fix: remove accidental type monomorphism in Id.run_seqLeft (#12936)

This PR fixes `Id.run_seqLeft` and `Id.run_seqRight` to apply when the
two monad results are different.

.claude/CLAUDE.md

@@ -20,9 +20,24 @@ CTEST_PARALLEL_LEVEL="$(nproc)" CTEST_OUTPUT_ON_FAILURE=1 \
 make -C build/release -j "$(nproc)" test ARGS='--rerun-failed'
 
 # Single test from tests/foo/bar/ (quick check during development)
-cd tests/foo/bar && ./run_test example_test.lean
+CTEST_PARALLEL_LEVEL="$(nproc)" CTEST_OUTPUT_ON_FAILURE=1 \
+make -C build/release -j "$(nproc)" test ARGS=-R testname'
 ```
 
+## Testing stage 2
+
+When requested to test stage 2, build it as follows:
+```
+make -C build/release stage2 -j$(nproc)
+```
+Stage 2 is *not* automatically invalidated by changes to `src/` which allows for faster iteration
+when fixing a specific file in the stage 2 build but for invalidating any files that already passed
+the stage 2 build as well as for final validation,
+```
+make -C build/release/stage2 clean-stdlib
+```
+must be run manually before building.
+
 ## New features
 
 When asked to implement new features:
@@ -40,6 +55,10 @@ When asked to implement new features:
 - ONLY use the project's documented build command: `make -j$(nproc) -C build/release`
 - If a build is broken, ask the user before attempting any manual cleanup
 
+## stage0 Is a Copy of src
+
+**Never manually edit files under `stage0/`.** The `stage0/` directory is a snapshot of `src/` produced by `make update-stage0`. To change anything in stage0 (CMakeLists.txt, C++ source, etc.), edit the corresponding file in `src/` and let `update-stage0` propagate it.
+
 ## LSP and IDE Diagnostics
 
 After rebuilding, LSP diagnostics may be stale until the user interacts with files. Trust command-line test results over IDE diagnostics.

.claude/commands/release.md

@@ -121,6 +121,24 @@ The nightly build system uses branches and tags across two repositories:
 
 When a nightly succeeds with mathlib, all three should point to the same commit. Don't confuse these: branches are in the main lean4 repo, dated tags are in lean4-nightly.
 
+## CI Failures: Investigate Immediately
+
+**CRITICAL: If the checklist reports `❌ CI: X check(s) failing` for any PR, investigate immediately.**
+
+Do NOT:
+- Report it as "CI in progress" or "some checks pending"
+- Wait for the remaining checks to finish before investigating
+- Assume it's a transient failure without checking
+
+DO:
+1. Run `gh pr checks <number> --repo <owner>/<repo>` to see which specific check failed
+2. Run `gh run view <run-id> --repo <owner>/<repo> --log-failed` to see the failure output
+3. Diagnose the failure and report clearly to the user: what failed and why
+4. Propose a fix if one is obvious (e.g., subverso version mismatch, transient elan install error)
+
+The checklist now distinguishes `❌ X check(s) failing, Y still in progress` from `🔄 Y check(s) in progress`.
+Any `❌` in CI status requires immediate investigation — do not move on.
+
 ## Waiting for CI or Merges
 
 Use `gh pr checks --watch` to block until a PR's CI checks complete (no polling needed).
@@ -135,6 +153,10 @@ For multiple PRs, launch one background command per PR in parallel. When each co
 you'll be notified automatically via a task-notification. Do NOT use sleep-based polling
 loops — `--watch` is event-driven and exits as soon as checks finish.
 
+Note: `gh pr checks --watch` exits as soon as ALL checks complete (pass or fail). If some checks
+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.
+
 ## Error Handling
 
 **CRITICAL**: If something goes wrong or a command fails:

.gitattributes

@@ -5,9 +5,3 @@ stage0/** binary linguist-generated
 # The following file is often manually edited, so do show it in diffs
 stage0/src/stdlib_flags.h -binary -linguist-generated
 doc/std/grove/GroveStdlib/Generated/** linguist-generated
-# These files should not have line endings translated on Windows, because
-# it throws off parser tests. Later lines override earlier ones, so the
-# runner code is still treated as ordinary text.
-tests/lean/docparse/* eol=lf
-tests/lean/docparse/*.lean eol=auto
-tests/lean/docparse/*.sh eol=auto

.github/workflows/ci.yml

@@ -166,7 +166,7 @@ jobs:
       # 0: PRs without special label
       # 1: PRs with `merge-ci` label, merge queue checks, master commits
       # 2: nightlies
-      # 3: PRs with `release-ci` label, full releases
+      # 3: PRs with `release-ci` or `lake-ci` label, full releases
       - name: Set check level
         id: set-level
         # We do not use github.event.pull_request.labels.*.name here because
@@ -175,6 +175,7 @@ jobs:
         run: |
           check_level=0
           fast=false
+          lake_ci=false
 
           if [[ -n "${{ steps.set-release.outputs.RELEASE_TAG }}" || -n "${{ steps.set-release-custom.outputs.RELEASE_TAG }}" ]]; then
             check_level=3
@@ -189,13 +190,19 @@ jobs:
             elif echo "$labels" | grep -q "merge-ci"; then
               check_level=1
             fi
+            if echo "$labels" | grep -q "lake-ci"; then
+              lake_ci=true
+            fi
             if echo "$labels" | grep -q "fast-ci"; then
               fast=true
             fi
           fi
 
-          echo "check-level=$check_level" >> "$GITHUB_OUTPUT"
-          echo "fast=$fast" >> "$GITHUB_OUTPUT"
+          {
+            echo "check-level=$check_level"
+            echo "fast=$fast"
+            echo "lake-ci=$lake_ci"
+          } >> "$GITHUB_OUTPUT"
         env:
           GH_TOKEN: ${{ github.token }}
 
@@ -206,6 +213,7 @@ jobs:
           script: |
             const level = ${{ steps.set-level.outputs.check-level }};
             const fast = ${{ steps.set-level.outputs.fast }};
+            const lakeCi = "${{ steps.set-level.outputs.lake-ci }}" == "true";
             console.log(`level: ${level}, fast: ${fast}`);
             // use large runners where available (original repo)
             let large = ${{ github.repository == 'leanprover/lean4' }};
@@ -379,6 +387,11 @@ jobs:
                 job["CMAKE_OPTIONS"] = (job["CMAKE_OPTIONS"] ? job["CMAKE_OPTIONS"] + " " : "") + "-DUSE_LAKE=OFF";
               }
             }
+            if (lakeCi) {
+              for (const job of matrix) {
+                job["CMAKE_OPTIONS"] = (job["CMAKE_OPTIONS"] ? job["CMAKE_OPTIONS"] + " " : "") + "-DLAKE_CI=ON";
+              }
+            }
             console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`);
             matrix = matrix.filter((job) => job["enabled"]);
             core.setOutput('matrix', matrix.filter((job) => !job["secondary"]));

.github/workflows/labels-from-comments.yml

@@ -1,5 +1,5 @@
 # This workflow allows any user to add one of the `awaiting-review`, `awaiting-author`, `WIP`,
-# `release-ci`, or a `changelog-XXX` label by commenting on the PR or issue.
+# `release-ci`, `lake-ci`, or a `changelog-XXX` label by commenting on the PR or issue.
 # If any labels from the set {`awaiting-review`, `awaiting-author`, `WIP`} are added, other labels
 # from that set are removed automatically at the same time.
 # Similarly, if any `changelog-XXX` label is added, other `changelog-YYY` labels are removed.
@@ -12,7 +12,7 @@ on:
 
 jobs:
   update-label:
-    if: github.event.issue.pull_request != null && (contains(github.event.comment.body, 'awaiting-review') || contains(github.event.comment.body, 'awaiting-author') || contains(github.event.comment.body, 'WIP') || contains(github.event.comment.body, 'release-ci') || contains(github.event.comment.body, 'changelog-'))
+    if: github.event.issue.pull_request != null && (contains(github.event.comment.body, 'awaiting-review') || contains(github.event.comment.body, 'awaiting-author') || contains(github.event.comment.body, 'WIP') || contains(github.event.comment.body, 'release-ci') || contains(github.event.comment.body, 'lake-ci') || contains(github.event.comment.body, 'changelog-'))
     runs-on: ubuntu-latest
 
     steps:
@@ -28,6 +28,7 @@ jobs:
           const awaitingAuthor = commentLines.includes('awaiting-author');
           const wip = commentLines.includes('WIP');
           const releaseCI = commentLines.includes('release-ci');
+          const lakeCI = commentLines.includes('lake-ci');
           const changelogMatch = commentLines.find(line => line.startsWith('changelog-'));
 
           if (awaitingReview || awaitingAuthor || wip) {
@@ -49,6 +50,9 @@ jobs:
           if (releaseCI) {
             await github.rest.issues.addLabels({ owner, repo, issue_number, labels: ['release-ci'] });
           }
+          if (lakeCI) {
+            await github.rest.issues.addLabels({ owner, repo, issue_number, labels: ['lake-ci'] });
+          }
 
           if (changelogMatch) {
             const changelogLabel = changelogMatch.trim();

.github/workflows/restart-on-label.yml

@@ -7,7 +7,7 @@ on:
 jobs:
   restart-on-label:
     runs-on: ubuntu-latest
-    if: contains(github.event.label.name, 'merge-ci') || contains(github.event.label.name, 'release-ci')
+    if: contains(github.event.label.name, 'merge-ci') || contains(github.event.label.name, 'release-ci') || contains(github.event.label.name, 'lake-ci')
     steps:
     - run: |
         # Finding latest CI workflow run on current pull request

.gitignore

@@ -20,6 +20,9 @@ settings.json
 !.claude/settings.json
 .gdb_history
 .vscode/*
+!.vscode/settings.json
+!.vscode/tasks.json
+!.vscode/extensions.json
 script/__pycache__
 *.produced.out
 CMakeSettings.json

.vscode/extensions.json

@@ -0,0 +1,5 @@
+{
+	"recommendations": [
+		"leanprover.lean4"
+	]
+}

.vscode/settings.json

@@ -0,0 +1,12 @@
+{
+	"files.insertFinalNewline": true,
+	"files.trimTrailingWhitespace": true,
+	// These require the CMake Tools extension (ms-vscode.cmake-tools).
+	"cmake.buildDirectory": "${workspaceFolder}/build/release",
+	"cmake.generator": "Unix Makefiles",
+	"[lean4]": {
+		"editor.rulers": [
+			100
+		]
+	}
+}

.vscode/tasks.json

@@ -0,0 +1,34 @@
+{
+	"version": "2.0.0",
+	"tasks": [
+		{
+			"label": "build",
+			"type": "shell",
+			"command": "make -C build/release -j$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4)",
+			"problemMatcher": [],
+			"group": {
+				"kind": "build",
+				"isDefault": true
+			}
+		},
+		{
+			"label": "build-old",
+			"type": "shell",
+			"command": "make -C build/release -j$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4) LAKE_EXTRA_ARGS=--old",
+			"problemMatcher": [],
+			"group": {
+				"kind": "build"
+			}
+		},
+		{
+			"label": "test",
+			"type": "shell",
+			"command": "NPROC=$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4); CTEST_OUTPUT_ON_FAILURE=1 make -C build/release test -j$NPROC ARGS=\"-j$NPROC\"",
+			"problemMatcher": [],
+			"group": {
+				"kind": "test",
+				"isDefault": true
+			}
+		}
+	]
+}

CMakeLists.txt

@@ -41,7 +41,7 @@ if(NOT (DEFINED STAGE0_CMAKE_EXECUTABLE_SUFFIX))
   set(STAGE0_CMAKE_EXECUTABLE_SUFFIX "${CMAKE_EXECUTABLE_SUFFIX}")
 endif()
 
-# Don't do anything with cadical on wasm
+# Don't do anything with cadical/leantar on wasm
 if(NOT CMAKE_SYSTEM_NAME MATCHES "Emscripten")
   find_program(CADICAL cadical)
   if(NOT CADICAL)
@@ -77,7 +77,44 @@ if(NOT CMAKE_SYSTEM_NAME MATCHES "Emscripten")
     set(CADICAL ${CMAKE_BINARY_DIR}/cadical/cadical${CMAKE_EXECUTABLE_SUFFIX})
     list(APPEND EXTRA_DEPENDS cadical)
   endif()
-  list(APPEND CL_ARGS -DCADICAL=${CADICAL})
+  find_program(LEANTAR leantar)
+  if(NOT LEANTAR)
+    set(LEANTAR_VERSION v0.1.19)
+    if(CMAKE_SYSTEM_NAME MATCHES "Windows")
+      set(LEANTAR_ARCHIVE_SUFFIX .zip)
+      set(LEANTAR_TARGET x86_64-pc-windows-msvc)
+    else()
+      set(LEANTAR_ARCHIVE_SUFFIX .tar.gz)
+      if(CMAKE_SYSTEM_PROCESSOR MATCHES "arm64")
+        set(LEANTAR_TARGET_ARCH aarch64)
+      else()
+        set(LEANTAR_TARGET_ARCH x86_64)
+      endif()
+      if(CMAKE_SYSTEM_NAME MATCHES "Darwin")
+        set(LEANTAR_TARGET_OS apple-darwin)
+      else()
+        set(LEANTAR_TARGET_OS unknown-linux-musl)
+      endif()
+      set(LEANTAR_TARGET ${LEANTAR_TARGET_ARCH}-${LEANTAR_TARGET_OS})
+    endif()
+    set(
+      LEANTAR
+      ${CMAKE_BINARY_DIR}/leantar/leantar-${LEANTAR_VERSION}-${LEANTAR_TARGET}/leantar${CMAKE_EXECUTABLE_SUFFIX}
+    )
+    if(NOT EXISTS "${LEANTAR}")
+      file(
+        DOWNLOAD
+          https://github.com/digama0/leangz/releases/download/${LEANTAR_VERSION}/leantar-${LEANTAR_VERSION}-${LEANTAR_TARGET}${LEANTAR_ARCHIVE_SUFFIX}
+        ${CMAKE_BINARY_DIR}/leantar${LEANTAR_ARCHIVE_SUFFIX}
+      )
+      file(
+        ARCHIVE_EXTRACT
+        INPUT ${CMAKE_BINARY_DIR}/leantar${LEANTAR_ARCHIVE_SUFFIX}
+        DESTINATION ${CMAKE_BINARY_DIR}/leantar
+      )
+    endif()
+  endif()
+  list(APPEND CL_ARGS -DCADICAL=${CADICAL} -DLEANTAR=${LEANTAR})
 endif()
 
 if(USE_MIMALLOC)

CONTRIBUTING.md

@@ -7,7 +7,7 @@ Helpful links
 -------
 
 * [Development Setup](./doc/dev/index.md)
-* [Testing](./doc/dev/testing.md)
+* [Testing](./tests/README.md)
 * [Commit convention](./doc/dev/commit_convention.md)
 
 Before You Submit a Pull Request (PR):

LICENSES

@@ -1370,4 +1370,208 @@ FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
-SOFTWARE.
+SOFTWARE.
+==============================================================================
+leantar is by Mario Carneiro and distributed under the Apache 2.0 License:
+==============================================================================
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
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+
+      "Legal Entity" shall mean the union of the acting entity and all
+      other entities that control, are controlled by, or are under common
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+
+      "You" (or "Your") shall mean an individual or Legal Entity
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+
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+      any Contribution intentionally submitted for inclusion in the Work
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+
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+
+      To apply the Apache License to your work, attach the following
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+   See the License for the specific language governing permissions and
+   limitations under the License.

doc/.gitignore

@@ -1 +0,0 @@
-out

doc/dev/index.md

@@ -1,7 +1,9 @@
 # Development Workflow
 
 If you want to make changes to Lean itself, start by [building Lean](../make/index.md) from a clean checkout to make sure that everything is set up correctly.
-After that, read on below to find out how to set up your editor for changing the Lean source code, followed by further sections of the development manual where applicable such as on the [test suite](testing.md) and [commit convention](commit_convention.md).
+After that, read on below to find out how to set up your editor for changing the Lean source code,
+followed by further sections of the development manual where applicable
+such as on the [test suite](../../tests/README.md) and [commit convention](commit_convention.md).
 
 If you are planning to make any changes that may affect the compilation of Lean itself, e.g. changes to the parser, elaborator, or compiler, you should first read about the [bootstrapping pipeline](bootstrap.md).
 You should not edit the `stage0` directory except using the commands described in that section when necessary.
@@ -61,10 +63,10 @@ you can then put `my_name/lean4:my-tag` in your `lean-toolchain` file in a proje
 
 ### VS Code
 
-There is a `lean.code-workspace` file that correctly sets up VS Code with workspace roots for the stage0/stage1 setup described above as well as with other settings.
-You should always load it when working on Lean, such as by invoking
+There is a `.vscode/` directory that correctly sets up VS Code with settings, tasks, and recommended extensions.
+Simply open the repository folder in VS Code, such as by invoking
 ```
-code lean.code-workspace
+code .
 ```
 on the command line.
 

doc/dev/testing.md

@@ -1,142 +0,0 @@
-# Test Suite
-
-**Warning:** This document is partially outdated.
-It describes the old test suite, which is currently in the process of being replaced.
-The new test suite's documentation can be found at [`tests/README.md`](../../tests/README.md).
-
-After [building Lean](../make/index.md) you can run all the tests using
-```
-cd build/release
-make test ARGS=-j4
-```
-Change the 4 to the maximum number of parallel tests you want to
-allow. The best choice is the number of CPU cores on your machine as
-the tests are mostly CPU bound.  You can find the number of processors
-on linux using `nproc` and on Windows it is the `NUMBER_OF_PROCESSORS`
-environment variable.
-
-You can run tests after [building a specific stage](bootstrap.md) by
-adding the `-C stageN` argument. The default when run as above is stage 1.  The
-Lean tests will automatically use that stage's corresponding Lean
-executables
-
-Running `make test` will not pick up new test files; run
-```bash
-cmake build/release/stage1
-```
-to update the list of tests.
-
-You can also use `ctest` directly if you are in the right folder.  So
-to run stage1 tests with a 300 second timeout run this:
-
-```bash
-cd build/release/stage1
-ctest -j 4 --output-on-failure --timeout 300
-```
-Useful `ctest` flags are `-R <name of test>` to run a single test, and
-`--rerun-failed` to run all tests that failed during the last run.
-You can also pass `ctest` flags via `make test ARGS="--rerun-failed"`.
-
-To get verbose output from ctest pass the `--verbose` command line
-option. Test output is normally suppressed and only summary
-information is displayed. This option will show all test output.
-
-## Test Suite Organization
-
-All these tests are included by [src/shell/CMakeLists.txt](https://github.com/leanprover/lean4/blob/master/src/shell/CMakeLists.txt):
-
-- [`tests/lean`](https://github.com/leanprover/lean4/tree/master/tests/lean/): contains tests that come equipped with a
-  .lean.expected.out file. The driver script [`test_single.sh`](https://github.com/leanprover/lean4/tree/master/tests/lean/test_single.sh) runs
-  each test and checks the actual output (*.produced.out) with the
-  checked in expected output.
-
-- [`tests/lean/run`](https://github.com/leanprover/lean4/tree/master/tests/lean/run/): contains tests that are run through the lean
-  command line one file at a time. These tests only look for error
-  codes and do not check the expected output even though output is
-  produced, it is ignored.
-
-  **Note:** Tests in this directory run with `-Dlinter.all=false` to reduce noise.
-  If your test needs to verify linter behavior (e.g., deprecation warnings),
-  explicitly enable the relevant linter with `set_option linter.<name> true`.
-
-- [`tests/lean/interactive`](https://github.com/leanprover/lean4/tree/master/tests/lean/interactive/): are designed to test server requests at a
-  given position in the input file. Each .lean file contains comments
-  that indicate how to simulate a client request at that position.
-  using a `--^` point to the line position. Example:
-    ```lean,ignore
-    open Foo in
-    theorem tst2 (h : a ≤ b) : a + 2 ≤ b + 2 :=
-    Bla.
-      --^ completion
-    ```
-    In this example, the test driver [`test_single.sh`](https://github.com/leanprover/lean4/tree/master/tests/lean/interactive/test_single.sh) will simulate an
-    auto-completion request at `Bla.`. The expected output is stored in
-    a .lean.expected.out in the json format that is part of the
-    [Language Server
-    Protocol](https://microsoft.github.io/language-server-protocol/).
-
-    This can also be used to test the following additional requests:
-    ```
-    --^ textDocument/hover
-    --^ textDocument/typeDefinition
-    --^ textDocument/definition
-    --^ $/lean/plainGoal
-    --^ $/lean/plainTermGoal
-    --^ insert: ...
-    --^ collectDiagnostics
-    ```
-
-- [`tests/lean/server`](https://github.com/leanprover/lean4/tree/master/tests/lean/server/): Tests more of the Lean `--server` protocol.
-  There are just a few of them, and it uses .log files containing
-  JSON.
-
-- [`tests/compiler`](https://github.com/leanprover/lean4/tree/master/tests/compiler/): contains tests that will run the Lean compiler and
-  build an executable that is executed and the output is compared to
-  the .lean.expected.out file. This test also contains a subfolder
-  [`foreign`](https://github.com/leanprover/lean4/tree/master/tests/compiler/foreign/) which shows how to extend Lean using C++.
-
-- [`tests/lean/trust0`](https://github.com/leanprover/lean4/tree/master/tests/lean/trust0): tests that run Lean in a mode that Lean doesn't
-  even trust the .olean files (i.e., trust 0).
-
-- [`tests/bench`](https://github.com/leanprover/lean4/tree/master/tests/bench/): contains performance tests.
-
-- [`tests/plugin`](https://github.com/leanprover/lean4/tree/master/tests/plugin/): tests that compiled Lean code can be loaded into
-  `lean` via the `--plugin` command line option.
-
-## Writing Good Tests
-
-Every test file should contain:
-* an initial `/-! -/` module docstring summarizing the test's purpose
-* a module docstring for each test section that describes what is tested
-  and, if not 100% clear, why that is the desirable behavior
-
-At the time of writing, most tests do not follow these new guidelines yet.
-For an example of a conforming test, see [`tests/lean/1971.lean`](https://github.com/leanprover/lean4/tree/master/tests/lean/1971.lean).
-
-## Fixing Tests
-
-When the Lean source code or the standard library are modified, some of the
-tests break because the produced output is slightly different, and we have
-to reflect the changes in the `.lean.expected.out` files.
-We should not blindly copy the new produced output since we may accidentally
-miss a bug introduced by recent changes.
-The test suite contains commands that allow us to see what changed in a convenient way.
-First, we must install [meld](http://meldmerge.org/). On Ubuntu, we can do it by simply executing
-
-```
-sudo apt-get install meld
-```
-
-Now, suppose `bad_class.lean` test is broken. We can see the problem by going to [`tests/lean`](https://github.com/leanprover/lean4/tree/master/tests/lean) directory and
-executing
-
-```
-./test_single.sh -i bad_class.lean
-```
-
-When the `-i` option is provided, `meld` is automatically invoked
-whenever there is discrepancy between the produced and expected
-outputs. `meld` can also be used to repair the problems.
-
-In Emacs, we can also execute `M-x lean4-diff-test-file` to check/diff the file of the current buffer.
-To mass-copy all `.produced.out` files to the respective `.expected.out` file, use `tests/lean/copy-produced`.

doc/examples/.gitignore

@@ -0,0 +1,2 @@
+*.out.produced
+*.exit.produced

doc/examples/bintree.lean.out.expected

@@ -0,0 +1,2 @@
+Tree.node (Tree.node (Tree.leaf) 1 "one" (Tree.leaf)) 2 "two" (Tree.node (Tree.leaf) 3 "three" (Tree.leaf))
+[(1, "one"), (2, "two"), (3, "three")]

doc/examples/compiler/run_test.sh

@@ -0,0 +1,4 @@
+leanmake --always-make bin
+
+capture ./build/bin/test hello world
+check_out_contains "[hello, world]"

doc/examples/compiler/test.lean.out.expected

@@ -0,0 +1 @@
+[hello, world]

doc/examples/interp.lean.out.expected

@@ -0,0 +1,3 @@
+30
+interp.lean:146:4: warning: declaration uses `sorry`
+3628800

doc/examples/palindromes.lean.out.expected

@@ -0,0 +1,2 @@
+true
+false

doc/examples/phoas.lean.out.expected

@@ -0,0 +1,2 @@
+"(((fun x_1 => (fun x_2 => (x_1 + x_2))) 1) 2)"
+"((((fun x_1 => (fun x_2 => (x_1 + x_2))) 1) 2) + 5)"

doc/examples/run_test.sh

@@ -0,0 +1,4 @@
+capture_only "$1" \
+  lean -Dlinter.all=false "$1"
+check_exit_is_success
+check_out_file

doc/examples/test_single.sh

@@ -1,4 +0,0 @@
-#!/usr/bin/env bash
-source ../../tests/common.sh
-
-exec_check_raw lean -Dlinter.all=false "$f"

lean.code-workspace

@@ -1,60 +0,0 @@
-{
-	"folders": [
-		{
-			"path": "."
-		}
-	],
-	"settings": {
-		"files.insertFinalNewline": true,
-		"files.trimTrailingWhitespace": true,
-		"cmake.buildDirectory": "${workspaceFolder}/build/release",
-		"cmake.generator": "Unix Makefiles",
-		"[markdown]": {
-			"rewrap.wrappingColumn": 70
-		},
-		"[lean4]": {
-			"editor.rulers": [
-				100
-			]
-		}
-	},
-	"tasks": {
-		"version": "2.0.0",
-		"tasks": [
-			{
-				"label": "build",
-				"type": "shell",
-				"command": "make -C build/release -j$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4)",
-				"problemMatcher": [],
-				"group": {
-					"kind": "build",
-					"isDefault": true
-				}
-			},
-			{
-				"label": "build-old",
-				"type": "shell",
-				"command": "make -C build/release -j$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4) LAKE_EXTRA_ARGS=--old",
-				"problemMatcher": [],
-				"group": {
-					"kind": "build"
-				}
-			},
-			{
-				"label": "test",
-				"type": "shell",
-				"command": "NPROC=$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4); CTEST_OUTPUT_ON_FAILURE=1 make -C build/release test -j$NPROC ARGS=\"-j$NPROC\"",
-				"problemMatcher": [],
-				"group": {
-					"kind": "test",
-					"isDefault": true
-				}
-			}
-		]
-	},
-	"extensions": {
-		"recommendations": [
-			"leanprover.lean4"
-		]
-	}
-}

script/gen_constants_cpp.py

@@ -1,4 +1,4 @@
-#!/usr/bin/env python
+#!/usr/bin/env python3
 # -*- coding: utf-8 -*-
 #
 # Copyright (c) 2015 Microsoft Corporation. All rights reserved.

script/gen_tokens_cpp.py

@@ -1,4 +1,4 @@
-#!/usr/bin/env python
+#!/usr/bin/env python3
 # -*- coding: utf-8 -*-
 #
 # Copyright (c) 2015 Microsoft Corporation. All rights reserved.

script/profiler/lean_demangle.py

@@ -1,9 +1,11 @@
 #!/usr/bin/env python3
 """
-Lean name demangler.
+Lean name demangler — thin wrapper around the Lean CLI tool.
 
-Demangles C symbol names produced by the Lean 4 compiler back into
-readable Lean hierarchical names.
+Spawns ``lean --run lean_demangle_cli.lean`` as a persistent subprocess
+and communicates via stdin/stdout pipes. This ensures a single source
+of truth for demangling logic (the Lean implementation in
+``Lean.Compiler.NameDemangling``).
 
 Usage as a filter (like c++filt):
     echo "l_Lean_Meta_Sym_main" | python lean_demangle.py
@@ -13,767 +15,68 @@ Usage as a module:
     print(demangle_lean_name("l_Lean_Meta_Sym_main"))
 """
 
+import atexit
+import os
+import subprocess
 import sys
 
-
-# ---------------------------------------------------------------------------
-# String.mangle / unmangle
-# ---------------------------------------------------------------------------
-
-def _is_ascii_alnum(ch):
-    """Check if ch is an ASCII letter or digit (matching Lean's isAlpha/isDigit)."""
-    return ('a' <= ch <= 'z') or ('A' <= ch <= 'Z') or ('0' <= ch <= '9')
-
-
-def mangle_string(s):
-    """Port of Lean's String.mangle: escape a single string for C identifiers."""
-    result = []
-    for ch in s:
-        if _is_ascii_alnum(ch):
-            result.append(ch)
-        elif ch == '_':
-            result.append('__')
-        else:
-            code = ord(ch)
-            if code < 0x100:
-                result.append('_x' + format(code, '02x'))
-            elif code < 0x10000:
-                result.append('_u' + format(code, '04x'))
-            else:
-                result.append('_U' + format(code, '08x'))
-    return ''.join(result)
-
-
-def _parse_hex(s, pos, n):
-    """Parse n lowercase hex digits at pos. Returns (new_pos, value) or None."""
-    if pos + n > len(s):
-        return None
-    val = 0
-    for i in range(n):
-        c = s[pos + i]
-        if '0' <= c <= '9':
-            val = (val << 4) | (ord(c) - ord('0'))
-        elif 'a' <= c <= 'f':
-            val = (val << 4) | (ord(c) - ord('a') + 10)
-        else:
-            return None
-    return (pos + n, val)
-
-
-# ---------------------------------------------------------------------------
-# Name mangling (for round-trip verification)
-# ---------------------------------------------------------------------------
-
-def _check_disambiguation(m):
-    """Port of Lean's checkDisambiguation: does mangled string m need a '00' prefix?"""
-    pos = 0
-    while pos < len(m):
-        ch = m[pos]
-        if ch == '_':
-            pos += 1
-            continue
-        if ch == 'x':
-            return _parse_hex(m, pos + 1, 2) is not None
-        if ch == 'u':
-            return _parse_hex(m, pos + 1, 4) is not None
-        if ch == 'U':
-            return _parse_hex(m, pos + 1, 8) is not None
-        if '0' <= ch <= '9':
-            return True
-        return False
-    # all underscores or empty
-    return True
-
-
-def _need_disambiguation(prev_component, mangled_next):
-    """Port of Lean's needDisambiguation."""
-    # Check if previous component (as a string) ends with '_'
-    prev_ends_underscore = (isinstance(prev_component, str) and
-                            len(prev_component) > 0 and
-                            prev_component[-1] == '_')
-    return prev_ends_underscore or _check_disambiguation(mangled_next)
-
-
-def mangle_name(components, prefix="l_"):
-    """
-    Mangle a list of name components (str or int) into a C symbol.
-    Port of Lean's Name.mangle.
-    """
-    if not components:
-        return prefix
-
-    parts = []
-    prev = None
-    for i, comp in enumerate(components):
-        if isinstance(comp, int):
-            if i == 0:
-                parts.append(str(comp) + '_')
-            else:
-                parts.append('_' + str(comp) + '_')
-        else:
-            m = mangle_string(comp)
-            if i == 0:
-                if _check_disambiguation(m):
-                    parts.append('00' + m)
-                else:
-                    parts.append(m)
-            else:
-                if _need_disambiguation(prev, m):
-                    parts.append('_00' + m)
-                else:
-                    parts.append('_' + m)
-        prev = comp
-
-    return prefix + ''.join(parts)
-
-
-# ---------------------------------------------------------------------------
-# Name demangling
-# ---------------------------------------------------------------------------
-
-def demangle_body(s):
-    """
-    Demangle a string produced by Name.mangleAux (without prefix).
-    Returns a list of components (str or int).
-
-    This is a faithful port of Lean's Name.demangleAux from NameMangling.lean.
-    """
-    components = []
-    length = len(s)
-
-    def emit(comp):
-        components.append(comp)
-
-    def decode_num(pos, n):
-        """Parse remaining digits, emit numeric component, continue."""
-        while pos < length:
-            ch = s[pos]
-            if '0' <= ch <= '9':
-                n = n * 10 + (ord(ch) - ord('0'))
-                pos += 1
-            else:
-                # Expect '_' (trailing underscore of numeric encoding)
-                pos += 1  # skip '_'
-                emit(n)
-                if pos >= length:
-                    return pos
-                # Skip separator '_' and go to name_start
-                pos += 1
-                return name_start(pos)
-        # End of string
-        emit(n)
-        return pos
-
-    def name_start(pos):
-        """Start parsing a new name component."""
-        if pos >= length:
-            return pos
-        ch = s[pos]
-        pos += 1
-        if '0' <= ch <= '9':
-            # Check for '00' disambiguation
-            if ch == '0' and pos < length and s[pos] == '0':
-                pos += 1
-                return demangle_main(pos, "", 0)
-            else:
-                return decode_num(pos, ord(ch) - ord('0'))
-        elif ch == '_':
-            return demangle_main(pos, "", 1)
-        else:
-            return demangle_main(pos, ch, 0)
-
-    def demangle_main(pos, acc, ucount):
-        """Main demangling loop."""
-        while pos < length:
-            ch = s[pos]
-            pos += 1
-
-            if ch == '_':
-                ucount += 1
-                continue
-
-            if ucount % 2 == 0:
-                # Even underscores: literal underscores in component name
-                acc += '_' * (ucount // 2) + ch
-                ucount = 0
-                continue
-
-            # Odd ucount: separator or escape
-            if '0' <= ch <= '9':
-                # End current str component, start number
-                emit(acc + '_' * (ucount // 2))
-                if ch == '0' and pos < length and s[pos] == '0':
-                    pos += 1
-                    return demangle_main(pos, "", 0)
-                else:
-                    return decode_num(pos, ord(ch) - ord('0'))
-
-            # Try hex escapes
-            if ch == 'x':
-                result = _parse_hex(s, pos, 2)
-                if result is not None:
-                    new_pos, val = result
-                    acc += '_' * (ucount // 2) + chr(val)
-                    pos = new_pos
-                    ucount = 0
-                    continue
-
-            if ch == 'u':
-                result = _parse_hex(s, pos, 4)
-                if result is not None:
-                    new_pos, val = result
-                    acc += '_' * (ucount // 2) + chr(val)
-                    pos = new_pos
-                    ucount = 0
-                    continue
-
-            if ch == 'U':
-                result = _parse_hex(s, pos, 8)
-                if result is not None:
-                    new_pos, val = result
-                    acc += '_' * (ucount // 2) + chr(val)
-                    pos = new_pos
-                    ucount = 0
-                    continue
-
-            # Name separator
-            emit(acc)
-            acc = '_' * (ucount // 2) + ch
-            ucount = 0
-
-        # End of string
-        acc += '_' * (ucount // 2)
-        if acc:
-            emit(acc)
-        return pos
-
-    name_start(0)
-    return components
-
-
-# ---------------------------------------------------------------------------
-# Prefix handling for lp_ (package prefix)
-# ---------------------------------------------------------------------------
-
-def _is_valid_string_mangle(s):
-    """Check if s is a valid output of String.mangle (no trailing bare _)."""
-    pos = 0
-    length = len(s)
-    while pos < length:
-        ch = s[pos]
-        if _is_ascii_alnum(ch):
-            pos += 1
-        elif ch == '_':
-            if pos + 1 >= length:
-                return False  # trailing bare _
-            nch = s[pos + 1]
-            if nch == '_':
-                pos += 2
-            elif nch == 'x' and _parse_hex(s, pos + 2, 2) is not None:
-                pos = _parse_hex(s, pos + 2, 2)[0]
-            elif nch == 'u' and _parse_hex(s, pos + 2, 4) is not None:
-                pos = _parse_hex(s, pos + 2, 4)[0]
-            elif nch == 'U' and _parse_hex(s, pos + 2, 8) is not None:
-                pos = _parse_hex(s, pos + 2, 8)[0]
-            else:
-                return False
-        else:
-            return False
-    return True
-
-
-def _skip_string_mangle(s, pos):
-    """
-    Skip past a String.mangle output in s starting at pos.
-    Returns the position after the mangled string (where we expect the separator '_').
-    This is a greedy scan.
-    """
-    length = len(s)
-    while pos < length:
-        ch = s[pos]
-        if _is_ascii_alnum(ch):
-            pos += 1
-        elif ch == '_':
-            if pos + 1 < length:
-                nch = s[pos + 1]
-                if nch == '_':
-                    pos += 2
-                elif nch == 'x' and _parse_hex(s, pos + 2, 2) is not None:
-                    pos = _parse_hex(s, pos + 2, 2)[0]
-                elif nch == 'u' and _parse_hex(s, pos + 2, 4) is not None:
-                    pos = _parse_hex(s, pos + 2, 4)[0]
-                elif nch == 'U' and _parse_hex(s, pos + 2, 8) is not None:
-                    pos = _parse_hex(s, pos + 2, 8)[0]
-                else:
-                    return pos  # bare '_': separator
-            else:
-                return pos
-        else:
-            return pos
-    return pos
-
-
-def _find_lp_body(s):
-    """
-    Given s = everything after 'lp_' in a symbol, find where the declaration
-    body (Name.mangleAux output) starts.
-    Returns the start index of the body within s, or None.
-
-    Strategy: try all candidate split points where the package part is a valid
-    String.mangle output and the body round-trips. Prefer the longest valid
-    package name (most specific match).
-    """
-    length = len(s)
-
-    # Collect candidate split positions: every '_' that could be the separator
-    candidates = []
-    pos = 0
-    while pos < length:
-        if s[pos] == '_':
-            candidates.append(pos)
-        pos += 1
-
-    # Try each candidate; collect all valid splits
-    valid_splits = []
-    for split_pos in candidates:
-        pkg_part = s[:split_pos]
-        if not pkg_part:
-            continue
-        if not _is_valid_string_mangle(pkg_part):
-            continue
-        body = s[split_pos + 1:]
-        if not body:
-            continue
-        components = demangle_body(body)
-        if not components:
-            continue
-        remangled = mangle_name(components, prefix="")
-        if remangled == body:
-            first = components[0]
-            # Score: prefer first component starting with uppercase
-            has_upper = isinstance(first, str) and first and first[0].isupper()
-            valid_splits.append((split_pos, has_upper))
-
-    if valid_splits:
-        # Among splits where first decl component starts uppercase, pick longest pkg.
-        # Otherwise pick shortest pkg.
-        upper_splits = [s for s in valid_splits if s[1]]
-        if upper_splits:
-            best = max(upper_splits, key=lambda x: x[0])
-        else:
-            best = min(valid_splits, key=lambda x: x[0])
-        return best[0] + 1
-
-    # Fallback: greedy String.mangle scan
-    greedy_pos = _skip_string_mangle(s, 0)
-    if greedy_pos < length and s[greedy_pos] == '_':
-        return greedy_pos + 1
-
-    return None
-
-
-# ---------------------------------------------------------------------------
-# Format name components for display
-# ---------------------------------------------------------------------------
-
-def format_name(components):
-    """Format a list of name components as a dot-separated string."""
-    return '.'.join(str(c) for c in components)
-
-
-# ---------------------------------------------------------------------------
-# Human-friendly postprocessing
-# ---------------------------------------------------------------------------
-
-# Compiler-generated suffix components — exact match
-_SUFFIX_FLAGS_EXACT = {
-    '_redArg':  'arity\u2193',
-    '_boxed':   'boxed',
-    '_impl':    'impl',
-}
-
-# Compiler-generated suffix prefixes — match with optional _N index
-# e.g., _lam, _lam_0, _lam_3, _lambda_0, _closed_2
-_SUFFIX_FLAGS_PREFIX = {
-    '_lam':     '\u03bb',
-    '_lambda':  '\u03bb',
-    '_elam':    '\u03bb',
-    '_jp':      'jp',
-    '_closed':  'closed',
-}
-
-
-def _match_suffix(component):
-    """
-    Check if a string component is a compiler-generated suffix.
-    Returns the flag label or None.
-
-    Handles both exact matches (_redArg, _boxed) and indexed suffixes
-    (_lam_0, _lambda_2, _closed_0) produced by appendIndexAfter.
-    """
-    if not isinstance(component, str):
-        return None
-    if component in _SUFFIX_FLAGS_EXACT:
-        return _SUFFIX_FLAGS_EXACT[component]
-    if component in _SUFFIX_FLAGS_PREFIX:
-        return _SUFFIX_FLAGS_PREFIX[component]
-    # Check for indexed suffix: prefix + _N
-    for prefix, label in _SUFFIX_FLAGS_PREFIX.items():
-        if component.startswith(prefix + '_'):
-            rest = component[len(prefix) + 1:]
-            if rest.isdigit():
-                return label
-    return None
-
-
-def _strip_private(components):
-    """Strip _private.Module.0. prefix. Returns (stripped_parts, is_private)."""
-    if (len(components) >= 3 and isinstance(components[0], str) and
-            components[0] == '_private'):
-        for i in range(1, len(components)):
-            if components[i] == 0:
-                if i + 1 < len(components):
-                    return components[i + 1:], True
-                break
-    return components, False
-
-
-def _strip_spec_suffixes(components):
-    """Strip trailing spec_N components (from appendIndexAfter)."""
-    parts = list(components)
-    while parts and isinstance(parts[-1], str) and parts[-1].startswith('spec_'):
-        rest = parts[-1][5:]
-        if rest.isdigit():
-            parts.pop()
-        else:
-            break
-    return parts
-
-
-def _is_spec_index(component):
-    """Check if a component is a spec_N index (from appendIndexAfter)."""
-    return (isinstance(component, str) and
-            component.startswith('spec_') and component[5:].isdigit())
-
-
-def _parse_spec_entries(rest):
-    """Parse _at_..._spec pairs into separate spec context entries.
-
-    Given components starting from the first _at_, returns:
-    - entries: list of component lists, one per _at_..._spec block
-    - remaining: components after the last _spec N (trailing suffixes)
-    """
-    entries = []
-    current_ctx = None
-    remaining = []
-    skip_next = False
-
-    for p in rest:
-        if skip_next:
-            skip_next = False
-            continue
-        if isinstance(p, str) and p == '_at_':
-            if current_ctx is not None:
-                entries.append(current_ctx)
-            current_ctx = []
-            continue
-        if isinstance(p, str) and p == '_spec':
-            if current_ctx is not None:
-                entries.append(current_ctx)
-                current_ctx = None
-            skip_next = True
-            continue
-        if isinstance(p, str) and p.startswith('_spec'):
-            if current_ctx is not None:
-                entries.append(current_ctx)
-                current_ctx = None
-            continue
-        if current_ctx is not None:
-            current_ctx.append(p)
-        else:
-            remaining.append(p)
-
-    if current_ctx is not None:
-        entries.append(current_ctx)
-
-    return entries, remaining
-
-
-def _process_spec_context(components):
-    """Process a spec context into a clean name and its flags.
-
-    Returns (name_parts, flags) where name_parts are the cleaned components
-    and flags is a deduplicated list of flag labels from compiler suffixes.
-    """
-    parts = list(components)
-    parts, _ = _strip_private(parts)
-
-    name_parts = []
-    ctx_flags = []
-    seen = set()
-
-    for p in parts:
-        flag = _match_suffix(p)
-        if flag is not None:
-            if flag not in seen:
-                ctx_flags.append(flag)
-                seen.add(flag)
-        elif _is_spec_index(p):
-            pass
-        else:
-            name_parts.append(p)
-
-    return name_parts, ctx_flags
-
-
-def postprocess_name(components):
-    """
-    Transform raw demangled components into a human-friendly display string.
-
-    Applies:
-    - Private name cleanup: _private.Module.0.Name.foo -> Name.foo [private]
-    - Hygienic name cleanup: strips _@.module._hygCtx._hyg.N
-    - Suffix folding: _redArg, _boxed, _lam_0, etc. -> [flags]
-    - Specialization: f._at_.g._spec.N -> f spec at g
-      Shown after base [flags], with context flags: spec at g[ctx_flags]
-    """
-    if not components:
-        return ""
-
-    parts = list(components)
-    flags = []
-    spec_entries = []
-
-    # --- Strip _private prefix ---
-    parts, is_private = _strip_private(parts)
-
-    # --- Strip hygienic suffixes: everything from _@ onward ---
-    at_idx = None
-    for i, p in enumerate(parts):
-        if isinstance(p, str) and p.startswith('_@'):
-            at_idx = i
-            break
-    if at_idx is not None:
-        parts = parts[:at_idx]
-
-    # --- Handle specialization: _at_ ... _spec N ---
-    at_positions = [i for i, p in enumerate(parts)
-                    if isinstance(p, str) and p == '_at_']
-    if at_positions:
-        first_at = at_positions[0]
-        base = parts[:first_at]
-        rest = parts[first_at:]
-
-        entries, remaining = _parse_spec_entries(rest)
-        for ctx_components in entries:
-            ctx_name, ctx_flags = _process_spec_context(ctx_components)
-            if ctx_name or ctx_flags:
-                spec_entries.append((ctx_name, ctx_flags))
-
-        parts = base + remaining
-
-    # --- Collect suffix flags from the end ---
-    while parts:
-        last = parts[-1]
-        flag = _match_suffix(last)
-        if flag is not None:
-            flags.append(flag)
-            parts.pop()
-        elif isinstance(last, int) and len(parts) >= 2:
-            prev_flag = _match_suffix(parts[-2])
-            if prev_flag is not None:
-                flags.append(prev_flag)
-                parts.pop()  # remove the number
-                parts.pop()  # remove the suffix
-            else:
-                break
-        else:
-            break
-
-    if is_private:
-        flags.append('private')
-
-    # --- Format result ---
-    name = '.'.join(str(c) for c in parts) if parts else '?'
-    result = name
-    if flags:
-        flag_str = ', '.join(flags)
-        result += f' [{flag_str}]'
-
-    for ctx_name, ctx_flags in spec_entries:
-        ctx_str = '.'.join(str(c) for c in ctx_name) if ctx_name else '?'
-        if ctx_flags:
-            ctx_flag_str = ', '.join(ctx_flags)
-            result += f' spec at {ctx_str}[{ctx_flag_str}]'
-        else:
-            result += f' spec at {ctx_str}'
-
-    return result
-
-
-# ---------------------------------------------------------------------------
-# Main demangling entry point
-# ---------------------------------------------------------------------------
-
-def demangle_lean_name_raw(mangled):
-    """
-    Demangle a Lean C symbol, preserving all internal name components.
-
-    Returns the exact demangled name with all compiler-generated suffixes
-    intact. Use demangle_lean_name() for human-friendly output.
-    """
-    try:
-        return _demangle_lean_name_inner(mangled, human_friendly=False)
-    except Exception:
-        return mangled
+_process = None
+_script_dir = os.path.dirname(os.path.abspath(__file__))
+_cli_script = os.path.join(_script_dir, "lean_demangle_cli.lean")
+
+
+def _get_process():
+    """Get or create the persistent Lean demangler subprocess."""
+    global _process
+    if _process is not None and _process.poll() is None:
+        return _process
+
+    lean = os.environ.get("LEAN", "lean")
+    _process = subprocess.Popen(
+        [lean, "--run", _cli_script],
+        stdin=subprocess.PIPE,
+        stdout=subprocess.PIPE,
+        stderr=subprocess.DEVNULL,
+        text=True,
+        bufsize=1,  # line buffered
+    )
+    atexit.register(_cleanup)
+    return _process
+
+
+def _cleanup():
+    global _process
+    if _process is not None:
+        try:
+            _process.stdin.close()
+            _process.wait(timeout=5)
+        except Exception:
+            _process.kill()
+        _process = None
 
 
 def demangle_lean_name(mangled):
     """
     Demangle a C symbol name produced by the Lean 4 compiler.
 
-    Returns a human-friendly demangled name with compiler suffixes folded
-    into readable flags. Use demangle_lean_name_raw() to preserve all
-    internal components.
+    Returns a human-friendly demangled name, or the original string
+    if it is not a Lean symbol.
     """
     try:
-        return _demangle_lean_name_inner(mangled, human_friendly=True)
+        proc = _get_process()
+        proc.stdin.write(mangled + "\n")
+        proc.stdin.flush()
+        result = proc.stdout.readline().rstrip("\n")
+        return result if result else mangled
     except Exception:
         return mangled
 
 
-def _demangle_lean_name_inner(mangled, human_friendly=True):
-    """Inner demangle that may raise on malformed input."""
-
-    if mangled == "_lean_main":
-        return "[lean] main"
-
-    # Handle lean_ runtime functions
-    if human_friendly and mangled.startswith("lean_apply_"):
-        rest = mangled[11:]
-        if rest.isdigit():
-            return f"<apply/{rest}>"
-
-    # Strip .cold.N suffix (LLVM linker cold function clones)
-    cold_suffix = ""
-    core = mangled
-    dot_pos = core.find('.cold.')
-    if dot_pos >= 0:
-        cold_suffix = " " + core[dot_pos:]
-        core = core[:dot_pos]
-    elif core.endswith('.cold'):
-        cold_suffix = " .cold"
-        core = core[:-5]
-
-    result = _demangle_core(core, human_friendly)
-    if result is None:
-        return mangled
-    return result + cold_suffix
-
-
-def _demangle_core(mangled, human_friendly=True):
-    """Demangle a symbol without .cold suffix. Returns None if not a Lean name."""
-
-    fmt = postprocess_name if human_friendly else format_name
-
-    # _init_ prefix
-    if mangled.startswith("_init_"):
-        rest = mangled[6:]
-        body, pkg_display = _strip_lean_prefix(rest)
-        if body is None:
-            return None
-        components = demangle_body(body)
-        if not components:
-            return None
-        name = fmt(components)
-        if pkg_display:
-            return f"[init] {name} ({pkg_display})"
-        return f"[init] {name}"
-
-    # initialize_ prefix (module init functions)
-    if mangled.startswith("initialize_"):
-        rest = mangled[11:]
-        # With package: initialize_lp_{pkg}_{body} or initialize_l_{body}
-        body, pkg_display = _strip_lean_prefix(rest)
-        if body is not None:
-            components = demangle_body(body)
-            if components:
-                name = fmt(components)
-                if pkg_display:
-                    return f"[module_init] {name} ({pkg_display})"
-                return f"[module_init] {name}"
-        # Without package: initialize_{Name.mangleAux(moduleName)}
-        if rest:
-            components = demangle_body(rest)
-            if components:
-                return f"[module_init] {fmt(components)}"
-        return None
-
-    # l_ or lp_ prefix
-    body, pkg_display = _strip_lean_prefix(mangled)
-    if body is None:
-        return None
-    components = demangle_body(body)
-    if not components:
-        return None
-    name = fmt(components)
-    if pkg_display:
-        return f"{name} ({pkg_display})"
-    return name
-
-
-def _strip_lean_prefix(s):
-    """
-    Strip the l_ or lp_ prefix from a mangled symbol.
-    Returns (body, pkg_display) where body is the Name.mangleAux output
-    and pkg_display is None or a string describing the package.
-    Returns (None, None) if the string doesn't have a recognized prefix.
-    """
-    if s.startswith("l_"):
-        return (s[2:], None)
-
-    if s.startswith("lp_"):
-        after_lp = s[3:]
-        body_start = _find_lp_body(after_lp)
-        if body_start is not None:
-            pkg_mangled = after_lp[:body_start - 1]
-            # Unmangle the package name
-            pkg_components = demangle_body(pkg_mangled)
-            if pkg_components and len(pkg_components) == 1 and isinstance(pkg_components[0], str):
-                pkg_display = pkg_components[0]
-            else:
-                pkg_display = pkg_mangled
-            return (after_lp[body_start:], pkg_display)
-        # Fallback: treat everything after lp_ as body
-        return (after_lp, "?")
-
-    return (None, None)
-
-
-# ---------------------------------------------------------------------------
-# CLI
-# ---------------------------------------------------------------------------
-
 def main():
-    """Filter stdin or arguments, demangling Lean names."""
-    import argparse
-    parser = argparse.ArgumentParser(
-        description="Demangle Lean 4 C symbol names (like c++filt for Lean)")
-    parser.add_argument('names', nargs='*',
-                        help='Names to demangle (reads stdin if none given)')
-    parser.add_argument('--raw', action='store_true',
-                        help='Output exact demangled names without postprocessing')
-    args = parser.parse_args()
-
-    demangle = demangle_lean_name_raw if args.raw else demangle_lean_name
-
-    if args.names:
-        for name in args.names:
-            print(demangle(name))
-    else:
-        for line in sys.stdin:
-            print(demangle(line.rstrip('\n')))
+    """Filter stdin, demangling Lean names."""
+    for line in sys.stdin:
+        print(demangle_lean_name(line.rstrip("\n")))
 
 
-if __name__ == '__main__':
+if __name__ == "__main__":
     main()

script/profiler/lean_demangle_cli.lean

@@ -0,0 +1,32 @@
+/-
+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
+
+import Lean.Compiler.NameDemangling
+
+/-!
+Lean name demangler CLI tool. Reads mangled symbol names from stdin (one per
+line) and writes demangled names to stdout. Non-Lean symbols pass through
+unchanged. Like `c++filt` but for Lean names.
+
+Usage:
+    echo "l_Lean_Meta_foo" | lean --run lean_demangle_cli.lean
+    cat symbols.txt | lean --run lean_demangle_cli.lean
+-/
+
+open Lean.Name.Demangle
+
+def main : IO Unit := do
+  let stdin ← IO.getStdin
+  let stdout ← IO.getStdout
+  repeat do
+    let line ← stdin.getLine
+    if line.isEmpty then break
+    let sym := line.trimRight
+    match demangleSymbol sym with
+    | some s => stdout.putStrLn s
+    | none => stdout.putStrLn sym
+    stdout.flush

script/profiler/test_demangle.py

@@ -1,670 +0,0 @@
-#!/usr/bin/env python3
-"""Tests for the Lean name demangler."""
-
-import unittest
-import json
-import gzip
-import tempfile
-import os
-
-from lean_demangle import (
-    mangle_string, mangle_name, demangle_body, format_name,
-    demangle_lean_name, demangle_lean_name_raw, postprocess_name,
-    _parse_hex, _check_disambiguation,
-)
-
-
-class TestStringMangle(unittest.TestCase):
-    """Test String.mangle (character-level escaping)."""
-
-    def test_alphanumeric(self):
-        self.assertEqual(mangle_string("hello"), "hello")
-        self.assertEqual(mangle_string("abc123"), "abc123")
-
-    def test_underscore(self):
-        self.assertEqual(mangle_string("a_b"), "a__b")
-        self.assertEqual(mangle_string("_"), "__")
-        self.assertEqual(mangle_string("__"), "____")
-
-    def test_special_chars(self):
-        self.assertEqual(mangle_string("."), "_x2e")
-        self.assertEqual(mangle_string("a.b"), "a_x2eb")
-
-    def test_unicode(self):
-        self.assertEqual(mangle_string("\u03bb"), "_u03bb")
-        self.assertEqual(mangle_string("\U0001d55c"), "_U0001d55c")
-
-    def test_empty(self):
-        self.assertEqual(mangle_string(""), "")
-
-
-class TestNameMangle(unittest.TestCase):
-    """Test Name.mangle (hierarchical name mangling)."""
-
-    def test_simple(self):
-        self.assertEqual(mangle_name(["Lean", "Meta", "Sym", "main"]),
-                         "l_Lean_Meta_Sym_main")
-
-    def test_single_component(self):
-        self.assertEqual(mangle_name(["main"]), "l_main")
-
-    def test_numeric_component(self):
-        self.assertEqual(
-            mangle_name(["_private", "Lean", "Meta", "Basic", 0,
-                         "Lean", "Meta", "withMVarContextImp"]),
-            "l___private_Lean_Meta_Basic_0__Lean_Meta_withMVarContextImp")
-
-    def test_component_with_underscore(self):
-        self.assertEqual(mangle_name(["a_b"]), "l_a__b")
-        self.assertEqual(mangle_name(["a_b", "c"]), "l_a__b_c")
-
-    def test_disambiguation_digit_start(self):
-        self.assertEqual(mangle_name(["0foo"]), "l_000foo")
-
-    def test_disambiguation_escape_start(self):
-        self.assertEqual(mangle_name(["a", "x27"]), "l_a_00x27")
-
-    def test_numeric_root(self):
-        self.assertEqual(mangle_name([42]), "l_42_")
-        self.assertEqual(mangle_name([42, "foo"]), "l_42__foo")
-
-    def test_component_ending_with_underscore(self):
-        self.assertEqual(mangle_name(["a_", "b"]), "l_a___00b")
-
-    def test_custom_prefix(self):
-        self.assertEqual(mangle_name(["foo"], prefix="lp_pkg_"),
-                         "lp_pkg_foo")
-
-
-class TestDemangleBody(unittest.TestCase):
-    """Test demangle_body (the core Name.demangleAux algorithm)."""
-
-    def test_simple(self):
-        self.assertEqual(demangle_body("Lean_Meta_Sym_main"),
-                         ["Lean", "Meta", "Sym", "main"])
-
-    def test_single(self):
-        self.assertEqual(demangle_body("main"), ["main"])
-
-    def test_empty(self):
-        self.assertEqual(demangle_body(""), [])
-
-    def test_underscore_in_component(self):
-        self.assertEqual(demangle_body("a__b"), ["a_b"])
-        self.assertEqual(demangle_body("a__b_c"), ["a_b", "c"])
-
-    def test_numeric_component(self):
-        self.assertEqual(demangle_body("foo_42__bar"), ["foo", 42, "bar"])
-
-    def test_numeric_root(self):
-        self.assertEqual(demangle_body("42_"), [42])
-
-    def test_numeric_at_end(self):
-        self.assertEqual(demangle_body("foo_42_"), ["foo", 42])
-
-    def test_disambiguation_00(self):
-        self.assertEqual(demangle_body("a_00x27"), ["a", "x27"])
-
-    def test_disambiguation_00_at_root(self):
-        self.assertEqual(demangle_body("000foo"), ["0foo"])
-
-    def test_hex_escape_x(self):
-        self.assertEqual(demangle_body("a_x2eb"), ["a.b"])
-
-    def test_hex_escape_u(self):
-        self.assertEqual(demangle_body("_u03bb"), ["\u03bb"])
-
-    def test_hex_escape_U(self):
-        self.assertEqual(demangle_body("_U0001d55c"), ["\U0001d55c"])
-
-    def test_private_name(self):
-        body = "__private_Lean_Meta_Basic_0__Lean_Meta_withMVarContextImp"
-        self.assertEqual(demangle_body(body),
-                         ["_private", "Lean", "Meta", "Basic", 0,
-                          "Lean", "Meta", "withMVarContextImp"])
-
-    def test_boxed_suffix(self):
-        body = "foo___boxed"
-        self.assertEqual(demangle_body(body), ["foo", "_boxed"])
-
-    def test_redArg_suffix(self):
-        body = "foo_bar___redArg"
-        self.assertEqual(demangle_body(body), ["foo", "bar", "_redArg"])
-
-    def test_component_ending_underscore_disambiguation(self):
-        self.assertEqual(demangle_body("a___00b"), ["a_", "b"])
-
-
-class TestRoundTrip(unittest.TestCase):
-    """Test that mangle(demangle(x)) == x for various names."""
-
-    def _check_roundtrip(self, components):
-        mangled = mangle_name(components, prefix="")
-        demangled = demangle_body(mangled)
-        self.assertEqual(demangled, components,
-                         f"Round-trip failed: {components} -> '{mangled}' -> {demangled}")
-        mangled_with_prefix = mangle_name(components, prefix="l_")
-        self.assertTrue(mangled_with_prefix.startswith("l_"))
-        body = mangled_with_prefix[2:]
-        demangled2 = demangle_body(body)
-        self.assertEqual(demangled2, components)
-
-    def test_simple_names(self):
-        self._check_roundtrip(["Lean", "Meta", "main"])
-        self._check_roundtrip(["a"])
-        self._check_roundtrip(["Foo", "Bar", "baz"])
-
-    def test_numeric(self):
-        self._check_roundtrip(["foo", 0, "bar"])
-        self._check_roundtrip([42])
-        self._check_roundtrip(["a", 1, "b", 2, "c"])
-
-    def test_underscores(self):
-        self._check_roundtrip(["_private"])
-        self._check_roundtrip(["a_b", "c_d"])
-        self._check_roundtrip(["_at_", "_spec"])
-
-    def test_private_name(self):
-        self._check_roundtrip(["_private", "Lean", "Meta", "Basic", 0,
-                                "Lean", "Meta", "withMVarContextImp"])
-
-    def test_boxed(self):
-        self._check_roundtrip(["Lean", "Meta", "foo", "_boxed"])
-
-    def test_redArg(self):
-        self._check_roundtrip(["Lean", "Meta", "foo", "_redArg"])
-
-    def test_specialization(self):
-        self._check_roundtrip(["List", "map", "_at_", "Foo", "bar", "_spec", 3])
-
-    def test_lambda(self):
-        self._check_roundtrip(["Foo", "bar", "_lambda", 0])
-        self._check_roundtrip(["Foo", "bar", "_lambda", 2])
-
-    def test_closed(self):
-        self._check_roundtrip(["myConst", "_closed", 0])
-
-    def test_special_chars(self):
-        self._check_roundtrip(["a.b"])
-        self._check_roundtrip(["\u03bb"])
-        self._check_roundtrip(["a", "b\u2192c"])
-
-    def test_disambiguation_cases(self):
-        self._check_roundtrip(["a", "x27"])
-        self._check_roundtrip(["0foo"])
-        self._check_roundtrip(["a_", "b"])
-
-    def test_complex_real_names(self):
-        """Names modeled after real Lean compiler output."""
-        self._check_roundtrip(
-            ["Lean", "MVarId", "withContext", "_at_",
-             "_private", "Lean", "Meta", "Sym", 0,
-             "Lean", "Meta", "Sym", "BackwardRule", "apply",
-             "_spec", 2, "_redArg", "_lambda", 0, "_boxed"])
-
-
-class TestDemangleRaw(unittest.TestCase):
-    """Test demangle_lean_name_raw (exact demangling, no postprocessing)."""
-
-    def test_l_prefix(self):
-        self.assertEqual(
-            demangle_lean_name_raw("l_Lean_Meta_Sym_main"),
-            "Lean.Meta.Sym.main")
-
-    def test_l_prefix_private(self):
-        result = demangle_lean_name_raw(
-            "l___private_Lean_Meta_Basic_0__Lean_Meta_withMVarContextImp")
-        self.assertEqual(result,
-                         "_private.Lean.Meta.Basic.0.Lean.Meta.withMVarContextImp")
-
-    def test_l_prefix_boxed(self):
-        result = demangle_lean_name_raw("l_foo___boxed")
-        self.assertEqual(result, "foo._boxed")
-
-    def test_l_prefix_redArg(self):
-        result = demangle_lean_name_raw(
-            "l___private_Lean_Meta_Basic_0__Lean_Meta_withMVarContextImp___redArg")
-        self.assertEqual(
-            result,
-            "_private.Lean.Meta.Basic.0.Lean.Meta.withMVarContextImp._redArg")
-
-    def test_lean_main(self):
-        self.assertEqual(demangle_lean_name_raw("_lean_main"), "[lean] main")
-
-    def test_non_lean_names(self):
-        self.assertEqual(demangle_lean_name_raw("printf"), "printf")
-        self.assertEqual(demangle_lean_name_raw("malloc"), "malloc")
-        self.assertEqual(demangle_lean_name_raw("lean_apply_5"), "lean_apply_5")
-        self.assertEqual(demangle_lean_name_raw(""), "")
-
-    def test_init_prefix(self):
-        result = demangle_lean_name_raw("_init_l_Lean_Meta_foo")
-        self.assertEqual(result, "[init] Lean.Meta.foo")
-
-    def test_lp_prefix_simple(self):
-        mangled = mangle_name(["Lean", "Meta", "foo"], prefix="lp_std_")
-        self.assertEqual(mangled, "lp_std_Lean_Meta_foo")
-        result = demangle_lean_name_raw(mangled)
-        self.assertEqual(result, "Lean.Meta.foo (std)")
-
-    def test_lp_prefix_underscore_pkg(self):
-        pkg_mangled = mangle_string("my_pkg")
-        self.assertEqual(pkg_mangled, "my__pkg")
-        mangled = mangle_name(["Lean", "Meta", "foo"],
-                              prefix=f"lp_{pkg_mangled}_")
-        self.assertEqual(mangled, "lp_my__pkg_Lean_Meta_foo")
-        result = demangle_lean_name_raw(mangled)
-        self.assertEqual(result, "Lean.Meta.foo (my_pkg)")
-
-    def test_lp_prefix_private_decl(self):
-        mangled = mangle_name(
-            ["_private", "X", 0, "Y", "foo"], prefix="lp_pkg_")
-        self.assertEqual(mangled, "lp_pkg___private_X_0__Y_foo")
-        result = demangle_lean_name_raw(mangled)
-        self.assertEqual(result, "_private.X.0.Y.foo (pkg)")
-
-    def test_complex_specialization(self):
-        components = [
-            "Lean", "MVarId", "withContext", "_at_",
-            "_private", "Lean", "Meta", "Sym", 0,
-            "Lean", "Meta", "Sym", "BackwardRule", "apply",
-            "_spec", 2, "_redArg", "_lambda", 0, "_boxed"
-        ]
-        mangled = mangle_name(components)
-        result = demangle_lean_name_raw(mangled)
-        expected = format_name(components)
-        self.assertEqual(result, expected)
-
-    def test_cold_suffix(self):
-        result = demangle_lean_name_raw("l_Lean_Meta_foo___redArg.cold.1")
-        self.assertEqual(result, "Lean.Meta.foo._redArg .cold.1")
-
-    def test_cold_suffix_plain(self):
-        result = demangle_lean_name_raw("l_Lean_Meta_foo.cold")
-        self.assertEqual(result, "Lean.Meta.foo .cold")
-
-    def test_initialize_no_pkg(self):
-        result = demangle_lean_name_raw("initialize_Init_Control_Basic")
-        self.assertEqual(result, "[module_init] Init.Control.Basic")
-
-    def test_initialize_with_l_prefix(self):
-        result = demangle_lean_name_raw("initialize_l_Lean_Meta_foo")
-        self.assertEqual(result, "[module_init] Lean.Meta.foo")
-
-    def test_never_crashes(self):
-        """Demangling should never raise, just return the original."""
-        weird_inputs = [
-            "", "l_", "lp_", "lp_x", "_init_", "initialize_",
-            "l_____", "lp____", "l_00", "l_0",
-            "some random string", "l_ space",
-        ]
-        for inp in weird_inputs:
-            result = demangle_lean_name_raw(inp)
-            self.assertIsInstance(result, str)
-
-
-class TestPostprocess(unittest.TestCase):
-    """Test postprocess_name (human-friendly suffix folding, etc.)."""
-
-    def test_no_change(self):
-        self.assertEqual(postprocess_name(["Lean", "Meta", "main"]),
-                         "Lean.Meta.main")
-
-    def test_boxed(self):
-        self.assertEqual(postprocess_name(["foo", "_boxed"]),
-                         "foo [boxed]")
-
-    def test_redArg(self):
-        self.assertEqual(postprocess_name(["foo", "bar", "_redArg"]),
-                         "foo.bar [arity\u2193]")
-
-    def test_lambda_separate(self):
-        # _lam as separate component + numeric index
-        self.assertEqual(postprocess_name(["foo", "_lam", 0]),
-                         "foo [\u03bb]")
-
-    def test_lambda_indexed(self):
-        # _lam_0 as single string (appendIndexAfter)
-        self.assertEqual(postprocess_name(["foo", "_lam_0"]),
-                         "foo [\u03bb]")
-        self.assertEqual(postprocess_name(["foo", "_lambda_2"]),
-                         "foo [\u03bb]")
-
-    def test_lambda_boxed(self):
-        # _lam_0 followed by _boxed
-        self.assertEqual(
-            postprocess_name(["Lean", "Meta", "Simp", "simpLambda",
-                              "_lam_0", "_boxed"]),
-            "Lean.Meta.Simp.simpLambda [boxed, \u03bb]")
-
-    def test_closed(self):
-        self.assertEqual(postprocess_name(["myConst", "_closed", 3]),
-                         "myConst [closed]")
-
-    def test_closed_indexed(self):
-        self.assertEqual(postprocess_name(["myConst", "_closed_0"]),
-                         "myConst [closed]")
-
-    def test_multiple_suffixes(self):
-        self.assertEqual(postprocess_name(["foo", "_redArg", "_boxed"]),
-                         "foo [boxed, arity\u2193]")
-
-    def test_redArg_lam(self):
-        # _redArg followed by _lam_0 (issue #4)
-        self.assertEqual(
-            postprocess_name(["Lean", "profileitIOUnsafe",
-                              "_redArg", "_lam_0"]),
-            "Lean.profileitIOUnsafe [\u03bb, arity\u2193]")
-
-    def test_private_name(self):
-        self.assertEqual(
-            postprocess_name(["_private", "Lean", "Meta", "Basic", 0,
-                              "Lean", "Meta", "withMVarContextImp"]),
-            "Lean.Meta.withMVarContextImp [private]")
-
-    def test_private_with_suffix(self):
-        self.assertEqual(
-            postprocess_name(["_private", "Lean", "Meta", "Basic", 0,
-                              "Lean", "Meta", "foo", "_redArg"]),
-            "Lean.Meta.foo [arity\u2193, private]")
-
-    def test_hygienic_strip(self):
-        self.assertEqual(
-            postprocess_name(["Lean", "Meta", "foo", "_@", "Lean", "Meta",
-                              "_hyg", 42]),
-            "Lean.Meta.foo")
-
-    def test_specialization(self):
-        self.assertEqual(
-            postprocess_name(["List", "map", "_at_", "Foo", "bar",
-                              "_spec", 3]),
-            "List.map spec at Foo.bar")
-
-    def test_specialization_with_suffix(self):
-        # Base suffix _boxed appears in [flags] before spec at
-        self.assertEqual(
-            postprocess_name(["Lean", "MVarId", "withContext", "_at_",
-                              "Foo", "bar", "_spec", 2, "_boxed"]),
-            "Lean.MVarId.withContext [boxed] spec at Foo.bar")
-
-    def test_spec_context_with_flags(self):
-        # Compiler suffixes in spec context become context flags
-        self.assertEqual(
-            postprocess_name(["Lean", "Meta", "foo", "_at_",
-                              "Lean", "Meta", "bar", "_elam_1", "_redArg",
-                              "_spec", 2]),
-            "Lean.Meta.foo spec at Lean.Meta.bar[\u03bb, arity\u2193]")
-
-    def test_spec_context_flags_dedup(self):
-        # Duplicate flag labels are deduplicated
-        self.assertEqual(
-            postprocess_name(["f", "_at_",
-                              "g", "_lam_0", "_elam_1", "_redArg",
-                              "_spec", 1]),
-            "f spec at g[\u03bb, arity\u2193]")
-
-    def test_multiple_at(self):
-        # Multiple _at_ entries become separate spec at clauses
-        self.assertEqual(
-            postprocess_name(["f", "_at_", "g", "_spec", 1,
-                              "_at_", "h", "_spec", 2]),
-            "f spec at g spec at h")
-
-    def test_multiple_at_with_flags(self):
-        # Multiple spec at with flags on base and contexts
-        self.assertEqual(
-            postprocess_name(["f", "_at_", "g", "_redArg", "_spec", 1,
-                              "_at_", "h", "_lam_0", "_spec", 2,
-                              "_boxed"]),
-            "f [boxed] spec at g[arity\u2193] spec at h[\u03bb]")
-
-    def test_base_flags_before_spec(self):
-        # Base trailing suffixes appear in [flags] before spec at
-        self.assertEqual(
-            postprocess_name(["f", "_at_", "g", "_spec", 1, "_lam_0"]),
-            "f [\u03bb] spec at g")
-
-    def test_spec_context_strip_spec_suffixes(self):
-        # spec_0 in context should be stripped
-        self.assertEqual(
-            postprocess_name(["Lean", "Meta", "transformWithCache", "visit",
-                              "_at_",
-                              "_private", "Lean", "Meta", "Transform", 0,
-                              "Lean", "Meta", "transform",
-                              "Lean", "Meta", "Sym", "unfoldReducible",
-                              "spec_0", "spec_0",
-                              "_spec", 1]),
-            "Lean.Meta.transformWithCache.visit "
-            "spec at Lean.Meta.transform.Lean.Meta.Sym.unfoldReducible")
-
-    def test_spec_context_strip_private(self):
-        # _private in spec context should be stripped
-        self.assertEqual(
-            postprocess_name(["Array", "mapMUnsafe", "map", "_at_",
-                              "_private", "Lean", "Meta", "Transform", 0,
-                              "Lean", "Meta", "transformWithCache", "visit",
-                              "_spec", 1]),
-            "Array.mapMUnsafe.map "
-            "spec at Lean.Meta.transformWithCache.visit")
-
-    def test_empty(self):
-        self.assertEqual(postprocess_name([]), "")
-
-
-class TestDemangleHumanFriendly(unittest.TestCase):
-    """Test demangle_lean_name (human-friendly output)."""
-
-    def test_simple(self):
-        self.assertEqual(demangle_lean_name("l_Lean_Meta_main"),
-                         "Lean.Meta.main")
-
-    def test_boxed(self):
-        self.assertEqual(demangle_lean_name("l_foo___boxed"),
-                         "foo [boxed]")
-
-    def test_redArg(self):
-        self.assertEqual(demangle_lean_name("l_foo___redArg"),
-                         "foo [arity\u2193]")
-
-    def test_private(self):
-        self.assertEqual(
-            demangle_lean_name(
-                "l___private_Lean_Meta_Basic_0__Lean_Meta_foo"),
-            "Lean.Meta.foo [private]")
-
-    def test_private_with_redArg(self):
-        self.assertEqual(
-            demangle_lean_name(
-                "l___private_Lean_Meta_Basic_0__Lean_Meta_foo___redArg"),
-            "Lean.Meta.foo [arity\u2193, private]")
-
-    def test_cold_with_suffix(self):
-        self.assertEqual(
-            demangle_lean_name("l_Lean_Meta_foo___redArg.cold.1"),
-            "Lean.Meta.foo [arity\u2193] .cold.1")
-
-    def test_lean_apply(self):
-        self.assertEqual(demangle_lean_name("lean_apply_5"), "<apply/5>")
-        self.assertEqual(demangle_lean_name("lean_apply_12"), "<apply/12>")
-
-    def test_lean_apply_raw_unchanged(self):
-        self.assertEqual(demangle_lean_name_raw("lean_apply_5"),
-                         "lean_apply_5")
-
-    def test_init_private(self):
-        self.assertEqual(
-            demangle_lean_name(
-                "_init_l___private_X_0__Y_foo"),
-            "[init] Y.foo [private]")
-
-    def test_complex_specialization(self):
-        components = [
-            "Lean", "MVarId", "withContext", "_at_",
-            "_private", "Lean", "Meta", "Sym", 0,
-            "Lean", "Meta", "Sym", "BackwardRule", "apply",
-            "_spec", 2, "_redArg", "_lambda", 0, "_boxed"
-        ]
-        mangled = mangle_name(components)
-        result = demangle_lean_name(mangled)
-        # Base: Lean.MVarId.withContext with trailing _redArg, _lambda 0, _boxed
-        # Spec context: Lean.Meta.Sym.BackwardRule.apply (private stripped)
-        self.assertEqual(
-            result,
-            "Lean.MVarId.withContext [boxed, \u03bb, arity\u2193] "
-            "spec at Lean.Meta.Sym.BackwardRule.apply")
-
-    def test_non_lean_unchanged(self):
-        self.assertEqual(demangle_lean_name("printf"), "printf")
-        self.assertEqual(demangle_lean_name("malloc"), "malloc")
-        self.assertEqual(demangle_lean_name(""), "")
-
-
-class TestDemangleProfile(unittest.TestCase):
-    """Test the profile rewriter."""
-
-    def _make_profile_shared(self, strings):
-        """Create a profile with shared.stringArray (newer format)."""
-        return {
-            "meta": {"version": 28},
-            "libs": [],
-            "shared": {
-                "stringArray": list(strings),
-            },
-            "threads": [{
-                "name": "main",
-                "pid": "1",
-                "tid": 1,
-                "funcTable": {
-                    "name": list(range(len(strings))),
-                    "isJS": [False] * len(strings),
-                    "relevantForJS": [False] * len(strings),
-                    "resource": [-1] * len(strings),
-                    "fileName": [None] * len(strings),
-                    "lineNumber": [None] * len(strings),
-                    "columnNumber": [None] * len(strings),
-                    "length": len(strings),
-                },
-                "frameTable": {"length": 0},
-                "stackTable": {"length": 0},
-                "samples": {"length": 0},
-                "markers": {"length": 0},
-                "resourceTable": {"length": 0},
-                "nativeSymbols": {"length": 0},
-            }],
-            "pages": [],
-            "counters": [],
-        }
-
-    def _make_profile_per_thread(self, strings):
-        """Create a profile with per-thread stringArray (samply format)."""
-        return {
-            "meta": {"version": 28},
-            "libs": [],
-            "threads": [{
-                "name": "main",
-                "pid": "1",
-                "tid": 1,
-                "stringArray": list(strings),
-                "funcTable": {
-                    "name": list(range(len(strings))),
-                    "isJS": [False] * len(strings),
-                    "relevantForJS": [False] * len(strings),
-                    "resource": [-1] * len(strings),
-                    "fileName": [None] * len(strings),
-                    "lineNumber": [None] * len(strings),
-                    "columnNumber": [None] * len(strings),
-                    "length": len(strings),
-                },
-                "frameTable": {"length": 0},
-                "stackTable": {"length": 0},
-                "samples": {"length": 0},
-                "markers": {"length": 0},
-                "resourceTable": {"length": 0},
-                "nativeSymbols": {"length": 0},
-            }],
-            "pages": [],
-            "counters": [],
-        }
-
-    def test_profile_rewrite_shared(self):
-        from lean_demangle_profile import rewrite_profile
-        strings = [
-            "l_Lean_Meta_Sym_main",
-            "printf",
-            "lean_apply_5",
-            "l___private_Lean_Meta_Basic_0__Lean_Meta_foo",
-        ]
-        profile = self._make_profile_shared(strings)
-        rewrite_profile(profile)
-        sa = profile["shared"]["stringArray"]
-        self.assertEqual(sa[0], "Lean.Meta.Sym.main")
-        self.assertEqual(sa[1], "printf")
-        self.assertEqual(sa[2], "<apply/5>")
-        self.assertEqual(sa[3], "Lean.Meta.foo [private]")
-
-    def test_profile_rewrite_per_thread(self):
-        from lean_demangle_profile import rewrite_profile
-        strings = [
-            "l_Lean_Meta_Sym_main",
-            "printf",
-            "lean_apply_5",
-            "l___private_Lean_Meta_Basic_0__Lean_Meta_foo",
-        ]
-        profile = self._make_profile_per_thread(strings)
-        count = rewrite_profile(profile)
-        sa = profile["threads"][0]["stringArray"]
-        self.assertEqual(sa[0], "Lean.Meta.Sym.main")
-        self.assertEqual(sa[1], "printf")
-        self.assertEqual(sa[2], "<apply/5>")
-        self.assertEqual(sa[3], "Lean.Meta.foo [private]")
-        self.assertEqual(count, 3)
-
-    def test_profile_json_roundtrip(self):
-        from lean_demangle_profile import process_profile_file
-        strings = ["l_Lean_Meta_main", "malloc"]
-        profile = self._make_profile_shared(strings)
-
-        with tempfile.NamedTemporaryFile(mode='w', suffix='.json',
-                                         delete=False) as f:
-            json.dump(profile, f)
-            inpath = f.name
-
-        outpath = inpath.replace('.json', '-demangled.json')
-        try:
-            process_profile_file(inpath, outpath)
-            with open(outpath) as f:
-                result = json.load(f)
-            self.assertEqual(result["shared"]["stringArray"][0],
-                             "Lean.Meta.main")
-            self.assertEqual(result["shared"]["stringArray"][1], "malloc")
-        finally:
-            os.unlink(inpath)
-            if os.path.exists(outpath):
-                os.unlink(outpath)
-
-    def test_profile_gzip_roundtrip(self):
-        from lean_demangle_profile import process_profile_file
-        strings = ["l_Lean_Meta_main", "malloc"]
-        profile = self._make_profile_shared(strings)
-
-        with tempfile.NamedTemporaryFile(suffix='.json.gz',
-                                         delete=False) as f:
-            with gzip.open(f, 'wt') as gz:
-                json.dump(profile, gz)
-            inpath = f.name
-
-        outpath = inpath.replace('.json.gz', '-demangled.json.gz')
-        try:
-            process_profile_file(inpath, outpath)
-            with gzip.open(outpath, 'rt') as f:
-                result = json.load(f)
-            self.assertEqual(result["shared"]["stringArray"][0],
-                             "Lean.Meta.main")
-        finally:
-            os.unlink(inpath)
-            if os.path.exists(outpath):
-                os.unlink(outpath)
-
-
-if __name__ == '__main__':
-    unittest.main()

script/release_checklist.py

@@ -11,7 +11,7 @@ IMPORTANT: Keep this documentation up-to-date when modifying the script's behavi
 What this script does:
 1. Validates preliminary Lean4 release infrastructure:
    - Checks that the release branch (releases/vX.Y.0) exists
-   - Verifies CMake version settings are correct
+   - Verifies CMake version settings are correct (both src/ and stage0/)
    - Confirms the release tag exists
    - Validates the release page exists on GitHub (created automatically by CI after tag push)
    - Checks the release notes page on lean-lang.org (updated while bumping the `reference-manual` repository)
@@ -326,6 +326,42 @@ def check_cmake_version(repo_url, branch, version_major, version_minor, github_t
     print(f"  ✅ CMake version settings are correct in {cmake_file_path}")
     return True
 
+def check_stage0_version(repo_url, branch, version_major, version_minor, github_token):
+    """Verify that stage0/src/CMakeLists.txt has the same version as src/CMakeLists.txt.
+
+    The stage0 pre-built binaries stamp .olean headers with their baked-in version.
+    If stage0 has a different version (e.g. from a 'begin development cycle' bump),
+    the release tarball will contain .olean files with the wrong version.
+    """
+    stage0_cmake = "stage0/src/CMakeLists.txt"
+    content = get_branch_content(repo_url, branch, stage0_cmake, github_token)
+    if content is None:
+        print(f"  ❌ Could not retrieve {stage0_cmake} from {branch}")
+        return False
+
+    errors = []
+    for line in content.splitlines():
+        stripped = line.strip()
+        if stripped.startswith("set(LEAN_VERSION_MAJOR "):
+            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(")")
+            if actual != str(version_minor):
+                errors.append(f"LEAN_VERSION_MINOR: expected {version_minor}, found {actual}")
+
+    if errors:
+        print(f"  ❌ stage0 version mismatch in {stage0_cmake}:")
+        for error in errors:
+            print(f"     {error}")
+        print(f"     The stage0 compiler stamps .olean headers with its baked-in version.")
+        print(f"     Run `make update-stage0` to rebuild stage0 with the correct version.")
+        return False
+
+    print(f"  ✅ stage0 version matches in {stage0_cmake}")
+    return True
+
 def extract_org_repo_from_url(repo_url):
     """Extract the 'org/repo' part from a GitHub URL."""
     if repo_url.startswith("https://github.com/"):
@@ -441,7 +477,10 @@ def get_pr_ci_status(repo_url, pr_number, github_token):
     conclusions = [run['conclusion'] for run in check_runs if run.get('status') == 'completed']
     in_progress = [run for run in check_runs if run.get('status') in ['queued', 'in_progress']]
 
+    failed = sum(1 for c in conclusions if c in ['failure', 'timed_out', 'action_required'])
     if in_progress:
+        if failed > 0:
+            return "failure", f"{failed} check(s) failing, {len(in_progress)} still in progress"
         return "pending", f"{len(in_progress)} check(s) in progress"
 
     if not conclusions:
@@ -450,7 +489,6 @@ def get_pr_ci_status(repo_url, pr_number, github_token):
     if all(c == 'success' for c in conclusions):
         return "success", f"All {len(conclusions)} checks passed"
 
-    failed = sum(1 for c in conclusions if c in ['failure', 'timed_out', 'action_required'])
     if failed > 0:
         return "failure", f"{failed} check(s) failed"
 
@@ -680,6 +718,9 @@ def main():
         # Check CMake version settings
         if not check_cmake_version(lean_repo_url, branch_name, version_major, version_minor, github_token):
             lean4_success = False
+        # Check that stage0 version matches (stage0 stamps .olean headers with its version)
+        if not check_stage0_version(lean_repo_url, branch_name, version_major, version_minor, github_token):
+            lean4_success = False
 
     # Check for tag and release page
     if not tag_exists(lean_repo_url, toolchain, github_token):
@@ -965,14 +1006,15 @@ def main():
         # Find the actual minor version in CMakeLists.txt
         for line in cmake_lines:
             if line.strip().startswith("set(LEAN_VERSION_MINOR "):
-                actual_minor = int(line.split()[-1].rstrip(")"))
+                m = re.search(r'set\(LEAN_VERSION_MINOR\s+(\d+)', line)
+                actual_minor = int(m.group(1)) if m else 0
                 version_minor_correct = actual_minor >= next_minor
                 break
         else:
             version_minor_correct = False
             
         is_release_correct = any(
-            l.strip().startswith("set(LEAN_VERSION_IS_RELEASE 0)") 
+            re.match(r'set\(LEAN_VERSION_IS_RELEASE\s+0[\s)]', l.strip())
             for l in cmake_lines
         )
         

script/release_steps.py

@@ -479,6 +479,25 @@ def execute_release_steps(repo, version, config):
         print(blue("Updating lakefile.toml..."))
         run_command(f'perl -pi -e \'s/"v4\\.[0-9]+(\\.[0-9]+)?(-rc[0-9]+)?"/"' + version + '"/g\' lakefile.*', cwd=repo_path)
         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. 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 = (
+            'ROOT_REV=$(jq -r \'.packages[] | select(.name == "subverso") | .rev\' lake-manifest.json); '
+            'SUBVERSO_URL=$(jq -r \'.packages[] | select(.name == "subverso") | .url\' lake-manifest.json); '
+            'DEMOD_REV=$(git ls-remote "$SUBVERSO_URL" "refs/tags/no-modules/$ROOT_REV" | awk \'{print $1}\'); '
+            'find test-projects -name lake-manifest.json -print0 | while IFS= read -r -d \'\' f; do '
+            'jq --arg rev "$DEMOD_REV" \'.packages |= map(if .name == "subverso" then .rev = $rev else . end)\' "$f" > /tmp/lm_tmp.json && mv /tmp/lm_tmp.json "$f"; '
+            'done'
+        )
+        run_command(sync_script, cwd=repo_path)
+        print(green("Synced de-modulized subverso rev to all test-project sub-manifests"))
     elif dependencies:
         run_command(f'perl -pi -e \'s/"v4\\.[0-9]+(\\.[0-9]+)?(-rc[0-9]+)?"/"' + version + '"/g\' lakefile.*', cwd=repo_path)
         run_command("lake update", cwd=repo_path, stream_output=True)

src/CMakeLists.txt

@@ -7,11 +7,17 @@ if(NOT DEFINED STAGE)
 endif()
 include(ExternalProject)
 project(LEAN CXX C)
-set(LEAN_VERSION_MAJOR 4)
-set(LEAN_VERSION_MINOR 30)
-set(LEAN_VERSION_PATCH 0)
-set(LEAN_VERSION_IS_RELEASE 0) # This number is 1 in the release revision, and 0 otherwise.
+set(LEAN_VERSION_MAJOR 4 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'")
+# project(LEAN) above implicitly creates empty LEAN_VERSION_{MAJOR,MINOR,PATCH}
+# normal variables (CMake sets <PROJECT>_VERSION_* for the project name). These
+# shadow the cache values. Remove them so ${VAR} falls through to the cache.
+unset(LEAN_VERSION_MAJOR)
+unset(LEAN_VERSION_MINOR)
+unset(LEAN_VERSION_PATCH)
 set(LEAN_VERSION_STRING "${LEAN_VERSION_MAJOR}.${LEAN_VERSION_MINOR}.${LEAN_VERSION_PATCH}")
 if(LEAN_SPECIAL_VERSION_DESC)
   string(APPEND LEAN_VERSION_STRING "-${LEAN_SPECIAL_VERSION_DESC}")
@@ -81,6 +87,8 @@ option(USE_GITHASH "GIT_HASH" ON)
 option(INSTALL_LICENSE "INSTALL_LICENSE" ON)
 # When ON we install a copy of cadical
 option(INSTALL_CADICAL "Install a copy of cadical" ON)
+# When ON we install a copy of leantar
+option(INSTALL_LEANTAR "Install a copy of leantar" ON)
 
 # FLAGS for disabling optimizations and debugging
 option(FREE_VAR_RANGE_OPT "FREE_VAR_RANGE_OPT" ON)
@@ -751,6 +759,14 @@ if(STAGE GREATER 0 AND CADICAL AND INSTALL_CADICAL)
   add_dependencies(leancpp copy-cadical)
 endif()
 
+if(STAGE GREATER 0 AND LEANTAR AND INSTALL_LEANTAR)
+  add_custom_target(
+    copy-leantar
+    COMMAND cmake -E copy_if_different "${LEANTAR}" "${CMAKE_BINARY_DIR}/bin/leantar${CMAKE_EXECUTABLE_SUFFIX}"
+  )
+  add_dependencies(leancpp copy-leantar)
+endif()
+
 # MSYS2 bash usually handles Windows paths relatively well, but not when putting them in the PATH
 string(REGEX REPLACE "^([a-zA-Z]):" "/\\1" LEAN_BIN "${CMAKE_BINARY_DIR}/bin")
 
@@ -907,6 +923,10 @@ if(STAGE GREATER 0 AND CADICAL AND INSTALL_CADICAL)
   install(PROGRAMS "${CADICAL}" DESTINATION bin)
 endif()
 
+if(STAGE GREATER 0 AND LEANTAR AND INSTALL_LEANTAR)
+  install(PROGRAMS "${LEANTAR}" DESTINATION bin)
+endif()
+
 add_custom_target(
   clean-stdlib
   COMMAND rm -rf "${CMAKE_BINARY_DIR}/lib" || true

src/Init.lean

@@ -30,6 +30,7 @@ public import Init.Hints
 public import Init.Conv
 public import Init.Guard
 public import Init.Simproc
+public import Init.CbvSimproc
 public import Init.SizeOfLemmas
 public import Init.BinderPredicates
 public import Init.Ext

src/Init/CbvSimproc.lean

@@ -0,0 +1,71 @@
+/-
+Copyright (c) 2026 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Wojciech Różowski
+-/
+module
+
+prelude
+public meta import Init.Data.ToString.Name  -- shake: keep (transitive public meta dep, fix)
+public import Init.Tactics
+import Init.Meta.Defs
+
+public section
+
+namespace Lean.Parser
+
+syntax cbvSimprocEval := "cbv_eval"
+
+/--
+A user-defined simplification procedure used by the `cbv` tactic.
+The body must have type `Lean.Meta.Sym.Simp.Simproc` (`Expr → SimpM Result`).
+Procedures are indexed by a discrimination tree pattern and fire at one of three phases:
+`↓` (pre), `cbv_eval` (eval), or `↑` (post, default).
+-/
+syntax (docComment)? attrKind "cbv_simproc " (Tactic.simpPre <|> Tactic.simpPost <|> cbvSimprocEval)? ident " (" term ")" " := " term : command
+
+/--
+A `cbv_simproc` declaration without automatically adding it to the cbv simproc set.
+To activate, use `attribute [cbv_simproc]`.
+-/
+syntax (docComment)? "cbv_simproc_decl " ident " (" term ")" " := " term : command
+
+syntax (docComment)? attrKind "builtin_cbv_simproc " (Tactic.simpPre <|> Tactic.simpPost <|> cbvSimprocEval)? ident " (" term ")" " := " term : command
+
+syntax (docComment)? "builtin_cbv_simproc_decl " ident " (" term ")" " := " term : command
+
+syntax (name := cbvSimprocPattern) "cbv_simproc_pattern% " term " => " ident : command
+
+syntax (name := cbvSimprocPatternBuiltin) "builtin_cbv_simproc_pattern% " term " => " ident : command
+
+namespace Attr
+
+syntax (name := cbvSimprocAttr) "cbv_simproc" (Tactic.simpPre <|> Tactic.simpPost <|> cbvSimprocEval)? : attr
+
+syntax (name := cbvSimprocBuiltinAttr) "builtin_cbv_simproc" (Tactic.simpPre <|> Tactic.simpPost <|> cbvSimprocEval)? : attr
+
+end Attr
+
+macro_rules
+  | `($[$doc?:docComment]? cbv_simproc_decl $n:ident ($pattern:term) := $body) => do
+    let simprocType := `Lean.Meta.Sym.Simp.Simproc
+    `($[$doc?:docComment]? meta def $n:ident : $(mkIdent simprocType) := $body
+      cbv_simproc_pattern% $pattern => $n)
+
+macro_rules
+  | `($[$doc?:docComment]? builtin_cbv_simproc_decl $n:ident ($pattern:term) := $body) => do
+    let simprocType := `Lean.Meta.Sym.Simp.Simproc
+    `($[$doc?:docComment]? def $n:ident : $(mkIdent simprocType) := $body
+      builtin_cbv_simproc_pattern% $pattern => $n)
+
+macro_rules
+  | `($[$doc?:docComment]? $kind:attrKind cbv_simproc $[$phase?]? $n:ident ($pattern:term) := $body) => do
+    `($[$doc?:docComment]? cbv_simproc_decl $n ($pattern) := $body
+      attribute [$kind cbv_simproc $[$phase?]?] $n)
+
+macro_rules
+  | `($[$doc?:docComment]? $kind:attrKind builtin_cbv_simproc $[$phase?]? $n:ident ($pattern:term) := $body) => do
+    `($[$doc?:docComment]? builtin_cbv_simproc_decl $n ($pattern) := $body
+      attribute [$kind builtin_cbv_simproc $[$phase?]?] $n)
+
+end Lean.Parser

src/Init/Classical.lean

@@ -69,9 +69,11 @@ theorem em (p : Prop) : p ∨ ¬p :=
 theorem exists_true_of_nonempty {α : Sort u} : Nonempty α → ∃ _ : α, True
   | ⟨x⟩ => ⟨x, trivial⟩
 
+@[implicit_reducible]
 noncomputable def inhabited_of_nonempty {α : Sort u} (h : Nonempty α) : Inhabited α :=
   ⟨choice h⟩
 
+@[implicit_reducible]
 noncomputable def inhabited_of_exists {α : Sort u} {p : α → Prop} (h : ∃ x, p x) : Inhabited α :=
   inhabited_of_nonempty (Exists.elim h (fun w _ => ⟨w⟩))
 
@@ -81,6 +83,7 @@ noncomputable scoped instance (priority := low) propDecidable (a : Prop) : Decid
     | Or.inl h => ⟨isTrue h⟩
     | Or.inr h => ⟨isFalse h⟩
 
+@[implicit_reducible]
 noncomputable def decidableInhabited (a : Prop) : Inhabited (Decidable a) where
   default := inferInstance
 

src/Init/Control.lean

@@ -18,3 +18,4 @@ public import Init.Control.StateCps
 public import Init.Control.ExceptCps
 public import Init.Control.MonadAttach
 public import Init.Control.EState
+public import Init.Control.Do

src/Init/Control/Id.lean

@@ -49,6 +49,7 @@ instance : Monad Id where
 /--
 The identity monad has a `bind` operator.
 -/
+@[implicit_reducible]
 def hasBind : Bind Id :=
   inferInstance
 
@@ -58,7 +59,7 @@ Runs a computation in the identity monad.
 This function is the identity function. Because its parameter has type `Id α`, it causes
 `do`-notation in its arguments to use the `Monad Id` instance.
 -/
-@[always_inline, inline, expose]
+@[always_inline, inline, expose, implicit_reducible]
 protected def run (x : Id α) : α := x
 
 instance [OfNat α n] : OfNat (Id α) n :=

src/Init/Control/Lawful/Basic.lean

@@ -254,8 +254,8 @@ instance : LawfulMonad Id := by
 @[simp, grind =] theorem run_bind (x : Id α) (f : α → Id β) : (x >>= f).run = (f x.run).run := rfl
 @[simp, grind =] theorem run_pure (a : α) : (pure a : Id α).run = a := rfl
 @[simp, grind =] theorem pure_run (a : Id α) : pure a.run = a := rfl
-@[simp] theorem run_seqRight (x y : Id α) : (x *> y).run = y.run := rfl
-@[simp] theorem run_seqLeft (x y : Id α) : (x <* y).run = x.run := rfl
+@[simp] theorem run_seqRight (x : Id α) (y : Id β) : (x *> y).run = y.run := rfl
+@[simp] theorem run_seqLeft (x : Id α) (y : Id β) : (x <* y).run = x.run := rfl
 @[simp] theorem run_seq (f : Id (α → β)) (x : Id α) : (f <*> x).run = f.run x.run := rfl
 
 end Id

src/Init/Conv.lean

@@ -280,7 +280,7 @@ resulting in `t'`, which becomes the new target subgoal. -/
 syntax (name := convConvSeq) "conv" " => " convSeq : conv
 
 /-- `· conv` focuses on the main conv goal and tries to solve it using `s`. -/
-macro dot:patternIgnore("· " <|> ". ") s:convSeq : conv => `(conv| {%$dot ($s) })
+macro dot:unicode("· ", ". ") s:convSeq : conv => `(conv| {%$dot ($s) })
 
 
 /-- `fail_if_success t` fails if the tactic `t` succeeds. -/

src/Init/Data/Array.lean

@@ -34,3 +34,4 @@ public import Init.Data.Array.MinMax
 public import Init.Data.Array.Nat
 public import Init.Data.Array.Int
 public import Init.Data.Array.Count
+public import Init.Data.Array.Sort

src/Init/Data/Array/Basic.lean

@@ -148,6 +148,9 @@ end List
 
 namespace Array
 
+@[simp, grind =] theorem getElem!_toList [Inhabited α] {xs : Array α} {i : Nat} : xs.toList[i]! = xs[i]! := by
+  rw [List.getElem!_toArray]
+
 theorem size_eq_length_toList {xs : Array α} : xs.size = xs.toList.length := rfl
 
 /-! ### Externs -/
@@ -283,7 +286,7 @@ Examples:
  * `#[1, 2].isEmpty = false`
  * `#[()].isEmpty = false`
 -/
-@[expose]
+@[expose, inline]
 def isEmpty (xs : Array α) : Bool :=
   xs.size = 0
 
@@ -377,6 +380,7 @@ Returns the last element of an array, or panics if the array is empty.
 Safer alternatives include `Array.back`, which requires a proof the array is non-empty, and
 `Array.back?`, which returns an `Option`.
 -/
+@[inline]
 def back! [Inhabited α] (xs : Array α) : α :=
   xs[xs.size - 1]!
 
@@ -386,6 +390,7 @@ Returns the last element of an array, given a proof that the array is not empty.
 See `Array.back!` for the version that panics if the array is empty, or `Array.back?` for the
 version that returns an option.
 -/
+@[inline]
 def back (xs : Array α) (h : 0 < xs.size := by get_elem_tactic) : α :=
   xs[xs.size - 1]'(Nat.sub_one_lt_of_lt h)
 
@@ -395,6 +400,7 @@ Returns the last element of an array, or `none` if the array is empty.
 See `Array.back!` for the version that panics if the array is empty, or `Array.back` for the version
 that requires a proof the array is non-empty.
 -/
+@[inline]
 def back? (xs : Array α) : Option α :=
   xs[xs.size - 1]?
 
@@ -2145,7 +2151,4 @@ protected def repr {α : Type u} [Repr α] (xs : Array α) : Std.Format :=
 instance {α : Type u} [Repr α] : Repr (Array α) where
   reprPrec xs _ := Array.repr xs
 
-instance [ToString α] : ToString (Array α) where
-  toString xs := String.Internal.append "#" (toString xs.toList)
-
 end Array

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

@@ -78,7 +78,7 @@ private theorem cons_lex_cons [BEq α] {lt : α → α → Bool} {a b : α} {xs
   simp only [lex, size_append, List.size_toArray, List.length_cons, List.length_nil, Nat.zero_add,
     Nat.add_min_add_left, Nat.add_lt_add_iff_left, Std.Rco.forIn'_eq_forIn'_toList]
   rw [cons_lex_cons.forIn'_congr_aux (Nat.toList_rco_eq_cons (by omega)) rfl (fun _ _ _ => rfl)]
-  simp only [bind_pure_comp, map_pure, Nat.toList_rco_succ_succ, Nat.add_comm 1]
+  simp only [Nat.toList_rco_succ_succ, Nat.add_comm 1]
   cases h : lt a b
   · cases h' : a == b <;> simp [bne, *]
   · simp [*]

src/Init/Data/Array/Sort.lean

@@ -0,0 +1,10 @@
+/-
+Copyright (c) 2026 Lean FRO. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+public import Init.Data.Array.Sort.Basic
+public import Init.Data.Array.Sort.Lemmas

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

@@ -0,0 +1,55 @@
+/-
+Copyright (c) 2026 Lean FRO. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+public import Init.Data.Array.Subarray.Split
+public import Init.Data.Slice.Array
+import Init.Omega
+
+public section
+
+private def Array.MergeSort.Internal.merge (xs ys : Array α) (le : α → α → Bool := by exact (· ≤ ·)) :
+    Array α :=
+  if hxs : 0 < xs.size then
+    if hys : 0 < ys.size then
+      go xs[*...*] ys[*...*] (by simp only [Array.size_mkSlice_rii]; omega) (by simp only [Array.size_mkSlice_rii]; omega) (Array.emptyWithCapacity (xs.size + ys.size))
+    else
+      xs
+  else
+    ys
+where
+  go (xs ys : Subarray α) (hxs : 0 < xs.size) (hys : 0 < ys.size) (acc : Array α) : Array α :=
+    let x := xs[0]
+    let y := ys[0]
+    if le x y then
+      if hi : 1 < xs.size then
+        go (xs.drop 1) ys (by simp only [Subarray.size_drop]; omega) hys (acc.push x)
+      else
+        ys.foldl (init := acc.push x) (fun acc y => acc.push y)
+    else
+      if hj : 1 < ys.size then
+        go xs (ys.drop 1) hxs (by simp only [Subarray.size_drop]; omega) (acc.push y)
+      else
+        xs.foldl (init := acc.push y) (fun acc x => acc.push x)
+  termination_by xs.size + ys.size
+
+def Subarray.mergeSort (xs : Subarray α) (le : α → α → Bool := by exact (· ≤ ·)) : Array α :=
+    if h : 1 < xs.size then
+      let splitIdx := (xs.size + 1) / 2 -- We follow the same splitting convention as `List.mergeSort`
+      let left := xs[*...splitIdx]
+      let right := xs[splitIdx...*]
+      Array.MergeSort.Internal.merge (mergeSort left le) (mergeSort right le) le
+    else
+      xs.toArray
+termination_by xs.size
+decreasing_by
+  · simp only [Subarray.size_mkSlice_rio]; omega
+  · simp only [Subarray.size_mkSlice_rci]; omega
+
+@[inline]
+def Array.mergeSort (xs : Array α) (le : α → α → Bool := by exact (· ≤ ·)) : Array α :=
+    xs[*...*].mergeSort le

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

@@ -0,0 +1,240 @@
+/-
+Copyright (c) 2026 Lean FRO. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+public import Init.Data.Array.Sort.Basic
+public import Init.Data.List.Sort.Basic
+public import Init.Data.Array.Perm
+import all Init.Data.Array.Sort.Basic
+import all Init.Data.List.Sort.Basic
+import Init.Data.List.Sort.Lemmas
+import Init.Data.Slice.Array.Lemmas
+import Init.Data.Slice.List.Lemmas
+import Init.Data.Array.Bootstrap
+import Init.Data.Array.Lemmas
+import Init.Data.Array.MapIdx
+import Init.ByCases
+
+public section
+
+private theorem Array.MergeSort.merge.go_eq_listMerge {xs ys : Subarray α} {hxs hys le acc} :
+    (Array.MergeSort.Internal.merge.go le xs ys hxs hys acc).toList = acc.toList ++ List.merge xs.toList ys.toList le := by
+  fun_induction Array.MergeSort.Internal.merge.go le xs ys hxs hys acc
+  · rename_i xs ys _ _ _ _ _ _ _ _
+    rw [List.merge.eq_def]
+    split
+    · have : xs.size = 0 := by simp [← Subarray.length_toList, *]
+      omega
+    · have : ys.size = 0 := by simp [← Subarray.length_toList, *]
+      omega
+    · rename_i x' xs' y' ys' _ _
+      simp +zetaDelta only at *
+      have h₁ : x' = xs[0] := by simp [Subarray.getElem_eq_getElem_toList, *]
+      have h₂ : y' = ys[0] := by simp [Subarray.getElem_eq_getElem_toList, *]
+      cases h₁
+      cases h₂
+      simp [Subarray.toList_drop, *]
+  · rename_i xs ys _ _ _ _ _ _ _
+    rw [List.merge.eq_def]
+    split
+    · have : xs.size = 0 := by simp [← Subarray.length_toList, *]
+      omega
+    · have : ys.size = 0 := by simp [← Subarray.length_toList, *]
+      omega
+    · rename_i x' xs' y' ys' _ _
+      simp +zetaDelta only at *
+      have h₁ : x' = xs[0] := by simp [Subarray.getElem_eq_getElem_toList, *]
+      have h₂ : y' = ys[0] := by simp [Subarray.getElem_eq_getElem_toList, *]
+      cases h₁
+      cases h₂
+      simp [*]
+      have : xs.size = xs'.length + 1 := by simp [← Subarray.length_toList, *]
+      have : xs' = [] := List.eq_nil_of_length_eq_zero (by omega)
+      simp only [this]
+      rw [← Subarray.foldl_toList]
+      simp [*]
+  · rename_i xs ys _ _ _ _ _ _ _ _
+    rw [List.merge.eq_def]
+    split
+    · have : xs.size = 0 := by simp [← Subarray.length_toList, *]
+      omega
+    · have : ys.size = 0 := by simp [← Subarray.length_toList, *]
+      omega
+    · rename_i x' xs' y' ys' _ _
+      simp +zetaDelta only at *
+      have h₁ : x' = xs[0] := by simp [Subarray.getElem_eq_getElem_toList, *]
+      have h₂ : y' = ys[0] := by simp [Subarray.getElem_eq_getElem_toList, *]
+      cases h₁
+      cases h₂
+      simp [Subarray.toList_drop, *]
+  · rename_i xs ys _ _ _ _ _ _ _
+    rw [List.merge.eq_def]
+    split
+    · have : xs.size = 0 := by simp [← Subarray.length_toList, *]
+      omega
+    · have : ys.size = 0 := by simp [← Subarray.length_toList, *]
+      omega
+    · rename_i x' xs' y' ys' _ _
+      simp +zetaDelta only at *
+      have h₁ : x' = xs[0] := by simp [Subarray.getElem_eq_getElem_toList, *]
+      have h₂ : y' = ys[0] := by simp [Subarray.getElem_eq_getElem_toList, *]
+      cases h₁
+      cases h₂
+      simp [*]
+      have : ys.size = ys'.length + 1 := by simp [← Subarray.length_toList, *]
+      have : ys' = [] := List.eq_nil_of_length_eq_zero (by omega)
+      simp [this]
+      rw [← Subarray.foldl_toList]
+      simp [*]
+
+private theorem Array.MergeSort.merge_eq_listMerge {xs ys : Array α} {le} :
+    (Array.MergeSort.Internal.merge xs ys le).toList = List.merge xs.toList ys.toList le := by
+  rw [Array.MergeSort.Internal.merge]
+  split <;> rename_i heq₁
+  · split <;> rename_i heq₂
+    · simp [Array.MergeSort.merge.go_eq_listMerge]
+    · have : ys.toList = [] := by simp_all
+      simp [this]
+  · have : xs.toList = [] := by simp_all
+    simp [this]
+
+private theorem List.mergeSort_eq_merge_mkSlice {xs : List α} :
+    xs.mergeSort le =
+      if 1 < xs.length then
+        merge (xs[*...((xs.length + 1) / 2)].toList.mergeSort le) (xs[((xs.length + 1) / 2)...*].toList.mergeSort le) le
+      else
+        xs := by
+  fun_cases xs.mergeSort le
+  · simp
+  · simp
+  · rename_i x y ys lr hl hr
+    simp [lr]
+
+theorem Subarray.toList_mergeSort {xs : Subarray α} {le : α → α → Bool} :
+    (xs.mergeSort le).toList = xs.toList.mergeSort le := by
+  fun_induction xs.mergeSort le
+  · rw [List.mergeSort_eq_merge_mkSlice]
+    simp +zetaDelta [Array.MergeSort.merge_eq_listMerge, *]
+  · simp [List.mergeSort_eq_merge_mkSlice, *]
+
+@[simp, grind =]
+theorem Subarray.mergeSort_eq_mergeSort_toArray {xs : Subarray α} {le : α → α → Bool} :
+    xs.mergeSort le = xs.toArray.mergeSort le := by
+  simp [← Array.toList_inj, toList_mergeSort, Array.mergeSort]
+
+theorem Subarray.mergeSort_toArray {xs : Subarray α} {le : α → α → Bool} :
+    xs.toArray.mergeSort le = xs.mergeSort le := by
+  simp
+
+theorem Array.toList_mergeSort {xs : Array α} {le : α → α → Bool} :
+    (xs.mergeSort le).toList = xs.toList.mergeSort le := by
+  rw [Array.mergeSort, Subarray.toList_mergeSort, Array.toList_mkSlice_rii]
+
+theorem Array.mergeSort_eq_toArray_mergeSort_toList {xs : Array α} {le : α → α → Bool} :
+    xs.mergeSort le = (xs.toList.mergeSort le).toArray := by
+  simp [← toList_mergeSort]
+
+/-!
+# Basic properties of `Array.mergeSort`.
+
+* `pairwise_mergeSort`: `mergeSort` produces a sorted array.
+* `mergeSort_perm`: `mergeSort` is a permutation of the input array.
+* `mergeSort_of_pairwise`: `mergeSort` does not change a sorted array.
+* `sublist_mergeSort`: if `c` is a sorted sublist of `l`, then `c` is still a sublist of `mergeSort le l`.
+-/
+
+namespace Array
+
+-- Enable this instance locally so we can write `Pairwise le` instead of `Pairwise (le · ·)` everywhere.
+attribute [local instance] boolRelToRel
+
+@[simp] theorem mergeSort_empty : (#[] : Array α).mergeSort r = #[] := by
+  simp [mergeSort_eq_toArray_mergeSort_toList]
+
+@[simp] theorem mergeSort_singleton {a : α} : #[a].mergeSort r = #[a] := by
+  simp [mergeSort_eq_toArray_mergeSort_toList]
+
+theorem mergeSort_perm {xs : Array α} {le} : (xs.mergeSort le).Perm xs := by
+  simpa [mergeSort_eq_toArray_mergeSort_toList, Array.perm_iff_toList_perm] using List.mergeSort_perm _ _
+
+@[simp] theorem size_mergeSort {xs : Array α} : (mergeSort xs le).size = xs.size := by
+  simp [mergeSort_eq_toArray_mergeSort_toList]
+
+@[simp] theorem mem_mergeSort {a : α} {xs : Array α} : a ∈ mergeSort xs le ↔ a ∈ xs := by
+  simp [mergeSort_eq_toArray_mergeSort_toList]
+
+/--
+The result of `Array.mergeSort` is sorted,
+as long as the comparison function is transitive (`le a b → le b c → le a c`)
+and total in the sense that `le a b || le b a`.
+
+The comparison function need not be irreflexive, i.e. `le a b` and `le b a` is allowed even when `a ≠ b`.
+-/
+theorem pairwise_mergeSort
+    (trans : ∀ (a b c : α), le a b → le b c → le a c)
+    (total : ∀ (a b : α), le a b || le b a)
+    {xs : Array α} :
+    (mergeSort xs le).toList.Pairwise (le · ·) := by
+  simpa [mergeSort_eq_toArray_mergeSort_toList] using List.pairwise_mergeSort trans total _
+
+/--
+If the input array is already sorted, then `mergeSort` does not change the array.
+-/
+theorem mergeSort_of_pairwise {le : α → α → Bool} {xs : Array α} (_ : xs.toList.Pairwise (le · ·)) :
+    mergeSort xs le = xs := by
+  simpa [mergeSort_eq_toArray_mergeSort_toList, List.toArray_eq_iff] using List.mergeSort_of_pairwise ‹_›
+
+/--
+This merge sort algorithm is stable,
+in the sense that breaking ties in the ordering function using the position in the array
+has no effect on the output.
+
+That is, elements which are equal with respect to the ordering function will remain
+in the same order in the output array as they were in the input array.
+
+See also:
+* `sublist_mergeSort`: if `c <+ l` and `c.Pairwise le`, then `c <+ (mergeSort le l).toList`.
+* `pair_sublist_mergeSort`: if `[a, b] <+ l` and `le a b`, then `[a, b] <+ (mergeSort le l).toList`)
+-/
+theorem mergeSort_zipIdx {xs : Array α} :
+    (mergeSort (xs.zipIdx.map fun (a, i) => (a, i)) (List.zipIdxLE le)).map (·.1) = mergeSort xs le := by
+  simpa [mergeSort_eq_toArray_mergeSort_toList, Array.toList_zipIdx] using List.mergeSort_zipIdx
+
+/--
+Another statement of stability of merge sort.
+If `c` is a sorted sublist of `xs.toList`,
+then `c` is still a sublist of `(mergeSort le xs).toList`.
+-/
+theorem sublist_mergeSort {le : α → α → Bool}
+    (trans : ∀ (a b c : α), le a b → le b c → le a c)
+    (total : ∀ (a b : α), le a b || le b a)
+    {ys : List α} (_ : ys.Pairwise (le · ·)) (_ : List.Sublist ys xs.toList) :
+    List.Sublist ys (mergeSort xs le).toList := by
+  simpa [mergeSort_eq_toArray_mergeSort_toList, Array.toList_zipIdx] using
+    List.sublist_mergeSort trans total ‹_› ‹_›
+
+/--
+Another statement of stability of merge sort.
+If a pair `[a, b]` is a sublist of `xs.toList` and `le a b`,
+then `[a, b]` is still a sublist of `(mergeSort le xs).toList`.
+-/
+theorem pair_sublist_mergeSort
+    (trans : ∀ (a b c : α), le a b → le b c → le a c)
+    (total : ∀ (a b : α), le a b || le b a)
+    (hab : le a b) (h : List.Sublist [a, b] xs.toList) :
+    List.Sublist [a, b] (mergeSort xs le).toList := by
+  simpa [mergeSort_eq_toArray_mergeSort_toList, Array.toList_zipIdx] using
+    List.pair_sublist_mergeSort trans total ‹_› ‹_›
+
+theorem map_mergeSort {r : α → α → Bool} {s : β → β → Bool} {f : α → β}
+    {xs : Array α} (hxs : ∀ a ∈ xs, ∀ b ∈ xs, r a b = s (f a) (f b)) :
+    (xs.mergeSort r).map f = (xs.map f).mergeSort s := by
+  simp only [mergeSort_eq_toArray_mergeSort_toList, List.map_toArray, toList_map, mk.injEq]
+  apply List.map_mergeSort
+  simpa
+
+end Array

src/Init/Data/BitVec/Bitblast.lean

@@ -2408,6 +2408,7 @@ def extractAndExtendAux (k len : Nat) (x : BitVec w) (acc : BitVec (k * len)) (h
   | n' + 1 =>
     let acc' := extractAndExtendBit k len x ++ acc
     extractAndExtendAux (k + 1) len x (acc'.cast (by simp [Nat.add_mul]; omega)) (by omega)
+termination_by w - k
 
 /-- We instantiate `extractAndExtendAux` to extend each bit to `len`, extending
   each bit in `x` to have width `w` and returning a `BitVec (w * w)`. -/
@@ -2443,6 +2444,7 @@ def cpopTree (l : BitVec (len * w)) : BitVec w :=
     l.cast (by simp [h])
   else
     cpopTree (cpopLayer l 0#(0 * w) (by omega))
+termination_by len
 
 /--
   Given flattened bitvector `x : BitVec w` and a length `l : Nat`,
@@ -2778,6 +2780,7 @@ private theorem addRecAux_cpopTree {x : BitVec (len * w)} :
       · rfl
       · intros j hj
         simp [extractLsb'_cpopLayer]
+termination_by len
 
 private theorem addRecAux_eq_cpopTree {x : BitVec (len * w)} :
     x.addRecAux len 0#w = (x.cpopTree).cast (by simp) := by

src/Init/Data/Bool.lean

@@ -629,6 +629,7 @@ export Bool (cond_eq_if cond_eq_ite xor and or not)
 This should not be turned on globally as an instance because it degrades performance in Mathlib,
 but may be used locally.
 -/
+@[implicit_reducible]
 def boolPredToPred : Coe (α → Bool) (α  → Prop) where
   coe r := fun a => Eq (r a) true
 

src/Init/Data/ByteArray/Basic.lean

@@ -469,5 +469,3 @@ def prevn : Iterator → Nat → Iterator
 
 end Iterator
 end ByteArray
-
-instance : ToString ByteArray := ⟨fun bs => bs.toList.toString⟩

src/Init/Data/Char/Basic.lean

@@ -129,6 +129,14 @@ The ASCII digits are the following: `0123456789`.
 @[inline] def isDigit (c : Char) : Bool :=
   c.val ≥ '0'.val && c.val ≤ '9'.val
 
+/--
+Returns `true` if the character is an ASCII hexadecimal digit.
+
+The ASCII hexadecimal digits are the following: `0123456789abcdefABCDEF`.
+-/
+@[inline] def isHexDigit (c : Char) : Bool :=
+  c.isDigit || (c.val ≥ 'a'.val && c.val ≤ 'f'.val) || (c.val ≥ 'A'.val && c.val ≤ 'F'.val)
+
 /--
 Returns `true` if the character is an ASCII letter or digit.
 

src/Init/Data/Char/Lemmas.lean

@@ -62,7 +62,7 @@ instance ltTrichotomous : Std.Trichotomous (· < · : Char → Char → Prop) wh
   trichotomous _ _ h₁ h₂ := Char.le_antisymm (by simpa using h₂) (by simpa using h₁)
 
 @[deprecated ltTrichotomous (since := "2025-10-27")]
-def notLTAntisymm : Std.Antisymm (¬ · < · : Char → Char → Prop) where
+theorem notLTAntisymm : Std.Antisymm (¬ · < · : Char → Char → Prop) where
   antisymm := Char.ltTrichotomous.trichotomous
 
 instance ltAsymm : Std.Asymm (· < · : Char → Char → Prop) where
@@ -73,7 +73,7 @@ instance leTotal : Std.Total (· ≤ · : Char → Char → Prop) where
 
 -- This instance is useful while setting up instances for `String`.
 @[deprecated ltAsymm (since := "2025-08-01")]
-def notLTTotal : Std.Total (¬ · < · : Char → Char → Prop) where
+theorem notLTTotal : Std.Total (¬ · < · : Char → Char → Prop) where
   total := fun x y => by simpa using Char.le_total y x
 
 @[simp] theorem ofNat_toNat (c : Char) : Char.ofNat c.toNat = c := by

src/Init/Data/FloatArray/Basic.lean

@@ -9,6 +9,7 @@ prelude
 public import Init.Data.Float
 import Init.Ext
 public import Init.GetElem
+public import Init.Data.ToString.Extra
 
 public section
 universe u

src/Init/Data/Format/Basic.lean

@@ -414,7 +414,7 @@ Renders a `Format` to a string.
 -/
 def pretty (f : Format) (width : Nat := defWidth) (indent : Nat := 0) (column := 0) : String :=
   let act : StateM State Unit := prettyM f width indent
-  State.out <| act (State.mk "" column) |>.snd
+  State.out <| act.run (State.mk "" column) |>.snd
 
 end Format
 

src/Init/Data/Int/Pow.lean

@@ -118,16 +118,19 @@ theorem toNat_pow_of_nonneg {x : Int} (h : 0 ≤ x) (k : Nat) : (x ^ k).toNat =
   | succ k ih =>
     rw [Int.pow_succ, Int.toNat_mul (Int.pow_nonneg h) h, ih, Nat.pow_succ]
 
-protected theorem sq_nonnneg (m : Int) : 0 ≤ m ^ 2 := by
+protected theorem sq_nonneg (m : Int) : 0 ≤ m ^ 2 := by
   rw [Int.pow_succ, Int.pow_one]
   cases m
   · apply Int.mul_nonneg <;> simp
   · apply Int.mul_nonneg_of_nonpos_of_nonpos <;> exact negSucc_le_zero _
 
+@[deprecated Int.sq_nonneg (since := "2026-03-13")]
+protected theorem sq_nonnneg (m : Int) : 0 ≤ m ^ 2 := Int.sq_nonneg m
+
 protected theorem pow_nonneg_of_even {m : Int} {n : Nat} (h : n % 2 = 0) : 0 ≤ m ^ n := by
   rw [← Nat.mod_add_div n 2, h, Nat.zero_add, Int.pow_mul]
   apply Int.pow_nonneg
-  exact Int.sq_nonnneg m
+  exact Int.sq_nonneg m
 
 protected theorem neg_pow {m : Int} {n : Nat} : (-m)^n = (-1)^(n % 2) * m^n := by
   rw [Int.neg_eq_neg_one_mul, Int.mul_pow]

src/Init/Data/Iterators/Combinators.lean

@@ -6,6 +6,7 @@ Authors: Paul Reichert
 module
 
 prelude
+public import Init.Data.Iterators.Combinators.Append
 public import Init.Data.Iterators.Combinators.Monadic
 public import Init.Data.Iterators.Combinators.FilterMap
 public import Init.Data.Iterators.Combinators.FlatMap

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

@@ -0,0 +1,79 @@
+/-
+Copyright (c) 2026 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+public import Init.Data.Iterators.Combinators.Monadic.Append
+
+public section
+
+namespace Std
+open Std.Iterators Std.Iterators.Types
+
+/--
+Given two iterators `it₁` and `it₂`, `it₁.append it₂` is an iterator that first outputs all values
+of `it₁` in order and then all values of `it₂` in order.
+
+**Marble diagram:**
+
+```text
+it₁                 ---a----b---c--⊥
+it₂                                 --d--e--⊥
+it₁.append it₂      ---a----b---c-----d--e--⊥
+```
+
+**Termination properties:**
+
+* `Finite` instance: only if `it₁` and `it₂` are finite
+* `Productive` instance: only if `it₁` and `it₂` are productive
+
+Note: If `it₁` is not finite, then `it₁.append it₂` can be productive while `it₂` is not.
+The standard library does not provide a `Productive` instance for this case.
+
+**Performance:**
+
+This combinator incurs an additional O(1) cost with each output of `it₁` and `it₂`.
+-/
+@[inline, expose]
+def Iter.append {α₁ : Type w} {α₂ : Type w} {β : Type w}
+    [Iterator α₁ Id β] [Iterator α₂ Id β]
+    (it₁ : Iter (α := α₁) β) (it₂ : Iter (α := α₂) β) :
+    Iter (α := Append α₁ α₂ Id β) β :=
+  (it₁.toIterM.append it₂.toIterM).toIter
+
+/--
+This combinator is only useful for advanced use cases.
+
+Given an iterator `it₂`, returns an iterator that behaves exactly like `it₂` but is of the same
+type as `it₁.append it₂` (after `it₁` has been exhausted).
+This is useful for constructing intermediate states of the append iterator.
+
+**Marble diagram:**
+
+```text
+it₂                        --a--b--⊥
+Iter.appendSnd α₁ it₂      --a--b--⊥
+```
+
+**Termination properties:**
+
+* `Finite` instance: only if `it₂` and iterators of type `α₁` are finite
+* `Productive` instance: only if `it₂` and iterators of type `α₁` are productive
+
+Note: If iterators of type `α₁` are not finite, then `append α₁ it₂` can be productive while `it₂` is not.
+The standard library does not provide a `Productive` instance for this case.
+
+**Performance:**
+
+This combinator incurs an additional O(1) cost with each output of `it₂`.
+-/
+@[inline, expose]
+def Iter.Intermediate.appendSnd {α₂ : Type w} {β : Type w}
+    [Iterator α₂ Id β] (α₁ : Type w) (it₂ : Iter (α := α₂) β) :
+    Iter (α := Append α₁ α₂ Id β) β :=
+  (IterM.Intermediate.appendSnd α₁ it₂.toIterM).toIter
+
+end Std

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

@@ -6,6 +6,7 @@ Authors: Paul Reichert
 module
 
 prelude
+public import Init.Data.Iterators.Combinators.Monadic.Append
 public import Init.Data.Iterators.Combinators.Monadic.FilterMap
 public import Init.Data.Iterators.Combinators.Monadic.FlatMap
 public import Init.Data.Iterators.Combinators.Monadic.Take

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

@@ -0,0 +1,261 @@
+/-
+Copyright (c) 2026 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+public import Init.Data.Iterators.Consumers.Monadic.Loop
+public import Init.Classical
+import Init.Data.Option.Lemmas
+import Init.ByCases
+import Init.Omega
+
+public section
+
+/-!
+This module provides the iterator combinator `IterM.append`.
+-/
+
+namespace Std
+
+variable {α : Type w} {m : Type w → Type w'} {β : Type w}
+
+/--
+The internal state of the `IterM.append` iterator combinator.
+-/
+inductive Iterators.Types.Append (α₁ α₂ : Type w) (m : Type w → Type w') (β : Type w) where
+  | fst : IterM (α := α₁) m β → IterM (α := α₂) m β → Append α₁ α₂ m β
+  | snd : IterM (α := α₂) m β → Append α₁ α₂ m β
+
+open Std.Iterators Std.Iterators.Types
+
+/--
+Given two iterators `it₁` and `it₂`, `it₁.append it₂` is an iterator that first outputs all values
+of `it₁` in order and then all values of `it₂` in order.
+
+**Marble diagram:**
+
+```text
+it₁                 ---a----b---c--⊥
+it₂                                 --d--e--⊥
+it₁.append it₂      ---a----b---c-----d--e--⊥
+```
+
+**Termination properties:**
+
+* `Finite` instance: only if `it₁` and `it₂` are finite
+* `Productive` instance: only if `it₁` and `it₂` are productive
+
+Note: If `it₁` is not finite, then `it₁.append it₂` can be productive while `it₂` is not.
+The standard library does not provide a `Productive` instance for this case.
+
+**Performance:**
+
+This combinator incurs an additional O(1) cost with each output of `it₁` and `it₂`.
+-/
+@[inline, expose]
+def IterM.append [Iterator α₁ m β] [Iterator α₂ m β]
+    (it₁ : IterM (α := α₁) m β) (it₂ : IterM (α := α₂) m β) :=
+  (⟨Iterators.Types.Append.fst it₁ it₂⟩ : IterM m β)
+
+/--
+This combinator is only useful for advanced use cases.
+
+Given an iterator `it₂`, `IterM.Intermediate.appendSnd α₁ it₂` returns an iterator that behaves
+exactly like `it₂` but has the same type as `it₁.append it₂` (after `it₁` has been exhausted).
+This is useful for constructing intermediate states of the append iterator.
+
+**Marble diagram:**
+
+```text
+it₂                                  --a--b--⊥
+IterM.Intermediate.appendSnd α₁ it₂  --a--b--⊥
+```
+
+**Termination properties:**
+
+* `Finite` instance: only if `it₂` and iterators of type `α₁` are finite
+* `Productive` instance: only if `it₂` and iterators of type `α₁` are productive
+
+Note: If iterators of type `α₁` are not finite, then `appendSnd α₁ it₂` can be productive
+while `it₂` is not. The standard library does not provide a `Productive` instance for this case.
+
+**Performance:**
+
+This combinator incurs an additional O(1) cost with each output of `it₂`.
+-/
+@[inline, expose]
+def IterM.Intermediate.appendSnd [Iterator α₂ m β] (α₁ : Type w) (it₂ : IterM (α := α₂) m β) :=
+  (⟨Iterators.Types.Append.snd (α₁ := α₁) it₂⟩ : IterM m β)
+
+namespace Iterators.Types
+
+inductive Append.PlausibleStep [Iterator α₁ m β] [Iterator α₂ m β] :
+    IterM (α := Append α₁ α₂ m β) m β → IterStep (IterM (α := Append α₁ α₂ m β) m β) β → Prop where
+  | fstYield {it₁ : IterM (α := α₁) m β}  {it₂ : IterM (α := α₂) m β} :
+    it₁.IsPlausibleStep (.yield it₁' out) → PlausibleStep (it₁.append it₂) (.yield (it₁'.append it₂) out)
+  | fstSkip {it₁ : IterM (α := α₁) m β} {it₂ : IterM (α := α₂) m β} :
+    it₁.IsPlausibleStep (.skip it₁') → PlausibleStep (it₁.append it₂) (.skip (it₁'.append it₂))
+  | fstDone {it₁ : IterM (α := α₁) m β} {it₂ : IterM (α := α₂) m β} :
+    it₁.IsPlausibleStep .done → PlausibleStep (it₁.append it₂) (.skip (IterM.Intermediate.appendSnd α₁ it₂))
+  | sndYield {it₂ : IterM (α := α₂) m β} :
+    it₂.IsPlausibleStep (.yield it₂' out) →
+      PlausibleStep (IterM.Intermediate.appendSnd α₁ it₂) (.yield (IterM.Intermediate.appendSnd α₁ it₂') out)
+  | sndSkip {it₂ : IterM (α := α₂) m β} :
+    it₂.IsPlausibleStep (.skip it₂') →
+      PlausibleStep (IterM.Intermediate.appendSnd α₁ it₂) (.skip (IterM.Intermediate.appendSnd α₁ it₂'))
+  | sndDone {it₂ : IterM (α := α₂) m β} :
+    it₂.IsPlausibleStep .done → PlausibleStep (IterM.Intermediate.appendSnd α₁ it₂) .done
+
+@[inline]
+instance Append.instIterator [Monad m] [Iterator α₁ m β] [Iterator α₂ m β] :
+    Iterator (Append α₁ α₂ m β) m β where
+  IsPlausibleStep := Append.PlausibleStep
+  step
+    | ⟨.fst it₁ it₂⟩ => do
+      match (← it₁.step).inflate with
+      | .yield it₁' out h => return .deflate <| .yield (it₁'.append it₂) out (.fstYield h)
+      | .skip it₁' h => return .deflate <| .skip (it₁'.append it₂) (.fstSkip h)
+      | .done h => return .deflate <| .skip (IterM.Intermediate.appendSnd α₁ it₂) (.fstDone h)
+    | ⟨.snd it₂⟩ => do
+      match (← it₂.step).inflate with
+      | .yield it₂' out h => return .deflate <| .yield (IterM.Intermediate.appendSnd α₁ it₂') out (.sndYield h)
+      | .skip it₂' h => return .deflate <| .skip (IterM.Intermediate.appendSnd α₁ it₂') (.sndSkip h)
+      | .done h => return .deflate <| .done (.sndDone h)
+
+instance Append.instIteratorLoop {n : Type x → Type x'} [Monad m] [Monad n]
+    [Iterator α₁ m β] [Iterator α₂ m β] :
+    IteratorLoop (Append α₁ α₂ m β) m n :=
+  .defaultImplementation
+
+section Finite
+
+variable {α₁ : Type w} {α₂ : Type w} {m : Type w → Type w'} {β : Type w}
+
+variable (α₁ α₂ m β) in
+def Append.Rel [Monad m] [Iterator α₁ m β] [Iterator α₂ m β] [Finite α₁ m] [Finite α₂ m] :
+    IterM (α := Append α₁ α₂ m β) m β → IterM (α := Append α₁ α₂ m β) m β → Prop :=
+  InvImage
+    (Prod.Lex
+      (Option.lt (InvImage IterM.TerminationMeasures.Finite.Rel IterM.finitelyManySteps))
+      (InvImage IterM.TerminationMeasures.Finite.Rel IterM.finitelyManySteps))
+    (fun it => match it.internalState with
+      | .fst it₁ it₂ => (some it₁, it₂)
+      | .snd it₂ => (none, it₂))
+
+theorem Append.rel_of_fst [Monad m] [Iterator α₁ m β] [Iterator α₂ m β]
+    [Finite α₁ m] [Finite α₂ m] {it₁ it₁' : IterM (α := α₁) m β} {it₂ : IterM (α := α₂) m β}
+    (h : it₁'.finitelyManySteps.Rel it₁.finitelyManySteps) :
+    Append.Rel α₁ α₂ m β (it₁'.append it₂) (it₁.append it₂) := by
+  exact Prod.Lex.left _ _ h
+
+theorem Append.rel_fstDone [Monad m] [Iterator α₁ m β] [Iterator α₂ m β]
+    [Finite α₁ m] [Finite α₂ m] {it₁ : IterM (α := α₁) m β} {it₂ : IterM (α := α₂) m β} :
+    Append.Rel α₁ α₂ m β (IterM.Intermediate.appendSnd α₁ it₂) (it₁.append it₂) := by
+  exact Prod.Lex.left _ _ trivial
+
+theorem Append.rel_of_snd [Monad m] [Iterator α₁ m β] [Iterator α₂ m β]
+    [Finite α₁ m] [Finite α₂ m] {it₂ it₂' : IterM (α := α₂) m β}
+    (h : it₂'.finitelyManySteps.Rel it₂.finitelyManySteps) :
+    Append.Rel α₁ α₂ m β (IterM.Intermediate.appendSnd α₁ it₂') (IterM.Intermediate.appendSnd α₁ it₂) := by
+  exact Prod.Lex.right _ h
+
+def Append.instFinitenessRelation [Monad m] [Iterator α₁ m β] [Iterator α₂ m β]
+    [Finite α₁ m] [Finite α₂ m] :
+    FinitenessRelation (Append α₁ α₂ m β) m where
+  Rel := Append.Rel α₁ α₂ m β
+  wf := by
+    apply InvImage.wf
+    refine ⟨fun (a, b) => Prod.lexAccessible (WellFounded.apply ?_ a) (WellFounded.apply ?_) b⟩
+    · exact Option.wellFounded_lt <| InvImage.wf _ WellFoundedRelation.wf
+    · exact InvImage.wf _ WellFoundedRelation.wf
+  subrelation {it it'} h := by
+    obtain ⟨step, h, h'⟩ := h
+    cases h' <;> cases h
+    case fstYield =>
+      apply Append.rel_of_fst
+      exact IterM.TerminationMeasures.Finite.rel_of_yield ‹_›
+    case fstSkip =>
+      apply Append.rel_of_fst
+      exact IterM.TerminationMeasures.Finite.rel_of_skip ‹_›
+    case fstDone =>
+      exact Append.rel_fstDone
+    case sndYield =>
+      apply Append.rel_of_snd
+      exact IterM.TerminationMeasures.Finite.rel_of_yield ‹_›
+    case sndSkip =>
+      apply Append.rel_of_snd
+      exact IterM.TerminationMeasures.Finite.rel_of_skip ‹_›
+
+@[no_expose]
+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
+
+end Finite
+
+section Productive
+
+variable {α₁ : Type w} {α₂ : Type w} {m : Type w → Type w'} {β : Type w}
+
+variable (α₁ α₂ m β) in
+def Append.ProductiveRel [Monad m] [Iterator α₁ m β] [Iterator α₂ m β]
+    [Productive α₁ m] [Productive α₂ m] :
+    IterM (α := Append α₁ α₂ m β) m β → IterM (α := Append α₁ α₂ m β) m β → Prop :=
+  InvImage
+    (Prod.Lex
+      (Option.lt (InvImage IterM.TerminationMeasures.Productive.Rel IterM.finitelyManySkips))
+      (InvImage IterM.TerminationMeasures.Productive.Rel IterM.finitelyManySkips))
+    (fun it => match it.internalState with
+      | .fst it₁ it₂ => (some it₁, it₂)
+      | .snd it₂ => (none, it₂))
+
+theorem Append.productiveRel_of_fst [Monad m] [Iterator α₁ m β] [Iterator α₂ m β]
+    [Productive α₁ m] [Productive α₂ m] {it₁ it₁' : IterM (α := α₁) m β}
+    {it₂ : IterM (α := α₂) m β}
+    (h : it₁'.finitelyManySkips.Rel it₁.finitelyManySkips) :
+    Append.ProductiveRel α₁ α₂ m β (it₁'.append it₂) (it₁.append it₂) := by
+  exact Prod.Lex.left _ _ h
+
+theorem Append.productiveRel_fstDone [Monad m] [Iterator α₁ m β] [Iterator α₂ m β]
+    [Productive α₁ m] [Productive α₂ m] {it₁ : IterM (α := α₁) m β}
+    {it₂ : IterM (α := α₂) m β} :
+    Append.ProductiveRel α₁ α₂ m β (IterM.Intermediate.appendSnd α₁ it₂) (it₁.append it₂) := by
+  exact Prod.Lex.left _ _ trivial
+
+theorem Append.productiveRel_of_snd [Monad m] [Iterator α₁ m β] [Iterator α₂ m β]
+    [Productive α₁ m] [Productive α₂ m] {it₂ it₂' : IterM (α := α₂) m β}
+    (h : it₂'.finitelyManySkips.Rel it₂.finitelyManySkips) :
+    Append.ProductiveRel α₁ α₂ m β
+      (IterM.Intermediate.appendSnd α₁ it₂') (IterM.Intermediate.appendSnd α₁ it₂) := by
+  exact Prod.Lex.right _ h
+
+private def Append.instProductivenessRelation [Monad m] [Iterator α₁ m β] [Iterator α₂ m β]
+    [Productive α₁ m] [Productive α₂ m] :
+    ProductivenessRelation (Append α₁ α₂ m β) m where
+  Rel := Append.ProductiveRel α₁ α₂ m β
+  wf := by
+    apply InvImage.wf
+    refine ⟨fun (a, b) => Prod.lexAccessible (WellFounded.apply ?_ a) (WellFounded.apply ?_) b⟩
+    · exact Option.wellFounded_lt <| InvImage.wf _ WellFoundedRelation.wf
+    · exact InvImage.wf _ WellFoundedRelation.wf
+  subrelation {it it'} h := by
+    cases h
+    case fstSkip =>
+      apply Append.productiveRel_of_fst
+      exact IterM.TerminationMeasures.Productive.rel_of_skip ‹_›
+    case fstDone =>
+      exact Append.productiveRel_fstDone
+    case sndSkip =>
+      apply Append.productiveRel_of_snd
+      exact IterM.TerminationMeasures.Productive.rel_of_skip ‹_›
+
+instance Append.instProductive [Monad m] [Iterator α₁ m β] [Iterator α₂ m β]
+    [Productive α₁ m] [Productive α₂ m] : Productive (Append α₁ α₂ m β) m :=
+  .of_productivenessRelation instProductivenessRelation
+
+end Productive
+
+end Std.Iterators.Types

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

@@ -362,8 +362,7 @@ def Flatten.instProductivenessRelation [Monad m] [Iterator α m (IterM (α := α
     case innerDone =>
       apply Flatten.productiveRel_of_right₂
 
-@[no_expose]
-public def Flatten.instProductive [Monad m] [Iterator α m (IterM (α := α₂) m β)] [Iterator α₂ m β]
+public theorem Flatten.instProductive [Monad m] [Iterator α m (IterM (α := α₂) m β)] [Iterator α₂ m β]
     [Finite α m] [Productive α₂ m] : Productive (Flatten α α₂ β m) m :=
   .of_productivenessRelation instProductivenessRelation
 

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

@@ -35,7 +35,7 @@ A `ForIn'` instance for iterators. Its generic membership relation is not easy t
 so this is not marked as `instance`. This way, more convenient instances can be built on top of it
 or future library improvements will make it more comfortable.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose, implicit_reducible]
 def Iter.instForIn' {α : Type w} {β : Type w} {n : Type x → Type x'} [Monad n]
     [Iterator α Id β] [IteratorLoop α Id n] :
     ForIn' n (Iter (α := α) β) β ⟨fun it out => it.IsPlausibleIndirectOutput out⟩ where
@@ -53,7 +53,7 @@ instance (α : Type w) (β : Type w) (n : Type x → Type x') [Monad n]
 /--
 An implementation of `for h : ... in ... do ...` notation for partial iterators.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose, implicit_reducible]
 def Iter.Partial.instForIn' {α : Type w} {β : Type w} {n : Type x → Type x'} [Monad n]
     [Iterator α Id β] [IteratorLoop α Id n] :
     ForIn' n (Iter.Partial (α := α) β) β ⟨fun it out => it.it.IsPlausibleIndirectOutput out⟩ where
@@ -71,7 +71,7 @@ instance (α : Type w) (β : Type w) (n : Type x → Type x') [Monad n]
 A `ForIn'` instance for iterators that is guaranteed to terminate after finitely many steps.
 It is not marked as an instance because the membership predicate is difficult to work with.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose, implicit_reducible]
 def Iter.Total.instForIn' {α : Type w} {β : Type w} {n : Type x → Type x'} [Monad n]
     [Iterator α Id β] [IteratorLoop α Id n] [Finite α Id] :
     ForIn' n (Iter.Total (α := α) β) β ⟨fun it out => it.it.IsPlausibleIndirectOutput out⟩ where

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

@@ -159,7 +159,7 @@ This is the default implementation of the `IteratorLoop` class.
 It simply iterates through the iterator using `IterM.step`. For certain iterators, more efficient
 implementations are possible and should be used instead.
 -/
-@[always_inline, inline, expose]
+@[always_inline, inline, expose, implicit_reducible]
 def IteratorLoop.defaultImplementation {α : Type w} {m : Type w → Type w'} {n : Type x → Type x'}
     [Monad n] [Iterator α m β] :
     IteratorLoop α m n where
@@ -211,7 +211,7 @@ theorem IteratorLoop.wellFounded_of_productive {α β : Type w} {m : Type w →
 /--
 This `ForIn'`-style loop construct traverses a finite iterator using an `IteratorLoop` instance.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose, implicit_reducible]
 def IteratorLoop.finiteForIn' {m : Type w → Type w'} {n : Type x → Type x'}
     {α : Type w} {β : Type w} [Iterator α m β] [IteratorLoop α m n] [Monad n]
     (lift : ∀ γ δ, (γ → n δ) → m γ → n δ) :
@@ -224,7 +224,7 @@ A `ForIn'` instance for iterators. Its generic membership relation is not easy t
 so this is not marked as `instance`. This way, more convenient instances can be built on top of it
 or future library improvements will make it more comfortable.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose, implicit_reducible]
 def IterM.instForIn' {m : Type w → Type w'} {n : Type w → Type w''}
     {α : Type w} {β : Type w} [Iterator α m β] [IteratorLoop α m n] [Monad n]
     [MonadLiftT m n] :
@@ -239,7 +239,7 @@ instance IterM.instForInOfIteratorLoop {m : Type w → Type w'} {n : Type w →
   instForInOfForIn'
 
 /-- Internal implementation detail of the iterator library. -/
-@[always_inline, inline]
+@[always_inline, inline, expose, implicit_reducible]
 def IterM.Partial.instForIn' {m : Type w → Type w'} {n : Type w → Type w''}
     {α : Type w} {β : Type w} [Iterator α m β] [IteratorLoop α m n] [MonadLiftT m n] [Monad n] :
     ForIn' n (IterM.Partial (α := α) m β) β ⟨fun it out => it.it.IsPlausibleIndirectOutput out⟩ where
@@ -247,7 +247,7 @@ def IterM.Partial.instForIn' {m : Type w → Type w'} {n : Type w → Type w''}
     haveI := @IterM.instForIn'; forIn' it.it init f
 
 /-- Internal implementation detail of the iterator library. -/
-@[always_inline, inline]
+@[always_inline, inline, expose, implicit_reducible]
 def IterM.Total.instForIn' {m : Type w → Type w'} {n : Type w → Type w''}
     {α : Type w} {β : Type w} [Iterator α m β] [IteratorLoop α m n] [MonadLiftT m n] [Monad n]
     [Finite α m] :

src/Init/Data/Iterators/Internal/LawfulMonadLiftFunction.lean

@@ -70,7 +70,7 @@ theorem LawfulMonadLiftFunction.lift_seqRight [LawfulMonad m] [LawfulMonad n]
 abbrev idToMonad [Monad m] ⦃α : Type u⦄ (x : Id α) : m α :=
     pure x.run
 
-def LawfulMonadLiftFunction.idToMonad [Monad m] [LawfulMonad m] :
+theorem LawfulMonadLiftFunction.idToMonad [LawfulMonad m] :
     LawfulMonadLiftFunction (m := Id) (n := m) idToMonad where
   lift_pure := by simp [Internal.idToMonad]
   lift_bind := by simp [Internal.idToMonad]
@@ -95,7 +95,7 @@ instance [LawfulMonadLiftBindFunction (n := n) (fun _ _ f x => lift x >>= f)] [L
     simpa using LawfulMonadLiftBindFunction.liftBind_bind (n := n)
       (liftBind := fun _ _ f x => lift x >>= f) (β := β) (γ := γ) (δ := γ) pure x g
 
-def LawfulMonadLiftBindFunction.id [Monad m] [LawfulMonad m] :
+theorem LawfulMonadLiftBindFunction.id [LawfulMonad m] :
     LawfulMonadLiftBindFunction (m := Id) (n := m) (fun _ _ f x => f x.run) where
   liftBind_pure := by simp
   liftBind_bind := by simp

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

@@ -6,6 +6,7 @@ Authors: Paul Reichert
 module
 
 prelude
+public import Init.Data.Iterators.Lemmas.Combinators.Append
 public import Init.Data.Iterators.Lemmas.Combinators.Attach
 public import Init.Data.Iterators.Lemmas.Combinators.Monadic
 public import Init.Data.Iterators.Lemmas.Combinators.FilterMap

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

@@ -0,0 +1,193 @@
+/-
+Copyright (c) 2026 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+public import Init.Data.Iterators.Combinators.Append
+public import Init.Data.Iterators.Lemmas.Combinators.Monadic.Append
+public import Init.Data.Iterators.Consumers.Collect
+public import Init.Data.Iterators.Consumers.Access
+import Init.Data.Iterators.Lemmas.Consumers.Collect
+import Init.Data.Iterators.Lemmas.Consumers.Access
+import Init.Data.Iterators.Lemmas.Basic
+import Init.Omega
+
+public section
+
+namespace Std
+open Std.Iterators Std.Iterators.Types
+
+theorem Iter.append_eq_toIter_append_toIterM {α₁ α₂ β : Type w}
+    [Iterator α₁ Id β] [Iterator α₂ Id β]
+    {it₁ : Iter (α := α₁) β} {it₂ : Iter (α := α₂) β} :
+    it₁.append it₂ = (it₁.toIterM.append it₂.toIterM).toIter :=
+  rfl
+
+theorem Iter.Intermediate.appendSnd_eq_toIter_appendSnd_toIterM {α₁ α₂ β : Type w}
+    [Iterator α₁ Id β] [Iterator α₂ Id β]
+    {it₂ : Iter (α := α₂) β} :
+    Iter.Intermediate.appendSnd α₁ it₂ = (IterM.Intermediate.appendSnd α₁ it₂.toIterM).toIter :=
+  rfl
+
+theorem Iter.step_append {α₁ α₂ β : Type w}
+    [Iterator α₁ Id β] [Iterator α₂ Id β]
+    {it₁ : Iter (α := α₁) β} {it₂ : Iter (α := α₂) β} :
+    (it₁.append it₂).step =
+      match it₁.step with
+      | .yield it₁' out h => .yield (it₁'.append it₂) out (.fstYield h)
+      | .skip it₁' h => .skip (it₁'.append it₂) (.fstSkip h)
+      | .done h => .skip (Iter.Intermediate.appendSnd α₁ it₂) (.fstDone h) := by
+  simp only [Iter.step, append_eq_toIter_append_toIterM, toIterM_toIter, IterM.step_append,
+    Id.run_bind]
+  cases it₁.toIterM.step.run.inflate using PlausibleIterStep.casesOn <;>
+    simp [Intermediate.appendSnd_eq_toIter_appendSnd_toIterM]
+
+theorem Iter.Intermediate.step_appendSnd {α₁ α₂ β : Type w}
+    [Iterator α₁ Id β] [Iterator α₂ Id β]
+    {it₂ : Iter (α := α₂) β} :
+    (Iter.Intermediate.appendSnd α₁ it₂).step =
+      match it₂.step with
+      | .yield it₂' out h => .yield (Iter.Intermediate.appendSnd α₁ it₂') out (.sndYield h)
+      | .skip it₂' h => .skip (Iter.Intermediate.appendSnd α₁ it₂') (.sndSkip h)
+      | .done h => .done (.sndDone h) := by
+  simp only [Iter.step, appendSnd, toIterM_toIter, IterM.Intermediate.step_appendSnd, Id.run_bind]
+  cases it₂.toIterM.step.run.inflate using PlausibleIterStep.casesOn <;> simp
+
+@[simp]
+theorem Iter.toList_append {α₁ α₂ β : Type w}
+    [Iterator α₁ Id β] [Iterator α₂ Id β] [Finite α₁ Id] [Finite α₂ Id]
+    {it₁ : Iter (α := α₁) β} {it₂ : Iter (α := α₂) β} :
+    (it₁.append it₂).toList = it₁.toList ++ it₂.toList := by
+  simp [append_eq_toIter_append_toIterM, toList_eq_toList_toIterM]
+
+@[simp]
+theorem Iter.toListRev_append {α₁ α₂ β : Type w}
+    [Iterator α₁ Id β] [Iterator α₂ Id β] [Finite α₁ Id] [Finite α₂ Id]
+    {it₁ : Iter (α := α₁) β} {it₂ : Iter (α := α₂) β} :
+    (it₁.append it₂).toListRev = it₂.toListRev ++ it₁.toListRev := by
+  simp [append_eq_toIter_append_toIterM, toListRev_eq_toListRev_toIterM]
+
+@[simp]
+theorem Iter.toArray_append {α₁ α₂ β : Type w}
+    [Iterator α₁ Id β] [Iterator α₂ Id β] [Finite α₁ Id] [Finite α₂ Id]
+    {it₁ : Iter (α := α₁) β} {it₂ : Iter (α := α₂) β} :
+    (it₁.append it₂).toArray = it₁.toArray ++ it₂.toArray := by
+  simp [append_eq_toIter_append_toIterM, toArray_eq_toArray_toIterM]
+
+@[simp]
+theorem Iter.atIdxSlow?_appendSnd {α₁ α₂ β : Type w}
+    [Iterator α₁ Id β] [Iterator α₂ Id β] [Productive α₁ Id] [Productive α₂ Id]
+    {it₂ : Iter (α := α₂) β} {n : Nat} :
+    (Iter.Intermediate.appendSnd α₁ it₂).atIdxSlow? n = it₂.atIdxSlow? n := by
+  induction n, it₂ using Iter.atIdxSlow?.induct_unfolding with
+  | yield_zero it it' out h h' =>
+    simp only [atIdxSlow?_eq_match (it := Iter.Intermediate.appendSnd α₁ it),
+      Intermediate.step_appendSnd, h']
+  | yield_succ it it' out h h' n ih =>
+    simp only [atIdxSlow?_eq_match (it := Iter.Intermediate.appendSnd α₁ it),
+      Intermediate.step_appendSnd, h', ih]
+  | skip_case n it it' h h' ih =>
+    simp only [atIdxSlow?_eq_match (it := Iter.Intermediate.appendSnd α₁ it),
+      Intermediate.step_appendSnd, h', ih]
+  | done_case n it h h' =>
+    simp only [atIdxSlow?_eq_match (it := Iter.Intermediate.appendSnd α₁ it),
+      Intermediate.step_appendSnd, h']
+
+theorem Iter.atIdxSlow?_append_of_eq_some {α₁ α₂ β : Type w}
+    [Iterator α₁ Id β] [Iterator α₂ Id β] [Productive α₁ Id] [Productive α₂ Id]
+    {it₁ : Iter (α := α₁) β} {it₂ : Iter (α := α₂) β} {n : Nat} {b : β}
+    (h : it₁.atIdxSlow? n = some b) :
+    (it₁.append it₂).atIdxSlow? n = some b := by
+  induction n, it₁ using Iter.atIdxSlow?.induct_unfolding generalizing it₂ with
+  | yield_zero it it' out hp h' =>
+    rw [atIdxSlow?_eq_match (it := it.append it₂)]
+    cases h
+    simp [step_append, h']
+  | yield_succ it it' out hp h' n ih =>
+    rw [atIdxSlow?_eq_match (it := it.append it₂)]
+    simp [step_append, h', ih h]
+  | skip_case n it it' hp h' ih =>
+    rw [atIdxSlow?_eq_match (it := it.append it₂)]
+    simp [step_append, h', ih h]
+  | done_case n it hp h' =>
+    cases h
+
+theorem Iter.atIdxSlow?_append {α₁ α₂ β : Type w}
+    [Iterator α₁ Id β] [Iterator α₂ Id β] [Finite α₁ Id] [Productive α₂ Id]
+    {it₁ : Iter (α := α₁) β} {it₂ : Iter (α := α₂) β} {n : Nat} :
+    (it₁.append it₂).atIdxSlow? n =
+      if n < it₁.toList.length then it₁.atIdxSlow? n
+      else it₂.atIdxSlow? (n - it₁.toList.length) := by
+  induction n, it₁ using Iter.atIdxSlow?.induct_unfolding generalizing it₂ with
+  | yield_zero it it' out h h' =>
+    simp only [atIdxSlow?_eq_match (it := it.append it₂), step_append, h']
+    rw [toList_eq_match_step (it := it)]
+    simp [h']
+  | yield_succ it it' out h h' n ih =>
+    simp only [atIdxSlow?_eq_match (it := it.append it₂), step_append, h', ih]
+    rw [toList_eq_match_step (it := it)]
+    simp [h', Nat.succ_lt_succ_iff, Nat.succ_sub_succ]
+  | skip_case n it it' h h' ih =>
+    simp only [atIdxSlow?_eq_match (it := it.append it₂), step_append, h', ih]
+    rw [toList_eq_match_step (it := it)]
+    simp [h']
+  | done_case n it h h' =>
+    simp [atIdxSlow?_eq_match (it := it.append it₂), step_append, h',
+      atIdxSlow?_appendSnd, toList_eq_match_step]
+
+theorem Iter.atIdxSlow?_append_of_productive {α₁ α₂ β : Type w}
+    [Iterator α₁ Id β] [Iterator α₂ Id β] [Productive α₁ Id] [Productive α₂ Id]
+    {it₁ : Iter (α := α₁) β} {it₂ : Iter (α := α₂) β} {n k : Nat}
+    (hk : it₁.atIdxSlow? k = none)
+    (hmin : ∀ j, j < k → (it₁.atIdxSlow? j).isSome)
+    (hle : k ≤ n) :
+    (it₁.append it₂).atIdxSlow? n = it₂.atIdxSlow? (n - k) := by
+  induction n, it₁ using Iter.atIdxSlow?.induct_unfolding generalizing k it₂ with
+  | yield_zero it it' out hp h' =>
+    exfalso
+    have : k = 0 := by omega
+    subst this
+    rw [atIdxSlow?_eq_match (it := it)] at hk
+    simp [h'] at hk
+  | yield_succ it it' out hp h' n ih =>
+    rw [atIdxSlow?_eq_match (it := it.append it₂)]
+    simp only [step_append, h']
+    match k with
+    | 0 =>
+      rw [atIdxSlow?_eq_match (it := it)] at hk
+      simp [h'] at hk
+    | k + 1 =>
+      rw [atIdxSlow?_eq_match (it := it)] at hk
+      simp [h'] at hk
+      have hmin' : ∀ j, j < k → (it'.atIdxSlow? j).isSome := by
+        intro j hj
+        have h := hmin (j + 1) (by omega)
+        rw [atIdxSlow?_eq_match (it := it)] at h
+        simpa [h'] using h
+      rw [ih hk hmin' (by omega)]
+      congr 1
+      omega
+  | skip_case n it it' hp h' ih =>
+    rw [atIdxSlow?_eq_match (it := it.append it₂)]
+    simp only [step_append, h']
+    rw [atIdxSlow?_eq_match (it := it)] at hk; simp [h'] at hk
+    have hmin' : ∀ j, j < k → (it'.atIdxSlow? j).isSome := by
+      intro j hj
+      have h := hmin j hj
+      rw [atIdxSlow?_eq_match (it := it)] at h
+      simpa [h'] using h
+    exact ih hk hmin' hle
+  | done_case n it hp h' =>
+    rw [atIdxSlow?_eq_match (it := it.append it₂)]
+    simp only [step_append, h', atIdxSlow?_appendSnd]
+    have hk0 : k = 0 := by
+      false_or_by_contra
+      have h := hmin 0 (by omega)
+      rw [atIdxSlow?_eq_match (it := it)] at h
+      simp [h'] at h
+    simp [hk0]
+
+end Std

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

@@ -435,8 +435,9 @@ theorem Iter.forIn_filterMapWithPostcondition
         match ← (f out).run with
         | some c => g c acc
         | none => return .yield acc) := by
-  simp +instances [Iter.forIn_eq_forIn_toIterM, filterMapWithPostcondition, IterM.forIn_filterMapWithPostcondition,
-    instMonadLiftTOfMonadLift_instMonadLiftTOfPure]; rfl
+  simp only [filterMapWithPostcondition, IterM.forIn_filterMapWithPostcondition, forIn_eq_forIn_toIterM]
+  rw [instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
+  rfl -- expressions are equal up to different matchers
 
 theorem Iter.forIn_filterMapM
     [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o]
@@ -448,8 +449,9 @@ theorem Iter.forIn_filterMapM
         match ← f out with
         | some c => g c acc
         | none => return .yield acc) := by
-  simp +instances [filterMapM, forIn_eq_forIn_toIterM, IterM.forIn_filterMapM,
-    instMonadLiftTOfMonadLift_instMonadLiftTOfPure]; rfl
+  simp [filterMapM, forIn_eq_forIn_toIterM, IterM.forIn_filterMapM]
+  rw [instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
+  rfl
 
 theorem Iter.forIn_filterMap
     [Monad n] [LawfulMonad n] [Finite α Id]
@@ -469,8 +471,8 @@ theorem Iter.forIn_mapWithPostcondition
     {g : β₂ → γ → o (ForInStep γ)} :
     forIn (it.mapWithPostcondition f) init g =
       forIn it init (fun out acc => do g (← (f out).run) acc) := by
-  simp +instances [mapWithPostcondition, forIn_eq_forIn_toIterM, IterM.forIn_mapWithPostcondition,
-    instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
+  simp only [mapWithPostcondition, forIn_eq_forIn_toIterM, IterM.forIn_mapWithPostcondition]
+  rw [instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
 
 theorem Iter.forIn_mapM
     [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o]
@@ -498,8 +500,8 @@ theorem Iter.forIn_filterWithPostcondition
     haveI : MonadLift n o := ⟨monadLift⟩
     forIn (it.filterWithPostcondition f) init g =
       forIn it init (fun out acc => do if (← (f out).run).down then g out acc else return .yield acc) := by
-  simp +instances [filterWithPostcondition, forIn_eq_forIn_toIterM, IterM.forIn_filterWithPostcondition,
-    instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
+  simp only [filterWithPostcondition, forIn_eq_forIn_toIterM, IterM.forIn_filterWithPostcondition]
+  rw [instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
 
 theorem Iter.forIn_filterM
     [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o]
@@ -508,8 +510,8 @@ theorem Iter.forIn_filterM
     [IteratorLoop α Id o] [LawfulIteratorLoop α Id o]
     {it : Iter (α := α) β} {f : β → n (ULift Bool)} {init : γ} {g : β → γ → o (ForInStep γ)} :
     forIn (it.filterM f) init g = forIn it init (fun out acc => do if (← f out).down then g out acc else return .yield acc) := by
-  simp +instances [filterM, forIn_eq_forIn_toIterM, IterM.forIn_filterM,
-    instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
+  simp only [filterM, forIn_eq_forIn_toIterM, IterM.forIn_filterM]
+  rw [instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
 
 theorem Iter.forIn_filter
     [Monad n] [LawfulMonad n]
@@ -550,8 +552,9 @@ theorem Iter.foldM_filterMapM {α β γ δ : Type w}
       it.foldM (init := init) (fun d b => do
           let some c ← f b | pure d
           g d c) := by
-  simp +instances [filterMapM, IterM.foldM_filterMapM, foldM_eq_foldM_toIterM,
-    instMonadLiftTOfMonadLift_instMonadLiftTOfPure]; rfl
+  simp only [filterMapM, IterM.foldM_filterMapM, foldM_eq_foldM_toIterM]
+  rw [instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
+  rfl
 
 theorem Iter.foldM_mapWithPostcondition {α β γ δ : Type w}
     {n : Type w → Type w''} {o : Type w → Type w'''}
@@ -563,8 +566,8 @@ theorem Iter.foldM_mapWithPostcondition {α β γ δ : Type w}
     {f : β → PostconditionT n γ} {g : δ → γ → o δ} {init : δ} {it : Iter (α := α) β} :
     (it.mapWithPostcondition f).foldM (init := init) g =
       it.foldM (init := init) (fun d b => do let c ← (f b).run; g d c) := by
-  simp +instances [mapWithPostcondition, IterM.foldM_mapWithPostcondition, foldM_eq_foldM_toIterM,
-    instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
+  simp only [mapWithPostcondition, IterM.foldM_mapWithPostcondition, foldM_eq_foldM_toIterM]
+  rw [instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
 
 theorem Iter.foldM_mapM {α β γ δ : Type w}
     {n : Type w → Type w''} {o : Type w → Type w'''}
@@ -578,8 +581,8 @@ theorem Iter.foldM_mapM {α β γ δ : Type w}
     haveI : MonadLift n o := ⟨MonadLiftT.monadLift⟩
     (it.mapM f).foldM (init := init) g =
       it.foldM (init := init) (fun d b => do let c ← f b; g d c) := by
-  simp +instances [mapM, IterM.foldM_mapM, foldM_eq_foldM_toIterM,
-    instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
+  simp only [mapM, IterM.foldM_mapM, foldM_eq_foldM_toIterM]
+  rw [instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
 
 theorem Iter.foldM_filterWithPostcondition {α β δ : Type w}
     {n : Type w → Type w''} {o : Type w → Type w'''}
@@ -591,8 +594,8 @@ theorem Iter.foldM_filterWithPostcondition {α β δ : Type w}
     {f : β → PostconditionT n (ULift Bool)} {g : δ → β → o δ} {init : δ} {it : Iter (α := α) β} :
     (it.filterWithPostcondition f).foldM (init := init) g =
       it.foldM (init := init) (fun d b => do if (← (f b).run).down then g d b else pure d) := by
-  simp +instances [filterWithPostcondition, IterM.foldM_filterWithPostcondition, foldM_eq_foldM_toIterM,
-    instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
+  simp only [filterWithPostcondition, IterM.foldM_filterWithPostcondition, foldM_eq_foldM_toIterM]
+  rw [instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
 
 theorem Iter.foldM_filterM {α β δ : Type w}
     {n : Type w → Type w''} {o : Type w → Type w'''}
@@ -605,8 +608,8 @@ theorem Iter.foldM_filterM {α β δ : Type w}
     {f : β → n (ULift Bool)} {g : δ → β → o δ} {init : δ} {it : Iter (α := α) β} :
     (it.filterM f).foldM (init := init) g =
       it.foldM (init := init) (fun d b => do if (← f b).down then g d b else pure d) := by
-  simp +instances [filterM, IterM.foldM_filterM, foldM_eq_foldM_toIterM,
-    instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
+  simp only [filterM, IterM.foldM_filterM, foldM_eq_foldM_toIterM]
+  rw [instMonadLiftTOfMonadLift_instMonadLiftTOfPure]
 
 theorem Iter.foldM_filterMap {α β γ δ : Type w} {n : Type w → Type w''}
     [Iterator α Id β] [Finite α Id] [Monad n] [LawfulMonad n]

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

@@ -121,22 +121,22 @@ public theorem Iter.step_flatMapAfterM {α : Type w} {β : Type w} {α₂ : Type
     [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] [Iterator α Id β] [Iterator α₂ m γ]
     {f : β → m (IterM (α := α₂) m γ)} {it₁ : Iter (α := α) β} {it₂ : Option (IterM (α := α₂) m γ)} :
   (it₁.flatMapAfterM f it₂).step = (do
-    match it₂ with
+    match hit : it₂ with
     | none =>
       match it₁.step with
       | .yield it₁' b h =>
         let fx ← MonadAttach.attach (f b)
-        return .deflate (.skip (it₁'.flatMapAfterM f (some fx.val)) (.outerYield_flatMapM_pure h fx.property))
-      | .skip it₁' h => return .deflate (.skip (it₁'.flatMapAfterM f none) (.outerSkip_flatMapM_pure h))
-      | .done h => return .deflate (.done (.outerDone_flatMapM_pure h))
+        return .deflate (.skip (it₁'.flatMapAfterM f (some fx.val)) (hit ▸ .outerYield_flatMapM_pure h fx.property))
+      | .skip it₁' h => return .deflate (.skip (it₁'.flatMapAfterM f it₂) (hit ▸ .outerSkip_flatMapM_pure h))
+      | .done h => return .deflate (.done (hit ▸ .outerDone_flatMapM_pure h))
     | some it₂ =>
       match (← it₂.step).inflate with
       | .yield it₂' out h =>
-        return .deflate (.yield (it₁.flatMapAfterM f (some it₂')) out (.innerYield_flatMapM_pure h))
+        return .deflate (.yield (it₁.flatMapAfterM f (some it₂')) out (hit ▸ .innerYield_flatMapM_pure h))
       | .skip it₂' h =>
-        return .deflate (.skip (it₁.flatMapAfterM f (some it₂')) (.innerSkip_flatMapM_pure h))
+        return .deflate (.skip (it₁.flatMapAfterM f (some it₂')) (hit ▸ .innerSkip_flatMapM_pure h))
       | .done h =>
-        return .deflate (.skip (it₁.flatMapAfterM f none) (.innerDone_flatMapM_pure h))) := by
+        return .deflate (.skip (it₁.flatMapAfterM f none) (hit ▸ .innerDone_flatMapM_pure h))) := by
   simp only [flatMapAfterM, IterM.step_flatMapAfterM, Iter.step_mapWithPostcondition,
     PostconditionT.operation_pure]
   split
@@ -232,7 +232,6 @@ public theorem Iter.toArray_flatMapM {α α₂ β γ : Type w} {m : Type w → T
     (it₁.flatMapM f).toArray = Array.flatten <$> (it₁.mapM fun b => do (← f b).toArray).toArray := by
   simp [flatMapM, toArray_flatMapAfterM]
 
-set_option backward.isDefEq.respectTransparency false in
 public theorem Iter.toList_flatMapAfter {α α₂ β γ : Type w} [Iterator α Id β] [Iterator α₂ Id γ]
     [Finite α Id] [Finite α₂ Id]
     {f : β → Iter (α := α₂) γ} {it₁ : Iter (α := α) β} {it₂ : Option (Iter (α := α₂) γ)} :
@@ -241,9 +240,9 @@ public theorem Iter.toList_flatMapAfter {α α₂ β γ : Type w} [Iterator α I
       | some it₂ => it₂.toList ++
           (it₁.map fun b => (f b).toList).toList.flatten := by
   simp only [flatMapAfter, Iter.toList, toIterM_toIter, IterM.toList_flatMapAfter]
-  cases it₂ <;> simp [map, IterM.toList_map_eq_toList_mapM, - IterM.toList_map]
+  unfold Iter.toList
+  cases it₂ <;> simp [map]
 
-set_option backward.isDefEq.respectTransparency false in
 public theorem Iter.toArray_flatMapAfter {α α₂ β γ : Type w} [Iterator α Id β] [Iterator α₂ Id γ]
     [Finite α Id] [Finite α₂ Id]
     {f : β → Iter (α := α₂) γ} {it₁ : Iter (α := α) β} {it₂ : Option (Iter (α := α₂) γ)} :
@@ -252,6 +251,7 @@ public theorem Iter.toArray_flatMapAfter {α α₂ β γ : Type w} [Iterator α
       | some it₂ => it₂.toArray ++
           (it₁.map fun b => (f b).toArray).toArray.flatten := by
   simp only [flatMapAfter, Iter.toArray, toIterM_toIter, IterM.toArray_flatMapAfter]
+  unfold Iter.toArray
   cases it₂ <;> simp [map, IterM.toArray_map_eq_toArray_mapM, - IterM.toArray_map]
 
 public theorem Iter.toList_flatMap {α α₂ β γ : Type w} [Iterator α Id β] [Iterator α₂ Id γ]

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

@@ -6,6 +6,7 @@ Authors: Paul Reichert
 module
 
 prelude
+public import Init.Data.Iterators.Lemmas.Combinators.Monadic.Append
 public import Init.Data.Iterators.Lemmas.Combinators.Monadic.Attach
 public import Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
 public import Init.Data.Iterators.Lemmas.Combinators.Monadic.FlatMap

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

@@ -0,0 +1,107 @@
+/-
+Copyright (c) 2026 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+public import Init.Data.Iterators.Combinators.Monadic.Append
+public import Init.Data.Iterators.Consumers.Monadic.Collect
+import Init.Data.Iterators.Lemmas.Consumers.Monadic.Collect
+import Init.Data.Iterators.Lemmas.Monadic.Basic
+import Init.Data.List.Lemmas
+import Init.Data.List.ToArray
+
+public section
+
+namespace Std
+open Std.Iterators Std.Iterators.Types
+
+variable {α₁ α₂ β : Type w} {m : Type w → Type w'}
+
+theorem IterM.step_append [Monad m] [Iterator α₁ m β] [Iterator α₂ m β]
+    {it₁ : IterM (α := α₁) m β} {it₂ : IterM (α := α₂) m β} :
+    (it₁.append it₂).step = (do
+      match (← it₁.step).inflate with
+      | .yield it₁' out h =>
+        pure <| .deflate <| .yield (it₁'.append it₂) out (.fstYield h)
+      | .skip it₁' h =>
+        pure <| .deflate <| .skip (it₁'.append it₂) (.fstSkip h)
+      | .done h =>
+        pure <| .deflate <| .skip (IterM.Intermediate.appendSnd α₁ it₂) (.fstDone h)) := by
+  simp only [append, Intermediate.appendSnd, step, Iterator.step]
+  apply bind_congr; intro step
+  cases step.inflate using PlausibleIterStep.casesOn <;> rfl
+
+theorem IterM.Intermediate.step_appendSnd [Monad m] [Iterator α₁ m β] [Iterator α₂ m β]
+    {it₂ : IterM (α := α₂) m β} :
+    (IterM.Intermediate.appendSnd α₁ it₂).step = (do
+      match (← it₂.step).inflate with
+      | .yield it₂' out h =>
+        pure <| .deflate <| .yield (IterM.Intermediate.appendSnd α₁ it₂') out (.sndYield h)
+      | .skip it₂' h =>
+        pure <| .deflate <| .skip (IterM.Intermediate.appendSnd α₁ it₂') (.sndSkip h)
+      | .done h =>
+        pure <| .deflate <| .done (.sndDone h)) := by
+  simp only [Intermediate.appendSnd, step, Iterator.step]
+  apply bind_congr; intro step
+  cases step.inflate using PlausibleIterStep.casesOn <;> rfl
+
+@[simp]
+theorem IterM.toList_appendSnd [Monad m] [LawfulMonad m]
+    [Iterator α₁ m β] [Iterator α₂ m β] [Finite α₁ m] [Finite α₂ m]
+    {it₂ : IterM (α := α₂) m β} :
+    (IterM.Intermediate.appendSnd α₁ it₂).toList = it₂.toList := by
+  induction it₂ using IterM.inductSteps with | step it₂ ihy ihs
+  rw [toList_eq_match_step (it := IterM.Intermediate.appendSnd α₁ it₂),
+      toList_eq_match_step (it := it₂)]
+  simp only [Intermediate.step_appendSnd, bind_assoc]
+  apply bind_congr; intro step
+  cases step.inflate using PlausibleIterStep.casesOn
+  · simp [ihy ‹_›]
+  · simp [ihs ‹_›]
+  · simp
+
+@[simp]
+theorem IterM.toList_append [Monad m] [LawfulMonad m]
+    [Iterator α₁ m β] [Iterator α₂ m β] [Finite α₁ m] [Finite α₂ m]
+    {it₁ : IterM (α := α₁) m β} {it₂ : IterM (α := α₂) m β} :
+    (it₁.append it₂).toList = (do
+      let l₁ ← it₁.toList
+      let l₂ ← it₂.toList
+      pure (l₁ ++ l₂)) := by
+  induction it₁ using IterM.inductSteps with | step it₁ ihy ihs
+  rw [toList_eq_match_step (it := it₁.append it₂), toList_eq_match_step (it := it₁)]
+  simp only [step_append, bind_assoc]
+  apply bind_congr; intro step
+  cases step.inflate using PlausibleIterStep.casesOn
+  · simp [ihy ‹_›, - bind_pure_comp]
+  · simp [ihs ‹_›]
+  · simp [toList_appendSnd, - bind_pure_comp]
+
+@[simp]
+theorem IterM.toListRev_append [Monad m] [LawfulMonad m]
+    [Iterator α₁ m β] [Iterator α₂ m β] [Finite α₁ m] [Finite α₂ m]
+    {it₁ : IterM (α := α₁) m β} {it₂ : IterM (α := α₂) m β} :
+    (it₁.append it₂).toListRev = (do
+      let l₁ ← it₁.toListRev
+      let l₂ ← it₂.toListRev
+      pure (l₂ ++ l₁)) := by
+  rw [toListRev_eq (it := it₁.append it₂), toList_append,
+      toListRev_eq (it := it₁), toListRev_eq (it := it₂)]
+  simp [map_bind, bind_pure_comp, List.reverse_append]
+
+@[simp]
+theorem IterM.toArray_append [Monad m] [LawfulMonad m]
+    [Iterator α₁ m β] [Iterator α₂ m β] [Finite α₁ m] [Finite α₂ m]
+    {it₁ : IterM (α := α₁) m β} {it₂ : IterM (α := α₂) m β} :
+    (it₁.append it₂).toArray = (do
+      let a₁ ← it₁.toArray
+      let a₂ ← it₂.toArray
+      pure (a₁ ++ a₂)) := by
+  rw [← toArray_toList (it := it₁.append it₂), toList_append,
+      ← toArray_toList (it := it₁), ← toArray_toList (it := it₂)]
+  simp [map_bind, - bind_pure_comp, ← List.toArray_appendList, - toArray_toList]
+
+end Std

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

@@ -374,7 +374,6 @@ theorem IterM.toList_map_eq_toList_filterMapM {α β γ : Type w} {m : Type w
   simp [toList_map_eq_toList_mapM, toList_mapM_eq_toList_filterMapM]
   congr <;> simp
 
-set_option backward.whnf.reducibleClassField false in
 /--
 Variant of `toList_filterMapWithPostcondition_filterMapWithPostcondition` that is intended to be
 used with the `apply` tactic. Because neither the LHS nor the RHS determine all implicit parameters,
@@ -395,7 +394,7 @@ private theorem IterM.toList_filterMapWithPostcondition_filterMapWithPostconditi
       (it.filterMapWithPostcondition (n := o) fg).toList := by
   induction it using IterM.inductSteps with | step it ihy ihs
   letI : MonadLift n o := ⟨monadLift⟩
-  haveI : LawfulMonadLift n o := ⟨by simp +instances [this], by simp +instances [this]⟩
+  haveI : LawfulMonadLift n o := ⟨LawfulMonadLiftT.monadLift_pure, LawfulMonadLiftT.monadLift_bind⟩
   rw [toList_eq_match_step, toList_eq_match_step, step_filterMapWithPostcondition,
     bind_assoc, step_filterMapWithPostcondition, step_filterMapWithPostcondition]
   simp only [bind_assoc, liftM_bind]
@@ -602,7 +601,6 @@ theorem IterM.toList_map_mapM {α β γ δ : Type w}
     toList_filterMapM_mapM]
   congr <;> simp
 
-set_option backward.isDefEq.respectTransparency false in
 @[simp]
 theorem IterM.toList_filterMapWithPostcondition {α β γ : Type w} {m : Type w → Type w'}
     [Monad m] [LawfulMonad m]
@@ -626,7 +624,6 @@ theorem IterM.toList_filterMapWithPostcondition {α β γ : Type w} {m : Type w
   · simp [ihs ‹_›, heq]
   · simp [heq]
 
-set_option backward.isDefEq.respectTransparency false in
 @[simp]
 theorem IterM.toList_mapWithPostcondition {α β γ : Type w} {m : Type w → Type w'}
     [Monad m] [LawfulMonad m] [Iterator α Id β] [Finite α Id]
@@ -647,25 +644,25 @@ theorem IterM.toList_mapWithPostcondition {α β γ : Type w} {m : Type w → Ty
   · simp [ihs ‹_›, heq]
   · simp [heq]
 
-set_option backward.isDefEq.respectTransparency false in
 @[simp]
 theorem IterM.toList_filterMapM {α β γ : Type w} {m : Type w → Type w'}
     [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m]
     [Iterator α Id β] [Finite α Id]
     {f : β → m (Option γ)} (it : IterM (α := α) Id β) :
     (it.filterMapM f).toList = it.toList.run.filterMapM f := by
-  simp [toList_filterMapM_eq_toList_filterMapWithPostcondition, toList_filterMapWithPostcondition,
-    PostconditionT.attachLift, PostconditionT.run_eq_map, WeaklyLawfulMonadAttach.map_attach]
+  simp only [toList_filterMapM_eq_toList_filterMapWithPostcondition,
+    toList_filterMapWithPostcondition, PostconditionT.run_eq_map]
+  simp [PostconditionT.attachLift, WeaklyLawfulMonadAttach.map_attach]
 
-set_option backward.isDefEq.respectTransparency false in
 @[simp]
 theorem IterM.toList_mapM {α β γ : Type w} {m : Type w → Type w'}
     [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m]
     [Iterator α Id β] [Finite α Id]
     {f : β → m γ} (it : IterM (α := α) Id β) :
     (it.mapM f).toList = it.toList.run.mapM f := by
-  simp [toList_mapM_eq_toList_mapWithPostcondition, toList_mapWithPostcondition,
-    PostconditionT.attachLift, PostconditionT.run_eq_map, WeaklyLawfulMonadAttach.map_attach]
+  simp only [toList_mapM_eq_toList_mapWithPostcondition, toList_mapWithPostcondition,
+    PostconditionT.run_eq_map]
+  simp [PostconditionT.attachLift, WeaklyLawfulMonadAttach.map_attach]
 
 @[simp]
 theorem IterM.toList_filterMap {α β γ : Type w} {m : Type w → Type w'}
@@ -1303,7 +1300,6 @@ theorem IterM.forIn_filterMap
   rw [filterMap, forIn_filterMapWithPostcondition]
   simp [PostconditionT.run_eq_map]
 
-set_option backward.isDefEq.respectTransparency false in
 theorem IterM.forIn_mapWithPostcondition
     [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o]
     [MonadLiftT m n] [LawfulMonadLiftT m n] [MonadLiftT n o] [LawfulMonadLiftT n o]
@@ -1314,9 +1310,9 @@ theorem IterM.forIn_mapWithPostcondition
     haveI : MonadLift n o := ⟨monadLift⟩
     forIn (it.mapWithPostcondition f) init g =
       forIn it init (fun out acc => do g (← (f out).run) acc) := by
-  rw [mapWithPostcondition, InternalCombinators.map, ← InternalCombinators.filterMap,
-    ← filterMapWithPostcondition, forIn_filterMapWithPostcondition]
-  simp [PostconditionT.run_eq_map]
+  unfold mapWithPostcondition InternalCombinators.map Map.instIterator Map.instIteratorLoop Map
+  rw [← InternalCombinators.filterMap, ← filterMapWithPostcondition, forIn_filterMapWithPostcondition]
+  simp
 
 theorem IterM.forIn_mapM
     [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o]
@@ -1480,7 +1476,7 @@ theorem IterM.foldM_filterM {α β δ : Type w}
   simp [filterM, foldM_filterMapWithPostcondition, PostconditionT.run_attachLift]
   congr 1; ext out acc
   apply bind_congr; intro fx
-  cases fx.down <;> simp [PostconditionT.run_eq_map]
+  cases fx.down <;> simp
 
 theorem IterM.foldM_filterMap {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''}
     [Iterator α m β] [Finite α m] [Monad m] [Monad n] [LawfulMonad m] [LawfulMonad n]

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

@@ -21,14 +21,14 @@ open Std.Internal Std.Iterators
 theorem IterM.step_flattenAfter {α α₂ β : Type w} {m : Type w → Type w'} [Monad m]
     [Iterator α m (IterM (α := α₂) m β)] [Iterator α₂ m β]
     {it₁ : IterM (α := α) m (IterM (α := α₂) m β)} {it₂ : Option (IterM (α := α₂) m β)} :
-  (it₁.flattenAfter it₂).step = (do
+  (it₁.flattenAfter it₂).step = (
     match it₂ with
-    | none =>
+    | none => do
       match (← it₁.step).inflate with
       | .yield it₁' it₂' h => return .deflate (.skip (it₁'.flattenAfter (some it₂')) (.outerYield h))
       | .skip it₁' h => return .deflate (.skip (it₁'.flattenAfter none) (.outerSkip h))
       | .done h => return .deflate (.done (.outerDone h))
-    | some it₂ =>
+    | some it₂ => do
       match (← it₂.step).inflate with
       | .yield it₂' out h => return .deflate (.yield (it₁.flattenAfter (some it₂')) out (.innerYield h))
       | .skip it₂' h => return .deflate (.skip (it₁.flattenAfter (some it₂')) (.innerSkip h))
@@ -130,16 +130,16 @@ public theorem IterM.step_flatMapAfterM {α : Type w} {β : Type w} {α₂ : Typ
     {γ : Type w} {m : Type w → Type w'} [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m]
     [Iterator α m β] [Iterator α₂ m γ] {f : β → m (IterM (α := α₂) m γ)} {it₁ : IterM (α := α) m β}
     {it₂ : Option (IterM (α := α₂) m γ)} :
-  (it₁.flatMapAfterM f it₂).step = (do
+  (it₁.flatMapAfterM f it₂).step = (
     match it₂ with
-    | none =>
+    | none => do
       match (← it₁.step).inflate with
       | .yield it₁' b h =>
         let fx ← MonadAttach.attach (f b)
         return .deflate (.skip (it₁'.flatMapAfterM f (some fx.val)) (.outerYield_flatMapM h fx.property))
       | .skip it₁' h => return .deflate (.skip (it₁'.flatMapAfterM f none) (.outerSkip_flatMapM h))
       | .done h => return .deflate (.done (.outerDone_flatMapM h))
-    | some it₂ =>
+    | some it₂ => do
       match (← it₂.step).inflate with
       | .yield it₂' out h => return .deflate (.yield (it₁.flatMapAfterM f (some it₂')) out (.innerYield_flatMapM h))
       | .skip it₂' h => return .deflate (.skip (it₁.flatMapAfterM f (some it₂')) (.innerSkip_flatMapM h))
@@ -171,15 +171,15 @@ public theorem IterM.step_flatMapM {α : Type w} {β : Type w} {α₂ : Type w}
 public theorem IterM.step_flatMapAfter {α : Type w} {β : Type w} {α₂ : Type w}
     {γ : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Iterator α m β] [Iterator α₂ m γ]
     {f : β → IterM (α := α₂) m γ} {it₁ : IterM (α := α) m β} {it₂ : Option (IterM (α := α₂) m γ)} :
-  (it₁.flatMapAfter f it₂).step = (do
+  (it₁.flatMapAfter f it₂).step = (
     match it₂ with
-    | none =>
+    | none => do
       match (← it₁.step).inflate with
       | .yield it₁' b h =>
         return .deflate (.skip (it₁'.flatMapAfter f (some (f b))) (.outerYield_flatMap h))
       | .skip it₁' h => return .deflate (.skip (it₁'.flatMapAfter f none) (.outerSkip_flatMap h))
       | .done h => return .deflate (.done (.outerDone_flatMap h))
-    | some it₂ =>
+    | some it₂ => do
       match (← it₂.step).inflate with
       | .yield it₂' out h => return .deflate (.yield (it₁.flatMapAfter f (some it₂')) out (.innerYield_flatMap h))
       | .skip it₂' h => return .deflate (.skip (it₁.flatMapAfter f (some it₂')) (.innerSkip_flatMap h))

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

@@ -32,11 +32,12 @@ theorem Iter.forIn'_eq {α β : Type w} [Iterator α Id β] [Finite α Id]
       IterM.DefaultConsumers.forIn' (n := m) (fun _ _ f x => f x.run) γ (fun _ _ _ => True)
         it.toIterM init _ (fun _ => id)
           (fun out h acc => return ⟨← f out (Iter.isPlausibleIndirectOutput_iff_isPlausibleIndirectOutput_toIterM.mpr h) acc, trivial⟩) := by
-  simp +instances only [instForIn', ForIn'.forIn', IteratorLoop.finiteForIn']
+  simp only [ForIn'.forIn']
   have : ∀ a b c, f a b c = (Subtype.val <$> (⟨·, trivial⟩) <$> f a b c) := by simp
   simp +singlePass only [this]
   rw [hl.lawful (fun _ _ f x => f x.run) (wf := IteratorLoop.wellFounded_of_finite)]
-  simp +instances [IteratorLoop.defaultImplementation]
+  simp only [IteratorLoop.forIn, Functor.map_map, id_map',
+    bind_pure_comp]
 
 theorem Iter.forIn_eq {α β : Type w} [Iterator α Id β] [Finite α Id]
     {m : Type x → Type x'} [Monad m] [LawfulMonad m] [IteratorLoop α Id m]
@@ -81,7 +82,7 @@ theorem Iter.forIn'_eq_forIn'_toIterM {α β : Type w} [Iterator α Id β]
       letI : ForIn' m (IterM (α := α) Id β) β _ := IterM.instForIn'
       ForIn'.forIn' it.toIterM init
         (fun out h acc => f out (isPlausibleIndirectOutput_iff_isPlausibleIndirectOutput_toIterM.mpr h) acc) := by
-  simp +instances [ForIn'.forIn', Iter.instForIn', IterM.instForIn', monadLift]
+  simp [ForIn'.forIn', monadLift]
 
 theorem Iter.forIn_eq_forIn_toIterM {α β : Type w} [Iterator α Id β]
     [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
@@ -395,7 +396,7 @@ theorem Iter.fold_eq_fold_toIterM {α β : Type w} {γ : Type w} [Iterator α Id
     [Finite α Id] [IteratorLoop α Id Id]
     {f : γ → β → γ} {init : γ} {it : Iter (α := α) β} :
     it.fold (init := init) f = (it.toIterM.fold (init := init) f).run := by
-  rw [fold_eq_foldM, foldM_eq_foldM_toIterM, IterM.fold_eq_foldM]; rfl
+  rw [fold_eq_foldM, foldM_eq_foldM_toIterM, IterM.fold_eq_foldM]
 
 @[simp]
 theorem Iter.forIn_pure_yield_eq_fold {α β : Type w} {γ : Type x} [Iterator α Id β]

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

@@ -109,10 +109,10 @@ theorem IterM.forIn'_eq {α β : Type w} {m : Type w → Type w'} [Iterator α m
     letI : ForIn' n (IterM (α := α) m β) β _ := IterM.instForIn'
     ForIn'.forIn' (α := β) (m := n) it init f = IterM.DefaultConsumers.forIn' (n := n)
         (fun _ _ f x => monadLift x >>= f) γ (fun _ _ _ => True) it init _ (fun _ => id) (return ⟨← f · · ·, trivial⟩) := by
-  simp +instances only [instForIn', ForIn'.forIn', IteratorLoop.finiteForIn']
+  simp only [ForIn'.forIn']
   have : f = (Subtype.val <$> (⟨·, trivial⟩) <$> f · · ·) := by simp
   rw [this, hl.lawful (fun _ _ f x => monadLift x >>= f) (wf := IteratorLoop.wellFounded_of_finite)]
-  simp +instances [IteratorLoop.defaultImplementation]
+  simp [IteratorLoop.forIn]
   try rfl
 
 theorem IterM.forIn_eq {α β : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]

src/Init/Data/Iterators/PostconditionMonad.lean

@@ -272,6 +272,12 @@ theorem PostconditionT.run_bind' {m : Type w → Type w'} [Monad m] [LawfulMonad
     (x >>= f).run = x.run >>= (f · |>.run) :=
   run_bind
 
+@[simp]
+protected theorem PostconditionT.run_pure {m : Type w → Type w'} [Monad m] [LawfulMonad m]
+    {α : Type w} {x : α} :
+    (pure x : PostconditionT m α).run = pure x := by
+  simp [run_eq_map]
+
 @[simp]
 theorem PostconditionT.property_lift {m : Type w → Type w'} [Functor m] {α : Type w}
     {x : m α} : (lift x : PostconditionT m α).Property = (fun _ => True) := by

src/Init/Data/Iterators/ToIterator.lean

@@ -32,14 +32,14 @@ def ToIterator.iter [ToIterator γ Id α β] (x : γ) : Iter (α := α) β :=
   ToIterator.iterM x |>.toIter
 
 /-- Creates a monadic `ToIterator` instance. -/
-@[always_inline, inline, expose, instance_reducible]
+@[always_inline, inline, expose, implicit_reducible]
 def ToIterator.ofM (α : Type w)
     (iterM : γ → IterM (α := α) m β) :
     ToIterator γ m α β where
   iterMInternal x := iterM x
 
 /-- Creates a pure `ToIterator` instance. -/
-@[always_inline, inline, expose, instance_reducible]
+@[always_inline, inline, expose, implicit_reducible]
 def ToIterator.of (α : Type w)
     (iter : γ → Iter (α := α) β) :
     ToIterator γ Id α β where

src/Init/Data/List/Lemmas.lean

@@ -236,7 +236,6 @@ theorem getElem?_eq_some_iff {l : List α} : l[i]? = some a ↔ ∃ h : i < l.le
     · match i, h with
       | i + 1, h => simp [getElem?_eq_some_iff, Nat.succ_lt_succ_iff]
 
-@[grind →]
 theorem getElem_of_getElem? {l : List α} : l[i]? = some a → ∃ h : i < l.length, l[i] = a :=
   getElem?_eq_some_iff.mp
 
@@ -937,6 +936,12 @@ theorem getElem_zero_eq_head {l : List α} (h : 0 < l.length) :
   | nil => simp at h
   | cons _ _ => simp
 
+theorem head!_eq_getElem! [Inhabited α] {l : List α} : head! l = l[0]! := by
+  cases l <;> rfl
+
+theorem headD_eq_getD {l : List α} {fallback} : headD l fallback = l.getD 0 fallback := by
+  cases l <;> rfl
+
 theorem head_eq_iff_head?_eq_some {xs : List α} (h) : xs.head h = a ↔ xs.head? = some a := by
   cases xs with
   | nil => simp at h

src/Init/Data/List/ToArray.lean

@@ -225,7 +225,7 @@ theorem forM_toArray [Monad m] (l : List α) (f : α → m PUnit) :
 @[simp, grind =] theorem findSomeM?_toArray [Monad m] [LawfulMonad m] (f : α → m (Option β)) (l : List α) :
     l.toArray.findSomeM? f = l.findSomeM? f := by
   rw [Array.findSomeM?]
-  simp only [bind_pure_comp, map_pure, forIn_toArray]
+  simp only [forIn_toArray]
   induction l with
   | nil => simp
   | cons a l ih =>
@@ -258,7 +258,7 @@ theorem findRevM?_toArray [Monad m] [LawfulMonad m] (f : α → m Bool) (l : Lis
 @[simp, grind =] theorem findM?_toArray [Monad m] [LawfulMonad m] (f : α → m Bool) (l : List α) :
     l.toArray.findM? f = l.findM? f := by
   rw [Array.findM?]
-  simp only [bind_pure_comp, map_pure, forIn_toArray]
+  simp only [forIn_toArray]
   induction l with
   | nil => simp
   | cons a l ih =>

src/Init/Data/Nat/Basic.lean

@@ -478,7 +478,7 @@ instance : Std.Trichotomous (. < . : Nat → Nat → Prop) where
 
 set_option linter.missingDocs false in
 @[deprecated Nat.instTrichotomousLt (since := "2025-10-27")]
-def Nat.instAntisymmNotLt : Std.Antisymm (¬ . < . : Nat → Nat → Prop) where
+theorem Nat.instAntisymmNotLt : Std.Antisymm (¬ . < . : Nat → Nat → Prop) where
   antisymm := Nat.instTrichotomousLt.trichotomous
 
 protected theorem add_le_add_left {n m : Nat} (h : n ≤ m) (k : Nat) : k + n ≤ k + m :=

src/Init/Data/Option/Instances.lean

@@ -172,10 +172,10 @@ instance [Monad m] : ForM m (Option α) α :=
   ⟨Option.forM⟩
 
 instance [Monad m] : ForIn' m (Option α) α inferInstance where
-  forIn' x init f := do
+  forIn' x init f :=
     match x with
     | none => return init
-    | some a =>
+    | some a => do
       match ← f a rfl init with
       | .done r | .yield r => return r
 

src/Init/Data/Order/Factories.lean

@@ -147,7 +147,7 @@ public theorem LawfulOrderMin.of_min_le {α : Type u} [Min α] [LE α]
 This lemma characterizes in terms of `LE α` when a `Max α` instance "behaves like a supremum
 operator".
 -/
-public def LawfulOrderSup.of_le {α : Type u} [Max α] [LE α]
+public theorem LawfulOrderSup.of_le {α : Type u} [Max α] [LE α]
     (max_le_iff : ∀ a b c : α, max a b ≤ c ↔ a ≤ c ∧ b ≤ c) : LawfulOrderSup α where
   max_le_iff := max_le_iff
 
@@ -159,7 +159,7 @@ instances.
 
 The produced instance entails `LawfulOrderSup α` and `MaxEqOr α`.
 -/
-public def LawfulOrderMax.of_max_le_iff {α : Type u} [Max α] [LE α]
+public theorem LawfulOrderMax.of_max_le_iff {α : Type u} [Max α] [LE α]
     (max_le_iff : ∀ a b c : α, max a b ≤ c ↔ a ≤ c ∧ b ≤ c := by exact LawfulOrderInf.le_min_iff)
     (max_eq_or : ∀ a b : α, max a b = a ∨ max a b = b := by exact MaxEqOr.max_eq_or) :
     LawfulOrderMax α where
@@ -196,7 +196,7 @@ Creates a *total* `LE α` instance from an `LT α` instance.
 
 This only makes sense for asymmetric `LT α` instances (see `Std.Asymm`).
 -/
-@[inline]
+@[inline, implicit_reducible, expose]
 public def _root_.LE.ofLT (α : Type u) [LT α] : LE α where
   le a b := ¬ b < a
 
@@ -208,7 +208,7 @@ public instance LawfulOrderLT.of_lt {α : Type u} [LT α] [i : Asymm (α := α)
     haveI := LE.ofLT α
     LawfulOrderLT α :=
   letI := LE.ofLT α
-  { lt_iff a b := by simp +instances [LE.ofLT, LE.le]; apply Asymm.asymm }
+  { lt_iff a b := by simp [LE.le]; apply Asymm.asymm }
 
 /--
 If an `LT α` instance is asymmetric and its negation is transitive, then `LE.ofLT α` represents a
@@ -253,8 +253,7 @@ public theorem LawfulOrderInf.of_lt {α : Type u} [Min α] [LT α]
   letI := LE.ofLT α
   { le_min_iff a b c := by
       open Classical in
-      simp +instances only [LE.ofLT, LE.le]
-      simp [← not_or, Decidable.not_iff_not]
+      simp only [LE.le, ← not_or, Decidable.not_iff_not]
       simpa [Decidable.imp_iff_not_or] using min_lt_iff a b c }
 
 /--
@@ -276,15 +275,14 @@ public theorem LawfulOrderMin.of_lt {α : Type u} [Min α] [LT α]
 This lemma characterizes in terms of `LT α` when a `Max α` instance
 "behaves like an supremum operator" with respect to `LE.ofLT α`.
 -/
-public def LawfulOrderSup.of_lt {α : Type u} [Max α] [LT α]
+public theorem LawfulOrderSup.of_lt {α : Type u} [Max α] [LT α]
     (lt_max_iff : ∀ a b c : α, c < max a b ↔ c < a ∨ c < b) :
     haveI := LE.ofLT α
     LawfulOrderSup α :=
   letI := LE.ofLT α
   { max_le_iff a b c := by
       open Classical in
-      simp +instances only [LE.ofLT, LE.le]
-      simp [← not_or, Decidable.not_iff_not]
+      simp only [LE.le, ← not_or, Decidable.not_iff_not]
       simpa [Decidable.imp_iff_not_or] using lt_max_iff a b c }
 
 /--
@@ -293,7 +291,7 @@ Derives a `LawfulOrderMax α` instance for `LE.ofLT` from two properties involvi
 
 The produced instance entails `LawfulOrderSup α` and `MaxEqOr α`.
 -/
-public def LawfulOrderMax.of_lt {α : Type u} [Max α] [LT α]
+public theorem LawfulOrderMax.of_lt {α : Type u} [Max α] [LT α]
     (lt_max_iff : ∀ a b c : α, c < max a b ↔ c < a ∨ c < b)
     (max_eq_or : ∀ a b : α, max a b = a ∨ max a b = b) :
     haveI := LE.ofLT α

src/Init/Data/Order/FactoriesExtra.lean

@@ -26,7 +26,7 @@ public def _root_.LE.ofOrd (α : Type u) [Ord α] : LE α where
 /--
 Creates an `DecidableLE α` instance using a well-behaved `Ord α` instance.
 -/
-@[inline, expose]
+@[inline, expose, implicit_reducible]
 public def _root_.DecidableLE.ofOrd (α : Type u) [LE α] [Ord α] [LawfulOrderOrd α] :
     DecidableLE α :=
   fun a b => match h : (compare a b).isLE with
@@ -93,7 +93,7 @@ grind_pattern compare_ne_eq => compare a b, Ordering.eq where
 /--
 Creates a `DecidableLT α` instance using a well-behaved `Ord α` instance.
 -/
-@[inline, expose]
+@[inline, expose, implicit_reducible]
 public def _root_.DecidableLT.ofOrd (α : Type u) [LE α] [LT α] [Ord α] [LawfulOrderOrd α]
     [LawfulOrderLT α] :
     DecidableLT α :=

src/Init/Data/Order/Opposite.lean

@@ -52,7 +52,8 @@ def max' [LE α] [DecidableLE α] (a b : α) : α :=
 Without the `open scoped` command, Lean would not find the required {lit}`DecidableLE α`
 instance for the opposite order.
 -/
-@[implicit_reducible] def LE.opposite (le : LE α) : LE α where
+@[implicit_reducible]
+def LE.opposite (le : LE α) : LE α where
   le a b := b ≤ a
 
 theorem LE.opposite_def {le : LE α} :
@@ -89,6 +90,7 @@ example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsLinearOrder α] {x y : α}
 Without the `open scoped` command, Lean would not find the {lit}`LawfulOrderLT α`
 and {lit}`IsLinearOrder α` instances for the opposite order that are required by {name}`not_le`.
 -/
+@[implicit_reducible]
 def LT.opposite (lt : LT α) : LT α where
   lt a b := b < a
 
@@ -125,6 +127,7 @@ example [LE α] [DecidableLE α] [Min α] [Std.LawfulOrderLeftLeaningMin α] {a
 Without the `open scoped` command, Lean would not find the {lit}`LawfulOrderLeftLeaningMax α`
 instance for the opposite order that is required by {name}`max_eq_if`.
 -/
+@[implicit_reducible]
 def Min.oppositeMax (min : Min α) : Max α where
   max a b := Min.min a b
 
@@ -161,6 +164,7 @@ example [LE α] [DecidableLE α] [Max α] [Std.LawfulOrderLeftLeaningMax α] {a
 Without the `open scoped` command, Lean would not find the {lit}`LawfulOrderLeftLeaningMin α`
 instance for the opposite order that is required by {name}`min_eq_if`.
 -/
+@[implicit_reducible]
 def Max.oppositeMin (max : Max α) : Min α where
   min a b := Max.max a b
 
@@ -283,7 +287,7 @@ scoped instance (priority := low) instLawfulOrderLTOpposite {il : LE α} {it : L
   letI := il.opposite
   letI := it.opposite
   { lt_iff a b := by
-      simp +instances only [LE.opposite, LT.opposite]
+      simp only [LE.le, LT.lt]
       letI := il; letI := it
       exact LawfulOrderLT.lt_iff b a }
 
@@ -293,7 +297,7 @@ scoped instance (priority := low) instLawfulOrderBEqOpposite {il : LE α} {ib :
     LawfulOrderBEq α :=
   letI := il.opposite
   { beq_iff_le_and_ge a b := by
-      simp +instances only [LE.opposite]
+      simp only [LE.le]
       letI := il; letI := ib
       rw [LawfulOrderBEq.beq_iff_le_and_ge]
       exact and_comm }
@@ -306,7 +310,7 @@ scoped instance (priority := low) instLawfulOrderInfOpposite {il : LE α} {im :
   letI := il.opposite
   letI := im.oppositeMax
   { max_le_iff a b c := by
-      simp +instances only [LE.opposite, Min.oppositeMax]
+      simp only [LE.le, Max.max]
       letI := il; letI := im
       exact LawfulOrderInf.le_min_iff c a b }
 
@@ -318,11 +322,11 @@ scoped instance (priority := low) instLawfulOrderMinOpposite {il : LE α} {im :
   letI := il.opposite
   letI := im.oppositeMax
   { max_eq_or a b := by
-      simp +instances only [Min.oppositeMax]
+      simp only [Max.max]
       letI := il; letI := im
       exact MinEqOr.min_eq_or a b
     max_le_iff a b c := by
-      simp +instances only [LE.opposite, Min.oppositeMax]
+      simp only [LE.le, Max.max]
       letI := il; letI := im
       exact LawfulOrderInf.le_min_iff c a b }
 
@@ -334,7 +338,7 @@ scoped instance (priority := low) instLawfulOrderSupOpposite {il : LE α} {im :
   letI := il.opposite
   letI := im.oppositeMin
   { le_min_iff a b c := by
-      simp +instances only [LE.opposite, Max.oppositeMin]
+      simp only [LE.le, Min.min]
       letI := il; letI := im
       exact LawfulOrderSup.max_le_iff b c a }
 
@@ -346,11 +350,11 @@ scoped instance (priority := low) instLawfulOrderMaxOpposite {il : LE α} {im :
   letI := il.opposite
   letI := im.oppositeMin
   { min_eq_or a b := by
-      simp +instances only [Max.oppositeMin]
+      simp only [Min.min]
       letI := il; letI := im
       exact MaxEqOr.max_eq_or a b
     le_min_iff a b c := by
-      simp +instances only [LE.opposite, Max.oppositeMin]
+      simp only [LE.le, Min.min]
       letI := il; letI := im
       exact LawfulOrderSup.max_le_iff b c a }
 
@@ -362,11 +366,11 @@ scoped instance (priority := low) instLawfulOrderLeftLeaningMinOpposite {il : LE
   letI := il.opposite
   letI := im.oppositeMax
   { max_eq_left a b hab := by
-      simp +instances only [Min.oppositeMax]
+      simp only [Max.max]
       letI := il; letI := im
       exact LawfulOrderLeftLeaningMin.min_eq_left a b hab
     max_eq_right a b hab := by
-      simp +instances only [Min.oppositeMax]
+      simp only [Max.max]
       letI := il; letI := im
       exact LawfulOrderLeftLeaningMin.min_eq_right a b hab }
 
@@ -378,11 +382,11 @@ scoped instance (priority := low) instLawfulOrderLeftLeaningMaxOpposite {il : LE
   letI := il.opposite
   letI := im.oppositeMin
   { min_eq_left a b hab := by
-      simp +instances only [Max.oppositeMin]
+      simp only [Min.min]
       letI := il; letI := im
       exact LawfulOrderLeftLeaningMax.max_eq_left a b hab
     min_eq_right a b hab := by
-      simp +instances only [Max.oppositeMin]
+      simp only [Min.min]
       letI := il; letI := im
       exact LawfulOrderLeftLeaningMax.max_eq_right a b hab }
 

src/Init/Data/Order/PackageFactories.lean

@@ -47,7 +47,7 @@ public instance instLawfulOrderBEqOfDecidableLE {α : Type u} [LE α] [Decidable
   beq_iff_le_and_ge := by simp [BEq.beq]
 
 /-- If `LT` can be characterized in terms of a decidable `LE`, then `LT` is decidable either. -/
-@[expose, instance_reducible]
+@[inline, expose, implicit_reducible]
 public def decidableLTOfLE {α : Type u} [LE α] {_ : LT α} [DecidableLE α] [LawfulOrderLT α] :
     DecidableLT α :=
   fun a b =>
@@ -171,7 +171,7 @@ automatically. If it fails, it is necessary to provide some of the fields manual
 * Other proof obligations, namely `le_refl` and `le_trans`, can be omitted if `Refl` and `Trans`
   instances can be synthesized.
 -/
-@[expose, implicit_reducible]
+@[inline, expose, implicit_reducible]
 public def PreorderPackage.ofLE (α : Type u)
     (args : Packages.PreorderOfLEArgs α := by exact {}) : PreorderPackage α where
   toLE := args.le
@@ -256,7 +256,7 @@ automatically. If it fails, it is necessary to provide some of the fields manual
 * Other proof obligations, namely `le_refl`, `le_trans` and `le_antisymm`, can be omitted if `Refl`,
   `Trans` and `Antisymm` instances can be synthesized.
 -/
-@[expose, implicit_reducible]
+@[inline, expose, implicit_reducible]
 public def PartialOrderPackage.ofLE (α : Type u)
     (args : Packages.PartialOrderOfLEArgs α := by exact {}) : PartialOrderPackage α where
   toPreorderPackage := .ofLE α args.toPreorderOfLEArgs
@@ -385,7 +385,7 @@ automatically. If it fails, it is necessary to provide some of the fields manual
 * Other proof obligations, namely `le_total` and `le_trans`, can be omitted if `Total` and `Trans`
   instances can be synthesized.
 -/
-@[expose, implicit_reducible]
+@[inline, expose, implicit_reducible]
 public def LinearPreorderPackage.ofLE (α : Type u)
     (args : Packages.LinearPreorderOfLEArgs α := by exact {}) : LinearPreorderPackage α where
   toPreorderPackage := .ofLE α args.toPreorderOfLEArgs
@@ -487,7 +487,7 @@ automatically. If it fails, it is necessary to provide some of the fields manual
 * Other proof obligations, namely `le_total`, `le_trans` and `le_antisymm`, can be omitted if
   `Total`, `Trans` and `Antisymm` instances can be synthesized.
 -/
-@[expose, implicit_reducible]
+@[inline, expose, implicit_reducible]
 public def LinearOrderPackage.ofLE (α : Type u)
     (args : Packages.LinearOrderOfLEArgs α := by exact {}) : LinearOrderPackage α where
   toLinearPreorderPackage := .ofLE α args.toLinearPreorderOfLEArgs
@@ -647,7 +647,7 @@ automatically. If it fails, it is necessary to provide some of the fields manual
 * Other proof obligations, for example `transOrd`, can be omitted if a matching instance can be
   synthesized.
 -/
-@[expose, instance_reducible]
+@[inline, expose, implicit_reducible]
 public def LinearPreorderPackage.ofOrd (α : Type u)
     (args : Packages.LinearPreorderOfOrdArgs α := by exact {}) : LinearPreorderPackage α :=
   letI := args.ord
@@ -793,10 +793,9 @@ automatically. If it fails, it is necessary to provide some of the fields manual
 * Other proof obligations, such as `transOrd`, can be omitted if matching instances can be
   synthesized.
 -/
-@[expose, instance_reducible]
+@[inline, expose, implicit_reducible]
 public def LinearOrderPackage.ofOrd (α : Type u)
     (args : Packages.LinearOrderOfOrdArgs α := by exact {}) : LinearOrderPackage α :=
-  -- set_option backward.isDefEq.respectTransparency false in
   letI := LinearPreorderPackage.ofOrd α args.toLinearPreorderOfOrdArgs
   haveI : LawfulEqOrd α := ⟨args.eq_of_compare _ _⟩
   letI : Min α := args.min

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

@@ -597,8 +597,7 @@ instance Iterator.instLawfulIteratorLoop [UpwardEnumerable α] [LE α] [Decidabl
     LawfulIteratorLoop (Rxc.Iterator α) Id n where
   lawful := by
     intro lift instLawfulMonadLiftFunction γ it init Pl wf f
-    simp +instances only [IteratorLoop.defaultImplementation, IteratorLoop.forIn,
-      IterM.DefaultConsumers.forIn'_eq_wf Pl wf]
+    simp only [IteratorLoop.forIn, IterM.DefaultConsumers.forIn'_eq_wf Pl wf]
     rw [IterM.DefaultConsumers.forIn'.wf]
     split; rotate_left
     · simp only [IterM.step_eq,
@@ -637,7 +636,7 @@ The pure function mapping a range iterator of type {name}`IterM` to the next ste
 This function is prefixed with {lit}`Monadic` in order to disambiguate it from the version for iterators
 of type {name}`Iter`.
 -/
-@[inline]
+@[inline, implicit_reducible]
 def Iterator.Monadic.step [UpwardEnumerable α] [LT α] [DecidableLT α]
     (it : IterM (α := Rxo.Iterator α) Id α) :
     IterStep (IterM (α := Rxo.Iterator α) Id α) α :=
@@ -1114,7 +1113,6 @@ private theorem Iterator.instIteratorLoop.loop_eq_wf [UpwardEnumerable α] [LT
     · rw [WellFounded.fix_eq]
       simp_all
 
-set_option backward.isDefEq.respectTransparency false in
 private theorem Iterator.instIteratorLoop.loopWf_eq [UpwardEnumerable α] [LT α] [DecidableLT α]
     [LawfulUpwardEnumerable α] [LawfulUpwardEnumerableLT α]
     {n : Type u → Type w} [Monad n] [LawfulMonad n] (γ : Type u)
@@ -1166,15 +1164,13 @@ termination_by IteratorLoop.WithWF.mk ⟨⟨some next, upperBound⟩⟩ acc (hwf
 decreasing_by
   simp [IteratorLoop.rel, Monadic.isPlausibleStep_iff, Monadic.step, *]
 
-set_option backward.isDefEq.respectTransparency false in
 instance Iterator.instLawfulIteratorLoop [UpwardEnumerable α] [LT α] [DecidableLT α]
     [LawfulUpwardEnumerable α] [LawfulUpwardEnumerableLT α]
     {n : Type u → Type w} [Monad n] [LawfulMonad n] :
     LawfulIteratorLoop (Rxo.Iterator α) Id n where
   lawful := by
     intro lift instLawfulMonadLiftFunction γ it init Pl wf f
-    simp +instances only [IteratorLoop.defaultImplementation, IteratorLoop.forIn,
-      IterM.DefaultConsumers.forIn'_eq_wf Pl wf]
+    simp only [IteratorLoop.forIn, IterM.DefaultConsumers.forIn'_eq_wf Pl wf]
     rw [IterM.DefaultConsumers.forIn'.wf]
     split; rotate_left
     · simp [IterM.step_eq, Monadic.step, Internal.LawfulMonadLiftBindFunction.liftBind_pure (liftBind := lift)]
@@ -1639,8 +1635,7 @@ instance Iterator.instLawfulIteratorLoop [UpwardEnumerable α]
     LawfulIteratorLoop (Rxi.Iterator α) Id n where
   lawful := by
     intro lift instLawfulMonadLiftFunction γ it init Pl wf f
-    simp +instances only [IteratorLoop.defaultImplementation, IteratorLoop.forIn,
-      IterM.DefaultConsumers.forIn'_eq_wf Pl wf]
+    simp only [IteratorLoop.forIn, IterM.DefaultConsumers.forIn'_eq_wf Pl wf]
     rw [IterM.DefaultConsumers.forIn'.wf]
     split; rotate_left
     · simp [Monadic.step_eq_step, Monadic.step, Internal.LawfulMonadLiftBindFunction.liftBind_pure]

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

@@ -248,7 +248,16 @@ 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]
 
-set_option backward.whnf.reducibleClassField false in
+private theorem succ?_eq_minValueSealed {x : Int8} :
+    UpwardEnumerable.succ? x = if x + 1 = minValueSealed then none else some (x + 1) :=
+  (rfl)
+
+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 :=
+  (rfl)
+
 theorem instUpwardEnumerable_eq :
     instUpwardEnumerable = HasModel.instUpwardEnumerable := by
   apply UpwardEnumerable.ext
@@ -256,16 +265,16 @@ theorem instUpwardEnumerable_eq :
     apply HasModel.succ?_eq_of_technicalCondition
     simp [HasModel.encode, succ?, ← Int8.toBitVec_inj, toBitVec_minValueSealed_eq_intMinSealed]
   · ext
-    simp +instances [HasModel.succMany?_eq, instUpwardEnumerable, HasModel.encode, HasModel.decode,
+    simp [HasModel.succMany?_eq, succMany?_eq_maxValueSealed, HasModel.encode, HasModel.decode,
       ← toInt_toBitVec, toBitVec_maxValueSealed_eq_intMaxSealed, ofIntLE_eq_ofInt]
 
 
 instance : LawfulUpwardEnumerable Int8 := by
-  simp +instances only [instUpwardEnumerable_eq]
+  rw [instUpwardEnumerable_eq]
   infer_instance
 
 instance : LawfulUpwardEnumerableLE Int8 := by
-  simp +instances only [instUpwardEnumerable_eq]
+  rw [instUpwardEnumerable_eq]
   infer_instance
 
 public instance instRxcHasSize : Rxc.HasSize Int8 where
@@ -277,7 +286,7 @@ theorem instRxcHasSize_eq :
     ← toInt_toBitVec, HasModel.toNat_toInt_add_one_sub_toInt (Nat.zero_lt_succ _)]
 
 public instance instRxcLawfulHasSize : Rxc.LawfulHasSize Int8 := by
-  simp +instances only [instUpwardEnumerable_eq, instRxcHasSize_eq]
+  rw [instUpwardEnumerable_eq, instRxcHasSize_eq]
   infer_instance
 public instance : Rxc.IsAlwaysFinite Int8 := by exact inferInstance
 
@@ -294,7 +303,7 @@ theorem instRxiHasSize_eq :
     HasModel.encode, HasModel.toNat_two_pow_sub_one_sub_toInt (show 8 > 0 by omega)]
 
 public instance instRxiLawfulHasSize : Rxi.LawfulHasSize Int8 := by
-  simp +instances only [instUpwardEnumerable_eq, instRxiHasSize_eq]
+  rw [instUpwardEnumerable_eq, instRxiHasSize_eq]
   infer_instance
 public instance instRxiIsAlwaysFinite : Rxi.IsAlwaysFinite Int8 := by exact inferInstance
 
@@ -344,7 +353,6 @@ instance : HasModel Int16 (BitVec 16) where
   le_iff_encode_le := by simp [LE.le, Int16.le]
   lt_iff_encode_lt := by simp [LT.lt, Int16.lt]
 
-set_option backward.whnf.reducibleClassField false in
 theorem instUpwardEnumerable_eq :
     instUpwardEnumerable = HasModel.instUpwardEnumerable := by
   apply UpwardEnumerable.ext
@@ -440,7 +448,6 @@ instance : HasModel Int32 (BitVec 32) where
   le_iff_encode_le := by simp [LE.le, Int32.le]
   lt_iff_encode_lt := by simp [LT.lt, Int32.lt]
 
-set_option backward.whnf.reducibleClassField false in
 theorem instUpwardEnumerable_eq :
     instUpwardEnumerable = HasModel.instUpwardEnumerable := by
   apply UpwardEnumerable.ext
@@ -536,7 +543,6 @@ instance : HasModel Int64 (BitVec 64) where
   le_iff_encode_le := by simp [LE.le, Int64.le]
   lt_iff_encode_lt := by simp [LT.lt, Int64.lt]
 
-set_option backward.whnf.reducibleClassField false in
 theorem instUpwardEnumerable_eq :
     instUpwardEnumerable = HasModel.instUpwardEnumerable := by
   apply UpwardEnumerable.ext
@@ -637,7 +643,6 @@ instance : HasModel ISize (BitVec System.Platform.numBits) where
   le_iff_encode_le := by simp [LE.le, ISize.le]
   lt_iff_encode_lt := by simp [LT.lt, ISize.lt]
 
-set_option backward.whnf.reducibleClassField false in
 theorem instUpwardEnumerable_eq :
     instUpwardEnumerable = HasModel.instUpwardEnumerable := by
   apply UpwardEnumerable.ext

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

@@ -438,6 +438,7 @@ protected theorem UpwardEnumerable.le_iff {α : Type u} [LE α] [UpwardEnumerabl
     [LawfulUpwardEnumerableLE α] {a b : α} : a ≤ b ↔ UpwardEnumerable.LE a b :=
   LawfulUpwardEnumerableLE.le_iff a b
 
+@[expose, implicit_reducible]
 def UpwardEnumerable.instLETransOfLawfulUpwardEnumerableLE {α : Type u} [LE α]
     [UpwardEnumerable α] [LawfulUpwardEnumerable α] [LawfulUpwardEnumerableLE α] :
     Trans (α := α) (· ≤ ·) (· ≤ ·) (· ≤ ·) where
@@ -502,12 +503,13 @@ protected theorem UpwardEnumerable.lt_succ_iff {α : Type u} [UpwardEnumerable
       ← succMany?_eq_some_iff_succMany] at hn
     exact ⟨n, hn⟩
 
+@[expose, implicit_reducible]
 def UpwardEnumerable.instLTTransOfLawfulUpwardEnumerableLT {α : Type u} [LT α]
     [UpwardEnumerable α] [LawfulUpwardEnumerable α] [LawfulUpwardEnumerableLT α] :
     Trans (α := α) (· < ·) (· < ·) (· < ·) where
   trans := by simpa [UpwardEnumerable.lt_iff] using @UpwardEnumerable.lt_trans
 
-def UpwardEnumerable.instLawfulOrderLTOfLawfulUpwardEnumerableLT {α : Type u} [LT α] [LE α]
+theorem UpwardEnumerable.instLawfulOrderLTOfLawfulUpwardEnumerableLT {α : Type u} [LT α] [LE α]
     [UpwardEnumerable α] [LawfulUpwardEnumerable α] [LawfulUpwardEnumerableLT α]
     [LawfulUpwardEnumerableLE α] :
     LawfulOrderLT α where

src/Init/Data/Rat/Basic.lean

@@ -11,6 +11,7 @@ public import Init.Data.OfScientific
 public import Init.Data.Int.DivMod.Basic
 public import Init.Data.String.Defs
 public import Init.Data.ToString.Macro
+public import Init.Data.ToString.Extra
 import Init.Data.Hashable
 import Init.Data.Int.DivMod.Bootstrap
 import Init.Data.Int.DivMod.Lemmas

src/Init/Data/SInt/Basic.lean

@@ -7,6 +7,7 @@ module
 
 prelude
 public import Init.Data.UInt.Basic
+public import Init.Data.ToString.Extra
 
 @[expose] public section
 

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

@@ -10,6 +10,7 @@ public import Init.Data.Slice.Operations
 import all Init.Data.Range.Polymorphic.Basic
 import Init.Omega
 public import Init.Data.Array.Subarray
+public import Init.Data.ToString.Extra
 
 public section
 
@@ -25,7 +26,7 @@ variable {shape : RangeShape} {α : Type u}
 structure SubarrayIterator (α : Type u) where
   xs : Subarray α
 
-@[inline, expose]
+@[inline, expose, implicit_reducible]
 def SubarrayIterator.step :
     IterM (α := SubarrayIterator α) Id α → IterStep (IterM (α := SubarrayIterator α) m α) α
   | ⟨⟨xs⟩⟩ =>

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

@@ -28,7 +28,6 @@ open Std Std.Iterators Std.PRange Std.Slice
 
 namespace SubarrayIterator
 
-set_option backward.isDefEq.respectTransparency false in
 theorem step_eq {it : Iter (α := SubarrayIterator α) α} :
     it.step = if h : it.1.xs.start < it.1.xs.stop then
         haveI := it.1.xs.start_le_stop
@@ -215,7 +214,6 @@ public theorem Array.stop_toSubarray {xs : Array α} {lo hi : Nat} :
     (xs.toSubarray lo hi).stop = min hi xs.size := by
   simp [toSubarray_eq_min, Subarray.stop]
 
-set_option backward.whnf.reducibleClassField false in
 public theorem Subarray.toList_eq {xs : Subarray α} :
     xs.toList = (xs.array.extract xs.start xs.stop).toList := by
   let aslice := xs

src/Init/Data/Slice/List/Iterator.lean

@@ -11,6 +11,7 @@ public import Init.Data.Iterators.Producers.List
 public import Init.Data.Iterators.Combinators.Take
 import all Init.Data.Range.Polymorphic.Basic
 public import Init.Data.Slice.Operations
+public import Init.Data.ToString.Extra
 
 public section
 

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

@@ -70,7 +70,6 @@ end ListSlice
 
 namespace List
 
-set_option backward.whnf.reducibleClassField false in
 @[simp, grind =]
 public theorem toList_mkSlice_rco {xs : List α} {lo hi : Nat} :
     xs[lo...hi].toList = (xs.take hi).drop lo := by
@@ -78,9 +77,9 @@ public theorem toList_mkSlice_rco {xs : List α} {lo hi : Nat} :
   simp only [Std.Rco.Sliceable.mkSlice, toSlice, ListSlice.toList_eq]
   by_cases h : lo < hi
   · have : lo ≤ hi := by omega
-    simp +instances [h, List.take_drop, Nat.add_sub_cancel' ‹_›, ← List.take_eq_take_min]
+    simp [h, List.take_drop, Nat.add_sub_cancel' ‹_›, ← List.take_eq_take_min]
   · have : min hi xs.length ≤ lo := by omega
-    simp +instances [h, Nat.min_eq_right this]
+    simp [h, Nat.min_eq_right this]
 
 @[simp, grind =]
 public theorem toArray_mkSlice_rco {xs : List α} {lo hi : Nat} :
@@ -111,12 +110,11 @@ public theorem size_mkSlice_rcc {xs : List α} {lo hi : Nat} :
     xs[lo...=hi].size = min (hi + 1) xs.length - lo := by
   simp [← length_toList_eq_size]
 
-set_option backward.whnf.reducibleClassField false in
 @[simp, grind =]
 public theorem toList_mkSlice_rci {xs : List α} {lo : Nat} :
     xs[lo...*].toList = xs.drop lo := by
   rw [List.drop_eq_drop_min]
-  simp +instances [ListSlice.toList_eq, Std.Rci.Sliceable.mkSlice, List.toUnboundedSlice]
+  simp [ListSlice.toList_eq, Std.Rci.Sliceable.mkSlice, List.toUnboundedSlice]
 
 @[simp, grind =]
 public theorem toArray_mkSlice_rci {xs : List α} {lo : Nat} :
@@ -290,11 +288,11 @@ section ListSubslices
 
 namespace ListSlice
 
-set_option backward.whnf.reducibleClassField false in
 @[simp, grind =]
 public theorem toList_mkSlice_rco {xs : ListSlice α} {lo hi : Nat} :
     xs[lo...hi].toList = (xs.toList.take hi).drop lo := by
-  simp +instances only [instSliceableListSliceNat_1, List.toList_mkSlice_rco, ListSlice.toList_eq (xs := xs)]
+  rw [instSliceableListSliceNat_1]
+  simp only [List.toList_mkSlice_rco, ListSlice.toList_eq (xs := xs)]
   obtain ⟨⟨xs, stop⟩⟩ := xs
   cases stop
   · simp
@@ -329,13 +327,13 @@ public theorem size_mkSlice_rcc {xs : ListSlice α} {lo hi : Nat} :
     xs[lo...=hi].size = min (hi + 1) xs.size - lo := by
   simp [← length_toList_eq_size]
 
-set_option backward.whnf.reducibleClassField false in
 @[simp, grind =]
 public theorem toList_mkSlice_rci {xs : ListSlice α} {lo : Nat} :
     xs[lo...*].toList = xs.toList.drop lo := by
-  simp +instances only [instSliceableListSliceNat_2, ListSlice.toList_eq (xs := xs)]
+  rw [instSliceableListSliceNat_2]
+  simp only [ListSlice.toList_eq (xs := xs)]
   obtain ⟨⟨xs, stop⟩⟩ := xs
-  simp +instances only
+  simp only
   split <;> simp
 
 @[simp, grind =]

src/Init/Data/String/Basic.lean

@@ -1724,14 +1724,15 @@ def pos! (s : String) (off : Pos.Raw) : s.Pos :=
 @[simp]
 theorem offset_pos {s : String} {off : Pos.Raw} {h} : (s.pos off h).offset = off := rfl
 
-/-- Constructs a valid position on `t` from a valid position on `s` and a proof that `s = t`. -/
+/-- Constructs a valid position on `t` from a valid position on `s` and a proof that
+`s.copy = t.copy`. -/
 @[inline]
-def Slice.Pos.cast {s t : Slice} (pos : s.Pos) (h : s = t) : t.Pos where
+def Slice.Pos.cast {s t : Slice} (pos : s.Pos) (h : s.copy = t.copy) : t.Pos where
   offset := pos.offset
-  isValidForSlice := h ▸ pos.isValidForSlice
+  isValidForSlice := Pos.Raw.isValid_copy_iff.mp (h ▸ Pos.Raw.isValid_copy_iff.mpr pos.isValidForSlice)
 
 @[simp]
-theorem Slice.Pos.offset_cast {s t : Slice} {pos : s.Pos} {h : s = t} :
+theorem Slice.Pos.offset_cast {s t : Slice} {pos : s.Pos} {h : s.copy = t.copy} :
     (pos.cast h).offset = pos.offset := (rfl)
 
 @[simp]
@@ -1739,14 +1740,14 @@ theorem Slice.Pos.cast_rfl {s : Slice} {pos : s.Pos} : pos.cast rfl = pos :=
   Slice.Pos.ext (by simp)
 
 @[simp]
-theorem Slice.Pos.cast_le_cast_iff {s t : Slice} {pos pos' : s.Pos} {h : s = t} :
+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
-  cases h; simp
+  simp [Slice.Pos.le_iff]
 
 @[simp]
-theorem Slice.Pos.cast_lt_cast_iff {s t : Slice} {pos pos' : s.Pos} {h : s = t} :
+theorem Slice.Pos.cast_lt_cast_iff {s t : Slice} {pos pos' : s.Pos} {h : s.copy = t.copy} :
     pos.cast h < pos'.cast h ↔ pos < pos' := by
-  cases h; simp
+  simp [Slice.Pos.lt_iff]
 
 /-- Constructs a valid position on `t` from a valid position on `s` and a proof that `s = t`. -/
 @[inline]
@@ -1977,6 +1978,7 @@ theorem Pos.ne_of_lt {s : String} {p q : s.Pos} : p < q → p ≠ q := by
 theorem Pos.lt_of_lt_of_le {s : String} {p q r : s.Pos} : p < q → q ≤ r → p < r := by
   simpa [Pos.lt_iff, Pos.le_iff] using Pos.Raw.lt_of_lt_of_le
 
+@[simp]
 theorem Pos.le_endPos {s : String} (p : s.Pos) : p ≤ s.endPos := by
   simpa [Pos.le_iff] using p.isValid.le_rawEndPos
 
@@ -2626,7 +2628,7 @@ taking `s.slice! p₀ p₁` already panicked. -/
 @[inline]
 def Slice.Pos.ofSlice! {s : Slice} {p₀ p₁ : s.Pos} (pos : (s.slice! p₀ p₁).Pos) : s.Pos :=
   if h : p₀ ≤ p₁ then
-    ofSlice (h := h) (pos.cast slice_eq_slice!.symm)
+    ofSlice (h := h) (pos.cast (congrArg Slice.copy slice_eq_slice!.symm))
   else
     panic! "Starting position must be less than or equal to end position."
 
@@ -2644,7 +2646,7 @@ taking `s.slice! p₀ p₁` already panicked or if the position is not between `
 def Slice.Pos.slice! {s : Slice} (pos : s.Pos) (p₀ p₁ : s.Pos) :
     (s.slice! p₀ p₁).Pos :=
   if h : p₀ ≤ pos ∧ pos ≤ p₁ then
-    (pos.slice _ _ h.1 h.2).cast slice_eq_slice!
+    (pos.slice _ _ h.1 h.2).cast (congrArg Slice.copy slice_eq_slice!)
   else
     panic! "Starting position must be less than or equal to end position and position must be between starting position and end position."
 

src/Init/Data/String/Bootstrap.lean

@@ -55,9 +55,11 @@ end String
 
 namespace String.Internal
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_posof"]
 opaque posOf (s : String) (c : Char) : Pos.Raw
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_offsetofpos"]
 opaque offsetOfPos (s : String) (pos : Pos.Raw) : Nat
 
@@ -67,6 +69,7 @@ opaque extract : (@& String) → (@& Pos.Raw) → (@& Pos.Raw) → String
 @[extern "lean_string_length"]
 opaque length : (@& String) → Nat
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_pushn"]
 opaque pushn (s : String) (c : Char) (n : Nat) : String
 
@@ -76,45 +79,57 @@ opaque append : String → (@& String) → String
 @[extern "lean_string_utf8_next"]
 opaque next (s : @& String) (p : @& Pos.Raw) : Pos.Raw
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_isempty"]
 opaque isEmpty (s : String) : Bool
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_foldl"]
 opaque foldl (f : String → Char → String) (init : String) (s : String) : String
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_isprefixof"]
 opaque isPrefixOf (p : String) (s : String) : Bool
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_any"]
 opaque any (s : String) (p : Char → Bool) : Bool
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_contains"]
 opaque contains (s : String) (c : Char) : Bool
 
 @[extern "lean_string_utf8_get"]
 opaque get (s : @& String) (p : @& Pos.Raw) : Char
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_capitalize"]
 opaque capitalize (s : String) : String
 
 @[extern "lean_string_utf8_at_end"]
 opaque atEnd : (@& String) → (@& Pos.Raw) → Bool
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_nextwhile"]
 opaque nextWhile (s : String) (p : Char → Bool) (i : String.Pos.Raw) : String.Pos.Raw
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_trim"]
 opaque trim (s : String) : String
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_intercalate"]
 opaque intercalate (s : String) : List String → String
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_front"]
 opaque front (s : String) : Char
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_drop"]
 opaque drop (s : String) (n : Nat) : String
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_dropright"]
 opaque dropRight (s : String) (n : Nat) : String
 
@@ -141,33 +156,43 @@ def List.asString (s : List Char) : String :=
 
 namespace Substring.Raw.Internal
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_substring_tostring"]
 opaque toString : Substring.Raw → String
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_substring_drop"]
 opaque drop : Substring.Raw → Nat → Substring.Raw
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_substring_front"]
 opaque front (s : Substring.Raw) : Char
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_substring_takewhile"]
 opaque takeWhile : Substring.Raw → (Char → Bool) → Substring.Raw
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_substring_extract"]
 opaque extract : Substring.Raw → String.Pos.Raw → String.Pos.Raw → Substring.Raw
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_substring_all"]
 opaque all (s : Substring.Raw) (p : Char → Bool) : Bool
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_substring_beq"]
 opaque beq (ss1 ss2 : Substring.Raw) : Bool
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_substring_isempty"]
 opaque isEmpty (ss : Substring.Raw) : Bool
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_substring_get"]
 opaque get : Substring.Raw → String.Pos.Raw → Char
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_substring_prev"]
 opaque prev : Substring.Raw → String.Pos.Raw → String.Pos.Raw
 
@@ -175,9 +200,11 @@ end Substring.Raw.Internal
 
 namespace String.Pos.Raw.Internal
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_pos_sub"]
 opaque sub : String.Pos.Raw → String.Pos.Raw → String.Pos.Raw
 
+set_option compiler.ignoreBorrowAnnotation true in
 @[extern "lean_string_pos_min"]
 opaque min (p₁ p₂ : Pos.Raw) : Pos.Raw
 

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

@@ -205,9 +205,10 @@ theorem Slice.copy_pos {s : Slice} {p : Pos.Raw} {h : Pos.Raw.IsValidForSlice s
   simp [String.Pos.ext_iff]
 
 @[simp]
-theorem Slice.cast_pos {s t : Slice} {p : Pos.Raw} {h : Pos.Raw.IsValidForSlice s p} {h' : s = t} :
-    (s.pos p h).cast h' = t.pos p (h' ▸ h) := by
-  simp [Pos.ext_iff]
+theorem Slice.cast_pos {s t : Slice} {p : Pos.Raw} {h : Pos.Raw.IsValidForSlice s p}
+    {h' : s.copy = t.copy} {h'' : Pos.Raw.IsValidForSlice t p} :
+    (s.pos p h).cast h' = t.pos p h'' := by
+  simp [Slice.Pos.ext_iff]
 
 @[simp]
 theorem cast_pos {s t : String} {p : Pos.Raw} {h : Pos.Raw.IsValid s p} {h' : s = t} :

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

@@ -16,6 +16,9 @@ import Init.ByCases
 import Init.Data.Iterators.Lemmas.Combinators.FilterMap
 import Init.Data.String.Lemmas.Basic
 import Init.Data.Iterators.Lemmas.Consumers.Loop
+public import Init.Data.String.Lemmas.Order
+import Init.Data.String.OrderInstances
+import Init.Data.Subtype.Basic
 
 set_option doc.verso true
 
@@ -47,6 +50,19 @@ theorem Model.positionsFrom_eq_cons {s : Slice} {p : s.Pos} (hp : p ≠ s.endPos
   rw [Model.positionsFrom]
   simp [hp]
 
+@[simp]
+theorem Model.mem_positionsFrom {s : Slice} {p : s.Pos} {q : { q : s.Pos // q ≠ s.endPos } } :
+    q ∈ Model.positionsFrom p ↔ p ≤ q := by
+  induction p using Pos.next_induction with
+  | next p h ih =>
+    rw [Model.positionsFrom_eq_cons h, List.mem_cons, ih]
+    simp [Subtype.ext_iff, Std.le_iff_lt_or_eq (a := p), or_comm, eq_comm]
+  | endPos => simp [q.property]
+
+theorem Model.mem_positionsFrom_startPos {s : Slice} {q : { q : s.Pos // q ≠ s.endPos} } :
+    q ∈ Model.positionsFrom s.startPos := by
+  simp
+
 theorem Model.map_get_positionsFrom_of_splits {s : Slice} {p : s.Pos} {t₁ t₂ : String}
     (hp : p.Splits t₁ t₂) : (Model.positionsFrom p).map (fun p => p.1.get p.2) = t₂.toList := by
   induction p using Pos.next_induction generalizing t₁ t₂ with
@@ -60,7 +76,6 @@ theorem Model.map_get_positionsFrom_startPos {s : Slice} :
     (Model.positionsFrom s.startPos).map (fun p => p.1.get p.2) = s.copy.toList :=
   Model.map_get_positionsFrom_of_splits (splits_startPos s)
 
-set_option backward.isDefEq.respectTransparency false in
 @[simp]
 theorem toList_positionsFrom {s : Slice} {p : s.Pos} :
     (s.positionsFrom p).toList = Model.positionsFrom p := by
@@ -80,6 +95,38 @@ theorem toList_positions {s : Slice} : s.positions.toList = Model.positionsFrom
 theorem toList_chars {s : Slice} : s.chars.toList = s.copy.toList := by
   simp [chars, Model.map_get_positionsFrom_startPos]
 
+theorem mem_toList_copy_iff_exists_get {s : Slice} {c : Char} :
+    c ∈ s.copy.toList ↔ ∃ (p : s.Pos) (h : p ≠ s.endPos), p.get h = c := by
+  simp [← Model.map_get_positionsFrom_startPos]
+
+theorem Pos.Splits.mem_toList_left_iff {s : Slice} {pos : s.Pos} {t u : String} {c : Char}
+    (hs : pos.Splits t u) :
+    c ∈ t.toList ↔ ∃ pos', ∃ (h : pos' < pos), pos'.get (Pos.ne_endPos_of_lt h) = c := by
+  rw [hs.eq_left pos.splits, mem_toList_copy_iff_exists_get]
+  refine ⟨?_, ?_⟩
+  · rintro ⟨p, hp, hpget⟩
+    have hlt : Pos.ofSliceTo p < pos := by
+      simpa using Pos.ofSliceTo_lt_ofSliceTo_iff.mpr ((Pos.lt_endPos_iff _).mpr hp)
+    exact ⟨_, hlt, by rwa [Pos.get_eq_get_ofSliceTo] at hpget⟩
+  · rintro ⟨pos', hlt, hget⟩
+    exact ⟨pos.sliceTo pos' (Std.le_of_lt hlt),
+      by simpa [← Pos.ofSliceTo_inj] using Std.ne_of_lt hlt,
+      by rw [Slice.Pos.get_eq_get_ofSliceTo]; simpa using hget⟩
+
+theorem Pos.Splits.mem_toList_right_iff {s : Slice} {pos : s.Pos} {t u : String} {c : Char}
+    (hs : pos.Splits t u) :
+    c ∈ u.toList ↔ ∃ pos', ∃ (_ : pos ≤ pos') (h : pos' ≠ s.endPos), pos'.get h = c := by
+  rw [hs.eq_right pos.splits, mem_toList_copy_iff_exists_get]
+  refine ⟨?_, ?_⟩
+  · rintro ⟨p, hp, hpget⟩
+    exact ⟨Pos.ofSliceFrom p, Pos.le_ofSliceFrom,
+      fun h => hp (Pos.ofSliceFrom_inj.mp (h.trans (Pos.ofSliceFrom_endPos (pos := pos)).symm)),
+      by rwa [Pos.get_eq_get_ofSliceFrom] at hpget⟩
+  · rintro ⟨pos', hle, hne, hget⟩
+    exact ⟨pos.sliceFrom pos' hle,
+      fun h => hne (by simpa using congrArg Pos.ofSliceFrom h),
+      by rw [Pos.get_eq_get_ofSliceFrom]; simpa using hget⟩
+
 /--
 A list of all positions strictly before {name}`p`, ordered from largest to smallest.
 
@@ -115,7 +162,6 @@ theorem Model.map_get_revPositionsFrom_endPos {s : Slice} :
     (Model.revPositionsFrom s.endPos).map (fun p => p.1.get p.2) = s.copy.toList.reverse :=
   Model.map_get_revPositionsFrom_of_splits (splits_endPos s)
 
-set_option backward.isDefEq.respectTransparency false in
 @[simp]
 theorem toList_revPositionsFrom {s : Slice} {p : s.Pos} :
     (s.revPositionsFrom p).toList = Model.revPositionsFrom p := by
@@ -168,6 +214,19 @@ theorem Model.positionsFrom_eq_cons {s : String} {p : s.Pos} (hp : p ≠ s.endPo
   rw [Model.positionsFrom]
   simp [hp]
 
+@[simp]
+theorem Model.mem_positionsFrom {s : String} {p : s.Pos} {q : { q : s.Pos // q ≠ s.endPos } } :
+    q ∈ Model.positionsFrom p ↔ p ≤ q := by
+  induction p using Pos.next_induction with
+  | next p h ih =>
+    rw [Model.positionsFrom_eq_cons h, List.mem_cons, ih]
+    simp [Subtype.ext_iff, Std.le_iff_lt_or_eq (a := p), or_comm, eq_comm]
+  | endPos => simp [q.property]
+
+theorem Model.mem_positionsFrom_startPos {s : String} {q : { q : s.Pos // q ≠ s.endPos} } :
+    q ∈ Model.positionsFrom s.startPos := by
+  simp
+
 theorem Model.positionsFrom_eq_map {s : String} {p : s.Pos} :
     Model.positionsFrom p = (Slice.Model.positionsFrom p.toSlice).map
       (fun p => ⟨Pos.ofToSlice p.1, by simpa [← Pos.toSlice_inj] using p.2⟩) := by
@@ -199,6 +258,38 @@ theorem toList_positions {s : String} : s.positions.toList = Model.positionsFrom
 theorem toList_chars {s : String} : s.chars.toList = s.toList := by
   simp [chars]
 
+theorem mem_toList_iff_exists_get {s : String} {c : Char} :
+    c ∈ s.toList ↔ ∃ (p : s.Pos) (h : p ≠ s.endPos), p.get h = c := by
+  simp [← Model.map_get_positionsFrom_startPos]
+
+theorem Pos.Splits.mem_toList_left_iff {s : String} {pos : s.Pos} {t u : String} {c : Char}
+    (hs : pos.Splits t u) :
+    c ∈ t.toList ↔ ∃ pos', ∃ (h : pos' < pos), pos'.get (Pos.ne_endPos_of_lt h) = c := by
+  rw [hs.eq_left pos.splits, Slice.mem_toList_copy_iff_exists_get]
+  refine ⟨?_, ?_⟩
+  · rintro ⟨p, hp, hpget⟩
+    have hlt : Pos.ofSliceTo p < pos := by
+      simpa using Pos.ofSliceTo_lt_ofSliceTo_iff.mpr ((Slice.Pos.lt_endPos_iff _).mpr hp)
+    exact ⟨_, hlt, by rwa [Pos.get_eq_get_ofSliceTo] at hpget⟩
+  · rintro ⟨pos', hlt, hget⟩
+    exact ⟨pos.sliceTo pos' (Std.le_of_lt hlt),
+      fun h => Std.ne_of_lt hlt (by simpa using congrArg Pos.ofSliceTo h),
+      by rw [Pos.get_eq_get_ofSliceTo]; simpa using hget⟩
+
+theorem Pos.Splits.mem_toList_right_iff {s : String} {pos : s.Pos} {t u : String} {c : Char}
+    (hs : pos.Splits t u) :
+    c ∈ u.toList ↔ ∃ pos', ∃ (_ : pos ≤ pos') (h : pos' ≠ s.endPos), pos'.get h = c := by
+  rw [hs.eq_right pos.splits, Slice.mem_toList_copy_iff_exists_get]
+  refine ⟨?_, ?_⟩
+  · rintro ⟨p, hp, hpget⟩
+    exact ⟨Pos.ofSliceFrom p, Pos.le_ofSliceFrom,
+      fun h => hp (Pos.ofSliceFrom_inj.mp (h.trans Pos.ofSliceFrom_endPos.symm)),
+      by rwa [Pos.get_eq_get_ofSliceFrom] at hpget⟩
+  · rintro ⟨pos', hle, hne, hget⟩
+    exact ⟨pos.sliceFrom pos' hle,
+      fun h => hne (by simpa using congrArg Pos.ofSliceFrom h),
+      by rw [Pos.get_eq_get_ofSliceFrom]; simpa using hget⟩
+
 /--
 A list of all positions strictly before {name}`p`, ordered from largest to smallest.
 

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

@@ -290,6 +290,70 @@ theorem Pos.ofSliceTo_le_iff {s : String} {p₀ : s.Pos} {p : (s.sliceTo p₀).P
     Pos.ofSliceTo p ≤ q ↔ ∀ h, p ≤ Pos.sliceTo p₀ q h := by
   simp [← Std.not_lt, Pos.lt_ofSliceTo_iff]
 
+theorem Slice.Pos.lt_sliceFrom_iff {s : Slice} {p₀ : s.Pos} {p : (s.sliceFrom p₀).Pos} {q : s.Pos} {h} :
+    p < Slice.Pos.sliceFrom p₀ q h ↔ Pos.ofSliceFrom p < q := by
+  simp [ofSliceFrom_lt_iff, h]
+
+theorem Slice.Pos.sliceFrom_le_iff {s : Slice} {p₀ : s.Pos} {p : (s.sliceFrom p₀).Pos} {q : s.Pos} {h} :
+    Slice.Pos.sliceFrom p₀ q h ≤ p ↔ q ≤ Pos.ofSliceFrom p := by
+  simp [← Std.not_lt, lt_sliceFrom_iff]
+
+theorem Slice.Pos.le_sliceFrom_iff {s : Slice} {p₀ : s.Pos} {p : (s.sliceFrom p₀).Pos} {q : s.Pos} {h} :
+    p ≤ Slice.Pos.sliceFrom p₀ q h ↔ Pos.ofSliceFrom p ≤ q := by
+  simp [ofSliceFrom_le_iff, h]
+
+theorem Slice.Pos.sliceFrom_lt_iff {s : Slice} {p₀ : s.Pos} {p : (s.sliceFrom p₀).Pos} {q : s.Pos} {h} :
+    Slice.Pos.sliceFrom p₀ q h < p ↔ q < Pos.ofSliceFrom p := by
+  simp [← Std.not_le, le_sliceFrom_iff]
+
+theorem Pos.lt_sliceFrom_iff {s : String} {p₀ : s.Pos} {p : (s.sliceFrom p₀).Pos} {q : s.Pos} {h} :
+    p < Pos.sliceFrom p₀ q h ↔ Pos.ofSliceFrom p < q := by
+  simp [ofSliceFrom_lt_iff, h]
+
+theorem Pos.sliceFrom_le_iff {s : String} {p₀ : s.Pos} {p : (s.sliceFrom p₀).Pos} {q : s.Pos} {h} :
+    Pos.sliceFrom p₀ q h ≤ p ↔ q ≤ Pos.ofSliceFrom p := by
+  simp [← Std.not_lt, lt_sliceFrom_iff]
+
+theorem Pos.le_sliceFrom_iff {s : String} {p₀ : s.Pos} {p : (s.sliceFrom p₀).Pos} {q : s.Pos} {h} :
+    p ≤ Pos.sliceFrom p₀ q h ↔ Pos.ofSliceFrom p ≤ q := by
+  simp [ofSliceFrom_le_iff, h]
+
+theorem Pos.sliceFrom_lt_iff {s : String} {p₀ : s.Pos} {p : (s.sliceFrom p₀).Pos} {q : s.Pos} {h} :
+    Pos.sliceFrom p₀ q h < p ↔ q < Pos.ofSliceFrom p := by
+  simp [← Std.not_le, le_sliceFrom_iff]
+
+theorem Slice.Pos.sliceTo_le_iff {s : Slice} {p₀ : s.Pos} {p : (s.sliceTo p₀).Pos} {q : s.Pos} {h} :
+    Pos.sliceTo p₀ q h ≤ p ↔ q ≤ Pos.ofSliceTo p := by
+  simp [le_ofSliceTo_iff, h]
+
+theorem Slice.Pos.lt_sliceTo_iff {s : Slice} {p₀ : s.Pos} {p : (s.sliceTo p₀).Pos} {q : s.Pos} {h} :
+    p < Pos.sliceTo p₀ q h ↔ Pos.ofSliceTo p < q := by
+  simp [← Std.not_le, sliceTo_le_iff]
+
+theorem Slice.Pos.sliceTo_lt_iff {s : Slice} {p₀ : s.Pos} {p : (s.sliceTo p₀).Pos} {q : s.Pos} {h} :
+    Slice.Pos.sliceTo p₀ q h < p ↔ q < Pos.ofSliceTo p := by
+  simp [lt_ofSliceTo_iff, h]
+
+theorem Slice.Pos.le_sliceTo_iff {s : Slice} {p₀ : s.Pos} {p : (s.sliceTo p₀).Pos} {q : s.Pos} {h} :
+    p ≤ Slice.Pos.sliceTo p₀ q h ↔ Pos.ofSliceTo p ≤ q := by
+  simp [← Std.not_lt, sliceTo_lt_iff]
+
+theorem Pos.sliceTo_le_iff {s : String} {p₀ : s.Pos} {p : (s.sliceTo p₀).Pos} {q : s.Pos} {h} :
+    Pos.sliceTo p₀ q h ≤ p ↔ q ≤ Pos.ofSliceTo p := by
+  simp [le_ofSliceTo_iff, h]
+
+theorem Pos.lt_sliceTo_iff {s : String} {p₀ : s.Pos} {p : (s.sliceTo p₀).Pos} {q : s.Pos} {h} :
+    p < Pos.sliceTo p₀ q h ↔ Pos.ofSliceTo p < q := by
+  simp [← Std.not_le, sliceTo_le_iff]
+
+theorem Pos.sliceTo_lt_iff {s : String} {p₀ : s.Pos} {p : (s.sliceTo p₀).Pos} {q : s.Pos} {h} :
+    Pos.sliceTo p₀ q h < p ↔ q < Pos.ofSliceTo p := by
+  simp [lt_ofSliceTo_iff, h]
+
+theorem Pos.le_sliceTo_iff {s : String} {p₀ : s.Pos} {p : (s.sliceTo p₀).Pos} {q : s.Pos} {h} :
+    p ≤ Pos.sliceTo p₀ q h ↔ Pos.ofSliceTo p ≤ q := by
+  simp [← Std.not_lt, sliceTo_lt_iff]
+
 theorem Slice.Pos.ofSliceTo_ne_endPos {s : Slice} {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))

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

@@ -12,3 +12,4 @@ public import Init.Data.String.Lemmas.Pattern.Pred
 public import Init.Data.String.Lemmas.Pattern.Char
 public import Init.Data.String.Lemmas.Pattern.String
 public import Init.Data.String.Lemmas.Pattern.Split
+public import Init.Data.String.Lemmas.Pattern.Find

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

@@ -12,6 +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
+import Init.Data.String.Lemmas.Basic
 import Init.Data.String.Lemmas.Order
 import Init.Data.String.Termination
 import Init.Data.Order.Lemmas
@@ -168,6 +169,24 @@ theorem IsLongestMatchAt.eq {pat : ρ} [ForwardPatternModel pat] {s : Slice} {st
     endPos = endPos' := by
   simpa using h.isLongestMatch_sliceFrom.eq h'.isLongestMatch_sliceFrom
 
+private theorem isLongestMatch_of_eq {pat : ρ} [ForwardPatternModel pat] {s t : Slice}
+    {pos : s.Pos} {pos' : t.Pos} (h_eq : s = t) (h_pos : pos.offset = pos'.offset)
+    (hm : IsLongestMatch pat pos) : IsLongestMatch pat pos' := by
+  subst h_eq; exact (Slice.Pos.ext h_pos) ▸ hm
+
+theorem isLongestMatchAt_iff_isLongestMatchAt_ofSliceFrom {pat : ρ} [ForwardPatternModel pat]
+    {s : Slice} {base : s.Pos} {startPos endPos : (s.sliceFrom base).Pos} :
+    IsLongestMatchAt pat startPos endPos ↔ IsLongestMatchAt pat (Pos.ofSliceFrom startPos) (Pos.ofSliceFrom endPos) := by
+  constructor
+  · intro h
+    refine ⟨Slice.Pos.ofSliceFrom_le_ofSliceFrom_iff.mpr h.le, ?_⟩
+    exact isLongestMatch_of_eq Slice.sliceFrom_sliceFrom
+      (by simp [Pos.Raw.ext_iff]; omega) h.isLongestMatch_sliceFrom
+  · intro h
+    refine ⟨Slice.Pos.ofSliceFrom_le_ofSliceFrom_iff.mp h.le, ?_⟩
+    exact isLongestMatch_of_eq Slice.sliceFrom_sliceFrom.symm
+      (by simp [Pos.Raw.ext_iff]; omega) h.isLongestMatch_sliceFrom
+
 theorem IsLongestMatch.isLongestMatchAt_ofSliceFrom {pat : ρ} [ForwardPatternModel pat] {s : Slice}
     {p₀ : s.Pos} {pos : (s.sliceFrom p₀).Pos} (h : IsLongestMatch pat pos) :
     IsLongestMatchAt pat p₀ (Slice.Pos.ofSliceFrom pos) where
@@ -198,6 +217,27 @@ theorem matchesAt_iff_exists_isMatch {pat : ρ} [ForwardPatternModel pat] {s : S
     ⟨Std.le_trans h₁ (by simpa [← Pos.ofSliceFrom_le_ofSliceFrom_iff] using hq.le_of_isMatch h₂),
      by simpa using hq⟩⟩
 
+@[simp]
+theorem not_matchesAt_endPos {pat : ρ} [ForwardPatternModel pat] {s : Slice} :
+    ¬ MatchesAt pat s.endPos := by
+  simp only [matchesAt_iff_exists_isMatch, Pos.endPos_le, exists_prop_eq]
+  intro h
+  simpa [← Pos.ofSliceFrom_inj] using h.ne_startPos
+
+theorem matchesAt_iff_matchesAt_ofSliceFrom {pat : ρ} [ForwardPatternModel pat] {s : Slice} {base : s.Pos}
+    {pos : (s.sliceFrom base).Pos} : MatchesAt pat pos ↔ MatchesAt pat (Pos.ofSliceFrom pos) := by
+  simp only [matchesAt_iff_exists_isLongestMatchAt]
+  constructor
+  · rintro ⟨endPos, h⟩
+    exact ⟨Pos.ofSliceFrom endPos, isLongestMatchAt_iff_isLongestMatchAt_ofSliceFrom.mp h⟩
+  · rintro ⟨endPos, h⟩
+    exact ⟨base.sliceFrom endPos (Std.le_trans Slice.Pos.le_ofSliceFrom h.le),
+           isLongestMatchAt_iff_isLongestMatchAt_ofSliceFrom.mpr (by simpa using h)⟩
+
+theorem IsLongestMatchAt.matchesAt {pat : ρ} [ForwardPatternModel pat] {s : Slice} {startPos endPos : s.Pos}
+    (h : IsLongestMatchAt pat startPos endPos) : MatchesAt pat startPos where
+  exists_isLongestMatchAt := ⟨_, h⟩
+
 open Classical in
 /--
 Noncomputable model function returning the end point of the longest match starting at the given

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

@@ -8,6 +8,12 @@ module
 prelude
 public import Init.Data.String.Pattern.Char
 public import Init.Data.String.Lemmas.Pattern.Basic
+public import Init.Data.String.Slice
+public import Init.Data.String.Lemmas.Pattern.Pred
+public import Init.Data.String.Search
+import all Init.Data.String.Slice
+import all Init.Data.String.Pattern.Char
+import all Init.Data.String.Search
 import Init.Data.Option.Lemmas
 import Init.Data.String.Lemmas.Basic
 import Init.Data.String.Lemmas.Order
@@ -54,13 +60,23 @@ instance {c : Char} : LawfulForwardPatternModel c where
   dropPrefix?_eq_some_iff {s} pos := by
     simp [isLongestMatch_iff, ForwardPattern.dropPrefix?, and_comm, eq_comm (b := pos)]
 
-instance {c : Char} : LawfulToForwardSearcherModel c :=
-  .defaultImplementation
+theorem toSearcher_eq {c : Char} {s : Slice} :
+  ToForwardSearcher.toSearcher c s = ToForwardSearcher.toSearcher (· == c) s := (rfl)
 
 theorem matchesAt_iff {c : Char} {s : Slice} {pos : s.Pos} :
     MatchesAt c pos ↔ ∃ (h : pos ≠ s.endPos), pos.get h = c := by
   simp [matchesAt_iff_exists_isLongestMatchAt, isLongestMatchAt_iff, exists_comm]
 
+theorem matchesAt_iff_splits {c : Char} {s : Slice} {pos : s.Pos} :
+    MatchesAt c pos ↔ ∃ t₁ t₂, pos.Splits t₁ (singleton c ++ t₂) := by
+  rw [matchesAt_iff]
+  refine ⟨?_, ?_⟩
+  · rintro ⟨h, rfl⟩
+    exact ⟨_, _, pos.splits_next_right h⟩
+  · rintro ⟨t₁, t₂, hs⟩
+    have hne := hs.ne_endPos_of_singleton
+    exact ⟨hne, (singleton_append_inj.mp (hs.eq_right (pos.splits_next_right hne))).1.symm⟩
+
 theorem not_matchesAt_of_get_ne {c : Char} {s : Slice} {pos : s.Pos} {h : pos ≠ s.endPos}
     (hc : pos.get h ≠ c) : ¬ MatchesAt c pos := by
   simp [matchesAt_iff, hc]
@@ -70,4 +86,153 @@ theorem matchAt?_eq {s : Slice} {pos : s.Pos} {c : Char} :
       if h₀ : ∃ (h : pos ≠ s.endPos), pos.get h = c then some (pos.next h₀.1) else none := by
   split <;> simp_all [isLongestMatchAt_iff, matchesAt_iff]
 
-end String.Slice.Pattern.Model.Char
+theorem isMatch_iff_isMatch_beq {c : Char} {s : Slice} {pos : s.Pos} :
+    IsMatch c pos ↔ IsMatch (· == c) pos := by
+  simp [isMatch_iff, CharPred.isMatch_iff, beq_iff_eq]
+
+theorem isLongestMatch_iff_isLongestMatch_beq {c : Char} {s : Slice} {pos : s.Pos} :
+    IsLongestMatch c pos ↔ IsLongestMatch (· == c) pos := by
+  simp [isLongestMatch_iff_isMatch, isMatch_iff_isMatch_beq]
+
+theorem isLongestMatchAt_iff_isLongestMatchAt_beq {c : Char} {s : Slice}
+    {pos pos' : s.Pos} :
+    IsLongestMatchAt c pos pos' ↔ IsLongestMatchAt (· == c) pos pos' := by
+  simp [Model.isLongestMatchAt_iff, isLongestMatch_iff_isLongestMatch_beq]
+
+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]
+
+theorem matchAt?_eq_matchAt?_beq {c : Char} {s : Slice} {pos : s.Pos} :
+    matchAt? c pos = matchAt? (· == c) pos := by
+  refine Option.ext (fun pos' => ?_)
+  simp [matchAt?_eq_some_iff, isLongestMatchAt_iff_isLongestMatchAt_beq]
+
+theorem isValidSearchFrom_iff_isValidSearchFrom_beq {c : Char} {s : Slice} {p : s.Pos}
+    {l : List (SearchStep s)} : IsValidSearchFrom c p l ↔ IsValidSearchFrom (· == c) p l := by
+  refine ⟨fun h => ?_, fun h => ?_⟩
+  · induction h with
+    | endPos => simpa using IsValidSearchFrom.endPos
+    | matched => simp_all [IsValidSearchFrom.matched, isLongestMatchAt_iff_isLongestMatchAt_beq]
+    | mismatched => simp_all [IsValidSearchFrom.mismatched, matchesAt_iff_matchesAt_beq]
+  · induction h with
+    | endPos => simpa using IsValidSearchFrom.endPos
+    | matched => simp_all [IsValidSearchFrom.matched, isLongestMatchAt_iff_isLongestMatchAt_beq]
+    | mismatched => simp_all [IsValidSearchFrom.mismatched, matchesAt_iff_matchesAt_beq]
+
+instance {c : Char} : LawfulToForwardSearcherModel c where
+  isValidSearchFrom_toList s := by
+    simpa [toSearcher_eq, isValidSearchFrom_iff_isValidSearchFrom_beq] using
+      LawfulToForwardSearcherModel.isValidSearchFrom_toList (pat := (· == c)) (s := s)
+
+end Pattern.Model.Char
+
+theorem startsWith_char_eq_startsWith_beq {c : Char} {s : Slice} :
+    s.startsWith c = s.startsWith (· == c) := (rfl)
+
+theorem dropPrefix?_char_eq_dropPrefix?_beq {c : Char} {s : Slice} :
+    s.dropPrefix? c = s.dropPrefix? (· == c) := (rfl)
+
+theorem dropPrefix_char_eq_dropPrefix_beq {c : Char} {s : Slice} :
+    s.dropPrefix c = s.dropPrefix (· == c) := (rfl)
+
+theorem Pattern.ForwardPattern.dropPrefix?_char_eq_dropPrefix?_beq {c : Char} {s : Slice} :
+    dropPrefix? c s = dropPrefix? (· == c) s := (rfl)
+
+private theorem dropWhileGo_eq {c : Char} {s : Slice} (curr : s.Pos) :
+    dropWhile.go s c curr = dropWhile.go s (· == c) curr := by
+  fun_induction dropWhile.go s c curr with
+  | case1 pos nextCurr h₁ h₂ ih =>
+    conv => rhs; rw [dropWhile.go]
+    simp [← Pattern.ForwardPattern.dropPrefix?_char_eq_dropPrefix?_beq, h₁, h₂, ih]
+  | case2 pos nextCurr h ih =>
+    conv => rhs; rw [dropWhile.go]
+    simp [← Pattern.ForwardPattern.dropPrefix?_char_eq_dropPrefix?_beq, h, ih]
+  | case3 pos h =>
+    conv => rhs; rw [dropWhile.go]
+    simp [← Pattern.ForwardPattern.dropPrefix?_char_eq_dropPrefix?_beq]
+
+theorem dropWhile_char_eq_dropWhile_beq {c : Char} {s : Slice} :
+    s.dropWhile c = s.dropWhile (· == c) := by
+  simpa only [dropWhile] using dropWhileGo_eq s.startPos
+
+private theorem takeWhileGo_eq {c : Char} {s : Slice} (curr : s.Pos) :
+    takeWhile.go s c curr = takeWhile.go s (· == c) curr := by
+  fun_induction takeWhile.go s c curr with
+  | case1 pos nextCurr h₁ h₂ ih =>
+    conv => rhs; rw [takeWhile.go]
+    simp [← Pattern.ForwardPattern.dropPrefix?_char_eq_dropPrefix?_beq, h₁, h₂, ih]
+  | case2 pos nextCurr h ih =>
+    conv => rhs; rw [takeWhile.go]
+    simp [← Pattern.ForwardPattern.dropPrefix?_char_eq_dropPrefix?_beq, h, ih]
+  | case3 pos h =>
+    conv => rhs; rw [takeWhile.go]
+    simp [← Pattern.ForwardPattern.dropPrefix?_char_eq_dropPrefix?_beq]
+
+theorem takeWhile_char_eq_takeWhile_beq {c : Char} {s : Slice} :
+    s.takeWhile c = s.takeWhile (· == c) := by
+  simp only [takeWhile]; exact takeWhileGo_eq s.startPos
+
+theorem all_char_eq_all_beq {c : Char} {s : Slice} :
+    s.all c = s.all (· == c) := by
+  simp only [all, dropWhile_char_eq_dropWhile_beq]
+
+theorem find?_char_eq_find?_beq {c : Char} {s : Slice} :
+    s.find? c = s.find? (· == c) :=
+  (rfl)
+
+theorem Pos.find?_char_eq_find?_beq {c : Char} {s : Slice} {p : s.Pos} :
+    p.find? c = p.find? (· == c) :=
+  (rfl)
+
+theorem contains_char_eq_contains_beq {c : Char} {s : Slice} :
+    s.contains c = s.contains (· == c) :=
+  (rfl)
+
+theorem endsWith_char_eq_endsWith_beq {c : Char} {s : Slice} :
+    s.endsWith c = s.endsWith (· == c) := (rfl)
+
+theorem dropSuffix?_char_eq_dropSuffix?_beq {c : Char} {s : Slice} :
+    s.dropSuffix? c = s.dropSuffix? (· == c) := (rfl)
+
+theorem dropSuffix_char_eq_dropSuffix_beq {c : Char} {s : Slice} :
+    s.dropSuffix c = s.dropSuffix (· == c) := (rfl)
+
+theorem Pattern.BackwardPattern.dropSuffix?_char_eq_dropSuffix?_beq {c : Char} {s : Slice} :
+    dropSuffix? c s = dropSuffix? (· == c) s := (rfl)
+
+private theorem dropEndWhileGo_eq {c : Char} {s : Slice} (curr : s.Pos) :
+    dropEndWhile.go s c curr = dropEndWhile.go s (· == c) curr := by
+  fun_induction dropEndWhile.go s c curr with
+  | case1 pos nextCurr h₁ h₂ ih =>
+    conv => rhs; rw [dropEndWhile.go]
+    simp [← Pattern.BackwardPattern.dropSuffix?_char_eq_dropSuffix?_beq, h₁, h₂, ih]
+  | case2 pos nextCurr h ih =>
+    conv => rhs; rw [dropEndWhile.go]
+    simp [← Pattern.BackwardPattern.dropSuffix?_char_eq_dropSuffix?_beq, h, ih]
+  | case3 pos h =>
+    conv => rhs; rw [dropEndWhile.go]
+    simp [← Pattern.BackwardPattern.dropSuffix?_char_eq_dropSuffix?_beq]
+
+theorem dropEndWhile_char_eq_dropEndWhile_beq {c : Char} {s : Slice} :
+    s.dropEndWhile c = s.dropEndWhile (· == c) := by
+  simpa only [dropEndWhile] using dropEndWhileGo_eq s.endPos
+
+private theorem takeEndWhileGo_eq {c : Char} {s : Slice} (curr : s.Pos) :
+    takeEndWhile.go s c curr = takeEndWhile.go s (· == c) curr := by
+  fun_induction takeEndWhile.go s c curr with
+  | case1 pos nextCurr h₁ h₂ ih =>
+    conv => rhs; rw [takeEndWhile.go]
+    simp [← Pattern.BackwardPattern.dropSuffix?_char_eq_dropSuffix?_beq, h₁, h₂, ih]
+  | case2 pos nextCurr h ih =>
+    conv => rhs; rw [takeEndWhile.go]
+    simp [← Pattern.BackwardPattern.dropSuffix?_char_eq_dropSuffix?_beq, h, ih]
+  | case3 pos h =>
+    conv => rhs; rw [takeEndWhile.go]
+    simp [← Pattern.BackwardPattern.dropSuffix?_char_eq_dropSuffix?_beq]
+
+theorem takeEndWhile_char_eq_takeEndWhile_beq {c : Char} {s : Slice} :
+    s.takeEndWhile c = s.takeEndWhile (· == c) := by
+  simpa only [takeEndWhile] using takeEndWhileGo_eq s.endPos
+
+end String.Slice