fix: verso test

Undo namespace collapses (e.g. `namespace Std.Time.Day.Offset`) back to
the original multi-line form (`namespace Std / namespace Time / namespace Day`),
keeping only functional formatting and parsing changes in this PR.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

.claude/CLAUDE.md

@@ -56,13 +56,6 @@ make -C build/release/stage2 clean-stdlib
 ```
 must be run manually before building.
 
-To rebuild individual stage 2 modules without a full `make stage2`, use Lake directly:
-```
-cd build/release/stage2 && lake build Init.Prelude
-```
-
-To run tests in stage2, replace `-C build/release` from above with `-C build/release/stage2`.
-
 ## New features
 
 When asked to implement new features:

.claude/commands/release.md

@@ -157,16 +157,6 @@ Note: `gh pr checks --watch` exits as soon as ALL checks complete (pass or fail)
 fail while others are still running, `--watch` will continue until everything settles, then exit
 with a non-zero code. So a background `--watch` finishing = all checks done; check which failed.
 
-## Mathlib Bump Branches
-
-Mathlib `bump/v4.X.0` branches live on the **fork** `leanprover-community/mathlib4-nightly-testing`,
-NOT on `leanprover-community/mathlib4`.
-
-## Never Force-Update Remote Refs Without Confirmation
-
-Never force-update an existing remote branch or tag via `git push --force` or the GitHub API
-without explicit user confirmation.
-
 ## Error Handling
 
 **CRITICAL**: If something goes wrong or a command fails:

.github/workflows/build-template.yml

@@ -131,7 +131,7 @@ jobs:
           [ -d build ] || mkdir build
           cd build
           # arguments passed to `cmake`
-          OPTIONS=(-DWFAIL=ON)
+          OPTIONS=(-DLEAN_EXTRA_MAKE_OPTS=-DwarningAsError=true)
           if [[ -n '${{ matrix.release }}' ]]; then
             # this also enables githash embedding into stage 1 library, which prohibits reusing
             # `.olean`s across commits, so we don't do it in the fast non-release CI

.github/workflows/ci.yml

@@ -143,7 +143,7 @@ jobs:
           CMAKE_MAJOR=$(grep -E "^set\(LEAN_VERSION_MAJOR " src/CMakeLists.txt | grep -oE '[0-9]+')
           CMAKE_MINOR=$(grep -E "^set\(LEAN_VERSION_MINOR " src/CMakeLists.txt | grep -oE '[0-9]+')
           CMAKE_PATCH=$(grep -E "^set\(LEAN_VERSION_PATCH " src/CMakeLists.txt | grep -oE '[0-9]+')
-          CMAKE_IS_RELEASE=$(grep -m 1 -E "^set\(LEAN_VERSION_IS_RELEASE " src/CMakeLists.txt | grep -oE '[0-9]+' | head -1)
+          CMAKE_IS_RELEASE=$(grep -m 1 -E "^set\(LEAN_VERSION_IS_RELEASE " src/CMakeLists.txt | sed -nE 's/^set\(LEAN_VERSION_IS_RELEASE ([0-9]+)\).*/\1/p')
 
           # Expected values from tag parsing
           TAG_MAJOR="${{ steps.set-release.outputs.LEAN_VERSION_MAJOR }}"
@@ -305,8 +305,7 @@ jobs:
                 "test": true,
                 "CMAKE_PRESET": "reldebug",
                 // * `elab_bench/big_do` crashes with exit code 134
-                // * `compile_bench/channel` randomly segfaults
-                "CTEST_OPTIONS": "-E 'elab_bench/big_do|compile_bench/channel'",
+                "CTEST_OPTIONS": "-E 'elab_bench/big_do'",
               },
               {
                 "name": "Linux fsanitize",

.github/workflows/update-stage0.yml

@@ -77,7 +77,7 @@ jobs:
       # sync options with `Linux Lake` to ensure cache reuse
       run: |
         mkdir -p build
-        cmake --preset release -B build -DWFAIL=ON
+        cmake --preset release -B build -DLEAN_EXTRA_MAKE_OPTS=-DwarningAsError=true
       shell: 'nix develop -c bash -euxo pipefail {0}'
     - if: env.should_update_stage0 == 'yes'
       run: |

.gitignore

@@ -34,4 +34,3 @@ wdErr.txt
 wdIn.txt
 wdOut.txt
 downstream_releases/
-.claude/worktrees/

.gitpod.yml

@@ -6,6 +6,6 @@ vscode:
     - leanprover.lean4
 
 tasks:
-  - name: Build
-    init: cmake --preset dev
+  - name: Release build
+    init: cmake --preset release
     command: make -C build/release -j$(nproc || sysctl -n hw.logicalcpu)

.vscode/tasks.json

@@ -11,15 +11,6 @@
 				"isDefault": true
 			}
 		},
-		{
-			"label": "build stage2",
-			"type": "shell",
-			"command": "make -C build/release stage2 -j$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4)",
-			"problemMatcher": [],
-			"group": {
-				"kind": "build"
-			}
-		},
 		{
 			"label": "build-old",
 			"type": "shell",

CMakeLists.txt

@@ -1,6 +1,4 @@
 cmake_minimum_required(VERSION 3.21)
-include(ExternalProject)
-include(FetchContent)
 
 if(NOT CMAKE_GENERATOR MATCHES "Makefiles")
   message(FATAL_ERROR "Only makefile generators are supported")
@@ -36,6 +34,7 @@ foreach(var ${vars})
   endif()
 endforeach()
 
+include(ExternalProject)
 project(LEAN CXX C)
 
 if(NOT (DEFINED STAGE0_CMAKE_EXECUTABLE_SUFFIX))
@@ -120,17 +119,17 @@ if(NOT CMAKE_SYSTEM_NAME MATCHES "Emscripten")
 endif()
 
 if(USE_MIMALLOC)
-  FetchContent_Declare(
+  ExternalProject_Add(
     mimalloc
+    PREFIX mimalloc
     GIT_REPOSITORY https://github.com/microsoft/mimalloc
     GIT_TAG v2.2.3
-    # Unnecessarily deep directory structure, but it saves us from a complicated
-    # stage0 update for now. If we ever update the other dependencies like
-    # cadical, it might be worth reorganizing the directory structure.
-    SOURCE_DIR
-    "${CMAKE_BINARY_DIR}/mimalloc/src/mimalloc"
+    # just download, we compile it as part of each stage as it is small
+    CONFIGURE_COMMAND ""
+    BUILD_COMMAND ""
+    INSTALL_COMMAND ""
   )
-  FetchContent_MakeAvailable(mimalloc)
+  list(APPEND EXTRA_DEPENDS mimalloc)
 endif()
 
 if(NOT STAGE1_PREV_STAGE)
@@ -220,9 +219,7 @@ add_custom_target(
   DEPENDS stage2
 )
 
-add_custom_target(clean-stdlib COMMAND $(MAKE) -C stage1 clean-stdlib DEPENDS stage1-configure)
-
-add_custom_target(cache-get COMMAND $(MAKE) -C stage1 cache-get DEPENDS stage1-configure)
+add_custom_target(clean-stdlib COMMAND $(MAKE) -C stage1 clean-stdlib DEPENDS stage1)
 
 install(CODE "execute_process(COMMAND make -C stage1 install)")
 

CMakePresets.json

@@ -8,26 +8,16 @@
   "configurePresets": [
     {
       "name": "release",
-      "displayName": "Release build config",
+      "displayName": "Default development optimized build config",
       "generator": "Unix Makefiles",
       "binaryDir": "${sourceDir}/build/release"
     },
-    {
-      "name": "dev",
-      "displayName": "Default development optimized build config",
-      "cacheVariables": {
-        "STRIP_BINARIES": "OFF"
-      },
-      "generator": "Unix Makefiles",
-      "binaryDir": "${sourceDir}/build/dev"
-    },
     {
       "name": "debug",
       "displayName": "Debug build config",
       "cacheVariables": {
-        "CMAKE_BUILD_TYPE": "Debug",
         "LEAN_EXTRA_CXX_FLAGS": "-DLEAN_DEFAULT_THREAD_STACK_SIZE=16*1024*1024",
-        "STRIP_BINARIES": "OFF"
+        "CMAKE_BUILD_TYPE": "Debug"
       },
       "generator": "Unix Makefiles",
       "binaryDir": "${sourceDir}/build/debug"
@@ -36,8 +26,7 @@
       "name": "reldebug",
       "displayName": "Release with assertions enabled",
       "cacheVariables": {
-        "CMAKE_BUILD_TYPE": "RelWithAssert",
-        "STRIP_BINARIES": "OFF"
+        "CMAKE_BUILD_TYPE": "RelWithAssert"
       },
       "generator": "Unix Makefiles",
       "binaryDir": "${sourceDir}/build/reldebug"
@@ -49,7 +38,6 @@
         "LEAN_EXTRA_CXX_FLAGS": "-fsanitize=address,undefined -DLEAN_DEFAULT_THREAD_STACK_SIZE=16*1024*1024",
         "LEANC_EXTRA_CC_FLAGS": "-fsanitize=address,undefined",
         "LEAN_EXTRA_LINKER_FLAGS": "-fsanitize=address,undefined -fsanitize-link-c++-runtime",
-        "STRIP_BINARIES": "OFF",
         "SMALL_ALLOCATOR": "OFF",
         "USE_MIMALLOC": "OFF",
         "BSYMBOLIC": "OFF",
@@ -70,10 +58,6 @@
       "name": "release",
       "configurePreset": "release"
     },
-    {
-      "name": "dev",
-      "configurePreset": "dev"
-    },
     {
       "name": "debug",
       "configurePreset": "debug"
@@ -97,11 +81,6 @@
       "configurePreset": "release",
       "output": {"outputOnFailure": true, "shortProgress": true}
     },
-    {
-      "name": "dev",
-      "configurePreset": "dev",
-      "output": {"outputOnFailure": true, "shortProgress": true}
-    },
     {
       "name": "debug",
       "configurePreset": "debug",

doc/make/index.md

@@ -30,9 +30,6 @@ cd lean4
 cmake --preset release
 make -C build/release -j$(nproc || sysctl -n hw.logicalcpu)
 ```
-
-For development, `cmake --preset dev` is recommended instead.
-
 You can replace `$(nproc || sysctl -n hw.logicalcpu)` with the desired parallelism amount.
 
 The above commands will compile the Lean library and binaries into the

script/release_checklist.py

@@ -311,16 +311,16 @@ def check_cmake_version(repo_url, branch, version_major, version_minor, github_t
         print(f"  ❌ Could not retrieve {cmake_file_path} from {branch}")
         return False
 
-    expected_patterns = [
-        (f"LEAN_VERSION_MAJOR", rf"^set\(LEAN_VERSION_MAJOR\s+{version_major}[\s)]", f"set(LEAN_VERSION_MAJOR {version_major} ...)"),
-        (f"LEAN_VERSION_MINOR", rf"^set\(LEAN_VERSION_MINOR\s+{version_minor}[\s)]", f"set(LEAN_VERSION_MINOR {version_minor} ...)"),
-        (f"LEAN_VERSION_PATCH", rf"^set\(LEAN_VERSION_PATCH\s+0[\s)]", f"set(LEAN_VERSION_PATCH 0 ...)"),
-        (f"LEAN_VERSION_IS_RELEASE", rf"^set\(LEAN_VERSION_IS_RELEASE\s+1[\s)]", f"set(LEAN_VERSION_IS_RELEASE 1 ...)"),
+    expected_lines = [
+        f"set(LEAN_VERSION_MAJOR {version_major})",
+        f"set(LEAN_VERSION_MINOR {version_minor})",
+        f"set(LEAN_VERSION_PATCH 0)",
+        f"set(LEAN_VERSION_IS_RELEASE 1)"
     ]
 
-    for name, pattern, display in expected_patterns:
-        if not any(re.match(pattern, l.strip()) for l in content.splitlines()):
-            print(f"  ❌ Missing or incorrect line in {cmake_file_path}: {display}")
+    for line in expected_lines:
+        if not any(l.strip().startswith(line) for l in content.splitlines()):
+            print(f"  ❌ Missing or incorrect line in {cmake_file_path}: {line}")
             return False
 
     print(f"  ✅ CMake version settings are correct in {cmake_file_path}")
@@ -343,11 +343,11 @@ def check_stage0_version(repo_url, branch, version_major, version_minor, github_
     for line in content.splitlines():
         stripped = line.strip()
         if stripped.startswith("set(LEAN_VERSION_MAJOR "):
-            actual = stripped.split()[1].rstrip(")")
+            actual = stripped.split()[-1].rstrip(")")
             if actual != str(version_major):
                 errors.append(f"LEAN_VERSION_MAJOR: expected {version_major}, found {actual}")
         elif stripped.startswith("set(LEAN_VERSION_MINOR "):
-            actual = stripped.split()[1].rstrip(")")
+            actual = stripped.split()[-1].rstrip(")")
             if actual != str(version_minor):
                 errors.append(f"LEAN_VERSION_MINOR: expected {version_minor}, found {actual}")
 

script/release_repos.yml

@@ -28,14 +28,6 @@ repositories:
     branch: main
     dependencies: []
 
-  - name: leansqlite
-    url: https://github.com/leanprover/leansqlite
-    toolchain-tag: true
-    stable-branch: false
-    branch: main
-    dependencies:
-      - plausible
-
   - name: verso
     url: https://github.com/leanprover/verso
     toolchain-tag: true
@@ -108,7 +100,7 @@ repositories:
     toolchain-tag: true
     stable-branch: false
     branch: main
-    dependencies: [lean4-cli, BibtexQuery, mathlib4, leansqlite]
+    dependencies: [lean4-cli, BibtexQuery, mathlib4]
 
   - name: cslib
     url: https://github.com/leanprover/cslib

script/release_steps.py

@@ -481,9 +481,11 @@ def execute_release_steps(repo, version, config):
         run_command("lake update", cwd=repo_path, stream_output=True)
     elif repo_name == "verso":
         # verso has nested Lake projects in test-projects/ that each have their own
-        # lake-manifest.json with a subverso pin and their own lean-toolchain.
-        # After updating the root manifest via `lake update`, sync the de-modulized
-        # subverso rev into all sub-manifests, and update their lean-toolchain files.
+        # lake-manifest.json with a subverso pin. After updating the root manifest via
+        # `lake update`, sync the de-modulized subverso rev into all sub-manifests.
+        # The sub-projects use an old toolchain (v4.21.0) that doesn't support module/prelude
+        # syntax, so they need the de-modulized version (tagged no-modules/<root-rev>).
+        # The "SubVerso version consistency" CI check accepts either the root or de-modulized rev.
         run_command("lake update", cwd=repo_path, stream_output=True)
         print(blue("Syncing de-modulized subverso rev to test-project sub-manifests..."))
         sync_script = (
@@ -496,15 +498,6 @@ def execute_release_steps(repo, version, config):
         )
         run_command(sync_script, cwd=repo_path)
         print(green("Synced de-modulized subverso rev to all test-project sub-manifests"))
-        # Update all lean-toolchain files in test-projects/ to match the root
-        print(blue("Updating lean-toolchain files in test-projects/..."))
-        find_result = run_command("find test-projects -name lean-toolchain", cwd=repo_path)
-        for tc_path in find_result.stdout.strip().splitlines():
-            if tc_path:
-                tc_file = repo_path / tc_path
-                with open(tc_file, "w") as f:
-                    f.write(f"leanprover/lean4:{version}\n")
-                print(green(f"  Updated {tc_path}"))
     elif dependencies:
         run_command(f'perl -pi -e \'s/"v4\\.[0-9]+(\\.[0-9]+)?(-rc[0-9]+)?"/"' + version + '"/g\' lakefile.*', cwd=repo_path)
         run_command("lake update", cwd=repo_path, stream_output=True)
@@ -666,61 +659,56 @@ def execute_release_steps(repo, version, config):
         # Fetch latest changes to ensure we have the most up-to-date nightly-testing branch
         print(blue("Fetching latest changes from origin..."))
         run_command("git fetch origin", cwd=repo_path)
-
-        # Check if nightly-testing branch exists on origin (use local ref after fetch for exact match)
-        nightly_check = run_command("git show-ref --verify --quiet refs/remotes/origin/nightly-testing", cwd=repo_path, check=False)
-        if nightly_check.returncode != 0:
-            print(yellow("No nightly-testing branch found on origin, skipping merge"))
-        else:
-            try:
-                print(blue("Merging origin/nightly-testing..."))
-                run_command("git merge origin/nightly-testing", cwd=repo_path)
-                print(green("Merge completed successfully"))
-            except subprocess.CalledProcessError:
-                # Merge failed due to conflicts - check which files are conflicted
-                print(blue("Merge conflicts detected, checking which files are affected..."))
-
-                # Get conflicted files using git status
-                status_result = run_command("git status --porcelain", cwd=repo_path)
-                conflicted_files = []
-
-                for line in status_result.stdout.splitlines():
-                    if len(line) >= 2 and line[:2] in ['UU', 'AA', 'DD', 'AU', 'UA', 'DU', 'UD']:
-                        # Extract filename (skip the first 3 characters which are status codes)
-                        conflicted_files.append(line[3:])
-
-                # Filter out allowed files
-                allowed_patterns = ['lean-toolchain', 'lake-manifest.json']
-                problematic_files = []
-
+        
+        try:
+            print(blue("Merging origin/nightly-testing..."))
+            run_command("git merge origin/nightly-testing", cwd=repo_path)
+            print(green("Merge completed successfully"))
+        except subprocess.CalledProcessError:
+            # Merge failed due to conflicts - check which files are conflicted
+            print(blue("Merge conflicts detected, checking which files are affected..."))
+            
+            # Get conflicted files using git status
+            status_result = run_command("git status --porcelain", cwd=repo_path)
+            conflicted_files = []
+            
+            for line in status_result.stdout.splitlines():
+                if len(line) >= 2 and line[:2] in ['UU', 'AA', 'DD', 'AU', 'UA', 'DU', 'UD']:
+                    # Extract filename (skip the first 3 characters which are status codes)
+                    conflicted_files.append(line[3:])
+            
+            # Filter out allowed files
+            allowed_patterns = ['lean-toolchain', 'lake-manifest.json']
+            problematic_files = []
+            
+            for file in conflicted_files:
+                is_allowed = any(pattern in file for pattern in allowed_patterns)
+                if not is_allowed:
+                    problematic_files.append(file)
+            
+            if problematic_files:
+                # There are conflicts in non-allowed files - fail
+                print(red("❌ Merge failed!"))
+                print(red(f"Merging nightly-testing resulted in conflicts in:"))
+                for file in problematic_files:
+                    print(red(f"  - {file}"))
+                print(red("Please resolve these conflicts manually."))
+                return
+            else:
+                # Only allowed files are conflicted - resolve them automatically
+                print(green(f"✅ Only allowed files conflicted: {', '.join(conflicted_files)}"))
+                print(blue("Resolving conflicts automatically..."))
+                
+                # For lean-toolchain and lake-manifest.json, keep our versions
                 for file in conflicted_files:
-                    is_allowed = any(pattern in file for pattern in allowed_patterns)
-                    if not is_allowed:
-                        problematic_files.append(file)
-
-                if problematic_files:
-                    # There are conflicts in non-allowed files - fail
-                    print(red("❌ Merge failed!"))
-                    print(red(f"Merging nightly-testing resulted in conflicts in:"))
-                    for file in problematic_files:
-                        print(red(f"  - {file}"))
-                    print(red("Please resolve these conflicts manually."))
-                    return
-                else:
-                    # Only allowed files are conflicted - resolve them automatically
-                    print(green(f"✅ Only allowed files conflicted: {', '.join(conflicted_files)}"))
-                    print(blue("Resolving conflicts automatically..."))
-
-                    # For lean-toolchain and lake-manifest.json, keep our versions
-                    for file in conflicted_files:
-                        print(blue(f"Keeping our version of {file}"))
-                        run_command(f"git checkout --ours {file}", cwd=repo_path)
-
-                    # Complete the merge
-                    run_command("git add .", cwd=repo_path)
-                    run_command("git commit --no-edit", cwd=repo_path)
-
-                    print(green("✅ Merge completed successfully with automatic conflict resolution"))
+                    print(blue(f"Keeping our version of {file}"))
+                    run_command(f"git checkout --ours {file}", cwd=repo_path)
+                
+                # Complete the merge
+                run_command("git add .", cwd=repo_path)
+                run_command("git commit --no-edit", cwd=repo_path)
+                
+                print(green("✅ Merge completed successfully with automatic conflict resolution"))
 
     # Build and test (skip for Mathlib)
     if repo_name not in ["mathlib4"]:

src/CMakeLists.txt

@@ -8,7 +8,7 @@ endif()
 include(ExternalProject)
 project(LEAN CXX C)
 set(LEAN_VERSION_MAJOR 4 CACHE STRING "")
-set(LEAN_VERSION_MINOR 31 CACHE STRING "")
+set(LEAN_VERSION_MINOR 30 CACHE STRING "")
 set(LEAN_VERSION_PATCH 0 CACHE STRING "")
 set(LEAN_VERSION_IS_RELEASE 0 CACHE STRING "") # 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'")
@@ -80,7 +80,6 @@ option(CCACHE "use ccache" ON)
 option(SPLIT_STACK "SPLIT_STACK" OFF)
 # When OFF we disable LLVM support
 option(LLVM "LLVM" OFF)
-option(STRIP_BINARIES "Strip produced binaries" ON)
 
 # When ON we include githash in the version string
 option(USE_GITHASH "GIT_HASH" ON)
@@ -110,26 +109,17 @@ option(RUNTIME_STATS "RUNTIME_STATS" OFF)
 option(BSYMBOLIC "Link with -Bsymbolic to reduce call overhead in shared libraries (Linux)" ON)
 option(USE_GMP "USE_GMP" ON)
 option(USE_MIMALLOC "use mimalloc" ON)
-set(LEAN_MI_SECURE 0 CACHE STRING "Configure mimalloc memory safety mitigations (https://github.com/microsoft/mimalloc/blob/v2.2.7/include/mimalloc/types.h#L56-L60)")
 
 # 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_CACHE "Use the Lake artifact cache for stage 1 builds (requires USE_LAKE)" OFF)
 
-set(LEAN_EXTRA_OPTS "" CACHE STRING "extra options to lean (via lake or make)")
-set(LEAN_EXTRA_MAKE_OPTS "" CACHE STRING "extra options to leanmake")
+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`")
 
 # Temporary, core-only flags. Must be synced with stdlib_flags.h.
-string(APPEND LEAN_EXTRA_OPTS " -Dbackward.do.legacy=false")
-
-# option used by the CI to fail on warnings
-option(WFAIL "Fail build if warnings are emitted by Lean" ON)
-if(WFAIL MATCHES "ON")
-  string(APPEND LAKE_EXTRA_ARGS " --wfail")
-  string(APPEND LEAN_EXTRA_MAKE_OPTS " -DwarningAsError=true")
-endif()
+string(APPEND LEAN_EXTRA_MAKE_OPTS " -Dbackward.do.legacy=false")
 
 if(LAZY_RC MATCHES "ON")
   set(LEAN_LAZY_RC "#define LEAN_LAZY_RC")
@@ -207,7 +197,7 @@ set(CMAKE_ARCHIVE_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/lib/lean")
 
 # OSX default thread stack size is very small. Moreover, in Debug mode, each new stack frame consumes a lot of extra memory.
 if((MULTI_THREAD MATCHES "ON") AND (CMAKE_SYSTEM_NAME MATCHES "Darwin"))
-  string(APPEND LEAN_EXTRA_OPTS " -s40000")
+  string(APPEND LEAN_EXTRA_MAKE_OPTS " -s40000")
 endif()
 
 # We want explicit stack probes in huge Lean stack frames for robust stack overflow detection
@@ -624,38 +614,6 @@ else()
       OUTPUT_VARIABLE GIT_SHA1
       OUTPUT_STRIP_TRAILING_WHITESPACE
     )
-    # Fallback for jj workspaces where git cannot find .git directly.
-    # Use `jj git root` to find the backing git repo, then `jj log` to
-    # resolve the current workspace's commit (git HEAD points to the root
-    # workspace, not the current one).
-    if("${GIT_SHA1}" STREQUAL "")
-      find_program(JJ_EXECUTABLE jj)
-      if(JJ_EXECUTABLE)
-        execute_process(
-          COMMAND "${JJ_EXECUTABLE}" git root
-          WORKING_DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}"
-          OUTPUT_VARIABLE _jj_git_dir
-          OUTPUT_STRIP_TRAILING_WHITESPACE
-          ERROR_QUIET
-          RESULT_VARIABLE _jj_git_root_result
-        )
-        execute_process(
-          COMMAND "${JJ_EXECUTABLE}" log -r @ --no-graph -T "commit_id"
-          WORKING_DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}"
-          OUTPUT_VARIABLE _jj_commit
-          OUTPUT_STRIP_TRAILING_WHITESPACE
-          ERROR_QUIET
-          RESULT_VARIABLE _jj_rev_result
-        )
-        if(_jj_git_root_result EQUAL 0 AND _jj_rev_result EQUAL 0)
-          execute_process(
-            COMMAND git --git-dir "${_jj_git_dir}" ls-tree "${_jj_commit}" stage0 --object-only
-            OUTPUT_VARIABLE GIT_SHA1
-            OUTPUT_STRIP_TRAILING_WHITESPACE
-          )
-        endif()
-      endif()
-    endif()
     message(STATUS "stage0 sha1: ${GIT_SHA1}")
     # Now that we've prepared the information for the next stage, we can forget that we will use
     # Lake in the future as we won't use it in this stage
@@ -679,9 +637,6 @@ else()
   set(LEAN_PATH_SEPARATOR ":")
 endif()
 
-# inherit genral options for lean.mk.in and stdlib.make.in
-string(APPEND LEAN_EXTRA_MAKE_OPTS " ${LEAN_EXTRA_OPTS}")
-
 # Version
 configure_file("${LEAN_SOURCE_DIR}/version.h.in" "${LEAN_BINARY_DIR}/include/lean/version.h")
 if(STAGE EQUAL 0)
@@ -842,14 +797,7 @@ if(LLVM AND STAGE GREATER 0)
   set(EXTRA_LEANMAKE_OPTS "LLVM=1")
 endif()
 
-set(
-  STDLIBS
-  Init
-  Std
-  Lean
-  Leanc
-  LeanIR
-)
+set(STDLIBS Init Std Lean Leanc LeanIR)
 if(NOT CMAKE_SYSTEM_NAME MATCHES "Emscripten")
   list(APPEND STDLIBS Lake LeanChecker)
 endif()
@@ -957,7 +905,10 @@ if(PREV_STAGE)
 endif()
 
 if(NOT CMAKE_SYSTEM_NAME MATCHES "Emscripten")
-  add_custom_target(leanir ALL DEPENDS leanshared COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make leanir VERBATIM)
+  add_custom_target(leanir ALL
+    DEPENDS leanshared
+    COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make leanir
+    VERBATIM)
 endif()
 
 # use Bash version for building, use Lean version in bin/ for tests & distribution
@@ -993,13 +944,6 @@ add_custom_target(
 
 add_custom_target(clean-olean DEPENDS clean-stdlib)
 
-if(USE_LAKE_CACHE)
-  add_custom_target(
-    cache-get
-    COMMAND ${PREV_STAGE}/bin/lake${CMAKE_EXECUTABLE_SUFFIX} cache get --repo=leanprover/lean4
-  )
-endif()
-
 install(
   DIRECTORY "${CMAKE_BINARY_DIR}/lib/"
   DESTINATION lib
@@ -1073,7 +1017,7 @@ string(REPLACE "ROOT" "${CMAKE_BINARY_DIR}" LEANC_CC "${LEANC_CC}")
 string(REPLACE "ROOT" "${CMAKE_BINARY_DIR}" LEANC_INTERNAL_FLAGS "${LEANC_INTERNAL_FLAGS}")
 string(REPLACE "ROOT" "${CMAKE_BINARY_DIR}" LEANC_INTERNAL_LINKER_FLAGS "${LEANC_INTERNAL_LINKER_FLAGS}")
 
-toml_escape("${LEAN_EXTRA_OPTS}" LEAN_EXTRA_OPTS_TOML)
+toml_escape("${LEAN_EXTRA_MAKE_OPTS}" LEAN_EXTRA_OPTS_TOML)
 
 if(CMAKE_BUILD_TYPE MATCHES "Debug|Release|RelWithDebInfo|MinSizeRel")
   set(CMAKE_BUILD_TYPE_TOML "${CMAKE_BUILD_TYPE}")

src/Init/Data/Array/Basic.lean

@@ -802,7 +802,6 @@ Examples:
 def firstM {α : Type u} {m : Type v → Type w} [Alternative m] (f : α → m β) (as : Array α) : m β :=
   go 0
 where
-  @[specialize]
   go (i : Nat) : m β :=
     if hlt : i < as.size then
       f as[i] <|> go (i+1)
@@ -1086,17 +1085,6 @@ Examples:
 def sum {α} [Add α] [Zero α] : Array α → α :=
   foldr (· + ·) 0
 
-/--
-Computes the product of the elements of an array.
-
-Examples:
- * `#[a, b, c].prod = a * (b * (c * 1))`
- * `#[1, 2, 5].prod = 10`
--/
-@[inline, expose]
-def prod {α} [Mul α] [One α] : Array α → α :=
-  foldr (· * ·) 1
-
 /--
 Counts the number of elements in the array `as` that satisfy the Boolean predicate `p`.
 
@@ -1265,7 +1253,7 @@ Examples:
 -/
 @[inline, expose]
 def findIdx? {α : Type u} (p : α → Bool) (as : Array α) : Option Nat :=
-  let rec @[specialize] loop (j : Nat) :=
+  let rec loop (j : Nat) :=
     if h : j < as.size then
       if p as[j] then some j else loop (j + 1)
     else none

src/Init/Data/Array/Int.lean

@@ -7,7 +7,6 @@ module
 
 prelude
 public import Init.Data.List.Int.Sum
-public import Init.Data.List.Int.Prod
 public import Init.Data.Array.MinMax
 import Init.Data.Int.Lemmas
 
@@ -75,17 +74,4 @@ theorem sum_div_length_le_max_of_max?_eq_some_int {xs : Array Int} (h : xs.max?
   simpa [List.max?_toArray, List.sum_toArray] using
     List.sum_div_length_le_max_of_max?_eq_some_int (by simpa using h)
 
-@[simp] theorem prod_replicate_int {n : Nat} {a : Int} : (replicate n a).prod = a ^ n := by
-  rw [← List.toArray_replicate, List.prod_toArray]
-  simp
-
-theorem prod_append_int {as₁ as₂ : Array Int} : (as₁ ++ as₂).prod = as₁.prod * as₂.prod := by
-  simp [prod_append]
-
-theorem prod_reverse_int (xs : Array Int) : xs.reverse.prod = xs.prod := by
-  simp [prod_reverse]
-
-theorem prod_eq_foldl_int {xs : Array Int} : xs.prod = xs.foldl (init := 1) (· * ·) := by
-  simp only [foldl_eq_foldr_reverse, Int.mul_comm, ← prod_eq_foldr, prod_reverse_int]
-
 end Array

src/Init/Data/Array/Lemmas.lean

@@ -3096,13 +3096,13 @@ theorem foldl_eq_foldlM {f : β → α → β} {b} {xs : Array α} {start stop :
 theorem foldr_eq_foldrM {f : α → β → β} {b} {xs : Array α} {start stop : Nat} :
     xs.foldr f b start stop = (xs.foldrM (m := Id) (pure <| f · ·) b start stop).run := rfl
 
-theorem foldl_eq_foldl_extract {xs : Array α} {f : β → α → β} {init : β} :
+public theorem foldl_eq_foldl_extract {xs : Array α} {f : β → α → β} {init : β} :
     xs.foldl (init := init) (start := start) (stop := stop) f =
       (xs.extract start stop).foldl (init := init) f := by
   simp only [foldl_eq_foldlM]
   rw [foldlM_start_stop]
 
-theorem foldr_eq_foldr_extract {xs : Array α} {f : α → β → β} {init : β} :
+public theorem foldr_eq_foldr_extract {xs : Array α} {f : α → β → β} {init : β} :
     xs.foldr (init := init) (start := start) (stop := stop) f =
       (xs.extract stop start).foldr (init := init) f := by
   simp only [foldr_eq_foldrM]
@@ -4380,47 +4380,6 @@ theorem sum_eq_foldl [Zero α] [Add α] [Std.Associative (α := α) (· + ·)]
     xs.sum = xs.foldl (init := 0) (· + ·) := by
   simp [← sum_toList, List.sum_eq_foldl]
 
-/-! ### prod -/
-
-@[simp, grind =] theorem prod_empty [Mul α] [One α] : (#[] : Array α).prod = 1 := rfl
-theorem prod_eq_foldr [Mul α] [One α] {xs : Array α} :
-    xs.prod = xs.foldr (init := 1) (· * ·) :=
-  rfl
-
-@[simp, grind =]
-theorem prod_toList [Mul α] [One α] {as : Array α} : as.toList.prod = as.prod := by
-  cases as
-  simp [Array.prod, List.prod]
-
-@[simp, grind =]
-theorem prod_append [One α] [Mul α] [Std.Associative (α := α) (· * ·)]
-    [Std.LawfulLeftIdentity (α := α) (· * ·) 1]
-    {as₁ as₂ : Array α} : (as₁ ++ as₂).prod = as₁.prod * as₂.prod := by
-  simp [← prod_toList, List.prod_append]
-
-@[simp, grind =]
-theorem prod_singleton [Mul α] [One α] [Std.LawfulRightIdentity (· * ·) (1 : α)] {x : α} :
-    #[x].prod = x := by
-  simp [Array.prod_eq_foldr, Std.LawfulRightIdentity.right_id x]
-
-@[simp, grind =]
-theorem prod_push [Mul α] [One α] [Std.Associative (α := α) (· * ·)]
-    [Std.LawfulIdentity (· * ·) (1 : α)] {xs : Array α} {x : α} :
-    (xs.push x).prod = xs.prod * x := by
-  simp [Array.prod_eq_foldr, Std.LawfulRightIdentity.right_id, Std.LawfulLeftIdentity.left_id,
-    ← Array.foldr_assoc]
-
-@[simp, grind =]
-theorem prod_reverse [One α] [Mul α] [Std.Associative (α := α) (· * ·)]
-    [Std.Commutative (α := α) (· * ·)]
-    [Std.LawfulLeftIdentity (α := α) (· * ·) 1] (xs : Array α) : xs.reverse.prod = xs.prod := by
-  simp [← prod_toList, List.prod_reverse]
-
-theorem prod_eq_foldl [One α] [Mul α] [Std.Associative (α := α) (· * ·)]
-    [Std.LawfulIdentity (· * ·) (1 : α)] {xs : Array α} :
-    xs.prod = xs.foldl (init := 1) (· * ·) := by
-  simp [← prod_toList, List.prod_eq_foldl]
-
 theorem foldl_toList_eq_flatMap {l : List α} {acc : Array β}
     {F : Array β → α → Array β} {G : α → List β}
     (H : ∀ acc a, (F acc a).toList = acc.toList ++ G a) :

src/Init/Data/Array/Nat.lean

@@ -8,7 +8,6 @@ module
 prelude
 public import Init.Data.Array.MinMax
 import Init.Data.List.Nat.Sum
-import Init.Data.List.Nat.Prod
 import Init.Data.Array.Lemmas
 
 public section
@@ -82,24 +81,4 @@ theorem sum_div_length_le_max_of_max?_eq_some_nat {xs : Array Nat} (h : xs.max?
   simpa [List.max?_toArray, List.sum_toArray] using
     List.sum_div_length_le_max_of_max?_eq_some_nat (by simpa using h)
 
-protected theorem prod_pos_iff_forall_pos_nat {xs : Array Nat} : 0 < xs.prod ↔ ∀ x ∈ xs, 0 < x := by
-  simp [← prod_toList, List.prod_pos_iff_forall_pos_nat]
-
-protected theorem prod_eq_zero_iff_exists_zero_nat {xs : Array Nat} :
-    xs.prod = 0 ↔ ∃ x ∈ xs, x = 0 := by
-  simp [← prod_toList, List.prod_eq_zero_iff_exists_zero_nat]
-
-@[simp] theorem prod_replicate_nat {n : Nat} {a : Nat} : (replicate n a).prod = a ^ n := by
-  rw [← List.toArray_replicate, List.prod_toArray]
-  simp
-
-theorem prod_append_nat {as₁ as₂ : Array Nat} : (as₁ ++ as₂).prod = as₁.prod * as₂.prod := by
-  simp [prod_append]
-
-theorem prod_reverse_nat (xs : Array Nat) : xs.reverse.prod = xs.prod := by
-  simp [prod_reverse]
-
-theorem prod_eq_foldl_nat {xs : Array Nat} : xs.prod = xs.foldl (init := 1) (· * ·) := by
-  simp only [foldl_eq_foldr_reverse, Nat.mul_comm, ← prod_eq_foldr, prod_reverse_nat]
-
 end Array

src/Init/Data/Array/Subarray.lean

@@ -80,7 +80,7 @@ instance : SliceSize (Internal.SubarrayData α) where
   size s := s.internalRepresentation.stop - s.internalRepresentation.start
 
 @[grind =, suggest_for Subarray.size]
-theorem size_eq {xs : Subarray α} :
+public theorem size_eq {xs : Subarray α} :
     xs.size = xs.stop - xs.start := by
   simp [Std.Slice.size, SliceSize.size, start, stop]
 

src/Init/Data/ByteArray/Basic.lean

@@ -20,20 +20,12 @@ universe u
 
 namespace ByteArray
 
-@[extern "lean_sarray_dec_eq"]
-def beq (lhs rhs : @& ByteArray) : Bool :=
-  lhs.data == rhs.data
-
-instance : BEq ByteArray where
-  beq := beq
+deriving instance BEq for ByteArray
 
 attribute [ext] ByteArray
 
-@[extern "lean_sarray_dec_eq"]
-def decEq (lhs rhs : @& ByteArray) : Decidable (lhs = rhs) :=
-  decidable_of_decidable_of_iff ByteArray.ext_iff.symm
-
-instance : DecidableEq ByteArray := decEq
+instance : DecidableEq ByteArray :=
+  fun _ _ => decidable_of_decidable_of_iff ByteArray.ext_iff.symm
 
 instance : Inhabited ByteArray where
   default := empty

src/Init/Data/Int/Compare.lean

@@ -74,7 +74,7 @@ protected theorem isGE_compare {a b : Int} :
   rw [← Int.compare_swap, Ordering.isGE_swap]
   exact Int.isLE_compare
 
-instance : Std.LawfulOrderOrd Int where
+public instance : Std.LawfulOrderOrd Int where
   isLE_compare _ _ := Int.isLE_compare
   isGE_compare _ _ := Int.isGE_compare
 

src/Init/Data/Iterators/Basic.lean

@@ -42,29 +42,29 @@ The conversion functions {name (scope := "Init.Data.Iterators.Basic")}`Shrink.de
 {name (scope := "Init.Data.Iterators.Basic")}`Shrink.inflate` form an equivalence between
 {name}`α` and {lean}`Shrink α`, but this equivalence is intentionally not definitional.
 -/
-def Shrink (α : Type u) : Type u := Internal.idOpaque.1 α
+public def Shrink (α : Type u) : Type u := Internal.idOpaque.1 α
 
 /-- Converts elements of {name}`α` into elements of {lean}`Shrink α`. -/
 @[always_inline]
-def Shrink.deflate {α} (x : α) : Shrink α :=
+public def Shrink.deflate {α} (x : α) : Shrink α :=
   cast (by simp [Shrink, Internal.idOpaque.property]) x
 
 /-- Converts elements of {lean}`Shrink α` into elements of {name}`α`. -/
 @[always_inline]
-def Shrink.inflate {α} (x : Shrink α) : α :=
+public def Shrink.inflate {α} (x : Shrink α) : α :=
   cast (by simp [Shrink, Internal.idOpaque.property]) x
 
 @[simp, grind =]
-theorem Shrink.deflate_inflate {α} {x : Shrink α} :
+public theorem Shrink.deflate_inflate {α} {x : Shrink α} :
     Shrink.deflate x.inflate = x := by
   simp [deflate, inflate]
 
 @[simp, grind =]
-theorem Shrink.inflate_deflate {α} {x : α} :
+public theorem Shrink.inflate_deflate {α} {x : α} :
     (Shrink.deflate x).inflate = x := by
   simp [deflate, inflate]
 
-theorem Shrink.inflate_inj {α} {x y : Shrink α} :
+public theorem Shrink.inflate_inj {α} {x y : Shrink α} :
     x.inflate = y.inflate ↔ x = y := by
   apply Iff.intro
   · intro h
@@ -72,7 +72,7 @@ theorem Shrink.inflate_inj {α} {x y : Shrink α} :
   · rintro rfl
     rfl
 
-theorem Shrink.deflate_inj {α} {x y : α} :
+public theorem Shrink.deflate_inj {α} {x y : α} :
     Shrink.deflate x = Shrink.deflate y ↔ x = y := by
   apply Iff.intro
   · intro h

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

@@ -190,7 +190,7 @@ def Append.instFinitenessRelation [Monad m] [Iterator α₁ m β] [Iterator α
       exact IterM.TerminationMeasures.Finite.rel_of_skip ‹_›
 
 @[no_expose]
-instance Append.instFinite [Monad m] [Iterator α₁ m β] [Iterator α₂ m β]
+public instance Append.instFinite [Monad m] [Iterator α₁ m β] [Iterator α₂ m β]
     [Finite α₁ m] [Finite α₂ m] : Finite (Append α₁ α₂ m β) m :=
   .of_finitenessRelation instFinitenessRelation
 

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

@@ -271,7 +271,7 @@ private def optionPelim' {α : Type u_1} (t : Option α) {β :  Sort u_2}
 
 /--
 Inserts an `Option` case distinction after the first computation of a call to `MonadAttach.pbind`.
-This lemma is useful for simplifying the second computation, which often involves `match` expressions
+This lemma is useful for simplifying the second computation, which often involes `match` expressions
 that use `pbind`'s proof term.
 -/
 private theorem pbind_eq_pbind_if_isSome [Monad m] [MonadAttach m] (x : m (Option α)) (f : (_ : _) → _ → m β) :

src/Init/Data/List/Basic.lean

@@ -282,7 +282,6 @@ The lexicographic order with respect to `lt` is:
 * `as.lex [] = false` is `false`
 * `(a :: as).lex (b :: bs)` is true if `lt a b` or `a == b` and `lex lt as bs` is true.
 -/
-@[specialize]
 def lex [BEq α] (l₁ l₂ : List α) (lt : α → α → Bool := by exact (· < ·)) : Bool :=
   match l₁, l₂ with
   | [],      _ :: _  => true
@@ -1005,7 +1004,6 @@ Examples:
  * `[8, 3, 2, 4, 2, 7, 4].dropWhile (· < 4) = [8, 3, 2, 4, 2, 7, 4]`
  * `[8, 3, 2, 4, 2, 7, 4].dropWhile (· < 100) = []`
 -/
-@[specialize]
 def dropWhile (p : α → Bool) : List α → List α
   | []   => []
   | a::l => match p a with
@@ -1462,11 +1460,9 @@ Examples:
 ["circle", "square", "triangle"]
 ```
 -/
-@[inline]
 def modifyTailIdx (l : List α) (i : Nat) (f : List α → List α) : List α :=
   go i l
 where
-  @[specialize]
   go : Nat → List α → List α
   | 0, l => f l
   | _+1, [] => []
@@ -1502,7 +1498,6 @@ Examples:
  * `[1, 2, 3].modify 2 (· * 10) = [1, 2, 30]`
  * `[1, 2, 3].modify 3 (· * 10) = [1, 2, 3]`
 -/
-@[inline]
 def modify (l : List α) (i : Nat) (f : α → α) : List α :=
   l.modifyTailIdx i (modifyHead f)
 
@@ -1609,7 +1604,6 @@ Examples:
 * `[7, 6, 5, 8, 1, 2, 6].find? (· < 5) = some 1`
 * `[7, 6, 5, 8, 1, 2, 6].find? (· < 1) = none`
 -/
-@[specialize]
 def find? (p : α → Bool) : List α → Option α
   | []    => none
   | a::as => match p a with
@@ -1632,7 +1626,6 @@ Examples:
  * `[7, 6, 5, 8, 1, 2, 6].findSome? (fun x => if x < 5 then some (10 * x) else none) = some 10`
  * `[7, 6, 5, 8, 1, 2, 6].findSome? (fun x => if x < 1 then some (10 * x) else none) = none`
 -/
-@[specialize]
 def findSome? (f : α → Option β) : List α → Option β
   | []    => none
   | a::as => match f a with
@@ -1656,7 +1649,6 @@ Examples:
 * `[7, 6, 5, 8, 1, 2, 6].findRev? (· < 5) = some 2`
 * `[7, 6, 5, 8, 1, 2, 6].findRev? (· < 1) = none`
 -/
-@[specialize]
 def findRev? (p : α → Bool) : List α → Option α
   | []    => none
   | a::as => match findRev? p as with
@@ -1675,7 +1667,6 @@ Examples:
  * `[7, 6, 5, 8, 1, 2, 6].findSomeRev? (fun x => if x < 5 then some (10 * x) else none) = some 20`
  * `[7, 6, 5, 8, 1, 2, 6].findSomeRev? (fun x => if x < 1 then some (10 * x) else none) = none`
 -/
-@[specialize]
 def findSomeRev? (f : α → Option β) : List α → Option β
   | []    => none
   | a::as => match findSomeRev? f as with
@@ -1726,11 +1717,9 @@ Examples:
 * `[7, 6, 5, 8, 1, 2, 6].findIdx (· < 5) = some 4`
 * `[7, 6, 5, 8, 1, 2, 6].findIdx (· < 1) = none`
 -/
-@[inline]
 def findIdx? (p : α → Bool) (l : List α) : Option Nat :=
   go l 0
 where
-  @[specialize]
   go : List α → Nat → Option Nat
   | [], _ => none
   | a :: l, i => if p a then some i else go l (i + 1)
@@ -1761,7 +1750,6 @@ Examples:
 @[inline] def findFinIdx? (p : α → Bool) (l : List α) : Option (Fin l.length) :=
   go l 0 (by simp)
 where
-  @[specialize]
   go : (l' : List α) → (i : Nat) → (h : l'.length + i = l.length) → Option (Fin l.length)
   | [], _, _ => none
   | a :: l, i, h =>
@@ -1898,7 +1886,7 @@ Examples:
 * `[2, 4, 5, 6].any (· % 2 = 0) = true`
 * `[2, 4, 5, 6].any (· % 2 = 1) = true`
 -/
-@[suggest_for List.some, specialize]
+@[suggest_for List.some]
 def any : (l : List α) → (p : α → Bool) → Bool
   | [], _ => false
   | h :: t, p => p h || any t p
@@ -1918,7 +1906,7 @@ Examples:
 * `[2, 4, 6].all (· % 2 = 0) = true`
 * `[2, 4, 5, 6].all (· % 2 = 0) = false`
 -/
-@[suggest_for List.every, specialize]
+@[suggest_for List.every]
 def all : List α → (α → Bool) → Bool
   | [], _ => true
   | h :: t, p => p h && all t p
@@ -2019,7 +2007,6 @@ Examples:
 * `[1, 2, 3].zipWithAll Prod.mk [5, 6] = [(some 1, some 5), (some 2, some 6), (some 3, none)]`
 * `[x₁, x₂].zipWithAll f [y] = [f (some x₁) (some y), f (some x₂) none]`
 -/
-@[specialize]
 def zipWithAll (f : Option α → Option β → γ) : List α → List β → List γ
   | [], bs => bs.map fun b => f none (some b)
   | a :: as, [] => (a :: as).map fun a => f (some a) none
@@ -2069,20 +2056,6 @@ def sum {α} [Add α] [Zero α] : List α → α :=
 @[simp, grind =] theorem sum_cons [Add α] [Zero α] {a : α} {l : List α} : (a::l).sum = a + l.sum := rfl
 theorem sum_eq_foldr [Add α] [Zero α] {l : List α} : l.sum = l.foldr (· + ·) 0 := rfl
 
-/--
-Computes the product of the elements of a list.
-
-Examples:
- * `[a, b, c].prod = a * (b * (c * 1))`
- * `[1, 2, 5].prod = 10`
--/
-def prod {α} [Mul α] [One α] : List α → α :=
-  foldr (· * ·) 1
-
-@[simp, grind =] theorem prod_nil [Mul α] [One α] : ([] : List α).prod = 1 := rfl
-@[simp, grind =] theorem prod_cons [Mul α] [One α] {a : α} {l : List α} : (a::l).prod = a * l.prod := rfl
-theorem prod_eq_foldr [Mul α] [One α] {l : List α} : l.prod = l.foldr (· * ·) 1 := rfl
-
 /-! ### range -/
 
 /--

src/Init/Data/List/Control.lean

@@ -444,8 +444,8 @@ theorem findM?_eq_findSomeM? [Monad m] [LawfulMonad m] {p : α → m Bool} {as :
     intro b
     cases b <;> simp
 
-@[inline, expose] protected def forIn' {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : @& List α) (init : β) (f : (a : α) → a ∈ as → β → m (ForInStep β)) : m β :=
-  let rec @[specialize] loop : (as' : @& List α) → (b : β) → Exists (fun bs => bs ++ as' = as) → m β
+@[inline, expose] protected def forIn' {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : List α) (init : β) (f : (a : α) → a ∈ as → β → m (ForInStep β)) : m β :=
+  let rec @[specialize] loop : (as' : List α) → (b : β) → Exists (fun bs => bs ++ as' = as) → m β
     | [], b, _    => pure b
     | a::as', b, h => do
       have : a ∈ as := by

src/Init/Data/List/Int.lean

@@ -7,4 +7,3 @@ module
 
 prelude
 public import Init.Data.List.Int.Sum
-public import Init.Data.List.Int.Prod

src/Init/Data/List/Int/Prod.lean

@@ -1,31 +0,0 @@
-/-
-Copyright (c) 2026 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.List.Lemmas
-import Init.Data.Int.Lemmas
-public import Init.Data.Int.Pow
-public import Init.Data.List.Basic
-
-public section
-
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
-namespace List
-
-@[simp]
-theorem prod_replicate_int {n : Nat} {a : Int} : (replicate n a).prod = a ^ n := by
-  induction n <;> simp_all [replicate_succ, Int.pow_succ, Int.mul_comm]
-
-theorem prod_append_int {l₁ l₂ : List Int} : (l₁ ++ l₂).prod = l₁.prod * l₂.prod := by
-  simp [prod_append]
-
-theorem prod_reverse_int (xs : List Int) : xs.reverse.prod = xs.prod := by
-  simp [prod_reverse]
-
-end List

src/Init/Data/List/Lemmas.lean

@@ -1878,24 +1878,6 @@ theorem sum_reverse [Zero α] [Add α] [Std.Associative (α := α) (· + ·)]
     simp_all [sum_append, Std.Commutative.comm (α := α) _ 0,
       Std.LawfulLeftIdentity.left_id, Std.Commutative.comm]
 
-@[simp, grind =]
-theorem prod_append [Mul α] [One α] [Std.LawfulLeftIdentity (α := α) (· * ·) 1]
-    [Std.Associative (α := α) (· * ·)] {l₁ l₂ : List α} : (l₁ ++ l₂).prod = l₁.prod * l₂.prod := by
-  induction l₁ generalizing l₂ <;> simp_all [Std.Associative.assoc, Std.LawfulLeftIdentity.left_id]
-
-@[simp, grind =]
-theorem prod_singleton [Mul α] [One α] [Std.LawfulRightIdentity (· * ·) (1 : α)] {x : α} :
-    [x].prod = x := by
-  simp [List.prod_eq_foldr, Std.LawfulRightIdentity.right_id x]
-
-@[simp, grind =]
-theorem prod_reverse [One α] [Mul α] [Std.Associative (α := α) (· * ·)]
-    [Std.Commutative (α := α) (· * ·)]
-    [Std.LawfulLeftIdentity (α := α) (· * ·) 1] (xs : List α) : xs.reverse.prod = xs.prod := by
-  induction xs <;>
-    simp_all [prod_append, Std.Commutative.comm (α := α) _ 1,
-      Std.LawfulLeftIdentity.left_id, Std.Commutative.comm]
-
 /-! ### concat
 
 Note that `concat_eq_append` is a `@[simp]` lemma, so `concat` should usually not appear in goals.
@@ -2802,11 +2784,6 @@ theorem sum_eq_foldl [Zero α] [Add α] [Std.Associative (α := α) (· + ·)]
     xs.sum = xs.foldl (init := 0) (· + ·) := by
   simp [sum_eq_foldr, foldl_eq_apply_foldr, Std.LawfulLeftIdentity.left_id]
 
-theorem prod_eq_foldl [One α] [Mul α] [Std.Associative (α := α) (· * ·)]
-    [Std.LawfulIdentity (· * ·) (1 : α)] {xs : List α} :
-    xs.prod = xs.foldl (init := 1) (· * ·) := by
-  simp [prod_eq_foldr, foldl_eq_apply_foldr, Std.LawfulLeftIdentity.left_id]
-
 -- The argument `f : α₁ → α₂` is intentionally explicit, as it is sometimes not found by unification.
 theorem foldl_hom (f : α₁ → α₂) {g₁ : α₁ → β → α₁} {g₂ : α₂ → β → α₂} {l : List β} {init : α₁}
     (H : ∀ x y, g₂ (f x) y = f (g₁ x y)) : l.foldl g₂ (f init) = f (l.foldl g₁ init) := by

src/Init/Data/List/MinMax.lean

@@ -37,7 +37,7 @@ open Nat
 @[simp, grind =] theorem min?_nil [Min α] : ([] : List α).min? = none := rfl
 
 @[simp, grind =]
-theorem min?_singleton [Min α] {x : α} : [x].min? = some x :=
+public theorem min?_singleton [Min α] {x : α} : [x].min? = some x :=
   (rfl)
 
 -- We don't put `@[simp]` on `min?_cons'`,
@@ -52,7 +52,7 @@ theorem min?_cons' [Min α] {xs : List α} : (x :: xs).min? = some (foldl min x
   cases xs <;> simp [min?]
 
 @[simp, grind =]
-theorem isSome_min?_iff [Min α] {xs : List α} : xs.min?.isSome ↔ xs ≠ [] := by
+public theorem isSome_min?_iff [Min α] {xs : List α} : xs.min?.isSome ↔ xs ≠ [] := by
   cases xs <;> simp [min?]
 
 @[grind .]
@@ -247,7 +247,7 @@ theorem foldl_min_eq_min [Min α] [Std.IdempotentOp (min : α → α → α)] [S
 @[simp, grind =] theorem max?_nil [Max α] : ([] : List α).max? = none := rfl
 
 @[simp, grind =]
-theorem max?_singleton [Max α] {x : α} : [x].max? = some x :=
+public theorem max?_singleton [Max α] {x : α} : [x].max? = some x :=
   (rfl)
 
 -- We don't put `@[simp]` on `max?_cons'`,
@@ -262,7 +262,7 @@ theorem max?_cons' [Max α] {xs : List α} : (x :: xs).max? = some (foldl max x
   cases xs <;> simp [max?]
 
 @[simp, grind =]
-theorem isSome_max?_iff [Max α] {xs : List α} : xs.max?.isSome ↔ xs ≠ [] := by
+public theorem isSome_max?_iff [Max α] {xs : List α} : xs.max?.isSome ↔ xs ≠ [] := by
   cases xs <;> simp [max?]
 
 @[grind .]

src/Init/Data/List/Nat.lean

@@ -13,7 +13,6 @@ public import Init.Data.List.Nat.Sublist
 public import Init.Data.List.Nat.TakeDrop
 public import Init.Data.List.Nat.Count
 public import Init.Data.List.Nat.Sum
-public import Init.Data.List.Nat.Prod
 public import Init.Data.List.Nat.Erase
 public import Init.Data.List.Nat.Find
 public import Init.Data.List.Nat.BEq

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

@@ -1,50 +0,0 @@
-/-
-Copyright (c) 2026 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.List.Lemmas
-public import Init.BinderPredicates
-public import Init.NotationExtra
-import Init.Data.Nat.Lemmas
-
-public section
-
-set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
-set_option linter.indexVariables true -- Enforce naming conventions for index variables.
-
-namespace List
-
-protected theorem prod_eq_zero_iff_exists_zero_nat {l : List Nat} : l.prod = 0 ↔ ∃ x ∈ l, x = 0 := by
-  induction l with
-  | nil => simp
-  | cons x xs ih =>
-    simp [Nat.mul_eq_zero, ih, eq_comm (a := (0 : Nat))]
-
-protected theorem prod_pos_iff_forall_pos_nat {l : List Nat} : 0 < l.prod ↔ ∀ x ∈ l, 0 < x := by
-  induction l with
-  | nil => simp
-  | cons x xs ih =>
-    simp only [prod_cons, mem_cons, forall_eq_or_imp, ← ih]
-    constructor
-    · intro h
-      exact ⟨Nat.pos_of_mul_pos_right h, Nat.pos_of_mul_pos_left h⟩
-    · exact fun ⟨hx, hxs⟩ => Nat.mul_pos hx hxs
-
-@[simp]
-theorem prod_replicate_nat {n : Nat} {a : Nat} : (replicate n a).prod = a ^ n := by
-  induction n <;> simp_all [replicate_succ, Nat.pow_succ, Nat.mul_comm]
-
-theorem prod_append_nat {l₁ l₂ : List Nat} : (l₁ ++ l₂).prod = l₁.prod * l₂.prod := by
-  simp [prod_append]
-
-theorem prod_reverse_nat (xs : List Nat) : xs.reverse.prod = xs.prod := by
-  simp [prod_reverse]
-
-theorem prod_eq_foldl_nat {xs : List Nat} : xs.prod = xs.foldl (init := 1) (· * ·) := by
-  simp only [foldl_eq_foldr_reverse, Nat.mul_comm, ← prod_eq_foldr, prod_reverse_nat]
-
-end List

src/Init/Data/List/Perm.lean

@@ -606,13 +606,6 @@ theorem sum_nat {l₁ l₂ : List Nat} (h : l₁ ~ l₂) : l₁.sum = l₂.sum :
   | swap => simpa [List.sum_cons] using Nat.add_left_comm ..
   | trans _ _ ih₁ ih₂ => simp [ih₁, ih₂]
 
-theorem prod_nat {l₁ l₂ : List Nat} (h : l₁ ~ l₂) : l₁.prod = l₂.prod := by
-  induction h with
-  | nil => simp
-  | cons _ _ ih => simp [ih]
-  | swap => simpa [List.prod_cons] using Nat.mul_left_comm ..
-  | trans _ _ ih₁ ih₂ => simp [ih₁, ih₂]
-
 theorem all_eq {l₁ l₂ : List α} {f : α → Bool} (hp : l₁.Perm l₂) : l₁.all f = l₂.all f := by
   rw [Bool.eq_iff_iff]; simp [hp.mem_iff]
 
@@ -622,9 +615,6 @@ theorem any_eq {l₁ l₂ : List α} {f : α → Bool} (hp : l₁.Perm l₂) : l
 grind_pattern Perm.sum_nat => l₁ ~ l₂, l₁.sum
 grind_pattern Perm.sum_nat => l₁ ~ l₂, l₂.sum
 
-grind_pattern Perm.prod_nat => l₁ ~ l₂, l₁.prod
-grind_pattern Perm.prod_nat => l₁ ~ l₂, l₂.prod
-
 end Perm
 
 end List

src/Init/Data/List/ToArray.lean

@@ -213,9 +213,6 @@ theorem forM_toArray [Monad m] (l : List α) (f : α → m PUnit) :
 @[simp, grind =] theorem sum_toArray [Add α] [Zero α] (l : List α) : l.toArray.sum = l.sum := by
   simp [Array.sum, List.sum]
 
-@[simp, grind =] theorem prod_toArray [Mul α] [One α] (l : List α) : l.toArray.prod = l.prod := by
-  simp [Array.prod, List.prod]
-
 @[simp, grind =] theorem append_toArray (l₁ l₂ : List α) :
     l₁.toArray ++ l₂.toArray = (l₁ ++ l₂).toArray := by
   apply ext'

src/Init/Data/Nat/Compare.lean

@@ -70,7 +70,7 @@ protected theorem isGE_compare {a b : Nat} :
   rw [← Nat.compare_swap, Ordering.isGE_swap]
   exact Nat.isLE_compare
 
-instance : Std.LawfulOrderOrd Nat where
+public instance : Std.LawfulOrderOrd Nat where
   isLE_compare _ _ := Nat.isLE_compare
   isGE_compare _ _ := Nat.isGE_compare
 

src/Init/Data/Nat/Gcd.lean

@@ -60,7 +60,7 @@ theorem gcd_def (x y : Nat) : gcd x y = if x = 0 then y else gcd (y % x) x := by
   cases n with
   | zero => simp
   | succ n =>
-    -- `simp [gcd_succ]` produces an invalid term unless `gcd_succ` is proved with `(rfl)` instead
+    -- `simp [gcd_succ]` produces an invalid term unless `gcd_succ` is proved with `id rfl` instead
     rw [gcd_succ]
     exact gcd_zero_left _
 instance : Std.LawfulIdentity gcd 0 where

src/Init/Data/Option/Attach.lean

@@ -444,7 +444,7 @@ instance : MonadAttach Option where
   CanReturn x a := x = some a
   attach x := x.attach
 
-instance : LawfulMonadAttach Option where
+public instance : LawfulMonadAttach Option where
   map_attach {α} x := by simp [MonadAttach.attach]
   canReturn_map_imp {α P x a} := by
     cases x
@@ -455,7 +455,7 @@ end Option
 
 namespace OptionT
 
-instance [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] :
+public instance [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] :
     WeaklyLawfulMonadAttach (OptionT m) where
   map_attach {α} x := by
     apply OptionT.ext
@@ -466,7 +466,7 @@ instance [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] :
     | ⟨some a, _⟩ => simp [OptionT.pure, OptionT.mk]
     | ⟨none, _⟩ => simp
 
-instance [Monad m] [MonadAttach m] [LawfulMonad m] [LawfulMonadAttach m] :
+public instance [Monad m] [MonadAttach m] [LawfulMonad m] [LawfulMonadAttach m] :
     LawfulMonadAttach (OptionT m) where
   canReturn_map_imp {α P x a} h := by
     simp only [MonadAttach.CanReturn, OptionT.run_map] at h

src/Init/Data/Ord/String.lean

@@ -9,7 +9,7 @@ prelude
 public import Init.Data.Order.Ord
 public import Init.Data.String.Basic
 import Init.Data.Char.Lemmas
-import Init.Data.String.Lemmas.StringOrder
+import Init.Data.String.Lemmas
 
 public section
 

src/Init/Data/Order/Lemmas.lean

@@ -243,10 +243,6 @@ public theorem lt_iff_le_and_ne [LE α] [LT α] [LawfulOrderLT α] [IsPartialOrd
     a < b ↔ a ≤ b ∧ a ≠ b := by
   simpa [le_iff_lt_or_eq, or_and_right] using Std.ne_of_lt
 
-public theorem lt_trichotomy [LT α] [Std.Trichotomous (α := α) (· < ·)] (a b : α) :
-    a < b ∨ a = b ∨ b < a :=
-  Trichotomous.rel_or_eq_or_rel_swap
-
 end LT
 end Std
 

src/Init/Data/Order/LemmasExtra.lean

@@ -152,7 +152,7 @@ public theorem max_eq_if_isGE_compare {α : Type u} [Ord α] [LE α] {_ : Max α
     {a b : α} : max a b = if (compare a b).isGE then a else b := by
   open Classical in simp [max_eq_if, isGE_compare]
 
-theorem min_le_min [LE α] [Min α] [Std.LawfulOrderLeftLeaningMin α] [IsLinearOrder α] (a b : α) : min a b ≤ min b a := by
+private theorem min_le_min [LE α] [Min α] [Std.LawfulOrderLeftLeaningMin α] [IsLinearOrder α] (a b : α) : min a b ≤ min b a := by
   apply (LawfulOrderInf.le_min_iff (min a b) b a).2
   rw [And.comm]
   by_cases h : a ≤ b

src/Init/Data/Range/Polymorphic/NatLemmas.lean

@@ -1718,7 +1718,7 @@ theorem toArray_roc_append_toArray_roc {l m n : Nat} (h : l ≤ m) (h' : m ≤ n
 @[simp]
 theorem getElem_toArray_roc {m n i : Nat} (_h : i < (m<...=n).toArray.size) :
     (m<...=n).toArray[i]'_h = m + 1 + i := by
-  simp [toArray_roc_eq_toArray_rco]
+simp [toArray_roc_eq_toArray_rco]
 
 theorem getElem?_toArray_roc {m n i : Nat} :
     (m<...=n).toArray[i]? = if i < n - m then some (m + 1 + i) else none := by

src/Init/Data/Range/Polymorphic/SInt.lean

@@ -248,11 +248,11 @@ instance : HasModel Int8 (BitVec 8) where
   le_iff_encode_le := by simp [LE.le, Int8.le]
   lt_iff_encode_lt := by simp [LT.lt, Int8.lt]
 
-theorem succ?_eq_minValueSealed {x : Int8} :
+private theorem succ?_eq_minValueSealed {x : Int8} :
     UpwardEnumerable.succ? x = if x + 1 = minValueSealed then none else some (x + 1) :=
   (rfl)
 
-theorem succMany?_eq_maxValueSealed {i : Int8} :
+private theorem succMany?_eq_maxValueSealed {i : Int8} :
     UpwardEnumerable.succMany? n i =
       have := i.minValue_le_toInt
       if h : i.toInt + n ≤ maxValueSealed.toInt then some (.ofIntLE _ (by omega) (maxValueSealed_def ▸ h)) else none :=
@@ -605,12 +605,12 @@ theorem minValueSealed_def : minValueSealed = ISize.minValue := (rfl)
 theorem maxValueSealed_def : maxValueSealed = ISize.maxValue := (rfl)
 seal minValueSealed maxValueSealed
 
-theorem toBitVec_minValueSealed_eq_intMinSealed :
+private theorem toBitVec_minValueSealed_eq_intMinSealed :
     minValueSealed.toBitVec = BitVec.Signed.intMinSealed System.Platform.numBits := by
   rw [minValueSealed_def, BitVec.Signed.intMinSealed_def, toBitVec_minValue]
   have := System.Platform.numBits_eq; generalize System.Platform.numBits = a at this ⊢
   rcases this with rfl | rfl <;> rfl
-theorem toBitVec_maxValueSealed_eq_intMaxSealed :
+private theorem toBitVec_maxValueSealed_eq_intMaxSealed :
     maxValueSealed.toBitVec = BitVec.Signed.intMaxSealed System.Platform.numBits := by
   rw [maxValueSealed_def, BitVec.Signed.intMaxSealed_def, toBitVec_maxValue]
   have := System.Platform.numBits_eq; generalize System.Platform.numBits = a at this ⊢

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

@@ -233,7 +233,7 @@ public theorem Subarray.toList_eq {xs : Subarray α} :
   simp [this, ListSlice.toList_eq, lslice]
 
 -- TODO: The current `List.extract_eq_drop_take` should be called `List.extract_eq_take_drop`
-theorem Std.Internal.List.extract_eq_drop_take' {l : List α} {start stop : Nat} :
+private theorem Std.Internal.List.extract_eq_drop_take' {l : List α} {start stop : Nat} :
     l.extract start stop = (l.take stop).drop start := by
   simp [List.take_drop]
   by_cases start ≤ stop

src/Init/Data/String/Basic.lean

@@ -1386,11 +1386,6 @@ theorem Slice.copy_eq_copy_sliceTo {s : Slice} {pos : s.Pos} :
   rw [Nat.max_eq_right]
   exact pos.offset_str_le_offset_endExclusive
 
-@[simp]
-theorem Slice.sliceTo_append_sliceFrom {s : Slice} {pos : s.Pos} :
-    (s.sliceTo pos).copy ++ (s.sliceFrom pos).copy = s.copy :=
-  copy_eq_copy_sliceTo.symm
-
 /-- Given a slice `s` and a position on `s.copy`, obtain the corresponding position on `s`. -/
 @[inline]
 def Pos.ofCopy {s : Slice} (pos : s.copy.Pos) : s.Pos where
@@ -1750,31 +1745,6 @@ theorem Slice.Pos.offset_cast {s t : Slice} {pos : s.Pos} {h : s.copy = t.copy}
 theorem Slice.Pos.cast_rfl {s : Slice} {pos : s.Pos} : pos.cast rfl = pos :=
   Slice.Pos.ext (by simp)
 
-@[simp]
-theorem Slice.Pos.cast_cast {s t u : Slice} {hst : s.copy = t.copy} {htu : t.copy = u.copy}
-    {pos : s.Pos} : (pos.cast hst).cast htu = pos.cast (hst.trans htu) :=
-  Slice.Pos.ext (by simp)
-
-@[simp]
-theorem Slice.Pos.cast_inj {s t : Slice} {hst : s.copy = t.copy} {p q : s.Pos} : p.cast hst = q.cast hst ↔ p = q := by
-  simp [Slice.Pos.ext_iff]
-
-@[simp]
-theorem Slice.Pos.cast_startPos {s t : Slice} {hst : s.copy = t.copy} : s.startPos.cast hst = t.startPos :=
-  Slice.Pos.ext (by simp)
-
-@[simp]
-theorem Slice.Pos.cast_eq_startPos {s t : Slice} {p : s.Pos} {hst : s.copy = t.copy} : p.cast hst = t.startPos ↔ p = s.startPos := by
-  rw [← cast_startPos (hst := hst), Pos.cast_inj]
-
-@[simp]
-theorem Slice.Pos.cast_endPos {s t : Slice} {hst : s.copy = t.copy} : s.endPos.cast hst = t.endPos :=
-  Slice.Pos.ext (by simp [← rawEndPos_copy, hst])
-
-@[simp]
-theorem Slice.Pos.cast_eq_endPos {s t : Slice} {p : s.Pos} {hst : s.copy = t.copy} : p.cast hst = t.endPos ↔ p = s.endPos := by
-  rw [← cast_endPos (hst := hst), Pos.cast_inj]
-
 @[simp]
 theorem Slice.Pos.cast_le_cast_iff {s t : Slice} {pos pos' : s.Pos} {h : s.copy = t.copy} :
     pos.cast h ≤ pos'.cast h ↔ pos ≤ pos' := by
@@ -1785,22 +1755,6 @@ theorem Slice.Pos.cast_lt_cast_iff {s t : Slice} {pos pos' : s.Pos} {h : s.copy
     pos.cast h < pos'.cast h ↔ pos < pos' := by
   simp [Slice.Pos.lt_iff]
 
-theorem Slice.Pos.cast_le_iff {s t : Slice} {pos : s.Pos} {pos' : t.Pos} {h : s.copy = t.copy} :
-    pos.cast h ≤ pos' ↔ pos ≤ pos'.cast h.symm := by
-  simp [Slice.Pos.le_iff]
-
-theorem Slice.Pos.le_cast_iff {s t : Slice} {pos : t.Pos} {pos' : s.Pos} {h : s.copy = t.copy} :
-    pos ≤ pos'.cast h ↔ pos.cast h.symm ≤ pos' := by
-  simp [Slice.Pos.le_iff]
-
-theorem Slice.Pos.cast_lt_iff {s t : Slice} {pos : s.Pos} {pos' : t.Pos} {h : s.copy = t.copy} :
-    pos.cast h < pos' ↔ pos < pos'.cast h.symm := by
-  simp [Slice.Pos.lt_iff]
-
-theorem Slice.Pos.lt_cast_iff {s t : Slice} {pos : t.Pos} {pos' : s.Pos} {h : s.copy = t.copy} :
-    pos < pos'.cast h ↔ pos.cast h.symm < pos' := by
-  simp [Slice.Pos.lt_iff]
-
 /-- Constructs a valid position on `t` from a valid position on `s` and a proof that `s = t`. -/
 @[inline]
 def Pos.cast {s t : String} (pos : s.Pos) (h : s = t) : t.Pos where
@@ -1815,31 +1769,6 @@ theorem Pos.offset_cast {s t : String} {pos : s.Pos} {h : s = t} :
 theorem Pos.cast_rfl {s : String} {pos : s.Pos} : pos.cast rfl = pos :=
   Pos.ext (by simp)
 
-@[simp]
-theorem Pos.cast_cast {s t u : String} {hst : s = t} {htu : t = u}
-    {pos : s.Pos} : (pos.cast hst).cast htu = pos.cast (hst.trans htu) :=
-  Pos.ext (by simp)
-
-@[simp]
-theorem Pos.cast_inj {s t : String} {hst : s = t} {p q : s.Pos} : p.cast hst = q.cast hst ↔ p = q := by
-  simp [Pos.ext_iff]
-
-@[simp]
-theorem Pos.cast_startPos {s t : String} {hst : s = t} : s.startPos.cast hst = t.startPos := by
-  subst hst; simp
-
-@[simp]
-theorem Pos.cast_eq_startPos {s t : String} {hst : s = t} {p : s.Pos} : p.cast hst = t.startPos ↔ p = s.startPos := by
-  rw [← Pos.cast_startPos (hst := hst), Pos.cast_inj]
-
-@[simp]
-theorem Pos.cast_endPos {s t : String} {hst : s = t} : s.endPos.cast hst = t.endPos := by
-  subst hst; simp
-
-@[simp]
-theorem Pos.cast_eq_endPos {s t : String} {hst : s = t} {p : s.Pos} : p.cast hst = t.endPos ↔ p = s.endPos := by
-  rw [← Pos.cast_endPos (hst := hst), Pos.cast_inj]
-
 @[simp]
 theorem Pos.cast_le_cast_iff {s t : String} {pos pos' : s.Pos} {h : s = t} :
     pos.cast h ≤ pos'.cast h ↔ pos ≤ pos' := by
@@ -1850,22 +1779,6 @@ theorem Pos.cast_lt_cast_iff {s t : String} {pos pos' : s.Pos} {h : s = t} :
     pos.cast h < pos'.cast h ↔ pos < pos' := by
   cases h; simp
 
-theorem Pos.cast_le_iff {s t : String} {pos : s.Pos} {pos' : t.Pos} {h : s = t} :
-    pos.cast h ≤ pos' ↔ pos ≤ pos'.cast h.symm := by
-  simp [Pos.le_iff]
-
-theorem Pos.le_cast_iff {s t : String} {pos : t.Pos} {pos' : s.Pos} {h : s = t} :
-    pos ≤ pos'.cast h ↔ pos.cast h.symm ≤ pos' := by
-  simp [Pos.le_iff]
-
-theorem Pos.cast_lt_iff {s t : String} {pos : s.Pos} {pos' : t.Pos} {h : s = t} :
-    pos.cast h < pos' ↔ pos < pos'.cast h.symm := by
-  simp [Pos.lt_iff]
-
-theorem Pos.lt_cast_iff {s t : String} {pos : t.Pos} {pos' : s.Pos} {h : s = t} :
-    pos < pos'.cast h ↔ pos.cast h.symm < pos' := by
-  simp [Pos.lt_iff]
-
 theorem Pos.copy_toSlice_eq_cast {s : String} (p : s.Pos) :
     p.toSlice.copy = p.cast copy_toSlice.symm :=
   Pos.ext (by simp)
@@ -2141,10 +2054,6 @@ theorem Pos.le_ofToSlice_iff {s : String} {p : s.Pos} {q : s.toSlice.Pos} :
 theorem Pos.toSlice_lt_toSlice_iff {s : String} {p q : s.Pos} :
     p.toSlice < q.toSlice ↔ p < q := Iff.rfl
 
-@[simp]
-theorem Pos.toSlice_le_toSlice_iff {s : String} {p q : s.Pos} :
-    p.toSlice ≤ q.toSlice ↔ p ≤ q := Iff.rfl
-
 theorem Pos.next_le_of_lt {s : String} {p q : s.Pos} {h} : p < q → p.next h ≤ q := by
   rw [next, Pos.ofToSlice_le_iff, ← Pos.toSlice_lt_toSlice_iff]
   exact Slice.Pos.next_le_of_lt

src/Init/Data/String/Decode.lean

@@ -94,7 +94,7 @@ public def String.utf8EncodeCharFast (c : Char) : List UInt8 :=
      (v >>>  6).toUInt8 &&& 0x3f ||| 0x80,
               v.toUInt8 &&& 0x3f ||| 0x80]
 
-theorem Nat.add_two_pow_eq_or_of_lt {b : Nat} (i : Nat) (b_lt : b < 2 ^ i) (a : Nat) :
+private theorem Nat.add_two_pow_eq_or_of_lt {b : Nat} (i : Nat) (b_lt : b < 2 ^ i) (a : Nat) :
     b + 2 ^ i * a = b ||| 2 ^ i * a := by
   rw [Nat.add_comm, Nat.or_comm, Nat.two_pow_add_eq_or_of_lt b_lt]
 
@@ -363,7 +363,7 @@ theorem toBitVec_eq_of_parseFirstByte_eq_threeMore {b : UInt8} (h : parseFirstBy
 public def isInvalidContinuationByte (b : UInt8) : Bool :=
   b &&& 0xc0 != 0x80
 
-theorem isInvalidContinuationByte_eq_false_iff {b : UInt8} :
+theorem isInvalidContinutationByte_eq_false_iff {b : UInt8} :
     isInvalidContinuationByte b = false ↔ b &&& 0xc0 = 0x80 := by
   simp [isInvalidContinuationByte]
 

src/Init/Data/String/Iter/Intercalate.lean

@@ -17,7 +17,6 @@ namespace Std
 /--
 Appends all the elements in the iterator, in order.
 -/
-@[inline]
 public def Iter.joinString {α β : Type} [Iterator α Id β] [ToString β]
     (it : Std.Iter (α := α) β) : String :=
   (it.map toString).fold (init := "") (· ++ ·)

src/Init/Data/String/Lemmas.lean

@@ -20,4 +20,49 @@ public import Init.Data.String.Lemmas.Intercalate
 public import Init.Data.String.Lemmas.Iter
 public import Init.Data.String.Lemmas.Hashable
 public import Init.Data.String.Lemmas.TakeDrop
-public import Init.Data.String.Lemmas.StringOrder
+import Init.Data.Order.Lemmas
+public import Init.Data.String.Basic
+import Init.Data.Char.Lemmas
+import Init.Data.Char.Order
+import Init.Data.List.Lex
+
+public section
+
+open Std
+
+namespace String
+
+@[deprecated toList_inj (since := "2025-10-30")]
+protected theorem data_eq_of_eq {a b : String} (h : a = b) : a.toList = b.toList :=
+  h ▸ rfl
+@[deprecated toList_inj (since := "2025-10-30")]
+protected theorem ne_of_data_ne {a b : String} (h : a.toList ≠ b.toList) : a ≠ b := by
+  simpa [← toList_inj]
+
+@[simp] protected theorem not_le {a b : String} : ¬ a ≤ b ↔ b < a := Decidable.not_not
+@[simp] protected theorem not_lt {a b : String} : ¬ a < b ↔ b ≤ a := Iff.rfl
+@[simp] protected theorem le_refl (a : String) : a ≤ a := List.le_refl _
+@[simp] protected theorem lt_irrefl (a : String) : ¬ a < a := List.lt_irrefl _
+
+attribute [local instance] Char.notLTTrans Char.ltTrichotomous Char.ltAsymm
+
+protected theorem le_trans {a b c : String} : a ≤ b → b ≤ c → a ≤ c := List.le_trans
+protected theorem lt_trans {a b c : String} : a < b → b < c → a < c := List.lt_trans
+protected theorem le_total (a b : String) : a ≤ b ∨ b ≤ a := List.le_total _ _
+protected theorem le_antisymm {a b : String} : a ≤ b → b ≤ a → a = b := fun h₁ h₂ => String.ext (List.le_antisymm (as := a.toList) (bs := b.toList) h₁ h₂)
+protected theorem lt_asymm {a b : String} (h : a < b) : ¬ b < a := List.lt_asymm h
+protected theorem ne_of_lt {a b : String} (h : a < b) : a ≠ b := by
+  have := String.lt_irrefl a
+  intro h; subst h; contradiction
+
+instance instIsLinearOrder : IsLinearOrder String := by
+  apply IsLinearOrder.of_le
+  case le_antisymm => constructor; apply String.le_antisymm
+  case le_trans => constructor; apply String.le_trans
+  case le_total => constructor; apply String.le_total
+
+instance : LawfulOrderLT String where
+  lt_iff a b := by
+    simp [← String.not_le, Decidable.imp_iff_not_or, Std.Total.total]
+
+end String

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

@@ -22,10 +22,6 @@ public section
 
 namespace String
 
-@[simp]
-theorem singleton_inj {c d : Char} : singleton c = singleton d ↔ c = d := by
-  simp [← toList_inj]
-
 @[simp]
 theorem singleton_append_inj : singleton c ++ s = singleton d ++ t ↔ c = d ∧ s = t := by
   simp [← toList_inj]
@@ -195,74 +191,18 @@ theorem sliceTo_slice {s : String} {p₁ p₂ h p} :
 theorem Slice.sliceFrom_startPos {s : Slice} : s.sliceFrom s.startPos = s := by
   ext <;> simp
 
-@[simp]
-theorem Slice.sliceFrom_eq_self_iff {s : Slice} {p : s.Pos} : s.sliceFrom p = s ↔ p = s.startPos := by
-  refine ⟨?_, by rintro rfl; simp⟩
-  rcases s with ⟨str, startInclusive, endExclusive, h⟩
-  simp [sliceFrom, Slice.startPos, String.Pos.ext_iff, Pos.Raw.ext_iff, Slice.Pos.ext_iff]
-
 @[simp]
 theorem Slice.sliceTo_endPos {s : Slice} : s.sliceTo s.endPos = s := by
   ext <;> simp
 
-@[simp]
-theorem Slice.sliceTo_eq_self_iff {s : Slice} {p : s.Pos} : s.sliceTo p = s ↔ p = s.endPos := by
-  refine ⟨?_, by rintro rfl; simp⟩
-  rcases s with ⟨str, startInclusive, endExclusive, h⟩
-  simp [sliceTo, Slice.endPos, String.Pos.ext_iff, Pos.Raw.ext_iff, Slice.Pos.ext_iff,
-    utf8ByteSize_eq]
-  omega
-
-@[simp]
-theorem Slice.slice_startPos {s : Slice} {p : s.Pos} :
-    s.slice s.startPos p (Pos.startPos_le _) = s.sliceTo p := by
-  ext <;> simp
-
-@[simp]
-theorem Slice.slice_eq_self_iff {s : Slice} {p₁ p₂ : s.Pos} {h} :
-    s.slice p₁ p₂ h = s ↔ p₁ = s.startPos ∧ p₂ = s.endPos := by
-  refine ⟨?_, by rintro ⟨rfl, rfl⟩; simp⟩
-  rcases s with ⟨str, startInclusive, endExclusive, h⟩
-  simp [slice, Slice.endPos, String.Pos.ext_iff, Pos.Raw.ext_iff, Slice.Pos.ext_iff,
-    utf8ByteSize_eq]
-  omega
-
-@[simp]
-theorem Slice.slice_endPos {s : Slice} {p : s.Pos} :
-    s.slice p s.endPos (Pos.le_endPos _) = s.sliceFrom p := by
-  ext <;> simp
-
 @[simp]
 theorem sliceFrom_startPos {s : String} : s.sliceFrom s.startPos = s := by
   ext <;> simp
 
-@[simp]
-theorem sliceFrom_eq_toSlice_iff {s : String} {p : s.Pos} : s.sliceFrom p = s.toSlice ↔ p = s.startPos := by
-  simp [← sliceFrom_toSlice]
-
 @[simp]
 theorem sliceTo_endPos {s : String} : s.sliceTo s.endPos = s := by
   ext <;> simp
 
-@[simp]
-theorem sliceTo_eq_toSlice_iff {s : String} {p : s.Pos} : s.sliceTo p = s.toSlice ↔ p = s.endPos := by
-  simp [← sliceTo_toSlice]
-
-@[simp]
-theorem slice_startPos {s : String} {p : s.Pos} :
-    s.slice s.startPos p (Pos.startPos_le _) = s.sliceTo p := by
-  ext <;> simp
-
-@[simp]
-theorem slice_endPos {s : String} {p : s.Pos} :
-    s.slice p s.endPos (Pos.le_endPos _) = s.sliceFrom p := by
-  ext <;> simp
-
-@[simp]
-theorem slice_eq_toSlice_iff {s : String} {p₁ p₂ : s.Pos} {h} :
-    s.slice p₁ p₂ h = s.toSlice ↔ p₁ = s.startPos ∧ p₂ = s.endPos := by
-  simp [← slice_toSlice]
-
 end Iterate
 
 theorem Slice.copy_eq_copy_slice {s : Slice} {pos₁ pos₂ : s.Pos} {h} :
@@ -352,39 +292,4 @@ theorem nextn_endPos {s : String} : s.endPos.nextn n = s.endPos := by
 
 end Pos
 
-@[simp]
-theorem Slice.Pos.cast_toSlice_copy {s : Slice} {pos : s.Pos} :
-    pos.copy.toSlice.cast (by simp) = pos := by
-  ext; simp
-
-@[simp]
-theorem Slice.Pos.sliceFrom_eq_startPos {s : Slice} {p : s.Pos} :
-    (Pos.sliceFrom p p (Pos.le_refl _)) = Slice.startPos _ := by
-  simp [← Pos.ofSliceFrom_inj]
-
-@[simp]
-theorem Slice.Pos.sliceFrom_endPos {s : Slice} {p : s.Pos} :
-    (Pos.sliceFrom p s.endPos (Pos.le_endPos _)) = Slice.endPos _ := by
-  simp [← Pos.ofSliceFrom_inj]
-
-@[simp]
-theorem Slice.Pos.sliceTo_startPos {s : Slice} {p : s.Pos} :
-    (Pos.sliceTo p s.startPos (Pos.startPos_le _)) = Slice.startPos _ := by
-  simp [← Pos.ofSliceTo_inj]
-
-@[simp]
-theorem Slice.Pos.sliceTo_eq_endPos {s : Slice} {p : s.Pos} :
-    (Pos.sliceTo p p (Pos.le_refl _)) = Slice.endPos _ := by
-  simp [← Pos.ofSliceTo_inj]
-
-@[simp]
-theorem Slice.Pos.slice_eq_startPos {s : Slice} {p₀ p₁ : s.Pos} {h} :
-    (Pos.slice p₀ p₀ p₁ (Pos.le_refl _) h) = Slice.startPos _ := by
-  simp [← Pos.ofSlice_inj]
-
-@[simp]
-theorem Slice.Pos.slice_eq_endPos {s : Slice} {p₀ p₁ : s.Pos} {h} :
-    (Pos.slice p₁ p₀ p₁ h (Pos.le_refl _)) = Slice.endPos _ := by
-  simp [← Pos.ofSlice_inj]
-
 end String

src/Init/Data/String/Lemmas/Intercalate.lean

@@ -77,15 +77,6 @@ theorem join_cons : join (s :: l) = s ++ join l := by
 theorem toList_join {l : List String} : (String.join l).toList = l.flatMap String.toList := by
   induction l <;> simp_all
 
-@[simp]
-theorem join_append {l m : List String} : String.join (l ++ m) = String.join l ++ String.join m := by
-  simp [← toList_inj]
-
-@[simp]
-theorem length_join {l : List String} : (String.join l).length = (l.map String.length).sum := by
-  simp only [← length_toList, toList_join, List.length_flatMap]
-  simp
-
 namespace Slice
 
 @[simp]

src/Init/Data/String/Lemmas/Iterate.lean

@@ -31,7 +31,7 @@ namespace Slice
 /--
 A list of all positions starting at {name}`p`.
 
-This function is not meant to be used in actual programs. Actual programs should use
+This function is not meant to be used in actual progams. Actual programs should use
 {name}`Slice.positionsFrom` or {name}`Slice.positions`.
 -/
 protected def Model.positionsFrom {s : Slice} (p : s.Pos) : List { p : s.Pos // p ≠ s.endPos } :=
@@ -206,7 +206,7 @@ end Slice
 /--
 A list of all positions starting at {name}`p`.
 
-This function is not meant to be used in actual programs. Actual programs should use
+This function is not meant to be used in actual progams. Actual programs should use
 {name}`Slice.positionsFrom` or {name}`Slice.positions`.
 -/
 protected def Model.positionsFrom {s : String} (p : s.Pos) : List { p : s.Pos // p ≠ s.endPos } :=

src/Init/Data/String/Lemmas/Order.lean

@@ -368,41 +368,21 @@ theorem Slice.Pos.ofSliceTo_ne_endPos {s : Slice} {p₀ : s.Pos} {p : (s.sliceTo
   refine (lt_endPos_iff _).1 (Std.lt_of_lt_of_le ?_ (le_endPos p₀))
   simpa [← lt_endPos_iff, ← ofSliceTo_lt_ofSliceTo_iff] using h
 
-theorem Slice.Pos.ne_endPos_of_sliceTo_ne_endPos {s : Slice} {p p₀ : s.Pos} {h₀}
-    (h : Pos.sliceTo p₀ p h₀ ≠ Slice.endPos _) : p ≠ s.endPos := by
-  rw [← Pos.ofSliceTo_sliceTo (h := h₀)]
-  apply Pos.ofSliceTo_ne_endPos h
-
 theorem Slice.Pos.ofSliceFrom_ne_startPos {s : Slice} {p₀ : s.Pos} {p : (s.sliceFrom p₀).Pos}
     (h : p ≠ (s.sliceFrom p₀).startPos) : Pos.ofSliceFrom p ≠ s.startPos := by
   refine (startPos_lt_iff _).1 (Std.lt_of_le_of_lt (startPos_le p₀) ?_)
   simpa [← startPos_lt_iff, ← ofSliceFrom_lt_ofSliceFrom_iff] using h
 
-theorem Slice.Pos.ne_startPos_of_sliceFrom_ne_startPos {s : Slice} {p p₀ : s.Pos} {h₀}
-    (h : Pos.sliceFrom p₀ p h₀ ≠ Slice.startPos _) : p ≠ s.startPos := by
-  rw [← Pos.ofSliceFrom_sliceFrom (h := h₀)]
-  apply Pos.ofSliceFrom_ne_startPos h
-
 theorem Pos.ofSliceTo_ne_endPos {s : String} {p₀ : s.Pos} {p : (s.sliceTo p₀).Pos}
     (h : p ≠ (s.sliceTo p₀).endPos) : Pos.ofSliceTo p ≠ s.endPos := by
   refine (lt_endPos_iff _).1 (Std.lt_of_lt_of_le ?_ (le_endPos p₀))
   simpa [← Slice.Pos.lt_endPos_iff, ← ofSliceTo_lt_ofSliceTo_iff] using h
 
-theorem Pos.ne_endPos_of_sliceTo_ne_endPos {s : String} {p p₀ : s.Pos} {h₀}
-    (h : Pos.sliceTo p₀ p h₀ ≠ Slice.endPos _) : p ≠ s.endPos := by
-  rw [← Pos.ofSliceTo_sliceTo (h := h₀)]
-  apply Pos.ofSliceTo_ne_endPos h
-
 theorem Pos.ofSliceFrom_ne_startPos {s : String} {p₀ : s.Pos} {p : (s.sliceFrom p₀).Pos}
     (h : p ≠ (s.sliceFrom p₀).startPos) : Pos.ofSliceFrom p ≠ s.startPos := by
   refine (startPos_lt_iff _).1 (Std.lt_of_le_of_lt (startPos_le p₀) ?_)
   simpa [← Slice.Pos.startPos_lt_iff, ← ofSliceFrom_lt_ofSliceFrom_iff] using h
 
-theorem Pos.ne_startPos_of_sliceFrom_ne_startPos {s : String} {p p₀ : s.Pos} {h₀}
-    (h : Pos.sliceFrom p₀ p h₀ ≠ Slice.startPos _) : p ≠ s.startPos := by
-  rw [← Pos.ofSliceFrom_sliceFrom (h := h₀)]
-  apply Pos.ofSliceFrom_ne_startPos h
-
 theorem Slice.Pos.ofSliceTo_next {s : Slice} {p₀ : s.Pos} {p : (s.sliceTo p₀).Pos} {h} :
     Pos.ofSliceTo (p.next h) = (Pos.ofSliceTo p).next (ofSliceTo_ne_endPos h) := by
   rw [eq_comm, Pos.next_eq_iff]
@@ -534,41 +514,21 @@ theorem Slice.Pos.ofSlice_ne_endPos {s : Slice} {p₀ p₁ : s.Pos} {h} {p : (s.
   refine (lt_endPos_iff _).1 (Std.lt_of_lt_of_le ?_ (le_endPos p₁))
   simpa [← lt_endPos_iff, ← ofSlice_lt_ofSlice_iff] using h
 
-theorem Slice.Pos.ne_endPos_of_slice_ne_endPos {s : Slice} {p p₀ p₁ : s.Pos} {h₁ h₂}
-    (h : Pos.slice p p₀ p₁ h₁ h₂ ≠ Slice.endPos _) : p ≠ s.endPos := by
-  rw [← Pos.ofSlice_slice (h₁ := h₁) (h₂ := h₂)]
-  apply Pos.ofSlice_ne_endPos h
-
 theorem Slice.Pos.ofSlice_ne_startPos {s : Slice} {p₀ p₁ : s.Pos} {h} {p : (s.slice p₀ p₁ h).Pos}
     (h : p ≠ (s.slice p₀ p₁ h).startPos) : Pos.ofSlice p ≠ s.startPos := by
   refine (startPos_lt_iff _).1 (Std.lt_of_le_of_lt (startPos_le p₀) ?_)
   simpa [← startPos_lt_iff, ← ofSlice_lt_ofSlice_iff] using h
 
-theorem Slice.Pos.ne_startPos_of_slice_ne_startPos {s : Slice} {p p₀ p₁ : s.Pos} {h₁ h₂}
-    (h : Pos.slice p p₀ p₁ h₁ h₂ ≠ Slice.startPos _) : p ≠ s.startPos := by
-  rw [← Pos.ofSlice_slice (h₁ := h₁) (h₂ := h₂)]
-  apply Pos.ofSlice_ne_startPos h
-
 theorem Pos.ofSlice_ne_endPos {s : String} {p₀ p₁ : s.Pos} {h} {p : (s.slice p₀ p₁ h).Pos}
     (h : p ≠ (s.slice p₀ p₁ h).endPos) : Pos.ofSlice p ≠ s.endPos := by
   refine (lt_endPos_iff _).1 (Std.lt_of_lt_of_le ?_ (le_endPos p₁))
   simpa [← Slice.Pos.lt_endPos_iff, ← ofSlice_lt_ofSlice_iff] using h
 
-theorem Pos.ne_endPos_of_slice_ne_endPos {s : String} {p p₀ p₁ : s.Pos} {h₁ h₂}
-    (h : Pos.slice p p₀ p₁ h₁ h₂ ≠ Slice.endPos _) : p ≠ s.endPos := by
-  rw [← Pos.ofSlice_slice (h₁ := h₁) (h₂ := h₂)]
-  apply Pos.ofSlice_ne_endPos h
-
 theorem Pos.ofSlice_ne_startPos {s : String} {p₀ p₁ : s.Pos} {h} {p : (s.slice p₀ p₁ h).Pos}
     (h : p ≠ (s.slice p₀ p₁ h).startPos) : Pos.ofSlice p ≠ s.startPos := by
   refine (startPos_lt_iff _).1 (Std.lt_of_le_of_lt (startPos_le p₀) ?_)
   simpa [← Slice.Pos.startPos_lt_iff, ← ofSlice_lt_ofSlice_iff] using h
 
-theorem Pos.ne_startPos_of_slice_ne_startPos {s : String} {p p₀ p₁ : s.Pos} {h₁ h₂}
-    (h : Pos.slice p p₀ p₁ h₁ h₂ ≠ Slice.startPos _) : p ≠ s.startPos := by
-  rw [← Pos.ofSlice_slice (h₁ := h₁) (h₂ := h₂)]
-  apply Pos.ofSlice_ne_startPos h
-
 @[simp]
 theorem Slice.Pos.offset_le_rawEndPos {s : Slice} {p : s.Pos} :
     p.offset ≤ s.rawEndPos :=
@@ -621,37 +581,21 @@ theorem Slice.Pos.get_eq_get_ofSliceTo {s : Slice} {p₀ : s.Pos} {pos : (s.slic
     pos.get h = (ofSliceTo pos).get (ofSliceTo_ne_endPos h) := by
   simp [Slice.Pos.get]
 
-theorem Slice.Pos.get_sliceTo {s : Slice} {p₀ p : s.Pos} {h h'} :
-    (Pos.sliceTo p₀ p h).get h' = p.get (ne_endPos_of_sliceTo_ne_endPos h') := by
-  simp [get_eq_get_ofSliceTo]
-
 theorem Pos.get_eq_get_ofSliceTo {s : String} {p₀ : s.Pos}
     {pos : (s.sliceTo p₀).Pos} {h} :
     pos.get h = (ofSliceTo pos).get (ofSliceTo_ne_endPos h) := by
   simp [Pos.get, Slice.Pos.get]
 
-theorem Pos.get_sliceTo {s : String} {p₀ p : s.Pos} {h h'} :
-    (Pos.sliceTo p₀ p h).get h' = p.get (ne_endPos_of_sliceTo_ne_endPos h') := by
-  simp [get_eq_get_ofSliceTo]
-
 theorem Slice.Pos.get_eq_get_ofSlice {s : Slice} {p₀ p₁ : s.Pos} {h}
     {pos : (s.slice p₀ p₁ h).Pos} {h'} :
     pos.get h' = (ofSlice pos).get (ofSlice_ne_endPos h') := by
   simp [Slice.Pos.get, Nat.add_assoc]
 
-theorem Slice.Pos.get_slice {s : Slice} {p p₀ p₁ : s.Pos} {h₁ h₂ h} :
-    (Pos.slice p p₀ p₁ h₁ h₂).get h = p.get (ne_endPos_of_slice_ne_endPos h) := by
-  simp [get_eq_get_ofSlice]
-
 theorem Pos.get_eq_get_ofSlice {s : String} {p₀ p₁ : s.Pos} {h}
     {pos : (s.slice p₀ p₁ h).Pos} {h'} :
     pos.get h' = (ofSlice pos).get (ofSlice_ne_endPos h') := by
   simp [Pos.get, Slice.Pos.get]
 
-theorem Pos.get_slice {s : String} {p p₀ p₁ : s.Pos} {h₁ h₂ h} :
-    (Pos.slice p p₀ p₁ h₁ h₂).get h = p.get (ne_endPos_of_slice_ne_endPos h) := by
-  simp [get_eq_get_ofSlice]
-
 theorem Slice.Pos.ofSlice_next {s : Slice} {p₀ p₁ : s.Pos} {h}
     {p : (s.slice p₀ p₁ h).Pos} {h'} :
     Pos.ofSlice (p.next h') = (Pos.ofSlice p).next (ofSlice_ne_endPos h') := by

src/Init/Data/String/Lemmas/Pattern/Basic.lean

@@ -12,7 +12,7 @@ public import Init.Data.Iterators.Consumers.Collect
 import all Init.Data.String.Pattern.Basic
 import Init.Data.String.OrderInstances
 import Init.Data.String.Lemmas.IsEmpty
-public import Init.Data.String.Lemmas.Basic
+import Init.Data.String.Lemmas.Basic
 import Init.Data.String.Lemmas.Order
 import Init.Data.String.Termination
 import Init.Data.Order.Lemmas
@@ -40,7 +40,7 @@ framework.
 /--
 This data-carrying typeclass is used to give semantics to a pattern type that implements
 {name}`ForwardPattern` and/or {name}`ToForwardSearcher` by providing an abstract, not necessarily
-decidable {name}`PatternModel.Matches` predicate that implementations of {name}`ForwardPattern`
+decidable {name}`PatternModel.Matches` predicate that implementates of {name}`ForwardPattern`
 and {name}`ToForwardSearcher` can be validated against.
 
 Correctness results for generic functions relying on the pattern infrastructure, for example the
@@ -52,23 +52,19 @@ The corresponding compatibility typeclasses are
 {name (scope := "Init.Data.String.Lemmas.Pattern.Basic")}`String.Slice.Pattern.Model.LawfulForwardPatternModel`
 and
 {name (scope := "Init.Data.String.Lemmas.Pattern.Basic")}`String.Slice.Pattern.Model.LawfulToForwardSearcherModel`.
+
+We include the condition that the empty string is not a match. This is necessary for the theory to
+work out as there is just no reasonable notion of searching that works for the empty string that is
+still specific enough to yield reasonably strong correctness results for operations based on
+searching.
+
+This means that pattern types that allow searching for the empty string will have to special-case
+the empty string in their correctness statements.
 -/
 class PatternModel {ρ : Type} (pat : ρ) : Type where
   /-- The predicate that says which strings match the pattern. -/
   Matches : String → Prop
-
-/--
-Type class for the condition that the empty string is not a match. This is necessary for the theory to
-work out as there is just no reasonable notion of searching that works for the empty string that is
-still specific enough to yield reasonably strong correctness results for operations based on
-searching.
--/
-class StrictPatternModel {ρ : Type} (pat : ρ) [PatternModel pat] : Prop where
-  not_matches_empty : ¬ PatternModel.Matches pat ""
-
-theorem not_matches_empty {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat] :
-    ¬ PatternModel.Matches pat "" :=
-  StrictPatternModel.not_matches_empty
+  not_matches_empty : ¬ Matches ""
 
 /--
 Predicate stating that the region between the start of the slice {name}`s` and the position
@@ -78,10 +74,10 @@ Predicate stating that the region between the start of the slice {name}`s` and t
 structure IsMatch (pat : ρ) [PatternModel pat] {s : Slice} (endPos : s.Pos) : Prop where
   matches_copy : PatternModel.Matches pat (s.sliceTo endPos).copy
 
-theorem IsMatch.ne_startPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {pos : s.Pos}
+theorem IsMatch.ne_startPos {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos}
     (h : IsMatch pat pos) : pos ≠ s.startPos := by
   intro hc
-  apply not_matches_empty (pat := pat)
+  apply PatternModel.not_matches_empty (pat := pat)
   simpa [hc] using h.matches_copy
 
 theorem isMatch_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos} :
@@ -94,21 +90,6 @@ theorem isMatch_iff_exists_splits {pat : ρ} [PatternModel pat] {s : Slice} {pos
   refine ⟨fun h => ⟨_, _, pos.splits, h⟩, fun ⟨t₁, t₂, h₁, h₂⟩ => ?_⟩
   rwa [h₁.eq_left pos.splits] at h₂
 
-@[simp]
-theorem isMatch_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (h : s.copy = t.copy) {pos : s.Pos} :
-    IsMatch pat (pos.cast h) ↔ IsMatch pat pos := by
-  simp [isMatch_iff]
-
-@[simp]
-theorem isMatch_sliceTo_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos p : s.Pos} {h} :
-    IsMatch pat (Pos.sliceTo p pos h) ↔ IsMatch pat pos := by
-  simp [isMatch_iff]
-
-@[simp]
-theorem isMatch_ofSliceTo_iff {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos} {pos : (s.sliceTo p).Pos} :
-    IsMatch pat (Pos.ofSliceTo pos) ↔ IsMatch pat pos := by
-  rw [← isMatch_sliceTo_iff (p := p) (h := Pos.ofSliceTo_le), Pos.sliceTo_ofSliceTo]
-
 /--
 Predicate stating that the region between the position {name}`startPos` and the end of the slice
 {name}`s` matches the pattern {name}`pat`. Note that there might be a longer match.
@@ -116,10 +97,10 @@ Predicate stating that the region between the position {name}`startPos` and the
 structure IsRevMatch (pat : ρ) [PatternModel pat] {s : Slice} (startPos : s.Pos) : Prop where
   matches_copy : PatternModel.Matches pat (s.sliceFrom startPos).copy
 
-theorem IsRevMatch.ne_endPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {pos : s.Pos}
+theorem IsRevMatch.ne_endPos {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos}
     (h : IsRevMatch pat pos) : pos ≠ s.endPos := by
   intro hc
-  apply not_matches_empty (pat := pat)
+  apply PatternModel.not_matches_empty (pat := pat)
   simpa [hc] using h.matches_copy
 
 theorem isRevMatch_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos} :
@@ -132,21 +113,6 @@ theorem isRevMatch_iff_exists_splits {pat : ρ} [PatternModel pat] {s : Slice} {
   refine ⟨fun h => ⟨_, _, pos.splits, h⟩, fun ⟨t₁, t₂, h₁, h₂⟩ => ?_⟩
   rwa [h₁.eq_right pos.splits] at h₂
 
-@[simp]
-theorem isRevMatch_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (h : s.copy = t.copy) {pos : s.Pos} :
-    IsRevMatch pat (pos.cast h) ↔ IsRevMatch pat pos := by
-  simp [isRevMatch_iff]
-
-@[simp]
-theorem isRevMatch_sliceFrom_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos p : s.Pos} {h} :
-    IsRevMatch pat (Pos.sliceFrom p pos h) ↔ IsRevMatch pat pos := by
-  simp [isRevMatch_iff]
-
-@[simp]
-theorem isRevMatch_ofSliceFrom_iff {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos} {pos : (s.sliceFrom p).Pos} :
-    IsRevMatch pat (Pos.ofSliceFrom pos) ↔ IsRevMatch pat pos := by
-  rw [← isRevMatch_sliceFrom_iff (p := p) (h := Pos.le_ofSliceFrom), Pos.sliceFrom_ofSliceFrom]
-
 /--
 Predicate stating that the region between the start of the slice {name}`s` and the position
 {name}`pos` matches the pattern {name}`pat`, and that there is no longer match starting at the
@@ -159,19 +125,10 @@ structure IsLongestMatch (pat : ρ) [PatternModel pat] {s : Slice} (pos : s.Pos)
   isMatch : IsMatch pat pos
   not_isMatch : ∀ pos', pos < pos' → ¬ IsMatch pat pos'
 
-theorem isLongestMatch_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos} :
-    IsLongestMatch pat pos ↔ IsMatch pat pos ∧ ∀ pos', pos < pos' → ¬ IsMatch pat pos' :=
-  ⟨fun ⟨h, h'⟩ => ⟨h, h'⟩, fun ⟨h, h'⟩ => ⟨h, h'⟩⟩
-
-theorem IsLongestMatch.ne_startPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {pos : s.Pos}
+theorem IsLongestMatch.ne_startPos {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos}
     (h : IsLongestMatch pat pos) : pos ≠ s.startPos :=
   h.isMatch.ne_startPos
 
-@[simp]
-theorem not_isLongestMatch_startPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} :
-    ¬IsLongestMatch pat s.startPos :=
-  fun h => h.ne_startPos rfl
-
 theorem IsLongestMatch.eq {pat : ρ} [PatternModel pat] {s : Slice} {pos pos' : s.Pos}
     (h : IsLongestMatch pat pos) (h' : IsLongestMatch pat pos') : pos = pos' := by
   apply Std.le_antisymm
@@ -192,37 +149,9 @@ theorem IsLongestMatch.le_of_isMatch {pat : ρ} [PatternModel pat] {s : Slice} {
     (h : IsLongestMatch pat pos) (h' : IsMatch pat pos') : pos' ≤ pos :=
   Std.not_lt.1 (fun hlt => h.not_isMatch _ hlt h')
 
-@[simp]
-theorem isLongestMatch_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice}
-    (hst : s.copy = t.copy) {pos : s.Pos} :
-    IsLongestMatch pat (pos.cast hst) ↔ IsLongestMatch pat pos := by
-  simp only [isLongestMatch_iff, isMatch_cast_iff, and_congr_right_iff]
-  refine fun _ => ⟨fun h p hp => ?_, fun h p hp => ?_⟩
-  · rw [← isMatch_cast_iff hst]
-    exact h _ (by simpa)
-  · have : p = (p.cast hst.symm).cast hst := by simp
-    rw [this, isMatch_cast_iff hst]
-    exact h _ (by rwa [this, Pos.cast_lt_cast_iff] at hp)
-
-theorem IsLongestMatch.of_eq {pat : ρ} [PatternModel pat] {s t : Slice} {pos : s.Pos} {pos' : t.Pos}
-    (h : IsLongestMatch pat pos) (h₁ : s.copy = t.copy) (h₂ : pos.cast h₁ = pos') :
-    IsLongestMatch pat pos' := by
-  subst h₂; simpa
-
-theorem IsLongestMatch.sliceTo {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos}
-    (h : IsLongestMatch pat pos) (p : s.Pos) (hp : pos ≤ p) : IsLongestMatch pat (Pos.sliceTo p pos hp) := by
-  simp [isLongestMatch_iff] at ⊢ h
-  refine ⟨h.1, fun p hp => ?_⟩
-  rw [← isMatch_ofSliceTo_iff]
-  exact h.2 _ (by simpa [Pos.sliceTo_lt_iff] using hp)
-
-theorem isLongestMatch_of_ofSliceTo {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos} {pos : (s.sliceTo p).Pos}
-    (h : IsLongestMatch pat (Pos.ofSliceTo pos)) : IsLongestMatch pat pos := by
-  simpa using h.sliceTo p
-
 /--
 Predicate stating that the region between the start of the slice {name}`s` and the position
-{name}`pos` matches the pattern {name}`pat`, and that there is no longer match starting at the
+{name}`pos` matches the patten {name}`pat`, and that there is no longer match starting at the
 beginning of the slice. This is what a correct matcher should match.
 
 In some cases, being a match and being a longest match will coincide, see
@@ -232,19 +161,10 @@ structure IsLongestRevMatch (pat : ρ) [PatternModel pat] {s : Slice} (pos : s.P
   isRevMatch : IsRevMatch pat pos
   not_isRevMatch : ∀ pos', pos' < pos → ¬ IsRevMatch pat pos'
 
-theorem isLongestRevMatch_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos} :
-    IsLongestRevMatch pat pos ↔ IsRevMatch pat pos ∧ ∀ pos', pos' < pos → ¬ IsRevMatch pat pos' :=
-  ⟨fun ⟨h, h'⟩ => ⟨h, h'⟩, fun ⟨h, h'⟩ => ⟨h, h'⟩⟩
-
-theorem IsLongestRevMatch.ne_endPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {pos : s.Pos}
+theorem IsLongestRevMatch.ne_endPos {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos}
     (h : IsLongestRevMatch pat pos) : pos ≠ s.endPos :=
   h.isRevMatch.ne_endPos
 
-@[simp]
-theorem not_isLongestRevMatch_endPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} :
-    ¬IsLongestRevMatch pat s.endPos :=
-  fun h => h.ne_endPos rfl
-
 theorem IsLongestRevMatch.eq {pat : ρ} [PatternModel pat] {s : Slice} {pos pos' : s.Pos}
     (h : IsLongestRevMatch pat pos) (h' : IsLongestRevMatch pat pos') : pos = pos' := by
   apply Std.le_antisymm
@@ -265,34 +185,6 @@ theorem IsLongestRevMatch.le_of_isRevMatch {pat : ρ} [PatternModel pat] {s : Sl
     (h : IsLongestRevMatch pat pos) (h' : IsRevMatch pat pos') : pos ≤ pos' :=
   Std.not_lt.1 (fun hlt => h.not_isRevMatch _ hlt h')
 
-@[simp]
-theorem isLongestRevMatch_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice}
-    (hst : s.copy = t.copy) {pos : s.Pos} :
-    IsLongestRevMatch pat (pos.cast hst) ↔ IsLongestRevMatch pat pos := by
-  simp only [isLongestRevMatch_iff, isRevMatch_cast_iff, and_congr_right_iff]
-  refine fun _ => ⟨fun h p hp => ?_, fun h p hp => ?_⟩
-  · rw [← isRevMatch_cast_iff hst]
-    exact h _ (by simpa)
-  · have : p = (p.cast hst.symm).cast hst := by simp
-    rw [this, isRevMatch_cast_iff hst]
-    exact h _ (by rwa [this, Pos.cast_lt_cast_iff] at hp)
-
-theorem IsLongestRevMatch.of_eq {pat : ρ} [PatternModel pat] {s t : Slice} {pos : s.Pos} {pos' : t.Pos}
-    (h : IsLongestRevMatch pat pos) (h₁ : s.copy = t.copy) (h₂ : pos.cast h₁ = pos') :
-    IsLongestRevMatch pat pos' := by
-  subst h₂; simpa
-
-theorem IsLongestRevMatch.sliceFrom {pat : ρ} [PatternModel pat] {s : Slice} {pos : s.Pos}
-    (h : IsLongestRevMatch pat pos) (p : s.Pos) (hp : p ≤ pos) : IsLongestRevMatch pat (Pos.sliceFrom p pos hp) := by
-  simp [isLongestRevMatch_iff] at ⊢ h
-  refine ⟨h.1, fun p' hp' => ?_⟩
-  rw [← isRevMatch_ofSliceFrom_iff]
-  exact h.2 _ (by simpa [Pos.lt_sliceFrom_iff] using hp')
-
-theorem isLongestRevMatch_of_ofSliceFrom {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos} {pos : (s.sliceFrom p).Pos}
-    (h : IsLongestRevMatch pat (Pos.ofSliceFrom pos)) : IsLongestRevMatch pat pos := by
-  simpa using h.sliceFrom p
-
 /--
 Predicate stating that a match for a given pattern is never a proper prefix of another match.
 
@@ -336,7 +228,7 @@ theorem isLongestRevMatch_iff_isRevMatch {ρ : Type} (pat : ρ) [PatternModel pa
   exact ht₅ (NoSuffixPatternModel.eq_empty _ _ ht₂ (ht₅'' ▸ ht₂'))
 
 /--
-Predicate stating that the slice formed by {name}`startPos` and {name}`endPos` contains a match
+Predicate stating that the slice formed by {name}`startPos` and {name}`endPos` contains is a match
 of {name}`pat` in {name}`s` and it is longest among matches starting at {name}`startPos`.
 -/
 structure IsLongestMatchAt (pat : ρ) [PatternModel pat] {s : Slice} (startPos endPos : s.Pos) : Prop where
@@ -348,21 +240,12 @@ theorem isLongestMatchAt_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos₁ p
       ∃ (h : pos₁ ≤ pos₂), IsLongestMatch pat (Slice.Pos.sliceFrom _ _ h) :=
   ⟨fun ⟨h, h'⟩ => ⟨h, h'⟩, fun ⟨h, h'⟩ => ⟨h, h'⟩⟩
 
-theorem IsLongestMatchAt.lt {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {startPos endPos : s.Pos}
+theorem IsLongestMatchAt.lt {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
     (h : IsLongestMatchAt pat startPos endPos) : startPos < endPos := by
   have := h.isLongestMatch_sliceFrom.ne_startPos
   rw [← Pos.startPos_lt_iff, ← Slice.Pos.ofSliceFrom_lt_ofSliceFrom_iff] at this
   simpa
 
-theorem IsLongestMatchAt.ne {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {startPos endPos : s.Pos}
-    (h : IsLongestMatchAt pat startPos endPos) : startPos ≠ endPos :=
-  Std.ne_of_lt h.lt
-
-@[simp]
-theorem not_isLongestMatchAt_self {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {startPos : s.Pos} :
-    ¬IsLongestMatchAt pat startPos startPos :=
-  fun h => h.ne rfl
-
 theorem IsLongestMatchAt.eq {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos endPos' : s.Pos}
     (h : IsLongestMatchAt pat startPos endPos) (h' : IsLongestMatchAt pat startPos endPos') :
     endPos = endPos' := by
@@ -399,77 +282,6 @@ theorem isLongestMatchAt_startPos_iff {pat : ρ} [PatternModel pat] {s : Slice}
     ⟨fun h => isLongestMatch_of_eq (by simp) (by simp) h,
      fun h => isLongestMatch_of_eq (by simp) (by simp) h⟩
 
-theorem isLongestMatch_iff_isLongestMatchAt_ofSliceFrom {pat : ρ} [PatternModel pat]
-    {s : Slice} {base : s.Pos} (endPos : (s.sliceFrom base).Pos) :
-    IsLongestMatch pat endPos ↔ IsLongestMatchAt pat base (Pos.ofSliceFrom endPos) := by
-  simp [← isLongestMatchAt_startPos_iff, isLongestMatchAt_iff_isLongestMatchAt_ofSliceFrom]
-
-theorem IsLongestMatchAt.matches_slice {pat : ρ} [PatternModel pat] {s : Slice}
-    {startPos endPos : s.Pos} (h : IsLongestMatchAt pat startPos endPos) :
-    PatternModel.Matches pat (s.slice startPos endPos h.le).copy := by
-  simpa using h.isLongestMatch_sliceFrom.isMatch.matches_copy
-
-@[simp]
-theorem isLongestMatchAt_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
-    {startPos endPos : s.Pos} :
-    IsLongestMatchAt pat (startPos.cast hst) (endPos.cast hst) ↔ IsLongestMatchAt pat startPos endPos := by
-  simp [isLongestMatchAt_iff, Pos.sliceFrom_cast]
-
-theorem IsLongestMatchAt.of_eq {pat : ρ} [PatternModel pat] {s t : Slice} {s₁ e₁ : s.Pos} {s₂ e₂ : t.Pos}
-    (h : IsLongestMatchAt pat s₁ e₁) (h₁ : s.copy = t.copy) (h₂ : s₁.cast h₁ = s₂) (h₃ : e₁.cast h₁ = e₂) :
-    IsLongestMatchAt pat s₂ e₂ := by
-  subst h₂ h₃; simpa
-
-theorem IsLongestMatchAt.sliceTo {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
-    (h : IsLongestMatchAt pat startPos endPos) (p : s.Pos) (hp : endPos ≤ p) :
-    IsLongestMatchAt pat (Pos.sliceTo p startPos (by exact Std.le_trans h.le hp)) (Pos.sliceTo p endPos hp) := by
-  simp only [isLongestMatchAt_iff, Pos.sliceTo_le_sliceTo_iff] at ⊢ h
-  obtain ⟨h, hp'⟩ := h
-  exact ⟨h, (hp'.sliceTo (Pos.sliceFrom startPos p (Std.le_trans h hp)) (by simpa)).of_eq (by simp) (by ext; simp)⟩
-
-theorem isLongestMatchAt_of_ofSliceTo {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos} {startPos endPos : (s.sliceTo p).Pos}
-    (h : IsLongestMatchAt pat (Pos.ofSliceTo startPos) (Pos.ofSliceTo endPos)) :
-    IsLongestMatchAt pat startPos endPos := by
-  simpa using h.sliceTo p Pos.ofSliceTo_le
-
-/--
-Predicate stating that the range between two positions of {name}`s` can be covered by longest
-matches of the pattern within {name}`s`.
--/
-inductive IsLongestMatchAtChain (pat : ρ) [PatternModel pat] {s : Slice} : s.Pos → s.Pos → Prop where
-  | nil (p : s.Pos) : IsLongestMatchAtChain pat p p
-  | cons (startPos middlePos endPos : s.Pos) : IsLongestMatchAt pat startPos middlePos →
-      IsLongestMatchAtChain pat middlePos endPos → IsLongestMatchAtChain pat startPos endPos
-
-attribute [simp] IsLongestMatchAtChain.nil
-
-theorem IsLongestMatchAtChain.eq_of_isLongestMatchAt_self {pat : ρ} [PatternModel pat] {s : Slice}
-    {startPos endPos : s.Pos} (h : IsLongestMatchAtChain pat startPos endPos) (h' : IsLongestMatchAt pat startPos startPos) :
-    startPos = endPos := by
-  induction h with
-  | nil => rfl
-  | cons p₁ p₂ p₃ h₁ h₂ ih =>
-    obtain rfl : p₁ = p₂ := h'.eq h₁
-    exact ih h₁
-
-theorem IsLongestMatchAtChain.le {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
-    (h : IsLongestMatchAtChain pat startPos endPos) : startPos ≤ endPos := by
-  induction h with
-  | nil => exact Std.le_refl _
-  | cons p₁ p₂ p₃ h₁ h₂ ih => exact Std.le_trans h₁.le ih
-
-theorem IsLongestMatchAtChain.sliceTo {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
-    (h : IsLongestMatchAtChain pat startPos endPos) (p : s.Pos) (hp : endPos ≤ p) :
-    IsLongestMatchAtChain pat (Pos.sliceTo p startPos (by exact Std.le_trans h.le hp)) (Pos.sliceTo p endPos hp) := by
-  induction h with
-  | nil => simp
-  | cons p₁ p₂ p₃ h₁ h₂ ih => exact .cons _ _ _ (h₁.sliceTo p (Std.le_trans h₂.le hp)) (ih hp)
-
-theorem isLongestMatchAtChain_of_ofSliceTo {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos}
-    {startPos endPos : (s.sliceTo p).Pos} (h : IsLongestMatchAtChain pat (Pos.ofSliceTo startPos) (Pos.ofSliceTo endPos)) :
-    IsLongestMatchAtChain pat startPos endPos := by
-  simpa using h.sliceTo p Pos.ofSliceTo_le
-
 /--
 Predicate stating that the slice formed by {name}`startPos` and {name}`endPos` contains is a match
 of {name}`pat` in {name}`s` and it is longest among matches ending at {name}`endPos`.
@@ -483,21 +295,12 @@ theorem isLongestRevMatchAt_iff {pat : ρ} [PatternModel pat] {s : Slice} {pos
       ∃ (h : pos₁ ≤ pos₂), IsLongestRevMatch pat (Slice.Pos.sliceTo _ _ h) :=
   ⟨fun ⟨h, h'⟩ => ⟨h, h'⟩, fun ⟨h, h'⟩ => ⟨h, h'⟩⟩
 
-theorem IsLongestRevMatchAt.lt {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {startPos endPos : s.Pos}
+theorem IsLongestRevMatchAt.lt {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
     (h : IsLongestRevMatchAt pat startPos endPos) : startPos < endPos := by
   have := h.isLongestRevMatch_sliceTo.ne_endPos
   rw [← Pos.lt_endPos_iff, ← Slice.Pos.ofSliceTo_lt_ofSliceTo_iff] at this
   simpa
 
-theorem IsLongestRevMatchAt.ne {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {startPos endPos : s.Pos}
-    (h : IsLongestRevMatchAt pat startPos endPos) : startPos ≠ endPos :=
-  Std.ne_of_lt h.lt
-
-@[simp]
-theorem not_isLongestRevMatchAt_self {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} {endPos : s.Pos} :
-    ¬IsLongestRevMatchAt pat endPos endPos :=
-  fun h => h.ne rfl
-
 theorem IsLongestRevMatchAt.eq {pat : ρ} [PatternModel pat] {s : Slice} {startPos startPos' endPos : s.Pos}
     (h : IsLongestRevMatchAt pat startPos endPos) (h' : IsLongestRevMatchAt pat startPos' endPos) :
     startPos = startPos' := by
@@ -532,77 +335,6 @@ theorem isLongestRevMatchAt_endPos_iff {pat : ρ} [PatternModel pat] {s : Slice}
     ⟨fun h => isLongestRevMatch_of_eq (by simp) (by simp) h,
      fun h => isLongestRevMatch_of_eq (by simp) (by simp) h⟩
 
-theorem isLongestRevMatch_iff_isLongestRevMatchAt_ofSliceTo {pat : ρ} [PatternModel pat]
-    {s : Slice} {base : s.Pos} (startPos : (s.sliceTo base).Pos) :
-    IsLongestRevMatch pat startPos ↔ IsLongestRevMatchAt pat (Pos.ofSliceTo startPos) base := by
-  simp [← isLongestRevMatchAt_endPos_iff, isLongestRevMatchAt_iff_isLongestRevMatchAt_ofSliceTo]
-
-theorem IsLongestRevMatchAt.matches_slice {pat : ρ} [PatternModel pat] {s : Slice}
-    {startPos endPos : s.Pos} (h : IsLongestRevMatchAt pat startPos endPos) :
-    PatternModel.Matches pat (s.slice startPos endPos h.le).copy := by
-  simpa using h.isLongestRevMatch_sliceTo.isRevMatch.matches_copy
-
-@[simp]
-theorem isLongestRevMatchAt_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
-    {startPos endPos : s.Pos} :
-    IsLongestRevMatchAt pat (startPos.cast hst) (endPos.cast hst) ↔ IsLongestRevMatchAt pat startPos endPos := by
-  simp [isLongestRevMatchAt_iff, Pos.sliceTo_cast]
-
-theorem IsLongestRevMatchAt.of_eq {pat : ρ} [PatternModel pat] {s t : Slice} {s₁ e₁ : s.Pos} {s₂ e₂ : t.Pos}
-    (h : IsLongestRevMatchAt pat s₁ e₁) (h₁ : s.copy = t.copy) (h₂ : s₁.cast h₁ = s₂) (h₃ : e₁.cast h₁ = e₂) :
-    IsLongestRevMatchAt pat s₂ e₂ := by
-  subst h₂ h₃; simpa
-
-theorem IsLongestRevMatchAt.sliceFrom {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
-    (h : IsLongestRevMatchAt pat startPos endPos) (p : s.Pos) (hp : p ≤ startPos) :
-    IsLongestRevMatchAt pat (Pos.sliceFrom p startPos hp) (Pos.sliceFrom p endPos (by exact Std.le_trans hp h.le)) := by
-  simp only [isLongestRevMatchAt_iff, Pos.sliceFrom_le_sliceFrom_iff] at ⊢ h
-  obtain ⟨h, hp'⟩ := h
-  exact ⟨h, (hp'.sliceFrom (Pos.sliceTo endPos p (Std.le_trans hp h)) (by simpa)).of_eq (by simp) (by ext; simp)⟩
-
-theorem isLongestRevMatchAt_of_ofSliceFrom {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos} {startPos endPos : (s.sliceFrom p).Pos}
-    (h : IsLongestRevMatchAt pat (Pos.ofSliceFrom startPos) (Pos.ofSliceFrom endPos)) :
-    IsLongestRevMatchAt pat startPos endPos := by
-  simpa using h.sliceFrom p Pos.le_ofSliceFrom
-
-/--
-Predicate stating that the range between two positions of {name}`s` can be covered by longest
-reverse matches of the pattern within {name}`s`.
--/
-inductive IsLongestRevMatchAtChain (pat : ρ) [PatternModel pat] {s : Slice} : s.Pos → s.Pos → Prop where
-  | nil (p : s.Pos) : IsLongestRevMatchAtChain pat p p
-  | cons (startPos middlePos endPos : s.Pos) : IsLongestRevMatchAtChain pat startPos middlePos →
-      IsLongestRevMatchAt pat middlePos endPos → IsLongestRevMatchAtChain pat startPos endPos
-
-attribute [simp] IsLongestRevMatchAtChain.nil
-
-theorem IsLongestRevMatchAtChain.eq_of_isLongestRevMatchAt_self {pat : ρ} [PatternModel pat] {s : Slice}
-    {startPos endPos : s.Pos} (h : IsLongestRevMatchAtChain pat startPos endPos) (h' : IsLongestRevMatchAt pat endPos endPos) :
-    startPos = endPos := by
-  induction h with
-  | nil => rfl
-  | cons mid endP hchain hmatch ih =>
-    obtain rfl := hmatch.eq h'
-    exact ih hmatch
-
-theorem IsLongestRevMatchAtChain.le {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
-    (h : IsLongestRevMatchAtChain pat startPos endPos) : startPos ≤ endPos := by
-  induction h with
-  | nil => exact Std.le_refl _
-  | cons mid endP hchain hmatch ih => exact Std.le_trans ih hmatch.le
-
-theorem IsLongestRevMatchAtChain.sliceFrom {pat : ρ} [PatternModel pat] {s : Slice} {startPos endPos : s.Pos}
-    (h : IsLongestRevMatchAtChain pat startPos endPos) (p : s.Pos) (hp : p ≤ startPos) :
-    IsLongestRevMatchAtChain pat (Pos.sliceFrom p startPos hp) (Pos.sliceFrom p endPos (by exact Std.le_trans hp h.le)) := by
-  induction h with
-  | nil => simp
-  | cons mid endP hchain hmatch ih => exact .cons _ _ _ ih (hmatch.sliceFrom p (Std.le_trans hp hchain.le))
-
-theorem isLongestRevMatchAtChain_of_ofSliceFrom {pat : ρ} [PatternModel pat] {s : Slice} {p : s.Pos}
-    {startPos endPos : (s.sliceFrom p).Pos} (h : IsLongestRevMatchAtChain pat (Pos.ofSliceFrom startPos) (Pos.ofSliceFrom endPos)) :
-    IsLongestRevMatchAtChain pat startPos endPos := by
-  simpa using h.sliceFrom p Pos.le_ofSliceFrom
-
 /--
 Predicate stating that there is a (longest) match starting at the given position.
 -/
@@ -628,7 +360,7 @@ theorem matchesAt_iff_exists_isMatch {pat : ρ} [PatternModel pat] {s : Slice}
      by simpa using hq⟩⟩
 
 @[simp]
-theorem not_matchesAt_endPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} :
+theorem not_matchesAt_endPos {pat : ρ} [PatternModel pat] {s : Slice} :
     ¬ MatchesAt pat s.endPos := by
   simp only [matchesAt_iff_exists_isMatch, Pos.endPos_le, exists_prop_eq]
   intro h
@@ -648,14 +380,6 @@ theorem IsLongestMatchAt.matchesAt {pat : ρ} [PatternModel pat] {s : Slice} {st
     (h : IsLongestMatchAt pat startPos endPos) : MatchesAt pat startPos where
   exists_isLongestMatchAt := ⟨_, h⟩
 
-@[simp]
-theorem matchesAt_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
-    {pos : s.Pos} : MatchesAt pat (pos.cast hst) ↔ MatchesAt pat pos := by
-  simp only [matchesAt_iff_exists_isLongestMatchAt]
-  refine ⟨fun ⟨endPos, h⟩ => ?_, fun ⟨endPos, h⟩ => ?_⟩
-  · exact ⟨endPos.cast hst.symm, by simpa [← isLongestMatchAt_cast_iff hst]⟩
-  · exact ⟨endPos.cast hst, by simpa⟩
-
 /--
 Predicate stating that there is a (longest) match ending at the given position.
 -/
@@ -681,13 +405,13 @@ theorem revMatchesAt_iff_exists_isRevMatch {pat : ρ} [PatternModel pat] {s : Sl
      by simpa using hq⟩⟩
 
 @[simp]
-theorem not_revMatchesAt_startPos {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice} :
+theorem not_revMatchesAt_startPos {pat : ρ} [PatternModel pat] {s : Slice} :
     ¬ RevMatchesAt pat s.startPos := by
   simp only [revMatchesAt_iff_exists_isRevMatch, Pos.le_startPos, exists_prop_eq]
   intro h
   simpa [← Pos.ofSliceTo_inj] using h.ne_endPos
 
-theorem revMatchesAt_iff_revMatchesAt_ofSliceTo {pat : ρ} [PatternModel pat] {s : Slice} {base : s.Pos}
+theorem revMatchesAt_iff_revMatchesAt_ofSliceto {pat : ρ} [PatternModel pat] {s : Slice} {base : s.Pos}
     {pos : (s.sliceTo base).Pos} : RevMatchesAt pat pos ↔ RevMatchesAt pat (Pos.ofSliceTo pos) := by
   simp only [revMatchesAt_iff_exists_isLongestRevMatchAt]
   constructor
@@ -701,14 +425,6 @@ theorem IsLongestRevMatchAt.revMatchesAt {pat : ρ} [PatternModel pat] {s : Slic
     (h : IsLongestRevMatchAt pat startPos endPos) : RevMatchesAt pat endPos where
   exists_isLongestRevMatchAt := ⟨_, h⟩
 
-@[simp]
-theorem revMatchesAt_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
-    {pos : s.Pos} : RevMatchesAt pat (pos.cast hst) ↔ RevMatchesAt pat pos := by
-  simp only [revMatchesAt_iff_exists_isLongestRevMatchAt]
-  refine ⟨fun ⟨endPos, h⟩ => ?_, fun ⟨endPos, h⟩ => ?_⟩
-  · exact ⟨endPos.cast hst.symm, by simpa [← isLongestRevMatchAt_cast_iff hst]⟩
-  · exact ⟨endPos.cast hst, by simpa⟩
-
 open Classical in
 /--
 Noncomputable model function returning the end point of the longest match starting at the given
@@ -734,21 +450,6 @@ theorem matchAt?_eq_none_iff {ρ : Type} {pat : ρ} [PatternModel pat]
   | case1 h => simpa using ⟨h⟩
   | case2 h => simpa using fun ⟨h'⟩ => h h'
 
-theorem lt_of_matchAt?_eq_some {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat]
-    {s : Slice} {startPos endPos : s.Pos} (h : matchAt? pat startPos = some endPos) :
-    startPos < endPos :=
-  (matchAt?_eq_some_iff.1 h).lt
-
-@[simp]
-theorem matchAt?_cast {ρ : Type} (pat : ρ) [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
-    {startPos : s.Pos} :
-    matchAt? pat (startPos.cast hst) = (matchAt? pat startPos).map (Slice.Pos.cast · hst) := by
-  refine Option.ext (fun endPos => ?_)
-  have : endPos = (endPos.cast hst.symm).cast hst := by simp
-  conv => lhs; rw [this, matchAt?_eq_some_iff, isLongestMatchAt_cast_iff]
-  simp only [Option.map_eq_some_iff, matchAt?_eq_some_iff]
-  exact ⟨fun h => ⟨_, ⟨h, by simp⟩⟩, by rintro ⟨pos, h, rfl⟩; simpa⟩
-
 open Classical in
 /--
 Noncomputable model function returning the start point of the longest match ending at the given
@@ -774,21 +475,6 @@ theorem revMatchAt?_eq_none_iff {ρ : Type} {pat : ρ} [PatternModel pat]
   | case1 h => simpa using ⟨h⟩
   | case2 h => simpa using fun ⟨h'⟩ => h h'
 
-theorem lt_of_revMatchAt?_eq_some {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat]
-    {s : Slice} {startPos endPos : s.Pos} (h : revMatchAt? pat endPos = some startPos) :
-    startPos < endPos :=
-  (revMatchAt?_eq_some_iff.1 h).lt
-
-@[simp]
-theorem revMatchAt?_cast {ρ : Type} (pat : ρ) [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
-    {startPos : s.Pos} :
-    revMatchAt? pat (startPos.cast hst) = (revMatchAt? pat startPos).map (Slice.Pos.cast · hst) := by
-  refine Option.ext (fun endPos => ?_)
-  have : endPos = (endPos.cast hst.symm).cast hst := by simp
-  conv => lhs; rw [this, revMatchAt?_eq_some_iff, isLongestRevMatchAt_cast_iff]
-  simp only [Option.map_eq_some_iff, revMatchAt?_eq_some_iff]
-  exact ⟨fun h => ⟨_, ⟨h, by simp⟩⟩, by rintro ⟨pos, h, rfl⟩; simpa⟩
-
 /--
 Predicate stating compatibility between {name}`PatternModel` and {name}`ForwardPattern`.
 
@@ -819,8 +505,8 @@ theorem LawfulForwardPatternModel.skipPrefix?_eq_none_iff {ρ : Type} {pat : ρ}
 /--
 Predicate stating compatibility between {name}`PatternModel` and {name}`BackwardPattern`.
 
-This extends {name}`LawfulBackwardPattern`, but it is much stronger because it forces the
-{name}`BackwardPattern` to match the longest prefix of the given slice that matches the property
+This extends {name}`LawfulForwardPattern`, but it is much stronger because it forces the
+{name}`ForwardPattern` to match the longest prefix of the given slice that matches the property
 supplied by the {name}`PatternModel` instance.
 -/
 class LawfulBackwardPatternModel {ρ : Type} (pat : ρ) [BackwardPattern pat]
@@ -884,24 +570,6 @@ theorem IsValidSearchFrom.endPos_of_eq {pat : ρ} [PatternModel pat] {s : Slice}
   cases hl
   exact IsValidSearchFrom.endPos
 
-theorem isValidSearchFrom_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
-    {pos : s.Pos} {l : List (SearchStep t)} :
-    IsValidSearchFrom pat (pos.cast hst) l ↔ IsValidSearchFrom pat pos (l.map (·.cast hst.symm)) := by
-  suffices ∀ (s t : Slice) (hst : s.copy = t.copy) (pos : s.Pos) (l : List (SearchStep s)),
-      IsValidSearchFrom pat pos l → IsValidSearchFrom pat (pos.cast hst) (l.map (·.cast hst)) from
-    ⟨fun h => by simpa using this _ _ hst.symm _ _ h, fun h => by
-      have hcomp : (SearchStep.cast hst) ∘ (SearchStep.cast hst.symm) = id := by ext; simp
-      simpa [hcomp] using this _ _ hst _ _ h⟩
-  intro s t hst pos l hl
-  induction hl with
-  | endPos => simpa using IsValidSearchFrom.endPos
-  | matched h₁ h₂ ih =>
-    simpa only [List.map_cons, SearchStep.cast_matched] using IsValidSearchFrom.matched (by simpa) ih
-  | mismatched h₁ h₂ h₃ ih =>
-    simp only [List.map_cons, SearchStep.cast_rejected]
-    refine IsValidSearchFrom.mismatched (by simpa) (fun p hp₁ hp₂ hp₃ => ?_) ih
-    exact h₂ (p.cast hst.symm) (by simpa [Pos.le_cast_iff]) (by simpa [Pos.cast_lt_iff]) (by simpa)
-
 /--
 Predicate stating compatibility between {name}`PatternModel` and {name}`ToForwardSearcher`.
 
@@ -995,24 +663,6 @@ theorem IsValidRevSearchFrom.startPos_of_eq {pat : ρ} [PatternModel pat] {s : S
   cases hl
   exact IsValidRevSearchFrom.startPos
 
-theorem isValidRevSearchFrom_cast_iff {pat : ρ} [PatternModel pat] {s t : Slice} (hst : s.copy = t.copy)
-    {pos : s.Pos} {l : List (SearchStep t)} :
-    IsValidRevSearchFrom pat (pos.cast hst) l ↔ IsValidRevSearchFrom pat pos (l.map (·.cast hst.symm)) := by
-  suffices ∀ (s t : Slice) (hst : s.copy = t.copy) (pos : s.Pos) (l : List (SearchStep s)),
-      IsValidRevSearchFrom pat pos l → IsValidRevSearchFrom pat (pos.cast hst) (l.map (·.cast hst)) from
-    ⟨fun h => by simpa using this _ _ hst.symm _ _ h, fun h => by
-      have hcomp : (SearchStep.cast hst) ∘ (SearchStep.cast hst.symm) = id := by ext; simp
-      simpa [hcomp] using this _ _ hst _ _ h⟩
-  intro s t hst pos l hl
-  induction hl with
-  | startPos => simpa using IsValidRevSearchFrom.startPos
-  | matched h₁ h₂ ih =>
-    simpa only [List.map_cons, SearchStep.cast_matched] using IsValidRevSearchFrom.matched (by simpa) ih
-  | mismatched h₁ h₂ h₃ ih =>
-    simp only [List.map_cons, SearchStep.cast_rejected]
-    refine IsValidRevSearchFrom.mismatched (by simpa) (fun p hp₁ hp₂ hp₃ => ?_) ih
-    exact h₂ (p.cast hst.symm) (by simpa [Pos.lt_cast_iff]) (by simpa [Pos.cast_le_iff]) (by simpa)
-
 /--
 Predicate stating compatibility between {name}`PatternModel` and {name}`ToBackwardSearcher`.
 

src/Init/Data/String/Lemmas/Pattern/Char.lean

@@ -28,9 +28,7 @@ namespace String.Slice.Pattern.Model.Char
 
 instance {c : Char} : PatternModel c where
   Matches s := s = String.singleton c
-
-instance {c : Char} : StrictPatternModel c where
-  not_matches_empty := by simp [PatternModel.Matches]
+  not_matches_empty := by simp
 
 instance {c : Char} : NoPrefixPatternModel c :=
   .of_length_eq (by simp +contextual [PatternModel.Matches])
@@ -170,61 +168,11 @@ theorem isLongestMatchAt_iff_isLongestMatchAt_beq {c : Char} {s : Slice}
     IsLongestMatchAt c pos pos' ↔ IsLongestMatchAt (· == c) pos pos' := by
   simp [Model.isLongestMatchAt_iff, isLongestMatch_iff_isLongestMatch_beq]
 
-theorem isLongestMatchAtChain_iff_isLongestMatchAtChain_beq {c : Char} {s : Slice} {pos pos' : s.Pos} :
-    IsLongestMatchAtChain c pos pos' ↔ IsLongestMatchAtChain (· == c) pos pos' := by
-  refine ⟨fun h => ?_, fun h => ?_⟩
-  · induction h with
-    | nil => simp
-    | cons p₁ p₂ p₃ h₁ h₂ ih => exact .cons _ _ _ (isLongestMatchAt_iff_isLongestMatchAt_beq.1 h₁) ih
-  · induction h with
-    | nil => simp
-    | cons p₁ p₂ p₃ h₁ h₂ ih => exact .cons _ _ _ (isLongestMatchAt_iff_isLongestMatchAt_beq.2 h₁) ih
-
-theorem isLongestMatchAtChain_iff {c : Char} {s : Slice} {pos pos' : s.Pos} :
-    IsLongestMatchAtChain c pos pos' ↔ pos ≤ pos' ∧ ∀ pos'', pos ≤ pos'' → (h : pos'' < pos') → pos''.get (Pos.ne_endPos_of_lt h) = c := by
-  simp [isLongestMatchAtChain_iff_isLongestMatchAtChain_beq, CharPred.isLongestMatchAtChain_iff]
-
-theorem isLongestMatchAtChain_iff_toList {c : Char} {s : Slice} {pos pos' : s.Pos} :
-    IsLongestMatchAtChain c pos pos' ↔
-      ∃ (h : pos ≤ pos'), (s.slice pos pos' h).copy.toList = List.replicate (s.slice pos pos' h).copy.length c := by
-  simp [isLongestMatchAtChain_iff_isLongestMatchAtChain_beq, CharPred.isLongestMatchAtChain_iff_toList,
-    List.eq_replicate_iff]
-
-theorem isLongestMatchAtChain_startPos_endPos_iff_toList {c : Char} {s : Slice} :
-    IsLongestMatchAtChain c s.startPos s.endPos ↔ s.copy.toList = List.replicate s.copy.length c := by
-  simp [isLongestMatchAtChain_iff_isLongestMatchAtChain_beq,
-    CharPred.isLongestMatchAtChain_startPos_endPos_iff_toList, List.eq_replicate_iff]
-
 theorem isLongestRevMatchAt_iff_isLongestRevMatchAt_beq {c : Char} {s : Slice}
     {pos pos' : s.Pos} :
     IsLongestRevMatchAt c pos pos' ↔ IsLongestRevMatchAt (· == c) pos pos' := by
   simp [Model.isLongestRevMatchAt_iff, isLongestRevMatch_iff_isLongestRevMatch_beq]
 
-theorem isLongestRevMatchAtChain_iff_isLongestRevMatchAtChain_beq {c : Char} {s : Slice} {pos pos' : s.Pos} :
-    IsLongestRevMatchAtChain c pos pos' ↔ IsLongestRevMatchAtChain (· == c) pos pos' := by
-  refine ⟨fun h => ?_, fun h => ?_⟩
-  · induction h with
-    | nil => simp
-    | cons p₂ p₃ _ hmatch ih => exact .cons _ _ _ ih (isLongestRevMatchAt_iff_isLongestRevMatchAt_beq.1 hmatch)
-  · induction h with
-    | nil => simp
-    | cons p₂ p₃ _ hmatch ih => exact .cons _ _ _ ih (isLongestRevMatchAt_iff_isLongestRevMatchAt_beq.2 hmatch)
-
-theorem isLongestRevMatchAtChain_iff {c : Char} {s : Slice} {pos pos' : s.Pos} :
-    IsLongestRevMatchAtChain c pos pos' ↔ pos ≤ pos' ∧ ∀ pos'', pos ≤ pos'' → (h : pos'' < pos') → pos''.get (Pos.ne_endPos_of_lt h) = c := by
-  simp [isLongestRevMatchAtChain_iff_isLongestRevMatchAtChain_beq, CharPred.isLongestRevMatchAtChain_iff]
-
-theorem isLongestRevMatchAtChain_iff_toList {c : Char} {s : Slice} {pos pos' : s.Pos} :
-    IsLongestRevMatchAtChain c pos pos' ↔
-      ∃ (h : pos ≤ pos'), (s.slice pos pos' h).copy.toList = List.replicate (s.slice pos pos' h).copy.length c := by
-  simp [isLongestRevMatchAtChain_iff_isLongestRevMatchAtChain_beq, CharPred.isLongestRevMatchAtChain_iff_toList,
-    List.eq_replicate_iff]
-
-theorem isLongestRevMatchAtChain_startPos_endPos_iff_toList {c : Char} {s : Slice} :
-    IsLongestRevMatchAtChain c s.startPos s.endPos ↔ s.copy.toList = List.replicate s.copy.length c := by
-  simp [isLongestRevMatchAtChain_iff_isLongestRevMatchAtChain_beq,
-    CharPred.isLongestRevMatchAtChain_startPos_endPos_iff_toList, List.eq_replicate_iff]
-
 theorem matchesAt_iff_matchesAt_beq {c : Char} {s : Slice} {pos : s.Pos} :
     MatchesAt c pos ↔ MatchesAt (· == c) pos := by
   simp [matchesAt_iff_exists_isLongestMatchAt, isLongestMatchAt_iff_isLongestMatchAt_beq]
@@ -294,21 +242,18 @@ theorem skipPrefix?_char_eq_skipPrefix?_beq {c : Char} {s : Slice} :
 theorem Pattern.ForwardPattern.skipPrefix?_char_eq_skipPrefix?_beq {c : Char} {s : Slice} :
     skipPrefix? c s = skipPrefix? (· == c) s := (rfl)
 
-theorem Pos.skip?_char_eq_skip?_beq {c : Char} {s : Slice} {pos : s.Pos} :
-    pos.skip? c = pos.skip? (· == c) := (rfl)
-
 theorem Pos.skipWhile_char_eq_skipWhile_beq {c : Char} {s : Slice} (curr : s.Pos) :
     Pos.skipWhile curr c = Pos.skipWhile curr (· == c) := by
   fun_induction Pos.skipWhile curr c with
   | case1 pos nextCurr h₁ h₂ ih =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pos.skip?_char_eq_skip?_beq, h₁, h₂, ih]
+    simp [← Pattern.ForwardPattern.skipPrefix?_char_eq_skipPrefix?_beq, h₁, h₂, ih]
   | case2 pos nextCurr h ih =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pos.skip?_char_eq_skip?_beq, h, ih]
+    simp [← Pattern.ForwardPattern.skipPrefix?_char_eq_skipPrefix?_beq, h, ih]
   | case3 pos h =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pos.skip?_char_eq_skip?_beq, h]
+    simp [← Pattern.ForwardPattern.skipPrefix?_char_eq_skipPrefix?_beq]
 
 theorem skipPrefixWhile_char_eq_skipPrefixWhile_beq {c : Char} {s : Slice} :
     s.skipPrefixWhile c = s.skipPrefixWhile (· == c) :=
@@ -324,7 +269,7 @@ theorem takeWhile_char_eq_takeWhile_beq {c : Char} {s : Slice} :
 
 theorem all_char_eq_all_beq {c : Char} {s : Slice} :
     s.all c = s.all (· == c) := by
-  simp only [all, skipPrefixWhile_char_eq_skipPrefixWhile_beq]
+  simp only [all, dropWhile_char_eq_dropWhile_beq]
 
 theorem find?_char_eq_find?_beq {c : Char} {s : Slice} :
     s.find? c = s.find? (· == c) :=
@@ -353,21 +298,18 @@ theorem dropSuffix_char_eq_dropSuffix_beq {c : Char} {s : Slice} :
 theorem Pattern.BackwardPattern.skipSuffix?_char_eq_skipSuffix?_beq {c : Char} {s : Slice} :
     skipSuffix? c s = skipSuffix? (· == c) s := (rfl)
 
-theorem Pos.revSkip?_char_eq_revSkip?_beq {c : Char} {s : Slice} {pos : s.Pos} :
-    pos.revSkip? c = pos.revSkip? (· == c) := (rfl)
-
 theorem Pos.revSkipWhile_char_eq_revSkipWhile_beq {c : Char} {s : Slice} (curr : s.Pos) :
     Pos.revSkipWhile curr c = Pos.revSkipWhile curr (· == c) := by
   fun_induction Pos.revSkipWhile curr c with
   | case1 pos nextCurr h₁ h₂ ih =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pos.revSkip?_char_eq_revSkip?_beq, h₁, h₂, ih]
+    simp [← Pattern.BackwardPattern.skipSuffix?_char_eq_skipSuffix?_beq, h₁, h₂, ih]
   | case2 pos nextCurr h ih =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pos.revSkip?_char_eq_revSkip?_beq, h, ih]
+    simp [← Pattern.BackwardPattern.skipSuffix?_char_eq_skipSuffix?_beq, h, ih]
   | case3 pos h =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pos.revSkip?_char_eq_revSkip?_beq, h]
+    simp [← Pattern.BackwardPattern.skipSuffix?_char_eq_skipSuffix?_beq]
 
 theorem skipSuffixWhile_char_eq_skipSuffixWhile_beq {c : Char} {s : Slice} :
     s.skipSuffixWhile c = s.skipSuffixWhile (· == c) :=
@@ -381,16 +323,4 @@ theorem takeEndWhile_char_eq_takeEndWhile_beq {c : Char} {s : Slice} :
     s.takeEndWhile c = s.takeEndWhile (· == c) := by
   simp only [takeEndWhile]; exact congrArg _ skipSuffixWhile_char_eq_skipSuffixWhile_beq
 
-theorem revFind?_char_eq_revFind?_beq {c : Char} {s : Slice} :
-    s.revFind? c = s.revFind? (· == c) :=
-  (rfl)
-
-theorem Pos.revFind?_char_eq_revFind?_beq {c : Char} {s : Slice} {p : s.Pos} :
-    p.revFind? c = p.revFind? (· == c) :=
-  (rfl)
-
-theorem revAll_char_eq_revAll_beq {c : Char} {s : Slice} :
-    s.revAll c = s.revAll (· == c) := by
-  simp [revAll, skipSuffixWhile_char_eq_skipSuffixWhile_beq]
-
 end String.Slice

src/Init/Data/String/Lemmas/Pattern/Find/Basic.lean

@@ -23,8 +23,8 @@ open Std String.Slice Pattern Pattern.Model
 
 namespace String.Slice
 
-theorem Pattern.Model.find?_eq_some_iff {ρ : Type} (pat : ρ) [PatternModel pat] [StrictPatternModel pat]
-    {σ : Slice → Type} [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
+theorem Pattern.Model.find?_eq_some_iff {ρ : Type} (pat : ρ) [PatternModel pat] {σ : Slice → Type}
+    [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
     [∀ s, IteratorLoop (σ s) Id Id] [∀ s, LawfulIteratorLoop (σ s) Id Id]
     [ToForwardSearcher pat σ] [LawfulToForwardSearcherModel pat] {s : Slice} {pos : s.Pos} :
     s.find? pat = some pos ↔ MatchesAt pat pos ∧ (∀ pos', pos' < pos → ¬ MatchesAt pat pos') := by
@@ -40,8 +40,8 @@ theorem Pattern.Model.find?_eq_some_iff {ρ : Type} (pat : ρ) [PatternModel pat
   | matched h₁ _ _ => have := h₁.matchesAt; grind
   | mismatched => grind
 
-theorem Pattern.Model.find?_eq_none_iff {ρ : Type} (pat : ρ) [PatternModel pat] [StrictPatternModel pat]
-    {σ : Slice → Type} [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
+theorem Pattern.Model.find?_eq_none_iff {ρ : Type} (pat : ρ) [PatternModel pat] {σ : Slice → Type}
+    [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
     [∀ s, IteratorLoop (σ s) Id Id] [∀ s, LawfulIteratorLoop (σ s) Id Id]
     [ToForwardSearcher pat σ] [LawfulToForwardSearcherModel pat] {s : Slice} :
     s.find? pat = none ↔ ∀ (pos : s.Pos), ¬ MatchesAt pat pos := by
@@ -65,15 +65,15 @@ theorem find?_eq_none_iff {ρ : Type} (pat : ρ) {σ : Slice → Type}
     [ToForwardSearcher pat σ] {s : Slice} : s.find? pat = none ↔ s.contains pat = false := by
   rw [← Option.isNone_iff_eq_none, ← Option.isSome_eq_false_iff, isSome_find?]
 
-theorem Pattern.Model.contains_eq_false_iff {ρ : Type} (pat : ρ) [PatternModel pat] [StrictPatternModel pat]
-    {σ : Slice → Type} [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
+theorem Pattern.Model.contains_eq_false_iff {ρ : Type} (pat : ρ) [PatternModel pat] {σ : Slice → Type}
+    [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
     [∀ s, IteratorLoop (σ s) Id Id] [∀ s, LawfulIteratorLoop (σ s) Id Id]
     [ToForwardSearcher pat σ] [LawfulToForwardSearcherModel pat] {s : Slice} :
     s.contains pat = false ↔ ∀ (pos : s.Pos), ¬ MatchesAt pat pos := by
   rw [← find?_eq_none_iff, Slice.find?_eq_none_iff]
 
-theorem Pattern.Model.contains_eq_true_iff {ρ : Type} (pat : ρ) [PatternModel pat] [StrictPatternModel pat]
-    {σ : Slice → Type} [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
+theorem Pattern.Model.contains_eq_true_iff {ρ : Type} (pat : ρ) [PatternModel pat] {σ : Slice → Type}
+    [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
     [∀ s, IteratorLoop (σ s) Id Id] [∀ s, LawfulIteratorLoop (σ s) Id Id]
     [ToForwardSearcher pat σ] [LawfulToForwardSearcherModel pat] {s : Slice} :
     s.contains pat ↔ ∃ (pos : s.Pos), MatchesAt pat pos := by
@@ -85,7 +85,7 @@ theorem Pos.find?_eq_find?_sliceFrom {ρ : Type} {pat : ρ} {σ : Slice → Type
     p.find? pat = ((s.sliceFrom p).find? pat).map Pos.ofSliceFrom :=
   (rfl)
 
-theorem Pattern.Model.posFind?_eq_some_iff {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {σ : Slice → Type}
+theorem Pattern.Model.posFind?_eq_some_iff {ρ : Type} {pat : ρ} [PatternModel pat] {σ : Slice → Type}
     [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
     [∀ s, IteratorLoop (σ s) Id Id] [∀ s, LawfulIteratorLoop (σ s) Id Id]
     [ToForwardSearcher pat σ] [LawfulToForwardSearcherModel pat] {s : Slice} {pos pos' : s.Pos} :
@@ -100,8 +100,8 @@ theorem Pattern.Model.posFind?_eq_some_iff {ρ : Type} {pat : ρ} [PatternModel
     refine ⟨Pos.sliceFrom _ _ h₁, ⟨by simpa using h₂, fun p hp₁ hp₂ => ?_⟩, by simp⟩
     exact h₃ (Pos.ofSliceFrom p) Slice.Pos.le_ofSliceFrom (Pos.lt_sliceFrom_iff.1 hp₁) hp₂
 
-theorem Pattern.Model.posFind?_eq_none_iff {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat]
-    {σ : Slice → Type} [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
+theorem Pattern.Model.posFind?_eq_none_iff {ρ : Type} {pat : ρ} [PatternModel pat] {σ : Slice → Type}
+    [∀ s, Iterator (σ s) Id (SearchStep s)] [∀ s, Iterators.Finite (σ s) Id]
     [∀ s, IteratorLoop (σ s) Id Id] [∀ s, LawfulIteratorLoop (σ s) Id Id]
     [ToForwardSearcher pat σ] [LawfulToForwardSearcherModel pat] {s : Slice} {pos : s.Pos} :
     pos.find? pat = none ↔ ∀ pos', pos ≤ pos' → ¬ MatchesAt pat pos' := by

src/Init/Data/String/Lemmas/Pattern/Find/String.lean

@@ -49,10 +49,9 @@ theorem contains_slice_iff {t s : Slice} :
   by_cases ht : t.isEmpty
   · simp [contains_eq_true_of_isEmpty ht s, copy_eq_empty_iff.mpr ht, String.toList_empty]
   · simp only [Bool.not_eq_true] at ht
-    have := Pattern.Model.ForwardSliceSearcher.strictPatternModel ht
     have := Pattern.Model.ForwardSliceSearcher.lawfulToForwardSearcherModel ht
     simp only [Pattern.Model.contains_eq_true_iff,
-      Pattern.Model.ForwardSliceSearcher.exists_matchesAt_iff_eq_append, isInfix_toList_iff]
+      Pattern.Model.ForwardSliceSearcher.exists_matchesAt_iff_eq_append ht, isInfix_toList_iff]
 
 @[simp]
 theorem contains_string_iff {t : String} {s : Slice} :

src/Init/Data/String/Lemmas/Pattern/Pred.lean

@@ -18,7 +18,6 @@ import Init.Data.String.Lemmas.Basic
 import Init.Data.String.Lemmas.Order
 import Init.Data.Order.Lemmas
 import Init.Data.String.OrderInstances
-import Init.Data.String.Lemmas.Iterate
 import Init.Omega
 import Init.Data.String.Lemmas.FindPos
 
@@ -28,9 +27,8 @@ namespace String.Slice.Pattern.Model.CharPred
 
 instance {p : Char → Bool} : PatternModel p where
   Matches s := ∃ c, s = singleton c ∧ p c
-
-instance {p : Char → Bool} : StrictPatternModel p where
-  not_matches_empty := by simp [PatternModel.Matches]
+  not_matches_empty := by
+    simp
 
 instance {p : Char → Bool} : NoPrefixPatternModel p :=
   .of_length_eq (by simp +contextual [PatternModel.Matches])
@@ -73,39 +71,6 @@ theorem isLongestMatchAt_iff {p : Char → Bool} {s : Slice} {pos pos' : s.Pos}
   simp +contextual [Model.isLongestMatchAt_iff, isLongestMatch_iff, ← Pos.ofSliceFrom_inj,
     Pos.get_eq_get_ofSliceFrom, Pos.ofSliceFrom_next]
 
-theorem isLongestMatchAtChain_iff {p : Char → Bool} {s : Slice} {pos pos' : s.Pos} :
-    IsLongestMatchAtChain p pos pos' ↔ pos ≤ pos' ∧ ∀ pos'', pos ≤ pos'' → (h : pos'' < pos') → p (pos''.get (Pos.ne_endPos_of_lt h)) := by
-  induction pos using WellFounded.induction Pos.wellFounded_gt with | h pos ih
-  obtain (h|rfl|h) := Std.lt_trichotomy pos pos'
-  · refine ⟨fun h => ?_, fun ⟨h₁, h₂⟩ => ?_⟩
-    · cases h with
-      | nil => exact (Std.lt_irrefl h).elim
-      | cons _ mid _ h₁ h₂ =>
-        obtain ⟨h₀, rfl, h₁'⟩ := isLongestMatchAt_iff.1 h₁
-        refine ⟨Std.le_of_lt h, fun pos'' hp₁ hp₂ => ?_⟩
-        obtain (hh|rfl) := Std.le_iff_lt_or_eq.1 hp₁
-        · exact ((ih (pos.next (Pos.ne_endPos_of_lt h)) Pos.lt_next).1 h₂).2 _ (by simpa) hp₂
-        · exact h₁'
-    · refine .cons _ (pos.next (Pos.ne_endPos_of_lt h)) _ ?_ ((ih _ Pos.lt_next).2 ?_)
-      · exact isLongestMatchAt_iff.2 ⟨Pos.ne_endPos_of_lt h, rfl, h₂ _ (by simp) h⟩
-      · exact ⟨by simpa, fun pos'' hp₁ hp₂ => h₂ _ (Std.le_trans Pos.le_next hp₁) hp₂⟩
-  · simpa using fun _ h₁ h₂ => (Std.lt_irrefl (Std.lt_of_le_of_lt h₁ h₂)).elim
-  · simpa [Std.not_le.2 h] using fun h' => (Std.not_le.2 h h'.le).elim
-
-theorem isLongestMatchAtChain_iff_toList {p : Char → Bool} {s : Slice} {pos pos' : s.Pos} :
-    IsLongestMatchAtChain p pos pos' ↔ ∃ (h : pos ≤ pos'), ∀ c, c ∈ (s.slice pos pos' h).copy.toList → p c := by
-  simp only [isLongestMatchAtChain_iff, mem_toList_copy_iff_exists_get, Pos.get_eq_get_ofSlice,
-    forall_exists_index]
-  refine ⟨fun ⟨h₁, h₂⟩ => ⟨h₁, fun c p' hp => ?_⟩, fun ⟨h₁, h₂⟩ => ⟨h₁, fun p' hp₁ hp₂ => ?_⟩⟩
-  · rintro rfl
-    exact h₂ _ Pos.le_ofSlice (by simp [Pos.ofSlice_lt_iff, h₁, hp])
-  · refine h₂ _ (Pos.slice p' _ _ hp₁ (Std.le_of_lt hp₂)) ?_ (by simp)
-    rwa [← Pos.lt_endPos_iff, ← Pos.slice_eq_endPos (h := h₁), Pos.slice_lt_slice_iff]
-
-theorem isLongestMatchAtChain_startPos_endPos_iff_toList {p : Char → Bool} {s : Slice} :
-    IsLongestMatchAtChain p s.startPos s.endPos ↔ ∀ c, c ∈ s.copy.toList → p c := by
-  simp [isLongestMatchAtChain_iff_toList]
-
 theorem isLongestRevMatchAt_iff {p : Char → Bool} {s : Slice} {pos pos' : s.Pos} :
     IsLongestRevMatchAt p pos pos' ↔ ∃ h, pos = pos'.prev h ∧ p ((pos'.prev h).get (by simp)) := by
   simp +contextual [Model.isLongestRevMatchAt_iff, isLongestRevMatch_iff, ← Pos.ofSliceTo_inj,
@@ -119,35 +84,6 @@ theorem isLongestRevMatchAt_of_get {p : Char → Bool} {s : Slice} {pos : s.Pos}
     (hc : p ((pos.prev h).get (by simp))) : IsLongestRevMatchAt p (pos.prev h) pos :=
   isLongestRevMatchAt_iff.2 ⟨h, by simp [hc]⟩
 
-theorem isLongestRevMatchAtChain_iff {p : Char → Bool} {s : Slice} {pos pos' : s.Pos} :
-    IsLongestRevMatchAtChain p pos pos' ↔ pos ≤ pos' ∧ ∀ pos'', pos ≤ pos'' → (h : pos'' < pos') → p (pos''.get (Pos.ne_endPos_of_lt h)) := by
-  induction pos' using WellFounded.induction Pos.wellFounded_lt with | h pos' ih
-  obtain (h|rfl|h) := Std.lt_trichotomy pos pos'
-  · refine ⟨fun h => ?_, fun ⟨h₁, h₂⟩ => ?_⟩
-    · cases h with
-      | nil => exact (Std.lt_irrefl h).elim
-      | cons _ _ hchain hmatch =>
-        obtain ⟨hne, hmid, hp⟩ := isLongestRevMatchAt_iff.1 hmatch
-        refine ⟨Std.le_of_lt h, fun pos'' hp₁ hp₂ => ?_⟩
-        rcases Std.le_iff_lt_or_eq.1 (Pos.le_prev_iff_lt.2 hp₂) with hh | heq
-        · exact ((ih _ Pos.prev_lt).1 (hmid ▸ hchain)).2 _ hp₁ hh
-        · exact heq ▸ hp
-    · have hne : pos' ≠ s.startPos := Slice.Pos.ne_startPos_of_lt h
-      refine .cons _ (pos'.prev hne) _ ((ih _ Pos.prev_lt).2 ?_)
-        (isLongestRevMatchAt_of_get (h₂ _ (Pos.le_prev_iff_lt.2 h) Pos.prev_lt))
-      exact ⟨Pos.le_prev_iff_lt.2 h, fun pos'' hp₁ hp₂ =>
-        h₂ _ hp₁ (Std.lt_trans hp₂ Pos.prev_lt)⟩
-  · simpa using fun _ h₁ h₂ => (Std.lt_irrefl (Std.lt_of_le_of_lt h₁ h₂)).elim
-  · simpa [Std.not_le.2 h] using fun h' => (Std.not_le.2 h h'.le).elim
-
-theorem isLongestRevMatchAtChain_iff_toList {p : Char → Bool} {s : Slice} {pos pos' : s.Pos} :
-    IsLongestRevMatchAtChain p pos pos' ↔ ∃ (h : pos ≤ pos'), ∀ c, c ∈ (s.slice pos pos' h).copy.toList → p c :=
-  isLongestRevMatchAtChain_iff.trans (isLongestMatchAtChain_iff.symm.trans isLongestMatchAtChain_iff_toList)
-
-theorem isLongestRevMatchAtChain_startPos_endPos_iff_toList {p : Char → Bool} {s : Slice} :
-    IsLongestRevMatchAtChain p s.startPos s.endPos ↔ ∀ c, c ∈ s.copy.toList → p c := by
-  simp [isLongestRevMatchAtChain_iff_toList]
-
 instance {p : Char → Bool} : LawfulForwardPatternModel p where
   skipPrefix?_eq_some_iff {s} pos := by
     simp [isLongestMatch_iff, ForwardPattern.skipPrefix?, and_comm, eq_comm (b := pos)]
@@ -192,9 +128,7 @@ namespace Decidable
 
 instance {p : Char → Prop} [DecidablePred p] : PatternModel p where
   Matches := PatternModel.Matches (decide <| p ·)
-
-instance {p : Char → Prop} [DecidablePred p] : StrictPatternModel p where
-  not_matches_empty := StrictPatternModel.not_matches_empty (pat := (decide <| p ·))
+  not_matches_empty := PatternModel.not_matches_empty (pat := (decide <| p ·))
 
 instance {p : Char → Prop} [DecidablePred p] : NoPrefixPatternModel p where
   eq_empty := NoPrefixPatternModel.eq_empty (pat := (decide <| p ·))
@@ -248,32 +182,6 @@ theorem isLongestRevMatchAt_iff_isLongestRevMatchAt_decide {p : Char → Prop} [
     IsLongestRevMatchAt p pos pos' ↔ IsLongestRevMatchAt (decide <| p ·) pos pos' := by
   simp [Model.isLongestRevMatchAt_iff, isLongestRevMatch_iff_isLongestRevMatch_decide]
 
-theorem isLongestMatchAtChain_iff_isLongestMatchAtChain_decide {p : Char → Prop} [DecidablePred p]
-    {s : Slice} {pos pos' : s.Pos} :
-    IsLongestMatchAtChain p pos pos' ↔ IsLongestMatchAtChain (decide <| p ·) pos pos' := by
-  constructor
-  · intro h; induction h with
-    | nil => exact .nil _
-    | cons _ mid _ hmatch hchain ih =>
-      exact .cons _ mid _ (isLongestMatchAt_iff_isLongestMatchAt_decide.1 hmatch) ih
-  · intro h; induction h with
-    | nil => exact .nil _
-    | cons _ mid _ hmatch hchain ih =>
-      exact .cons _ mid _ (isLongestMatchAt_iff_isLongestMatchAt_decide.2 hmatch) ih
-
-theorem isLongestRevMatchAtChain_iff_isLongestRevMatchAtChain_decide {p : Char → Prop} [DecidablePred p]
-    {s : Slice} {pos pos' : s.Pos} :
-    IsLongestRevMatchAtChain p pos pos' ↔ IsLongestRevMatchAtChain (decide <| p ·) pos pos' := by
-  constructor
-  · intro h; induction h with
-    | nil => exact .nil _
-    | cons _ _ hchain hmatch ih =>
-      exact .cons _ _ _ ih (isLongestRevMatchAt_iff_isLongestRevMatchAt_decide.1 hmatch)
-  · intro h; induction h with
-    | nil => exact .nil _
-    | cons _ _ hchain hmatch ih =>
-      exact .cons _ _ _ ih (isLongestRevMatchAt_iff_isLongestRevMatchAt_decide.2 hmatch)
-
 theorem isLongestMatchAt_iff {p : Char → Prop} [DecidablePred p] {s : Slice}
     {pos pos' : s.Pos} :
     IsLongestMatchAt p pos pos' ↔ ∃ h, pos' = pos.next h ∧ p (pos.get h) := by
@@ -411,9 +319,6 @@ theorem dropPrefix_prop_eq_dropPrefix_decide {p : Char → Prop} [DecidablePred
 theorem skipPrefix?_prop_eq_skipPrefix?_decide {p : Char → Prop} [DecidablePred p] {s : Slice} :
     s.skipPrefix? p = s.skipPrefix? (decide <| p ·) := (rfl)
 
-theorem Pos.skip?_prop_eq_skip?_decide {p : Char → Prop} [DecidablePred p] {s : Slice} {pos : s.Pos} :
-    pos.skip? p = pos.skip? (decide <| p ·) := (rfl)
-
 theorem Pattern.ForwardPattern.skipPrefix?_prop_eq_skipPrefix?_decide
     {p : Char → Prop} [DecidablePred p] {s : Slice} :
     skipPrefix? p s = skipPrefix? (decide <| p ·) s := (rfl)
@@ -424,13 +329,13 @@ theorem Pos.skipWhile_prop_eq_skipWhile_decide {p : Char → Prop} [DecidablePre
   fun_induction Pos.skipWhile curr p with
   | case1 pos nextCurr h₁ h₂ ih =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pos.skip?_prop_eq_skip?_decide, h₁, h₂, ih]
+    simp [← Pattern.ForwardPattern.skipPrefix?_prop_eq_skipPrefix?_decide, h₁, h₂, ih]
   | case2 pos nextCurr h ih =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pos.skip?_prop_eq_skip?_decide, h, ih]
+    simp [← Pattern.ForwardPattern.skipPrefix?_prop_eq_skipPrefix?_decide, h, ih]
   | case3 pos h =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pos.skip?_prop_eq_skip?_decide, h]
+    simp [← Pattern.ForwardPattern.skipPrefix?_prop_eq_skipPrefix?_decide]
 
 theorem skipPrefixWhile_prop_eq_skipPrefixWhile_decide {p : Char → Prop} [DecidablePred p]
     {s : Slice} :
@@ -447,7 +352,7 @@ theorem takeWhile_prop_eq_takeWhile_decide {p : Char → Prop} [DecidablePred p]
 
 theorem all_prop_eq_all_decide {p : Char → Prop} [DecidablePred p] {s : Slice} :
     s.all p = s.all (decide <| p ·) := by
-  simp only [all, skipPrefixWhile_prop_eq_skipPrefixWhile_decide]
+  simp only [all, dropWhile_prop_eq_dropWhile_decide]
 
 theorem find?_prop_eq_find?_decide {p : Char → Prop} [DecidablePred p] {s : Slice} :
     s.find? p = s.find? (decide <| p ·) :=
@@ -478,22 +383,19 @@ theorem Pattern.BackwardPattern.skipSuffix?_prop_eq_skipSuffix?_decide
     {p : Char → Prop} [DecidablePred p] {s : Slice} :
     skipSuffix? p s = skipSuffix? (decide <| p ·) s := (rfl)
 
-theorem Pos.revSkip?_prop_eq_revSkip?_decide {p : Char → Prop} [DecidablePred p] {s : Slice} {pos : s.Pos} :
-    pos.revSkip? p = pos.revSkip? (decide <| p ·) := (rfl)
-
 theorem Pos.revSkipWhile_prop_eq_revSkipWhile_decide {p : Char → Prop} [DecidablePred p]
     {s : Slice} (curr : s.Pos) :
     Pos.revSkipWhile curr p = Pos.revSkipWhile curr (decide <| p ·) := by
   fun_induction Pos.revSkipWhile curr p with
   | case1 pos nextCurr h₁ h₂ ih =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pos.revSkip?_prop_eq_revSkip?_decide, h₁, h₂, ih]
+    simp [← Pattern.BackwardPattern.skipSuffix?_prop_eq_skipSuffix?_decide, h₁, h₂, ih]
   | case2 pos nextCurr h ih =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pos.revSkip?_prop_eq_revSkip?_decide, h, ih]
+    simp [← Pattern.BackwardPattern.skipSuffix?_prop_eq_skipSuffix?_decide, h, ih]
   | case3 pos h =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pos.revSkip?_prop_eq_revSkip?_decide, h]
+    simp [← Pattern.BackwardPattern.skipSuffix?_prop_eq_skipSuffix?_decide]
 
 theorem skipSuffixWhile_prop_eq_skipSuffixWhile_decide {p : Char → Prop} [DecidablePred p]
     {s : Slice} :
@@ -510,8 +412,4 @@ theorem takeEndWhile_prop_eq_takeEndWhile_decide {p : Char → Prop} [DecidableP
     s.takeEndWhile p = s.takeEndWhile (decide <| p ·) := by
   simp only [takeEndWhile]; exact congrArg _ skipSuffixWhile_prop_eq_skipSuffixWhile_decide
 
-theorem revAll_prop_eq_revAll_decide {p : Char → Prop} [DecidablePred p] {s : Slice} :
-    s.revAll p = s.revAll (decide <| p ·) := by
-  simp only [revAll, skipSuffixWhile_prop_eq_skipSuffixWhile_decide]
-
 end String.Slice

src/Init/Data/String/Lemmas/Pattern/Split/Basic.lean

@@ -36,7 +36,7 @@ This gives a low-level correctness proof from which higher-level API lemmas can
 namespace String.Slice.Pattern.Model
 
 @[cbv_opaque]
-public protected noncomputable def split {ρ : Type} (pat : ρ) [PatternModel pat] [StrictPatternModel pat] {s : Slice}
+public protected noncomputable def split {ρ : Type} (pat : ρ) [PatternModel pat] {s : Slice}
     (firstRejected curr : s.Pos) (hle : firstRejected ≤ curr) : List s.Subslice :=
   if h : curr = s.endPos then
     [s.subslice _ _ hle]
@@ -49,12 +49,12 @@ public protected noncomputable def split {ρ : Type} (pat : ρ) [PatternModel pa
 termination_by curr
 
 @[simp]
-public theorem split_endPos {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat] {s : Slice}
+public theorem split_endPos {ρ : Type} {pat : ρ} [PatternModel pat] {s : Slice}
     {firstRejected : s.Pos} :
     Model.split (s := s) pat firstRejected s.endPos (by simp) = [s.subslice firstRejected s.endPos (by simp)] := by
   simp [Model.split]
 
-public theorem split_eq_of_isLongestMatchAt {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat]
+public theorem split_eq_of_isLongestMatchAt {ρ : Type} {pat : ρ} [PatternModel pat]
     {s : Slice} {firstRejected start stop : s.Pos} {hle} (h : IsLongestMatchAt pat start stop) :
     Model.split pat firstRejected start hle =
       s.subslice _ _ hle :: Model.split pat stop stop (by exact Std.le_refl _) := by
@@ -63,7 +63,7 @@ public theorem split_eq_of_isLongestMatchAt {ρ : Type} {pat : ρ} [PatternModel
   · congr <;> exact (matchAt?_eq_some_iff.1 ‹_›).eq h
   · simp [matchAt?_eq_some_iff.2 ‹_›] at *
 
-public theorem split_eq_of_not_matchesAt {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat]
+public theorem split_eq_of_not_matchesAt {ρ : Type} {pat : ρ} [PatternModel pat]
     {s : Slice} {firstRejected start} (stop : s.Pos) (h₀ : start ≤ stop) {hle}
     (h : ∀ p, start ≤ p → p < stop → ¬ MatchesAt pat p) :
     Model.split pat firstRejected start hle =
@@ -80,7 +80,7 @@ public theorem split_eq_of_not_matchesAt {ρ : Type} {pat : ρ} [PatternModel pa
   · obtain rfl : start = stop := Std.le_antisymm h₀ (Std.not_lt.1 h')
     simp
 
-public theorem split_eq_next_of_not_matchesAt {ρ : Type} {pat : ρ} [PatternModel pat] [StrictPatternModel pat]
+public theorem split_eq_next_of_not_matchesAt {ρ : Type} {pat : ρ} [PatternModel pat]
     {s : Slice} {firstRejected start} {hle} (hs : start ≠ s.endPos) (h : ¬ MatchesAt pat start) :
     Model.split pat firstRejected start hle =
       Model.split pat firstRejected (start.next hs) (by exact Std.le_trans hle (by simp)) := by
@@ -103,7 +103,7 @@ def splitFromSteps {s : Slice} (currPos : s.Pos) (l : List (SearchStep s)) : Lis
   | .matched p q :: l => s.subslice! currPos p :: splitFromSteps q l
 
 theorem IsValidSearchFrom.splitFromSteps_eq_extend_split {ρ : Type} (pat : ρ)
-    [PatternModel pat] [StrictPatternModel pat] (l : List (SearchStep s)) (pos pos' : s.Pos) (h₀ : pos ≤ pos')
+    [PatternModel pat] (l : List (SearchStep s)) (pos pos' : s.Pos) (h₀ : pos ≤ pos')
     (h' : ∀ p, pos ≤ p → p < pos' → ¬ MatchesAt pat p)
     (h : IsValidSearchFrom pat pos' l) :
     splitFromSteps pos l = Model.split pat pos pos' h₀ := by
@@ -155,7 +155,7 @@ end Model
 open Model
 
 @[cbv_eval]
-public theorem toList_splitToSubslice_eq_modelSplit {ρ : Type} (pat : ρ) [PatternModel pat] [StrictPatternModel pat]
+public theorem toList_splitToSubslice_eq_modelSplit {ρ : Type} (pat : ρ) [PatternModel pat]
     {σ : Slice → Type} [ToForwardSearcher pat σ] [∀ s, Std.Iterator (σ s) Id (SearchStep s)]
     [∀ s, Std.Iterators.Finite (σ s) Id] [LawfulToForwardSearcherModel pat] (s : Slice) :
     (s.splitToSubslice pat).toList = Model.split pat s.startPos s.startPos (by exact Std.le_refl _) := by
@@ -168,7 +168,7 @@ end Pattern
 open Pattern
 
 public theorem toList_splitToSubslice_of_isEmpty {ρ : Type} (pat : ρ)
-    [Model.PatternModel pat] [Model.StrictPatternModel pat] {σ : Slice → Type}
+    [Model.PatternModel pat] {σ : Slice → Type}
     [ToForwardSearcher pat σ] [∀ s, Std.Iterator (σ s) Id (SearchStep s)]
     [∀ s, Std.Iterators.Finite (σ s) Id] [Model.LawfulToForwardSearcherModel pat] {s : Slice}
     (h : s.isEmpty = true) :
@@ -182,7 +182,7 @@ public theorem toList_split_eq_splitToSubslice {ρ : Type} (pat : ρ) {σ : Slic
   simp [split, Std.Iter.toList_map]
 
 public theorem toList_split_of_isEmpty {ρ : Type} (pat : ρ)
-    [Model.PatternModel pat] [Model.StrictPatternModel pat] {σ : Slice → Type}
+    [Model.PatternModel pat] {σ : Slice → Type}
     [ToForwardSearcher pat σ] [∀ s, Std.Iterator (σ s) Id (SearchStep s)]
     [∀ s, Std.Iterators.Finite (σ s) Id] [Model.LawfulToForwardSearcherModel pat] {s : Slice}
     (h : s.isEmpty = true) :
@@ -200,7 +200,7 @@ public theorem split_eq_split_toSlice {ρ : Type} {pat : ρ} {σ : Slice → Typ
 
 @[simp]
 public theorem toList_split_empty {ρ : Type} (pat : ρ)
-    [Model.PatternModel pat] [Model.StrictPatternModel pat] {σ : Slice → Type}
+    [Model.PatternModel pat] {σ : Slice → Type}
     [ToForwardSearcher pat σ] [∀ s, Std.Iterator (σ s) Id (SearchStep s)]
     [∀ s, Std.Iterators.Finite (σ s) Id] [Model.LawfulToForwardSearcherModel pat] :
     ("".split pat).toList.map Slice.copy = [""] := by

src/Init/Data/String/Lemmas/Pattern/String/Basic.lean

@@ -10,9 +10,6 @@ public import Init.Data.String.Pattern.String
 public import Init.Data.String.Lemmas.Pattern.Basic
 import Init.Data.String.Lemmas.IsEmpty
 import Init.Data.String.Lemmas.Basic
-import Init.Data.String.Lemmas.Intercalate
-import Init.Data.String.OrderInstances
-import Init.Data.String.Lemmas.Splits
 import Init.Data.ByteArray.Lemmas
 import Init.Omega
 
@@ -23,10 +20,17 @@ namespace String.Slice.Pattern.Model
 namespace ForwardSliceSearcher
 
 instance {pat : Slice} : PatternModel pat where
-  Matches s := s = pat.copy
+  /-
+  See the docstring of `PatternModel` for an explanation about why we disallow matching the
+  empty string.
 
-theorem strictPatternModel {pat : Slice} (hpat : pat.isEmpty = false) : StrictPatternModel pat where
-  not_matches_empty := by simpa [PatternModel.Matches]
+  Requiring `s ≠ ""` is a trick that allows us to give a `PatternModel` instance
+  unconditionally, without forcing `pat.copy` to be non-empty (which would make it very awkward
+  to state theorems about the instance). It does not change anything about the fact that all lemmas
+  about this instance require `pat.isEmpty = false`.
+  -/
+  Matches s := s ≠ "" ∧ s = pat.copy
+  not_matches_empty := by simp
 
 instance {pat : Slice} : NoPrefixPatternModel pat :=
   .of_length_eq (by simp +contextual [PatternModel.Matches])
@@ -34,111 +38,59 @@ instance {pat : Slice} : NoPrefixPatternModel pat :=
 instance {pat : Slice} : NoSuffixPatternModel pat :=
   .of_length_eq (by simp +contextual [PatternModel.Matches])
 
-theorem isMatch_iff {pat s : Slice} {pos : s.Pos} :
+theorem isMatch_iff {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
     IsMatch pat pos ↔ (s.sliceTo pos).copy = pat.copy := by
-  simp [Model.isMatch_iff, PatternModel.Matches]
+  simp only [Model.isMatch_iff, PatternModel.Matches, ne_eq, copy_eq_empty_iff,
+    Bool.not_eq_true, and_iff_right_iff_imp]
+  intro h'
+  rw [← isEmpty_copy (s := s.sliceTo pos), h', isEmpty_copy, h]
 
-theorem isRevMatch_iff {pat s : Slice} {pos : s.Pos} :
+theorem isRevMatch_iff {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
     IsRevMatch pat pos ↔ (s.sliceFrom pos).copy = pat.copy := by
-  simp [Model.isRevMatch_iff, PatternModel.Matches]
+  simp only [Model.isRevMatch_iff, PatternModel.Matches, ne_eq, copy_eq_empty_iff,
+    Bool.not_eq_true, and_iff_right_iff_imp]
+  intro h'
+  rw [← isEmpty_copy (s := s.sliceFrom pos), h', isEmpty_copy, h]
 
-theorem isLongestMatch_iff {pat s : Slice} {pos : s.Pos} :
+theorem isLongestMatch_iff {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
     IsLongestMatch pat pos ↔ (s.sliceTo pos).copy = pat.copy := by
-  rw [isLongestMatch_iff_isMatch, isMatch_iff]
+  rw [isLongestMatch_iff_isMatch, isMatch_iff h]
 
-theorem isLongestRevMatch_iff {pat s : Slice} {pos : s.Pos} :
+theorem isLongestRevMatch_iff {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
     IsLongestRevMatch pat pos ↔ (s.sliceFrom pos).copy = pat.copy := by
-  rw [isLongestRevMatch_iff_isRevMatch, isRevMatch_iff]
+  rw [isLongestRevMatch_iff_isRevMatch, isRevMatch_iff h]
 
-theorem isLongestMatchAt_iff {pat s : Slice} {pos₁ pos₂ : s.Pos} :
+theorem isLongestMatchAt_iff {pat s : Slice} {pos₁ pos₂ : s.Pos} (h : pat.isEmpty = false) :
     IsLongestMatchAt pat pos₁ pos₂ ↔ ∃ h, (s.slice pos₁ pos₂ h).copy = pat.copy := by
-  simp [Model.isLongestMatchAt_iff, isLongestMatch_iff]
+  simp [Model.isLongestMatchAt_iff, isLongestMatch_iff h]
 
-theorem isLongestMatchAtChain_iff {pat s : Slice} {pos₁ pos₂ : s.Pos} :
-    IsLongestMatchAtChain pat pos₁ pos₂ ↔
-      ∃ h n, (s.slice pos₁ pos₂ h).copy = String.join (List.replicate n pat.copy) := by
-  refine ⟨fun h => ⟨h.le, ?_⟩, fun ⟨h, n, h'⟩ => ?_⟩
-  · induction h with
-    | nil => simpa using ⟨0, by simp⟩
-    | cons p₁ p₂ p₃ h₁ h₂ ih =>
-      rw [isLongestMatchAt_iff] at h₁
-      obtain ⟨n, ih⟩ := ih
-      obtain ⟨h₀, h₁⟩ := h₁
-      have : (s.slice p₁ p₃ (Std.le_trans h₀ h₂.le)).copy = (s.slice p₁ p₂ h₀).copy ++ (s.slice p₂ p₃ h₂.le).copy := by
-        simp [(Slice.Pos.slice p₂ _ _ h₀ h₂.le).splits.eq_append]
-      refine ⟨n + 1, ?_⟩
-      rw [this, h₁, ih]
-      simp [← String.join_cons, ← List.replicate_succ]
-  · induction n generalizing pos₁ pos₂ with
-    | zero => simp_all
-    | succ n ih =>
-      rw [List.replicate_succ, String.join_cons] at h'
-      refine .cons _ (Pos.ofSlice (Pos.ofEqAppend h')) _ ?_ (ih ?_ Pos.ofSlice_le ?_)
-      · simpa [isLongestMatchAt_iff] using (Pos.splits_ofEqAppend h').copy_sliceTo_eq
-      · simpa [sliceFrom_slice ▸ (Pos.splits_ofEqAppend h').copy_sliceFrom_eq] using ⟨n, rfl⟩
-      · simpa using (Pos.splits_ofEqAppend h').copy_sliceFrom_eq
-
-theorem isLongestMatchAtChain_startPos_endPos_iff {pat s : Slice} :
-    IsLongestMatchAtChain pat s.startPos s.endPos ↔
-      ∃ n, s.copy = String.join (List.replicate n pat.copy) := by
-  simp [isLongestMatchAtChain_iff]
-
-theorem isLongestRevMatchAt_iff {pat s : Slice} {pos₁ pos₂ : s.Pos} :
+theorem isLongestRevMatchAt_iff {pat s : Slice} {pos₁ pos₂ : s.Pos} (h : pat.isEmpty = false) :
     IsLongestRevMatchAt pat pos₁ pos₂ ↔ ∃ h, (s.slice pos₁ pos₂ h).copy = pat.copy := by
-  simp [Model.isLongestRevMatchAt_iff, isLongestRevMatch_iff]
+  simp [Model.isLongestRevMatchAt_iff, isLongestRevMatch_iff h]
 
-theorem isLongestRevMatchAtChain_iff {pat s : Slice} {pos₁ pos₂ : s.Pos} :
-    IsLongestRevMatchAtChain pat pos₁ pos₂ ↔
-      ∃ h n, (s.slice pos₁ pos₂ h).copy = String.join (List.replicate n pat.copy) := by
-  refine ⟨fun h => ⟨h.le, ?_⟩, fun ⟨h, n, h'⟩ => ?_⟩
-  · induction h with
-    | nil => simpa using ⟨0, by simp⟩
-    | cons p₂ p₃ h₁ h₂ ih =>
-      rw [isLongestRevMatchAt_iff] at h₂
-      obtain ⟨n, ih⟩ := ih
-      obtain ⟨h₀, h₂⟩ := h₂
-      have : (s.slice pos₁ p₃ (Std.le_trans h₁.le h₀)).copy = (s.slice pos₁ p₂ h₁.le).copy ++ (s.slice p₂ p₃ h₀).copy := by
-        simp [(Slice.Pos.slice p₂ _ _ (IsLongestRevMatchAtChain.le ‹_›) h₀).splits.eq_append]
-      refine ⟨n + 1, ?_⟩
-      rw [this, h₂, ih]
-      simp [← List.replicate_append_replicate]
-  · induction n generalizing pos₁ pos₂ with
-    | zero => simp_all
-    | succ n ih =>
-      have h'' : (s.slice pos₁ pos₂ h).copy = String.join (List.replicate n pat.copy) ++ pat.copy := by
-        rw [h', List.replicate_succ', String.join_append]; simp
-      refine .cons _ (Pos.ofSlice (Pos.ofEqAppend h'')) _ (ih ?_ Pos.le_ofSlice ?_) ?_
-      · simpa [sliceTo_slice ▸ (Pos.splits_ofEqAppend h'').copy_sliceTo_eq] using ⟨n, rfl⟩
-      · simpa using (Pos.splits_ofEqAppend h'').copy_sliceTo_eq
-      · simpa [isLongestRevMatchAt_iff] using (Pos.splits_ofEqAppend h'').copy_sliceFrom_eq
-
-theorem isLongestRevMatchAtChain_startPos_endPos_iff {pat s : Slice} :
-    IsLongestRevMatchAtChain pat s.startPos s.endPos ↔
-      ∃ n, s.copy = String.join (List.replicate n pat.copy) := by
-  simp [isLongestRevMatchAtChain_iff]
-
-theorem isLongestMatchAt_iff_splits {pat s : Slice} {pos₁ pos₂ : s.Pos} :
+theorem isLongestMatchAt_iff_splits {pat s : Slice} {pos₁ pos₂ : s.Pos} (h : pat.isEmpty = false) :
     IsLongestMatchAt pat pos₁ pos₂ ↔ ∃ t₁ t₂, pos₁.Splits t₁ (pat.copy ++ t₂) ∧
       pos₂.Splits (t₁ ++ pat.copy) t₂ := by
-  simp only [isLongestMatchAt_iff, copy_slice_eq_iff_splits]
+  simp only [isLongestMatchAt_iff h, copy_slice_eq_iff_splits]
 
-theorem isLongestRevMatchAt_iff_splits {pat s : Slice} {pos₁ pos₂ : s.Pos} :
+theorem isLongestRevMatchAt_iff_splits {pat s : Slice} {pos₁ pos₂ : s.Pos}
+    (h : pat.isEmpty = false) :
     IsLongestRevMatchAt pat pos₁ pos₂ ↔ ∃ t₁ t₂, pos₁.Splits t₁ (pat.copy ++ t₂) ∧
       pos₂.Splits (t₁ ++ pat.copy) t₂ := by
-  simp only [isLongestRevMatchAt_iff, copy_slice_eq_iff_splits]
+  simp only [isLongestRevMatchAt_iff h, copy_slice_eq_iff_splits]
 
-theorem isLongestMatch_iff_splits {pat s : Slice} {pos : s.Pos} :
+theorem isLongestMatch_iff_splits {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
     IsLongestMatch pat pos ↔ ∃ t, pos.Splits pat.copy t := by
-  rw [isLongestMatch_iff, copy_sliceTo_eq_iff_exists_splits]
+  rw [isLongestMatch_iff h, copy_sliceTo_eq_iff_exists_splits]
 
-theorem isLongestRevMatch_iff_splits {pat s : Slice} {pos : s.Pos} :
+theorem isLongestRevMatch_iff_splits {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
     IsLongestRevMatch pat pos ↔ ∃ t, pos.Splits t pat.copy := by
-  rw [isLongestRevMatch_iff, copy_sliceFrom_eq_iff_exists_splits]
+  rw [isLongestRevMatch_iff h, copy_sliceFrom_eq_iff_exists_splits]
 
 theorem isLongestMatchAt_iff_extract {pat s : Slice} {pos₁ pos₂ : s.Pos} (h : pat.isEmpty = false) :
     IsLongestMatchAt pat pos₁ pos₂ ↔
       s.copy.toByteArray.extract pos₁.offset.byteIdx pos₂.offset.byteIdx = pat.copy.toByteArray := by
-  rw [isLongestMatchAt_iff]
+  rw [isLongestMatchAt_iff h]
   refine ⟨fun ⟨h, h'⟩ => ?_, fun h' => ?_⟩
   · simp [← h', toByteArray_copy_slice]
   · rw [← Slice.toByteArray_copy_ne_empty_iff, ← h', ne_eq, ByteArray.extract_eq_empty_iff] at h
@@ -150,7 +102,7 @@ theorem isLongestRevMatchAt_iff_extract {pat s : Slice} {pos₁ pos₂ : s.Pos}
     IsLongestRevMatchAt pat pos₁ pos₂ ↔
       s.copy.toByteArray.extract pos₁.offset.byteIdx pos₂.offset.byteIdx =
         pat.copy.toByteArray := by
-  rw [isLongestRevMatchAt_iff]
+  rw [isLongestRevMatchAt_iff h]
   refine ⟨fun ⟨h, h'⟩ => ?_, fun h' => ?_⟩
   · simp [← h', toByteArray_copy_slice]
   · rw [← Slice.toByteArray_copy_ne_empty_iff, ← h', ne_eq, ByteArray.extract_eq_empty_iff] at h
@@ -178,21 +130,21 @@ theorem offset_of_isLongestRevMatchAt {pat s : Slice} {pos₁ pos₂ : s.Pos}
   suffices pos₂.offset.byteIdx ≤ s.utf8ByteSize by omega
   simpa [Pos.le_iff, Pos.Raw.le_iff] using pos₂.le_endPos
 
-theorem matchesAt_iff_splits {pat s : Slice} {pos : s.Pos} :
+theorem matchesAt_iff_splits {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
     MatchesAt pat pos ↔ ∃ t₁ t₂, pos.Splits t₁ (pat.copy ++ t₂) := by
-  simp only [matchesAt_iff_exists_isLongestMatchAt, isLongestMatchAt_iff_splits]
+  simp only [matchesAt_iff_exists_isLongestMatchAt, isLongestMatchAt_iff_splits h]
   exact ⟨fun ⟨e, t₁, t₂, ht₁, ht₂⟩ => ⟨t₁, t₂, ht₁⟩,
     fun ⟨t₁, t₂, ht⟩ => ⟨ht.rotateRight, t₁, t₂, ht, ht.splits_rotateRight⟩⟩
 
-theorem revMatchesAt_iff_splits {pat s : Slice} {pos : s.Pos} :
+theorem revMatchesAt_iff_splits {pat s : Slice} {pos : s.Pos} (h : pat.isEmpty = false) :
     RevMatchesAt pat pos ↔ ∃ t₁ t₂, pos.Splits (t₁ ++ pat.copy) t₂ := by
-  simp only [revMatchesAt_iff_exists_isLongestRevMatchAt, isLongestRevMatchAt_iff_splits]
+  simp only [revMatchesAt_iff_exists_isLongestRevMatchAt, isLongestRevMatchAt_iff_splits h]
   exact ⟨fun ⟨e, t₁, t₂, ht₁, ht₂⟩ => ⟨t₁, t₂, ht₂⟩,
     fun ⟨t₁, t₂, ht⟩ => ⟨ht.rotateLeft, t₁, t₂, ht.splits_rotateLeft, ht⟩⟩
 
-theorem exists_matchesAt_iff_eq_append {pat s : Slice} :
+theorem exists_matchesAt_iff_eq_append {pat s : Slice} (h : pat.isEmpty = false) :
     (∃ (pos : s.Pos), MatchesAt pat pos) ↔ ∃ t₁ t₂, s.copy = t₁ ++ pat.copy ++ t₂ := by
-  simp only [matchesAt_iff_splits]
+  simp only [matchesAt_iff_splits h]
   constructor
   · rintro ⟨pos, t₁, t₂, hsplit⟩
     exact ⟨t₁, t₂, by rw [hsplit.eq_append, append_assoc]⟩
@@ -202,9 +154,9 @@ theorem exists_matchesAt_iff_eq_append {pat s : Slice} :
         ⟨t₁, pat.copy ++ t₂, by rw [← append_assoc]; exact heq, rfl⟩
     exact ⟨s.pos _ hvalid, t₁, t₂, ⟨by rw [← append_assoc]; exact heq, by simp⟩⟩
 
-theorem exists_revMatchesAt_iff_eq_append {pat s : Slice} :
+theorem exists_revMatchesAt_iff_eq_append {pat s : Slice} (h : pat.isEmpty = false) :
     (∃ (pos : s.Pos), RevMatchesAt pat pos) ↔ ∃ t₁ t₂, s.copy = t₁ ++ pat.copy ++ t₂ := by
-  simp only [revMatchesAt_iff_splits]
+  simp only [revMatchesAt_iff_splits h]
   constructor
   · rintro ⟨pos, t₁, t₂, hsplit⟩
     exact ⟨t₁, t₂, by rw [hsplit.eq_append, append_assoc]⟩
@@ -281,10 +233,8 @@ end ForwardSliceSearcher
 namespace ForwardStringSearcher
 
 instance {pat : String} : PatternModel pat where
-  Matches s := s = pat
-
-theorem strictPatternModel {pat : String} (h : pat ≠ "") : StrictPatternModel pat where
-  not_matches_empty := by simpa [PatternModel.Matches]
+  Matches s := s ≠ "" ∧ s = pat
+  not_matches_empty := by simp
 
 instance {pat : String} : NoPrefixPatternModel pat :=
   .of_length_eq (by simp +contextual [PatternModel.Matches])
@@ -317,60 +267,12 @@ theorem isLongestMatchAt_iff_isLongestMatchAt_toSlice {pat : String} {s : Slice}
       IsLongestMatchAt (ρ := Slice) pat.toSlice pos₁ pos₂ := by
   simp [Model.isLongestMatchAt_iff, isLongestMatch_iff_isLongestMatch_toSlice]
 
-theorem isLongestMatchAtChain_iff_isLongestMatchAtChain_toSlice {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
-    IsLongestMatchAtChain pat pos₁ pos₂ ↔
-      IsLongestMatchAtChain pat.toSlice pos₁ pos₂ := by
-  refine ⟨fun h => ?_, fun h => ?_⟩
-  · induction h with
-    | nil => simp
-    | cons p₁ p₂ p₃ h₁ h₂ ih =>
-      exact .cons _ _ _ (isLongestMatchAt_iff_isLongestMatchAt_toSlice.1 h₁) ih
-  · induction h with
-    | nil => simp
-    | cons p₁ p₂ p₃ h₁ h₂ ih =>
-      exact .cons _ _ _ (isLongestMatchAt_iff_isLongestMatchAt_toSlice.2 h₁) ih
-
-theorem isLongestMatchAtChain_iff {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
-    IsLongestMatchAtChain pat pos₁ pos₂ ↔
-      ∃ h n, (s.slice pos₁ pos₂ h).copy = String.join (List.replicate n pat) := by
-  simp [isLongestMatchAtChain_iff_isLongestMatchAtChain_toSlice,
-    ForwardSliceSearcher.isLongestMatchAtChain_iff]
-
-theorem isLongestMatchAtChain_startPos_endPos_iff {pat : String} {s : Slice} :
-    IsLongestMatchAtChain pat s.startPos s.endPos ↔
-      ∃ n, s.copy = String.join (List.replicate n pat) := by
-  simp [isLongestMatchAtChain_iff]
-
 theorem isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice {pat : String} {s : Slice}
     {pos₁ pos₂ : s.Pos} :
     IsLongestRevMatchAt (ρ := String) pat pos₁ pos₂ ↔
       IsLongestRevMatchAt (ρ := Slice) pat.toSlice pos₁ pos₂ := by
   simp [Model.isLongestRevMatchAt_iff, isLongestRevMatch_iff_isLongestRevMatch_toSlice]
 
-theorem isLongestRevMatchAtChain_iff_isLongestRevMatchAtChain_toSlice {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
-    IsLongestRevMatchAtChain pat pos₁ pos₂ ↔
-      IsLongestRevMatchAtChain pat.toSlice pos₁ pos₂ := by
-  refine ⟨fun h => ?_, fun h => ?_⟩
-  · induction h with
-    | nil => simp
-    | cons p₂ p₃ _ hmatch ih =>
-      exact .cons _ _ _ ih (isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice.1 hmatch)
-  · induction h with
-    | nil => simp
-    | cons p₂ p₃ _ hmatch ih =>
-      exact .cons _ _ _ ih (isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice.2 hmatch)
-
-theorem isLongestRevMatchAtChain_iff {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
-    IsLongestRevMatchAtChain pat pos₁ pos₂ ↔
-      ∃ h n, (s.slice pos₁ pos₂ h).copy = String.join (List.replicate n pat) := by
-  simp [isLongestRevMatchAtChain_iff_isLongestRevMatchAtChain_toSlice,
-    ForwardSliceSearcher.isLongestRevMatchAtChain_iff]
-
-theorem isLongestRevMatchAtChain_startPos_endPos_iff {pat : String} {s : Slice} :
-    IsLongestRevMatchAtChain pat s.startPos s.endPos ↔
-      ∃ n, s.copy = String.join (List.replicate n pat) := by
-  simp [isLongestRevMatchAtChain_iff]
-
 theorem matchesAt_iff_toSlice {pat : String} {s : Slice} {pos : s.Pos} :
     MatchesAt (ρ := String) pat pos ↔ MatchesAt (ρ := Slice) pat.toSlice pos := by
   simp [matchesAt_iff_exists_isLongestMatchAt, isLongestMatchAt_iff_isLongestMatchAt_toSlice]
@@ -380,55 +282,61 @@ theorem revMatchesAt_iff_toSlice {pat : String} {s : Slice} {pos : s.Pos} :
   simp [revMatchesAt_iff_exists_isLongestRevMatchAt,
     isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice]
 
-theorem isMatch_iff {pat : String} {s : Slice} {pos : s.Pos} :
+private theorem toSlice_isEmpty (h : pat ≠ "") : pat.toSlice.isEmpty = false := by
+  rwa [isEmpty_toSlice, isEmpty_eq_false_iff]
+
+theorem isMatch_iff {pat : String} {s : Slice} {pos : s.Pos} (h : pat ≠ "") :
     IsMatch pat pos ↔ (s.sliceTo pos).copy = pat := by
-  rw [isMatch_iff_slice, ForwardSliceSearcher.isMatch_iff]
+  rw [isMatch_iff_slice, ForwardSliceSearcher.isMatch_iff (toSlice_isEmpty h)]
   simp
 
-theorem isRevMatch_iff {pat : String} {s : Slice} {pos : s.Pos} :
+theorem isRevMatch_iff {pat : String} {s : Slice} {pos : s.Pos} (h : pat ≠ "") :
     IsRevMatch pat pos ↔ (s.sliceFrom pos).copy = pat := by
-  rw [isRevMatch_iff_slice, ForwardSliceSearcher.isRevMatch_iff]
+  rw [isRevMatch_iff_slice, ForwardSliceSearcher.isRevMatch_iff (toSlice_isEmpty h)]
   simp
 
-theorem isLongestMatch_iff {pat : String} {s : Slice} {pos : s.Pos} :
+theorem isLongestMatch_iff {pat : String} {s : Slice} {pos : s.Pos} (h : pat ≠ "") :
     IsLongestMatch pat pos ↔ (s.sliceTo pos).copy = pat := by
-  rw [isLongestMatch_iff_isMatch, isMatch_iff]
+  rw [isLongestMatch_iff_isMatch, isMatch_iff h]
 
-theorem isLongestRevMatch_iff {pat : String} {s : Slice} {pos : s.Pos} :
+theorem isLongestRevMatch_iff {pat : String} {s : Slice} {pos : s.Pos} (h : pat ≠ "") :
     IsLongestRevMatch pat pos ↔ (s.sliceFrom pos).copy = pat := by
-  rw [isLongestRevMatch_iff_isRevMatch, isRevMatch_iff]
+  rw [isLongestRevMatch_iff_isRevMatch, isRevMatch_iff h]
 
-theorem isLongestMatchAt_iff {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
+theorem isLongestMatchAt_iff {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} (h : pat ≠ "") :
     IsLongestMatchAt pat pos₁ pos₂ ↔ ∃ h, (s.slice pos₁ pos₂ h).copy = pat := by
   rw [isLongestMatchAt_iff_isLongestMatchAt_toSlice,
-    ForwardSliceSearcher.isLongestMatchAt_iff]
+    ForwardSliceSearcher.isLongestMatchAt_iff (toSlice_isEmpty h)]
   simp
 
-theorem isLongestRevMatchAt_iff {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
+theorem isLongestRevMatchAt_iff {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} (h : pat ≠ "") :
     IsLongestRevMatchAt pat pos₁ pos₂ ↔ ∃ h, (s.slice pos₁ pos₂ h).copy = pat := by
   rw [isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice,
-    ForwardSliceSearcher.isLongestRevMatchAt_iff]
+    ForwardSliceSearcher.isLongestRevMatchAt_iff (toSlice_isEmpty h)]
   simp
 
-theorem isLongestMatchAt_iff_splits {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
+theorem isLongestMatchAt_iff_splits {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos}
+    (h : pat ≠ "") :
     IsLongestMatchAt pat pos₁ pos₂ ↔
       ∃ t₁ t₂, pos₁.Splits t₁ (pat ++ t₂) ∧ pos₂.Splits (t₁ ++ pat) t₂ := by
   rw [isLongestMatchAt_iff_isLongestMatchAt_toSlice,
-    ForwardSliceSearcher.isLongestMatchAt_iff_splits]
+    ForwardSliceSearcher.isLongestMatchAt_iff_splits (toSlice_isEmpty h)]
   simp
 
-theorem isLongestRevMatchAt_iff_splits {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} :
+theorem isLongestRevMatchAt_iff_splits {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos}
+    (h : pat ≠ "") :
     IsLongestRevMatchAt pat pos₁ pos₂ ↔
       ∃ t₁ t₂, pos₁.Splits t₁ (pat ++ t₂) ∧ pos₂.Splits (t₁ ++ pat) t₂ := by
   rw [isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice,
-    ForwardSliceSearcher.isLongestRevMatchAt_iff_splits]
+    ForwardSliceSearcher.isLongestRevMatchAt_iff_splits (toSlice_isEmpty h)]
   simp
 
-theorem isLongestMatchAt_iff_extract {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos} (h : pat ≠ "") :
+theorem isLongestMatchAt_iff_extract {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos}
+    (h : pat ≠ "") :
     IsLongestMatchAt pat pos₁ pos₂ ↔
       s.copy.toByteArray.extract pos₁.offset.byteIdx pos₂.offset.byteIdx = pat.toByteArray := by
   rw [isLongestMatchAt_iff_isLongestMatchAt_toSlice,
-    ForwardSliceSearcher.isLongestMatchAt_iff_extract (by simpa)]
+    ForwardSliceSearcher.isLongestMatchAt_iff_extract (toSlice_isEmpty h)]
   simp
 
 theorem isLongestRevMatchAt_iff_extract {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos}
@@ -436,38 +344,38 @@ theorem isLongestRevMatchAt_iff_extract {pat : String} {s : Slice} {pos₁ pos
     IsLongestRevMatchAt pat pos₁ pos₂ ↔
       s.copy.toByteArray.extract pos₁.offset.byteIdx pos₂.offset.byteIdx = pat.toByteArray := by
   rw [isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice,
-    ForwardSliceSearcher.isLongestRevMatchAt_iff_extract (by simpa)]
+    ForwardSliceSearcher.isLongestRevMatchAt_iff_extract (toSlice_isEmpty h)]
   simp
 
 theorem offset_of_isLongestMatchAt {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos}
     (h : pat ≠ "") (h' : IsLongestMatchAt pat pos₁ pos₂) :
     pos₂.offset = pos₁.offset.increaseBy pat.utf8ByteSize := by
   rw [show pat.utf8ByteSize = pat.toSlice.utf8ByteSize from utf8ByteSize_toSlice.symm]
-  exact ForwardSliceSearcher.offset_of_isLongestMatchAt (by simpa)
+  exact ForwardSliceSearcher.offset_of_isLongestMatchAt (toSlice_isEmpty h)
     (isLongestMatchAt_iff_isLongestMatchAt_toSlice.1 h')
 
 theorem offset_of_isLongestRevMatchAt {pat : String} {s : Slice} {pos₁ pos₂ : s.Pos}
     (h : pat ≠ "") (h' : IsLongestRevMatchAt pat pos₁ pos₂) :
     pos₂.offset = pos₁.offset.increaseBy pat.utf8ByteSize := by
   rw [show pat.utf8ByteSize = pat.toSlice.utf8ByteSize from utf8ByteSize_toSlice.symm]
-  exact ForwardSliceSearcher.offset_of_isLongestRevMatchAt (by simpa)
+  exact ForwardSliceSearcher.offset_of_isLongestRevMatchAt (toSlice_isEmpty h)
     (isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice.1 h')
 
-theorem matchesAt_iff_splits {pat : String} {s : Slice} {pos : s.Pos} :
+theorem matchesAt_iff_splits {pat : String} {s : Slice} {pos : s.Pos} (h : pat ≠ "") :
     MatchesAt pat pos ↔ ∃ t₁ t₂, pos.Splits t₁ (pat ++ t₂) := by
   rw [matchesAt_iff_toSlice,
-    ForwardSliceSearcher.matchesAt_iff_splits]
+    ForwardSliceSearcher.matchesAt_iff_splits (toSlice_isEmpty h)]
   simp
 
-theorem revMatchesAt_iff_splits {pat : String} {s : Slice} {pos : s.Pos} :
+theorem revMatchesAt_iff_splits {pat : String} {s : Slice} {pos : s.Pos} (h : pat ≠ "") :
     RevMatchesAt pat pos ↔ ∃ t₁ t₂, pos.Splits (t₁ ++ pat) t₂ := by
   rw [revMatchesAt_iff_toSlice,
-    ForwardSliceSearcher.revMatchesAt_iff_splits]
+    ForwardSliceSearcher.revMatchesAt_iff_splits (toSlice_isEmpty h)]
   simp
 
-theorem exists_matchesAt_iff_eq_append {pat : String} {s : Slice} :
+theorem exists_matchesAt_iff_eq_append {pat : String} {s : Slice} (h : pat ≠ "") :
     (∃ (pos : s.Pos), MatchesAt pat pos) ↔ ∃ t₁ t₂, s.copy = t₁ ++ pat ++ t₂ := by
-  simp only [matchesAt_iff_splits]
+  simp only [matchesAt_iff_splits h]
   constructor
   · rintro ⟨pos, t₁, t₂, hsplit⟩
     exact ⟨t₁, t₂, by rw [hsplit.eq_append, append_assoc]⟩
@@ -477,12 +385,12 @@ theorem exists_matchesAt_iff_eq_append {pat : String} {s : Slice} :
         ⟨t₁, pat ++ t₂, by rw [← append_assoc]; exact heq, rfl⟩
     exact ⟨s.pos _ hvalid, t₁, t₂, ⟨by rw [← append_assoc]; exact heq, by simp⟩⟩
 
-theorem exists_revMatchesAt_iff_eq_append {pat : String} {s : Slice} :
+theorem exists_revMatchesAt_iff_eq_append {pat : String} {s : Slice} (h : pat ≠ "") :
     (∃ (pos : s.Pos), RevMatchesAt pat pos) ↔ ∃ t₁ t₂, s.copy = t₁ ++ pat ++ t₂ := by
   rw [show (∃ (pos : s.Pos), RevMatchesAt (ρ := String) pat pos) ↔
       (∃ (pos : s.Pos), RevMatchesAt (ρ := Slice) pat.toSlice pos) from by
     simp [revMatchesAt_iff_toSlice],
-    ForwardSliceSearcher.exists_revMatchesAt_iff_eq_append]
+    ForwardSliceSearcher.exists_revMatchesAt_iff_eq_append (toSlice_isEmpty h)]
   simp
 
 theorem matchesAt_iff_isLongestMatchAt {pat : String} {s : Slice} {pos : s.Pos}
@@ -490,7 +398,7 @@ theorem matchesAt_iff_isLongestMatchAt {pat : String} {s : Slice} {pos : s.Pos}
     MatchesAt pat pos ↔ ∃ (h : (pos.offset.increaseBy pat.utf8ByteSize).IsValidForSlice s),
       IsLongestMatchAt pat pos (s.pos _ h) := by
   have key := ForwardSliceSearcher.matchesAt_iff_isLongestMatchAt (pat := pat.toSlice)
-    (by simpa) (pos := pos)
+    (toSlice_isEmpty h) (pos := pos)
   simp only [utf8ByteSize_toSlice, ← isLongestMatchAt_iff_isLongestMatchAt_toSlice] at key
   rwa [matchesAt_iff_toSlice]
 
@@ -500,7 +408,7 @@ theorem revMatchesAt_iff_isLongestRevMatchAt {pat : String} {s : Slice} {pos : s
       ∃ (h : (pos.offset.decreaseBy pat.utf8ByteSize).IsValidForSlice s),
         IsLongestRevMatchAt pat (s.pos _ h) pos := by
   have key := ForwardSliceSearcher.revMatchesAt_iff_isLongestRevMatchAt (pat := pat.toSlice)
-    (by simpa) (pos := pos)
+    (toSlice_isEmpty h) (pos := pos)
   simp only [utf8ByteSize_toSlice, ← isLongestRevMatchAt_iff_isLongestRevMatchAt_toSlice] at key
   rwa [revMatchesAt_iff_toSlice]
 
@@ -510,14 +418,14 @@ theorem matchesAt_iff_getElem {pat : String} {s : Slice} {pos : s.Pos} (h : pat
         ∀ (j), (hj : j < pat.toByteArray.size) →
           pat.toByteArray[j] = s.copy.toByteArray[pos.offset.byteIdx + j] := by
   have key := ForwardSliceSearcher.matchesAt_iff_getElem (pat := pat.toSlice)
-    (by simpa) (pos := pos)
+    (toSlice_isEmpty h) (pos := pos)
   simp only [copy_toSlice] at key
   rwa [matchesAt_iff_toSlice]
 
 theorem le_of_matchesAt {pat : String} {s : Slice} {pos : s.Pos} (h : pat ≠ "")
     (h' : MatchesAt pat pos) : pos.offset.increaseBy pat.utf8ByteSize ≤ s.rawEndPos := by
   rw [show pat.utf8ByteSize = pat.toSlice.utf8ByteSize from utf8ByteSize_toSlice.symm]
-  exact ForwardSliceSearcher.le_of_matchesAt (by simpa)
+  exact ForwardSliceSearcher.le_of_matchesAt (toSlice_isEmpty h)
     (matchesAt_iff_toSlice.1 h')
 
 theorem matchesAt_iff_matchesAt_toSlice {pat : String} {s : Slice}

src/Init/Data/String/Lemmas/Pattern/String/ForwardPattern.lean

@@ -56,7 +56,7 @@ theorem skipPrefix?_eq_some_iff {pat s : Slice} {pos : s.Pos} :
     simp only [reduceCtorEq, false_iff]
     intro heq
     have := h (s.sliceFrom pos).copy
-    simp [← heq, -sliceTo_append_sliceFrom, pos.splits.eq_append] at this
+    simp [← heq, pos.splits.eq_append] at this
 
 theorem isSome_skipPrefix? {pat s : Slice} : (skipPrefix? pat s).isSome = startsWith pat s := by
   fun_cases skipPrefix? <;> simp_all
@@ -76,11 +76,14 @@ namespace Model.ForwardSliceSearcher
 
 open Pattern.ForwardSliceSearcher
 
-public instance {pat : Slice} : LawfulForwardPatternModel pat where
+public instance {pat : Slice} : LawfulForwardPattern pat where
   skipPrefixOfNonempty?_eq _ := rfl
   startsWith_eq _ := isSome_skipPrefix?.symm
+
+public theorem lawfulForwardPatternModel {pat : Slice} (hpat : pat.isEmpty = false) :
+    LawfulForwardPatternModel pat where
   skipPrefix?_eq_some_iff pos := by
-    simp [ForwardPattern.skipPrefix?, skipPrefix?_eq_some_iff, isLongestMatch_iff]
+    simp [ForwardPattern.skipPrefix?, skipPrefix?_eq_some_iff, isLongestMatch_iff hpat]
 
 end Model.ForwardSliceSearcher
 
@@ -88,11 +91,14 @@ namespace Model.ForwardStringSearcher
 
 open Pattern.ForwardSliceSearcher
 
-public instance {pat : String} : LawfulForwardPatternModel pat where
+public instance {pat : String} : LawfulForwardPattern pat where
   skipPrefixOfNonempty?_eq _ := rfl
   startsWith_eq _ := isSome_skipPrefix?.symm
+
+public theorem lawfulForwardPatternModel {pat : String} (hpat : pat ≠ "") :
+    LawfulForwardPatternModel pat where
   skipPrefix?_eq_some_iff pos := by
-    simp [ForwardPattern.skipPrefix?, skipPrefix?_eq_some_iff, isLongestMatch_iff]
+    simp [ForwardPattern.skipPrefix?, skipPrefix?_eq_some_iff, isLongestMatch_iff hpat]
 
 end Model.ForwardStringSearcher
 
@@ -147,7 +153,7 @@ theorem skipSuffix?_eq_some_iff {pat s : Slice} {pos : s.Pos} :
     simp only [reduceCtorEq, false_iff]
     intro heq
     have := h (s.sliceTo pos).copy
-    simp [← heq, -sliceTo_append_sliceFrom, pos.splits.eq_append] at this
+    simp [← heq, pos.splits.eq_append] at this
 
 theorem isSome_skipSuffix? {pat s : Slice} : (skipSuffix? pat s).isSome = endsWith pat s := by
   fun_cases skipSuffix? <;> simp_all
@@ -167,12 +173,15 @@ namespace Model.BackwardSliceSearcher
 
 open Pattern.BackwardSliceSearcher
 
-public instance {pat : Slice} : LawfulBackwardPatternModel pat where
+public instance {pat : Slice} : LawfulBackwardPattern pat where
   skipSuffixOfNonempty?_eq _ := rfl
   endsWith_eq _ := isSome_skipSuffix?.symm
+
+public theorem lawfulBackwardPatternModel {pat : Slice} (hpat : pat.isEmpty = false) :
+    LawfulBackwardPatternModel pat where
   skipSuffix?_eq_some_iff pos := by
     simp [BackwardPattern.skipSuffix?, skipSuffix?_eq_some_iff,
-      ForwardSliceSearcher.isLongestRevMatch_iff]
+      ForwardSliceSearcher.isLongestRevMatch_iff hpat]
 
 end Model.BackwardSliceSearcher
 
@@ -180,12 +189,15 @@ namespace Model.BackwardStringSearcher
 
 open Pattern.BackwardSliceSearcher
 
-public instance {pat : String} : LawfulBackwardPatternModel pat where
+public instance {pat : String} : LawfulBackwardPattern pat where
   skipSuffixOfNonempty?_eq _ := rfl
   endsWith_eq _ := isSome_skipSuffix?.symm
+
+public theorem lawfulBackwardPatternModel {pat : String} (hpat : pat ≠ "") :
+    LawfulBackwardPatternModel pat where
   skipSuffix?_eq_some_iff pos := by
     simp [BackwardPattern.skipSuffix?, skipSuffix?_eq_some_iff,
-      ForwardStringSearcher.isLongestRevMatch_iff]
+      ForwardStringSearcher.isLongestRevMatch_iff hpat]
 
 end Model.BackwardStringSearcher
 
@@ -207,22 +219,19 @@ public theorem Pattern.ForwardPattern.skipPrefix?_string_eq_skipPrefix?_toSlice
     {pat : String} {s : Slice} :
     skipPrefix? pat s = skipPrefix? pat.toSlice s := (rfl)
 
-public theorem Pos.skip?_string_eq_skip?_toSlice {pat : String} {s : Slice} {pos : s.Pos} :
-    pos.skip? pat = pos.skip? pat.toSlice := (rfl)
-
 public theorem Pos.skipWhile_string_eq_skipWhile_toSlice {pat : String} {s : Slice}
     (curr : s.Pos) :
     Pos.skipWhile curr pat = Pos.skipWhile curr pat.toSlice := by
   fun_induction Pos.skipWhile curr pat with
   | case1 pos nextCurr h₁ h₂ ih =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pos.skip?_string_eq_skip?_toSlice, h₁, h₂, ih]
+    simp [← Pattern.ForwardPattern.skipPrefix?_string_eq_skipPrefix?_toSlice, h₁, h₂, ih]
   | case2 pos nextCurr h ih =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pos.skip?_string_eq_skip?_toSlice, h, ih]
+    simp [← Pattern.ForwardPattern.skipPrefix?_string_eq_skipPrefix?_toSlice, h, ih]
   | case3 pos h =>
     conv => rhs; rw [Pos.skipWhile]
-    simp [← Pos.skip?_string_eq_skip?_toSlice, h]
+    simp [← Pattern.ForwardPattern.skipPrefix?_string_eq_skipPrefix?_toSlice]
 
 public theorem skipPrefixWhile_string_eq_skipPrefixWhile_toSlice {pat : String} {s : Slice} :
     s.skipPrefixWhile pat = s.skipPrefixWhile pat.toSlice :=
@@ -238,7 +247,7 @@ public theorem takeWhile_string_eq_takeWhile_toSlice {pat : String} {s : Slice}
 
 public theorem all_string_eq_all_toSlice {pat : String} {s : Slice} :
     s.all pat = s.all pat.toSlice := by
-  simp only [all, skipPrefixWhile_string_eq_skipPrefixWhile_toSlice]
+  simp only [all, dropWhile_string_eq_dropWhile_toSlice]
 
 public theorem endsWith_string_eq_endsWith_toSlice {pat : String} {s : Slice} :
     s.endsWith pat = s.endsWith pat.toSlice := (rfl)
@@ -256,22 +265,19 @@ public theorem Pattern.BackwardPattern.skipSuffix?_string_eq_skipSuffix?_toSlice
     {pat : String} {s : Slice} :
     skipSuffix? pat s = skipSuffix? pat.toSlice s := (rfl)
 
-public theorem Pos.revSkip?_string_eq_revSkip?_toSlice {pat : String} {s : Slice} {pos : s.Pos} :
-    pos.revSkip? pat = pos.revSkip? pat.toSlice := (rfl)
-
 public theorem Pos.revSkipWhile_string_eq_revSkipWhile_toSlice {pat : String} {s : Slice}
     (curr : s.Pos) :
     Pos.revSkipWhile curr pat = Pos.revSkipWhile curr pat.toSlice := by
   fun_induction Pos.revSkipWhile curr pat with
   | case1 pos nextCurr h₁ h₂ ih =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pos.revSkip?_string_eq_revSkip?_toSlice, h₁, h₂, ih]
+    simp [← Pattern.BackwardPattern.skipSuffix?_string_eq_skipSuffix?_toSlice, h₁, h₂, ih]
   | case2 pos nextCurr h ih =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pos.revSkip?_string_eq_revSkip?_toSlice, h, ih]
+    simp [← Pattern.BackwardPattern.skipSuffix?_string_eq_skipSuffix?_toSlice, h, ih]
   | case3 pos h =>
     conv => rhs; rw [Pos.revSkipWhile]
-    simp [← Pos.revSkip?_string_eq_revSkip?_toSlice, h]
+    simp [← Pattern.BackwardPattern.skipSuffix?_string_eq_skipSuffix?_toSlice]
 
 public theorem skipSuffixWhile_string_eq_skipSuffixWhile_toSlice {pat : String} {s : Slice} :
     s.skipSuffixWhile pat = s.skipSuffixWhile pat.toSlice :=
@@ -285,8 +291,4 @@ public theorem takeEndWhile_string_eq_takeEndWhile_toSlice {pat : String} {s : S
     s.takeEndWhile pat = s.takeEndWhile pat.toSlice := by
   simp only [takeEndWhile]; exact congrArg _ skipSuffixWhile_string_eq_skipSuffixWhile_toSlice
 
-public theorem revAll_string_eq_revAll_toSlice {pat : String} {s : Slice} :
-    s.revAll pat = s.revAll pat.toSlice := by
-  simp [revAll, skipSuffixWhile_string_eq_skipSuffixWhile_toSlice]
-
 end String.Slice

src/Init/Data/String/Lemmas/Pattern/TakeDrop/Char.lean

@@ -56,77 +56,6 @@ theorem eq_append_of_dropPrefix?_char_eq_some {c : Char} {s res : Slice} (h : s.
     s.copy = singleton c ++ res.copy := by
   simpa [PatternModel.Matches] using Pattern.Model.eq_append_of_dropPrefix?_eq_some h
 
-theorem Pos.skip?_char_eq_some_iff {c : Char} {s : Slice} {pos res : s.Pos} :
-    pos.skip? c = some res ↔ ∃ h, res = pos.next h ∧ pos.get h = c := by
-  simp [Pattern.Model.Pos.skip?_eq_some_iff, Char.isLongestMatchAt_iff]
-
-@[simp]
-theorem Pos.skip?_char_eq_none_iff {c : Char} {s : Slice} {pos : s.Pos} :
-    pos.skip? c = none ↔ ∀ h, pos.get h ≠ c := by
-  simp [Pattern.Model.Pos.skip?_eq_none_iff, Char.matchesAt_iff]
-
-theorem Pos.get_skipWhile_char_ne {c : Char} {s : Slice} {pos : s.Pos} {h} :
-    (pos.skipWhile c).get h ≠ c := by
-  have := Pattern.Model.Pos.not_matchesAt_skipWhile c pos
-  simp_all [Char.matchesAt_iff]
-
-theorem Pos.skipWhile_char_eq_self_iff_get {c : Char} {s : Slice} {pos : s.Pos} :
-    pos.skipWhile c = pos ↔ ∀ h, pos.get h ≠ c := by
-  simp [Pattern.Model.Pos.skipWhile_eq_self_iff, Char.matchesAt_iff]
-
-theorem Pos.get_eq_of_lt_skipWhile_char {c : Char} {s : Slice} {pos pos' : s.Pos}
-    (h₁ : pos ≤ pos') (h₂ : pos' < pos.skipWhile c) : pos'.get (ne_endPos_of_lt h₂) = c :=
-  (Char.isLongestMatchAtChain_iff.1 (Pattern.Model.Pos.isLongestMatchAtChain_skipWhile c pos)).2 _ h₁ h₂
-
-theorem get_skipPrefixWhile_char_ne {c : Char} {s : Slice} {h} :
-    (s.skipPrefixWhile c).get h ≠ c := by
-  simp [skipPrefixWhile_eq_skipWhile_startPos, Pos.get_skipWhile_char_ne]
-
-theorem get_eq_of_lt_skipPrefixWhile_char {c : Char} {s : Slice} {pos : s.Pos} (h : pos < s.skipPrefixWhile c) :
-    pos.get (Pos.ne_endPos_of_lt h) = c :=
-  Pos.get_eq_of_lt_skipWhile_char (Pos.startPos_le _) (by rwa [skipPrefixWhile_eq_skipWhile_startPos] at h)
-
-@[simp]
-theorem all_char_iff {c : Char} {s : Slice} : s.all c ↔ s.copy.toList = List.replicate s.copy.length c := by
-  rw [Bool.eq_iff_iff]
-  simp [Pattern.Model.all_eq_true_iff, Char.isLongestMatchAtChain_startPos_endPos_iff_toList]
-
-theorem Pos.revSkip?_char_eq_some_iff {c : Char} {s : Slice} {pos res : s.Pos} :
-    pos.revSkip? c = some res ↔ ∃ h, res = pos.prev h ∧ (pos.prev h).get (by simp) = c := by
-  simp [Pattern.Model.Pos.revSkip?_eq_some_iff, Char.isLongestRevMatchAt_iff]
-
-@[simp]
-theorem Pos.revSkip?_char_eq_none_iff {c : Char} {s : Slice} {pos : s.Pos} :
-    pos.revSkip? c = none ↔ ∀ h, (pos.prev h).get (by simp) ≠ c := by
-  simp [Pattern.Model.Pos.revSkip?_eq_none_iff, Char.revMatchesAt_iff]
-
-theorem Pos.get_revSkipWhile_char_ne {c : Char} {s : Slice} {pos : s.Pos} {h} :
-    ((pos.revSkipWhile c).prev h).get (by simp) ≠ c := by
-  have := Pattern.Model.Pos.not_revMatchesAt_revSkipWhile c pos
-  simp_all [Char.revMatchesAt_iff]
-
-theorem Pos.revSkipWhile_char_eq_self_iff_get {c : Char} {s : Slice} {pos : s.Pos} :
-    pos.revSkipWhile c = pos ↔ ∀ h, (pos.prev h).get (by simp) ≠ c := by
-  simp [Pattern.Model.Pos.revSkipWhile_eq_self_iff, Char.revMatchesAt_iff]
-
-theorem Pos.get_eq_of_revSkipWhile_le_char {c : Char} {s : Slice} {pos pos' : s.Pos}
-    (h₁ : pos' < pos) (h₂ : pos.revSkipWhile c ≤ pos') : pos'.get (Pos.ne_endPos_of_lt h₁) = c :=
-  (Char.isLongestRevMatchAtChain_iff.1 (Pattern.Model.Pos.isLongestRevMatchAtChain_revSkipWhile c pos)).2 _ h₂ h₁
-
-theorem get_skipSuffixWhile_char_ne {c : Char} {s : Slice} {h} :
-    ((s.skipSuffixWhile c).prev h).get (by simp) ≠ c := by
-  simp [skipSuffixWhile_eq_revSkipWhile_endPos, Pos.get_revSkipWhile_char_ne]
-
-theorem get_eq_of_skipSuffixWhile_le_char {c : Char} {s : Slice} {pos : s.Pos}
-    (h : s.skipSuffixWhile c ≤ pos) (h' : pos < s.endPos) :
-    pos.get (Pos.ne_endPos_of_lt h') = c :=
-  Pos.get_eq_of_revSkipWhile_le_char h' (by rwa [skipSuffixWhile_eq_revSkipWhile_endPos] at h)
-
-@[simp]
-theorem revAll_char_iff {c : Char} {s : Slice} : s.revAll c ↔ s.copy.toList = List.replicate s.copy.length c := by
-  rw [Bool.eq_iff_iff]
-  simp [Pattern.Model.revAll_eq_true_iff, Char.isLongestRevMatchAtChain_startPos_endPos_iff_toList]
-
 theorem skipSuffix?_char_eq_some_iff {c : Char} {s : Slice} {pos : s.Pos} :
     s.skipSuffix? c = some pos ↔ ∃ h, pos = s.endPos.prev h ∧ (s.endPos.prev h).get (by simp) = c := by
   rw [Pattern.Model.skipSuffix?_eq_some_iff, Char.isLongestRevMatch_iff]
@@ -171,19 +100,19 @@ theorem skipPrefix?_char_eq_some_iff {c : Char} {s : String} {pos : s.Pos} :
 
 theorem startsWith_char_iff_get {c : Char} {s : String} :
     s.startsWith c ↔ ∃ h, s.startPos.get h = c := by
-  simp [← startsWith_toSlice, Slice.startsWith_char_iff_get]
+  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_char_iff_get]
 
 theorem startsWith_char_eq_false_iff_get {c : Char} {s : String} :
     s.startsWith c = false ↔ ∀ h, s.startPos.get h ≠ c := by
-  simp [← startsWith_toSlice, Slice.startsWith_char_eq_false_iff_get]
+  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_char_eq_false_iff_get]
 
 theorem startsWith_char_eq_head? {c : Char} {s : String} :
     s.startsWith c = (s.toList.head? == some c) := by
-  simp [← startsWith_toSlice, Slice.startsWith_char_eq_head?]
+  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_char_eq_head?]
 
 theorem startsWith_char_iff_exists_append {c : Char} {s : String} :
     s.startsWith c ↔ ∃ t, s = singleton c ++ t := by
-  simp [← startsWith_toSlice, Slice.startsWith_char_iff_exists_append]
+  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_char_iff_exists_append]
 
 theorem startsWith_char_eq_false_iff_forall_append {c : Char} {s : String} :
     s.startsWith c = false ↔ ∀ t, s ≠ singleton c ++ t := by
@@ -201,19 +130,19 @@ theorem skipSuffix?_char_eq_some_iff {c : Char} {s : String} {pos : s.Pos} :
 
 theorem endsWith_char_iff_get {c : Char} {s : String} :
     s.endsWith c ↔ ∃ h, (s.endPos.prev h).get (by simp) = c := by
-  simp [← endsWith_toSlice, Slice.endsWith_char_iff_get, Pos.prev_toSlice]
+  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_char_iff_get, Pos.prev_toSlice]
 
 theorem endsWith_char_eq_false_iff_get {c : Char} {s : String} :
     s.endsWith c = false ↔ ∀ h, (s.endPos.prev h).get (by simp) ≠ c := by
-  simp [← endsWith_toSlice, Slice.endsWith_char_eq_false_iff_get, Pos.prev_toSlice]
+  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_char_eq_false_iff_get, Pos.prev_toSlice]
 
 theorem endsWith_char_eq_getLast? {c : Char} {s : String} :
     s.endsWith c = (s.toList.getLast? == some c) := by
-  simp [← endsWith_toSlice, Slice.endsWith_char_eq_getLast?]
+  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_char_eq_getLast?]
 
 theorem endsWith_char_iff_exists_append {c : Char} {s : String} :
     s.endsWith c ↔ ∃ t, s = t ++ singleton c := by
-  simp [← endsWith_toSlice, Slice.endsWith_char_iff_exists_append]
+  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_char_iff_exists_append]
 
 theorem endsWith_char_eq_false_iff_forall_append {c : Char} {s : String} :
     s.endsWith c = false ↔ ∀ t, s ≠ t ++ singleton c := by

src/Init/Data/String/Lemmas/Pattern/TakeDrop/Pred.lean

@@ -8,16 +8,11 @@ module
 prelude
 public import Init.Data.String.Slice
 public import Init.Data.String.TakeDrop
-public import Init.Data.String.Lemmas.Order
 import Init.Data.String.Lemmas.Pattern.TakeDrop.Basic
 import Init.Data.String.Lemmas.Pattern.Pred
 import Init.Data.Option.Lemmas
 import Init.Data.String.Lemmas.FindPos
-import Init.Data.String.Lemmas.Intercalate
 import Init.ByCases
-import Init.Data.Order.Lemmas
-import Init.Data.String.OrderInstances
-import Init.Data.String.Lemmas.Basic
 
 public section
 
@@ -54,80 +49,6 @@ theorem eq_append_of_dropPrefix?_bool_eq_some {p : Char → Bool} {s res : Slice
   obtain ⟨_, ⟨c, ⟨rfl, h₁⟩⟩, h₂⟩ := by simpa [PatternModel.Matches] using Pattern.Model.eq_append_of_dropPrefix?_eq_some h
   exact ⟨_, h₂, h₁⟩
 
-@[simp]
-theorem Pos.skip?_bool_eq_some_iff {p : Char → Bool} {s : Slice} {pos res : s.Pos} :
-    pos.skip? p = some res ↔ ∃ h, res = pos.next h ∧ p (pos.get h) := by
-  simp [Pattern.Model.Pos.skip?_eq_some_iff, CharPred.isLongestMatchAt_iff]
-
-@[simp]
-theorem Pos.skip?_bool_eq_none_iff {p : Char → Bool} {s : Slice} {pos : s.Pos} :
-    pos.skip? p = none ↔ ∀ h, p (pos.get h) = false := by
-  simp [Pattern.Model.Pos.skip?_eq_none_iff, CharPred.matchesAt_iff]
-
-theorem Pos.apply_skipWhile_bool_eq_false {p : Char → Bool} {s : Slice} {pos : s.Pos} {h} :
-    p ((pos.skipWhile p).get h) = false := by
-  have := Pattern.Model.Pos.not_matchesAt_skipWhile p pos
-  simp_all [CharPred.matchesAt_iff]
-
-theorem Pos.skipWhile_bool_eq_self_iff_get {p : Char → Bool} {s : Slice} {pos : s.Pos} :
-    pos.skipWhile p = pos ↔ ∀ h, p (pos.get h) = false := by
-  simp [Pattern.Model.Pos.skipWhile_eq_self_iff, CharPred.matchesAt_iff]
-
-theorem Pos.apply_eq_true_of_lt_skipWhile_bool {p : Char → Bool} {s : Slice} {pos pos' : s.Pos}
-    (h₁ : pos ≤ pos') (h₂ : pos' < pos.skipWhile p) : p (pos'.get (ne_endPos_of_lt h₂)) = true :=
-  (CharPred.isLongestMatchAtChain_iff.1 (Pattern.Model.Pos.isLongestMatchAtChain_skipWhile p pos)).2 _ h₁ h₂
-
-theorem apply_skipPrefixWhile_bool_eq_false {p : Char → Bool} {s : Slice} {h} :
-    p ((s.skipPrefixWhile p).get h) = false := by
-  simp [skipPrefixWhile_eq_skipWhile_startPos, Pos.apply_skipWhile_bool_eq_false]
-
-theorem apply_eq_true_of_lt_skipPrefixWhile_bool {p : Char → Bool} {s : Slice} {pos : s.Pos} (h : pos < s.skipPrefixWhile p) :
-    p (pos.get (Pos.ne_endPos_of_lt h)) = true :=
-  Pos.apply_eq_true_of_lt_skipWhile_bool (Pos.startPos_le _) (skipPrefixWhile_eq_skipWhile_startPos ▸ h)
-
-@[simp]
-theorem all_bool_eq {p : Char → Bool} {s : Slice} : s.all p = s.copy.toList.all p := by
-  rw [Bool.eq_iff_iff, Pattern.Model.all_eq_true_iff,
-    CharPred.isLongestMatchAtChain_startPos_endPos_iff_toList, List.all_eq_true]
-
-@[simp]
-theorem Pos.skip?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s : Slice} {pos res : s.Pos} :
-    pos.skip? P = some res ↔ ∃ h, res = pos.next h ∧ P (pos.get h) := by
-  simp [Pos.skip?_prop_eq_skip?_decide, skip?_bool_eq_some_iff]
-
-@[simp]
-theorem Pos.skip?_prop_eq_none_iff {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos} :
-    pos.skip? P = none ↔ ∀ h, ¬ P (pos.get h) := by
-  simp [Pos.skip?_prop_eq_skip?_decide, skip?_bool_eq_none_iff]
-
-theorem Pos.apply_skipWhile_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos} {h} :
-    ¬ P ((pos.skipWhile P).get h) := by
-  have := Pattern.Model.Pos.not_matchesAt_skipWhile P pos
-  simp_all [CharPred.Decidable.matchesAt_iff]
-
-theorem Pos.skipWhile_prop_eq_self_iff_get {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos} :
-    pos.skipWhile P = pos ↔ ∀ h, ¬ P (pos.get h) := by
-  simp [Pos.skipWhile_prop_eq_skipWhile_decide, skipWhile_bool_eq_self_iff_get]
-
-theorem Pos.apply_of_lt_skipWhile_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {pos pos' : s.Pos}
-    (h₁ : pos ≤ pos') (h₂ : pos' < pos.skipWhile P) : P (pos'.get (ne_endPos_of_lt h₂)) := by
-  simp [Pos.skipWhile_prop_eq_skipWhile_decide] at h₂
-  simpa using apply_eq_true_of_lt_skipWhile_bool h₁ h₂
-
-theorem apply_skipPrefixWhile_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {h} :
-    ¬ P ((s.skipPrefixWhile P).get h) := by
-  simp [skipPrefixWhile_eq_skipWhile_startPos, Pos.apply_skipWhile_prop]
-
-theorem apply_of_lt_skipPrefixWhile_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos}
-    (h : pos < s.skipPrefixWhile P) : P (pos.get (Pos.ne_endPos_of_lt h)) := by
-  simp [skipPrefixWhile_prop_eq_skipPrefixWhile_decide] at h
-  simpa using apply_eq_true_of_lt_skipPrefixWhile_bool h
-
-@[simp]
-theorem all_prop_eq {P : Char → Prop} [DecidablePred P] {s : Slice} :
-    s.all P = s.copy.toList.all (decide <| P ·) := by
-  simp [all_prop_eq_all_decide]
-
 theorem skipPrefix?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos} :
     s.skipPrefix? P = some pos ↔ ∃ h, pos = s.startPos.next h ∧ P (s.startPos.get h) := by
   simp [skipPrefix?_prop_eq_skipPrefix?_decide, skipPrefix?_bool_eq_some_iff]
@@ -144,7 +65,7 @@ theorem startsWith_prop_eq_head? {P : Char → Prop} [DecidablePred P] {s : Slic
     s.startsWith P = s.copy.toList.head?.any (decide <| P ·) := by
   simp [startsWith_prop_eq_startsWith_decide, startsWith_bool_eq_head?]
 
-theorem eq_append_of_dropPrefix?_prop_eq_some {P : Char → Prop} [DecidablePred P] {s res : Slice} (h : s.dropPrefix? P = some res) :
+theorem eq_append_of_dropPrefix_prop_eq_some {P : Char → Prop} [DecidablePred P] {s res : Slice} (h : s.dropPrefix? P = some res) :
     ∃ c, s.copy = singleton c ++ res.copy ∧ P c := by
   rw [dropPrefix?_prop_eq_dropPrefix?_decide] at h
   simpa using eq_append_of_dropPrefix?_bool_eq_some h
@@ -197,83 +118,6 @@ theorem eq_append_of_dropSuffix?_prop_eq_some {P : Char → Prop} [DecidablePred
   rw [dropSuffix?_prop_eq_dropSuffix?_decide] at h
   simpa using eq_append_of_dropSuffix?_bool_eq_some h
 
-@[simp]
-theorem Pos.revSkip?_bool_eq_some_iff {p : Char → Bool} {s : Slice} {pos res : s.Pos} :
-    pos.revSkip? p = some res ↔ ∃ h, res = pos.prev h ∧ p ((pos.prev h).get (by simp)) := by
-  simp [Pattern.Model.Pos.revSkip?_eq_some_iff, CharPred.isLongestRevMatchAt_iff]
-
-@[simp]
-theorem Pos.revSkip?_bool_eq_none_iff {p : Char → Bool} {s : Slice} {pos : s.Pos} :
-    pos.revSkip? p = none ↔ ∀ h, p ((pos.prev h).get (by simp)) = false := by
-  simp [Pattern.Model.Pos.revSkip?_eq_none_iff, CharPred.revMatchesAt_iff]
-
-theorem Pos.apply_revSkipWhile_bool_eq_false {p : Char → Bool} {s : Slice} {pos : s.Pos} {h} :
-    p (((pos.revSkipWhile p).prev h).get (by simp)) = false := by
-  have := Pattern.Model.Pos.not_revMatchesAt_revSkipWhile p pos
-  simp_all [CharPred.revMatchesAt_iff]
-
-theorem Pos.revSkipWhile_bool_eq_self_iff_get {p : Char → Bool} {s : Slice} {pos : s.Pos} :
-    pos.revSkipWhile p = pos ↔ ∀ h, p ((pos.prev h).get (by simp)) = false := by
-  simp [Pattern.Model.Pos.revSkipWhile_eq_self_iff, CharPred.revMatchesAt_iff]
-
-theorem Pos.apply_eq_true_of_revSkipWhile_le_bool {p : Char → Bool} {s : Slice} {pos pos' : s.Pos}
-    (h₁ : pos' < pos) (h₂ : pos.revSkipWhile p ≤ pos') : p (pos'.get (Pos.ne_endPos_of_lt h₁)) = true :=
-  (CharPred.isLongestRevMatchAtChain_iff.1 (Pattern.Model.Pos.isLongestRevMatchAtChain_revSkipWhile p pos)).2 _ h₂ h₁
-
-theorem apply_skipSuffixWhile_bool_eq_false {p : Char → Bool} {s : Slice} {h} :
-    p (((s.skipSuffixWhile p).prev h).get (by simp)) = false := by
-  simp [skipSuffixWhile_eq_revSkipWhile_endPos, Pos.apply_revSkipWhile_bool_eq_false]
-
-theorem apply_eq_true_of_skipSuffixWhile_le_bool {p : Char → Bool} {s : Slice} {pos : s.Pos}
-    (h : s.skipSuffixWhile p ≤ pos) (h' : pos < s.endPos) :
-    p (pos.get (Pos.ne_endPos_of_lt h')) = true :=
-  Pos.apply_eq_true_of_revSkipWhile_le_bool h' (skipSuffixWhile_eq_revSkipWhile_endPos ▸ h)
-
-@[simp]
-theorem revAll_bool_eq {p : Char → Bool} {s : Slice} : s.revAll p = s.copy.toList.all p := by
-  rw [Bool.eq_iff_iff, Pattern.Model.revAll_eq_true_iff,
-    CharPred.isLongestRevMatchAtChain_startPos_endPos_iff_toList, List.all_eq_true]
-
-@[simp]
-theorem Pos.revSkip?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s : Slice} {pos res : s.Pos} :
-    pos.revSkip? P = some res ↔ ∃ h, res = pos.prev h ∧ P ((pos.prev h).get (by simp)) := by
-  simp [Pos.revSkip?_prop_eq_revSkip?_decide, revSkip?_bool_eq_some_iff]
-
-@[simp]
-theorem Pos.revSkip?_prop_eq_none_iff {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos} :
-    pos.revSkip? P = none ↔ ∀ h, ¬ P ((pos.prev h).get (by simp)) := by
-  simp [Pos.revSkip?_prop_eq_revSkip?_decide, revSkip?_bool_eq_none_iff]
-
-theorem Pos.apply_revSkipWhile_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos} {h} :
-    ¬ P (((pos.revSkipWhile P).prev h).get (by simp)) := by
-  have := Pattern.Model.Pos.not_revMatchesAt_revSkipWhile P pos
-  simp_all [CharPred.Decidable.revMatchesAt_iff]
-
-theorem Pos.revSkipWhile_prop_eq_self_iff_get {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos} :
-    pos.revSkipWhile P = pos ↔ ∀ h, ¬ P ((pos.prev h).get (by simp)) := by
-  simp [Pos.revSkipWhile_prop_eq_revSkipWhile_decide, revSkipWhile_bool_eq_self_iff_get]
-
-theorem Pos.apply_of_revSkipWhile_le_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {pos pos' : s.Pos}
-    (h₁ : pos' < pos) (h₂ : pos.revSkipWhile P ≤ pos') : P (pos'.get (Pos.ne_endPos_of_lt h₁)) := by
-  have h₂' : pos.revSkipWhile (decide <| P ·) ≤ pos' :=
-    Pos.revSkipWhile_prop_eq_revSkipWhile_decide (p := P) pos ▸ h₂
-  simpa using Pos.apply_eq_true_of_revSkipWhile_le_bool h₁ h₂'
-
-theorem apply_skipSuffixWhile_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {h} :
-    ¬ P (((s.skipSuffixWhile P).prev h).get (by simp)) := by
-  have := Pattern.Model.Pos.not_revMatchesAt_revSkipWhile P s.endPos
-  simp_all [CharPred.Decidable.revMatchesAt_iff, skipSuffixWhile_eq_revSkipWhile_endPos]
-
-theorem apply_of_skipSuffixWhile_le_prop {P : Char → Prop} [DecidablePred P] {s : Slice} {pos : s.Pos}
-    (h : s.skipSuffixWhile P ≤ pos) (h' : pos < s.endPos) :
-    P (pos.get (Pos.ne_endPos_of_lt h')) :=
-  Pos.apply_of_revSkipWhile_le_prop h' (skipSuffixWhile_eq_revSkipWhile_endPos (pat := P) ▸ h)
-
-@[simp]
-theorem revAll_prop_eq {P : Char → Prop} [DecidablePred P] {s : Slice} :
-    s.revAll P = s.copy.toList.all (decide <| P ·) := by
-  simp [revAll_prop_eq_revAll_decide, revAll_bool_eq]
-
 end Slice
 
 theorem skipPrefix?_bool_eq_some_iff {p : Char → Bool} {s : String} {pos : s.Pos} :
@@ -283,58 +127,21 @@ theorem skipPrefix?_bool_eq_some_iff {p : Char → Bool} {s : String} {pos : s.P
 
 theorem startsWith_bool_iff_get {p : Char → Bool} {s : String} :
     s.startsWith p ↔ ∃ h, p (s.startPos.get h) = true := by
-  simp [← startsWith_toSlice, Slice.startsWith_bool_iff_get]
+  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_bool_iff_get]
 
 theorem startsWith_bool_eq_false_iff_get {p : Char → Bool} {s : String} :
     s.startsWith p = false ↔ ∀ h, p (s.startPos.get h) = false := by
-  simp [← startsWith_toSlice, Slice.startsWith_bool_eq_false_iff_get]
+  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_bool_eq_false_iff_get]
 
 theorem startsWith_bool_eq_head? {p : Char → Bool} {s : String} :
     s.startsWith p = s.toList.head?.any p := by
-  simp [← startsWith_toSlice, Slice.startsWith_bool_eq_head?]
+  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_bool_eq_head?]
 
 theorem eq_append_of_dropPrefix?_bool_eq_some {p : Char → Bool} {s : String} {res : Slice} (h : s.dropPrefix? p = some res) :
     ∃ c, s = singleton c ++ res.copy ∧ p c = true := by
   rw [dropPrefix?_eq_dropPrefix?_toSlice] at h
   simpa using Slice.eq_append_of_dropPrefix?_bool_eq_some h
 
-@[simp]
-theorem Pos.skip?_bool_eq_some_iff {p : Char → Bool} {s : String} {pos res : s.Pos} :
-    pos.skip? p = some res ↔ ∃ h, res = pos.next h ∧ p (pos.get h) := by
-  simp [skip?_eq_skip?_toSlice, ← toSlice_inj, toSlice_next]
-
-@[simp]
-theorem Pos.skip?_bool_eq_none_iff {p : Char → Bool} {s : String} {pos : s.Pos} :
-    pos.skip? p = none ↔ ∀ h, p (pos.get h) = false := by
-  simp [skip?_eq_skip?_toSlice]
-
-theorem Pos.apply_skipWhile_bool_eq_false {p : Char → Bool} {s : String} {pos : s.Pos} {h} :
-    p ((pos.skipWhile p).get h) = false := by
-  simp [skipWhile_eq_skipWhile_toSlice, Slice.Pos.apply_skipWhile_bool_eq_false]
-
-theorem Pos.skipWhile_bool_eq_self_iff_get {p : Char → Bool} {s : String} {pos : s.Pos} :
-    pos.skipWhile p = pos ↔ ∀ h, p (pos.get h) = false := by
-  simp [skipWhile_eq_skipWhile_toSlice, ← toSlice_inj, Slice.Pos.skipWhile_bool_eq_self_iff_get]
-
-theorem Pos.apply_eq_true_of_lt_skipWhile_bool {p : Char → Bool} {s : String} {pos pos' : s.Pos}
-    (h₁ : pos ≤ pos') (h₂ : pos' < pos.skipWhile p) : p (pos'.get (ne_endPos_of_lt h₂)) = true := by
-  rw [Pos.get_eq_get_toSlice]
-  exact Slice.Pos.apply_eq_true_of_lt_skipWhile_bool (toSlice_le_toSlice_iff.2 h₁)
-    (by simpa [skipWhile_eq_skipWhile_toSlice] using h₂)
-
-theorem apply_skipPrefixWhile_bool_eq_false {p : Char → Bool} {s : String} {h} :
-    p ((s.skipPrefixWhile p).get h) = false := by
-  simp [skipPrefixWhile_eq_skipPrefixWhile_toSlice, Slice.apply_skipPrefixWhile_bool_eq_false]
-
-theorem apply_eq_true_of_lt_skipPrefixWhile_bool {p : Char → Bool} {s : String} {pos : s.Pos} (h : pos < s.skipPrefixWhile p) :
-    p (pos.get (Pos.ne_endPos_of_lt h)) = true := by
-  rw [Pos.get_eq_get_toSlice]
-  exact Slice.apply_eq_true_of_lt_skipPrefixWhile_bool (by simpa [skipPrefixWhile_eq_skipPrefixWhile_toSlice] using h)
-
-@[simp]
-theorem all_bool_eq {p : Char → Bool} {s : String} : s.all p = s.toList.all p := by
-  simp [← all_toSlice]
-
 theorem skipPrefix?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos} :
     s.skipPrefix? P = some pos ↔ ∃ h, pos = s.startPos.next h ∧ P (s.startPos.get h) := by
   simp [skipPrefix?_eq_skipPrefix?_toSlice, Slice.skipPrefix?_prop_eq_some_iff, ← Pos.toSlice_inj,
@@ -342,20 +149,20 @@ theorem skipPrefix?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s :
 
 theorem startsWith_prop_iff_get {P : Char → Prop} [DecidablePred P] {s : String} :
     s.startsWith P ↔ ∃ h, P (s.startPos.get h) := by
-  simp [← startsWith_toSlice, Slice.startsWith_prop_iff_get]
+  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_prop_iff_get]
 
 theorem startsWith_prop_eq_false_iff_get {P : Char → Prop} [DecidablePred P] {s : String} :
     s.startsWith P = false ↔ ∀ h, ¬ P (s.startPos.get h) := by
-  simp [← startsWith_toSlice, Slice.startsWith_prop_eq_false_iff_get]
+  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_prop_eq_false_iff_get]
 
 theorem startsWith_prop_eq_head? {P : Char → Prop} [DecidablePred P] {s : String} :
     s.startsWith P = s.toList.head?.any (decide <| P ·) := by
-  simp [← startsWith_toSlice, Slice.startsWith_prop_eq_head?]
+  simp [startsWith_eq_startsWith_toSlice, Slice.startsWith_prop_eq_head?]
 
 theorem eq_append_of_dropPrefix?_prop_eq_some {P : Char → Prop} [DecidablePred P] {s : String} {res : Slice}
     (h : s.dropPrefix? P = some res) : ∃ c, s = singleton c ++ res.copy ∧ P c := by
   rw [dropPrefix?_eq_dropPrefix?_toSlice] at h
-  simpa using Slice.eq_append_of_dropPrefix?_prop_eq_some h
+  simpa using Slice.eq_append_of_dropPrefix_prop_eq_some h
 
 theorem skipSuffix?_bool_eq_some_iff {p : Char → Bool} {s : String} {pos : s.Pos} :
     s.skipSuffix? p = some pos ↔ ∃ h, pos = s.endPos.prev h ∧ p ((s.endPos.prev h).get (by simp)) = true := by
@@ -364,15 +171,15 @@ theorem skipSuffix?_bool_eq_some_iff {p : Char → Bool} {s : String} {pos : s.P
 
 theorem endsWith_bool_iff_get {p : Char → Bool} {s : String} :
     s.endsWith p ↔ ∃ h, p ((s.endPos.prev h).get (by simp)) = true := by
-  simp [← endsWith_toSlice, Slice.endsWith_bool_iff_get, Pos.prev_toSlice]
+  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_bool_iff_get, Pos.prev_toSlice]
 
 theorem endsWith_bool_eq_false_iff_get {p : Char → Bool} {s : String} :
     s.endsWith p = false ↔ ∀ h, p ((s.endPos.prev h).get (by simp)) = false := by
-  simp [← endsWith_toSlice, Slice.endsWith_bool_eq_false_iff_get, Pos.prev_toSlice]
+  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_bool_eq_false_iff_get, Pos.prev_toSlice]
 
 theorem endsWith_bool_eq_getLast? {p : Char → Bool} {s : String} :
     s.endsWith p = s.toList.getLast?.any p := by
-  simp [← endsWith_toSlice, Slice.endsWith_bool_eq_getLast?]
+  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_bool_eq_getLast?]
 
 theorem eq_append_of_dropSuffix?_bool_eq_some {p : Char → Bool} {s : String} {res : Slice} (h : s.dropSuffix? p = some res) :
     ∃ c, s = res.copy ++ singleton c ∧ p c = true := by
@@ -386,154 +193,19 @@ theorem skipSuffix?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s :
 
 theorem endsWith_prop_iff_get {P : Char → Prop} [DecidablePred P] {s : String} :
     s.endsWith P ↔ ∃ h, P ((s.endPos.prev h).get (by simp)) := by
-  simp [← endsWith_toSlice, Slice.endsWith_prop_iff_get, Pos.prev_toSlice]
+  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_prop_iff_get, Pos.prev_toSlice]
 
 theorem endsWith_prop_eq_false_iff_get {P : Char → Prop} [DecidablePred P] {s : String} :
     s.endsWith P = false ↔ ∀ h, ¬ P ((s.endPos.prev h).get (by simp)) := by
-  simp [← endsWith_toSlice, Slice.endsWith_prop_eq_false_iff_get, Pos.prev_toSlice]
+  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_prop_eq_false_iff_get, Pos.prev_toSlice]
 
 theorem endsWith_prop_eq_getLast? {P : Char → Prop} [DecidablePred P] {s : String} :
     s.endsWith P = s.toList.getLast?.any (decide <| P ·) := by
-  simp [← endsWith_toSlice, Slice.endsWith_prop_eq_getLast?]
+  simp [endsWith_eq_endsWith_toSlice, Slice.endsWith_prop_eq_getLast?]
 
 theorem eq_append_of_dropSuffix?_prop_eq_some {P : Char → Prop} [DecidablePred P] {s : String} {res : Slice}
     (h : s.dropSuffix? P = some res) : ∃ c, s = res.copy ++ singleton c ∧ P c := by
   rw [dropSuffix?_eq_dropSuffix?_toSlice] at h
   simpa using Slice.eq_append_of_dropSuffix?_prop_eq_some h
 
-@[simp]
-theorem Pos.skip?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s : String} {pos res : s.Pos} :
-    pos.skip? P = some res ↔ ∃ h, res = pos.next h ∧ P (pos.get h) := by
-  simp [skip?_eq_skip?_toSlice, ← toSlice_inj, toSlice_next]
-
-@[simp]
-theorem Pos.skip?_prop_eq_none_iff {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos} :
-    pos.skip? P = none ↔ ∀ h, ¬ P (pos.get h) := by
-  simp [skip?_eq_skip?_toSlice]
-
-theorem Pos.apply_skipWhile_prop {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos} {h} :
-    ¬ P ((pos.skipWhile P).get h) := by
-  simp [skipWhile_eq_skipWhile_toSlice, Slice.Pos.apply_skipWhile_prop]
-
-theorem Pos.skipWhile_prop_eq_self_iff_get {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos} :
-    pos.skipWhile P = pos ↔ ∀ h, ¬ P (pos.get h) := by
-  simp [skipWhile_eq_skipWhile_toSlice, ← toSlice_inj, Slice.Pos.skipWhile_prop_eq_self_iff_get]
-
-theorem Pos.apply_of_lt_skipWhile_prop {P : Char → Prop} [DecidablePred P] {s : String} {pos pos' : s.Pos}
-    (h₁ : pos ≤ pos') (h₂ : pos' < pos.skipWhile P) : P (pos'.get (ne_endPos_of_lt h₂)) := by
-  rw [Pos.get_eq_get_toSlice]
-  exact Slice.Pos.apply_of_lt_skipWhile_prop (toSlice_le_toSlice_iff.2 h₁)
-    (by simpa [skipWhile_eq_skipWhile_toSlice] using h₂)
-
-theorem apply_skipPrefixWhile_prop {P : Char → Prop} [DecidablePred P] {s : String} {h} :
-    ¬ P ((s.skipPrefixWhile P).get h) := by
-  simp [skipPrefixWhile_eq_skipPrefixWhile_toSlice, Slice.apply_skipPrefixWhile_prop]
-
-theorem apply_of_lt_skipPrefixWhile_prop {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos}
-    (h : pos < s.skipPrefixWhile P) : P (pos.get (Pos.ne_endPos_of_lt h)) := by
-  rw [Pos.get_eq_get_toSlice]
-  exact Slice.apply_of_lt_skipPrefixWhile_prop (by simpa [skipPrefixWhile_eq_skipPrefixWhile_toSlice] using h)
-
-@[simp]
-theorem all_prop_eq {P : Char → Prop} [DecidablePred P] {s : String} :
-    s.all P = s.toList.all (decide <| P ·) := by
-  simp [← all_toSlice]
-
-@[simp]
-theorem Pos.revSkip?_bool_eq_some_iff {p : Char → Bool} {s : String} {pos res : s.Pos} :
-    pos.revSkip? p = some res ↔ ∃ h, res = pos.prev h ∧ p ((pos.prev h).get (by simp)) := by
-  simp [revSkip?_eq_revSkip?_toSlice, ← toSlice_inj, toSlice_prev, get_eq_get_toSlice]
-
-@[simp]
-theorem Pos.revSkip?_bool_eq_none_iff {p : Char → Bool} {s : String} {pos : s.Pos} :
-    pos.revSkip? p = none ↔ ∀ h, p ((pos.prev h).get (by simp)) = false := by
-  simp [revSkip?_eq_revSkip?_toSlice, Pos.prev_toSlice]
-
-theorem Pos.apply_revSkipWhile_bool_eq_false {p : Char → Bool} {s : String} {pos : s.Pos} {h} :
-    p (((pos.revSkipWhile p).prev h).get (by simp)) = false := by
-  have h' : pos.toSlice.revSkipWhile p ≠ s.toSlice.startPos := by
-    simpa [Pos.revSkipWhile_eq_revSkipWhile_toSlice, ← toSlice_inj] using h
-  have := Slice.Pos.apply_revSkipWhile_bool_eq_false (pos := pos.toSlice) (h := h')
-  simpa [Pos.revSkipWhile_eq_revSkipWhile_toSlice, Pos.prev_ofToSlice]
-
-theorem Pos.revSkipWhile_bool_eq_self_iff_get {p : Char → Bool} {s : String} {pos : s.Pos} :
-    pos.revSkipWhile p = pos ↔ ∀ h, p ((pos.prev h).get (by simp)) = false := by
-  simp [Pos.revSkipWhile_eq_revSkipWhile_toSlice, ← toSlice_inj, Slice.Pos.revSkipWhile_bool_eq_self_iff_get,
-    Pos.prev_toSlice]
-
-theorem Pos.apply_eq_true_of_revSkipWhile_le_bool {p : Char → Bool} {s : String} {pos pos' : s.Pos}
-    (h₁ : pos' < pos) (h₂ : pos.revSkipWhile p ≤ pos') : p (pos'.get (ne_endPos_of_lt h₁)) = true := by
-  rw [Pos.get_eq_get_toSlice]
-  exact Slice.Pos.apply_eq_true_of_revSkipWhile_le_bool
-    (Pos.toSlice_lt_toSlice_iff.2 h₁)
-    (by simpa [Pos.revSkipWhile_eq_revSkipWhile_toSlice, Pos.ofToSlice_le_iff] using h₂)
-
-theorem apply_skipSuffixWhile_bool_eq_false {p : Char → Bool} {s : String} {h} :
-    p (((s.skipSuffixWhile p).prev h).get (by simp)) = false := by
-  have h' : s.toSlice.skipSuffixWhile p ≠ s.toSlice.startPos := by
-    simpa [skipSuffixWhile_eq_skipSuffixWhile_toSlice, ← Pos.toSlice_inj] using h
-  have := Slice.apply_skipSuffixWhile_bool_eq_false (s := s.toSlice) (h := h')
-  simpa [skipSuffixWhile_eq_skipSuffixWhile_toSlice, Pos.prev_ofToSlice]
-
-theorem apply_eq_true_of_skipSuffixWhile_le_bool {p : Char → Bool} {s : String} {pos : s.Pos}
-    (h : s.skipSuffixWhile p ≤ pos) (h' : pos < s.endPos) :
-    p (pos.get (Pos.ne_endPos_of_lt h')) = true := by
-  rw [Pos.get_eq_get_toSlice]
-  exact Slice.apply_eq_true_of_skipSuffixWhile_le_bool
-    (by simpa [skipSuffixWhile_eq_skipSuffixWhile_toSlice, Pos.ofToSlice_le_iff] using h)
-    (by simpa [Pos.toSlice_lt_toSlice_iff] using h')
-
-@[simp]
-theorem revAll_bool_eq {p : Char → Bool} {s : String} : s.revAll p = s.toList.all p := by
-  simp [← revAll_toSlice]
-
-@[simp]
-theorem Pos.revSkip?_prop_eq_some_iff {P : Char → Prop} [DecidablePred P] {s : String} {pos res : s.Pos} :
-    pos.revSkip? P = some res ↔ ∃ h, res = pos.prev h ∧ P ((pos.prev h).get (by simp)) := by
-  simp [revSkip?_eq_revSkip?_toSlice, ← toSlice_inj, toSlice_prev, get_eq_get_toSlice]
-
-@[simp]
-theorem Pos.revSkip?_prop_eq_none_iff {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos} :
-    pos.revSkip? P = none ↔ ∀ h, ¬ P ((pos.prev h).get (by simp)) := by
-  simp [revSkip?_eq_revSkip?_toSlice, Pos.prev_toSlice]
-
-theorem Pos.apply_revSkipWhile_prop {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos} {h} :
-    ¬ P (((pos.revSkipWhile P).prev h).get (by simp)) := by
-  have h' : pos.toSlice.revSkipWhile P ≠ s.toSlice.startPos := by
-    simpa [Pos.revSkipWhile_eq_revSkipWhile_toSlice, ← toSlice_inj] using h
-  have := Slice.Pos.apply_revSkipWhile_prop (pos := pos.toSlice) (h := h')
-  simpa [Pos.revSkipWhile_eq_revSkipWhile_toSlice, Pos.prev_ofToSlice]
-
-theorem Pos.revSkipWhile_prop_eq_self_iff_get {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos} :
-    pos.revSkipWhile P = pos ↔ ∀ h, ¬ P ((pos.prev h).get (by simp)) := by
-  simp [Pos.revSkipWhile_eq_revSkipWhile_toSlice, ← toSlice_inj,
-    Slice.Pos.revSkipWhile_prop_eq_self_iff_get, Pos.prev_toSlice]
-
-theorem Pos.apply_of_revSkipWhile_le_prop {P : Char → Prop} [DecidablePred P] {s : String} {pos pos' : s.Pos}
-    (h₁ : pos' < pos) (h₂ : pos.revSkipWhile P ≤ pos') : P (pos'.get (ne_endPos_of_lt h₁)) := by
-  rw [Pos.get_eq_get_toSlice]
-  exact Slice.Pos.apply_of_revSkipWhile_le_prop
-    (Pos.toSlice_lt_toSlice_iff.2 h₁)
-    (by simpa [Pos.revSkipWhile_eq_revSkipWhile_toSlice, Pos.ofToSlice_le_iff] using h₂)
-
-theorem apply_skipSuffixWhile_prop {P : Char → Prop} [DecidablePred P] {s : String} {h} :
-    ¬ P (((s.skipSuffixWhile P).prev h).get (by simp)) := by
-  have h' : s.toSlice.skipSuffixWhile P ≠ s.toSlice.startPos := by
-    simpa [skipSuffixWhile_eq_skipSuffixWhile_toSlice, ← Pos.toSlice_inj] using h
-  have := Slice.apply_skipSuffixWhile_prop (s := s.toSlice) (h := h')
-  simpa [skipSuffixWhile_eq_skipSuffixWhile_toSlice, Pos.prev_ofToSlice]
-
-theorem apply_of_skipSuffixWhile_le_prop {P : Char → Prop} [DecidablePred P] {s : String} {pos : s.Pos}
-    (h : s.skipSuffixWhile P ≤ pos) (h' : pos < s.endPos) :
-    P (pos.get (Pos.ne_endPos_of_lt h')) := by
-  rw [Pos.get_eq_get_toSlice]
-  exact Slice.apply_of_skipSuffixWhile_le_prop
-    (by simpa [skipSuffixWhile_eq_skipSuffixWhile_toSlice, Pos.ofToSlice_le_iff] using h)
-    (by simpa [Pos.toSlice_lt_toSlice_iff] using h')
-
-@[simp]
-theorem revAll_prop_eq {P : Char → Prop} [DecidablePred P] {s : String} :
-    s.revAll P = s.toList.all (decide <| P ·) := by
-  simp [← revAll_toSlice]
-
 end String

src/Init/Data/String/Lemmas/Pattern/TakeDrop/String.lean

@@ -30,7 +30,11 @@ theorem skipPrefix?_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true)
 @[simp]
 theorem skipPrefix?_slice_eq_some_iff {pat s : Slice} {pos : s.Pos} :
     s.skipPrefix? pat = some pos ↔ ∃ t, pos.Splits pat.copy t := by
-  rw [Pattern.Model.skipPrefix?_eq_some_iff, ForwardSliceSearcher.isLongestMatch_iff_splits]
+  match h : pat.isEmpty with
+  | false =>
+    have := ForwardSliceSearcher.lawfulForwardPatternModel h
+    rw [Pattern.Model.skipPrefix?_eq_some_iff, ForwardSliceSearcher.isLongestMatch_iff_splits h]
+  | true => simp [skipPrefix?_slice_of_isEmpty h, (show pat.copy = "" by simpa), eq_comm]
 
 theorem startsWith_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true) :
     s.startsWith pat = true := by
@@ -39,10 +43,14 @@ theorem startsWith_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true)
 @[simp]
 theorem startsWith_slice_iff {pat s : Slice} :
     s.startsWith pat ↔ pat.copy.toList <+: s.copy.toList := by
-  simp only [Model.startsWith_iff, ForwardSliceSearcher.matchesAt_iff_splits,
-    splits_startPos_iff, exists_and_left, exists_eq_left]
-  simp only [← toList_inj, toList_append, List.prefix_iff_exists_append_eq]
-  exact ⟨fun ⟨t, ht⟩ => ⟨t.toList, by simp [ht]⟩, fun ⟨t, ht⟩ => ⟨String.ofList t, by simp [← ht]⟩⟩
+  match h : pat.isEmpty with
+  | false =>
+    have := ForwardSliceSearcher.lawfulForwardPatternModel h
+    simp only [Model.startsWith_iff, ForwardSliceSearcher.matchesAt_iff_splits h,
+      splits_startPos_iff, exists_and_left, exists_eq_left]
+    simp only [← toList_inj, toList_append, List.prefix_iff_exists_append_eq]
+    exact ⟨fun ⟨t, ht⟩ => ⟨t.toList, by simp [ht]⟩, fun ⟨t, ht⟩ => ⟨String.ofList t, by simp [← ht]⟩⟩
+  | true => simp [startsWith_slice_of_isEmpty h, (show pat.copy = "" by simpa)]
 
 @[simp]
 theorem startsWith_slice_eq_false_iff {pat s : Slice} :
@@ -55,18 +63,14 @@ theorem dropPrefix?_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true)
 
 theorem eq_append_of_dropPrefix?_slice_eq_some {pat s res : Slice} (h : s.dropPrefix? pat = some res) :
     s.copy = pat.copy ++ res.copy := by
-  have := Pattern.Model.eq_append_of_dropPrefix?_eq_some h
-  simp only [PatternModel.Matches] at this
-  obtain ⟨_, ⟨-, rfl⟩, h⟩ := this
-  exact h
-
-@[simp]
-theorem all_slice_iff {pat s : Slice} : s.all pat ↔ ∃ n, s.copy = String.join (List.replicate n pat.copy) := by
-  simp [Pattern.Model.all_eq_true_iff, ForwardSliceSearcher.isLongestMatchAtChain_startPos_endPos_iff]
-
-@[simp]
-theorem revAll_slice_iff {pat s : Slice} : s.revAll pat ↔ ∃ n, s.copy = String.join (List.replicate n pat.copy) := by
-  simp [Pattern.Model.revAll_eq_true_iff, ForwardSliceSearcher.isLongestRevMatchAtChain_startPos_endPos_iff]
+  match hpat : pat.isEmpty with
+  | false =>
+    have := ForwardSliceSearcher.lawfulForwardPatternModel hpat
+    have := Pattern.Model.eq_append_of_dropPrefix?_eq_some h
+    simp only [PatternModel.Matches] at this
+    obtain ⟨_, ⟨-, rfl⟩, h⟩ := this
+    exact h
+  | true => simp [Option.some.inj (h ▸ dropPrefix?_slice_of_isEmpty hpat), (show pat.copy = "" by simpa)]
 
 @[simp]
 theorem skipPrefix?_string_eq_some_iff {pat : String} {s : Slice} {pos : s.Pos} :
@@ -100,7 +104,6 @@ theorem eq_append_of_dropPrefix?_string_eq_some {pat : String} {s res : Slice} (
   rw [dropPrefix?_string_eq_dropPrefix?_toSlice] at h
   simpa using eq_append_of_dropPrefix?_slice_eq_some h
 
-
 theorem skipSuffix?_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true) :
     s.skipSuffix? pat = some s.endPos := by
   rw [skipSuffix?_eq_backwardPatternSkipSuffix?, BackwardSliceSearcher.skipSuffix?_of_isEmpty hpat]
@@ -108,7 +111,11 @@ theorem skipSuffix?_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true)
 @[simp]
 theorem skipSuffix?_slice_eq_some_iff {pat s : Slice} {pos : s.Pos} :
     s.skipSuffix? pat = some pos ↔ ∃ t, pos.Splits t pat.copy := by
-  rw [Pattern.Model.skipSuffix?_eq_some_iff, ForwardSliceSearcher.isLongestRevMatch_iff_splits]
+  match h : pat.isEmpty with
+  | false =>
+    have := BackwardSliceSearcher.lawfulBackwardPatternModel h
+    rw [Pattern.Model.skipSuffix?_eq_some_iff, ForwardSliceSearcher.isLongestRevMatch_iff_splits h]
+  | true => simp [skipSuffix?_slice_of_isEmpty h, (show pat.copy = "" by simpa), eq_comm]
 
 theorem endsWith_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true) :
     s.endsWith pat = true := by
@@ -117,10 +124,14 @@ theorem endsWith_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true) :
 @[simp]
 theorem endsWith_slice_iff {pat s : Slice} :
     s.endsWith pat ↔ pat.copy.toList <:+ s.copy.toList := by
-  simp only [Model.endsWith_iff, ForwardSliceSearcher.revMatchesAt_iff_splits,
-    splits_endPos_iff, exists_eq_right]
-  simp only [← toList_inj, toList_append, List.suffix_iff_exists_append_eq]
-  exact ⟨fun ⟨t, ht⟩ => ⟨t.toList, by simp [ht]⟩, fun ⟨t, ht⟩ => ⟨String.ofList t, by simp [← ht]⟩⟩
+  match h : pat.isEmpty with
+  | false =>
+    have := BackwardSliceSearcher.lawfulBackwardPatternModel h
+    simp only [Model.endsWith_iff, ForwardSliceSearcher.revMatchesAt_iff_splits h,
+      splits_endPos_iff, exists_eq_right]
+    simp only [← toList_inj, toList_append, List.suffix_iff_exists_append_eq]
+    exact ⟨fun ⟨t, ht⟩ => ⟨t.toList, by simp [ht]⟩, fun ⟨t, ht⟩ => ⟨String.ofList t, by simp [← ht]⟩⟩
+  | true => simp [endsWith_slice_of_isEmpty h, (show pat.copy = "" by simpa)]
 
 @[simp]
 theorem endsWith_slice_eq_false_iff {pat s : Slice} :
@@ -133,10 +144,14 @@ theorem dropSuffix?_slice_of_isEmpty {pat s : Slice} (hpat : pat.isEmpty = true)
 
 theorem eq_append_of_dropSuffix?_slice_eq_some {pat s res : Slice} (h : s.dropSuffix? pat = some res) :
     s.copy = res.copy ++ pat.copy := by
-  have := Pattern.Model.eq_append_of_dropSuffix?_eq_some h
-  simp only [PatternModel.Matches] at this
-  obtain ⟨_, ⟨-, rfl⟩, h⟩ := this
-  exact h
+  match hpat : pat.isEmpty with
+  | false =>
+    have := BackwardSliceSearcher.lawfulBackwardPatternModel hpat
+    have := Pattern.Model.eq_append_of_dropSuffix?_eq_some h
+    simp only [PatternModel.Matches] at this
+    obtain ⟨_, ⟨-, rfl⟩, h⟩ := this
+    exact h
+  | true => simp [Option.some.inj (h ▸ dropSuffix?_slice_of_isEmpty hpat), (show pat.copy = "" by simpa)]
 
 @[simp]
 theorem skipSuffix?_string_eq_some_iff' {pat : String} {s : Slice} {pos : s.Pos} :
@@ -193,12 +208,12 @@ theorem startsWith_slice_of_isEmpty {pat : Slice} {s : String} (hpat : pat.isEmp
 @[simp]
 theorem startsWith_slice_iff {pat : Slice} {s : String} :
     s.startsWith pat ↔ pat.copy.toList <+: s.toList := by
-  simp [← startsWith_toSlice]
+  simp [startsWith_eq_startsWith_toSlice]
 
 @[simp]
 theorem startsWith_slice_eq_false_iff {pat : Slice} {s : String} :
     s.startsWith pat = false ↔ ¬ (pat.copy.toList <+: s.toList) := by
-  simp [← startsWith_toSlice]
+  simp [startsWith_eq_startsWith_toSlice]
 
 theorem dropPrefix?_slice_of_isEmpty {pat : Slice} {s : String} (hpat : pat.isEmpty = true) :
     s.dropPrefix? pat = some s.toSlice := by
@@ -224,21 +239,21 @@ theorem skipPrefix?_string_eq_some_iff {pat s : String} {pos : s.Pos} :
 
 @[simp]
 theorem startsWith_string_empty {s : String} : s.startsWith "" = true := by
-  simp [← startsWith_toSlice]
+  simp [startsWith_eq_startsWith_toSlice]
 
 @[simp]
 theorem startsWith_string_iff {pat s : String} :
     s.startsWith pat ↔ pat.toList <+: s.toList := by
-  simp [← startsWith_toSlice]
+  simp [startsWith_eq_startsWith_toSlice]
 
 @[simp]
 theorem startsWith_string_eq_false_iff {pat s : String} :
     s.startsWith pat = false ↔ ¬ (pat.toList <+: s.toList) := by
-  simp [← startsWith_toSlice]
+  simp [startsWith_eq_startsWith_toSlice]
 
 @[simp]
 theorem dropPrefix?_string_empty {s : String} : s.dropPrefix? "" = some s.toSlice := by
-  simp [← dropPrefix?_toSlice]
+  simp [dropPrefix?_eq_dropPrefix?_toSlice]
 
 theorem eq_append_of_dropPrefix?_string_eq_some {s pat : String} {res : Slice} (h : s.dropPrefix? pat = some res) :
     s = pat ++ res.copy := by

src/Init/Data/String/Lemmas/Splits.lean

@@ -99,11 +99,6 @@ theorem Pos.splits {s : String} (p : s.Pos) :
   eq_append := by simp [← toByteArray_inj, Slice.toByteArray_copy, ← size_toByteArray]
   offset_eq_rawEndPos := by simp
 
-@[simp]
-theorem sliceTo_append_sliceFrom {s : String} {pos : s.Pos} :
-    (s.sliceTo pos).copy ++ (s.sliceFrom pos).copy = s :=
-  pos.splits.eq_append.symm
-
 theorem Slice.Pos.splits {s : Slice} (p : s.Pos) :
     p.Splits (s.sliceTo p).copy (s.sliceFrom p).copy where
   eq_append := copy_eq_copy_sliceTo
@@ -380,10 +375,6 @@ theorem Slice.copy_sliceTo_eq_iff_exists_splits {s : Slice} {p : s.Pos} {t₁ :
   · rintro ⟨t₂, h⟩
     exact p.splits.eq_left h
 
-theorem Slice.copy_sliceTo_eq_iff_splits {s : Slice} {p : s.Pos} {t₁ : String} :
-    (s.sliceTo p).copy = t₁ ↔ p.Splits t₁ (s.sliceFrom p).copy :=
-  ⟨fun h => h ▸ p.splits, p.splits.eq_left⟩
-
 theorem Slice.copy_sliceFrom_eq_iff_exists_splits {s : Slice} {p : s.Pos} {t₂ : String} :
     (s.sliceFrom p).copy = t₂ ↔ ∃ t₁, p.Splits t₁ t₂ := by
   refine ⟨?_, ?_⟩
@@ -392,26 +383,14 @@ theorem Slice.copy_sliceFrom_eq_iff_exists_splits {s : Slice} {p : s.Pos} {t₂
   · rintro ⟨t₂, h⟩
     exact p.splits.eq_right h
 
-theorem Slice.copy_sliceFrom_eq_iff_splits {s : Slice} {p : s.Pos} {t₂ : String} :
-    (s.sliceFrom p).copy = t₂ ↔ p.Splits (s.sliceTo p).copy t₂ :=
-  ⟨fun h => h ▸ p.splits, p.splits.eq_right⟩
-
 theorem copy_sliceTo_eq_iff_exists_splits {s : String} {p : s.Pos} {t₁ : String} :
     (s.sliceTo p).copy = t₁ ↔ ∃ t₂, p.Splits t₁ t₂ := by
   simp [← Pos.splits_toSlice_iff, ← Slice.copy_sliceTo_eq_iff_exists_splits]
 
-theorem copy_sliceTo_eq_iff_splits {s : String} {p : s.Pos} {t₁ : String} :
-    (s.sliceTo p).copy = t₁ ↔ p.Splits t₁ (s.sliceFrom p).copy :=
-  ⟨fun h => h ▸ p.splits, p.splits.eq_left⟩
-
 theorem copy_sliceFrom_eq_iff_exists_splits {s : String} {p : s.Pos} {t₂ : String} :
     (s.sliceFrom p).copy = t₂ ↔ ∃ t₁, p.Splits t₁ t₂ := by
   simp [← Pos.splits_toSlice_iff, ← Slice.copy_sliceFrom_eq_iff_exists_splits]
 
-theorem copy_sliceFrom_eq_iff_splits {s : String} {p : s.Pos} {t₂ : String} :
-    (s.sliceFrom p).copy = t₂ ↔ p.Splits (s.sliceTo p).copy t₂ :=
-  ⟨fun h => h ▸ p.splits, p.splits.eq_right⟩
-
 theorem Pos.Splits.offset_eq_decreaseBy {s : String} {p : s.Pos} (h : p.Splits t₁ t₂) :
     p.offset = s.rawEndPos.decreaseBy t₂.utf8ByteSize := by
   simp [h.offset_eq_rawEndPos, h.eq_append, Pos.Raw.ext_iff]
@@ -662,28 +641,6 @@ theorem Pos.splits_append_rawEndPos {s t : String} :
   eq_append := rfl
   offset_eq_rawEndPos := rfl
 
-/--
-Given a slice `s` such that `s.copy = t₁ ++ t₂`, obtain the position sitting between `t₁` and `t₂`.
--/
-def Slice.Pos.ofEqAppend {s : Slice} {t₁ t₂ : String} (h : s.copy = t₁ ++ t₂) : s.Pos :=
-  s.pos t₁.rawEndPos
-    (by simpa [← Pos.Raw.isValid_copy_iff, h] using ((Pos.Raw.isValid_rawEndPos).append_right t₂))
-
-theorem Slice.Pos.splits_ofEqAppend {s : Slice} {t₁ t₂ : String} (h : s.copy = t₁ ++ t₂) :
-    (ofEqAppend h).Splits t₁ t₂ where
-  eq_append := h
-  offset_eq_rawEndPos := by simp [ofEqAppend]
-
-/--
-Given a string `s` such that `s = t₁ ++ t₂`, obtain the position sitting between `t₁` and `t₂`.
--/
-def Pos.ofEqAppend {s t₁ t₂ : String} (h : s = t₁ ++ t₂) : s.Pos :=
-  ((t₁ ++ t₂).pos t₁.rawEndPos ((Pos.Raw.isValid_rawEndPos).append_right t₂)).cast h.symm
-
-theorem Pos.splits_ofEqAppend {s t₁ t₂ : String} (h : s = t₁ ++ t₂) : (ofEqAppend h).Splits t₁ t₂ where
-  eq_append := h
-  offset_eq_rawEndPos := by simp [ofEqAppend]
-
 theorem Pos.Splits.copy_sliceTo_eq {s : String} {p : s.Pos} (h : p.Splits t₁ t₂) :
     (s.sliceTo p).copy = t₁ :=
   p.splits.eq_left h
@@ -783,44 +740,4 @@ theorem splits_prevn_endPos (s : String) (n : Nat) :
     (s.endPos.prevn n).Splits (String.ofList (s.toList.take (s.length - n))) (String.ofList (s.toList.drop (s.length - n))) := by
   simpa using s.splits_endPos.prevn n
 
-@[simp]
-theorem Slice.copy_sliceFrom_cast {s t : Slice} (hst : s.copy = t.copy) {pos : s.Pos} :
-    (t.sliceFrom (pos.cast hst)).copy = (s.sliceFrom pos).copy := by
-  simpa [copy_sliceFrom_eq_iff_exists_splits] using ⟨_, pos.splits⟩
-
-@[simp]
-theorem Slice.copy_sliceTo_cast {s t : Slice} (hst : s.copy = t.copy) {pos : s.Pos} :
-    (t.sliceTo (pos.cast hst)).copy = (s.sliceTo pos).copy := by
-  simpa [copy_sliceTo_eq_iff_exists_splits] using ⟨_, pos.splits⟩
-
-@[simp]
-theorem copy_sliceFrom_cast {s t : String} (hst : s = t) {pos : s.Pos} :
-    (t.sliceFrom (pos.cast hst)).copy = (s.sliceFrom pos).copy := by
-  simpa [copy_sliceFrom_eq_iff_exists_splits] using ⟨_, pos.splits⟩
-
-@[simp]
-theorem copy_sliceTo_cast {s t : String} (hst : s = t) {pos : s.Pos} :
-    (t.sliceTo (pos.cast hst)).copy = (s.sliceTo pos).copy := by
-  simpa [copy_sliceTo_eq_iff_exists_splits] using ⟨_, pos.splits⟩
-
-theorem Slice.Pos.sliceFrom_cast {s t : Slice} {hst : s.copy = t.copy} (p q : s.Pos) {h} :
-    Slice.Pos.sliceFrom (p.cast hst) (q.cast hst) h =
-      (Slice.Pos.sliceFrom p q (by simpa using h)).cast (by simp) := by
-  ext1; simp
-
-theorem Slice.Pos.sliceTo_cast {s t : Slice} {hst : s.copy = t.copy} (p q : s.Pos) {h} :
-    Slice.Pos.sliceTo (p.cast hst) (q.cast hst) h =
-      (Slice.Pos.sliceTo p q (by simpa using h)).cast (by simp) := by
-  ext1; simp
-
-theorem Pos.sliceFrom_cast {s t : String} {hst : s = t} (p q : s.Pos) {h} :
-    Pos.sliceFrom (p.cast hst) (q.cast hst) h =
-      (Pos.sliceFrom p q (by simpa using h)).cast (by simp) := by
-  ext1; simp
-
-theorem Pos.sliceTo_cast {s t : String} {hst : s = t} (p q : s.Pos) {h} :
-    Pos.sliceTo (p.cast hst) (q.cast hst) h =
-      (Pos.sliceTo p q (by simpa using h)).cast (by simp) := by
-  ext1; simp
-
 end String

src/Init/Data/String/Lemmas/StringOrder.lean

@@ -1,49 +0,0 @@
-/-
-Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-module
-
-prelude
-public import Init.Data.String.Basic
-public import Init.Data.Order.Classes
-import Init.Data.List.Lex
-import Init.Data.Char.Lemmas
-import Init.Data.Char.Order
-import Init.Data.Order.Factories
-import Init.Data.Order.Lemmas
-
-public section
-
-open Std
-
-namespace String
-
-@[simp] protected theorem not_le {a b : String} : ¬ a ≤ b ↔ b < a := Decidable.not_not
-@[simp] protected theorem not_lt {a b : String} : ¬ a < b ↔ b ≤ a := Iff.rfl
-@[simp] protected theorem le_refl (a : String) : a ≤ a := List.le_refl _
-@[simp] protected theorem lt_irrefl (a : String) : ¬ a < a := List.lt_irrefl _
-
-attribute [local instance] Char.notLTTrans Char.ltTrichotomous Char.ltAsymm
-
-protected theorem le_trans {a b c : String} : a ≤ b → b ≤ c → a ≤ c := List.le_trans
-protected theorem lt_trans {a b c : String} : a < b → b < c → a < c := List.lt_trans
-protected theorem le_total (a b : String) : a ≤ b ∨ b ≤ a := List.le_total _ _
-protected theorem le_antisymm {a b : String} : a ≤ b → b ≤ a → a = b := fun h₁ h₂ => String.ext (List.le_antisymm (as := a.toList) (bs := b.toList) h₁ h₂)
-protected theorem lt_asymm {a b : String} (h : a < b) : ¬ b < a := List.lt_asymm h
-protected theorem ne_of_lt {a b : String} (h : a < b) : a ≠ b := by
-  have := String.lt_irrefl a
-  intro h; subst h; contradiction
-
-instance instIsLinearOrder : IsLinearOrder String := by
-  apply IsLinearOrder.of_le
-  case le_antisymm => constructor; apply String.le_antisymm
-  case le_trans => constructor; apply String.le_trans
-  case le_total => constructor; apply String.le_total
-
-instance : LawfulOrderLT String where
-  lt_iff a b := by
-    simp [← String.not_le, Decidable.imp_iff_not_or, Std.Total.total]
-
-end String

src/Init/Data/String/Pattern/Basic.lean

@@ -96,44 +96,6 @@ theorem endPos_ofSliceFrom {s : Slice} {p : s.Pos} {st : SearchStep (s.sliceFrom
     st.ofSliceFrom.endPos = Slice.Pos.ofSliceFrom st.endPos := by
   cases st <;> simp [ofSliceFrom]
 
-/--
-Converts a {lean}`SearchStep s` into a {lean}`SearchStep t` by applying {name}`Slice.Pos.cast` to the
-start and end position.
--/
-@[inline]
-def cast {s t : Slice} (hst : s.copy = t.copy) : SearchStep s → SearchStep t
-  | .rejected startPos endPos => .rejected (startPos.cast hst) (endPos.cast hst)
-  | .matched startPos endPos => .matched (startPos.cast hst) (endPos.cast hst)
-
-@[simp]
-theorem cast_rejected {s t : Slice} {hst : s.copy = t.copy} {startPos endPos : s.Pos} :
-    (SearchStep.rejected startPos endPos).cast hst = .rejected (startPos.cast hst) (endPos.cast hst) :=
-  (rfl)
-
-@[simp]
-theorem cast_matched {s t : Slice} {hst : s.copy = t.copy} {startPos endPos : s.Pos} :
-    (SearchStep.matched startPos endPos).cast hst = .matched (startPos.cast hst) (endPos.cast hst) :=
-  (rfl)
-
-@[simp]
-theorem startPos_cast {s t : Slice} (hst : s.copy = t.copy) {st : SearchStep s} :
-    (st.cast hst).startPos = st.startPos.cast hst := by
-  cases st <;> simp
-
-@[simp]
-theorem endPos_cast {s t : Slice} (hst : s.copy = t.copy) {st : SearchStep s} :
-    (st.cast hst).endPos = st.endPos.cast hst := by
-  cases st <;> simp
-
-@[simp]
-theorem cast_rfl {s : Slice} {st : SearchStep s} : st.cast rfl = st := by
-  cases st <;> simp
-
-@[simp]
-theorem cast_cast {s t u : Slice} {hst : s.copy = t.copy} {htu : t.copy = u.copy} {st : SearchStep s} :
-    (st.cast hst).cast htu = st.cast (hst.trans htu) := by
-  cases st <;> simp
-
 end SearchStep
 
 /--

src/Init/Data/String/Search.lean

@@ -311,6 +311,23 @@ def Internal.containsImpl (s : String) (c : Char) : Bool :=
 def Internal.anyImpl (s : String) (p : Char → Bool) :=
   String.any s p
 
+/--
+Checks whether a slice only consists of matches of the pattern {name}`pat`.
+
+Short-circuits at the first pattern mis-match.
+
+This function is generic over all currently supported patterns.
+
+Examples:
+ * {lean}`"brown".all Char.isLower = true`
+ * {lean}`"brown and orange".all Char.isLower = false`
+ * {lean}`"aaaaaa".all 'a' = true`
+ * {lean}`"aaaaaa".all "aa" = true`
+ * {lean}`"aaaaaaa".all "aa" = false`
+-/
+@[inline, suggest_for String.every] def all (s : String) (pat : ρ) [ForwardPattern pat] : Bool :=
+  s.toSlice.all pat
+
 /--
 Checks whether the string can be interpreted as the decimal representation of a natural number.
 

src/Init/Data/String/Slice.lean

@@ -426,13 +426,13 @@ Advances {name}`pos` as long as {name}`pat` matches.
 -/
 @[specialize pat]
 def Pos.skipWhile {s : Slice} (pos : s.Pos) (pat : ρ) [ForwardPattern pat] : s.Pos :=
-  match pos.skip? pat with
-  | some nextCurr =>
-    if pos < nextCurr then
-      skipWhile nextCurr pat
+  if let some nextCurr := ForwardPattern.skipPrefix? pat (s.sliceFrom pos) then
+    if pos < Pos.ofSliceFrom nextCurr then
+      skipWhile (Pos.ofSliceFrom nextCurr) pat
     else
       pos
-  | none => pos
+  else
+    pos
 termination_by pos
 
 /--
@@ -572,7 +572,7 @@ Examples:
 -/
 @[inline]
 def all (s : Slice) (pat : ρ) [ForwardPattern pat] : Bool :=
-  s.skipPrefixWhile pat == s.endPos
+  s.dropWhile pat |>.isEmpty
 
 end ForwardPatternUsers
 
@@ -706,14 +706,14 @@ Returns {name}`none` otherwise.
 This function is generic over all currently supported patterns.
 -/
 @[inline]
-def Pos.revSkip? {s : Slice} (pos : s.Pos) (pat : ρ) [BackwardPattern pat] : Option s.Pos :=
-  ((s.sliceTo pos).skipSuffix? pat).map Pos.ofSliceTo
+def Pos.revSkip? {s : Slice} (pos : s.Pos) (pat : ρ) [ForwardPattern pat] : Option s.Pos :=
+  ((s.sliceFrom pos).skipPrefix? pat).map Pos.ofSliceFrom
 
 /--
 If {name}`pat` matches a suffix of {name}`s`, returns the remainder. Returns {name}`none` otherwise.
 
 Use {name (scope := "Init.Data.String.Slice")}`String.Slice.dropSuffix` to return the slice
-unchanged when {name}`pat` does not match a suffix.
+unchanged when {name}`pat` does not match a prefix.
 
 This function is generic over all currently supported patterns.
 
@@ -765,53 +765,23 @@ Rewinds {name}`pos` as long as {name}`pat` matches.
 -/
 @[specialize pat]
 def Pos.revSkipWhile {s : Slice} (pos : s.Pos) (pat : ρ) [BackwardPattern pat] : s.Pos :=
-  match pos.revSkip? pat with
-  | some nextCurr =>
-    if nextCurr < pos then
-      revSkipWhile nextCurr pat
+  if let some nextCurr := BackwardPattern.skipSuffix? pat (s.sliceTo pos) then
+    if Pos.ofSliceTo nextCurr < pos then
+      revSkipWhile (Pos.ofSliceTo nextCurr) pat
     else
       pos
-  | none => pos
+  else
+    pos
 termination_by pos.down
 
 /--
-Returns the position at the start of the longest suffix of {name}`s` for which {name}`pat` matches
+Returns the position a the start of the longest suffix of {name}`s` for which {name}`pat` matches
 (potentially repeatedly).
 -/
 @[inline]
 def skipSuffixWhile (s : Slice) (pat : ρ) [BackwardPattern pat] : s.Pos :=
   s.endPos.revSkipWhile pat
 
-/--
-Checks whether a slice only consists of matches of the pattern {name}`pat`, starting from the back
-of the string.
-
-Short-circuits at the first pattern mis-match.
-
-This function is generic over all currently supported patterns.
-
-For many types of patterns, this function can be expected to return the same result as
-{name}`Slice.all`. If mismatches are expected to occur close to the end of the string, this function
-might be more efficient.
-
-For some types of patterns, this function will return a different result than {name}`Slice.all`.
-Consider, for example, a pattern that matches the longest string at the given position that matches
-the regular expression {lean}`"a|aa|ab"`. Then, given the input string {lean}`"aab"`, performing
-{name}`Slice.all` will greedily match the prefix {lean}`"aa"` and then get stuck on the remainder
-{lean}`"b"`, causing it to return {lean}`false`. On the other hand, {name}`Slice.revAll` will match
-the suffix {lean}`"ab"` and then match the remainder {lean}`"a"`, so it will return {lean}`true`.
-
-Examples:
- * {lean}`"brown".toSlice.revAll Char.isLower = true`
- * {lean}`"brown and orange".toSlice.revAll Char.isLower = false`
- * {lean}`"aaaaaa".toSlice.revAll 'a' = true`
- * {lean}`"aaaaaa".toSlice.revAll "aa" = true`
- * {lean}`"aaaaaaa".toSlice.revAll "aa" = false`
--/
-@[inline]
-def revAll (s : Slice) (pat : ρ) [BackwardPattern pat] : Bool :=
-  s.skipSuffixWhile pat == s.startPos
-
 /--
 Creates a new slice that contains the longest suffix of {name}`s` for which {name}`pat` matched
 (potentially repeatedly).

src/Init/Data/String/Subslice.lean

@@ -23,7 +23,7 @@ Given a {name}`Slice` {name}`s`, the type {lean}`s.Subslice` is the type of half
 in {name}`s` delineated by a valid position on both sides.
 
 This type is useful to track regions of interest within some larger slice that is also of interest.
-In contrast, {name}`Slice` is used to track regions of interest within some larger string that is
+In contrast, {name}`Slice` is used to track regions of interest whithin some larger string that is
 not or no longer relevant.
 
 Equality on {name}`Subslice` is somewhat better behaved than on {name}`Slice`, but note that there

src/Init/Data/String/TakeDrop.lean

@@ -224,53 +224,6 @@ Returns the position after the longest prefix of {name}`s` for which {name}`pat`
 @[inline] def skipPrefixWhile (s : String) (pat : ρ) [ForwardPattern pat] : s.Pos :=
   Pos.ofToSlice (s.toSlice.skipPrefixWhile pat)
 
-/--
-Checks whether a string only consists of matches of the pattern {name}`pat`.
-
-Short-circuits at the first pattern mis-match.
-
-This function is generic over all currently supported patterns.
-
-Examples:
- * {lean}`"brown".all Char.isLower = true`
- * {lean}`"brown and orange".all Char.isLower = false`
- * {lean}`"aaaaaa".all 'a' = true`
- * {lean}`"aaaaaa".all "aa" = true`
- * {lean}`"aaaaaaa".all "aa" = false`
--/
-@[inline, suggest_for String.every] def all (s : String) (pat : ρ) [ForwardPattern pat] : Bool :=
-  s.toSlice.all pat
-
-/--
-Checks whether a string only consists of matches of the pattern {name}`pat`, starting from the back
-of the string.
-
-Short-circuits at the first pattern mis-match.
-
-This function is generic over all currently supported patterns.
-
-For many types of patterns, this function can be expected to return the same result as
-{name}`String.all`. If mismatches are expected to occur close to the end of the string, this function
-might be more efficient.
-
-For some types of patterns, this function will return a different result than {name}`String.all`.
-Consider, for example, a pattern that matches the longest string at the given position that matches
-the regular expression {lean}`"a|aa|ab"`. Then, given the input string {lean}`"aab"`, performing
-{name}`String.all` will greedily match the prefix {lean}`"aa"` and then get stuck on the remainder
-{lean}`"b"`, causing it to return {lean}`false`. On the other hand, {name}`String.revAll` will match
-the suffix {lean}`"ab"` and then match the remainder {lean}`"a"`, so it will return {lean}`true`.
-
-Examples:
- * {lean}`"brown".revAll Char.isLower = true`
- * {lean}`"brown and orange".revAll Char.isLower = false`
- * {lean}`"aaaaaa".revAll 'a' = true`
- * {lean}`"aaaaaa".revAll "aa" = true`
- * {lean}`"aaaaaaa".revAll "aa" = false`
--/
-@[inline]
-def revAll (s : String) (pat : ρ) [BackwardPattern pat] : Bool :=
-  s.toSlice.revAll pat
-
 /--
 If {name}`pat` matches at {name}`pos`, returns the position after the end of the match.
 Returns {name}`none` otherwise.
@@ -361,7 +314,7 @@ Returns {name}`none` otherwise.
 This function is generic over all currently supported patterns.
 -/
 @[inline]
-def Pos.revSkip? {s : String} (pos : s.Pos) (pat : ρ) [BackwardPattern pat] : Option s.Pos :=
+def Pos.revSkip? {s : String} (pos : s.Pos) (pat : ρ) [ForwardPattern pat] : Option s.Pos :=
   (pos.toSlice.revSkip? pat).map Pos.ofToSlice
 
 /--
@@ -508,7 +461,7 @@ def dropPrefix? (s : String) (pat : ρ) [ForwardPattern pat] : Option String.Sli
 If {name}`pat` matches a suffix of {name}`s`, returns the remainder. Returns {name}`none` otherwise.
 
 Use {name (scope := "Init.Data.String.TakeDrop")}`String.dropSuffix` to return the slice
-unchanged when {name}`pat` does not match a suffix.
+unchanged when {name}`pat` does not match a prefix.
 
 This is a cheap operation because it does not allocate a new string to hold the result.
 To convert the result into a string, use {name}`String.Slice.copy`.

src/Init/Data/Vector/Basic.lean

@@ -506,16 +506,6 @@ Examples:
 @[inline, expose] def sum [Add α] [Zero α] (xs : Vector α n) : α :=
   xs.toArray.sum
 
-/--
-Computes the product of the elements of a vector.
-
-Examples:
- * `#v[a, b, c].prod = a * (b * (c * 1))`
- * `#v[1, 2, 5].prod = 10`
--/
-@[inline, expose] def prod [Mul α] [One α] (xs : Vector α n) : α :=
-  xs.toArray.prod
-
 /--
 Pad a vector on the left with a given element.
 

src/Init/Data/Vector/Int.lean

@@ -30,16 +30,4 @@ theorem sum_reverse_int (xs : Vector Int n) : xs.reverse.sum = xs.sum := by
 theorem sum_eq_foldl_int {xs : Vector Int n} : xs.sum = xs.foldl (b := 0) (· + ·) := by
   simp only [foldl_eq_foldr_reverse, Int.add_comm, ← sum_eq_foldr, sum_reverse_int]
 
-@[simp] theorem prod_replicate_int {n : Nat} {a : Int} : (replicate n a).prod = a ^ n := by
-  simp [← prod_toArray, Array.prod_replicate_int]
-
-theorem prod_append_int {as₁ as₂ : Vector Int n} : (as₁ ++ as₂).prod = as₁.prod * as₂.prod := by
-  simp [← prod_toArray]
-
-theorem prod_reverse_int (xs : Vector Int n) : xs.reverse.prod = xs.prod := by
-  simp [prod_reverse]
-
-theorem prod_eq_foldl_int {xs : Vector Int n} : xs.prod = xs.foldl (b := 1) (· * ·) := by
-  simp only [foldl_eq_foldr_reverse, Int.mul_comm, ← prod_eq_foldr, prod_reverse_int]
-
 end Vector

src/Init/Data/Vector/Lemmas.lean

@@ -278,12 +278,6 @@ theorem toArray_mk {xs : Array α} (h : xs.size = n) : (Vector.mk xs h).toArray
 @[simp, grind =] theorem sum_toArray [Add α] [Zero α] {xs : Vector α n} :
     xs.toArray.sum = xs.sum := rfl
 
-@[simp] theorem prod_mk [Mul α] [One α] {xs : Array α} (h : xs.size = n) :
-    (Vector.mk xs h).prod = xs.prod := rfl
-
-@[simp, grind =] theorem prod_toArray [Mul α] [One α] {xs : Vector α n} :
-    xs.toArray.prod = xs.prod := rfl
-
 @[simp] theorem eq_mk : xs = Vector.mk as h ↔ xs.toArray = as := by
   cases xs
   simp
@@ -557,10 +551,6 @@ theorem toArray_toList {xs : Vector α n} : xs.toList.toArray = xs.toArray := rf
     xs.toList.sum = xs.sum := by
   rw [← toList_toArray, Array.sum_toList, sum_toArray]
 
-@[simp, grind =] theorem prod_toList [Mul α] [One α] {xs : Vector α n} :
-    xs.toList.prod = xs.prod := by
-  rw [← toList_toArray, Array.prod_toList, prod_toArray]
-
 @[simp] theorem getElem_toList {xs : Vector α n} {i : Nat} (h : i < xs.toList.length) :
     xs.toList[i] = xs[i]'(by simpa using h) := by
   cases xs
@@ -3144,39 +3134,3 @@ theorem sum_eq_foldl [Zero α] [Add α]
     {xs : Vector α n} :
     xs.sum = xs.foldl (b := 0) (· + ·) := by
   simp [← sum_toList, List.sum_eq_foldl]
-
-/-! ### prod -/
-
-@[simp, grind =] theorem prod_empty [Mul α] [One α] : (#v[] : Vector α 0).prod = 1 := rfl
-theorem prod_eq_foldr [Mul α] [One α] {xs : Vector α n} :
-    xs.prod = xs.foldr (b := 1) (· * ·) :=
-  rfl
-
-@[simp, grind =]
-theorem prod_append [One α] [Mul α] [Std.Associative (α := α) (· * ·)]
-    [Std.LeftIdentity (α := α) (· * ·) 1] [Std.LawfulLeftIdentity (α := α) (· * ·) 1]
-    {as₁ as₂ : Vector α n} : (as₁ ++ as₂).prod = as₁.prod * as₂.prod := by
-  simp [← prod_toList, List.prod_append]
-
-@[simp, grind =]
-theorem prod_singleton [Mul α] [One α] [Std.LawfulRightIdentity (· * ·) (1 : α)] {x : α} :
-    #v[x].prod = x := by
-  simp [← prod_toList, Std.LawfulRightIdentity.right_id x]
-
-@[simp, grind =]
-theorem prod_push [Mul α] [One α] [Std.Associative (α := α) (· * ·)]
-    [Std.LawfulIdentity (· * ·) (1 : α)] {xs : Vector α n} {x : α} :
-    (xs.push x).prod = xs.prod * x := by
-  simp [← prod_toArray]
-
-@[simp, grind =]
-theorem prod_reverse [One α] [Mul α] [Std.Associative (α := α) (· * ·)]
-    [Std.Commutative (α := α) (· * ·)]
-    [Std.LawfulLeftIdentity (α := α) (· * ·) 1] (xs : Vector α n) : xs.reverse.prod = xs.prod := by
-  simp [← prod_toList, List.prod_reverse]
-
-theorem prod_eq_foldl [One α] [Mul α]
-    [Std.Associative (α := α) (· * ·)] [Std.LawfulIdentity (· * ·) (1 : α)]
-    {xs : Vector α n} :
-    xs.prod = xs.foldl (b := 1) (· * ·) := by
-  simp [← prod_toList, List.prod_eq_foldl]

src/Init/Data/Vector/Nat.lean

@@ -37,23 +37,4 @@ theorem sum_reverse_nat (xs : Vector Nat n) : xs.reverse.sum = xs.sum := by
 theorem sum_eq_foldl_nat {xs : Vector Nat n} : xs.sum = xs.foldl (b := 0) (· + ·) := by
   simp only [foldl_eq_foldr_reverse, Nat.add_comm, ← sum_eq_foldr, sum_reverse_nat]
 
-protected theorem prod_pos_iff_forall_pos_nat {xs : Vector Nat n} : 0 < xs.prod ↔ ∀ x ∈ xs, 0 < x := by
-  simp [← prod_toArray, Array.prod_pos_iff_forall_pos_nat]
-
-protected theorem prod_eq_zero_iff_exists_zero_nat {xs : Vector Nat n} :
-    xs.prod = 0 ↔ ∃ x ∈ xs, x = 0 := by
-  simp [← prod_toArray, Array.prod_eq_zero_iff_exists_zero_nat]
-
-@[simp] theorem prod_replicate_nat {n : Nat} {a : Nat} : (replicate n a).prod = a ^ n := by
-  simp [← prod_toArray, Array.prod_replicate_nat]
-
-theorem prod_append_nat {as₁ as₂ : Vector Nat n} : (as₁ ++ as₂).prod = as₁.prod * as₂.prod := by
-  simp [← prod_toArray]
-
-theorem prod_reverse_nat (xs : Vector Nat n) : xs.reverse.prod = xs.prod := by
-  simp [prod_reverse]
-
-theorem prod_eq_foldl_nat {xs : Vector Nat n} : xs.prod = xs.foldl (b := 1) (· * ·) := by
-  simp only [foldl_eq_foldr_reverse, Nat.mul_comm, ← prod_eq_foldr, prod_reverse_nat]
-
 end Vector

src/Init/Grind/Ring/Basic.lean

@@ -564,28 +564,6 @@ end Ring
 
 end IsCharP
 
-/--
-`PowIdentity α p` states that `x ^ p = x` holds for all elements of `α`.
-
-The primary source of instances is Fermat's little theorem: for a finite field with `q` elements,
-`x ^ q = x` for every `x`. For `Fin p` or `ZMod p` with prime `p`, this gives `x ^ p = x`.
-
-The `grind` ring solver uses this typeclass to add the relation `x ^ p - x = 0` to the
-Groebner basis, which allows it to reduce high-degree polynomials. Mathlib can provide
-instances for general finite fields via `FiniteField.pow_card`.
--/
-class PowIdentity (α : Type u) [CommSemiring α] (p : outParam Nat) : Prop where
-  /-- Every element satisfies `x ^ p = x`. -/
-  pow_eq (x : α) : x ^ p = x
-
-namespace PowIdentity
-
-variable [CommSemiring α] [PowIdentity α p]
-
-theorem pow (x : α) : x ^ p = x := pow_eq x
-
-end PowIdentity
-
 open AddCommGroup
 
 theorem no_int_zero_divisors {α : Type u} [IntModule α] [NoNatZeroDivisors α] {k : Int} {a : α}

src/Init/Grind/Ring/Envelope.lean

@@ -193,7 +193,7 @@ theorem mul_assoc (a b c : Q α) : mul (mul a b) c = mul a (mul b c) := by
   simp [Semiring.left_distrib, Semiring.right_distrib]; refine ⟨0, ?_⟩; ac_rfl
 
 theorem mul_one (a : Q α) : mul a (natCast 1) = a := by
-  obtain ⟨⟨_, _⟩⟩ := a; simp
+obtain ⟨⟨_, _⟩⟩ := a; simp
 
 theorem one_mul (a : Q α) : mul (natCast 1) a = a := by
   obtain ⟨⟨_, _⟩⟩ := a; simp

src/Init/Grind/Util.lean

@@ -30,13 +30,13 @@ simpMatchDiscrsOnly (match 0 with | 0 => true | _ => false) = true
 ```
 using `eq_self`.
 -/
-@[expose] def simpMatchDiscrsOnly {α : Sort u} (a : α) : α := a
+def simpMatchDiscrsOnly {α : Sort u} (a : α) : α := a
 
 /--
 Gadget for protecting lambda abstractions created by `abstractGroundMismatches?`
 from beta reduction during preprocessing. See `ProveEq.lean` for details.
 -/
-@[expose] def abstractFn {α : Sort u} (a : α) : α := a
+def abstractFn {α : Sort u} (a : α) : α := a
 
 /-- Gadget for representing offsets `t+k` in patterns. -/
 def offset (a b : Nat) : Nat := a + b

src/Init/GrindInstances/Ring/Fin.lean

@@ -156,12 +156,6 @@ instance [i : NeZero n] : ToInt.Pow (Fin n) (.co 0 n) where
       rw [pow_succ, ToInt.Mul.toInt_mul, ih, ← ToInt.wrap_toInt,
         ← IntInterval.wrap_mul (by simp), Int.pow_succ, ToInt.wrap_toInt]
 
-instance : PowIdentity (Fin 2) 2 where
-  pow_eq x := by
-    match x with
-    | ⟨0, _⟩ => rfl
-    | ⟨1, _⟩ => rfl
-
 end Fin
 
 end Lean.Grind

src/Init/Notation.lean

@@ -624,23 +624,6 @@ existing code. It may be removed in a future version of the library.
 syntax (name := deprecated) "deprecated" (ppSpace ident)? (ppSpace str)?
     (" (" &"since" " := " str ")")? : attr
 
-/--
-The attribute `@[deprecated_arg old new]` marks a named parameter as deprecated.
-
-When a caller uses the old name with a replacement available, a deprecation warning is emitted
-and the argument is silently forwarded to the new parameter. When no replacement is provided,
-the parameter is treated as removed and using it produces an error.
-
-* `@[deprecated_arg old new (since := "2026-03-18")]` marks `old` as a deprecated alias for `new`.
-* `@[deprecated_arg old new "use foo instead" (since := "2026-03-18")]` adds a custom message.
-* `@[deprecated_arg old (since := "2026-03-18")]` marks `old` as a removed parameter (no replacement).
-* `@[deprecated_arg old "no longer needed" (since := "2026-03-18")]` removed with a custom message.
-
-A warning is emitted if `(since := "...")` is omitted.
--/
-syntax (name := deprecated_arg) "deprecated_arg" ppSpace ident (ppSpace ident)? (ppSpace str)?
-    (" (" &"since" " := " str ")")? : attr
-
 /--
 The attribute `@[suggest_for ..]` on a declaration suggests likely ways in which
 someone might **incorrectly** refer to a definition.

src/Init/Omega/LinearCombo.lean

@@ -36,6 +36,9 @@ private local instance : ToString Int where
 private local instance : Repr Int where
   reprPrec i prec := if i < 0 then Repr.addAppParen (toString i) prec else toString i
 
+private local instance : Append String where
+  append := String.Internal.append
+
 /-- Internal representation of a linear combination of atoms, and a constant term. -/
 structure LinearCombo where
   /-- Constant term. -/

src/Init/Prelude.lean

@@ -145,7 +145,7 @@ Examples:
 The constant function that ignores its argument.
 
 If `a : α`, then `Function.const β a : β → α` is the “constant function with value `a`”. For all
-arguments `b : β`, `Function.const β a b = a`. It is often written directly as `fun _ => a`.
+arguments `b : β`, `Function.const β a b = a`.
 
 Examples:
  * `Function.const Bool 10 true = 10`
@@ -3754,7 +3754,7 @@ class Functor (f : Type u → Type v) : Type (max (u+1) v) where
   /--
   Mapping a constant function.
 
-  Given `a : α` and `v : f β`, `mapConst a v` is equivalent to `(fun _ => a) <$> v`. For some
+  Given `a : α` and `v : f α`, `mapConst a v` is equivalent to `Function.const _ a <$> v`. For some
   functors, this can be implemented more efficiently; for all other functors, the default
   implementation may be used.
   -/

src/Init/System/IO.lean

@@ -1880,12 +1880,3 @@ lead to undefined behavior.
 -/
 @[extern "lean_runtime_forget"]
 def Runtime.forget (a : α) : BaseIO Unit := return
-
-set_option linter.unusedVariables false in
-/--
-Ensures `a` remains at least alive until the call site by holding a reference to `a`. This can be useful
-for unsafe code (such as an FFI) that relies on a Lean object not being freed until after some point
-in the program. At runtime, this will be a no-op as the C compiler will optimize away this call.
--/
-@[extern "lean_runtime_hold"]
-def Runtime.hold (a : @& α) : BaseIO Unit := return

src/Lean/AddDecl.lean

@@ -9,7 +9,6 @@ prelude
 public import Lean.Meta.Sorry
 public import Lean.Util.CollectAxioms
 public import Lean.OriginalConstKind
-import Lean.Compiler.MetaAttr
 import all Lean.OriginalConstKind  -- for accessing `privateConstKindsExt`
 
 public section
@@ -209,12 +208,8 @@ where
       catch _ => pure ()
 
 
-def addAndCompile (decl : Declaration) (logCompileErrors : Bool := true)
-    (markMeta : Bool := false) : CoreM Unit := do
+def addAndCompile (decl : Declaration) (logCompileErrors : Bool := true) : CoreM Unit := do
   addDecl decl
-  if markMeta then
-    for n in decl.getNames do
-      modifyEnv (Lean.markMeta · n)
   compileDecl decl (logErrors := logCompileErrors)
 
 end Lean

src/Lean/AuxRecursor.lean

@@ -56,11 +56,11 @@ def markSparseCasesOn (env : Environment) (declName : Name) : Environment :=
   sparseCasesOnExt.tag env declName
 
 /-- Is this a constructor elimination or a sparse casesOn? -/
-def isSparseCasesOn (env : Environment) (declName : Name) : Bool :=
+public def isSparseCasesOn (env : Environment) (declName : Name) : Bool :=
   sparseCasesOnExt.isTagged env declName
 
 /-- Is this a `.casesOn`, a constructor elimination or a sparse casesOn? -/
-def isCasesOnLike (env : Environment) (declName : Name) : Bool :=
+public def isCasesOnLike (env : Environment) (declName : Name) : Bool :=
   isCasesOnRecursor env declName || isSparseCasesOn env declName
 
 /--

src/Lean/Compiler/InitAttr.lean

@@ -54,7 +54,7 @@ unsafe def registerInitAttrUnsafe (attrName : Name) (runAfterImport : Bool) (ref
     descr := "initialization procedure for global references"
     -- We want to run `[init]` in declaration order
     preserveOrder := true
-    getParam := fun declName stx => withoutExporting do
+    getParam := fun declName stx => do
       let decl ← getConstInfo declName
       match (← Attribute.Builtin.getIdent? stx) with
       | some initFnName =>
@@ -149,6 +149,8 @@ def setBuiltinInitAttr (env : Environment) (declName : Name) (initFnName : Name
 def declareBuiltin (forDecl : Name) (value : Expr) : CoreM Unit :=
   -- can always be private, not referenced directly except through emitted C code
   withoutExporting do
+  -- TODO: needs an update-stage0 + prefer_native=true for breaking symbol name
+  withExporting do
     let name ← mkAuxDeclName (kind := `_regBuiltin ++ forDecl)
     let type := mkApp (mkConst `IO) (mkConst `Unit)
     let decl := Declaration.defnDecl { name, levelParams := [], type, value, hints := ReducibilityHints.opaque,

src/Lean/Compiler/LCNF/Basic.lean

@@ -1230,14 +1230,7 @@ def instantiateRevRangeArgs (e : Expr) (beginIdx endIdx : Nat) (args : Array (Ar
   else
     e.instantiateRevRange beginIdx endIdx (args.map (·.toExpr))
 
-/--
-Lookup function for compiler extensions with sorted persisted state that works in both `lean` and
-`leanir`.
-
-`preferImported` defaults to false because in `leanir`, we do not want to mix information from
-`meta` compilation in `lean` with our own state. But in `lean`, setting `preferImported` can help
-with avoiding unnecessary task blocks.
--/
+/-- Lookup function for compiler extensions with sorted persisted state that works in both `lean` and `leanir`. -/
 @[inline] def findExtEntry? [Inhabited σ] (env : Environment) (ext : PersistentEnvExtension α β σ) (declName : Name)
     (findAtSorted? : Array α → Name → Option α')
     (findInState? : σ → Name → Option α') : Option α' :=

src/Lean/Compiler/LCNF/Check.lean

@@ -232,7 +232,6 @@ partial def checkCases (c : Cases .pure) : CheckM Unit := do
       withParams params do check k
 
 partial def check (code : Code .pure) : CheckM Unit := do
-  checkSystem "LCNF check"
   match code with
   | .let decl k => checkLetDecl decl; withFVarId decl.fvarId do check k
   | .fun decl k =>

src/Lean/Compiler/LCNF/CoalesceRC.lean

@@ -21,7 +21,7 @@ Within a basic block, it is always safe to:
   until the later inc) and thus doing all relevant `inc` in the beginning doesn't change
   semantics.
 - Move all decrements on a variable to the last `dec` location (summing the counts). Because the
-  value is guaranteed to stay alive until at least the last `dec` anyway so a similar argument to
+  value is guaranteed to stay alive until at least the last `dec` anyway so a similiar argument to
   `inc` holds.
 
 Crucially this pass must be placed after `expandResetReuse` as that one relies on `inc`s still being

src/Lean/Compiler/LCNF/EmitC.lean

@@ -774,7 +774,7 @@ where
 
 mutual
 
-partial def emitBasicBlock (code : Code .impure) : EmitM Unit := do
+private partial def emitBasicBlock (code : Code .impure) : EmitM Unit := do
   match code with
   | .jp (k := k) .. => emitBasicBlock k
   | .let decl k =>
@@ -896,7 +896,7 @@ where
   emitUnreach : EmitM Unit := do
     emitLn "lean_internal_panic_unreachable();"
 
-partial def emitJoinPoints (code : Code .impure) : EmitM Unit := do
+private partial def emitJoinPoints (code : Code .impure) : EmitM Unit := do
   match code with
   | .jp decl k =>
     emit decl.binderName; emitLn ":"
@@ -906,7 +906,7 @@ partial def emitJoinPoints (code : Code .impure) : EmitM Unit := do
   | .sset (k := k) .. | .uset (k := k) .. | .oset (k := k) .. => emitJoinPoints k
   | .cases .. | .return .. | .jmp .. | .unreach .. => return ()
 
-partial def emitCode (code : Code .impure) : EmitM Unit := do
+private partial def emitCode (code : Code .impure) : EmitM Unit := do
   withEmitBlock do
     let declared ← declareVars code
     if declared then emitLn ""

src/Lean/Compiler/LCNF/EmitUtil.lean

@@ -12,7 +12,7 @@ import Lean.Compiler.InitAttr
 
 namespace Lean.Compiler.LCNF
 
-structure CollectUsedDeclsState where
+private structure CollectUsedDeclsState where
   visited : NameSet := {}
   localDecls : Array (Decl .impure) := #[]
   extSigs : Array (Signature .impure) := #[]

src/Lean/Compiler/LCNF/ExpandResetReuse.lean

@@ -69,8 +69,8 @@ open ImpureType
 abbrev Mask := Array (Option FVarId)
 
 /--
-Try to erase `inc` instructions on projections of `targetId` occurring in the tail of `ds`.
-Return the updated `ds` and mask containing the `FVarId`s whose `inc` was removed.
+Try to erase `inc` instructions on projections of `targetId` occuring in the tail of `ds`.
+Return the updated `ds` and mask contianing the `FVarId`s whose `inc` was removed.
 -/
 partial def eraseProjIncFor (nFields : Nat) (targetId : FVarId) (ds : Array (CodeDecl .impure)) :
     CompilerM (Array (CodeDecl .impure) × Mask) := do

src/Lean/Compiler/LCNF/InferBorrow.lean

@@ -67,7 +67,7 @@ structure ParamMap where
   The set of fvars that were already annotated as borrowed before arriving at this pass. We try to
   preserve the annotations here if possible.
   -/
-  annotatedBorrows : Std.HashSet FVarId := {}
+  annoatedBorrows : Std.HashSet FVarId := {}
 
 namespace ParamMap
 
@@ -95,7 +95,7 @@ where
         modify fun m =>
           { m with
             map := m.map.insert (.decl decl.name) (initParamsIfNotExported exported decl.params),
-            annotatedBorrows := decl.params.foldl (init := m.annotatedBorrows) fun acc p =>
+            annoatedBorrows := decl.params.foldl (init := m.annoatedBorrows) fun acc p =>
               if p.borrow then acc.insert p.fvarId else acc
           }
         goCode decl.name code
@@ -116,7 +116,7 @@ where
       modify fun m =>
         { m with
           map := m.map.insert (.jp declName decl.fvarId) (initParams decl.params),
-          annotatedBorrows := decl.params.foldl (init := m.annotatedBorrows) fun acc p =>
+          annoatedBorrows := decl.params.foldl (init := m.annoatedBorrows) fun acc p =>
             if p.borrow then acc.insert p.fvarId else acc
         }
       goCode declName decl.value
@@ -286,7 +286,7 @@ where
 
   ownFVar (fvarId : FVarId) (reason : OwnReason) : InferM Unit := do
     unless (← get).owned.contains fvarId do
-      if !reason.isForced && (← get).paramMap.annotatedBorrows.contains fvarId then
+      if !reason.isForced && (← get).paramMap.annoatedBorrows.contains fvarId then
         trace[Compiler.inferBorrow] "user annotation blocked owning {← PP.run <| PP.ppFVar fvarId}: {← reason.toString}"
       else
         trace[Compiler.inferBorrow] "own {← PP.run <| PP.ppFVar fvarId}: {← reason.toString}"

src/Lean/Compiler/LCNF/Main.lean

@@ -78,13 +78,9 @@ def isValidMainType (type : Expr) : Bool :=
     isValidResultName resultName
   | _ => false
 
-/-- A postponed call of `compileDecls`. -/
 structure PostponedCompileDecls where
-  /-- Declaration names of this mutual group. -/
   declNames : Array Name
-  /-- Options at time of original call, to be restored for tracing etc. -/
-  options : Options
-deriving BEq
+deriving BEq, Hashable
 
 /--
 Saves postponed `compileDecls` calls.
@@ -105,20 +101,16 @@ builtin_initialize postponedCompileDeclsExt : SimplePersistentEnvExtension Postp
       { exported := #[], server := #[], «private» := es.toArray }
   }
 
-def resumeCompilation (declName : Name) (baseOpts : Options) : CoreM Unit := do
+def resumeCompilation (declName : Name) : CoreM Unit := do
   let some decls := postponedCompileDeclsExt.getState (← getEnv) |>.find? declName | return
-  let opts := baseOpts.mergeBy (fun _ base _ => base) decls.options
-  let opts := compiler.postponeCompile.set opts false
   modifyEnv (postponedCompileDeclsExt.modifyState · fun s => decls.declNames.foldl (·.erase) s)
-  -- NOTE: we *must* throw away the current options as they could depend on the specific recursion
-  -- we did to get here.
-  withOptions (fun _ => opts) do
+  withOptions (compiler.postponeCompile.set · false) do
   Core.prependError m!"Failed to compile `{declName}`" do
-    (← compileDeclsRef.get) decls.declNames baseOpts
+    (← compileDeclsRef.get) decls.declNames
 
 namespace PassManager
 
-partial def run (declNames : Array Name) (baseOpts : Options) : CompilerM Unit := withAtLeastMaxRecDepth 8192 do
+partial def run (declNames : Array Name) : CompilerM Unit := withAtLeastMaxRecDepth 8192 do
   /-
   Note: we need to increase the recursion depth because we currently do to save phase1
   declarations in .olean files. Then, we have to recursively compile all dependencies,
@@ -149,14 +141,11 @@ partial def run (declNames : Array Name) (baseOpts : Options) : CompilerM Unit :
 
   -- Now that we have done all input checks, check for postponement
   if (← getEnv).header.isModule && (← compiler.postponeCompile.getM) then
-    modifyEnv (postponedCompileDeclsExt.addEntry · { declNames := decls.map (·.name), options := ← getOptions })
+    modifyEnv (postponedCompileDeclsExt.addEntry · { declNames := decls.map (·.name) })
     -- meta defs are compiled locally so they are available for execution/compilation without
     -- importing `.ir` but still marked for `leanir` compilation so that we do not have to persist
     -- module-local compilation information between the two processes
-    if decls.any (isMarkedMeta (← getEnv) ·.name) then
-      -- avoid re-compiling the meta defs in this process; the entry for `leanir` is not affected
-      modifyEnv (postponedCompileDeclsExt.modifyState · fun s => decls.foldl (·.erase ·.name) s)
-    else
+    if !decls.any (isMarkedMeta (← getEnv) ·.name) then
       trace[Compiler] "postponing compilation of {decls.map (·.name)}"
       return
 
@@ -168,7 +157,7 @@ partial def run (declNames : Array Name) (baseOpts : Options) : CompilerM Unit :
       let .let { value := .const c .., .. } .. := c | return
       -- Need to do some lookups to get the actual name passed to `compileDecls`
       let c := Compiler.getImplementedBy? (← getEnv) c |>.getD c
-      resumeCompilation c baseOpts
+      resumeCompilation c
 
   let decls := markRecDecls decls
   let manager ← getPassManager
@@ -199,7 +188,6 @@ where
     profileitM Exception profilerName (← getOptions) do
       let mut state : (pu : Purity) × Array (Decl pu) := ⟨inPhase, decls⟩
       for pass in passes do
-        checkSystem "LCNF compiler"
         state ← withTraceNode `Compiler (fun _ => return m!"compiler phase: {pass.phase}, pass: {pass.name}") do
           let decls ← withPhase pass.phase do
             state.fst.withAssertPurity pass.phase.toPurity fun h => do
@@ -211,9 +199,9 @@ where
 
 end PassManager
 
-def main (declNames : Array Name) (baseOpts : Options) : CoreM Unit := do
+def main (declNames : Array Name) : CoreM Unit := do
   withTraceNode `Compiler (fun _ => return m!"compiling: {declNames}") do
-    CompilerM.run <| PassManager.run declNames baseOpts
+    CompilerM.run <| PassManager.run declNames
 
 builtin_initialize
   compileDeclsRef.set main

src/Lean/Compiler/LCNF/PassManager.lean

@@ -121,7 +121,7 @@ def mkPerDeclaration (name : Name) (phase : Phase)
   occurrence := occurrence
   phase := phase
   name := name
-  run := fun xs => xs.mapM fun decl => do checkSystem "LCNF compiler"; run decl
+  run := fun xs => xs.mapM run
 
 end Pass
 

src/Lean/Compiler/LCNF/PublicDeclsExt.lean

@@ -29,7 +29,7 @@ public def mkOrderedDeclSetExt : IO (EnvExtension (List Name × NameSet)) :=
 /--
 Set of declarations to be exported to other modules; visibility shared by base/mono/IR phases.
 -/
-builtin_initialize publicDeclsExt : EnvExtension (List Name × NameSet) ← mkOrderedDeclSetExt
+private builtin_initialize publicDeclsExt : EnvExtension (List Name × NameSet) ← mkOrderedDeclSetExt
 
 public def isDeclPublic (env : Environment) (declName : Name) : Bool := Id.run do
   if !env.header.isModule then

src/Lean/Compiler/LCNF/ResetReuse.lean

@@ -28,7 +28,7 @@ inserts addition instructions to attempt to reuse the memory right away instead
 allocator.
 
 For this the paper defines three functions:
-- `R` (called `Decl.insertResetReuse` here) which looks for candidates that might be eligible for
+- `R` (called `Decl.insertResetReuse` here) which looks for candidates that might be elligible for
   reuse. For these variables it invokes `D`.
 - `D` which looks for code regions in which the target variable is dead (i.e. no longer read from),
   it then invokes `S`. If `S` succeeds it inserts a `reset` instruction to match the `reuse`

src/Lean/Compiler/LCNF/Simp/Main.lean

@@ -217,8 +217,6 @@ Simplify `code`
 -/
 partial def simp (code : Code .pure) : SimpM (Code .pure) := withIncRecDepth do
   incVisited
-  if (← get).visited % 128 == 0 then
-    checkSystem "LCNF simp"
   match code with
   | .let decl k =>
     let baseDecl := decl

src/Lean/Compiler/LCNF/Simp/SimpM.lean

@@ -146,7 +146,7 @@ Similar to the default `Lean.withIncRecDepth`, but include the `inlineStack` in
 @[inline] def withIncRecDepth (x : SimpM α) : SimpM α := do
   let curr ← MonadRecDepth.getRecDepth
   let max  ← MonadRecDepth.getMaxRecDepth
-  if max != 0 && curr == max then
+  if curr == max then
     throwMaxRecDepth
   else
     MonadRecDepth.withRecDepth (curr+1) x