feat: warn grind redundant parameters

This PR produces a warning for redundant `grind` arguments.

.github/workflows/build-template.yml

@@ -36,7 +36,7 @@ jobs:
         include: ${{fromJson(inputs.config)}}
       # complete all jobs
       fail-fast: false
-    runs-on: ${{ endsWith(matrix.os, '-with-cache') && fromJSON(format('["{0}", "nscloud-git-mirror-1gb"]', matrix.os)) || matrix.os }}
+    runs-on: ${{ matrix.os }}
     defaults:
       run:
         shell: ${{ matrix.shell || 'nix develop -c bash -euxo pipefail {0}' }}
@@ -69,16 +69,10 @@ jobs:
           brew install ccache tree zstd coreutils gmp libuv
         if: runner.os == 'macOS'
       - name: Checkout
-        if: (!endsWith(matrix.os, '-with-cache'))
         uses: actions/checkout@v4
         with:
           # the default is to use a virtual merge commit between the PR and master: just use the PR
           ref: ${{ github.event.pull_request.head.sha }}
-      - name: Namespace Checkout
-        if: endsWith(matrix.os, '-with-cache')
-        uses: namespacelabs/nscloud-checkout-action@v7
-        with:
-          ref: ${{ github.event.pull_request.head.sha }}
       - name: Open Nix shell once
         run: true
         if: runner.os == 'Linux'
@@ -110,7 +104,7 @@ jobs:
           # NOTE: must be in sync with `save` below and with `restore-cache` in `update-stage0.yml`
           path: |
             .ccache
-            ${{ matrix.name == 'Linux Lake' && 'build/stage1/**/*.trace
+            ${{ matrix.name == 'Linux Lake (cached)' && 'build/stage1/**/*.trace
             build/stage1/**/*.olean*
             build/stage1/**/*.ilean
             build/stage1/**/*.ir
@@ -172,24 +166,6 @@ jobs:
           # contortion to support empty OPTIONS with old macOS bash
           cmake .. --preset ${{ matrix.CMAKE_PRESET || 'release' }} -B . ${{ matrix.CMAKE_OPTIONS }} ${OPTIONS[@]+"${OPTIONS[@]}"} -DLEAN_INSTALL_PREFIX=$PWD/..
           time make $TARGET_STAGE -j$NPROC
-      # Should be done as early as possible and in particular *before* "Check rebootstrap" which
-      # changes the state of stage1/
-      - name: Save Cache
-        # Caching on cancellation created some mysterious issues perhaps related to improper build
-        # shutdown
-        if: steps.restore-cache.outputs.cache-hit != 'true' && !cancelled()
-        uses: actions/cache/save@v4
-        with:
-          # NOTE: must be in sync with `restore` above
-          path: |
-            .ccache
-            ${{ matrix.name == 'Linux Lake' && 'build/stage1/**/*.trace
-            build/stage1/**/*.olean*
-            build/stage1/**/*.ilean
-            build/stage1/**/*.ir
-            build/stage1/**/*.c
-            build/stage1/**/*.c.o*' || '' }}
-          key: ${{ steps.restore-cache.outputs.cache-primary-key }}
       - name: Install
         run: |
           make -C build/$TARGET_STAGE install
@@ -223,13 +199,13 @@ jobs:
           path: pack/*
       - name: Lean stats
         run: |
-          build/$TARGET_STAGE/bin/lean --stats src/Lean.lean -Dexperimental.module=true
+          build/stage1/bin/lean --stats src/Lean.lean -Dexperimental.module=true
         if: ${{ !matrix.cross }}
       - name: Test
         id: test
         run: |
           ulimit -c unlimited  # coredumps
-          time ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/$TARGET_STAGE -j$NPROC --output-junit test-results.xml ${{ matrix.CTEST_OPTIONS }}
+          time ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/$TARGET_STAGE -j$NPROC --output-junit test-results.xml ${{ matrix.CTARGET_OPTIONS }}
         if: (matrix.wasm || !matrix.cross) && (inputs.check-level >= 1 || matrix.test)
       - name: Test Summary
         uses: test-summary/action@v2
@@ -259,13 +235,9 @@ jobs:
         if: matrix.test-speedcenter
       - name: Check rebootstrap
         run: |
-          set -e
           # clean rebuild in case of Makefile changes/Lake does not detect uncommited stage 0
           # changes yet
-          make -C build update-stage0
-          make -C build/stage1 clean-stdlib
-          time make -C build -j$NPROC
-          time ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/stage1 -j$NPROC
+          make -C build update-stage0 && make -C build/stage1 clean-stdlib && make -C build -j$NPROC
         if: matrix.check-rebootstrap
       - name: CCache stats
         if: always()
@@ -277,3 +249,22 @@ jobs:
             progbin="$(file $c | sed "s/.*execfn: '\([^']*\)'.*/\1/")"
             echo bt | $GDB/bin/gdb -q $progbin $c || true
           done
+      - name: Save Cache
+        if: always() && steps.restore-cache.outputs.cache-hit != 'true'
+        uses: actions/cache/save@v4
+        with:
+          # NOTE: must be in sync with `restore` above
+          path: |
+            .ccache
+            ${{ matrix.name == 'Linux Lake (cached)' && 'build/stage1/**/*.trace
+            build/stage1/**/*.olean*
+            build/stage1/**/*.ilean
+            build/stage1/**/*.ir
+            build/stage1/**/*.c
+            build/stage1/**/*.c.o*' || '' }}
+          key: ${{ steps.restore-cache.outputs.cache-primary-key }}
+      - name: Upload Build Artifact
+        if: always() && matrix.name == 'Linux Lake (cached)'
+        uses: actions/upload-artifact@v4
+        with:
+          path: build

.github/workflows/ci.yml

@@ -181,18 +181,24 @@ jobs:
                 "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
                 "binary-check": "ldd -v",
                 // foreign code may be linked against more recent glibc
-                "CTEST_OPTIONS": "-E 'foreign'",
+                "CTEST_OPTIONS": "-E 'foreign'"
               },
               {
                 "name": "Linux Lake",
-                "os": large ? "nscloud-ubuntu-22.04-amd64-8x16-with-cache" : "ubuntu-latest",
+                "os": large ? "nscloud-ubuntu-22.04-amd64-8x16" : "ubuntu-latest",
                 "check-level": 0,
                 "test": true,
                 "check-rebootstrap": level >= 1,
                 "check-stage3": level >= 2,
                 // NOTE: `test-speedcenter` currently seems to be broken on `ubuntu-latest`
                 "test-speedcenter": large && level >= 2,
-                // made explicit until it can be assumed to have propagated to PRs
+                "CMAKE_OPTIONS": "-DUSE_LAKE=ON",
+              },
+              {
+                "name": "Linux Lake (cached)",
+                "os": "ubuntu-latest",
+                "check-level": (isPr || isPushToMaster) ? 0 : 2,
+                "secondary": true,
                 "CMAKE_OPTIONS": "-DUSE_LAKE=ON",
               },
               {
@@ -200,6 +206,8 @@ jobs:
                 "os": "ubuntu-latest",
                 "check-level": 2,
                 "CMAKE_PRESET": "reldebug",
+                // exclude seriously slow/stackoverflowing tests
+                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest|bv_bitblast_stress|3807'"
               },
               // TODO: suddenly started failing in CI
               /*{
@@ -220,8 +228,7 @@ jobs:
                 "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-apple-darwin.tar.zst",
                 "prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm*",
                 "binary-check": "otool -L",
-                "tar": "gtar", // https://github.com/actions/runner-images/issues/2619
-                "CTEST_OPTIONS": "-E 'leanlaketest_hello'", // started failing from unpack
+                "tar": "gtar" // https://github.com/actions/runner-images/issues/2619
               },
               {
                 "name": "macOS aarch64",
@@ -245,9 +252,11 @@ jobs:
                 "check-level": 2,
                 "shell": "msys2 {0}",
                 "CMAKE_OPTIONS": "-G \"Unix Makefiles\"",
+                // for reasons unknown, interactivetests are flaky on Windows
+                "CTEST_OPTIONS": "--repeat until-pass:2",
                 "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-w64-windows-gnu.tar.zst",
                 "prepare-llvm": "../script/prepare-llvm-mingw.sh lean-llvm*",
-                "binary-check": "ldd",
+                "binary-check": "ldd"
               },
               {
                 "name": "Linux aarch64",
@@ -257,7 +266,7 @@ jobs:
                 "check-level": 2,
                 "shell": "nix develop .#oldGlibcAArch -c bash -euxo pipefail {0}",
                 "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-aarch64-linux-gnu.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
+                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*"
               },
               // Started running out of memory building expensive modules, a 2GB heap is just not that much even before fragmentation
               //{
@@ -286,12 +295,6 @@ jobs:
               //   "CTEST_OPTIONS": "-R \"leantest_1007\\.lean|leantest_Format\\.lean|leanruntest\\_1037.lean|leanruntest_ac_rfl\\.lean|leanruntest_tempfile.lean\\.|leanruntest_libuv\\.lean\""
               // }
             ];
-            for (const job of matrix) {
-              if (job["prepare-llvm"]) {
-                // `USE_LAKE` is not compatible with `prepare-llvm` currently
-                job["CMAKE_OPTIONS"] = (job["CMAKE_OPTIONS"] ? job["CMAKE_OPTIONS"] + " " : "") + "-DUSE_LAKE=OFF";
-              }
-            }
             console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`);
             matrix = matrix.filter((job) => level >= job["check-level"]);
             core.setOutput('matrix', matrix.filter((job) => !job["secondary"]));

.github/workflows/update-stage0.yml

@@ -19,8 +19,6 @@ concurrency:
 jobs:
   update-stage0:
     runs-on: nscloud-ubuntu-22.04-amd64-8x16
-    env:
-      CCACHE_DIR: ${{ github.workspace }}/.ccache
     steps:
     # This action should push to an otherwise protected branch, so it
     # uses a deploy key with write permissions, as suggested at
@@ -59,14 +57,9 @@ jobs:
       uses: actions/cache/restore@v4
       with:
         # NOTE: must be in sync with `restore-cache` in `build-template.yml`
+        # TODO: actually switch to USE_LAKE once it caches more; for now it just caches more often than any other build type so let's use its cache
         path: |
           .ccache
-          build/stage1/**/*.trace
-          build/stage1/**/*.olean*
-          build/stage1/**/*.ilean
-          build/stage1/**/*.ir
-          build/stage1/**/*.c
-          build/stage1/**/*.c.o*
         key: Linux Lake-build-v3-${{ github.sha }}
         # fall back to (latest) previous cache
         restore-keys: |

CMakeLists.txt

@@ -147,10 +147,6 @@ add_custom_target(test
   COMMAND $(MAKE) -C stage1 test
   DEPENDS stage1)
 
-add_custom_target(clean-stdlib
-  COMMAND $(MAKE) -C stage1 clean-stdlib
-  DEPENDS stage1)
-
 install(CODE "execute_process(COMMAND make -C stage1 install)")
 
 add_custom_target(check-stage3

README.md

@@ -9,7 +9,7 @@ This is the repository for **Lean 4**.
 - [Documentation Overview](https://lean-lang.org/documentation/)
 - [Language Reference](https://lean-lang.org/doc/reference/latest/)
 - [Release notes](RELEASES.md) starting at v4.0.0-m3
-- [Examples](https://lean-lang.org/lean4/doc/examples.html)
+- [Examples](https://lean-lang.org/documentation/examples/)
 - [External Contribution Guidelines](CONTRIBUTING.md)
 
 # Installation

doc/dev/bootstrap.md

@@ -1,6 +1,6 @@
 # Lean Build Bootstrapping
 
-Lean is a bootstrapped program: the
+Since version 4, Lean is a partially bootstrapped program: most parts of the
 frontend and compiler are written in Lean itself and thus need to be built before
 building Lean itself - which is needed to again build those parts. This cycle is
 broken by using pre-built C files checked into the repository (which ultimately
@@ -73,11 +73,6 @@ update the archived C source code of the stage 0 compiler in `stage0/src`.
 The github repository will automatically update stage0 on `master` once
 `src/stdlib_flags.h` and `stage0/src/stdlib_flags.h` are out of sync.
 
-NOTE: A full rebuild of stage 1 will only be triggered when the *committed* contents of `stage0/` are changed.
-Thus if you change files in it manually instead of through `update-stage0-commit` (see below) or fetching updates from git, you either need to commit those changes first or run `make -C build/release clean-stdlib`.
-The same is true for further stages except that a rebuild of them is retriggered on any committed change, not just to a specific directory.
-Thus when debugging e.g. stage 2 failures, you can resume the build from these failures on but may want to explicitly call `clean-stdlib` to either observe changes from `.olean` files of modules that built successfully or to check that you did not break modules that built successfully at some prior point.
-
 If you have write access to the lean4 repository, you can also manually
 trigger that process, for example to be able to use new features in the compiler itself.
 You can do that on <https://github.com/leanprover/lean4/actions/workflows/update-stage0.yml>
@@ -87,13 +82,13 @@ gh workflow run update-stage0.yml
 ```
 
 Leaving stage0 updates to the CI automation is preferable, but should you need
-to do it locally, you can use `make -C build/release update-stage0-commit` to
-update `stage0` from `stage1` or `make -C build/release/stageN update-stage0-commit` to
+to do it locally, you can use `make update-stage0-commit` in `build/release` to
+update `stage0` from `stage1` or `make -C stageN update-stage0-commit` to
 update from another stage. This command will automatically stage the updated files
-and introduce a commit, so make sure to commit your work before that.
+and introduce a commit,so make sure to commit your work before that.
 
 If you rebased the branch (either onto a newer version of `master`, or fixing
-up some commits prior to the stage0 update), recreate the stage0 update commits.
+up some commits prior to the stage0 update, recreate the stage0 update commits.
 The script `script/rebase-stage0.sh` can be used for that.
 
 The CI should prevent PRs with changes to stage0 (besides `stdlib_flags.h`)

doc/dev/index.md

@@ -8,8 +8,8 @@ You should not edit the `stage0` directory except using the commands described i
 
 ## Development Setup
 
-You can use any of the [supported editors](https://lean-lang.org/install/manual/) for editing the Lean source code.
-Please see below for specific instructions for VS Code.
+You can use any of the [supported editors](../setup.md) for editing the Lean source code.
+If you set up `elan` as below, opening `src/` as a *workspace folder* should ensure that stage 0 (i.e. the stage that first compiles `src/`) will be used for files in that directory.
 
 ### Dev setup using elan
 
@@ -68,10 +68,6 @@ code lean.code-workspace
 ```
 on the command line.
 
-You can use the `Refresh File Dependencies` command as in other projects to rebuild modules from inside VS Code but be aware that this does not trigger any non-Lake build targets.
-In particular, after updating `stage0/` (or fetching an update to it), you will want to invoke `make` directly to rebuild `stage0/bin/lean` as described in [building Lean](../make/index.md).
-You should then run the `Restart Server` command to update all open files and the server watchdog process as well.
-
 ### `ccache`
 
 Lean's build process uses [`ccache`](https://ccache.dev/) if it is

doc/examples/bintree.lean

@@ -282,7 +282,7 @@ theorem BinTree.find_insert_of_ne (b : BinTree β) (ne : k ≠ k') (v : β)
   let ⟨t, h⟩ := b; simp
   induction t with simp
   | leaf =>
-    intro le
+    intros le
     exact Nat.lt_of_le_of_ne le ne
   | node left key value right ihl ihr =>
     let .node hl hr bl br := h

doc/make/index.md

@@ -1,6 +1,6 @@
 These are instructions to set up a working development environment for those who wish to make changes to Lean itself. It is part of the [Development Guide](../dev/index.md).
 
-We strongly suggest that new users instead follow the [Installation Instructions](https://lean-lang.org/install/) to get started using Lean, since this sets up an environment that can automatically manage multiple Lean toolchain versions, which is necessary when working within the Lean ecosystem.
+We strongly suggest that new users instead follow the [Quickstart](../quickstart.md) to get started using Lean, since this sets up an environment that can automatically manage multiple Lean toolchain versions, which is necessary when working within the Lean ecosystem.
 
 Requirements
 ------------
@@ -53,6 +53,11 @@ There are also two alternative presets that combine some of these options you ca
   Select the C/C++ compilers to use. Official Lean releases currently use Clang;
   see also `.github/workflows/ci.yml` for the CI config.
 
+* `-DUSE_LAKE=ON`\
+  Experimental option to build the core libraries using Lake instead of `lean.mk`.  Caveats:
+  * As native code compilation is still handled by cmake, changes to stage0/ (such as from `git pull`) are picked up only when invoking the build via `make`, not via `Refresh Dependencies` in the editor.
+  * `USE_LAKE` is not yet compatible with `LAKE_ARTIFACT_CACHE`
+
 Lean will automatically use [CCache](https://ccache.dev/) if available to avoid
 redundant builds, especially after stage 0 has been updated.
 

flake.nix

@@ -18,14 +18,14 @@
       # An old nixpkgs for creating releases with an old glibc
       pkgsDist-old-aarch = import inputs.nixpkgs-old { localSystem.config = "aarch64-unknown-linux-gnu"; };
 
-      llvmPackages = pkgs.llvmPackages_15;
+      lean-packages = pkgs.callPackage (./nix/packages.nix) { src = ./.; };
 
       devShellWithDist = pkgsDist: pkgs.mkShell.override {
-          stdenv = pkgs.overrideCC pkgs.stdenv llvmPackages.clang;
+          stdenv = pkgs.overrideCC pkgs.stdenv lean-packages.llvmPackages.clang;
         } ({
           buildInputs = with pkgs; [
             cmake gmp libuv ccache pkg-config
-            llvmPackages.llvm  # llvm-symbolizer for asan/lsan
+            lean-packages.llvmPackages.llvm  # llvm-symbolizer for asan/lsan
             gdb
             tree  # for CI
           ];
@@ -60,6 +60,12 @@
           GDB = pkgsDist.gdb;
         });
     in {
+      packages.${system} = {
+        # to be removed when Nix CI is not needed anymore
+        inherit (lean-packages) cacheRoots test update-stage0-commit ciShell;
+        deprecated = lean-packages;
+      };
+
       devShells.${system} = {
         # The default development shell for working on lean itself
         default = devShellWithDist pkgs;

nix/bareStdenv/setup

@@ -0,0 +1,7 @@
+set -eo pipefail
+
+for pkg in $buildInputs; do
+  export PATH=$PATH:$pkg/bin
+done
+
+: ${outputs:=out}

nix/bootstrap.nix

@@ -0,0 +1,208 @@
+{ 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,
+  ... } @ args:
+with builtins;
+lib.warn "The Nix-based build is deprecated" rec {
+  inherit stdenv;
+  sourceByRegex = p: rs: lib.sourceByRegex p (map (r: "(/src/)?${r}") rs);
+  buildCMake = args: stdenv.mkDerivation ({
+    nativeBuildInputs = [ cmake pkg-config ];
+    buildInputs = [ gmp libuv llvmPackages.llvm ];
+    # https://github.com/NixOS/nixpkgs/issues/60919
+    hardeningDisable = [ "all" ];
+    dontStrip = (args.debug or debug);
+
+    postConfigure = ''
+      patchShebangs .
+    '';
+  } // args // {
+    src = args.realSrc or (sourceByRegex args.src [ "[a-z].*" "CMakeLists\.txt" ]);
+    cmakeFlags = ["-DSMALL_ALLOCATOR=ON" "-DUSE_MIMALLOC=OFF"] ++ (args.cmakeFlags or [ "-DSTAGE=1" "-DPREV_STAGE=./faux-prev-stage" "-DUSE_GITHASH=OFF" "-DCADICAL=${cadical}/bin/cadical" ]) ++ (args.extraCMakeFlags or extraCMakeFlags) ++ lib.optional (args.debug or debug) [ "-DCMAKE_BUILD_TYPE=Debug" ];
+    preConfigure = args.preConfigure or "" + ''
+      # ignore absence of submodule
+      sed -i 's!lake/Lake.lean!!' CMakeLists.txt
+    '';
+  });
+  lean-bin-tools-unwrapped = buildCMake {
+    name = "lean-bin-tools";
+    outputs = [ "out" "leanc_src" ];
+    realSrc = sourceByRegex (src + "/src") [ "CMakeLists\.txt" "[a-z].*" ".*\.in" "Leanc\.lean" ];
+    dontBuild = true;
+    installPhase = ''
+      mkdir $out $leanc_src
+      mv bin/ include/ share/ $out/
+      mv leanc.sh $out/bin/leanc
+      mv leanc/Leanc.lean $leanc_src/
+      substituteInPlace $out/bin/leanc --replace '$root' "$out" --replace " sed " " ${gnused}/bin/sed "
+      substituteInPlace $out/bin/leanmake --replace "make" "${gnumake}/bin/make"
+      substituteInPlace $out/share/lean/lean.mk --replace "/usr/bin/env bash" "${bash}/bin/bash"
+    '';
+  };
+  leancpp = buildCMake {
+    name = "leancpp";
+    src = src + "/src";
+    buildFlags = [ "leancpp" "leanrt" "leanrt_initial-exec" "leanshell" "leanmain" ];
+    installPhase = ''
+      mkdir -p $out
+      mv lib/ $out/
+      mv runtime/libleanrt_initial-exec.a $out/lib
+    '';
+  };
+  stage0 = args.stage0 or (buildCMake {
+    name = "lean-stage0";
+    realSrc = src + "/stage0/src";
+    debug = stage0debug;
+    cmakeFlags = [ "-DSTAGE=0" ];
+    extraCMakeFlags = [];
+    preConfigure = ''
+      ln -s ${src + "/stage0/stdlib"} ../stdlib
+    '';
+    installPhase = ''
+      mkdir -p $out/bin $out/lib/lean
+      mv bin/lean $out/bin/
+      mv lib/lean/*.{so,dylib} $out/lib/lean
+    '';
+    meta.mainProgram = "lean";
+  });
+  stage = { stage, prevStage, self }:
+    let
+      desc = "stage${toString stage}";
+      build = args: buildLeanPackage.override {
+        lean = prevStage;
+        leanc = lean-bin-tools-unwrapped;
+        # use same stage for retrieving dependencies
+        lean-leanDeps = stage0;
+        lean-final = self;
+      } ({
+        src = src + "/src";
+        roots = [ { mod = args.name; glob = "andSubmodules"; } ];
+        fullSrc = src;
+        srcPath = "$PWD/src:$PWD/src/lake";
+        inherit debug;
+        leanFlags = [ "-DwarningAsError=true" ];
+      } // args);
+      Init' = build { name = "Init"; deps = []; };
+      Std' = build { name = "Std"; deps = [ Init' ]; };
+      Lean' = build { name = "Lean"; deps = [ Std' ]; };
+      attachSharedLib = sharedLib: pkg: pkg // {
+        inherit sharedLib;
+        mods = mapAttrs (_: m: m // { inherit sharedLib; propagatedLoadDynlibs = []; }) pkg.mods;
+      };
+    in (all: all // all.lean) rec {
+      inherit (Lean) emacs-dev emacs-package vscode-dev vscode-package;
+      Init = attachSharedLib leanshared Init';
+      Std = attachSharedLib leanshared Std' // { allExternalDeps = [ Init ]; };
+      Lean = attachSharedLib leanshared Lean' // { allExternalDeps = [ Std ]; };
+      Lake = build {
+        name = "Lake";
+        sharedLibName = "Lake_shared";
+        src = src + "/src/lake";
+        deps = [ Init Lean ];
+      };
+      Lake-Main = build {
+        name = "LakeMain";
+        roots = [{ glob = "one"; mod = "LakeMain"; }];
+        executableName = "lake";
+        deps = [ Lake ];
+        linkFlags = lib.optional stdenv.isLinux "-rdynamic";
+        src = src + "/src/lake";
+      };
+      stdlib = [ Init Std Lean Lake ];
+      modDepsFiles = symlinkJoin { name = "modDepsFiles"; paths = map (l: l.modDepsFile) (stdlib ++ [ Leanc ]); };
+      depRoots = symlinkJoin { name = "depRoots"; paths = map (l: l.depRoots) stdlib; };
+      iTree = symlinkJoin { name = "ileans"; paths = map (l: l.iTree) stdlib; };
+      Leanc = build { name = "Leanc"; src = lean-bin-tools-unwrapped.leanc_src; deps = stdlib; roots = [ "Leanc" ]; };
+      stdlibLinkFlags = "${lib.concatMapStringsSep " " (l: "-L${l.staticLib}") stdlib} -L${leancpp}/lib/lean";
+      libInit_shared = runCommand "libInit_shared" { buildInputs = [ stdenv.cc ]; libName = "libInit_shared${stdenv.hostPlatform.extensions.sharedLibrary}"; } ''
+        mkdir $out
+        touch empty.c
+        ${stdenv.cc}/bin/cc -shared -o $out/$libName empty.c
+      '';
+      leanshared_1 = runCommand "leanshared_1" { buildInputs = [ stdenv.cc ]; libName = "leanshared_1${stdenv.hostPlatform.extensions.sharedLibrary}"; } ''
+        mkdir $out
+        touch empty.c
+        ${stdenv.cc}/bin/cc -shared -o $out/$libName empty.c
+      '';
+      leanshared = runCommand "leanshared" { buildInputs = [ stdenv.cc ]; libName = "libleanshared${stdenv.hostPlatform.extensions.sharedLibrary}"; } ''
+        mkdir $out
+        LEAN_CC=${stdenv.cc}/bin/cc ${lean-bin-tools-unwrapped}/bin/leanc -shared ${lib.optionalString stdenv.isLinux "-Wl,-Bsymbolic"} \
+          -Wl,--whole-archive ${leancpp}/lib/temp/libleanshell.a -lInit -lStd -lLean -lleancpp ${leancpp}/lib/libleanrt_initial-exec.a -Wl,--no-whole-archive -lstdc++ \
+          -lm ${stdlibLinkFlags} \
+          $(${llvmPackages.libllvm.dev}/bin/llvm-config --ldflags --libs) \
+          -o $out/$libName
+      '';
+      mods = foldl' (mods: pkg: mods // pkg.mods) {} stdlib;
+      print-paths = Lean.makePrintPathsFor [] mods;
+      leanc = writeShellScriptBin "leanc" ''
+        LEAN_CC=${stdenv.cc}/bin/cc ${Leanc.executable}/bin/leanc -I${lean-bin-tools-unwrapped}/include ${stdlibLinkFlags} -L${libInit_shared} -L${leanshared_1} -L${leanshared} -L${Lake.sharedLib} "$@"
+      '';
+      lean = runCommand "lean" { buildInputs = lib.optional stdenv.isDarwin darwin.cctools; } ''
+        mkdir -p $out/bin
+        ${leanc}/bin/leanc ${leancpp}/lib/temp/libleanmain.a ${libInit_shared}/* ${leanshared_1}/* ${leanshared}/* -o $out/bin/lean
+      '';
+      # derivation following the directory layout of the "basic" setup, mostly useful for running tests
+      lean-all = stdenv.mkDerivation {
+        name = "lean-${desc}";
+        buildCommand = ''
+          mkdir -p $out/bin $out/lib/lean
+          ln -sf ${leancpp}/lib/lean/* ${lib.concatMapStringsSep " " (l: "${l.modRoot}/* ${l.staticLib}/*") (lib.reverseList stdlib)} ${libInit_shared}/* ${leanshared_1}/* ${leanshared}/* ${Lake.sharedLib}/* $out/lib/lean/
+          # put everything in a single final derivation so `IO.appDir` references work
+          cp ${lean}/bin/lean ${leanc}/bin/leanc ${Lake-Main.executable}/bin/lake $out/bin
+          # NOTE: `lndir` will not override existing `bin/leanc`
+          ${lndir}/bin/lndir -silent ${lean-bin-tools-unwrapped} $out
+        '';
+        meta.mainProgram = "lean";
+      };
+      cacheRoots = linkFarmFromDrvs "cacheRoots" ([
+        stage0 lean leanc lean-all iTree modDepsFiles depRoots Leanc.src
+      ] ++ map (lib: lib.oTree) stdlib);
+      test = buildCMake {
+        name = "lean-test-${desc}";
+        realSrc = lib.sourceByRegex src [ "src.*" "tests.*" ];
+        buildInputs = [ gmp libuv perl git cadical ];
+        preConfigure = ''
+          cd src
+        '';
+        extraCMakeFlags = [ "-DLLVM=OFF" ];
+        postConfigure = ''
+          patchShebangs ../../tests ../lake
+          rm -r bin lib include share
+          ln -sf ${lean-all}/* .
+        '';
+        buildPhase = ''
+         ctest --output-junit test-results.xml --output-on-failure -E 'leancomptest_(doc_example|foreign)|leanlaketest_reverse-ffi|leanruntest_timeIO' -j$NIX_BUILD_CORES
+        '';
+        installPhase = ''
+          mkdir $out
+          mv test-results.xml $out
+        '';
+      };
+      update-stage0 =
+        let cTree = symlinkJoin { name = "cs"; paths = map (lib: lib.cTree) (stdlib ++ [Lake-Main]); }; in
+        writeShellScriptBin "update-stage0" ''
+          CSRCS=${cTree} CP_C_PARAMS="--dereference --no-preserve=all" ${src + "/script/lib/update-stage0"}
+        '';
+      update-stage0-commit = writeShellScriptBin "update-stage0-commit" ''
+        set -euo pipefail
+        ${update-stage0}/bin/update-stage0
+        git commit -m "chore: update stage0"
+      '';
+      link-ilean = writeShellScriptBin "link-ilean" ''
+        dest=''${1:-src}
+        rm -rf $dest/build/lib || true
+        mkdir -p $dest/build/lib
+        ln -s ${iTree}/* $dest/build/lib
+      '';
+      benchmarks =
+        let
+          entries = attrNames (readDir (src + "/tests/bench"));
+          leanFiles = map (n: elemAt n 0) (filter (n: n != null) (map (match "(.*)\.lean") entries));
+        in lib.genAttrs leanFiles (n: (buildLeanPackage {
+          name = n;
+          src = filterSource (e: _: baseNameOf e == "${n}.lean") (src + "/tests/bench");
+        }).executable);
+    };
+  stage1 = stage { stage = 1; prevStage = stage0; self = stage1; };
+  stage2 = stage { stage = 2; prevStage = stage1; self = stage2; };
+  stage3 = stage { stage = 3; prevStage = stage2; self = stage3; };
+}

nix/buildLeanPackage.nix

@@ -0,0 +1,247 @@
+{ lean, lean-leanDeps ? lean, lean-final ? lean, leanc,
+  stdenv, lib, coreutils, gnused, writeShellScriptBin, bash, substituteAll, symlinkJoin, linkFarmFromDrvs,
+  runCommand, darwin, mkShell, ... }:
+let lean-final' = lean-final; in
+lib.makeOverridable (
+{ name, src, fullSrc ? src, srcPrefix ? "", srcPath ? "$PWD/${srcPrefix}",
+  # Lean dependencies. Each entry should be an output of buildLeanPackage.
+  deps ? [ lean.Init lean.Std lean.Lean ],
+  # Static library dependencies. Each derivation `static` should contain a static library in the directory `${static}`.
+  staticLibDeps ? [],
+  # Whether to wrap static library inputs in a -Wl,--start-group [...] -Wl,--end-group to ensure dependencies are resolved.
+  groupStaticLibs ? false,
+  # Shared library dependencies included at interpretation with --load-dynlib and linked to. Each derivation `shared` should contain a
+  # shared library at the path `${shared}/${shared.libName or shared.name}` and a name to link to like `-l${shared.linkName or shared.name}`.
+  # These libs are also linked to in packages that depend on this one.
+  nativeSharedLibs ? [],
+  # Lean modules to include.
+  # A set of Lean modules names as strings (`"Foo.Bar"`) or attrsets (`{ name = "Foo.Bar"; glob = "one" | "submodules" | "andSubmodules"; }`);
+  # see Lake README for glob meanings. Dependencies of selected modules are always included.
+  roots ? [ name ],
+  # Output from `lean --deps-json` on package source files. Persist the corresponding output attribute to a file and pass it back in here to avoid IFD.
+  # Must be refreshed on any change in `import`s or set of source file names.
+  modDepsFile ? null,
+  # Whether to compile each module into a native shared library that is loaded whenever the module is imported in order to accelerate evaluation
+  precompileModules ? false,
+  # Whether to compile the package into a native shared library that is loaded whenever *any* of the package's modules is imported into another package.
+  # If `precompileModules` is also `true`, the latter only affects imports within the current package.
+  precompilePackage ? precompileModules,
+  # Lean plugin dependencies. Each derivation `plugin` should contain a plugin library at path `${plugin}/${plugin.name}`.
+  pluginDeps ? [],
+  # `overrideAttrs` for `buildMod`
+  overrideBuildModAttrs ? null,
+  debug ? false, leanFlags ? [], leancFlags ? [], linkFlags ? [], executableName ? lib.toLower name, libName ? name, sharedLibName ? libName,
+  srcTarget ? "..#stage0", srcArgs ? "(\${args[*]})", lean-final ? lean-final' }@args:
+with builtins; let
+  # "Init.Core" ~> "Init/Core"
+  modToPath = mod: replaceStrings ["."] ["/"] mod;
+  modToAbsPath = mod: "${src}/${modToPath mod}";
+  # sanitize file name before copying to store, except when already in store
+  copyToStoreSafe = base: suffix: if lib.isDerivation base then base + suffix else
+    builtins.path { name = lib.strings.sanitizeDerivationName (baseNameOf suffix); path = base + suffix; };
+  modToLean = mod: copyToStoreSafe src "/${modToPath mod}.lean";
+  bareStdenv = ./bareStdenv;
+  mkBareDerivation = args: derivation (args // {
+    name = lib.strings.sanitizeDerivationName args.name;
+    stdenv = bareStdenv;
+    inherit (stdenv) system;
+    buildInputs = (args.buildInputs or []) ++ [ coreutils ];
+    builder = stdenv.shell;
+    args = [ "-c" ''
+      source $stdenv/setup
+      set -u
+      ${args.buildCommand}
+    '' ];
+  }) // { overrideAttrs = f: mkBareDerivation (lib.fix (lib.extends f (_: args))); };
+  runBareCommand = name: args: buildCommand: mkBareDerivation (args // { inherit name buildCommand; });
+  runBareCommandLocal = name: args: buildCommand: runBareCommand name (args // {
+    preferLocalBuild = true;
+    allowSubstitutes = false;
+  }) buildCommand;
+  mkSharedLib = name: args: runBareCommand "${name}-dynlib" {
+    buildInputs = [ stdenv.cc ] ++ lib.optional stdenv.isDarwin darwin.cctools;
+    libName = "${name}${stdenv.hostPlatform.extensions.sharedLibrary}";
+  } ''
+    mkdir -p $out
+    ${leanc}/bin/leanc -shared ${args} -o $out/$libName
+  '';
+  depRoot = name: deps: mkBareDerivation {
+    name = "${name}-depRoot";
+    inherit deps;
+    depRoots = map (drv: drv.LEAN_PATH) deps;
+
+    passAsFile = [ "deps" "depRoots" ];
+    buildCommand = ''
+      mkdir -p $out
+      for i in $(cat $depRootsPath); do
+        cp -dru --no-preserve=mode $i/. $out
+      done
+      for i in $(cat $depsPath); do
+        cp -drsu --no-preserve=mode $i/. $out
+      done
+    '';
+  };
+  srcRoot = src;
+
+  # A flattened list of Lean-module dependencies (`deps`)
+  allExternalDeps = lib.unique (lib.foldr (dep: allExternalDeps: allExternalDeps ++ [ dep ] ++ dep.allExternalDeps) [] deps);
+  allNativeSharedLibs =
+    lib.unique (lib.flatten (nativeSharedLibs ++ (map (dep: dep.allNativeSharedLibs or []) allExternalDeps)));
+
+  # A flattened list of all static library dependencies: this and every dep module's explicitly provided `staticLibDeps`,
+  # plus every dep module itself: `dep.staticLib`
+  allStaticLibDeps =
+    lib.unique (lib.flatten (staticLibDeps ++ (map (dep: [dep.staticLib] ++ dep.staticLibDeps or []) allExternalDeps)));
+
+  pathOfSharedLib = dep: dep.libPath or "${dep}/${dep.libName or dep.name}";
+
+  leanPluginFlags = lib.concatStringsSep " " (map (dep: "--plugin=${pathOfSharedLib dep}") pluginDeps);
+  loadDynlibsOfDeps = deps: lib.unique (concatMap (d: d.propagatedLoadDynlibs) deps);
+
+  # submodules "Init" = ["Init.List.Basic", "Init.Core", ...]
+  submodules = mod: let
+    dir = readDir (modToAbsPath mod);
+    f = p: t:
+      if t == "directory" then
+        submodules "${mod}.${p}"
+      else
+        let m = builtins.match "(.*)\.lean" p;
+        in lib.optional (m != null) "${mod}.${head m}";
+  in concatLists (lib.mapAttrsToList f dir);
+
+  # conservatively approximate list of source files matched by glob
+  expandGlobAllApprox = g:
+    if typeOf g == "string" then
+      # we can't know the required files without parsing dependencies (which is what we want this
+      # function for), so we approximate to the entire package.
+      let root = (head (split "\\." g));
+      in lib.optional (pathExists (src + "/${modToPath root}.lean")) root ++ lib.optionals (pathExists (modToAbsPath root)) (submodules root)
+    else if g.glob == "one" then expandGlobAllApprox g.mod
+    else if g.glob == "submodules" then submodules g.mod
+    else if g.glob == "andSubmodules" then [g.mod] ++ submodules g.mod
+    else throw "unknown glob kind '${g}'";
+  # list of modules that could potentially be involved in the build
+  candidateMods = lib.unique (concatMap expandGlobAllApprox roots);
+  candidateFiles = map modToLean candidateMods;
+  modDepsFile = args.modDepsFile or mkBareDerivation {
+    name = "${name}-deps.json";
+    candidateFiles = lib.concatStringsSep " " candidateFiles;
+    passAsFile = [ "candidateFiles" ];
+    buildCommand = ''
+      mkdir $out
+      ${lean-leanDeps}/bin/lean --deps-json --stdin < $candidateFilesPath > $out/$name
+    '';
+  };
+  modDeps = fromJSON (
+    # the only possible references to store paths in the JSON should be inside errors, so no chance of missed dependencies from this
+    unsafeDiscardStringContext (readFile "${modDepsFile}/${modDepsFile.name}"));
+  # map from module name to list of imports
+  modDepsMap = listToAttrs (lib.zipListsWith lib.nameValuePair candidateMods modDeps.imports);
+  maybeOverrideAttrs = f: x: if f != null then x.overrideAttrs f else x;
+  # build module (.olean and .c) given derivations of all (immediate) dependencies
+  # TODO: make `rec` parts override-compatible?
+  buildMod = mod: deps: maybeOverrideAttrs overrideBuildModAttrs (mkBareDerivation rec {
+    name = "${mod}";
+    LEAN_PATH = depRoot mod deps;
+    LEAN_ABORT_ON_PANIC = "1";
+    relpath = modToPath mod;
+    buildInputs = [ lean ];
+    leanPath = relpath + ".lean";
+    # should be either single .lean file or directory directly containing .lean file plus dependencies
+    src = copyToStoreSafe srcRoot ("/" + leanPath);
+    outputs = [ "out" "ilean" "c" ];
+    oleanPath = relpath + ".olean";
+    ileanPath = relpath + ".ilean";
+    cPath = relpath + ".c";
+    inherit leanFlags leanPluginFlags;
+    leanLoadDynlibFlags = map (p: "--load-dynlib=${pathOfSharedLib p}") (loadDynlibsOfDeps deps);
+    buildCommand = ''
+      dir=$(dirname $relpath)
+      mkdir -p $dir $out/$dir $ilean/$dir $c/$dir
+      if [ -d $src ]; then cp -r $src/. .; else cp $src $leanPath; fi
+      lean -o $out/$oleanPath -i $out/$ileanPath -c $c/$cPath $leanPath $leanFlags $leanPluginFlags $leanLoadDynlibFlags
+    '';
+  }) // {
+    inherit deps;
+    propagatedLoadDynlibs = loadDynlibsOfDeps deps;
+  };
+  compileMod = mod: drv: mkBareDerivation {
+    name = "${mod}-cc";
+    buildInputs = [ leanc stdenv.cc ];
+    hardeningDisable = [ "all" ];
+    oPath = drv.relpath + ".o";
+    inherit leancFlags;
+    buildCommand = ''
+      mkdir -p $out/$(dirname ${drv.relpath})
+      # make local "copy" so `drv`'s Nix store path doesn't end up in ccache's hash
+      ln -s ${drv.c}/${drv.cPath} src.c
+      # on the other hand, a debug build is pretty fast anyway, so preserve the path for gdb
+      leanc -c -o $out/$oPath $leancFlags -fPIC ${if debug then "${drv.c}/${drv.cPath} -g" else "src.c -O3 -DNDEBUG -DLEAN_EXPORTING"}
+    '';
+  };
+  mkMod = mod: deps:
+    let drv = buildMod mod deps;
+        obj = compileMod mod drv;
+        # this attribute will only be used if any dependent module is precompiled
+        sharedLib = mkSharedLib mod "${obj}/${obj.oPath} ${lib.concatStringsSep " " (map (d: pathOfSharedLib d.sharedLib) deps)}";
+    in drv // {
+      inherit obj sharedLib;
+    } // lib.optionalAttrs precompileModules {
+      propagatedLoadDynlibs = [sharedLib];
+    };
+  externalModMap = lib.foldr (dep: depMap: depMap // dep.mods) {} allExternalDeps;
+  # map from module name to derivation
+  modCandidates = mapAttrs (mod: header:
+    let
+      deps = if header.errors == []
+             then map (m: m.module) header.result.imports
+             else abort "errors while parsing imports of ${mod}:\n${lib.concatStringsSep "\n" header.errors}";
+    in mkMod mod (map (dep: if modDepsMap ? ${dep} then modCandidates.${dep} else externalModMap.${dep}) deps)) modDepsMap;
+  expandGlob = g:
+    if typeOf g == "string" then [g]
+    else if g.glob == "one" then [g.mod]
+    else if g.glob == "submodules" then submodules g.mod
+    else if g.glob == "andSubmodules" then [g.mod] ++ submodules g.mod
+    else throw "unknown glob kind '${g}'";
+  # subset of `modCandidates` that is transitively reachable from `roots`
+  mods' = listToAttrs (map (e: { name = e.key; value = modCandidates.${e.key}; }) (genericClosure {
+    startSet = map (m: { key = m; }) (concatMap expandGlob roots);
+    operator = e: if modDepsMap ? ${e.key} then map (m: { key = m.module; }) (filter (m: modCandidates ? ${m.module}) modDepsMap.${e.key}.result.imports) else [];
+  }));
+  allLinkFlags = lib.foldr (shared: acc: acc ++ [ "-L${shared}" "-l${shared.linkName or shared.name}" ]) linkFlags allNativeSharedLibs;
+
+  objects   = mapAttrs (_: m: m.obj) mods';
+  bintools = if stdenv.isDarwin then darwin.cctools else stdenv.cc.bintools.bintools;
+  staticLib = runCommand "${name}-lib" { buildInputs = [ bintools ]; } ''
+    mkdir -p $out
+    ar Trcs $out/lib${libName}.a ${lib.concatStringsSep " " (map (drv: "${drv}/${drv.oPath}") (attrValues objects))};
+  '';
+
+  staticLibLinkWrapper = libs: if groupStaticLibs && !stdenv.isDarwin
+    then "-Wl,--start-group ${libs} -Wl,--end-group"
+    else "${libs}";
+in rec {
+  inherit name lean deps staticLibDeps allNativeSharedLibs allLinkFlags allExternalDeps src objects staticLib modDepsFile;
+  mods = mapAttrs (_: m:
+      m //
+      # if neither precompilation option was set but a dependent module wants to be precompiled, default to precompiling this package whole
+      lib.optionalAttrs (precompilePackage || !precompileModules) { inherit sharedLib; } //
+      lib.optionalAttrs precompilePackage { propagatedLoadDynlibs = [sharedLib]; })
+    mods';
+  modRoot   = depRoot name (attrValues mods);
+  depRoots  = linkFarmFromDrvs "depRoots" (map (m: m.LEAN_PATH) (attrValues mods));
+  cTree     = symlinkJoin { name = "${name}-cTree"; paths = map (mod: mod.c) (attrValues mods); };
+  oTree     = symlinkJoin { name = "${name}-oTree"; paths = (attrValues objects); };
+  iTree     = symlinkJoin { name = "${name}-iTree"; paths = map (mod: mod.ilean) (attrValues mods); };
+  sharedLib = mkSharedLib "lib${sharedLibName}" ''
+    ${if stdenv.isDarwin then "-Wl,-force_load,${staticLib}/lib${libName}.a" else "-Wl,--whole-archive ${staticLib}/lib${libName}.a -Wl,--no-whole-archive"} \
+    ${lib.concatStringsSep " " (map (d: "${d.sharedLib}/*") deps)}'';
+  executable = lib.makeOverridable ({ withSharedStdlib ? true }: let
+      objPaths = map (drv: "${drv}/${drv.oPath}") (attrValues objects) ++ lib.optional withSharedStdlib "${lean-final.leanshared}/*";
+    in runCommand executableName { buildInputs = [ stdenv.cc leanc ]; } ''
+      mkdir -p $out/bin
+      leanc ${staticLibLinkWrapper (lib.concatStringsSep " " (objPaths ++ map (d: "${d}/*.a") allStaticLibDeps))} \
+        -o $out/bin/${executableName} \
+        ${lib.concatStringsSep " " allLinkFlags}
+    '') {};
+})

nix/lake-dev.in

@@ -0,0 +1,42 @@
+#!@bash@/bin/bash
+
+set -euo pipefail
+
+function pebkac() {
+    echo 'This is just a simple Nix adapter for `lake print-paths|serve`.'
+    exit 1
+}
+
+[[ $# -gt 0 ]] || pebkac
+case $1 in
+    --version)
+        # minimum version for `lake serve` with fallback
+        echo 3.1.0
+        ;;
+    print-paths)
+        shift
+        deps="$@"
+        root=.
+        # fall back to initial package if not in package
+        [[ ! -f "$root/flake.nix" ]] && root="@srcRoot@"
+        target="$root#print-paths"
+        args=()
+        # HACK: use stage 0 instead of 1 inside Lean's own `src/`
+        [[ -d Lean && -f ../flake.nix ]] && target="@srcTarget@print-paths" && args=@srcArgs@
+        for dep in $deps; do
+            target="$target.\"$dep\""
+        done
+        echo "Building dependencies..." >&2
+        # -v only has "built ...", but "-vv" is a bit too verbose
+        exec @nix@/bin/nix run "$target" ${args[*]} -v
+        ;;
+    serve)
+        shift
+        [[ ${1:-} == "--" ]] && shift
+        # `link-ilean` puts them there
+        LEAN_PATH=${LEAN_PATH:+$LEAN_PATH:}$PWD/build/lib exec $(dirname $0)/lean --server "$@"
+        ;;
+    *)
+        pebkac
+        ;;
+esac

nix/lean-dev.in

@@ -0,0 +1,28 @@
+#!@bash@/bin/bash
+
+set -euo pipefail
+
+root="."
+# find package root
+while [[ "$root" != / ]]; do
+    [ -f "$root/flake.nix" ] && break
+    root="$(realpath "$root/..")"
+done
+# fall back to initial package if not in package
+[[ ! -f "$root/flake.nix" ]] && root="@srcRoot@"
+
+# use Lean w/ package unless in server mode (which has its own LEAN_PATH logic)
+target="$root#lean-package"
+for arg in "$@"; do
+    case $arg in
+        --server | --worker | -v | --version)
+            target="$root#lean"
+            ;;
+    esac
+done
+
+args=(-- "$@")
+# HACK: use stage 0 instead of 1 inside Lean's own `src/`
+[[ -d Lean && -f ../flake.nix ]] && target="@srcTarget@" && args=@srcArgs@
+
+LEAN_SYSROOT="$(dirname "$0")/.." exec @nix@/bin/nix ${LEAN_NIX_ARGS:-} run "$target" ${args[*]}

nix/packages.nix

@@ -0,0 +1,52 @@
+{ src, pkgs, ... } @ args:
+with pkgs;
+let
+  # https://github.com/NixOS/nixpkgs/issues/130963
+  llvmPackages = if stdenv.isDarwin then llvmPackages_11 else llvmPackages_15;
+  cc = (ccacheWrapper.override rec {
+    cc = llvmPackages.clang;
+    extraConfig = ''
+      export CCACHE_DIR=/nix/var/cache/ccache
+      export CCACHE_UMASK=007
+      export CCACHE_BASE_DIR=$NIX_BUILD_TOP
+      # https://github.com/NixOS/nixpkgs/issues/109033
+      args=("$@")
+      for ((i=0; i<"''${#args[@]}"; i++)); do
+        case ''${args[i]} in
+          -frandom-seed=*) unset args[i]; break;;
+        esac
+      done
+      set -- "''${args[@]}"
+      [ -d $CCACHE_DIR ] || exec ${cc}/bin/$(basename "$0") "$@"
+    '';
+  }).overrideAttrs (old: {
+    # https://github.com/NixOS/nixpkgs/issues/119779
+    installPhase = builtins.replaceStrings ["use_response_file_by_default=1"] ["use_response_file_by_default=0"] old.installPhase;
+  });
+  stdenv' = if stdenv.isLinux then useGoldLinker stdenv else stdenv;
+  lean = callPackage (import ./bootstrap.nix) (args // {
+    stdenv = overrideCC stdenv' cc;
+    inherit src buildLeanPackage llvmPackages;
+  });
+  makeOverridableLeanPackage = f:
+    let newF = origArgs: f origArgs // {
+      overrideArgs = newArgs: makeOverridableLeanPackage f (origArgs // newArgs);
+    };
+    in lib.setFunctionArgs newF (lib.getFunctionArgs f) // {
+      override = args: makeOverridableLeanPackage (f.override args);
+    };
+  buildLeanPackage = makeOverridableLeanPackage (callPackage (import ./buildLeanPackage.nix) (args // {
+    inherit (lean) stdenv;
+    lean = lean.stage1;
+    inherit (lean.stage1) leanc;
+  }));
+in {
+  inherit cc buildLeanPackage llvmPackages;
+  nixpkgs = pkgs;
+  ciShell = writeShellScriptBin "ciShell" ''
+    set -o pipefail
+    export PATH=${moreutils}/bin:$PATH
+    # prefix lines with cumulative and individual execution time
+    "$@" |& ts -i "(%.S)]" | ts -s "[%M:%S"
+  '';
+} // lean.stage1

nix/templates/pkg/MyPackage.lean

@@ -0,0 +1 @@
+#eval "Hello, world!"

nix/templates/pkg/flake.nix

@@ -0,0 +1,21 @@
+{
+  description = "My Lean package";
+
+  inputs.lean.url = "github:leanprover/lean4";
+  inputs.flake-utils.url = "github:numtide/flake-utils";
+
+  outputs = { self, lean, flake-utils }: flake-utils.lib.eachDefaultSystem (system:
+    let
+      leanPkgs = lean.packages.${system};
+      pkg = leanPkgs.buildLeanPackage {
+        name = "MyPackage";  # must match the name of the top-level .lean file
+        src = ./.;
+      };
+    in {
+      packages = pkg // {
+        inherit (leanPkgs) lean;
+      };
+
+      defaultPackage = pkg.modRoot;
+    });
+}

script/AnalyzeGrindAnnotations.lean

@@ -1,132 +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
--/
-import Lean
-
-namespace Lean.Meta.Grind.Analyzer
-
-
-/-!
-A simple E-matching annotation analyzer.
-For each theorem annotated as an E-matching candidate, it creates an artificial goal, executes `grind` and shows the
-number of instances created.
-For a theorem of the form `params -> type`, the artificial goal is of the form `params -> type -> False`.
--/
-
-/--
-`grind` configuration for the analyzer. We disable case-splits and lookahead,
-increase the number of generations, and limit the number of instances generated.
--/
-def config : Grind.Config := {
-  splits       := 0
-  lookahead    := false
-  mbtc         := false
-  ematch       := 20
-  instances    := 100
-  gen          := 10
-}
-
-structure Config where
-  /-- Minimum number of instantiations to trigger summary report -/
-  min : Nat := 10
-  /-- Minimum number of instantiations to trigger detailed report -/
-  detailed : Nat := 50
-
-def mkParams : MetaM Params := do
-  let params ← Grind.mkParams config
-  let ematch ← getEMatchTheorems
-  let casesTypes ← Grind.getCasesTypes
-  return { params with ematch, casesTypes }
-
-/-- Returns the total number of generated instances.  -/
-private def sum (cs : PHashMap Origin Nat) : Nat := Id.run do
-  let mut r := 0
-  for (_, c) in cs do
-    r := r + c
-  return r
-
-private def thmsToMessageData (thms : PHashMap Origin Nat) : MetaM MessageData := do
-  let data := thms.toArray.filterMap fun (origin, c) =>
-    match origin with
-    | .decl declName => some (declName, c)
-    | _ => none
-  let data := data.qsort fun (d₁, c₁) (d₂, c₂) => if c₁ == c₂ then Name.lt d₁ d₂ else c₁ > c₂
-  let data ← data.mapM fun (declName, counter) =>
-    return .trace { cls := `thm } m!"{.ofConst (← mkConstWithLevelParams declName)} ↦ {counter}" #[]
-  return .trace { cls := `thm } "instances" data
-
-/--
-Analyzes theorem `declName`. That is, creates the artificial goal based on `declName` type,
-and invokes `grind` on it.
--/
-def analyzeEMatchTheorem (declName : Name) (c : Config) : MetaM Unit := do
-  let info ← getConstInfo declName
-  let mvarId ← forallTelescope info.type fun _ type => do
-    withLocalDeclD `h type fun _ => do
-      return (← mkFreshExprMVar (mkConst ``False)).mvarId!
-  let result ← Grind.main mvarId (← mkParams) (pure ())
-  let thms := result.counters.thm
-  let s := sum thms
-  if s > c.min then
-    IO.println s!"{declName} : {s}"
-  if s > c.detailed then
-    logInfo m!"{declName}\n{← thmsToMessageData thms}"
-
--- Not sure why this is failing: `down_pure` perhaps has an unnecessary universe parameter?
-run_meta analyzeEMatchTheorem ``Std.Do.SPred.down_pure {}
-
-/-- Analyzes all theorems in the standard library marked as E-matching theorems. -/
-def analyzeEMatchTheorems (c : Config := {}) : MetaM Unit := do
-  let origins := (← getEMatchTheorems).getOrigins
-  let decls := origins.filterMap fun | .decl declName => some declName | _ => none
-  for declName in decls.mergeSort Name.lt do
-    try
-      analyzeEMatchTheorem declName c
-    catch e =>
-      logError m!"{declName} failed with {e.toMessageData}"
-  logInfo m!"Finished analyzing {decls.length} theorems"
-
-/-- Macro for analyzing E-match theorems with unlimited heartbeats -/
-macro "#analyzeEMatchTheorems" : command => `(
-  set_option maxHeartbeats 0 in
-  run_meta analyzeEMatchTheorems
-)
-
-#analyzeEMatchTheorems
-
--- -- We can analyze specific theorems using commands such as
-set_option trace.grind.ematch.instance true
-
--- 1. grind immediately sees `(#[] : Array α) = ([] : List α).toArray` but probably this should be hidden.
--- 2. `Vector.toArray_empty` keys on `Array.mk []` rather than `#v[].toArray`
--- I guess we could add `(#[].extract _ _).extract _ _` as a stop pattern.
-run_meta analyzeEMatchTheorem ``Array.extract_empty {}
-
--- Neither `Option.bind_some` nor `Option.bind_fun_some` fire, because the terms appear inside
--- lambdas. So we get crazy things like:
--- `fun x => ((some x).bind some).bind fun x => (some x).bind fun x => (some x).bind some`
--- We could consider replacing `filterMap_some` with
--- `filterMap g (filterMap f xs) = filterMap (f >=> g) xs`
--- to avoid the lambda that `grind` struggles with, but this would require more API around the fish.
-run_meta analyzeEMatchTheorem ``Array.filterMap_some {}
-
--- Not entirely certain what is wrong here, but certainly
--- `eq_empty_of_append_eq_empty` is firing too often.
--- Ideally we could instantiate this is we fine `xs ++ ys` in the same equivalence class,
--- note just as soon as we see `xs ++ ys`.
--- I've tried removing this in https://github.com/leanprover/lean4/pull/10162
-run_meta analyzeEMatchTheorem ``Array.range'_succ {}
-
--- Perhaps the same story here.
-run_meta analyzeEMatchTheorem ``Array.range_succ {}
-
--- `zip_map_left` and `zip_map_right` are bad grind lemmas,
--- checking if they can be removed in https://github.com/leanprover/lean4/pull/10163
-run_meta analyzeEMatchTheorem ``Array.zip_map {}
-
--- It seems crazy to me that as soon as we have `0 >>> n = 0`, we instantiate based on the
--- pattern `0 >>> n >>> m` by substituting `0` into `0 >>> n` to produce the `0 >>> n >>> n`.
--- I don't think any forbidden subterms can help us here. I don't know what to do. :-(
-run_meta analyzeEMatchTheorem ``Int.zero_shiftRight {}

script/bench.sh

@@ -1,9 +1,9 @@
 #!/usr/bin/env bash
-set -euxo pipefail
+set -euo pipefail
 
-cmake --preset release 1>&2
+cmake --preset release -DUSE_LAKE=ON 1>&2
 
-# We benchmark against stage2/bin to test new optimizations.
+# We benchmark against stage 2 to test new optimizations.
 timeout -s KILL 1h time make -C build/release -j$(nproc) stage3 1>&2
 export PATH=$PWD/build/release/stage2/bin:$PATH
 
@@ -11,86 +11,6 @@ export PATH=$PWD/build/release/stage2/bin:$PATH
 # easier to configure them statically.
 cmake -B build/release/stage3 -S src -DLEAN_EXTRA_LAKEFILE_TOML='weakLeanArgs=["-Dprofiler=true", "-Dprofiler.threshold=9999999", "--stats"]' 1>&2
 
-(
 cd tests/bench
 timeout -s KILL 1h time temci exec --config speedcenter.yaml --in speedcenter.exec.velcom.yaml 1>&2
 temci report run_output.yaml --reporter codespeed2
-)
-
-if [ -d .git ]; then
-    DIR="$(git rev-parse @)"
-    BASE_URL="https://speed.lean-lang.org/lean4-out/$DIR"
-    {
-        cat <<'EOF'
-<!DOCTYPE html>
-<html>
-<head>
-  <meta charset="UTF-8">
-  <title>Lakeprof Report</title>
-</head>
-<h1>Lakeprof Report</h1>
-<button type="button" id="btn_fetch">View build trace in Perfetto</button>
-<script type="text/javascript">
-const ORIGIN = 'https://ui.perfetto.dev';
-
-const btnFetch = document.getElementById('btn_fetch');
-
-async function fetchAndOpen(traceUrl) {
-  const resp = await fetch(traceUrl);
-  // Error checking is left as an exercise to the reader.
-  const blob = await resp.blob();
-  const arrayBuffer = await blob.arrayBuffer();
-  openTrace(arrayBuffer, traceUrl);
-}
-
-function openTrace(arrayBuffer, traceUrl) {
-  const win = window.open(ORIGIN);
-  if (!win) {
-    btnFetch.style.background = '#f3ca63';
-  	btnFetch.onclick = () => openTrace(arrayBuffer);
-    btnFetch.innerText = 'Popups blocked, click here to open the trace file';
-    return;
-  }
-
-  const timer = setInterval(() => win.postMessage('PING', ORIGIN), 50);
-
-  const onMessageHandler = (evt) => {
-    if (evt.data !== 'PONG') return;
-
-    // We got a PONG, the UI is ready.
-    window.clearInterval(timer);
-    window.removeEventListener('message', onMessageHandler);
-
-    const reopenUrl = new URL(location.href);
-    reopenUrl.hash = `#reopen=${traceUrl}`;
-    win.postMessage({
-      perfetto: {
-        buffer: arrayBuffer,
-        title: 'Lake Build Trace',
-        url: reopenUrl.toString(),
-    }}, ORIGIN);
-  };
-
-  window.addEventListener('message', onMessageHandler);
-}
-
-// This is triggered when following the link from the Perfetto UI's sidebar.
-if (location.hash.startsWith('#reopen=')) {
- const traceUrl = location.hash.substr(8);
- fetchAndOpen(traceUrl);
-}
-EOF
-        cat <<EOF
-btnFetch.onclick = () => fetchAndOpen("$BASE_URL/lakeprof.trace_event");
-</script>
-EOF
-        echo "<pre><code>"
-        (cd src; lakeprof report -prc)
-        echo "</code></pre>"
-        echo "</body></html>"
-    } | tee index.html
-
-    curl -T index.html $BASE_URL/index.html
-    curl -T src/lakeprof.log $BASE_URL/lakeprof.log
-    curl -T src/lakeprof.trace_event $BASE_URL/lakeprof.trace_event
-fi

script/release_repos.yml

@@ -28,28 +28,6 @@ repositories:
     branch: main
     dependencies: []
 
-  - name: verso
-    url: https://github.com/leanprover/verso
-    toolchain-tag: true
-    stable-branch: false
-    branch: main
-    dependencies: []
-
-  - name: plausible
-    url: https://github.com/leanprover-community/plausible
-    toolchain-tag: true
-    stable-branch: false
-    branch: main
-    dependencies: []
-
-  - name: import-graph
-    url: https://github.com/leanprover-community/import-graph
-    toolchain-tag: true
-    stable-branch: false
-    branch: main
-    dependencies:
-      - lean4-cli
-
   - name: doc-gen4
     url: https://github.com/leanprover/doc-gen4
     toolchain-tag: true
@@ -57,6 +35,13 @@ repositories:
     branch: main
     dependencies: [lean4-cli]
 
+  - name: verso
+    url: https://github.com/leanprover/verso
+    toolchain-tag: true
+    stable-branch: false
+    branch: main
+    dependencies: []
+
   - name: reference-manual
     url: https://github.com/leanprover/reference-manual
     toolchain-tag: true
@@ -80,6 +65,22 @@ repositories:
     dependencies:
       - batteries
 
+  - name: import-graph
+    url: https://github.com/leanprover-community/import-graph
+    toolchain-tag: true
+    stable-branch: false
+    branch: main
+    dependencies:
+      - lean4-cli
+      - batteries
+
+  - name: plausible
+    url: https://github.com/leanprover-community/plausible
+    toolchain-tag: true
+    stable-branch: false
+    branch: main
+    dependencies: []
+
   - name: mathlib4
     url: https://github.com/leanprover-community/mathlib4
     toolchain-tag: true

src/CMakeLists.txt

@@ -10,7 +10,7 @@ endif()
 include(ExternalProject)
 project(LEAN CXX C)
 set(LEAN_VERSION_MAJOR 4)
-set(LEAN_VERSION_MINOR 24)
+set(LEAN_VERSION_MINOR 23)
 set(LEAN_VERSION_PATCH 0)
 set(LEAN_VERSION_IS_RELEASE 0)  # This number is 1 in the release revision, and 0 otherwise.
 set(LEAN_SPECIAL_VERSION_DESC "" CACHE STRING "Additional version description like 'nightly-2018-03-11'")
@@ -81,7 +81,7 @@ option(USE_MIMALLOC "use mimalloc" ON)
 
 # development-specific options
 option(CHECK_OLEAN_VERSION "Only load .olean files compiled with the current version of Lean" OFF)
-option(USE_LAKE "Use Lake instead of lean.mk for building core libs from language server" ON)
+option(USE_LAKE "Use Lake instead of lean.mk for building core libs from language server" OFF)
 
 set(LEAN_EXTRA_MAKE_OPTS  ""                           CACHE STRING "extra options to lean --make")
 set(LEANC_CC              ${CMAKE_C_COMPILER}          CACHE STRING "C compiler to use in `leanc`")
@@ -469,7 +469,6 @@ elseif(${CMAKE_SYSTEM_NAME} MATCHES "Darwin")
   string(APPEND CMAKE_CXX_FLAGS " -ftls-model=initial-exec")
   string(APPEND INIT_SHARED_LINKER_FLAGS " -install_name @rpath/libInit_shared.dylib")
   string(APPEND LEANSHARED_1_LINKER_FLAGS " -install_name @rpath/libleanshared_1.dylib")
-  string(APPEND LEANSHARED_2_LINKER_FLAGS " -install_name @rpath/libleanshared_2.dylib")
   string(APPEND LEANSHARED_LINKER_FLAGS " -install_name @rpath/libleanshared.dylib")
   string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libLake.a.export -install_name @rpath/libLake_shared.dylib")
   string(APPEND CMAKE_EXE_LINKER_FLAGS " -Wl,-rpath,@executable_path/../lib -Wl,-rpath,@executable_path/../lib/lean")
@@ -503,7 +502,7 @@ endif()
 # are already loaded) and probably fail unless we set up LD_LIBRARY_PATH.
 if(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
   # import libraries created by the stdlib.make targets
-  string(APPEND LEANC_SHARED_LINKER_FLAGS " -lInit_shared -lleanshared_2 -lleanshared_1 -lleanshared")
+  string(APPEND LEANC_SHARED_LINKER_FLAGS " -lInit_shared -lleanshared_1 -lleanshared")
 elseif("${CMAKE_SYSTEM_NAME}" MATCHES "Darwin")
   # The second flag is necessary to even *load* dylibs without resolved symbols, as can happen
   # if a Lake `extern_lib` depends on a symbols defined by the Lean library but is loaded even
@@ -590,7 +589,7 @@ endif()
 
 add_subdirectory(initialize)
 add_subdirectory(shell)
-# to be included in `leanshared` but not the smaller `leanshared_*` (as it would pull
+# to be included in `leanshared` but not the smaller `leanshared_1` (as it would pull
 # in the world)
 add_library(leaninitialize STATIC $<TARGET_OBJECTS:initialize>)
 set_target_properties(leaninitialize PROPERTIES
@@ -685,17 +684,12 @@ if (LLVM AND ${STAGE} GREATER 0)
   set(EXTRA_LEANMAKE_OPTS "LLVM=1")
 endif()
 
-set(STDLIBS Init Std Lean Leanc)
-if(NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
-  list(APPEND STDLIBS Lake)
-endif()
-
 add_custom_target(make_stdlib ALL
   WORKING_DIRECTORY ${LEAN_SOURCE_DIR}
   # The actual rule is in a separate makefile because we want to prefix it with '+' to use the Make job server
   # for a parallelized nested build, but CMake doesn't let us do that.
   # We use `lean` from the previous stage, but `leanc`, headers, etc. from the current stage
-  COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make ${STDLIBS}
+  COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make Init Std Lean Leanc
   VERBATIM)
 
 # if we have LLVM enabled, then build `lean.h.bc` which has the LLVM bitcode
@@ -715,7 +709,6 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
   )
   add_custom_target(leanshared ALL
     DEPENDS Init_shared leancpp
-    COMMAND touch ${CMAKE_LIBRARY_OUTPUT_DIRECTORY}/libleanshared_2${CMAKE_SHARED_LIBRARY_SUFFIX}
     COMMAND touch ${CMAKE_LIBRARY_OUTPUT_DIRECTORY}/libleanshared_1${CMAKE_SHARED_LIBRARY_SUFFIX}
     COMMAND touch ${CMAKE_LIBRARY_OUTPUT_DIRECTORY}/libleanshared${CMAKE_SHARED_LIBRARY_SUFFIX}
   )
@@ -736,13 +729,18 @@ else()
     COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make leanshared
     VERBATIM)
 
-  string(APPEND CMAKE_EXE_LINKER_FLAGS " -lInit_shared -lleanshared_2 -lleanshared_1 -lleanshared")
+  string(APPEND CMAKE_EXE_LINKER_FLAGS " -lInit_shared -lleanshared_1 -lleanshared")
 endif()
 
 if(NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
-  add_custom_target(lake_shared
+  add_custom_target(lake_lib
     WORKING_DIRECTORY ${LEAN_SOURCE_DIR}
     DEPENDS leanshared
+    COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make Lake
+    VERBATIM)
+  add_custom_target(lake_shared
+    WORKING_DIRECTORY ${LEAN_SOURCE_DIR}
+    DEPENDS lake_lib
     COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make libLake_shared
     VERBATIM)
   add_custom_target(lake ALL

src/Init/Control/EState.lean

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

src/Init/Control/Lawful/Instances.lean

@@ -7,10 +7,8 @@ module
 
 prelude
 public import Init.Control.Lawful.Basic
-public import Init.Control.Except
-import all Init.Control.Except
-public import Init.Control.State
-import all Init.Control.State
+public import all Init.Control.Except
+public import all Init.Control.State
 public import Init.Control.StateRef
 public import Init.Ext
 
@@ -22,24 +20,23 @@ open Function
 
 namespace ExceptT
 
-@[ext, grind ext] theorem ext {x y : ExceptT ε m α} (h : x.run = y.run) : x = y := by
+@[ext] theorem ext {x y : ExceptT ε m α} (h : x.run = y.run) : x = y := by
   simp [run] at h
   assumption
 
-@[simp, grind =] theorem run_pure [Monad m] (x : α) : run (pure x : ExceptT ε m α) = pure (Except.ok x) := rfl
+@[simp] theorem run_pure [Monad m] (x : α) : run (pure x : ExceptT ε m α) = pure (Except.ok x) := rfl
 
-@[simp, grind =] theorem run_lift  [Monad.{u, v} m] (x : m α) : run (ExceptT.lift x : ExceptT ε m α) = (Except.ok <$> x : m (Except ε α)) := rfl
+@[simp] theorem run_lift  [Monad.{u, v} m] (x : m α) : run (ExceptT.lift x : ExceptT ε m α) = (Except.ok <$> x : m (Except ε α)) := rfl
 
-@[simp, grind =] theorem run_throw [Monad m] : run (throw e : ExceptT ε m β) = pure (Except.error e) := rfl
+@[simp] theorem run_throw [Monad m] : run (throw e : ExceptT ε m β) = pure (Except.error e) := rfl
 
-@[simp, grind =] theorem run_bind_lift [Monad m] [LawfulMonad m] (x : m α) (f : α → ExceptT ε m β) : run (ExceptT.lift x >>= f : ExceptT ε m β) = x >>= fun a => run (f a) := by
+@[simp] theorem run_bind_lift [Monad m] [LawfulMonad m] (x : m α) (f : α → ExceptT ε m β) : run (ExceptT.lift x >>= f : ExceptT ε m β) = x >>= fun a => run (f a) := by
   simp [ExceptT.run, ExceptT.lift, bind, ExceptT.bind, ExceptT.mk, ExceptT.bindCont]
 
-@[simp, grind =] theorem bind_throw [Monad m] [LawfulMonad m] (f : α → ExceptT ε m β) : (throw e >>= f) = throw e := by
+@[simp] theorem bind_throw [Monad m] [LawfulMonad m] (f : α → ExceptT ε m β) : (throw e >>= f) = throw e := by
   simp [throw, throwThe, MonadExceptOf.throw, bind, ExceptT.bind, ExceptT.bindCont, ExceptT.mk]
 
-@[grind =]
-theorem run_bind [Monad m] (x : ExceptT ε m α) (f : α → ExceptT ε m β)
+theorem run_bind [Monad m] (x : ExceptT ε m α)
         : run (x >>= f : ExceptT ε m β)
           =
           run x >>= fun
@@ -47,10 +44,10 @@ theorem run_bind [Monad m] (x : ExceptT ε m α) (f : α → ExceptT ε m β)
                      | Except.error e => pure (Except.error e) :=
   rfl
 
-@[simp, grind =] theorem lift_pure [Monad m] [LawfulMonad m] (a : α) : ExceptT.lift (pure a) = (pure a : ExceptT ε m α) := by
+@[simp] theorem lift_pure [Monad m] [LawfulMonad m] (a : α) : ExceptT.lift (pure a) = (pure a : ExceptT ε m α) := by
   simp [ExceptT.lift, pure, ExceptT.pure]
 
-@[simp, grind =] theorem run_map [Monad m] [LawfulMonad m] (f : α → β) (x : ExceptT ε m α)
+@[simp] theorem run_map [Monad m] [LawfulMonad m] (f : α → β) (x : ExceptT ε m α)
     : (f <$> x).run = Except.map f <$> x.run := by
   simp [Functor.map, ExceptT.map, ←bind_pure_comp]
   apply bind_congr
@@ -114,28 +111,28 @@ instance : LawfulFunctor (Except ε) := inferInstance
 
 namespace ReaderT
 
-@[ext, grind ext] theorem ext {x y : ReaderT ρ m α} (h : ∀ ctx, x.run ctx = y.run ctx) : x = y := by
+@[ext] theorem ext {x y : ReaderT ρ m α} (h : ∀ ctx, x.run ctx = y.run ctx) : x = y := by
   simp [run] at h
   exact funext h
 
-@[simp, grind =] theorem run_pure [Monad m] (a : α) (ctx : ρ) : (pure a : ReaderT ρ m α).run ctx = pure a := rfl
+@[simp] theorem run_pure [Monad m] (a : α) (ctx : ρ) : (pure a : ReaderT ρ m α).run ctx = pure a := rfl
 
-@[simp, grind =] theorem run_bind [Monad m] (x : ReaderT ρ m α) (f : α → ReaderT ρ m β) (ctx : ρ)
+@[simp] theorem run_bind [Monad m] (x : ReaderT ρ m α) (f : α → ReaderT ρ m β) (ctx : ρ)
     : (x >>= f).run ctx = x.run ctx >>= λ a => (f a).run ctx := rfl
 
-@[simp, grind =] theorem run_mapConst [Monad m] (a : α) (x : ReaderT ρ m β) (ctx : ρ)
+@[simp] theorem run_mapConst [Monad m] (a : α) (x : ReaderT ρ m β) (ctx : ρ)
     : (Functor.mapConst a x).run ctx = Functor.mapConst a (x.run ctx) := rfl
 
-@[simp, grind =] theorem run_map [Monad m] (f : α → β) (x : ReaderT ρ m α) (ctx : ρ)
+@[simp] theorem run_map [Monad m] (f : α → β) (x : ReaderT ρ m α) (ctx : ρ)
     : (f <$> x).run ctx = f <$> x.run ctx := rfl
 
-@[simp, grind =] theorem run_monadLift [MonadLiftT n m] (x : n α) (ctx : ρ)
+@[simp] theorem run_monadLift [MonadLiftT n m] (x : n α) (ctx : ρ)
     : (monadLift x : ReaderT ρ m α).run ctx = (monadLift x : m α) := rfl
 
-@[simp, grind =] theorem run_monadMap [MonadFunctorT n m] (f : {β : Type u} → n β → n β) (x : ReaderT ρ m α) (ctx : ρ)
+@[simp] theorem run_monadMap [MonadFunctorT n m] (f : {β : Type u} → n β → n β) (x : ReaderT ρ m α) (ctx : ρ)
     : (monadMap @f x : ReaderT ρ m α).run ctx = monadMap @f (x.run ctx) := rfl
 
-@[simp, grind =] theorem run_read [Monad m] (ctx : ρ) : (ReaderT.read : ReaderT ρ m ρ).run ctx = pure ctx := rfl
+@[simp] theorem run_read [Monad m] (ctx : ρ) : (ReaderT.read : ReaderT ρ m ρ).run ctx = pure ctx := rfl
 
 @[simp] theorem run_seq {α β : Type u} [Monad m] (f : ReaderT ρ m (α → β)) (x : ReaderT ρ m α) (ctx : ρ)
     : (f <*> x).run ctx = (f.run ctx <*> x.run ctx) := rfl
@@ -176,39 +173,38 @@ instance [Monad m] [LawfulMonad m] : LawfulMonad (StateRefT' ω σ m) :=
 
 namespace StateT
 
-@[ext, grind ext] theorem ext {x y : StateT σ m α} (h : ∀ s, x.run s = y.run s) : x = y :=
+@[ext] theorem ext {x y : StateT σ m α} (h : ∀ s, x.run s = y.run s) : x = y :=
   funext h
 
-@[simp, grind =] theorem run'_eq [Monad m] (x : StateT σ m α) (s : σ) : run' x s = (·.1) <$> run x s :=
+@[simp] theorem run'_eq [Monad m] (x : StateT σ m α) (s : σ) : run' x s = (·.1) <$> run x s :=
   rfl
 
-@[simp, grind =] theorem run_pure [Monad m] (a : α) (s : σ) : (pure a : StateT σ m α).run s = pure (a, s) := rfl
+@[simp] theorem run_pure [Monad m] (a : α) (s : σ) : (pure a : StateT σ m α).run s = pure (a, s) := rfl
 
-@[simp, grind =] theorem run_bind [Monad m] (x : StateT σ m α) (f : α → StateT σ m β) (s : σ)
+@[simp] theorem run_bind [Monad m] (x : StateT σ m α) (f : α → StateT σ m β) (s : σ)
     : (x >>= f).run s = x.run s >>= λ p => (f p.1).run p.2 := by
   simp [bind, StateT.bind, run]
 
-@[simp, grind =] theorem run_map {α β σ : Type u} [Monad m] [LawfulMonad m] (f : α → β) (x : StateT σ m α) (s : σ) : (f <$> x).run s = (fun (p : α × σ) => (f p.1, p.2)) <$> x.run s := by
+@[simp] theorem run_map {α β σ : Type u} [Monad m] [LawfulMonad m] (f : α → β) (x : StateT σ m α) (s : σ) : (f <$> x).run s = (fun (p : α × σ) => (f p.1, p.2)) <$> x.run s := by
   simp [Functor.map, StateT.map, run, ←bind_pure_comp]
 
-@[simp, grind =] theorem run_get [Monad m] (s : σ)    : (get : StateT σ m σ).run s = pure (s, s) := rfl
+@[simp] theorem run_get [Monad m] (s : σ)    : (get : StateT σ m σ).run s = pure (s, s) := rfl
 
-@[simp, grind =] theorem run_set [Monad m] (s s' : σ) : (set s' : StateT σ m PUnit).run s = pure (⟨⟩, s') := rfl
+@[simp] theorem run_set [Monad m] (s s' : σ) : (set s' : StateT σ m PUnit).run s = pure (⟨⟩, s') := rfl
 
-@[simp, grind =] theorem run_modify [Monad m] (f : σ → σ) (s : σ) : (modify f : StateT σ m PUnit).run s = pure (⟨⟩, f s) := rfl
+@[simp] theorem run_modify [Monad m] (f : σ → σ) (s : σ) : (modify f : StateT σ m PUnit).run s = pure (⟨⟩, f s) := rfl
 
-@[simp, grind =] theorem run_modifyGet [Monad m] (f : σ → α × σ) (s : σ) : (modifyGet f : StateT σ m α).run s = pure ((f s).1, (f s).2) := by
+@[simp] theorem run_modifyGet [Monad m] (f : σ → α × σ) (s : σ) : (modifyGet f : StateT σ m α).run s = pure ((f s).1, (f s).2) := by
   simp [modifyGet, MonadStateOf.modifyGet, StateT.modifyGet, run]
 
-@[simp, grind =] theorem run_lift {α σ : Type u} [Monad m] (x : m α) (s : σ) : (StateT.lift x : StateT σ m α).run s = x >>= fun a => pure (a, s) := rfl
+@[simp] theorem run_lift {α σ : Type u} [Monad m] (x : m α) (s : σ) : (StateT.lift x : StateT σ m α).run s = x >>= fun a => pure (a, s) := rfl
 
-@[grind =]
 theorem run_bind_lift {α σ : Type u} [Monad m] [LawfulMonad m] (x : m α) (f : α → StateT σ m β) (s : σ) : (StateT.lift x >>= f).run s = x >>= fun a => (f a).run s := by
   simp [StateT.lift, StateT.run, bind, StateT.bind]
 
-@[simp, grind =] theorem run_monadLift {α σ : Type u} [Monad m] [MonadLiftT n m] (x : n α) (s : σ) : (monadLift x : StateT σ m α).run s = (monadLift x : m α) >>= fun a => pure (a, s) := rfl
+@[simp] theorem run_monadLift {α σ : Type u} [Monad m] [MonadLiftT n m] (x : n α) (s : σ) : (monadLift x : StateT σ m α).run s = (monadLift x : m α) >>= fun a => pure (a, s) := rfl
 
-@[simp, grind =] theorem run_monadMap [MonadFunctorT n m] (f : {β : Type u} → n β → n β) (x : StateT σ m α) (s : σ) :
+@[simp] theorem run_monadMap [MonadFunctorT n m] (f : {β : Type u} → n β → n β) (x : StateT σ m α) (s : σ) :
     (monadMap @f x : StateT σ m α).run s = monadMap @f (x.run s) := rfl
 
 @[simp] theorem run_seq {α β σ : Type u} [Monad m] [LawfulMonad m] (f : StateT σ m (α → β)) (x : StateT σ m α) (s : σ) : (f <*> x).run s = (f.run s >>= fun fs => (fun (p : α × σ) => (fs.1 p.1, p.2)) <$> x.run fs.2) := by

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

@@ -6,18 +6,12 @@ Authors: Quang Dao, Paul Reichert
 module
 
 prelude
-public import Init.Control.Option
-import all Init.Control.Option
-public import Init.Control.Except
-import all Init.Control.Except
-public import Init.Control.ExceptCps
-import all Init.Control.ExceptCps
-public import Init.Control.StateRef
-import all Init.Control.StateRef
-public import Init.Control.StateCps
-import all Init.Control.StateCps
-public import Init.Control.Id
-import all Init.Control.Id
+public import all Init.Control.Option
+public import all Init.Control.Except
+public import all Init.Control.ExceptCps
+public import all Init.Control.StateRef
+public import all Init.Control.StateCps
+public import all Init.Control.Id
 public import Init.Control.Lawful.MonadLift.Lemmas
 public import Init.Control.Lawful.Instances
 

src/Init/Conv.lean

@@ -290,17 +290,13 @@ macro "right" : conv => `(conv| rhs)
 /-- `intro` traverses into binders. Synonym for `ext`. -/
 macro "intro" xs:(ppSpace colGt binderIdent)* : conv => `(conv| ext $xs*)
 
-syntax enterPattern := "in " (occs)? term
-
-syntax enterArg := binderIdent <|> argArg <|> enterPattern
+syntax enterArg := binderIdent <|> argArg
 
 /-- `enter [arg, ...]` is a compact way to describe a path to a subterm.
 It is a shorthand for other conv tactics as follows:
 * `enter [i]` is equivalent to `arg i`.
 * `enter [@i]` is equivalent to `arg @i`.
 * `enter [x]` (where `x` is an identifier) is equivalent to `ext x`.
-* `enter [in e]` (where `e` is a term) is equivalent to `pattern e`.
-  Occurrences can be specified with `enter [in (occs := ...) e]`.
 For example, given the target `f (g a (fun x => x b))`, `enter [1, 2, x, 1]`
 will traverse to the subterm `b`. -/
 syntax (name := enter) "enter" " [" withoutPosition(enterArg,+) "]" : conv

src/Init/Core.lean

@@ -29,29 +29,6 @@ theorem id_def {α : Sort u} (a : α) : id a = a := rfl
 
 attribute [grind] id
 
-/--
-A helper gadget for instructing the kernel to eagerly reduce terms.
-
-When the gadget wraps the argument of an application, then when checking that
-the expected and inferred type of the argument match, the kernel will evaluate terms more eagerly.
-It is often used to wrap `Eq.refl true` proof terms as `eagerReduce (Eq.refl true)`
-when using proof by reflection.
-As an example, consider the theorem:
-```
-theorem eq_norm (ctx : Context) (p₁ p₂ : Poly) (h : (p₁.norm == p₂) = true) :
-  p₁.denote ctx = 0 → p₂.denote ctx = 0
-```
-The argument `h : (p₁.norm == p₂) = true` is a candidate for `eagerReduce`.
-When applying this theorem, we would write:
-
-```
-eq_norm ctx p q (eagerReduce (Eq.refl true)) h
-```
-to instruct the kernel to use eager reduction when establishing that `(p.norm == q) = true` is
-definitionally equal to `true = true`.
--/
-@[expose] def eagerReduce {α : Sort u} (a : α) : α := a
-
 /--
 `flip f a b` is `f b a`. It is useful for "point-free" programming,
 since it can sometimes be used to avoid introducing variables.
@@ -2522,17 +2499,12 @@ class Antisymm (r : α → α → Prop) : Prop where
   /-- An antisymmetric relation `r` satisfies `r a b → r b a → a = b`. -/
   antisymm (a b : α) : r a b → r b a → a = b
 
-/-- `Asymm r` means that the binary relation `r` is asymmetric, that is,
+/-- `Asymm X r` means that the binary relation `r` on `X` is asymmetric, that is,
 `r a b → ¬ r b a`. -/
 class Asymm (r : α → α → Prop) : Prop where
   /-- An asymmetric relation satisfies `r a b → ¬ r b a`. -/
   asymm : ∀ a b, r a b → ¬r b a
 
-/-- `Symm r` means that the binary relation `r` is symmetric, that is, `r a b → r b a`.  -/
-class Symm (r : α → α → Prop) : Prop where
-  /-- A symmetric relation satisfies `r a b → r b a`. -/
-  symm : ∀ a b, r a b → r b a
-
 /-- `Total X r` means that the binary relation `r` on `X` is total, that is, that for any
 `x y : X` we have `r x y` or `r y x`. -/
 class Total (r : α → α → Prop) : Prop where

src/Init/Data.lean

@@ -49,8 +49,5 @@ public import Init.Data.Vector
 public import Init.Data.Iterators
 public import Init.Data.Range.Polymorphic
 public import Init.Data.Slice
-public import Init.Data.Order
-public import Init.Data.Rat
-public import Init.Data.Dyadic
 
 public section

src/Init/Data/Array/Attach.lean

@@ -9,8 +9,7 @@ prelude
 public import Init.Data.Array.Mem
 public import Init.Data.Array.Lemmas
 public import Init.Data.Array.Count
-public import Init.Data.List.Attach
-import all Init.Data.List.Attach
+public import all Init.Data.List.Attach
 
 public section
 

src/Init/Data/Array/Basic.lean

@@ -10,11 +10,11 @@ public import Init.WFTactics
 public import Init.Data.Nat.Basic
 public import Init.Data.Fin.Basic
 public import Init.Data.UInt.BasicAux
+public import Init.Data.Repr
+public import Init.Data.ToString.Basic
 public import Init.GetElem
-public import Init.Data.List.ToArrayImpl
-import all Init.Data.List.ToArrayImpl
-public import Init.Data.Array.Set
-import all Init.Data.Array.Set
+public import all Init.Data.List.ToArrayImpl
+public import all Init.Data.Array.Set
 
 public section
 
@@ -162,8 +162,8 @@ This is a low-level version of `Array.size` that directly queries the runtime sy
 representation of arrays. While this is not provable, `Array.usize` always returns the exact size of
 the array since the implementation only supports arrays of size less than `USize.size`.
 -/
-@[extern "lean_array_size", simp, expose]
-def usize (xs : @& Array α) : USize := xs.size.toUSize
+@[extern "lean_array_size", simp]
+def usize (a : @& Array α) : USize := a.size.toUSize
 
 /--
 Low-level indexing operator which is as fast as a C array read.
@@ -171,8 +171,8 @@ Low-level indexing operator which is as fast as a C array read.
 This avoids overhead due to unboxing a `Nat` used as an index.
 -/
 @[extern "lean_array_uget", simp, expose]
-def uget (xs : @& Array α) (i : USize) (h : i.toNat < xs.size) : α :=
-  xs[i.toNat]
+def uget (a : @& Array α) (i : USize) (h : i.toNat < a.size) : α :=
+  a[i.toNat]
 
 /--
 Low-level modification operator which is as fast as a C array write. The modification is performed
@@ -441,7 +441,7 @@ def swapAt! (xs : Array α) (i : Nat) (v : α) : α × Array α :=
     swapAt xs i v
   else
     have : Inhabited (α × Array α) := ⟨(v, xs)⟩
-    panic! String.Internal.append (String.Internal.append "index " (toString i)) " out of bounds"
+    panic! ("index " ++ toString i ++ " out of bounds")
 
 /--
 Returns the first `n` elements of an array. The resulting array is produced by repeatedly calling
@@ -1165,7 +1165,7 @@ Examples:
 def zipIdx (xs : Array α) (start := 0) : Array (α × Nat) :=
   xs.mapIdx fun i a => (a, start + i)
 
-
+@[deprecated zipIdx (since := "2025-01-21")] abbrev zipWithIndex := @zipIdx
 
 /--
 Returns the first element of the array for which the predicate `p` returns `true`, or `none` if no
@@ -1285,7 +1285,7 @@ def findFinIdx? {α : Type u} (p : α → Bool) (as : Array α) : Option (Fin as
     decreasing_by simp_wf; decreasing_trivial_pre_omega
   loop 0
 
-private theorem findIdx?_loop_eq_map_findFinIdx?_loop_val {xs : Array α} {p : α → Bool} {j} :
+theorem findIdx?_loop_eq_map_findFinIdx?_loop_val {xs : Array α} {p : α → Bool} {j} :
     findIdx?.loop p xs j = (findFinIdx?.loop p xs j).map (·.val) := by
   unfold findIdx?.loop
   unfold findFinIdx?.loop
@@ -1322,7 +1322,8 @@ def idxOfAux [BEq α] (xs : Array α) (v : α) (i : Nat) : Option (Fin xs.size)
   else none
 decreasing_by simp_wf; decreasing_trivial_pre_omega
 
-
+@[deprecated idxOfAux (since := "2025-01-29")]
+abbrev indexOfAux := @idxOfAux
 
 /--
 Returns the index of the first element equal to `a`, or the size of the array if no element is equal
@@ -1337,7 +1338,8 @@ Examples:
 def finIdxOf? [BEq α] (xs : Array α) (v : α) : Option (Fin xs.size) :=
   idxOfAux xs v 0
 
-
+@[deprecated "`Array.indexOf?` has been deprecated, use `idxOf?` or `finIdxOf?` instead." (since := "2025-01-29")]
+abbrev indexOf? := @finIdxOf?
 
 /--
 Returns the index of the first element equal to `a`, or the size of the array if no element is equal
@@ -2167,7 +2169,7 @@ instance {α : Type u} [Repr α] : Repr (Array α) where
   reprPrec xs _ := Array.repr xs
 
 instance [ToString α] : ToString (Array α) where
-  toString xs := String.Internal.append "#" (toString xs.toList)
+  toString xs := "#" ++ toString xs.toList
 
 end Array
 

src/Init/Data/Array/BasicAux.lean

@@ -6,8 +6,7 @@ Authors: Leonardo de Moura
 module
 
 prelude
-public import Init.Data.Array.Basic
-import all Init.Data.Array.Basic
+public import all Init.Data.Array.Basic
 public import Init.Data.Nat.Linear
 public import Init.NotationExtra
 

src/Init/Data/Array/Bootstrap.lean

@@ -8,8 +8,7 @@ module
 
 prelude
 public import Init.Data.List.TakeDrop
-public import Init.Data.Array.Basic
-import all Init.Data.Array.Basic
+public import all Init.Data.Array.Basic
 
 public section
 
@@ -35,8 +34,8 @@ the index is in bounds. This is because the tactic itself needs to look up value
 arrays.
 -/
 @[deprecated "Use indexing notation `as[i]` instead" (since := "2025-02-17")]
-def get {α : Type u} (xs : @& Array α) (i : @& Nat) (h : LT.lt i xs.size) : α :=
-  xs.toList.get ⟨i, h⟩
+def get {α : Type u} (a : @& Array α) (i : @& Nat) (h : LT.lt i a.size) : α :=
+  a.toList.get ⟨i, h⟩
 
 /--
 Use the indexing notation `a[i]!` instead.
@@ -44,8 +43,8 @@ Use the indexing notation `a[i]!` instead.
 Access an element from an array, or panic if the index is out of bounds.
 -/
 @[deprecated "Use indexing notation `as[i]!` instead" (since := "2025-02-17"), expose]
-def get! {α : Type u} [Inhabited α] (xs : @& Array α) (i : @& Nat) : α :=
-  Array.getD xs i default
+def get! {α : Type u} [Inhabited α] (a : @& Array α) (i : @& Nat) : α :=
+  Array.getD a i default
 
 theorem foldlM_toList.aux [Monad m]
     {f : β → α → m β} {xs : Array α} {i j} (H : xs.size ≤ i + j) {b} :
@@ -124,9 +123,15 @@ abbrev pop_toList := @Array.toList_pop
 @[simp, grind =] theorem append_empty {xs : Array α} : xs ++ #[] = xs := by
   apply ext'; simp only [toList_append, List.append_nil]
 
+@[deprecated append_empty (since := "2025-01-13")]
+abbrev append_nil := @append_empty
+
 @[simp, grind =] theorem empty_append {xs : Array α} : #[] ++ xs = xs := by
   apply ext'; simp only [toList_append, List.nil_append]
 
+@[deprecated empty_append (since := "2025-01-13")]
+abbrev nil_append := @empty_append
+
 @[simp, grind _=_] theorem append_assoc {xs ys zs : Array α} : xs ++ ys ++ zs = xs ++ (ys ++ zs) := by
   apply ext'; simp only [toList_append, List.append_assoc]
 
@@ -137,6 +142,7 @@ abbrev pop_toList := @Array.toList_pop
   rw [← appendList_eq_append]; unfold Array.appendList
   induction l generalizing xs <;> simp [*]
 
-
+@[deprecated toList_appendList (since := "2024-12-11")]
+abbrev appendList_toList := @toList_appendList
 
 end Array

src/Init/Data/Array/Count.lean

@@ -6,8 +6,7 @@ Authors: Kim Morrison
 module
 
 prelude
-public import Init.Data.Array.Basic
-import all Init.Data.Array.Basic
+public import all Init.Data.Array.Basic
 public import Init.Data.Array.Lemmas
 public import Init.Data.List.Nat.Count
 

src/Init/Data/Array/DecidableEq.lean

@@ -6,8 +6,7 @@ Authors: Leonardo de Moura
 module
 
 prelude
-public import Init.Data.Array.Basic
-import all Init.Data.Array.Basic
+public import all Init.Data.Array.Basic
 public import Init.Data.BEq
 public import Init.Data.List.Nat.BEq
 public import Init.ByCases

src/Init/Data/Array/Erase.lean

@@ -6,8 +6,7 @@ Authors: Kim Morrison
 module
 
 prelude
-public import Init.Data.Array.Basic
-import all Init.Data.Array.Basic
+public import all Init.Data.Array.Basic
 public import Init.Data.Array.Lemmas
 public import Init.Data.List.Nat.Erase
 public import Init.Data.List.Nat.Basic

src/Init/Data/Array/Find.lean

@@ -7,8 +7,7 @@ module
 
 prelude
 public import Init.Data.List.Nat.Find
-public import Init.Data.Array.Basic
-import all Init.Data.Array.Basic
+public import all Init.Data.Array.Basic
 public import Init.Data.Array.Lemmas
 public import Init.Data.Array.Attach
 public import Init.Data.Array.Range
@@ -728,7 +727,7 @@ theorem isNone_findFinIdx? {xs : Array α} {p : α → Bool} :
   cases xs
   simp only [List.findFinIdx?_toArray, hf, List.findFinIdx?_subtype]
   rw [findFinIdx?_congr List.unattach_toArray]
-  simp only [Option.map_map, Function.comp_def, Fin.cast_cast]
+  simp only [Option.map_map, Function.comp_def, Fin.cast_trans]
   simp [Array.size]
 
 /-! ### idxOf

src/Init/Data/Array/Lemmas.lean

@@ -8,19 +8,19 @@ module
 prelude
 public import Init.Data.Nat.Lemmas
 public import Init.Data.List.Range
+public import all Init.Data.List.Control
 public import Init.Data.List.Nat.TakeDrop
 public import Init.Data.List.Nat.Modify
 public import Init.Data.List.Nat.Basic
 public import Init.Data.List.Monadic
 public import Init.Data.List.OfFn
+public import all Init.Data.Array.Bootstrap
 public import Init.Data.Array.Mem
 public import Init.Data.Array.DecidableEq
+public import Init.Data.Array.Lex.Basic
 public import Init.Data.Range.Lemmas
 public import Init.TacticsExtra
 public import Init.Data.List.ToArray
-import all Init.Data.List.Control
-import all Init.Data.Array.Basic
-import all Init.Data.Array.Bootstrap
 
 public section
 
@@ -311,7 +311,7 @@ theorem eq_push_pop_back!_of_size_ne_zero [Inhabited α] {xs : Array α} (h : xs
     xs = xs.pop.push xs.back! := by
   apply ext
   · simp [Nat.sub_add_cancel (Nat.zero_lt_of_ne_zero h)]
-  · intro i h h'
+  · intros i h h'
     if hlt : i < xs.pop.size then
       rw [getElem_push_lt (h:=hlt), getElem_pop]
     else
@@ -837,10 +837,15 @@ theorem mem_of_contains_eq_true [BEq α] [LawfulBEq α] {a : α} {as : Array α}
   cases as
   simp
 
-theorem contains_eq_true_of_mem [BEq α] [ReflBEq α] {a : α} {as : Array α} (h : a ∈ as) :
-    as.contains a = true := by
+@[deprecated mem_of_contains_eq_true (since := "2024-12-12")]
+abbrev mem_of_elem_eq_true := @mem_of_contains_eq_true
+
+theorem contains_eq_true_of_mem [BEq α] [LawfulBEq α] {a : α} {as : Array α} (h : a ∈ as) : as.contains a = true := by
   cases as
-  simpa using List.elem_eq_true_of_mem (Array.mem_toList_iff.mpr h)
+  simpa using h
+
+@[deprecated contains_eq_true_of_mem (since := "2024-12-12")]
+abbrev elem_eq_true_of_mem := @contains_eq_true_of_mem
 
 @[simp] theorem elem_eq_contains [BEq α] {a : α} {xs : Array α} :
     elem a xs = xs.contains a := by
@@ -899,9 +904,15 @@ theorem all_push {xs : Array α} {a : α} {p : α → Bool} :
   cases xs
   simp
 
+@[deprecated getElem_set_self (since := "2024-12-11")]
+abbrev getElem_set_eq := @getElem_set_self
+
 @[simp] theorem getElem?_set_self {xs : Array α} {i : Nat} (h : i < xs.size) {v : α} :
     (xs.set i v)[i]? = some v := by simp [h]
 
+@[deprecated getElem?_set_self (since := "2024-12-11")]
+abbrev getElem?_set_eq := @getElem?_set_self
+
 @[simp] theorem getElem_set_ne {xs : Array α} {i : Nat} (h' : i < xs.size) {v : α} {j : Nat}
     (pj : j < xs.size) (h : i ≠ j) :
     (xs.set i v)[j]'(by simp [*]) = xs[j] := by
@@ -992,6 +1003,9 @@ grind_pattern mem_or_eq_of_mem_set => a ∈ xs.set i b
 theorem setIfInBounds_def (xs : Array α) (i : Nat) (a : α) :
     xs.setIfInBounds i a = if h : i < xs.size then xs.set i a else xs := rfl
 
+@[deprecated set!_eq_setIfInBounds (since := "2024-12-12")]
+abbrev set!_is_setIfInBounds := @set!_eq_setIfInBounds
+
 @[simp, grind] theorem size_setIfInBounds {xs : Array α} {i : Nat} {a : α} :
     (xs.setIfInBounds i a).size = xs.size := by
   if h : i < xs.size  then
@@ -1013,6 +1027,9 @@ theorem setIfInBounds_def (xs : Array α) (i : Nat) (a : α) :
   simp at h
   simp only [setIfInBounds, h, ↓reduceDIte, getElem_set_self]
 
+@[deprecated getElem_setIfInBounds_self (since := "2024-12-11")]
+abbrev getElem_setIfInBounds_eq := @getElem_setIfInBounds_self
+
 @[simp] theorem getElem_setIfInBounds_ne {xs : Array α} {i : Nat} {a : α} {j : Nat}
     (hj : j < xs.size) (h : i ≠ j) :
     (xs.setIfInBounds i a)[j]'(by simpa using hj) = xs[j] := by
@@ -1032,6 +1049,9 @@ theorem getElem?_setIfInBounds_self_of_lt {xs : Array α} {i : Nat} {a : α} (h
     (xs.setIfInBounds i a)[i]? = some a := by
   simp [h]
 
+@[deprecated getElem?_setIfInBounds_self (since := "2024-12-11")]
+abbrev getElem?_setIfInBounds_eq := @getElem?_setIfInBounds_self
+
 @[simp] theorem getElem?_setIfInBounds_ne {xs : Array α} {i j : Nat} (h : i ≠ j) {a : α}  :
     (xs.setIfInBounds i a)[j]? = xs[j]? := by
   simp [getElem?_setIfInBounds, h]
@@ -1357,6 +1377,23 @@ theorem mapM_eq_mapM_toList [Monad m] [LawfulMonad m] {f : α → m β} {xs : Ar
     toList <$> xs.mapM f = xs.toList.mapM f := by
   simp [mapM_eq_mapM_toList]
 
+@[deprecated "Use `mapM_eq_foldlM` instead" (since := "2025-01-08")]
+theorem mapM_map_eq_foldl {as : Array α} {f : α → β} {i : Nat} :
+    mapM.map (m := Id) (pure <| f ·) as i b = pure (as.foldl (start := i) (fun acc a => acc.push (f a)) b) := by
+  unfold mapM.map
+  split <;> rename_i h
+  · ext : 1
+    dsimp [foldl, foldlM]
+    rw [mapM_map_eq_foldl, dif_pos (by omega), foldlM.loop, dif_pos h]
+    -- Calling `split` here gives a bad goal.
+    have : size as - i = Nat.succ (size as - i - 1) := by omega
+    rw [this]
+    simp [foldl, foldlM, Nat.sub_add_eq]
+  · dsimp [foldl, foldlM]
+    rw [dif_pos (by omega), foldlM.loop, dif_neg h]
+    rfl
+termination_by as.size - i
+
 /--
 Use this as `induction ass using array₂_induction` on a hypothesis of the form `ass : Array (Array α)`.
 The hypothesis `ass` will be replaced with a hypothesis `ass : List (List α)`,
@@ -2893,14 +2930,14 @@ theorem getElem_extract_loop_ge_aux {xs ys : Array α} {size start : Nat} (hge :
   exact Nat.sub_lt_left_of_lt_add hge h
 
 theorem getElem_extract_loop_ge {xs ys : Array α} {size start : Nat} (hge : i ≥ ys.size)
-    (h : i < (extract.loop xs size start ys).size) :
-    (extract.loop xs size start ys)[i] = xs[start + i - ys.size]'(getElem_extract_loop_ge_aux hge h) := by
+    (h : i < (extract.loop xs size start ys).size)
+    (h' := getElem_extract_loop_ge_aux hge h) :
+    (extract.loop xs size start ys)[i] = xs[start + i - ys.size] := by
   induction size using Nat.recAux generalizing start ys with
   | zero =>
     rw [size_extract_loop, Nat.zero_min, Nat.add_zero] at h
     omega
   | succ size ih =>
-    have h' : start + i - ys.size < xs.size := getElem_extract_loop_ge_aux hge h
     have : start < xs.size := by
       apply Nat.lt_of_le_of_lt (Nat.le_add_right start (i - ys.size))
       rwa [← Nat.add_sub_assoc hge]
@@ -2954,7 +2991,7 @@ theorem getElem?_extract {xs : Array α} {start stop : Nat} :
   apply List.ext_getElem
   · simp only [length_toList, size_extract, List.length_take, List.length_drop]
     omega
-  · intro n h₁ h₂
+  · intros n h₁ h₂
     simp
 
 @[simp] theorem extract_size {xs : Array α} : xs.extract 0 xs.size = xs := by
@@ -2962,6 +2999,9 @@ theorem getElem?_extract {xs : Array α} {start stop : Nat} :
   · rw [size_extract, Nat.min_self, Nat.sub_zero]
   · intros; rw [getElem_extract]; congr; rw [Nat.zero_add]
 
+@[deprecated extract_size (since := "2025-01-19")]
+abbrev extract_all := @extract_size
+
 theorem extract_empty_of_stop_le_start {xs : Array α} {start stop : Nat} (h : stop ≤ start) :
     xs.extract start stop = #[] := by
   simp only [extract, Nat.sub_eq, emptyWithCapacity_eq]
@@ -2996,14 +3036,14 @@ theorem take_size {xs : Array α} : xs.take xs.size = xs := by
 
 /-! ### shrink -/
 
-@[simp] private theorem size_shrink_loop {xs : Array α} {n : Nat} : (shrink.loop n xs).size = xs.size - n := by
+@[simp] theorem size_shrink_loop {xs : Array α} {n : Nat} : (shrink.loop n xs).size = xs.size - n := by
   induction n generalizing xs with
   | zero => simp [shrink.loop]
   | succ n ih =>
     simp [shrink.loop, ih]
     omega
 
-@[simp] private theorem getElem_shrink_loop {xs : Array α} {n i : Nat} (h : i < (shrink.loop n xs).size) :
+@[simp] theorem getElem_shrink_loop {xs : Array α} {n i : Nat} (h : i < (shrink.loop n xs).size) :
     (shrink.loop n xs)[i] = xs[i]'(by simp at h; omega) := by
   induction n generalizing xs i with
   | zero => simp [shrink.loop]
@@ -4279,7 +4319,7 @@ Examples:
 
 /-! ### Preliminaries about `ofFn` -/
 
-@[simp] private theorem size_ofFn_go {n} {f : Fin n → α} {i acc h} :
+@[simp] theorem size_ofFn_go {n} {f : Fin n → α} {i acc h} :
     (ofFn.go f acc i h).size = acc.size + i := by
   induction i generalizing acc with
   | zero => simp [ofFn.go]
@@ -4289,7 +4329,7 @@ Examples:
 @[simp] theorem size_ofFn {n : Nat} {f : Fin n → α} : (ofFn f).size = n := by simp [ofFn]
 
 -- Recall `ofFn.go f acc i h = acc ++ #[f (n - i), ..., f(n - 1)]`
-private theorem getElem_ofFn_go {f : Fin n → α} {acc i k} (h : i ≤ n) (w₁ : k < acc.size + i) :
+theorem getElem_ofFn_go {f : Fin n → α} {acc i k} (h : i ≤ n) (w₁ : k < acc.size + i) :
     (ofFn.go f acc i h)[k]'(by simpa using w₁) =
       if w₂ : k < acc.size then acc[k] else f ⟨n - i + k - acc.size, by omega⟩ := by
   induction i generalizing acc k with
@@ -4694,10 +4734,27 @@ end List
 /-! ### Deprecations -/
 namespace Array
 
+@[deprecated size_toArray (since := "2024-12-11")]
+theorem size_mk (as : List α) : (Array.mk as).size = as.length := by simp
+
+@[deprecated getElem?_eq_getElem (since := "2024-12-11")]
+theorem getElem?_lt
+    (xs : Array α) {i : Nat} (h : i < xs.size) : xs[i]? = some xs[i] := dif_pos h
+
+@[deprecated getElem?_eq_none (since := "2024-12-11")]
+theorem getElem?_ge
+    (xs : Array α) {i : Nat} (h : i ≥ xs.size) : xs[i]? = none := dif_neg (Nat.not_lt_of_le h)
+
 set_option linter.deprecated false in
 @[deprecated "`get?` is deprecated" (since := "2025-02-12"), simp]
 theorem get?_eq_getElem? (xs : Array α) (i : Nat) : xs.get? i = xs[i]? := rfl
 
+@[deprecated getElem?_eq_none (since := "2024-12-11")]
+theorem getElem?_len_le (xs : Array α) {i : Nat} (h : xs.size ≤ i) : xs[i]? = none := by
+  simp [h]
+
+@[deprecated getD_getElem? (since := "2024-12-11")] abbrev getD_get? := @getD_getElem?
+
 @[deprecated getD_eq_getD_getElem? (since := "2025-02-12")] abbrev getD_eq_get? := @getD_eq_getD_getElem?
 
 set_option linter.deprecated false in
@@ -4722,9 +4779,64 @@ theorem get?_eq_get?_toList (xs : Array α) (i : Nat) : xs.get? i = xs.toList.ge
 set_option linter.deprecated false in
 @[deprecated get!_eq_getD_getElem? (since := "2025-02-12")] abbrev get!_eq_get? := @get!_eq_getD_getElem?
 
+@[deprecated getElem_set_self (since := "2025-01-17")]
+theorem get_set_eq (xs : Array α) (i : Nat) (v : α) (h : i < xs.size) :
+    (xs.set i v h)[i]'(by simp [h]) = v := by
+  simp only [set, ← getElem_toList, List.getElem_set_self]
+
+@[deprecated Array.getElem_toList (since := "2024-12-08")]
+theorem getElem_eq_getElem_toList {xs : Array α} (h : i < xs.size) : xs[i] = xs.toList[i] := rfl
+
+@[deprecated Array.getElem?_toList (since := "2024-12-08")]
+theorem getElem?_eq_getElem?_toList (xs : Array α) (i : Nat) : xs[i]? = xs.toList[i]? := by
+  rw [getElem?_def]
+  split <;> simp_all
+
+@[deprecated LawfulGetElem.getElem?_def (since := "2024-12-08")]
+theorem getElem?_eq {xs : Array α} {i : Nat} :
+    xs[i]? = if h : i < xs.size then some xs[i] else none := by
+  rw [getElem?_def]
+
+/-! ### map -/
+
+@[deprecated "Use `toList_map` or `List.map_toArray` to characterize `Array.map`." (since := "2025-01-06")]
+theorem map_induction (xs : Array α) (f : α → β) (motive : Nat → Prop) (h0 : motive 0)
+    (p : Fin xs.size → β → Prop) (hs : ∀ i, motive i.1 → p i (f xs[i]) ∧ motive (i+1)) :
+    motive xs.size ∧
+      ∃ eq : (xs.map f).size = xs.size, ∀ i h, p ⟨i, h⟩ ((xs.map f)[i]) := by
+  have t := foldl_induction (as := xs) (β := Array β)
+    (motive := fun i xs => motive i ∧ xs.size = i ∧ ∀ i h2, p i xs[i.1])
+    (init := #[]) (f := fun acc a => acc.push (f a)) ?_ ?_
+  obtain ⟨m, eq, w⟩ := t
+  · refine ⟨m, by simp, ?_⟩
+    intro i h
+    simp only [eq] at w
+    specialize w ⟨i, h⟩ h
+    simpa using w
+  · exact ⟨h0, rfl, nofun⟩
+  · intro i bs ⟨m, ⟨eq, w⟩⟩
+    refine ⟨?_, ?_, ?_⟩
+    · exact (hs _ m).2
+    · simp_all
+    · intro j h
+      simp at h ⊢
+      by_cases h' : j < size bs
+      · rw [getElem_push]
+        simp_all
+      · rw [getElem_push, dif_neg h']
+        simp only [show j = i by omega]
+        exact (hs _ m).1
+
+set_option linter.deprecated false in
+@[deprecated "Use `toList_map` or `List.map_toArray` to characterize `Array.map`." (since := "2025-01-06")]
+theorem map_spec (xs : Array α) (f : α → β) (p : Fin xs.size → β → Prop)
+    (hs : ∀ i, p i (f xs[i])) :
+    ∃ eq : (xs.map f).size = xs.size, ∀ i h, p ⟨i, h⟩ ((xs.map f)[i]) := by
+  simpa using map_induction xs f (fun _ => True) trivial p (by simp_all)
+
 /-! ### set -/
 
-@[deprecated getElem?_set_self (since := "2025-02-27")] abbrev get?_set_eq := @getElem?_set_self
+@[deprecated getElem?_set_eq (since := "2025-02-27")] abbrev get?_set_eq := @getElem?_set_self
 @[deprecated getElem?_set_ne (since := "2025-02-27")] abbrev get?_set_ne := @getElem?_set_ne
 @[deprecated getElem?_set (since := "2025-02-27")] abbrev get?_set := @getElem?_set
 @[deprecated get_set (since := "2025-02-27")] abbrev get_set := @getElem_set

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

@@ -12,12 +12,9 @@ public import Init.Data.Array.Lemmas
 public import Init.Data.List.Lex
 import Init.Data.Range.Polymorphic.Lemmas
 import Init.Data.Range.Polymorphic.NatLemmas
-import Init.Data.Order.Lemmas
 
 public section
 
-open Std
-
 set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
 set_option linter.indexVariables true -- Enforce naming conventions for index variables.
 
@@ -31,8 +28,8 @@ namespace Array
 @[simp] theorem lt_toList [LT α] {xs ys : Array α} : xs.toList < ys.toList ↔ xs < ys := Iff.rfl
 @[simp] theorem le_toList [LT α] {xs ys : Array α} : xs.toList ≤ ys.toList ↔ xs ≤ ys := Iff.rfl
 
-grind_pattern _root_.List.lt_toArray => l₁.toArray < l₂.toArray
-grind_pattern _root_.List.le_toArray => l₁.toArray ≤ l₂.toArray
+grind_pattern _root_.List.lt_toArray =>  l₁.toArray < l₂.toArray
+grind_pattern _root_.List.le_toArray =>  l₁.toArray ≤ l₂.toArray
 grind_pattern lt_toList => xs.toList < ys.toList
 grind_pattern le_toList => xs.toList ≤ ys.toList
 
@@ -70,8 +67,8 @@ private theorem cons_lex_cons [BEq α] {lt : α → α → Bool} {a b : α} {xs
     rw [cons_lex_cons.forIn'_congr_aux Std.PRange.toList_eq_match rfl (fun _ _ _ => rfl)]
     simp only [Std.PRange.SupportsUpperBound.IsSatisfied, bind_pure_comp, map_pure]
     rw [cons_lex_cons.forIn'_congr_aux (if_pos (by omega)) rfl (fun _ _ _ => rfl)]
-  simp only [Std.PRange.toList_Rox_eq_toList_Rcx_of_isSome_succ? (lo := 0) (h := rfl),
-    Std.PRange.UpwardEnumerable.succ?, Nat.add_comm 1, Std.PRange.Nat.toList_Rco_succ_succ,
+  simp only [Std.PRange.toList_open_eq_toList_closed_of_isSome_succ? (lo := 0) (h := rfl),
+    Std.PRange.UpwardEnumerable.succ?, Nat.add_comm 1, Std.PRange.Nat.ClosedOpen.toList_succ_succ,
     Option.get_some, List.forIn'_cons, List.size_toArray, List.length_cons, List.length_nil,
     Nat.lt_add_one, getElem_append_left, List.getElem_toArray, List.getElem_cons_zero]
   cases lt a b
@@ -103,14 +100,6 @@ theorem singleton_lex_singleton [BEq α] {lt : α → α → Bool} : #[a].lex #[
     xs.toList.lex ys.toList lt = xs.lex ys lt := by
   cases xs <;> cases ys <;> simp
 
-instance [LT α] [LE α] [LawfulOrderLT α] [IsLinearOrder α] : IsLinearOrder (Array α) := by
-  apply IsLinearOrder.of_le
-  · constructor
-    intro _ _ hab hba
-    simpa using Std.le_antisymm (α := List α) hab hba
-  · constructor; exact Std.le_trans (α := List α)
-  · constructor; exact fun _ _ => Std.le_total (α := List α)
-
 protected theorem lt_irrefl [LT α] [Std.Irrefl (· < · : α → α → Prop)] (xs : Array α) : ¬ xs < xs :=
   List.lt_irrefl xs.toList
 
@@ -142,35 +131,27 @@ instance [LT α] [Trans (· < · : α → α → Prop) (· < ·) (· < ·)] :
     Trans (· < · : Array α → Array α → Prop) (· < ·) (· < ·) where
   trans h₁ h₂ := Array.lt_trans h₁ h₂
 
-protected theorem lt_of_le_of_lt [LE α] [LT α] [LawfulOrderLT α] [IsLinearOrder α]
-    {xs ys zs : Array α} (h₁ : xs ≤ ys) (h₂ : ys < zs) : xs < zs :=
-  Std.lt_of_le_of_lt (α := List α) h₁ h₂
-
-@[deprecated Array.lt_of_le_of_lt (since := "2025-08-01")]
-protected theorem lt_of_le_of_lt' [LT α]
+protected theorem lt_of_le_of_lt [LT α]
+    [i₀ : Std.Irrefl (· < · : α → α → Prop)]
     [i₁ : Std.Asymm (· < · : α → α → Prop)]
     [i₂ : Std.Antisymm (¬ · < · : α → α → Prop)]
     [i₃ : Trans (¬ · < · : α → α → Prop) (¬ · < ·) (¬ · < ·)]
     {xs ys zs : Array α} (h₁ : xs ≤ ys) (h₂ : ys < zs) : xs < zs :=
-  letI := LE.ofLT α
-  haveI : IsLinearOrder α := IsLinearOrder.of_lt
-  Array.lt_of_le_of_lt h₁ h₂
+  List.lt_of_le_of_lt h₁ h₂
 
-protected theorem le_trans [LE α] [LT α] [LawfulOrderLT α] [IsLinearOrder α]
+protected theorem le_trans [LT α]
+    [Std.Irrefl (· < · : α → α → Prop)]
+    [Std.Asymm (· < · : α → α → Prop)]
+    [Std.Antisymm (¬ · < · : α → α → Prop)]
+    [Trans (¬ · < · : α → α → Prop) (¬ · < ·) (¬ · < ·)]
     {xs ys zs : Array α} (h₁ : xs ≤ ys) (h₂ : ys ≤ zs) : xs ≤ zs :=
   fun h₃ => h₁ (Array.lt_of_le_of_lt h₂ h₃)
 
-@[deprecated Array.le_trans (since := "2025-08-01")]
-protected theorem le_trans' [LT α]
-    [i₁ : Std.Asymm (· < · : α → α → Prop)]
-    [i₂ : Std.Antisymm (¬ · < · : α → α → Prop)]
-    [i₃ : Trans (¬ · < · : α → α → Prop) (¬ · < ·) (¬ · < ·)]
-    {xs ys zs : Array α} (h₁ : xs ≤ ys) (h₂ : ys ≤ zs) : xs ≤ zs :=
-  letI := LE.ofLT α
-  haveI : IsLinearOrder α := IsLinearOrder.of_lt
-  Array.le_trans h₁ h₂
-
-instance [LE α] [LT α] [LawfulOrderLT α] [IsLinearOrder α] :
+instance [LT α]
+    [Std.Irrefl (· < · : α → α → Prop)]
+    [Std.Asymm (· < · : α → α → Prop)]
+    [Std.Antisymm (¬ · < · : α → α → Prop)]
+    [Trans (¬ · < · : α → α → Prop) (¬ · < ·) (¬ · < ·)] :
     Trans (· ≤ · : Array α → Array α → Prop) (· ≤ ·) (· ≤ ·) where
   trans h₁ h₂ := Array.le_trans h₁ h₂
 
@@ -184,7 +165,7 @@ instance [LT α]
   asymm _ _ := Array.lt_asymm
 
 protected theorem le_total [LT α]
-    [i : Std.Asymm (· < · : α → α → Prop)] (xs ys : Array α) : xs ≤ ys ∨ ys ≤ xs :=
+    [i : Std.Total (¬ · < · : α → α → Prop)] (xs ys : Array α) : xs ≤ ys ∨ ys ≤ xs :=
   List.le_total xs.toList ys.toList
 
 @[simp] protected theorem not_lt [LT α]
@@ -194,22 +175,19 @@ protected theorem le_total [LT α]
     {xs ys : Array α} : ¬ ys ≤ xs ↔ xs < ys := Classical.not_not
 
 protected theorem le_of_lt [LT α]
-    [i : Std.Asymm (· < · : α → α → Prop)]
+    [i : Std.Total (¬ · < · : α → α → Prop)]
     {xs ys : Array α} (h : xs < ys) : xs ≤ ys :=
   List.le_of_lt h
 
 protected theorem le_iff_lt_or_eq [LT α]
     [Std.Irrefl (· < · : α → α → Prop)]
     [Std.Antisymm (¬ · < · : α → α → Prop)]
-    [Std.Asymm (· < · : α → α → Prop)]
+    [Std.Total (¬ · < · : α → α → Prop)]
     {xs ys : Array α} : xs ≤ ys ↔ xs < ys ∨ xs = ys := by
   simpa using List.le_iff_lt_or_eq (l₁ := xs.toList) (l₂ := ys.toList)
 
-protected theorem le_antisymm [LT α] [LE α] [IsLinearOrder α] [LawfulOrderLT α]
-    {xs ys : Array α} : xs ≤ ys → ys ≤ xs → xs = ys := by
-  simpa using List.le_antisymm (as := xs.toList) (bs := ys.toList)
-
-instance [LT α] [Std.Asymm (· < · : α → α → Prop)] :
+instance [LT α]
+    [Std.Total (¬ · < · : α → α → Prop)] :
     Std.Total (· ≤ · : Array α → Array α → Prop) where
   total := Array.le_total
 
@@ -288,6 +266,7 @@ protected theorem lt_iff_exists [LT α] {xs ys : Array α} :
   simp [List.lt_iff_exists]
 
 protected theorem le_iff_exists [LT α]
+    [Std.Irrefl (· < · : α → α → Prop)]
     [Std.Asymm (· < · : α → α → Prop)]
     [Std.Antisymm (¬ · < · : α → α → Prop)] {xs ys : Array α} :
     xs ≤ ys ↔
@@ -307,6 +286,7 @@ theorem append_left_lt [LT α] {xs ys zs : Array α} (h : ys < zs) :
   simpa using List.append_left_lt h
 
 theorem append_left_le [LT α]
+    [Std.Irrefl (· < · : α → α → Prop)]
     [Std.Asymm (· < · : α → α → Prop)]
     [Std.Antisymm (¬ · < · : α → α → Prop)]
     {xs ys zs : Array α} (h : ys ≤ zs) :
@@ -330,8 +310,10 @@ protected theorem map_lt [LT α] [LT β]
   simpa using List.map_lt w h
 
 protected theorem map_le [LT α] [LT β]
+    [Std.Irrefl (· < · : α → α → Prop)]
     [Std.Asymm (· < · : α → α → Prop)]
     [Std.Antisymm (¬ · < · : α → α → Prop)]
+    [Std.Irrefl (· < · : β → β → Prop)]
     [Std.Asymm (· < · : β → β → Prop)]
     [Std.Antisymm (¬ · < · : β → β → Prop)]
     {xs ys : Array α} {f : α → β} (w : ∀ x y, x < y → f x < f y) (h : xs ≤ ys) :

src/Init/Data/Array/MapIdx.lean

@@ -6,13 +6,11 @@ Authors: Mario Carneiro, Kim Morrison
 module
 
 prelude
-public import Init.Data.Array.Basic
-import all Init.Data.Array.Basic
+public import all Init.Data.Array.Basic
 public import Init.Data.Array.Lemmas
 public import Init.Data.Array.Attach
 public import Init.Data.Array.OfFn
-public import Init.Data.List.MapIdx
-import all Init.Data.List.MapIdx
+public import all Init.Data.List.MapIdx
 
 public section
 
@@ -62,7 +60,7 @@ theorem mapFinIdx_spec {xs : Array α} {f : (i : Nat) → α → (h : i < xs.siz
 @[simp, grind =] theorem size_zipIdx {xs : Array α} {k : Nat} : (xs.zipIdx k).size = xs.size :=
   Array.size_mapFinIdx
 
-
+@[deprecated size_zipIdx (since := "2025-01-21")] abbrev size_zipWithIndex := @size_zipIdx
 
 @[simp, grind =] theorem getElem_mapFinIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {i : Nat}
     (h : i < (xs.mapFinIdx f).size) :
@@ -134,20 +132,23 @@ namespace Array
     (xs.zipIdx k)[i] = (xs[i]'(by simp_all), k + i) := by
   simp [zipIdx]
 
-
+@[deprecated getElem_zipIdx (since := "2025-01-21")]
+abbrev getElem_zipWithIndex := @getElem_zipIdx
 
 @[simp, grind =] theorem zipIdx_toArray {l : List α} {k : Nat} :
     l.toArray.zipIdx k = (l.zipIdx k).toArray := by
   ext i hi₁ hi₂ <;> simp
 
-
+@[deprecated zipIdx_toArray (since := "2025-01-21")]
+abbrev zipWithIndex_toArray := @zipIdx_toArray
 
 @[simp, grind =] theorem toList_zipIdx {xs : Array α} {k : Nat} :
     (xs.zipIdx k).toList = xs.toList.zipIdx k := by
   rcases xs with ⟨xs⟩
   simp
 
-
+@[deprecated toList_zipIdx (since := "2025-01-21")]
+abbrev toList_zipWithIndex := @toList_zipIdx
 
 theorem mk_mem_zipIdx_iff_le_and_getElem?_sub {k i : Nat} {x : α} {xs : Array α} :
     (x, i) ∈ xs.zipIdx k ↔ k ≤ i ∧ xs[i - k]? = some x := by
@@ -172,7 +173,11 @@ theorem mem_zipIdx_iff_getElem? {x : α × Nat} {xs : Array α} :
     x ∈ xs.zipIdx ↔ xs[x.2]? = some x.1 := by
   rw [mk_mem_zipIdx_iff_getElem?]
 
+@[deprecated mk_mem_zipIdx_iff_getElem? (since := "2025-01-21")]
+abbrev mk_mem_zipWithIndex_iff_getElem? := @mk_mem_zipIdx_iff_getElem?
 
+@[deprecated mem_zipIdx_iff_getElem? (since := "2025-01-21")]
+abbrev mem_zipWithIndex_iff_getElem? := @mem_zipIdx_iff_getElem?
 
 /-! ### mapFinIdx -/
 
@@ -217,7 +222,8 @@ theorem mapFinIdx_eq_zipIdx_map {xs : Array α} {f : (i : Nat) → α → (h : i
         f i x (by simp [mk_mem_zipIdx_iff_getElem?, getElem?_eq_some_iff] at m; exact m.1) := by
   ext <;> simp
 
-
+@[deprecated mapFinIdx_eq_zipIdx_map (since := "2025-01-21")]
+abbrev mapFinIdx_eq_zipWithIndex_map := @mapFinIdx_eq_zipIdx_map
 
 @[simp]
 theorem mapFinIdx_eq_empty_iff {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
@@ -326,7 +332,8 @@ theorem mapIdx_eq_zipIdx_map {xs : Array α} {f : Nat → α → β} :
     xs.mapIdx f = xs.zipIdx.map fun ⟨a, i⟩ => f i a := by
   ext <;> simp
 
-
+@[deprecated mapIdx_eq_zipIdx_map (since := "2025-01-21")]
+abbrev mapIdx_eq_zipWithIndex_map := @mapIdx_eq_zipIdx_map
 
 @[grind =]
 theorem mapIdx_append {xs ys : Array α} :

src/Init/Data/Array/Monadic.lean

@@ -6,10 +6,8 @@ Authors: Kim Morrison
 module
 
 prelude
-public import Init.Data.List.Control
-import all Init.Data.List.Control
-public import Init.Data.Array.Basic
-import all Init.Data.Array.Basic
+public import all Init.Data.List.Control
+public import all Init.Data.Array.Basic
 public import Init.Data.Array.Lemmas
 public import Init.Data.Array.Attach
 public import Init.Data.List.Monadic

src/Init/Data/Array/OfFn.lean

@@ -6,8 +6,7 @@ Authors: Kim Morrison
 module
 
 prelude
-public import Init.Data.Array.Basic
-import all Init.Data.Array.Basic
+public import all Init.Data.Array.Basic
 public import Init.Data.Array.Lemmas
 public import Init.Data.Array.Monadic
 public import Init.Data.List.OfFn

src/Init/Data/Array/Perm.lean

@@ -7,8 +7,7 @@ module
 
 prelude
 public import Init.Data.List.Nat.Perm
-public import Init.Data.Array.Basic
-import all Init.Data.Array.Basic
+public import all Init.Data.Array.Basic
 public import Init.Data.Array.Lemmas
 
 public section

src/Init/Data/Array/QSort/Basic.lean

@@ -7,7 +7,7 @@ module
 
 prelude
 public import Init.Data.Vector.Basic
-public import Init.Data.Ord.Basic
+public import Init.Data.Ord
 
 public section
 

src/Init/Data/Array/Range.lean

@@ -7,10 +7,8 @@ module
 
 prelude
 public import Init.Data.Array.Lemmas
-public import Init.Data.Array.Basic
-import all Init.Data.Array.Basic
-public import Init.Data.Array.OfFn
-import all Init.Data.Array.OfFn
+public import all Init.Data.Array.Basic
+public import all Init.Data.Array.OfFn
 public import Init.Data.Array.MapIdx
 public import Init.Data.Array.Zip
 public import Init.Data.List.Nat.Range

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

@@ -8,8 +8,7 @@ module
 
 prelude
 public import Init.Data.Array.Basic
-public import Init.Data.Array.Subarray
-import all Init.Data.Array.Subarray
+public import all Init.Data.Array.Subarray
 public import Init.Omega
 
 public section

src/Init/Data/Array/TakeDrop.lean

@@ -6,8 +6,7 @@ Authors: Markus Himmel
 module
 
 prelude
-public import Init.Data.Array.Basic
-import all Init.Data.Array.Basic
+public import all Init.Data.Array.Basic
 public import Init.Data.Array.Lemmas
 public import Init.Data.List.Nat.TakeDrop
 

src/Init/Data/Array/Zip.lean

@@ -6,8 +6,7 @@ Authors: Kim Morrison
 module
 
 prelude
-public import Init.Data.Array.Basic
-import all Init.Data.Array.Basic
+public import all Init.Data.Array.Basic
 public import Init.Data.Array.TakeDrop
 public import Init.Data.List.Zip
 
@@ -231,9 +230,11 @@ theorem zip_map {f : α → γ} {g : β → δ} {as : Array α} {bs : Array β}
   cases bs
   simp [List.zip_map]
 
+@[grind _=_]
 theorem zip_map_left {f : α → γ} {as : Array α} {bs : Array β} :
     zip (as.map f) bs = (zip as bs).map (Prod.map f id) := by rw [← zip_map, map_id]
 
+@[grind _=_]
 theorem zip_map_right {f : β → γ} {as : Array α} {bs : Array β} :
     zip as (bs.map f) = (zip as bs).map (Prod.map id f) := by rw [← zip_map, map_id]
 

src/Init/Data/BEq.lean

@@ -23,14 +23,11 @@ class PartialEquivBEq (α) [BEq α] : Prop where
   /-- Transitivity for `BEq`. If `a == b` and `b == c` then `a == c`. -/
   trans : (a : α) == b → b == c → a == c
 
-instance [BEq α] [PartialEquivBEq α] : Std.Symm (α := α) (· == ·) where
-  symm _ _ h := PartialEquivBEq.symm h
-
 /-- `EquivBEq` says that the `BEq` implementation is an equivalence relation. -/
 class EquivBEq (α) [BEq α] : Prop extends PartialEquivBEq α, ReflBEq α
 
-theorem BEq.symm [BEq α] [Std.Symm (α := α) (· == ·)] {a b : α} : a == b → b == a :=
-  Std.Symm.symm a b (r := (· == ·))
+theorem BEq.symm [BEq α] [PartialEquivBEq α] {a b : α} : a == b → b == a :=
+  PartialEquivBEq.symm
 
 theorem BEq.comm [BEq α] [PartialEquivBEq α] {a b : α} : (a == b) = (b == a) :=
   Bool.eq_iff_iff.2 ⟨BEq.symm, BEq.symm⟩

src/Init/Data/BitVec/Basic.lean

@@ -9,7 +9,7 @@ prelude
 public import Init.Data.Fin.Basic
 public import Init.Data.Nat.Bitwise.Lemmas
 public import Init.Data.Nat.Power2
-public import Init.Data.Int.Bitwise.Basic
+public import Init.Data.Int.Bitwise
 public import Init.Data.BitVec.BasicAux
 
 @[expose] public section
@@ -206,13 +206,10 @@ Converts a bitvector into a fixed-width hexadecimal number with enough digits to
 
 If `n` is `0`, then one digit is returned. Otherwise, `⌊(n + 3) / 4⌋` digits are returned.
 -/
--- If we ever want to prove something about this, we can avoid having to use the opaque
--- `Internal` string functions by moving this definition out to a separate file that can live
--- downstream of `Init.Data.String.Basic`.
 protected def toHex {n : Nat} (x : BitVec n) : String :=
   let s := (Nat.toDigits 16 x.toNat).asString
-  let t := (List.replicate ((n+3) / 4 - String.Internal.length s) '0').asString
-  String.Internal.append t s
+  let t := (List.replicate ((n+3) / 4 - s.length) '0').asString
+  t ++ s
 
 /-- `BitVec` representation. -/
 protected def BitVec.repr (a : BitVec n) : Std.Format :=

src/Init/Data/BitVec/BasicAux.lean

@@ -21,6 +21,13 @@ namespace BitVec
 
 section Nat
 
+/--
+The bitvector with value `i mod 2^n`.
+-/
+@[expose, match_pattern]
+protected def ofNat (n : Nat) (i : Nat) : BitVec n where
+  toFin := Fin.ofNat (2^n) i
+
 instance instOfNat : OfNat (BitVec n) i where ofNat := .ofNat n i
 
 /-- Return the bound in terms of toNat. -/

src/Init/Data/BitVec/Bitblast.lean

@@ -6,14 +6,11 @@ Authors: Harun Khan, Abdalrhman M Mohamed, Joe Hendrix, Siddharth Bhat
 module
 
 prelude
-public import Init.Data.Nat.Bitwise.Basic
-import all Init.Data.Nat.Bitwise.Basic
+public import all Init.Data.Nat.Bitwise.Basic
 public import Init.Data.Nat.Mod
-public import Init.Data.Int.DivMod
-import all Init.Data.Int.DivMod
+public import all Init.Data.Int.DivMod
 public import Init.Data.Int.LemmasAux
-public import Init.Data.BitVec.Basic
-import all Init.Data.BitVec.Basic
+public import all Init.Data.BitVec.Basic
 public import Init.Data.BitVec.Decidable
 public import Init.Data.BitVec.Lemmas
 public import Init.Data.BitVec.Folds
@@ -341,11 +338,11 @@ theorem add_eq_or_of_and_eq_zero {w : Nat} (x y : BitVec w)
   · rfl
   · simp only [adcb, atLeastTwo, Bool.and_false, Bool.or_false, bne_false,
     Prod.mk.injEq, and_eq_false_imp]
-    intro i
+    intros i
     replace h : (x &&& y).getLsbD i = (0#w).getLsbD i := by rw [h]
     simp only [getLsbD_and, getLsbD_zero, and_eq_false_imp] at h
     constructor
-    · intro hx
+    · intros hx
       simp_all
     · by_cases hx : x.getLsbD i <;> simp_all
 
@@ -1669,7 +1666,7 @@ private theorem neg_udiv_eq_intMin_iff_eq_intMin_eq_one_of_msb_eq_true
     {x y : BitVec w} (hx : x.msb = true) (hy : y.msb = false) :
     -x / y = intMin w ↔ (x = intMin w ∧ y = 1#w) := by
   constructor
-  · intro h
+  · intros h
     rcases w with _ | w; decide +revert
     have : (-x / y).msb = true := by simp [h, msb_intMin]
     rw [msb_udiv] at this
@@ -1745,7 +1742,7 @@ theorem msb_sdiv_eq_decide {x y : BitVec w} :
         Bool.and_self, ne_zero_of_msb_true, decide_false, Bool.and_true, Bool.true_and, Bool.not_true,
         Bool.false_and, Bool.or_false, bool_to_prop]
       have : x / -y ≠ intMin (w + 1) := by
-        intro h
+        intros h
         have : (x / -y).msb = (intMin (w + 1)).msb := by simp only [h]
         simp only [msb_udiv, msb_intMin, show 0 < w + 1 by omega, decide_true, and_eq_true, beq_iff_eq] at this
         obtain ⟨hcontra, _⟩ := this
@@ -1874,7 +1871,7 @@ theorem toInt_dvd_toInt_iff {x y : BitVec w} :
     y.toInt ∣ x.toInt ↔ (if x.msb then -x else x) % (if y.msb then -y else y) = 0#w := by
   constructor
   <;> by_cases hxmsb : x.msb <;> by_cases hymsb: y.msb
-  <;> intro h
+  <;> intros h
   <;> simp only [hxmsb, hymsb, reduceIte, false_eq_true, toNat_eq, toNat_umod, toNat_ofNat,
         zero_mod, toInt_eq_neg_toNat_neg_of_msb_true, Int.dvd_neg, Int.neg_dvd,
         toInt_eq_toNat_of_msb] at h
@@ -2144,7 +2141,7 @@ theorem add_shiftLeft_eq_or_shiftLeft {x y : BitVec w} :
   ext i hi
   simp only [shiftLeft_eq', getElem_and, getElem_shiftLeft, getElem_zero, and_eq_false_imp,
     not_eq_eq_eq_not, Bool.not_true, decide_eq_false_iff_not, Nat.not_lt]
-  intro hxi hxval
+  intros hxi hxval
   have : 2^i ≤ x.toNat := two_pow_le_toNat_of_getElem_eq_true hi hxi
   have : i < 2^i := by exact Nat.lt_two_pow_self
   omega
@@ -2155,238 +2152,4 @@ theorem shiftLeft_add_eq_shiftLeft_or {x y : BitVec w} :
     (y <<< x) + x =  (y <<< x) ||| x := by
   rw [BitVec.add_comm, add_shiftLeft_eq_or_shiftLeft, or_comm]
 
-/- ### Fast Circuit For Unsigned Overflow Detection -/
-
-/-!
-# Note [Fast Unsigned Multiplication Overflow Detection]
-
-The fast unsigned multiplication overflow detection circuit is described in
-`Efficient integer multiplication overflow detection circuits` (https://ieeexplore.ieee.org/abstract/document/987767).
-With this circuit, the computation of the overflow flag for the unsigned multiplication of
-two bitvectors `x` and `y` with bitwidth `w` requires:
-· extending the operands by `1` bit and performing the multiplication with the extended operands,
-· computing the preliminary overflow flag, which describes whether `x` and `y` together have at most
-  `w - 2` leading zeros.
-If the most significant bit of the extended operands' multiplication is `true` or if the
-preliminary overflow flag is `true`, overflow happens.
-In particular, the conditions check two different cases:
-· if the most significant bit of the extended operands' multiplication is `true`, the result of the
-  multiplication 2 ^ w ≤ x.toNat * y.toNat < 2 ^ (w + 1),
-· if the preliminary flag is true, then 2 ^ (w + 1) ≤ x.toNat * y.toNat.
-
-The computation of the preliminary overflow flag `resRec` relies on two quantities:
-· `uppcRec`: the unsigned parallel prefix circuit for the bits until a certain `i`,
-· `aandRec`: the conjunction between the parallel prefix circuit at of the first operand until a certain `i`
-  and the `i`-th bit in the second operand.
--/
-
-/--
-  `uppcRec` is the unsigned parallel prefix, `x.uppcRec s = true` iff `x.toNat` is greater or equal
-  than `2 ^ (w - 1 - (s - 1))`.
--/
-def uppcRec {w} (x : BitVec w) (s : Nat) (hs : s < w) : Bool :=
-  match s with
-  | 0 => x.msb
-  | i + 1 =>  x[w - 1 - i] || uppcRec x i (by omega)
-
-/-- The unsigned parallel prefix of `x` at `s` is `true` if and only if x interpreted
-  as a natural number is greater or equal than `2 ^ (w - 1 - (s - 1))`. -/
-@[simp]
-theorem uppcRec_true_iff (x : BitVec w) (s : Nat) (h : s < w) :
-    uppcRec x s h ↔ 2 ^ (w - 1 - (s - 1)) ≤ x.toNat := by
-  rcases w with _|w
-  · omega
-  · induction s
-    · case succ.zero =>
-      simp only [uppcRec, msb_eq_true_iff_two_mul_ge, Nat.pow_add, Nat.pow_one,
-        Nat.mul_comm (2 ^ w) 2, ge_iff_le, Nat.add_one_sub_one, zero_le, Nat.sub_eq_zero_of_le,
-        Nat.sub_zero]
-      apply Nat.mul_le_mul_left_iff (by omega)
-    · case succ.succ s ihs =>
-      simp only [uppcRec, or_eq_true, ihs, Nat.add_one_sub_one]
-      have := Nat.pow_le_pow_of_le (a := 2) ( n := (w - s)) (m := (w - (s - 1))) (by omega) (by omega)
-      constructor
-      · intro h'
-        rcases h' with h'|h'
-        · apply ge_two_pow_of_testBit h'
-        · omega
-      · intro h'
-        by_cases hbit: x[w - s]
-        · simp [hbit]
-        · have := BitVec.le_toNat_iff_getLsbD_eq_true (x := x) (i := w - s) (by omega)
-          simp only [h', true_iff] at this
-          obtain ⟨k, hk⟩ := this
-          by_cases hwk : w - s + k < w + 1
-          · by_cases hk' : 0 < k
-            · have hle := ge_two_pow_of_testBit hk
-              have hpowle := Nat.pow_le_pow_of_le (a := 2) ( n := (w - (s - 1))) (m := (w - s + k)) (by omega) (by omega)
-              omega
-            · rw [getLsbD_eq_getElem (by omega)] at hk
-              simp [hbit, show k = 0 by omega] at hk
-          · simp_all
-
-/--
-  Conjunction for fast umulOverflow circuit
--/
-def aandRec (x y : BitVec w) (s : Nat) (hs : s < w) : Bool :=
-  y[s] && uppcRec x s (by omega)
-
-
-/--
-  Preliminary overflow flag for fast umulOverflow circuit as introduced in
-  `Efficient integer multiplication overflow detection circuits` (https://ieeexplore.ieee.org/abstract/document/987767).
--/
-def resRec (x y : BitVec w) (s : Nat) (hs : s < w) (hslt : 0 < s) : Bool :=
-  match hs0 : s with
-  | 0 => by omega
-  | s' + 1 =>
-    match hs' : s' with
-    | 0 => aandRec x y 1 (by omega)
-    | s'' + 1 =>
-      (resRec x y s' (by omega) (by omega)) || (aandRec x y s (by omega))
-
-/-- The preliminary overflow flag is true for a certain `s` if and only if the conjunction returns true at
-  any `k` smaller than or equal to `s`. -/
-theorem resRec_true_iff (x y : BitVec w) (s : Nat) (hs : s < w) (hs' : 0 < s) :
-    resRec x y s hs hs' = true ↔ ∃ (k : Nat), ∃ (h : k ≤ s), ∃ (_ : 0 < k), aandRec x y k (by omega) := by
-  unfold resRec
-  rcases s with _|s
-  · omega
-  · rcases s
-    · case zero =>
-      constructor
-      · intro ha
-        exists 1, by omega, by omega
-      · intro hr
-        obtain ⟨k, hk, hk', hk''⟩ := hr
-        simp only [show k = 1 by omega] at hk''
-        exact hk''
-    · case succ s =>
-      induction s
-      · case zero =>
-        unfold resRec
-        simp only [Nat.zero_add, Nat.reduceAdd, or_eq_true]
-        constructor
-        · intro h
-          rcases h with h|h
-          · exists 1, by omega, by omega
-          · exists 2, by omega, by omega
-        · intro h
-          obtain ⟨k, hk, hk', hk''⟩ := h
-          have h : k = 1 ∨ k = 2 := by omega
-          rcases h with h|h
-          <;> simp only [h] at hk''
-          <;> simp [hk'']
-      · case succ s ihs =>
-        specialize ihs (by omega) (by omega)
-        unfold resRec
-        simp only [or_eq_true, ihs]
-        constructor
-        · intro h
-          rcases h with h|h
-          · obtain ⟨k, hk, hk', hk''⟩ := h
-            exists k, by omega, by omega
-          · exists s + 1 + 1 + 1, by omega, by omega
-        · intro h
-          obtain ⟨k, hk, hk', hk''⟩ := h
-          by_cases h' : x.aandRec y (s + 1 + 1 + 1) (by omega) = true
-          · simp [h']
-          · simp only [h', false_eq_true, _root_.or_false]
-            by_cases h'' : k ≤ s + 1 + 1
-            · exists k, h'', by omega
-            · have : k = s + 1 + 1 + 1 := by omega
-              simp_all
-
-/-- If the sum of the leading zeroes of two bitvecs with bitwidth `w` is less than or equal to
-  (`w - 2`), then the preliminary overflow flag is true and their unsigned multiplication overflows.
-  The explanation is in `Efficient integer multiplication overflow detection circuits`
-  https://ieeexplore.ieee.org/abstract/document/987767
-  -/
-theorem resRec_of_clz_le {x y : BitVec w} (hw : 1 < w) (hx : x ≠ 0#w) (hy : y ≠ 0#w):
-    (clz x).toNat + (clz y).toNat ≤ w - 2 → resRec x y (w - 1) (by omega) (by omega) := by
-  intro h
-  rw [resRec_true_iff]
-  exists (w - 1 - y.clz.toNat), by omega, by omega
-  simp only [aandRec]
-  by_cases hw0 : w - 1 - y.clz.toNat = 0
-  · have := clz_lt_iff_ne_zero.mpr (by omega)
-    omega
-  · simp only [and_eq_true, getLsbD_true_clz_of_ne_zero (x := y) (by omega) (by omega),
-    getElem_of_getLsbD_eq_true, uppcRec_true_iff,
-    show w - 1 - (w - 1 - y.clz.toNat - 1) = y.clz.toNat + 1 by omega, _root_.true_and]
-    exact Nat.le_trans (Nat.pow_le_pow_of_le (a := 2) (n := y.clz.toNat + 1)
-          (m := w - 1 - x.clz.toNat) (by omega) (by omega))
-          (BitVec.two_pow_sub_clz_le_toNat_of_ne_zero (x := x) (by omega) (by omega))
-
-/--
-  Complete fast overflow detection circuit for unsigned multiplication.
--/
-theorem fastUmulOverflow (x y : BitVec w) :
-    umulOverflow x y = if hw : w ≤ 1 then false
-      else (setWidth (w + 1) x * setWidth (w + 1) y)[w] || x.resRec y (w - 1) (by omega) (by omega) := by
-  rcases w with _|_|w
-  · simp [of_length_zero, umulOverflow]
-  · have hx : x.toNat ≤ 1 := by omega
-    have hy : y.toNat ≤ 1 := by omega
-    have := Nat.mul_le_mul (n₁ := x.toNat) (m₁ := y.toNat) (n₂ := 1) (m₂ := 1) hx hy
-    simp [umulOverflow]
-    omega
-  · by_cases h : umulOverflow x y
-    · simp only [h, Nat.reduceLeDiff, reduceDIte, Nat.add_one_sub_one, true_eq, or_eq_true]
-      simp only [umulOverflow, ge_iff_le, decide_eq_true_eq] at h
-      by_cases h' : x.toNat * y.toNat < 2 ^ (w + 1 + 1 + 1)
-      · have hlt := BitVec.getElem_eq_true_of_lt_of_le
-          (x := (setWidth (w + 1 + 1 + 1) x * setWidth (w + 1 + 1 + 1) y))
-          (k := w + 1 + 1)  (by omega)
-        simp only [toNat_mul, toNat_setWidth, Nat.lt_add_one, toNat_mod_cancel_of_lt,
-          Nat.mod_eq_of_lt (a := x.toNat * y.toNat) (b := 2 ^ (w + 1 + 1 + 1)) (by omega), h', h,
-          forall_const] at hlt
-        simp [hlt]
-      · by_cases hsw : (setWidth (w + 1 + 1 + 1) x * setWidth (w + 1 + 1 + 1) y)[w + 1 + 1] = true
-        · simp [hsw]
-        · simp only [hsw, false_eq_true, _root_.false_or]
-          have := Nat.two_pow_pos (w := w + 1 + 1)
-          have hltx := BitVec.toNat_lt_two_pow_sub_clz (x := x)
-          have hlty := BitVec.toNat_lt_two_pow_sub_clz (x := y)
-          have := Nat.mul_ne_zero_iff (m := y.toNat) (n := x.toNat)
-          simp only [ne_eq, show ¬x.toNat * y.toNat = 0 by omega, not_false_eq_true,
-            true_iff] at this
-          obtain ⟨hxz,hyz⟩ := this
-          apply resRec_of_clz_le (x := x) (y := y) (by omega) (by simp [toNat_eq]; exact hxz) (by simp [toNat_eq]; exact hyz)
-          by_cases hzxy : x.clz.toNat + y.clz.toNat ≤ w
-          · omega
-          · by_cases heq : w + 1 - y.clz.toNat = 0
-            · by_cases heq' : w + 1 + 1 - y.clz.toNat = 0
-              · simp [heq', hyz] at hlty
-              · simp only [show y.clz.toNat = w + 1 by omega, Nat.add_sub_cancel_left,
-                  Nat.pow_one] at hlty
-                simp only [show y.toNat = 1 by omega, Nat.mul_one, Nat.not_lt] at h'
-                omega
-            · by_cases w + 1 < y.clz.toNat
-              · omega
-              · simp only [Nat.not_lt] at h'
-                have := Nat.mul_lt_mul'' (a := x.toNat) (b := y.toNat) (c := 2 ^ (w + 1 + 1 - x.clz.toNat)) (d := 2 ^ (w + 1 + 1 - y.clz.toNat)) hltx hlty
-                simp only [← Nat.pow_add] at this
-                have := Nat.pow_le_pow_of_le (a := 2) (n := w + 1 + 1 - x.clz.toNat + (w + 1 + 1 - y.clz.toNat)) (m := w + 1 + 1 + 1)
-                 (by omega) (by omega)
-                omega
-    · simp only [h, Nat.reduceLeDiff, reduceDIte, Nat.add_one_sub_one, false_eq, or_eq_false_iff]
-      simp only [umulOverflow, ge_iff_le, decide_eq_true_eq, Nat.not_le] at h
-      and_intros
-      · simp only [← getLsbD_eq_getElem, getLsbD_eq_getMsbD, Nat.lt_add_one, decide_true,
-          Nat.add_one_sub_one, Nat.sub_self, ← msb_eq_getMsbD_zero, Bool.true_and,
-          msb_eq_false_iff_two_mul_lt, toNat_mul, toNat_setWidth, toNat_mod_cancel_of_lt]
-        rw [Nat.mod_eq_of_lt (by omega),Nat.pow_add (m := w + 1 + 1) (n := 1)]
-        simp [Nat.mul_comm 2 (x.toNat * y.toNat), h]
-      · apply Classical.byContradiction
-        intro hcontra
-        simp only [not_eq_false, resRec_true_iff, exists_prop, exists_and_left] at hcontra
-        obtain ⟨k,hk,hk',hk''⟩ := hcontra
-        simp only [aandRec, and_eq_true, uppcRec_true_iff, Nat.add_one_sub_one] at hk''
-        obtain ⟨hky, hkx⟩ := hk''
-        have hyle := two_pow_le_toNat_of_getElem_eq_true (x := y) (i := k) (by omega) hky
-        have := Nat.mul_le_mul (n₁ := 2 ^ (w + 1 - (k - 1))) (m₁ := 2 ^ k) (n₂ := x.toNat) (m₂ := y.toNat) hkx hyle
-        simp [← Nat.pow_add, show w + 1 - (k - 1) + k = w + 1 + 1 by omega] at this
-        omega
-
 end BitVec

src/Init/Data/BitVec/Bootstrap.lean

@@ -6,9 +6,7 @@ Authors: Joe Hendrix, Harun Khan, Alex Keizer, Abdalrhman M Mohamed, Siddharth B
 module
 
 prelude
-public import Init.Data.BitVec.Basic
-import all Init.Data.BitVec.Basic
-import Init.Data.Int.Bitwise.Lemmas
+public import all Init.Data.BitVec.Basic
 
 public section
 

src/Init/Data/BitVec/Folds.lean

@@ -6,8 +6,7 @@ Authors: Joe Hendrix, Harun Khan
 module
 
 prelude
-public import Init.Data.BitVec.Basic
-import all Init.Data.BitVec.Basic
+public import all Init.Data.BitVec.Basic
 public import Init.Data.BitVec.Lemmas
 public import Init.Data.Nat.Lemmas
 public import Init.Data.Fin.Iterate

src/Init/Data/BitVec/Lemmas.lean

@@ -7,10 +7,8 @@ module
 
 prelude
 public import Init.Data.Bool
-public import Init.Data.BitVec.Basic
-import all Init.Data.BitVec.Basic
-public import Init.Data.BitVec.BasicAux
-import all Init.Data.BitVec.BasicAux
+public import all Init.Data.BitVec.Basic
+public import all Init.Data.BitVec.BasicAux
 public import Init.Data.Fin.Lemmas
 public import Init.Data.Nat.Lemmas
 public import Init.Data.Nat.Div.Lemmas
@@ -21,12 +19,9 @@ public import Init.Data.Int.LemmasAux
 public import Init.Data.Int.Pow
 public import Init.Data.Int.LemmasAux
 public import Init.Data.BitVec.Bootstrap
-public import Init.Data.Order.Factories
 
 public section
 
-open Std
-
 set_option linter.missingDocs true
 
 namespace BitVec
@@ -122,7 +117,7 @@ theorem getElem_of_getLsbD_eq_true {x : BitVec w} {i : Nat} (h : x.getLsbD i = t
 This normalized a bitvec using `ofFin` to `ofNat`.
 -/
 theorem ofFin_eq_ofNat : @BitVec.ofFin w (Fin.mk x lt) = BitVec.ofNat w x := by
-  simp only [BitVec.ofNat, Fin.Internal.ofNat_eq_ofNat, Fin.ofNat, lt, Nat.mod_eq_of_lt]
+  simp only [BitVec.ofNat, Fin.ofNat, lt, Nat.mod_eq_of_lt]
 
 /-- Prove nonequality of bitvectors in terms of nat operations. -/
 theorem toNat_ne_iff_ne {n} {x y : BitVec n} : x.toNat ≠ y.toNat ↔ x ≠ y := by
@@ -243,11 +238,11 @@ theorem eq_of_getLsbD_eq_iff {w : Nat} {x y : BitVec w} :
     x = y ↔ ∀ (i : Nat), i < w → x.getLsbD i = y.getLsbD i := by
   have iff := @BitVec.eq_of_getElem_eq_iff w x y
   constructor
-  · intro heq i lt
+  · intros heq i lt
     have hext := iff.mp heq i lt
     simp only [← getLsbD_eq_getElem] at hext
     exact hext
-  · intro heq
+  · intros heq
     exact iff.mpr heq
 
 theorem eq_of_getMsbD_eq {x y : BitVec w}
@@ -299,7 +294,7 @@ theorem length_pos_of_ne {x y : BitVec w} (h : x ≠ y) : 0 < w :=
 
 theorem ofFin_ofNat (n : Nat) :
     ofFin (no_index (OfNat.ofNat n : Fin (2^w))) = OfNat.ofNat n := by
-  simp only [OfNat.ofNat, Fin.Internal.ofNat_eq_ofNat, Fin.ofNat, BitVec.ofNat]
+  simp only [OfNat.ofNat, Fin.ofNat, BitVec.ofNat]
 
 -- We use a `grind_pattern` as `@[grind]` will not use the `no_index` term.
 grind_pattern ofFin_ofNat => ofFin (OfNat.ofNat n : Fin (2^w))
@@ -510,18 +505,6 @@ theorem getElem_ofBool {b : Bool} {h : i < 1}: (ofBool b)[i] = b := by
 @[simp] theorem zero_eq_one_iff (w : Nat) : (0#w = 1#w) ↔ (w = 0) := by
   rw [← one_eq_zero_iff, eq_comm]
 
-/-- A bitvector is equal to 0#w if and only if all bits are `false` -/
-theorem zero_iff_eq_false {x: BitVec w} :
-    x = 0#w ↔ ∀ i, x.getLsbD i = false := by
-  rcases w with _|w
-  · simp [of_length_zero]
-  · constructor
-    · intro hzero
-      simp [hzero]
-    · intro hfalse
-      ext j hj
-      simp [← getLsbD_eq_getElem, hfalse]
-
 /-! ### msb -/
 
 @[simp] theorem msb_zero : (0#w).msb = false := by simp [BitVec.msb, getMsbD]
@@ -835,14 +818,14 @@ its most significant bit is true.
 theorem slt_zero_iff_msb_cond {x : BitVec w} : x.slt 0#w ↔ x.msb = true := by
   have := toInt_eq_msb_cond x
   constructor
-  · intro h
+  · intros h
     apply Classical.byContradiction
-    intro hmsb
+    intros hmsb
     simp only [Bool.not_eq_true] at hmsb
     simp only [hmsb, Bool.false_eq_true, ↓reduceIte] at this
     simp only [BitVec.slt, toInt_zero, decide_eq_true_eq] at h
     omega /- Can't have `x.toInt` which is equal to `x.toNat` be strictly less than zero -/
-  · intro h
+  · intros h
     simp only [h, ↓reduceIte] at this
     simp only [BitVec.slt, this, toInt_zero, decide_eq_true_eq]
     omega
@@ -2111,7 +2094,7 @@ theorem toInt_ushiftRight_of_lt {x : BitVec w} {n : Nat} (hn : 0 < n) :
     (x >>> n).toInt = x.toNat >>> n := by
   rw [toInt_eq_toNat_cond]
   simp only [toNat_ushiftRight, ite_eq_left_iff, Nat.not_lt]
-  intro h
+  intros h
   by_cases hn : n ≤ w
   · have h1 := Nat.mul_lt_mul_of_pos_left (toNat_ushiftRight_lt x n hn) Nat.two_pos
     simp only [toNat_ushiftRight, Nat.zero_lt_succ, Nat.mul_lt_mul_left] at h1
@@ -2206,7 +2189,8 @@ theorem sshiftRight_eq_of_msb_false {x : BitVec w} {s : Nat} (h : x.msb = false)
   apply BitVec.eq_of_toNat_eq
   rw [BitVec.sshiftRight_eq, BitVec.toInt_eq_toNat_cond]
   have hxbound : 2 * x.toNat < 2 ^ w := BitVec.msb_eq_false_iff_two_mul_lt.mp h
-  simp only [hxbound, ↓reduceIte, toNat_ushiftRight]
+  simp only [hxbound, ↓reduceIte, Int.natCast_shiftRight, ofInt_natCast,
+    toNat_ofNat, toNat_ushiftRight]
   replace hxbound : x.toNat >>> s < 2 ^ w := by
     rw [Nat.shiftRight_eq_div_pow]
     exact Nat.lt_of_le_of_lt (Nat.div_le_self ..) x.isLt
@@ -2248,7 +2232,7 @@ theorem getLsbD_sshiftRight (x : BitVec w) (s i : Nat) :
       omega
     · simp only [hi, decide_false, Bool.not_false, Bool.true_and, Bool.eq_and_self,
         decide_eq_true_eq]
-      intro hlsb
+      intros hlsb
       apply BitVec.lt_of_getLsbD hlsb
   · by_cases hi : i ≥ w
     · simp [hi]
@@ -2302,7 +2286,7 @@ theorem msb_sshiftRight {n : Nat} {x : BitVec w} :
   · simp [hw₀]
   · simp only [show ¬(w ≤ w - 1) by omega, decide_false, Bool.not_false, Bool.true_and,
       ite_eq_right_iff]
-    intro h
+    intros h
     simp [show n = 0 by omega]
 
 @[simp] theorem sshiftRight_zero {x : BitVec w} : x.sshiftRight 0 = x := by
@@ -2790,7 +2774,7 @@ theorem toInt_append {x : BitVec n} {y : BitVec m} :
     (x ++ 0#m).toInt = (2 ^ m) * x.toInt := by
   simp only [toInt_append, beq_iff_eq, toInt_zero, toNat_ofNat, Nat.zero_mod, Int.cast_ofNat_Int, Int.add_zero,
     ite_eq_right_iff]
-  intro h
+  intros h
   subst h
   simp [BitVec.eq_nil x]
 
@@ -2974,7 +2958,7 @@ theorem extractLsb'_append_extractLsb'_eq_extractLsb' {x : BitVec w} (h : start
   ext i h
   simp only [getElem_append, getElem_extractLsb', dite_eq_ite, getElem_cast, ite_eq_left_iff,
     Nat.not_lt]
-  intro hi
+  intros hi
   congr 1
   omega
 
@@ -3001,7 +2985,7 @@ theorem signExtend_eq_append_extractLsb' {w v : Nat} {x : BitVec w} :
   · simp only [hx, signExtend_eq_setWidth_of_msb_false, getElem_setWidth, Bool.false_eq_true,
       ↓reduceIte, getElem_append, getElem_extractLsb', Nat.zero_add, getElem_zero, dite_eq_ite,
       Bool.if_false_right, Bool.eq_and_self, decide_eq_true_eq]
-    intro hi
+    intros hi
     have hw : i < w := lt_of_getLsbD hi
     omega
   · simp [signExtend_eq_not_setWidth_not_of_msb_true hx, getElem_append, Nat.lt_min, hi]
@@ -3049,7 +3033,7 @@ theorem extractLsb'_append_eq_ite {v w} {xhi : BitVec v} {xlo : BitVec w} {start
     · simp only [hlen, ↓reduceDIte]
       ext i hi
       simp only [getElem_extractLsb', getLsbD_append, ite_eq_left_iff, Nat.not_lt]
-      intro hcontra
+      intros hcontra
       omega
     · simp only [hlen, ↓reduceDIte]
       ext i hi
@@ -3496,7 +3480,7 @@ theorem toInt_sub_toInt_lt_twoPow_iff {x y : BitVec w} :
     have := two_mul_toInt_lt (x := y)
     simp only [Nat.add_one_sub_one]
     constructor
-    · intro h
+    · intros h
       rw_mod_cast [← Int.add_bmod_right, Int.bmod_eq_of_le]
       <;> omega
     · have := Int.bmod_neg_iff (x := x.toInt - y.toInt) (m := 2 ^ (w + 1))
@@ -3512,7 +3496,7 @@ theorem twoPow_le_toInt_sub_toInt_iff {x y : BitVec w} :
     have := le_two_mul_toInt (x := y); have := two_mul_toInt_lt (x := y)
     simp only [Nat.add_one_sub_one]
     constructor
-    · intro h
+    · intros h
       simp only [show 0 ≤ x.toInt by omega, show y.toInt < 0 by omega, _root_.true_and]
       rw_mod_cast [← Int.sub_bmod_right, Int.bmod_eq_of_le (by omega) (by omega)]
       omega
@@ -4031,16 +4015,6 @@ protected theorem ne_of_lt {x y : BitVec n} : x < y → x ≠ y := by
   simp only [lt_def, ne_eq, toNat_eq]
   apply Nat.ne_of_lt
 
-instance instIsLinearOrder : IsLinearOrder (BitVec n) := by
-  apply IsLinearOrder.of_le
-  case le_antisymm => constructor; apply BitVec.le_antisymm
-  case le_trans => constructor; apply BitVec.le_trans
-  case le_total => constructor; apply BitVec.le_total
-
-instance instLawfulOrderLT : LawfulOrderLT (BitVec n) := by
-  apply LawfulOrderLT.of_le
-  simpa using fun _ _ => BitVec.lt_asymm
-
 protected theorem umod_lt (x : BitVec n) {y : BitVec n} : 0 < y → x % y < y := by
   simp only [ofNat_eq_ofNat, lt_def, toNat_ofNat, Nat.zero_mod]
   apply Nat.mod_lt
@@ -5779,6 +5753,40 @@ theorem msb_replicate {n w : Nat} {x : BitVec w} :
   simp only [BitVec.msb, getMsbD_replicate, Nat.zero_mod]
   cases n <;> cases w <;> simp
 
+/-! ### Count leading zeros -/
+
+theorem clzAuxRec_zero (x : BitVec w) :
+    x.clzAuxRec 0 = if x.getLsbD 0 then BitVec.ofNat w (w - 1) else BitVec.ofNat w w := by rfl
+
+theorem clzAuxRec_succ (x : BitVec w) :
+    x.clzAuxRec (n + 1) = if x.getLsbD (n + 1) then BitVec.ofNat w (w - 1 - (n + 1)) else BitVec.clzAuxRec x n := by rfl
+
+theorem clzAuxRec_eq_clzAuxRec_of_le (x : BitVec w) (h : w - 1 ≤ n) :
+    x.clzAuxRec n = x.clzAuxRec (w - 1) := by
+  let k := n - (w - 1)
+  rw [show n = (w - 1) + k by omega]
+  induction k
+  case zero => simp
+  case succ k ihk =>
+    simp [show w - 1 + (k + 1) = (w - 1 + k) + 1 by omega, clzAuxRec_succ, ihk,
+      show x.getLsbD (w - 1 + k + 1) = false by simp only [show w ≤ w - 1 + k + 1 by omega, getLsbD_of_ge]]
+
+theorem clzAuxRec_eq_clzAuxRec_of_getLsbD_false {x : BitVec w} (h : ∀ i, n < i → x.getLsbD i = false) :
+    x.clzAuxRec n = x.clzAuxRec (n + k) := by
+  induction k
+  case zero => simp
+  case succ k ihk =>
+    simp only [show n + (k + 1) = (n + k) + 1 by omega, clzAuxRec_succ]
+    by_cases hxn : x.getLsbD (n + k + 1)
+    · have : ¬ ∀ (i : Nat), n < i → x.getLsbD i = false := by
+        simp only [Classical.not_forall, Bool.not_eq_false]
+        exists n + k + 1
+        simp [show n < n + k + 1 by omega, hxn]
+      contradiction
+    · simp only [hxn, Bool.false_eq_true, ↓reduceIte]
+      exact ihk
+
+
 /-! ### Inequalities (le / lt) -/
 
 theorem ule_eq_not_ult (x y : BitVec w) : x.ule y = !y.ult x := by
@@ -5827,362 +5835,6 @@ theorem sle_eq_ule {x y : BitVec w} : x.sle y = (x.msb != y.msb ^^ x.ule y) := b
 theorem sle_eq_ule_of_msb_eq {x y : BitVec w} (h : x.msb = y.msb) : x.sle y = x.ule y := by
   simp [BitVec.sle_eq_ule, h]
 
-/-- A bitvector interpreted as a natural number is greater than or equal to `2 ^ i` if and only if
-  there exists at least one bit with `true` value at position `i` or higher. -/
-theorem le_toNat_iff_getLsbD_eq_true {x : BitVec w} (hi : i < w ) :
-    (2 ^ i ≤ x.toNat) ↔ (∃ k, x.getLsbD (i + k) = true) := by
-  rcases w with _|w
-  · simp [of_length_zero]
-  · constructor
-    · intro hle
-      apply Classical.byContradiction
-      intros hcontra
-      let x' := setWidth (i + 1) x
-      have hx' : setWidth (i + 1) x = x' := by rfl
-      have hcast : w - i + (i + 1) = w + 1 := by omega
-      simp only [not_exists, Bool.not_eq_true] at hcontra
-      have hx'' : x = BitVec.cast hcast (0#(w - i) ++ x') := by
-        ext j
-        by_cases hj : j < i + 1
-        · simp only [← hx', getElem_cast, getElem_append, hj, reduceDIte, getElem_setWidth]
-          rw [getLsbD_eq_getElem]
-        · simp only [getElem_cast, getElem_append, hj, reduceDIte, getElem_zero]
-          let j' := j - i
-          simp only [show j = i + j' by omega]
-          apply hcontra
-      have : x'.toNat < 2 ^ i := by
-        apply Nat.lt_pow_two_of_testBit (n := i) x'.toNat
-        intro j hj
-        let j' := j - i
-        specialize hcontra j'
-        have : x'.getLsbD (i + j') = x.getLsbD (i + j') := by
-          subst x'
-          simp [hcontra]
-        simp [show j = i + j' by omega, testBit_toNat, this, hcontra]
-      have : x'.toNat = x.toNat := by
-        have := BitVec.setWidth_eq_append (w := (w + 1)) (v := i + 1) (x := x')
-        specialize this (by omega)
-        rw [toNat_eq, toNat_setWidth, Nat.mod_eq_of_lt (by omega)] at this
-        simp [hx'']
-      omega
-    · intro h
-      obtain ⟨k, hk⟩ := h
-      by_cases hk' : i + k < w + 1
-      · have := Nat.ge_two_pow_of_testBit hk
-        have := Nat.pow_le_pow_of_le (a := 2) (n := i) (m := i + k) (by omega) (by omega)
-        omega
-      · simp [show w + 1 ≤ i + k by omega] at hk
-
-/-- A bitvector interpreted as a natural number is strictly smaller than `2 ^ i` if and only if
-  all bits at position `i` or higher are false. -/
-theorem toNat_lt_iff_getLsbD_eq_false {x : BitVec w} (i : Nat) (hi : i < w) :
-    x.toNat < 2 ^ i ↔ (∀ k, x.getLsbD (i + k) = false) := by
-  constructor
-  · intro h
-    apply Classical.byContradiction
-    intro hcontra
-    simp only [Classical.not_forall, Bool.not_eq_false] at hcontra
-    obtain ⟨k, hk⟩ := hcontra
-    have hle := Nat.ge_two_pow_of_testBit hk
-    by_cases hlt : i + k < w
-    · have := Nat.pow_le_pow_of_le (a := 2) (n := i) (m := i + k) (by omega) (by omega)
-      omega
-    · simp [show w ≤ i + k by omega] at hk
-  · intro h
-    apply Classical.byContradiction
-    intro hcontra
-    simp [BitVec.le_toNat_iff_getLsbD_eq_true (x := x) (i := i) hi, h] at hcontra
-
-/-- If a bitvector interpreted as a natural number is strictly smaller than `2 ^ (k + 1)` and greater than or
-  equal to 2 ^ k, then the bit at position `k` must be `true` -/
-theorem getElem_eq_true_of_lt_of_le {x : BitVec w} (hk' : k < w) (hlt: x.toNat < 2 ^ (k + 1)) (hle : 2 ^ k ≤ x.toNat) :
-    x[k] = true := by
-  have := le_toNat_iff_getLsbD_eq_true (x := x) (i := k) hk'
-  simp only [hle, true_iff] at this
-  obtain ⟨k',hk'⟩ := this
-  by_cases hkk' : k + k' < w
-  · have := Nat.ge_two_pow_of_testBit hk'
-    by_cases hzk' : k' = 0
-    · simp [hzk'] at hk'; exact hk'
-    · have := Nat.pow_lt_pow_of_lt (a := 2) (n := k) (m := k + k') (by omega) (by omega)
-      have := Nat.pow_le_pow_of_le (a := 2) (n := k + 1) (m := k + k') (by omega) (by omega)
-      omega
-  · simp [show w ≤ k + k' by omega] at hk'
-
-/-! ### Count leading zeros -/
-
-theorem clzAuxRec_zero (x : BitVec w) :
-    x.clzAuxRec 0 = if x.getLsbD 0 then BitVec.ofNat w (w - 1) else BitVec.ofNat w w := by rfl
-
-theorem clzAuxRec_succ (x : BitVec w) :
-    x.clzAuxRec (n + 1) = if x.getLsbD (n + 1) then BitVec.ofNat w (w - 1 - (n + 1)) else BitVec.clzAuxRec x n := by rfl
-
-theorem clzAuxRec_eq_clzAuxRec_of_le {x : BitVec w} (h : w - 1 ≤ n) :
-    x.clzAuxRec n = x.clzAuxRec (w - 1) := by
-  let k := n - (w - 1)
-  rw [show n = (w - 1) + k by omega]
-  induction k
-  · case zero => simp
-  · case succ k ihk =>
-    simp [show w - 1 + (k + 1) = (w - 1 + k) + 1 by omega, clzAuxRec_succ, ihk,
-      show x.getLsbD (w - 1 + k + 1) = false by simp only [show w ≤ w - 1 + k + 1 by omega, getLsbD_of_ge]]
-
-theorem clzAuxRec_eq_clzAuxRec_of_getLsbD_false {x : BitVec w} (h : ∀ i, n < i → x.getLsbD i = false) :
-    x.clzAuxRec n = x.clzAuxRec (n + k) := by
-  induction k
-  · case zero => simp
-  · case succ k ihk =>
-    simp only [show n + (k + 1) = (n + k) + 1 by omega, clzAuxRec_succ]
-    by_cases hxn : x.getLsbD (n + k + 1)
-    · have : ¬ ∀ (i : Nat), n < i → x.getLsbD i = false := by
-        simp only [Classical.not_forall, Bool.not_eq_false]
-        exists n + k + 1
-        simp [show n < n + k + 1 by omega, hxn]
-      contradiction
-    · simp only [hxn, Bool.false_eq_true, ↓reduceIte]
-      exact ihk
-
-theorem clzAuxRec_le {x : BitVec w} (n : Nat) :
-    clzAuxRec x n ≤ w := by
-  have := Nat.lt_pow_self (a := 2) (n := w) (by omega)
-  rcases w with _|w
-  · simp [of_length_zero]
-  · induction n
-    · case zero =>
-      simp only  [clzAuxRec_zero]
-      by_cases hx0 : x.getLsbD 0
-      · simp only [hx0, Nat.add_one_sub_one, reduceIte, natCast_eq_ofNat, ofNat_le_ofNat,
-          Nat.mod_two_pow_self, ge_iff_le, Nat.mod_eq_of_lt (a := w) (b := 2 ^ (w + 1)) (by omega)]
-        omega
-      · simp only [hx0, Bool.false_eq_true, reduceIte, natCast_eq_ofNat, BitVec.le_refl]
-    · case succ n ihn =>
-      simp only [clzAuxRec_succ, Nat.add_one_sub_one, natCast_eq_ofNat, ge_iff_le]
-      by_cases hxn : x.getLsbD (n + 1)
-      · simp [hxn, Nat.mod_eq_of_lt (a := w - (n + 1)) (b := 2 ^(w + 1)) (by omega)]
-        omega
-      · simp only [hxn, Bool.false_eq_true, reduceIte]
-        exact ihn
-
-theorem clzAuxRec_eq_iff_of_getLsbD_false {x : BitVec w} (h : ∀ i, n < i → x.getLsbD i = false) :
-    x.clzAuxRec n = BitVec.ofNat w w ↔ ∀ j, j ≤ n → x.getLsbD j = false := by
-  rcases w with _|w
-  · simp [of_length_zero]
-  · have := Nat.lt_pow_self (a := 2) (n := w + 1)
-    induction n
-    · case zero =>
-      simp only [clzAuxRec_zero, Nat.zero_lt_succ, getLsbD_eq_getElem, Nat.add_one_sub_one,
-        ite_eq_right_iff, Nat.le_zero_eq, forall_eq]
-      by_cases hx0 : x.getLsbD 0
-      · simp [hx0, toNat_eq, toNat_ofNat, Nat.mod_eq_of_lt (a := w) (b := 2 ^ (w + 1)) (by omega)]
-      · simp only [Nat.zero_lt_succ, getLsbD_eq_getElem, Bool.not_eq_true] at hx0
-        simp [hx0]
-    · case succ n ihn =>
-      simp only [clzAuxRec_succ, Nat.add_one_sub_one]
-      by_cases hxn : x.getLsbD (n + 1)
-      · simp only [hxn, reduceIte, toNat_eq, toNat_ofNat,
-          Nat.mod_eq_of_lt (a := w - (n + 1)) (b := 2 ^ (w + 1)) (by omega), Nat.mod_two_pow_self,
-          show ¬w - (n + 1) = w + 1 by omega, false_iff, Classical.not_forall,
-          Bool.not_eq_false]
-        exists n + 1, by omega
-      · have : ∀ (i : Nat), n < i → x.getLsbD i = false := by
-          intro i hi
-          by_cases hi' : i = n + 1
-          · simp [hi', hxn]
-          · apply h; omega
-        specialize ihn this
-        simp only [Bool.not_eq_true] at ihn hxn
-        simp only [hxn, Bool.false_eq_true, reduceIte, ihn]
-        constructor
-        <;> intro h' j hj
-        <;> (by_cases hj' : j = n + 1; simp [hj', hxn]; (apply h'; omega))
-
-theorem clz_le {x : BitVec w} :
-    clz x ≤ w := by
-  unfold clz
-  rcases w with _|w
-  · simp [of_length_zero]
-  · exact clzAuxRec_le (n := w)
-
-@[simp]
-theorem clz_eq_iff_eq_zero {x : BitVec w} :
-    clz x = w ↔ x = 0#w := by
-  rcases w with _|w
-  · simp [clz, of_length_zero]
-  · simp only [clz, Nat.add_one_sub_one, natCast_eq_ofNat, zero_iff_eq_false]
-    rw [clzAuxRec_eq_iff_of_getLsbD_false (x := x) (n := w) (w := w + 1) (by intros i hi; simp [show w + 1 ≤ i by omega])]
-    constructor
-    · intro h i
-      by_cases i ≤ w
-      · apply h; omega
-      · simp [show w + 1 ≤ i by omega]
-    · intro h j hj
-      apply h
-
-theorem clzAuxRec_eq_zero_iff {x : BitVec w} (h : ∀ i, n < i → x.getLsbD i = false) (hw : 0 < w) :
-    (x.clzAuxRec n).toNat = 0 ↔ x[w - 1] = true := by
-  have := Nat.lt_pow_self (a := 2) (n := w)
-  induction n
-  · case zero =>
-    simp only [clzAuxRec_zero]
-    by_cases hw1 : w - 1 = 0
-    · by_cases hx0 : x.getLsbD 0
-      · simp [hw1, hx0]
-      · simp [hw1, show ¬ w = 0 by omega, hx0, ← getLsbD_eq_getElem]
-    · by_cases hx0 : x.getLsbD 0
-      · simp only [hx0, ↓reduceIte, toNat_ofNat,
-          Nat.mod_eq_of_lt (a := w - 1) (b := 2 ^ w) (by omega), show ¬w - 1 = 0 by omega, false_iff,
-          Bool.not_eq_true]
-        specialize h (w - 1) (by omega)
-        exact h
-      · simp [hx0, show ¬ w = 0 by omega]
-        specialize h (w - 1) (by omega)
-        exact h
-  · case succ n ihn =>
-    by_cases hxn : x.getLsbD (n + 1)
-    · simp only [clzAuxRec_succ, hxn, reduceIte, toNat_ofNat]
-      rw [Nat.mod_eq_of_lt (by omega)]
-      by_cases hwn : w - 1 - (n + 1) = 0
-      · have := lt_of_getLsbD hxn
-        simp only [show w - 1 = n + 1 by omega, Nat.sub_self, true_iff]
-        exact hxn
-      · simp only [hwn, false_iff, Bool.not_eq_true]
-        specialize h (w - 1) (by omega)
-        exact h
-    · simp only [clzAuxRec_succ, hxn, Bool.false_eq_true, reduceIte]
-      apply ihn
-      intro i hi
-      by_cases hi : i = n + 1
-      · simp [hi, hxn]
-      · apply h; omega
-
-theorem clz_eq_zero_iff {x : BitVec w} (hw : 0 < w) :
-    (clz x).toNat = 0 ↔ 2 ^ (w - 1) ≤ x.toNat := by
-  simp only [clz, clzAuxRec_eq_zero_iff (x := x) (n := w - 1) (by intro i hi; simp [show w ≤ i by omega]) hw]
-  by_cases hxw : x[w - 1]
-  · simp [hxw, two_pow_le_toNat_of_getElem_eq_true (x := x) (i := w - 1) (by omega) hxw]
-  · simp only [hxw, Bool.false_eq_true, false_iff, Nat.not_le]
-    simp only [← getLsbD_eq_getElem, ← msb_eq_getLsbD_last, Bool.not_eq_true] at hxw
-    exact toNat_lt_of_msb_false hxw
-
-/-- The number of leading zeroes is strictly less than the bitwidth iff the bitvector is nonzero. -/
-theorem clz_lt_iff_ne_zero {x : BitVec w} :
-    clz x < w ↔ x ≠ 0#w := by
-  have hle := clz_le (x := x)
-  have heq := clz_eq_iff_eq_zero (x := x)
-  constructor
-  · intro h
-    simp only [natCast_eq_ofNat, BitVec.ne_of_lt (x := x.clz) (y := BitVec.ofNat w w) h,
-      false_iff] at heq
-    simp only [ne_eq, heq, not_false_eq_true]
-  · intro h
-    simp only [natCast_eq_ofNat, h, iff_false] at heq
-    apply BitVec.lt_of_le_ne (x := x.clz) (y := BitVec.ofNat w w) hle heq
-
-theorem getLsbD_false_of_clzAuxRec {x : BitVec w} (h : ∀ i, n < i → x.getLsbD i = false) :
-    ∀ j, x.getLsbD (w - (x.clzAuxRec n).toNat + j) = false := by
-  rcases w with _|w
-  · simp
-  · have := Nat.lt_pow_self (a := 2) (n := w + 1)
-    induction n
-    · case zero =>
-      intro j
-      simp only [clzAuxRec_zero, Nat.zero_lt_succ, getLsbD_eq_getElem, Nat.add_one_sub_one]
-      by_cases hx0 : x[0]
-      · specialize h (1 + j) (by omega)
-        simp [h, hx0, Nat.mod_eq_of_lt (a := w) (b := 2 ^ (w + 1)) (by omega)]
-      · simp only [hx0, Bool.false_eq_true, ↓reduceIte, toNat_ofNat, Nat.mod_two_pow_self,
-          Nat.sub_self, Nat.zero_add]
-        by_cases hj0 : j = 0
-        · simp [hj0, hx0]
-        · specialize h j (by omega)
-          exact h
-    · case succ n ihn =>
-      intro j
-      by_cases hxn : x.getLsbD (n + 1)
-      · have := lt_of_getLsbD hxn
-        specialize h (n + j + 1 + 1) (by omega)
-        simp [h, clzAuxRec_succ, hxn, Nat.mod_eq_of_lt (a := w - (n + 1)) (b := 2 ^ (w + 1)) (by omega),
-          show (w + 1 - (w - (n + 1)) + j) = n + j + 1 + 1 by omega]
-      · simp only [clzAuxRec_succ, hxn, Bool.false_eq_true, reduceIte]
-        apply ihn
-        intro i hi
-        by_cases hin : i = n + 1
-        · simp [hin, hxn]
-        · specialize h i (by omega)
-          exact h
-
-theorem getLsbD_true_of_eq_clzAuxRec_of_ne_zero {x : BitVec w} (hx : ¬ x = 0#w) (hn : ∀ i, n < i → x.getLsbD i = false) :
-    x.getLsbD (w - 1 - (x.clzAuxRec n).toNat) = true := by
-  rcases w with _|w
-  · simp [of_length_zero] at hx
-  · have := Nat.lt_pow_self (a := 2) (n := w + 1)
-    induction n
-    · case zero =>
-      by_cases hx0 : x[0]
-      · simp only [Nat.add_one_sub_one, clzAuxRec_zero, Nat.zero_lt_succ, getLsbD_eq_getElem, hx0,
-          reduceIte, toNat_ofNat, Nat.mod_eq_of_lt (a := w) (b := 2 ^(w + 1)) (by omega), show w - w = 0 by omega]
-      · simp only [zero_iff_eq_false, Classical.not_forall, Bool.not_eq_false] at hx
-        obtain ⟨m,hm⟩ := hx
-        specialize hn m
-        by_cases hm0 : m = 0
-        · simp [hm0, hx0] at hm
-        · simp [show 0 < m by omega, hm] at hn
-    · case succ n ihn =>
-      by_cases hxn : x.getLsbD (n + 1)
-      · have := lt_of_getLsbD hxn
-        simp [clzAuxRec_succ, hxn, toNat_ofNat, Nat.mod_eq_of_lt (a := w - (n + 1)) (b := 2 ^ (w + 1)) (by omega),
-          show w - (w - (n + 1)) = n + 1 by omega]
-      · simp only [Nat.add_one_sub_one, clzAuxRec_succ, hxn, Bool.false_eq_true, reduceIte]
-        simp only [Nat.add_one_sub_one] at ihn
-        apply ihn
-        intro j hj
-        by_cases hjn : j = n + 1
-        · simp [hjn, hxn]
-        · specialize hn j (by omega)
-          exact hn
-
-theorem getLsbD_true_clz_of_ne_zero {x : BitVec w} (hw : 0 < w) (hx : x ≠ 0#w) :
-    x.getLsbD (w - 1 - (clz x).toNat) = true := by
-  unfold clz
-  apply getLsbD_true_of_eq_clzAuxRec_of_ne_zero (x := x) (n := w - 1) (by omega)
-  intro i hi
-  simp [show w ≤ i by omega]
-
-/-- A nonzero bitvector is lower-bounded by its leading zeroes. -/
-theorem two_pow_sub_clz_le_toNat_of_ne_zero {x : BitVec w} (hw : 0 < w) (hx : x ≠ 0#w) :
-    2 ^ (w - 1 - (clz x).toNat) ≤ x.toNat := by
-  by_cases hc0 : x.clz.toNat  = 0
-  · simp [hc0, ← clz_eq_zero_iff (x := x) hw]
-  · have hclz := getLsbD_true_clz_of_ne_zero (x := x) hw hx
-    rw [getLsbD_eq_getElem (by omega)] at hclz
-    have hge := Nat.ge_two_pow_of_testBit hclz
-    push_cast at hge
-    exact hge
-
-/-- A bitvector is upper bounded by the number of leading zeroes. -/
-theorem toNat_lt_two_pow_sub_clz {x : BitVec w} :
-    x.toNat < 2 ^ (w - (clz x).toNat) := by
-  rcases w with _|w
-  · simp [of_length_zero]
-  · unfold clz
-    have hlt := toNat_lt_iff_getLsbD_eq_false (x := x)
-    have hzero := clzAuxRec_eq_zero_iff (x := x) (n := w) (by intro i hi; simp [show w + 1 ≤ i by omega]) (by omega)
-    simp only [Nat.add_one_sub_one] at hzero
-    by_cases hxw : x[w]
-    · simp only [hxw, iff_true] at hzero
-      simp only [Nat.add_one_sub_one, hzero, Nat.sub_zero, gt_iff_lt]
-      omega
-    · simp only [hxw, Bool.false_eq_true, iff_false] at hzero
-      rw [hlt]
-      · intro k
-        apply getLsbD_false_of_clzAuxRec (x := x) (n := w)
-        intro i hi
-        by_cases hiw : i = w
-        · simp [hiw, hxw]
-        · simp [show w + 1 ≤ i by omega]
-      · simp; omega
-
-
 /-! ### Deprecations -/
 
 set_option linter.missingDocs false
@@ -6190,8 +5842,13 @@ set_option linter.missingDocs false
 @[deprecated toFin_uShiftRight (since := "2025-02-18")]
 abbrev toFin_uShiftRight := @toFin_ushiftRight
 
+@[deprecated signExtend_eq_setWidth_of_msb_false (since := "2024-12-08")]
+abbrev signExtend_eq_not_setWidth_not_of_msb_false := @signExtend_eq_setWidth_of_msb_false
 
+@[deprecated replicate_zero (since := "2025-01-08")]
+abbrev replicate_zero_eq := @replicate_zero
 
-
+@[deprecated replicate_succ (since := "2025-01-08")]
+abbrev replicate_succ_eq := @replicate_succ
 
 end BitVec

src/Init/Data/Bool.lean

@@ -10,6 +10,7 @@ public import Init.NotationExtra
 
 public section
 
+
 namespace Bool
 
 /--
@@ -698,13 +699,13 @@ but may be used locally.
 
 /-! ### Proof by reflection support  -/
 
-@[expose] protected noncomputable def Bool.and' (a b : Bool) : Bool :=
+protected noncomputable def Bool.and' (a b : Bool) : Bool :=
   Bool.rec false b a
 
-@[expose] protected noncomputable def Bool.or' (a b : Bool) : Bool :=
+protected noncomputable def Bool.or' (a b : Bool) : Bool :=
   Bool.rec b true a
 
-@[expose] protected noncomputable def Bool.not' (a : Bool) : Bool :=
+protected noncomputable def Bool.not' (a : Bool) : Bool :=
   Bool.rec true false a
 
 @[simp] theorem Bool.and'_eq_and (a b : Bool) : a.and' b = a.and b := by

src/Init/Data/ByteArray.lean

@@ -7,6 +7,5 @@ module
 
 prelude
 public import Init.Data.ByteArray.Basic
-public import Init.Data.ByteArray.Extra
 
 public section

src/Init/Data/ByteArray/Basic.lean

@@ -6,10 +6,10 @@ Author: Leonardo de Moura
 module
 
 prelude
+public import Init.Data.Array.Basic
 public import Init.Data.Array.DecidableEq
 public import Init.Data.UInt.Basic
-public import Init.Data.UInt.BasicAux
-import all Init.Data.UInt.BasicAux
+public import all Init.Data.UInt.BasicAux
 public import Init.Data.Option.Basic
 
 @[expose] public section
@@ -360,3 +360,27 @@ def List.toByteArray (bs : List UInt8) : ByteArray :=
   loop bs ByteArray.empty
 
 instance : ToString ByteArray := ⟨fun bs => bs.toList.toString⟩
+
+/-- Interpret a `ByteArray` of size 8 as a little-endian `UInt64`. -/
+def ByteArray.toUInt64LE! (bs : ByteArray) : UInt64 :=
+  assert! bs.size == 8
+  (bs.get! 7).toUInt64 <<< 0x38 |||
+  (bs.get! 6).toUInt64 <<< 0x30 |||
+  (bs.get! 5).toUInt64 <<< 0x28 |||
+  (bs.get! 4).toUInt64 <<< 0x20 |||
+  (bs.get! 3).toUInt64 <<< 0x18 |||
+  (bs.get! 2).toUInt64 <<< 0x10 |||
+  (bs.get! 1).toUInt64 <<< 0x8  |||
+  (bs.get! 0).toUInt64
+
+/-- Interpret a `ByteArray` of size 8 as a big-endian `UInt64`. -/
+def ByteArray.toUInt64BE! (bs : ByteArray) : UInt64 :=
+  assert! bs.size == 8
+  (bs.get! 0).toUInt64 <<< 0x38 |||
+  (bs.get! 1).toUInt64 <<< 0x30 |||
+  (bs.get! 2).toUInt64 <<< 0x28 |||
+  (bs.get! 3).toUInt64 <<< 0x20 |||
+  (bs.get! 4).toUInt64 <<< 0x18 |||
+  (bs.get! 5).toUInt64 <<< 0x10 |||
+  (bs.get! 6).toUInt64 <<< 0x8  |||
+  (bs.get! 7).toUInt64

src/Init/Data/ByteArray/Extra.lean

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

src/Init/Data/Char.lean

@@ -8,6 +8,5 @@ module
 prelude
 public import Init.Data.Char.Basic
 public import Init.Data.Char.Lemmas
-public import Init.Data.Char.Order
 
 public section

src/Init/Data/Char/Lemmas.lean

@@ -6,8 +6,7 @@ Authors: Leonardo de Moura
 module
 
 prelude
-public import Init.Data.Char.Basic
-import all Init.Data.Char.Basic
+public import all Init.Data.Char.Basic
 public import Init.Data.UInt.Lemmas
 
 public section
@@ -62,10 +61,14 @@ instance leTotal : Std.Total (· ≤ · : Char → Char → Prop) where
   total := Char.le_total
 
 -- This instance is useful while setting up instances for `String`.
-@[deprecated ltAsymm (since := "2025-08-01")]
 def notLTTotal : Std.Total (¬ · < · : Char → Char → Prop) where
   total := fun x y => by simpa using Char.le_total y x
 
+theorem utf8Size_eq (c : Char) : c.utf8Size = 1 ∨ c.utf8Size = 2 ∨ c.utf8Size = 3 ∨ c.utf8Size = 4 := by
+  have := c.utf8Size_pos
+  have := c.utf8Size_le_four
+  omega
+
 @[simp] theorem ofNat_toNat (c : Char) : Char.ofNat c.toNat = c := by
   rw [Char.ofNat, dif_pos]
   rfl

src/Init/Data/Char/Order.lean

@@ -1,27 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Paul Reichert
--/
-module
-
-prelude
-public import Init.Data.Char.Basic
-import Init.Data.Char.Lemmas
-public import Init.Data.Order.Factories
-
-open Std
-
-namespace Char
-
-public instance instIsLinearOrder : IsLinearOrder Char := by
-  apply IsLinearOrder.of_le
-  case le_antisymm => constructor; apply Char.le_antisymm
-  case le_trans => constructor; apply Char.le_trans
-  case le_total => constructor; apply Char.le_total
-
-public instance : LawfulOrderLT Char where
-  lt_iff a b := by
-    simp [← Char.not_le, Decidable.imp_iff_not_or, Std.Total.total]
-
-end Char

src/Init/Data/Dyadic.lean

@@ -1,12 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison
--/
-module
-prelude
-
-public import Init.Data.Dyadic.Basic
-public import Init.Data.Dyadic.Instances
-public import Init.Data.Dyadic.Round
-public import Init.Data.Dyadic.Inv

src/Init/Data/Dyadic/Basic.lean

@@ -1,747 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison, Robin Arnez
--/
-module
-
-prelude
-public import Init.Data.Rat.Lemmas
-import Init.Data.Int.Bitwise.Lemmas
-import Init.Data.Int.DivMod.Lemmas
-
-/-!
-# The dyadic rationals
-
-Constructs the dyadic rationals as an ordered ring, equipped with a compatible embedding into the rationals.
--/
-
-set_option linter.missingDocs true
-
-@[expose] public section
-
-open Nat
-
-namespace Int
-
-/-- The number of trailing zeros in the binary representation of `i`. -/
-def trailingZeros (i : Int) : Nat :=
-  if h : i = 0 then 0 else aux i.natAbs i h (Nat.le_refl _) 0
-where
-  aux (k : Nat) (i : Int) (hi : i ≠ 0) (hk : i.natAbs ≤ k) (acc : Nat) : Nat :=
-    match k, (by omega : k ≠ 0) with
-    | k + 1, _ =>
-      if h : i % 2 = 0 then aux k (i / 2) (by omega) (by omega) (acc + 1)
-      else acc
-
--- TODO: check performance of `trailingZeros` in the kernel and VM.
-
-private theorem trailingZeros_aux_irrel (hi : i ≠ 0) (hk : i.natAbs ≤ k) (hk' : i.natAbs ≤ k') :
-    trailingZeros.aux k i hi hk acc = trailingZeros.aux k' i hi hk' acc := by
-  fun_induction trailingZeros.aux k i hi hk acc generalizing k' <;>
-    fun_cases trailingZeros.aux k' _ _ hk' _
-  · rename_i ih _ _ _ _ _
-    exact ih _
-  · contradiction
-  · contradiction
-  · rfl
-
-private theorem trailingZeros_aux_succ :
-    trailingZeros.aux k i hi hk (acc + 1) = trailingZeros.aux k i hi hk acc + 1 := by
-  fun_induction trailingZeros.aux k i hi hk acc <;> simp_all [trailingZeros.aux]
-
-theorem trailingZeros_zero : trailingZeros 0 = 0 := rfl
-
-theorem trailingZeros_two_mul_add_one (i : Int) :
-    Int.trailingZeros (2 * i + 1) = 0 := by
-  unfold trailingZeros trailingZeros.aux
-  rw [dif_neg (by omega)]
-  split <;> simp_all
-
-theorem trailingZeros_eq_zero_of_mod_eq {i : Int} (h : i % 2 = 1) :
-    Int.trailingZeros i = 0 := by
-  unfold trailingZeros trailingZeros.aux
-  rw [dif_neg (by omega)]
-  split <;> simp_all
-
-theorem trailingZeros_two_mul {i : Int} (h : i ≠ 0) :
-    Int.trailingZeros (2 * i) = Int.trailingZeros i + 1 := by
-  rw [Int.trailingZeros, dif_neg (Int.mul_ne_zero (by decide) h), Int.trailingZeros.aux.eq_def]
-  simp only [ne_eq, mul_emod_right, ↓reduceDIte, Int.reduceEq, not_false_eq_true,
-    mul_ediv_cancel_left, Nat.zero_add]
-  split
-  rw [trailingZeros, trailingZeros_aux_succ, dif_neg h]
-  apply congrArg Nat.succ (trailingZeros_aux_irrel ..) <;> omega
-
-theorem shiftRight_trailingZeros_mod_two {i : Int} (h : i ≠ 0) :
-    (i >>> i.trailingZeros) % 2 = 1 := by
-  rw (occs := .pos [2]) [← Int.emod_add_mul_ediv i 2]
-  rcases i.emod_two_eq with h' | h' <;> rw [h']
-  · rcases Int.dvd_of_emod_eq_zero h' with ⟨a, rfl⟩
-    simp only [ne_eq, Int.mul_eq_zero, Int.reduceEq, false_or] at h
-    rw [Int.zero_add, mul_ediv_cancel_left _ (by decide), trailingZeros_two_mul h, Nat.add_comm,
-      shiftRight_add, shiftRight_eq_div_pow _ 1]
-    simpa using shiftRight_trailingZeros_mod_two h
-  · rwa [Int.add_comm, trailingZeros_two_mul_add_one, shiftRight_zero]
-termination_by i.natAbs
-
-theorem two_pow_trailingZeros_dvd {i : Int} (h : i ≠ 0) :
-    2 ^ i.trailingZeros ∣ i := by
-  rcases i.emod_two_eq with h' | h'
-  · rcases Int.dvd_of_emod_eq_zero h' with ⟨a, rfl⟩
-    simp only [ne_eq, Int.mul_eq_zero, Int.reduceEq, false_or] at h
-    rw [trailingZeros_two_mul h, Int.pow_succ']
-    exact Int.mul_dvd_mul_left _ (two_pow_trailingZeros_dvd h)
-  · rw (occs := .pos [1]) [← Int.emod_add_mul_ediv i 2, h', Int.add_comm, trailingZeros_two_mul_add_one]
-    exact Int.one_dvd _
-termination_by i.natAbs
-
-theorem trailingZeros_shiftLeft {x : Int} (hx : x ≠ 0) (n : Nat) :
-    trailingZeros (x <<< n) = x.trailingZeros + n := by
-  have : NeZero x := ⟨hx⟩
-  induction n <;> simp [Int.shiftLeft_succ', trailingZeros_two_mul (NeZero.ne _), *, Nat.add_assoc]
-
-@[simp]
-theorem trailingZeros_neg (x : Int) : trailingZeros (-x) = x.trailingZeros := by
-  by_cases hx : x = 0
-  · simp [hx]
-  rcases x.emod_two_eq with h | h
-  · rcases Int.dvd_of_emod_eq_zero h with ⟨a, rfl⟩
-    simp only [Int.mul_ne_zero_iff, ne_eq, Int.reduceEq, not_false_eq_true, true_and] at hx
-    rw [← Int.mul_neg, trailingZeros_two_mul hx, trailingZeros_two_mul (Int.neg_ne_zero.mpr hx)]
-    rw [trailingZeros_neg]
-  · simp [trailingZeros_eq_zero_of_mod_eq, h]
-termination_by x.natAbs
-
-end Int
-
-/--
-A dyadic rational is either zero or of the form `n * 2^(-k)` for some (unique) `n k : Int`
-where `n` is odd.
--/
-inductive Dyadic where
-  /-- The dyadic number `0`. -/
-  | zero
-  /-- The dyadic number `n * 2^(-k)` for some odd `n` and integer `k`. -/
-  | ofOdd (n : Int) (k : Int) (hn : n % 2 = 1)
-deriving DecidableEq
-
-namespace Dyadic
-
-/-- Returns the dyadic number representation of `i * 2 ^ (-exp)`. -/
-def ofIntWithPrec (i : Int) (prec : Int) : Dyadic :=
-  if h : i = 0 then .zero
-  else .ofOdd (i >>> i.trailingZeros) (prec - i.trailingZeros) (Int.shiftRight_trailingZeros_mod_two h)
-
-/-- Convert an integer to a dyadic number (which will necessarily have non-positive precision). -/
-def ofInt (i : Int) : Dyadic :=
-  Dyadic.ofIntWithPrec i 0
-
-instance (n : Nat) : OfNat Dyadic n where
-  ofNat := Dyadic.ofInt n
-
-instance : IntCast Dyadic := ⟨ofInt⟩
-instance : NatCast Dyadic := ⟨fun x => ofInt x⟩
-
-/-- Add two dyadic numbers. -/
-protected def add (x y : Dyadic) : Dyadic :=
-  match x, y with
-  | .zero, y => y
-  | x, .zero => x
-  | .ofOdd n₁ k₁ hn₁, .ofOdd n₂ k₂ hn₂ =>
-    match k₁ - k₂ with
-    | 0 => .ofIntWithPrec (n₁ + n₂) k₁
-    -- TODO: these `simp_all` calls where previously factored out into a `where finally` clause,
-    -- but there is apparently a bad interaction with the module system.
-    | (d@hd:(d' + 1) : Nat) => .ofOdd (n₁ + (n₂ <<< d)) k₁ (by simp_all [Int.shiftLeft_eq, Int.pow_succ, ← Int.mul_assoc])
-    | -(d + 1 : Nat) => .ofOdd (n₁ <<< (d + 1) + n₂) k₂ (by simp_all [Int.shiftLeft_eq, Int.pow_succ, ← Int.mul_assoc])
-
-instance : Add Dyadic := ⟨Dyadic.add⟩
-
-/-- Multiply two dyadic numbers. -/
-protected def mul (x y : Dyadic) : Dyadic :=
-  match x, y with
-  | .zero, _ => .zero
-  | _, .zero => .zero
-  | .ofOdd n₁ k₁ hn₁, .ofOdd n₂ k₂ hn₂ =>
-    .ofOdd (n₁ * n₂) (k₁ + k₂) (by rw [Int.mul_emod, hn₁, hn₂]; rfl)
-
-instance : Mul Dyadic := ⟨Dyadic.mul⟩
-
-/-- Multiply two dyadic numbers. -/
-protected def pow (x : Dyadic) (i : Nat) : Dyadic :=
-  match x with
-  | .zero => if i = 0 then 1 else 0
-  | .ofOdd n k hn =>
-    .ofOdd (n ^ i) (k * i) (by induction i <;> simp [Int.pow_succ, Int.mul_emod, *])
-
-instance : Pow Dyadic Nat := ⟨Dyadic.pow⟩
-
-/-- Negate a dyadic number. -/
-protected def neg (x : Dyadic) : Dyadic :=
-  match x with
-  | .zero => .zero
-  | .ofOdd n k hn => .ofOdd (-n) k (by rwa [Int.neg_emod_two])
-
-instance : Neg Dyadic := ⟨Dyadic.neg⟩
-
-/-- Subtract two dyadic numbers. -/
-protected def sub (x y : Dyadic) : Dyadic := x + (- y)
-
-instance : Sub Dyadic := ⟨Dyadic.sub⟩
-
-/-- Shift a dyadic number left by `i` bits. -/
-protected def shiftLeft (x : Dyadic) (i : Int) : Dyadic :=
-  match x with
-  | .zero => .zero
-  | .ofOdd n k hn => .ofOdd n (k - i) hn
-
-/-- Shift a dyadic number right by `i` bits. -/
-protected def shiftRight (x : Dyadic) (i : Int) : Dyadic :=
-  match x with
-  | .zero => .zero
-  | .ofOdd n k hn => .ofOdd n (k + i) hn
-
-instance : HShiftLeft Dyadic Int Dyadic := ⟨Dyadic.shiftLeft⟩
-instance : HShiftRight Dyadic Int Dyadic := ⟨Dyadic.shiftRight⟩
-
-instance : HShiftLeft Dyadic Nat Dyadic := ⟨fun x y => x <<< (y : Int)⟩
-instance : HShiftRight Dyadic Nat Dyadic := ⟨fun x y => x >>> (y : Int)⟩
-
--- TODO: move this
-theorem _root_.Int.natAbs_emod_two (i : Int) : i.natAbs % 2 = (i % 2).natAbs := by omega
-
-/-- Convert a dyadic number to a rational number. -/
-def toRat (x : Dyadic) : Rat :=
-  match x with
-  | .zero => 0
-  | .ofOdd n (k : Nat) hn =>
-    have reduced : n.natAbs.Coprime (2 ^ k) := by
-      apply Coprime.pow_right
-      rw [coprime_iff_gcd_eq_one, Nat.gcd_comm, Nat.gcd_def]
-      simp [hn, Int.natAbs_emod_two]
-    ⟨n, 2 ^ k, Nat.ne_of_gt (Nat.pow_pos (by decide)), reduced⟩
-  | .ofOdd n (-((k : Nat) + 1)) hn =>
-    (n * (2 ^ (k + 1) : Nat) : Int)
-
-@[simp] protected theorem zero_eq : Dyadic.zero = 0 := rfl
-@[simp] protected theorem add_zero (x : Dyadic) : x + 0 = x := by cases x <;> rfl
-@[simp] protected theorem zero_add (x : Dyadic) : 0 + x = x := by cases x <;> rfl
-@[simp] protected theorem neg_zero : (-0 : Dyadic) = 0 := rfl
-@[simp] protected theorem mul_zero (x : Dyadic) : x * 0 = 0 := by cases x <;> rfl
-@[simp] protected theorem zero_mul (x : Dyadic) : 0 * x = 0 := by cases x <;> rfl
-
-@[simp] theorem toRat_zero : toRat 0 = 0 := rfl
-
-theorem _root_.Rat.mkRat_one (x : Int) : mkRat x 1 = x := by
-  rw [← Rat.mk_den_one, Rat.mk_eq_mkRat]
-
-theorem toRat_ofOdd_eq_mkRat :
-    toRat (.ofOdd n k hn) = mkRat (n <<< (-k).toNat) (1 <<< k.toNat) := by
-  cases k
-  · simp [toRat, Rat.mk_eq_mkRat, Int.shiftLeft_eq, Nat.shiftLeft_eq]
-  · simp [toRat, Int.neg_negSucc, Rat.mkRat_one, Int.shiftLeft_eq]
-
-theorem toRat_ofIntWithPrec_eq_mkRat :
-    toRat (.ofIntWithPrec n k) = mkRat (n <<< (-k).toNat) (1 <<< k.toNat) := by
-  simp only [ofIntWithPrec]
-  split
-  · simp_all
-  rw [toRat_ofOdd_eq_mkRat, Rat.mkRat_eq_iff (NeZero.ne _) (NeZero.ne _)]
-  simp only [Int.natCast_shiftLeft, Int.cast_ofNat_Int, Int.shiftLeft_mul_shiftLeft, Int.mul_one]
-  have : (-(k - n.trailingZeros) : Int).toNat + k.toNat =
-      n.trailingZeros + ((-k).toNat + (k - n.trailingZeros).toNat) := by omega
-  rw [this, Int.shiftLeft_add, Int.shiftRight_shiftLeft_cancel]
-  exact Int.two_pow_trailingZeros_dvd ‹_›
-
-theorem toRat_ofIntWithPrec_eq_mul_two_pow : toRat (.ofIntWithPrec n k) = n * 2 ^ (-k) := by
-  rw [toRat_ofIntWithPrec_eq_mkRat, Rat.zpow_neg, Int.shiftLeft_eq, Nat.one_shiftLeft]
-  rw [Rat.mkRat_eq_div, Rat.div_def]
-  have : ((2 : Int) : Rat) ≠ 0 := by decide
-  simp only [Rat.intCast_mul, Rat.intCast_pow, ← Rat.zpow_natCast, ← Rat.intCast_natCast,
-    Int.natCast_pow, Int.cast_ofNat_Int, ← Rat.zpow_neg, Rat.mul_assoc, ne_eq,
-    Rat.intCast_eq_zero_iff, Int.reduceEq, not_false_eq_true, ← Rat.zpow_add]
-  rw [Int.add_neg_eq_sub, ← Int.neg_sub, Int.toNat_sub_toNat_neg]
-  rfl
-
-example : ((3 : Dyadic) >>> 2) + ((3 : Dyadic) >>> 2) = ((3 : Dyadic) >>> 1) := rfl -- 3/4 + 3/4 = 3/2
-example : ((7 : Dyadic) >>> 3) + ((1 : Dyadic) >>> 3) = 1 := rfl -- 7/8 + 1/8 = 1
-example : (12 : Dyadic) + ((3 : Dyadic) >>> 1) = (27 : Dyadic) >>> 1 := rfl -- 12 + 3/2 = 27/2 = (2 * 13 + 1)/2^1
-example : ((3 : Dyadic) >>> 1).add 12 =  (27 : Dyadic) >>> 1 := rfl -- 3/2 + 12 = 27/2 = (2 * 13 + 1)/2^1
-example : (12 : Dyadic).add 12 = 24 := rfl -- 12 + 12 = 24
-
-@[simp]
-theorem toRat_add (x y : Dyadic) : toRat (x + y) = toRat x + toRat y := by
-  match x, y with
-  | .zero, _ => simp [toRat, Rat.zero_add]
-  | _, .zero => simp [toRat, Rat.add_zero]
-  | .ofOdd n₁ k₁ hn₁, .ofOdd n₂ k₂ hn₂ =>
-    change (Dyadic.add _ _).toRat = _
-    rw [Dyadic.add, toRat_ofOdd_eq_mkRat, toRat_ofOdd_eq_mkRat]
-    rw [Rat.mkRat_add_mkRat _ _ (NeZero.ne _) (NeZero.ne _)]
-    split
-    · rename_i h
-      cases Int.sub_eq_zero.mp h
-      rw [toRat_ofIntWithPrec_eq_mkRat, Rat.mkRat_eq_iff (NeZero.ne _) (NeZero.ne _)]
-      simp [Int.shiftLeft_mul_shiftLeft, Int.add_shiftLeft, Int.add_mul, Nat.add_assoc]
-    · rename_i h
-      cases Int.sub_eq_iff_eq_add.mp h
-      rw [toRat_ofOdd_eq_mkRat, Rat.mkRat_eq_iff (NeZero.ne _) (NeZero.ne _)]
-      simp only [succ_eq_add_one, Int.ofNat_eq_coe, Int.add_shiftLeft, ← Int.shiftLeft_add,
-        Int.natCast_mul, Int.natCast_shiftLeft, Int.shiftLeft_mul_shiftLeft, Int.add_mul]
-      congr 2 <;> omega
-    · rename_i h
-      cases Int.sub_eq_iff_eq_add.mp h
-      rw [toRat_ofOdd_eq_mkRat, Rat.mkRat_eq_iff (NeZero.ne _) (NeZero.ne _)]
-      simp only [Int.add_shiftLeft, ← Int.shiftLeft_add, Int.natCast_mul, Int.natCast_shiftLeft,
-        Int.cast_ofNat_Int, Int.shiftLeft_mul_shiftLeft, Int.mul_one, Int.add_mul]
-      congr 2 <;> omega
-
-@[simp]
-theorem toRat_neg (x : Dyadic) : toRat (-x) = - toRat x := by
-  change x.neg.toRat = _
-  cases x
-  · rfl
-  · simp [Dyadic.neg, Rat.neg_mkRat, Int.neg_shiftLeft, toRat_ofOdd_eq_mkRat]
-
-@[simp]
-theorem toRat_sub (x y : Dyadic) : toRat (x - y) = toRat x - toRat y := by
-  change toRat (x + -y) = _
-  simp [Rat.sub_eq_add_neg]
-
-@[simp]
-theorem toRat_mul (x y : Dyadic) : toRat (x * y) = toRat x * toRat y := by
-  match x, y with
-  | .zero, _ => simp
-  | _, .zero => simp
-  | .ofOdd n₁ k₁ hn₁, .ofOdd n₂ k₂ hn₂ =>
-    change (Dyadic.mul _ _).toRat = _
-    rw [Dyadic.mul, toRat_ofOdd_eq_mkRat, toRat_ofOdd_eq_mkRat, toRat_ofOdd_eq_mkRat,
-      Rat.mkRat_mul_mkRat, Rat.mkRat_eq_iff (NeZero.ne _) (NeZero.ne _)]
-    simp only [Int.natCast_mul, Int.natCast_shiftLeft, Int.cast_ofNat_Int,
-      Int.shiftLeft_mul_shiftLeft, Int.mul_one]
-    congr 1; omega
-
-@[simp]
-protected theorem pow_zero (x : Dyadic) : x ^ 0 = 1 := by
-  change x.pow 0 = 1
-  cases x <;> simp [Dyadic.pow] <;> rfl
-
-protected theorem pow_succ (x : Dyadic) (n : Nat) : x ^ (n + 1) = x ^ n * x := by
-  change x.pow (n + 1) = x.pow n * x
-  cases x
-  · simp [Dyadic.pow]
-  · change _ = Dyadic.mul _ _
-    simp [Dyadic.pow, Dyadic.mul, Int.pow_succ, Int.mul_add]
-
-@[simp]
-theorem toRat_pow (x : Dyadic) (n : Nat) : toRat (x ^ n) = toRat x ^ n := by
-  induction n with
-  | zero => simp; rfl
-  | succ k ih => simp [Dyadic.pow_succ, Rat.pow_succ, ih]
-
-@[simp]
-theorem toRat_intCast (x : Int) : (x : Dyadic).toRat = x := by
-  change (ofInt x).toRat = x
-  simp [ofInt, toRat_ofIntWithPrec_eq_mul_two_pow]
-
-@[simp]
-theorem toRat_natCast (x : Nat) : (x : Dyadic).toRat = x := by
-  change (ofInt x).toRat = x
-  simp [ofInt, toRat_ofIntWithPrec_eq_mul_two_pow, Rat.intCast_natCast]
-
-@[simp] theorem of_ne_zero : ofOdd n k hn ≠ 0 := Dyadic.noConfusion
-@[simp] theorem zero_ne_of : 0 ≠ ofOdd n k hn := Dyadic.noConfusion
-
-@[simp]
-theorem toRat_eq_zero_iff {x : Dyadic} : x.toRat = 0 ↔ x = 0 := by
-  refine ⟨fun h => ?_, fun h => h ▸ rfl⟩
-  cases x
-  · rfl
-  · simp only [toRat_ofOdd_eq_mkRat, ne_eq, shiftLeft_eq_zero_iff, succ_ne_self, not_false_eq_true,
-      Rat.mkRat_eq_zero, Int.shiftLeft_eq_zero_iff] at h
-    cases h
-    contradiction
-
-theorem ofOdd_eq_ofIntWithPrec : ofOdd n k hn = ofIntWithPrec n k := by
-  simp only [ofIntWithPrec, Dyadic.zero_eq, Int.trailingZeros_eq_zero_of_mod_eq hn,
-    Int.shiftRight_zero, Int.cast_ofNat_Int, Int.sub_zero, right_eq_dite_iff, of_ne_zero, imp_false]
-  intro rfl; contradiction
-
-theorem toRat_ofOdd_eq_mul_two_pow : toRat (.ofOdd n k hn) = n * 2 ^ (-k) := by
-  rw [ofOdd_eq_ofIntWithPrec, toRat_ofIntWithPrec_eq_mul_two_pow]
-
-@[simp]
-theorem ofIntWithPrec_zero {i : Int} : ofIntWithPrec 0 i = 0 := rfl
-
-@[simp]
-theorem neg_ofOdd : -ofOdd n k hn = ofOdd (-n) k (by simpa using hn) := rfl
-
-@[simp]
-theorem neg_ofIntWithPrec {i prec : Int} : -ofIntWithPrec i prec = ofIntWithPrec (-i) prec := by
-  rw [ofIntWithPrec, ofIntWithPrec]
-  simp only [Dyadic.zero_eq, Int.neg_eq_zero, Int.trailingZeros_neg]
-  split
-  · rfl
-  · obtain ⟨a, h⟩ := Int.two_pow_trailingZeros_dvd ‹_›
-    rw [Int.mul_comm, ← Int.shiftLeft_eq] at h
-    conv => enter [1, 1, 1, 1]; rw [h]
-    conv => enter [2, 1, 1]; rw [h]
-    simp only [Int.shiftLeft_shiftRight_cancel, neg_ofOdd, ← Int.neg_shiftLeft]
-
-theorem ofIntWithPrec_shiftLeft_add {n : Nat} :
-    ofIntWithPrec ((x : Int) <<< n) (i + n) = ofIntWithPrec x i := by
-  rw [ofIntWithPrec, ofIntWithPrec]
-  simp only [Int.shiftLeft_eq_zero_iff]
-  split
-  · rfl
-  · simp [Int.trailingZeros_shiftLeft, *, Int.shiftLeft_shiftRight_eq_shiftRight_of_le,
-      Int.add_comm x.trailingZeros n, ← Int.sub_sub]
-
-/-- The "precision" of a dyadic number, i.e. in `n * 2^(-p)` with `n` odd the precision is `p`. -/
--- TODO: If `WithBot` is upstreamed, replace this with `WithBot Int`.
-def precision : Dyadic → Option Int
-  | .zero => none
-  | .ofOdd _ p _ => some p
-
-theorem precision_ofIntWithPrec_le {i : Int} (h : i ≠ 0) (prec : Int) :
-    (ofIntWithPrec i prec).precision ≤ some prec := by
-  simp [ofIntWithPrec, h, precision]
-  omega
-
-@[simp] theorem precision_zero : (0 : Dyadic).precision = none := rfl
-@[simp] theorem precision_neg {x : Dyadic} : (-x).precision = x.precision :=
-  match x with
-  | .zero => rfl
-  | .ofOdd _ _ _ => rfl
-
-end Dyadic
-
-namespace Rat
-
-open Dyadic
-
-/--
-Convert a rational number `x` to the greatest dyadic number with precision at most `prec`
-which is less than or equal to `x`.
--/
-def toDyadic (x : Rat) (prec : Int) : Dyadic :=
-  match prec with
-  | (n : Nat) => .ofIntWithPrec ((x.num <<< n) / x.den) prec
-  | -(n + 1 : Nat) => .ofIntWithPrec (x.num / (x.den <<< (n + 1))) prec
-
-theorem toDyadic_mkRat (a : Int) (b : Nat) (prec : Int) :
-    Rat.toDyadic (mkRat a b) prec =
-      .ofIntWithPrec ((a <<< prec.toNat) / (b <<< (-prec).toNat)) prec := by
-  by_cases hb : b = 0
-  · cases prec <;> simp [hb, Rat.toDyadic]
-  rcases h : mkRat a b with ⟨n, d, hnz, hr⟩
-  obtain ⟨m, hm, rfl, rfl⟩ := Rat.mkRat_num_den hb h
-  cases prec
-  · simp only [Rat.toDyadic, Int.ofNat_eq_coe, Int.toNat_natCast, Int.toNat_neg_natCast,
-      shiftLeft_zero, Int.natCast_mul]
-    rw [Int.mul_comm d, ← Int.ediv_ediv (by simp), ← Int.shiftLeft_mul,
-      Int.mul_ediv_cancel _ (by simpa using hm)]
-  · simp only [Rat.toDyadic, Int.natCast_shiftLeft, Int.negSucc_eq, ← Int.natCast_add_one,
-      Int.toNat_neg_natCast, Int.shiftLeft_zero, Int.neg_neg, Int.toNat_natCast, Int.natCast_mul]
-    rw [Int.mul_comm d, ← Int.mul_shiftLeft, ← Int.ediv_ediv (by simp),
-      Int.mul_ediv_cancel _ (by simpa using hm)]
-
-theorem toDyadic_eq_ofIntWithPrec (x : Rat) (prec : Int) :
-    x.toDyadic prec = .ofIntWithPrec ((x.num <<< prec.toNat) / (x.den <<< (-prec).toNat)) prec := by
-  conv => lhs; rw [← Rat.mkRat_self x]
-  rw [Rat.toDyadic_mkRat]
-
-/--
-Converting a rational to a dyadic at a given precision and then back to a rational
-gives the same result as taking the floor of the rational at precision `2 ^ prec`.
--/
-theorem toRat_toDyadic (x : Rat) (prec : Int) :
-    (x.toDyadic prec).toRat = (x * 2 ^ prec).floor / 2 ^ prec := by
-  rw [Rat.toDyadic_eq_ofIntWithPrec, toRat_ofIntWithPrec_eq_mul_two_pow, Rat.zpow_neg, Rat.div_def]
-  congr 2
-  rw [Rat.floor_def, Int.shiftLeft_eq, Nat.shiftLeft_eq]
-  match prec with
-  | .ofNat prec =>
-    simp only [Int.ofNat_eq_coe, Int.toNat_natCast, Int.toNat_neg_natCast, Nat.pow_zero,
-      Nat.mul_one]
-    have : (2 ^ prec : Rat) = ((2 ^ prec : Nat) : Rat) := by simp
-    rw [Rat.zpow_natCast, this, Rat.mul_def']
-    simp only [Rat.num_mkRat, Rat.den_mkRat]
-    simp only [Rat.natCast_pow, Rat.natCast_ofNat, Rat.num_pow, Rat.num_ofNat, Rat.den_pow,
-      Rat.den_ofNat, Nat.one_pow, Nat.mul_one]
-    split
-    · simp_all
-    · rw [Int.ediv_ediv (Int.ofNat_zero_le _)]
-      congr 1
-      rw [Int.natCast_ediv, Int.mul_ediv_cancel']
-      rw [Int.natCast_dvd_natCast]
-      apply gcd_dvd_left
-  | .negSucc prec =>
-    simp only [Int.toNat_negSucc, Int.pow_zero, Int.mul_one, Int.neg_negSucc, Int.natCast_mul,
-      Int.natCast_pow, Int.cast_ofNat_Int]
-    have : (2 ^ ((prec : Int) + 1)) = ((2 ^ (prec + 1) : Nat) : Rat) := by simp; rfl
-    rw [Int.negSucc_eq, Rat.zpow_neg, this, Rat.mul_def']
-    simp only [Rat.num_mkRat, Rat.den_mkRat]
-    simp only [natCast_pow, natCast_ofNat, den_inv, num_pow, num_ofNat, Int.natAbs_pow,
-      Int.reduceAbs, num_inv, den_pow, den_ofNat, Nat.one_pow, Int.cast_ofNat_Int, Int.mul_one]
-    have : ¬ (2 ^ (prec + 1) : Int) = 0 := NeZero.out
-    simp only [if_neg this]
-    have : (2 ^ (prec + 1) : Int).sign = 1 := by simpa using Int.pow_pos (by decide)
-    simp only [this]
-    have : x.den * 2 ^ (prec + 1) = 0 ↔ x.den = 0 := by
-      rw [Nat.mul_eq_zero]
-      simp_all
-    simp only [this, Int.mul_one]
-    split
-    · simp_all
-    · rw [Int.ediv_ediv (Int.ofNat_zero_le _)]
-      congr 1
-      rw [Int.natCast_ediv, Int.mul_ediv_cancel']
-      · simp
-      · rw [Int.natCast_dvd_natCast]
-        apply gcd_dvd_left
-
-theorem toRat_toDyadic_le {x : Rat} {prec : Int} : (x.toDyadic prec).toRat ≤ x := by
-  rw [toRat_toDyadic]
-  have : (x * 2 ^ prec).floor ≤ x * 2 ^ prec := Rat.floor_le _
-  apply Rat.le_of_mul_le_mul_right (c := 2 ^ prec)
-  rw [Rat.div_mul_cancel]
-  exact this
-  · apply Rat.ne_of_gt (Rat.zpow_pos (by decide))
-  · exact Rat.zpow_pos (by decide)
-
-theorem lt_toRat_toDyadic_add {x : Rat} {prec : Int} :
-    x < (x.toDyadic prec + ofIntWithPrec 1 prec).toRat := by
-  rw [toRat_add, toRat_toDyadic, toRat_ofIntWithPrec_eq_mul_two_pow]
-  have := Rat.lt_floor_add_one (x * 2 ^ prec)
-  rw [Rat.zpow_neg, Rat.div_def, ← Rat.add_mul]
-  apply Rat.lt_of_mul_lt_mul_right (c := 2 ^ prec)
-  rw [Rat.mul_assoc, Rat.inv_mul_cancel, Rat.mul_one]
-  exact mod_cast this
-  · apply Rat.ne_of_gt (Rat.zpow_pos (by decide))
-  · exact Rat.zpow_nonneg (by decide)
-
--- TODO: `x.toDyadic prec` is the unique dyadic with the given precision satisfying the two inequalities above.
-
-end Rat
-
-namespace Dyadic
-
-/--
-Rounds a dyadic rational `x` down to the greatest dyadic number with precision at most `prec`
-which is less than or equal to `x`.
--/
-def roundDown (x : Dyadic) (prec : Int) : Dyadic :=
-  match x with
-  | .zero => .zero
-  | .ofOdd n k _ =>
-    match k - prec with
-    | .ofNat l => .ofIntWithPrec (n >>> l) prec
-    | .negSucc _ => x
-
-theorem roundDown_eq_self_of_le {x : Dyadic} {prec : Int} (h : x.precision ≤ some prec) :
-    roundDown x prec = x := by
-  rcases x with _ | ⟨n, k, hn⟩
-  · rfl
-  · simp only [precision] at h
-    obtain ⟨a, rfl⟩ := h.dest
-    rcases a with _ | a
-    · simp [roundDown, ofOdd_eq_ofIntWithPrec]
-    · have : k - (k + (a + 1 : Nat)) = Int.negSucc a := by omega
-      simp only [roundDown, this]
-
-@[simp]
-theorem toDyadic_toRat (x : Dyadic) (prec : Int) :
-    x.toRat.toDyadic prec = x.roundDown prec := by
-  rcases x with _ | ⟨n, k, hn⟩
-  · cases prec <;> simp [Rat.toDyadic, roundDown]
-  · simp only [toRat_ofOdd_eq_mkRat, roundDown]
-    rw [Rat.toDyadic_mkRat]
-    simp only [← Int.shiftLeft_add, Int.natCast_shiftLeft, Int.cast_ofNat_Int]
-    rw [Int.shiftLeft_eq' 1, Int.one_mul, ← Int.shiftRight_eq_div_pow]
-    rw [Int.shiftLeft_shiftRight_eq, ← Int.toNat_sub, ← Int.toNat_sub, ← Int.neg_sub]
-    have : ((k.toNat + (-prec).toNat : Nat) - ((-k).toNat + prec.toNat : Nat) : Int) = k - prec := by
-      omega
-    rw [this]
-    cases h : k - prec
-    · simp
-    · simp only [Int.neg_negSucc, Int.natCast_add, Int.cast_ofNat_Int, Int.toNat_natCast_add_one,
-        Int.toNat_negSucc, Int.shiftRight_zero]
-      rw [Int.negSucc_eq, Int.eq_neg_comm, Int.neg_sub, eq_comm, Int.sub_eq_iff_eq_add] at h
-      simp only [h, ← Int.natCast_add_one, Int.add_comm _ k, ofIntWithPrec_shiftLeft_add,
-        ofOdd_eq_ofIntWithPrec]
-
-theorem toRat_inj {x y : Dyadic} : x.toRat = y.toRat ↔ x = y := by
-  refine ⟨fun h => ?_, fun h => h ▸ rfl⟩
-  cases x <;> cases y
-  · rfl
-  · simp [eq_comm (a := (0 : Rat))] at h
-  · simp at h
-  · rename_i n₁ k₁ hn₁ n₂ k₂ hn₂
-    replace h := congrArg (·.toDyadic (max k₁ k₂)) h
-    simpa [toDyadic_toRat, roundDown_eq_self_of_le, precision, Int.le_max_left, Int.le_max_right]
-      using h
-
-theorem add_comm (x y : Dyadic) : x + y = y + x := by
-  rw [← toRat_inj, toRat_add, toRat_add, Rat.add_comm]
-
-theorem add_assoc (x y z : Dyadic) : (x + y) + z = x + (y + z) := by
-  rw [← toRat_inj, toRat_add, toRat_add, toRat_add, toRat_add, Rat.add_assoc]
-
-theorem mul_comm (x y : Dyadic) : x * y = y * x := by
-  rw [← toRat_inj, toRat_mul, toRat_mul, Rat.mul_comm]
-
-theorem mul_assoc (x y z : Dyadic) : (x * y) * z = x * (y * z) := by
-  rw [← toRat_inj, toRat_mul, toRat_mul, toRat_mul, toRat_mul, Rat.mul_assoc]
-
-theorem mul_one (x : Dyadic) : x * 1 = x := by
-  rw [← toRat_inj, toRat_mul]
-  exact Rat.mul_one x.toRat
-
-theorem one_mul (x : Dyadic) : 1 * x = x := by
-  rw [← toRat_inj, toRat_mul]
-  exact Rat.one_mul x.toRat
-
-theorem add_mul (x y z : Dyadic) : (x + y) * z = x * z + y * z := by
-  simp [← toRat_inj, Rat.add_mul]
-
-theorem mul_add (x y z : Dyadic) : x * (y + z) = x * y + x * z := by
-  simp [← toRat_inj, Rat.mul_add]
-
-theorem neg_add_cancel (x : Dyadic) : -x + x = 0 := by
-  simp [← toRat_inj, Rat.neg_add_cancel]
-
-theorem neg_mul (x y : Dyadic) : -x * y = -(x * y) := by
-  simp [← toRat_inj, Rat.neg_mul]
-
-/-- Determine if a dyadic rational is strictly less than another. -/
-def blt (x y : Dyadic) : Bool :=
-  match x, y with
-  | .zero, .zero => false
-  | .zero, .ofOdd n₂ _ _ => 0 < n₂
-  | .ofOdd n₁ _ _, .zero => n₁ < 0
-  | .ofOdd n₁ k₁ _, .ofOdd n₂ k₂ _ =>
-    match k₂ - k₁ with
-    | (l : Nat) => (n₁ <<< l) < n₂
-    | -((l+1 : Nat)) => n₁ < (n₂ <<< (l + 1))
-
-/-- Determine if a dyadic rational is less than or equal to another. -/
-def ble (x y : Dyadic) : Bool :=
-  match x, y with
-  | .zero, .zero => true
-  | .zero, .ofOdd n₂ _ _ => 0 ≤ n₂
-  | .ofOdd n₁ _ _, .zero => n₁ ≤ 0
-  | .ofOdd n₁ k₁ _, .ofOdd n₂ k₂ _ =>
-    match k₂ - k₁ with
-    | (l : Nat) => (n₁ <<< l) ≤ n₂
-    | -((l+1 : Nat)) => n₁ ≤ (n₂ <<< (l + 1))
-
-theorem blt_iff_toRat {x y : Dyadic} : blt x y ↔ x.toRat < y.toRat := by
-  rcases x with _ | ⟨n₁, k₁, hn₁⟩ <;> rcases y with _ | ⟨n₂, k₂, hn₂⟩
-  · decide
-  · simp only [blt, decide_eq_true_eq, Dyadic.zero_eq, toRat_zero, toRat_ofOdd_eq_mul_two_pow,
-      Rat.mul_pos_iff_of_pos_right (Rat.zpow_pos (by decide : (0 : Rat) < 2)), Rat.intCast_pos]
-  · simp only [blt, decide_eq_true_eq, Dyadic.zero_eq, toRat_zero, toRat_ofOdd_eq_mul_two_pow,
-      Rat.mul_neg_iff_of_pos_right (Rat.zpow_pos (by decide : (0 : Rat) < 2)), Rat.intCast_neg_iff]
-  · simp only [blt, toRat_ofOdd_eq_mul_two_pow,
-      ← Rat.div_lt_iff (Rat.zpow_pos (by decide : (0 : Rat) < 2)), Rat.div_def, ← Rat.zpow_neg,
-      Int.neg_neg, Rat.mul_assoc, ne_eq, Rat.ofNat_eq_ofNat, reduceCtorEq, not_false_eq_true,
-      ← Rat.zpow_add, Int.shiftLeft_eq]
-    rw [Int.add_comm, Int.add_neg_eq_sub]
-    split
-    · simp [decide_eq_true_eq, ← Rat.intCast_lt_intCast, Rat.zpow_natCast, *]
-    · simp only [decide_eq_true_eq, Int.negSucc_eq, *]
-      rw [Rat.zpow_neg, ← Rat.div_def, Rat.div_lt_iff (Rat.zpow_pos (by decide))]
-      simp [← Rat.intCast_lt_intCast, ← Rat.zpow_natCast, *]
-
-theorem blt_eq_false_iff : blt x y = false ↔ ble y x = true := by
-  cases x <;> cases y
-  · simp [ble, blt]
-  · simp [ble, blt]
-  · simp [ble, blt]
-  · rename_i n₁ k₁ hn₁ n₂ k₂ hn₂
-    simp only [blt, ble]
-    rw [← Int.neg_sub]
-    rcases k₁ - k₂ with (_ | _) | _
-    · simp
-    · simp [← Int.negSucc_eq]
-    · simp only [Int.neg_negSucc, decide_eq_false_iff_not, Int.not_lt,
-        decide_eq_true_eq]
-
-theorem ble_iff_toRat : ble x y ↔ x.toRat ≤ y.toRat := by
-  rw [← blt_eq_false_iff, Bool.eq_false_iff]
-  simp only [ne_eq, blt_iff_toRat, Rat.not_lt]
-
-instance : LT Dyadic where
-  lt x y := blt x y
-
-instance : LE Dyadic where
-  le x y := ble x y
-
-instance : DecidableLT Dyadic := fun _ _ => inferInstanceAs (Decidable (_ = true))
-instance : DecidableLE Dyadic := fun _ _ => inferInstanceAs (Decidable (_ = true))
-
-theorem lt_iff_toRat {x y : Dyadic} : x < y ↔ x.toRat < y.toRat := blt_iff_toRat
-
-theorem le_iff_toRat {x y : Dyadic} : x ≤ y ↔ x.toRat ≤ y.toRat := ble_iff_toRat
-
-@[simp]
-protected theorem not_le {x y : Dyadic} : ¬x < y ↔ y ≤ x := by
-  simp only [· ≤ ·, · < ·, Bool.not_eq_true, blt_eq_false_iff]
-
-@[simp]
-protected theorem not_lt {x y : Dyadic} : ¬x ≤ y ↔ y < x := by
-  rw [← Dyadic.not_le, Decidable.not_not]
-
-@[simp]
-protected theorem le_refl (x : Dyadic) : x ≤ x := by
-  rw [le_iff_toRat]
-  exact Rat.le_refl
-
-protected theorem le_trans {x y z : Dyadic} (h : x ≤ y) (h' : y ≤ z) : x ≤ z := by
-  rw [le_iff_toRat] at h h' ⊢
-  exact Rat.le_trans h h'
-
-protected theorem le_antisymm {x y : Dyadic} (h : x ≤ y) (h' : y ≤ x) : x = y := by
-  rw [le_iff_toRat] at h h'
-  rw [← toRat_inj]
-  exact Rat.le_antisymm h h'
-
-protected theorem le_total (x y : Dyadic) : x ≤ y ∨ y ≤ x := by
-  rw [le_iff_toRat, le_iff_toRat]
-  exact Rat.le_total
-
-instance : Std.LawfulOrderLT Dyadic where
-  lt_iff a b := by rw [← Dyadic.not_lt, iff_and_self]; exact (Dyadic.le_total _ _).resolve_left
-
-instance : Std.IsPreorder Dyadic where
-  le_refl := Dyadic.le_refl
-  le_trans _ _ _ := Dyadic.le_trans
-
-instance : Std.IsPartialOrder Dyadic where
-  le_antisymm _ _ := Dyadic.le_antisymm
-
-instance : Std.IsLinearPreorder Dyadic where
-  le_total := Dyadic.le_total
-
-instance : Std.IsLinearOrder Dyadic where
-
-/-- `roundUp x prec` is the least dyadic number with precision at most `prec` which is greater than or equal to `x`. -/
-def roundUp (x : Dyadic) (prec : Int) : Dyadic :=
-  match x with
-  | .zero => .zero
-  | .ofOdd n k _ =>
-    match k - prec with
-    | .ofNat l => .ofIntWithPrec (-((-n) >>> l)) prec
-    | .negSucc _ => x
-
-theorem roundUp_eq_neg_roundDown_neg (x : Dyadic) (prec : Int) :
-    x.roundUp prec = -((-x).roundDown prec) := by
-  rcases x with _ | ⟨n, k, hn⟩
-  · rfl
-  · change _ = -(ofOdd ..).roundDown prec
-    rw [roundDown, roundUp]
-    split <;> simp
-
-end Dyadic

src/Init/Data/Dyadic/Instances.lean

@@ -1,60 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison, Robin Arnez
--/
-module
-
-prelude
-public import Init.Data.Dyadic.Basic
-public import Init.Grind.Ring.Basic
-public import Init.Grind.Ordered.Ring
-
-/-! # Internal `grind` algebra instances for `Dyadic`. -/
-
-open Lean.Grind
-
-namespace Dyadic
-
-instance : CommRing Dyadic where
-  nsmul := ⟨(· * ·)⟩
-  zsmul := ⟨(· * ·)⟩
-  add_zero := Dyadic.add_zero
-  add_comm := Dyadic.add_comm
-  add_assoc := Dyadic.add_assoc
-  mul_assoc := Dyadic.mul_assoc
-  mul_one := Dyadic.mul_one
-  one_mul := Dyadic.one_mul
-  zero_mul := Dyadic.zero_mul
-  mul_zero := Dyadic.mul_zero
-  mul_comm := Dyadic.mul_comm
-  pow_zero := Dyadic.pow_zero
-  pow_succ := Dyadic.pow_succ
-  sub_eq_add_neg _ _ := rfl
-  neg_add_cancel := Dyadic.neg_add_cancel
-  neg_zsmul i a := by
-    change ((-i : Int) : Dyadic) * a = -(i * a)
-    simp [← toRat_inj, Rat.neg_mul]
-  left_distrib := Dyadic.mul_add
-  right_distrib := Dyadic.add_mul
-  intCast_neg _ := by simp [← toRat_inj]
-  ofNat_succ n := by
-    change ((n + 1 : Int) : Dyadic) = ((n : Int) : Dyadic) + 1
-    simp [← toRat_inj, Rat.intCast_add]; rfl
-
-instance : IsCharP Dyadic 0 := IsCharP.mk' _ _
-  (ofNat_eq_zero_iff := fun x => by change (x : Dyadic) = 0 ↔ _; simp [← toRat_inj])
-
-instance : NoNatZeroDivisors Dyadic where
-  no_nat_zero_divisors k a b h₁ h₂ := by
-    change k * a = k * b at h₂
-    simp only [← toRat_inj, toRat_mul, toRat_natCast] at h₂ ⊢
-    simpa [← Rat.mul_assoc, Rat.inv_mul_cancel, h₁] using congrArg ((k : Rat)⁻¹ * ·) h₂
-
-instance : OrderedRing Dyadic where
-  zero_lt_one := by decide
-  add_le_left_iff _ := by simp [le_iff_toRat, Rat.add_le_add_right]
-  mul_lt_mul_of_pos_left {_ _ _} := by simpa [lt_iff_toRat] using Rat.mul_lt_mul_of_pos_left
-  mul_lt_mul_of_pos_right {_ _ _} := by simpa [lt_iff_toRat] using Rat.mul_lt_mul_of_pos_right
-
-end Dyadic

src/Init/Data/Dyadic/Inv.lean

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

src/Init/Data/Dyadic/Round.lean

@@ -1,77 +0,0 @@
-/-
-Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison
--/
-module
-
-prelude
-public import Init.Data.Dyadic.Basic
-import all Init.Data.Dyadic.Instances
-import Init.Data.Int.Bitwise.Lemmas
-import Init.Grind.Ordered.Rat
-import Init.Grind.Ordered.Field
-
-namespace Dyadic
-
-/-!
-Theorems about `roundUp` and `roundDown`.
--/
-
-public section
-
-theorem roundDown_le {x : Dyadic} {prec : Int} : roundDown x prec ≤ x :=
-  match x with
-  | .zero => Dyadic.le_refl _
-  | .ofOdd n k _ => by
-    unfold roundDown
-    dsimp
-    match h : k - prec with
-    | .ofNat l =>
-      dsimp
-      rw [ofOdd_eq_ofIntWithPrec, le_iff_toRat]
-      replace h : k = Int.ofNat l + prec := by omega
-      subst h
-      simp only [toRat_ofIntWithPrec_eq_mul_two_pow]
-      rw [Int.neg_add, Rat.zpow_add (by decide), ← Rat.mul_assoc]
-      refine Lean.Grind.OrderedRing.mul_le_mul_of_nonneg_right ?_ (Rat.zpow_nonneg (by decide))
-      rw [Int.shiftRight_eq_div_pow]
-      rw [← Lean.Grind.Field.IsOrdered.mul_le_mul_iff_of_pos_right (c := 2^(Int.ofNat l)) (Rat.zpow_pos (by decide))]
-      simp only [Int.natCast_pow, Int.cast_ofNat_Int, Int.ofNat_eq_coe]
-      rw [Rat.mul_assoc, ← Rat.zpow_add (by decide), Int.add_left_neg, Rat.zpow_zero, Rat.mul_one]
-      have : (2 : Rat) ^ (l : Int) = (2 ^ l : Int) := by
-        rw [Rat.zpow_natCast, Rat.intCast_pow, Rat.intCast_ofNat]
-      rw [this, ← Rat.intCast_mul, Rat.intCast_le_intCast]
-      exact Int.ediv_mul_le n (Int.pow_ne_zero (by decide))
-    | .negSucc _ =>
-      apply Dyadic.le_refl
-
-theorem precision_roundDown {x : Dyadic} {prec : Int} : (roundDown x prec).precision ≤ some prec := by
-  unfold roundDown
-  match x with
-  | zero => simp [precision]
-  | ofOdd n k hn =>
-    dsimp
-    split
-    · rename_i n' h
-      by_cases h' : n >>> n' = 0
-      · simp [h']
-      · exact precision_ofIntWithPrec_le h' _
-    · simp [precision]
-      omega
-
--- This theorem would characterize `roundDown` in terms of the order and `precision`.
--- theorem le_roundDown {x y : Dyadic} {prec : Int} (h : y.precision ≤ some prec) (h' : y ≤ x) :
---     y ≤ x.roundDown prec := sorry
-
-theorem le_roundUp {x : Dyadic} {prec : Int} : x ≤ roundUp x prec := by
-  rw [roundUp_eq_neg_roundDown_neg, Lean.Grind.OrderedAdd.le_neg_iff]
-  apply roundDown_le
-
-theorem precision_roundUp {x : Dyadic} {prec : Int} : (roundUp x prec).precision ≤ some prec := by
-  rw [roundUp_eq_neg_roundDown_neg, precision_neg]
-  exact precision_roundDown
-
--- This theorem would characterize `roundUp` in terms of the order and `precision`.
--- theorem roundUp_le {x y : Dyadic} {prec : Int} (h : y.precision ≤ some prec) (h' : x ≤ y) :
---    x.roundUp prec ≤ y := sorry

src/Init/Data/Fin/Basic.lean

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

src/Init/Data/Fin/Fold.lean

@@ -107,14 +107,14 @@ Fin.foldrM n f xₙ = do
   subst w
   rfl
 
-private theorem foldlM_loop_lt [Monad m] (f : α → Fin n → m α) (x) (h : i < n) :
+theorem foldlM_loop_lt [Monad m] (f : α → Fin n → m α) (x) (h : i < n) :
     foldlM.loop n f x i = f x ⟨i, h⟩ >>= (foldlM.loop n f . (i+1)) := by
   rw [foldlM.loop, dif_pos h]
 
-private theorem foldlM_loop_eq [Monad m] (f : α → Fin n → m α) (x) : foldlM.loop n f x n = pure x := by
+theorem foldlM_loop_eq [Monad m] (f : α → Fin n → m α) (x) : foldlM.loop n f x n = pure x := by
   rw [foldlM.loop, dif_neg (Nat.lt_irrefl _)]
 
-private theorem foldlM_loop [Monad m] (f : α → Fin (n+1) → m α) (x) (h : i < n+1) :
+theorem foldlM_loop [Monad m] (f : α → Fin (n+1) → m α) (x) (h : i < n+1) :
     foldlM.loop (n+1) f x i = f x ⟨i, h⟩ >>= (foldlM.loop n (fun x j => f x j.succ) . i) := by
   if h' : i < n then
     rw [foldlM_loop_lt _ _ h]
@@ -170,15 +170,15 @@ theorem foldlM_add [Monad m] [LawfulMonad m] (f : α → Fin (n + k) → m α) :
   subst w
   rfl
 
-private theorem foldrM_loop_zero [Monad m] (f : Fin n → α → m α) (x) :
+theorem foldrM_loop_zero [Monad m] (f : Fin n → α → m α) (x) :
     foldrM.loop n f ⟨0, Nat.zero_le _⟩ x = pure x := by
   rw [foldrM.loop]
 
-private theorem foldrM_loop_succ [Monad m] (f : Fin n → α → m α) (x) (h : i < n) :
+theorem foldrM_loop_succ [Monad m] (f : Fin n → α → m α) (x) (h : i < n) :
     foldrM.loop n f ⟨i+1, h⟩ x = f ⟨i, h⟩ x >>= foldrM.loop n f ⟨i, Nat.le_of_lt h⟩ := by
   rw [foldrM.loop]
 
-private theorem foldrM_loop [Monad m] [LawfulMonad m] (f : Fin (n+1) → α → m α) (x) (h : i+1 ≤ n+1) :
+theorem foldrM_loop [Monad m] [LawfulMonad m] (f : Fin (n+1) → α → m α) (x) (h : i+1 ≤ n+1) :
     foldrM.loop (n+1) f ⟨i+1, h⟩ x =
       foldrM.loop n (fun j => f j.succ) ⟨i, Nat.le_of_succ_le_succ h⟩ x >>= f 0 := by
   induction i generalizing x with
@@ -228,14 +228,14 @@ theorem foldrM_add [Monad m] [LawfulMonad m] (f : Fin (n + k) → α → m α) :
   subst w
   rfl
 
-private theorem foldl_loop_lt (f : α → Fin n → α) (x) (h : i < n) :
+theorem foldl_loop_lt (f : α → Fin n → α) (x) (h : i < n) :
     foldl.loop n f x i = foldl.loop n f (f x ⟨i, h⟩) (i+1) := by
   rw [foldl.loop, dif_pos h]
 
-private theorem foldl_loop_eq (f : α → Fin n → α) (x) : foldl.loop n f x n = x := by
+theorem foldl_loop_eq (f : α → Fin n → α) (x) : foldl.loop n f x n = x := by
   rw [foldl.loop, dif_neg (Nat.lt_irrefl _)]
 
-private theorem foldl_loop (f : α → Fin (n+1) → α) (x) (h : i < n+1) :
+theorem foldl_loop (f : α → Fin (n+1) → α) (x) (h : i < n+1) :
     foldl.loop (n+1) f x i = foldl.loop n (fun x j => f x j.succ) (f x ⟨i, h⟩) i := by
   if h' : i < n then
     rw [foldl_loop_lt _ _ h]
@@ -285,15 +285,15 @@ theorem foldlM_pure [Monad m] [LawfulMonad m] {n} {f : α → Fin n → α} :
   subst w
   rfl
 
-private theorem foldr_loop_zero (f : Fin n → α → α) (x) :
+theorem foldr_loop_zero (f : Fin n → α → α) (x) :
     foldr.loop n f 0 (Nat.zero_le _) x = x := by
   rw [foldr.loop]
 
-private theorem foldr_loop_succ (f : Fin n → α → α) (x) (h : i < n) :
+theorem foldr_loop_succ (f : Fin n → α → α) (x) (h : i < n) :
     foldr.loop n f (i+1) h x = foldr.loop n f i (Nat.le_of_lt h) (f ⟨i, h⟩ x) := by
   rw [foldr.loop]
 
-private theorem foldr_loop (f : Fin (n+1) → α → α) (x) (h : i+1 ≤ n+1) :
+theorem foldr_loop (f : Fin (n+1) → α → α) (x) (h : i+1 ≤ n+1) :
     foldr.loop (n+1) f (i+1) h x =
       f 0 (foldr.loop n (fun j => f j.succ) i (Nat.le_of_succ_le_succ h) x) := by
   induction i generalizing x with

src/Init/Data/Fin/Lemmas.lean

@@ -12,25 +12,21 @@ public import Init.Ext
 public import Init.ByCases
 public import Init.Conv
 public import Init.Omega
-public import Init.Data.Order.Factories
-import Init.Data.Order.Lemmas
 
 public section
 
-open Std
-
 namespace Fin
 
 @[simp] theorem ofNat_zero (n : Nat) [NeZero n] : Fin.ofNat n 0 = 0 := rfl
 
 @[deprecated ofNat_zero (since := "2025-05-28")] abbrev ofNat'_zero := @ofNat_zero
 
-theorem mod_def (a m : Fin n) : a % m = Fin.mk (a.val % m.val) (Nat.lt_of_le_of_lt (Nat.mod_le _ _) a.2) :=
+theorem mod_def (a m : Fin n) : a % m = Fin.mk (a % m) (Nat.lt_of_le_of_lt (Nat.mod_le _ _) a.2) :=
   rfl
 
-theorem mul_def (a b : Fin n) : a * b = Fin.mk ((a.val * b.val) % n) (Nat.mod_lt _ a.pos) := rfl
+theorem mul_def (a b : Fin n) : a * b = Fin.mk ((a * b) % n) (Nat.mod_lt _ a.pos) := rfl
 
-theorem sub_def (a b : Fin n) : a - b = Fin.mk (((n - b.val) + a.val) % n) (Nat.mod_lt _ a.pos) := rfl
+theorem sub_def (a b : Fin n) : a - b = Fin.mk (((n - b) + a) % n) (Nat.mod_lt _ a.pos) := rfl
 
 theorem pos' : ∀ [Nonempty (Fin n)], 0 < n | ⟨i⟩ => i.pos
 
@@ -81,7 +77,7 @@ theorem mk_val (i : Fin n) : (⟨i, i.isLt⟩ : Fin n) = i := Fin.eta ..
 
 @[deprecated ofNat_self (since := "2025-05-28")] abbrev ofNat'_self := @ofNat_self
 
-@[simp] theorem ofNat_val_eq_self [NeZero n] (x : Fin n) : (Fin.ofNat n x.val) = x := by
+@[simp] theorem ofNat_val_eq_self [NeZero n] (x : Fin n) : (Fin.ofNat n x) = x := by
   ext
   rw [val_ofNat, Nat.mod_eq_of_lt]
   exact x.2
@@ -121,6 +117,8 @@ Non-trivial loops lead to undesirable and counterintuitive elaboration behavior.
 For example, for `x : Fin k` and `n : Nat`,
 it causes `x < n` to be elaborated as `x < ↑n` rather than `↑x < n`,
 silently introducing wraparound arithmetic.
+
+Note: as of 2025-06-03, Mathlib has such a coercion for `Fin n` anyway!
 -/
 @[expose]
 def instNatCast (n : Nat) [NeZero n] : NatCast (Fin n) where
@@ -253,17 +251,7 @@ protected theorem le_antisymm_iff {x y : Fin n} : x = y ↔ x ≤ y ∧ y ≤ x
 protected theorem le_antisymm {x y : Fin n} (h1 : x ≤ y) (h2 : y ≤ x) : x = y :=
   Fin.le_antisymm_iff.2 ⟨h1, h2⟩
 
-instance instIsLinearOrder : IsLinearOrder (Fin n) := by
-  apply IsLinearOrder.of_le
-  case le_antisymm => constructor; apply Fin.le_antisymm
-  case le_total => constructor; apply Fin.le_total
-  case le_trans => constructor; apply Fin.le_trans
-
-instance : LawfulOrderLT (Fin n) where
-  lt_iff := by
-    simp [← Fin.not_le, Decidable.imp_iff_not_or, Std.Total.total]
-
-@[simp, grind =] theorem val_rev (i : Fin n) : (rev i).val = n - (i + 1) := rfl
+@[simp, grind =] theorem val_rev (i : Fin n) : rev i = n - (i + 1) := rfl
 
 @[simp] theorem rev_rev (i : Fin n) : rev (rev i) = i := Fin.ext <| by
   rw [val_rev, val_rev, ← Nat.sub_sub, Nat.sub_sub_self (by exact i.2), Nat.add_sub_cancel]
@@ -498,11 +486,9 @@ theorem succ_succ_ne_one (a : Fin n) : Fin.succ (Fin.succ a) ≠ 1 :=
   ext
   simp
 
-@[simp, grind =] theorem cast_cast {k : Nat} (h : n = m) (h' : m = k) {i : Fin n} :
+@[simp] theorem cast_trans {k : Nat} (h : n = m) (h' : m = k) {i : Fin n} :
     (i.cast h).cast h' = i.cast (Eq.trans h h') := rfl
 
-@[deprecated cast_cast (since := "2025-09-03")] abbrev cast_trans := @cast_cast
-
 theorem castLE_of_eq {m n : Nat} (h : m = n) {h' : m ≤ n} : castLE h' = Fin.cast h := rfl
 
 @[simp] theorem coe_castAdd (m : Nat) (i : Fin n) : (castAdd m i : Nat) = i := rfl
@@ -531,7 +517,7 @@ theorem cast_castAdd_left {n n' m : Nat} (i : Fin n') (h : n' + m = n + m) :
     (i.castAdd m').cast h = i.castAdd m := rfl
 
 theorem castAdd_castAdd {m n p : Nat} (i : Fin m) :
-    (i.castAdd n).castAdd p = (i.castAdd (n + p)).cast (Nat.add_assoc ..).symm := rfl
+    (i.castAdd n).castAdd p = (i.castAdd (n + p)).cast (Nat.add_assoc ..).symm  := rfl
 
 /-- The cast of the successor is the successor of the cast. See `Fin.succ_cast_eq` for rewriting in
 the reverse direction. -/
@@ -952,7 +938,7 @@ For the induction:
     (reverseInduction zero succ (Fin.last n) : motive (Fin.last n)) = zero := by
   rw [reverseInduction, reverseInduction.go]; simp
 
-private theorem reverseInduction_castSucc_aux {n : Nat} {motive : Fin (n + 1) → Sort _} {succ}
+@[simp] theorem reverseInduction_castSucc_aux {n : Nat} {motive : Fin (n + 1) → Sort _} {succ}
     (i : Fin n) (j : Nat) (h) (h2 : i.1 < j) (zero : motive ⟨j, h⟩) :
     reverseInduction.go (motive := motive) succ i.castSucc j h (Nat.le_of_lt h2) zero =
       succ i (reverseInduction.go succ i.succ j h h2 zero) := by

src/Init/Data/Format/Basic.lean

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

src/Init/Data/Format/Instances.lean

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

src/Init/Data/Format/Syntax.lean

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

src/Init/Data/Int/Basic.lean

@@ -31,7 +31,6 @@ This file defines the `Int` type as well as
 Division and modulus operations are defined in `Init.Data.Int.DivMod.Basic`.
 -/
 
-set_option genCtorIdx false in
 /--
 The integers.
 
@@ -315,14 +314,12 @@ Examples:
  * `(0 : Int).natAbs = 0`
  * `((-11 : Int).natAbs = 11`
 -/
-@[extern "lean_nat_abs", expose]
+@[extern "lean_nat_abs"]
 def natAbs (m : @& Int) : Nat :=
   match m with
   | ofNat m => m
   | -[m +1] => m.succ
 
-attribute [gen_constructor_elims] Int
-
 /-! ## sign -/
 
 /--
@@ -408,25 +405,11 @@ instance : Min Int := minOfLe
 instance : Max Int := maxOfLe
 
 /-- Equality predicate for kernel reduction. -/
-@[expose] protected noncomputable def beq' (a b : Int) : Bool :=
+protected noncomputable def beq' (a b : Int) : Bool :=
   Int.rec
     (fun a => Int.rec (fun b => Nat.beq a b) (fun _ => false) b)
     (fun a => Int.rec (fun _ => false) (fun b => Nat.beq a b) b) a
 
-/-- `x ≤ y` for kernel reduction. -/
-@[expose] protected noncomputable def ble' (a b : Int) : Bool :=
-  Int.rec
-    (fun a => Int.rec (fun b => Nat.ble a b) (fun _ => false) b)
-    (fun a => Int.rec (fun _ => true) (fun b => Nat.ble b a) b)
-    a
-
-/-- `x < y` for kernel reduction. -/
-@[expose] protected noncomputable def blt' (a b : Int) : Bool :=
-  Int.rec
-    (fun a => Int.rec (fun b => Nat.blt a b) (fun _ => false) b)
-    (fun a => Int.rec (fun _ => true) (fun b => Nat.blt b a) b)
-    a
-
 end Int
 
 /--

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

@@ -50,21 +50,4 @@ protected def shiftRight : Int → Nat → Int
 
 instance : HShiftRight Int Nat Int := ⟨.shiftRight⟩
 
-/--
-Bitwise left shift, usually accessed via the `<<<` operator.
-
-Examples:
- * `1 <<< 2 = 4`
- * `1 <<< 3 = 8`
- * `0 <<< 3 = 0`
- * `0xf1 <<< 4 = 0xf10`
- * `(-1) <<< 3 = -8`
--/
-@[expose]
-protected def shiftLeft : Int → Nat → Int
-  | Int.ofNat n, s => Int.ofNat (n <<< s)
-  | Int.negSucc n, s => Int.negSucc (((n + 1) <<< s) - 1)
-
-instance : HShiftLeft Int Nat Int := ⟨.shiftLeft⟩
-
 end Int

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

@@ -7,8 +7,7 @@ module
 
 prelude
 public import Init.Data.Nat.Bitwise.Lemmas
-public import Init.Data.Int.Bitwise.Basic
-import all Init.Data.Int.Bitwise.Basic
+public import all Init.Data.Int.Bitwise.Basic
 public import Init.Data.Int.DivMod.Lemmas
 
 public section
@@ -17,8 +16,8 @@ namespace Int
 
 theorem shiftRight_eq (n : Int) (s : Nat) : n >>> s = Int.shiftRight n s := rfl
 
-@[simp, norm_cast]
-theorem natCast_shiftRight (n s : Nat) : n >>> s = (n : Int) >>> s := rfl
+@[simp]
+theorem natCast_shiftRight (n s : Nat) : (n : Int) >>> s = n >>> s := rfl
 
 @[simp]
 theorem negSucc_shiftRight (m n : Nat) :
@@ -38,11 +37,11 @@ theorem shiftRight_eq_div_pow (m : Int) (n : Nat) :
   · rw [negSucc_ediv _ (by norm_cast; exact Nat.pow_pos (Nat.zero_lt_two))]
     rfl
 
-@[simp, grind =]
+@[simp]
 theorem zero_shiftRight (n : Nat) : (0 : Int) >>> n = 0 := by
   simp [Int.shiftRight_eq_div_pow]
 
-@[simp, grind =]
+@[simp]
 theorem shiftRight_zero (n : Int) : n >>> 0 = n := by
   simp [Int.shiftRight_eq_div_pow]
 
@@ -68,7 +67,7 @@ theorem shiftRight_le_of_nonneg {n : Int} {s : Nat} (h : 0 ≤ n) : n >>> s ≤
     by_cases hm : m = 0
     · simp [hm]
     · have := Nat.shiftRight_le m s
-      rw [ofNat_eq_coe]
+      simp
       omega
   case _ _ _ m =>
     omega
@@ -89,94 +88,4 @@ theorem shiftRight_le_of_nonpos {n : Int} {s : Nat} (h : n ≤ 0) : (n >>> s)
     have rl : n / 2 ^ s ≤ 0 := Int.ediv_nonpos_of_nonpos_of_neg (by omega) (by norm_cast at *; omega)
     norm_cast at *
 
-@[simp, norm_cast]
-theorem natCast_shiftLeft (n s : Nat) : n <<< s = (n : Int) <<< s := rfl
-
-@[simp, grind =]
-theorem zero_shiftLeft (n : Nat) : (0 : Int) <<< n = 0 := by
-  change ((0 <<< n : Nat) : Int) = 0
-  simp
-
-@[simp, grind =]
-theorem shiftLeft_zero (n : Int) : n <<< 0 = n := by
-  change Int.shiftLeft _ _ = _
-  match n with
-  | Int.ofNat n
-  | Int.negSucc n => simp [Int.shiftLeft]
-
-theorem shiftLeft_succ (m : Int) (n : Nat) : m <<< (n + 1) = (m <<< n) * 2 := by
-  change Int.shiftLeft _ _ = Int.shiftLeft _ _ * 2
-  match m with
-  | (m : Nat) =>
-    dsimp only [Int.shiftLeft, Int.ofNat_eq_coe]
-    rw [Nat.shiftLeft_succ, Nat.mul_comm, natCast_mul, ofNat_two]
-  | Int.negSucc m =>
-    dsimp only [Int.shiftLeft]
-    rw [Nat.shiftLeft_succ, Nat.mul_comm, Int.negSucc_eq]
-    have := Nat.le_shiftLeft (a := m + 1) (b := n)
-    omega
-
-theorem shiftLeft_succ' (m : Int) (n : Nat) : m <<< (n + 1) = 2 * (m <<< n) := by
-  rw [shiftLeft_succ, Int.mul_comm]
-
-theorem shiftLeft_eq (a : Int) (b : Nat) : a <<< b = a * 2 ^ b := by
-  induction b with
-  | zero => simp
-  | succ b ih =>
-    rw [shiftLeft_succ, ih, Int.pow_succ, Int.mul_assoc]
-
-theorem shiftLeft_eq' (a : Int) (b : Nat) : a <<< b = a * (2 ^ b : Nat) := by
-  simp [shiftLeft_eq]
-
-theorem shiftLeft_add (a : Int) (b c : Nat) : a <<< (b + c) = a <<< b <<< c := by
-  simp [shiftLeft_eq, Int.pow_add, Int.mul_assoc]
-
-@[simp]
-theorem shiftLeft_shiftRight_cancel (a : Int) (b : Nat) : a <<< b >>> b = a := by
-  simp [shiftLeft_eq, shiftRight_eq_div_pow, mul_ediv_cancel _ (NeZero.ne _)]
-
-theorem shiftLeft_shiftRight_eq_shiftLeft_of_le {b c : Nat} (h : c ≤ b) (a : Int) :
-    a <<< b >>> c = a <<< (b - c) := by
-  obtain ⟨b, rfl⟩ := h.dest
-  simp [shiftLeft_eq, Int.pow_add, shiftRight_eq_div_pow, Int.mul_left_comm a,
-    Int.mul_ediv_cancel_left _ (NeZero.ne _)]
-
-theorem shiftLeft_shiftRight_eq_shiftRight_of_le {b c : Nat} (h : b ≤ c) (a : Int) :
-    a <<< b >>> c = a >>> (c - b) := by
-  obtain ⟨c, rfl⟩ := h.dest
-  simp [shiftRight_add]
-
-theorem shiftLeft_shiftRight_eq (a : Int) (b c : Nat) :
-    a <<< b >>> c = a <<< (b - c) >>> (c - b) := by
-  rcases Nat.le_total b c with h | h
-  · simp [shiftLeft_shiftRight_eq_shiftRight_of_le h, Nat.sub_eq_zero_of_le h]
-  · simp [shiftLeft_shiftRight_eq_shiftLeft_of_le h, Nat.sub_eq_zero_of_le h]
-
-@[simp]
-theorem shiftRight_shiftLeft_cancel {a : Int} {b : Nat} (h : 2 ^ b ∣ a) : a >>> b <<< b = a := by
-  simp [shiftLeft_eq, shiftRight_eq_div_pow, Int.ediv_mul_cancel h]
-
-theorem add_shiftLeft (a b : Int) (n : Nat) : (a + b) <<< n = a <<< n + b <<< n := by
-  simp [shiftLeft_eq, Int.add_mul]
-
-theorem neg_shiftLeft (a : Int) (n : Nat) : (-a) <<< n = -a <<< n := by
-  simp [Int.shiftLeft_eq, Int.neg_mul]
-
-theorem shiftLeft_mul (a b : Int) (n : Nat) : a <<< n * b = (a * b) <<< n := by
-  simp [shiftLeft_eq, Int.mul_right_comm]
-
-theorem mul_shiftLeft (a b : Int) (n : Nat) : a * b <<< n = (a * b) <<< n := by
-  simp [shiftLeft_eq, Int.mul_assoc]
-
-theorem shiftLeft_mul_shiftLeft (a b : Int) (m n : Nat) :
-    a <<< m * b <<< n = (a * b) <<< (m + n) := by
-  simp [shiftLeft_mul, mul_shiftLeft, shiftLeft_add]
-
-@[simp]
-theorem shiftLeft_eq_zero_iff {a : Int} {n : Nat} : a <<< n = 0 ↔ a = 0 := by
-  simp [shiftLeft_eq, Int.mul_eq_zero, NeZero.ne]
-
-instance {a : Int} {n : Nat} [NeZero a] : NeZero (a <<< n) :=
-  ⟨mt shiftLeft_eq_zero_iff.mp (NeZero.ne _)⟩
-
 end Int

src/Init/Data/Int/Compare.lean

@@ -6,8 +6,7 @@ Authors: Leonardo de Moura, Jeremy Avigad, Mario Carneiro, Paul Reichert
 module
 
 prelude
-public import Init.Data.Ord.Basic
-import all Init.Data.Ord.Basic
+public import all Init.Data.Ord
 public import Init.Data.Int.Order
 
 public section

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

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

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

@@ -26,10 +26,6 @@ namespace Int
 
 @[simp high] theorem natCast_eq_zero {n : Nat} : (n : Int) = 0 ↔ n = 0 := by omega
 
-instance {n : Nat} [NeZero n] : NeZero (n : Int) := ⟨mt Int.natCast_eq_zero.mp (NeZero.ne _)⟩
-instance {n : Nat} [NeZero n] : NeZero (no_index (OfNat.ofNat n) : Int) :=
-  ⟨mt Int.natCast_eq_zero.mp (NeZero.ne _)⟩
-
 protected theorem exists_add_of_le {a b : Int} (h : a ≤ b) : ∃ (c : Nat), b = a + c :=
   ⟨(b - a).toNat, by omega⟩
 
@@ -334,7 +330,7 @@ theorem fdiv_eq_ediv_of_dvd {a b : Int} (h : b ∣ a) : a.fdiv b = a / b := by
 
 /-! ### mod definitions -/
 
-theorem tmod_add_mul_tdiv : ∀ a b : Int, tmod a b + b * (a.tdiv b) = a
+theorem tmod_add_tdiv : ∀ a b : Int, tmod a b + b * (a.tdiv b) = a
   | ofNat _, ofNat _ => congrArg ofNat (Nat.mod_add_div ..)
   | ofNat m, -[n+1] => by
     change (m % succ n + -↑(succ n) * -↑(m / succ n) : Int) = m
@@ -351,37 +347,21 @@ theorem tmod_add_mul_tdiv : ∀ a b : Int, tmod a b + b * (a.tdiv b) = a
     rw [Int.neg_mul, ← Int.neg_add]
     exact congrArg (-ofNat ·) (Nat.mod_add_div ..)
 
-@[deprecated tmod_add_mul_tdiv (since := "2025-09-01")]
-def tmod_add_tdiv := @tmod_add_mul_tdiv
+theorem tdiv_add_tmod (a b : Int) : b * a.tdiv b + tmod a b = a := by
+  rw [Int.add_comm]; apply tmod_add_tdiv ..
 
-theorem mul_tdiv_add_tmod (a b : Int) : b * a.tdiv b + tmod a b = a := by
-  rw [Int.add_comm]; apply tmod_add_mul_tdiv ..
+/-- Variant of `tmod_add_tdiv` with the multiplication written the other way around. -/
+theorem tmod_add_tdiv' (m k : Int) : tmod m k + m.tdiv k * k = m := by
+  rw [Int.mul_comm]; apply tmod_add_tdiv
 
-@[deprecated mul_tdiv_add_tmod (since := "2025-09-01")]
-def tdiv_add_tmod := @mul_tdiv_add_tmod
-
-theorem tmod_add_tdiv_mul (m k : Int) : tmod m k + m.tdiv k * k = m := by
-  rw [Int.mul_comm]; apply tmod_add_mul_tdiv
-
-@[deprecated tmod_add_tdiv_mul (since := "2025-09-01")]
-def tmod_add_tdiv' := @tmod_add_mul_tdiv
-
-theorem tdiv_mul_add_tmod (m k : Int) : m.tdiv k * k + tmod m k = m := by
-  rw [Int.mul_comm]; apply mul_tdiv_add_tmod
-
-@[deprecated tdiv_mul_add_tmod (since := "2025-09-01")]
-def tdiv_add_tmod' := @tdiv_mul_add_tmod
+/-- Variant of `tdiv_add_tmod` with the multiplication written the other way around. -/
+theorem tdiv_add_tmod' (m k : Int) : m.tdiv k * k + tmod m k = m := by
+  rw [Int.mul_comm]; apply tdiv_add_tmod
 
 theorem tmod_def (a b : Int) : tmod a b = a - b * a.tdiv b := by
-  rw [← Int.add_sub_cancel (tmod a b), tmod_add_mul_tdiv]
+  rw [← Int.add_sub_cancel (tmod a b), tmod_add_tdiv]
 
-theorem mul_tdiv_self (a b : Int) : b * (a.tdiv b) = a - a.tmod b := by
-  rw [tmod_def, Int.sub_sub_self]
-
-theorem tdiv_mul_self (a b : Int) : a.tdiv b * b = a - a.tmod b := by
-  rw [Int.mul_comm, tmod_def, Int.sub_sub_self]
-
-theorem fmod_add_mul_fdiv : ∀ a b : Int, a.fmod b + b * a.fdiv b = a
+theorem fmod_add_fdiv : ∀ a b : Int, a.fmod b + b * a.fdiv b = a
   | 0, ofNat _ | 0, -[_+1] => congrArg ofNat <| by simp
   | succ _, ofNat _ => congrArg ofNat <| Nat.mod_add_div ..
   | succ m, -[n+1] => by
@@ -398,35 +378,19 @@ theorem fmod_add_mul_fdiv : ∀ a b : Int, a.fmod b + b * a.fdiv b = a
     change -(↑(succ m % succ n) : Int) + -↑(succ n * (succ m / succ n)) = -↑(succ m)
     rw [← Int.neg_add]; exact congrArg (-ofNat ·) <| Nat.mod_add_div ..
 
-@[deprecated fmod_add_mul_fdiv (since := "2025-09-01")]
-def fmod_add_fdiv := @fmod_add_mul_fdiv
+/-- Variant of `fmod_add_fdiv` with the multiplication written the other way around. -/
+theorem fmod_add_fdiv' (a b : Int) : a.fmod b + (a.fdiv b) * b = a := by
+  rw [Int.mul_comm]; exact fmod_add_fdiv ..
 
-theorem fmod_add_fdiv_mul (a b : Int) : a.fmod b + (a.fdiv b) * b = a := by
-  rw [Int.mul_comm]; exact fmod_add_mul_fdiv ..
+theorem fdiv_add_fmod (a b : Int) : b * a.fdiv b + a.fmod b = a := by
+  rw [Int.add_comm]; exact fmod_add_fdiv ..
 
-@[deprecated fmod_add_fdiv_mul (since := "2025-09-01")]
-def fmod_add_fdiv' := @fmod_add_fdiv_mul
-
-theorem mul_fdiv_add_fmod (a b : Int) : b * a.fdiv b + a.fmod b = a := by
-  rw [Int.add_comm]; exact fmod_add_mul_fdiv ..
-
-@[deprecated mul_fdiv_add_fmod (since := "2025-09-01")]
-def fdiv_add_fmod := @mul_fdiv_add_fmod
-
-theorem fdiv_mul_add_fmod (a b : Int) : (a.fdiv b) * b + a.fmod b = a := by
-  rw [Int.mul_comm]; exact mul_fdiv_add_fmod ..
-
-@[deprecated mul_fdiv_add_fmod (since := "2025-09-01")]
-def fdiv_add_fmod' := @mul_fdiv_add_fmod
+/-- Variant of `fdiv_add_fmod` with the multiplication written the other way around. -/
+theorem fdiv_add_fmod' (a b : Int) : (a.fdiv b) * b + a.fmod b = a := by
+  rw [Int.mul_comm]; exact fdiv_add_fmod ..
 
 theorem fmod_def (a b : Int) : a.fmod b = a - b * a.fdiv b := by
-  rw [← Int.add_sub_cancel (a.fmod b), fmod_add_mul_fdiv]
-
-theorem mul_fdiv_self (a b : Int) : b * (a.fdiv b) = a - a.fmod b := by
-  rw [fmod_def, Int.sub_sub_self]
-
-theorem fdiv_mul_self (a b : Int) : a.fdiv b * b = a - a.fmod b := by
-  rw [Int.mul_comm, fmod_def, Int.sub_sub_self]
+  rw [← Int.add_sub_cancel (a.fmod b), fmod_add_fdiv]
 
 /-! ### mod equivalences  -/
 
@@ -805,7 +769,7 @@ protected theorem ediv_emod_unique {a b r q : Int} (h : 0 < b) :
     a / b = q ∧ a % b = r ↔ r + b * q = a ∧ 0 ≤ r ∧ r < b := by
   constructor
   · intro ⟨rfl, rfl⟩
-    exact ⟨emod_add_mul_ediv a b, emod_nonneg _ (Int.ne_of_gt h), emod_lt_of_pos _ h⟩
+    exact ⟨emod_add_ediv a b, emod_nonneg _ (Int.ne_of_gt h), emod_lt_of_pos _ h⟩
   · intro ⟨rfl, hz, hb⟩
     constructor
     · rw [Int.add_mul_ediv_left r q (Int.ne_of_gt h), ediv_eq_zero_of_lt hz hb]
@@ -829,7 +793,7 @@ theorem neg_ediv {a b : Int} : (-a) / b = -(a / b) - if b ∣ a then 0 else b.si
   if hb : b = 0 then
     simp [hb]
   else
-    conv => lhs; rw [← mul_ediv_add_emod a b]
+    conv => lhs; rw [← ediv_add_emod a b]
     rw [Int.neg_add, ← Int.mul_neg, mul_add_ediv_left _ _ hb, Int.add_comm]
     split <;> rename_i h
     · rw [emod_eq_zero_of_dvd h]
@@ -992,12 +956,6 @@ theorem neg_mul_ediv_cancel_left (a b : Int) (h : a ≠ 0) : -(a * b) / a = -b :
 @[simp] theorem emod_one (a : Int) : a % 1 = 0 := by
   simp [emod_def, Int.one_mul, Int.sub_self]
 
-theorem ediv_minus_one (a : Int) : a / (-1) = -a := by
-  simp
-
-theorem emod_minus_one (a : Int) : a % (-1) = 0 := by
-  simp
-
 @[deprecated sub_emod_right (since := "2025-04-11")]
 theorem emod_sub_cancel (x y : Int) : (x - y) % y = x % y :=
   sub_emod_right ..
@@ -1119,10 +1077,6 @@ theorem emod_natAbs_of_neg {x : Int} (h : x < 0) {n : Nat} (w : n ≠ 0) :
 protected theorem ediv_mul_le (a : Int) {b : Int} (H : b ≠ 0) : a / b * b ≤ a :=
   Int.le_of_sub_nonneg <| by rw [Int.mul_comm, ← emod_def]; apply emod_nonneg _ H
 
-protected theorem lt_ediv_mul (a : Int) {b : Int} (H : 0 < b) : a - b < a / b * b := by
-  rw [ediv_mul_self, Int.sub_lt_sub_left_iff]
-  exact emod_lt_of_pos a H
-
 theorem le_of_mul_le_mul_left {a b c : Int} (w : a * b ≤ a * c) (h : 0 < a) : b ≤ c := by
   have w := Int.sub_nonneg_of_le w
   rw [← Int.mul_sub] at w
@@ -1213,9 +1167,9 @@ theorem ediv_eq_iff_of_pos {k x y : Int} (h : 0 < k) : x / k = y ↔ y * k ≤ x
 theorem add_ediv_of_pos {a b c : Int} (h : 0 < c) :
     (a + b) / c = a / c + b / c + if c ≤ a % c + b % c then 1 else 0 := by
   have h' : c ≠ 0 := by omega
-  conv => lhs; rw [← Int.mul_ediv_add_emod a c]
+  conv => lhs; rw [← Int.ediv_add_emod a c]
   rw [Int.add_assoc, Int.mul_add_ediv_left _ _ h']
-  conv => lhs; rw [← Int.mul_ediv_add_emod b c]
+  conv => lhs; rw [← Int.ediv_add_emod b c]
   rw [Int.add_comm (a % c), Int.add_assoc, Int.mul_add_ediv_left _ _ h',
     ← Int.add_assoc, Int.add_comm (b % c)]
   congr
@@ -1246,7 +1200,7 @@ theorem not_dvd_iff_lt_mul_succ (m : Int) (hn : 0 < n) :
     ¬n ∣ m ↔ (∃ k, n * k < m ∧ m < n * (k + 1)) := by
   refine ⟨fun h ↦ ?_, ?_⟩
   · rw [dvd_iff_emod_eq_zero, ← Ne] at h
-    rw [← emod_add_mul_ediv m n]
+    rw [← emod_add_ediv m n]
     refine ⟨m / n, Int.lt_add_of_pos_left _ ?_, ?_⟩
     · have := emod_nonneg m (Int.ne_of_gt hn)
       omega
@@ -1258,26 +1212,6 @@ theorem not_dvd_iff_lt_mul_succ (m : Int) (hn : 0 < n) :
     rw [Int.lt_add_one_iff, ← Int.not_lt] at h2k
     exact h2k h1k
 
-private theorem ediv_ediv_of_pos {x y z : Int} (hy : 0 < y) (hz : 0 < z) :
-    x / y / z = x / (y * z) := by
-  rw [eq_comm, Int.ediv_eq_iff_of_pos (Int.mul_pos hy hz)]
-  constructor
-  · rw [Int.mul_comm y, ← Int.mul_assoc]
-    exact Int.le_trans
-      (Int.mul_le_mul_of_nonneg_right (Int.ediv_mul_le _ (Int.ne_of_gt hz)) (Int.le_of_lt hy))
-      (Int.ediv_mul_le x (Int.ne_of_gt hy))
-  · rw [Int.mul_comm y, ← Int.mul_assoc, ← Int.add_mul, Int.mul_comm _ z]
-    exact Int.lt_mul_of_ediv_lt hy (Int.lt_mul_ediv_self_add hz)
-
-theorem ediv_ediv {x y z : Int} (hy : 0 ≤ y) : x / y / z = x / (y * z) := by
-  rcases y with (_ | a) | a
-  · simp
-  · rcases z with (_ | b) | b
-    · simp
-    · simp [ediv_ediv_of_pos]
-    · simp [Int.negSucc_eq, Int.mul_neg, ediv_ediv_of_pos]
-  · simp at hy
-
 /-! ### tdiv -/
 
 -- `tdiv` analogues of `ediv` lemmas from `Bootstrap.lean`
@@ -1521,7 +1455,7 @@ theorem sign_tmod (a b : Int) : sign (tmod a b) = if b ∣ a then 0 else sign a
 -- Analogues of statements about `ediv` and `emod` from `Bootstrap.lean`
 
 theorem mul_tdiv_cancel_of_tmod_eq_zero {a b : Int} (H : a.tmod b = 0) : b * (a.tdiv b) = a := by
-  have := tmod_add_mul_tdiv a b; rwa [H, Int.zero_add] at this
+  have := tmod_add_tdiv a b; rwa [H, Int.zero_add] at this
 
 theorem tdiv_mul_cancel_of_tmod_eq_zero {a b : Int} (H : a.tmod b = 0) : a.tdiv b * b = a := by
   rw [Int.mul_comm, mul_tdiv_cancel_of_tmod_eq_zero H]
@@ -2246,7 +2180,7 @@ theorem fmod_add_cancel_right {m n k : Int} (i) : (m + i).fmod n = (k + i).fmod
 
 theorem mul_fmod (a b n : Int) : (a * b).fmod n = (a.fmod n * b.fmod n).fmod n := by
   conv => lhs; rw [
-    ← fmod_add_mul_fdiv a n, ← fmod_add_fdiv_mul b n, Int.add_mul, Int.mul_add, Int.mul_add,
+    ← fmod_add_fdiv a n, ← fmod_add_fdiv' b n, Int.add_mul, Int.mul_add, Int.mul_add,
     Int.mul_assoc, Int.mul_assoc, ← Int.mul_add n _ _, add_mul_fmod_self_left,
     ← Int.mul_assoc, add_mul_fmod_self_right]
 
@@ -2255,7 +2189,7 @@ theorem mul_fmod (a b n : Int) : (a * b).fmod n = (a.fmod n * b.fmod n).fmod n :
 
 @[simp] theorem fmod_fmod_of_dvd (n : Int) {m k : Int}
     (h : m ∣ k) : (n.fmod k).fmod m = n.fmod m := by
-  conv => rhs; rw [← fmod_add_mul_fdiv n k]
+  conv => rhs; rw [← fmod_add_fdiv n k]
   match k, h with
   | _, ⟨t, rfl⟩ => rw [Int.mul_assoc, add_mul_fmod_self_left]
 
@@ -2285,7 +2219,7 @@ theorem fmod_eq_of_lt {a b : Int} (H1 : 0 ≤ a) (H2 : a < b) : a.fmod b = a :=
 -- Analogues of properties of `ediv` and `emod` from `Bootstrap.lean`
 
 theorem mul_fdiv_cancel_of_fmod_eq_zero {a b : Int} (H : a.fmod b = 0) : b * (a.fdiv b) = a := by
-  have := fmod_add_mul_fdiv a b; rwa [H, Int.zero_add] at this
+  have := fmod_add_fdiv a b; rwa [H, Int.zero_add] at this
 
 theorem fdiv_mul_cancel_of_fmod_eq_zero {a b : Int} (H : a.fmod b = 0) : (a.fdiv b) * b= a := by
   rw [Int.mul_comm, mul_fdiv_cancel_of_fmod_eq_zero H]
@@ -2527,9 +2461,9 @@ theorem bdiv_add_bmod (x : Int) (m : Nat) : m * bdiv x m + bmod x m = x := by
       ite_self]
   · dsimp only
     split
-    · exact mul_ediv_add_emod x m
+    · exact ediv_add_emod x m
     · rw [Int.mul_add, Int.mul_one, Int.add_assoc, Int.add_comm m, Int.sub_add_cancel]
-      exact mul_ediv_add_emod x m
+      exact ediv_add_emod x m
 
 theorem bmod_add_bdiv (x : Int) (m : Nat) : bmod x m + m * bdiv x m = x := by
   rw [Int.add_comm]; exact bdiv_add_bmod x m
@@ -2786,7 +2720,7 @@ theorem le_bmod {x : Int} {m : Nat} (h : 0 < m) : - (m/2) ≤ Int.bmod x m := by
     · exact Int.ne_of_gt (natCast_pos.mpr h)
   · simp [Int.not_lt] at w
     refine Int.le_trans ?_ (Int.sub_le_sub_right w _)
-    rw [← mul_ediv_add_emod m 2]
+    rw [← ediv_add_emod m 2]
     generalize (m : Int) / 2 = q
     generalize h : (m : Int) % 2 = r at *
     rcases v with rfl | rfl
@@ -2947,7 +2881,7 @@ theorem neg_bmod {a : Int} {b : Nat} :
           simp only [gt_iff_lt, Nat.zero_lt_succ, Nat.mul_pos_iff_of_pos_left, Int.natCast_mul,
             cast_ofNat_Int, Int.not_lt] at *
           rw [Int.mul_dvd_mul_iff_left (by omega)]
-          have := mul_ediv_add_emod a (2 * c)
+          have := ediv_add_emod a (2 * c)
           rw [(by omega : a % (2 * c) = c)] at this
           rw [← this]
           apply Int.dvd_add _ (by simp)

src/Init/Data/Int/Lemmas.lean

@@ -40,7 +40,7 @@ theorem ofNat_succ (n : Nat) : (succ n : Int) = n + 1 := rfl
 
 theorem neg_ofNat_zero : -((0 : Nat) : Int) = 0 := rfl
 theorem neg_ofNat_succ (n : Nat) : -(succ n : Int) = -[n+1] := rfl
-@[simp] theorem neg_negSucc (n : Nat) : -(-[n+1]) = ((n + 1 : Nat) : Int) := rfl
+theorem neg_negSucc (n : Nat) : -(-[n+1]) = succ n := rfl
 
 theorem negOfNat_eq : negOfNat n = -ofNat n := rfl
 
@@ -361,10 +361,10 @@ theorem negSucc_coe' (n : Nat) : -[n+1] = -↑n - 1 := by
 
 protected theorem subNatNat_eq_coe {m n : Nat} : subNatNat m n = ↑m - ↑n := by
   apply subNatNat_elim m n fun m n i => i = m - n
-  · intro i n
+  · intros i n
     rw [Int.natCast_add, Int.sub_eq_add_neg, Int.add_assoc, Int.add_left_comm,
       Int.add_right_neg, Int.add_zero]
-  · intro i n
+  · intros i n
     simp only [negSucc_eq, natCast_add, ofNat_one, Int.sub_eq_add_neg, Int.neg_add, ← Int.add_assoc]
     rw [Int.add_neg_eq_sub (a := n), ← ofNat_sub, Nat.sub_self, ofNat_zero, Int.zero_add]
     apply Nat.le_refl
@@ -566,9 +566,6 @@ protected theorem mul_eq_zero {a b : Int} : a * b = 0 ↔ a = 0 ∨ b = 0 := by
 protected theorem mul_ne_zero {a b : Int} (a0 : a ≠ 0) (b0 : b ≠ 0) : a * b ≠ 0 :=
   Or.rec a0 b0 ∘ Int.mul_eq_zero.mp
 
-instance {a b : Int} [NeZero a] [NeZero b] : NeZero (a * b) :=
-  ⟨Int.mul_ne_zero (NeZero.ne _) (NeZero.ne _)⟩
-
 @[simp] protected theorem mul_ne_zero_iff {a b : Int} : a * b ≠ 0 ↔ a ≠ 0 ∧ b ≠ 0 := by
   rw [ne_eq, Int.mul_eq_zero, not_or, ne_eq]
 

src/Init/Data/Int/LemmasAux.lean

@@ -69,18 +69,6 @@ theorem natCast_succ_pos (n : Nat) : 0 < (n.succ : Int) := natCast_pos.2 n.succ_
 
 @[simp, norm_cast] theorem cast_id {n : Int} : Int.cast n = n := rfl
 
-@[simp] theorem ble'_eq_true (a b : Int) : (Int.ble' a b = true) = (a ≤ b) := by
-  cases a <;> cases b <;> simp [Int.ble'] <;> omega
-
-@[simp] theorem blt'_eq_true (a b : Int) : (Int.blt' a b = true) = (a < b) := by
-  cases a <;> cases b <;> simp [Int.blt'] <;> omega
-
-@[simp] theorem ble'_eq_false (a b : Int) : (Int.ble' a b = false) = ¬(a ≤ b) := by
-  simp [← Bool.not_eq_true]
-
-@[simp] theorem blt'_eq_false (a b : Int) : (Int.blt' a b = false) = ¬ (a < b) := by
-  simp [← Bool.not_eq_true]
-
 /-! ### toNat -/
 
 @[simp] theorem toNat_sub' (a : Int) (b : Nat) : (a - b).toNat = a.toNat - b := by

src/Init/Data/Int/Order.lean

@@ -8,13 +8,9 @@ module
 prelude
 public import Init.Data.Int.Lemmas
 public import Init.ByCases
-public import Init.Data.Order.Factories
-import Init.Data.Order.Lemmas
 
 public section
 
-open Std
-
 /-!
 # Results about the order properties of the integers, and the integers as an ordered ring.
 -/
@@ -701,13 +697,10 @@ theorem toNat_sub_toNat_neg : ∀ n : Int, ↑n.toNat - ↑(-n).toNat = n
   | (_+1:Nat) => Nat.add_zero _
   | -[_+1] => Nat.zero_add _
 
-@[simp] theorem toNat_neg_natCast : ∀ n : Nat, (-(n : Int)).toNat = 0
+@[simp] theorem toNat_neg_nat : ∀ n : Nat, (-(n : Int)).toNat = 0
   | 0 => rfl
   | _+1 => rfl
 
-@[deprecated toNat_neg_natCast (since := "2025-08-29")]
-theorem toNat_neg_nat : ∀ n : Nat, (-(n : Int)).toNat = 0 := toNat_neg_natCast
-
 /-! ### toNat? -/
 
 theorem mem_toNat? : ∀ {a : Int} {n : Nat}, toNat? a = some n ↔ a = n
@@ -1422,14 +1415,4 @@ theorem natAbs_eq_iff_mul_eq_zero : natAbs a = n ↔ (a - n) * (a + n) = 0 := by
 @[deprecated natAbs_eq_iff_mul_eq_zero (since := "2025-03-11")]
 abbrev eq_natAbs_iff_mul_eq_zero := @natAbs_eq_iff_mul_eq_zero
 
-instance instIsLinearOrder : IsLinearOrder Int := by
-  apply IsLinearOrder.of_le
-  case le_antisymm => constructor; apply Int.le_antisymm
-  case le_total => constructor; apply Int.le_total
-  case le_trans => constructor; apply Int.le_trans
-
-instance : LawfulOrderLT Int where
-  lt_iff := by
-    simp [← Int.not_le, Decidable.imp_iff_not_or, Std.Total.total]
-
 end Int

src/Init/Data/Int/Pow.lean

@@ -21,11 +21,6 @@ protected theorem pow_succ (b : Int) (e : Nat) : b ^ (e+1) = (b ^ e) * b := rfl
 protected theorem pow_succ' (b : Int) (e : Nat) : b ^ (e+1) = b * (b ^ e) := by
   rw [Int.mul_comm, Int.pow_succ]
 
-protected theorem pow_add (a : Int) (m n : Nat) : a ^ (m + n) = a ^ m * a ^ n := by
-  induction n with
-  | zero => rw [Nat.add_zero, Int.pow_zero, Int.mul_one]
-  | succ _ ih => rw [Nat.add_succ, Int.pow_succ, Int.pow_succ, ih, Int.mul_assoc]
-
 protected theorem zero_pow {n : Nat} (h : n ≠ 0) : (0 : Int) ^ n = 0 := by
   match n, h with
   | n + 1, _ => simp [Int.pow_succ]
@@ -48,8 +43,6 @@ protected theorem pow_ne_zero {n : Int} {m : Nat} : n ≠ 0 → n ^ m ≠ 0 := b
   | zero => simp
   | succ m ih => exact fun h => Int.mul_ne_zero (ih h) h
 
-instance {n : Int} {m : Nat} [NeZero n] : NeZero (n ^ m) := ⟨Int.pow_ne_zero (NeZero.ne _)⟩
-
 @[deprecated Nat.pow_le_pow_left (since := "2025-02-17")]
 abbrev pow_le_pow_of_le_left := @Nat.pow_le_pow_left
 

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

@@ -6,10 +6,8 @@ Authors: Paul Reichert
 module
 
 prelude
-public import Init.Data.Iterators.Combinators.Attach
-import all Init.Data.Iterators.Combinators.Attach
-public import Init.Data.Iterators.Combinators.Monadic.Attach
-import all Init.Data.Iterators.Combinators.Monadic.Attach
+public import all Init.Data.Iterators.Combinators.Attach
+public import all Init.Data.Iterators.Combinators.Monadic.Attach
 public import Init.Data.Iterators.Lemmas.Combinators.Monadic.Attach
 public import Init.Data.Iterators.Lemmas.Consumers.Collect
 public import Init.Data.Array.Attach

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

@@ -6,8 +6,7 @@ Authors: Paul Reichert
 module
 
 prelude
-public import Init.Data.Iterators.Combinators.Monadic.Attach
-import all Init.Data.Iterators.Combinators.Monadic.Attach
+public import all Init.Data.Iterators.Combinators.Monadic.Attach
 public import Init.Data.Iterators.Lemmas.Consumers.Monadic.Collect
 
 public section

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

@@ -9,8 +9,7 @@ prelude
 public import Init.Data.Iterators.Internal.LawfulMonadLiftFunction
 public import Init.Data.Iterators.Combinators.Monadic.FilterMap
 public import Init.Data.Iterators.Lemmas.Consumers.Monadic
-public import Init.Data.Iterators.Consumers.Monadic.Collect
-import all Init.Data.Iterators.Consumers.Monadic.Collect
+public import all Init.Data.Iterators.Consumers.Monadic.Collect
 
 public section
 

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

@@ -6,8 +6,7 @@ Authors: Paul Reichert
 module
 
 prelude
-public import Init.Data.Iterators.Combinators.Monadic.ULift
-import all Init.Data.Iterators.Combinators.Monadic.ULift
+public import all Init.Data.Iterators.Combinators.Monadic.ULift
 public import Init.Data.Iterators.Lemmas.Consumers.Monadic.Collect
 
 public section

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

@@ -6,8 +6,7 @@ Authors: Paul Reichert
 module
 
 prelude
-public import Init.Data.Iterators.Combinators.ULift
-import all Init.Data.Iterators.Combinators.ULift
+public import all Init.Data.Iterators.Combinators.ULift
 public import Init.Data.Iterators.Lemmas.Combinators.Monadic.ULift
 public import Init.Data.Iterators.Lemmas.Consumers.Collect
 

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

@@ -8,10 +8,8 @@ module
 prelude
 public import Init.Data.Iterators.Lemmas.Basic
 public import Init.Data.Iterators.Lemmas.Consumers.Monadic.Collect
-public import Init.Data.Iterators.Consumers.Access
-import all Init.Data.Iterators.Consumers.Access
-public import Init.Data.Iterators.Consumers.Collect
-import all Init.Data.Iterators.Consumers.Collect
+public import all Init.Data.Iterators.Consumers.Access
+public import all Init.Data.Iterators.Consumers.Collect
 
 public section
 

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

@@ -8,12 +8,9 @@ module
 prelude
 public import Init.Control.Lawful.MonadLift.Instances
 public import Init.Data.Iterators.Lemmas.Consumers.Collect
-public import Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop
-import all Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop
-public import Init.Data.Iterators.Consumers.Loop
-import all Init.Data.Iterators.Consumers.Loop
-public import Init.Data.Iterators.Consumers.Monadic.Collect
-import all Init.Data.Iterators.Consumers.Monadic.Collect
+public import all Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop
+public import all Init.Data.Iterators.Consumers.Loop
+public import all Init.Data.Iterators.Consumers.Monadic.Collect
 
 public section
 

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

@@ -8,8 +8,7 @@ module
 prelude
 public import Init.Data.Array.Lemmas
 public import Init.Data.Iterators.Lemmas.Monadic.Basic
-public import Init.Data.Iterators.Consumers.Monadic.Collect
-import all Init.Data.Iterators.Consumers.Monadic.Collect
+public import all Init.Data.Iterators.Consumers.Monadic.Collect
 
 public section
 

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

@@ -7,8 +7,7 @@ module
 
 prelude
 public import Init.Data.Iterators.Lemmas.Consumers.Monadic.Collect
-public import Init.Data.Iterators.Consumers.Monadic.Loop
-import all Init.Data.Iterators.Consumers.Monadic.Loop
+public import all Init.Data.Iterators.Consumers.Monadic.Loop
 
 public section
 

src/Init/Data/Iterators/PostconditionMonad.lean

@@ -7,7 +7,7 @@ module
 
 prelude
 public import Init.Control.Lawful.Basic
-public import Init.Data.Subtype.Basic
+public import Init.Data.Subtype
 public import Init.PropLemmas
 
 public section

src/Init/Data/List/Attach.lean

@@ -6,10 +6,9 @@ Authors: Mario Carneiro
 module
 
 prelude
-public import Init.Data.List.Lemmas  -- for dsimping with `getElem?_cons_succ`
-import all Init.Data.List.Lemmas  -- for dsimping with `getElem?_cons_succ`
+public import all Init.Data.List.Lemmas  -- for dsimping with `getElem?_cons_succ`
 public import Init.Data.List.Count
-public import Init.Data.Subtype.Basic
+public import Init.Data.Subtype
 public import Init.BinderNameHint
 
 public section
@@ -124,7 +123,7 @@ theorem attachWith_congr {l₁ l₂ : List α} (w : l₁ = l₂) {P : α → Pro
       ⟨x, mem_cons_self⟩ :: xs.attach.map fun ⟨y, h⟩ => ⟨y, mem_cons_of_mem x h⟩ := by
   simp only [attach, attachWith, pmap, map_pmap, cons.injEq, true_and]
   apply pmap_congr_left
-  intro a _ m' _
+  intros a _ m' _
   rfl
 
 @[simp, grind =]

src/Init/Data/List/Basic.lean

@@ -242,7 +242,8 @@ instance instLT [LT α] : LT (List α) := ⟨List.lt⟩
 instance decidableLT [DecidableEq α] [LT α] [DecidableLT α] (l₁ l₂ : List α) :
     Decidable (l₁ < l₂) := decidableLex (· < ·) l₁ l₂
 
-
+@[deprecated decidableLT (since := "2024-12-13"), inherit_doc decidableLT]
+abbrev hasDecidableLt := @decidableLT
 
 /--
 Non-strict ordering of lists with respect to a strict ordering of their elements.
@@ -1721,8 +1722,14 @@ Examples:
 -/
 def idxOf [BEq α] (a : α) : List α → Nat := findIdx (· == a)
 
+/-- Returns the index of the first element equal to `a`, or the length of the list otherwise. -/
+@[deprecated idxOf (since := "2025-01-29")] abbrev indexOf := @idxOf
+
 @[simp] theorem idxOf_nil [BEq α] : ([] : List α).idxOf x = 0 := rfl
 
+@[deprecated idxOf_nil (since := "2025-01-29")]
+theorem indexOf_nil [BEq α] : ([] : List α).idxOf x = 0 := rfl
+
 /-! ### findIdx? -/
 
 /--
@@ -1753,6 +1760,10 @@ Examples:
 -/
 @[inline] def idxOf? [BEq α] (a : α) : List α → Option Nat := findIdx? (· == a)
 
+/-- Return the index of the first occurrence of `a` in the list. -/
+@[deprecated idxOf? (since := "2025-01-29")]
+abbrev indexOf? := @idxOf?
+
 /-! ### findFinIdx? -/
 
 /--
@@ -2108,10 +2119,21 @@ def range' : (start len : Nat) → (step : Nat := 1) → List Nat
   | _, 0, _ => []
   | s, n+1, step => s :: range' (s+step) n step
 
-@[simp, grind =] theorem range'_zero : range' s 0 step = [] := rfl
-@[simp, grind =] theorem range'_one {s step : Nat} : range' s 1 step = [s] := rfl
--- The following theorem is intentionally not a simp lemma.
-theorem range'_succ : range' s (n + 1) step = s :: range' (s + step) n step := rfl
+/-! ### iota -/
+
+/--
+`O(n)`. `iota n` is the numbers from `1` to `n` inclusive, in decreasing order.
+* `iota 5 = [5, 4, 3, 2, 1]`
+-/
+@[deprecated "Use `(List.range' 1 n).reverse` instead of `iota n`." (since := "2025-01-20")]
+def iota : Nat → List Nat
+  | 0       => []
+  | m@(n+1) => m :: iota n
+
+set_option linter.deprecated false in
+@[simp] theorem iota_zero : iota 0 = [] := rfl
+set_option linter.deprecated false in
+@[simp] theorem iota_succ : iota (i+1) = (i+1) :: iota i := rfl
 
 /-! ### zipIdx -/
 
@@ -2131,6 +2153,38 @@ def zipIdx : (l : List α) → (n : Nat := 0) → List (α × Nat)
 @[simp] theorem zipIdx_nil : ([] : List α).zipIdx i = [] := rfl
 @[simp] theorem zipIdx_cons : (a::as).zipIdx i = (a, i) :: as.zipIdx (i+1) := rfl
 
+/-! ### enumFrom -/
+
+/--
+`O(|l|)`. `enumFrom n l` is like `enum` but it allows you to specify the initial index.
+* `enumFrom 5 [a, b, c] = [(5, a), (6, b), (7, c)]`
+-/
+@[deprecated "Use `zipIdx` instead; note the signature change." (since := "2025-01-21")]
+def enumFrom : Nat → List α → List (Nat × α)
+  | _, [] => nil
+  | n, x :: xs   => (n, x) :: enumFrom (n + 1) xs
+
+set_option linter.deprecated false in
+@[deprecated zipIdx_nil (since := "2025-01-21"), simp]
+theorem enumFrom_nil : ([] : List α).enumFrom i = [] := rfl
+set_option linter.deprecated false in
+@[deprecated zipIdx_cons (since := "2025-01-21"), simp]
+theorem enumFrom_cons : (a::as).enumFrom i = (i, a) :: as.enumFrom (i+1) := rfl
+
+/-! ### enum -/
+
+set_option linter.deprecated false in
+/--
+`O(|l|)`. `enum l` pairs up each element with its index in the list.
+* `enum [a, b, c] = [(0, a), (1, b), (2, c)]`
+-/
+@[deprecated "Use `zipIdx` instead; note the signature change." (since := "2025-01-21")]
+def enum : List α → List (Nat × α) := enumFrom 0
+
+set_option linter.deprecated false in
+@[deprecated zipIdx_nil (since := "2025-01-21"), simp]
+theorem enum_nil : ([] : List α).enum = [] := rfl
+
 /-! ## Minima and maxima -/
 
 /-! ### min? -/
@@ -2550,6 +2604,25 @@ Examples:
     exact go s n (m + 1)
   exact (go s n 0).symm
 
+/-! ### iota -/
+
+/-- Tail-recursive version of `List.iota`. -/
+@[deprecated "Use `List.range' 1 n` instead of `iota n`." (since := "2025-01-20")]
+def iotaTR (n : Nat) : List Nat :=
+  let rec go : Nat → List Nat → List Nat
+    | 0, r => r.reverse
+    | m@(n+1), r => go n (m::r)
+  go n []
+
+set_option linter.deprecated false in
+@[csimp]
+theorem iota_eq_iotaTR : @iota = @iotaTR :=
+  have aux (n : Nat) (r : List Nat) : iotaTR.go n r = r.reverse ++ iota n := by
+    induction n generalizing r with
+    | zero => simp [iota, iotaTR.go]
+    | succ n ih => simp [iota, iotaTR.go, ih, append_assoc]
+  funext fun n => by simp [iotaTR, aux]
+
 /-! ## Other list operations -/
 
 /-! ### intersperse -/

src/Init/Data/List/Erase.lean

@@ -57,9 +57,15 @@ theorem eraseP_of_forall_not {l : List α} (h : ∀ a, a ∈ l → ¬p a) : l.er
       rintro x h' rfl
       simp_all
 
+@[deprecated eraseP_eq_nil_iff (since := "2025-01-30")]
+abbrev eraseP_eq_nil := @eraseP_eq_nil_iff
+
 theorem eraseP_ne_nil_iff {xs : List α} {p : α → Bool} : xs.eraseP p ≠ [] ↔ xs ≠ [] ∧ ∀ x, p x → xs ≠ [x] := by
   simp
 
+@[deprecated eraseP_ne_nil_iff (since := "2025-01-30")]
+abbrev eraseP_ne_nil := @eraseP_ne_nil_iff
+
 theorem exists_of_eraseP : ∀ {l : List α} {a} (_ : a ∈ l) (_ : p a),
     ∃ a l₁ l₂, (∀ b ∈ l₁, ¬p b) ∧ p a ∧ l = l₁ ++ a :: l₂ ∧ l.eraseP p = l₁ ++ l₂
   | b :: l, _, al, pa =>
@@ -346,11 +352,17 @@ theorem erase_eq_eraseP [LawfulBEq α] (a : α) : ∀ (l : List α), l.erase a =
   rw [erase_eq_eraseP]
   simp
 
+@[deprecated erase_eq_nil_iff (since := "2025-01-30")]
+abbrev erase_eq_nil := @erase_eq_nil_iff
+
 theorem erase_ne_nil_iff [LawfulBEq α] {xs : List α} {a : α} :
     xs.erase a ≠ [] ↔ xs ≠ [] ∧ xs ≠ [a] := by
   rw [erase_eq_eraseP]
   simp
 
+@[deprecated erase_ne_nil_iff (since := "2025-01-30")]
+abbrev erase_ne_nil := @erase_ne_nil_iff
+
 theorem exists_erase_eq [LawfulBEq α] {a : α} {l : List α} (h : a ∈ l) :
     ∃ l₁ l₂, a ∉ l₁ ∧ l = l₁ ++ a :: l₂ ∧ l.erase a = l₁ ++ l₂ := by
   let ⟨_, l₁, l₂, h₁, e, h₂, h₃⟩ := exists_of_eraseP h (beq_self_eq_true _)
@@ -427,7 +439,7 @@ theorem erase_append_left [LawfulBEq α] {l₁ : List α} (l₂) (h : a ∈ l₁
 theorem erase_append_right [LawfulBEq α] {a : α} {l₁ : List α} (l₂ : List α) (h : a ∉ l₁) :
     (l₁ ++ l₂).erase a = (l₁ ++ l₂.erase a) := by
   rw [erase_eq_eraseP, erase_eq_eraseP, eraseP_append_right]
-  intro b h' h''; rw [eq_of_beq h''] at h; exact h h'
+  intros b h' h''; rw [eq_of_beq h''] at h; exact h h'
 
 @[grind =]
 theorem erase_append [LawfulBEq α] {a : α} {l₁ l₂ : List α} :
@@ -570,7 +582,8 @@ theorem eraseIdx_eq_take_drop_succ :
   | a::l, 0
   | a::l, i + 1 => simp
 
-
+@[deprecated eraseIdx_eq_nil_iff (since := "2025-01-30")]
+abbrev eraseIdx_eq_nil := @eraseIdx_eq_nil_iff
 
 theorem eraseIdx_ne_nil_iff {l : List α} {i : Nat} : eraseIdx l i ≠ [] ↔ 2 ≤ l.length ∨ (l.length = 1 ∧ i ≠ 0) := by
   match l with
@@ -578,7 +591,8 @@ theorem eraseIdx_ne_nil_iff {l : List α} {i : Nat} : eraseIdx l i ≠ [] ↔ 2
   | [a]
   | a::b::l => simp
 
-
+@[deprecated eraseIdx_ne_nil_iff (since := "2025-01-30")]
+abbrev eraseIdx_ne_nil := @eraseIdx_ne_nil_iff
 
 @[grind]
 theorem eraseIdx_sublist : ∀ (l : List α) (k : Nat), eraseIdx l k <+ l
@@ -686,6 +700,7 @@ theorem erase_eq_eraseIdx_of_idxOf [BEq α] [LawfulBEq α]
     rw [eq_comm, eraseIdx_eq_self]
     exact Nat.le_of_eq (idxOf_eq_length h).symm
 
-
+@[deprecated erase_eq_eraseIdx_of_idxOf (since := "2025-01-29")]
+abbrev erase_eq_eraseIdx_of_indexOf := @erase_eq_eraseIdx_of_idxOf
 
 end List

src/Init/Data/List/FinRange.lean

@@ -6,8 +6,7 @@ Authors: François G. Dorais
 module
 
 prelude
-public import Init.Data.List.OfFn
-import all Init.Data.List.OfFn
+public import all Init.Data.List.OfFn
 public import Init.Data.List.Monadic
 
 public section

src/Init/Data/List/Find.lean

@@ -11,8 +11,7 @@ public import Init.Data.List.Lemmas
 public import Init.Data.List.Sublist
 public import Init.Data.List.Range
 public import Init.Data.List.Impl
-public import Init.Data.List.Attach
-import all Init.Data.List.Attach
+public import all Init.Data.List.Attach
 public import Init.Data.Fin.Lemmas
 
 public section
@@ -1099,9 +1098,15 @@ theorem idxOf_cons [BEq α] :
   dsimp [idxOf]
   simp [findIdx_cons]
 
+@[deprecated idxOf_cons (since := "2025-01-29")]
+abbrev indexOf_cons := @idxOf_cons
+
 @[simp] theorem idxOf_cons_self [BEq α] [ReflBEq α] {l : List α} : (a :: l).idxOf a = 0 := by
   simp [idxOf_cons]
 
+@[deprecated idxOf_cons_self (since := "2025-01-29")]
+abbrev indexOf_cons_self := @idxOf_cons_self
+
 @[grind =]
 theorem idxOf_append [BEq α] [LawfulBEq α] {l₁ l₂ : List α} {a : α} :
     (l₁ ++ l₂).idxOf a = if a ∈ l₁ then l₁.idxOf a else l₂.idxOf a + l₁.length := by
@@ -1112,7 +1117,8 @@ theorem idxOf_append [BEq α] [LawfulBEq α] {l₁ l₂ : List α} {a : α} :
   · rw [if_neg]
     simpa using h
 
-
+@[deprecated idxOf_append (since := "2025-01-29")]
+abbrev indexOf_append := @idxOf_append
 
 theorem idxOf_eq_length [BEq α] [LawfulBEq α] {l : List α} (h : a ∉ l) : l.idxOf a = l.length := by
   induction l with
@@ -1122,7 +1128,8 @@ theorem idxOf_eq_length [BEq α] [LawfulBEq α] {l : List α} (h : a ∉ l) : l.
     simp only [idxOf_cons, cond_eq_if, beq_iff_eq]
     split <;> simp_all
 
-
+@[deprecated idxOf_eq_length (since := "2025-01-29")]
+abbrev indexOf_eq_length := @idxOf_eq_length
 
 theorem idxOf_lt_length_of_mem [BEq α] [EquivBEq α] {l : List α} (h : a ∈ l) : l.idxOf a < l.length := by
   induction l with
@@ -1152,7 +1159,8 @@ theorem idxOf_lt_length_iff [BEq α] [LawfulBEq α] {l : List α} {a : α} :
 
 grind_pattern idxOf_lt_length_iff => l.idxOf a, l.length
 
-
+@[deprecated idxOf_lt_length_of_mem (since := "2025-01-29")]
+abbrev indexOf_lt_length := @idxOf_lt_length_of_mem
 
 /-! ### finIdxOf?
 
@@ -1223,7 +1231,8 @@ The lemmas below should be made consistent with those for `findIdx?` (and proved
   · rintro w x h rfl
     contradiction
 
-
+@[deprecated idxOf?_eq_none_iff (since := "2025-01-29")]
+abbrev indexOf?_eq_none_iff := @idxOf?_eq_none_iff
 
 @[simp, grind =]
 theorem isSome_idxOf? [BEq α] [LawfulBEq α] {l : List α} {a : α} :
@@ -1242,9 +1251,9 @@ theorem isNone_idxOf? [BEq α] [LawfulBEq α] {l : List α} {a : α} :
 /-! ### lookup -/
 
 section lookup
-variable [BEq α]
+variable [BEq α] [LawfulBEq α]
 
-@[simp] theorem lookup_cons_self [ReflBEq α] {k : α} : ((k,b) :: es).lookup k = some b := by
+@[simp] theorem lookup_cons_self  {k : α} : ((k,b) :: es).lookup k = some b := by
   simp [lookup_cons]
 
 @[simp] theorem lookup_singleton {a b : α} : [(a,b)].lookup c = if c == a then some b else none := by
@@ -1263,13 +1272,13 @@ theorem lookup_eq_findSome? {l : List (α × β)} {k : α} :
 
 @[simp, grind =] theorem lookup_eq_none_iff {l : List (α × β)} {k : α} :
     l.lookup k = none ↔ ∀ p ∈ l, k != p.1 := by
-  simp [lookup_eq_findSome?, bne]
+  simp [lookup_eq_findSome?]
 
 @[simp] theorem lookup_isSome_iff {l : List (α × β)} {k : α} :
     (l.lookup k).isSome ↔ ∃ p ∈ l, k == p.1 := by
   simp [lookup_eq_findSome?]
 
-theorem lookup_eq_some_iff [LawfulBEq α] {l : List (α × β)} {k : α} {b : β} :
+theorem lookup_eq_some_iff {l : List (α × β)} {k : α} {b : β} :
     l.lookup k = some b ↔ ∃ l₁ l₂, l = l₁ ++ (k, b) :: l₂ ∧ ∀ p ∈ l₁, k != p.1 := by
   simp only [lookup_eq_findSome?, findSome?_eq_some_iff]
   constructor
@@ -1299,11 +1308,11 @@ theorem lookup_replicate_of_pos {k : α} (h : 0 < n) :
     (replicate n (a, b)).lookup k = if k == a then some b else none := by
   simp [lookup_replicate, Nat.ne_of_gt h]
 
-theorem lookup_replicate_self [ReflBEq α] {a : α} :
+theorem lookup_replicate_self {a : α} :
     (replicate n (a, b)).lookup a = if n = 0 then none else some b := by
   simp [lookup_replicate]
 
-@[simp] theorem lookup_replicate_self_of_pos [ReflBEq α] {a : α} (h : 0 < n) :
+@[simp] theorem lookup_replicate_self_of_pos {a : α} (h : 0 < n) :
     (replicate n (a, b)).lookup a = some b := by
   simp [lookup_replicate_self, Nat.ne_of_gt h]
 

src/Init/Data/List/Impl.lean

@@ -98,7 +98,7 @@ Example:
 [10, 14, 14]
 ```
 -/
-@[inline, expose] def filterMapTR (f : α → Option β) (l : List α) : List β := go l #[] where
+@[inline] def filterMapTR (f : α → Option β) (l : List α) : List β := go l #[] where
   /-- Auxiliary for `filterMap`: `filterMap.go f l = acc.toList ++ filterMap f l` -/
   @[specialize] go : List α → Array β → List β
   | [], acc => acc.toList
@@ -367,7 +367,7 @@ def modifyTR (l : List α) (i : Nat) (f : α → α) : List α := go l i #[] whe
   | a :: l, 0, acc => acc.toListAppend (f a :: l)
   | a :: l, i+1, acc => go l i (acc.push a)
 
-private theorem modifyTR_go_eq : ∀ l i, modifyTR.go f l i acc = acc.toList ++ modify l i f
+theorem modifyTR_go_eq : ∀ l i, modifyTR.go f l i acc = acc.toList ++ modify l i f
   | [], i => by cases i <;> simp [modifyTR.go, modify]
   | a :: l, 0 => by simp [modifyTR.go, modify]
   | a :: l, i+1 => by simp [modifyTR.go, modify, modifyTR_go_eq l]
@@ -399,7 +399,7 @@ Examples:
   | _, [], acc => acc.toList
   | n+1, a :: l, acc => go n l (acc.push a)
 
-private theorem insertIdxTR_go_eq : ∀ i l, insertIdxTR.go a i l acc = acc.toList ++ insertIdx l i a
+theorem insertIdxTR_go_eq : ∀ i l, insertIdxTR.go a i l acc = acc.toList ++ insertIdx l i a
   | 0, l | _+1, [] => by simp [insertIdxTR.go, insertIdx]
   | n+1, a :: l => by simp [insertIdxTR.go, insertIdx, insertIdxTR_go_eq n l]
 
@@ -564,7 +564,24 @@ def zipIdxTR (l : List α) (n : Nat := 0) : List (α × Nat) :=
 
 /-! ### enumFrom -/
 
+/-- Tail recursive version of `List.enumFrom`. -/
+@[deprecated zipIdxTR (since := "2025-01-21")]
+def enumFromTR (n : Nat) (l : List α) : List (Nat × α) :=
+  let as := l.toArray
+  (as.foldr (fun a (n, acc) => (n-1, (n-1, a) :: acc)) (n + as.size, [])).2
 
+set_option linter.deprecated false in
+@[deprecated zipIdx_eq_zipIdxTR (since := "2025-01-21"), csimp]
+theorem enumFrom_eq_enumFromTR : @enumFrom = @enumFromTR := by
+  funext α n l; simp only [enumFromTR]
+  let f := fun (a : α) (n, acc) => (n-1, (n-1, a) :: acc)
+  let rec go : ∀ l n, l.foldr f (n + l.length, []) = (n, enumFrom n l)
+    | [], n => rfl
+    | a::as, n => by
+      rw [← show _ + as.length = n + (a::as).length from Nat.succ_add .., foldr, go as]
+      simp [enumFrom, f]
+  rw [← Array.foldr_toList]
+  simp +zetaDelta [go]
 
 /-! ## Other list operations -/
 

src/Init/Data/List/Lemmas.lean

@@ -9,10 +9,8 @@ module
 prelude
 public import Init.Data.Bool
 public import Init.Data.Option.Lemmas
-public import Init.Data.List.BasicAux
-import all Init.Data.List.BasicAux
-public import Init.Data.List.Control
-import all Init.Data.List.Control
+public import all Init.Data.List.BasicAux
+public import all Init.Data.List.Control
 public import Init.Control.Lawful.Basic
 public import Init.BinderPredicates
 
@@ -72,7 +70,7 @@ See also
 
 Further results, which first require developing further automation around `Nat`, appear in
 * `Init.Data.List.Nat.Basic`: miscellaneous lemmas
-* `Init.Data.List.Nat.Range`: `List.range`, `List.range'` and `List.enum`
+* `Init.Data.List.Nat.Range`: `List.range` and `List.enum`
 * `Init.Data.List.Nat.TakeDrop`: `List.take` and `List.drop`
 
 Also
@@ -1086,12 +1084,6 @@ theorem getLast?_tail {l : List α} : (tail l).getLast? = if l.length = 1 then n
     rw [if_neg]
     rintro ⟨⟩
 
-@[simp, grind =]
-theorem cons_head_tail (h : l ≠ []) : l.head h :: l.tail = l := by
-  induction l with
-  | nil => contradiction
-  | cons ih => simp_all
-
 /-! ## Basic operations -/
 
 /-! ### map -/
@@ -1594,7 +1586,9 @@ theorem filterMap_eq_cons_iff {l} {b} {bs} :
 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
 
 /--
 See also `eq_append_cons_of_mem`, which proves a stronger version
@@ -1704,7 +1698,7 @@ theorem getLast_concat {a : α} : ∀ {l : List α}, getLast (l ++ [a]) (by simp
 @[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
 
 theorem nil_eq_append_iff : [] = a ++ b ↔ a = [] ∧ b = [] := by
   simp
@@ -1859,10 +1853,6 @@ theorem append_eq_map_iff {f : α → β} :
 theorem sum_append_nat {l₁ l₂ : List Nat} : (l₁ ++ l₂).sum = l₁.sum + l₂.sum := by
   induction l₁ generalizing l₂ <;> simp_all [Nat.add_assoc]
 
-@[simp, grind =]
-theorem sum_reverse_nat (xs : List Nat) : xs.reverse.sum = xs.sum := by
-  induction xs <;> simp_all [Nat.add_comm]
-
 /-! ### concat
 
 Note that `concat_eq_append` is a `@[simp]` lemma, so `concat` should usually not appear in goals.
@@ -2278,7 +2268,8 @@ theorem map_const' {l : List α} {b : β} : map (fun _ => b) l = replicate l.len
     simp only [mem_append, mem_replicate, ne_eq]
     rintro (⟨-, rfl⟩ | ⟨_, rfl⟩) <;> rfl
 
-
+@[deprecated replicate_append_replicate (since := "2025-01-16")]
+abbrev append_replicate_replicate := @replicate_append_replicate
 
 theorem append_eq_replicate_iff {l₁ l₂ : List α} {a : α} :
     l₁ ++ l₂ = replicate n a ↔
@@ -2666,6 +2657,8 @@ theorem foldl_map_hom {g : α → β} {f : α → α → α} {f' : β → β →
   · simp
   · simp [*]
 
+@[deprecated foldl_map_hom (since := "2025-01-20")] abbrev foldl_map' := @foldl_map_hom
+
 theorem foldr_map_hom {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
@@ -2673,6 +2666,8 @@ theorem foldr_map_hom {g : α → β} {f : α → α → α} {f' : β → β →
   · simp
   · simp [*]
 
+@[deprecated foldr_map_hom (since := "2025-01-20")] abbrev foldr_map' := @foldr_map_hom
+
 @[simp] theorem foldrM_append [Monad m] [LawfulMonad m] {f : α → β → m β} {b : β} {l l' : List α} :
     (l ++ l').foldrM f b = l'.foldrM f b >>= l.foldrM f := by
   induction l <;> simp [*]
@@ -3740,6 +3735,12 @@ theorem mem_iff_get? {a} {l : List α} : a ∈ l ↔ ∃ n, l.get? n = some a :=
 
 /-! ### Deprecations -/
 
+@[deprecated _root_.isSome_getElem? (since := "2024-12-09")]
+theorem isSome_getElem? {l : List α} {i : Nat} : l[i]?.isSome ↔ i < l.length := by
+  simp
 
+@[deprecated _root_.isNone_getElem? (since := "2024-12-09")]
+theorem isNone_getElem? {l : List α} {i : Nat} : l[i]?.isNone ↔ l.length ≤ i := by
+  simp
 
 end List