for builtin '{forDecl}': {msg}"
+  | Except.ok env  => IO.ofExcept (setBuiltinInitAttr env name) >>= setEnv
 
 end Lean

src/Lean/Compiler/LCNF/MonoTypes.lean

@@ -74,6 +74,8 @@ partial def toMonoType (type : Expr) : CoreM Expr := do
   let type := type.headBeta
   if type.isErased then
     return erasedExpr
+  else if type.isErased then
+    return erasedExpr
   else if isTypeFormerType type then
     return erasedExpr
   else match type with

src/Lean/Compiler/Old.lean

@@ -53,3 +53,18 @@ def isUnsafeRecName? : Name → Option Name
   | _ => none
 
 end Compiler
+
+namespace Environment
+
+/--
+Compile the given block of mutual declarations.
+Assumes the declarations have already been added to the environment using `addDecl`.
+-/
+@[extern "lean_compile_decls"]
+opaque compileDecls (env : Environment) (opt : @& Options) (decls : @& List Name) : Except KernelException Environment
+
+/-- Compile the given declaration, it assumes the declaration has already been added to the environment using `addDecl`. -/
+def compileDecl (env : Environment) (opt : @& Options) (decl : @& Declaration) : Except KernelException Environment :=
+  compileDecls env opt (Compiler.getDeclNamesForCodeGen decl)
+
+end Environment

src/Lean/CoreM.lean

@@ -514,16 +514,13 @@ register_builtin_option compiler.enableNew : Bool := {
 @[extern "lean_lcnf_compile_decls"]
 opaque compileDeclsNew (declNames : List Name) : CoreM Unit
 
-@[extern "lean_compile_decls"]
-opaque compileDeclsOld (env : Environment) (opt : @& Options) (decls : @& List Name) : Except KernelException Environment
-
 def compileDecl (decl : Declaration) : CoreM Unit := do
   let opts ← getOptions
   let decls := Compiler.getDeclNamesForCodeGen decl
   if compiler.enableNew.get opts then
     compileDeclsNew decls
   let res ← withTraceNode `compiler (fun _ => return m!"compiling old: {decls}") do
-    return compileDeclsOld (← getEnv) opts decls
+    return (← getEnv).compileDecl opts decl
   match res with
   | Except.ok env => setEnv env
   | Except.error (KernelException.other msg) =>
@@ -536,7 +533,7 @@ def compileDecls (decls : List Name) : CoreM Unit := do
   let opts ← getOptions
   if compiler.enableNew.get opts then
     compileDeclsNew decls
-  match compileDeclsOld (← getEnv) opts decls with
+  match (← getEnv).compileDecls opts decls with
   | Except.ok env   => setEnv env
   | Except.error (KernelException.other msg) =>
     throwError msg

src/Lean/Data/AssocList.lean

@@ -24,7 +24,7 @@ abbrev empty : AssocList α β :=
 
 instance : EmptyCollection (AssocList α β) := ⟨empty⟩
 
-abbrev insertNew (m : AssocList α β) (k : α) (v : β) : AssocList α β :=
+abbrev insert (m : AssocList α β) (k : α) (v : β) : AssocList α β :=
   m.cons k v
 
 def isEmpty : AssocList α β → Bool
@@ -77,12 +77,6 @@ def replace [BEq α] (a : α) (b : β) : AssocList α β → AssocList α β
     | true  => cons a b es
     | false => cons k v (replace a b es)
 
-def insert [BEq α] (m : AssocList α β) (k : α) (v : β) : AssocList α β :=
-  if m.contains k then
-    m.replace k v
-  else
-    m.insertNew k v
-
 def erase [BEq α] (a : α) : AssocList α β → AssocList α β
   | nil         => nil
   | cons k v es => match k == a with

src/Lean/Data/Json/Printer.lean

@@ -11,22 +11,6 @@ import Init.Data.List.Impl
 namespace Lean
 namespace Json
 
-set_option maxRecDepth 1024 in
-/--
-This table contains for each UTF-8 byte whether we need to escape a string that contains it.
--/
-private def escapeTable : { xs : ByteArray // xs.size = 256 } :=
-  ⟨ByteArray.mk #[
-    1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
-    0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-    0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
-    0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-    1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
-    1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
-    1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
-    1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
-  ], by rfl⟩
-
 private def escapeAux (acc : String) (c : Char) : String :=
   -- escape ", \, \n and \r, keep all other characters ≥ 0x20 and render characters < 0x20 with \u
   if c = '"' then -- hack to prevent emacs from regarding the rest of the file as a string: "
@@ -55,27 +39,8 @@ private def escapeAux (acc : String) (c : Char) : String :=
     let d4 := Nat.digitChar (n % 16)
     acc ++ "\\u" |>.push d1 |>.push d2 |>.push d3 |>.push d4
 
-private def needEscape (s : String) : Bool :=
-  go s 0
-where
-  go (s : String) (i : Nat) : Bool :=
-    if h : i < s.utf8ByteSize then
-      let byte := s.getUtf8Byte i h
-      have h1 : byte.toNat < 256 := UInt8.toNat_lt_size byte
-      have h2 : escapeTable.val.size = 256 := escapeTable.property
-      if escapeTable.val.get byte.toNat (Nat.lt_of_lt_of_eq h1 h2.symm) == 0 then
-        go s (i + 1)
-      else
-        true
-    else
-      false
-
 def escape (s : String) (acc : String := "") : String :=
-  -- If we don't have any characters that need to be escaped we can just append right away.
-  if needEscape s then
-    s.foldl escapeAux acc
-  else
-    acc ++ s
+  s.foldl escapeAux acc
 
 def renderString (s : String) (acc : String := "") : String :=
   let acc := acc ++ "\""

src/Lean/Data/Lsp.lean

@@ -6,7 +6,6 @@ Authors: Marc Huisinga, Wojciech Nawrocki
 -/
 prelude
 import Lean.Data.Lsp.Basic
-import Lean.Data.Lsp.CancelParams
 import Lean.Data.Lsp.Capabilities
 import Lean.Data.Lsp.Client
 import Lean.Data.Lsp.Communication

src/Lean/Data/Lsp/Basic.lean

@@ -6,6 +6,7 @@ Authors: Marc Huisinga, Wojciech Nawrocki
 -/
 prelude
 import Lean.Data.Json
+import Lean.Data.JsonRpc
 
 /-! Defines most of the 'Basic Structures' in the LSP specification
 (https://microsoft.github.io/language-server-protocol/specifications/specification-current/),
@@ -18,6 +19,10 @@ namespace Lsp
 
 open Json
 
+structure CancelParams where
+  id : JsonRpc.RequestID
+  deriving Inhabited, BEq, ToJson, FromJson
+
 abbrev DocumentUri := String
 
 /-- We adopt the convention that zero-based UTF-16 positions as sent by LSP clients

src/Lean/Data/Lsp/CancelParams.lean

@@ -1,25 +0,0 @@
-/-
-Copyright (c) 2020 Marc Huisinga. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-
-Authors: Marc Huisinga, Wojciech Nawrocki
--/
-prelude
-import Lean.Data.JsonRpc
-
-/-! # Defines `Lean.Lsp.CancelParams`.
-
-This is separate from `Lean.Data.Lsp.Basic` to reduce transitive dependencies.
--/
-
-namespace Lean
-namespace Lsp
-
-open Json
-
-structure CancelParams where
-  id : JsonRpc.RequestID
-  deriving Inhabited, BEq, ToJson, FromJson
-
-end Lsp
-end Lean

src/Lean/Data/Lsp/Utf16.lean

@@ -6,6 +6,7 @@ Authors: Marc Huisinga, Wojciech Nawrocki
 -/
 prelude
 import Init.Data.String
+import Init.Data.Array
 import Lean.Data.Lsp.Basic
 import Lean.Data.Position
 import Lean.DeclarationRange

src/Lean/Elab/App.lean

@@ -1474,7 +1474,7 @@ where
     | field::fields, false => .fieldName field field.getId.getString! none fIdent :: toLVals fields false
 
 /-- Resolve `(.$id:ident)` using the expected type to infer namespace. -/
-private partial def resolveDotName (id : Syntax) (expectedType? : Option Expr) : TermElabM Expr := do
+private partial def resolveDotName (id : Syntax) (expectedType? : Option Expr) : TermElabM Name := do
   tryPostponeIfNoneOrMVar expectedType?
   let some expectedType := expectedType?
     | throwError "invalid dotted identifier notation, expected type must be known"
@@ -1489,7 +1489,7 @@ where
         withForallBody body k
       else
         k body
-  go (resultType : Expr) (expectedType : Expr) (previousExceptions : Array Exception) : TermElabM Expr := do
+  go (resultType : Expr) (expectedType : Expr) (previousExceptions : Array Exception) : TermElabM Name := do
     let resultType ← instantiateMVars resultType
     let resultTypeFn := resultType.cleanupAnnotations.getAppFn
     try
@@ -1497,12 +1497,9 @@ where
       let .const declName .. := resultTypeFn.cleanupAnnotations
         | throwError "invalid dotted identifier notation, expected type is not of the form (... → C ...) where C is a constant{indentExpr expectedType}"
       let idNew := declName ++ id.getId.eraseMacroScopes
-      if (← getEnv).contains idNew then
-        mkConst idNew
-      else if let some (fvar, []) ← resolveLocalName idNew then
-        return fvar
-      else
+      unless (← getEnv).contains idNew do
         throwError "invalid dotted identifier notation, unknown identifier `{idNew}` from expected type{indentExpr expectedType}"
+      return idNew
     catch
       | ex@(.error ..) =>
         match (← unfoldDefinition? resultType) with
@@ -1551,7 +1548,7 @@ private partial def elabAppFn (f : Syntax) (lvals : List LVal) (namedArgs : Arra
     | `(_)       => throwError "placeholders '_' cannot be used where a function is expected"
     | `(.$id:ident) =>
         addCompletionInfo <| CompletionInfo.dotId f id.getId (← getLCtx) expectedType?
-        let fConst ← resolveDotName id expectedType?
+        let fConst ← mkConst (← resolveDotName id expectedType?)
         let s ← observing do
           -- Use (force := true) because we want to record the result of .ident resolution even in patterns
           let fConst ← addTermInfo f fConst expectedType? (force := true)

src/Lean/Elab/Import.lean

@@ -5,7 +5,7 @@ Authors: Leonardo de Moura, Sebastian Ullrich
 -/
 prelude
 import Lean.Parser.Module
-import Lean.Util.Paths
+import Lean.Data.Json
 
 namespace Lean.Elab
 
@@ -42,12 +42,4 @@ def printImports (input : String) (fileName : Option String) : IO Unit := do
     let fname ← findOLean dep.module
     IO.println fname
 
-@[export lean_print_import_srcs]
-def printImportSrcs (input : String) (fileName : Option String) : IO Unit := do
-  let sp ← initSrcSearchPath
-  let (deps, _, _) ← parseImports input fileName
-  for dep in deps do
-    let fname ← findLean sp dep.module
-    IO.println fname
-
 end Lean.Elab

src/Lean/Elab/Tactic/BVDecide/Frontend/Attr.lean

@@ -38,9 +38,6 @@ declare_config_elab elabBVDecideConfig Lean.Elab.Tactic.BVDecide.Frontend.BVDeci
 builtin_initialize bvNormalizeExt : Meta.SimpExtension ←
   Meta.registerSimpAttr `bv_normalize "simp theorems used by bv_normalize"
 
-builtin_initialize intToBitVecExt : Meta.SimpExtension ←
-  Meta.registerSimpAttr `int_toBitVec "simp theorems used to convert UIntX/IntX statements into BitVec ones"
-
 /-- Builtin `bv_normalize` simprocs. -/
 builtin_initialize builtinBVNormalizeSimprocsRef : IO.Ref Meta.Simp.Simprocs ← IO.mkRef {}
 

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize.lean

@@ -4,28 +4,342 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Henrik Böving
 -/
 prelude
+import Lean.Meta.AppBuilder
+import Lean.Meta.Tactic.AC.Main
+import Lean.Elab.Tactic.Simp
 import Lean.Elab.Tactic.FalseOrByContra
-import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Basic
-import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Simproc
-import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Rewrite
-import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AndFlatten
-import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.EmbeddedConstraint
-import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AC
+import Lean.Elab.Tactic.BVDecide.Frontend.Attr
+import Std.Tactic.BVDecide.Normalize
+import Std.Tactic.BVDecide.Syntax
 
 /-!
-This module contains the implementation of `bv_normalize`, the preprocessing tactic for `bv_decide`.
-It is in essence a (slightly reduced) version of the Bitwuzla preprocessor together with Lean
-specific details.
+This module contains the implementation of `bv_normalize` which is effectively a custom `bv_normalize`
+simp set that is called like this: `simp only [seval, bv_normalize]`. The rules in `bv_normalize`
+fulfill two goals:
+1. Turn all hypothesis involving `Bool` and `BitVec` into the form `x = true` where `x` only consists
+   of a operations on `Bool` and `BitVec`. In particular no `Prop` should be contained. This makes
+   the reflection procedure further down the pipeline much easier to implement.
+2. Apply simplification rules from the Bitwuzla SMT solver.
 -/
 
 namespace Lean.Elab.Tactic.BVDecide
 namespace Frontend.Normalize
 
 open Lean.Meta
+open Std.Tactic.BVDecide.Normalize
 
-def passPipeline : PreProcessM (List Pass) := do
-  let mut passPipeline := [rewriteRulesPass]
-  let cfg ← PreProcessM.getConfig
+builtin_simproc ↓ [bv_normalize] reduceCond (cond _ _ _) := fun e => do
+  let_expr f@cond α c tb eb := e | return .continue
+  let r ← Simp.simp c
+  if r.expr.cleanupAnnotations.isConstOf ``Bool.true then
+    let pr := mkApp (mkApp4 (mkConst ``Bool.cond_pos f.constLevels!) α c tb eb) (← r.getProof)
+    return .visit { expr := tb, proof? := pr }
+  else if r.expr.cleanupAnnotations.isConstOf ``Bool.false then
+    let pr := mkApp (mkApp4 (mkConst ``Bool.cond_neg f.constLevels!) α c tb eb) (← r.getProof)
+    return .visit { expr := eb, proof? := pr }
+  else
+    return .continue
+
+builtin_simproc [bv_normalize] eqToBEq (((_ : Bool) = (_ : Bool))) := fun e => do
+  let_expr Eq _ lhs rhs := e | return .continue
+  match_expr rhs with
+  | Bool.true => return .continue
+  | _ =>
+    let beqApp ← mkAppM ``BEq.beq #[lhs, rhs]
+    let new := mkApp3 (mkConst ``Eq [1]) (mkConst ``Bool) beqApp (mkConst ``Bool.true)
+    let proof := mkApp2 (mkConst ``Bool.eq_to_beq) lhs rhs
+    return .done { expr := new, proof? := some proof }
+
+builtin_simproc [bv_normalize] andOnes ((_ : BitVec _) &&& (_ : BitVec _)) := fun e => do
+  let_expr HAnd.hAnd _ _ _ _ lhs rhs := e | return .continue
+  let some ⟨w, rhsValue⟩ ← getBitVecValue? rhs | return .continue
+  if rhsValue == -1#w then
+    let proof := mkApp2 (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.and_ones) (toExpr w) lhs
+    return .visit { expr := lhs, proof? := some proof }
+  else
+    return .continue
+
+builtin_simproc [bv_normalize] onesAnd ((_ : BitVec _) &&& (_ : BitVec _)) := fun e => do
+  let_expr HAnd.hAnd _ _ _ _ lhs rhs := e | return .continue
+  let some ⟨w, lhsValue⟩ ← getBitVecValue? lhs | return .continue
+  if lhsValue == -1#w then
+    let proof := mkApp2 (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.ones_and) (toExpr w) rhs
+    return .visit { expr := rhs, proof? := some proof }
+  else
+    return .continue
+
+builtin_simproc [bv_normalize] maxUlt (BitVec.ult (_ : BitVec _) (_ : BitVec _)) := fun e => do
+  let_expr BitVec.ult _ lhs rhs := e | return .continue
+  let some ⟨w, lhsValue⟩ ← getBitVecValue? lhs | return .continue
+  if lhsValue == -1#w then
+    let proof := mkApp2 (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.max_ult') (toExpr w) rhs
+    return .visit { expr := toExpr Bool.false, proof? := some proof }
+  else
+    return .continue
+
+-- A specialised version of BitVec.neg_eq_not_add so it doesn't trigger on -constant
+builtin_simproc [bv_normalize] neg_eq_not_add (-(_ : BitVec _)) := fun e => do
+  let_expr Neg.neg typ _ val := e | return .continue
+  let_expr BitVec widthExpr := typ | return .continue
+  let some w ← getNatValue? widthExpr | return .continue
+  match ← getBitVecValue? val with
+  | some _ => return .continue
+  | none =>
+    let proof := mkApp2 (mkConst ``BitVec.neg_eq_not_add) (toExpr w) val
+    let expr ← mkAppM ``HAdd.hAdd #[← mkAppM ``Complement.complement #[val], (toExpr 1#w)]
+    return .visit { expr := expr, proof? := some proof }
+
+builtin_simproc [bv_normalize] bv_add_const ((_ : BitVec _) + ((_ : BitVec _) + (_ : BitVec _))) :=
+  fun e => do
+    let_expr HAdd.hAdd _ _ _ _ exp1 rhs := e | return .continue
+    let_expr HAdd.hAdd _ _ _ _ exp2 exp3 := rhs | return .continue
+    let some ⟨w, exp1Val⟩ ←  getBitVecValue? exp1 | return .continue
+    let proofBuilder thm := mkApp4 (mkConst thm) (toExpr w) exp1 exp2 exp3
+    match ← getBitVecValue? exp2 with
+    | some ⟨w', exp2Val⟩ =>
+      if h : w = w' then
+        let newLhs := exp1Val + h ▸ exp2Val
+        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp3]
+        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_left
+        return .visit { expr := expr, proof? := some proof }
+      else
+        return .continue
+    | none =>
+      let some ⟨w', exp3Val⟩ ← getBitVecValue? exp3 | return .continue
+      if h : w = w' then
+        let newLhs := exp1Val + h ▸ exp3Val
+        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp2]
+        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_right
+        return .visit { expr := expr, proof? := some proof }
+      else
+        return .continue
+
+builtin_simproc [bv_normalize] bv_add_const' (((_ : BitVec _) + (_ : BitVec _)) + (_ : BitVec _)) :=
+  fun e => do
+    let_expr HAdd.hAdd _ _ _ _ lhs exp3 := e | return .continue
+    let_expr HAdd.hAdd _ _ _ _ exp1 exp2 := lhs | return .continue
+    let some ⟨w, exp3Val⟩ ←  getBitVecValue? exp3 | return .continue
+    let proofBuilder thm := mkApp4 (mkConst thm) (toExpr w) exp1 exp2 exp3
+    match ← getBitVecValue? exp1 with
+    | some ⟨w', exp1Val⟩ =>
+      if h : w = w' then
+        let newLhs := exp3Val + h ▸ exp1Val
+        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp2]
+        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_left'
+        return .visit { expr := expr, proof? := some proof }
+      else
+        return .continue
+    | none =>
+      let some ⟨w', exp2Val⟩ ← getBitVecValue? exp2 | return .continue
+      if h : w = w' then
+        let newLhs := exp3Val + h ▸ exp2Val
+        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp1]
+        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_right'
+        return .visit { expr := expr, proof? := some proof }
+      else
+        return .continue
+
+/-- Return a number `k` such that `2^k = n`. -/
+private def Nat.log2Exact (n : Nat) : Option Nat := do
+  guard <| n ≠ 0
+  let k := n.log2
+  guard <| Nat.pow 2 k == n
+  return k
+
+-- Build an expression for `x ^ y`.
+def mkPow (x y : Expr) : MetaM Expr := mkAppM ``HPow.hPow #[x, y]
+
+builtin_simproc [bv_normalize] bv_udiv_of_two_pow (((_ : BitVec _) / (BitVec.ofNat _ _) : BitVec _)) := fun e => do
+  let_expr HDiv.hDiv _α _β _γ _self x y := e | return .continue
+  let some ⟨w, yVal⟩ ← getBitVecValue? y | return .continue
+  let n := yVal.toNat
+  -- BitVec.ofNat w n, where n =def= 2^k
+  let some k := Nat.log2Exact n | return .continue
+  -- check that k < w.
+  if k ≥ w then return .continue
+  let rhs ← mkAppM ``HShiftRight.hShiftRight #[x, mkNatLit k]
+  -- 2^k = n
+  let hk ← mkDecideProof (← mkEq (← mkPow (mkNatLit 2) (mkNatLit k)) (mkNatLit n))
+  -- k < w
+  let hlt ← mkDecideProof (← mkLt (mkNatLit k) (mkNatLit w))
+  let proof := mkAppN (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.udiv_ofNat_eq_of_lt)
+    #[mkNatLit w, x, mkNatLit n, mkNatLit k, hk, hlt]
+  return .done {
+      expr :=  rhs
+      proof? := some proof
+  }
+
+/--
+A pass in the normalization pipeline. Takes the current goal and produces a refined one or closes
+the goal fully, indicated by returning `none`.
+-/
+structure Pass where
+  name : Name
+  run : MVarId → MetaM (Option MVarId)
+
+namespace Pass
+
+/--
+Repeatedly run a list of `Pass` until they either close the goal or an iteration doesn't change
+the goal anymore.
+-/
+partial def fixpointPipeline (passes : List Pass) (goal : MVarId) : MetaM (Option MVarId) := do
+  let runPass (goal? : Option MVarId) (pass : Pass) : MetaM (Option MVarId) := do
+    let some goal := goal? | return none
+    withTraceNode `bv (fun _ => return s!"Running pass: {pass.name}") do
+      pass.run goal
+
+  let some newGoal := ← passes.foldlM (init := some goal) runPass | return none
+  if goal != newGoal then
+    trace[Meta.Tactic.bv] m!"Rerunning pipeline on:\n{newGoal}"
+    fixpointPipeline passes newGoal
+  else
+    trace[Meta.Tactic.bv] "Pipeline reached a fixpoint"
+    return newGoal
+
+/--
+Responsible for applying the Bitwuzla style rewrite rules.
+-/
+def rewriteRulesPass (maxSteps : Nat) : Pass where
+  name := `rewriteRules
+  run goal := do
+    let bvThms ← bvNormalizeExt.getTheorems
+    let bvSimprocs ← bvNormalizeSimprocExt.getSimprocs
+    let sevalThms ← getSEvalTheorems
+    let sevalSimprocs ← Simp.getSEvalSimprocs
+
+    let simpCtx ← Simp.mkContext
+      (config := { failIfUnchanged := false, zetaDelta := true, maxSteps })
+      (simpTheorems := #[bvThms, sevalThms])
+      (congrTheorems := (← getSimpCongrTheorems))
+
+    let hyps ← goal.getNondepPropHyps
+    let ⟨result?, _⟩ ← simpGoal goal
+      (ctx := simpCtx)
+      (simprocs := #[bvSimprocs, sevalSimprocs])
+      (fvarIdsToSimp := hyps)
+    let some (_, newGoal) := result? | return none
+    return newGoal
+
+/--
+Flatten out ands. That is look for hypotheses of the form `h : (x && y) = true` and replace them
+with `h.left : x = true` and `h.right : y = true`. This can enable more fine grained substitutions
+in embedded constraint substitution.
+-/
+partial def andFlatteningPass : Pass where
+  name := `andFlattening
+  run goal := do
+    goal.withContext do
+      let hyps ← goal.getNondepPropHyps
+      let mut newHyps := #[]
+      let mut oldHyps := #[]
+      for fvar in hyps do
+        let hyp : Hypothesis := {
+          userName := (← fvar.getDecl).userName
+          type := ← fvar.getType
+          value := mkFVar fvar
+        }
+        let sizeBefore := newHyps.size
+        newHyps ← splitAnds hyp newHyps
+        if newHyps.size > sizeBefore then
+          oldHyps := oldHyps.push fvar
+      if newHyps.size == 0 then
+        return goal
+      else
+        let (_, goal) ← goal.assertHypotheses newHyps
+        -- Given that we collected the hypotheses in the correct order above the invariant is given
+        let goal ← goal.tryClearMany oldHyps
+        return goal
+where
+  splitAnds (hyp : Hypothesis) (hyps : Array Hypothesis) (first : Bool := true) :
+      MetaM (Array Hypothesis) := do
+    match ← trySplit hyp with
+    | some (left, right) =>
+      let hyps ← splitAnds left hyps false
+      splitAnds right hyps false
+    | none =>
+      if first then
+        return hyps
+      else
+        return hyps.push hyp
+
+  trySplit (hyp : Hypothesis) : MetaM (Option (Hypothesis × Hypothesis)) := do
+    let typ := hyp.type
+    let_expr Eq α eqLhs eqRhs := typ | return none
+    let_expr Bool.and lhs rhs := eqLhs | return none
+    let_expr Bool.true := eqRhs | return none
+    let_expr Bool := α | return none
+    let mkEqTrue (lhs : Expr) : Expr :=
+      mkApp3 (mkConst ``Eq [1]) (mkConst ``Bool) lhs (mkConst ``Bool.true)
+    let leftHyp : Hypothesis := {
+      userName := hyp.userName,
+      type := mkEqTrue lhs,
+      value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_left) lhs rhs hyp.value
+    }
+    let rightHyp : Hypothesis := {
+      userName := hyp.userName,
+      type := mkEqTrue rhs,
+      value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_right) lhs rhs hyp.value
+    }
+    return some (leftHyp, rightHyp)
+
+/--
+Substitute embedded constraints. That is look for hypotheses of the form `h : x = true` and use
+them to substitute occurences of `x` within other hypotheses. Additionally this drops all
+redundant top level hypotheses.
+-/
+def embeddedConstraintPass (maxSteps : Nat) : Pass where
+  name := `embeddedConstraintSubsitution
+  run goal := do
+    goal.withContext do
+      let hyps ← goal.getNondepPropHyps
+      let mut relevantHyps : SimpTheoremsArray := #[]
+      let mut seen : Std.HashSet Expr := {}
+      let mut duplicates : Array FVarId := #[]
+      for hyp in hyps do
+        let typ ← hyp.getType
+        let_expr Eq α lhs rhs := typ | continue
+        let_expr Bool.true := rhs | continue
+        let_expr Bool := α | continue
+        if seen.contains lhs then
+          -- collect and later remove duplicates on the fly
+          duplicates := duplicates.push hyp
+        else
+          seen := seen.insert lhs
+          let localDecl ← hyp.getDecl
+          let proof  := localDecl.toExpr
+          relevantHyps ← relevantHyps.addTheorem (.fvar hyp) proof
+
+      let goal ← goal.tryClearMany duplicates
+
+      let simpCtx ← Simp.mkContext
+        (config := { failIfUnchanged := false, maxSteps })
+        (simpTheorems := relevantHyps)
+        (congrTheorems := (← getSimpCongrTheorems))
+
+      let ⟨result?, _⟩ ← simpGoal goal (ctx := simpCtx) (fvarIdsToSimp := ← goal.getNondepPropHyps)
+      let some (_, newGoal) := result? | return none
+      return newGoal
+
+/--
+Normalize with respect to Associativity and Commutativity.
+-/
+def acNormalizePass : Pass where
+  name := `ac_nf
+  run goal := do
+    let mut newGoal := goal
+    for hyp in (← goal.getNondepPropHyps) do
+      let result ← Lean.Meta.AC.acNfHypMeta newGoal hyp
+
+      if let .some nextGoal := result then
+        newGoal := nextGoal
+      else
+        return none
+
+    return newGoal
+
+def passPipeline (cfg : BVDecideConfig) : List Pass := Id.run do
+  let mut passPipeline := [rewriteRulesPass cfg.maxSteps]
 
   if cfg.acNf then
     passPipeline := passPipeline ++ [acNormalizePass]
@@ -34,20 +348,18 @@ def passPipeline : PreProcessM (List Pass) := do
     passPipeline := passPipeline ++ [andFlatteningPass]
 
   if cfg.embeddedConstraintSubst then
-    passPipeline := passPipeline ++ [embeddedConstraintPass]
+    passPipeline := passPipeline ++ [embeddedConstraintPass cfg.maxSteps]
 
   return passPipeline
 
-def bvNormalize (g : MVarId) (cfg : BVDecideConfig) : MetaM (Option MVarId) := do
-  withTraceNode `bv (fun _ => return "Preprocessing goal") do
-    (go g).run cfg g
-where
-  go (g : MVarId) : PreProcessM (Option MVarId) := do
-    let some g ← g.falseOrByContra | return none
+end Pass
 
+def bvNormalize (g : MVarId) (cfg : BVDecideConfig) : MetaM (Option MVarId) := do
+  withTraceNode `bv (fun _ => return "Normalizing goal") do
+    -- Contradiction proof
+    let some g ← g.falseOrByContra | return none
     trace[Meta.Tactic.bv] m!"Running preprocessing pipeline on:\n{g}"
-    let pipeline ← passPipeline
-    Pass.fixpointPipeline pipeline g
+    Pass.fixpointPipeline (Pass.passPipeline cfg) g
 
 @[builtin_tactic Lean.Parser.Tactic.bvNormalize]
 def evalBVNormalize : Tactic := fun

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize/AC.lean

@@ -1,39 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-prelude
-import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Basic
-import Lean.Meta.Tactic.AC.Main
-
-/-!
-This module contains the implementation of the associativity and commutativity normalisation pass
-in the fixpoint pipeline.
--/
-
-namespace Lean.Elab.Tactic.BVDecide
-namespace Frontend.Normalize
-
-open Lean.Meta
-
-/--
-Normalize with respect to Associativity and Commutativity.
--/
-def acNormalizePass : Pass where
-  name := `ac_nf
-  run' goal := do
-    let mut newGoal := goal
-    for hyp in (← goal.getNondepPropHyps) do
-      let result ← AC.acNfHypMeta newGoal hyp
-
-      if let .some nextGoal := result then
-        newGoal := nextGoal
-      else
-        return none
-
-    return newGoal
-
-
-end Frontend.Normalize
-end Lean.Elab.Tactic.BVDecide

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize/AndFlatten.lean

@@ -1,99 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-prelude
-import Std.Tactic.BVDecide.Normalize.Bool
-import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Basic
-import Lean.Meta.Tactic.Assert
-
-/-!
-This module contains the implementation of the and flattening pass in the fixpoint pipeline, taking
-hypotheses of the form `h : x && y = true` and splitting them into `h1 : x = true` and
-`h2 : y = true` recursively.
--/
-
-namespace Lean.Elab.Tactic.BVDecide
-namespace Frontend.Normalize
-
-open Lean.Meta
-
-structure AndFlattenState where
-  hypsToDelete : Array FVarId := #[]
-  hypsToAdd : Array Hypothesis := #[]
-  cache : Std.HashSet Expr := {}
-
-/--
-Flatten out ands. That is look for hypotheses of the form `h : (x && y) = true` and replace them
-with `h.left : x = true` and `h.right : y = true`. This can enable more fine grained substitutions
-in embedded constraint substitution.
--/
-partial def andFlatteningPass : Pass where
-  name := `andFlattening
-  run' goal := do
-    let (_, { hypsToDelete, hypsToAdd, .. }) ← processGoal goal |>.run {}
-    if hypsToAdd.isEmpty then
-      return goal
-    else
-      let (_, goal) ← goal.assertHypotheses hypsToAdd
-      -- Given that we collected the hypotheses in the correct order above the invariant is given
-      let goal ← goal.tryClearMany hypsToDelete
-      return goal
-where
-  processGoal (goal : MVarId) : StateRefT AndFlattenState MetaM Unit := do
-    goal.withContext do
-      let hyps ← goal.getNondepPropHyps
-      hyps.forM processFVar
-
-  processFVar (fvar : FVarId) : StateRefT AndFlattenState MetaM Unit := do
-    let type ← fvar.getType
-    if (← get).cache.contains type then
-      modify (fun s => { s with hypsToDelete := s.hypsToDelete.push fvar })
-    else
-      let hyp := {
-        userName := (← fvar.getDecl).userName
-        type := type
-        value := mkFVar fvar
-      }
-      let some (lhs, rhs) ← trySplit hyp | return ()
-      modify (fun s => { s with hypsToDelete := s.hypsToDelete.push fvar })
-      splitAnds [lhs, rhs]
-
-  splitAnds (worklist : List Hypothesis) : StateRefT AndFlattenState MetaM Unit := do
-    match worklist with
-    | [] => return ()
-    | hyp :: worklist =>
-      match ← trySplit hyp with
-      | some (left, right) => splitAnds <| left :: right :: worklist
-      | none =>
-        modify (fun s => { s with hypsToAdd := s.hypsToAdd.push hyp })
-        splitAnds worklist
-
-  trySplit (hyp : Hypothesis) :
-      StateRefT AndFlattenState MetaM (Option (Hypothesis × Hypothesis)) := do
-    let typ := hyp.type
-    if (← get).cache.contains typ then
-      return none
-    else
-      modify (fun s => { s with cache := s.cache.insert typ })
-      let_expr Eq _ eqLhs eqRhs := typ | return none
-      let_expr Bool.and lhs rhs := eqLhs | return none
-      let_expr Bool.true := eqRhs | return none
-      let mkEqTrue (lhs : Expr) : Expr :=
-        mkApp3 (mkConst ``Eq [1]) (mkConst ``Bool) lhs (mkConst ``Bool.true)
-      let leftHyp : Hypothesis := {
-        userName := hyp.userName,
-        type := mkEqTrue lhs,
-        value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_left) lhs rhs hyp.value
-      }
-      let rightHyp : Hypothesis := {
-        userName := hyp.userName,
-        type := mkEqTrue rhs,
-        value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_right) lhs rhs hyp.value
-      }
-      return some (leftHyp, rightHyp)
-
-
-end Frontend.Normalize
-end Lean.Elab.Tactic.BVDecide

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize/Basic.lean

@@ -1,86 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-prelude
-import Lean.Meta.Basic
-import Lean.Elab.Tactic.BVDecide.Frontend.Attr
-
-/-!
-This module contains the basic preprocessing pipeline framework for `bv_normalize`.
--/
-
-namespace Lean.Elab.Tactic.BVDecide
-namespace Frontend.Normalize
-
-open Lean.Meta
-
-structure PreProcessState where
-  /--
-  Contains `FVarId` that we already know are in `bv_normalize` simp normal form and thus don't
-  need to be processed again when we visit the next time.
-  -/
-  rewriteCache : Std.HashSet FVarId := {}
-
-abbrev PreProcessM : Type → Type := ReaderT BVDecideConfig <| StateRefT PreProcessState MetaM
-
-namespace PreProcessM
-
-def getConfig : PreProcessM BVDecideConfig := read
-
-@[inline]
-def checkRewritten (fvar : FVarId) : PreProcessM Bool := do
-  let val := (← get).rewriteCache.contains fvar
-  trace[Meta.Tactic.bv] m!"{mkFVar fvar} was already rewritten? {val}"
-  return val
-
-@[inline]
-def rewriteFinished (fvar : FVarId) : PreProcessM Unit := do
-  trace[Meta.Tactic.bv] m!"Adding {mkFVar fvar} to the rewritten set"
-  modify (fun s => { s with rewriteCache := s.rewriteCache.insert fvar })
-
-def run (cfg : BVDecideConfig) (goal : MVarId) (x : PreProcessM α) : MetaM α := do
-  let hyps ← goal.getNondepPropHyps
-  ReaderT.run x cfg |>.run' { rewriteCache := Std.HashSet.empty hyps.size }
-
-end PreProcessM
-
-/--
-A pass in the normalization pipeline. Takes the current goal and produces a refined one or closes
-the goal fully, indicated by returning `none`.
--/
-structure Pass where
-  name : Name
-  run' : MVarId → PreProcessM (Option MVarId)
-
-namespace Pass
-
-def run (pass : Pass) (goal : MVarId) : PreProcessM (Option MVarId) := do
-  withTraceNode `bv (fun _ => return m!"Running pass: {pass.name} on\n{goal}") do
-    pass.run' goal
-
-/--
-Repeatedly run a list of `Pass` until they either close the goal or an iteration doesn't change
-the goal anymore.
--/
-partial def fixpointPipeline (passes : List Pass) (goal : MVarId) : PreProcessM (Option MVarId) := do
-  let mut newGoal := goal
-  for pass in passes do
-    if let some nextGoal ← pass.run newGoal then
-      newGoal := nextGoal
-    else
-      trace[Meta.Tactic.bv] "Fixpoint iteration solved the goal"
-      return none
-
-  if goal != newGoal then
-    trace[Meta.Tactic.bv] m!"Rerunning pipeline on:\n{newGoal}"
-    fixpointPipeline passes newGoal
-  else
-    trace[Meta.Tactic.bv] "Pipeline reached a fixpoint"
-    return newGoal
-
-end Pass
-
-end Frontend.Normalize
-end Lean.Elab.Tactic.BVDecide

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize/EmbeddedConstraint.lean

@@ -1,62 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-prelude
-import Std.Tactic.BVDecide.Normalize.Bool
-import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Basic
-import Lean.Meta.Tactic.Simp
-
-/-!
-This module contains the implementation of the embedded constraint substitution pass in the fixpoint
-pipeline, substituting hypotheses of the form `h : x = true` in other hypotheses.
--/
-
-namespace Lean.Elab.Tactic.BVDecide
-namespace Frontend.Normalize
-
-open Lean.Meta
-
-/--
-Substitute embedded constraints. That is look for hypotheses of the form `h : x = true` and use
-them to substitute occurences of `x` within other hypotheses. Additionally this drops all
-redundant top level hypotheses.
--/
-def embeddedConstraintPass : Pass where
-  name := `embeddedConstraintSubsitution
-  run' goal := do
-    goal.withContext do
-      let hyps ← goal.getNondepPropHyps
-      let mut relevantHyps : SimpTheoremsArray := #[]
-      let mut seen : Std.HashSet Expr := {}
-      let mut duplicates : Array FVarId := #[]
-      for hyp in hyps do
-        let typ ← hyp.getType
-        let_expr Eq _ lhs rhs := typ | continue
-        let_expr Bool.true := rhs | continue
-        if seen.contains lhs then
-          duplicates := duplicates.push hyp
-        else
-          seen := seen.insert lhs
-          let localDecl ← hyp.getDecl
-          let proof := localDecl.toExpr
-          relevantHyps ← relevantHyps.addTheorem (.fvar hyp) proof
-
-      let goal ← goal.tryClearMany duplicates
-
-      if relevantHyps.isEmpty then
-        return goal
-
-      let cfg ← PreProcessM.getConfig
-      let simpCtx ← Simp.mkContext
-        (config := { failIfUnchanged := false, maxSteps := cfg.maxSteps })
-        (simpTheorems := relevantHyps)
-        (congrTheorems := (← getSimpCongrTheorems))
-      let ⟨result?, _⟩ ← simpGoal goal (ctx := simpCtx) (fvarIdsToSimp := ← goal.getNondepPropHyps)
-      let some (_, newGoal) := result? | return none
-      return newGoal
-
-
-end Frontend.Normalize
-end Lean.Elab.Tactic.BVDecide

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize/Rewrite.lean

@@ -1,61 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-prelude
-import Lean.Elab.Tactic.Simp
-import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Basic
-import Lean.Elab.Tactic.BVDecide.Frontend.Attr
-
-/-!
-This module contains the implementation of the rewriting pass in the fixpoint pipeline, applying
-rules from the `bv_normalize` simp set.
--/
-
-namespace Lean.Elab.Tactic.BVDecide
-namespace Frontend.Normalize
-
-open Lean.Meta
-
-/--
-Responsible for applying the Bitwuzla style rewrite rules.
--/
-def rewriteRulesPass : Pass where
-  name := `rewriteRules
-  run' goal := do
-    let bvThms ← bvNormalizeExt.getTheorems
-    let bvSimprocs ← bvNormalizeSimprocExt.getSimprocs
-    let sevalThms ← getSEvalTheorems
-    let sevalSimprocs ← Simp.getSEvalSimprocs
-    let cfg ← PreProcessM.getConfig
-
-    let simpCtx ← Simp.mkContext
-      (config := { failIfUnchanged := false, zetaDelta := true, maxSteps := cfg.maxSteps })
-      (simpTheorems := #[bvThms, sevalThms])
-      (congrTheorems := (← getSimpCongrTheorems))
-
-    let hyps ← getHyps goal
-    if hyps.isEmpty then
-      return goal
-    else
-      let ⟨result?, _⟩ ← simpGoal goal
-        (ctx := simpCtx)
-        (simprocs := #[bvSimprocs, sevalSimprocs])
-        (fvarIdsToSimp := hyps)
-
-      let some (_, newGoal) := result? | return none
-      newGoal.withContext do
-        (← newGoal.getNondepPropHyps).forM PreProcessM.rewriteFinished
-      return newGoal
-where
-  getHyps (goal : MVarId) : PreProcessM (Array FVarId) := do
-    goal.withContext do
-      let mut hyps ← goal.getNondepPropHyps
-      let filter hyp := do
-        return !(← PreProcessM.checkRewritten hyp)
-      hyps.filterM filter
-
-
-end Frontend.Normalize
-end Lean.Elab.Tactic.BVDecide

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize/Simproc.lean

@@ -1,164 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Henrik Böving
--/
-prelude
-import Std.Tactic.BVDecide.Normalize
-import Std.Tactic.BVDecide.Syntax
-import Lean.Elab.Tactic.Simp
-import Lean.Elab.Tactic.BVDecide.Frontend.Attr
-
-/-!
-This module contains implementations of simprocs used in the `bv_normalize` simp set.
--/
-
-namespace Lean.Elab.Tactic.BVDecide
-namespace Frontend.Normalize
-
-open Lean.Meta
-open Std.Tactic.BVDecide.Normalize
-
-builtin_simproc ↓ [bv_normalize] reduceCond (cond _ _ _) := fun e => do
-  let_expr f@cond α c tb eb := e | return .continue
-  let r ← Simp.simp c
-  if r.expr.cleanupAnnotations.isConstOf ``Bool.true then
-    let pr := mkApp (mkApp4 (mkConst ``Bool.cond_pos f.constLevels!) α c tb eb) (← r.getProof)
-    return .visit { expr := tb, proof? := pr }
-  else if r.expr.cleanupAnnotations.isConstOf ``Bool.false then
-    let pr := mkApp (mkApp4 (mkConst ``Bool.cond_neg f.constLevels!) α c tb eb) (← r.getProof)
-    return .visit { expr := eb, proof? := pr }
-  else
-    return .continue
-
-builtin_simproc [bv_normalize] eqToBEq (((_ : Bool) = (_ : Bool))) := fun e => do
-  let_expr Eq _ lhs rhs := e | return .continue
-  match_expr rhs with
-  | Bool.true => return .continue
-  | _ =>
-    let beqApp ← mkAppM ``BEq.beq #[lhs, rhs]
-    let new := mkApp3 (mkConst ``Eq [1]) (mkConst ``Bool) beqApp (mkConst ``Bool.true)
-    let proof := mkApp2 (mkConst ``Bool.eq_to_beq) lhs rhs
-    return .done { expr := new, proof? := some proof }
-
-builtin_simproc [bv_normalize] andOnes ((_ : BitVec _) &&& (_ : BitVec _)) := fun e => do
-  let_expr HAnd.hAnd _ _ _ _ lhs rhs := e | return .continue
-  let some ⟨w, rhsValue⟩ ← getBitVecValue? rhs | return .continue
-  if rhsValue == -1#w then
-    let proof := mkApp2 (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.and_ones) (toExpr w) lhs
-    return .visit { expr := lhs, proof? := some proof }
-  else
-    return .continue
-
-builtin_simproc [bv_normalize] onesAnd ((_ : BitVec _) &&& (_ : BitVec _)) := fun e => do
-  let_expr HAnd.hAnd _ _ _ _ lhs rhs := e | return .continue
-  let some ⟨w, lhsValue⟩ ← getBitVecValue? lhs | return .continue
-  if lhsValue == -1#w then
-    let proof := mkApp2 (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.ones_and) (toExpr w) rhs
-    return .visit { expr := rhs, proof? := some proof }
-  else
-    return .continue
-
-builtin_simproc [bv_normalize] maxUlt (BitVec.ult (_ : BitVec _) (_ : BitVec _)) := fun e => do
-  let_expr BitVec.ult _ lhs rhs := e | return .continue
-  let some ⟨w, lhsValue⟩ ← getBitVecValue? lhs | return .continue
-  if lhsValue == -1#w then
-    let proof := mkApp2 (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.max_ult') (toExpr w) rhs
-    return .visit { expr := toExpr Bool.false, proof? := some proof }
-  else
-    return .continue
-
--- A specialised version of BitVec.neg_eq_not_add so it doesn't trigger on -constant
-builtin_simproc [bv_normalize] neg_eq_not_add (-(_ : BitVec _)) := fun e => do
-  let_expr Neg.neg typ _ val := e | return .continue
-  let_expr BitVec widthExpr := typ | return .continue
-  let some w ← getNatValue? widthExpr | return .continue
-  match ← getBitVecValue? val with
-  | some _ => return .continue
-  | none =>
-    let proof := mkApp2 (mkConst ``BitVec.neg_eq_not_add) (toExpr w) val
-    let expr ← mkAppM ``HAdd.hAdd #[← mkAppM ``Complement.complement #[val], (toExpr 1#w)]
-    return .visit { expr := expr, proof? := some proof }
-
-builtin_simproc [bv_normalize] bv_add_const ((_ : BitVec _) + ((_ : BitVec _) + (_ : BitVec _))) :=
-  fun e => do
-    let_expr HAdd.hAdd _ _ _ _ exp1 rhs := e | return .continue
-    let_expr HAdd.hAdd _ _ _ _ exp2 exp3 := rhs | return .continue
-    let some ⟨w, exp1Val⟩ ←  getBitVecValue? exp1 | return .continue
-    let proofBuilder thm := mkApp4 (mkConst thm) (toExpr w) exp1 exp2 exp3
-    match ← getBitVecValue? exp2 with
-    | some ⟨w', exp2Val⟩ =>
-      if h : w = w' then
-        let newLhs := exp1Val + h ▸ exp2Val
-        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp3]
-        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_left
-        return .visit { expr := expr, proof? := some proof }
-      else
-        return .continue
-    | none =>
-      let some ⟨w', exp3Val⟩ ← getBitVecValue? exp3 | return .continue
-      if h : w = w' then
-        let newLhs := exp1Val + h ▸ exp3Val
-        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp2]
-        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_right
-        return .visit { expr := expr, proof? := some proof }
-      else
-        return .continue
-
-builtin_simproc [bv_normalize] bv_add_const' (((_ : BitVec _) + (_ : BitVec _)) + (_ : BitVec _)) :=
-  fun e => do
-    let_expr HAdd.hAdd _ _ _ _ lhs exp3 := e | return .continue
-    let_expr HAdd.hAdd _ _ _ _ exp1 exp2 := lhs | return .continue
-    let some ⟨w, exp3Val⟩ ←  getBitVecValue? exp3 | return .continue
-    let proofBuilder thm := mkApp4 (mkConst thm) (toExpr w) exp1 exp2 exp3
-    match ← getBitVecValue? exp1 with
-    | some ⟨w', exp1Val⟩ =>
-      if h : w = w' then
-        let newLhs := exp3Val + h ▸ exp1Val
-        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp2]
-        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_left'
-        return .visit { expr := expr, proof? := some proof }
-      else
-        return .continue
-    | none =>
-      let some ⟨w', exp2Val⟩ ← getBitVecValue? exp2 | return .continue
-      if h : w = w' then
-        let newLhs := exp3Val + h ▸ exp2Val
-        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp1]
-        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_right'
-        return .visit { expr := expr, proof? := some proof }
-      else
-        return .continue
-
-/-- Return a number `k` such that `2^k = n`. -/
-private def Nat.log2Exact (n : Nat) : Option Nat := do
-  guard <| n ≠ 0
-  let k := n.log2
-  guard <| Nat.pow 2 k == n
-  return k
-
--- Build an expression for `x ^ y`.
-def mkPow (x y : Expr) : MetaM Expr := mkAppM ``HPow.hPow #[x, y]
-
-builtin_simproc [bv_normalize] bv_udiv_of_two_pow (((_ : BitVec _) / (BitVec.ofNat _ _) : BitVec _)) := fun e => do
-  let_expr HDiv.hDiv _α _β _γ _self x y := e | return .continue
-  let some ⟨w, yVal⟩ ← getBitVecValue? y | return .continue
-  let n := yVal.toNat
-  -- BitVec.ofNat w n, where n =def= 2^k
-  let some k := Nat.log2Exact n | return .continue
-  -- check that k < w.
-  if k ≥ w then return .continue
-  let rhs ← mkAppM ``HShiftRight.hShiftRight #[x, mkNatLit k]
-  -- 2^k = n
-  let hk ← mkDecideProof (← mkEq (← mkPow (mkNatLit 2) (mkNatLit k)) (mkNatLit n))
-  -- k < w
-  let hlt ← mkDecideProof (← mkLt (mkNatLit k) (mkNatLit w))
-  let proof := mkAppN (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.udiv_ofNat_eq_of_lt)
-    #[mkNatLit w, x, mkNatLit n, mkNatLit k, hk, hlt]
-  return .done {
-      expr :=  rhs
-      proof? := some proof
-  }
-
-end Frontend.Normalize
-end Lean.Elab.Tactic.BVDecide

src/Lean/Elab/Tactic/BuiltinTactic.lean

@@ -362,9 +362,9 @@ partial def evalChoiceAux (tactics : Array Syntax) (i : Nat) : TacticM Unit :=
   | `(tactic| intro $h:term $hs:term*) => evalTactic (← `(tactic| intro $h:term; intro $hs:term*))
   | _ => throwUnsupportedSyntax
 where
-  introStep (ref? : Option Syntax) (n : Name) (typeStx? : Option Syntax := none) : TacticM Unit := do
+  introStep (ref : Option Syntax) (n : Name) (typeStx? : Option Syntax := none) : TacticM Unit := do
     let fvarId ← liftMetaTacticAux fun mvarId => do
-      let (fvarId, mvarId) ← withRef? ref? <| mvarId.intro n
+      let (fvarId, mvarId) ← mvarId.intro n
       pure (fvarId, [mvarId])
     if let some typeStx := typeStx? then
       withMainContext do
@@ -374,9 +374,9 @@ where
         unless (← isDefEqGuarded type fvarType) do
           throwError "type mismatch at `intro {fvar}`{← mkHasTypeButIsExpectedMsg fvarType type}"
         liftMetaTactic fun mvarId => return [← mvarId.replaceLocalDeclDefEq fvarId type]
-    if let some ref := ref? then
+    if let some stx := ref then
       withMainContext do
-        Term.addLocalVarInfo ref (mkFVar fvarId)
+        Term.addLocalVarInfo stx (mkFVar fvarId)
 
 @[builtin_tactic Lean.Parser.Tactic.introMatch] def evalIntroMatch : Tactic := fun stx => do
   let matchAlts := stx[1]

src/Lean/Elab/Tactic/Classical.lean

@@ -24,8 +24,11 @@ def classical [Monad m] [MonadEnv m] [MonadFinally m] [MonadLiftT MetaM m] (t :
   finally
     modifyEnv Meta.instanceExtension.popScope
 
-@[builtin_tactic Lean.Parser.Tactic.classical, builtin_incremental]
-def evalClassical : Tactic := fun stx =>
-  classical <| Term.withNarrowedArgTacticReuse (argIdx := 1) Elab.Tactic.evalTactic stx
+@[builtin_tactic Lean.Parser.Tactic.classical]
+def evalClassical : Tactic := fun stx => do
+  match stx with
+  | `(tactic| classical $tacs:tacticSeq) =>
+     classical <| Elab.Tactic.evalTactic tacs
+  | _ => throwUnsupportedSyntax
 
 end Lean.Elab.Tactic

src/Lean/Elab/Tactic/Conv/Simp.lean

@@ -7,10 +7,9 @@ prelude
 import Lean.Elab.Tactic.Simp
 import Lean.Elab.Tactic.Split
 import Lean.Elab.Tactic.Conv.Basic
-import Lean.Elab.Tactic.SimpTrace
 
 namespace Lean.Elab.Tactic.Conv
-open Meta Tactic TryThis
+open Meta
 
 def applySimpResult (result : Simp.Result) : TacticM Unit := do
   if result.proof?.isNone then
@@ -24,19 +23,6 @@ def applySimpResult (result : Simp.Result) : TacticM Unit := do
   let (result, _) ← dischargeWrapper.with fun d? => simp lhs ctx (simprocs := simprocs) (discharge? := d?)
   applySimpResult result
 
-@[builtin_tactic Lean.Parser.Tactic.Conv.simpTrace] def evalSimpTrace : Tactic := fun stx => withMainContext do
-  match stx with
-  | `(conv| simp?%$tk $cfg:optConfig $(discharger)? $[only%$o]? $[[$args,*]]?) => do
-    let stx ← `(tactic| simp%$tk $cfg:optConfig $[$discharger]? $[only%$o]? $[[$args,*]]?)
-    let { ctx, simprocs, dischargeWrapper, .. } ← mkSimpContext stx (eraseLocal := false)
-    let lhs ← getLhs
-    let (result, stats) ← dischargeWrapper.with fun d? =>
-      simp lhs ctx (simprocs := simprocs) (discharge? := d?)
-    applySimpResult result
-    let stx ← mkSimpCallStx stx stats.usedTheorems
-    addSuggestion tk stx (origSpan? := ← getRef)
-  | _ => throwUnsupportedSyntax
-
 @[builtin_tactic Lean.Parser.Tactic.Conv.simpMatch] def evalSimpMatch : Tactic := fun _ => withMainContext do
   applySimpResult (← Split.simpMatch (← getLhs))
 
@@ -44,15 +30,4 @@ def applySimpResult (result : Simp.Result) : TacticM Unit := do
   let { ctx, .. } ← mkSimpContext stx (eraseLocal := false) (kind := .dsimp)
   changeLhs (← Lean.Meta.dsimp (← getLhs) ctx).1
 
-@[builtin_tactic Lean.Parser.Tactic.Conv.dsimpTrace] def evalDSimpTrace : Tactic := fun stx => withMainContext do
-  match stx with
-  | `(conv| dsimp?%$tk $cfg:optConfig $[only%$o]? $[[$args,*]]?) =>
-    let stx ← `(tactic| dsimp%$tk $cfg:optConfig $[only%$o]? $[[$args,*]]?)
-    let { ctx, .. } ← mkSimpContext stx (eraseLocal := false) (kind := .dsimp)
-    let (result, stats) ← Lean.Meta.dsimp (← getLhs) ctx
-    changeLhs result
-    let stx ← mkSimpCallStx stx stats.usedTheorems
-    addSuggestion tk stx (origSpan? := ← getRef)
-  | _ => throwUnsupportedSyntax
-
 end Lean.Elab.Tactic.Conv

src/Lean/Elab/Tactic/Grind.lean

@@ -26,18 +26,16 @@ def elabGrindPattern : CommandElab := fun stx => do
       let info ← getConstInfo declName
       forallTelescope info.type fun xs _ => do
         let patterns ← terms.getElems.mapM fun term => do
-          let pattern ← elabTerm term none
-          synthesizeSyntheticMVarsUsingDefault
-          let pattern ← instantiateMVars pattern
-          let pattern ← Grind.preprocessPattern pattern
+          let pattern ← instantiateMVars (← elabTerm term none)
+          let pattern ← Grind.unfoldReducible pattern
           return pattern.abstract xs
         Grind.addEMatchTheorem declName xs.size patterns.toList
   | _ => throwUnsupportedSyntax
 
 def grind (mvarId : MVarId) (config : Grind.Config) (mainDeclName : Name) (fallback : Grind.Fallback) : MetaM Unit := do
-  let goals ← Grind.main mvarId config mainDeclName fallback
-  unless goals.isEmpty do
-    throwError "`grind` failed\n{← Grind.goalsToMessageData goals config}"
+  let mvarIds ← Grind.main mvarId config mainDeclName fallback
+  unless mvarIds.isEmpty do
+    throwError "`grind` failed\n{goalsToMessageData mvarIds}"
 
 private def elabFallback (fallback? : Option Term) : TermElabM (Grind.GoalM Unit) := do
   let some fallback := fallback? | return (pure ())

src/Lean/Elab/Tactic/Induction.lean

@@ -258,11 +258,11 @@ private def saveAltVarsInfo (altMVarId : MVarId) (altStx : Syntax) (fvarIds : Ar
           i := i + 1
 
 open Language in
-def evalAlts (elimInfo : ElimInfo) (alts : Array Alt) (optPreTac : Syntax) (altStxs? : Option (Array Syntax))
+def evalAlts (elimInfo : ElimInfo) (alts : Array Alt) (optPreTac : Syntax) (altStxs : Array Syntax)
     (initialInfo : Info)
     (numEqs : Nat := 0) (numGeneralized : Nat := 0) (toClear : Array FVarId := #[])
     (toTag : Array (Ident × FVarId) := #[]) : TacticM Unit := do
-  let hasAlts := altStxs?.isSome
+  let hasAlts := altStxs.size > 0
   if hasAlts then
     -- default to initial state outside of alts
     -- HACK: because this node has the same span as the original tactic,
@@ -274,7 +274,9 @@ def evalAlts (elimInfo : ElimInfo) (alts : Array Alt) (optPreTac : Syntax) (altS
 where
   -- continuation in the correct info context
   goWithInfo := do
-    if let some altStxs := altStxs? then
+    let hasAlts := altStxs.size > 0
+
+    if hasAlts then
       if let some tacSnap := (← readThe Term.Context).tacSnap? then
         -- incrementality: create a new promise for each alternative, resolve current snapshot to
         -- them, eventually put each of them back in `Context.tacSnap?` in `applyAltStx`
@@ -307,8 +309,7 @@ where
 
   -- continuation in the correct incrementality context
   goWithIncremental (tacSnaps : Array (SnapshotBundle TacticParsedSnapshot)) := do
-    let hasAlts := altStxs?.isSome
-    let altStxs := altStxs?.getD #[]
+    let hasAlts := altStxs.size > 0
     let mut alts := alts
 
     -- initial sanity checks: named cases should be known, wildcards should be last
@@ -342,12 +343,12 @@ where
       let altName := getAltName altStx
       if let some i := alts.findFinIdx? (·.1 == altName) then
         -- cover named alternative
-        applyAltStx tacSnaps altStxs altStxIdx altStx alts[i]
+        applyAltStx tacSnaps altStxIdx altStx alts[i]
         alts := alts.eraseIdx i
       else if !alts.isEmpty && isWildcard altStx then
         -- cover all alternatives
         for alt in alts do
-          applyAltStx tacSnaps altStxs altStxIdx altStx alt
+          applyAltStx tacSnaps altStxIdx altStx alt
         alts := #[]
       else
         throwErrorAt altStx "unused alternative '{altName}'"
@@ -378,7 +379,7 @@ where
         altMVarIds.forM fun mvarId => admitGoal mvarId
 
   /-- Applies syntactic alternative to alternative goal. -/
-  applyAltStx tacSnaps altStxs altStxIdx altStx alt := withRef altStx do
+  applyAltStx tacSnaps altStxIdx altStx alt := withRef altStx do
     let { name := altName, info, mvarId := altMVarId } := alt
     -- also checks for unknown alternatives
     let numFields ← getAltNumFields elimInfo altName
@@ -475,7 +476,7 @@ private def generalizeVars (mvarId : MVarId) (stx : Syntax) (targets : Array Exp
 /--
 Given `inductionAlts` of the form
 ```
-syntax inductionAlts := "with " (tactic)? withPosition( (colGe inductionAlt)*)
+syntax inductionAlts := "with " (tactic)? withPosition( (colGe inductionAlt)+)
 ```
 Return an array containing its alternatives.
 -/
@@ -485,30 +486,21 @@ private def getAltsOfInductionAlts (inductionAlts : Syntax) : Array Syntax :=
 /--
 Given `inductionAlts` of the form
 ```
-syntax inductionAlts := "with " (tactic)? withPosition( (colGe inductionAlt)*)
+syntax inductionAlts := "with " (tactic)? withPosition( (colGe inductionAlt)+)
 ```
-runs `cont (some alts)` where `alts` is an array containing all `inductionAlt`s while disabling incremental
-reuse if any other syntax changed. If there's no `with` clause, then runs `cont none`.
+runs `cont alts` where `alts` is an array containing all `inductionAlt`s while disabling incremental
+reuse if any other syntax changed.
 -/
 private def withAltsOfOptInductionAlts (optInductionAlts : Syntax)
-    (cont : Option (Array Syntax) → TacticM α) : TacticM α :=
+    (cont : Array Syntax → TacticM α) : TacticM α :=
   Term.withNarrowedTacticReuse (stx := optInductionAlts) (fun optInductionAlts =>
     if optInductionAlts.isNone then
       -- if there are no alternatives, what to compare is irrelevant as there will be no reuse
       (mkNullNode #[], mkNullNode #[])
     else
-      -- if there are no alts, then use the `with` token for `inner` for a ref for messages
-      let altStxs := optInductionAlts[0].getArg 2
-      let inner := if altStxs.getNumArgs > 0 then altStxs else optInductionAlts[0][0]
       -- `with` and tactic applied to all branches must be unchanged for reuse
-      (mkNullNode optInductionAlts[0].getArgs[:2], inner))
-    (fun alts? =>
-      if optInductionAlts.isNone then      -- no `with` clause
-        cont none
-      else if alts?.isOfKind nullKind then -- has alts
-        cont (some alts?.getArgs)
-      else                                 -- has `with` clause, but no alts
-        cont (some #[]))
+      (mkNullNode optInductionAlts[0].getArgs[:2], optInductionAlts[0].getArg 2))
+    (fun alts => cont alts.getArgs)
 
 private def getOptPreTacOfOptInductionAlts (optInductionAlts : Syntax) : Syntax :=
   if optInductionAlts.isNone then mkNullNode else optInductionAlts[0][1]
@@ -526,7 +518,7 @@ private def expandMultiAlt? (alt : Syntax) : Option (Array Syntax) := Id.run do
 /--
 Given `inductionAlts` of the form
 ```
-syntax inductionAlts := "with " (tactic)? withPosition( (colGe inductionAlt)*)
+syntax inductionAlts := "with " (tactic)? withPosition( (colGe inductionAlt)+)
 ```
 Return `some inductionAlts'` if one of the alternatives have multiple LHSs, in the new `inductionAlts'`
 all alternatives have a single LHS.
@@ -708,10 +700,10 @@ def evalInduction : Tactic := fun stx =>
         -- unchanged
         -- everything up to the alternatives must be unchanged for reuse
         Term.withNarrowedArgTacticReuse (stx := stx) (argIdx := 4) fun optInductionAlts => do
-        withAltsOfOptInductionAlts optInductionAlts fun alts? => do
+        withAltsOfOptInductionAlts optInductionAlts fun alts => do
           let optPreTac := getOptPreTacOfOptInductionAlts optInductionAlts
           mvarId.assign result.elimApp
-          ElimApp.evalAlts elimInfo result.alts optPreTac alts? initInfo (numGeneralized := n) (toClear := targetFVarIds)
+          ElimApp.evalAlts elimInfo result.alts optPreTac alts initInfo (numGeneralized := n) (toClear := targetFVarIds)
           appendGoals result.others.toList
 where
   checkTargets (targets : Array Expr) : MetaM Unit := do

src/Lean/Elab/Tactic/Omega/Frontend.lean

@@ -680,7 +680,7 @@ def omegaTactic (cfg : OmegaConfig) : TacticM Unit := do
 
 /-- The `omega` tactic, for resolving integer and natural linear arithmetic problems. This
 `TacticM Unit` frontend with default configuration can be used as an Aesop rule, for example via
-the tactic call `aesop (add 50% tactic Lean.Elab.Tactic.Omega.omegaDefault)`. -/
+the tactic call `aesop (add 50% tactic Lean.Omega.omegaDefault)`. -/
 def omegaDefault : TacticM Unit := omegaTactic {}
 
 @[builtin_tactic Lean.Parser.Tactic.omega]

src/Lean/Elab/Tactic/RCases.lean

@@ -507,7 +507,7 @@ partial def rintroCore (g : MVarId) (fs : FVarSubst) (clears : Array FVarId) (a
   match pat with
   | `(rintroPat| $pat:rcasesPat) =>
     let pat := (← RCasesPatt.parse pat).typed? ref ty?
-    let (v, g) ← withRef pat.ref <| g.intro (pat.name?.getD `_)
+    let (v, g) ← g.intro (pat.name?.getD `_)
     rcasesCore g fs clears (.fvar v) a pat cont
   | `(rintroPat| ($(pats)* $[: $ty?']?)) =>
     let ref := if pats.size == 1 then pat.raw else .missing

src/Lean/Linter/MissingDocs.lean

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro
 -/
 prelude
-import Lean.Parser.Syntax
 import Lean.Meta.Tactic.Simp.RegisterCommand
 import Lean.Elab.Command
 import Lean.Elab.SetOption

src/Lean/Meta/AppBuilder.lean

@@ -11,14 +11,14 @@ import Lean.Meta.DecLevel
 
 namespace Lean.Meta
 
-/-- Returns `id e` -/
+/-- Return `id e` -/
 def mkId (e : Expr) : MetaM Expr := do
   let type ← inferType e
   let u    ← getLevel type
   return mkApp2 (mkConst ``id [u]) type e
 
 /--
-  Given `e` s.t. `inferType e` is definitionally equal to `expectedType`, returns
+  Given `e` s.t. `inferType e` is definitionally equal to `expectedType`, return
   term `@id expectedType e`. -/
 def mkExpectedTypeHint (e : Expr) (expectedType : Expr) : MetaM Expr := do
   let u ← getLevel expectedType
@@ -38,13 +38,13 @@ def mkLetFun (x : Expr) (v : Expr) (e : Expr) : MetaM Expr := do
   let u2 ← getLevel ety
   return mkAppN (.const ``letFun [u1, u2]) #[α, β, v, f]
 
-/-- Returns `a = b`. -/
+/-- Return `a = b`. -/
 def mkEq (a b : Expr) : MetaM Expr := do
   let aType ← inferType a
   let u ← getLevel aType
   return mkApp3 (mkConst ``Eq [u]) aType a b
 
-/-- Returns `HEq a b`. -/
+/-- Return `HEq a b`. -/
 def mkHEq (a b : Expr) : MetaM Expr := do
   let aType ← inferType a
   let bType ← inferType b
@@ -52,7 +52,7 @@ def mkHEq (a b : Expr) : MetaM Expr := do
   return mkApp4 (mkConst ``HEq [u]) aType a bType b
 
 /--
-  If `a` and `b` have definitionally equal types, returns `Eq a b`, otherwise returns `HEq a b`.
+  If `a` and `b` have definitionally equal types, return `Eq a b`, otherwise return `HEq a b`.
 -/
 def mkEqHEq (a b : Expr) : MetaM Expr := do
   let aType ← inferType a
@@ -63,25 +63,25 @@ def mkEqHEq (a b : Expr) : MetaM Expr := do
   else
     return mkApp4 (mkConst ``HEq [u]) aType a bType b
 
-/-- Returns a proof of `a = a`. -/
+/-- Return a proof of `a = a`. -/
 def mkEqRefl (a : Expr) : MetaM Expr := do
   let aType ← inferType a
   let u ← getLevel aType
   return mkApp2 (mkConst ``Eq.refl [u]) aType a
 
-/-- Returns a proof of `HEq a a`. -/
+/-- Return a proof of `HEq a a`. -/
 def mkHEqRefl (a : Expr) : MetaM Expr := do
   let aType ← inferType a
   let u ← getLevel aType
   return mkApp2 (mkConst ``HEq.refl [u]) aType a
 
-/-- Given `hp : P` and `nhp : Not P`, returns an instance of type `e`. -/
+/-- Given `hp : P` and `nhp : Not P` returns an instance of type `e`. -/
 def mkAbsurd (e : Expr) (hp hnp : Expr) : MetaM Expr := do
   let p ← inferType hp
   let u ← getLevel e
   return mkApp4 (mkConst ``absurd [u]) p e hp hnp
 
-/-- Given `h : False`, returns an instance of type `e`. -/
+/-- Given `h : False`, return an instance of type `e`. -/
 def mkFalseElim (e : Expr) (h : Expr) : MetaM Expr := do
   let u ← getLevel e
   return mkApp2 (mkConst ``False.elim [u]) e h
@@ -108,7 +108,7 @@ def mkEqSymm (h : Expr) : MetaM Expr := do
       return mkApp4 (mkConst ``Eq.symm [u]) α a b h
     | none => throwAppBuilderException ``Eq.symm ("equality proof expected" ++ hasTypeMsg h hType)
 
-/-- Given `h₁ : a = b` and `h₂ : b = c`, returns a proof of `a = c`. -/
+/-- Given `h₁ : a = b` and `h₂ : b = c` returns a proof of `a = c`. -/
 def mkEqTrans (h₁ h₂ : Expr) : MetaM Expr := do
   if h₁.isAppOf ``Eq.refl then
     return h₂
@@ -185,7 +185,7 @@ def mkHEqOfEq (h : Expr) : MetaM Expr := do
   return mkApp4 (mkConst ``heq_of_eq [u]) α a b h
 
 /--
-If `e` is `@Eq.refl α a`, returns `a`.
+If `e` is `@Eq.refl α a`, return `a`.
 -/
 def isRefl? (e : Expr) : Option Expr := do
   if e.isAppOfArity ``Eq.refl 2 then
@@ -194,7 +194,7 @@ def isRefl? (e : Expr) : Option Expr := do
     none
 
 /--
-If `e` is `@congrArg α β a b f h`, returns `α`, `f` and `h`.
+If `e` is `@congrArg α β a b f h`, return `α`, `f` and `h`.
 Also works if `e` can be turned into such an application (e.g. `congrFun`).
 -/
 def congrArg? (e : Expr) : MetaM (Option (Expr × Expr × Expr)) := do
@@ -336,14 +336,13 @@ private def withAppBuilderTrace [ToMessageData α] [ToMessageData β]
       throw ex
 
 /--
-  Returns the application `constName xs`.
+  Return the application `constName xs`.
   It tries to fill the implicit arguments before the last element in `xs`.
 
   Remark:
   ``mkAppM `arbitrary #[α]`` returns `@arbitrary.{u} α` without synthesizing
   the implicit argument occurring after `α`.
-  Given a `x : ([Decidable p] → Bool) × Nat`, ``mkAppM `Prod.fst #[x]``,
-  returns `@Prod.fst ([Decidable p] → Bool) Nat x`.
+  Given a `x : ([Decidable p] → Bool) × Nat`, ``mkAppM `Prod.fst #[x]`` returns `@Prod.fst ([Decidable p] → Bool) Nat x`.
 -/
 def mkAppM (constName : Name) (xs : Array Expr) : MetaM Expr := do
   withAppBuilderTrace constName xs do withNewMCtxDepth do
@@ -466,9 +465,8 @@ def mkPure (monad : Expr) (e : Expr) : MetaM Expr :=
   mkAppOptM ``Pure.pure #[monad, none, none, e]
 
 /--
-`mkProjection s fieldName` returns an expression for accessing field `fieldName` of the structure `s`.
-Remark: `fieldName` may be a subfield of `s`.
--/
+  `mkProjection s fieldName` returns an expression for accessing field `fieldName` of the structure `s`.
+  Remark: `fieldName` may be a subfield of `s`. -/
 partial def mkProjection (s : Expr) (fieldName : Name) : MetaM Expr := do
   let type ← inferType s
   let type ← whnf type
@@ -522,11 +520,11 @@ def mkSome (type value : Expr) : MetaM Expr := do
   let u ← getDecLevel type
   return mkApp2 (mkConst ``Option.some [u]) type value
 
-/-- Returns `Decidable.decide p` -/
+/-- Return `Decidable.decide p` -/
 def mkDecide (p : Expr) : MetaM Expr :=
   mkAppOptM ``Decidable.decide #[p, none]
 
-/-- Returns a proof for `p : Prop` using `decide p` -/
+/-- Return a proof for `p : Prop` using `decide p` -/
 def mkDecideProof (p : Expr) : MetaM Expr := do
   let decP      ← mkDecide p
   let decEqTrue ← mkEq decP (mkConst ``Bool.true)
@@ -534,75 +532,59 @@ def mkDecideProof (p : Expr) : MetaM Expr := do
   let h         ← mkExpectedTypeHint h decEqTrue
   mkAppM ``of_decide_eq_true #[h]
 
-/-- Returns `a < b` -/
+/-- Return `a < b` -/
 def mkLt (a b : Expr) : MetaM Expr :=
   mkAppM ``LT.lt #[a, b]
 
-/-- Returns `a <= b` -/
+/-- Return `a <= b` -/
 def mkLe (a b : Expr) : MetaM Expr :=
   mkAppM ``LE.le #[a, b]
 
-/-- Returns `Inhabited.default α` -/
+/-- Return `Inhabited.default α` -/
 def mkDefault (α : Expr) : MetaM Expr :=
   mkAppOptM ``Inhabited.default #[α, none]
 
-/-- Returns `@Classical.ofNonempty α _` -/
+/-- Return `@Classical.ofNonempty α _` -/
 def mkOfNonempty (α : Expr) : MetaM Expr := do
   mkAppOptM ``Classical.ofNonempty #[α, none]
 
-/-- Returns `funext h` -/
+/-- Return `funext h` -/
 def mkFunExt (h : Expr) : MetaM Expr :=
   mkAppM ``funext #[h]
 
-/-- Returns `propext h` -/
+/-- Return `propext h` -/
 def mkPropExt (h : Expr) : MetaM Expr :=
   mkAppM ``propext #[h]
 
-/-- Returns `let_congr h₁ h₂` -/
+/-- Return `let_congr h₁ h₂` -/
 def mkLetCongr (h₁ h₂ : Expr) : MetaM Expr :=
   mkAppM ``let_congr #[h₁, h₂]
 
-/-- Returns `let_val_congr b h` -/
+/-- Return `let_val_congr b h` -/
 def mkLetValCongr (b h : Expr) : MetaM Expr :=
   mkAppM ``let_val_congr #[b, h]
 
-/-- Returns `let_body_congr a h` -/
+/-- Return `let_body_congr a h` -/
 def mkLetBodyCongr (a h : Expr) : MetaM Expr :=
   mkAppM ``let_body_congr #[a, h]
 
-/-- Returns `@of_eq_true p h` -/
-def mkOfEqTrueCore (p : Expr) (h : Expr) : Expr :=
-  match_expr h with
-  | eq_true _ h => h
-  | _ => mkApp2 (mkConst ``of_eq_true) p h
+/-- Return `of_eq_true h` -/
+def mkOfEqTrue (h : Expr) : MetaM Expr :=
+  mkAppM ``of_eq_true #[h]
 
-/-- Returns `of_eq_true h` -/
-def mkOfEqTrue (h : Expr) : MetaM Expr := do
-  match_expr h with
-  | eq_true _ h => return h
-  | _ => mkAppM ``of_eq_true #[h]
-
-/-- Returns `eq_true h` -/
-def mkEqTrueCore (p : Expr) (h : Expr) : Expr :=
-  match_expr h with
-  | of_eq_true _ h => h
-  | _ => mkApp2 (mkConst ``eq_true) p h
-
-/-- Returns `eq_true h` -/
-def mkEqTrue (h : Expr) : MetaM Expr := do
-  match_expr h with
-  | of_eq_true _ h => return h
-  | _ => return mkApp2 (mkConst ``eq_true) (← inferType h) h
+/-- Return `eq_true h` -/
+def mkEqTrue (h : Expr) : MetaM Expr :=
+  mkAppM ``eq_true #[h]
 
 /--
-  Returns `eq_false h`
+  Return `eq_false h`
   `h` must have type definitionally equal to `¬ p` in the current
   reducibility setting. -/
 def mkEqFalse (h : Expr) : MetaM Expr :=
   mkAppM ``eq_false #[h]
 
 /--
-  Returns `eq_false' h`
+  Return `eq_false' h`
   `h` must have type definitionally equal to `p → False` in the current
   reducibility setting. -/
 def mkEqFalse' (h : Expr) : MetaM Expr :=
@@ -620,7 +602,7 @@ def mkImpDepCongrCtx (h₁ h₂ : Expr) : MetaM Expr :=
 def mkForallCongr (h : Expr) : MetaM Expr :=
   mkAppM ``forall_congr #[h]
 
-/-- Returns instance for `[Monad m]` if there is one -/
+/-- Return instance for `[Monad m]` if there is one -/
 def isMonad? (m : Expr) : MetaM (Option Expr) :=
   try
     let monadType ← mkAppM `Monad #[m]
@@ -631,52 +613,52 @@ def isMonad? (m : Expr) : MetaM (Option Expr) :=
   catch _ =>
     pure none
 
-/-- Returns `(n : type)`, a numeric literal of type `type`. The method fails if we don't have an instance `OfNat type n` -/
+/-- Return `(n : type)`, a numeric literal of type `type`. The method fails if we don't have an instance `OfNat type n` -/
 def mkNumeral (type : Expr) (n : Nat) : MetaM Expr := do
   let u ← getDecLevel type
   let inst ← synthInstance (mkApp2 (mkConst ``OfNat [u]) type (mkRawNatLit n))
   return mkApp3 (mkConst ``OfNat.ofNat [u]) type (mkRawNatLit n) inst
 
 /--
-Returns `a op b`, where `op` has name `opName` and is implemented using the typeclass `className`.
-This method assumes `a` and `b` have the same type, and typeclass `className` is heterogeneous.
-Examples of supported classes: `HAdd`, `HSub`, `HMul`.
-We use heterogeneous operators to ensure we have a uniform representation.
--/
+  Return `a op b`, where `op` has name `opName` and is implemented using the typeclass `className`.
+  This method assumes `a` and `b` have the same type, and typeclass `className` is heterogeneous.
+  Examples of supported classes: `HAdd`, `HSub`, `HMul`.
+  We use heterogeneous operators to ensure we have a uniform representation.
+  -/
 private def mkBinaryOp (className : Name) (opName : Name) (a b : Expr) : MetaM Expr := do
   let aType ← inferType a
   let u ← getDecLevel aType
   let inst ← synthInstance (mkApp3 (mkConst className [u, u, u]) aType aType aType)
   return mkApp6 (mkConst opName [u, u, u]) aType aType aType inst a b
 
-/-- Returns `a + b` using a heterogeneous `+`. This method assumes `a` and `b` have the same type. -/
+/-- Return `a + b` using a heterogeneous `+`. This method assumes `a` and `b` have the same type. -/
 def mkAdd (a b : Expr) : MetaM Expr := mkBinaryOp ``HAdd ``HAdd.hAdd a b
 
-/-- Returns `a - b` using a heterogeneous `-`. This method assumes `a` and `b` have the same type. -/
+/-- Return `a - b` using a heterogeneous `-`. This method assumes `a` and `b` have the same type. -/
 def mkSub (a b : Expr) : MetaM Expr := mkBinaryOp ``HSub ``HSub.hSub a b
 
-/-- Returns `a * b` using a heterogeneous `*`. This method assumes `a` and `b` have the same type. -/
+/-- Return `a * b` using a heterogeneous `*`. This method assumes `a` and `b` have the same type. -/
 def mkMul (a b : Expr) : MetaM Expr := mkBinaryOp ``HMul ``HMul.hMul a b
 
 /--
-Returns `a r b`, where `r` has name `rName` and is implemented using the typeclass `className`.
-This method assumes `a` and `b` have the same type.
-Examples of supported classes: `LE` and `LT`.
-We use heterogeneous operators to ensure we have a uniform representation.
--/
+  Return `a r b`, where `r` has name `rName` and is implemented using the typeclass `className`.
+  This method assumes `a` and `b` have the same type.
+  Examples of supported classes: `LE` and `LT`.
+  We use heterogeneous operators to ensure we have a uniform representation.
+  -/
 private def mkBinaryRel (className : Name) (rName : Name) (a b : Expr) : MetaM Expr := do
   let aType ← inferType a
   let u ← getDecLevel aType
   let inst ← synthInstance (mkApp (mkConst className [u]) aType)
   return mkApp4 (mkConst rName [u]) aType inst a b
 
-/-- Returns `a ≤ b`. This method assumes `a` and `b` have the same type. -/
+/-- Return `a ≤ b`. This method assumes `a` and `b` have the same type. -/
 def mkLE (a b : Expr) : MetaM Expr := mkBinaryRel ``LE ``LE.le a b
 
-/-- Returns `a < b`. This method assumes `a` and `b` have the same type. -/
+/-- Return `a < b`. This method assumes `a` and `b` have the same type. -/
 def mkLT (a b : Expr) : MetaM Expr := mkBinaryRel ``LT ``LT.lt a b
 
-/-- Given `h : a = b`, returns a proof for `a ↔ b`. -/
+/-- Given `h : a = b`, return a proof for `a ↔ b`. -/
 def mkIffOfEq (h : Expr) : MetaM Expr := do
   if h.isAppOfArity ``propext 3 then
     return h.appArg!

src/Lean/Meta/Basic.lean

@@ -1964,22 +1964,15 @@ def sortFVarIds (fvarIds : Array FVarId) : MetaM (Array FVarId) := do
 
 end Methods
 
-/--
-Return `some info` if `declName` is an inductive predicate where `info : InductiveVal`.
-That is, `inductive` type in `Prop`.
--/
-def isInductivePredicate? (declName : Name) : MetaM (Option InductiveVal) := do
-  match (← getEnv).find? declName with
-  | some (.inductInfo info) =>
-    forallTelescopeReducing info.type fun _ type => do
-      match (← whnfD type) with
-      | .sort u .. => if u == levelZero then return some info else return none
-      | _ => return none
-  | _ => return none
-
 /-- Return `true` if `declName` is an inductive predicate. That is, `inductive` type in `Prop`. -/
 def isInductivePredicate (declName : Name) : MetaM Bool := do
-  return (← isInductivePredicate? declName).isSome
+  match (← getEnv).find? declName with
+  | some (.inductInfo { type := type, ..}) =>
+    forallTelescopeReducing type fun _ type => do
+      match (← whnfD type) with
+      | .sort u .. => return u == levelZero
+      | _ => return false
+  | _ => return false
 
 def isListLevelDefEqAux : List Level → List Level → MetaM Bool
   | [],    []    => return true

src/Lean/Meta/Tactic/Cases.lean

@@ -33,7 +33,7 @@ private def mkEqAndProof (lhs rhs : Expr) : MetaM (Expr × Expr) := do
   else
     pure (mkApp4 (mkConst ``HEq [u]) lhsType lhs rhsType rhs, mkApp2 (mkConst ``HEq.refl [u]) lhsType lhs)
 
-partial def withNewEqs (targets targetsNew : Array Expr) (k : Array Expr → Array Expr → MetaM α) : MetaM α :=
+private partial def withNewEqs (targets targetsNew : Array Expr) (k : Array Expr → Array Expr → MetaM α) : MetaM α :=
   let rec loop (i : Nat) (newEqs : Array Expr) (newRefls : Array Expr) := do
     if i < targets.size then
       let (newEqType, newRefl) ← mkEqAndProof targets[i]! targetsNew[i]!
@@ -66,31 +66,30 @@ structure GeneralizeIndicesSubgoal where
   numEqs         : Nat
 
 /--
-Given a metavariable `mvarId` representing the goal
-```
-Ctx |- T
-```
-and an expression `e : I A j`, where `I A j` is an inductive datatype where `A` are parameters,
-and `j` the indices. Generate the goal
-```
-Ctx, j' : J, h' : I A j' |- j == j' -> e == h' -> T
-```
-Remark: `(j == j' -> e == h')` is a "telescopic" equality.
-Remark: `j` is sequence of terms, and `j'` a sequence of free variables.
-The result contains the fields
-- `mvarId`: the new goal
-- `indicesFVarIds`: `j'` ids
-- `fvarId`: `h'` id
-- `numEqs`: number of equations in the target
-
-If `varName?` is not none, it is used to name `h'`.
--/
-def generalizeIndices' (mvarId : MVarId) (e : Expr) (varName? : Option Name := none) : MetaM GeneralizeIndicesSubgoal :=
+  Similar to `generalizeTargets` but customized for the `casesOn` motive.
+  Given a metavariable `mvarId` representing the
+  ```
+  Ctx, h : I A j, D |- T
+  ```
+  where `fvarId` is `h`s id, and the type `I A j` is an inductive datatype where `A` are parameters,
+  and `j` the indices. Generate the goal
+  ```
+  Ctx, h : I A j, D, j' : J, h' : I A j' |- j == j' -> h == h' -> T
+  ```
+  Remark: `(j == j' -> h == h')` is a "telescopic" equality.
+  Remark: `j` is sequence of terms, and `j'` a sequence of free variables.
+  The result contains the fields
+  - `mvarId`: the new goal
+  - `indicesFVarIds`: `j'` ids
+  - `fvarId`: `h'` id
+  - `numEqs`: number of equations in the target -/
+def generalizeIndices (mvarId : MVarId) (fvarId : FVarId) : MetaM GeneralizeIndicesSubgoal :=
   mvarId.withContext do
     let lctx       ← getLCtx
     let localInsts ← getLocalInstances
     mvarId.checkNotAssigned `generalizeIndices
-    let type ← whnfD (← inferType e)
+    let fvarDecl ← fvarId.getDecl
+    let type ← whnf fvarDecl.type
     type.withApp fun f args => matchConstInduct f (fun _ => throwTacticEx `generalizeIndices mvarId "inductive type expected") fun val _ => do
       unless val.numIndices > 0 do throwTacticEx `generalizeIndices mvarId "indexed inductive type expected"
       unless args.size == val.numIndices + val.numParams do throwTacticEx `generalizeIndices mvarId "ill-formed inductive datatype"
@@ -99,10 +98,9 @@ def generalizeIndices' (mvarId : MVarId) (e : Expr) (varName? : Option Name := n
       let IAType ← inferType IA
       forallTelescopeReducing IAType fun newIndices _ => do
       let newType := mkAppN IA newIndices
-      let varName ← if let some varName := varName? then pure varName else mkFreshUserName `x
-      withLocalDeclD varName newType fun h' =>
+      withLocalDeclD fvarDecl.userName newType fun h' =>
       withNewEqs indices newIndices fun newEqs newRefls => do
-      let (newEqType, newRefl) ← mkEqAndProof e h'
+      let (newEqType, newRefl) ← mkEqAndProof fvarDecl.toExpr h'
       let newRefls := newRefls.push newRefl
       withLocalDeclD `h newEqType fun newEq => do
       let newEqs := newEqs.push newEq
@@ -114,7 +112,7 @@ def generalizeIndices' (mvarId : MVarId) (e : Expr) (varName? : Option Name := n
       let auxType ← mkForallFVars newIndices auxType
       let newMVar ← mkFreshExprMVarAt lctx localInsts auxType MetavarKind.syntheticOpaque tag
       /- assign mvarId := newMVar indices h refls -/
-      mvarId.assign (mkAppN (mkApp (mkAppN newMVar indices) e) newRefls)
+      mvarId.assign (mkAppN (mkApp (mkAppN newMVar indices) fvarDecl.toExpr) newRefls)
       let (indicesFVarIds, newMVarId) ← newMVar.mvarId!.introNP newIndices.size
       let (fvarId, newMVarId) ← newMVarId.intro1P
       return {
@@ -124,29 +122,6 @@ def generalizeIndices' (mvarId : MVarId) (e : Expr) (varName? : Option Name := n
         numEqs         := newEqs.size
       }
 
-/--
-Similar to `generalizeTargets` but customized for the `casesOn` motive.
-Given a metavariable `mvarId` representing the
-```
-Ctx, h : I A j, D |- T
-```
-where `fvarId` is `h`s id, and the type `I A j` is an inductive datatype where `A` are parameters,
-and `j` the indices. Generate the goal
-```
-Ctx, h : I A j, D, j' : J, h' : I A j' |- j == j' -> h == h' -> T
-```
-Remark: `(j == j' -> h == h')` is a "telescopic" equality.
-Remark: `j` is sequence of terms, and `j'` a sequence of free variables.
-The result contains the fields
-- `mvarId`: the new goal
-- `indicesFVarIds`: `j'` ids
-- `fvarId`: `h'` id
-- `numEqs`: number of equations in the target -/
-def generalizeIndices (mvarId : MVarId) (fvarId : FVarId) : MetaM GeneralizeIndicesSubgoal :=
-  mvarId.withContext do
-    let fvarDecl ← fvarId.getDecl
-    generalizeIndices' mvarId fvarDecl.toExpr fvarDecl.userName
-
 structure CasesSubgoal extends InductionSubgoal where
   ctorName : Name
 

src/Lean/Meta/Tactic/FVarSubst.lean

@@ -35,7 +35,7 @@ def insert (s : FVarSubst) (fvarId : FVarId) (v : Expr) : FVarSubst :=
   if s.contains fvarId then s
   else
     let map := s.map.mapVal fun e => e.replaceFVarId fvarId v;
-    { map := map.insertNew fvarId v }
+    { map := map.insert fvarId v }
 
 def erase (s : FVarSubst) (fvarId : FVarId) : FVarSubst :=
   { map := s.map.erase fvarId }

src/Lean/Meta/Tactic/Grind.lean

@@ -23,8 +23,7 @@ import Lean.Meta.Tactic.Grind.Parser
 import Lean.Meta.Tactic.Grind.EMatchTheorem
 import Lean.Meta.Tactic.Grind.EMatch
 import Lean.Meta.Tactic.Grind.Main
-import Lean.Meta.Tactic.Grind.CasesMatch
-import Lean.Meta.Tactic.Grind.Arith
+
 
 namespace Lean
 
@@ -35,22 +34,10 @@ builtin_initialize registerTraceClass `grind.eqc
 builtin_initialize registerTraceClass `grind.internalize
 builtin_initialize registerTraceClass `grind.ematch
 builtin_initialize registerTraceClass `grind.ematch.pattern
-builtin_initialize registerTraceClass `grind.ematch.pattern.search
 builtin_initialize registerTraceClass `grind.ematch.instance
 builtin_initialize registerTraceClass `grind.ematch.instance.assignment
 builtin_initialize registerTraceClass `grind.issues
 builtin_initialize registerTraceClass `grind.simp
-builtin_initialize registerTraceClass `grind.split
-builtin_initialize registerTraceClass `grind.split.candidate
-builtin_initialize registerTraceClass `grind.split.resolved
-builtin_initialize registerTraceClass `grind.offset
-builtin_initialize registerTraceClass `grind.offset.dist
-builtin_initialize registerTraceClass `grind.offset.internalize
-builtin_initialize registerTraceClass `grind.offset.internalize.term (inherited := true)
-builtin_initialize registerTraceClass `grind.offset.propagate
-builtin_initialize registerTraceClass `grind.offset.eq
-builtin_initialize registerTraceClass `grind.offset.eq.to (inherited := true)
-builtin_initialize registerTraceClass `grind.offset.eq.from (inherited := true)
 
 /-! Trace options for `grind` developers -/
 builtin_initialize registerTraceClass `grind.debug
@@ -60,9 +47,5 @@ builtin_initialize registerTraceClass `grind.debug.proof
 builtin_initialize registerTraceClass `grind.debug.proj
 builtin_initialize registerTraceClass `grind.debug.parent
 builtin_initialize registerTraceClass `grind.debug.final
-builtin_initialize registerTraceClass `grind.debug.forallPropagator
-builtin_initialize registerTraceClass `grind.debug.split
-builtin_initialize registerTraceClass `grind.debug.canon
-builtin_initialize registerTraceClass `grind.debug.offset
-builtin_initialize registerTraceClass `grind.debug.offset.proof
+
 end Lean

src/Lean/Meta/Tactic/Grind/Arith.lean

@@ -1,10 +0,0 @@
-/-
-Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Lean.Meta.Tactic.Grind.Arith.Util
-import Lean.Meta.Tactic.Grind.Arith.Types
-import Lean.Meta.Tactic.Grind.Arith.Offset
-import Lean.Meta.Tactic.Grind.Arith.Main

src/Lean/Meta/Tactic/Grind/Arith/Internalize.lean

@@ -1,14 +0,0 @@
-/-
-Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Lean.Meta.Tactic.Grind.Arith.Offset
-
-namespace Lean.Meta.Grind.Arith
-
-def internalize (e : Expr) (parent? : Option Expr) : GoalM Unit := do
-  Offset.internalize e parent?
-
-end Lean.Meta.Grind.Arith

src/Lean/Meta/Tactic/Grind/Arith/Inv.lean

@@ -1,14 +0,0 @@
-/-
-Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Lean.Meta.Tactic.Grind.Arith.Offset
-
-namespace Lean.Meta.Grind.Arith
-
-def checkInvariants : GoalM Unit :=
-  Offset.checkInvariants
-
-end Lean.Meta.Grind.Arith

src/Lean/Meta/Tactic/Grind/Arith/Main.lean

@@ -1,34 +0,0 @@
-/-
-Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Lean.Meta.Tactic.Grind.PropagatorAttr
-import Lean.Meta.Tactic.Grind.Arith.Offset
-
-namespace Lean.Meta.Grind.Arith
-
-namespace Offset
-def isCnstr? (e : Expr) : GoalM (Option (Cnstr NodeId)) :=
-  return (← get).arith.offset.cnstrs.find? { expr := e }
-
-def assertTrue (c : Cnstr NodeId) (p : Expr) : GoalM Unit := do
-  addEdge c.u c.v c.k (← mkOfEqTrue p)
-
-def assertFalse (c : Cnstr NodeId) (p : Expr) : GoalM Unit := do
-  let p := mkOfNegEqFalse (← get').nodes c p
-  let c := c.neg
-  addEdge c.u c.v c.k p
-
-end Offset
-
-builtin_grind_propagator propagateLE ↓LE.le := fun e => do
-  if (← isEqTrue e) then
-    if let some c ← Offset.isCnstr? e then
-      Offset.assertTrue c (← mkEqTrueProof e)
-  if (← isEqFalse e) then
-    if let some c ← Offset.isCnstr? e then
-      Offset.assertFalse c (← mkEqFalseProof e)
-
-end Lean.Meta.Grind.Arith

src/Lean/Meta/Tactic/Grind/Arith/Model.lean

@@ -1,46 +0,0 @@
-/-
-Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Lean.Meta.Basic
-import Lean.Meta.Tactic.Grind.Types
-import Lean.Meta.Tactic.Grind.Util
-
-namespace Lean.Meta.Grind.Arith.Offset
-/-- Construct a model that statisfies all offset constraints -/
-def mkModel (goal : Goal) : MetaM (Array (Expr × Nat)) := do
-  let s := goal.arith.offset
-  let nodes := s.nodes
-  let mut pre : Array (Option Int) := mkArray nodes.size none
-  for u in [:nodes.size] do
-    let val? := s.sources[u]!.foldl (init := @none Int) fun val? v k => Id.run do
-      let some va := pre[v]! | return val?
-      let val' := va - k
-      let some val := val? | return val'
-      if val' > val then return val' else val?
-    let val? := s.targets[u]!.foldl (init := val?) fun val? v k => Id.run do
-      let some va := pre[v]! | return val?
-      let val' := va + k
-      let some val := val? | return val'
-      if val' < val then return val' else val?
-    let val := val?.getD 0
-    pre := pre.set! u (some val)
-  let min := pre.foldl (init := 0) fun min val? => Id.run do
-    let some val := val? | return min
-    if val < min then val else min
-  let mut r := {}
-  for u in [:nodes.size] do
-    let some val := pre[u]! | unreachable!
-    let val := (val - min).toNat
-    let e := nodes[u]!
-    /-
-    We should not include the assignment for auxiliary offset terms since
-    they do not provide any additional information.
-    -/
-    if (isNatOffset? e).isNone && isNatNum? e != some 0 then
-      r := r.push (e, val)
-  return r
-
-end Lean.Meta.Grind.Arith.Offset

src/Lean/Meta/Tactic/Grind/Arith/Offset.lean

@@ -1,335 +0,0 @@
-/-
-Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Init.Grind.Offset
-import Lean.Meta.Tactic.Grind.Types
-import Lean.Meta.Tactic.Grind.Arith.ProofUtil
-
-namespace Lean.Meta.Grind.Arith.Offset
-/-!
-This module implements a decision procedure for offset constraints of the form:
-```
-x + k ≤ y
-x ≤ y + k
-```
-where `k` is a numeral.
-Each constraint is represented as an edge in a weighted graph.
-The constraint `x + k ≤ y` is represented as a negative edge.
-The shortest path between two nodes in the graph corresponds to an implied inequality.
-When adding a new edge, the state is considered unsatisfiable if the new edge creates a negative cycle.
-An incremental Floyd-Warshall algorithm is used to find the shortest paths between all nodes.
-This module can also handle offset equalities of the form `x + k = y` by representing them with two edges:
-```
-x + k ≤ y
-y ≤ x + k
-```
-The main advantage of this module over a full linear integer arithmetic procedure is
-its ability to efficiently detect all implied equalities and inequalities.
--/
-
-def get' : GoalM State := do
-  return (← get).arith.offset
-
-@[inline] def modify' (f : State → State) : GoalM Unit := do
-  modify fun s => { s with arith.offset := f s.arith.offset }
-
-def mkNode (expr : Expr) : GoalM NodeId := do
-  if let some nodeId := (← get').nodeMap.find? { expr } then
-    return nodeId
-  let nodeId : NodeId := (← get').nodes.size
-  trace[grind.offset.internalize.term] "{expr} ↦ #{nodeId}"
-  modify' fun s => { s with
-    nodes   := s.nodes.push expr
-    nodeMap := s.nodeMap.insert { expr } nodeId
-    sources := s.sources.push {}
-    targets := s.targets.push {}
-    proofs  := s.proofs.push {}
-  }
-  markAsOffsetTerm expr
-  return nodeId
-
-private def getExpr (u : NodeId) : GoalM Expr := do
-  return (← get').nodes[u]!
-
-private def getDist? (u v : NodeId) : GoalM (Option Int) := do
-  return (← get').targets[u]!.find? v
-
-private def getProof? (u v : NodeId) : GoalM (Option ProofInfo) := do
-  return (← get').proofs[u]!.find? v
-
-private def getNodeId (e : Expr) : GoalM NodeId := do
-  let some nodeId := (← get').nodeMap.find? { expr := e }
-    | throwError "internal `grind` error, term has not been internalized by offset module{indentExpr e}"
-  return nodeId
-
-/--
-Returns a proof for `u + k ≤ v` (or `u ≤ v + k`) where `k` is the
-shortest path between `u` and `v`.
--/
-private partial def mkProofForPath (u v : NodeId) : GoalM Expr := do
-  go (← getProof? u v).get!
-where
-  go (p : ProofInfo) : GoalM Expr := do
-    if u == p.w then
-      return p.proof
-    else
-      let p' := (← getProof? u p.w).get!
-      go (mkTrans (← get').nodes p' p v)
-
-/--
-Given a new edge edge `u --(kuv)--> v` justified by proof `huv` s.t.
-it creates a negative cycle with the existing path `v --{kvu}-->* u`, i.e., `kuv + kvu < 0`,
-this function closes the current goal by constructing a proof of `False`.
--/
-private def setUnsat (u v : NodeId) (kuv : Int) (huv : Expr) (kvu : Int) : GoalM Unit := do
-  assert! kuv + kvu < 0
-  let hvu ← mkProofForPath v u
-  let u ← getExpr u
-  let v ← getExpr v
-  closeGoal (mkUnsatProof u v kuv huv kvu hvu)
-
-/-- Sets the new shortest distance `k` between nodes `u` and `v`. -/
-private def setDist (u v : NodeId) (k : Int) : GoalM Unit := do
-  trace[grind.offset.dist] "{({ u, v, k : Cnstr NodeId})}"
-  modify' fun s => { s with
-    targets := s.targets.modify u fun es => es.insert v k
-    sources := s.sources.modify v fun es => es.insert u k
-  }
-
-private def setProof (u v : NodeId) (p : ProofInfo) : GoalM Unit := do
-  modify' fun s => { s with
-    proofs := s.proofs.modify u fun es => es.insert v p
-  }
-
-@[inline]
-private def forEachSourceOf (u : NodeId) (f : NodeId → Int → GoalM Unit) : GoalM Unit := do
-  (← get').sources[u]!.forM f
-
-@[inline]
-private def forEachTargetOf (u : NodeId) (f : NodeId → Int → GoalM Unit) : GoalM Unit := do
-  (← get').targets[u]!.forM f
-
-/-- Returns `true` if `k` is smaller than the shortest distance between `u` and `v` -/
-private def isShorter (u v : NodeId) (k : Int) : GoalM Bool := do
-  if let some k' ← getDist? u v then
-    return k < k'
-  else
-    return true
-
-/--
-Tries to assign `e` to `True`, which is represented by constraint `c` (from `u` to `v`), using the
-path `u --(k)--> v`.
--/
-private def propagateTrue (u v : NodeId) (k : Int) (c : Cnstr NodeId) (e : Expr) : GoalM Bool := do
-  if k ≤ c.k then
-    trace[grind.offset.propagate] "{{ u, v, k : Cnstr NodeId}} ==> {e} = True"
-    let kuv ← mkProofForPath u v
-    let u ← getExpr u
-    let v ← getExpr v
-    pushEqTrue e <| mkPropagateEqTrueProof u v k kuv c.k
-    return true
-  return false
-
-/--
-Tries to assign `e` to `False`, which is represented by constraint `c` (from `v` to `u`), using the
-path `u --(k)--> v`.
--/
-private def propagateFalse (u v : NodeId) (k : Int) (c : Cnstr NodeId) (e : Expr) : GoalM Bool := do
-  if k + c.k < 0 then
-    trace[grind.offset.propagate] "{{ u, v, k : Cnstr NodeId}} ==> {e} = False"
-    let kuv ← mkProofForPath u v
-    let u ← getExpr u
-    let v ← getExpr v
-    pushEqFalse e <| mkPropagateEqFalseProof u v k kuv c.k
-  return false
-
-/--
-Auxiliary function for implementing `propagateAll`.
-Traverses the constraints `c` (representing an expression `e`) s.t.
-`c.u = u` and `c.v = v`, it removes `c` from the list of constraints
-associated with `(u, v)` IF
-- `e` is already assigned, or
-- `f c e` returns true
--/
-@[inline]
-private def updateCnstrsOf (u v : NodeId) (f : Cnstr NodeId → Expr → GoalM Bool) : GoalM Unit := do
-  if let some cs := (← get').cnstrsOf.find? (u, v) then
-    let cs' ← cs.filterM fun (c, e) => do
-      if (← isEqTrue e <||> isEqFalse e) then
-        return false -- constraint was already assigned
-      else
-        return !(← f c e)
-    modify' fun s => { s with cnstrsOf := s.cnstrsOf.insert (u, v) cs' }
-
-/-- Equality propagation. -/
-private def propagateEq (u v : NodeId) (k : Int) : GoalM Unit := do
-  if k != 0 then return ()
-  let some k' ← getDist? v u | return ()
-  if k' != 0 then return ()
-  let ue ← getExpr u
-  let ve ← getExpr v
-  if (← isEqv ue ve) then return ()
-  let huv ← mkProofForPath u v
-  let hvu ← mkProofForPath v u
-  trace[grind.offset.eq.from] "{ue}, {ve}"
-  pushEq ue ve <| mkApp4 (mkConst ``Grind.Nat.eq_of_le_of_le) ue ve huv hvu
-
-/-- Performs constraint propagation. -/
-private def propagateAll (u v : NodeId) (k : Int) : GoalM Unit := do
-  updateCnstrsOf u v fun c e => return !(← propagateTrue u v k c e)
-  updateCnstrsOf v u fun c e => return !(← propagateFalse u v k c e)
-  propagateEq u v k
-
-/--
-If `isShorter u v k`, updates the shortest distance between `u` and `v`.
-`w` is the penultimate node in the path from `u` to `v`.
--/
-private def updateIfShorter (u v : NodeId) (k : Int) (w : NodeId) : GoalM Unit := do
-  if (← isShorter u v k) then
-    setDist u v k
-    setProof u v (← getProof? w v).get!
-    propagateAll u v k
-
-/--
-Adds an edge `u --(k) --> v` justified by the proof term `p`, and then
-if no negative cycle was created, updates the shortest distance of affected
-node pairs.
--/
-def addEdge (u : NodeId) (v : NodeId) (k : Int) (p : Expr) : GoalM Unit := do
-  if (← isInconsistent) then return ()
-  if let some k' ← getDist? v u then
-    if k'+k < 0 then
-      setUnsat u v k p k'
-      return ()
-  if (← isShorter u v k) then
-    setDist u v k
-    setProof u v { w := u, k, proof := p }
-    propagateAll u v k
-    update
-where
-  update : GoalM Unit := do
-    forEachTargetOf v fun j k₂ => do
-      /- Check whether new path: `u -(k)-> v -(k₂)-> j` is shorter -/
-      updateIfShorter u j (k+k₂) v
-    forEachSourceOf u fun i k₁ => do
-      /- Check whether new path: `i -(k₁)-> u -(k)-> v` is shorter -/
-      updateIfShorter i v (k₁+k) u
-      forEachTargetOf v fun j k₂ => do
-        /- Check whether new path: `i -(k₁)-> u -(k)-> v -(k₂) -> j` is shorter -/
-        updateIfShorter i j (k₁+k+k₂) v
-
-private def internalizeCnstr (e : Expr) (c : Cnstr Expr) : GoalM Unit := do
-  let u ← mkNode c.u
-  let v ← mkNode c.v
-  let c := { c with u, v }
-  if let some k ← getDist? u v then
-    if (← propagateTrue u v k c e) then
-      return ()
-  if let some k ← getDist? v u then
-    if (← propagateFalse v u k c e) then
-      return ()
-  trace[grind.offset.internalize] "{e} ↦ {c}"
-  modify' fun s => { s with
-    cnstrs   := s.cnstrs.insert { expr := e } c
-    cnstrsOf :=
-      let cs := if let some cs := s.cnstrsOf.find? (u, v) then (c, e) :: cs else [(c, e)]
-      s.cnstrsOf.insert (u, v) cs
-  }
-
-private def getZeroNode : GoalM NodeId := do
-  mkNode (← getNatZeroExpr)
-
-/-- Internalize `e` of the form `b + k` -/
-private def internalizeTerm (e : Expr) (b : Expr) (k : Nat) : GoalM Unit := do
-  -- `e` is of the form `b + k`
-  let u ← mkNode e
-  let v ← mkNode b
-  -- `u = v + k`. So, we add edges for `u ≤ v + k` and `v + k ≤ u`.
-  let h := mkApp (mkConst ``Nat.le_refl) e
-  addEdge u v k h
-  addEdge v u (-k) h
-  -- `0 + k ≤ u`
-  let z ← getZeroNode
-  addEdge z u (-k) <| mkApp2 (mkConst ``Grind.Nat.le_offset) b (toExpr k)
-
-/--
-Returns `true`, if `parent?` is relevant for internalization.
-For example, we do not want to internalize an offset term that
-is the child of an addition. This kind of term will be processed by the
-more general linear arithmetic module.
--/
-private def isRelevantParent (parent? : Option Expr) : GoalM Bool := do
-  let some parent := parent? | return false
-  let z ← getNatZeroExpr
-  return !isNatAdd parent && (isNatOffsetCnstr? parent z).isNone
-
-private def isEqParent (parent? : Option Expr) : Bool := Id.run do
-  let some parent := parent? | return false
-  return parent.isEq
-
-def internalize (e : Expr) (parent? : Option Expr) : GoalM Unit := do
-  let z ← getNatZeroExpr
-  if let some c := isNatOffsetCnstr? e z then
-    internalizeCnstr e c
-  else if (← isRelevantParent parent?) then
-    if let some (b, k) := isNatOffset? e then
-      internalizeTerm e b k
-    else if let some k := isNatNum? e then
-      -- core module has support for detecting equality between literals
-      unless isEqParent parent? do
-        internalizeTerm e z k
-
-@[export lean_process_new_offset_eq]
-def processNewOffsetEqImpl (a b : Expr) : GoalM Unit := do
-  unless isSameExpr a b do
-    trace[grind.offset.eq.to] "{a}, {b}"
-    let u ← getNodeId a
-    let v ← getNodeId b
-    let h ← mkEqProof a b
-    addEdge u v 0 <| mkApp3 (mkConst ``Grind.Nat.le_of_eq_1) a b h
-    addEdge v u 0 <| mkApp3 (mkConst ``Grind.Nat.le_of_eq_2) a b h
-
-@[export lean_process_new_offset_eq_lit]
-def processNewOffsetEqLitImpl (a b : Expr) : GoalM Unit := do
-  unless isSameExpr a b do
-    trace[grind.offset.eq.to] "{a}, {b}"
-    let some k := isNatNum? b | unreachable!
-    let u ← getNodeId a
-    let z ← mkNode (← getNatZeroExpr)
-    let h ← mkEqProof a b
-    addEdge u z k <| mkApp3 (mkConst ``Grind.Nat.le_of_eq_1) a b h
-    addEdge z u (-k) <| mkApp3 (mkConst ``Grind.Nat.le_of_eq_2) a b h
-
-def traceDists : GoalM Unit := do
-  let s ← get'
-  for u in [:s.targets.size], es in s.targets.toArray do
-    for (v, k) in es do
-      trace[grind.offset.dist] "#{u} -({k})-> #{v}"
-
-def Cnstr.toExpr (c : Cnstr NodeId) : GoalM Expr := do
-  let u := (← get').nodes[c.u]!
-  let v := (← get').nodes[c.v]!
-  if c.k == 0 then
-    return mkNatLE u v
-  else if c.k < 0 then
-    return mkNatLE (mkNatAdd u (Lean.toExpr ((-c.k).toNat))) v
-  else
-    return mkNatLE u (mkNatAdd v (Lean.toExpr c.k.toNat))
-
-def checkInvariants : GoalM Unit := do
-  let s ← get'
-  for u in [:s.targets.size], es in s.targets.toArray do
-    for (v, k) in es do
-      let c : Cnstr NodeId := { u, v, k }
-      trace[grind.debug.offset] "{c}"
-      let p ← mkProofForPath u v
-      trace[grind.debug.offset.proof] "{p} : {← inferType p}"
-      check p
-      unless (← withDefault <| isDefEq (← inferType p) (← Cnstr.toExpr c)) do
-        trace[grind.debug.offset.proof] "failed: {← inferType p} =?= {← Cnstr.toExpr c}"
-        unreachable!
-
-end Lean.Meta.Grind.Arith.Offset

src/Lean/Meta/Tactic/Grind/Arith/ProofUtil.lean

@@ -1,168 +0,0 @@
-/-
-Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Init.Grind.Offset
-import Init.Grind.Lemmas
-import Lean.Meta.Tactic.Grind.Types
-
-namespace Lean.Meta.Grind.Arith
-
-/-!
-Helper functions for constructing proof terms in the arithmetic procedures.
--/
-
-namespace Offset
-
-/-- Returns a proof for `true = true` -/
-def rfl_true : Expr := mkConst ``Grind.rfl_true
-
-private def toExprN (n : Int) :=
-  assert! n >= 0
-  toExpr n.toNat
-
-open Lean.Grind in
-/--
-Assume `pi₁` is `{ w := u, k := k₁, proof := p₁ }` and `pi₂` is `{ w := w, k := k₂, proof := p₂ }`
-`p₁` is the proof for edge `u -(k₁) → w` and `p₂` the proof for edge `w -(k₂)-> v`.
-Then, this function returns a proof for edge `u -(k₁+k₂) -> v`.
--/
-def mkTrans (nodes : PArray Expr) (pi₁ : ProofInfo) (pi₂ : ProofInfo) (v : NodeId) : ProofInfo :=
-  let { w := u, k := k₁, proof := p₁ } := pi₁
-  let { w, k := k₂, proof := p₂ } := pi₂
-  let u := nodes[u]!
-  let w := nodes[w]!
-  let v := nodes[v]!
-  let p := if k₁ == 0 then
-    if k₂ == 0 then
-      -- u ≤ w, w ≤ v
-      mkApp5 (mkConst ``Nat.le_trans) u w v p₁ p₂
-    else if k₂ > 0 then
-      -- u ≤ v, w ≤ v + k₂
-      mkApp6 (mkConst ``Nat.le_ro) u w v (toExprN k₂) p₁ p₂
-    else
-      let k₂ := - k₂
-      -- u ≤ w, w + k₂ ≤ v
-      mkApp6 (mkConst ``Nat.le_lo) u w v (toExprN k₂) p₁ p₂
-  else if k₁ < 0 then
-    let k₁ := -k₁
-    if k₂ == 0 then
-      mkApp6 (mkConst ``Nat.lo_le) u w v (toExprN k₁) p₁ p₂
-    else if k₂ < 0 then
-      let k₂ := -k₂
-      mkApp7 (mkConst ``Nat.lo_lo) u w v (toExprN k₁) (toExprN k₂) p₁ p₂
-    else
-      let ke₁ := toExprN k₁
-      let ke₂ := toExprN k₂
-      if k₁ > k₂ then
-        mkApp8 (mkConst ``Nat.lo_ro_1) u w v ke₁ ke₂ rfl_true p₁ p₂
-      else
-        mkApp7 (mkConst ``Nat.lo_ro_2) u w v ke₁ ke₂ p₁ p₂
-  else
-    let ke₁ := toExprN k₁
-    if k₂ == 0 then
-      mkApp6 (mkConst ``Nat.ro_le) u w v ke₁ p₁ p₂
-    else if k₂ < 0 then
-      let k₂  := -k₂
-      let ke₂ := toExprN k₂
-       if k₂ > k₁ then
-         mkApp8 (mkConst ``Nat.ro_lo_2) u w v ke₁ ke₂ rfl_true p₁ p₂
-       else
-         mkApp7 (mkConst ``Nat.ro_lo_1) u w v ke₁ ke₂ p₁ p₂
-    else
-      let ke₂ := toExprN k₂
-      mkApp7 (mkConst ``Nat.ro_ro) u w v ke₁ ke₂ p₁ p₂
-  { w := pi₁.w, k := k₁+k₂, proof := p }
-
-open Lean.Grind in
-def mkOfNegEqFalse (nodes : PArray Expr) (c : Cnstr NodeId) (h : Expr) : Expr :=
-  let u := nodes[c.u]!
-  let v := nodes[c.v]!
-  if c.k == 0 then
-    mkApp3 (mkConst ``Nat.of_le_eq_false) u v h
-  else if c.k == -1 then
-    mkApp3 (mkConst ``Nat.of_lo_eq_false_1) u v h
-  else if c.k < 0 then
-    mkApp4 (mkConst ``Nat.of_lo_eq_false) u v (toExprN (-c.k)) h
-  else
-    mkApp4 (mkConst ``Nat.of_ro_eq_false) u v (toExprN c.k) h
-
-/--
-Returns a proof of `False` using a negative cycle composed of
-- `u --(kuv)--> v` with proof `huv`
-- `v --(kvu)--> u` with proof `hvu`
--/
-def mkUnsatProof (u v : Expr) (kuv : Int) (huv : Expr) (kvu : Int) (hvu : Expr) : Expr :=
-  if kuv == 0 then
-    assert! kvu < 0
-    mkApp6 (mkConst ``Grind.Nat.unsat_le_lo) u v (toExprN (-kvu)) rfl_true huv hvu
-  else if kvu == 0 then
-    mkApp6 (mkConst ``Grind.Nat.unsat_le_lo) v u (toExprN (-kuv)) rfl_true hvu huv
-  else if kuv < 0 then
-    if kvu > 0 then
-      mkApp7 (mkConst ``Grind.Nat.unsat_lo_ro) u v (toExprN (-kuv)) (toExprN kvu) rfl_true huv hvu
-    else
-      assert! kvu < 0
-      mkApp7 (mkConst ``Grind.Nat.unsat_lo_lo) u v (toExprN (-kuv)) (toExprN (-kvu)) rfl_true huv hvu
-  else
-    assert! kuv > 0 && kvu < 0
-    mkApp7 (mkConst ``Grind.Nat.unsat_lo_ro) v u (toExprN (-kvu)) (toExprN kuv) rfl_true hvu huv
-
-/--
-Given a path `u --(kuv)--> v` justified by proof `huv`,
-construct a proof of `e = True` where `e` is a term corresponding to the edgen `u --(k') --> v`
-s.t. `k ≤ k'`
--/
-def mkPropagateEqTrueProof (u v : Expr) (k : Int) (huv : Expr) (k' : Int) : Expr :=
-  if k == 0 then
-    if k' == 0 then
-      mkApp3 (mkConst ``Grind.Nat.le_eq_true_of_le) u v huv
-    else
-      assert! k' > 0
-      mkApp4 (mkConst ``Grind.Nat.ro_eq_true_of_le) u v (toExprN k') huv
-  else if k < 0 then
-    let k := -k
-    if k' == 0 then
-      mkApp4 (mkConst ``Grind.Nat.le_eq_true_of_lo) u v (toExprN k) huv
-    else if k' < 0 then
-      let k' := -k'
-      mkApp6 (mkConst ``Grind.Nat.lo_eq_true_of_lo) u v (toExprN k) (toExprN k') rfl_true huv
-    else
-      assert! k' > 0
-      mkApp5 (mkConst ``Grind.Nat.ro_eq_true_of_lo) u v (toExprN k) (toExprN k') huv
-  else
-    assert! k > 0
-    assert! k' > 0
-    mkApp6 (mkConst ``Grind.Nat.ro_eq_true_of_ro) u v (toExprN k) (toExprN k') rfl_true huv
-
-/--
-Given a path `u --(kuv)--> v` justified by proof `huv`,
-construct a proof of `e = False` where `e` is a term corresponding to the edgen `v --(k') --> u`
-s.t. `k+k' < 0`
--/
-def mkPropagateEqFalseProof (u v : Expr) (k : Int) (huv : Expr) (k' : Int) : Expr :=
-  if k == 0 then
-    assert! k' < 0
-    let k' := -k'
-    mkApp5 (mkConst ``Grind.Nat.lo_eq_false_of_le) u v (toExprN k') rfl_true huv
-  else if k < 0 then
-    let k := -k
-    if k' == 0 then
-      mkApp5 (mkConst ``Grind.Nat.le_eq_false_of_lo) u v (toExprN k) rfl_true huv
-    else if k' < 0 then
-      let k' := -k'
-      mkApp6 (mkConst ``Grind.Nat.lo_eq_false_of_lo) u v (toExprN k) (toExprN k') rfl_true huv
-    else
-      assert! k' > 0
-      mkApp6 (mkConst ``Grind.Nat.ro_eq_false_of_lo) u v (toExprN k) (toExprN k') rfl_true huv
-  else
-    assert! k > 0
-    assert! k' < 0
-    let k' := -k'
-    mkApp6 (mkConst ``Grind.Nat.lo_eq_false_of_ro) u v (toExprN k) (toExprN k') rfl_true huv
-
-end Offset
-
-end Lean.Meta.Grind.Arith

src/Lean/Meta/Tactic/Grind/Arith/Types.lean

@@ -1,66 +0,0 @@
-/-
-Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Lean.Data.PersistentArray
-import Lean.Meta.Tactic.Grind.ENodeKey
-import Lean.Meta.Tactic.Grind.Arith.Util
-
-namespace Lean.Meta.Grind.Arith
-
-namespace Offset
-
-abbrev NodeId := Nat
-
-instance : ToMessageData (Offset.Cnstr NodeId) where
-  toMessageData c := Offset.toMessageData (α := NodeId) (inst := { toMessageData n := m!"#{n}" }) c
-
-/-- Auxiliary structure used for proof extraction.  -/
-structure ProofInfo where
-  w     : NodeId
-  k     : Int
-  proof : Expr
-  deriving Inhabited
-
-/-- State of the constraint offset procedure. -/
-structure State where
-  /-- Mapping from `NodeId` to the `Expr` represented by the node. -/
-  nodes    : PArray Expr := {}
-  /-- Mapping from `Expr` to a node representing it. -/
-  nodeMap  : PHashMap ENodeKey NodeId := {}
-  /-- Mapping from `Expr` representing inequalites to constraints. -/
-  cnstrs   : PHashMap ENodeKey (Cnstr NodeId) := {}
-  /--
-  Mapping from pairs `(u, v)` to a list of offset constraints on `u` and `v`.
-  We use this mapping to implement exhaustive constraint propagation.
-  -/
-  cnstrsOf : PHashMap (NodeId × NodeId) (List (Cnstr NodeId × Expr)) := {}
-  /--
-  For each node with id `u`, `sources[u]` contains
-  pairs `(v, k)` s.t. there is a path from `v` to `u` with weight `k`.
-  -/
-  sources  : PArray (AssocList NodeId Int) := {}
-  /--
-  For each node with id `u`, `targets[u]` contains
-  pairs `(v, k)` s.t. there is a path from `u` to `v` with weight `k`.
-  -/
-  targets  : PArray (AssocList NodeId Int) := {}
-  /--
-  Proof reconstruction information. For each node with id `u`, `proofs[u]` contains
-  pairs `(v, { w, proof })` s.t. there is a path from `u` to `v`, and
-  `w` is the penultimate node in the path, and `proof` is the justification for
-  the last edge.
-  -/
-  proofs   : PArray (AssocList NodeId ProofInfo) := {}
-  deriving Inhabited
-
-end Offset
-
-/-- State for the arithmetic procedures. -/
-structure State where
-  offset : Offset.State := {}
-  deriving Inhabited
-
-end Lean.Meta.Grind.Arith

src/Lean/Meta/Tactic/Grind/Arith/Util.lean

@@ -1,102 +0,0 @@
-/-
-Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Lean.Expr
-import Lean.Message
-
-namespace Lean.Meta.Grind.Arith
-
-/-- Returns `true` if `e` is of the form `Nat` -/
-def isNatType (e : Expr) : Bool :=
-  e.isConstOf ``Nat
-
-/-- Returns `true` if `e` is of the form `@instHAdd Nat instAddNat` -/
-def isInstAddNat (e : Expr) : Bool :=
-  let_expr instHAdd a b := e | false
-  isNatType a && b.isConstOf ``instAddNat
-
-/-- Returns `true` if `e` is `instLENat` -/
-def isInstLENat (e : Expr) : Bool :=
-  e.isConstOf ``instLENat
-
-/--
-Returns `some (a, b)` if `e` is of the form
-```
-@HAdd.hAdd Nat Nat Nat (instHAdd Nat instAddNat) a b
-```
--/
-def isNatAdd? (e : Expr) : Option (Expr × Expr) :=
-  let_expr HAdd.hAdd _ _ _ i a b := e | none
-  if isInstAddNat i then some (a, b) else none
-
-/--
-Returns `true` if `e` is of the form
-```
-@HAdd.hAdd Nat Nat Nat (instHAdd Nat instAddNat) _ _
-```
--/
-def isNatAdd (e : Expr) : Bool :=
-  let_expr HAdd.hAdd _ _ _ i _ _ := e | false
-  isInstAddNat i
-
-/-- Returns `some k` if `e` `@OfNat.ofNat Nat _ (instOfNatNat k)` -/
-def isNatNum? (e : Expr) : Option Nat := Id.run do
-  let_expr OfNat.ofNat _ _ inst := e | none
-  let_expr instOfNatNat k := inst | none
-  let .lit (.natVal k) := k | none
-  some k
-
-/-- Returns `some (a, k)` if `e` is of the form `a + k`.  -/
-def isNatOffset? (e : Expr) : Option (Expr × Nat) := Id.run do
-  let some (a, b) := isNatAdd? e | none
-  let some k := isNatNum? b | none
-  some (a, k)
-
-/-- An offset constraint. -/
-structure Offset.Cnstr (α : Type) where
-  u  : α
-  v  : α
-  k  : Int := 0
-  deriving Inhabited
-
-def Offset.Cnstr.neg : Cnstr α → Cnstr α
-  | { u, v, k } => { u := v, v := u, k := -k - 1 }
-
-example (c : Offset.Cnstr α) : c.neg.neg = c := by
-  cases c; simp [Offset.Cnstr.neg]; omega
-
-def Offset.toMessageData [inst : ToMessageData α] (c : Offset.Cnstr α) : MessageData :=
-  match c.k with
-  | .ofNat 0   => m!"{c.u} ≤ {c.v}"
-  | .ofNat k   => m!"{c.u} ≤ {c.v} + {k}"
-  | .negSucc k => m!"{c.u} + {k + 1} ≤ {c.v}"
-
-instance : ToMessageData (Offset.Cnstr Expr) where
-  toMessageData c := Offset.toMessageData c
-
-/--
-Returns `some cnstr` if `e` is offset constraint.
-Remark: `z` is `0` numeral. It is an extra argument because we
-want to be able to provide the one that has already been internalized.
--/
-def isNatOffsetCnstr? (e : Expr) (z : Expr) : Option (Offset.Cnstr Expr) :=
-  match_expr e with
-  | LE.le _ inst a b => if isInstLENat inst then go a b else none
-  | _ => none
-where
-  go (u v : Expr) :=
-    if let some (u, k) := isNatOffset? u then
-      some { u, k := - k, v }
-    else if let some (v, k) := isNatOffset? v then
-      some { u, v, k }
-    else if let some k := isNatNum? u then
-      some { u := z, v, k := - k }
-    else if let some k := isNatNum? v then
-      some { u, v := z, k }
-    else
-      some { u, v }
-
-end Lean.Meta.Grind.Arith

src/Lean/Meta/Tactic/Grind/Canon.lean

@@ -10,7 +10,6 @@ import Lean.Meta.FunInfo
 import Lean.Util.FVarSubset
 import Lean.Util.PtrSet
 import Lean.Util.FVarSubset
-import Lean.Meta.Tactic.Grind.Types
 
 namespace Lean.Meta.Grind
 namespace Canon
@@ -23,7 +22,7 @@ to detect when two structurally different atoms are definitionally equal.
 The `grind` tactic, on the other hand, uses congruence closure. Moreover, types, type formers, proofs, and instances
 are considered supporting elements and are not factored into congruence detection.
 
-This module minimizes the number of `isDefEq` checks by comparing two terms `a` and `b` only if they are instances,
+This module minimizes the number of `isDefEq` checks by comparing two terms `a` and `b` only if they instances,
 types, or type formers and are the `i`-th arguments of two different `f`-applications. This approach is
 sufficient for the congruence closure procedure used by the `grind` tactic.
 
@@ -41,37 +40,22 @@ additions will still use structurally different (and definitionally different) i
 Furthermore, `grind` will not be able to infer that  `HEq (a + a) (b + b)` even if we add the assumptions `n = m` and `HEq a b`.
 -/
 
-@[inline] private def get' : GoalM State :=
-  return (← get).canon
-
-@[inline] private def modify' (f : State → State) : GoalM Unit :=
-  modify fun s => { s with canon := f s.canon }
-
-/--
-Helper function for `canonElemCore`. It tries `isDefEq a b` with default transparency, but using
-at most `canonHeartbeats` heartbeats. It reports an issue if the threshold is reached.
-Remark: `parent` is use only to report an issue
--/
-private def isDefEqBounded (a b : Expr) (parent : Expr) : GoalM Bool := do
-  withCurrHeartbeats do
-  let config ← getConfig
-  tryCatchRuntimeEx
-    (withTheReader Core.Context (fun ctx => { ctx with maxHeartbeats := config.canonHeartbeats }) do
-      withDefault <| isDefEq a b)
-    fun ex => do
-      if ex.isRuntime then
-        let curr := (← getConfig).canonHeartbeats
-        reportIssue m!"failed to show that{indentExpr a}\nis definitionally equal to{indentExpr b}\nwhile canonicalizing{indentExpr parent}\nusing `{curr}*1000` heartbeats, `(canonHeartbeats := {curr})`"
-        return false
-      else
-        throw ex
+structure State where
+  argMap     : PHashMap (Expr × Nat) (List Expr) := {}
+  canon      : PHashMap Expr Expr := {}
+  proofCanon : PHashMap Expr Expr := {}
+  deriving Inhabited
 
 /--
 Helper function for canonicalizing `e` occurring as the `i`th argument of an `f`-application.
-If `useIsDefEqBounded` is `true`, we try `isDefEqBounded` before returning false
+`isInst` is true if `e` is an type class instance.
+
+Recall that we use `TransparencyMode.instances` for checking whether two instances are definitionally equal or not.
+Thus, if diagnostics are enabled, we also check them using `TransparencyMode.default`. If the result is different
+we report to the user.
 -/
-def canonElemCore (parent : Expr) (f : Expr) (i : Nat) (e : Expr) (useIsDefEqBounded : Bool) : GoalM Expr := do
-  let s ← get'
+def canonElemCore (f : Expr) (i : Nat) (e : Expr) (isInst : Bool) : StateT State MetaM Expr := do
+  let s ← get
   if let some c := s.canon.find? e then
     return c
   let key := (f, i)
@@ -81,23 +65,17 @@ def canonElemCore (parent : Expr) (f : Expr) (i : Nat) (e : Expr) (useIsDefEqBou
       -- We used to check `c.fvarsSubset e` because it is not
       -- in general safe to replace `e` with `c` if `c` has more free variables than `e`.
       -- However, we don't revert previously canonicalized elements in the `grind` tactic.
-      -- Moreover, we store the canonicalizer state in the `Goal` because we case-split
-      -- and different locals are added in different branches.
-      modify' fun s => { s with canon := s.canon.insert e c }
-      trace[grind.debugn.canon] "found {e} ===> {c}"
+      modify fun s => { s with canon := s.canon.insert e c }
       return c
-    if useIsDefEqBounded then
-      if (← isDefEqBounded e c parent) then
-        modify' fun s => { s with canon := s.canon.insert e c }
-        trace[grind.debugn.canon] "found using `isDefEqBounded`: {e} ===> {c}"
-        return c
-  trace[grind.debug.canon] "({f}, {i}) ↦ {e}"
-  modify' fun s => { s with canon := s.canon.insert e e, argMap := s.argMap.insert key (e::cs) }
+    if isInst then
+      if (← isDiagnosticsEnabled <&&> pure (c.fvarsSubset e) <&&> (withDefault <| isDefEq e c)) then
+        -- TODO: consider storing this information in some structure that can be browsed later.
+        trace[grind.issues] "the following `grind` static elements are definitionally equal with `default` transparency, but not with `instances` transparency{indentExpr e}\nand{indentExpr c}"
+  modify fun s => { s with canon := s.canon.insert e e, argMap := s.argMap.insert key (e::cs) }
   return e
 
-abbrev canonType (parent f : Expr) (i : Nat) (e : Expr) := withDefault <| canonElemCore parent f i e (useIsDefEqBounded := false)
-abbrev canonInst (parent f : Expr) (i : Nat) (e : Expr) := withReducibleAndInstances <| canonElemCore parent f i e (useIsDefEqBounded := true)
-abbrev canonImplicit (parent f : Expr) (i : Nat) (e : Expr) := withReducible <| canonElemCore parent f i e (useIsDefEqBounded := true)
+abbrev canonType (f : Expr) (i : Nat) (e : Expr) := withDefault <| canonElemCore f i e false
+abbrev canonInst (f : Expr) (i : Nat) (e : Expr) := withReducibleAndInstances <| canonElemCore f i e true
 
 /--
 Return type for the `shouldCanon` function.
@@ -107,8 +85,6 @@ private inductive ShouldCanonResult where
     canonType
   | /- Nested instances are canonicalized. -/
     canonInst
-  | /- Implicit argument that is not an instance nor a type. -/
-    canonImplicit
   | /-
     Term is not a proof, type (former), nor an instance.
     Thus, it must be recursively visited by the canonizer.
@@ -116,13 +92,6 @@ private inductive ShouldCanonResult where
     visit
   deriving Inhabited
 
-instance : Repr ShouldCanonResult where
-  reprPrec r _ := match r with
-    | .canonType => "canonType"
-    | .canonInst => "canonInst"
-    | .canonImplicit => "canonImplicit"
-    | .visit => "visit"
-
 /--
 See comments at `ShouldCanonResult`.
 -/
@@ -133,68 +102,62 @@ def shouldCanon (pinfos : Array ParamInfo) (i : Nat) (arg : Expr) : MetaM Should
       return .canonInst
     else if pinfo.isProp then
       return .visit
-    else if pinfo.isImplicit then
-      if (← isTypeFormer arg) then
-        return .canonType
-      else
-        return .canonImplicit
-  if (← isProp arg) then
-    return .visit
-  else if (← isTypeFormer arg) then
+  if (← isTypeFormer arg) then
     return .canonType
   else
     return .visit
 
-unsafe def canonImpl (e : Expr) : GoalM Expr := do
+unsafe def canonImpl (e : Expr) : StateT State MetaM Expr := do
   visit e |>.run' mkPtrMap
 where
-  visit (e : Expr) : StateRefT (PtrMap Expr Expr) GoalM Expr := do
-    unless e.isApp || e.isForall do return e
-    -- Check whether it is cached
-    if let some r := (← get).find? e then
-      return r
-    let e' ← match e with
-      | .app .. => e.withApp fun f args => do
-        if f.isConstOf ``Lean.Grind.nestedProof && args.size == 2 then
+  visit (e : Expr) : StateRefT (PtrMap Expr Expr) (StateT State MetaM) Expr := do
+    match e with
+    | .bvar .. => unreachable!
+    -- Recall that `grind` treats `let`, `forall`, and `lambda` as atomic terms.
+    | .letE .. | .forallE .. | .lam ..
+    | .const .. | .lit .. | .mvar .. | .sort .. | .fvar ..
+    -- Recall that the `grind` preprocessor uses the `foldProjs` preprocessing step.
+    | .proj ..
+    -- Recall that the `grind` preprocessor uses the `eraseIrrelevantMData` preprocessing step.
+    | .mdata ..  => return e
+    -- We only visit applications
+    | .app .. =>
+      -- Check whether it is cached
+      if let some r := (← get).find? e then
+        return r
+      e.withApp fun f args => do
+        let e' ← if f.isConstOf ``Lean.Grind.nestedProof && args.size == 2 then
           let prop := args[0]!
           let prop' ← visit prop
-          if let some r := (← get').proofCanon.find? prop' then
+          if let some r := (← getThe State).proofCanon.find? prop' then
             pure r
           else
             let e' := if ptrEq prop prop' then e else mkAppN f (args.set! 0 prop')
-            modify' fun s => { s with proofCanon := s.proofCanon.insert prop' e' }
+            modifyThe State fun s => { s with proofCanon := s.proofCanon.insert prop' e' }
             pure e'
         else
           let pinfos := (← getFunInfo f).paramInfo
           let mut modified := false
-          let mut args := args.toVector
-          for h : i in [:args.size] do
-            let arg := args[i]
-            trace[grind.debug.canon] "[{repr (← shouldCanon pinfos i arg)}]: {arg} : {← inferType arg}"
+          let mut args := args
+          for i in [:args.size] do
+            let arg := args[i]!
             let arg' ← match (← shouldCanon pinfos i arg) with
-            | .canonType  => canonType e f i arg
-            | .canonInst  => canonInst e f i arg
-            | .canonImplicit => canonImplicit e f i (← visit arg)
+            | .canonType  => canonType f i arg
+            | .canonInst  => canonInst f i arg
             | .visit      => visit arg
             unless ptrEq arg arg' do
-              args := args.set i arg'
+              args := args.set! i arg'
               modified := true
-          pure <| if modified then mkAppN f args.toArray else e
-      | .forallE _ d b _ =>
-        -- Recall that we have `ForallProp.lean`.
-        let d' ← visit d
-        -- Remark: users may not want to convert `p → q` into `¬p ∨ q`
-        let b' ← if b.hasLooseBVars then pure b else visit b
-        pure <| e.updateForallE! d' b'
-      | _ => unreachable!
-    modify fun s => s.insert e e'
-    return e'
+          pure <| if modified then mkAppN f args else e
+        modify fun s => s.insert e e'
+        return e'
+
+/--
+Canonicalizes nested types, type formers, and instances in `e`.
+-/
+def canon (e : Expr) : StateT State MetaM Expr :=
+  unsafe canonImpl e
 
 end Canon
 
-/-- Canonicalizes nested types, type formers, and instances in `e`. -/
-def canon (e : Expr) : GoalM Expr := do
-  trace[grind.debug.canon] "{e}"
-  unsafe Canon.canonImpl e
-
 end Lean.Meta.Grind

src/Lean/Meta/Tactic/Grind/Cases.lean

@@ -11,56 +11,52 @@ namespace Lean.Meta.Grind
 The `grind` tactic includes an auxiliary `cases` tactic that is not intended for direct use by users.
 This method implements it.
 This tactic is automatically applied when introducing local declarations with a type tagged with `[grind_cases]`.
-It is also used for "case-splitting" on terms during the search.
-
 It differs from the user-facing Lean `cases` tactic in the following ways:
 
 - It avoids unnecessary `revert` and `intro` operations.
 
 - It does not introduce new local declarations for each minor premise. Instead, the `grind` tactic preprocessor is responsible for introducing them.
 
+- It assumes that the major premise (i.e., the parameter `fvarId`) is the latest local declaration in the current goal.
+
 - If the major premise type is an indexed family, auxiliary declarations and (heterogeneous) equalities are introduced.
   However, these equalities are not resolved using `unifyEqs`. Instead, the `grind` tactic employs union-find and
   congruence closure to process these auxiliary equalities. This approach avoids applying substitution to propositions
   that have already been internalized by `grind`.
 -/
-def cases (mvarId : MVarId) (e : Expr) : MetaM (List MVarId) := mvarId.withContext do
+def cases (mvarId : MVarId) (fvarId : FVarId) : MetaM (List MVarId) := mvarId.withContext do
   let tag ← mvarId.getTag
-  let type ← whnf (← inferType e)
+  let type ← whnf (← fvarId.getType)
   let .const declName _ := type.getAppFn | throwInductiveExpected type
   let .inductInfo _ ← getConstInfo declName | throwInductiveExpected type
   let recursorInfo ← mkRecursorInfo (mkCasesOnName declName)
-  let k (mvarId : MVarId) (fvarId : FVarId) (indices : Array FVarId) : MetaM (List MVarId) := do
-    let indicesExpr := indices.map mkFVar
-    let recursor ← mkRecursorAppPrefix mvarId `grind.cases fvarId recursorInfo indicesExpr
-    let mut recursor := mkApp (mkAppN recursor indicesExpr) (mkFVar fvarId)
+  let k (mvarId : MVarId) (fvarId : FVarId) (indices : Array Expr) (clearMajor : Bool) : MetaM (List MVarId) := do
+    let recursor ← mkRecursorAppPrefix mvarId `grind.cases fvarId recursorInfo indices
+    let mut recursor := mkApp (mkAppN recursor indices) (mkFVar fvarId)
     let mut recursorType ← inferType recursor
     let mut mvarIdsNew := #[]
-    let mut idx := 1
     for _ in [:recursorInfo.numMinors] do
       let .forallE _ targetNew recursorTypeNew _ ← whnf recursorType
         | throwTacticEx `grind.cases mvarId "unexpected recursor type"
       recursorType := recursorTypeNew
-      let tagNew := if recursorInfo.numMinors > 1 then Name.num tag idx else tag
-      let mvar ← mkFreshExprSyntheticOpaqueMVar targetNew tagNew
+      let mvar ← mkFreshExprSyntheticOpaqueMVar targetNew tag
       recursor := mkApp recursor mvar
-      let mvarIdNew ← mvar.mvarId!.tryClearMany (indices.push fvarId)
+      let mvarIdNew ← if clearMajor then
+        mvar.mvarId!.clear fvarId
+      else
+        pure mvar.mvarId!
       mvarIdsNew := mvarIdsNew.push mvarIdNew
-      idx := idx + 1
     mvarId.assign recursor
     return mvarIdsNew.toList
   if recursorInfo.numIndices > 0 then
-    let s ← generalizeIndices' mvarId e
+    let s ← generalizeIndices mvarId fvarId
     s.mvarId.withContext do
-      k s.mvarId s.fvarId s.indicesFVarIds
-  else if let .fvar fvarId := e then
-    k mvarId fvarId #[]
+      k s.mvarId s.fvarId (s.indicesFVarIds.map mkFVar) (clearMajor := false)
   else
-    let mvarId ← mvarId.assert (← mkFreshUserName `x) type e
-    let (fvarId, mvarId) ← mvarId.intro1
-    mvarId.withContext do k mvarId fvarId #[]
+    let indices ← getMajorTypeIndices mvarId `grind.cases recursorInfo type
+    k mvarId fvarId indices (clearMajor := true)
 where
   throwInductiveExpected {α} (type : Expr) : MetaM α := do
-    throwTacticEx `grind.cases mvarId m!"(non-recursive) inductive type expected at {e}{indentExpr type}"
+    throwTacticEx `grind.cases mvarId m!"(non-recursive) inductive type expected at {mkFVar fvarId}{indentExpr type}"
 
 end Lean.Meta.Grind

src/Lean/Meta/Tactic/Grind/CasesMatch.lean

@@ -1,53 +0,0 @@
-/-
-Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Lean.Meta.Tactic.Util
-import Lean.Meta.Tactic.Cases
-import Lean.Meta.Match.MatcherApp
-
-namespace Lean.Meta.Grind
-
-def casesMatch (mvarId : MVarId) (e : Expr) : MetaM (List MVarId) := mvarId.withContext do
-  let some app ← matchMatcherApp? e
-    | throwTacticEx `grind.casesMatch mvarId m!"`match`-expression expected{indentExpr e}"
-  let (motive, eqRefls) ← mkMotiveAndRefls app
-  let target ← mvarId.getType
-  let mut us := app.matcherLevels
-  if let some i := app.uElimPos? then
-    us := us.set! i (← getLevel target)
-  let splitterName := (← Match.getEquationsFor app.matcherName).splitterName
-  let splitterApp := mkConst splitterName us.toList
-  let splitterApp := mkAppN splitterApp app.params
-  let splitterApp := mkApp splitterApp motive
-  let splitterApp := mkAppN splitterApp app.discrs
-  let (mvars, _, _) ← forallMetaBoundedTelescope (← inferType splitterApp) app.alts.size (kind := .syntheticOpaque)
-  let splitterApp := mkAppN splitterApp mvars
-  let val := mkAppN splitterApp eqRefls
-  mvarId.assign val
-  updateTags mvars
-  return mvars.toList.map (·.mvarId!)
-where
-  mkMotiveAndRefls (app : MatcherApp) : MetaM (Expr × Array Expr) := do
-    let dummy := mkSort 0
-    let aux := mkApp (mkAppN e.getAppFn app.params) dummy
-    forallBoundedTelescope (← inferType aux) app.discrs.size fun xs _ => do
-    withNewEqs app.discrs xs fun eqs eqRefls => do
-      let type ← mvarId.getType
-      let type ← mkForallFVars eqs type
-      let motive ← mkLambdaFVars xs type
-      return (motive, eqRefls)
-
-  updateTags (mvars : Array Expr) : MetaM Unit := do
-    let tag ← mvarId.getTag
-    if mvars.size == 1 then
-      mvars[0]!.mvarId!.setTag tag
-    else
-      let mut idx := 1
-      for mvar in mvars do
-        mvar.mvarId!.setTag (Name.num tag idx)
-        idx := idx + 1
-
-end Lean.Meta.Grind

src/Lean/Meta/Tactic/Grind/Combinators.lean

@@ -1,71 +0,0 @@
-/-
-Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-prelude
-import Lean.Meta.Tactic.Grind.Types
-
-namespace Lean.Meta.Grind
-
-/-!
-Combinators for manipulating `GrindTactic`s.
-TODO: a proper tactic language for `grind`.
--/
-
-def GrindTactic := Goal → GrindM (Option (List Goal))
-
-def GrindTactic.try (x : GrindTactic) : GrindTactic := fun g => do
-  let some gs ← x g | return some [g]
-  return some gs
-
-def applyToAll (x : GrindTactic)  (goals : List Goal) : GrindM (List Goal) := do
-  go goals []
-where
-  go (goals : List Goal) (acc : List Goal) : GrindM (List Goal) := do
-    match goals with
-    | [] => return acc.reverse
-    | goal :: goals => match (← x goal) with
-      | none => go goals (goal :: acc)
-      | some goals' => go goals (goals' ++ acc)
-
-partial def GrindTactic.andThen (x y : GrindTactic) : GrindTactic := fun goal => do
-  let some goals ← x goal | return none
-  applyToAll y goals
-
-instance : AndThen GrindTactic where
-  andThen a b := GrindTactic.andThen a (b ())
-
-partial def GrindTactic.iterate (x : GrindTactic) : GrindTactic := fun goal => do
-  go [goal] []
-where
-  go (todo : List Goal) (result : List Goal) : GrindM (List Goal) := do
-    match todo with
-    | [] => return result
-    | goal :: todo =>
-      if let some goalsNew ← x goal then
-        go (goalsNew ++ todo) result
-      else
-        go todo (goal :: result)
-
-partial def GrindTactic.orElse (x y : GrindTactic) : GrindTactic := fun goal => do
-  let some goals ← x goal | y goal
-  return goals
-
-instance : OrElse GrindTactic where
-  orElse a b := GrindTactic.andThen a (b ())
-
-def toGrindTactic (f : GoalM Unit) : GrindTactic := fun goal => do
-  let goal ← GoalM.run' goal f
-  if goal.inconsistent then
-    return some []
-  else
-    return some [goal]
-
-def GrindTactic' := Goal → GrindM (List Goal)
-
-def GrindTactic'.toGrindTactic (x : GrindTactic') : GrindTactic := fun goal => do
-  let goals ← x goal
-  return some goals
-
-end Lean.Meta.Grind

src/Lean/Meta/Tactic/Grind/Core.lean

@@ -10,7 +10,6 @@ import Lean.Meta.Tactic.Grind.Types
 import Lean.Meta.Tactic.Grind.Inv
 import Lean.Meta.Tactic.Grind.PP
 import Lean.Meta.Tactic.Grind.Ctor
-import Lean.Meta.Tactic.Grind.Util
 import Lean.Meta.Tactic.Grind.Internalize
 
 namespace Lean.Meta.Grind
@@ -42,9 +41,8 @@ This is an auxiliary function performed while merging equivalence classes.
 private def removeParents (root : Expr) : GoalM ParentSet := do
   let parents ← getParentsAndReset root
   for parent in parents do
-    -- Recall that we may have `Expr.forallE` in `parents` because of `ForallProp.lean`
-    if (← pure parent.isApp <&&> isCongrRoot parent) then
-      trace_goal[grind.debug.parent] "remove: {parent}"
+    if (← isCongrRoot parent) then
+      trace[grind.debug.parent] "remove: {parent}"
       modify fun s => { s with congrTable := s.congrTable.erase { e := parent } }
   return parents
 
@@ -54,8 +52,8 @@ This is an auxiliary function performed while merging equivalence classes.
 -/
 private def reinsertParents (parents : ParentSet) : GoalM Unit := do
   for parent in parents do
-    if (← pure parent.isApp <&&> isCongrRoot parent) then
-      trace_goal[grind.debug.parent] "reinsert: {parent}"
+    if (← isCongrRoot parent) then
+      trace[grind.debug.parent] "reinsert: {parent}"
       addCongrTable parent
 
 /-- Closes the goal when `True` and `False` are in the same equivalence class. -/
@@ -87,34 +85,14 @@ private partial def updateMT (root : Expr) : GoalM Unit := do
       setENode parent { node with mt := gmt }
       updateMT parent
 
-/--
-Helper function for combining `ENode.offset?` fields and propagating an equality
-to the offset constraint module.
--/
-private def propagateOffsetEq (rhsRoot lhsRoot : ENode) : GoalM Unit := do
-  match lhsRoot.offset? with
-  | some lhsOffset =>
-    if let some rhsOffset := rhsRoot.offset? then
-      Arith.processNewOffsetEq lhsOffset rhsOffset
-    else if isNatNum rhsRoot.self then
-      Arith.processNewOffsetEqLit lhsOffset rhsRoot.self
-    else
-      -- We have to retrieve the node because other fields have been updated
-      let rhsRoot ← getENode rhsRoot.self
-      setENode rhsRoot.self { rhsRoot with offset? := lhsOffset }
-  | none =>
-    if isNatNum lhsRoot.self then
-    if let some rhsOffset := rhsRoot.offset? then
-      Arith.processNewOffsetEqLit rhsOffset lhsRoot.self
-
 private partial def addEqStep (lhs rhs proof : Expr) (isHEq : Bool) : GoalM Unit := do
   let lhsNode ← getENode lhs
   let rhsNode ← getENode rhs
   if isSameExpr lhsNode.root rhsNode.root then
     -- `lhs` and `rhs` are already in the same equivalence class.
-    trace_goal[grind.debug] "{← ppENodeRef lhs} and {← ppENodeRef rhs} are already in the same equivalence class"
+    trace[grind.debug] "{← ppENodeRef lhs} and {← ppENodeRef rhs} are already in the same equivalence class"
     return ()
-  trace_goal[grind.eqc] "{← if isHEq then mkHEq lhs rhs else mkEq lhs rhs}"
+  trace[grind.eqc] "{← if isHEq then mkHEq lhs rhs else mkEq lhs rhs}"
   let lhsRoot ← getENode lhsNode.root
   let rhsRoot ← getENode rhsNode.root
   let mut valueInconsistency := false
@@ -139,11 +117,11 @@ private partial def addEqStep (lhs rhs proof : Expr) (isHEq : Bool) : GoalM Unit
   unless (← isInconsistent) do
     if valueInconsistency then
       closeGoalWithValuesEq lhsRoot.self rhsRoot.self
-  trace_goal[grind.debug] "after addEqStep, {← (← get).ppState}"
+  trace[grind.debug] "after addEqStep, {← ppState}"
   checkInvariants
 where
   go (lhs rhs : Expr) (lhsNode rhsNode lhsRoot rhsRoot : ENode) (flipped : Bool) : GoalM Unit := do
-    trace_goal[grind.debug] "adding {← ppENodeRef lhs} ↦ {← ppENodeRef rhs}"
+    trace[grind.debug] "adding {← ppENodeRef lhs} ↦ {← ppENodeRef rhs}"
     /-
     We have the following `target?/proof?`
     `lhs -> ... -> lhsNode.root`
@@ -160,34 +138,33 @@ where
     }
     let parents ← removeParents lhsRoot.self
     updateRoots lhs rhsNode.root
-    trace_goal[grind.debug] "{← ppENodeRef lhs} new root {← ppENodeRef rhsNode.root}, {← ppENodeRef (← getRoot lhs)}"
+    trace[grind.debug] "{← ppENodeRef lhs} new root {← ppENodeRef rhsNode.root}, {← ppENodeRef (← getRoot lhs)}"
     reinsertParents parents
-    propagateEqcDown lhs
     setENode lhsNode.root { (← getENode lhsRoot.self) with -- We must retrieve `lhsRoot` since it was updated.
       next := rhsRoot.next
     }
     setENode rhsNode.root { rhsRoot with
-      next       := lhsRoot.next
-      size       := rhsRoot.size + lhsRoot.size
+      next := lhsRoot.next
+      size := rhsRoot.size + lhsRoot.size
       hasLambdas := rhsRoot.hasLambdas || lhsRoot.hasLambdas
       heqProofs  := isHEq || rhsRoot.heqProofs || lhsRoot.heqProofs
     }
     copyParentsTo parents rhsNode.root
-    unless (← isInconsistent) do
-      updateMT rhsRoot.self
-    propagateOffsetEq rhsRoot lhsRoot
     unless (← isInconsistent) do
       for parent in parents do
         propagateUp parent
+    unless (← isInconsistent) do
+      updateMT rhsRoot.self
 
   updateRoots (lhs : Expr) (rootNew : Expr) : GoalM Unit := do
-    traverseEqc lhs fun n =>
-      setENode n.self { n with root := rootNew }
-
-  propagateEqcDown (lhs : Expr) : GoalM Unit := do
-    traverseEqc lhs fun n =>
+    let rec loop (e : Expr) : GoalM Unit := do
+      let n ← getENode e
+      setENode e { n with root := rootNew }
       unless (← isInconsistent) do
-        propagateDown n.self
+        propagateDown e
+      if isSameExpr lhs n.next then return ()
+      loop n.next
+    loop lhs
 
 /-- Ensures collection of equations to be processed is empty. -/
 private def resetNewEqs : GoalM Unit :=
@@ -213,30 +190,17 @@ where
     addEqStep lhs rhs proof isHEq
     processTodo
 
-/-- Adds a new equality `lhs = rhs`. It assumes `lhs` and `rhs` have already been internalized. -/
-private def addEq (lhs rhs proof : Expr) : GoalM Unit := do
+def addEq (lhs rhs proof : Expr) : GoalM Unit := do
   addEqCore lhs rhs proof false
 
-/-- Adds a new heterogeneous equality `HEq lhs rhs`. It assumes `lhs` and `rhs` have already been internalized. -/
-private def addHEq (lhs rhs proof : Expr) : GoalM Unit := do
+def addHEq (lhs rhs proof : Expr) : GoalM Unit := do
   addEqCore lhs rhs proof true
 
-/-- Save asserted facts for pretty printing goal. -/
-private def storeFact (fact : Expr) : GoalM Unit := do
-  modify fun s => { s with facts := s.facts.push fact }
-
-/-- Internalizes `lhs` and `rhs`, and then adds equality `lhs = rhs`. -/
-def addNewEq (lhs rhs proof : Expr) (generation : Nat) : GoalM Unit := do
-  let eq ← mkEq lhs rhs
-  storeFact eq
-  internalize lhs generation eq
-  internalize rhs generation eq
-  addEq lhs rhs proof
-
-/-- Adds a new `fact` justified by the given proof and using the given generation. -/
+/--
+Adds a new `fact` justified by the given proof and using the given generation.
+-/
 def add (fact : Expr) (proof : Expr) (generation := 0) : GoalM Unit := do
-  storeFact fact
-  trace_goal[grind.assert] "{fact}"
+  trace[grind.assert] "{fact}"
   if (← isInconsistent) then return ()
   resetNewEqs
   let_expr Not p := fact
@@ -245,30 +209,22 @@ def add (fact : Expr) (proof : Expr) (generation := 0) : GoalM Unit := do
 where
   go (p : Expr) (isNeg : Bool) : GoalM Unit := do
     match_expr p with
-    | Eq α lhs rhs =>
-      if α.isProp then
-        -- It is morally an iff.
-        -- We do not use the `goEq` optimization because we want to register `p` as a case-split
-        goFact p isNeg
-      else
-        goEq p lhs rhs isNeg false
+    | Eq _ lhs rhs => goEq p lhs rhs isNeg false
     | HEq _ lhs _ rhs => goEq p lhs rhs isNeg true
-    | _ => goFact p isNeg
-
-  goFact (p : Expr) (isNeg : Bool) : GoalM Unit := do
-    internalize p generation
-    if isNeg then
-      addEq p (← getFalseExpr) (← mkEqFalse proof)
-    else
-      addEq p (← getTrueExpr) (← mkEqTrue proof)
+    | _ =>
+      internalize p generation
+      if isNeg then
+        addEq p (← getFalseExpr) (← mkEqFalse proof)
+      else
+        addEq p (← getTrueExpr) (← mkEqTrue proof)
 
   goEq (p : Expr) (lhs rhs : Expr) (isNeg : Bool) (isHEq : Bool) : GoalM Unit := do
     if isNeg then
       internalize p generation
       addEq p (← getFalseExpr) (← mkEqFalse proof)
     else
-      internalize lhs generation p
-      internalize rhs generation p
+      internalize lhs generation
+      internalize rhs generation
       addEqCore lhs rhs proof isHEq
 
 /-- Adds a new hypothesis. -/

src/Lean/Meta/Tactic/Grind/Ctor.lean

@@ -9,18 +9,14 @@ import Lean.Meta.Tactic.Grind.Types
 namespace Lean.Meta.Grind
 
 private partial def propagateInjEqs (eqs : Expr) (proof : Expr) : GoalM Unit := do
-  -- Remark: we must use `shareCommon` before using `pushEq` and `pushHEq`.
-  -- This is needed because the result type of the injection theorem may allocate
   match_expr eqs with
   | And left right =>
     propagateInjEqs left (.proj ``And 0 proof)
     propagateInjEqs right (.proj ``And 1 proof)
-  | Eq _ lhs rhs    =>
-    pushEq (← shareCommon lhs) (← shareCommon rhs) proof
-  | HEq _ lhs _ rhs =>
-    pushHEq (← shareCommon lhs) (← shareCommon rhs) proof
+  | Eq _ lhs rhs    => pushEq lhs rhs proof
+  | HEq _ lhs _ rhs => pushHEq lhs rhs proof
   | _ =>
-   reportIssue m!"unexpected injectivity theorem result type{indentExpr eqs}"
+   trace[grind.issues] "unexpected injectivity theorem result type{indentExpr eqs}"
    return ()
 
 /--