chore: basic functionality tests for modify/alter

feat: interim implementation of HashMap.modify/alter
2026-03-18 10:54:09 +00:00 · 2024-10-31 10:41:46 +11:00 · 2024-10-30 12:05:28 +11:00
1516 changed files with 8657 additions and 36666 deletions
--- a/.github/ISSUE_TEMPLATE/bug_report.md
+++ b/.github/ISSUE_TEMPLATE/bug_report.md
@@ -39,7 +39,7 @@ Please put an X between the brackets as you perform the following steps:

 ### Versions

-[Output of `#version` or `#eval Lean.versionString`]
+[Output of `#eval Lean.versionString`]
 [OS version, if not using live.lean-lang.org.]

 ### Additional Information
--- a/.github/PULL_REQUEST_TEMPLATE.md
+++ b/.github/PULL_REQUEST_TEMPLATE.md
@@ -5,10 +5,6 @@
 * Include the link to your `RFC` or `bug` issue in the description.
 * If the issue does not already have approval from a developer, submit the PR as draft.
 * The PR title/description will become the commit message. Keep it up-to-date as the PR evolves.
-* For `feat/fix` PRs, the first paragraph starting with "This PR" must be present and will become a
-  changelog entry unless the PR is labeled with `no-changelog`. If the PR does not have this label,
-  it must instead be categorized with one of the `changelog-*` labels (which will be done by a
-  reviewer for external PRs).
 * A toolchain of the form `leanprover/lean4-pr-releases:pr-release-NNNN` for Linux and M-series Macs will be generated upon build. To generate binaries for Windows and Intel-based Macs as well, write a comment containing `release-ci` on its own line.
 * If you rebase your PR onto `nightly-with-mathlib` then CI will test Mathlib against your PR.
 * You can manage the `awaiting-review`, `awaiting-author`, and `WIP` labels yourself, by writing a comment containing one of these labels on its own line.
@@ -16,6 +12,4 @@

 ---

-This PR <short changelog summary for feat/fix, see above>.
-
-Closes <`RFC` or `bug` issue number fixed by this PR, if any>
+Closes #0000 (`RFC` or `bug` issue number fixed by this PR, if any)
--- a/.github/dependabot.yml
+++ b/.github/dependabot.yml
@@ -1,8 +0,0 @@
-version: 2
-updates:
-  - package-ecosystem: "github-actions"
-    directory: "/"
-    schedule:
-      interval: "monthly"
-    commit-message:
-      prefix: "chore: CI"
--- a/.github/workflows/actionlint.yml
+++ b/.github/workflows/actionlint.yml
@@ -17,6 +17,6 @@ jobs:
    - name: Checkout
      uses: actions/checkout@v4
    - name: actionlint
-      uses: raven-actions/actionlint@v2
+      uses: raven-actions/actionlint@v1
      with:
        pyflakes: false # we do not use python scripts
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -217,7 +217,7 @@ jobs:
                "release": true,
                "check-level": 2,
                "shell": "msys2 {0}",
-                "CMAKE_OPTIONS": "-G \"Unix Makefiles\"",
+                "CMAKE_OPTIONS": "-G \"Unix Makefiles\" -DUSE_GMP=OFF",
                // for reasons unknown, interactivetests are flaky on Windows
                "CTEST_OPTIONS": "--repeat until-pass:2",
                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-w64-windows-gnu.tar.zst",
@@ -227,7 +227,7 @@ jobs:
              {
                "name": "Linux aarch64",
                "os": "nscloud-ubuntu-22.04-arm64-4x8",
-                "CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-linux_aarch64",
+                "CMAKE_OPTIONS": "-DUSE_GMP=OFF -DLEAN_INSTALL_SUFFIX=-linux_aarch64",
                "release": true,
                "check-level": 2,
                "shell": "nix develop .#oldGlibcAArch -c bash -euxo pipefail {0}",
@@ -318,7 +318,7 @@ jobs:
        if: github.event_name == 'pull_request'
      # (needs to be after "Checkout" so files don't get overridden)
      - name: Setup emsdk
-        uses: mymindstorm/setup-emsdk@v14
+        uses: mymindstorm/setup-emsdk@v12
        with:
          version: 3.1.44
          actions-cache-folder: emsdk
@@ -492,7 +492,7 @@ jobs:
        with:
          path: artifacts
      - name: Release
-        uses: softprops/action-gh-release@v2
+        uses: softprops/action-gh-release@v1
        with:
          files: artifacts/*/*
          fail_on_unmatched_files: true
@@ -536,7 +536,7 @@ jobs:
          echo -e "\n*Full commit log*\n" >> diff.md
          git log --oneline "$last_tag"..HEAD | sed 's/^/* /' >> diff.md
      - name: Release Nightly
-        uses: softprops/action-gh-release@v2
+        uses: softprops/action-gh-release@v1
        with:
          body_path: diff.md
          prerelease: true
--- a/.github/workflows/labels-from-comments.yml
+++ b/.github/workflows/labels-from-comments.yml
@@ -1,8 +1,7 @@
 # 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.
+# or `release-ci` labels 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.

 name: Label PR based on Comment

@@ -12,7 +11,7 @@ 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'))
    runs-on: ubuntu-latest

    steps:
@@ -21,14 +20,13 @@ jobs:
      with:
        github-token: ${{ secrets.GITHUB_TOKEN }}
        script: |
-          const { owner, repo, number: issue_number } = context.issue;
+          const { owner, repo, number: issue_number  } = context.issue;
          const commentLines = context.payload.comment.body.split('\r\n');

          const awaitingReview = commentLines.includes('awaiting-review');
          const awaitingAuthor = commentLines.includes('awaiting-author');
          const wip = commentLines.includes('WIP');
          const releaseCI = commentLines.includes('release-ci');
-          const changelogMatch = commentLines.find(line => line.startsWith('changelog-'));

          if (awaitingReview || awaitingAuthor || wip) {
            await github.rest.issues.removeLabel({ owner, repo, issue_number, name: 'awaiting-review' }).catch(() => {});
@@ -49,19 +47,3 @@ jobs:
          if (releaseCI) {
            await github.rest.issues.addLabels({ owner, repo, issue_number, labels: ['release-ci'] });
          }
-
-          if (changelogMatch) {
-            const changelogLabel = changelogMatch.trim();
-            const { data: existingLabels } = await github.rest.issues.listLabelsOnIssue({ owner, repo, issue_number });
-            const changelogLabels = existingLabels.filter(label => label.name.startsWith('changelog-'));
-
-            // Remove all other changelog labels
-            for (const label of changelogLabels) {
-              if (label.name !== changelogLabel) {
-                await github.rest.issues.removeLabel({ owner, repo, issue_number, name: label.name }).catch(() => {});
-              }
-            }
-
-            // Add the new changelog label
-            await github.rest.issues.addLabels({ owner, repo, issue_number, labels: [changelogLabel] });
-          }
--- a/.github/workflows/nix-ci.yml
+++ b/.github/workflows/nix-ci.yml
@@ -110,6 +110,14 @@ jobs:
          # https://github.com/netlify/cli/issues/1809
          cp -r --dereference ./result ./dist
        if: matrix.name == 'Nix Linux'
+      - name: Check manual for broken links
+        id: lychee
+        uses: lycheeverse/lychee-action@v1.9.0
+        with:
+          fail: false  # report errors but do not block CI on temporary failures
+          # gmplib.org consistently times out from GH actions
+          # the GitHub token is to avoid rate limiting
+          args: --base './dist' --no-progress --github-token ${{ secrets.GITHUB_TOKEN }} --exclude 'gmplib.org' './dist/**/*.html'
      - name: Rebuild Nix Store Cache
        run: |
          rm -rf nix-store-cache || true
@@ -121,7 +129,7 @@ jobs:
          python3 -c 'import base64; print("alias="+base64.urlsafe_b64encode(bytes.fromhex("${{github.sha}}")).decode("utf-8").rstrip("="))' >> "$GITHUB_OUTPUT"
          echo "message=`git log -1 --pretty=format:"%s"`" >> "$GITHUB_OUTPUT"
      - name: Publish manual to Netlify
-        uses: nwtgck/actions-netlify@v3.0
+        uses: nwtgck/actions-netlify@v2.0
        id: publish-manual
        with:
          publish-dir: ./dist
--- a/.github/workflows/pr-body.yml
+++ b/.github/workflows/pr-body.yml
@@ -1,25 +0,0 @@
-name: Check PR body for changelog convention
-
-on:
-  merge_group:
-  pull_request:
-    types: [opened, synchronize, reopened, edited, labeled, converted_to_draft, ready_for_review]
-
-jobs:
-  check-pr-body:
-    runs-on: ubuntu-latest
-    steps:
-      - name: Check PR body
-        if: github.event_name == 'pull_request'
-        uses: actions/github-script@v7
-        with:
-          script: |
-            const { title, body, labels, draft } = context.payload.pull_request;
-            if (!draft && /^(feat|fix):/.test(title) && !labels.some(label => label.name == "changelog-no")) {
-              if (!labels.some(label => label.name.startsWith("changelog-"))) {
-                core.setFailed('feat/fix PR must have a `changelog-*` label');
-              }
-              if (!/^This PR [^<]/.test(body)) {
-                core.setFailed('feat/fix PR must have changelog summary starting with "This PR ..." as first line.');
-              }
-            }
--- a/.github/workflows/pr-release.yml
+++ b/.github/workflows/pr-release.yml
@@ -34,7 +34,7 @@ jobs:
      - name: Download artifact from the previous workflow.
        if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
        id: download-artifact
-        uses: dawidd6/action-download-artifact@v6 # https://github.com/marketplace/actions/download-workflow-artifact
+        uses: dawidd6/action-download-artifact@v2 # https://github.com/marketplace/actions/download-workflow-artifact
        with:
          run_id: ${{ github.event.workflow_run.id }}
          path: artifacts
@@ -60,7 +60,7 @@ jobs:
          GH_TOKEN: ${{ secrets.PR_RELEASES_TOKEN }}
      - name: Release
        if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
-        uses: softprops/action-gh-release@v2
+        uses: softprops/action-gh-release@v1
        with:
          name: Release for PR ${{ steps.workflow-info.outputs.pullRequestNumber }}
          # There are coredumps files here as well, but all in deeper subdirectories.
@@ -75,7 +75,7 @@ jobs:

      - name: Report release status
        if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
-        uses: actions/github-script@v7
+        uses: actions/github-script@v6
        with:
          script: |
            await github.rest.repos.createCommitStatus({
@@ -111,7 +111,7 @@ jobs:

      - name: 'Setup jq'
        if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
-        uses: dcarbone/install-jq-action@v2.1.0
+        uses: dcarbone/install-jq-action@v1.0.1

      # Check that the most recently nightly coincides with 'git merge-base HEAD master'
      - name: Check merge-base and nightly-testing-YYYY-MM-DD
@@ -208,7 +208,7 @@ jobs:

      - name: Report mathlib base
        if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true' }}
-        uses: actions/github-script@v7
+        uses: actions/github-script@v6
        with:
          script: |
            const description =
--- a/.github/workflows/stale.yml
+++ b/.github/workflows/stale.yml
@@ -11,7 +11,7 @@ jobs:
  stale:
    runs-on: ubuntu-latest
    steps:
-      - uses: actions/stale@v9
+      - uses: actions/stale@v8
        with:
          days-before-stale: -1
          days-before-pr-stale: 30
--- a/RELEASES.md
+++ b/RELEASES.md
@@ -8,329 +8,6 @@ This file contains work-in-progress notes for the upcoming release, as well as p
 Please check the [releases](https://github.com/leanprover/lean4/releases) page for the current status
 of each version.

-v4.15.0
----------
-
-Development in progress.
-
-v4.14.0
----------
-
-Release candidate, release notes will be copied from the branch `releases/v4.14.0` once completed.
-
-v4.13.0
----------
-
-**Full Changelog**: https://github.com/leanprover/lean4/compare/v4.12.0...v4.13.0
-
-### Language features, tactics, and metaprograms
-
-* `structure` command
-  * [#5511](https://github.com/leanprover/lean4/pull/5511) allows structure parents to be type synonyms.
-  * [#5531](https://github.com/leanprover/lean4/pull/5531) allows default values for structure fields to be noncomputable.
-
-* `rfl` and `apply_rfl` tactics
-  * [#3714](https://github.com/leanprover/lean4/pull/3714), [#3718](https://github.com/leanprover/lean4/pull/3718) improve the `rfl` tactic and give better error messages.
-  * [#3772](https://github.com/leanprover/lean4/pull/3772) makes `rfl` no longer use kernel defeq for ground terms.
-  * [#5329](https://github.com/leanprover/lean4/pull/5329) tags `Iff.refl` with `@[refl]` (@Parcly-Taxel)
-  * [#5359](https://github.com/leanprover/lean4/pull/5359) ensures that the `rfl` tactic tries `Iff.rfl` (@Parcly-Taxel)
-
-* `unfold` tactic
-  * [#4834](https://github.com/leanprover/lean4/pull/4834) let `unfold` do zeta-delta reduction of local definitions, incorporating functionality of the Mathlib `unfold_let` tactic.
-
-* `omega` tactic
-  * [#5382](https://github.com/leanprover/lean4/pull/5382) fixes spurious error in [#5315](https://github.com/leanprover/lean4/issues/5315)
-  * [#5523](https://github.com/leanprover/lean4/pull/5523) supports `Int.toNat`
-
-* `simp` tactic
-  * [#5479](https://github.com/leanprover/lean4/pull/5479) lets `simp` apply rules with higher-order patterns.
-
-* `induction` tactic
-  * [#5494](https://github.com/leanprover/lean4/pull/5494) fixes `induction`’s "pre-tactic" block to always be indented, avoiding unintended uses of it.
-
-* `ac_nf` tactic
-  * [#5524](https://github.com/leanprover/lean4/pull/5524) adds `ac_nf`, a counterpart to `ac_rfl`, for normalizing expressions with respect to associativity and commutativity. Tests it with `BitVec` expressions.
-
-* `bv_decide`
-  * [#5211](https://github.com/leanprover/lean4/pull/5211) makes `extractLsb'` the primitive `bv_decide` understands, rather than `extractLsb` (@alexkeizer)
-  * [#5365](https://github.com/leanprover/lean4/pull/5365) adds `bv_decide` diagnoses.
-  * [#5375](https://github.com/leanprover/lean4/pull/5375) adds `bv_decide` normalization rules for `ofBool (a.getLsbD i)` and `ofBool a[i]` (@alexkeizer)
-  * [#5423](https://github.com/leanprover/lean4/pull/5423) enhances the rewriting rules of `bv_decide`
-  * [#5433](https://github.com/leanprover/lean4/pull/5433) presents the `bv_decide` counterexample at the API
-  * [#5484](https://github.com/leanprover/lean4/pull/5484) handles `BitVec.ofNat` with `Nat` fvars in `bv_decide`
-  * [#5506](https://github.com/leanprover/lean4/pull/5506), [#5507](https://github.com/leanprover/lean4/pull/5507) add `bv_normalize` rules.
-  * [#5568](https://github.com/leanprover/lean4/pull/5568) generalize the `bv_normalize` pipeline to support more general preprocessing passes
-  * [#5573](https://github.com/leanprover/lean4/pull/5573) gets `bv_normalize` up-to-date with the current `BitVec` rewrites
-  * Cleanups: [#5408](https://github.com/leanprover/lean4/pull/5408), [#5493](https://github.com/leanprover/lean4/pull/5493), [#5578](https://github.com/leanprover/lean4/pull/5578)
-
-
-* Elaboration improvements
-  * [#5266](https://github.com/leanprover/lean4/pull/5266) preserve order of overapplied arguments in `elab_as_elim` procedure.
-  * [#5510](https://github.com/leanprover/lean4/pull/5510) generalizes `elab_as_elim` to allow arbitrary motive applications.
-  * [#5283](https://github.com/leanprover/lean4/pull/5283), [#5512](https://github.com/leanprover/lean4/pull/5512) refine how named arguments suppress explicit arguments. Breaking change: some previously omitted explicit arguments may need explicit `_` arguments now.
-  * [#5376](https://github.com/leanprover/lean4/pull/5376) modifies projection instance binder info for instances, making parameters that are instance implicit in the type be implicit.
-  * [#5402](https://github.com/leanprover/lean4/pull/5402) localizes universe metavariable errors to `let` bindings and `fun` binders if possible. Makes "cannot synthesize metavariable" errors take precedence over unsolved universe level errors.
-  * [#5419](https://github.com/leanprover/lean4/pull/5419) must not reduce `ite` in the discriminant of `match`-expression when reducibility setting is `.reducible`
-  * [#5474](https://github.com/leanprover/lean4/pull/5474) have autoparams report parameter/field on failure
-  * [#5530](https://github.com/leanprover/lean4/pull/5530) makes automatic instance names about types with hygienic names be hygienic.
-
-* Deriving handlers
-  * [#5432](https://github.com/leanprover/lean4/pull/5432) makes `Repr` deriving instance handle explicit type parameters
-
-* Functional induction
-  * [#5364](https://github.com/leanprover/lean4/pull/5364) adds more equalities in context, more careful cleanup.
-
-* Linters
-  * [#5335](https://github.com/leanprover/lean4/pull/5335) fixes the unused variables linter complaining about match/tactic combinations
-  * [#5337](https://github.com/leanprover/lean4/pull/5337) fixes the unused variables linter complaining about some wildcard patterns
-
-* Other fixes
-  * [#4768](https://github.com/leanprover/lean4/pull/4768) fixes a parse error when `..` appears with a `.` on the next line
-
-* Metaprogramming
-  * [#3090](https://github.com/leanprover/lean4/pull/3090) handles level parameters in `Meta.evalExpr` (@eric-wieser)  
-  * [#5401](https://github.com/leanprover/lean4/pull/5401) instance for `Inhabited (TacticM α)` (@alexkeizer)
-  * [#5412](https://github.com/leanprover/lean4/pull/5412) expose Kernel.check for debugging purposes
-  * [#5556](https://github.com/leanprover/lean4/pull/5556) improves the "invalid projection" type inference error in `inferType`.
-  * [#5587](https://github.com/leanprover/lean4/pull/5587) allows `MVarId.assertHypotheses` to set `BinderInfo` and `LocalDeclKind`.
-  * [#5588](https://github.com/leanprover/lean4/pull/5588) adds `MVarId.tryClearMany'`, a variant of `MVarId.tryClearMany`.
-
-
-
-### Language server, widgets, and IDE extensions
-
-* [#5205](https://github.com/leanprover/lean4/pull/5205) decreases the latency of auto-completion in tactic blocks.
-* [#5237](https://github.com/leanprover/lean4/pull/5237) fixes symbol occurrence highlighting in VS Code not highlighting occurrences when moving the text cursor into the identifier from the right.
-* [#5257](https://github.com/leanprover/lean4/pull/5257) fixes several instances of incorrect auto-completions being reported.
-* [#5299](https://github.com/leanprover/lean4/pull/5299) allows auto-completion to report completions for global identifiers when the elaborator fails to provide context-specific auto-completions.
-* [#5312](https://github.com/leanprover/lean4/pull/5312) fixes the server breaking when changing whitespace after the module header.
-* [#5322](https://github.com/leanprover/lean4/pull/5322) fixes several instances of auto-completion reporting non-existent namespaces.
-* [#5428](https://github.com/leanprover/lean4/pull/5428) makes sure to always report some recent file range as progress when waiting for elaboration.
-
-
-### Pretty printing
-
-* [#4979](https://github.com/leanprover/lean4/pull/4979) make pretty printer escape identifiers that are tokens.
-* [#5389](https://github.com/leanprover/lean4/pull/5389) makes formatter use the current token table.
-* [#5513](https://github.com/leanprover/lean4/pull/5513) use breakable instead of unbreakable whitespace when formatting tokens.
-
-
-### Library
-
-* [#5222](https://github.com/leanprover/lean4/pull/5222) reduces allocations in `Json.compress`.
-* [#5231](https://github.com/leanprover/lean4/pull/5231) upstreams `Zero` and `NeZero`
-* [#5292](https://github.com/leanprover/lean4/pull/5292) refactors `Lean.Elab.Deriving.FromToJson` (@arthur-adjedj)
-* [#5415](https://github.com/leanprover/lean4/pull/5415) implements `Repr Empty` (@TomasPuverle)
-* [#5421](https://github.com/leanprover/lean4/pull/5421) implements `To/FromJSON Empty` (@TomasPuverle)
-
-* Logic
-  * [#5263](https://github.com/leanprover/lean4/pull/5263) allows simplifying `dite_not`/`decide_not` with only `Decidable (¬p)`.
-  * [#5268](https://github.com/leanprover/lean4/pull/5268) fixes binders on `ite_eq_left_iff`
-  * [#5284](https://github.com/leanprover/lean4/pull/5284) turns off `Inhabited (Sum α β)` instances
-  * [#5355](https://github.com/leanprover/lean4/pull/5355) adds simp lemmas for `LawfulBEq`
-  * [#5374](https://github.com/leanprover/lean4/pull/5374) add `Nonempty` instances for products, allowing more `partial` functions to elaborate successfully
-  * [#5447](https://github.com/leanprover/lean4/pull/5447) updates Pi instance names
-  * [#5454](https://github.com/leanprover/lean4/pull/5454) makes some instance arguments implicit
-  * [#5456](https://github.com/leanprover/lean4/pull/5456) adds `heq_comm`
-  * [#5529](https://github.com/leanprover/lean4/pull/5529) moves `@[simp]` from `exists_prop'` to `exists_prop`
-
-* `Bool`
-  * [#5228](https://github.com/leanprover/lean4/pull/5228) fills gaps in Bool lemmas
-  * [#5332](https://github.com/leanprover/lean4/pull/5332) adds notation `^^` for Bool.xor
-  * [#5351](https://github.com/leanprover/lean4/pull/5351) removes `_root_.and` (and or/not/xor) and instead exports/uses `Bool.and` (etc.).
-
-* `BitVec`
-  * [#5240](https://github.com/leanprover/lean4/pull/5240) removes BitVec simps with complicated RHS
-  * [#5247](https://github.com/leanprover/lean4/pull/5247) `BitVec.getElem_zeroExtend`
-  * [#5248](https://github.com/leanprover/lean4/pull/5248) simp lemmas for BitVec, improving confluence
-  * [#5249](https://github.com/leanprover/lean4/pull/5249) removes `@[simp]` from some BitVec lemmas
-  * [#5252](https://github.com/leanprover/lean4/pull/5252) changes `BitVec.intMin/Max` from abbrev to def
-  * [#5278](https://github.com/leanprover/lean4/pull/5278) adds `BitVec.getElem_truncate` (@tobiasgrosser)
-  * [#5281](https://github.com/leanprover/lean4/pull/5281) adds udiv/umod bitblasting for `bv_decide` (@bollu)
-  * [#5297](https://github.com/leanprover/lean4/pull/5297) `BitVec` unsigned order theoretic results
-  * [#5313](https://github.com/leanprover/lean4/pull/5313) adds more basic BitVec ordering theory for UInt
-  * [#5314](https://github.com/leanprover/lean4/pull/5314) adds `toNat_sub_of_le` (@bollu)
-  * [#5357](https://github.com/leanprover/lean4/pull/5357) adds `BitVec.truncate` lemmas
-  * [#5358](https://github.com/leanprover/lean4/pull/5358) introduces `BitVec.setWidth` to unify zeroExtend and truncate (@tobiasgrosser)
-  * [#5361](https://github.com/leanprover/lean4/pull/5361) some BitVec GetElem lemmas
-  * [#5385](https://github.com/leanprover/lean4/pull/5385) adds `BitVec.ofBool_[and|or|xor]_ofBool` theorems (@tobiasgrosser)
-  * [#5404](https://github.com/leanprover/lean4/pull/5404) more of `BitVec.getElem_*` (@tobiasgrosser)
-  * [#5410](https://github.com/leanprover/lean4/pull/5410) BitVec analogues of `Nat.{mul_two, two_mul, mul_succ, succ_mul}` (@bollu)
-  * [#5411](https://github.com/leanprover/lean4/pull/5411) `BitVec.toNat_{add,sub,mul_of_lt}` for BitVector non-overflow reasoning (@bollu)
-  * [#5413](https://github.com/leanprover/lean4/pull/5413) adds `_self`, `_zero`, and `_allOnes` for `BitVec.[and|or|xor]` (@tobiasgrosser)
-  * [#5416](https://github.com/leanprover/lean4/pull/5416) adds LawCommIdentity + IdempotentOp for `BitVec.[and|or|xor]` (@tobiasgrosser)
-  * [#5418](https://github.com/leanprover/lean4/pull/5418) decidable quantifers for BitVec
-  * [#5450](https://github.com/leanprover/lean4/pull/5450) adds `BitVec.toInt_[intMin|neg|neg_of_ne_intMin]` (@tobiasgrosser)
-  * [#5459](https://github.com/leanprover/lean4/pull/5459) missing BitVec lemmas
-  * [#5469](https://github.com/leanprover/lean4/pull/5469) adds `BitVec.[not_not, allOnes_shiftLeft_or_shiftLeft, allOnes_shiftLeft_and_shiftLeft]` (@luisacicolini)
-  * [#5478](https://github.com/leanprover/lean4/pull/5478) adds `BitVec.(shiftLeft_add_distrib, shiftLeft_ushiftRight)` (@luisacicolini)
-  * [#5487](https://github.com/leanprover/lean4/pull/5487) adds `sdiv_eq`, `smod_eq` to allow `sdiv`/`smod` bitblasting (@bollu)
-  * [#5491](https://github.com/leanprover/lean4/pull/5491) adds `BitVec.toNat_[abs|sdiv|smod]` (@tobiasgrosser)
-  * [#5492](https://github.com/leanprover/lean4/pull/5492) `BitVec.(not_sshiftRight, not_sshiftRight_not, getMsb_not, msb_not)` (@luisacicolini)
-  * [#5499](https://github.com/leanprover/lean4/pull/5499) `BitVec.Lemmas` - drop non-terminal simps (@tobiasgrosser)
-  * [#5505](https://github.com/leanprover/lean4/pull/5505) unsimps `BitVec.divRec_succ'`
-  * [#5508](https://github.com/leanprover/lean4/pull/5508) adds `BitVec.getElem_[add|add_add_bool|mul|rotateLeft|rotateRight…` (@tobiasgrosser)
-  * [#5554](https://github.com/leanprover/lean4/pull/5554) adds `Bitvec.[add, sub, mul]_eq_xor` and `width_one_cases` (@luisacicolini)
-
-* `List`
-  * [#5242](https://github.com/leanprover/lean4/pull/5242) improve naming for `List.mergeSort` lemmas
-  * [#5302](https://github.com/leanprover/lean4/pull/5302) provide `mergeSort` comparator autoParam
-  * [#5373](https://github.com/leanprover/lean4/pull/5373) fix name of `List.length_mergeSort`
-  * [#5377](https://github.com/leanprover/lean4/pull/5377) upstream `map_mergeSort`
-  * [#5378](https://github.com/leanprover/lean4/pull/5378) modify signature of lemmas about `mergeSort`
-  * [#5245](https://github.com/leanprover/lean4/pull/5245) avoid importing `List.Basic` without List.Impl
-  * [#5260](https://github.com/leanprover/lean4/pull/5260) review of List API
-  * [#5264](https://github.com/leanprover/lean4/pull/5264) review of List API
-  * [#5269](https://github.com/leanprover/lean4/pull/5269) remove HashMap's duplicated Pairwise and Sublist
-  * [#5271](https://github.com/leanprover/lean4/pull/5271) remove @[simp] from `List.head_mem` and similar
-  * [#5273](https://github.com/leanprover/lean4/pull/5273) lemmas about `List.attach`
-  * [#5275](https://github.com/leanprover/lean4/pull/5275) reverse direction of `List.tail_map`
-  * [#5277](https://github.com/leanprover/lean4/pull/5277) more `List.attach` lemmas
-  * [#5285](https://github.com/leanprover/lean4/pull/5285) `List.count` lemmas
-  * [#5287](https://github.com/leanprover/lean4/pull/5287) use boolean predicates in `List.filter`
-  * [#5289](https://github.com/leanprover/lean4/pull/5289) `List.mem_ite_nil_left` and analogues
-  * [#5293](https://github.com/leanprover/lean4/pull/5293) cleanup of `List.findIdx` / `List.take` lemmas
-  * [#5294](https://github.com/leanprover/lean4/pull/5294) switch primes on `List.getElem_take`
-  * [#5300](https://github.com/leanprover/lean4/pull/5300) more `List.findIdx` theorems
-  * [#5310](https://github.com/leanprover/lean4/pull/5310) fix `List.all/any` lemmas
-  * [#5311](https://github.com/leanprover/lean4/pull/5311) fix `List.countP` lemmas
-  * [#5316](https://github.com/leanprover/lean4/pull/5316) `List.tail` lemma
-  * [#5331](https://github.com/leanprover/lean4/pull/5331) fix implicitness of `List.getElem_mem`
-  * [#5350](https://github.com/leanprover/lean4/pull/5350) `List.replicate` lemmas
-  * [#5352](https://github.com/leanprover/lean4/pull/5352) `List.attachWith` lemmas
-  * [#5353](https://github.com/leanprover/lean4/pull/5353) `List.head_mem_head?`
-  * [#5360](https://github.com/leanprover/lean4/pull/5360) lemmas about `List.tail`
-  * [#5391](https://github.com/leanprover/lean4/pull/5391) review of `List.erase` / `List.find` lemmas
-  * [#5392](https://github.com/leanprover/lean4/pull/5392) `List.fold` / `attach` lemmas
-  * [#5393](https://github.com/leanprover/lean4/pull/5393) `List.fold` relators
-  * [#5394](https://github.com/leanprover/lean4/pull/5394) lemmas about `List.maximum?`
-  * [#5403](https://github.com/leanprover/lean4/pull/5403) theorems about `List.toArray`
-  * [#5405](https://github.com/leanprover/lean4/pull/5405) reverse direction of `List.set_map`
-  * [#5448](https://github.com/leanprover/lean4/pull/5448) add lemmas about `List.IsPrefix` (@Command-Master)
-  * [#5460](https://github.com/leanprover/lean4/pull/5460) missing `List.set_replicate_self`
-  * [#5518](https://github.com/leanprover/lean4/pull/5518) rename `List.maximum?` to `max?`
-  * [#5519](https://github.com/leanprover/lean4/pull/5519) upstream `List.fold` lemmas
-  * [#5520](https://github.com/leanprover/lean4/pull/5520) restore `@[simp]` on `List.getElem_mem` etc.
-  * [#5521](https://github.com/leanprover/lean4/pull/5521) List simp fixes
-  * [#5550](https://github.com/leanprover/lean4/pull/5550) `List.unattach` and simp lemmas
-  * [#5594](https://github.com/leanprover/lean4/pull/5594) induction-friendly `List.min?_cons`
-
-* `Array`
-  * [#5246](https://github.com/leanprover/lean4/pull/5246) cleanup imports of Array.Lemmas
-  * [#5255](https://github.com/leanprover/lean4/pull/5255) split Init.Data.Array.Lemmas for better bootstrapping
-  * [#5288](https://github.com/leanprover/lean4/pull/5288) rename `Array.data` to `Array.toList`
-  * [#5303](https://github.com/leanprover/lean4/pull/5303) cleanup of `List.getElem_append` variants
-  * [#5304](https://github.com/leanprover/lean4/pull/5304) `Array.not_mem_empty`
-  * [#5400](https://github.com/leanprover/lean4/pull/5400) reorganization in Array/Basic
-  * [#5420](https://github.com/leanprover/lean4/pull/5420) make `Array` functions either semireducible or use structural recursion
-  * [#5422](https://github.com/leanprover/lean4/pull/5422) refactor `DecidableEq (Array α)`
-  * [#5452](https://github.com/leanprover/lean4/pull/5452) refactor of Array
-  * [#5458](https://github.com/leanprover/lean4/pull/5458) cleanup of Array docstrings after refactor
-  * [#5461](https://github.com/leanprover/lean4/pull/5461) restore `@[simp]` on `Array.swapAt!_def`
-  * [#5465](https://github.com/leanprover/lean4/pull/5465) improve Array GetElem lemmas
-  * [#5466](https://github.com/leanprover/lean4/pull/5466) `Array.foldX` lemmas
-  * [#5472](https://github.com/leanprover/lean4/pull/5472) @[simp] lemmas about `List.toArray`
-  * [#5485](https://github.com/leanprover/lean4/pull/5485) reverse simp direction for `toArray_concat`
-  * [#5514](https://github.com/leanprover/lean4/pull/5514) `Array.eraseReps`
-  * [#5515](https://github.com/leanprover/lean4/pull/5515) upstream `Array.qsortOrd`
-  * [#5516](https://github.com/leanprover/lean4/pull/5516) upstream `Subarray.empty`
-  * [#5526](https://github.com/leanprover/lean4/pull/5526) fix name of `Array.length_toList`
-  * [#5527](https://github.com/leanprover/lean4/pull/5527) reduce use of deprecated lemmas in Array
-  * [#5534](https://github.com/leanprover/lean4/pull/5534) cleanup of Array GetElem lemmas
-  * [#5536](https://github.com/leanprover/lean4/pull/5536) fix `Array.modify` lemmas
-  * [#5551](https://github.com/leanprover/lean4/pull/5551) upstream `Array.flatten` lemmas
-  * [#5552](https://github.com/leanprover/lean4/pull/5552) switch obvious cases of array "bang"`[]!` indexing to rely on hypothesis (@TomasPuverle)
-  * [#5577](https://github.com/leanprover/lean4/pull/5577) add missing simp to `Array.size_feraseIdx`
-  * [#5586](https://github.com/leanprover/lean4/pull/5586) `Array/Option.unattach`
-
-* `Option`
-  * [#5272](https://github.com/leanprover/lean4/pull/5272) remove @[simp] from `Option.pmap/pbind` and add simp lemmas
-  * [#5307](https://github.com/leanprover/lean4/pull/5307) restoring Option simp confluence
-  * [#5354](https://github.com/leanprover/lean4/pull/5354) remove @[simp] from `Option.bind_map`
-  * [#5532](https://github.com/leanprover/lean4/pull/5532) `Option.attach`
-  * [#5539](https://github.com/leanprover/lean4/pull/5539) fix explicitness of `Option.mem_toList`
-
-* `Nat`
-  * [#5241](https://github.com/leanprover/lean4/pull/5241) add @[simp] to `Nat.add_eq_zero_iff`
-  * [#5261](https://github.com/leanprover/lean4/pull/5261) Nat bitwise lemmas
-  * [#5262](https://github.com/leanprover/lean4/pull/5262) `Nat.testBit_add_one` should not be a global simp lemma
-  * [#5267](https://github.com/leanprover/lean4/pull/5267) protect some Nat bitwise theorems
-  * [#5305](https://github.com/leanprover/lean4/pull/5305) rename Nat bitwise lemmas
-  * [#5306](https://github.com/leanprover/lean4/pull/5306) add `Nat.self_sub_mod` lemma
-  * [#5503](https://github.com/leanprover/lean4/pull/5503) restore @[simp] to upstreamed `Nat.lt_off_iff`
-
-* `Int`
-  * [#5301](https://github.com/leanprover/lean4/pull/5301) rename `Int.div/mod` to `Int.tdiv/tmod`
-  * [#5320](https://github.com/leanprover/lean4/pull/5320) add `ediv_nonneg_of_nonpos_of_nonpos` to DivModLemmas (@sakehl)
-
-* `Fin`
-  * [#5250](https://github.com/leanprover/lean4/pull/5250) missing lemma about `Fin.ofNat'`
-  * [#5356](https://github.com/leanprover/lean4/pull/5356) `Fin.ofNat'` uses `NeZero`
-  * [#5379](https://github.com/leanprover/lean4/pull/5379) remove some @[simp]s from Fin lemmas
-  * [#5380](https://github.com/leanprover/lean4/pull/5380) missing Fin @[simp] lemmas
-
-* `HashMap`
-  * [#5244](https://github.com/leanprover/lean4/pull/5244) (`DHashMap`|`HashMap`|`HashSet`).(`getKey?`|`getKey`|`getKey!`|`getKeyD`)
-  * [#5362](https://github.com/leanprover/lean4/pull/5362) remove the last use of `Lean.(HashSet|HashMap)`
-  * [#5369](https://github.com/leanprover/lean4/pull/5369) `HashSet.ofArray`
-  * [#5370](https://github.com/leanprover/lean4/pull/5370) `HashSet.partition`
-  * [#5581](https://github.com/leanprover/lean4/pull/5581) `Singleton`/`Insert`/`Union` instances for `HashMap`/`Set`
-  * [#5582](https://github.com/leanprover/lean4/pull/5582) `HashSet.all`/`any`
-  * [#5590](https://github.com/leanprover/lean4/pull/5590) adding `Insert`/`Singleton`/`Union` instances for `HashMap`/`Set.Raw`
-  * [#5591](https://github.com/leanprover/lean4/pull/5591) `HashSet.Raw.all/any`
-
-* `Monads`
-  * [#5463](https://github.com/leanprover/lean4/pull/5463) upstream some monad lemmas
-  * [#5464](https://github.com/leanprover/lean4/pull/5464) adjust simp attributes on monad lemmas
-  * [#5522](https://github.com/leanprover/lean4/pull/5522) more monadic simp lemmas
-
-* Simp lemma cleanup
-  * [#5251](https://github.com/leanprover/lean4/pull/5251) remove redundant simp annotations
-  * [#5253](https://github.com/leanprover/lean4/pull/5253) remove Int simp lemmas that can't fire
-  * [#5254](https://github.com/leanprover/lean4/pull/5254) variables appearing on both sides of an iff should be implicit
-  * [#5381](https://github.com/leanprover/lean4/pull/5381) cleaning up redundant simp lemmas
-
-
-### Compiler, runtime, and FFI
-
-* [#4685](https://github.com/leanprover/lean4/pull/4685) fixes a typo in the C `run_new_frontend` signature
-* [#4729](https://github.com/leanprover/lean4/pull/4729) has IR checker suggest using `noncomputable`
-* [#5143](https://github.com/leanprover/lean4/pull/5143) adds a shared library for Lake
-* [#5437](https://github.com/leanprover/lean4/pull/5437) removes (syntactically) duplicate imports (@euprunin)
-* [#5462](https://github.com/leanprover/lean4/pull/5462) updates `src/lake/lakefile.toml` to the adjusted Lake build process
-* [#5541](https://github.com/leanprover/lean4/pull/5541) removes new shared libs before build to better support Windows
-* [#5558](https://github.com/leanprover/lean4/pull/5558) make `lean.h` compile with MSVC (@kant2002)
-* [#5564](https://github.com/leanprover/lean4/pull/5564) removes non-conforming size-0 arrays (@eric-wieser)
-
-
-### Lake
-  * Reservoir build cache. Lake will now attempt to fetch a pre-built copy of the package from Reservoir before building it. This is only enabled for packages in the leanprover or leanprover-community organizations on versions indexed by Reservoir. Users can force Lake to build packages from the source by passing --no-cache on the CLI or by setting the  LAKE_NO_CACHE environment variable to true. [#5486](https://github.com/leanprover/lean4/pull/5486), [#5572](https://github.com/leanprover/lean4/pull/5572), [#5583](https://github.com/leanprover/lean4/pull/5583), [#5600](https://github.com/leanprover/lean4/pull/5600), [#5641](https://github.com/leanprover/lean4/pull/5641), [#5642](https://github.com/leanprover/lean4/pull/5642).
-  * [#5504](https://github.com/leanprover/lean4/pull/5504) lake new and lake init now produce TOML configurations by default.
-  * [#5878](https://github.com/leanprover/lean4/pull/5878) fixes a serious issue where Lake would delete path dependencies when attempting to cleanup a dependency required with an incorrect name.
-
-  * **Breaking changes**
-    * [#5641](https://github.com/leanprover/lean4/pull/5641) A Lake build of target within a package will no longer build a package's dependencies package-level extra target dependencies. At the technical level, a package's extraDep facet no longer transitively builds its dependencies’ extraDep facets (which include their extraDepTargets).
-
-### Documentation fixes
-
-* [#3918](https://github.com/leanprover/lean4/pull/3918) `@[builtin_doc]` attribute (@digama0)
-* [#4305](https://github.com/leanprover/lean4/pull/4305) explains the borrow syntax (@eric-wieser)
-* [#5349](https://github.com/leanprover/lean4/pull/5349) adds documentation for `groupBy.loop` (@vihdzp)
-* [#5473](https://github.com/leanprover/lean4/pull/5473) fixes typo in `BitVec.mul` docstring (@llllvvuu)
-* [#5476](https://github.com/leanprover/lean4/pull/5476) fixes typos in `Lean.MetavarContext`
-* [#5481](https://github.com/leanprover/lean4/pull/5481) removes mention of `Lean.withSeconds` (@alexkeizer)
-* [#5497](https://github.com/leanprover/lean4/pull/5497) updates documentation and tests for `toUIntX` functions (@TomasPuverle)
-* [#5087](https://github.com/leanprover/lean4/pull/5087) mentions that `inferType` does not ensure type correctness
-* Many fixes to spelling across the doc-strings, (@euprunin): [#5425](https://github.com/leanprover/lean4/pull/5425) [#5426](https://github.com/leanprover/lean4/pull/5426) [#5427](https://github.com/leanprover/lean4/pull/5427) [#5430](https://github.com/leanprover/lean4/pull/5430)  [#5431](https://github.com/leanprover/lean4/pull/5431) [#5434](https://github.com/leanprover/lean4/pull/5434) [#5435](https://github.com/leanprover/lean4/pull/5435) [#5436](https://github.com/leanprover/lean4/pull/5436) [#5438](https://github.com/leanprover/lean4/pull/5438) [#5439](https://github.com/leanprover/lean4/pull/5439) [#5440](https://github.com/leanprover/lean4/pull/5440) [#5599](https://github.com/leanprover/lean4/pull/5599)
-
-### Changes to CI
-
-* [#5343](https://github.com/leanprover/lean4/pull/5343) allows addition of `release-ci` label via comment (@thorimur)
-* [#5344](https://github.com/leanprover/lean4/pull/5344) sets check level correctly during workflow (@thorimur)
-* [#5444](https://github.com/leanprover/lean4/pull/5444) Mathlib's `lean-pr-testing-NNNN` branches should use Batteries' `lean-pr-testing-NNNN` branches
-* [#5489](https://github.com/leanprover/lean4/pull/5489) commit `lake-manifest.json` when updating `lean-pr-testing` branches
-* [#5490](https://github.com/leanprover/lean4/pull/5490) use separate secrets for commenting and branching in `pr-release.yml`
-
 v4.12.0
 ----------

--- a/doc/dev/bootstrap.md
+++ b/doc/dev/bootstrap.md
@@ -103,21 +103,10 @@ your PR using rebase merge, bypassing the merge queue.
 As written above, changes in meta code in the current stage usually will only
 affect later stages. This is an issue in two specific cases.

-* For the special case of *quotations*, it is desirable to have changes in builtin parsers affect them immediately: when the changes in the parser become active in the next stage, builtin macros implemented via quotations should generate syntax trees compatible with the new parser, and quotation patterns in builtin macros and elaborators should be able to match syntax created by the new parser and macros.
-  Since quotations capture the syntax tree structure during execution of the current stage and turn it into code for the next stage, we need to run the current stage's builtin parsers in quotations via the interpreter for this to work.
-  Caveats:
-  * We activate this behavior by default when building stage 1 by setting `-Dinternal.parseQuotWithCurrentStage=true`.
-    We force-disable it inside `macro/macro_rules/elab/elab_rules` via `suppressInsideQuot` as they are guaranteed not to run in the next stage and may need to be run in the current one, so the stage 0 parser is the correct one to use for them.
-    It may be necessary to extend this disabling to functions that contain quotations and are (exclusively) used by one of the mentioned commands. A function using quotations should never be used by both builtin and non-builtin macros/elaborators. Example: https://github.com/leanprover/lean4/blob/f70b7e5722da6101572869d87832494e2f8534b7/src/Lean/Elab/Tactic/Config.lean#L118-L122
-  * The parser needs to be reachable via an `import` statement, otherwise the version of the previous stage will silently be used.
-  * Only the parser code (`Parser.fn`) is affected; all metadata such as leading tokens is taken from the previous stage.
-
-  For an example, see https://github.com/leanprover/lean4/commit/f9dcbbddc48ccab22c7674ba20c5f409823b4cc1#diff-371387aed38bb02bf7761084fd9460e4168ae16d1ffe5de041b47d3ad2d22422R13
-
 * For *non-builtin* meta code such as `notation`s or `macro`s in
  `Notation.lean`, we expect changes to affect the current file and all later
  files of the same stage immediately, just like outside the stdlib. To ensure
-  this, we build stage 1 using `-Dinterpreter.prefer_native=false` -
+  this, we need to build the stage using `-Dinterpreter.prefer_native=false` -
  otherwise, when executing a macro, the interpreter would notice that there is
  already a native symbol available for this function and run it instead of the
  new IR, but the symbol is from the previous stage!
@@ -135,11 +124,26 @@ affect later stages. This is an issue in two specific cases.
  further stages (e.g. after an `update-stage0`) will then need to be compiled
  with the flag set to `false` again since they will expect the new signature.

-  When enabling `prefer_native`, we usually want to *disable* `parseQuotWithCurrentStage` as it would otherwise make quotations use the interpreter after all.
-  However, there is a specific case where we want to set both options to `true`: when we make changes to a non-builtin parser like `simp` that has a builtin elaborator, we cannot have the new parser be active outside of quotations in stage 1 as the builtin elaborator from stage 0 would not understand them; on the other hand, we need quotations in e.g. the builtin `simp` elaborator to produce the new syntax in the next stage.
-  As this issue usually affects only tactics, enabling `debug.byAsSorry` instead of `prefer_native` can be a simpler solution.
+  For an example, see https://github.com/leanprover/lean4/commit/da4c46370d85add64ef7ca5e7cc4638b62823fbb.

-  For a `prefer_native` example, see https://github.com/leanprover/lean4/commit/da4c46370d85add64ef7ca5e7cc4638b62823fbb.
+* For the special case of *quotations*, it is desirable to have changes in
+  built-in parsers affect them immediately: when the changes in the parser
+  become active in the next stage, macros implemented via quotations should
+  generate syntax trees compatible with the new parser, and quotation patterns
+  in macro and elaborators should be able to match syntax created by the new
+  parser and macros. Since quotations capture the syntax tree structure during
+  execution of the current stage and turn it into code for the next stage, we
+  need to run the current stage's built-in parsers in quotation via the
+  interpreter for this to work. Caveats:
+  * Since interpreting full parsers is not nearly as cheap and we rarely change
+    built-in syntax, this needs to be opted in using `-Dinternal.parseQuotWithCurrentStage=true`.
+  * The parser needs to be reachable via an `import` statement, otherwise the
+    version of the previous stage will silently be used.
+  * Only the parser code (`Parser.fn`) is affected; all metadata such as leading
+    tokens is taken from the previous stage.
+
+  For an example, see https://github.com/leanprover/lean4/commit/f9dcbbddc48ccab22c7674ba20c5f409823b4cc1#diff-371387aed38bb02bf7761084fd9460e4168ae16d1ffe5de041b47d3ad2d22422
+  (from before the flag defaulted to `false`).

 To modify either of these flags both for building and editing the stdlib, adjust
 the code in `stage0/src/stdlib_flags.h`. The flags will automatically be reset
--- a/doc/examples/interp.lean
+++ b/doc/examples/interp.lean
@@ -12,17 +12,17 @@ Remark: this example is based on an example found in the Idris manual.
 Vectors
 --------

-A `Vec` is a list of size `n` whose elements belong to a type `α`.
+A `Vector` is a list of size `n` whose elements belong to a type `α`.
 -/

-inductive Vec (α : Type u) : Nat → Type u
-  | nil : Vec α 0
-  | cons : α → Vec α n → Vec α (n+1)
+inductive Vector (α : Type u) : Nat → Type u
+  | nil : Vector α 0
+  | cons : α → Vector α n → Vector α (n+1)

 /-!
-We can overload the `List.cons` notation `::` and use it to create `Vec`s.
+We can overload the `List.cons` notation `::` and use it to create `Vector`s.
 -/
-infix:67 " :: " => Vec.cons
+infix:67 " :: " => Vector.cons

 /-!
 Now, we define the types of our simple functional language.
@@ -50,11 +50,11 @@ the builtin instance for `Add Int` as the solution.
 /-!
 Expressions are indexed by the types of the local variables, and the type of the expression itself.
 -/
-inductive HasType : Fin n → Vec Ty n → Ty → Type where
+inductive HasType : Fin n → Vector Ty n → Ty → Type where
  | stop : HasType 0 (ty :: ctx) ty
  | pop  : HasType k ctx ty → HasType k.succ (u :: ctx) ty

-inductive Expr : Vec Ty n → Ty → Type where
+inductive Expr : Vector Ty n → Ty → Type where
  | var   : HasType i ctx ty → Expr ctx ty
  | val   : Int → Expr ctx Ty.int
  | lam   : Expr (a :: ctx) ty → Expr ctx (Ty.fn a ty)
@@ -102,8 +102,8 @@ indexed over the types in scope. Since an environment is just another form of li
 to the vector of local variable types, we overload again the notation `::` so that we can use the usual list syntax.
 Given a proof that a variable is defined in the context, we can then produce a value from the environment.
 -/
-inductive Env : Vec Ty n → Type where
-  | nil  : Env Vec.nil
+inductive Env : Vector Ty n → Type where
+  | nil  : Env Vector.nil
  | cons : Ty.interp a → Env ctx → Env (a :: ctx)

 infix:67 " :: " => Env.cons
--- a/doc/examples/tc.lean
+++ b/doc/examples/tc.lean
@@ -82,7 +82,9 @@ theorem Expr.typeCheck_correct (h₁ : HasType e ty) (h₂ : e.typeCheck ≠ .un
 /-!
 Now, we prove that if `Expr.typeCheck e` returns `Maybe.unknown`, then forall `ty`, `HasType e ty` does not hold.
 The notation `e.typeCheck` is sugar for `Expr.typeCheck e`. Lean can infer this because we explicitly said that `e` has type `Expr`.
-The proof is by induction on `e` and case analysis. Note that the tactic `simp [typeCheck]` is applied to all goal generated by the `induction` tactic, and closes
+The proof is by induction on `e` and case analysis. The tactic `rename_i` is used to rename "inaccessible" variables.
+We say a variable is inaccessible if it is introduced by a tactic (e.g., `cases`) or has been shadowed by another variable introduced
+by the user. Note that the tactic `simp [typeCheck]` is applied to all goal generated by the `induction` tactic, and closes
 the cases corresponding to the constructors `Expr.nat` and `Expr.bool`.
 -/
 theorem Expr.typeCheck_complete {e : Expr} : e.typeCheck = .unknown → ¬ HasType e ty := by
--- a/doc/make/index.md
+++ b/doc/make/index.md
@@ -1,6 +1,6 @@
-These are instructions to set up a working development environment for those who wish to make changes to Lean itself. It is part of the [Development Guide](../dev/index.md).
+These are instructions to set up a working development environment for those who wish to make changes to Lean itself. It is part of the [Development Guide](doc/dev/index.md).

-We strongly suggest that new users instead follow the [Quickstart](../quickstart.md) to get started using Lean, since this sets up an environment that can automatically manage multiple Lean toolchain versions, which is necessary when working within the Lean ecosystem.
+We strongly suggest that new users instead follow the [Quickstart](doc/quickstart.md) to get started using Lean, since this sets up an environment that can automatically manage multiple Lean toolchain versions, which is necessary when working within the Lean ecosystem.

 Requirements
 ------------
--- a/flake.nix
+++ b/flake.nix
@@ -38,11 +38,7 @@
          # more convenient `ctest` output
          CTEST_OUTPUT_ON_FAILURE = 1;
        } // pkgs.lib.optionalAttrs pkgs.stdenv.isLinux {
-          GMP = (pkgsDist.gmp.override { withStatic = true; }).overrideAttrs (attrs:
-            pkgs.lib.optionalAttrs (pkgs.stdenv.system == "aarch64-linux") {
-              # would need additional linking setup on Linux aarch64, we don't use it anywhere else either
-              hardeningDisable = [ "stackprotector" ];
-            });
+          GMP = pkgsDist.gmp.override { withStatic = true; };
          LIBUV = pkgsDist.libuv.overrideAttrs (attrs: {
            configureFlags = ["--enable-static"];
            hardeningDisable = [ "stackprotector" ];
--- a/nix/bootstrap.nix
+++ b/nix/bootstrap.nix
@@ -170,7 +170,7 @@ lib.warn "The Nix-based build is deprecated" rec {
          ln -sf ${lean-all}/* .
        '';
        buildPhase = ''
-         ctest --output-junit test-results.xml --output-on-failure -E 'leancomptest_(doc_example|foreign)|leanlaketest_reverse-ffi|leanruntest_timeIO' -j$NIX_BUILD_CORES
+          ctest --output-junit test-results.xml --output-on-failure -E 'leancomptest_(doc_example|foreign)|leanlaketest_reverse-ffi' -j$NIX_BUILD_CORES
        '';
        installPhase = ''
          mkdir $out
--- a/script/prepare-llvm-linux.sh
+++ b/script/prepare-llvm-linux.sh
@@ -64,7 +64,7 @@ fi
 # use `-nostdinc` to make sure headers are not visible by default (in particular, not to `#include_next` in the clang headers),
 # but do not change sysroot so users can still link against system libs
 echo -n " -DLEANC_INTERNAL_FLAGS='-nostdinc -isystem ROOT/include/clang' -DLEANC_CC=ROOT/bin/clang"
-echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='-L ROOT/lib -L ROOT/lib/glibc ROOT/lib/glibc/libc_nonshared.a ROOT/lib/glibc/libpthread_nonshared.a -Wl,--as-needed -Wl,-Bstatic -lgmp -lunwind -luv -Wl,-Bdynamic -Wl,--no-as-needed -fuse-ld=lld'"
+echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='-L ROOT/lib -L ROOT/lib/glibc ROOT/lib/glibc/libc_nonshared.a ROOT/lib/glibc/libpthread_nonshared.a -Wl,--as-needed -Wl,-Bstatic -lgmp -lunwind -luv -lpthread -ldl -lrt -Wl,-Bdynamic -Wl,--no-as-needed -fuse-ld=lld'"
 # when not using the above flags, link GMP dynamically/as usual
 echo -n " -DLEAN_EXTRA_LINKER_FLAGS='-Wl,--as-needed -lgmp -luv -lpthread -ldl -lrt -Wl,--no-as-needed'"
 # do not set `LEAN_CC` for tests
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -10,15 +10,13 @@ endif()
 include(ExternalProject)
 project(LEAN CXX C)
 set(LEAN_VERSION_MAJOR 4)
-set(LEAN_VERSION_MINOR 15)
+set(LEAN_VERSION_MINOR 12)
 set(LEAN_VERSION_PATCH 0)
 set(LEAN_VERSION_IS_RELEASE 0)  # This number is 1 in the release revision, and 0 otherwise.
 set(LEAN_SPECIAL_VERSION_DESC "" CACHE STRING "Additional version description like 'nightly-2018-03-11'")
 set(LEAN_VERSION_STRING "${LEAN_VERSION_MAJOR}.${LEAN_VERSION_MINOR}.${LEAN_VERSION_PATCH}")
 if (LEAN_SPECIAL_VERSION_DESC)
  string(APPEND LEAN_VERSION_STRING "-${LEAN_SPECIAL_VERSION_DESC}")
-elseif (NOT LEAN_VERSION_IS_RELEASE)
-  string(APPEND LEAN_VERSION_STRING "-pre")
 endif()

 set(LEAN_PLATFORM_TARGET "" CACHE STRING "LLVM triple of the target platform")
@@ -51,8 +49,6 @@ option(LLVM               "LLVM"               OFF)
 option(USE_GITHASH        "GIT_HASH"           ON)
 # When ON we install LICENSE files to CMAKE_INSTALL_PREFIX
 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 thread storage is automatically finalized, it assumes platform support pthreads.
 # This option is important when using Lean as library that is invoked from a different programming language (e.g., Haskell).
 option(AUTO_THREAD_FINALIZATION "AUTO_THREAD_FINALIZATION" ON)
@@ -618,7 +614,7 @@ else()
    OUTPUT_NAME leancpp)
 endif()

-if((${STAGE} GREATER 0) AND CADICAL AND INSTALL_CADICAL)
+if((${STAGE} GREATER 0) AND CADICAL)
  add_custom_target(copy-cadical
    COMMAND cmake -E copy_if_different "${CADICAL}" "${CMAKE_BINARY_DIR}/bin/cadical${CMAKE_EXECUTABLE_SUFFIX}")
  add_dependencies(leancpp copy-cadical)
@@ -740,7 +736,7 @@ file(COPY ${LEAN_SOURCE_DIR}/bin/leanmake DESTINATION ${CMAKE_BINARY_DIR}/bin)

 install(DIRECTORY "${CMAKE_BINARY_DIR}/bin/" USE_SOURCE_PERMISSIONS DESTINATION bin)

-if (${STAGE} GREATER 0 AND CADICAL AND INSTALL_CADICAL)
+if (${STAGE} GREATER 0 AND CADICAL)
  install(PROGRAMS "${CADICAL}" DESTINATION bin)
 endif()

--- a/src/Init.lean
+++ b/src/Init.lean
@@ -36,4 +36,3 @@ import Init.Omega
 import Init.MacroTrace
 import Init.Grind
 import Init.While
-import Init.Syntax
--- a/src/Init/Control/Basic.lean
+++ b/src/Init/Control/Basic.lean
@@ -11,13 +11,8 @@ universe u v w
 /--
 A `ForIn'` instance, which handles `for h : x in c do`,
 can also handle `for x in x do` by ignoring `h`, and so provides a `ForIn` instance.
-
-Note that this instance will cause a potentially non-defeq duplication if both `ForIn` and `ForIn'`
-instances are provided for the same type.
 -/
-- We set the priority to 500 so it is below the default,
-- but still above the low priority instance from `Stream`.
-instance (priority := 500) instForInOfForIn' [ForIn' m ρ α d] : ForIn m ρ α where
+instance (priority := low) instForInOfForIn' [ForIn' m ρ α d] : ForIn m ρ α where
  forIn x b f := forIn' x b fun a _ => f a

@[simp] theorem forIn'_eq_forIn [d : Membership α ρ] [ForIn' m ρ α d] {β} [Monad m] (x : ρ) (b : β)
@@ -35,15 +30,6 @@ instance (priority := 500) instForInOfForIn' [ForIn' m ρ α d] : ForIn m ρ α
  simp [h]
  rfl

-/-- Extract the value from a `ForInStep`, ignoring whether it is `done` or `yield`. -/
-def ForInStep.value (x : ForInStep α) : α :=
-  match x with
-  | ForInStep.done b => b
-  | ForInStep.yield b => b
-
-@[simp] theorem ForInStep.value_done (b : β) : (ForInStep.done b).value = b := rfl
-@[simp] theorem ForInStep.value_yield (b : β) : (ForInStep.yield b).value = b := rfl
-
@[reducible]
 def Functor.mapRev {f : Type u → Type v} [Functor f] {α β : Type u} : f α → (α → β) → f β :=
  fun a f => f <$> a
--- a/src/Init/Control/Lawful/Instances.lean
+++ b/src/Init/Control/Lawful/Instances.lean
@@ -7,7 +7,6 @@ prelude
 import Init.Control.Lawful.Basic
 import Init.Control.Except
 import Init.Control.StateRef
-import Init.Ext

 open Function

@@ -15,7 +14,7 @@ open Function

 namespace ExceptT

-@[ext] theorem ext {x y : ExceptT ε m α} (h : x.run = y.run) : x = y := by
+theorem ext {x y : ExceptT ε m α} (h : x.run = y.run) : x = y := by
  simp [run] at h
  assumption

@@ -106,7 +105,7 @@ instance : LawfulFunctor (Except ε) := inferInstance

 namespace ReaderT

-@[ext] theorem ext {x y : ReaderT ρ m α} (h : ∀ ctx, x.run ctx = y.run ctx) : x = y := by
+theorem ext {x y : ReaderT ρ m α} (h : ∀ ctx, x.run ctx = y.run ctx) : x = y := by
  simp [run] at h
  exact funext h

@@ -168,7 +167,7 @@ instance [Monad m] [LawfulMonad m] : LawfulMonad (StateRefT' ω σ m) :=

 namespace StateT

-@[ext] theorem ext {x y : StateT σ m α} (h : ∀ s, x.run s = y.run s) : x = y :=
+theorem ext {x y : StateT σ m α} (h : ∀ s, x.run s = y.run s) : x = y :=
  funext h

@[simp] theorem run'_eq [Monad m] (x : StateT σ m α) (s : σ) : run' x s = (·.1) <$> run x s :=
--- a/src/Init/Conv.lean
+++ b/src/Init/Conv.lean
@@ -7,7 +7,6 @@ Notation for operators defined at Prelude.lean
 -/
 prelude
 import Init.Tactics
-import Init.Meta

 namespace Lean.Parser.Tactic.Conv

@@ -47,20 +46,12 @@ scoped syntax (name := withAnnotateState)
 /-- `skip` does nothing. -/
 syntax (name := skip) "skip" : conv

-/--
-Traverses into the left subterm of a binary operator.
-
-In general, for an `n`-ary operator, it traverses into the second to last argument.
-It is a synonym for `arg -2`.
-/
+/-- Traverses into the left subterm of a binary operator.
+(In general, for an `n`-ary operator, it traverses into the second to last argument.) -/
 syntax (name := lhs) "lhs" : conv

-/--
-Traverses into the right subterm of a binary operator.
-
-In general, for an `n`-ary operator, it traverses into the last argument.
-It is a synonym for `arg -1`.
-/
+/-- Traverses into the right subterm of a binary operator.
+(In general, for an `n`-ary operator, it traverses into the last argument.) -/
 syntax (name := rhs) "rhs" : conv

 /-- Traverses into the function of a (unary) function application.
@@ -83,17 +74,13 @@ subgoals for all the function arguments. For example, if the target is `f x y` t
 `congr` produces two subgoals, one for `x` and one for `y`. -/
 syntax (name := congr) "congr" : conv

-syntax argArg := "@"? "-"? num
-
 /--
 * `arg i` traverses into the `i`'th argument of the target. For example if the
  target is `f a b c d` then `arg 1` traverses to `a` and `arg 3` traverses to `c`.
-  The index may be negative; `arg -1` traverses into the last argument,
-  `arg -2` into the second-to-last argument, and so on.
 * `arg @i` is the same as `arg i` but it counts all arguments instead of just the
  explicit arguments.
 * `arg 0` traverses into the function. If the target is `f a b c d`, `arg 0` traverses into `f`. -/
-syntax (name := arg) "arg " argArg : conv
+syntax (name := arg) "arg " "@"? num : conv

 /-- `ext x` traverses into a binder (a `fun x => e` or `∀ x, e` expression)
 to target `e`, introducing name `x` in the process. -/
@@ -143,11 +130,11 @@ For example, if we are searching for `f _` in `f (f a) = f b`:
 syntax (name := pattern) "pattern " (occs)? term : conv

 /-- `rw [thm]` rewrites the target using `thm`. See the `rw` tactic for more information. -/
-syntax (name := rewrite) "rewrite" optConfig rwRuleSeq : conv
+syntax (name := rewrite) "rewrite" (config)? rwRuleSeq : conv

 /-- `simp [thm]` performs simplification using `thm` and marked `@[simp]` lemmas.
 See the `simp` tactic for more information. -/
-syntax (name := simp) "simp" optConfig (discharger)? (&" only")?
+syntax (name := simp) "simp" (config)? (discharger)? (&" only")?
  (" [" withoutPosition((simpStar <|> simpErase <|> simpLemma),*) "]")? : conv

 /--
@@ -164,7 +151,7 @@ example (a : Nat): (0 + 0) = a - a := by
    rw [← Nat.sub_self a]
 ```
 -/
-syntax (name := dsimp) "dsimp" optConfig (discharger)? (&" only")?
+syntax (name := dsimp) "dsimp" (config)? (discharger)? (&" only")?
  (" [" withoutPosition((simpErase <|> simpLemma),*) "]")? : conv

 /-- `simp_match` simplifies match expressions. For example,
@@ -260,12 +247,12 @@ macro (name := failIfSuccess) tk:"fail_if_success " s:convSeq : conv =>

 /-- `rw [rules]` applies the given list of rewrite rules to the target.
 See the `rw` tactic for more information. -/
-macro "rw" c:optConfig s:rwRuleSeq : conv => `(conv| rewrite $c:optConfig $s)
+macro "rw" c:(config)? s:rwRuleSeq : conv => `(conv| rewrite $[$c]? $s)

-/-- `erw [rules]` is a shorthand for `rw (transparency := .default) [rules]`.
+/-- `erw [rules]` is a shorthand for `rw (config := { transparency := .default }) [rules]`.
 This does rewriting up to unfolding of regular definitions (by comparison to regular `rw`
 which only unfolds `@[reducible]` definitions). -/
-macro "erw" c:optConfig s:rwRuleSeq : conv => `(conv| rw $[$(getConfigItems c)]* (transparency := .default) $s:rwRuleSeq)
+macro "erw" s:rwRuleSeq : conv => `(conv| rw (config := { transparency := .default }) $s)

 /-- `args` traverses into all arguments. Synonym for `congr`. -/
 macro "args" : conv => `(conv| congr)
@@ -276,7 +263,7 @@ macro "right" : conv => `(conv| rhs)
 /-- `intro` traverses into binders. Synonym for `ext`. -/
 macro "intro" xs:(ppSpace colGt ident)* : conv => `(conv| ext $xs*)

-syntax enterArg := ident <|> argArg
+syntax enterArg := ident <|> ("@"? num)

 /-- `enter [arg, ...]` is a compact way to describe a path to a subterm.
 It is a shorthand for other conv tactics as follows:
@@ -285,7 +272,12 @@ It is a shorthand for other conv tactics as follows:
 * `enter [x]` (where `x` is an identifier) is equivalent to `ext x`.
 For example, given the target `f (g a (fun x => x b))`, `enter [1, 2, x, 1]`
 will traverse to the subterm `b`. -/
-syntax (name := enter) "enter" " [" withoutPosition(enterArg,+) "]" : conv
+syntax "enter" " [" withoutPosition(enterArg,+) "]" : conv
+macro_rules
+  | `(conv| enter [$i:num]) => `(conv| arg $i)
+  | `(conv| enter [@$i]) => `(conv| arg @$i)
+  | `(conv| enter [$id:ident]) => `(conv| ext $id)
+  | `(conv| enter [$arg, $args,*]) => `(conv| (enter [$arg]; enter [$args,*]))

 /-- The `apply thm` conv tactic is the same as `apply thm` the tactic.
 There are no restrictions on `thm`, but strange results may occur if `thm`
--- a/src/Init/Core.lean
+++ b/src/Init/Core.lean
@@ -861,21 +861,16 @@ theorem Exists.elim {α : Sort u} {p : α → Prop} {b : Prop}

 /-! # Decidable -/

-@[simp] theorem decide_true (h : Decidable True) : @decide True h = true :=
+theorem decide_true_eq_true (h : Decidable True) : @decide True h = true :=
  match h with
  | isTrue _  => rfl
  | isFalse h => False.elim <| h ⟨⟩

-@[simp] theorem decide_false (h : Decidable False) : @decide False h = false :=
+theorem decide_false_eq_false (h : Decidable False) : @decide False h = false :=
  match h with
  | isFalse _ => rfl
  | isTrue h  => False.elim h

-set_option linter.missingDocs false in
-@[deprecated decide_true (since := "2024-11-05")] abbrev decide_true_eq_true := decide_true
-set_option linter.missingDocs false in
-@[deprecated decide_false (since := "2024-11-05")] abbrev decide_false_eq_false := decide_false
-
 /-- Similar to `decide`, but uses an explicit instance -/
@[inline] def toBoolUsing {p : Prop} (d : Decidable p) : Bool :=
  decide (h := d)
@@ -1922,12 +1917,12 @@ represents an element of `Squash α` the same as `α` itself
 `Squash.lift` will extract a value in any subsingleton `β` from a function on `α`,
 while `Nonempty.rec` can only do the same when `β` is a proposition.
 -/
-def Squash (α : Sort u) := Quot (fun (_ _ : α) => True)
+def Squash (α : Type u) := Quot (fun (_ _ : α) => True)

 /-- The canonical quotient map into `Squash α`. -/
-def Squash.mk {α : Sort u} (x : α) : Squash α := Quot.mk _ x
+def Squash.mk {α : Type u} (x : α) : Squash α := Quot.mk _ x

-theorem Squash.ind {α : Sort u} {motive : Squash α → Prop} (h : ∀ (a : α), motive (Squash.mk a)) : ∀ (q : Squash α), motive q :=
+theorem Squash.ind {α : Type u} {motive : Squash α → Prop} (h : ∀ (a : α), motive (Squash.mk a)) : ∀ (q : Squash α), motive q :=
  Quot.ind h

 /-- If `β` is a subsingleton, then a function `α → β` lifts to `Squash α → β`. -/
--- a/src/Init/Data.lean
+++ b/src/Init/Data.lean
@@ -42,5 +42,3 @@ import Init.Data.PLift
 import Init.Data.Zero
 import Init.Data.NeZero
 import Init.Data.Function
-import Init.Data.RArray
-import Init.Data.Vector
--- a/src/Init/Data/Array.lean
+++ b/src/Init/Data/Array.lean
@@ -17,6 +17,3 @@ import Init.Data.Array.TakeDrop
 import Init.Data.Array.Bootstrap
 import Init.Data.Array.GetLit
 import Init.Data.Array.MapIdx
-import Init.Data.Array.Set
-import Init.Data.Array.Monadic
-import Init.Data.Array.FinRange
--- a/src/Init/Data/Array/Attach.lean
+++ b/src/Init/Data/Array/Attach.lean
@@ -10,17 +10,6 @@ import Init.Data.List.Attach

 namespace Array

-/--
-`O(n)`. Partial map. If `f : Π a, P a → β` is a partial function defined on
-`a : α` satisfying `P`, then `pmap f l h` is essentially the same as `map f l`
-but is defined only when all members of `l` satisfy `P`, using the proof
-to apply `f`.
-
-We replace this at runtime with a more efficient version via the `csimp` lemma `pmap_eq_pmapImpl`.
-/
-def pmap {P : α → Prop} (f : ∀ a, P a → β) (l : Array α) (H : ∀ a ∈ l, P a) : Array β :=
-  (l.toList.pmap f (fun a m => H a (mem_def.mpr m))).toArray
-
 /--
 Unsafe implementation of `attachWith`, taking advantage of the fact that the representation of
 `Array {x // P x}` is the same as the input `Array α`.
@@ -46,10 +35,6 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
    l.toArray.attach = (l.attachWith (· ∈ l.toArray) (by simp)).toArray := by
  simp [attach]

-@[simp] theorem _root_.List.pmap_toArray {l : List α} {P : α → Prop} {f : ∀ a, P a → β} {H : ∀ a ∈ l.toArray, P a} :
-    l.toArray.pmap f H = (l.pmap f (by simpa using H)).toArray := by
-  simp [pmap]
-
@[simp] theorem toList_attachWith {l : Array α} {P : α → Prop} {H : ∀ x ∈ l, P x} :
   (l.attachWith P H).toList = l.toList.attachWith P (by simpa [mem_toList] using H) := by
  simp [attachWith]
@@ -58,387 +43,6 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
    l.attach.toList = l.toList.attachWith (· ∈ l) (by simp [mem_toList]) := by
  simp [attach]

-@[simp] theorem toList_pmap {l : Array α} {P : α → Prop} {f : ∀ a, P a → β} {H : ∀ a ∈ l, P a} :
-    (l.pmap f H).toList = l.toList.pmap f (fun a m => H a (mem_def.mpr m)) := by
-  simp [pmap]
-
-/-- Implementation of `pmap` using the zero-copy version of `attach`. -/
-@[inline] private def pmapImpl {P : α → Prop} (f : ∀ a, P a → β) (l : Array α) (H : ∀ a ∈ l, P a) :
-    Array β := (l.attachWith _ H).map fun ⟨x, h'⟩ => f x h'
-
-@[csimp] private theorem pmap_eq_pmapImpl : @pmap = @pmapImpl := by
-  funext α β p f L h'
-  cases L
-  simp only [pmap, pmapImpl, List.attachWith_toArray, List.map_toArray, mk.injEq, List.map_attachWith]
-  apply List.pmap_congr_left
-  intro a m h₁ h₂
-  congr
-
-@[simp] theorem pmap_empty {P : α → Prop} (f : ∀ a, P a → β) : pmap f #[] (by simp) = #[] := rfl
-
-@[simp] theorem pmap_push {P : α → Prop} (f : ∀ a, P a → β) (a : α) (l : Array α) (h : ∀ b ∈ l.push a, P b) :
-    pmap f (l.push a) h =
-      (pmap f l (fun a m => by simp at h; exact h a (.inl m))).push (f a (h a (by simp))) := by
-  simp [pmap]
-
-@[simp] theorem attach_empty : (#[] : Array α).attach = #[] := rfl
-
-@[simp] theorem attachWith_empty {P : α → Prop} (H : ∀ x ∈ #[], P x) : (#[] : Array α).attachWith P H = #[] := rfl
-
-@[simp] theorem _root_.List.attachWith_mem_toArray {l : List α} :
-    l.attachWith (fun x => x ∈ l.toArray) (fun x h => by simpa using h) =
-      l.attach.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
-  simp only [List.attachWith, List.attach, List.map_pmap]
-  apply List.pmap_congr_left
-  simp
-
-@[simp]
-theorem pmap_eq_map (p : α → Prop) (f : α → β) (l : Array α) (H) :
-    @pmap _ _ p (fun a _ => f a) l H = map f l := by
-  cases l; simp
-
-theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a, q a → β} (l : Array α) {H₁ H₂}
-    (h : ∀ a ∈ l, ∀ (h₁ h₂), f a h₁ = g a h₂) : pmap f l H₁ = pmap g l H₂ := by
-  cases l
-  simp only [mem_toArray] at h
-  simp only [List.pmap_toArray, mk.injEq]
-  rw [List.pmap_congr_left _ h]
-
-theorem map_pmap {p : α → Prop} (g : β → γ) (f : ∀ a, p a → β) (l H) :
-    map g (pmap f l H) = pmap (fun a h => g (f a h)) l H := by
-  cases l
-  simp [List.map_pmap]
-
-theorem pmap_map {p : β → Prop} (g : ∀ b, p b → γ) (f : α → β) (l H) :
-    pmap g (map f l) H = pmap (fun a h => g (f a) h) l fun _ h => H _ (mem_map_of_mem _ h) := by
-  cases l
-  simp [List.pmap_map]
-
-theorem attach_congr {l₁ l₂ : Array α} (h : l₁ = l₂) :
-    l₁.attach = l₂.attach.map (fun x => ⟨x.1, h ▸ x.2⟩) := by
-  subst h
-  simp
-
-theorem attachWith_congr {l₁ l₂ : Array α} (w : l₁ = l₂) {P : α → Prop} {H : ∀ x ∈ l₁, P x} :
-    l₁.attachWith P H = l₂.attachWith P fun _ h => H _ (w ▸ h) := by
-  subst w
-  simp
-
-@[simp] theorem attach_push {a : α} {l : Array α} :
-    (l.push a).attach =
-      (l.attach.map (fun ⟨x, h⟩ => ⟨x, mem_push_of_mem a h⟩)).push ⟨a, by simp⟩ := by
-  cases l
-  rw [attach_congr (List.push_toArray _ _)]
-  simp [Function.comp_def]
-
-@[simp] theorem attachWith_push {a : α} {l : Array α} {P : α → Prop} {H : ∀ x ∈ l.push a, P x} :
-    (l.push a).attachWith P H =
-      (l.attachWith P (fun x h => by simp at H; exact H x (.inl h))).push ⟨a, H a (by simp)⟩ := by
-  cases l
-  simp [attachWith_congr (List.push_toArray _ _)]
-
-theorem pmap_eq_map_attach {p : α → Prop} (f : ∀ a, p a → β) (l H) :
-    pmap f l H = l.attach.map fun x => f x.1 (H _ x.2) := by
-  cases l
-  simp [List.pmap_eq_map_attach]
-
-theorem attach_map_coe (l : Array α) (f : α → β) :
-    (l.attach.map fun (i : {i // i ∈ l}) => f i) = l.map f := by
-  cases l
-  simp [List.attach_map_coe]
-
-theorem attach_map_val (l : Array α) (f : α → β) : (l.attach.map fun i => f i.val) = l.map f :=
-  attach_map_coe _ _
-
-@[simp]
-theorem attach_map_subtype_val (l : Array α) : l.attach.map Subtype.val = l := by
-  cases l; simp
-
-theorem attachWith_map_coe {p : α → Prop} (f : α → β) (l : Array α) (H : ∀ a ∈ l, p a) :
-    ((l.attachWith p H).map fun (i : { i // p i}) => f i) = l.map f := by
-  cases l; simp
-
-theorem attachWith_map_val {p : α → Prop} (f : α → β) (l : Array α) (H : ∀ a ∈ l, p a) :
-    ((l.attachWith p H).map fun i => f i.val) = l.map f :=
-  attachWith_map_coe _ _ _
-
-@[simp]
-theorem attachWith_map_subtype_val {p : α → Prop} (l : Array α) (H : ∀ a ∈ l, p a) :
-    (l.attachWith p H).map Subtype.val = l := by
-  cases l; simp
-
-@[simp]
-theorem mem_attach (l : Array α) : ∀ x, x ∈ l.attach
-  | ⟨a, h⟩ => by
-    have := mem_map.1 (by rw [attach_map_subtype_val] <;> exact h)
-    rcases this with ⟨⟨_, _⟩, m, rfl⟩
-    exact m
-
-@[simp]
-theorem mem_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H b} :
-    b ∈ pmap f l H ↔ ∃ (a : _) (h : a ∈ l), f a (H a h) = b := by
-  simp only [pmap_eq_map_attach, mem_map, mem_attach, true_and, Subtype.exists, eq_comm]
-
-theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {l H} {a} (h : a ∈ l) :
-    f a (H a h) ∈ pmap f l H := by
-  rw [mem_pmap]
-  exact ⟨a, h, rfl⟩
-
-@[simp]
-theorem size_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H} : (pmap f l H).size = l.size := by
-  cases l; simp
-
-@[simp]
-theorem size_attach {L : Array α} : L.attach.size = L.size := by
-  cases L; simp
-
-@[simp]
-theorem size_attachWith {p : α → Prop} {l : Array α} {H} : (l.attachWith p H).size = l.size := by
-  cases l; simp
-
-@[simp]
-theorem pmap_eq_empty_iff {p : α → Prop} {f : ∀ a, p a → β} {l H} : pmap f l H = #[] ↔ l = #[] := by
-  cases l; simp
-
-theorem pmap_ne_empty_iff {P : α → Prop} (f : (a : α) → P a → β) {xs : Array α}
-    (H : ∀ (a : α), a ∈ xs → P a) : xs.pmap f H ≠ #[] ↔ xs ≠ #[] := by
-  cases xs; simp
-
-theorem pmap_eq_self {l : Array α} {p : α → Prop} (hp : ∀ (a : α), a ∈ l → p a)
-    (f : (a : α) → p a → α) : l.pmap f hp = l ↔ ∀ a (h : a ∈ l), f a (hp a h) = a := by
-  cases l; simp [List.pmap_eq_self]
-
-@[simp]
-theorem attach_eq_empty_iff {l : Array α} : l.attach = #[] ↔ l = #[] := by
-  cases l; simp
-
-theorem attach_ne_empty_iff {l : Array α} : l.attach ≠ #[] ↔ l ≠ #[] := by
-  cases l; simp
-
-@[simp]
-theorem attachWith_eq_empty_iff {l : Array α} {P : α → Prop} {H : ∀ a ∈ l, P a} :
-    l.attachWith P H = #[] ↔ l = #[] := by
-  cases l; simp
-
-theorem attachWith_ne_empty_iff {l : Array α} {P : α → Prop} {H : ∀ a ∈ l, P a} :
-    l.attachWith P H ≠ #[] ↔ l ≠ #[] := by
-  cases l; simp
-
-@[simp]
-theorem getElem?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : Array α} (h : ∀ a ∈ l, p a) (n : Nat) :
-    (pmap f l h)[n]? = Option.pmap f l[n]? fun x H => h x (mem_of_getElem? H) := by
-  cases l; simp
-
-@[simp]
-theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : Array α} (h : ∀ a ∈ l, p a) {n : Nat}
-    (hn : n < (pmap f l h).size) :
-    (pmap f l h)[n] =
-      f (l[n]'(@size_pmap _ _ p f l h ▸ hn))
-        (h _ (getElem_mem (@size_pmap _ _ p f l h ▸ hn))) := by
-  cases l; simp
-
-@[simp]
-theorem getElem?_attachWith {xs : Array α} {i : Nat} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
-    (xs.attachWith P H)[i]? = xs[i]?.pmap Subtype.mk (fun _ a => H _ (mem_of_getElem? a)) :=
-  getElem?_pmap ..
-
-@[simp]
-theorem getElem?_attach {xs : Array α} {i : Nat} :
-    xs.attach[i]? = xs[i]?.pmap Subtype.mk (fun _ a => mem_of_getElem? a) :=
-  getElem?_attachWith
-
-@[simp]
-theorem getElem_attachWith {xs : Array α} {P : α → Prop} {H : ∀ a ∈ xs, P a}
-    {i : Nat} (h : i < (xs.attachWith P H).size) :
-    (xs.attachWith P H)[i] = ⟨xs[i]'(by simpa using h), H _ (getElem_mem (by simpa using h))⟩ :=
-  getElem_pmap ..
-
-@[simp]
-theorem getElem_attach {xs : Array α} {i : Nat} (h : i < xs.attach.size) :
-    xs.attach[i] = ⟨xs[i]'(by simpa using h), getElem_mem (by simpa using h)⟩ :=
-  getElem_attachWith h
-
-theorem foldl_pmap (l : Array α) {P : α → Prop} (f : (a : α) → P a → β)
-  (H : ∀ (a : α), a ∈ l → P a) (g : γ → β → γ) (x : γ) :
-    (l.pmap f H).foldl g x = l.attach.foldl (fun acc a => g acc (f a.1 (H _ a.2))) x := by
-  rw [pmap_eq_map_attach, foldl_map]
-
-theorem foldr_pmap (l : Array α) {P : α → Prop} (f : (a : α) → P a → β)
-  (H : ∀ (a : α), a ∈ l → P a) (g : β → γ → γ) (x : γ) :
-    (l.pmap f H).foldr g x = l.attach.foldr (fun a acc => g (f a.1 (H _ a.2)) acc) x := by
-  rw [pmap_eq_map_attach, foldr_map]
-
-/--
-If we fold over `l.attach` with a function that ignores the membership predicate,
-we get the same results as folding over `l` directly.
-
-This is useful when we need to use `attach` to show termination.
-
-Unfortunately this can't be applied by `simp` because of the higher order unification problem,
-and even when rewriting we need to specify the function explicitly.
-See however `foldl_subtype` below.
-/
-theorem foldl_attach (l : Array α) (f : β → α → β) (b : β) :
-    l.attach.foldl (fun acc t => f acc t.1) b = l.foldl f b := by
-  rcases l with ⟨l⟩
-  simp only [List.attach_toArray, List.attachWith_mem_toArray, List.map_attach, size_toArray,
-    List.length_pmap, List.foldl_toArray', mem_toArray, List.foldl_subtype]
-  congr
-  ext
-  simpa using fun a => List.mem_of_getElem? a
-
-/--
-If we fold over `l.attach` with a function that ignores the membership predicate,
-we get the same results as folding over `l` directly.
-
-This is useful when we need to use `attach` to show termination.
-
-Unfortunately this can't be applied by `simp` because of the higher order unification problem,
-and even when rewriting we need to specify the function explicitly.
-See however `foldr_subtype` below.
-/
-theorem foldr_attach (l : Array α) (f : α → β → β) (b : β) :
-    l.attach.foldr (fun t acc => f t.1 acc) b = l.foldr f b := by
-  rcases l with ⟨l⟩
-  simp only [List.attach_toArray, List.attachWith_mem_toArray, List.map_attach, size_toArray,
-    List.length_pmap, List.foldr_toArray', mem_toArray, List.foldr_subtype]
-  congr
-  ext
-  simpa using fun a => List.mem_of_getElem? a
-
-theorem attach_map {l : Array α} (f : α → β) :
-    (l.map f).attach = l.attach.map (fun ⟨x, h⟩ => ⟨f x, mem_map_of_mem f h⟩) := by
-  cases l
-  ext <;> simp
-
-theorem attachWith_map {l : Array α} (f : α → β) {P : β → Prop} {H : ∀ (b : β), b ∈ l.map f → P b} :
-    (l.map f).attachWith P H = (l.attachWith (P ∘ f) (fun _ h => H _ (mem_map_of_mem f h))).map
-      fun ⟨x, h⟩ => ⟨f x, h⟩ := by
-  cases l
-  ext
-  · simp
-  · simp only [List.map_toArray, List.attachWith_toArray, List.getElem_toArray,
-      List.getElem_attachWith, List.getElem_map, Function.comp_apply]
-    erw [List.getElem_attachWith] -- Why is `erw` needed here?
-
-theorem map_attachWith {l : Array α} {P : α → Prop} {H : ∀ (a : α), a ∈ l → P a}
-    (f : { x // P x } → β) :
-    (l.attachWith P H).map f =
-      l.pmap (fun a (h : a ∈ l ∧ P a) => f ⟨a, H _ h.1⟩) (fun a h => ⟨h, H a h⟩) := by
-  cases l
-  ext <;> simp
-
-/-- See also `pmap_eq_map_attach` for writing `pmap` in terms of `map` and `attach`. -/
-theorem map_attach {l : Array α} (f : { x // x ∈ l } → β) :
-    l.attach.map f = l.pmap (fun a h => f ⟨a, h⟩) (fun _ => id) := by
-  cases l
-  ext <;> simp
-
-theorem attach_filterMap {l : Array α} {f : α → Option β} :
-    (l.filterMap f).attach = l.attach.filterMap
-      fun ⟨x, h⟩ => (f x).pbind (fun b m => some ⟨b, mem_filterMap.mpr ⟨x, h, m⟩⟩) := by
-  cases l
-  rw [attach_congr (List.filterMap_toArray f _)]
-  simp [List.attach_filterMap, List.map_filterMap, Function.comp_def]
-
-theorem attach_filter {l : Array α} (p : α → Bool) :
-    (l.filter p).attach = l.attach.filterMap
-      fun x => if w : p x.1 then some ⟨x.1, mem_filter.mpr ⟨x.2, w⟩⟩ else none := by
-  cases l
-  rw [attach_congr (List.filter_toArray p _)]
-  simp [List.attach_filter, List.map_filterMap, Function.comp_def]
-
-- We are still missing here `attachWith_filterMap` and `attachWith_filter`.
-- Also missing are `filterMap_attach`, `filter_attach`, `filterMap_attachWith` and `filter_attachWith`.
-
-theorem pmap_pmap {p : α → Prop} {q : β → Prop} (g : ∀ a, p a → β) (f : ∀ b, q b → γ) (l H₁ H₂) :
-    pmap f (pmap g l H₁) H₂ =
-      pmap (α := { x // x ∈ l }) (fun a h => f (g a h) (H₂ (g a h) (mem_pmap_of_mem a.2))) l.attach
-        (fun a _ => H₁ a a.2) := by
-  cases l
-  simp [List.pmap_pmap, List.pmap_map]
-
-@[simp] theorem pmap_append {p : ι → Prop} (f : ∀ a : ι, p a → α) (l₁ l₂ : Array ι)
-    (h : ∀ a ∈ l₁ ++ l₂, p a) :
-    (l₁ ++ l₂).pmap f h =
-      (l₁.pmap f fun a ha => h a (mem_append_left l₂ ha)) ++
-        l₂.pmap f fun a ha => h a (mem_append_right l₁ ha) := by
-  cases l₁
-  cases l₂
-  simp
-
-theorem pmap_append' {p : α → Prop} (f : ∀ a : α, p a → β) (l₁ l₂ : Array α)
-    (h₁ : ∀ a ∈ l₁, p a) (h₂ : ∀ a ∈ l₂, p a) :
-    ((l₁ ++ l₂).pmap f fun a ha => (mem_append.1 ha).elim (h₁ a) (h₂ a)) =
-      l₁.pmap f h₁ ++ l₂.pmap f h₂ :=
-  pmap_append f l₁ l₂ _
-
-@[simp] theorem attach_append (xs ys : Array α) :
-    (xs ++ ys).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_append_left ys h⟩) ++
-      ys.attach.map fun ⟨x, h⟩ => ⟨x, mem_append_right xs h⟩ := by
-  cases xs
-  cases ys
-  rw [attach_congr (List.append_toArray _ _)]
-  simp [List.attach_append, Function.comp_def]
-
-@[simp] theorem attachWith_append {P : α → Prop} {xs ys : Array α}
-    {H : ∀ (a : α), a ∈ xs ++ ys → P a} :
-    (xs ++ ys).attachWith P H = xs.attachWith P (fun a h => H a (mem_append_left ys h)) ++
-      ys.attachWith P (fun a h => H a (mem_append_right xs h)) := by
-  simp [attachWith, attach_append, map_pmap, pmap_append]
-
-@[simp] theorem pmap_reverse {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
-    (H : ∀ (a : α), a ∈ xs.reverse → P a) :
-    xs.reverse.pmap f H = (xs.pmap f (fun a h => H a (by simpa using h))).reverse := by
-  induction xs <;> simp_all
-
-theorem reverse_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
-    (H : ∀ (a : α), a ∈ xs → P a) :
-    (xs.pmap f H).reverse = xs.reverse.pmap f (fun a h => H a (by simpa using h)) := by
-  rw [pmap_reverse]
-
-@[simp] theorem attachWith_reverse {P : α → Prop} {xs : Array α}
-    {H : ∀ (a : α), a ∈ xs.reverse → P a} :
-    xs.reverse.attachWith P H =
-      (xs.attachWith P (fun a h => H a (by simpa using h))).reverse := by
-  cases xs
-  simp
-
-theorem reverse_attachWith {P : α → Prop} {xs : Array α}
-    {H : ∀ (a : α), a ∈ xs → P a} :
-    (xs.attachWith P H).reverse = (xs.reverse.attachWith P (fun a h => H a (by simpa using h))) := by
-  cases xs
-  simp
-
-@[simp] theorem attach_reverse (xs : Array α) :
-    xs.reverse.attach = xs.attach.reverse.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
-  cases xs
-  rw [attach_congr (List.reverse_toArray _)]
-  simp
-
-theorem reverse_attach (xs : Array α) :
-    xs.attach.reverse = xs.reverse.attach.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
-  cases xs
-  simp
-
-@[simp] theorem back?_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
-    (H : ∀ (a : α), a ∈ xs → P a) :
-    (xs.pmap f H).back? = xs.attach.back?.map fun ⟨a, m⟩ => f a (H a m) := by
-  cases xs
-  simp
-
-@[simp] theorem back?_attachWith {P : α → Prop} {xs : Array α}
-    {H : ∀ (a : α), a ∈ xs → P a} :
-    (xs.attachWith P H).back? = xs.back?.pbind (fun a h => some ⟨a, H _ (mem_of_back?_eq_some h)⟩) := by
-  cases xs
-  simp
-
-@[simp]
-theorem back?_attach {xs : Array α} :
-    xs.attach.back? = xs.back?.pbind fun a h => some ⟨a, mem_of_back?_eq_some h⟩ := by
-  cases xs
-  simp
-
 /-! ## unattach

 `Array.unattach` is the (one-sided) inverse of `Array.attach`. It is a synonym for `Array.map Subtype.val`.
@@ -479,7 +83,7 @@ def unattach {α : Type _} {p : α → Prop} (l : Array { x // p x }) := l.map (

@[simp] theorem unattach_attach {l : Array α} : l.attach.unattach = l := by
  cases l
-  simp only [List.attach_toArray, List.unattach_toArray, List.unattach_attachWith]
+  simp

@[simp] theorem unattach_attachWith {p : α → Prop} {l : Array α}
    {H : ∀ a ∈ l, p a} :
@@ -487,15 +91,6 @@ def unattach {α : Type _} {p : α → Prop} (l : Array { x // p x }) := l.map (
  cases l
  simp

-@[simp] theorem getElem?_unattach {p : α → Prop} {l : Array { x // p x }} (i : Nat) :
-    l.unattach[i]? = l[i]?.map Subtype.val := by
-  simp [unattach]
-
-@[simp] theorem getElem_unattach
-    {p : α → Prop} {l : Array { x // p x }} (i : Nat) (h : i < l.unattach.size) :
-    l.unattach[i] = (l[i]'(by simpa using h)).1 := by
-  simp [unattach]
-
 /-! ### Recognizing higher order functions using a function that only depends on the value. -/

 /--
--- a/src/Init/Data/Array/Basic.lean
+++ b/src/Init/Data/Array/Basic.lean
@@ -12,8 +12,6 @@ import Init.Data.Repr
 import Init.Data.ToString.Basic
 import Init.GetElem
 import Init.Data.List.ToArray
-import Init.Data.Array.Set
-
 universe u v w

 /-! ### Array literal syntax -/
@@ -31,8 +29,7 @@ namespace Array

 /-! ### Preliminary theorems -/

-@[simp] theorem size_set (a : Array α) (i : Nat) (v : α) (h : i < a.size) :
-    (set a i v h).size = a.size :=
+@[simp] theorem size_set (a : Array α) (i : Fin a.size) (v : α) : (set a i v).size = a.size :=
  List.length_set ..

@[simp] theorem size_push (a : Array α) (v : α) : (push a v).size = a.size + 1 :=
@@ -144,7 +141,7 @@ def uget (a : @& Array α) (i : USize) (h : i.toNat < a.size) : α :=
   `fset` may be slightly slower than `uset`. -/
@[extern "lean_array_uset"]
 def uset (a : Array α) (i : USize) (v : α) (h : i.toNat < a.size) : Array α :=
-  a.set i.toNat v h
+  a.set ⟨i.toNat, h⟩ v

@[extern "lean_array_pop"]
 def pop (a : Array α) : Array α where
@@ -166,15 +163,14 @@ This will perform the update destructively provided that `a` has a reference
 count of 1 when called.
 -/
@[extern "lean_array_fswap"]
-def swap (a : Array α) (i j : @& Nat) (hi : i < a.size := by get_elem_tactic) (hj : j < a.size := by get_elem_tactic) : Array α :=
-  let v₁ := a[i]
-  let v₂ := a[j]
+def swap (a : Array α) (i j : @& Fin a.size) : Array α :=
+  let v₁ := a.get i
+  let v₂ := a.get j
  let a'  := a.set i v₂
-  a'.set j v₁ (Nat.lt_of_lt_of_eq hj (size_set a i v₂ _).symm)
+  a'.set (size_set a i v₂ ▸ j) v₁

-@[simp] theorem size_swap (a : Array α) (i j : Nat) {hi hj} : (a.swap i j hi hj).size = a.size := by
-  show ((a.set i a[j]).set j a[i]
-    (Nat.lt_of_lt_of_eq hj (size_set a i a[j] _).symm)).size = a.size
+@[simp] theorem size_swap (a : Array α) (i j : Fin a.size) : (a.swap i j).size = a.size := by
+  show ((a.set i (a.get j)).set (size_set a i _ ▸ j) (a.get i)).size = a.size
  rw [size_set, size_set]

 /--
@@ -184,14 +180,12 @@ This will perform the update destructively provided that `a` has a reference
 count of 1 when called.
 -/
@[extern "lean_array_swap"]
-def swapIfInBounds (a : Array α) (i j : @& Nat) : Array α :=
+def swap! (a : Array α) (i j : @& Nat) : Array α :=
  if h₁ : i < a.size then
-  if h₂ : j < a.size then swap a i j
+  if h₂ : j < a.size then swap a ⟨i, h₁⟩ ⟨j, h₂⟩
  else a
  else a

-@[deprecated swapIfInBounds (since := "2024-11-24")] abbrev swap! := @swapIfInBounds
-
 /-! ### GetElem instance for `USize`, backed by `uget` -/

 instance : GetElem (Array α) USize α fun xs i => i.toNat < xs.size where
@@ -236,31 +230,29 @@ def ofFn {n} (f : Fin n → α) : Array α := go 0 (mkEmpty n) where

 /-- The array `#[0, 1, ..., n - 1]`. -/
 def range (n : Nat) : Array Nat :=
-  ofFn fun (i : Fin n) => i
+  n.fold (flip Array.push) (mkEmpty n)

 def singleton (v : α) : Array α :=
  mkArray 1 v

-def back! [Inhabited α] (a : Array α) : α :=
+def back [Inhabited α] (a : Array α) : α :=
  a.get! (a.size - 1)

-@[deprecated back! (since := "2024-10-31")] abbrev back := @back!
-
 def get? (a : Array α) (i : Nat) : Option α :=
  if h : i < a.size then some a[i] else none

 def back? (a : Array α) : Option α :=
-  a[a.size - 1]?
+  a.get? (a.size - 1)

-@[inline] def swapAt (a : Array α) (i : Nat) (v : α) (hi : i < a.size := by get_elem_tactic) : α × Array α :=
-  let e := a[i]
+@[inline] def swapAt (a : Array α) (i : Fin a.size) (v : α) : α × Array α :=
+  let e := a.get i
  let a := a.set i v
  (e, a)

@[inline]
 def swapAt! (a : Array α) (i : Nat) (v : α) : α × Array α :=
  if h : i < a.size then
-    swapAt a i v
+    swapAt a ⟨i, h⟩ v
  else
    have : Inhabited (α × Array α) := ⟨(v, a)⟩
    panic! ("index " ++ toString i ++ " out of bounds")
@@ -277,22 +269,24 @@ def take (a : Array α) (n : Nat) : Array α :=
@[inline]
 unsafe def modifyMUnsafe [Monad m] (a : Array α) (i : Nat) (f : α → m α) : m (Array α) := do
  if h : i < a.size then
-    let v                := a[i]
+    let idx : Fin a.size := ⟨i, h⟩
+    let v                := a.get idx
    -- Replace a[i] by `box(0)`.  This ensures that `v` remains unshared if possible.
    -- Note: we assume that arrays have a uniform representation irrespective
    -- of the element type, and that it is valid to store `box(0)` in any array.
-    let a'               := a.set i (unsafeCast ())
+    let a'               := a.set idx (unsafeCast ())
    let v ← f v
-    pure <| a'.set i v (Nat.lt_of_lt_of_eq h (size_set a ..).symm)
+    pure <| a'.set (size_set a .. ▸ idx) v
  else
    pure a

@[implemented_by modifyMUnsafe]
 def modifyM [Monad m] (a : Array α) (i : Nat) (f : α → m α) : m (Array α) := do
  if h : i < a.size then
-    let v   := a[i]
+    let idx := ⟨i, h⟩
+    let v   := a.get idx
    let v ← f v
-    pure <| a.set i v
+    pure <| a.set idx v
  else
    pure a

@@ -308,6 +302,37 @@ def modifyOp (self : Array α) (idx : Nat) (f : α → α) : Array α :=
  We claim this unsafe implementation is correct because an array cannot have more than `usizeSz` elements in our runtime.

  This kind of low level trick can be removed with a little bit of compiler support. For example, if the compiler simplifies `as.size < usizeSz` to true. -/
+@[inline] unsafe def forInUnsafe {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (b : β) (f : α → β → m (ForInStep β)) : m β :=
+  let sz := as.usize
+  let rec @[specialize] loop (i : USize) (b : β) : m β := do
+    if i < sz then
+      let a := as.uget i lcProof
+      match (← f a b) with
+      | ForInStep.done  b => pure b
+      | ForInStep.yield b => loop (i+1) b
+    else
+      pure b
+  loop 0 b
+
+/-- Reference implementation for `forIn` -/
+@[implemented_by Array.forInUnsafe]
+protected def forIn {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (b : β) (f : α → β → m (ForInStep β)) : m β :=
+  let rec loop (i : Nat) (h : i ≤ as.size) (b : β) : m β := do
+    match i, h with
+    | 0,   _ => pure b
+    | i+1, h =>
+      have h' : i < as.size            := Nat.lt_of_lt_of_le (Nat.lt_succ_self i) h
+      have : as.size - 1 < as.size     := Nat.sub_lt (Nat.zero_lt_of_lt h') (by decide)
+      have : as.size - 1 - i < as.size := Nat.lt_of_le_of_lt (Nat.sub_le (as.size - 1) i) this
+      match (← f as[as.size - 1 - i] b) with
+      | ForInStep.done b  => pure b
+      | ForInStep.yield b => loop i (Nat.le_of_lt h') b
+  loop as.size (Nat.le_refl _) b
+
+instance : ForIn m (Array α) α where
+  forIn := Array.forIn
+
+/-- See comment at `forInUnsafe` -/
@[inline] unsafe def forIn'Unsafe {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (b : β) (f : (a : α) → a ∈ as → β → m (ForInStep β)) : m β :=
  let sz := as.usize
  let rec @[specialize] loop (i : USize) (b : β) : m β := do
@@ -338,9 +363,7 @@ protected def forIn' {α : Type u} {β : Type v} {m : Type v → Type w} [Monad
 instance : ForIn' m (Array α) α inferInstance where
  forIn' := Array.forIn'

-- No separate `ForIn` instance is required because it can be derived from `ForIn'`.
-
-/-- See comment at `forIn'Unsafe` -/
+/-- See comment at `forInUnsafe` -/
@[inline]
 unsafe def foldlMUnsafe {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : β → α → m β) (init : β) (as : Array α) (start := 0) (stop := as.size) : m β :=
  let rec @[specialize] fold (i : USize) (stop : USize) (b : β) : m β := do
@@ -375,7 +398,7 @@ def foldlM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : β
  else
    fold as.size (Nat.le_refl _)

-/-- See comment at `forIn'Unsafe` -/
+/-- See comment at `forInUnsafe` -/
@[inline]
 unsafe def foldrMUnsafe {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → β → m β) (init : β) (as : Array α) (start := as.size) (stop := 0) : m β :=
  let rec @[specialize] fold (i : USize) (stop : USize) (b : β) : m β := do
@@ -414,7 +437,7 @@ def foldrM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α
  else
    pure init

-/-- See comment at `forIn'Unsafe` -/
+/-- See comment at `forInUnsafe` -/
@[inline]
 unsafe def mapMUnsafe {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m β) (as : Array α) : m (Array β) :=
  let sz := as.usize
@@ -445,8 +468,6 @@ def mapM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α
  decreasing_by simp_wf; decreasing_trivial_pre_omega
  map 0 (mkEmpty as.size)

-@[deprecated mapM (since := "2024-11-11")] abbrev sequenceMap := @mapM
-
 /-- Variant of `mapIdxM` which receives the index as a `Fin as.size`. -/
@[inline]
 def mapFinIdxM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m]
@@ -459,15 +480,15 @@ def mapFinIdxM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m]
        rw [← inv, Nat.add_assoc, Nat.add_comm 1 j, Nat.add_comm]
        apply Nat.le_add_right
      have : i + (j + 1) = as.size := by rw [← inv, Nat.add_comm j 1, Nat.add_assoc]
-      map i (j+1) this (bs.push (← f ⟨j, j_lt⟩ (as.get j j_lt)))
+      map i (j+1) this (bs.push (← f ⟨j, j_lt⟩ (as.get ⟨j, j_lt⟩)))
  map as.size 0 rfl (mkEmpty as.size)

@[inline]
-def mapIdxM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : Nat → α → m β) (as : Array α) : m (Array β) :=
+def mapIdxM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (f : Nat → α → m β) : m (Array β) :=
  as.mapFinIdxM fun i a => f i a

@[inline]
-def findSomeM? {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m (Option β)) (as : Array α) : m (Option β) := do
+def findSomeM? {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (f : α → m (Option β)) : m (Option β) := do
  for a in as do
    match (← f a) with
    | some b => return b
@@ -475,14 +496,14 @@ def findSomeM? {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f
  return none

@[inline]
-def findM? {α : Type} {m : Type → Type} [Monad m] (p : α → m Bool) (as : Array α) : m (Option α) := do
+def findM? {α : Type} {m : Type → Type} [Monad m] (as : Array α) (p : α → m Bool) : m (Option α) := do
  for a in as do
    if (← p a) then
      return a
  return none

@[inline]
-def findIdxM? [Monad m] (p : α → m Bool) (as : Array α) : m (Option Nat) := do
+def findIdxM? [Monad m] (as : Array α) (p : α → m Bool) : m (Option Nat) := do
  let mut i := 0
  for a in as do
    if (← p a) then
@@ -534,7 +555,7 @@ def allM {α : Type u} {m : Type → Type w} [Monad m] (p : α → m Bool) (as :
  return !(← as.anyM (start := start) (stop := stop) fun v => return !(← p v))

@[inline]
-def findSomeRevM? {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m (Option β)) (as : Array α) : m (Option β) :=
+def findSomeRevM? {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (f : α → m (Option β)) : m (Option β) :=
  let rec @[specialize] find : (i : Nat) → i ≤ as.size → m (Option β)
    | 0,   _ => pure none
    | i+1, h => do
@@ -548,7 +569,7 @@ def findSomeRevM? {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m]
  find as.size (Nat.le_refl _)

@[inline]
-def findRevM? {α : Type} {m : Type → Type w} [Monad m] (p : α → m Bool) (as : Array α) : m (Option α) :=
+def findRevM? {α : Type} {m : Type → Type w} [Monad m] (as : Array α) (p : α → m Bool) : m (Option α) :=
  as.findSomeRevM? fun a => return if (← p a) then some a else none

@[inline]
@@ -577,7 +598,7 @@ def mapFinIdx {α : Type u} {β : Type v} (as : Array α) (f : Fin as.size →
  Id.run <| as.mapFinIdxM f

@[inline]
-def mapIdx {α : Type u} {β : Type v} (f : Nat → α → β) (as : Array α) : Array β :=
+def mapIdx {α : Type u} {β : Type v} (as : Array α) (f : Nat → α → β) : Array β :=
  Id.run <| as.mapIdxM f

 /-- Turns `#[a, b]` into `#[(a, 0), (b, 1)]`. -/
@@ -585,29 +606,29 @@ def zipWithIndex (arr : Array α) : Array (α × Nat) :=
  arr.mapIdx fun i a => (a, i)

@[inline]
-def find? {α : Type} (p : α → Bool) (as : Array α) : Option α :=
+def find? {α : Type} (as : Array α) (p : α → Bool) : Option α :=
  Id.run <| as.findM? p

@[inline]
-def findSome? {α : Type u} {β : Type v} (f : α → Option β) (as : Array α) : Option β :=
+def findSome? {α : Type u} {β : Type v} (as : Array α) (f : α → Option β) : Option β :=
  Id.run <| as.findSomeM? f

@[inline]
-def findSome! {α : Type u} {β : Type v} [Inhabited β] (f : α → Option β) (a : Array α) : β :=
-  match a.findSome? f with
+def findSome! {α : Type u} {β : Type v} [Inhabited β] (a : Array α) (f : α → Option β) : β :=
+  match findSome? a f with
  | some b => b
  | none   => panic! "failed to find element"

@[inline]
-def findSomeRev? {α : Type u} {β : Type v} (f : α → Option β) (as : Array α) : Option β :=
+def findSomeRev? {α : Type u} {β : Type v} (as : Array α) (f : α → Option β) : Option β :=
  Id.run <| as.findSomeRevM? f

@[inline]
-def findRev? {α : Type} (p : α → Bool) (as : Array α) : Option α :=
+def findRev? {α : Type} (as : Array α) (p : α → Bool) : Option α :=
  Id.run <| as.findRevM? p

@[inline]
-def findIdx? {α : Type u} (p : α → Bool) (as : Array α) : Option Nat :=
+def findIdx? {α : Type u} (as : Array α) (p : α → Bool) : Option Nat :=
  let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
  loop (j : Nat) :=
    if h : j < as.size then
@@ -616,20 +637,14 @@ def findIdx? {α : Type u} (p : α → Bool) (as : Array α) : Option Nat :=
    decreasing_by simp_wf; decreasing_trivial_pre_omega
  loop 0

-@[inline]
-def findFinIdx? {α : Type u} (p : α → Bool) (as : Array α) : Option (Fin as.size) :=
-  let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
-  loop (j : Nat) :=
-    if h : j < as.size then
-      if p as[j] then some ⟨j, h⟩ else loop (j + 1)
-    else none
-    decreasing_by simp_wf; decreasing_trivial_pre_omega
-  loop 0
+def getIdx? [BEq α] (a : Array α) (v : α) : Option Nat :=
+  a.findIdx? fun a => a == v

@[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
 def indexOfAux [BEq α] (a : Array α) (v : α) (i : Nat) : Option (Fin a.size) :=
  if h : i < a.size then
-    if a[i] == v then some ⟨i, h⟩
+    let idx : Fin a.size := ⟨i, h⟩;
+    if a.get idx == v then some idx
    else indexOfAux a v (i+1)
  else none
 decreasing_by simp_wf; decreasing_trivial_pre_omega
@@ -637,10 +652,6 @@ decreasing_by simp_wf; decreasing_trivial_pre_omega
 def indexOf? [BEq α] (a : Array α) (v : α) : Option (Fin a.size) :=
  indexOfAux a v 0

-@[deprecated indexOf? (since := "2024-11-20")]
-def getIdx? [BEq α] (a : Array α) (v : α) : Option Nat :=
-  a.findIdx? fun a => a == v
-
@[inline]
 def any (as : Array α) (p : α → Bool) (start := 0) (stop := as.size) : Bool :=
  Id.run <| as.anyM p start stop
@@ -749,7 +760,7 @@ where
  loop (as : Array α) (i : Nat) (j : Fin as.size) :=
    if h : i < j then
      have := termination h
-      let as := as.swap i j (Nat.lt_trans h j.2)
+      let as := as.swap ⟨i, Nat.lt_trans h j.2⟩ j
      have : j-1 < as.size := by rw [size_swap]; exact Nat.lt_of_le_of_lt (Nat.pred_le _) j.2
      loop as (i+1) ⟨j-1, this⟩
    else
@@ -758,7 +769,7 @@ where
@[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
 def popWhile (p : α → Bool) (as : Array α) : Array α :=
  if h : as.size > 0 then
-    if p (as[as.size - 1]'(Nat.sub_lt h (by decide))) then
+    if p (as.get ⟨as.size - 1, Nat.sub_lt h (by decide)⟩) then
      popWhile p as.pop
    else
      as
@@ -770,7 +781,7 @@ def takeWhile (p : α → Bool) (as : Array α) : Array α :=
  let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
  go (i : Nat) (r : Array α) : Array α :=
    if h : i < as.size then
-      let a := as[i]
+      let a := as.get ⟨i, h⟩
      if p a then
        go (i+1) (r.push a)
      else
@@ -780,63 +791,49 @@ def takeWhile (p : α → Bool) (as : Array α) : Array α :=
    decreasing_by simp_wf; decreasing_trivial_pre_omega
  go 0 #[]

-/--
-Remove the element at a given index from an array without a runtime bounds checks,
-using a `Nat` index and a tactic-provided bound.
+/-- Remove the element at a given index from an array without bounds checks, using a `Fin` index.

-This function takes worst case O(n) time because
-it has to backshift all elements at positions greater than `i`.-/
+  This function takes worst case O(n) time because
+  it has to backshift all elements at positions greater than `i`.-/
@[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
-def eraseIdx (a : Array α) (i : Nat) (h : i < a.size := by get_elem_tactic) : Array α :=
-  if h' : i + 1 < a.size then
-    let a' := a.swap (i + 1) i
-    a'.eraseIdx (i + 1) (by simp [a', h'])
+def feraseIdx (a : Array α) (i : Fin a.size) : Array α :=
+  if h : i.val + 1 < a.size then
+    let a' := a.swap ⟨i.val + 1, h⟩ i
+    let i' : Fin a'.size := ⟨i.val + 1, by simp [a', h]⟩
+    a'.feraseIdx i'
  else
    a.pop
-termination_by a.size - i
-decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ h
+termination_by a.size - i.val
+decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ i.isLt

 -- This is required in `Lean.Data.PersistentHashMap`.
-@[simp] theorem size_eraseIdx (a : Array α) (i : Nat) (h) : (a.eraseIdx i h).size = a.size - 1 := by
-  induction a, i, h using Array.eraseIdx.induct with
-  | @case1 a i h h' a' ih =>
-    unfold eraseIdx
-    simp [h', a', ih]
-  | case2 a i h h' =>
-    unfold eraseIdx
-    simp [h']
+@[simp] theorem size_feraseIdx (a : Array α) (i : Fin a.size) : (a.feraseIdx i).size = a.size - 1 := by
+  induction a, i using Array.feraseIdx.induct with
+  | @case1 a i h a' _ ih =>
+    unfold feraseIdx
+    simp [h, a', ih]
+  | case2 a i h =>
+    unfold feraseIdx
+    simp [h]

 /-- Remove the element at a given index from an array, or do nothing if the index is out of bounds.

  This function takes worst case O(n) time because
  it has to backshift all elements at positions greater than `i`.-/
-def eraseIdxIfInBounds (a : Array α) (i : Nat) : Array α :=
-  if h : i < a.size then a.eraseIdx i h else a
-
-/-- Remove the element at a given index from an array, or panic if the index is out of bounds.
-
-This function takes worst case O(n) time because
-it has to backshift all elements at positions greater than `i`. -/
-def eraseIdx! (a : Array α) (i : Nat) : Array α :=
-  if h : i < a.size then a.eraseIdx i h else panic! "invalid index"
+def eraseIdx (a : Array α) (i : Nat) : Array α :=
+  if h : i < a.size then a.feraseIdx ⟨i, h⟩ else a

 def erase [BEq α] (as : Array α) (a : α) : Array α :=
  match as.indexOf? a with
  | none   => as
-  | some i => as.eraseIdx i
-
-/-- Erase the first element that satisfies the predicate `p`. -/
-def eraseP (as : Array α) (p : α → Bool) : Array α :=
-  match as.findIdx? p with
-  | none   => as
-  | some i => as.eraseIdxIfInBounds i
+  | some i => as.feraseIdx i

 /-- Insert element `a` at position `i`. -/
-@[inline] def insertIdx (as : Array α) (i : Nat) (a : α) (_ : i ≤ as.size := by get_elem_tactic) : Array α :=
+@[inline] def insertAt (as : Array α) (i : Fin (as.size + 1)) (a : α) : Array α :=
  let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
  loop (as : Array α) (j : Fin as.size) :=
-    if i < j then
-      let j' : Fin as.size := ⟨j-1, Nat.lt_of_le_of_lt (Nat.pred_le _) j.2⟩
+    if i.1 < j then
+      let j' := ⟨j-1, Nat.lt_of_le_of_lt (Nat.pred_le _) j.2⟩
      let as := as.swap j' j
      loop as ⟨j', by rw [size_swap]; exact j'.2⟩
    else
@@ -846,23 +843,12 @@ def eraseP (as : Array α) (p : α → Bool) : Array α :=
  let as := as.push a
  loop as ⟨j, size_push .. ▸ j.lt_succ_self⟩

-@[deprecated insertIdx (since := "2024-11-20")] abbrev insertAt := @insertIdx
-
 /-- Insert element `a` at position `i`. Panics if `i` is not `i ≤ as.size`. -/
-def insertIdx! (as : Array α) (i : Nat) (a : α) : Array α :=
+def insertAt! (as : Array α) (i : Nat) (a : α) : Array α :=
  if h : i ≤ as.size then
-    insertIdx as i a
+    insertAt as ⟨i, Nat.lt_succ_of_le h⟩ a
  else panic! "invalid index"

-@[deprecated insertIdx! (since := "2024-11-20")] abbrev insertAt! := @insertIdx!
-
-/-- Insert element `a` at position `i`, or do nothing if `as.size < i`. -/
-def insertIdxIfInBounds (as : Array α) (i : Nat) (a : α) : Array α :=
-  if h : i ≤ as.size then
-    insertIdx as i a
-  else
-    as
-
@[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
 def isPrefixOfAux [BEq α] (as bs : Array α) (hle : as.size ≤ bs.size) (i : Nat) : Bool :=
  if h : i < as.size then
@@ -886,12 +872,12 @@ def isPrefixOf [BEq α] (as bs : Array α) : Bool :=
    false

@[semireducible, specialize] -- This is otherwise irreducible because it uses well-founded recursion.
-def zipWithAux (as : Array α) (bs : Array β) (f : α → β → γ) (i : Nat) (cs : Array γ) : Array γ :=
+def zipWithAux (f : α → β → γ) (as : Array α) (bs : Array β) (i : Nat) (cs : Array γ) : Array γ :=
  if h : i < as.size then
    let a := as[i]
    if h : i < bs.size then
      let b := bs[i]
-      zipWithAux as bs f (i+1) <| cs.push <| f a b
+      zipWithAux f as bs (i+1) <| cs.push <| f a b
    else
      cs
  else
@@ -899,27 +885,14 @@ def zipWithAux (as : Array α) (bs : Array β) (f : α → β → γ) (i : Nat)
 decreasing_by simp_wf; decreasing_trivial_pre_omega

@[inline] def zipWith (as : Array α) (bs : Array β) (f : α → β → γ) : Array γ :=
-  zipWithAux as bs f 0 #[]
+  zipWithAux f as bs 0 #[]

 def zip (as : Array α) (bs : Array β) : Array (α × β) :=
  zipWith as bs Prod.mk

-def zipWithAll (as : Array α) (bs : Array β) (f : Option α → Option β → γ) : Array γ :=
-  go as bs 0 #[]
-where go (as : Array α) (bs : Array β) (i : Nat) (cs : Array γ) :=
-  if i < max as.size bs.size then
-    let a := as[i]?
-    let b := bs[i]?
-    go as bs (i+1) (cs.push (f a b))
-  else
-    cs
-  termination_by max as.size bs.size - i
-  decreasing_by simp_wf; decreasing_trivial_pre_omega
-
 def unzip (as : Array (α × β)) : Array α × Array β :=
  as.foldl (init := (#[], #[])) fun (as, bs) (a, b) => (as.push a, bs.push b)

-@[deprecated partition (since := "2024-11-06")]
 def split (as : Array α) (p : α → Bool) : Array α × Array α :=
  as.foldl (init := (#[], #[])) fun (as, bs) a =>
    if p a then (as.push a, bs) else (as, bs.push a)
--- a/src/Init/Data/Array/BasicAux.lean
+++ b/src/Init/Data/Array/BasicAux.lean
@@ -60,7 +60,7 @@ where
      if ptrEq a b then
        go (i+1) as
      else
-        go (i+1) (as.set i b h)
+        go (i+1) (as.set ⟨i, h⟩ b)
    else
      return as

--- a/src/Init/Data/Array/BinSearch.lean
+++ b/src/Init/Data/Array/BinSearch.lean
@@ -5,64 +5,59 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Init.Data.Array.Basic
-import Init.Omega
 universe u v

-namespace Array
+-- TODO: CLEANUP

-@[specialize] def binSearchAux {α : Type u} {β : Type v} (lt : α → α → Bool) (found : Option α → β) (as : Array α) (k : α) :
-    (lo : Fin (as.size + 1)) → (hi : Fin as.size) → (lo.1 ≤ hi.1) → β
-  | lo, hi, h =>
-    let m := (lo.1 + hi.1)/2
-    let a := as[m]
-    if lt a k then
-      if h' : m + 1 ≤ hi.1 then
-        binSearchAux lt found as k ⟨m+1, by omega⟩ hi h'
-      else found none
-    else if lt k a then
-      if h' : m = 0 ∨ m - 1 < lo.1 then found none
-      else binSearchAux lt found as k lo ⟨m-1, by omega⟩ (by simp; omega)
-    else found (some a)
-termination_by lo hi => hi.1 - lo.1
+namespace Array
+-- TODO: remove the [Inhabited α] parameters as soon as we have the tactic framework for automating proof generation and using Array.fget
+-- TODO: remove `partial` using well-founded recursion
+
+@[specialize] partial def binSearchAux {α : Type u} {β : Type v} [Inhabited β] (lt : α → α → Bool) (found : Option α → β) (as : Array α) (k : α) : Nat → Nat → β
+  | lo, hi =>
+    if lo <= hi then
+      let _ := Inhabited.mk k
+      let m := (lo + hi)/2
+      let a := as.get! m
+      if lt a k then binSearchAux lt found as k (m+1) hi
+      else if lt k a then
+        if m == 0 then found none
+        else binSearchAux lt found as k lo (m-1)
+      else found (some a)
+    else found none

@[inline] def binSearch {α : Type} (as : Array α) (k : α) (lt : α → α → Bool) (lo := 0) (hi := as.size - 1) : Option α :=
-  if h : lo < as.size then
+  if lo < as.size then
    let hi := if hi < as.size then hi else as.size - 1
-    if w : lo ≤ hi then
-      binSearchAux lt id as k ⟨lo, by omega⟩ ⟨hi, by simp [hi]; split <;> omega⟩ (by simp [hi]; omega)
-    else
-      none
+    binSearchAux lt id as k lo hi
  else
    none

@[inline] def binSearchContains {α : Type} (as : Array α) (k : α) (lt : α → α → Bool) (lo := 0) (hi := as.size - 1) : Bool :=
-  if h : lo < as.size then
+  if lo < as.size then
    let hi := if hi < as.size then hi else as.size - 1
-    if w : lo ≤ hi then
-      binSearchAux lt Option.isSome as k ⟨lo, by omega⟩ ⟨hi, by simp [hi]; split <;> omega⟩ (by simp [hi]; omega)
-    else
-      false
+    binSearchAux lt Option.isSome as k lo hi
  else
    false

-@[specialize] private def binInsertAux {α : Type u} {m : Type u → Type v} [Monad m]
+@[specialize] private partial def binInsertAux {α : Type u} {m : Type u → Type v} [Monad m]
    (lt : α → α → Bool)
    (merge : α → m α)
    (add : Unit → m α)
    (as : Array α)
-    (k : α) : (lo : Fin as.size) → (hi : Fin as.size) → (lo.1 ≤ hi.1) → (lt as[lo] k) → m (Array α)
-  | lo, hi, h, w =>
-    let mid    := (lo.1 + hi.1)/2
-    let midVal := as[mid]
-    if w₁ : lt midVal k then
-      if h' : mid = lo then do let v ← add (); pure <| as.insertIdx (lo+1) v
-      else binInsertAux lt merge add as k ⟨mid, by omega⟩ hi (by simp; omega) w₁
-    else if w₂ : lt k midVal then
-      have : mid ≠ lo := fun z => by simp [midVal, z] at w₁; simp_all
-      binInsertAux lt merge add as k lo ⟨mid, by omega⟩ (by simp; omega) w
+    (k : α) : Nat → Nat → m (Array α)
+  | lo, hi =>
+    let _ := Inhabited.mk k
+    -- as[lo] < k < as[hi]
+    let mid    := (lo + hi)/2
+    let midVal := as.get! mid
+    if lt midVal k then
+      if mid == lo then do let v ← add (); pure <| as.insertAt! (lo+1) v
+      else binInsertAux lt merge add as k mid hi
+    else if lt k midVal then
+      binInsertAux lt merge add as k lo mid
    else do
      as.modifyM mid <| fun v => merge v
-termination_by lo hi => hi.1 - lo.1

@[specialize] def binInsertM {α : Type u} {m : Type u → Type v} [Monad m]
    (lt : α → α → Bool)
@@ -70,12 +65,13 @@ termination_by lo hi => hi.1 - lo.1
    (add : Unit → m α)
    (as : Array α)
    (k : α) : m (Array α) :=
-  if h : as.size = 0 then do let v ← add (); pure <| as.push v
-  else if lt k as[0] then do let v ← add (); pure <| as.insertIdx 0 v
-  else if h' : !lt as[0] k then as.modifyM 0 <| merge
-  else if lt as[as.size - 1] k then do let v ← add (); pure <| as.push v
-  else if !lt k as[as.size - 1] then as.modifyM (as.size - 1) <| merge
-  else binInsertAux lt merge add as k ⟨0, by omega⟩ ⟨as.size - 1, by omega⟩ (by simp) (by simpa using h')
+  let _ := Inhabited.mk k
+  if as.isEmpty then do let v ← add (); pure <| as.push v
+  else if lt k (as.get! 0) then do let v ← add (); pure <| as.insertAt! 0 v
+  else if !lt (as.get! 0) k then as.modifyM 0 <| merge
+  else if lt as.back k then do let v ← add (); pure <| as.push v
+  else if !lt k as.back then as.modifyM (as.size - 1) <| merge
+  else binInsertAux lt merge add as k 0 (as.size - 1)

@[inline] def binInsert {α : Type u} (lt : α → α → Bool) (as : Array α) (k : α) : Array α :=
  Id.run <| binInsertM lt (fun _ => k) (fun _ => k) as k
--- a/src/Init/Data/Array/Bootstrap.lean
+++ b/src/Init/Data/Array/Bootstrap.lean
@@ -15,26 +15,26 @@ This file contains some theorems about `Array` and `List` needed for `Init.Data.

 namespace Array

-theorem foldlM_toList.aux [Monad m]
+theorem foldlM_eq_foldlM_toList.aux [Monad m]
    (f : β → α → m β) (arr : Array α) (i j) (H : arr.size ≤ i + j) (b) :
    foldlM.loop f arr arr.size (Nat.le_refl _) i j b = (arr.toList.drop j).foldlM f b := by
  unfold foldlM.loop
  split; split
  · cases Nat.not_le_of_gt ‹_› (Nat.zero_add _ ▸ H)
  · rename_i i; rw [Nat.succ_add] at H
-    simp [foldlM_toList.aux f arr i (j+1) H]
-    rw (occs := [2]) [← List.getElem_cons_drop_succ_eq_drop ‹_›]
+    simp [foldlM_eq_foldlM_toList.aux f arr i (j+1) H]
+    rw (config := {occs := .pos [2]}) [← List.get_drop_eq_drop _ _ ‹_›]
    rfl
  · rw [List.drop_of_length_le (Nat.ge_of_not_lt ‹_›)]; rfl

-@[simp] theorem foldlM_toList [Monad m]
+theorem foldlM_eq_foldlM_toList [Monad m]
    (f : β → α → m β) (init : β) (arr : Array α) :
-    arr.toList.foldlM f init = arr.foldlM f init := by
-  simp [foldlM, foldlM_toList.aux]
+    arr.foldlM f init = arr.toList.foldlM f init := by
+  simp [foldlM, foldlM_eq_foldlM_toList.aux]

-@[simp] theorem foldl_toList (f : β → α → β) (init : β) (arr : Array α) :
-    arr.toList.foldl f init = arr.foldl f init :=
-  List.foldl_eq_foldlM .. ▸ foldlM_toList ..
+theorem foldl_eq_foldl_toList (f : β → α → β) (init : β) (arr : Array α) :
+    arr.foldl f init = arr.toList.foldl f init :=
+  List.foldl_eq_foldlM .. ▸ foldlM_eq_foldlM_toList ..

 theorem foldrM_eq_reverse_foldlM_toList.aux [Monad m]
    (f : α → β → m β) (arr : Array α) (init : β) (i h) :
@@ -51,23 +51,23 @@ theorem foldrM_eq_reverse_foldlM_toList [Monad m] (f : α → β → m β) (init
  match arr, this with | _, .inl rfl => rfl | arr, .inr h => ?_
  simp [foldrM, h, ← foldrM_eq_reverse_foldlM_toList.aux, List.take_length]

-@[simp] theorem foldrM_toList [Monad m]
+theorem foldrM_eq_foldrM_toList [Monad m]
    (f : α → β → m β) (init : β) (arr : Array α) :
-    arr.toList.foldrM f init = arr.foldrM f init := by
+    arr.foldrM f init = arr.toList.foldrM f init := by
  rw [foldrM_eq_reverse_foldlM_toList, List.foldlM_reverse]

-@[simp] theorem foldr_toList (f : α → β → β) (init : β) (arr : Array α) :
-    arr.toList.foldr f init = arr.foldr f init :=
-  List.foldr_eq_foldrM .. ▸ foldrM_toList ..
+theorem foldr_eq_foldr_toList (f : α → β → β) (init : β) (arr : Array α) :
+    arr.foldr f init = arr.toList.foldr f init :=
+  List.foldr_eq_foldrM .. ▸ foldrM_eq_foldrM_toList ..

@[simp] theorem push_toList (arr : Array α) (a : α) : (arr.push a).toList = arr.toList ++ [a] := by
  simp [push, List.concat_eq_append]

@[simp] theorem toListAppend_eq (arr : Array α) (l) : arr.toListAppend l = arr.toList ++ l := by
-  simp [toListAppend, ← foldr_toList]
+  simp [toListAppend, foldr_eq_foldr_toList]

@[simp] theorem toListImpl_eq (arr : Array α) : arr.toListImpl = arr.toList := by
-  simp [toListImpl, ← foldr_toList]
+  simp [toListImpl, foldr_eq_foldr_toList]

@[simp] theorem pop_toList (arr : Array α) : arr.pop.toList = arr.toList.dropLast := rfl

@@ -76,20 +76,9 @@ theorem foldrM_eq_reverse_foldlM_toList [Monad m] (f : α → β → m β) (init
@[simp] theorem toList_append (arr arr' : Array α) :
    (arr ++ arr').toList = arr.toList ++ arr'.toList := by
  rw [← append_eq_append]; unfold Array.append
-  rw [← foldl_toList]
+  rw [foldl_eq_foldl_toList]
  induction arr'.toList generalizing arr <;> simp [*]

-@[simp] theorem toList_empty : (#[] : Array α).toList = [] := rfl
-
-@[simp] theorem append_nil (as : Array α) : as ++ #[] = as := by
-  apply ext'; simp only [toList_append, toList_empty, List.append_nil]
-
-@[simp] theorem nil_append (as : Array α) : #[] ++ as = as := by
-  apply ext'; simp only [toList_append, toList_empty, List.nil_append]
-
-@[simp] theorem append_assoc (as bs cs : Array α) : as ++ bs ++ cs = as ++ (bs ++ cs) := by
-  apply ext'; simp only [toList_append, List.append_assoc]
-
@[simp] theorem appendList_eq_append
    (arr : Array α) (l : List α) : arr.appendList l = arr ++ l := rfl

@@ -98,44 +87,20 @@ theorem foldrM_eq_reverse_foldlM_toList [Monad m] (f : α → β → m β) (init
  rw [← appendList_eq_append]; unfold Array.appendList
  induction l generalizing arr <;> simp [*]

-@[deprecated "Use the reverse direction of `foldrM_toList`." (since := "2024-11-13")]
-theorem foldrM_eq_foldrM_toList [Monad m]
-    (f : α → β → m β) (init : β) (arr : Array α) :
-    arr.foldrM f init = arr.toList.foldrM f init := by
-  simp
+@[deprecated foldlM_eq_foldlM_toList (since := "2024-09-09")]
+abbrev foldlM_eq_foldlM_data := @foldlM_eq_foldlM_toList

-@[deprecated "Use the reverse direction of `foldlM_toList`." (since := "2024-11-13")]
-theorem foldlM_eq_foldlM_toList [Monad m]
-    (f : β → α → m β) (init : β) (arr : Array α) :
-    arr.foldlM f init = arr.toList.foldlM f init:= by
-  simp
-
-@[deprecated "Use the reverse direction of `foldr_toList`." (since := "2024-11-13")]
-theorem foldr_eq_foldr_toList
-    (f : α → β → β) (init : β) (arr : Array α) :
-    arr.foldr f init = arr.toList.foldr f init := by
-  simp
-
-@[deprecated "Use the reverse direction of `foldl_toList`." (since := "2024-11-13")]
-theorem foldl_eq_foldl_toList
-    (f : β → α → β) (init : β) (arr : Array α) :
-    arr.foldl f init = arr.toList.foldl f init:= by
-  simp
-
-@[deprecated foldlM_toList (since := "2024-09-09")]
-abbrev foldlM_eq_foldlM_data := @foldlM_toList
-
-@[deprecated foldl_toList (since := "2024-09-09")]
-abbrev foldl_eq_foldl_data := @foldl_toList
+@[deprecated foldl_eq_foldl_toList (since := "2024-09-09")]
+abbrev foldl_eq_foldl_data := @foldl_eq_foldl_toList

@[deprecated foldrM_eq_reverse_foldlM_toList (since := "2024-09-09")]
 abbrev foldrM_eq_reverse_foldlM_data := @foldrM_eq_reverse_foldlM_toList

-@[deprecated foldrM_toList (since := "2024-09-09")]
-abbrev foldrM_eq_foldrM_data := @foldrM_toList
+@[deprecated foldrM_eq_foldrM_toList (since := "2024-09-09")]
+abbrev foldrM_eq_foldrM_data := @foldrM_eq_foldrM_toList

-@[deprecated foldr_toList (since := "2024-09-09")]
-abbrev foldr_eq_foldr_data := @foldr_toList
+@[deprecated foldr_eq_foldr_toList (since := "2024-09-09")]
+abbrev foldr_eq_foldr_data := @foldr_eq_foldr_toList

@[deprecated push_toList (since := "2024-09-09")]
 abbrev push_data := @push_toList
--- a/src/Init/Data/Array/DecidableEq.lean
+++ b/src/Init/Data/Array/DecidableEq.lean
@@ -6,15 +6,16 @@ Authors: Leonardo de Moura
 prelude
 import Init.Data.Array.Basic
 import Init.Data.BEq
+import Init.Data.Nat.Lemmas
 import Init.Data.List.Nat.BEq
 import Init.ByCases

 namespace Array

 theorem rel_of_isEqvAux
-    {r : α → α → Bool} {a b : Array α} (hsz : a.size = b.size) {i : Nat} (hi : i ≤ a.size)
+    (r : α → α → Bool) (a b : Array α) (hsz : a.size = b.size) (i : Nat) (hi : i ≤ a.size)
    (heqv : Array.isEqvAux a b hsz r i hi)
-    {j : Nat} (hj : j < i) : r (a[j]'(Nat.lt_of_lt_of_le hj hi)) (b[j]'(Nat.lt_of_lt_of_le hj (hsz ▸ hi))) := by
+    (j : Nat) (hj : j < i) : r (a[j]'(Nat.lt_of_lt_of_le hj hi)) (b[j]'(Nat.lt_of_lt_of_le hj (hsz ▸ hi))) := by
  induction i with
  | zero => contradiction
  | succ i ih =>
@@ -27,7 +28,7 @@ theorem rel_of_isEqvAux
      subst hj'
      exact heqv.left

-theorem isEqvAux_of_rel {r : α → α → Bool} {a b : Array α} (hsz : a.size = b.size) {i : Nat} (hi : i ≤ a.size)
+theorem isEqvAux_of_rel (r : α → α → Bool) (a b : Array α) (hsz : a.size = b.size) (i : Nat) (hi : i ≤ a.size)
    (w : ∀ j, (hj : j < i) → r (a[j]'(Nat.lt_of_lt_of_le hj hi)) (b[j]'(Nat.lt_of_lt_of_le hj (hsz ▸ hi)))) : Array.isEqvAux a b hsz r i hi := by
  induction i with
  | zero => simp [Array.isEqvAux]
@@ -35,18 +36,18 @@ theorem isEqvAux_of_rel {r : α → α → Bool} {a b : Array α} (hsz : a.size
    simp only [isEqvAux, Bool.and_eq_true]
    exact ⟨w i (Nat.lt_add_one i), ih _ fun j hj => w j (Nat.lt_add_right 1 hj)⟩

-theorem rel_of_isEqv {r : α → α → Bool} {a b : Array α} :
+theorem rel_of_isEqv (r : α → α → Bool) (a b : Array α) :
    Array.isEqv a b r → ∃ h : a.size = b.size, ∀ (i : Nat) (h' : i < a.size), r (a[i]) (b[i]'(h ▸ h')) := by
  simp only [isEqv]
  split <;> rename_i h
-  · exact fun h' => ⟨h, fun i => rel_of_isEqvAux h (Nat.le_refl ..) h'⟩
+  · exact fun h' => ⟨h, rel_of_isEqvAux r a b h a.size (Nat.le_refl ..) h'⟩
  · intro; contradiction

 theorem isEqv_iff_rel (a b : Array α) (r) :
    Array.isEqv a b r ↔ ∃ h : a.size = b.size, ∀ (i : Nat) (h' : i < a.size), r (a[i]) (b[i]'(h ▸ h')) :=
-  ⟨rel_of_isEqv, fun ⟨h, w⟩ => by
+  ⟨rel_of_isEqv r a b, fun ⟨h, w⟩ => by
    simp only [isEqv, ← h, ↓reduceDIte]
-    exact isEqvAux_of_rel h (by simp [h]) w⟩
+    exact isEqvAux_of_rel r a b h a.size (by simp [h]) w⟩

 theorem isEqv_eq_decide (a b : Array α) (r) :
    Array.isEqv a b r =
@@ -66,7 +67,7 @@ theorem isEqv_eq_decide (a b : Array α) (r) :
  simp [isEqv_eq_decide, List.isEqv_eq_decide]

 theorem eq_of_isEqv [DecidableEq α] (a b : Array α) (h : Array.isEqv a b (fun x y => x = y)) : a = b := by
-  have ⟨h, h'⟩ := rel_of_isEqv h
+  have ⟨h, h'⟩ := rel_of_isEqv (fun x y => x = y) a b h
  exact ext _ _ h (fun i lt _ => by simpa using h' i lt)

 theorem isEqvAux_self (r : α → α → Bool) (hr : ∀ a, r a a) (a : Array α) (i : Nat) (h : i ≤ a.size) :
--- a/src/Init/Data/Array/FinRange.lean
+++ b/src/Init/Data/Array/FinRange.lean
@@ -1,14 +0,0 @@
-/-
-Copyright (c) 2024 François G. Dorais. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: François G. Dorais
-/
-prelude
-import Init.Data.List.FinRange
-
-namespace Array
-
-/-- `finRange n` is the array of all elements of `Fin n` in order. -/
-protected def finRange (n : Nat) : Array (Fin n) := ofFn fun i => i
-
-end Array
--- a/src/Init/Data/Array/Find.lean
+++ b/src/Init/Data/Array/Find.lean
@@ -1,281 +0,0 @@
-/-
-Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison
-/
-prelude
-import Init.Data.List.Find
-import Init.Data.Array.Lemmas
-import Init.Data.Array.Attach
-
-/-!
-# Lemmas about `Array.findSome?`, `Array.find?`.
-/
-
-namespace Array
-
-open Nat
-
-/-! ### findSome? -/
-
-@[simp] theorem findSomeRev?_push_of_isSome (l : Array α) (h : (f a).isSome) : (l.push a).findSomeRev? f = f a := by
-  cases l; simp_all
-
-@[simp] theorem findSomeRev?_push_of_isNone (l : Array α) (h : (f a).isNone) : (l.push a).findSomeRev? f = l.findSomeRev? f := by
-  cases l; simp_all
-
-theorem exists_of_findSome?_eq_some {f : α → Option β} {l : Array α} (w : l.findSome? f = some b) :
-    ∃ a, a ∈ l ∧ f a = b := by
-  cases l; simp_all [List.exists_of_findSome?_eq_some]
-
-@[simp] theorem findSome?_eq_none_iff : findSome? p l = none ↔ ∀ x ∈ l, p x = none := by
-  cases l; simp
-
-@[simp] theorem findSome?_isSome_iff {f : α → Option β} {l : Array α} :
-    (l.findSome? f).isSome ↔ ∃ x, x ∈ l ∧ (f x).isSome := by
-  cases l; simp
-
-theorem findSome?_eq_some_iff {f : α → Option β} {l : Array α} {b : β} :
-    l.findSome? f = some b ↔ ∃ (l₁ : Array α) (a : α) (l₂ : Array α), l = l₁.push a ++ l₂ ∧ f a = some b ∧ ∀ x ∈ l₁, f x = none := by
-  cases l
-  simp only [List.findSome?_toArray, List.findSome?_eq_some_iff]
-  constructor
-  · rintro ⟨l₁, a, l₂, rfl, h₁, h₂⟩
-    exact ⟨l₁.toArray, a, l₂.toArray, by simp_all⟩
-  · rintro ⟨l₁, a, l₂, h₀, h₁, h₂⟩
-    exact ⟨l₁.toList, a, l₂.toList, by simpa using congrArg toList h₀, h₁, by simpa⟩
-
-@[simp] theorem findSome?_guard (l : Array α) : findSome? (Option.guard fun x => p x) l = find? p l := by
-  cases l; simp
-
-@[simp] theorem getElem?_zero_filterMap (f : α → Option β) (l : Array α) : (l.filterMap f)[0]? = l.findSome? f := by
-  cases l; simp [← List.head?_eq_getElem?]
-
-@[simp] theorem getElem_zero_filterMap (f : α → Option β) (l : Array α) (h) :
-    (l.filterMap f)[0] = (l.findSome? f).get (by cases l; simpa [List.length_filterMap_eq_countP] using h) := by
-  cases l; simp [← List.head_eq_getElem, ← getElem?_zero_filterMap]
-
-@[simp] theorem back?_filterMap (f : α → Option β) (l : Array α) : (l.filterMap f).back? = l.findSomeRev? f := by
-  cases l; simp
-
-@[simp] theorem back!_filterMap [Inhabited β] (f : α → Option β) (l : Array α) :
-    (l.filterMap f).back! = (l.findSomeRev? f).getD default := by
-  cases l; simp
-
-@[simp] theorem map_findSome? (f : α → Option β) (g : β → γ) (l : Array α) :
-    (l.findSome? f).map g = l.findSome? (Option.map g ∘ f) := by
-  cases l; simp
-
-theorem findSome?_map (f : β → γ) (l : Array β) : findSome? p (l.map f) = l.findSome? (p ∘ f) := by
-  cases l; simp [List.findSome?_map]
-
-theorem findSome?_append {l₁ l₂ : Array α} : (l₁ ++ l₂).findSome? f = (l₁.findSome? f).or (l₂.findSome? f) := by
-  cases l₁; cases l₂; simp [List.findSome?_append]
-
-theorem getElem?_zero_flatten (L : Array (Array α)) :
-    (flatten L)[0]? = L.findSome? fun l => l[0]? := by
-  cases L using array_array_induction
-  simp [← List.head?_eq_getElem?, List.head?_flatten, List.findSome?_map, Function.comp_def]
-
-theorem getElem_zero_flatten.proof {L : Array (Array α)} (h : 0 < L.flatten.size) :
-    (L.findSome? fun l => l[0]?).isSome := by
-  cases L using array_array_induction
-  simp only [List.findSome?_toArray, List.findSome?_map, Function.comp_def, List.getElem?_toArray,
-    List.findSome?_isSome_iff, List.isSome_getElem?]
-  simp only [flatten_toArray_map_toArray, size_toArray, List.length_flatten,
-    Nat.sum_pos_iff_exists_pos, List.mem_map] at h
-  obtain ⟨_, ⟨xs, m, rfl⟩, h⟩ := h
-  exact ⟨xs, m, by simpa using h⟩
-
-theorem getElem_zero_flatten {L : Array (Array α)} (h) :
-    (flatten L)[0] = (L.findSome? fun l => l[0]?).get (getElem_zero_flatten.proof h) := by
-  have t := getElem?_zero_flatten L
-  simp [getElem?_eq_getElem, h] at t
-  simp [← t]
-
-theorem back?_flatten {L : Array (Array α)} :
-    (flatten L).back? = (L.findSomeRev? fun l => l.back?) := by
-  cases L using array_array_induction
-  simp [List.getLast?_flatten, ← List.map_reverse, List.findSome?_map, Function.comp_def]
-
-theorem findSome?_mkArray : findSome? f (mkArray n a) = if n = 0 then none else f a := by
-  simp [mkArray_eq_toArray_replicate, List.findSome?_replicate]
-
-@[simp] theorem findSome?_mkArray_of_pos (h : 0 < n) : findSome? f (mkArray n a) = f a := by
-  simp [findSome?_mkArray, Nat.ne_of_gt h]
-
-- Argument is unused, but used to decide whether `simp` should unfold.
-@[simp] theorem findSome?_mkArray_of_isSome (_ : (f a).isSome) :
-   findSome? f (mkArray n a) = if n = 0 then none else f a := by
-  simp [findSome?_mkArray]
-
-@[simp] theorem findSome?_mkArray_of_isNone (h : (f a).isNone) :
-    findSome? f (mkArray n a) = none := by
-  rw [Option.isNone_iff_eq_none] at h
-  simp [findSome?_mkArray, h]
-
-/-! ### find? -/
-
-@[simp] theorem find?_singleton (a : α) (p : α → Bool) :
-    #[a].find? p = if p a then some a else none := by
-  simp [singleton_eq_toArray_singleton]
-
-@[simp] theorem findRev?_push_of_pos (l : Array α) (h : p a) :
-    findRev? p (l.push a) = some a := by
-  cases l; simp [h]
-
-@[simp] theorem findRev?_cons_of_neg (l : Array α) (h : ¬p a) :
-    findRev? p (l.push a) = findRev? p l := by
-  cases l; simp [h]
-
-@[simp] theorem find?_eq_none : find? p l = none ↔ ∀ x ∈ l, ¬ p x := by
-  cases l; simp
-
-theorem find?_eq_some_iff_append {xs : Array α} :
-    xs.find? p = some b ↔ p b ∧ ∃ (as bs : Array α), xs = as.push b ++ bs ∧ ∀ a ∈ as, !p a := by
-  rcases xs with ⟨xs⟩
-  simp only [List.find?_toArray, List.find?_eq_some_iff_append, Bool.not_eq_eq_eq_not,
-    Bool.not_true, exists_and_right, and_congr_right_iff]
-  intro w
-  constructor
-  · rintro ⟨as, ⟨⟨x, rfl⟩, h⟩⟩
-    exact ⟨as.toArray, ⟨x.toArray, by simp⟩ , by simpa using h⟩
-  · rintro ⟨as, ⟨⟨x, h'⟩, h⟩⟩
-    exact ⟨as.toList, ⟨x.toList, by simpa using congrArg Array.toList h'⟩,
-      by simpa using h⟩
-
-@[simp]
-theorem find?_push_eq_some {xs : Array α} :
-    (xs.push a).find? p = some b ↔ xs.find? p = some b ∨ (xs.find? p = none ∧ (p a ∧ a = b)) := by
-  cases xs; simp
-
-@[simp] theorem find?_isSome {xs : Array α} {p : α → Bool} : (xs.find? p).isSome ↔ ∃ x, x ∈ xs ∧ p x := by
-  cases xs; simp
-
-theorem find?_some {xs : Array α} (h : find? p xs = some a) : p a := by
-  cases xs
-  simp at h
-  exact List.find?_some h
-
-theorem mem_of_find?_eq_some {xs : Array α} (h : find? p xs = some a) : a ∈ xs := by
-  cases xs
-  simp at h
-  simpa using List.mem_of_find?_eq_some h
-
-theorem get_find?_mem {xs : Array α} (h) : (xs.find? p).get h ∈ xs := by
-  cases xs
-  simp [List.get_find?_mem]
-
-@[simp] theorem find?_filter {xs : Array α} (p q : α → Bool) :
-    (xs.filter p).find? q = xs.find? (fun a => p a ∧ q a) := by
-  cases xs; simp
-
-@[simp] theorem getElem?_zero_filter (p : α → Bool) (l : Array α) :
-    (l.filter p)[0]? = l.find? p := by
-  cases l; simp [← List.head?_eq_getElem?]
-
-@[simp] theorem getElem_zero_filter (p : α → Bool) (l : Array α) (h) :
-    (l.filter p)[0] =
-      (l.find? p).get (by cases l; simpa [← List.countP_eq_length_filter] using h) := by
-  cases l
-  simp [List.getElem_zero_eq_head]
-
-@[simp] theorem back?_filter (p : α → Bool) (l : Array α) : (l.filter p).back? = l.findRev? p := by
-  cases l; simp
-
-@[simp] theorem back!_filter [Inhabited α] (p : α → Bool) (l : Array α) :
-    (l.filter p).back! = (l.findRev? p).get! := by
-  cases l; simp [Option.get!_eq_getD]
-
-@[simp] theorem find?_filterMap (xs : Array α) (f : α → Option β) (p : β → Bool) :
-    (xs.filterMap f).find? p = (xs.find? (fun a => (f a).any p)).bind f := by
-  cases xs; simp
-
-@[simp] theorem find?_map (f : β → α) (xs : Array β) :
-    find? p (xs.map f) = (xs.find? (p ∘ f)).map f := by
-  cases xs; simp
-
-@[simp] theorem find?_append {l₁ l₂ : Array α} :
-    (l₁ ++ l₂).find? p = (l₁.find? p).or (l₂.find? p) := by
-  cases l₁
-  cases l₂
-  simp
-
-@[simp] theorem find?_flatten (xs : Array (Array α)) (p : α → Bool) :
-    xs.flatten.find? p = xs.findSome? (·.find? p) := by
-  cases xs using array_array_induction
-  simp [List.findSome?_map, Function.comp_def]
-
-theorem find?_flatten_eq_none {xs : Array (Array α)} {p : α → Bool} :
-    xs.flatten.find? p = none ↔ ∀ ys ∈ xs, ∀ x ∈ ys, !p x := by
-  simp
-
-/--
-If `find? p` returns `some a` from `xs.flatten`, then `p a` holds, and
-some array in `xs` contains `a`, and no earlier element of that array satisfies `p`.
-Moreover, no earlier array in `xs` has an element satisfying `p`.
-/
-theorem find?_flatten_eq_some {xs : Array (Array α)} {p : α → Bool} {a : α} :
-    xs.flatten.find? p = some a ↔
-      p a ∧ ∃ (as : Array (Array α)) (ys zs : Array α) (bs : Array (Array α)),
-        xs = as.push (ys.push a ++ zs) ++ bs ∧
-        (∀ a ∈ as, ∀ x ∈ a, !p x) ∧ (∀ x ∈ ys, !p x) := by
-  cases xs using array_array_induction
-  simp only [flatten_toArray_map_toArray, List.find?_toArray, List.find?_flatten_eq_some]
-  simp only [Bool.not_eq_eq_eq_not, Bool.not_true, exists_and_right, and_congr_right_iff]
-  intro w
-  constructor
-  · rintro ⟨as, ys, ⟨⟨zs, bs, rfl⟩, h₁, h₂⟩⟩
-    exact ⟨as.toArray.map List.toArray, ys.toArray,
-      ⟨zs.toArray, bs.toArray.map List.toArray, by simp⟩, by simpa using h₁, by simpa using h₂⟩
-  · rintro ⟨as, ys, ⟨⟨zs, bs, h⟩, h₁, h₂⟩⟩
-    replace h := congrArg (·.map Array.toList) (congrArg Array.toList h)
-    simp [Function.comp_def] at h
-    exact ⟨as.toList.map Array.toList, ys.toList,
-      ⟨zs.toList, bs.toList.map Array.toList, by simpa using h⟩,
-        by simpa using h₁, by simpa using h₂⟩
-
-@[simp] theorem find?_flatMap (xs : Array α) (f : α → Array β) (p : β → Bool) :
-    (xs.flatMap f).find? p = xs.findSome? (fun x => (f x).find? p) := by
-  cases xs
-  simp [List.find?_flatMap, Array.flatMap_toArray]
-
-theorem find?_flatMap_eq_none {xs : Array α} {f : α → Array β} {p : β → Bool} :
-    (xs.flatMap f).find? p = none ↔ ∀ x ∈ xs, ∀ y ∈ f x, !p y := by
-  simp
-
-theorem find?_mkArray :
-    find? p (mkArray n a) = if n = 0 then none else if p a then some a else none := by
-  simp [mkArray_eq_toArray_replicate, List.find?_replicate]
-
-@[simp] theorem find?_mkArray_of_length_pos (h : 0 < n) :
-    find? p (mkArray n a) = if p a then some a else none := by
-  simp [find?_mkArray, Nat.ne_of_gt h]
-
-@[simp] theorem find?_mkArray_of_pos (h : p a) :
-    find? p (mkArray n a) = if n = 0 then none else some a := by
-  simp [find?_mkArray, h]
-
-@[simp] theorem find?_mkArray_of_neg (h : ¬ p a) : find? p (mkArray n a) = none := by
-  simp [find?_mkArray, h]
-
-- This isn't a `@[simp]` lemma since there is already a lemma for `l.find? p = none` for any `l`.
-theorem find?_mkArray_eq_none {n : Nat} {a : α} {p : α → Bool} :
-    (mkArray n a).find? p = none ↔ n = 0 ∨ !p a := by
-  simp [mkArray_eq_toArray_replicate, List.find?_replicate_eq_none, Classical.or_iff_not_imp_left]
-
-@[simp] theorem find?_mkArray_eq_some {n : Nat} {a b : α} {p : α → Bool} :
-    (mkArray n a).find? p = some b ↔ n ≠ 0 ∧ p a ∧ a = b := by
-  simp [mkArray_eq_toArray_replicate]
-
-@[simp] theorem get_find?_mkArray (n : Nat) (a : α) (p : α → Bool) (h) :
-    ((mkArray n a).find? p).get h = a := by
-  simp [mkArray_eq_toArray_replicate]
-
-theorem find?_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
-    (H : ∀ (a : α), a ∈ xs → P a) (p : β → Bool) :
-    (xs.pmap f H).find? p = (xs.attach.find? (fun ⟨a, m⟩ => p (f a (H a m)))).map fun ⟨a, m⟩ => f a (H a m) := by
-  simp only [pmap_eq_map_attach, find?_map]
-  rfl
-
-end Array
--- a/src/Init/Data/Array/GetLit.lean
+++ b/src/Init/Data/Array/GetLit.lean
@@ -41,6 +41,6 @@ where
  getLit_eq (as : Array α) (i : Nat) (h₁ : as.size = n) (h₂ : i < n) : as.getLit i h₁ h₂ = getElem as.toList i ((id (α := as.toList.length = n) h₁) ▸ h₂) :=
    rfl
  go (i : Nat) (hi : i ≤ as.size) : toListLitAux as n hsz i hi (as.toList.drop i) = as.toList := by
-    induction i <;> simp only [List.drop, toListLitAux, getLit_eq, List.getElem_cons_drop_succ_eq_drop, *]
+    induction i <;> simp only [List.drop, toListLitAux, getLit_eq, List.get_drop_eq_drop, *]

 end Array
--- a/src/Init/Data/Array/InsertionSort.lean
+++ b/src/Init/Data/Array/InsertionSort.lean
@@ -5,91 +5,24 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Init.Data.Array.Basic
-import Init.Data.Nat.Fold
-import Init.Data.Vector.Lemmas

-namespace Vector
-
-/-- Swap the `i`-th element repeatedly to the left, while the element to its left is not `lt` it. -/
-@[specialize, inline] def swapLeftWhileLT {n} (a : Vector α n) (i : Nat) (h : i < n)
-    (lt : α → α → Bool := by exact (· < ·)) : Vector α n :=
-  match h' : i with
-  | 0 => a
-  | i'+1 =>
-    if lt a[i] a[i'] then
-      swapLeftWhileLT (a.swap i' i) i' (by omega) lt
-    else
-      a
-
-end Vector
-
-open Vector
-namespace Array
-
-/-- Sort an array in place using insertion sort. -/
-@[inline] def insertionSort (a : Array α) (lt : α → α → Bool := by exact (· < ·)) : Array α :=
-  a.size.fold (init := ⟨a, rfl⟩) (fun i h acc => swapLeftWhileLT acc i h lt) |>.toArray
-
-/-- Insert an element into an array, after the last element which is not `lt` the inserted element. -/
-def orderedInsert (a : Array α) (x : α) (lt : α → α → Bool := by exact (· < ·)) : Array α :=
- swapLeftWhileLT ⟨a.push x, rfl⟩ a.size (by simp) lt |>.toArray
-
-end Array
-
-/-! ### Verification -/
-
-namespace Vector
-
-theorem swapLeftWhileLT_push {n} (a : Vector α n) (x : α) (j : Nat) (h : j < n) :
-    swapLeftWhileLT (a.push x) j (by omega) lt = (swapLeftWhileLT a j h lt).push x := by
-  induction j generalizing a with
-  | zero => simp [swapLeftWhileLT]
-  | succ j ih =>
-    simp [swapLeftWhileLT]
-    split <;> rename_i h
-    · rw [Vector.getElem_push_lt (by omega), Vector.getElem_push_lt (by omega)] at h
-      rw [← Vector.push_swap, ih, if_pos h]
-    · rw [Vector.getElem_push_lt (by omega), Vector.getElem_push_lt (by omega)] at h
-      rw [if_neg h]
-
-theorem swapLeftWhileLT_cast {n m} (a : Vector α n) (j : Nat) (h : j < n) (h' : n = m) :
-    swapLeftWhileLT (a.cast h') j (by omega) lt = (swapLeftWhileLT a j h lt).cast h' := by
-  subst h'
-  simp
-
-end Vector
-
-namespace Array
-
-@[simp] theorem size_insertionSort (a : Array α) : (a.insertionSort lt).size = a.size := by
-  simp [insertionSort]
-
-private theorem insertionSort_push' (a : Array α) (x : α) :
-    (a.push x).insertionSort lt =
-      (swapLeftWhileLT ⟨(a.insertionSort lt).push x, rfl⟩ a.size (by simp) lt).toArray := by
-  rw [insertionSort, Nat.fold_congr (size_push a x), Nat.fold]
-  have : (a.size.fold (fun i h acc => swapLeftWhileLT acc i (by simp; omega) lt) ⟨a.push x, rfl⟩) =
-      ((a.size.fold (fun i h acc => swapLeftWhileLT acc i h lt) ⟨a, rfl⟩).push x).cast (by simp) := by
-    rw [Vector.eq_cast_iff]
-    simp only [Nat.fold_eq_finRange_foldl]
-    rw [← List.foldl_hom (fun a => (Vector.push x a)) _ (fun v ⟨i, h⟩ => swapLeftWhileLT v i (by omega) lt)]
-    rw [Vector.push_mk]
-    rw [← List.foldl_hom (Vector.cast _) _ (fun v ⟨i, h⟩ => swapLeftWhileLT v i (by omega) lt)]
-    · simp
-    · intro v i
-      simp only
-      rw [swapLeftWhileLT_cast]
-    · simp [swapLeftWhileLT_push]
-  rw [this]
-  simp only [Nat.lt_add_one, swapLeftWhileLT_cast, Vector.toArray_cast]
-  unfold insertionSort
-  simp only [Vector.push]
-  congr
-  all_goals simp
-
-theorem insertionSort_push (a : Array α) (x : α) :
-    (a.push x).insertionSort lt = (a.insertionSort lt).orderedInsert x lt := by
-  rw [insertionSort_push', orderedInsert]
-  simp
-
-end Array
+@[inline] def Array.insertionSort (a : Array α) (lt : α → α → Bool) : Array α :=
+  traverse a 0 a.size
+where
+  @[specialize] traverse (a : Array α) (i : Nat) (fuel : Nat) : Array α :=
+    match fuel with
+    | 0      => a
+    | fuel+1 =>
+      if h : i < a.size then
+        traverse (swapLoop a i h) (i+1) fuel
+      else
+        a
+  @[specialize] swapLoop (a : Array α) (j : Nat) (h : j < a.size) : Array α :=
+    match (generalizing := false) he:j with -- using `generalizing` because we don't want to refine the type of `h`
+    | 0    => a
+    | j'+1 =>
+      have h' : j' < a.size := by subst j; exact Nat.lt_trans (Nat.lt_succ_self _) h
+      if lt a[j] a[j'] then
+        swapLoop (a.swap ⟨j, h⟩ ⟨j', h'⟩) j' (by rw [size_swap]; assumption; done)
+      else
+        a
--- a/src/Init/Data/Array/Lemmas.lean
+++ b/src/Init/Data/Array/Lemmas.lean
--- a/src/Init/Data/Array/MapIdx.lean
+++ b/src/Init/Data/Array/MapIdx.lean
@@ -60,53 +60,33 @@ theorem mapFinIdx_spec (as : Array α) (f : Fin as.size → α → β)
  simp only [getElem?_def, size_mapFinIdx, getElem_mapFinIdx]
  split <;> simp_all

-@[simp] theorem toList_mapFinIdx (a : Array α) (f : Fin a.size → α → β) :
-    (a.mapFinIdx f).toList = a.toList.mapFinIdx (fun i a => f ⟨i, by simp⟩ a) := by
-  apply List.ext_getElem <;> simp
-
 /-! ### mapIdx -/

-theorem mapIdx_induction (f : Nat → α → β) (as : Array α)
+theorem mapIdx_induction (as : Array α) (f : Nat → α → β)
    (motive : Nat → Prop) (h0 : motive 0)
    (p : Fin as.size → β → Prop)
    (hs : ∀ i, motive i.1 → p i (f i as[i]) ∧ motive (i + 1)) :
-    motive as.size ∧ ∃ eq : (as.mapIdx f).size = as.size,
-      ∀ i h, p ⟨i, h⟩ ((as.mapIdx f)[i]) :=
+    motive as.size ∧ ∃ eq : (Array.mapIdx as f).size = as.size,
+      ∀ i h, p ⟨i, h⟩ ((Array.mapIdx as f)[i]) :=
  mapFinIdx_induction as (fun i a => f i a) motive h0 p hs

-theorem mapIdx_spec (f : Nat → α → β) (as : Array α)
+theorem mapIdx_spec (as : Array α) (f : Nat → α → β)
    (p : Fin as.size → β → Prop) (hs : ∀ i, p i (f i as[i])) :
-    ∃ eq : (as.mapIdx f).size = as.size,
-      ∀ i h, p ⟨i, h⟩ ((as.mapIdx f)[i]) :=
+    ∃ eq : (Array.mapIdx as f).size = as.size,
+      ∀ i h, p ⟨i, h⟩ ((Array.mapIdx as f)[i]) :=
  (mapIdx_induction _ _ (fun _ => True) trivial p fun _ _ => ⟨hs .., trivial⟩).2

-@[simp] theorem size_mapIdx (f : Nat → α → β) (as : Array α) : (as.mapIdx f).size = as.size :=
+@[simp] theorem size_mapIdx (a : Array α) (f : Nat → α → β) : (a.mapIdx f).size = a.size :=
  (mapIdx_spec (p := fun _ _ => True) (hs := fun _ => trivial)).1

-@[simp] theorem getElem_mapIdx (f : Nat → α → β) (as : Array α) (i : Nat)
-    (h : i < (as.mapIdx f).size) :
-    (as.mapIdx f)[i] = f i (as[i]'(by simp_all)) :=
-  (mapIdx_spec _ _ (fun i b => b = f i as[i]) fun _ => rfl).2 i (by simp_all)
+@[simp] theorem getElem_mapIdx (a : Array α) (f : Nat → α → β) (i : Nat)
+    (h : i < (mapIdx a f).size) :
+    (a.mapIdx f)[i] = f i (a[i]'(by simp_all)) :=
+  (mapIdx_spec _ _ (fun i b => b = f i a[i]) fun _ => rfl).2 i (by simp_all)

-@[simp] theorem getElem?_mapIdx (f : Nat → α → β) (as : Array α) (i : Nat) :
-    (as.mapIdx f)[i]? =
-      as[i]?.map (f i) := by
+@[simp] theorem getElem?_mapIdx (a : Array α) (f : Nat → α → β) (i : Nat) :
+    (a.mapIdx f)[i]? =
+      a[i]?.map (f i) := by
  simp [getElem?_def, size_mapIdx, getElem_mapIdx]

-@[simp] theorem toList_mapIdx (f : Nat → α → β) (as : Array α) :
-    (as.mapIdx f).toList = as.toList.mapIdx (fun i a => f i a) := by
-  apply List.ext_getElem <;> simp
-
 end Array
-
-namespace List
-
-@[simp] theorem mapFinIdx_toArray (l : List α) (f : Fin l.length → α → β) :
-    l.toArray.mapFinIdx f = (l.mapFinIdx f).toArray := by
-  ext <;> simp
-
-@[simp] theorem mapIdx_toArray (f : Nat → α → β) (l : List α) :
-    l.toArray.mapIdx f = (l.mapIdx f).toArray := by
-  ext <;> simp
-
-end List
--- a/src/Init/Data/Array/Mem.lean
+++ b/src/Init/Data/Array/Mem.lean
@@ -14,12 +14,12 @@ theorem sizeOf_lt_of_mem [SizeOf α] {as : Array α} (h : a ∈ as) : sizeOf a <
  cases as with | _ as =>
  exact Nat.lt_trans (List.sizeOf_lt_of_mem h.val) (by simp_arith)

-theorem sizeOf_get [SizeOf α] (as : Array α) (i : Nat) (h : i < as.size) : sizeOf (as.get i h) < sizeOf as := by
+theorem sizeOf_get [SizeOf α] (as : Array α) (i : Fin as.size) : sizeOf (as.get i) < sizeOf as := by
  cases as with | _ as =>
-  simpa using Nat.lt_trans (List.sizeOf_get _ ⟨i, h⟩) (by simp_arith)
+  exact Nat.lt_trans (List.sizeOf_get ..) (by simp_arith)

@[simp] theorem sizeOf_getElem [SizeOf α] (as : Array α) (i : Nat) (h : i < as.size) :
-  sizeOf (as[i]'h) < sizeOf as := sizeOf_get _ _ h
+  sizeOf (as[i]'h) < sizeOf as := sizeOf_get _ _

 /-- This tactic, added to the `decreasing_trivial` toolbox, proves that
 `sizeOf arr[i] < sizeOf arr`, which is useful for well founded recursions
--- a/src/Init/Data/Array/Monadic.lean
+++ b/src/Init/Data/Array/Monadic.lean
@@ -1,159 +0,0 @@
-/-
-Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison
-/
-prelude
-import Init.Data.Array.Lemmas
-import Init.Data.Array.Attach
-import Init.Data.List.Monadic
-
-/-!
-# Lemmas about `Array.forIn'` and `Array.forIn`.
-/
-
-namespace Array
-
-open Nat
-
-/-! ## Monadic operations -/
-
-/-! ### mapM -/
-
-theorem mapM_eq_foldlM_push [Monad m] [LawfulMonad m] (f : α → m β) (l : Array α) :
-    mapM f l = l.foldlM (fun acc a => return (acc.push (← f a))) #[] := by
-  rcases l with ⟨l⟩
-  simp only [List.mapM_toArray, bind_pure_comp, size_toArray, List.foldlM_toArray']
-  rw [List.mapM_eq_reverse_foldlM_cons]
-  simp only [bind_pure_comp, Functor.map_map]
-  suffices ∀ (k), (fun a => a.reverse.toArray) <$> List.foldlM (fun acc a => (fun a => a :: acc) <$> f a) k l =
-      List.foldlM (fun acc a => acc.push <$> f a) k.reverse.toArray l by
-    exact this []
-  intro k
-  induction l generalizing k with
-  | nil => simp
-  | cons a as ih =>
-    simp [ih, List.foldlM_cons]
-
-/-! ### foldlM and foldrM -/
-
-theorem foldlM_map [Monad m] (f : β₁ → β₂) (g : α → β₂ → m α) (l : Array β₁) (init : α) :
-    (l.map f).foldlM g init = l.foldlM (fun x y => g x (f y)) init := by
-  cases l
-  rw [List.map_toArray] -- Why doesn't this fire via `simp`?
-  simp [List.foldlM_map]
-
-theorem foldrM_map [Monad m] [LawfulMonad m] (f : β₁ → β₂) (g : β₂ → α → m α) (l : Array β₁)
-    (init : α) : (l.map f).foldrM g init = l.foldrM (fun x y => g (f x) y) init := by
-  cases l
-  rw [List.map_toArray] -- Why doesn't this fire via `simp`?
-  simp [List.foldrM_map]
-
-theorem foldlM_filterMap [Monad m] [LawfulMonad m] (f : α → Option β) (g : γ → β → m γ) (l : Array α) (init : γ) :
-    (l.filterMap f).foldlM g init =
-      l.foldlM (fun x y => match f y with | some b => g x b | none => pure x) init := by
-  cases l
-  rw [List.filterMap_toArray] -- Why doesn't this fire via `simp`?
-  simp [List.foldlM_filterMap]
-  rfl
-
-theorem foldrM_filterMap [Monad m] [LawfulMonad m] (f : α → Option β) (g : β → γ → m γ) (l : Array α) (init : γ) :
-    (l.filterMap f).foldrM g init =
-      l.foldrM (fun x y => match f x with | some b => g b y | none => pure y) init := by
-  cases l
-  rw [List.filterMap_toArray] -- Why doesn't this fire via `simp`?
-  simp [List.foldrM_filterMap]
-  rfl
-
-theorem foldlM_filter [Monad m] [LawfulMonad m] (p : α → Bool) (g : β → α → m β) (l : Array α) (init : β) :
-    (l.filter p).foldlM g init =
-      l.foldlM (fun x y => if p y then g x y else pure x) init := by
-  cases l
-  rw [List.filter_toArray] -- Why doesn't this fire via `simp`?
-  simp [List.foldlM_filter]
-
-theorem foldrM_filter [Monad m] [LawfulMonad m] (p : α → Bool) (g : α → β → m β) (l : Array α) (init : β) :
-    (l.filter p).foldrM g init =
-      l.foldrM (fun x y => if p x then g x y else pure y) init := by
-  cases l
-  rw [List.filter_toArray] -- Why doesn't this fire via `simp`?
-  simp [List.foldrM_filter]
-
-/-! ### forIn' -/
-
-/--
-We can express a for loop over an array as a fold,
-in which whenever we reach `.done b` we keep that value through the rest of the fold.
-/
-theorem forIn'_eq_foldlM [Monad m] [LawfulMonad m]
-    (l : Array α) (f : (a : α) → a ∈ l → β → m (ForInStep β)) (init : β) :
-    forIn' l init f = ForInStep.value <$>
-      l.attach.foldlM (fun b ⟨a, m⟩ => match b with
-        | .yield b => f a m b
-        | .done b => pure (.done b)) (ForInStep.yield init) := by
-  cases l
-  rw [List.attach_toArray] -- Why doesn't this fire via `simp`?
-  simp only [List.forIn'_toArray, List.forIn'_eq_foldlM, List.attachWith_mem_toArray, size_toArray,
-    List.length_map, List.length_attach, List.foldlM_toArray', List.foldlM_map]
-  congr
-
-/-- We can express a for loop over an array which always yields as a fold. -/
-@[simp] theorem forIn'_yield_eq_foldlM [Monad m] [LawfulMonad m]
-    (l : Array α) (f : (a : α) → a ∈ l → β → m γ) (g : (a : α) → a ∈ l → β → γ → β) (init : β) :
-    forIn' l init (fun a m b => (fun c => .yield (g a m b c)) <$> f a m b) =
-      l.attach.foldlM (fun b ⟨a, m⟩ => g a m b <$> f a m b) init := by
-  cases l
-  rw [List.attach_toArray] -- Why doesn't this fire via `simp`?
-  simp [List.foldlM_map]
-
-theorem forIn'_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
-    (l : Array α) (f : (a : α) → a ∈ l → β → β) (init : β) :
-    forIn' l init (fun a m b => pure (.yield (f a m b))) =
-      pure (f := m) (l.attach.foldl (fun b ⟨a, h⟩ => f a h b) init) := by
-  cases l
-  simp [List.forIn'_pure_yield_eq_foldl, List.foldl_map]
-
-@[simp] theorem forIn'_yield_eq_foldl
-    (l : Array α) (f : (a : α) → a ∈ l → β → β) (init : β) :
-    forIn' (m := Id) l init (fun a m b => .yield (f a m b)) =
-      l.attach.foldl (fun b ⟨a, h⟩ => f a h b) init := by
-  cases l
-  simp [List.foldl_map]
-
-/--
-We can express a for loop over an array as a fold,
-in which whenever we reach `.done b` we keep that value through the rest of the fold.
-/
-theorem forIn_eq_foldlM [Monad m] [LawfulMonad m]
-    (f : α → β → m (ForInStep β)) (init : β) (l : Array α) :
-    forIn l init f = ForInStep.value <$>
-      l.foldlM (fun b a => match b with
-        | .yield b => f a b
-        | .done b => pure (.done b)) (ForInStep.yield init) := by
-  cases l
-  simp only [List.forIn_toArray, List.forIn_eq_foldlM, size_toArray, List.foldlM_toArray']
-  congr
-
-/-- We can express a for loop over an array which always yields as a fold. -/
-@[simp] theorem forIn_yield_eq_foldlM [Monad m] [LawfulMonad m]
-    (l : Array α) (f : α → β → m γ) (g : α → β → γ → β) (init : β) :
-    forIn l init (fun a b => (fun c => .yield (g a b c)) <$> f a b) =
-      l.foldlM (fun b a => g a b <$> f a b) init := by
-  cases l
-  simp [List.foldlM_map]
-
-theorem forIn_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
-    (l : Array α) (f : α → β → β) (init : β) :
-    forIn l init (fun a b => pure (.yield (f a b))) =
-      pure (f := m) (l.foldl (fun b a => f a b) init) := by
-  cases l
-  simp [List.forIn_pure_yield_eq_foldl, List.foldl_map]
-
-@[simp] theorem forIn_yield_eq_foldl
-    (l : Array α) (f : α → β → β) (init : β) :
-    forIn (m := Id) l init (fun a b => .yield (f a b)) =
-      l.foldl (fun b a => f a b) init := by
-  cases l
-  simp [List.foldl_map]
-
-end Array
--- a/src/Init/Data/Array/QSort.lean
+++ b/src/Init/Data/Array/QSort.lean
@@ -13,19 +13,19 @@ namespace Array
 def qpartition (as : Array α) (lt : α → α → Bool) (lo hi : Nat) : Nat × Array α :=
  if h : as.size = 0 then (0, as) else have : Inhabited α := ⟨as[0]'(by revert h; cases as.size <;> simp)⟩ -- TODO: remove
  let mid := (lo + hi) / 2
-  let as  := if lt (as.get! mid) (as.get! lo) then as.swapIfInBounds lo mid else as
-  let as  := if lt (as.get! hi)  (as.get! lo) then as.swapIfInBounds lo hi  else as
-  let as  := if lt (as.get! mid) (as.get! hi) then as.swapIfInBounds mid hi else as
+  let as  := if lt (as.get! mid) (as.get! lo) then as.swap! lo mid else as
+  let as  := if lt (as.get! hi)  (as.get! lo) then as.swap! lo hi  else as
+  let as  := if lt (as.get! mid) (as.get! hi) then as.swap! mid hi else as
  let pivot := as.get! hi
  let rec loop (as : Array α) (i j : Nat) :=
    if h : j < hi then
      if lt (as.get! j) pivot then
-        let as := as.swapIfInBounds i j
+        let as := as.swap! i j
        loop as (i+1) (j+1)
      else
        loop as i (j+1)
    else
-      let as := as.swapIfInBounds i hi
+      let as := as.swap! i hi
      (i, as)
    termination_by hi - j
    decreasing_by all_goals simp_wf; decreasing_trivial_pre_omega
--- a/src/Init/Data/Array/Set.lean
+++ b/src/Init/Data/Array/Set.lean
@@ -1,41 +0,0 @@
-/-
-Copyright (c) 2020 Microsoft Corporation. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura, Mario Carneiro
-/
-prelude
-import Init.Tactics
-
-
-/--
-Set an element in an array, using a proof that the index is in bounds.
-(This proof can usually be omitted, and will be synthesized automatically.)
-
-This will perform the update destructively provided that `a` has a reference
-count of 1 when called.
-/
-@[extern "lean_array_fset"]
-def Array.set (a : Array α) (i : @& Nat) (v : α) (h : i < a.size := by get_elem_tactic) :
-    Array α where
-  toList := a.toList.set i v
-
-/--
-Set an element in an array, or do nothing if the index is out of bounds.
-
-This will perform the update destructively provided that `a` has a reference
-count of 1 when called.
-/
-@[inline] def Array.setIfInBounds (a : Array α) (i : Nat) (v : α) : Array α :=
-  dite (LT.lt i a.size) (fun h => a.set i v h) (fun _ => a)
-
-@[deprecated Array.setIfInBounds (since := "2024-11-24")] abbrev Array.setD := @Array.setIfInBounds
-
-/--
-Set an element in an array, or panic if the index is out of bounds.
-
-This will perform the update destructively provided that `a` has a reference
-count of 1 when called.
-/
-@[extern "lean_array_set"]
-def Array.set! (a : Array α) (i : @& Nat) (v : α) : Array α :=
-  Array.setIfInBounds a i v
--- a/src/Init/Data/Array/Subarray.lean
+++ b/src/Init/Data/Array/Subarray.lean
@@ -15,6 +15,15 @@ structure Subarray (α : Type u)  where
  start_le_stop : start ≤ stop
  stop_le_array_size : stop ≤ array.size

+@[deprecated Subarray.array (since := "2024-04-13")]
+abbrev Subarray.as (s : Subarray α) : Array α := s.array
+
+@[deprecated Subarray.start_le_stop (since := "2024-04-13")]
+theorem Subarray.h₁ (s : Subarray α) : s.start ≤ s.stop := s.start_le_stop
+
+@[deprecated Subarray.stop_le_array_size (since := "2024-04-13")]
+theorem Subarray.h₂ (s : Subarray α) : s.stop ≤ s.array.size := s.stop_le_array_size
+
 namespace Subarray

 def size (s : Subarray α) : Nat :=
@@ -39,7 +48,7 @@ instance : GetElem (Subarray α) Nat α fun xs i => i < xs.size where
  getElem xs i h := xs.get ⟨i, h⟩

@[inline] def getD (s : Subarray α) (i : Nat) (v₀ : α) : α :=
-  if h : i < s.size then s[i] else v₀
+  if h : i < s.size then s.get ⟨i, h⟩ else v₀

 abbrev get! [Inhabited α] (s : Subarray α) (i : Nat) : α :=
  getD s i default
--- a/src/Init/Data/Array/Subarray/Split.lean
+++ b/src/Init/Data/Array/Subarray/Split.lean
@@ -23,13 +23,16 @@ def split (s : Subarray α) (i : Fin s.size.succ) : (Subarray α × Subarray α)
  let ⟨i', isLt⟩ := i
  have := s.start_le_stop
  have := s.stop_le_array_size
+  have : i' ≤ s.stop - s.start := Nat.lt_succ.mp isLt
+  have : s.start + i' ≤ s.stop := by omega
+  have : s.start + i' ≤ s.array.size := by omega
  have : s.start + i' ≤ s.stop := by
    simp only [size] at isLt
    omega
  let pre := {s with
    stop := s.start + i',
    start_le_stop := by omega,
-    stop_le_array_size := by omega
+    stop_le_array_size := by assumption
  }
  let post := {s with
    start := s.start + i'
@@ -45,7 +48,9 @@ def drop (arr : Subarray α) (i : Nat) : Subarray α where
  array := arr.array
  start := min (arr.start + i) arr.stop
  stop := arr.stop
-  start_le_stop := by omega
+  start_le_stop := by
+    rw [Nat.min_def]
+    split <;> simp only [Nat.le_refl, *]
  stop_le_array_size := arr.stop_le_array_size

 /--
@@ -58,7 +63,9 @@ def take (arr : Subarray α) (i : Nat) : Subarray α where
  stop := min (arr.start + i) arr.stop
  start_le_stop := by
    have := arr.start_le_stop
-    omega
+    rw [Nat.min_def]
+    split <;> omega
  stop_le_array_size := by
    have := arr.stop_le_array_size
-    omega
+    rw [Nat.min_def]
+    split <;> omega
--- a/src/Init/Data/BitVec/Basic.lean
+++ b/src/Init/Data/BitVec/Basic.lean
@@ -29,6 +29,9 @@ section Nat

 instance natCastInst : NatCast (BitVec w) := ⟨BitVec.ofNat w⟩

+@[deprecated isLt (since := "2024-03-12")]
+theorem toNat_lt (x : BitVec n) : x.toNat < 2^n := x.isLt
+
 /-- Theorem for normalizing the bit vector literal representation. -/
 -- TODO: This needs more usage data to assess which direction the simp should go.
@[simp, bv_toNat] theorem ofNat_eq_ofNat : @OfNat.ofNat (BitVec n) i _ = .ofNat n i := rfl
@@ -631,16 +634,6 @@ def twoPow (w : Nat) (i : Nat) : BitVec w := 1#w <<< i

 end bitwise

-/-- Compute a hash of a bitvector, combining 64-bit words using `mixHash`. -/
-def hash (bv : BitVec n) : UInt64 :=
-  if n ≤ 64 then
-    bv.toFin.val.toUInt64
-  else
-    mixHash (bv.toFin.val.toUInt64) (hash ((bv >>> 64).setWidth (n - 64)))
-
-instance : Hashable (BitVec n) where
-  hash := hash
-
 section normalization_eqs
 /-! We add simp-lemmas that rewrite bitvector operations into the equivalent notation -/
@[simp] theorem append_eq (x : BitVec w) (y : BitVec v)   : BitVec.append x y = x ++ y        := rfl
--- a/src/Init/Data/BitVec/Bitblast.lean
+++ b/src/Init/Data/BitVec/Bitblast.lean
@@ -76,7 +76,7 @@ to prove the correctness of the circuit that is built by `bv_decide`.
 def blastMul (aig : AIG BVBit) (input : AIG.BinaryRefVec aig w) : AIG.RefVecEntry BVBit w
 theorem denote_blastMul (aig : AIG BVBit) (lhs rhs : BitVec w) (assign : Assignment) :
   ...
-   ⟦(blastMul aig input).aig, (blastMul aig input).vec[idx], assign.toAIGAssignment⟧
+   ⟦(blastMul aig input).aig, (blastMul aig input).vec.get idx hidx, assign.toAIGAssignment⟧
     =
   (lhs * rhs).getLsbD idx
 ```
@@ -174,30 +174,6 @@ theorem carry_succ (i : Nat) (x y : BitVec w) (c : Bool) :
    exact mod_two_pow_add_mod_two_pow_add_bool_lt_two_pow_succ ..
  cases x.toNat.testBit i <;> cases y.toNat.testBit i <;> (simp; omega)

-theorem carry_succ_one (i : Nat) (x : BitVec w) (h : 0 < w) :
-    carry (i+1) x (1#w) false = decide (∀ j ≤ i, x.getLsbD j = true) := by
-  induction i with
-  | zero => simp [carry_succ, h]
-  | succ i ih =>
-    rw [carry_succ, ih]
-    simp only [getLsbD_one, add_one_ne_zero, decide_false, Bool.and_false, atLeastTwo_false_mid]
-    cases hx : x.getLsbD (i+1)
-    case false =>
-      have : ∃ j ≤ i + 1, x.getLsbD j = false :=
-        ⟨i+1, by omega, hx⟩
-      simpa
-    case true =>
-      suffices
-          (∀ (j : Nat), j ≤ i → x.getLsbD j = true)
-          ↔ (∀ (j : Nat), j ≤ i + 1 → x.getLsbD j = true) by
-        simpa
-      constructor
-      · intro h j hj
-        rcases Nat.le_or_eq_of_le_succ hj with (hj' | rfl)
-        · apply h; assumption
-        · exact hx
-      · intro h j hj; apply h; omega
-
 /--
 If `x &&& y = 0`, then the carry bit `(x + y + 0)` is always `false` for any index `i`.
 Intuitively, this is because a carry is only produced when at least two of `x`, `y`, and the
@@ -249,7 +225,7 @@ theorem getLsbD_add_add_bool {i : Nat} (i_lt : i < w) (x y : BitVec w) (c : Bool
    [ Nat.testBit_mod_two_pow,
      Nat.testBit_mul_two_pow_add_eq,
      i_lt,
-      decide_true,
+      decide_True,
      Bool.true_and,
      Nat.add_assoc,
      Nat.add_left_comm (_%_) (_ * _) _,
@@ -346,10 +322,6 @@ theorem getMsbD_sub {i : Nat} {i_lt : i < w} {x y : BitVec w} :
  · rfl
  · omega

-theorem getElem_sub {i : Nat} {x y : BitVec w} (h : i < w) :
-    (x - y)[i] = (x[i] ^^ ((~~~y + 1#w)[i] ^^ carry i x (~~~y + 1#w) false)) := by
-  simp [← getLsbD_eq_getElem, getLsbD_sub, h]
-
 theorem msb_sub {x y: BitVec w} :
    (x - y).msb
      = (x.msb ^^ ((~~~y + 1#w).msb ^^ carry (w - 1 - 0) x (~~~y + 1#w) false)) := by
@@ -380,121 +352,6 @@ theorem bit_neg_eq_neg (x : BitVec w) : -x = (adc (((iunfoldr (fun (i : Fin w) c
    simp [← sub_toAdd, BitVec.sub_add_cancel]
  · simp [bit_not_testBit x _]

-/--
-Remember that negating a bitvector is equal to incrementing the complement
-by one, i.e., `-x = ~~~x + 1`. See also `neg_eq_not_add`.
-
-This computation has two crucial properties:
- The least significant bit of `-x` is the same as the least significant bit of `x`, and
- The `i+1`-th least significant bit of `-x` is the complement of the `i+1`-th bit of `x`, unless
-  all of the preceding bits are `false`, in which case the bit is equal to the `i+1`-th bit of `x`
-/
-theorem getLsbD_neg {i : Nat} {x : BitVec w} :
-    getLsbD (-x) i =
-      (getLsbD x i ^^ decide (i < w) && decide (∃ j < i, getLsbD x j = true)) := by
-  rw [neg_eq_not_add]
-  by_cases hi : i < w
-  · rw [getLsbD_add hi]
-    have : 0 < w := by omega
-    simp only [getLsbD_not, hi, decide_true, Bool.true_and, getLsbD_one, this, not_bne,
-      _root_.true_and, not_eq_eq_eq_not]
-    cases i with
-    | zero =>
-      have carry_zero : carry 0 ?x ?y false = false := by
-        simp [carry]; omega
-      simp [hi, carry_zero]
-    | succ =>
-      rw [carry_succ_one _ _ (by omega), ← Bool.xor_not, ← decide_not]
-      simp only [add_one_ne_zero, decide_false, getLsbD_not, and_eq_true, decide_eq_true_eq,
-        not_eq_eq_eq_not, Bool.not_true, false_bne, not_exists, _root_.not_and, not_eq_true,
-        bne_right_inj, decide_eq_decide]
-      constructor
-      · rintro h j hj; exact And.right <| h j (by omega)
-      · rintro h j hj; exact ⟨by omega, h j (by omega)⟩
-  · have h_ge : w ≤ i := by omega
-    simp [getLsbD_ge _ _ h_ge, h_ge, hi]
-
-theorem getElem_neg {i : Nat} {x : BitVec w} (h : i < w) :
-    (-x)[i] = (x[i] ^^ decide (∃ j < i, x.getLsbD j = true)) := by
-  simp [← getLsbD_eq_getElem, getLsbD_neg, h]
-
-theorem getMsbD_neg {i : Nat} {x : BitVec w} :
-    getMsbD (-x) i =
-      (getMsbD x i ^^ decide (∃ j < w, i < j ∧ getMsbD x j = true)) := by
-  simp only [getMsbD, getLsbD_neg, Bool.decide_and, Bool.and_eq_true, decide_eq_true_eq]
-  by_cases hi : i < w
-  case neg =>
-    simp [hi]; omega
-  case pos =>
-    have h₁ : w - 1 - i < w := by omega
-    simp only [hi, decide_true, h₁, Bool.true_and, Bool.bne_right_inj, decide_eq_decide]
-    constructor
-    · rintro ⟨j, hj, h⟩
-      refine ⟨w - 1 - j, by omega, by omega, by omega, _root_.cast ?_ h⟩
-      congr; omega
-    · rintro ⟨j, hj₁, hj₂, -, h⟩
-      exact ⟨w - 1 - j, by omega, h⟩
-
-theorem msb_neg {w : Nat} {x : BitVec w} :
-    (-x).msb = ((x != 0#w && x != intMin w) ^^ x.msb) := by
-  simp only [BitVec.msb, getMsbD_neg]
-  by_cases hmin : x = intMin _
-  case pos =>
-    have : (∃ j, j < w ∧ 0 < j ∧ 0 < w ∧ j = 0) ↔ False := by
-      simp; omega
-    simp [hmin, getMsbD_intMin, this]
-  case neg =>
-    by_cases hzero : x = 0#w
-    case pos => simp [hzero]
-    case neg =>
-      have w_pos : 0 < w := by
-        cases w
-        · rw [@of_length_zero x] at hzero
-          contradiction
-        · omega
-      suffices ∃ j, j < w ∧ 0 < j ∧ x.getMsbD j = true
-        by simp [show x != 0#w by simpa, show x != intMin w by simpa, this]
-      false_or_by_contra
-      rename_i getMsbD_x
-      simp only [not_exists, _root_.not_and, not_eq_true] at getMsbD_x
-      /- `getMsbD` says that all bits except the msb are `false` -/
-      cases hmsb : x.msb
-      case true =>
-        apply hmin
-        apply eq_of_getMsbD_eq
-        rintro ⟨i, hi⟩
-        simp only [getMsbD_intMin, w_pos, decide_true, Bool.true_and]
-        cases i
-        case zero => exact hmsb
-        case succ => exact getMsbD_x _ hi (by omega)
-      case false =>
-        apply hzero
-        apply eq_of_getMsbD_eq
-        rintro ⟨i, hi⟩
-        simp only [getMsbD_zero]
-        cases i
-        case zero => exact hmsb
-        case succ => exact getMsbD_x _ hi (by omega)
-
-/-! ### abs -/
-
-theorem msb_abs {w : Nat} {x : BitVec w} :
-    x.abs.msb = (decide (x = intMin w) && decide (0 < w)) := by
-  simp only [BitVec.abs, getMsbD_neg, ne_eq, decide_not, Bool.not_bne]
-  by_cases h₀ : 0 < w
-  · by_cases h₁ : x = intMin w
-    · simp [h₁, msb_intMin]
-    · simp only [neg_eq, h₁, decide_false]
-      by_cases h₂ : x.msb
-      · simp [h₂, msb_neg]
-        and_intros
-        · by_cases h₃ : x = 0#w
-          · simp [h₃] at h₂
-          · simp [h₃]
-        · simp [h₁]
-      · simp [h₂]
-  · simp [BitVec.msb, show w = 0 by omega]
-
 /-! ### Inequalities (le / lt) -/

 theorem ult_eq_not_carry (x y : BitVec w) : x.ult y = !carry w x (~~~y) true := by
@@ -574,18 +431,18 @@ theorem setWidth_setWidth_succ_eq_setWidth_setWidth_add_twoPow (x : BitVec w) (i
      setWidth w (x.setWidth i) + (x &&& twoPow w i) := by
  rw [add_eq_or_of_and_eq_zero]
  · ext k
-    simp only [getLsbD_setWidth, Fin.is_lt, decide_true, Bool.true_and, getLsbD_or, getLsbD_and]
+    simp only [getLsbD_setWidth, Fin.is_lt, decide_True, Bool.true_and, getLsbD_or, getLsbD_and]
    by_cases hik : i = k
    · subst hik
      simp
-    · simp only [getLsbD_twoPow, hik, decide_false, Bool.and_false, Bool.or_false]
+    · simp only [getLsbD_twoPow, hik, decide_False, Bool.and_false, Bool.or_false]
      by_cases hik' : k < (i + 1)
      · have hik'' : k < i := by omega
        simp [hik', hik'']
      · have hik'' : ¬ (k < i) := by omega
        simp [hik', hik'']
  · ext k
-    simp only [and_twoPow, getLsbD_and, getLsbD_setWidth, Fin.is_lt, decide_true, Bool.true_and,
+    simp only [and_twoPow, getLsbD_and, getLsbD_setWidth, Fin.is_lt, decide_True, Bool.true_and,
      getLsbD_zero, and_eq_false_imp, and_eq_true, decide_eq_true_eq, and_imp]
    by_cases hi : x.getLsbD i <;> simp [hi] <;> omega

@@ -1100,8 +957,8 @@ def sshiftRightRec (x : BitVec w₁) (y : BitVec w₂) (n : Nat) : BitVec w₁ :

@[simp]
 theorem sshiftRightRec_zero_eq (x : BitVec w₁) (y : BitVec w₂) :
-    sshiftRightRec x y 0 = x.sshiftRight' (y &&& twoPow w₂ 0) := by
-  simp only [sshiftRightRec]
+    sshiftRightRec x y 0 = x.sshiftRight' (y &&& 1#w₂) := by
+  simp only [sshiftRightRec, twoPow_zero]

@[simp]
 theorem sshiftRightRec_succ_eq (x : BitVec w₁) (y : BitVec w₂) (n : Nat) :
--- a/src/Init/Data/BitVec/Folds.lean
+++ b/src/Init/Data/BitVec/Folds.lean
@@ -65,7 +65,7 @@ theorem iunfoldr_getLsbD' {f : Fin w → α → α × Bool} (state : Nat → α)
    intro
    apply And.intro
    · intro i
-      have := Fin.pos i
+      have := Fin.size_pos i
      contradiction
    · rfl
  case step =>
--- a/src/Init/Data/BitVec/Lemmas.lean
+++ b/src/Init/Data/BitVec/Lemmas.lean
@@ -123,7 +123,7 @@ theorem getMsbD_eq_getLsbD (x : BitVec w) (i : Nat) : x.getMsbD i = (decide (i <
 theorem getLsbD_eq_getMsbD (x : BitVec w) (i : Nat) : x.getLsbD i = (decide (i < w) && x.getMsbD (w - 1 - i)) := by
  rw [getMsbD]
  by_cases h₁ : i < w <;> by_cases h₂ : w - 1 - i < w <;>
-    simp only [h₁, h₂] <;> simp only [decide_true, decide_false, Bool.false_and, Bool.and_false, Bool.true_and, Bool.and_true]
+    simp only [h₁, h₂] <;> simp only [decide_True, decide_False, Bool.false_and, Bool.and_false, Bool.true_and, Bool.and_true]
  · congr
    omega
  all_goals
@@ -269,10 +269,6 @@ theorem ofBool_eq_iff_eq : ∀ {b b' : Bool}, BitVec.ofBool b = BitVec.ofBool b'
  getLsbD (x#'lt) i = x.testBit i := by
  simp [getLsbD, BitVec.ofNatLt]

-@[simp] theorem getMsbD_ofNatLt {n x i : Nat} (h : x < 2^n) :
-    getMsbD (x#'h) i = (decide (i < n) && x.testBit (n - 1 - i)) := by
-  simp [getMsbD, getLsbD]
-
@[simp, bv_toNat] theorem toNat_ofNat (x w : Nat) : (BitVec.ofNat w x).toNat = x % 2^w := by
  simp [BitVec.toNat, BitVec.ofNat, Fin.ofNat']

@@ -390,7 +386,7 @@ theorem msb_eq_getLsbD_last (x : BitVec w) :
    · simp [Nat.div_eq_of_lt h, h]
    · simp only [h]
      rw [Nat.div_eq_sub_div (Nat.two_pow_pos w) h, Nat.div_eq_of_lt]
-      · simp
+      · decide
      · omega

@[bv_toNat] theorem getLsbD_succ_last (x : BitVec (w + 1)) :
@@ -516,31 +512,6 @@ theorem eq_zero_or_eq_one (a : BitVec 1) : a = 0#1 ∨ a = 1#1 := by
    subst h
    simp

-@[simp]
-theorem toInt_zero {w : Nat} : (0#w).toInt = 0 := by
-  simp [BitVec.toInt, show 0 < 2^w by exact Nat.two_pow_pos w]
-
-/-! ### slt -/
-
-/--
-A bitvector, when interpreted as an integer, is less than zero iff
-its most significant bit is true.
-/
-theorem slt_zero_iff_msb_cond (x : BitVec w) : x.slt 0#w ↔ x.msb = true := by
-  have := toInt_eq_msb_cond x
-  constructor
-  · intros h
-    apply Classical.byContradiction
-    intros hmsb
-    simp only [Bool.not_eq_true] at hmsb
-    simp only [hmsb, Bool.false_eq_true, ↓reduceIte] at this
-    simp only [BitVec.slt, toInt_zero, decide_eq_true_eq] at h
-    omega /- Can't have `x.toInt` which is equal to `x.toNat` be strictly less than zero -/
-  · intros h
-    simp only [h, ↓reduceIte] at this
-    simp [BitVec.slt, this]
-    omega
-
 /-! ### setWidth, zeroExtend and truncate -/

@[simp]
@@ -565,10 +536,6 @@ theorem zeroExtend_eq_setWidth {v : Nat} {x : BitVec w} :
  else
    simp [n_le_i, toNat_ofNat]

-@[simp] theorem toInt_setWidth (x : BitVec w) :
-    (x.setWidth v).toInt = Int.bmod x.toNat (2^v) := by
-  simp [toInt_eq_toNat_bmod, toNat_setWidth, Int.emod_bmod]
-
 theorem setWidth'_eq {x : BitVec w} (h : w ≤ v) : x.setWidth' h = x.setWidth v := by
  apply eq_of_toNat_eq
  rw [toNat_setWidth, toNat_setWidth']
@@ -666,7 +633,7 @@ theorem getElem?_setWidth (m : Nat) (x : BitVec n) (i : Nat) :
@[simp] theorem setWidth_setWidth_of_le (x : BitVec w) (h : k ≤ l) :
    (x.setWidth l).setWidth k = x.setWidth k := by
  ext i
-  simp only [getLsbD_setWidth, Fin.is_lt, decide_true, Bool.true_and]
+  simp only [getLsbD_setWidth, Fin.is_lt, decide_True, Bool.true_and]
  have p := lt_of_getLsbD (x := x) (i := i)
  revert p
  cases getLsbD x i <;> simp; omega
@@ -696,7 +663,7 @@ theorem setWidth_one_eq_ofBool_getLsb_zero (x : BitVec w) :
 theorem setWidth_ofNat_one_eq_ofNat_one_of_lt {v w : Nat} (hv : 0 < v) :
    (BitVec.ofNat v 1).setWidth w = BitVec.ofNat w 1 := by
  ext ⟨i, hilt⟩
-  simp only [getLsbD_setWidth, hilt, decide_true, getLsbD_ofNat, Bool.true_and,
+  simp only [getLsbD_setWidth, hilt, decide_True, getLsbD_ofNat, Bool.true_and,
    Bool.and_iff_right_iff_imp, decide_eq_true_eq]
  intros hi₁
  have hv := Nat.testBit_one_eq_true_iff_self_eq_zero.mp hi₁
@@ -763,18 +730,14 @@ theorem extractLsb'_eq_extractLsb {w : Nat} (x : BitVec w) (start len : Nat) (h
@[simp] theorem getLsbD_allOnes : (allOnes v).getLsbD i = decide (i < v) := by
  simp [allOnes]

-@[simp] theorem getMsbD_allOnes : (allOnes v).getMsbD i = decide (i < v) := by
-  simp [allOnes]
-  omega
-
@[simp] theorem getElem_allOnes (i : Nat) (h : i < v) : (allOnes v)[i] = true := by
  simp [getElem_eq_testBit_toNat, h]

@[simp] theorem ofFin_add_rev (x : Fin (2^n)) : ofFin (x + x.rev) = allOnes n := by
  ext
-  simp only [Fin.rev, getLsbD_ofFin, getLsbD_allOnes, Fin.is_lt, decide_true]
+  simp only [Fin.rev, getLsbD_ofFin, getLsbD_allOnes, Fin.is_lt, decide_True]
  rw [Fin.add_def]
-  simp only [Nat.testBit_mod_two_pow, Fin.is_lt, decide_true, Bool.true_and]
+  simp only [Nat.testBit_mod_two_pow, Fin.is_lt, decide_True, Bool.true_and]
  have h : (x : Nat) + (2 ^ n - (x + 1)) = 2 ^ n - 1 := by omega
  rw [h, Nat.testBit_two_pow_sub_one]
  simp
@@ -784,12 +747,6 @@ theorem extractLsb'_eq_extractLsb {w : Nat} (x : BitVec w) (start len : Nat) (h
@[simp] theorem toNat_or (x y : BitVec v) :
    BitVec.toNat (x ||| y) = BitVec.toNat x ||| BitVec.toNat y := rfl

-@[simp] theorem toInt_or (x y : BitVec w) :
-    BitVec.toInt (x ||| y) = Int.bmod (BitVec.toNat x ||| BitVec.toNat y) (2^w) := by
-  rw_mod_cast [Int.bmod_def, BitVec.toInt, toNat_or, Nat.mod_eq_of_lt
-    (Nat.or_lt_two_pow (BitVec.isLt x) (BitVec.isLt y))]
-  omega
-
@[simp] theorem toFin_or (x y : BitVec v) :
    BitVec.toFin (x ||| y) = BitVec.toFin x ||| BitVec.toFin y := by
  apply Fin.eq_of_val_eq
@@ -857,12 +814,6 @@ instance : Std.LawfulCommIdentity (α := BitVec n) (· ||| · ) (0#n) where
@[simp] theorem toNat_and (x y : BitVec v) :
    BitVec.toNat (x &&& y) = BitVec.toNat x &&& BitVec.toNat y := rfl

-@[simp] theorem toInt_and (x y : BitVec w) :
-    BitVec.toInt (x &&& y) = Int.bmod (BitVec.toNat x &&& BitVec.toNat y) (2^w) := by
-  rw_mod_cast [Int.bmod_def, BitVec.toInt, toNat_and, Nat.mod_eq_of_lt
-    (Nat.and_lt_two_pow x.toNat (BitVec.isLt y))]
-  omega
-
@[simp] theorem toFin_and (x y : BitVec v) :
    BitVec.toFin (x &&& y) = BitVec.toFin x &&& BitVec.toFin y := by
  apply Fin.eq_of_val_eq
@@ -930,12 +881,6 @@ instance : Std.LawfulCommIdentity (α := BitVec n) (· &&& · ) (allOnes n) wher
@[simp] theorem toNat_xor (x y : BitVec v) :
    BitVec.toNat (x ^^^ y) = BitVec.toNat x ^^^ BitVec.toNat y := rfl

-@[simp] theorem toInt_xor (x y : BitVec w) :
-    BitVec.toInt (x ^^^ y) = Int.bmod (BitVec.toNat x ^^^ BitVec.toNat y) (2^w) := by
-  rw_mod_cast [Int.bmod_def, BitVec.toInt, toNat_xor, Nat.mod_eq_of_lt
-    (Nat.xor_lt_two_pow (BitVec.isLt x) (BitVec.isLt y))]
-  omega
-
@[simp] theorem toFin_xor (x y : BitVec v) :
    BitVec.toFin (x ^^^ y) = BitVec.toFin x ^^^ BitVec.toFin y := by
  apply Fin.eq_of_val_eq
@@ -1013,13 +958,6 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
          _ ≤ 2 ^ i := Nat.pow_le_pow_of_le_right Nat.zero_lt_two w
      · simp

-@[simp] theorem toInt_not {x : BitVec w} :
-    (~~~x).toInt = Int.bmod (2^w - 1 - x.toNat) (2^w) := by
-  rw_mod_cast [BitVec.toInt, BitVec.toNat_not, Int.bmod_def]
-  simp [show ((2^w : Nat) : Int) - 1 - x.toNat = ((2^w - 1 - x.toNat) : Nat) by omega]
-  rw_mod_cast [Nat.mod_eq_of_lt (by omega)]
-  omega
-
@[simp] theorem ofInt_negSucc_eq_not_ofNat {w n : Nat} :
    BitVec.ofInt w (Int.negSucc n) = ~~~.ofNat w n := by
  simp only [BitVec.ofInt, Int.toNat, Int.ofNat_eq_coe, toNat_eq, toNat_ofNatLt, toNat_not,
@@ -1044,10 +982,6 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
@[simp] theorem getLsbD_not {x : BitVec v} : (~~~x).getLsbD i = (decide (i < v) && ! x.getLsbD i) := by
  by_cases h' : i < v <;> simp_all [not_def]

-@[simp] theorem getMsbD_not {x : BitVec v} :
-    (~~~x).getMsbD i = (decide (i < v) && ! x.getMsbD i) := by
-  by_cases h' : i < v <;> simp_all [not_def]
-
@[simp] theorem getElem_not {x : BitVec w} {i : Nat} (h : i < w) : (~~~x)[i] = !x[i] := by
  simp only [getElem_eq_testBit_toNat, toNat_not]
  rw [← Nat.sub_add_eq, Nat.add_comm 1]
@@ -1155,21 +1089,21 @@ theorem zero_shiftLeft (n : Nat) : 0#w <<< n = 0#w := by
 theorem shiftLeft_xor_distrib (x y : BitVec w) (n : Nat) :
    (x ^^^ y) <<< n = (x <<< n) ^^^ (y <<< n) := by
  ext i
-  simp only [getLsbD_shiftLeft, Fin.is_lt, decide_true, Bool.true_and, getLsbD_xor]
+  simp only [getLsbD_shiftLeft, Fin.is_lt, decide_True, Bool.true_and, getLsbD_xor]
  by_cases h : i < n
    <;> simp [h]

 theorem shiftLeft_and_distrib (x y : BitVec w) (n : Nat) :
    (x &&& y) <<< n = (x <<< n) &&& (y <<< n) := by
  ext i
-  simp only [getLsbD_shiftLeft, Fin.is_lt, decide_true, Bool.true_and, getLsbD_and]
+  simp only [getLsbD_shiftLeft, Fin.is_lt, decide_True, Bool.true_and, getLsbD_and]
  by_cases h : i < n
    <;> simp [h]

 theorem shiftLeft_or_distrib (x y : BitVec w) (n : Nat) :
    (x ||| y) <<< n = (x <<< n) ||| (y <<< n) := by
  ext i
-  simp only [getLsbD_shiftLeft, Fin.is_lt, decide_true, Bool.true_and, getLsbD_or]
+  simp only [getLsbD_shiftLeft, Fin.is_lt, decide_True, Bool.true_and, getLsbD_or]
  by_cases h : i < n
    <;> simp [h]

@@ -1180,9 +1114,9 @@ theorem shiftLeft_or_distrib (x y : BitVec w) (n : Nat) :
  · subst h; simp
  have t : w - 1 - k < w := by omega
  simp only [t]
-  simp only [decide_true, Nat.sub_sub, Bool.true_and, Nat.add_assoc]
+  simp only [decide_True, Nat.sub_sub, Bool.true_and, Nat.add_assoc]
  by_cases h₁ : k < w <;> by_cases h₂ : w - (1 + k) < i <;> by_cases h₃ : k + i < w
-    <;> simp only [h₁, h₂, h₃, decide_false, h₂, decide_true, Bool.not_true, Bool.false_and, Bool.and_self,
+    <;> simp only [h₁, h₂, h₃, decide_False, h₂, decide_True, Bool.not_true, Bool.false_and, Bool.and_self,
      Bool.true_and, Bool.false_eq, Bool.false_and, Bool.not_false]
    <;> (first | apply getLsbD_ge | apply Eq.symm; apply getLsbD_ge)
    <;> omega
@@ -1226,7 +1160,7 @@ theorem shiftLeftZeroExtend_eq {x : BitVec w} :
 theorem shiftLeft_add {w : Nat} (x : BitVec w) (n m : Nat) :
    x <<< (n + m) = (x <<< n) <<< m := by
  ext i
-  simp only [getLsbD_shiftLeft, Fin.is_lt, decide_true, Bool.true_and]
+  simp only [getLsbD_shiftLeft, Fin.is_lt, decide_True, Bool.true_and]
  rw [show i - (n + m) = (i - m - n) by omega]
  cases h₂ : decide (i < m) <;>
  cases h₃ : decide (i - m < w) <;>
@@ -1324,8 +1258,7 @@ theorem getMsbD_ushiftRight {x : BitVec w} {i n : Nat} :
  · simp [getLsbD_ge, show w ≤ (n + (w - 1 - i)) by omega]
    omega
  · by_cases h₁ : i < w
-    · simp only [h, decide_false, Bool.not_false, show i - n < w by omega, decide_true,
-        Bool.true_and]
+    · simp only [h, ushiftRight_eq, getLsbD_ushiftRight, show i - n < w by omega]
      congr
      omega
    · simp [h, h₁]
@@ -1394,17 +1327,17 @@ theorem getLsbD_sshiftRight (x : BitVec w) (s i : Nat) :
  rcases hmsb : x.msb with rfl | rfl
  · simp only [sshiftRight_eq_of_msb_false hmsb, getLsbD_ushiftRight, Bool.if_false_right]
    by_cases hi : i ≥ w
-    · simp only [hi, decide_true, Bool.not_true, Bool.false_and]
+    · simp only [hi, decide_True, Bool.not_true, Bool.false_and]
      apply getLsbD_ge
      omega
-    · simp only [hi, decide_false, Bool.not_false, Bool.true_and, Bool.iff_and_self,
+    · simp only [hi, decide_False, Bool.not_false, Bool.true_and, Bool.iff_and_self,
        decide_eq_true_eq]
      intros hlsb
      apply BitVec.lt_of_getLsbD hlsb
  · by_cases hi : i ≥ w
    · simp [hi]
    · simp only [sshiftRight_eq_of_msb_true hmsb, getLsbD_not, getLsbD_ushiftRight, Bool.not_and,
-        Bool.not_not, hi, decide_false, Bool.not_false, Bool.if_true_right, Bool.true_and,
+        Bool.not_not, hi, decide_False, Bool.not_false, Bool.if_true_right, Bool.true_and,
        Bool.and_iff_right_iff_imp, Bool.or_eq_true, Bool.not_eq_true', decide_eq_false_iff_not,
        Nat.not_lt, decide_eq_true_eq]
      omega
@@ -1449,7 +1382,7 @@ theorem msb_sshiftRight {n : Nat} {x : BitVec w} :
  rw [msb_eq_getLsbD_last, getLsbD_sshiftRight, msb_eq_getLsbD_last]
  by_cases hw₀ : w = 0
  · simp [hw₀]
-  · simp only [show ¬(w ≤ w - 1) by omega, decide_false, Bool.not_false, Bool.true_and,
+  · simp only [show ¬(w ≤ w - 1) by omega, decide_False, Bool.not_false, Bool.true_and,
      ite_eq_right_iff]
    intros h
    simp [show n = 0 by omega]
@@ -1468,7 +1401,7 @@ theorem sshiftRight_add {x : BitVec w} {m n : Nat} :
  simp only [getLsbD_sshiftRight, Nat.add_assoc]
  by_cases h₁ : w ≤ (i : Nat)
  · simp [h₁]
-  · simp only [h₁, decide_false, Bool.not_false, Bool.true_and]
+  · simp only [h₁, decide_False, Bool.not_false, Bool.true_and]
    by_cases h₂ : n + ↑i < w
    · simp [h₂]
    · simp only [h₂, ↓reduceIte]
@@ -1480,7 +1413,7 @@ theorem sshiftRight_add {x : BitVec w} {m n : Nat} :
 theorem not_sshiftRight {b : BitVec w} :
    ~~~b.sshiftRight n = (~~~b).sshiftRight n := by
  ext i
-  simp only [getLsbD_not, Fin.is_lt, decide_true, getLsbD_sshiftRight, Bool.not_and, Bool.not_not,
+  simp only [getLsbD_not, Fin.is_lt, decide_True, getLsbD_sshiftRight, Bool.not_and, Bool.not_not,
    Bool.true_and, msb_not]
  by_cases h : w ≤ i
  <;> by_cases h' : n + i < w
@@ -1498,15 +1431,15 @@ theorem getMsbD_sshiftRight {x : BitVec w} {i n : Nat} :
    getMsbD (x.sshiftRight n) i = (decide (i < w) && if i < n then x.msb else getMsbD x (i - n)) := by
  simp only [getMsbD, BitVec.getLsbD_sshiftRight]
  by_cases h : i < w
-  · simp only [h, decide_true, Bool.true_and]
+  · simp only [h, decide_True, Bool.true_and]
    by_cases h₁ : w ≤ w - 1 - i
    · simp [h₁]
      omega
-    · simp only [h₁, decide_false, Bool.not_false, Bool.true_and]
+    · simp only [h₁, decide_False, Bool.not_false, Bool.true_and]
      by_cases h₂ : i < n
      · simp only [h₂, ↓reduceIte, ite_eq_right_iff]
        omega
-      · simp only [show i - n < w by omega, h₂, ↓reduceIte, decide_true, Bool.true_and]
+      · simp only [show i - n < w by omega, h₂, ↓reduceIte, decide_True, Bool.true_and]
        by_cases h₄ : n + (w - 1 - i) < w <;> (simp only [h₄, ↓reduceIte]; congr; omega)
  · simp [h]

@@ -1521,26 +1454,20 @@ theorem getLsbD_sshiftRight' {x y: BitVec w} {i : Nat} :
      (!decide (w ≤ i) && if y.toNat + i < w then x.getLsbD (y.toNat + i) else x.msb) := by
  simp only [BitVec.sshiftRight', BitVec.getLsbD_sshiftRight]

-@[simp]
-theorem getElem_sshiftRight' {x y : BitVec w} {i : Nat} (h : i < w) :
-    (x.sshiftRight' y)[i] =
-      (!decide (w ≤ i) && if y.toNat + i < w then x.getLsbD (y.toNat + i) else x.msb) := by
-  simp only [← getLsbD_eq_getElem, BitVec.sshiftRight', BitVec.getLsbD_sshiftRight]
-
@[simp]
 theorem getMsbD_sshiftRight' {x y: BitVec w} {i : Nat} :
    (x.sshiftRight y.toNat).getMsbD i = (decide (i < w) && if i < y.toNat then x.msb else x.getMsbD (i - y.toNat)) := by
  simp only [BitVec.sshiftRight', getMsbD, BitVec.getLsbD_sshiftRight]
  by_cases h : i < w
-  · simp only [h, decide_true, Bool.true_and]
+  · simp only [h, decide_True, Bool.true_and]
    by_cases h₁ : w ≤ w - 1 - i
    · simp [h₁]
      omega
-    · simp only [h₁, decide_false, Bool.not_false, Bool.true_and]
+    · simp only [h₁, decide_False, Bool.not_false, Bool.true_and]
      by_cases h₂ : i < y.toNat
      · simp only [h₂, ↓reduceIte, ite_eq_right_iff]
        omega
-      · simp only [show i - y.toNat < w by omega, h₂, ↓reduceIte, decide_true, Bool.true_and]
+      · simp only [show i - y.toNat < w by omega, h₂, ↓reduceIte, decide_True, Bool.true_and]
        by_cases h₄ : y.toNat + (w - 1 - i) < w <;> (simp only [h₄, ↓reduceIte]; congr; omega)
  · simp [h]

@@ -1565,11 +1492,11 @@ theorem signExtend_eq_not_setWidth_not_of_msb_false {x : BitVec w} {v : Nat} (hm
    x.signExtend v = x.setWidth v := by
  ext i
  by_cases hv : i < v
-  · simp only [signExtend, getLsbD, getLsbD_setWidth, hv, decide_true, Bool.true_and, toNat_ofInt,
+  · simp only [signExtend, getLsbD, getLsbD_setWidth, hv, decide_True, Bool.true_and, toNat_ofInt,
      BitVec.toInt_eq_msb_cond, hmsb, ↓reduceIte, reduceCtorEq]
    rw [Int.ofNat_mod_ofNat, Int.toNat_ofNat, Nat.testBit_mod_two_pow]
    simp [BitVec.testBit_toNat]
-  · simp only [getLsbD_setWidth, hv, decide_false, Bool.false_and]
+  · simp only [getLsbD_setWidth, hv, decide_False, Bool.false_and]
    apply getLsbD_ge
    omega

@@ -1611,7 +1538,7 @@ theorem getElem_signExtend {x  : BitVec w} {v i : Nat} (h : i < v) :
 theorem signExtend_eq_setWidth_of_lt (x : BitVec w) {v : Nat} (hv : v ≤ w):
  x.signExtend v = x.setWidth v := by
  ext i
-  simp only [getLsbD_signExtend, Fin.is_lt, decide_true, Bool.true_and, getLsbD_setWidth,
+  simp only [getLsbD_signExtend, Fin.is_lt, decide_True, Bool.true_and, getLsbD_setWidth,
    ite_eq_left_iff, Nat.not_lt]
  omega

@@ -1619,82 +1546,6 @@ theorem signExtend_eq_setWidth_of_lt (x : BitVec w) {v : Nat} (hv : v ≤ w):
 theorem signExtend_eq (x : BitVec w) : x.signExtend w = x := by
  rw [signExtend_eq_setWidth_of_lt _ (Nat.le_refl _), setWidth_eq]

-/-- Sign extending to a larger bitwidth depends on the msb.
-If the msb is false, then the result equals the original value.
-If the msb is true, then we add a value of `(2^v - 2^w)`, which arises from the sign extension. -/
-private theorem toNat_signExtend_of_le (x : BitVec w) {v : Nat} (hv : w ≤ v) :
-    (x.signExtend v).toNat = x.toNat + if x.msb then 2^v - 2^w else 0 := by
-  apply Nat.eq_of_testBit_eq
-  intro i
-  have ⟨k, hk⟩ := Nat.exists_eq_add_of_le hv
-  rw [hk, testBit_toNat, getLsbD_signExtend, Nat.pow_add, ← Nat.mul_sub_one, Nat.add_comm (x.toNat)]
-  by_cases hx : x.msb
-  · simp only [hx, Bool.if_true_right, ↓reduceIte,
-      Nat.testBit_mul_pow_two_add _ x.isLt,
-      testBit_toNat, Nat.testBit_two_pow_sub_one]
-    -- Case analysis on i being in the intervals [0..w), [w..w + k), [w+k..∞)
-    have hi : i < w ∨ (w ≤ i ∧ i < w + k) ∨ w + k ≤ i := by omega
-    rcases hi with hi | hi | hi
-    · simp [hi]; omega
-    · simp [hi]; omega
-    · simp [hi, show ¬ (i < w + k) by omega, show ¬ (i < w) by omega]
-      omega
-  · simp only [hx, Bool.if_false_right,
-      Bool.false_eq_true, ↓reduceIte, Nat.zero_add, testBit_toNat]
-    have hi : i < w ∨ (w ≤ i ∧ i < w + k) ∨ w + k ≤ i := by omega
-    rcases hi with hi | hi | hi
-    · simp [hi]; omega
-    · simp [hi]
-    · simp [hi, show ¬ (i < w + k) by omega, show ¬ (i < w) by omega, getLsbD_ge x i (by omega)]
-
-/-- Sign extending to a larger bitwidth depends on the msb.
-If the msb is false, then the result equals the original value.
-If the msb is true, then we add a value of `(2^v - 2^w)`, which arises from the sign extension. -/
-theorem toNat_signExtend (x : BitVec w) {v : Nat} :
-    (x.signExtend v).toNat = (x.setWidth v).toNat + if x.msb then 2^v - 2^w else 0 := by
-  by_cases h : v ≤ w
-  · have : 2^v ≤ 2^w := Nat.pow_le_pow_of_le_right Nat.two_pos h
-    simp [signExtend_eq_setWidth_of_lt x h, toNat_setWidth, Nat.sub_eq_zero_of_le this]
-  · have : 2^w ≤ 2^v := Nat.pow_le_pow_of_le_right Nat.two_pos (by omega)
-    rw [toNat_signExtend_of_le x (by omega), toNat_setWidth, Nat.mod_eq_of_lt (by omega)]
-
-/-
-If the current width `w` is smaller than the extended width `v`,
-then the value when interpreted as an integer does not change.
-/
-theorem toInt_signExtend_of_lt {x : BitVec w} (hv : w < v):
-    (x.signExtend v).toInt = x.toInt := by
-  simp only [toInt_eq_msb_cond, toNat_signExtend]
-  have : (x.signExtend v).msb = x.msb := by
-    rw [msb_eq_getLsbD_last, getLsbD_eq_getElem (Nat.sub_one_lt_of_lt hv)]
-    simp [getElem_signExtend, Nat.le_sub_one_of_lt hv]
-  have H : 2^w ≤ 2^v := Nat.pow_le_pow_of_le_right (by omega) (by omega)
-  simp only [this, toNat_setWidth, Int.natCast_add, Int.ofNat_emod, Int.natCast_mul]
-  by_cases h : x.msb
-  <;> norm_cast
-  <;> simp [h, Nat.mod_eq_of_lt (Nat.lt_of_lt_of_le x.isLt H)]
-  omega
-
-/-
-If the current width `w` is larger than the extended width `v`,
-then the value when interpreted as an integer is truncated,
-and we compute a modulo by `2^v`.
-/
-theorem toInt_signExtend_of_le {x : BitVec w} (hv : v ≤ w) :
-    (x.signExtend v).toInt = Int.bmod x.toNat (2^v) := by
-  simp [signExtend_eq_setWidth_of_lt _ hv]
-
-/-
-Interpreting the sign extension of `(x : BitVec w)` to width `v`
-computes `x % 2^v` (where `%` is the balanced mod).
-/
-theorem toInt_signExtend (x : BitVec w) :
-    (x.signExtend v).toInt = Int.bmod x.toNat (2^(min v w)) := by
-  by_cases hv : v ≤ w
-  · simp [toInt_signExtend_of_le hv, Nat.min_eq_left hv]
-  · simp only [Nat.not_le] at hv
-    rw [toInt_signExtend_of_lt hv, Nat.min_eq_right (by omega), toInt_eq_toNat_bmod]
-
 /-! ### append -/

 theorem append_def (x : BitVec v) (y : BitVec w) :
@@ -1771,7 +1622,7 @@ theorem setWidth_append {x : BitVec w} {y : BitVec v} :
    (x ++ y).setWidth k = if h : k ≤ v then y.setWidth k else (x.setWidth (k - v) ++ y).cast (by omega) := by
  apply eq_of_getLsbD_eq
  intro i
-  simp only [getLsbD_setWidth, Fin.is_lt, decide_true, getLsbD_append, Bool.true_and]
+  simp only [getLsbD_setWidth, Fin.is_lt, decide_True, getLsbD_append, Bool.true_and]
  split
  · have t : i < v := by omega
    simp [t]
@@ -1783,7 +1634,7 @@ theorem setWidth_append {x : BitVec w} {y : BitVec v} :
@[simp] theorem setWidth_append_of_eq {x : BitVec v} {y : BitVec w} (h : w' = w) : setWidth (v' + w') (x ++ y) = setWidth v' x ++ setWidth w' y := by
  subst h
  ext i
-  simp only [getLsbD_setWidth, Fin.is_lt, decide_true, getLsbD_append, cond_eq_if,
+  simp only [getLsbD_setWidth, Fin.is_lt, decide_True, getLsbD_append, cond_eq_if,
    decide_eq_true_eq, Bool.true_and, setWidth_eq]
  split
  · simp_all
@@ -1854,13 +1705,13 @@ theorem shiftRight_shiftRight {w : Nat} (x : BitVec w) (n m : Nat) :

 theorem getLsbD_rev (x : BitVec w) (i : Fin w) :
    x.getLsbD i.rev = x.getMsbD i := by
-  simp only [getLsbD, Fin.val_rev, getMsbD, Fin.is_lt, decide_true, Bool.true_and]
+  simp only [getLsbD, Fin.val_rev, getMsbD, Fin.is_lt, decide_True, Bool.true_and]
  congr 1
  omega

 theorem getElem_rev {x : BitVec w} {i : Fin w}:
    x[i.rev] = x.getMsbD i := by
-  simp only [Fin.getElem_fin, Fin.val_rev, getMsbD, Fin.is_lt, decide_true, Bool.true_and]
+  simp only [Fin.getElem_fin, Fin.val_rev, getMsbD, Fin.is_lt, decide_True, Bool.true_and]
  congr 1
  omega

@@ -1890,7 +1741,7 @@ theorem getLsbD_cons (b : Bool) {n} (x : BitVec n) (i : Nat) :
  · have p1 : ¬(n ≤ i) := by omega
    have p2 : i ≠ n := by omega
    simp [p1, p2]
-  · simp only [i_eq_n, ge_iff_le, Nat.le_refl, decide_true, Nat.sub_self, Nat.testBit_zero,
+  · simp only [i_eq_n, ge_iff_le, Nat.le_refl, decide_True, Nat.sub_self, Nat.testBit_zero,
    Bool.true_and, testBit_toNat, getLsbD_ge, Bool.or_false, ↓reduceIte]
    cases b <;> trivial
  · have p1 : i ≠ n := by omega
@@ -1905,7 +1756,7 @@ theorem getElem_cons {b : Bool} {n} {x : BitVec n} {i : Nat} (h : i < n + 1) :
  · have p1 : ¬(n ≤ i) := by omega
    have p2 : i ≠ n := by omega
    simp [p1, p2]
-  · simp only [i_eq_n, ge_iff_le, Nat.le_refl, decide_true, Nat.sub_self, Nat.testBit_zero,
+  · simp only [i_eq_n, ge_iff_le, Nat.le_refl, decide_True, Nat.sub_self, Nat.testBit_zero,
    Bool.true_and, testBit_toNat, getLsbD_ge, Bool.or_false, ↓reduceIte]
    cases b <;> trivial
  · have p1 : i ≠ n := by omega
@@ -1925,7 +1776,7 @@ theorem setWidth_succ (x : BitVec w) :
    setWidth (i+1) x = cons (getLsbD x i) (setWidth i x) := by
  apply eq_of_getLsbD_eq
  intro j
-  simp only [getLsbD_setWidth, getLsbD_cons, j.isLt, decide_true, Bool.true_and]
+  simp only [getLsbD_setWidth, getLsbD_cons, j.isLt, decide_True, Bool.true_and]
  if j_eq : j.val = i then
    simp [j_eq]
  else
@@ -1941,7 +1792,7 @@ theorem setWidth_succ (x : BitVec w) :
    · simp_all
    · omega

-@[deprecated "Use the reverse direction of `cons_msb_setWidth`" (since := "2024-09-23")]
+@[deprecated "Use the reverse direction of `cons_msb_setWidth`"]
 theorem eq_msb_cons_setWidth (x : BitVec (w+1)) : x = (cons x.msb (x.setWidth w)) := by
  simp

@@ -2033,7 +1884,7 @@ theorem getLsbD_shiftConcat_eq_decide (x : BitVec w) (b : Bool) (i : Nat) :
 theorem shiftRight_sub_one_eq_shiftConcat (n : BitVec w) (hwn : 0 < wn) :
    n >>> (wn - 1) = (n >>> wn).shiftConcat (n.getLsbD (wn - 1)) := by
  ext i
-  simp only [getLsbD_ushiftRight, getLsbD_shiftConcat, Fin.is_lt, decide_true, Bool.true_and]
+  simp only [getLsbD_ushiftRight, getLsbD_shiftConcat, Fin.is_lt, decide_True, Bool.true_and]
  split
  · simp [*]
  · congr 1; omega
@@ -2074,7 +1925,7 @@ theorem getMsbD_concat {i w : Nat} {b : Bool} {x : BitVec w} :
  · simp [h₀]
  · by_cases h₁ : i < w
    · simp [h₀, h₁, show ¬ w - i = 0 by omega, show i < w + 1 by omega, Nat.sub_sub, Nat.add_comm]
-    · simp only [show w - i = 0 by omega, ↓reduceIte, h₁, h₀, decide_false, Bool.false_and,
+    · simp only [show w - i = 0 by omega, ↓reduceIte, h₁, h₀, decide_False, Bool.false_and,
        Bool.and_eq_false_imp, decide_eq_true_eq]
      intro
      omega
@@ -2082,10 +1933,10 @@ theorem getMsbD_concat {i w : Nat} {b : Bool} {x : BitVec w} :
@[simp]
 theorem msb_concat {w : Nat} {b : Bool} {x : BitVec w} :
    (x.concat b).msb = if 0 < w then x.msb else b := by
-  simp only [BitVec.msb, getMsbD_eq_getLsbD, Nat.zero_lt_succ, decide_true, Nat.add_one_sub_one,
+  simp only [BitVec.msb, getMsbD_eq_getLsbD, Nat.zero_lt_succ, decide_True, Nat.add_one_sub_one,
    Nat.sub_zero, Bool.true_and]
  by_cases h₀ : 0 < w
-  · simp only [Nat.lt_add_one, getLsbD_eq_getElem, getElem_concat, h₀, ↓reduceIte, decide_true,
+  · simp only [Nat.lt_add_one, getLsbD_eq_getElem, getElem_concat, h₀, ↓reduceIte, decide_True,
      Bool.true_and, ite_eq_right_iff]
    intro
    omega
@@ -2175,9 +2026,9 @@ theorem sub_def {n} (x y : BitVec n) : x - y = .ofNat n ((2^n - y.toNat) + x.toN

@[simp] theorem toFin_sub (x y : BitVec n) : (x - y).toFin = toFin x - toFin y := rfl

-theorem ofFin_sub (x : Fin (2^n)) (y : BitVec n) : .ofFin x - y = .ofFin (x - y.toFin) :=
+@[simp] theorem ofFin_sub (x : Fin (2^n)) (y : BitVec n) : .ofFin x - y = .ofFin (x - y.toFin) :=
  rfl
-theorem sub_ofFin (x : BitVec n) (y : Fin (2^n)) : x - .ofFin y = .ofFin (x.toFin - y) :=
+@[simp] theorem sub_ofFin (x : BitVec n) (y : Fin (2^n)) : x - .ofFin y = .ofFin (x.toFin - y) :=
  rfl

 -- Remark: we don't use `[simp]` here because simproc` subsumes it for literals.
@@ -2295,6 +2146,19 @@ theorem not_neg (x : BitVec w) : ~~~(-x) = x + -1#w := by
        show (_ - x.toNat) % _ = _ by rw [Nat.mod_eq_of_lt (by omega)]]
      omega

+/-! ### abs -/
+
+theorem abs_eq (x : BitVec w) : x.abs = if x.msb then -x else x := by rfl
+
+@[simp, bv_toNat]
+theorem toNat_abs {x : BitVec w} : x.abs.toNat = if x.msb then 2^w - x.toNat else x.toNat := by
+  simp only [BitVec.abs, neg_eq]
+  by_cases h : x.msb = true
+  · simp only [h, ↓reduceIte, toNat_neg]
+    have : 2 * x.toNat ≥ 2 ^ w := BitVec.msb_eq_true_iff_two_mul_ge.mp h
+    rw [Nat.mod_eq_of_lt (by omega)]
+  · simp [h]
+
 /-! ### mul -/

 theorem mul_def {n} {x y : BitVec n} : x * y = (ofFin <| x.toFin * y.toFin) := by rfl
@@ -2524,9 +2388,6 @@ theorem umod_eq_and {x y : BitVec 1} : x % y = x &&& (~~~y) := by
 theorem smtUDiv_eq (x y : BitVec w) : smtUDiv x y = if y = 0#w then allOnes w else x / y := by
  simp [smtUDiv]

-@[simp]
-theorem smtUDiv_zero {x : BitVec n} : x.smtUDiv 0#n = allOnes n := rfl
-
 /-! ### sdiv -/

 /-- Equation theorem for `sdiv` in terms of `udiv`. -/
@@ -2594,10 +2455,6 @@ theorem smtSDiv_eq (x y : BitVec w) : smtSDiv x y =
  rw [BitVec.smtSDiv]
  rcases x.msb <;> rcases y.msb <;> simp

-@[simp]
-theorem smtSDiv_zero {x : BitVec n} : x.smtSDiv 0#n = if x.slt 0#n then 1#n else (allOnes n) := by
-  rcases hx : x.msb <;> simp [smtSDiv, slt_zero_iff_msb_cond x, hx, ← negOne_eq_allOnes]
-
 /-! ### srem -/

 theorem srem_eq (x y : BitVec w) : srem x y =
@@ -2662,7 +2519,7 @@ theorem smod_zero {x : BitVec n} : x.smod 0#n = x := by
@[simp] theorem getElem_ofBoolListBE (h : i < bs.length) :
    (ofBoolListBE bs)[i] = bs[bs.length - 1 - i] := by
  rw [← getLsbD_eq_getElem, getLsbD_ofBoolListBE]
-  simp only [h, decide_true, List.getD_eq_getElem?_getD, Bool.true_and]
+  simp only [h, decide_True, List.getD_eq_getElem?_getD, Bool.true_and]
  rw [List.getElem?_eq_getElem (by omega)]
  simp

@@ -2734,7 +2591,7 @@ theorem getLsbD_rotateLeftAux_of_geq {x : BitVec w} {r : Nat} {i : Nat} (hi : i
  apply getLsbD_ge
  omega

-/-- When `r < w`, we give a formula for `(x.rotateLeft r).getLsbD i`. -/
+/-- When `r < w`, we give a formula for `(x.rotateRight r).getLsbD i`. -/
 theorem getLsbD_rotateLeft_of_le {x : BitVec w} {r i : Nat} (hr: r < w) :
    (x.rotateLeft r).getLsbD i =
      cond (i < r)
@@ -2761,64 +2618,6 @@ theorem getElem_rotateLeft {x : BitVec w} {r i : Nat} (h : i < w) :
      if h' : i < r % w then x[(w - (r % w) + i)] else x[i - (r % w)] := by
  simp [← BitVec.getLsbD_eq_getElem, h]

-theorem getMsbD_rotateLeftAux_of_lt {x : BitVec w} {r : Nat} {i : Nat} (hi : i < w - r) :
-    (x.rotateLeftAux r).getMsbD i = x.getMsbD (r + i) := by
-  rw [rotateLeftAux, getMsbD_or]
-  simp [show i < w - r by omega, Nat.add_comm]
-
-theorem getMsbD_rotateLeftAux_of_ge {x : BitVec w} {r : Nat} {i : Nat} (hi : i ≥ w - r) :
-    (x.rotateLeftAux r).getMsbD i = (decide (i < w) && x.getMsbD (i - (w - r))) := by
-  simp [rotateLeftAux, getMsbD_or, show i + r ≥ w by omega, show ¬i < w - r by omega]
-
-/--
-If a number `w * n ≤ i < w * (n + 1)`, then `i - w * n` equals `i % w`.
-This is true by subtracting `w * n` from the inequality, giving
-`0 ≤ i - w * n < w`, which uniquely identifies `i % w`.
-/
-private theorem Nat.sub_mul_eq_mod_of_lt_of_le (hlo : w * n ≤ i) (hhi : i < w * (n + 1)) :
-    i - w * n = i % w := by
-  rw [Nat.mod_def]
-  congr
-  symm
-  apply Nat.div_eq_of_lt_le
-    (by rw [Nat.mul_comm]; omega)
-    (by rw [Nat.mul_comm]; omega)
-
-/-- When `r < w`, we give a formula for `(x.rotateLeft r).getMsbD i`. -/
-theorem getMsbD_rotateLeft_of_lt {n w : Nat} {x : BitVec w} (hi : r < w):
-    (x.rotateLeft r).getMsbD n = (decide (n < w) && x.getMsbD ((r + n) % w)) := by
-  rcases w with rfl | w
-  · simp
-  · rw [BitVec.rotateLeft_eq_rotateLeftAux_of_lt (by omega)]
-    by_cases h : n < (w + 1) - r
-    · simp [getMsbD_rotateLeftAux_of_lt h, Nat.mod_eq_of_lt, show r + n < (w + 1) by omega, show n < w + 1 by omega]
-    · simp [getMsbD_rotateLeftAux_of_ge <| Nat.ge_of_not_lt h]
-      by_cases h₁ : n < w + 1
-      · simp only [h₁, decide_true, Bool.true_and]
-        have h₂ : (r + n) < 2 * (w + 1) := by omega
-        congr 1
-        rw [← Nat.sub_mul_eq_mod_of_lt_of_le (n := 1) (by omega) (by omega), Nat.mul_one]
-        omega
-      · simp [h₁]
-
-theorem getMsbD_rotateLeft {r n w : Nat} {x : BitVec w} :
-    (x.rotateLeft r).getMsbD n = (decide (n < w) && x.getMsbD ((r + n) % w)) := by
-  rcases w with rfl | w
-  · simp
-  · by_cases h : r < w
-    · rw [getMsbD_rotateLeft_of_lt (by omega)]
-    · rw [← rotateLeft_mod_eq_rotateLeft, getMsbD_rotateLeft_of_lt (by apply Nat.mod_lt; simp)]
-      simp
-
-@[simp]
-theorem msb_rotateLeft {m w : Nat} {x : BitVec w} :
-    (x.rotateLeft m).msb = x.getMsbD (m % w) := by
-  simp only [BitVec.msb, getMsbD_rotateLeft]
-  by_cases h : w = 0
-  · simp [h]
-  · simp
-    omega
-
 /-! ## Rotate Right -/

 /--
@@ -2880,7 +2679,7 @@ theorem rotateRight_mod_eq_rotateRight {x : BitVec w} {r : Nat} :
  simp only [rotateRight, Nat.mod_mod]

 /-- When `r < w`, we give a formula for `(x.rotateRight r).getLsb i`. -/
-theorem getLsbD_rotateRight_of_lt {x : BitVec w} {r i : Nat} (hr: r < w) :
+theorem getLsbD_rotateRight_of_le {x : BitVec w} {r i : Nat} (hr: r < w) :
    (x.rotateRight r).getLsbD i =
      cond (i < w - r)
      (x.getLsbD (r + i))
@@ -2898,7 +2697,7 @@ theorem getLsbD_rotateRight {x : BitVec w} {r i : Nat} :
      (decide (i < w) && x.getLsbD (i - (w - (r % w)))) := by
  rcases w with ⟨rfl, w⟩
  · simp
-  · rw [← rotateRight_mod_eq_rotateRight, getLsbD_rotateRight_of_lt (Nat.mod_lt _ (by omega))]
+  · rw [← rotateRight_mod_eq_rotateRight, getLsbD_rotateRight_of_le (Nat.mod_lt _ (by omega))]

@[simp]
 theorem getElem_rotateRight {x : BitVec w} {r i : Nat} (h : i < w) :
@@ -2906,61 +2705,8 @@ theorem getElem_rotateRight {x : BitVec w} {r i : Nat} (h : i < w) :
  simp only [← BitVec.getLsbD_eq_getElem]
  simp [getLsbD_rotateRight, h]

-theorem getMsbD_rotateRightAux_of_lt {x : BitVec w} {r : Nat} {i : Nat} (hi : i < r) :
-    (x.rotateRightAux r).getMsbD i = x.getMsbD (i + (w - r)) := by
-  rw [rotateRightAux, getMsbD_or, getMsbD_ushiftRight]
-  simp [show i < r by omega]
-
-theorem getMsbD_rotateRightAux_of_ge {x : BitVec w} {r : Nat} {i : Nat} (hi : i ≥ r) :
-    (x.rotateRightAux r).getMsbD i = (decide (i < w) && x.getMsbD (i - r)) := by
-  simp [rotateRightAux, show ¬ i < r by omega, show i + (w - r) ≥ w by omega]
-
-/-- When `m < w`, we give a formula for `(x.rotateLeft m).getMsbD i`. -/
-@[simp]
-theorem getMsbD_rotateRight_of_lt {w n m : Nat} {x : BitVec w} (hr : m < w):
-    (x.rotateRight m).getMsbD n = (decide (n < w) && (if (n < m % w)
-    then x.getMsbD ((w + n - m % w) % w) else x.getMsbD (n - m % w))):= by
-  rcases w with rfl | w
-  · simp
-  · rw [rotateRight_eq_rotateRightAux_of_lt (by omega)]
-    by_cases h : n < m
-    · simp only [getMsbD_rotateRightAux_of_lt h, show n < w + 1 by omega, decide_true,
-        show m % (w + 1) = m by rw [Nat.mod_eq_of_lt hr], h, ↓reduceIte,
-        show (w + 1 + n - m) < (w + 1) by omega, Nat.mod_eq_of_lt, Bool.true_and]
-      congr 1
-      omega
-    · simp [h, getMsbD_rotateRightAux_of_ge <| Nat.ge_of_not_lt h]
-      by_cases h₁ : n < w + 1
-      · simp [h, h₁, decide_true, Bool.true_and, Nat.mod_eq_of_lt hr]
-      · simp [h₁]
-
-@[simp]
-theorem getMsbD_rotateRight {w n m : Nat} {x : BitVec w} :
-    (x.rotateRight m).getMsbD n = (decide (n < w) && (if (n < m % w)
-    then x.getMsbD ((w + n - m % w) % w) else x.getMsbD (n - m % w))):= by
-  rcases w with rfl | w
-  · simp
-  · by_cases h₀ : m < w
-    · rw [getMsbD_rotateRight_of_lt (by omega)]
-    · rw [← rotateRight_mod_eq_rotateRight, getMsbD_rotateRight_of_lt (by apply Nat.mod_lt; simp)]
-      simp
-
-@[simp]
-theorem msb_rotateRight {r w : Nat} {x : BitVec w} :
-    (x.rotateRight r).msb = x.getMsbD ((w - r % w) % w) := by
-  simp only [BitVec.msb, getMsbD_rotateRight]
-  by_cases h₀ : 0 < w
-  · simp only [h₀, decide_true, Nat.add_zero, Nat.zero_le, Nat.sub_eq_zero_of_le, Bool.true_and,
-    ite_eq_left_iff, Nat.not_lt, Nat.le_zero_eq]
-    intro h₁
-    simp [h₁]
-  · simp [show w = 0 by omega]
-
 /- ## twoPow -/

-theorem twoPow_eq (w : Nat) (i : Nat) : twoPow w i = 1#w <<< i := by
-  dsimp [twoPow]
-
@[simp, bv_toNat]
 theorem toNat_twoPow (w : Nat) (i : Nat) : (twoPow w i).toNat = 2^i % 2^w := by
  rcases w with rfl | w
@@ -2975,7 +2721,7 @@ theorem getLsbD_twoPow (i j : Nat) : (twoPow w i).getLsbD j = ((i < w) && (i = j
  · simp
  · simp only [twoPow, getLsbD_shiftLeft, getLsbD_ofNat]
    by_cases hj : j < i
-    · simp only [hj, decide_true, Bool.not_true, Bool.and_false, Bool.false_and, Bool.false_eq,
+    · simp only [hj, decide_True, Bool.not_true, Bool.and_false, Bool.false_and, Bool.false_eq,
      Bool.and_eq_false_imp, decide_eq_true_eq, decide_eq_false_iff_not]
      omega
    · by_cases hi : Nat.testBit 1 (j - i)
@@ -3038,15 +2784,7 @@ theorem twoPow_zero {w : Nat} : twoPow w 0 = 1#w := by
 theorem shiftLeft_eq_mul_twoPow (x : BitVec w) (n : Nat) :
    x <<< n = x * (BitVec.twoPow w n) := by
  ext i
-  simp [getLsbD_shiftLeft, Fin.is_lt, decide_true, Bool.true_and, mul_twoPow_eq_shiftLeft]
-
-/--
-The unsigned division of `x` by `2^k` equals shifting `x` right by `k`,
-when `k` is less than the bitwidth `w`.
-/
-theorem udiv_twoPow_eq_of_lt {w : Nat} {x : BitVec w} {k : Nat} (hk : k < w) : x / (twoPow w k) = x >>> k := by
-  have : 2^k < 2^w := Nat.pow_lt_pow_of_lt (by decide) hk
-  simp [bv_toNat, Nat.shiftRight_eq_div_pow, Nat.mod_eq_of_lt this]
+  simp [getLsbD_shiftLeft, Fin.is_lt, decide_True, Bool.true_and, mul_twoPow_eq_shiftLeft]

 /- ### cons -/

@@ -3074,7 +2812,7 @@ theorem setWidth_setWidth_succ_eq_setWidth_setWidth_of_getLsbD_false
    setWidth w (x.setWidth (i + 1)) =
      setWidth w (x.setWidth i) := by
  ext k
-  simp only [getLsbD_setWidth, Fin.is_lt, decide_true, Bool.true_and, getLsbD_or, getLsbD_and]
+  simp only [getLsbD_setWidth, Fin.is_lt, decide_True, Bool.true_and, getLsbD_or, getLsbD_and]
  by_cases hik : i = k
  · subst hik
    simp [hx]
@@ -3090,7 +2828,7 @@ theorem setWidth_setWidth_succ_eq_setWidth_setWidth_or_twoPow_of_getLsbD_true
    setWidth w (x.setWidth (i + 1)) =
      setWidth w (x.setWidth i) ||| (twoPow w i) := by
  ext k
-  simp only [getLsbD_setWidth, Fin.is_lt, decide_true, Bool.true_and, getLsbD_or, getLsbD_and]
+  simp only [getLsbD_setWidth, Fin.is_lt, decide_True, Bool.true_and, getLsbD_or, getLsbD_and]
  by_cases hik : i = k
  · subst hik
    simp [hx]
@@ -3100,7 +2838,7 @@ theorem setWidth_setWidth_succ_eq_setWidth_setWidth_or_twoPow_of_getLsbD_true
 theorem and_one_eq_setWidth_ofBool_getLsbD {x : BitVec w} :
    (x &&& 1#w) = setWidth w (ofBool (x.getLsbD 0)) := by
  ext i
-  simp only [getLsbD_and, getLsbD_one, getLsbD_setWidth, Fin.is_lt, decide_true, getLsbD_ofBool,
+  simp only [getLsbD_and, getLsbD_one, getLsbD_setWidth, Fin.is_lt, decide_True, getLsbD_ofBool,
    Bool.true_and]
  by_cases h : ((i : Nat) = 0) <;> simp [h] <;> omega

@@ -3114,6 +2852,20 @@ theorem replicate_succ_eq {x : BitVec w} :
    (x ++ replicate n x).cast (by rw [Nat.mul_succ]; omega) := by
  simp [replicate]

+/--
+If a number `w * n ≤ i < w * (n + 1)`, then `i - w * n` equals `i % w`.
+This is true by subtracting `w * n` from the inequality, giving
+`0 ≤ i - w * n < w`, which uniquely identifies `i % w`.
+-/
+private theorem Nat.sub_mul_eq_mod_of_lt_of_le (hlo : w * n ≤ i) (hhi : i < w * (n + 1)) :
+    i - w * n = i % w := by
+  rw [Nat.mod_def]
+  congr
+  symm
+  apply Nat.div_eq_of_lt_le
+    (by rw [Nat.mul_comm]; omega)
+    (by rw [Nat.mul_comm]; omega)
+
@[simp]
 theorem getLsbD_replicate {n w : Nat} (x : BitVec w) :
    (x.replicate n).getLsbD i =
@@ -3123,13 +2875,13 @@ theorem getLsbD_replicate {n w : Nat} (x : BitVec w) :
  case succ n ih =>
    simp only [replicate_succ_eq, getLsbD_cast, getLsbD_append]
    by_cases hi : i < w * (n + 1)
-    · simp only [hi, decide_true, Bool.true_and]
+    · simp only [hi, decide_True, Bool.true_and]
      by_cases hi' : i < w * n
      · simp [hi', ih]
-      · simp only [hi', decide_false, cond_false]
+      · simp only [hi', decide_False, cond_false]
        rw [Nat.sub_mul_eq_mod_of_lt_of_le] <;> omega
    · rw [Nat.mul_succ] at hi ⊢
-      simp only [show ¬i < w * n by omega, decide_false, cond_false, hi, Bool.false_and]
+      simp only [show ¬i < w * n by omega, decide_False, cond_false, hi, Bool.false_and]
      apply BitVec.getLsbD_ge (x := x) (i := i - w * n) (ge := by omega)

@[simp]
@@ -3147,14 +2899,6 @@ theorem getLsbD_intMin (w : Nat) : (intMin w).getLsbD i = decide (i + 1 = w) :=
  simp only [intMin, getLsbD_twoPow, boolToPropSimps]
  omega

-theorem getMsbD_intMin {w i : Nat} :
-    (intMin w).getMsbD i = (decide (0 < w) && decide (i = 0)) := by
-  simp only [getMsbD, getLsbD_intMin]
-  match w, i with
-  | 0,   _    => simp
-  | w+1, 0    => simp
-  | w+1, i+1  => simp; omega
-
 /--
 The RHS is zero in case `w = 0` which is modeled by wrapping the expression in `... % 2 ^ w`.
 -/
@@ -3177,21 +2921,6 @@ theorem toInt_intMin {w : Nat} :
    rw [Nat.mul_comm]
    simp [w_pos]

-theorem toInt_intMin_le (x : BitVec w) :
-    (intMin w).toInt ≤ x.toInt := by
-  cases w
-  case zero => simp [@of_length_zero x]
-  case succ w =>
-    simp only [toInt_intMin, Nat.add_one_sub_one, Int.ofNat_emod]
-    have : 0 < 2 ^ w := Nat.two_pow_pos w
-    rw [Int.emod_eq_of_lt (by omega) (by omega)]
-    rw [BitVec.toInt_eq_toNat_bmod]
-    rw [show (2 ^ w : Nat) = ((2 ^ (w + 1) : Nat) : Int) / 2 by omega]
-    apply Int.le_bmod (by omega)
-
-theorem intMin_sle (x : BitVec w) : (intMin w).sle x := by
-  simp only [BitVec.sle, toInt_intMin_le x, decide_true]
-
@[simp]
 theorem neg_intMin {w : Nat} : -intMin w = intMin w := by
  by_cases h : 0 < w
@@ -3199,10 +2928,6 @@ theorem neg_intMin {w : Nat} : -intMin w = intMin w := by
  · simp only [Nat.not_lt, Nat.le_zero_eq] at h
    simp [bv_toNat, h]

-@[simp]
-theorem abs_intMin {w : Nat} : (intMin w).abs = intMin w := by
-  simp [BitVec.abs, bv_toNat]
-
 theorem toInt_neg_of_ne_intMin {x : BitVec w} (rs : x ≠ intMin w) :
    (-x).toInt = -(x.toInt) := by
  simp only [ne_eq, toNat_eq, toNat_intMin] at rs
@@ -3219,15 +2944,6 @@ theorem toInt_neg_of_ne_intMin {x : BitVec w} (rs : x ≠ intMin w) :
  have := @Nat.two_pow_pred_mul_two w (by omega)
  split <;> split <;> omega

-theorem toInt_neg_eq_ite {x : BitVec w} :
-    (-x).toInt = if x = intMin w then x.toInt else -(x.toInt) := by
-  by_cases hx : x = intMin w <;>
-    simp [hx, neg_intMin, toInt_neg_of_ne_intMin]
-
-theorem msb_intMin {w : Nat} : (intMin w).msb = decide (0 < w) := by
-  simp only [msb_eq_decide, toNat_intMin, decide_eq_decide]
-  by_cases h : 0 < w <;> simp_all
-
 /-! ### intMax -/

 /-- The bitvector of width `w` that has the largest value when interpreted as an integer. -/
@@ -3320,109 +3036,6 @@ theorem sub_le_sub_iff_le {x y z : BitVec w} (hxz : z ≤ x) (hyz : z ≤ y) :
    BitVec.toNat_sub_of_le (by rw [BitVec.le_def]; omega)]
  omega

-/-! ### neg -/
-
-theorem msb_eq_toInt {x : BitVec w}:
-    x.msb = decide (x.toInt < 0) := by
-  by_cases h : x.msb <;>
-  · simp [h, toInt_eq_msb_cond]
-    omega
-
-theorem msb_eq_toNat {x : BitVec w}:
-    x.msb = decide (x.toNat ≥ 2 ^ (w - 1)) := by
-  simp only [msb_eq_decide, ge_iff_le]
-
-/-! ### abs -/
-
-theorem abs_eq (x : BitVec w) : x.abs = if x.msb then -x else x := by rfl
-
-@[simp, bv_toNat]
-theorem toNat_abs {x : BitVec w} : x.abs.toNat = if x.msb then 2^w - x.toNat else x.toNat := by
-  simp only [BitVec.abs, neg_eq]
-  by_cases h : x.msb = true
-  · simp only [h, ↓reduceIte, toNat_neg]
-    have : 2 * x.toNat ≥ 2 ^ w := BitVec.msb_eq_true_iff_two_mul_ge.mp h
-    rw [Nat.mod_eq_of_lt (by omega)]
-  · simp [h]
-
-theorem getLsbD_abs {i : Nat} {x : BitVec w} :
-    getLsbD x.abs i = if x.msb then getLsbD (-x) i else getLsbD x i := by
-  by_cases h : x.msb <;> simp [BitVec.abs, h]
-
-theorem getElem_abs {i : Nat} {x : BitVec w} (h : i < w) :
-    x.abs[i] = if x.msb then (-x)[i] else x[i] := by
-  by_cases h : x.msb <;> simp [BitVec.abs, h]
-
-theorem getMsbD_abs {i : Nat} {x : BitVec w} :
-    getMsbD (x.abs) i = if x.msb then getMsbD (-x) i else getMsbD x i := by
-  by_cases h : x.msb <;> simp [BitVec.abs, h]
-
-/-
-The absolute value of `x : BitVec w` is naively a case split on the sign of `x`.
-However, recall that when `x = intMin w`, `-x = x`.
-Thus, the full value of `abs x` is computed by the case split:
- If `x : BitVec w` is `intMin`, then its absolute value is also `intMin w`, and
-  thus `toInt` will equal `intMin.toInt`.
- Otherwise, if `x` is negative, then `x.abs.toInt = (-x).toInt`.
- If `x` is positive, then it is equal to `x.abs.toInt = x.toInt`.
-/
-theorem toInt_abs_eq_ite {x : BitVec w} :
-  x.abs.toInt =
-    if x = intMin w then (intMin w).toInt
-    else if x.msb then -x.toInt
-    else x.toInt := by
-  by_cases hx : x = intMin w
-  · simp [hx]
-  · simp [hx]
-    by_cases hx₂ : x.msb
-    · simp [hx₂, abs_eq, toInt_neg_of_ne_intMin hx]
-    · simp [hx₂, abs_eq]
-
-
-
-/-
-The absolute value of `x : BitVec w` is a case split on the sign of `x`, when `x ≠ intMin w`.
-This is a variant of `toInt_abs_eq_ite`.
-/
-theorem toInt_abs_eq_ite_of_ne_intMin {x : BitVec w} (hx : x ≠ intMin w) :
-  x.abs.toInt = if x.msb then -x.toInt else x.toInt := by
-  simp [toInt_abs_eq_ite, hx]
-
-
-/--
-The absolute value of `x : BitVec w`, interpreted as an integer, is a case split:
- When `x = intMin w`, then `x.abs = intMin w`
- Otherwise, `x.abs.toInt` equals the absolute value (`x.toInt.natAbs`).
-
-This is a simpler version of `BitVec.toInt_abs_eq_ite`, which hides a case split on `x.msb`.
-/
-theorem toInt_abs_eq_natAbs {x : BitVec w} : x.abs.toInt =
-    if x = intMin w then (intMin w).toInt else x.toInt.natAbs := by
-  rw [toInt_abs_eq_ite]
-  by_cases hx : x = intMin w
-  · simp [hx]
-  · simp [hx]
-    by_cases h : x.msb
-    · simp only [h, ↓reduceIte]
-      have : x.toInt < 0 := by
-        rw [toInt_neg_iff]
-        have := msb_eq_true_iff_two_mul_ge.mp h
-        omega
-      omega
-    · simp only [h, Bool.false_eq_true, ↓reduceIte]
-      have : 0 ≤ x.toInt := by
-        rw [toInt_pos_iff]
-        exact msb_eq_false_iff_two_mul_lt.mp (by simp [h])
-      omega
-
-/-
-The absolute value of `(x : BitVec w)`, when interpreted as an integer,
-is the absolute value of `x.toInt` when `(x ≠ intMin)`.
-/
-theorem toInt_abs_eq_natAbs_of_ne_intMin {x : BitVec w} (hx : x ≠ intMin w) :
-    x.abs.toInt = x.toInt.natAbs := by
-  simp [toInt_abs_eq_natAbs, hx]
-

 /-! ### Decidable quantifiers -/

--- a/src/Init/Data/Bool.lean
+++ b/src/Init/Data/Bool.lean
@@ -238,8 +238,8 @@ theorem not_bne_not : ∀ (x y : Bool), ((!x) != (!y)) = (x != y) := by simp
@[simp] theorem bne_assoc : ∀ (x y z : Bool), ((x != y) != z) = (x != (y != z)) := by decide
 instance : Std.Associative (· != ·) := ⟨bne_assoc⟩

-@[simp] theorem bne_right_inj  : ∀ {x y z : Bool}, (x != y) = (x != z) ↔ y = z := by decide
-@[simp] theorem bne_left_inj : ∀ {x y z : Bool}, (x != z) = (y != z) ↔ x = y := by decide
+@[simp] theorem bne_left_inj  : ∀ {x y z : Bool}, (x != y) = (x != z) ↔ y = z := by decide
+@[simp] theorem bne_right_inj : ∀ {x y z : Bool}, (x != z) = (y != z) ↔ x = y := by decide

 theorem eq_not_of_ne : ∀ {x y : Bool}, x ≠ y → x = !y := by decide

@@ -295,9 +295,9 @@ theorem xor_right_comm : ∀ (x y z : Bool), ((x ^^ y) ^^ z) = ((x ^^ z) ^^ y) :

 theorem xor_assoc : ∀ (x y z : Bool), ((x ^^ y) ^^ z) = (x ^^ (y ^^ z)) := bne_assoc

-theorem xor_right_inj : ∀ {x y z : Bool}, (x ^^ y) = (x ^^ z) ↔ y = z := bne_right_inj
+theorem xor_left_inj : ∀ {x y z : Bool}, (x ^^ y) = (x ^^ z) ↔ y = z := bne_left_inj

-theorem xor_left_inj : ∀ {x y z : Bool}, (x ^^ z) = (y ^^ z) ↔ x = y := bne_left_inj
+theorem xor_right_inj : ∀ {x y z : Bool}, (x ^^ z) = (y ^^ z) ↔ x = y := bne_right_inj

 /-! ### le/lt -/

--- a/src/Init/Data/ByteArray/Basic.lean
+++ b/src/Init/Data/ByteArray/Basic.lean
@@ -42,7 +42,7 @@ def usize (a : @& ByteArray) : USize :=
  a.size.toUSize

@[extern "lean_byte_array_uget"]
-def uget : (a : @& ByteArray) → (i : USize) → (h : i.toNat < a.size := by get_elem_tactic) → UInt8
+def uget : (a : @& ByteArray) → (i : USize) → i.toNat < a.size → UInt8
  | ⟨bs⟩, i, h => bs[i]

@[extern "lean_byte_array_get"]
@@ -50,11 +50,11 @@ def get! : (@& ByteArray) → (@& Nat) → UInt8
  | ⟨bs⟩, i => bs.get! i

@[extern "lean_byte_array_fget"]
-def get : (a : @& ByteArray) → (i : @& Nat) → (h : i < a.size := by get_elem_tactic) → UInt8
-  | ⟨bs⟩, i, _ => bs[i]
+def get : (a : @& ByteArray) → (@& Fin a.size) → UInt8
+  | ⟨bs⟩, i => bs.get i

 instance : GetElem ByteArray Nat UInt8 fun xs i => i < xs.size where
-  getElem xs i h := xs.get i
+  getElem xs i h := xs.get ⟨i, h⟩

 instance : GetElem ByteArray USize UInt8 fun xs i => i.val < xs.size where
  getElem xs i h := xs.uget i h
@@ -64,11 +64,11 @@ def set! : ByteArray → (@& Nat) → UInt8 → ByteArray
  | ⟨bs⟩, i, b => ⟨bs.set! i b⟩

@[extern "lean_byte_array_fset"]
-def set : (a : ByteArray) → (i : @& Nat) → UInt8 → (h : i < a.size := by get_elem_tactic) → ByteArray
-  | ⟨bs⟩, i, b, h => ⟨bs.set i b h⟩
+def set : (a : ByteArray) → (@& Fin a.size) → UInt8 → ByteArray
+  | ⟨bs⟩, i, b => ⟨bs.set i b⟩

@[extern "lean_byte_array_uset"]
-def uset : (a : ByteArray) → (i : USize) → UInt8 → (h : i.toNat < a.size := by get_elem_tactic) → ByteArray
+def uset : (a : ByteArray) → (i : USize) → UInt8 → i.toNat < a.size → ByteArray
  | ⟨bs⟩, i, v, h => ⟨bs.uset i v h⟩

@[extern "lean_byte_array_hash"]
@@ -108,18 +108,8 @@ def toList (bs : ByteArray) : List UInt8 :=

@[inline] def findIdx? (a : ByteArray) (p : UInt8 → Bool) (start := 0) : Option Nat :=
  let rec @[specialize] loop (i : Nat) :=
-    if h : i < a.size then
-      if p a[i] then some i else loop (i+1)
-    else
-      none
-    termination_by a.size - i
-    decreasing_by decreasing_trivial_pre_omega
-  loop start
-
-@[inline] def findFinIdx? (a : ByteArray) (p : UInt8 → Bool) (start := 0) : Option (Fin a.size) :=
-  let rec @[specialize] loop (i : Nat) :=
-    if h : i < a.size then
-      if p a[i] then some ⟨i, h⟩ else loop (i+1)
+    if i < a.size then
+      if p (a.get! i) then some i else loop (i+1)
    else
      none
    termination_by a.size - i
@@ -154,7 +144,7 @@ protected def forIn {β : Type v} {m : Type v → Type w} [Monad m] (as : ByteAr
      have h' : i < as.size            := Nat.lt_of_lt_of_le (Nat.lt_succ_self i) h
      have : as.size - 1 < as.size     := Nat.sub_lt (Nat.zero_lt_of_lt h') (by decide)
      have : as.size - 1 - i < as.size := Nat.lt_of_le_of_lt (Nat.sub_le (as.size - 1) i) this
-      match (← f as[as.size - 1 - i] b) with
+      match (← f (as.get ⟨as.size - 1 - i, this⟩) b) with
      | ForInStep.done b  => pure b
      | ForInStep.yield b => loop i (Nat.le_of_lt h') b
  loop as.size (Nat.le_refl _) b
@@ -188,7 +178,7 @@ def foldlM {β : Type v} {m : Type v → Type w} [Monad m] (f : β → UInt8 →
        match i with
        | 0    => pure b
        | i'+1 =>
-          loop i' (j+1) (← f b as[j])
+          loop i' (j+1) (← f b (as.get ⟨j, Nat.lt_of_lt_of_le hlt h⟩))
      else
        pure b
    loop (stop - start) start init
--- a/src/Init/Data/Fin/Basic.lean
+++ b/src/Init/Data/Fin/Basic.lean
@@ -165,7 +165,6 @@ theorem modn_lt : ∀ {m : Nat} (i : Fin n), m > 0 → (modn i m).val < m
 theorem val_lt_of_le (i : Fin b) (h : b ≤ n) : i.val < n :=
  Nat.lt_of_lt_of_le i.isLt h

-/-- If you actually have an element of `Fin n`, then the `n` is always positive -/
 protected theorem pos (i : Fin n) : 0 < n :=
  Nat.lt_of_le_of_lt (Nat.zero_le _) i.2

--- a/src/Init/Data/Fin/Fold.lean
+++ b/src/Init/Data/Fin/Fold.lean
@@ -5,217 +5,22 @@ Authors: François G. Dorais
 -/
 prelude
 import Init.Data.Nat.Linear
-import Init.Control.Lawful.Basic
-import Init.Data.Fin.Lemmas

 namespace Fin

 /-- Folds over `Fin n` from the left: `foldl 3 f x = f (f (f x 0) 1) 2`. -/
@[inline] def foldl (n) (f : α → Fin n → α) (init : α) : α := loop init 0 where
  /-- Inner loop for `Fin.foldl`. `Fin.foldl.loop n f x i = f (f (f x i) ...) (n-1)`  -/
-  @[semireducible] loop (x : α) (i : Nat) : α :=
+  loop (x : α) (i : Nat) : α :=
    if h : i < n then loop (f x ⟨i, h⟩) (i+1) else x
  termination_by n - i
-
-/-- Folds over `Fin n` from the right: `foldr 3 f x = f 0 (f 1 (f 2 x))`. -/
-@[inline] def foldr (n) (f : Fin n → α → α) (init : α) : α := loop n (Nat.le_refl n) init where
-  /-- Inner loop for `Fin.foldr`. `Fin.foldr.loop n f i x = f 0 (f ... (f (i-1) x))`  -/
-  loop : (i : _) → i ≤ n → α → α
-  | 0, _, x => x
-  | i+1, h, x => loop i (Nat.le_of_lt h) (f ⟨i, h⟩ x)
-  termination_by structural i => i
-
-/--
-Folds a monadic function over `Fin n` from left to right:
-```
-Fin.foldlM n f x₀ = do
-  let x₁ ← f x₀ 0
-  let x₂ ← f x₁ 1
-  ...
-  let xₙ ← f xₙ₋₁ (n-1)
-  pure xₙ
-```
-/
-@[inline] def foldlM [Monad m] (n) (f : α → Fin n → m α) (init : α) : m α := loop init 0 where
-  /--
-  Inner loop for `Fin.foldlM`.
-  ```
-  Fin.foldlM.loop n f xᵢ i = do
-    let xᵢ₊₁ ← f xᵢ i
-    ...
-    let xₙ ← f xₙ₋₁ (n-1)
-    pure xₙ
-  ```
-  -/
-  loop (x : α) (i : Nat) : m α := do
-    if h : i < n then f x ⟨i, h⟩ >>= (loop · (i+1)) else pure x
-  termination_by n - i
  decreasing_by decreasing_trivial_pre_omega

-/--
-Folds a monadic function over `Fin n` from right to left:
-```
-Fin.foldrM n f xₙ = do
-  let xₙ₋₁ ← f (n-1) xₙ
-  let xₙ₋₂ ← f (n-2) xₙ₋₁
-  ...
-  let x₀ ← f 0 x₁
-  pure x₀
-```
-/
-@[inline] def foldrM [Monad m] (n) (f : Fin n → α → m α) (init : α) : m α :=
-  loop ⟨n, Nat.le_refl n⟩ init where
-  /--
-  Inner loop for `Fin.foldrM`.
-  ```
-  Fin.foldrM.loop n f i xᵢ = do
-    let xᵢ₋₁ ← f (i-1) xᵢ
-    ...
-    let x₁ ← f 1 x₂
-    let x₀ ← f 0 x₁
-    pure x₀
-  ```
-  -/
-  loop : {i // i ≤ n} → α → m α
-  | ⟨0, _⟩, x => pure x
-  | ⟨i+1, h⟩, x => f ⟨i, h⟩ x >>= loop ⟨i, Nat.le_of_lt h⟩
-
-/-! ### foldlM -/
-
-theorem foldlM_loop_lt [Monad m] (f : α → Fin n → m α) (x) (h : i < n) :
-    foldlM.loop n f x i = f x ⟨i, h⟩ >>= (foldlM.loop n f . (i+1)) := by
-  rw [foldlM.loop, dif_pos h]
-
-theorem foldlM_loop_eq [Monad m] (f : α → Fin n → m α) (x) : foldlM.loop n f x n = pure x := by
-  rw [foldlM.loop, dif_neg (Nat.lt_irrefl _)]
-
-theorem foldlM_loop [Monad m] (f : α → Fin (n+1) → m α) (x) (h : i < n+1) :
-    foldlM.loop (n+1) f x i = f x ⟨i, h⟩ >>= (foldlM.loop n (fun x j => f x j.succ) . i) := by
-  if h' : i < n then
-    rw [foldlM_loop_lt _ _ h]
-    congr; funext
-    rw [foldlM_loop_lt _ _ h', foldlM_loop]; rfl
-  else
-    cases Nat.le_antisymm (Nat.le_of_lt_succ h) (Nat.not_lt.1 h')
-    rw [foldlM_loop_lt]
-    congr; funext
-    rw [foldlM_loop_eq, foldlM_loop_eq]
-termination_by n - i
-
-@[simp] theorem foldlM_zero [Monad m] (f : α → Fin 0 → m α) (x) : foldlM 0 f x = pure x :=
-  foldlM_loop_eq ..
-
-theorem foldlM_succ [Monad m] (f : α → Fin (n+1) → m α) (x) :
-    foldlM (n+1) f x = f x 0 >>= foldlM n (fun x j => f x j.succ) := foldlM_loop ..
-
-/-! ### foldrM -/
-
-theorem foldrM_loop_zero [Monad m] (f : Fin n → α → m α) (x) :
-    foldrM.loop n f ⟨0, Nat.zero_le _⟩ x = pure x := by
-  rw [foldrM.loop]
-
-theorem foldrM_loop_succ [Monad m] (f : Fin n → α → m α) (x) (h : i < n) :
-    foldrM.loop n f ⟨i+1, h⟩ x = f ⟨i, h⟩ x >>= foldrM.loop n f ⟨i, Nat.le_of_lt h⟩ := by
-  rw [foldrM.loop]
-
-theorem foldrM_loop [Monad m] [LawfulMonad m] (f : Fin (n+1) → α → m α) (x) (h : i+1 ≤ n+1) :
-    foldrM.loop (n+1) f ⟨i+1, h⟩ x =
-      foldrM.loop n (fun j => f j.succ) ⟨i, Nat.le_of_succ_le_succ h⟩ x >>= f 0 := by
-  induction i generalizing x with
-  | zero =>
-    rw [foldrM_loop_zero, foldrM_loop_succ, pure_bind]
-    conv => rhs; rw [←bind_pure (f 0 x)]
-    congr; funext; exact foldrM_loop_zero ..
-  | succ i ih =>
-    rw [foldrM_loop_succ, foldrM_loop_succ, bind_assoc]
-    congr; funext; exact ih ..
-
-@[simp] theorem foldrM_zero [Monad m] (f : Fin 0 → α → m α) (x) : foldrM 0 f x = pure x :=
-  foldrM_loop_zero ..
-
-theorem foldrM_succ [Monad m] [LawfulMonad m] (f : Fin (n+1) → α → m α) (x) :
-    foldrM (n+1) f x = foldrM n (fun i => f i.succ) x >>= f 0 := foldrM_loop ..
-
-/-! ### foldl -/
-
-theorem foldl_loop_lt (f : α → Fin n → α) (x) (h : i < n) :
-    foldl.loop n f x i = foldl.loop n f (f x ⟨i, h⟩) (i+1) := by
-  rw [foldl.loop, dif_pos h]
-
-theorem foldl_loop_eq (f : α → Fin n → α) (x) : foldl.loop n f x n = x := by
-  rw [foldl.loop, dif_neg (Nat.lt_irrefl _)]
-
-theorem foldl_loop (f : α → Fin (n+1) → α) (x) (h : i < n+1) :
-    foldl.loop (n+1) f x i = foldl.loop n (fun x j => f x j.succ) (f x ⟨i, h⟩) i := by
-  if h' : i < n then
-    rw [foldl_loop_lt _ _ h]
-    rw [foldl_loop_lt _ _ h', foldl_loop]; rfl
-  else
-    cases Nat.le_antisymm (Nat.le_of_lt_succ h) (Nat.not_lt.1 h')
-    rw [foldl_loop_lt]
-    rw [foldl_loop_eq, foldl_loop_eq]
-
-@[simp] theorem foldl_zero (f : α → Fin 0 → α) (x) : foldl 0 f x = x :=
-  foldl_loop_eq ..
-
-theorem foldl_succ (f : α → Fin (n+1) → α) (x) :
-    foldl (n+1) f x = foldl n (fun x i => f x i.succ) (f x 0) :=
-  foldl_loop ..
-
-theorem foldl_succ_last (f : α → Fin (n+1) → α) (x) :
-    foldl (n+1) f x = f (foldl n (f · ·.castSucc) x) (last n) := by
-  rw [foldl_succ]
-  induction n generalizing x with
-  | zero => simp [foldl_succ, Fin.last]
-  | succ n ih => rw [foldl_succ, ih (f · ·.succ), foldl_succ]; simp [succ_castSucc]
-
-theorem foldl_eq_foldlM (f : α → Fin n → α) (x) :
-    foldl n f x = foldlM (m:=Id) n f x := by
-  induction n generalizing x <;> simp [foldl_succ, foldlM_succ, *]
-
-/-! ### foldr -/
-
-theorem foldr_loop_zero (f : Fin n → α → α) (x) :
-    foldr.loop n f 0 (Nat.zero_le _) x = x := by
-  rw [foldr.loop]
-
-theorem foldr_loop_succ (f : Fin n → α → α) (x) (h : i < n) :
-    foldr.loop n f (i+1) h x = foldr.loop n f i (Nat.le_of_lt h) (f ⟨i, h⟩ x) := by
-  rw [foldr.loop]
-
-theorem foldr_loop (f : Fin (n+1) → α → α) (x) (h : i+1 ≤ n+1) :
-    foldr.loop (n+1) f (i+1) h x =
-      f 0 (foldr.loop n (fun j => f j.succ) i (Nat.le_of_succ_le_succ h) x) := by
-  induction i generalizing x with
-  | zero => simp [foldr_loop_succ, foldr_loop_zero]
-  | succ i ih => rw [foldr_loop_succ, ih]; rfl
-
-@[simp] theorem foldr_zero (f : Fin 0 → α → α) (x) : foldr 0 f x = x :=
-  foldr_loop_zero ..
-
-theorem foldr_succ (f : Fin (n+1) → α → α) (x) :
-    foldr (n+1) f x = f 0 (foldr n (fun i => f i.succ) x) := foldr_loop ..
-
-theorem foldr_succ_last (f : Fin (n+1) → α → α) (x) :
-    foldr (n+1) f x = foldr n (f ·.castSucc) (f (last n) x) := by
-  induction n generalizing x with
-  | zero => simp [foldr_succ, Fin.last]
-  | succ n ih => rw [foldr_succ, ih (f ·.succ), foldr_succ]; simp [succ_castSucc]
-
-theorem foldr_eq_foldrM (f : Fin n → α → α) (x) :
-    foldr n f x = foldrM (m:=Id) n f x := by
-  induction n <;> simp [foldr_succ, foldrM_succ, *]
-
-theorem foldl_rev (f : Fin n → α → α) (x) :
-    foldl n (fun x i => f i.rev x) x = foldr n f x := by
-  induction n generalizing x with
-  | zero => simp
-  | succ n ih => rw [foldl_succ, foldr_succ_last, ← ih]; simp [rev_succ]
-
-theorem foldr_rev (f : α → Fin n → α) (x) :
-     foldr n (fun i x => f x i.rev) x = foldl n f x := by
-  induction n generalizing x with
-  | zero => simp
-  | succ n ih => rw [foldl_succ_last, foldr_succ, ← ih]; simp [rev_succ]
+/-- Folds over `Fin n` from the right: `foldr 3 f x = f 0 (f 1 (f 2 x))`. -/
+@[inline] def foldr (n) (f : Fin n → α → α) (init : α) : α := loop ⟨n, Nat.le_refl n⟩ init where
+  /-- Inner loop for `Fin.foldr`. `Fin.foldr.loop n f i x = f 0 (f ... (f (i-1) x))`  -/
+  loop : {i // i ≤ n} → α → α
+  | ⟨0, _⟩, x => x
+  | ⟨i+1, h⟩, x => loop ⟨i, Nat.le_of_lt h⟩ (f ⟨i, h⟩ x)

 end Fin
--- a/src/Init/Data/Fin/Lemmas.lean
+++ b/src/Init/Data/Fin/Lemmas.lean
@@ -13,19 +13,17 @@ import Init.Omega

 namespace Fin

-@[deprecated Fin.pos (since := "2024-11-11")]
-theorem size_pos (i : Fin n) : 0 < n := i.pos
+/-- If you actually have an element of `Fin n`, then the `n` is always positive -/
+theorem size_pos (i : Fin n) : 0 < n := Nat.lt_of_le_of_lt (Nat.zero_le _) i.2

 theorem mod_def (a m : Fin n) : a % m = Fin.mk (a % m) (Nat.lt_of_le_of_lt (Nat.mod_le _ _) a.2) :=
  rfl

-theorem mul_def (a b : Fin n) : a * b = Fin.mk ((a * b) % n) (Nat.mod_lt _ a.pos) := rfl
+theorem mul_def (a b : Fin n) : a * b = Fin.mk ((a * b) % n) (Nat.mod_lt _ a.size_pos) := rfl

-theorem sub_def (a b : Fin n) : a - b = Fin.mk (((n - b) + a) % n) (Nat.mod_lt _ a.pos) := rfl
+theorem sub_def (a b : Fin n) : a - b = Fin.mk (((n - b) + a) % n) (Nat.mod_lt _ a.size_pos) := rfl

-theorem pos' : ∀ [Nonempty (Fin n)], 0 < n | ⟨i⟩ => i.pos
-
-@[deprecated pos' (since := "2024-11-11")] abbrev size_pos' := @pos'
+theorem size_pos' : ∀ [Nonempty (Fin n)], 0 < n | ⟨i⟩ => i.size_pos

@[simp] theorem is_lt (a : Fin n) : (a : Nat) < n := a.2

@@ -242,7 +240,7 @@ theorem fin_one_eq_zero (a : Fin 1) : a = 0 := Subsingleton.elim a 0
  rw [eq_comm]
  simp

-theorem add_def (a b : Fin n) : a + b = Fin.mk ((a + b) % n) (Nat.mod_lt _ a.pos) := rfl
+theorem add_def (a b : Fin n) : a + b = Fin.mk ((a + b) % n) (Nat.mod_lt _ a.size_pos) := rfl

 theorem val_add (a b : Fin n) : (a + b).val = (a.val + b.val) % n := rfl

@@ -642,7 +640,7 @@ theorem pred_add_one (i : Fin (n + 2)) (h : (i : Nat) < n + 1) :
  ext
  simp

-@[simp] theorem subNat_one_succ (i : Fin (n + 1)) (h : 1 ≤ (i : Nat)) : (subNat 1 i h).succ = i := by
+@[simp] theorem subNat_one_succ (i : Fin (n + 1)) (h : 1 ≤ ↑i) : (subNat 1 i h).succ = i := by
  ext
  simp
  omega
--- a/src/Init/Data/Float.lean
+++ b/src/Init/Data/Float.lean
@@ -31,7 +31,7 @@ opaque floatSpec : FloatSpec := {
 structure Float where
  val : floatSpec.float

-instance : Nonempty Float := ⟨{ val := floatSpec.val }⟩
+instance : Inhabited Float := ⟨{ val := floatSpec.val }⟩

@[extern "lean_float_add"] opaque Float.add : Float → Float → Float
@[extern "lean_float_sub"] opaque Float.sub : Float → Float → Float
@@ -47,25 +47,6 @@ def Float.lt : Float → Float → Prop := fun a b =>
 def Float.le : Float → Float → Prop := fun a b =>
  floatSpec.le a.val b.val

-/--
-Raw transmutation from `UInt64`.
-
-Floats and UInts have the same endianness on all supported platforms.
-IEEE 754 very precisely specifies the bit layout of floats.
-/
-@[extern "lean_float_of_bits"] opaque Float.ofBits : UInt64 → Float
-
-/--
-Raw transmutation to `UInt64`.
-
-Floats and UInts have the same endianness on all supported platforms.
-IEEE 754 very precisely specifies the bit layout of floats.
-
-Note that this function is distinct from `Float.toUInt64`, which attempts
-to preserve the numeric value, and not the bitwise value.
-/
-@[extern "lean_float_to_bits"] opaque Float.toBits : Float → UInt64
-
 instance : Add Float := ⟨Float.add⟩
 instance : Sub Float := ⟨Float.sub⟩
 instance : Mul Float := ⟨Float.mul⟩
@@ -136,9 +117,6 @@ instance : ToString Float where

@[extern "lean_uint64_to_float"] opaque UInt64.toFloat (n : UInt64) : Float

-instance : Inhabited Float where
-  default := UInt64.toFloat 0
-
 instance : Repr Float where
  reprPrec n prec := if n < UInt64.toFloat 0 then Repr.addAppParen (toString n) prec else toString n

--- a/src/Init/Data/FloatArray/Basic.lean
+++ b/src/Init/Data/FloatArray/Basic.lean
@@ -46,8 +46,8 @@ def uget : (a : @& FloatArray) → (i : USize) → i.toNat < a.size → Float
  | ⟨ds⟩, i, h => ds[i]

@[extern "lean_float_array_fget"]
-def get : (ds : @& FloatArray) → (i : @& Nat) → (h : i < ds.size := by get_elem_tactic) → Float
-  | ⟨ds⟩, i, h => ds.get i h
+def get : (ds : @& FloatArray) → (@& Fin ds.size) → Float
+  | ⟨ds⟩, i => ds.get i

@[extern "lean_float_array_get"]
 def get! : (@& FloatArray) → (@& Nat) → Float
@@ -55,23 +55,23 @@ def get! : (@& FloatArray) → (@& Nat) → Float

 def get? (ds : FloatArray) (i : Nat) : Option Float :=
  if h : i < ds.size then
-    some (ds.get i h)
+    ds.get ⟨i, h⟩
  else
    none

 instance : GetElem FloatArray Nat Float fun xs i => i < xs.size where
-  getElem xs i h := xs.get i h
+  getElem xs i h := xs.get ⟨i, h⟩

 instance : GetElem FloatArray USize Float fun xs i => i.val < xs.size where
  getElem xs i h := xs.uget i h

@[extern "lean_float_array_uset"]
-def uset : (a : FloatArray) → (i : USize) → Float → (h : i.toNat < a.size := by get_elem_tactic) → FloatArray
+def uset : (a : FloatArray) → (i : USize) → Float → i.toNat < a.size → FloatArray
  | ⟨ds⟩, i, v, h => ⟨ds.uset i v h⟩

@[extern "lean_float_array_fset"]
-def set : (ds : FloatArray) → (i : @& Nat) → Float → (h : i < ds.size := by get_elem_tactic) → FloatArray
-  | ⟨ds⟩, i, d, h => ⟨ds.set i d h⟩
+def set : (ds : FloatArray) → (@& Fin ds.size) → Float → FloatArray
+  | ⟨ds⟩, i, d => ⟨ds.set i d⟩

@[extern "lean_float_array_set"]
 def set! : FloatArray → (@& Nat) → Float → FloatArray
@@ -83,7 +83,7 @@ def isEmpty (s : FloatArray) : Bool :=
 partial def toList (ds : FloatArray) : List Float :=
  let rec loop (i r) :=
    if h : i < ds.size then
-      loop (i+1) (ds[i] :: r)
+      loop (i+1) (ds.get ⟨i, h⟩ :: r)
    else
      r.reverse
  loop 0 []
@@ -115,7 +115,7 @@ protected def forIn {β : Type v} {m : Type v → Type w} [Monad m] (as : FloatA
      have h' : i < as.size            := Nat.lt_of_lt_of_le (Nat.lt_succ_self i) h
      have : as.size - 1 < as.size     := Nat.sub_lt (Nat.zero_lt_of_lt h') (by decide)
      have : as.size - 1 - i < as.size := Nat.lt_of_le_of_lt (Nat.sub_le (as.size - 1) i) this
-      match (← f as[as.size - 1 - i] b) with
+      match (← f (as.get ⟨as.size - 1 - i, this⟩) b) with
      | ForInStep.done b  => pure b
      | ForInStep.yield b => loop i (Nat.le_of_lt h') b
  loop as.size (Nat.le_refl _) b
@@ -149,7 +149,7 @@ def foldlM {β : Type v} {m : Type v → Type w} [Monad m] (f : β → Float →
        match i with
        | 0    => pure b
        | i'+1 =>
-          loop i' (j+1) (← f b (as[j]'(Nat.lt_of_lt_of_le hlt h)))
+          loop i' (j+1) (← f b (as.get ⟨j, Nat.lt_of_lt_of_le hlt h⟩))
      else
        pure b
    loop (stop - start) start init
--- a/src/Init/Data/Hashable.lean
+++ b/src/Init/Data/Hashable.lean
@@ -48,9 +48,6 @@ instance : Hashable UInt64 where
 instance : Hashable USize where
  hash n := n.toUInt64

-instance : Hashable ByteArray where
-  hash as := as.foldl (fun r a => mixHash r (hash a)) 7
-
 instance : Hashable (Fin n) where
  hash v := v.val.toUInt64

--- a/src/Init/Data/Int/DivModLemmas.lean
+++ b/src/Init/Data/Int/DivModLemmas.lean
@@ -1267,7 +1267,7 @@ theorem bmod_le {x : Int} {m : Nat} (h : 0 < m) : bmod x m ≤ (m - 1) / 2 := by
    _ = ((m + 1 - 2) + 2)/2 := by simp
    _ = (m - 1) / 2 + 1     := by
      rw [add_ediv_of_dvd_right]
-      · simp +decide only [Int.ediv_self]
+      · simp (config := {decide := true}) only [Int.ediv_self]
        congr 2
        rw [Int.add_sub_assoc, ← Int.sub_neg]
        congr
@@ -1285,7 +1285,7 @@ theorem bmod_natAbs_plus_one (x : Int) (w : 1 < x.natAbs) : bmod x (x.natAbs + 1
    simp only [bmod, ofNat_eq_coe, natAbs_ofNat, natCast_add, ofNat_one,
      emod_self_add_one (ofNat_nonneg x)]
    match x with
-    | 0 => rw [if_pos] <;> simp +decide
+    | 0 => rw [if_pos] <;> simp (config := {decide := true})
    | (x+1) =>
      rw [if_neg]
      · simp [← Int.sub_sub]
--- a/src/Init/Data/Int/Lemmas.lean
+++ b/src/Init/Data/Int/Lemmas.lean
@@ -329,22 +329,22 @@ theorem toNat_sub (m n : Nat) : toNat (m - n) = m - n := by
 /- ## add/sub injectivity -/

@[simp]
-protected theorem add_left_inj {i j : Int} (k : Int) : (i + k = j + k) ↔ i = j := by
+protected theorem add_right_inj {i j : Int} (k : Int) : (i + k = j + k) ↔ i = j := by
  apply Iff.intro
  · intro p
    rw [←Int.add_sub_cancel i k, ←Int.add_sub_cancel j k, p]
  · exact congrArg (· + k)

@[simp]
-protected theorem add_right_inj {i j : Int} (k : Int) : (k + i = k + j) ↔ i = j := by
+protected theorem add_left_inj {i j : Int} (k : Int) : (k + i = k + j) ↔ i = j := by
  simp [Int.add_comm k]

@[simp]
-protected theorem sub_right_inj {i j : Int} (k : Int) : (k - i = k - j) ↔ i = j := by
+protected theorem sub_left_inj {i j : Int} (k : Int) : (k - i = k - j) ↔ i = j := by
  simp [Int.sub_eq_add_neg, Int.neg_inj]

@[simp]
-protected theorem sub_left_inj {i j : Int} (k : Int) : (i - k = j - k) ↔ i = j := by
+protected theorem sub_right_inj {i j : Int} (k : Int) : (i - k = j - k) ↔ i = j := by
  simp [Int.sub_eq_add_neg]

 /- ## Ring properties -/
--- a/src/Init/Data/Int/Order.lean
+++ b/src/Init/Data/Int/Order.lean
@@ -1007,9 +1007,9 @@ theorem sign_eq_neg_one_iff_neg {a : Int} : sign a = -1 ↔ a < 0 :=
  match x with
  | 0 => rfl
  | .ofNat (_ + 1) =>
-    simp +decide only [sign, true_iff]
+    simp (config := { decide := true }) only [sign, true_iff]
    exact Int.le_add_one (ofNat_nonneg _)
-  | .negSucc _ => simp +decide [sign]
+  | .negSucc _ => simp (config := { decide := true }) [sign]

 theorem mul_sign : ∀ i : Int, i * sign i = natAbs i
  | succ _ => Int.mul_one _
--- a/src/Init/Data/List.lean
+++ b/src/Init/Data/List.lean
@@ -25,5 +25,3 @@ import Init.Data.List.Perm
 import Init.Data.List.Sort
 import Init.Data.List.ToArray
 import Init.Data.List.MapIdx
-import Init.Data.List.OfFn
-import Init.Data.List.FinRange
--- a/src/Init/Data/List/Attach.lean
+++ b/src/Init/Data/List/Attach.lean
@@ -13,7 +13,7 @@ namespace List
  `a : α` satisfying `P`, then `pmap f l h` is essentially the same as `map f l`
  but is defined only when all members of `l` satisfy `P`, using the proof
  to apply `f`. -/
-def pmap {P : α → Prop} (f : ∀ a, P a → β) : ∀ l : List α, (H : ∀ a ∈ l, P a) → List β
+@[simp] def pmap {P : α → Prop} (f : ∀ a, P a → β) : ∀ l : List α, (H : ∀ a ∈ l, P a) → List β
  | [], _ => []
  | a :: l, H => f a (forall_mem_cons.1 H).1 :: pmap f l (forall_mem_cons.1 H).2

@@ -46,11 +46,6 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
  | cons _ L', hL' => congrArg _ <| go L' fun _ hx => hL' (.tail _ hx)
  exact go L h'

-@[simp] theorem pmap_nil {P : α → Prop} (f : ∀ a, P a → β) : pmap f [] (by simp) = [] := rfl
-
-@[simp] theorem pmap_cons {P : α → Prop} (f : ∀ a, P a → β) (a : α) (l : List α) (h : ∀ b ∈ a :: l, P b) :
-    pmap f (a :: l) h = f a (forall_mem_cons.1 h).1 :: pmap f l (forall_mem_cons.1 h).2 := rfl
-
@[simp] theorem attach_nil : ([] : List α).attach = [] := rfl

@[simp] theorem attachWith_nil : ([] : List α).attachWith P H = [] := rfl
@@ -153,7 +148,7 @@ theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {l H} {a} (h :
  exact ⟨a, h, rfl⟩

@[simp]
-theorem length_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H} : (pmap f l H).length = l.length := by
+theorem length_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H} : length (pmap f l H) = length l := by
  induction l
  · rfl
  · simp only [*, pmap, length]
@@ -174,13 +169,6 @@ theorem pmap_ne_nil_iff {P : α → Prop} (f : (a : α) → P a → β) {xs : Li
    (H : ∀ (a : α), a ∈ xs → P a) : xs.pmap f H ≠ [] ↔ xs ≠ [] := by
  simp

-theorem pmap_eq_self {l : List α} {p : α → Prop} (hp : ∀ (a : α), a ∈ l → p a)
-    (f : (a : α) → p a → α) : l.pmap f hp = l ↔ ∀ a (h : a ∈ l), f a (hp a h) = a := by
-  rw [pmap_eq_map_attach]
-  conv => lhs; rhs; rw [← attach_map_subtype_val l]
-  rw [map_inj_left]
-  simp
-
@[simp]
 theorem attach_eq_nil_iff {l : List α} : l.attach = [] ↔ l = [] :=
  pmap_eq_nil_iff
@@ -204,7 +192,7 @@ theorem attachWith_ne_nil_iff {l : List α} {P : α → Prop} {H : ∀ a ∈ l,

@[simp]
 theorem getElem?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h : ∀ a ∈ l, p a) (n : Nat) :
-    (pmap f l h)[n]? = Option.pmap f l[n]? fun x H => h x (mem_of_getElem? H) := by
+    (pmap f l h)[n]? = Option.pmap f l[n]? fun x H => h x (getElem?_mem H) := by
  induction l generalizing n with
  | nil => simp
  | cons hd tl hl =>
@@ -220,7 +208,7 @@ theorem getElem?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h
      · simp_all

 theorem get?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h : ∀ a ∈ l, p a) (n : Nat) :
-    get? (pmap f l h) n = Option.pmap f (get? l n) fun x H => h x (mem_of_get? H) := by
+    get? (pmap f l h) n = Option.pmap f (get? l n) fun x H => h x (get?_mem H) := by
  simp only [get?_eq_getElem?]
  simp [getElem?_pmap, h]

@@ -243,18 +231,18 @@ theorem get_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h :
    (hn : n < (pmap f l h).length) :
    get (pmap f l h) ⟨n, hn⟩ =
      f (get l ⟨n, @length_pmap _ _ p f l h ▸ hn⟩)
-        (h _ (getElem_mem (@length_pmap _ _ p f l h ▸ hn))) := by
+        (h _ (get_mem l n (@length_pmap _ _ p f l h ▸ hn))) := by
  simp only [get_eq_getElem]
  simp [getElem_pmap]

@[simp]
 theorem getElem?_attachWith {xs : List α} {i : Nat} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
-    (xs.attachWith P H)[i]? = xs[i]?.pmap Subtype.mk (fun _ a => H _ (mem_of_getElem? a)) :=
+    (xs.attachWith P H)[i]? = xs[i]?.pmap Subtype.mk (fun _ a => H _ (getElem?_mem a)) :=
  getElem?_pmap ..

@[simp]
 theorem getElem?_attach {xs : List α} {i : Nat} :
-    xs.attach[i]? = xs[i]?.pmap Subtype.mk (fun _ a => mem_of_getElem? a) :=
+    xs.attach[i]? = xs[i]?.pmap Subtype.mk (fun _ a => getElem?_mem a) :=
  getElem?_attachWith

@[simp]
@@ -338,7 +326,6 @@ This is useful when we need to use `attach` to show termination.

 Unfortunately this can't be applied by `simp` because of the higher order unification problem,
 and even when rewriting we need to specify the function explicitly.
-See however `foldl_subtype` below.
 -/
 theorem foldl_attach (l : List α) (f : β → α → β) (b : β) :
    l.attach.foldl (fun acc t => f acc t.1) b = l.foldl f b := by
@@ -354,7 +341,6 @@ This is useful when we need to use `attach` to show termination.

 Unfortunately this can't be applied by `simp` because of the higher order unification problem,
 and even when rewriting we need to specify the function explicitly.
-See however `foldr_subtype` below.
 -/
 theorem foldr_attach (l : List α) (f : α → β → β) (b : β) :
    l.attach.foldr (fun t acc => f t.1 acc) b = l.foldr f b := by
@@ -459,16 +445,16 @@ theorem pmap_append' {p : α → Prop} (f : ∀ a : α, p a → β) (l₁ l₂ :
  pmap_append f l₁ l₂ _

@[simp] theorem attach_append (xs ys : List α) :
-    (xs ++ ys).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_append_left ys h⟩) ++
-      ys.attach.map fun ⟨x, h⟩ => ⟨x, mem_append_right xs h⟩ := by
+    (xs ++ ys).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_append_of_mem_left ys h⟩) ++
+      ys.attach.map fun ⟨x, h⟩ => ⟨x, mem_append_of_mem_right xs h⟩ := by
  simp only [attach, attachWith, pmap, map_pmap, pmap_append]
  congr 1 <;>
  exact pmap_congr_left _ fun _ _ _ _ => rfl

@[simp] theorem attachWith_append {P : α → Prop} {xs ys : List α}
    {H : ∀ (a : α), a ∈ xs ++ ys → P a} :
-    (xs ++ ys).attachWith P H = xs.attachWith P (fun a h => H a (mem_append_left ys h)) ++
-      ys.attachWith P (fun a h => H a (mem_append_right xs h)) := by
+    (xs ++ ys).attachWith P H = xs.attachWith P (fun a h => H a (mem_append_of_mem_left ys h)) ++
+      ys.attachWith P (fun a h => H a (mem_append_of_mem_right xs h)) := by
  simp only [attachWith, attach_append, map_pmap, pmap_append]

@[simp] theorem pmap_reverse {P : α → Prop} (f : (a : α) → P a → β) (xs : List α)
@@ -605,15 +591,6 @@ def unattach {α : Type _} {p : α → Prop} (l : List { x // p x }) := l.map (
  | nil => simp
  | cons a l ih => simp [ih, Function.comp_def]

-@[simp] theorem getElem?_unattach {p : α → Prop} {l : List { x // p x }} (i : Nat) :
-    l.unattach[i]? = l[i]?.map Subtype.val := by
-  simp [unattach]
-
-@[simp] theorem getElem_unattach
-    {p : α → Prop} {l : List { x // p x }} (i : Nat) (h : i < l.unattach.length) :
-    l.unattach[i] = (l[i]'(by simpa using h)).1 := by
-  simp [unattach]
-
 /-! ### Recognizing higher order functions on subtypes using a function that only depends on the value. -/

 /--
--- a/src/Init/Data/List/Basic.lean
+++ b/src/Init/Data/List/Basic.lean
@@ -38,14 +38,14 @@ The operations are organized as follow:
 * Sublists: `take`, `drop`, `takeWhile`, `dropWhile`, `partition`, `dropLast`,
  `isPrefixOf`, `isPrefixOf?`, `isSuffixOf`, `isSuffixOf?`, `Subset`, `Sublist`,
  `rotateLeft` and `rotateRight`.
-* Manipulating elements: `replace`, `modify`, `insert`, `insertIdx`, `erase`, `eraseP`, `eraseIdx`.
+* Manipulating elements: `replace`, `insert`, `modify`, `erase`, `eraseP`, `eraseIdx`.
 * Finding elements: `find?`, `findSome?`, `findIdx`, `indexOf`, `findIdx?`, `indexOf?`,
 `countP`, `count`, and `lookup`.
 * Logic: `any`, `all`, `or`, and `and`.
 * Zippers: `zipWith`, `zip`, `zipWithAll`, and `unzip`.
 * Ranges and enumeration: `range`, `iota`, `enumFrom`, and `enum`.
 * Minima and maxima: `min?` and `max?`.
-* Other functions: `intersperse`, `intercalate`, `eraseDups`, `eraseReps`, `span`, `splitBy`,
+* Other functions: `intersperse`, `intercalate`, `eraseDups`, `eraseReps`, `span`, `groupBy`,
  `removeAll`
  (currently these functions are mostly only used in meta code,
  and do not have API suitable for verification).
@@ -231,7 +231,7 @@ theorem ext_get? : ∀ {l₁ l₂ : List α}, (∀ n, l₁.get? n = l₂.get? n)
    injection h0 with aa; simp only [aa, ext_get? fun n => h (n+1)]

 /-- Deprecated alias for `ext_get?`. The preferred extensionality theorem is now `ext_getElem?`. -/
-@[deprecated ext_get? (since := "2024-06-07")] abbrev ext := @ext_get?
+@[deprecated (since := "2024-06-07")] abbrev ext := @ext_get?

 /-! ### getD -/

@@ -551,7 +551,7 @@ theorem reverseAux_eq_append (as bs : List α) : reverseAux as bs = reverseAux a
 /-! ### flatten -/

 /--
-`O(|flatten L|)`. `flatten L` concatenates all the lists in `L` into one list.
+`O(|flatten L|)`. `join L` concatenates all the lists in `L` into one list.
 * `flatten [[a], [], [b, c], [d, e, f]] = [a, b, c, d, e, f]`
 -/
 def flatten : List (List α) → List α
@@ -682,7 +682,7 @@ theorem elem_cons [BEq α] {a : α} :
    (b::bs).elem a = match a == b with | true => true | false => bs.elem a := rfl

 /-- `notElem a l` is `!(elem a l)`. -/
-@[deprecated "Use `!(elem a l)` instead."(since := "2024-06-15")]
+@[deprecated (since := "2024-06-15")]
 def notElem [BEq α] (a : α) (as : List α) : Bool :=
  !(as.elem a)

@@ -726,13 +726,13 @@ theorem elem_eq_true_of_mem [BEq α] [LawfulBEq α] {a : α} {as : List α} (h :
 instance [BEq α] [LawfulBEq α] (a : α) (as : List α) : Decidable (a ∈ as) :=
  decidable_of_decidable_of_iff (Iff.intro mem_of_elem_eq_true elem_eq_true_of_mem)

-theorem mem_append_left {a : α} {as : List α} (bs : List α) : a ∈ as → a ∈ as ++ bs := by
+theorem mem_append_of_mem_left {a : α} {as : List α} (bs : List α) : a ∈ as → a ∈ as ++ bs := by
  intro h
  induction h with
  | head => apply Mem.head
  | tail => apply Mem.tail; assumption

-theorem mem_append_right {b : α} {bs : List α} (as : List α) : b ∈ bs → b ∈ as ++ bs := by
+theorem mem_append_of_mem_right {b : α} {bs : List α} (as : List α) : b ∈ bs → b ∈ as ++ bs := by
  intro h
  induction as with
  | nil  => simp [h]
@@ -1113,6 +1113,12 @@ theorem replace_cons [BEq α] {a : α} :
    (a::as).replace b c = match b == a with | true => c::as | false => a :: replace as b c :=
  rfl

+/-! ### insert -/
+
+/-- Inserts an element into a list without duplication. -/
+@[inline] protected def insert [BEq α] (a : α) (l : List α) : List α :=
+  if l.elem a then l else a :: l
+
 /-! ### modify -/

 /--
@@ -1142,21 +1148,6 @@ Apply `f` to the nth element of the list, if it exists, replacing that element w
 def modify (f : α → α) : Nat → List α → List α :=
  modifyTailIdx (modifyHead f)

-/-! ### insert -/
-
-/-- Inserts an element into a list without duplication. -/
-@[inline] protected def insert [BEq α] (a : α) (l : List α) : List α :=
-  if l.elem a then l else a :: l
-
-/--
-`insertIdx n a l` inserts `a` into the list `l` after the first `n` elements of `l`
-```
-insertIdx 2 1 [1, 2, 3, 4] = [1, 2, 1, 3, 4]
-```
-/
-def insertIdx (n : Nat) (a : α) : List α → List α :=
-  modifyTailIdx (cons a) n
-
 /-! ### erase -/

 /--
@@ -1427,10 +1418,10 @@ def zipWithAll (f : Option α → Option β → γ) : List α → List β → Li
  | a :: as, [] => (a :: as).map fun a => f (some a) none
  | a :: as, b :: bs => f a b :: zipWithAll f as bs

-@[simp] theorem zipWithAll_nil :
+@[simp] theorem zipWithAll_nil_right :
    zipWithAll f as [] = as.map fun a => f (some a) none := by
  cases as <;> rfl
-@[simp] theorem nil_zipWithAll :
+@[simp] theorem zipWithAll_nil_left :
    zipWithAll f [] bs = bs.map fun b => f none (some b) := rfl
@[simp] theorem zipWithAll_cons_cons :
    zipWithAll f (a :: as) (b :: bs) = f (some a) (some b) :: zipWithAll f as bs := rfl
@@ -1648,23 +1639,23 @@ where
    | true  => loop as (a::rs)
    | false => (rs.reverse, a::as)

-/-! ### splitBy -/
+/-! ### groupBy -/

 /--
-`O(|l|)`. `splitBy R l` splits `l` into chains of elements
+`O(|l|)`. `groupBy R l` splits `l` into chains of elements
 such that adjacent elements are related by `R`.

-* `splitBy (·==·) [1, 1, 2, 2, 2, 3, 2] = [[1, 1], [2, 2, 2], [3], [2]]`
-* `splitBy (·<·) [1, 2, 5, 4, 5, 1, 4] = [[1, 2, 5], [4, 5], [1, 4]]`
+* `groupBy (·==·) [1, 1, 2, 2, 2, 3, 2] = [[1, 1], [2, 2, 2], [3], [2]]`
+* `groupBy (·<·) [1, 2, 5, 4, 5, 1, 4] = [[1, 2, 5], [4, 5], [1, 4]]`
 -/
-@[specialize] def splitBy (R : α → α → Bool) : List α → List (List α)
+@[specialize] def groupBy (R : α → α → Bool) : List α → List (List α)
  | []    => []
  | a::as => loop as a [] []
 where
  /--
-  The arguments of `splitBy.loop l ag g gs` represent the following:
+  The arguments of `groupBy.loop l ag g gs` represent the following:

-  - `l : List α` are the elements which we still need to split.
+  - `l : List α` are the elements which we still need to group.
  - `ag : α` is the previous element for which a comparison was performed.
  - `g : List α` is the group currently being assembled, in **reverse order**.
  - `gs : List (List α)` is all of the groups that have been completed, in **reverse order**.
@@ -1675,8 +1666,6 @@ where
    | false => loop as a [] ((ag::g).reverse::gs)
  | [], ag, g, gs => ((ag::g).reverse::gs).reverse

-@[deprecated splitBy (since := "2024-10-30"), inherit_doc splitBy] abbrev groupBy := @splitBy
-
 /-! ### removeAll -/

 /-- `O(|xs|)`. Computes the "set difference" of lists,
--- a/src/Init/Data/List/Control.lean
+++ b/src/Init/Data/List/Control.lean
@@ -5,8 +5,6 @@ Author: Leonardo de Moura
 -/
 prelude
 import Init.Control.Basic
-import Init.Control.Id
-import Init.Control.Lawful
 import Init.Data.List.Basic

 namespace List
@@ -209,16 +207,6 @@ def findM? {m : Type → Type u} [Monad m] {α : Type} (p : α → m Bool) : Lis
    | true  => pure (some a)
    | false => findM? p as

-@[simp]
-theorem findM?_id (p : α → Bool) (as : List α) : findM? (m := Id) p as = as.find? p := by
-  induction as with
-  | nil => rfl
-  | cons a as ih =>
-    simp only [findM?, find?]
-    cases p a with
-    | true  => rfl
-    | false => rw [ih]; rfl
-
@[specialize]
 def findSomeM? {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f : α → m (Option β)) : List α → m (Option β)
  | []    => pure none
@@ -227,27 +215,26 @@ def findSomeM? {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f
    | some b => pure (some b)
    | none   => findSomeM? f as

-@[simp]
-theorem findSomeM?_id (f : α → Option β) (as : List α) : findSomeM? (m := Id) f as = as.findSome? f := by
-  induction as with
-  | nil => rfl
-  | cons a as ih =>
-    simp only [findSomeM?, findSome?]
-    cases f a with
-    | some b => rfl
-    | none   => rw [ih]; rfl
+@[inline] protected def forIn {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : List α) (init : β) (f : α → β → m (ForInStep β)) : m β :=
+  let rec @[specialize] loop
+    | [], b    => pure b
+    | a::as, b => do
+      match (← f a b) with
+      | ForInStep.done b  => pure b
+      | ForInStep.yield b => loop as b
+  loop as init

-theorem findM?_eq_findSomeM? [Monad m] [LawfulMonad m] (p : α → m Bool) (as : List α) :
-    as.findM? p = as.findSomeM? fun a => return if (← p a) then some a else none := by
-  induction as with
-  | nil => rfl
-  | cons a as ih =>
-    simp only [findM?, findSomeM?]
-    simp [ih]
-    congr
-    apply funext
-    intro b
-    cases b <;> simp
+instance : ForIn m (List α) α where
+  forIn := List.forIn
+
+@[simp] theorem forIn_eq_forIn [Monad m] : @List.forIn α β m _ = forIn := rfl
+
+@[simp] theorem forIn_nil [Monad m] (f : α → β → m (ForInStep β)) (b : β) : forIn [] b f = pure b :=
+  rfl
+
+@[simp] theorem forIn_cons [Monad m] (f : α → β → m (ForInStep β)) (a : α) (as : List α) (b : β)
+    : forIn (a::as) b f = f a b >>= fun | ForInStep.done b => pure b | ForInStep.yield b => forIn as b f :=
+  rfl

@[inline] protected def forIn' {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : List α) (init : β) (f : (a : α) → a ∈ as → β → m (ForInStep β)) : m β :=
  let rec @[specialize] loop : (as' : List α) → (b : β) → Exists (fun bs => bs ++ as' = as) → m β
@@ -256,7 +243,7 @@ theorem findM?_eq_findSomeM? [Monad m] [LawfulMonad m] (p : α → m Bool) (as :
      have : a ∈ as := by
        have ⟨bs, h⟩ := h
        subst h
-        exact mem_append_right _ (Mem.head ..)
+        exact mem_append_of_mem_right _ (Mem.head ..)
      match (← f a this b) with
      | ForInStep.done b  => pure b
      | ForInStep.yield b =>
@@ -267,15 +254,16 @@ theorem findM?_eq_findSomeM? [Monad m] [LawfulMonad m] (p : α → m Bool) (as :
 instance : ForIn' m (List α) α inferInstance where
  forIn' := List.forIn'

-- No separate `ForIn` instance is required because it can be derived from `ForIn'`.
-
@[simp] theorem forIn'_eq_forIn' [Monad m] : @List.forIn' α β m _ = forIn' := rfl

-@[simp] theorem forIn'_nil [Monad m] (f : (a : α) → a ∈ [] → β → m (ForInStep β)) (b : β) : forIn' [] b f = pure b :=
-  rfl
-
-@[simp] theorem forIn_nil [Monad m] (f : α → β → m (ForInStep β)) (b : β) : forIn [] b f = pure b :=
-  rfl
+@[simp] theorem forIn'_eq_forIn {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : List α) (init : β) (f : α → β → m (ForInStep β)) : forIn' as init (fun a _ b => f a b) = forIn as init f := by
+  simp [forIn', forIn, List.forIn, List.forIn']
+  have : ∀ cs h, List.forIn'.loop cs (fun a _ b => f a b) as init h = List.forIn.loop f as init := by
+    intro cs h
+    induction as generalizing cs init with
+    | nil => intros; rfl
+    | cons a as ih => intros; simp [List.forIn.loop, List.forIn'.loop, ih]
+  apply this

 instance : ForM m (List α) α where
  forM := List.forM
--- a/src/Init/Data/List/Count.lean
+++ b/src/Init/Data/List/Count.lean
@@ -153,7 +153,7 @@ theorem countP_filterMap (p : β → Bool) (f : α → Option β) (l : List α)
  simp only [length_filterMap_eq_countP]
  congr
  ext a
-  simp +contextual [Option.getD_eq_iff, Option.isSome_eq_isSome]
+  simp (config := { contextual := true }) [Option.getD_eq_iff, Option.isSome_eq_isSome]

@[simp] theorem countP_flatten (l : List (List α)) :
    countP p l.flatten = (l.map (countP p)).sum := by
@@ -315,7 +315,7 @@ theorem replicate_count_eq_of_count_eq_length {l : List α} (h : count a l = len
 theorem count_le_count_map [DecidableEq β] (l : List α) (f : α → β) (x : α) :
    count x l ≤ count (f x) (map f l) := by
  rw [count, count, countP_map]
-  apply countP_mono_left; simp +contextual
+  apply countP_mono_left; simp (config := { contextual := true })

 theorem count_filterMap {α} [BEq β] (b : β) (f : α → Option β) (l : List α) :
    count b (filterMap f l) = countP (fun a => f a == some b) l := by
--- a/src/Init/Data/List/FinRange.lean
+++ b/src/Init/Data/List/FinRange.lean
@@ -1,48 +0,0 @@
-/-
-Copyright (c) 2024 François G. Dorais. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: François G. Dorais
-/
-prelude
-import Init.Data.List.OfFn
-
-namespace List
-
-/-- `finRange n` lists all elements of `Fin n` in order -/
-def finRange (n : Nat) : List (Fin n) := ofFn fun i => i
-
-@[simp] theorem length_finRange (n) : (List.finRange n).length = n := by
-  simp [List.finRange]
-
-@[simp] theorem getElem_finRange (i : Nat) (h : i < (List.finRange n).length) :
-    (finRange n)[i] = Fin.cast (length_finRange n) ⟨i, h⟩ := by
-  simp [List.finRange]
-
-@[simp] theorem finRange_zero : finRange 0 = [] := by simp [finRange, ofFn]
-
-theorem finRange_succ (n) : finRange (n+1) = 0 :: (finRange n).map Fin.succ := by
-  apply List.ext_getElem; simp; intro i; cases i <;> simp
-
-theorem finRange_succ_last (n) :
-    finRange (n+1) = (finRange n).map Fin.castSucc ++ [Fin.last n] := by
-  apply List.ext_getElem
-  · simp
-  · intros
-    simp only [List.finRange, List.getElem_ofFn, getElem_append, length_map, length_ofFn,
-      getElem_map, Fin.castSucc_mk, getElem_singleton]
-    split
-    · rfl
-    · next h => exact Fin.eq_last_of_not_lt h
-
-theorem finRange_reverse (n) : (finRange n).reverse = (finRange n).map Fin.rev := by
-  induction n with
-  | zero => simp
-  | succ n ih =>
-    conv => lhs; rw [finRange_succ_last]
-    conv => rhs; rw [finRange_succ]
-    rw [reverse_append, reverse_cons, reverse_nil, nil_append, singleton_append, ← map_reverse,
-      map_cons, ih, map_map, map_map]
-    congr; funext
-    simp [Fin.rev_succ]
-
-end List
--- a/src/Init/Data/List/Find.lean
+++ b/src/Init/Data/List/Find.lean
@@ -10,8 +10,7 @@ import Init.Data.List.Sublist
 import Init.Data.List.Range

 /-!
-Lemmas about `List.findSome?`, `List.find?`, `List.findIdx`, `List.findIdx?`, `List.indexOf`,
-and `List.lookup`.
+# Lemmas about `List.findSome?`, `List.find?`, `List.findIdx`, `List.findIdx?`, and `List.indexOf`.
 -/

 namespace List
@@ -96,22 +95,22 @@ theorem findSome?_eq_some_iff {f : α → Option β} {l : List α} {b : β} :
    · simp only [Option.guard_eq_none] at h
      simp [ih, h]

-@[simp] theorem head?_filterMap (f : α → Option β) (l : List α) : (l.filterMap f).head? = l.findSome? f := by
+@[simp] theorem filterMap_head? (f : α → Option β) (l : List α) : (l.filterMap f).head? = l.findSome? f := by
  induction l with
  | nil => simp
  | cons x xs ih =>
    simp only [filterMap_cons, findSome?_cons]
    split <;> simp [*]

-@[simp] theorem head_filterMap (f : α → Option β) (l : List α) (h) :
-    (l.filterMap f).head h = (l.findSome? f).get (by simp_all [Option.isSome_iff_ne_none]) := by
+@[simp] theorem filterMap_head (f : α → Option β) (l : List α) (h) :
+    (l.filterMap f).head h = (l.findSome? f).get (by simp_all [Option.isSome_iff_ne_none])  := by
  simp [head_eq_iff_head?_eq_some]

-@[simp] theorem getLast?_filterMap (f : α → Option β) (l : List α) : (l.filterMap f).getLast? = l.reverse.findSome? f := by
+@[simp] theorem filterMap_getLast? (f : α → Option β) (l : List α) : (l.filterMap f).getLast? = l.reverse.findSome? f := by
  rw [getLast?_eq_head?_reverse]
  simp [← filterMap_reverse]

-@[simp] theorem getLast_filterMap (f : α → Option β) (l : List α) (h) :
+@[simp] theorem filterMap_getLast (f : α → Option β) (l : List α) (h) :
    (l.filterMap f).getLast h = (l.reverse.findSome? f).get (by simp_all [Option.isSome_iff_ne_none]) := by
  simp [getLast_eq_iff_getLast_eq_some]

@@ -180,7 +179,7 @@ theorem IsPrefix.findSome?_eq_some {l₁ l₂ : List α} {f : α → Option β}
    List.findSome? f l₁ = some b → List.findSome? f l₂ = some b := by
  rw [IsPrefix] at h
  obtain ⟨t, rfl⟩ := h
-  simp +contextual [findSome?_append]
+  simp (config := {contextual := true}) [findSome?_append]

 theorem IsPrefix.findSome?_eq_none {l₁ l₂ : List α} {f : α → Option β} (h : l₁ <+: l₂) :
    List.findSome? f l₂ = none → List.findSome? f l₁ = none :=
@@ -207,8 +206,7 @@ theorem IsInfix.findSome?_eq_none {l₁ l₂ : List α} {f : α → Option β} (
@[simp] theorem find?_eq_none : find? p l = none ↔ ∀ x ∈ l, ¬ p x := by
  induction l <;> simp [find?_cons]; split <;> simp [*]

-theorem find?_eq_some_iff_append :
-    xs.find? p = some b ↔ p b ∧ ∃ as bs, xs = as ++ b :: bs ∧ ∀ a ∈ as, !p a := by
+theorem find?_eq_some : xs.find? p = some b ↔ p b ∧ ∃ as bs, xs = as ++ b :: bs ∧ ∀ a ∈ as, !p a := by
  induction xs with
  | nil => simp
  | cons x xs ih =>
@@ -244,9 +242,6 @@ theorem find?_eq_some_iff_append :
          cases h₁
          simp

-@[deprecated find?_eq_some_iff_append (since := "2024-11-06")]
-abbrev find?_eq_some := @find?_eq_some_iff_append
-
@[simp]
 theorem find?_cons_eq_some : (a :: xs).find? p = some b ↔ (p a ∧ a = b) ∨ (!p a ∧ xs.find? p = some b) := by
  rw [find?_cons]
@@ -292,18 +287,18 @@ theorem get_find?_mem (xs : List α) (p : α → Bool) (h) : (xs.find? p).get h
    · simp only [find?_cons]
      split <;> simp_all

-@[simp] theorem head?_filter (p : α → Bool) (l : List α) : (l.filter p).head? = l.find? p := by
-  rw [← filterMap_eq_filter, head?_filterMap, findSome?_guard]
+@[simp] theorem filter_head? (p : α → Bool) (l : List α) : (l.filter p).head? = l.find? p := by
+  rw [← filterMap_eq_filter, filterMap_head?, findSome?_guard]

-@[simp] theorem head_filter (p : α → Bool) (l : List α) (h) :
+@[simp] theorem filter_head (p : α → Bool) (l : List α) (h) :
    (l.filter p).head h = (l.find? p).get (by simp_all [Option.isSome_iff_ne_none]) := by
  simp [head_eq_iff_head?_eq_some]

-@[simp] theorem getLast?_filter (p : α → Bool) (l : List α) : (l.filter p).getLast? = l.reverse.find? p := by
+@[simp] theorem filter_getLast? (p : α → Bool) (l : List α) : (l.filter p).getLast? = l.reverse.find? p := by
  rw [getLast?_eq_head?_reverse]
  simp [← filter_reverse]

-@[simp] theorem getLast_filter (p : α → Bool) (l : List α) (h) :
+@[simp] theorem filter_getLast (p : α → Bool) (l : List α) (h) :
    (l.filter p).getLast h = (l.reverse.find? p).get (by simp_all [Option.isSome_iff_ne_none]) := by
  simp [getLast_eq_iff_getLast_eq_some]

@@ -352,7 +347,7 @@ theorem find?_flatten_eq_some {xs : List (List α)} {p : α → Bool} {a : α} :
    xs.flatten.find? p = some a ↔
      p a ∧ ∃ as ys zs bs, xs = as ++ (ys ++ a :: zs) :: bs ∧
        (∀ a ∈ as, ∀ x ∈ a, !p x) ∧ (∀ x ∈ ys, !p x) := by
-  rw [find?_eq_some_iff_append]
+  rw [find?_eq_some]
  constructor
  · rintro ⟨h, ⟨ys, zs, h₁, h₂⟩⟩
    refine ⟨h, ?_⟩
@@ -441,7 +436,7 @@ theorem IsPrefix.find?_eq_some {l₁ l₂ : List α} {p : α → Bool} (h : l₁
    List.find? p l₁ = some b → List.find? p l₂ = some b := by
  rw [IsPrefix] at h
  obtain ⟨t, rfl⟩ := h
-  simp +contextual [find?_append]
+  simp (config := {contextual := true}) [find?_append]

 theorem IsPrefix.find?_eq_none {l₁ l₂ : List α} {p : α → Bool} (h : l₁ <+: l₂) :
    List.find? p l₂ = none → List.find? p l₁ = none :=
@@ -567,7 +562,7 @@ theorem not_of_lt_findIdx {p : α → Bool} {xs : List α} {i : Nat} (h : i < xs
    | inr e =>
      have ipm := Nat.succ_pred_eq_of_pos e
      have ilt := Nat.le_trans ho (findIdx_le_length p)
-      simp +singlePass only [← ipm, getElem_cons_succ]
+      simp (config := { singlePass := true }) only [← ipm, getElem_cons_succ]
      rw [← ipm, Nat.succ_lt_succ_iff] at h
      simpa using ih h

--- a/src/Init/Data/List/Impl.lean
+++ b/src/Init/Data/List/Impl.lean
@@ -23,7 +23,7 @@ namespace List
 The following operations are already tail-recursive, and do not need `@[csimp]` replacements:
 `get`, `foldl`, `beq`, `isEqv`, `reverse`, `elem` (and hence `contains`), `drop`, `dropWhile`,
 `partition`, `isPrefixOf`, `isPrefixOf?`, `find?`, `findSome?`, `lookup`, `any` (and hence `or`),
-`all` (and hence `and`) , `range`, `eraseDups`, `eraseReps`, `span`, `splitBy`.
+`all` (and hence `and`) , `range`, `eraseDups`, `eraseReps`, `span`, `groupBy`.

 The following operations are still missing `@[csimp]` replacements:
 `concat`, `zipWithAll`.
@@ -38,7 +38,7 @@ The following operations were already given `@[csimp]` replacements in `Init/Dat

 The following operations are given `@[csimp]` replacements below:
 `set`, `filterMap`, `foldr`, `append`, `bind`, `join`,
-`take`, `takeWhile`, `dropLast`, `replace`, `modify`, `insertIdx`, `erase`, `eraseIdx`, `zipWith`,
+`take`, `takeWhile`, `dropLast`, `replace`, `modify`, `erase`, `eraseIdx`, `zipWith`,
 `enumFrom`, and `intercalate`.

 -/
@@ -91,7 +91,7 @@ The following operations are given `@[csimp]` replacements below:
@[specialize] def foldrTR (f : α → β → β) (init : β) (l : List α) : β := l.toArray.foldr f init

@[csimp] theorem foldr_eq_foldrTR : @foldr = @foldrTR := by
-  funext α β f init l; simp [foldrTR, ← Array.foldr_toList, -Array.size_toArray]
+  funext α β f init l; simp [foldrTR, Array.foldr_eq_foldr_toList, -Array.size_toArray]

 /-! ### flatMap  -/

@@ -215,23 +215,6 @@ theorem modifyTR_go_eq : ∀ l n, modifyTR.go f l n acc = acc.toList ++ modify f
@[csimp] theorem modify_eq_modifyTR : @modify = @modifyTR := by
  funext α f n l; simp [modifyTR, modifyTR_go_eq]

-/-! ### insertIdx -/
-
-/-- Tail-recursive version of `insertIdx`. -/
-@[inline] def insertIdxTR (n : Nat) (a : α) (l : List α) : List α := go n l #[] where
-  /-- Auxiliary for `insertIdxTR`: `insertIdxTR.go a n l acc = acc.toList ++ insertIdx n a l`. -/
-  go : Nat → List α → Array α → List α
-  | 0, l, acc => acc.toListAppend (a :: l)
-  | _, [], acc => acc.toList
-  | n+1, a :: l, acc => go n l (acc.push a)
-
-theorem insertIdxTR_go_eq : ∀ n l, insertIdxTR.go a n l acc = acc.toList ++ insertIdx n a l
-  | 0, l | _+1, [] => by simp [insertIdxTR.go, insertIdx]
-  | n+1, a :: l => by simp [insertIdxTR.go, insertIdx, insertIdxTR_go_eq n l]
-
-@[csimp] theorem insertIdx_eq_insertIdxTR : @insertIdx = @insertIdxTR := by
-  funext α f n l; simp [insertIdxTR, insertIdxTR_go_eq]
-
 /-! ### erase -/

 /-- Tail recursive version of `List.erase`. -/
@@ -331,7 +314,7 @@ def enumFromTR (n : Nat) (l : List α) : List (Nat × α) :=
    | a::as, n => by
      rw [← show _ + as.length = n + (a::as).length from Nat.succ_add .., foldr, go as]
      simp [enumFrom, f]
-  rw [← Array.foldr_toList]
+  rw [Array.foldr_eq_foldr_toList]
  simp [go]

 /-! ## Other list operations -/
--- a/src/Init/Data/List/Lemmas.lean
+++ b/src/Init/Data/List/Lemmas.lean
@@ -101,7 +101,7 @@ theorem tail_eq_of_cons_eq (H : h₁ :: t₁ = h₂ :: t₂) : t₁ = t₂ := (c
 theorem cons_inj_right (a : α) {l l' : List α} : a :: l = a :: l' ↔ l = l' :=
  ⟨tail_eq_of_cons_eq, congrArg _⟩

-@[deprecated cons_inj_right (since := "2024-06-15")] abbrev cons_inj := @cons_inj_right
+@[deprecated (since := "2024-06-15")] abbrev cons_inj := @cons_inj_right

 theorem cons_eq_cons {a b : α} {l l' : List α} : a :: l = b :: l' ↔ a = b ∧ l = l' :=
  List.cons.injEq .. ▸ .rfl
@@ -171,7 +171,7 @@ theorem get_cons_succ {as : List α} {h : i + 1 < (a :: as).length} :
 theorem get_cons_succ' {as : List α} {i : Fin as.length} :
  (a :: as).get i.succ = as.get i := rfl

-@[deprecated "Deprecated without replacement." (since := "2024-07-09")]
+@[deprecated (since := "2024-07-09")]
 theorem get_cons_cons_one : (a₁ :: a₂ :: as).get (1 : Fin (as.length + 2)) = a₂ := rfl

 theorem get_mk_zero : ∀ {l : List α} (h : 0 < l.length), l.get ⟨0, h⟩ = l.head (length_pos.mp h)
@@ -372,17 +372,6 @@ theorem getElem?_concat_length (l : List α) (a : α) : (l ++ [a])[l.length]? =
@[deprecated getElem?_concat_length (since := "2024-06-12")]
 theorem get?_concat_length (l : List α) (a : α) : (l ++ [a]).get? l.length = some a := by simp

-@[simp] theorem isSome_getElem? {l : List α} {n : Nat} : l[n]?.isSome ↔ n < l.length := by
-  by_cases h : n < l.length
-  · simp_all
-  · simp [h]
-    simp_all
-
-@[simp] theorem isNone_getElem? {l : List α} {n : Nat} : l[n]?.isNone ↔ l.length ≤ n := by
-  by_cases h : n < l.length
-  · simp_all
-  · simp [h]
-
 /-! ### mem -/

@[simp] theorem not_mem_nil (a : α) : ¬ a ∈ [] := nofun
@@ -394,9 +383,9 @@ theorem get?_concat_length (l : List α) (a : α) : (l ++ [a]).get? l.length = s
 theorem mem_cons_self (a : α) (l : List α) : a ∈ a :: l := .head ..

 theorem mem_concat_self (xs : List α) (a : α) : a ∈ xs ++ [a] :=
-  mem_append_right xs (mem_cons_self a _)
+  mem_append_of_mem_right xs (mem_cons_self a _)

-theorem mem_append_cons_self : a ∈ xs ++ a :: ys := mem_append_right _ (mem_cons_self _ _)
+theorem mem_append_cons_self : a ∈ xs ++ a :: ys := mem_append_of_mem_right _ (mem_cons_self _ _)

 theorem eq_append_cons_of_mem {a : α} {xs : List α} (h : a ∈ xs) :
    ∃ as bs, xs = as ++ a :: bs ∧ a ∉ as := by
@@ -503,20 +492,16 @@ theorem getElem?_of_mem {a} {l : List α} (h : a ∈ l) : ∃ n : Nat, l[n]? = s
 theorem get?_of_mem {a} {l : List α} (h : a ∈ l) : ∃ n, l.get? n = some a :=
  let ⟨⟨n, _⟩, e⟩ := get_of_mem h; ⟨n, e ▸ get?_eq_get _⟩

-theorem get_mem : ∀ (l : List α) n, get l n ∈ l
-  | _ :: _, ⟨0, _⟩ => .head ..
-  | _ :: l, ⟨_+1, _⟩ => .tail _ (get_mem l ..)
+theorem get_mem : ∀ (l : List α) n h, get l ⟨n, h⟩ ∈ l
+  | _ :: _, 0, _ => .head ..
+  | _ :: l, _+1, _ => .tail _ (get_mem l ..)

-theorem mem_of_getElem? {l : List α} {n : Nat} {a : α} (e : l[n]? = some a) : a ∈ l :=
+theorem getElem?_mem {l : List α} {n : Nat} {a : α} (e : l[n]? = some a) : a ∈ l :=
  let ⟨_, e⟩ := getElem?_eq_some_iff.1 e; e ▸ getElem_mem ..

-@[deprecated mem_of_getElem? (since := "2024-09-06")] abbrev getElem?_mem := @mem_of_getElem?
-
-theorem mem_of_get? {l : List α} {n a} (e : l.get? n = some a) : a ∈ l :=
+theorem get?_mem {l : List α} {n a} (e : l.get? n = some a) : a ∈ l :=
  let ⟨_, e⟩ := get?_eq_some.1 e; e ▸ get_mem ..

-@[deprecated mem_of_get? (since := "2024-09-06")] abbrev get?_mem := @mem_of_get?
-
 theorem mem_iff_getElem {a} {l : List α} : a ∈ l ↔ ∃ (n : Nat) (h : n < l.length), l[n]'h = a :=
  ⟨getElem_of_mem, fun ⟨_, _, e⟩ => e ▸ getElem_mem ..⟩

@@ -791,24 +776,6 @@ theorem mem_or_eq_of_mem_set : ∀ {l : List α} {n : Nat} {a b : α}, a ∈ l.s
    · intro a
      simp

-@[simp] theorem beq_nil_iff [BEq α] {l : List α} : (l == []) = l.isEmpty := by
-  cases l <;> rfl
-
-@[simp] theorem nil_beq_iff [BEq α] {l : List α} : ([] == l) = l.isEmpty := by
-  cases l <;> rfl
-
-@[simp] theorem cons_beq_cons [BEq α] {a b : α} {l₁ l₂ : List α} :
-    (a :: l₁ == b :: l₂) = (a == b && l₁ == l₂) := rfl
-
-theorem length_eq_of_beq [BEq α] {l₁ l₂ : List α} (h : l₁ == l₂) : l₁.length = l₂.length :=
-  match l₁, l₂ with
-  | [], [] => rfl
-  | [], _ :: _ => by simp [beq_nil_iff] at h
-  | _ :: _, [] => by simp [nil_beq_iff] at h
-  | a :: l₁, b :: l₂ => by
-    simp at h
-    simpa [Nat.add_one_inj]using length_eq_of_beq h.2
-
 /-! ### Lexicographic ordering -/

 protected theorem lt_irrefl [LT α] (lt_irrefl : ∀ x : α, ¬x < x) (l : List α) : ¬l < l := by
@@ -874,12 +841,6 @@ theorem foldr_eq_foldrM (f : α → β → β) (b) (l : List α) :
    l.foldr f b = l.foldrM (m := Id) f b := by
  induction l <;> simp [*, foldr]

-@[simp] theorem id_run_foldlM (f : β → α → Id β) (b) (l : List α) :
-    Id.run (l.foldlM f b) = l.foldl f b := (foldl_eq_foldlM f b l).symm
-
-@[simp] theorem id_run_foldrM (f : α → β → Id β) (b) (l : List α) :
-    Id.run (l.foldrM f b) = l.foldr f b := (foldr_eq_foldrM f b l).symm
-
 /-! ### foldl and foldr -/

@[simp] theorem foldr_cons_eq_append (l : List α) : l.foldr cons l' = l ++ l' := by
@@ -902,30 +863,14 @@ theorem foldr_map (f : α₁ → α₂) (g : α₂ → β → β) (l : List α
    (l.map f).foldr g init = l.foldr (fun x y => g (f x) y) init := by
  induction l generalizing init <;> simp [*]

-theorem foldl_filterMap (f : α → Option β) (g : γ → β → γ) (l : List α) (init : γ) :
-    (l.filterMap f).foldl g init = l.foldl (fun x y => match f y with | some b => g x b | none => x) init := by
-  induction l generalizing init with
-  | nil => rfl
-  | cons a l ih =>
-    simp only [filterMap_cons, foldl_cons]
-    cases f a <;> simp [ih]
-
-theorem foldr_filterMap (f : α → Option β) (g : β → γ → γ) (l : List α) (init : γ) :
-    (l.filterMap f).foldr g init = l.foldr (fun x y => match f x with | some b => g b y | none => y) init := by
-  induction l generalizing init with
-  | nil => rfl
-  | cons a l ih =>
-    simp only [filterMap_cons, foldr_cons]
-    cases f a <;> simp [ih]
-
-theorem foldl_map' (g : α → β) (f : α → α → α) (f' : β → β → β) (a : α) (l : List α)
+theorem foldl_map' {α β : Type u} (g : α → β) (f : α → α → α) (f' : β → β → β) (a : α) (l : List α)
    (h : ∀ x y, f' (g x) (g y) = g (f x y)) :
    (l.map g).foldl f' (g a) = g (l.foldl f a) := by
  induction l generalizing a
  · simp
  · simp [*, h]

-theorem foldr_map' (g : α → β) (f : α → α → α) (f' : β → β → β) (a : α) (l : List α)
+theorem foldr_map' {α β : Type u} (g : α → β) (f : α → α → α) (f' : β → β → β) (a : α) (l : List α)
    (h : ∀ x y, f' (g x) (g y) = g (f x y)) :
    (l.map g).foldr f' (g a) = g (l.foldr f a) := by
  induction l generalizing a
@@ -1038,21 +983,6 @@ theorem foldr_rel {l : List α} {f g : α → β → β} {a b : β} (r : β →
    · simp
    · exact ih h fun a m c c' h => h' _ (by simp_all) _ _ h

-@[simp] theorem foldl_add_const (l : List α) (a b : Nat) :
-    l.foldl (fun x _ => x + a) b = b + a * l.length := by
-  induction l generalizing b with
-  | nil => simp
-  | cons y l ih =>
-    simp only [foldl_cons, ih, length_cons, Nat.mul_add, Nat.mul_one, Nat.add_assoc,
-      Nat.add_comm a]
-
-@[simp] theorem foldr_add_const (l : List α) (a b : Nat) :
-    l.foldr (fun _ x => x + a) b = b + a * l.length := by
-  induction l generalizing b with
-  | nil => simp
-  | cons y l ih =>
-    simp only [foldr_cons, ih, length_cons, Nat.mul_add, Nat.mul_one, Nat.add_assoc]
-
 /-! ### getLast -/

 theorem getLast_eq_getElem : ∀ (l : List α) (h : l ≠ []),
@@ -1064,10 +994,6 @@ theorem getLast_eq_getElem : ∀ (l : List α) (h : l ≠ []),
  | _ :: _ :: _, _ => by
    simp [getLast, get, Nat.succ_sub_succ, getLast_eq_getElem]

-theorem getElem_length_sub_one_eq_getLast (l : List α) (h) :
-    l[l.length - 1] = getLast l (by cases l; simp at h; simp) := by
-  rw [← getLast_eq_getElem]
-
@[deprecated getLast_eq_getElem (since := "2024-07-15")]
 theorem getLast_eq_get (l : List α) (h : l ≠ []) :
    getLast l h = l.get ⟨l.length - 1, by
@@ -1088,7 +1014,7 @@ theorem getLast_eq_getLastD (a l h) : @getLast α (a::l) h = getLastD l a := by

@[simp] theorem getLast_singleton (a h) : @getLast α [a] h = a := rfl

-theorem getLast!_cons_eq_getLastD [Inhabited α] : @getLast! α _ (a::l) = getLastD l a := by
+theorem getLast!_cons [Inhabited α] : @getLast! α _ (a::l) = getLastD l a := by
  simp [getLast!, getLast_eq_getLastD]

@[simp] theorem getLast_mem : ∀ {l : List α} (h : l ≠ []), getLast l h ∈ l
@@ -1152,12 +1078,7 @@ theorem getLastD_concat (a b l) : @getLastD α (l ++ [b]) a = b := by

 /-! ### getLast! -/

-theorem getLast!_nil [Inhabited α] : ([] : List α).getLast! = default := rfl
-
-@[simp] theorem getLast!_eq_getLast?_getD [Inhabited α] {l : List α} : getLast! l = (getLast? l).getD default := by
-  cases l with
-  | nil => simp [getLast!_nil]
-  | cons _ _ => simp [getLast!, getLast?_eq_getLast]
+@[simp] theorem getLast!_nil [Inhabited α] : ([] : List α).getLast! = default := rfl

 theorem getLast!_of_getLast? [Inhabited α] : ∀ {l : List α}, getLast? l = some a → getLast! l = a
  | _ :: _, rfl => rfl
@@ -1192,11 +1113,6 @@ theorem head_eq_getElem (l : List α) (h : l ≠ []) : head l h = l[0]'(length_p
  | nil => simp at h
  | cons _ _ => simp

-theorem getElem_zero_eq_head (l : List α) (h) : l[0] = head l (by simpa [length_pos] using h) := by
-  cases l with
-  | nil => simp at h
-  | cons _ _ => simp
-
 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
@@ -1541,22 +1457,6 @@ theorem forall_mem_filter {l : List α} {p : α → Bool} {P : α → Prop} :
  | [] => rfl
  | a :: l => by by_cases hp : p a <;> by_cases hq : q a <;> simp [hp, hq, filter_filter _ l]

-theorem foldl_filter (p : α → Bool) (f : β → α → β) (l : List α) (init : β) :
-    (l.filter p).foldl f init = l.foldl (fun x y => if p y then f x y else x) init := by
-  induction l generalizing init with
-  | nil => rfl
-  | cons a l ih =>
-    simp only [filter_cons, foldl_cons]
-    split <;> simp [ih]
-
-theorem foldr_filter (p : α → Bool) (f : α → β → β) (l : List α) (init : β) :
-    (l.filter p).foldr f init = l.foldr (fun x y => if p x then f x y else y) init := by
-  induction l generalizing init with
-  | nil => rfl
-  | cons a l ih =>
-    simp only [filter_cons, foldr_cons]
-    split <;> simp [ih]
-
 theorem filter_map (f : β → α) (l : List β) : filter p (map f l) = map f (filter (p ∘ f) l) := by
  induction l with
  | nil => rfl
@@ -1824,7 +1724,7 @@ theorem getElem_append_right' (l₁ : List α) {l₂ : List α} {n : Nat} (hn :
    l₂[n] = (l₁ ++ l₂)[n + l₁.length]'(by simpa [Nat.add_comm] using Nat.add_lt_add_left hn _) := by
  rw [getElem_append_right] <;> simp [*, le_add_left]

-@[deprecated "Deprecated without replacement." (since := "2024-06-12")]
+@[deprecated (since := "2024-06-12")]
 theorem get_append_right_aux {l₁ l₂ : List α} {n : Nat}
  (h₁ : l₁.length ≤ n) (h₂ : n < (l₁ ++ l₂).length) : n - l₁.length < l₂.length := by
  rw [length_append] at h₂
@@ -1841,7 +1741,7 @@ theorem getElem_of_append {l : List α} (eq : l = l₁ ++ a :: l₂) (h : l₁.l
  rw [← getElem?_eq_getElem, eq, getElem?_append_right (h ▸ Nat.le_refl _), h]
  simp

-@[deprecated "Deprecated without replacement." (since := "2024-06-12")]
+@[deprecated (since := "2024-06-12")]
 theorem get_of_append_proof {l : List α}
    (eq : l = l₁ ++ a :: l₂) (h : l₁.length = n) : n < length l := eq ▸ h ▸ by simp_arith

@@ -2025,8 +1925,11 @@ theorem not_mem_append {a : α} {s t : List α} (h₁ : a ∉ s) (h₂ : a ∉ t
 theorem mem_append_eq (a : α) (s t : List α) : (a ∈ s ++ t) = (a ∈ s ∨ a ∈ t) :=
  propext mem_append

-@[deprecated mem_append_left (since := "2024-11-20")] abbrev mem_append_of_mem_left := @mem_append_left
-@[deprecated mem_append_right (since := "2024-11-20")] abbrev mem_append_of_mem_right := @mem_append_right
+theorem mem_append_left {a : α} {l₁ : List α} (l₂ : List α) (h : a ∈ l₁) : a ∈ l₁ ++ l₂ :=
+  mem_append.2 (Or.inl h)
+
+theorem mem_append_right {a : α} (l₁ : List α) {l₂ : List α} (h : a ∈ l₂) : a ∈ l₁ ++ l₂ :=
+  mem_append.2 (Or.inr h)

 theorem mem_iff_append {a : α} {l : List α} : a ∈ l ↔ ∃ s t : List α, l = s ++ a :: t :=
  ⟨append_of_mem, fun ⟨s, t, e⟩ => e ▸ by simp⟩
@@ -2440,7 +2343,7 @@ theorem forall_mem_replicate {p : α → Prop} {a : α} {n} :

@[simp] theorem getElem_replicate (a : α) {n : Nat} {m} (h : m < (replicate n a).length) :
    (replicate n a)[m] = a :=
-  eq_of_mem_replicate (getElem_mem _)
+  eq_of_mem_replicate (get_mem _ _ _)

@[deprecated getElem_replicate (since := "2024-06-12")]
 theorem get_replicate (a : α) {n : Nat} (m : Fin _) : (replicate n a).get m = a := by
@@ -2797,12 +2700,6 @@ theorem flatMap_reverse {β} (l : List α) (f : α → List β) : (l.reverse.fla
    l.reverse.foldr f b = l.foldl (fun x y => f y x) b :=
  (foldl_reverse ..).symm.trans <| by simp

-theorem foldl_eq_foldr_reverse (l : List α) (f : β → α → β) (b) :
-    l.foldl f b = l.reverse.foldr (fun x y => f y x) b := by simp
-
-theorem foldr_eq_foldl_reverse (l : List α) (f : α → β → β) (b) :
-    l.foldr f b = l.reverse.foldl (fun x y => f y x) b := by simp
-
@[simp] theorem reverse_replicate (n) (a : α) : reverse (replicate n a) = replicate n a :=
  eq_replicate_iff.2
    ⟨by rw [length_reverse, length_replicate],
@@ -2946,10 +2843,6 @@ theorem contains_iff_exists_mem_beq [BEq α] {l : List α} {a : α} :
    l.contains a ↔ ∃ a' ∈ l, a == a' := by
  induction l <;> simp_all

-theorem contains_iff_mem [BEq α] [LawfulBEq α] {l : List α} {a : α} :
-    l.contains a ↔ a ∈ l := by
-  simp
-
 /-! ## Sublists -/

 /-! ### partition
@@ -3357,10 +3250,10 @@ theorem any_eq_not_all_not (l : List α) (p : α → Bool) : l.any p = !l.all (!
 theorem all_eq_not_any_not (l : List α) (p : α → Bool) : l.all p = !l.any (!p .) := by
  simp only [not_any_eq_all_not, Bool.not_not]

-@[simp] theorem any_map {l : List α} {p : β → Bool} : (l.map f).any p = l.any (p ∘ f) := by
+@[simp] theorem any_map {l : List α} {p : α → Bool} : (l.map f).any p = l.any (p ∘ f) := by
  induction l with simp | cons _ _ ih => rw [ih]

-@[simp] theorem all_map {l : List α} {p : β → Bool} : (l.map f).all p = l.all (p ∘ f) := by
+@[simp] theorem all_map {l : List α} {p : α → Bool} : (l.map f).all p = l.all (p ∘ f) := by
  induction l with simp | cons _ _ ih => rw [ih]

@[simp] theorem any_filter {l : List α} {p q : α → Bool} :
@@ -3435,7 +3328,7 @@ theorem all_eq_not_any_not (l : List α) (p : α → Bool) : l.all p = !l.any (!

@[simp] theorem all_replicate {n : Nat} {a : α} :
    (replicate n a).all f = if n = 0 then true else f a := by
-  cases n <;> simp +contextual [replicate_succ]
+  cases n <;> simp (config := {contextual := true}) [replicate_succ]

@[simp] theorem any_insert [BEq α] [LawfulBEq α] {l : List α} {a : α} :
    (l.insert a).any f = (f a || l.any f) := by
--- a/src/Init/Data/List/MapIdx.lean
+++ b/src/Init/Data/List/MapIdx.lean
@@ -7,9 +7,6 @@ Authors: Kim Morrison, Mario Carneiro
 prelude
 import Init.Data.Array.Lemmas
 import Init.Data.List.Nat.Range
-import Init.Data.List.OfFn
-import Init.Data.Fin.Lemmas
-import Init.Data.Option.Attach

 namespace List

@@ -17,21 +14,8 @@ namespace List

 /-! ### mapIdx -/

-
 /--
-Given a list `as = [a₀, a₁, ...]` function `f : Fin as.length → α → β`, returns the list
-`[f 0 a₀, f 1 a₁, ...]`.
-/
-@[inline] def mapFinIdx (as : List α) (f : Fin as.length → α → β) : List β := go as #[] (by simp) where
-  /-- Auxiliary for `mapFinIdx`:
-  `mapFinIdx.go [a₀, a₁, ...] acc = acc.toList ++ [f 0 a₀, f 1 a₁, ...]` -/
-  @[specialize] go : (bs : List α) → (acc : Array β) → bs.length + acc.size = as.length → List β
-  | [], acc, h => acc.toList
-  | a :: as, acc, h =>
-    go as (acc.push (f ⟨acc.size, by simp at h; omega⟩ a)) (by simp at h ⊢; omega)
-
-/--
-Given a function `f : Nat → α → β` and `as : List α`, `as = [a₀, a₁, ...]`, returns the list
+Given a function `f : Nat → α → β` and `as : list α`, `as = [a₀, a₁, ...]`, returns the list
 `[f 0 a₀, f 1 a₁, ...]`.
 -/
@[inline] def mapIdx (f : Nat → α → β) (as : List α) : List β := go as #[] where
@@ -41,177 +25,34 @@ Given a function `f : Nat → α → β` and `as : List α`, `as = [a₀, a₁,
  | [], acc => acc.toList
  | a :: as, acc => go as (acc.push (f acc.size a))

-/-! ### mapFinIdx -/
-
-@[simp]
-theorem mapFinIdx_nil {f : Fin 0 → α → β} : mapFinIdx [] f = [] :=
-  rfl
-
-@[simp] theorem length_mapFinIdx_go :
-    (mapFinIdx.go as f bs acc h).length = as.length := by
-  induction bs generalizing acc with
-  | nil => simpa using h
-  | cons _ _ ih => simp [mapFinIdx.go, ih]
-
-@[simp] theorem length_mapFinIdx {as : List α} {f : Fin as.length → α → β} :
-    (as.mapFinIdx f).length = as.length := by
-  simp [mapFinIdx, length_mapFinIdx_go]
-
-theorem getElem_mapFinIdx_go {as : List α} {f : Fin as.length → α → β} {i : Nat} {h} {w} :
-    (mapFinIdx.go as f bs acc h)[i] =
-      if w' : i < acc.size then acc[i] else f ⟨i, by simp at w; omega⟩ (bs[i - acc.size]'(by simp at w; omega)) := by
-  induction bs generalizing acc with
-  | nil =>
-    simp only [length_mapFinIdx_go, length_nil, Nat.zero_add] at w h
-    simp only [mapFinIdx.go, Array.getElem_toList]
-    rw [dif_pos]
-  | cons _ _ ih =>
-    simp [mapFinIdx.go]
-    rw [ih]
-    simp
-    split <;> rename_i h₁ <;> split <;> rename_i h₂
-    · rw [Array.getElem_push_lt]
-    · have h₃ : i = acc.size := by omega
-      subst h₃
-      simp
-    · omega
-    · have h₃ : i - acc.size = (i - (acc.size + 1)) + 1 := by omega
-      simp [h₃]
-
-@[simp] theorem getElem_mapFinIdx {as : List α} {f : Fin as.length → α → β} {i : Nat} {h} :
-    (as.mapFinIdx f)[i] = f ⟨i, by simp at h; omega⟩ (as[i]'(by simp at h; omega)) := by
-  simp [mapFinIdx, getElem_mapFinIdx_go]
-
-theorem mapFinIdx_eq_ofFn {as : List α} {f : Fin as.length → α → β} :
-    as.mapFinIdx f = List.ofFn fun i : Fin as.length => f i as[i] := by
-  apply ext_getElem <;> simp
-
-@[simp] theorem getElem?_mapFinIdx {l : List α} {f : Fin l.length → α → β} {i : Nat} :
-    (l.mapFinIdx f)[i]? = l[i]?.pbind fun x m => f ⟨i, by simp [getElem?_eq_some] at m; exact m.1⟩ x := by
-  simp only [getElem?_eq, length_mapFinIdx, getElem_mapFinIdx]
-  split <;> simp
-
-@[simp]
-theorem mapFinIdx_cons {l : List α} {a : α} {f : Fin (l.length + 1) → α → β} :
-    mapFinIdx (a :: l) f = f 0 a :: mapFinIdx l (fun i => f i.succ) := by
-  apply ext_getElem
-  · simp
-  · rintro (_|i) h₁ h₂ <;> simp
-
-theorem mapFinIdx_append {K L : List α} {f : Fin (K ++ L).length → α → β} :
-    (K ++ L).mapFinIdx f =
-      K.mapFinIdx (fun i => f (i.castLE (by simp))) ++ L.mapFinIdx (fun i => f ((i.natAdd K.length).cast (by simp))) := by
-  apply ext_getElem
-  · simp
-  · intro i h₁ h₂
-    rw [getElem_append]
-    simp only [getElem_mapFinIdx, length_mapFinIdx]
-    split <;> rename_i h
-    · rw [getElem_append_left]
-      congr
-    · simp only [Nat.not_lt] at h
-      rw [getElem_append_right h]
-      congr
-      simp
-      omega
-
-@[simp] theorem mapFinIdx_concat {l : List α} {e : α} {f : Fin (l ++ [e]).length → α → β}:
-    (l ++ [e]).mapFinIdx f = l.mapFinIdx (fun i => f (i.castLE (by simp))) ++ [f ⟨l.length, by simp⟩ e] := by
-  simp [mapFinIdx_append]
-  congr
-
-theorem mapFinIdx_singleton {a : α} {f : Fin 1 → α → β} :
-    [a].mapFinIdx f = [f ⟨0, by simp⟩ a] := by
-  simp
-
-theorem mapFinIdx_eq_enum_map {l : List α} {f : Fin l.length → α → β} :
-    l.mapFinIdx f = l.enum.attach.map
-      fun ⟨⟨i, x⟩, m⟩ => f ⟨i, by rw [mk_mem_enum_iff_getElem?, getElem?_eq_some] at m; exact m.1⟩ x := by
-  apply ext_getElem <;> simp
-
-@[simp]
-theorem mapFinIdx_eq_nil_iff {l : List α} {f : Fin l.length → α → β} :
-    l.mapFinIdx f = [] ↔ l = [] := by
-  rw [mapFinIdx_eq_enum_map, map_eq_nil_iff, attach_eq_nil_iff, enum_eq_nil_iff]
-
-theorem mapFinIdx_ne_nil_iff {l : List α} {f : Fin l.length → α → β} :
-    l.mapFinIdx f ≠ [] ↔ l ≠ [] := by
-  simp
-
-theorem exists_of_mem_mapFinIdx {b : β} {l : List α} {f : Fin l.length → α → β}
-    (h : b ∈ l.mapFinIdx f) : ∃ (i : Fin l.length), f i l[i] = b := by
-  rw [mapFinIdx_eq_enum_map] at h
-  replace h := exists_of_mem_map h
-  simp only [mem_attach, true_and, Subtype.exists, Prod.exists, mk_mem_enum_iff_getElem?] at h
-  obtain ⟨i, b, h, rfl⟩ := h
-  rw [getElem?_eq_some_iff] at h
-  obtain ⟨h', rfl⟩ := h
-  exact ⟨⟨i, h'⟩, rfl⟩
-
-@[simp] theorem mem_mapFinIdx {b : β} {l : List α} {f : Fin l.length → α → β} :
-    b ∈ l.mapFinIdx f ↔ ∃ (i : Fin l.length), f i l[i] = b := by
-  constructor
-  · intro h
-    exact exists_of_mem_mapFinIdx h
-  · rintro ⟨i, h, rfl⟩
-    rw [mem_iff_getElem]
-    exact ⟨i, by simp⟩
-
-theorem mapFinIdx_eq_cons_iff {l : List α} {b : β} {f : Fin l.length → α → β} :
-    l.mapFinIdx f = b :: l₂ ↔
-      ∃ (a : α) (l₁ : List α) (h : l = a :: l₁),
-        f ⟨0, by simp [h]⟩ a = b ∧ l₁.mapFinIdx (fun i => f (i.succ.cast (by simp [h]))) = l₂ := by
-  cases l with
-  | nil => simp
-  | cons x l' =>
-    simp only [mapFinIdx_cons, cons.injEq, length_cons, Fin.zero_eta, Fin.cast_succ_eq,
-      exists_and_left]
-    constructor
-    · rintro ⟨rfl, rfl⟩
-      refine ⟨x, rfl, l', by simp⟩
-    · rintro ⟨a, ⟨rfl, h⟩, ⟨_, ⟨rfl, rfl⟩, h⟩⟩
-      exact ⟨rfl, h⟩
-
-theorem mapFinIdx_eq_cons_iff' {l : List α} {b : β} {f : Fin l.length → α → β} :
-    l.mapFinIdx f = b :: l₂ ↔
-      l.head?.pbind (fun x m => (f ⟨0, by cases l <;> simp_all⟩ x)) = some b ∧
-        l.tail?.attach.map (fun ⟨t, m⟩ => t.mapFinIdx fun i => f (i.succ.cast (by cases l <;> simp_all))) = some l₂ := by
-  cases l <;> simp
-
-theorem mapFinIdx_eq_iff {l : List α} {f : Fin l.length → α → β} :
-    l.mapFinIdx f = l' ↔ ∃ h : l'.length = l.length, ∀ (i : Nat) (h : i < l.length), l'[i] = f ⟨i, h⟩ l[i] := by
-  constructor
-  · rintro rfl
-    simp
-  · rintro ⟨h, w⟩
-    apply ext_getElem <;> simp_all
-
-theorem mapFinIdx_eq_mapFinIdx_iff {l : List α} {f g : Fin l.length → α → β} :
-    l.mapFinIdx f = l.mapFinIdx g ↔ ∀ (i : Fin l.length), f i l[i] = g i l[i] := by
-  rw [eq_comm, mapFinIdx_eq_iff]
-  simp [Fin.forall_iff]
-
-@[simp] theorem mapFinIdx_mapFinIdx {l : List α} {f : Fin l.length → α → β} {g : Fin _ → β → γ} :
-    (l.mapFinIdx f).mapFinIdx g = l.mapFinIdx (fun i => g (i.cast (by simp)) ∘ f i) := by
-  simp [mapFinIdx_eq_iff]
-
-theorem mapFinIdx_eq_replicate_iff {l : List α} {f : Fin l.length → α → β} {b : β} :
-    l.mapFinIdx f = replicate l.length b ↔ ∀ (i : Fin l.length), f i l[i] = b := by
-  simp [eq_replicate_iff, length_mapFinIdx, mem_mapFinIdx, forall_exists_index, true_and]
-
-@[simp] theorem mapFinIdx_reverse {l : List α} {f : Fin l.reverse.length → α → β} :
-    l.reverse.mapFinIdx f = (l.mapFinIdx (fun i => f ⟨l.length - 1 - i, by simp; omega⟩)).reverse := by
-  simp [mapFinIdx_eq_iff]
-  intro i h
-  congr
-  omega
-
-/-! ### mapIdx -/
-
@[simp]
 theorem mapIdx_nil {f : Nat → α → β} : mapIdx f [] = [] :=
  rfl

+theorem mapIdx_go_append  {l₁ l₂ : List α} {arr : Array β} :
+    mapIdx.go f (l₁ ++ l₂) arr = mapIdx.go f l₂ (List.toArray (mapIdx.go f l₁ arr)) := by
+  generalize h : (l₁ ++ l₂).length = len
+  induction len generalizing l₁ arr with
+  | zero =>
+    have l₁_nil : l₁ = [] := by
+      cases l₁
+      · rfl
+      · contradiction
+    have l₂_nil : l₂ = [] := by
+      cases l₂
+      · rfl
+      · rw [List.length_append] at h; contradiction
+    rw [l₁_nil, l₂_nil]; simp only [mapIdx.go, List.toArray_toList]
+  | succ len ih =>
+    cases l₁ with
+    | nil =>
+      simp only [mapIdx.go, nil_append, List.toArray_toList]
+    | cons head tail =>
+      simp only [mapIdx.go, List.append_eq]
+      rw [ih]
+      · simp only [cons_append, length_cons, length_append, Nat.succ.injEq] at h
+        simp only [length_append, h]
+
 theorem mapIdx_go_length {arr : Array β} :
    length (mapIdx.go f l arr) = length l + arr.size := by
  induction l generalizing arr with
@@ -219,6 +60,16 @@ theorem mapIdx_go_length {arr : Array β} :
  | cons _ _ ih =>
    simp only [mapIdx.go, ih, Array.size_push, Nat.add_succ, length_cons, Nat.add_comm]

+@[simp] theorem mapIdx_concat {l : List α} {e : α} :
+    mapIdx f (l ++ [e]) = mapIdx f l ++ [f l.length e] := by
+  unfold mapIdx
+  rw [mapIdx_go_append]
+  simp only [mapIdx.go, Array.size_toArray, mapIdx_go_length, length_nil, Nat.add_zero,
+    Array.push_toList]
+
+@[simp] theorem mapIdx_singleton {a : α} : mapIdx f [a] = [f 0 a] := by
+  simpa using mapIdx_concat (l := [])
+
 theorem length_mapIdx_go : ∀ {l : List α} {arr : Array β},
    (mapIdx.go f l arr).length = l.length + arr.size
  | [], _ => by simp [mapIdx.go]
@@ -261,15 +112,6 @@ theorem getElem?_mapIdx_go : ∀ {l : List α} {arr : Array β} {i : Nat},
  rw [← getElem?_eq_getElem, getElem?_mapIdx, getElem?_eq_getElem (by simpa using h)]
  simp

-@[simp] theorem mapFinIdx_eq_mapIdx {l : List α} {f : Fin l.length → α → β} {g : Nat → α → β}
-    (h : ∀ (i : Fin l.length), f i l[i] = g i l[i]) :
-    l.mapFinIdx f = l.mapIdx g := by
-  simp_all [mapFinIdx_eq_iff]
-
-theorem mapIdx_eq_mapFinIdx {l : List α} {f : Nat → α → β} :
-    l.mapIdx f = l.mapFinIdx (fun i => f i) := by
-  simp [mapFinIdx_eq_mapIdx]
-
 theorem mapIdx_eq_enum_map {l : List α} :
    l.mapIdx f = l.enum.map (Function.uncurry f) := by
  ext1 i
@@ -288,16 +130,9 @@ theorem mapIdx_append {K L : List α} :
  | nil => rfl
  | cons _ _ ih => simp [ih (f := fun i => f (i + 1)), Nat.add_assoc]

-@[simp] theorem mapIdx_concat {l : List α} {e : α} :
-    mapIdx f (l ++ [e]) = mapIdx f l ++ [f l.length e] := by
-  simp [mapIdx_append]
-
-theorem mapIdx_singleton {a : α} : mapIdx f [a] = [f 0 a] := by
-  simp
-
@[simp]
 theorem mapIdx_eq_nil_iff {l : List α} : List.mapIdx f l = [] ↔ l = [] := by
-  rw [List.mapIdx_eq_enum_map, List.map_eq_nil_iff, List.enum_eq_nil_iff]
+  rw [List.mapIdx_eq_enum_map, List.map_eq_nil_iff, List.enum_eq_nil]

 theorem mapIdx_ne_nil_iff {l : List α} :
    List.mapIdx f l ≠ [] ↔ l ≠ [] := by
@@ -305,8 +140,13 @@ theorem mapIdx_ne_nil_iff {l : List α} :

 theorem exists_of_mem_mapIdx {b : β} {l : List α}
    (h : b ∈ mapIdx f l) : ∃ (i : Nat) (h : i < l.length), f i l[i] = b := by
-  rw [mapIdx_eq_mapFinIdx] at h
-  simpa [Fin.exists_iff] using exists_of_mem_mapFinIdx h
+  rw [mapIdx_eq_enum_map] at h
+  replace h := exists_of_mem_map h
+  simp only [Prod.exists, mk_mem_enum_iff_getElem?, Function.uncurry_apply_pair] at h
+  obtain ⟨i, b, h, rfl⟩ := h
+  rw [getElem?_eq_some_iff] at h
+  obtain ⟨h, rfl⟩ := h
+  exact ⟨i, h, rfl⟩

@[simp] theorem mem_mapIdx {b : β} {l : List α} :
    b ∈ mapIdx f l ↔ ∃ (i : Nat) (h : i < l.length), f i l[i] = b := by
--- a/src/Init/Data/List/Monadic.lean
+++ b/src/Init/Data/List/Monadic.lean
@@ -5,7 +5,6 @@ Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, M
 -/
 prelude
 import Init.Data.List.TakeDrop
-import Init.Data.List.Attach

 /-!
 # Lemmas about `List.mapM` and `List.forM`.
@@ -49,9 +48,6 @@ theorem mapM'_eq_mapM [Monad m] [LawfulMonad m] (f : α → m β) (l : List α)
@[simp] theorem mapM_cons [Monad m] [LawfulMonad m] (f : α → m β) :
    (a :: l).mapM f = (return (← f a) :: (← l.mapM f)) := by simp [← mapM'_eq_mapM, mapM']

-@[simp] theorem mapM_id {l : List α} {f : α → Id β} : l.mapM f = l.map f := by
-  induction l <;> simp_all
-
@[simp] theorem mapM_append [Monad m] [LawfulMonad m] (f : α → m β) {l₁ l₂ : List α} :
    (l₁ ++ l₂).mapM f = (return (← l₁.mapM f) ++ (← l₂.mapM f)) := by induction l₁ <;> simp [*]

@@ -76,52 +72,6 @@ theorem mapM_eq_reverse_foldlM_cons [Monad m] [LawfulMonad m] (f : α → m β)
      reverse_cons, reverse_nil, nil_append, singleton_append]
    simp [bind_pure_comp]

-/-! ### foldlM and foldrM -/
-
-theorem foldlM_map [Monad m] (f : β₁ → β₂) (g : α → β₂ → m α) (l : List β₁) (init : α) :
-    (l.map f).foldlM g init = l.foldlM (fun x y => g x (f y)) init := by
-  induction l generalizing g init <;> simp [*]
-
-theorem foldrM_map [Monad m] [LawfulMonad m] (f : β₁ → β₂) (g : β₂ → α → m α) (l : List β₁)
-    (init : α) : (l.map f).foldrM g init = l.foldrM (fun x y => g (f x) y) init := by
-  induction l generalizing g init <;> simp [*]
-
-theorem foldlM_filterMap [Monad m] [LawfulMonad m] (f : α → Option β) (g : γ → β → m γ) (l : List α) (init : γ) :
-    (l.filterMap f).foldlM g init =
-      l.foldlM (fun x y => match f y with | some b => g x b | none => pure x) init := by
-  induction l generalizing init with
-  | nil => rfl
-  | cons a l ih =>
-    simp only [filterMap_cons, foldlM_cons]
-    cases f a <;> simp [ih]
-
-theorem foldrM_filterMap [Monad m] [LawfulMonad m] (f : α → Option β) (g : β → γ → m γ) (l : List α) (init : γ) :
-    (l.filterMap f).foldrM g init =
-      l.foldrM (fun x y => match f x with | some b => g b y | none => pure y) init := by
-  induction l generalizing init with
-  | nil => rfl
-  | cons a l ih =>
-    simp only [filterMap_cons, foldrM_cons]
-    cases f a <;> simp [ih]
-
-theorem foldlM_filter [Monad m] [LawfulMonad m] (p : α → Bool) (g : β → α → m β) (l : List α) (init : β) :
-    (l.filter p).foldlM g init =
-      l.foldlM (fun x y => if p y then g x y else pure x) init := by
-  induction l generalizing init with
-  | nil => rfl
-  | cons a l ih =>
-    simp only [filter_cons, foldlM_cons]
-    split <;> simp [ih]
-
-theorem foldrM_filter [Monad m] [LawfulMonad m] (p : α → Bool) (g : α → β → m β) (l : List α) (init : β) :
-    (l.filter p).foldrM g init =
-      l.foldrM (fun x y => if p x then g x y else pure y) init := by
-  induction l generalizing init with
-  | nil => rfl
-  | cons a l ih =>
-    simp only [filter_cons, foldrM_cons]
-    split <;> simp [ih]
-
 /-! ### forM -/

 -- We use `List.forM` as the simp normal form, rather that `ForM.forM`.
@@ -139,6 +89,9 @@ theorem foldrM_filter [Monad m] [LawfulMonad m] (p : α → Bool) (g : α → β

 /-! ### forIn' -/

+@[simp] theorem forIn'_nil [Monad m] (f : (a : α) → a ∈ [] → β → m (ForInStep β)) (b : β) : forIn' [] b f = pure b :=
+  rfl
+
 theorem forIn'_loop_congr [Monad m] {as bs : List α}
    {f : (a' : α) → a' ∈ as → β → m (ForInStep β)}
    {g : (a' : α) → a' ∈ bs → β → m (ForInStep β)}
@@ -169,11 +122,6 @@ theorem forIn'_loop_congr [Monad m] {as bs : List α}
    intros
    rfl

-@[simp] theorem forIn_cons [Monad m] (f : α → β → m (ForInStep β)) (a : α) (as : List α) (b : β) :
-    forIn (a::as) b f = f a b >>= fun | ForInStep.done b => pure b | ForInStep.yield b => forIn as b f := by
-  have := forIn'_cons (a := a) (as := as) (fun a' _ b => f a' b) b
-  simpa only [forIn'_eq_forIn]
-
@[congr] theorem forIn'_congr [Monad m] {as bs : List α} (w : as = bs)
    {b b' : β} (hb : b = b')
    {f : (a' : α) → a' ∈ as → β → m (ForInStep β)}
@@ -201,112 +149,6 @@ theorem forIn'_loop_congr [Monad m] {as bs : List α}
          intro a m b
          exact h a (mem_cons_of_mem _ m) b

-/--
-We can express a for loop over a list as a fold,
-in which whenever we reach `.done b` we keep that value through the rest of the fold.
-/
-theorem forIn'_eq_foldlM [Monad m] [LawfulMonad m]
-    (l : List α) (f : (a : α) → a ∈ l → β → m (ForInStep β)) (init : β) :
-    forIn' l init f = ForInStep.value <$>
-      l.attach.foldlM (fun b ⟨a, m⟩ => match b with
-        | .yield b => f a m b
-        | .done b => pure (.done b)) (ForInStep.yield init) := by
-  induction l generalizing init with
-  | nil => simp
-  | cons a as ih =>
-    simp only [forIn'_cons, attach_cons, foldlM_cons, _root_.map_bind]
-    congr 1
-    funext x
-    match x with
-    | .done b =>
-      clear ih
-      dsimp
-      induction as with
-      | nil => simp
-      | cons a as ih =>
-        simp only [attach_cons, map_cons, map_map, Function.comp_def, foldlM_cons, pure_bind]
-        specialize ih (fun a m b => f a (by
-          simp only [mem_cons] at m
-          rcases m with rfl|m
-          · apply mem_cons_self
-          · exact mem_cons_of_mem _ (mem_cons_of_mem _ m)) b)
-        simp [ih, List.foldlM_map]
-    | .yield b =>
-      simp [ih, List.foldlM_map]
-
-/-- We can express a for loop over a list which always yields as a fold. -/
-@[simp] theorem forIn'_yield_eq_foldlM [Monad m] [LawfulMonad m]
-    (l : List α) (f : (a : α) → a ∈ l → β → m γ) (g : (a : α) → a ∈ l → β → γ → β) (init : β) :
-    forIn' l init (fun a m b => (fun c => .yield (g a m b c)) <$> f a m b) =
-      l.attach.foldlM (fun b ⟨a, m⟩ => g a m b <$> f a m b) init := by
-  simp only [forIn'_eq_foldlM]
-  generalize l.attach = l'
-  induction l' generalizing init <;> simp_all
-
-theorem forIn'_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
-    (l : List α) (f : (a : α) → a ∈ l → β → β) (init : β) :
-    forIn' l init (fun a m b => pure (.yield (f a m b))) =
-      pure (f := m) (l.attach.foldl (fun b ⟨a, h⟩ => f a h b) init) := by
-  simp only [forIn'_eq_foldlM]
-  generalize l.attach = l'
-  induction l' generalizing init <;> simp_all
-
-@[simp] theorem forIn'_yield_eq_foldl
-    (l : List α) (f : (a : α) → a ∈ l → β → β) (init : β) :
-    forIn' (m := Id) l init (fun a m b => .yield (f a m b)) =
-      l.attach.foldl (fun b ⟨a, h⟩ => f a h b) init := by
-  simp only [forIn'_eq_foldlM]
-  generalize l.attach = l'
-  induction l' generalizing init <;> simp_all
-
-/--
-We can express a for loop over a list as a fold,
-in which whenever we reach `.done b` we keep that value through the rest of the fold.
-/
-theorem forIn_eq_foldlM [Monad m] [LawfulMonad m]
-    (f : α → β → m (ForInStep β)) (init : β) (l : List α) :
-    forIn l init f = ForInStep.value <$>
-      l.foldlM (fun b a => match b with
-        | .yield b => f a b
-        | .done b => pure (.done b)) (ForInStep.yield init) := by
-  induction l generalizing init with
-  | nil => simp
-  | cons a as ih =>
-    simp only [foldlM_cons, bind_pure_comp, forIn_cons, _root_.map_bind]
-    congr 1
-    funext x
-    match x with
-    | .done b =>
-      clear ih
-      dsimp
-      induction as with
-      | nil => simp
-      | cons a as ih => simp [ih]
-    | .yield b =>
-      simp [ih]
-
-/-- We can express a for loop over a list which always yields as a fold. -/
-@[simp] theorem forIn_yield_eq_foldlM [Monad m] [LawfulMonad m]
-    (l : List α) (f : α → β → m γ) (g : α → β → γ → β) (init : β) :
-    forIn l init (fun a b => (fun c => .yield (g a b c)) <$> f a b) =
-      l.foldlM (fun b a => g a b <$> f a b) init := by
-  simp only [forIn_eq_foldlM]
-  induction l generalizing init <;> simp_all
-
-theorem forIn_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
-    (l : List α) (f : α → β → β) (init : β) :
-    forIn l init (fun a b => pure (.yield (f a b))) =
-      pure (f := m) (l.foldl (fun b a => f a b) init) := by
-  simp only [forIn_eq_foldlM]
-  induction l generalizing init <;> simp_all
-
-@[simp] theorem forIn_yield_eq_foldl
-    (l : List α) (f : α → β → β) (init : β) :
-    forIn (m := Id) l init (fun a b => .yield (f a b)) =
-      l.foldl (fun b a => f a b) init := by
-  simp only [forIn_eq_foldlM]
-  induction l generalizing init <;> simp_all
-
 /-! ### allM -/

 theorem allM_eq_not_anyM_not [Monad m] [LawfulMonad m] (p : α → m Bool) (as : List α) :
@@ -319,4 +161,14 @@ theorem allM_eq_not_anyM_not [Monad m] [LawfulMonad m] (p : α → m Bool) (as :
    funext b
    split <;> simp_all

+/-! ### foldlM and foldrM -/
+
+theorem foldlM_map [Monad m] (f : β₁ → β₂) (g : α → β₂ → m α) (l : List β₁) (init : α) :
+    (l.map f).foldlM g init = l.foldlM (fun x y => g x (f y)) init := by
+  induction l generalizing g init <;> simp [*]
+
+theorem foldrM_map [Monad m] [LawfulMonad m] (f : β₁ → β₂) (g : β₂ → α → m α) (l : List β₁)
+    (init : α) : (l.map f).foldrM g init = l.foldrM (fun x y => g (f x) y) init := by
+  induction l generalizing g init <;> simp [*]
+
 end List
--- a/src/Init/Data/List/Nat.lean
+++ b/src/Init/Data/List/Nat.lean
@@ -14,4 +14,3 @@ import Init.Data.List.Nat.Erase
 import Init.Data.List.Nat.Find
 import Init.Data.List.Nat.BEq
 import Init.Data.List.Nat.Modify
-import Init.Data.List.Nat.InsertIdx
--- a/src/Init/Data/List/Nat/BEq.lean
+++ b/src/Init/Data/List/Nat/BEq.lean
@@ -9,7 +9,7 @@ import Init.Data.List.Basic

 namespace List

-/-! ### isEqv -/
+/-! ### isEqv-/

 theorem isEqv_eq_decide (a b : List α) (r) :
    isEqv a b r = if h : a.length = b.length then
--- a/src/Init/Data/List/Nat/Erase.lean
+++ b/src/Init/Data/List/Nat/Erase.lean
@@ -64,82 +64,3 @@ theorem getElem_eraseIdx_of_ge (l : List α) (i : Nat) (j : Nat) (h : j < (l.era
    (l.eraseIdx i)[j] = l[j + 1]'(by rw [length_eraseIdx] at h; split at h <;> omega) := by
  rw [getElem_eraseIdx, dif_neg]
  omega
-
-theorem eraseIdx_set_eq {l : List α} {i : Nat} {a : α} :
-    (l.set i a).eraseIdx i = l.eraseIdx i := by
-  apply ext_getElem
-  · simp [length_eraseIdx]
-  · intro n h₁ h₂
-    rw [getElem_eraseIdx, getElem_eraseIdx]
-    split <;>
-    · rw [getElem_set_ne]
-      omega
-
-theorem eraseIdx_set_lt {l : List α} {i : Nat} {j : Nat} {a : α} (h : j < i) :
-    (l.set i a).eraseIdx j = (l.eraseIdx j).set (i - 1) a := by
-  apply ext_getElem
-  · simp [length_eraseIdx]
-  · intro n h₁ h₂
-    simp only [length_eraseIdx, length_set] at h₁
-    simp only [getElem_eraseIdx, getElem_set]
-    split
-    · split
-      · split
-        · rfl
-        · omega
-      · split
-        · omega
-        · rfl
-    · split
-      · split
-        · rfl
-        · omega
-      · have t : i - 1 ≠ n := by omega
-        simp [t]
-
-theorem eraseIdx_set_gt {l : List α} {i : Nat} {j : Nat} {a : α} (h : i < j) :
-    (l.set i a).eraseIdx j = (l.eraseIdx j).set i a := by
-  apply ext_getElem
-  · simp [length_eraseIdx]
-  · intro n h₁ h₂
-    simp only [length_eraseIdx, length_set] at h₁
-    simp only [getElem_eraseIdx, getElem_set]
-    split
-    · rfl
-    · split
-      · split
-        · rfl
-        · omega
-      · have t : i ≠ n := by omega
-        simp [t]
-
-@[simp] theorem set_getElem_succ_eraseIdx_succ
-    {l : List α} {i : Nat} (h : i + 1 < l.length) :
-    (l.eraseIdx (i + 1)).set i l[i + 1] = l.eraseIdx i := by
-  apply ext_getElem
-  · simp only [length_set, length_eraseIdx, h, ↓reduceIte]
-    rw [if_pos]
-    omega
-  · intro n h₁ h₂
-    simp [getElem_set, getElem_eraseIdx]
-    split
-    · split
-      · omega
-      · simp_all
-    · split
-      · split
-        · rfl
-        · omega
-      · have t : ¬ n < i := by omega
-        simp [t]
-
-@[simp] theorem eraseIdx_length_sub_one (l : List α) :
-    (l.eraseIdx (l.length - 1)) = l.dropLast := by
-  apply ext_getElem
-  · simp [length_eraseIdx]
-    omega
-  · intro n h₁ h₂
-    rw [getElem_eraseIdx_of_lt, getElem_dropLast]
-    simp_all
-
-end List
--- a/src/Init/Data/List/Nat/Find.lean
+++ b/src/Init/Data/List/Nat/Find.lean
@@ -9,32 +9,6 @@ import Init.Data.List.Find

 namespace List

-open Nat
-
-theorem find?_eq_some_iff_getElem {xs : List α} {p : α → Bool} {b : α} :
-    xs.find? p = some b ↔ p b ∧ ∃ i h, xs[i] = b ∧ ∀ j : Nat, (hj : j < i) → !p xs[j] := by
-  rw [find?_eq_some_iff_append]
-  simp only [Bool.not_eq_eq_eq_not, Bool.not_true, exists_and_right, and_congr_right_iff]
-  intro w
-  constructor
-  · rintro ⟨as, ⟨bs, rfl⟩, h⟩
-    refine ⟨as.length, ⟨?_, ?_, ?_⟩⟩
-    · simp only [length_append, length_cons]
-      refine Nat.lt_add_of_pos_right (zero_lt_succ bs.length)
-    · rw [getElem_append_right (Nat.le_refl as.length)]
-      simp
-    · intro j h'
-      rw [getElem_append_left h']
-      exact h _ (getElem_mem h')
-  · rintro ⟨i, h, rfl, h'⟩
-    refine ⟨xs.take i, ⟨xs.drop (i+1), ?_⟩, ?_⟩
-    · rw [getElem_cons_drop, take_append_drop]
-    · intro a m
-      rw [mem_take_iff_getElem] at m
-      obtain ⟨j, h, rfl⟩ := m
-      apply h'
-      omega
-
 theorem findIdx?_eq_some_le_of_findIdx?_eq_some {xs : List α} {p q : α → Bool} (w : ∀ x ∈ xs, p x → q x) {i : Nat}
    (h : xs.findIdx? p = some i) : ∃ j, j ≤ i ∧ xs.findIdx? q = some j := by
  simp only [findIdx?_eq_findSome?_enum] at h
--- a/src/Init/Data/List/Nat/InsertIdx.lean
+++ b/src/Init/Data/List/Nat/InsertIdx.lean
@@ -1,242 +0,0 @@
-/-
-Copyright (c) 2014 Parikshit Khanna. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
-/
-prelude
-import Init.Data.List.Nat.Modify
-
-/-!
-# insertIdx
-
-Proves various lemmas about `List.insertIdx`.
-/
-
-open Function
-
-open Nat
-
-namespace List
-
-universe u
-
-variable {α : Type u}
-
-section InsertIdx
-
-variable {a : α}
-
-@[simp]
-theorem insertIdx_zero (s : List α) (x : α) : insertIdx 0 x s = x :: s :=
-  rfl
-
-@[simp]
-theorem insertIdx_succ_nil (n : Nat) (a : α) : insertIdx (n + 1) a [] = [] :=
-  rfl
-
-@[simp]
-theorem insertIdx_succ_cons (s : List α) (hd x : α) (n : Nat) :
-    insertIdx (n + 1) x (hd :: s) = hd :: insertIdx n x s :=
-  rfl
-
-theorem length_insertIdx : ∀ n as, (insertIdx n a as).length = if n ≤ as.length then as.length + 1 else as.length
-  | 0, _ => by simp
-  | n + 1, [] => by simp
-  | n + 1, a :: as => by
-    simp only [insertIdx_succ_cons, length_cons, length_insertIdx, Nat.add_le_add_iff_right]
-    split <;> rfl
-
-theorem length_insertIdx_of_le_length (h : n ≤ length as) : length (insertIdx n a as) = length as + 1 := by
-  simp [length_insertIdx, h]
-
-theorem length_insertIdx_of_length_lt (h : length as < n) : length (insertIdx n a as) = length as := by
-  simp [length_insertIdx, h]
-
-theorem eraseIdx_insertIdx (n : Nat) (l : List α) : (l.insertIdx n a).eraseIdx n = l := by
-  rw [eraseIdx_eq_modifyTailIdx, insertIdx, modifyTailIdx_modifyTailIdx_self]
-  exact modifyTailIdx_id _ _
-
-theorem insertIdx_eraseIdx_of_ge :
-    ∀ n m as,
-      n < length as → n ≤ m → insertIdx m a (as.eraseIdx n) = (as.insertIdx (m + 1) a).eraseIdx n
-  | 0, 0, [], has, _ => (Nat.lt_irrefl _ has).elim
-  | 0, 0, _ :: as, _, _ => by simp [eraseIdx, insertIdx]
-  | 0, _ + 1, _ :: _, _, _ => rfl
-  | n + 1, m + 1, a :: as, has, hmn =>
-    congrArg (cons a) <|
-      insertIdx_eraseIdx_of_ge n m as (Nat.lt_of_succ_lt_succ has) (Nat.le_of_succ_le_succ hmn)
-
-theorem insertIdx_eraseIdx_of_le :
-    ∀ n m as,
-      n < length as → m ≤ n → insertIdx m a (as.eraseIdx n) = (as.insertIdx m a).eraseIdx (n + 1)
-  | _, 0, _ :: _, _, _ => rfl
-  | n + 1, m + 1, a :: as, has, hmn =>
-    congrArg (cons a) <|
-      insertIdx_eraseIdx_of_le n m as (Nat.lt_of_succ_lt_succ has) (Nat.le_of_succ_le_succ hmn)
-
-theorem insertIdx_comm (a b : α) :
-    ∀ (i j : Nat) (l : List α) (_ : i ≤ j) (_ : j ≤ length l),
-      (l.insertIdx i a).insertIdx (j + 1) b = (l.insertIdx j b).insertIdx i a
-  | 0, j, l => by simp [insertIdx]
-  | _ + 1, 0, _ => fun h => (Nat.not_lt_zero _ h).elim
-  | i + 1, j + 1, [] => by simp
-  | i + 1, j + 1, c :: l => fun h₀ h₁ => by
-    simp only [insertIdx_succ_cons, cons.injEq, true_and]
-    exact insertIdx_comm a b i j l (Nat.le_of_succ_le_succ h₀) (Nat.le_of_succ_le_succ h₁)
-
-theorem mem_insertIdx {a b : α} :
-    ∀ {n : Nat} {l : List α} (_ : n ≤ l.length), a ∈ l.insertIdx n b ↔ a = b ∨ a ∈ l
-  | 0, as, _ => by simp
-  | _ + 1, [], h => (Nat.not_succ_le_zero _ h).elim
-  | n + 1, a' :: as, h => by
-    rw [List.insertIdx_succ_cons, mem_cons, mem_insertIdx (Nat.le_of_succ_le_succ h),
-      ← or_assoc, @or_comm (a = a'), or_assoc, mem_cons]
-
-theorem insertIdx_of_length_lt (l : List α) (x : α) (n : Nat) (h : l.length < n) :
-    insertIdx n x l = l := by
-  induction l generalizing n with
-  | nil =>
-    cases n
-    · simp at h
-    · simp
-  | cons x l ih =>
-    cases n
-    · simp at h
-    · simp only [Nat.succ_lt_succ_iff, length] at h
-      simpa using ih _ h
-
-@[simp]
-theorem insertIdx_length_self (l : List α) (x : α) : insertIdx l.length x l = l ++ [x] := by
-  induction l with
-  | nil => simp
-  | cons x l ih => simpa using ih
-
-theorem length_le_length_insertIdx (l : List α) (x : α) (n : Nat) :
-    l.length ≤ (insertIdx n x l).length := by
-  simp only [length_insertIdx]
-  split <;> simp
-
-theorem length_insertIdx_le_succ (l : List α) (x : α) (n : Nat) :
-    (insertIdx n x l).length ≤ l.length + 1 := by
-  simp only [length_insertIdx]
-  split <;> simp
-
-theorem getElem_insertIdx_of_lt {l : List α} {x : α} {n k : Nat} (hn : k < n)
-    (hk : k < (insertIdx n x l).length) :
-    (insertIdx n x l)[k] = l[k]'(by simp [length_insertIdx] at hk; split at hk <;> omega) := by
-  induction n generalizing k l with
-  | zero => simp at hn
-  | succ n ih =>
-    cases l with
-    | nil => simp
-    | cons _ _=>
-      cases k
-      · simp [get]
-      · rw [Nat.succ_lt_succ_iff] at hn
-        simpa using ih hn _
-
-@[simp]
-theorem getElem_insertIdx_self {l : List α} {x : α} {n : Nat} (hn : n < (insertIdx n x l).length) :
-    (insertIdx n x l)[n] = x := by
-  induction l generalizing n with
-  | nil =>
-    simp [length_insertIdx] at hn
-    split at hn
-    · simp_all
-    · omega
-  | cons _ _ ih =>
-    cases n
-    · simp
-    · simp only [insertIdx_succ_cons, length_cons, length_insertIdx, Nat.add_lt_add_iff_right] at hn ih
-      simpa using ih hn
-
-theorem getElem_insertIdx_of_ge {l : List α} {x : α} {n k : Nat} (hn : n + 1 ≤ k)
-    (hk : k < (insertIdx n x l).length) :
-    (insertIdx n x l)[k] = l[k - 1]'(by simp [length_insertIdx] at hk; split at hk <;> omega) := by
-  induction l generalizing n k with
-  | nil =>
-    cases n with
-    | zero =>
-      simp only [insertIdx_zero, length_singleton, lt_one_iff] at hk
-      omega
-    | succ n => simp at hk
-  | cons _ _ ih =>
-    cases n with
-    | zero =>
-      simp only [insertIdx_zero] at hk
-      cases k with
-      | zero => omega
-      | succ k => simp
-    | succ n =>
-      cases k with
-      | zero => simp
-      | succ k =>
-        simp only [insertIdx_succ_cons, getElem_cons_succ]
-        rw [ih (by omega)]
-        cases k with
-        | zero => omega
-        | succ k => simp
-
-theorem getElem_insertIdx {l : List α} {x : α} {n k : Nat} (h : k < (insertIdx n x l).length) :
-    (insertIdx n x l)[k] =
-      if h₁ : k < n then
-        l[k]'(by simp [length_insertIdx] at h; split at h <;> omega)
-      else
-        if h₂ : k = n then
-          x
-        else
-          l[k-1]'(by simp [length_insertIdx] at h; split at h <;> omega) := by
-  split <;> rename_i h₁
-  · rw [getElem_insertIdx_of_lt h₁]
-  · split <;> rename_i h₂
-    · subst h₂
-      rw [getElem_insertIdx_self h]
-    · rw [getElem_insertIdx_of_ge (by omega)]
-
-theorem getElem?_insertIdx {l : List α} {x : α} {n k : Nat} :
-    (insertIdx n x l)[k]? =
-      if k < n then
-        l[k]?
-      else
-        if k = n then
-          if k ≤ l.length then some x else none
-        else
-          l[k-1]? := by
-  rw [getElem?_def]
-  split <;> rename_i h
-  · rw [getElem_insertIdx h]
-    simp only [length_insertIdx] at h
-    split <;> rename_i h₁
-    · rw [getElem?_def, dif_pos]
-    · split <;> rename_i h₂
-      · rw [if_pos]
-        split at h <;> omega
-      · rw [getElem?_def]
-        simp only [Option.some_eq_dite_none_right, exists_prop, and_true]
-        split at h <;> omega
-  · simp only [length_insertIdx] at h
-    split <;> rename_i h₁
-    · rw [getElem?_eq_none]
-      split at h <;> omega
-    · split <;> rename_i h₂
-      · rw [if_neg]
-        split at h <;> omega
-      · rw [getElem?_eq_none]
-        split at h <;> omega
-
-theorem getElem?_insertIdx_of_lt {l : List α} {x : α} {n k : Nat} (h : k < n) :
-    (insertIdx n x l)[k]? = l[k]? := by
-  rw [getElem?_insertIdx, if_pos h]
-
-theorem getElem?_insertIdx_self {l : List α} {x : α} {n : Nat} :
-    (insertIdx n x l)[n]? = if n ≤ l.length then some x else none := by
-  rw [getElem?_insertIdx, if_neg (by omega)]
-  simp
-
-theorem getElem?_insertIdx_of_ge {l : List α} {x : α} {n k : Nat} (h : n + 1 ≤ k) :
-    (insertIdx n x l)[k]? = l[k - 1]? := by
-  rw [getElem?_insertIdx, if_neg (by omega), if_neg (by omega)]
-
-end InsertIdx
-
-end List
--- a/src/Init/Data/List/Nat/Modify.lean
+++ b/src/Init/Data/List/Nat/Modify.lean
@@ -110,25 +110,6 @@ theorem exists_of_modifyTailIdx (f : List α → List α) {n} {l : List α} (h :
    ⟨_, _, (take_append_drop n l).symm, length_take_of_le h⟩
  ⟨_, _, eq, hl, hl ▸ eq ▸ modifyTailIdx_add (n := 0) ..⟩

-theorem modifyTailIdx_modifyTailIdx {f g : List α → List α} (m : Nat) :
-    ∀ (n) (l : List α),
-      (l.modifyTailIdx f n).modifyTailIdx g (m + n) =
-        l.modifyTailIdx (fun l => (f l).modifyTailIdx g m) n
-  | 0, _ => rfl
-  | _ + 1, [] => rfl
-  | n + 1, a :: l => congrArg (List.cons a) (modifyTailIdx_modifyTailIdx m n l)
-
-theorem modifyTailIdx_modifyTailIdx_le {f g : List α → List α} (m n : Nat) (l : List α)
-    (h : n ≤ m) :
-    (l.modifyTailIdx f n).modifyTailIdx g m =
-      l.modifyTailIdx (fun l => (f l).modifyTailIdx g (m - n)) n := by
-  rcases Nat.exists_eq_add_of_le h with ⟨m, rfl⟩
-  rw [Nat.add_comm, modifyTailIdx_modifyTailIdx, Nat.add_sub_cancel]
-
-theorem modifyTailIdx_modifyTailIdx_self {f g : List α → List α} (n : Nat) (l : List α) :
-    (l.modifyTailIdx f n).modifyTailIdx g n = l.modifyTailIdx (g ∘ f) n := by
-  rw [modifyTailIdx_modifyTailIdx_le n n l (Nat.le_refl n), Nat.sub_self]; rfl
-
 /-! ### modify -/

@[simp] theorem modify_nil (f : α → α) (n) : [].modify f n = [] := by cases n <;> rfl
--- a/src/Init/Data/List/Nat/Range.lean
+++ b/src/Init/Data/List/Nat/Range.lean
@@ -108,7 +108,7 @@ theorem range'_eq_append_iff : range' s n = xs ++ ys ↔ ∃ k, k ≤ n ∧ xs =

@[simp] theorem find?_range'_eq_some {s n : Nat} {i : Nat} {p : Nat → Bool} :
    (range' s n).find? p = some i ↔ p i ∧ i ∈ range' s n ∧ ∀ j, s ≤ j → j < i → !p j := by
-  rw [find?_eq_some_iff_append]
+  rw [find?_eq_some]
  simp only [Bool.not_eq_eq_eq_not, Bool.not_true, exists_and_right, mem_range'_1,
    and_congr_right_iff]
  simp only [range'_eq_append_iff, eq_comm (a := i :: _), range'_eq_cons_iff]
@@ -169,7 +169,7 @@ theorem not_mem_range_self {n : Nat} : n ∉ range n := by simp
 theorem self_mem_range_succ (n : Nat) : n ∈ range (n + 1) := by simp

 theorem pairwise_lt_range (n : Nat) : Pairwise (· < ·) (range n) := by
-  simp +decide only [range_eq_range', pairwise_lt_range']
+  simp (config := {decide := true}) only [range_eq_range', pairwise_lt_range']

 theorem pairwise_le_range (n : Nat) : Pairwise (· ≤ ·) (range n) :=
  Pairwise.imp Nat.le_of_lt (pairwise_lt_range _)
@@ -177,10 +177,10 @@ theorem pairwise_le_range (n : Nat) : Pairwise (· ≤ ·) (range n) :=
 theorem take_range (m n : Nat) : take m (range n) = range (min m n) := by
  apply List.ext_getElem
  · simp
-  · simp +contextual [getElem_take, Nat.lt_min]
+  · simp (config := { contextual := true }) [getElem_take, Nat.lt_min]

 theorem nodup_range (n : Nat) : Nodup (range n) := by
-  simp +decide only [range_eq_range', nodup_range']
+  simp (config := {decide := true}) only [range_eq_range', nodup_range']

@[simp] theorem find?_range_eq_some {n : Nat} {i : Nat} {p : Nat → Bool} :
    (range n).find? p = some i ↔ p i ∧ i ∈ range n ∧ ∀ j, j < i → !p j := by
@@ -282,7 +282,7 @@ theorem find?_iota_eq_none {n : Nat} {p : Nat → Bool} :

@[simp] theorem find?_iota_eq_some {n : Nat} {i : Nat} {p : Nat → Bool} :
    (iota n).find? p = some i ↔ p i ∧ i ∈ iota n ∧ ∀ j, i < j → j ≤ n → !p j := by
-  rw [find?_eq_some_iff_append]
+  rw [find?_eq_some]
  simp only [iota_eq_reverse_range', reverse_eq_append_iff, reverse_cons, append_assoc, cons_append,
    nil_append, Bool.not_eq_eq_eq_not, Bool.not_true, exists_and_right, mem_reverse, mem_range'_1,
    and_congr_right_iff]
@@ -430,10 +430,7 @@ theorem enumFrom_eq_append_iff {l : List α} {n : Nat} :
 /-! ### enum -/

@[simp]
-theorem enum_eq_nil_iff {l : List α} : List.enum l = [] ↔ l = [] := enumFrom_eq_nil
-
-@[deprecated enum_eq_nil_iff (since := "2024-11-04")]
-theorem enum_eq_nil {l : List α} : List.enum l = [] ↔ l = [] := enum_eq_nil_iff
+theorem enum_eq_nil {l : List α} : List.enum l = [] ↔ l = [] := enumFrom_eq_nil

@[simp] theorem enum_singleton (x : α) : enum [x] = [(0, x)] := rfl

--- a/src/Init/Data/List/OfFn.lean
+++ b/src/Init/Data/List/OfFn.lean
@@ -1,80 +0,0 @@
-/-
-Copyright (c) 2024 Lean FRO. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Mario Carneiro, Kim Morrison
-/
-prelude
-import Init.Data.List.Basic
-import Init.Data.Fin.Fold
-
-/-!
-# Theorems about `List.ofFn`
-/
-
-namespace List
-
-/--
-`ofFn f` with `f : fin n → α` returns the list whose ith element is `f i`
-```
-ofFn f = [f 0, f 1, ... , f (n - 1)]
-```
-/
-def ofFn {n} (f : Fin n → α) : List α := Fin.foldr n (f · :: ·) []
-
-@[simp]
-theorem length_ofFn (f : Fin n → α) : (ofFn f).length = n := by
-  simp only [ofFn]
-  induction n with
-  | zero => simp
-  | succ n ih => simp [Fin.foldr_succ, ih]
-
-@[simp]
-protected theorem getElem_ofFn (f : Fin n → α) (i : Nat) (h : i < (ofFn f).length) :
-    (ofFn f)[i] = f ⟨i, by simp_all⟩ := by
-  simp only [ofFn]
-  induction n generalizing i with
-  | zero => simp at h
-  | succ n ih =>
-    match i with
-    | 0 => simp [Fin.foldr_succ]
-    | i+1 =>
-      simp only [Fin.foldr_succ]
-      apply ih
-      simp_all
-
-@[simp]
-protected theorem getElem?_ofFn (f : Fin n → α) (i) : (ofFn f)[i]? = if h : i < n then some (f ⟨i, h⟩) else none :=
-  if h : i < (ofFn f).length
-  then by
-    rw [getElem?_eq_getElem h, List.getElem_ofFn]
-    · simp only [length_ofFn] at h; simp [h]
-  else by
-    rw [dif_neg] <;>
-    simpa using h
-
-/-- `ofFn` on an empty domain is the empty list. -/
-@[simp]
-theorem ofFn_zero (f : Fin 0 → α) : ofFn f = [] :=
-  ext_get (by simp) (fun i hi₁ hi₂ => by contradiction)
-
-@[simp]
-theorem ofFn_succ {n} (f : Fin (n + 1) → α) : ofFn f = f 0 :: ofFn fun i => f i.succ :=
-  ext_get (by simp) (fun i hi₁ hi₂ => by
-    cases i
-    · simp
-    · simp)
-
-@[simp]
-theorem ofFn_eq_nil_iff {f : Fin n → α} : ofFn f = [] ↔ n = 0 := by
-  cases n <;> simp only [ofFn_zero, ofFn_succ, eq_self_iff_true, Nat.succ_ne_zero, reduceCtorEq]
-
-theorem head_ofFn {n} (f : Fin n → α) (h : ofFn f ≠ []) :
-    (ofFn f).head h = f ⟨0, Nat.pos_of_ne_zero (mt ofFn_eq_nil_iff.2 h)⟩ := by
-  rw [← getElem_zero (length_ofFn _ ▸ Nat.pos_of_ne_zero (mt ofFn_eq_nil_iff.2 h)),
-    List.getElem_ofFn]
-
-theorem getLast_ofFn {n} (f : Fin n → α) (h : ofFn f ≠ []) :
-    (ofFn f).getLast h = f ⟨n - 1, Nat.sub_one_lt (mt ofFn_eq_nil_iff.2 h)⟩ := by
-  simp [getLast_eq_getElem, length_ofFn, List.getElem_ofFn]
-
-end List
--- a/src/Init/Data/List/Pairwise.lean
+++ b/src/Init/Data/List/Pairwise.lean
@@ -76,11 +76,11 @@ theorem pairwise_of_forall {l : List α} (H : ∀ x y, R x y) : Pairwise R l :=

 theorem Pairwise.and_mem {l : List α} :
    Pairwise R l ↔ Pairwise (fun x y => x ∈ l ∧ y ∈ l ∧ R x y) l :=
-  Pairwise.iff_of_mem <| by simp +contextual
+  Pairwise.iff_of_mem <| by simp (config := { contextual := true })

 theorem Pairwise.imp_mem {l : List α} :
    Pairwise R l ↔ Pairwise (fun x y => x ∈ l → y ∈ l → R x y) l :=
-  Pairwise.iff_of_mem <| by simp +contextual
+  Pairwise.iff_of_mem <| by simp (config := { contextual := true })

 theorem Pairwise.forall_of_forall_of_flip (h₁ : ∀ x ∈ l, R x x) (h₂ : Pairwise R l)
    (h₃ : l.Pairwise (flip R)) : ∀ ⦃x⦄, x ∈ l → ∀ ⦃y⦄, y ∈ l → R x y := by
--- a/src/Init/Data/List/Perm.lean
+++ b/src/Init/Data/List/Perm.lean
@@ -114,14 +114,6 @@ theorem Perm.length_eq {l₁ l₂ : List α} (p : l₁ ~ l₂) : length l₁ = l
  | swap => rfl
  | trans _ _ ih₁ ih₂ => simp only [ih₁, ih₂]

-theorem Perm.contains_eq [BEq α] {l₁ l₂ : List α} (h : l₁ ~ l₂) {a : α} :
-    l₁.contains a = l₂.contains a := by
-  induction h with
-  | nil => rfl
-  | cons => simp_all
-  | swap => simp only [contains_cons, ← Bool.or_assoc, Bool.or_comm]
-  | trans => simp_all
-
 theorem Perm.eq_nil {l : List α} (p : l ~ []) : l = [] := eq_nil_of_length_eq_zero p.length_eq

 theorem Perm.nil_eq {l : List α} (p : [] ~ l) : [] = l := p.symm.eq_nil.symm
--- a/src/Init/Data/List/Sort/Lemmas.lean
+++ b/src/Init/Data/List/Sort/Lemmas.lean
@@ -293,7 +293,7 @@ theorem sorted_mergeSort
    apply sorted_mergeSort trans total
 termination_by l => l.length

-@[deprecated sorted_mergeSort (since := "2024-09-02")] abbrev mergeSort_sorted := @sorted_mergeSort
+@[deprecated (since := "2024-09-02")] abbrev mergeSort_sorted := @sorted_mergeSort

 /--
 If the input list is already sorted, then `mergeSort` does not change the list.
@@ -429,8 +429,7 @@ theorem sublist_mergeSort
        ((fun w => Sublist.of_sublist_append_right w h') fun b m₁ m₃ =>
          (Bool.eq_not_self true).mp ((rel_of_pairwise_cons hc m₁).symm.trans (h₃ b m₃))))

-@[deprecated sublist_mergeSort (since := "2024-09-02")]
-abbrev mergeSort_stable := @sublist_mergeSort
+@[deprecated (since := "2024-09-02")] abbrev mergeSort_stable := @sublist_mergeSort

 /--
 Another statement of stability of merge sort.
@@ -443,8 +442,7 @@ theorem pair_sublist_mergeSort
    (hab : le a b) (h : [a, b] <+ l) : [a, b] <+ mergeSort l le :=
  sublist_mergeSort trans total (pairwise_pair.mpr hab) h

-@[deprecated pair_sublist_mergeSort(since := "2024-09-02")]
-abbrev mergeSort_stable_pair := @pair_sublist_mergeSort
+@[deprecated (since := "2024-09-02")] abbrev mergeSort_stable_pair := @pair_sublist_mergeSort

 theorem map_merge {f : α → β} {r : α → α → Bool} {s : β → β → Bool} {l l' : List α}
    (hl : ∀ a ∈ l, ∀ b ∈ l', r a b = s (f a) (f b)) :
--- a/src/Init/Data/List/Sublist.lean
+++ b/src/Init/Data/List/Sublist.lean
@@ -116,7 +116,7 @@ fun s => Subset.trans s <| subset_append_right _ _
 theorem replicate_subset {n : Nat} {a : α} {l : List α} : replicate n a ⊆ l ↔ n = 0 ∨ a ∈ l := by
  induction n with
  | zero => simp
-  | succ n ih => simp +contextual [replicate_succ, ih, cons_subset]
+  | succ n ih => simp (config := {contextual := true}) [replicate_succ, ih, cons_subset]

 theorem subset_replicate {n : Nat} {a : α} {l : List α} (h : n ≠ 0) : l ⊆ replicate n a ↔ ∀ x ∈ l, x = a := by
  induction l with
@@ -417,7 +417,7 @@ theorem Sublist.of_sublist_append_left (w : ∀ a, a ∈ l → a ∉ l₂) (h :
  obtain ⟨l₁', l₂', rfl, h₁, h₂⟩ := h
  have : l₂' = [] := by
    rw [eq_nil_iff_forall_not_mem]
-    exact fun x m => w x (mem_append_right l₁' m) (h₂.mem m)
+    exact fun x m => w x (mem_append_of_mem_right l₁' m) (h₂.mem m)
  simp_all

 theorem Sublist.of_sublist_append_right (w : ∀ a, a ∈ l → a ∉ l₁) (h : l <+ l₁ ++ l₂) : l <+ l₂ := by
@@ -425,7 +425,7 @@ theorem Sublist.of_sublist_append_right (w : ∀ a, a ∈ l → a ∉ l₁) (h :
  obtain ⟨l₁', l₂', rfl, h₁, h₂⟩ := h
  have : l₁' = [] := by
    rw [eq_nil_iff_forall_not_mem]
-    exact fun x m => w x (mem_append_left l₂' m) (h₁.mem m)
+    exact fun x m => w x (mem_append_of_mem_left l₂' m) (h₁.mem m)
  simp_all

 theorem Sublist.middle {l : List α} (h : l <+ l₁ ++ l₂) (a : α) : l <+ l₁ ++ a :: l₂ := by
@@ -835,7 +835,7 @@ theorem isPrefix_iff : l₁ <+: l₂ ↔ ∀ i (h : i < l₁.length), l₂[i]? =
      simpa using ⟨0, by simp⟩
    | cons b l₂ =>
      simp only [cons_append, cons_prefix_cons, ih]
-      rw (occs := [2]) [← Nat.and_forall_add_one]
+      rw (config := {occs := .pos [2]}) [← Nat.and_forall_add_one]
      simp [Nat.succ_lt_succ_iff, eq_comm]

 theorem isPrefix_iff_getElem {l₁ l₂ : List α} :
--- a/src/Init/Data/List/TakeDrop.lean
+++ b/src/Init/Data/List/TakeDrop.lean
@@ -190,7 +190,7 @@ theorem set_drop {l : List α} {n m : Nat} {a : α} :
 theorem take_concat_get (l : List α) (i : Nat) (h : i < l.length) :
    (l.take i).concat l[i] = l.take (i+1) :=
  Eq.symm <| (append_left_inj _).1 <| (take_append_drop (i+1) l).trans <| by
-    rw [concat_eq_append, append_assoc, singleton_append, getElem_cons_drop_succ_eq_drop, take_append_drop]
+    rw [concat_eq_append, append_assoc, singleton_append, get_drop_eq_drop, take_append_drop]

@[deprecated take_succ_cons (since := "2024-07-25")]
 theorem take_cons_succ : (a::as).take (i+1) = a :: as.take i := rfl
@@ -224,7 +224,7 @@ theorem take_succ {l : List α} {n : Nat} : l.take (n + 1) = l.take n ++ l[n]?.t
    · simp only [take, Option.toList, getElem?_cons_zero, nil_append]
    · simp only [take, hl, getElem?_cons_succ, cons_append]

-@[deprecated "Deprecated without replacement." (since := "2024-07-25")]
+@[deprecated (since := "2024-07-25")]
 theorem drop_sizeOf_le [SizeOf α] (l : List α) (n : Nat) : sizeOf (l.drop n) ≤ sizeOf l := by
  induction l generalizing n with
  | nil => rw [drop_nil]; apply Nat.le_refl
--- a/src/Init/Data/Nat.lean
+++ b/src/Init/Data/Nat.lean
@@ -20,4 +20,3 @@ import Init.Data.Nat.Mod
 import Init.Data.Nat.Lcm
 import Init.Data.Nat.Compare
 import Init.Data.Nat.Simproc
-import Init.Data.Nat.Fold
--- a/src/Init/Data/Nat/Basic.lean
+++ b/src/Init/Data/Nat/Basic.lean
@@ -35,6 +35,52 @@ Used as the default `Nat` eliminator by the `cases` tactic. -/
 protected abbrev casesAuxOn {motive : Nat → Sort u} (t : Nat) (zero : motive 0) (succ : (n : Nat) → motive (n + 1)) : motive t :=
  Nat.casesOn t zero succ

+/--
+`Nat.fold` evaluates `f` on the numbers up to `n` exclusive, in increasing order:
+* `Nat.fold f 3 init = init |> f 0 |> f 1 |> f 2`
+-/
+@[specialize] def fold {α : Type u} (f : Nat → α → α) : (n : Nat) → (init : α) → α
+  | 0,      a => a
+  | succ n, a => f n (fold f n a)
+
+/-- Tail-recursive version of `Nat.fold`. -/
+@[inline] def foldTR {α : Type u} (f : Nat → α → α) (n : Nat) (init : α) : α :=
+  let rec @[specialize] loop
+    | 0,      a => a
+    | succ m, a => loop m (f (n - succ m) a)
+  loop n init
+
+/--
+`Nat.foldRev` evaluates `f` on the numbers up to `n` exclusive, in decreasing order:
+* `Nat.foldRev f 3 init = f 0 <| f 1 <| f 2 <| init`
+-/
+@[specialize] def foldRev {α : Type u} (f : Nat → α → α) : (n : Nat) → (init : α) → α
+  | 0,      a => a
+  | succ n, a => foldRev f n (f n a)
+
+/-- `any f n = true` iff there is `i in [0, n-1]` s.t. `f i = true` -/
+@[specialize] def any (f : Nat → Bool) : Nat → Bool
+  | 0      => false
+  | succ n => any f n || f n
+
+/-- Tail-recursive version of `Nat.any`. -/
+@[inline] def anyTR (f : Nat → Bool) (n : Nat) : Bool :=
+  let rec @[specialize] loop : Nat → Bool
+    | 0      => false
+    | succ m => f (n - succ m) || loop m
+  loop n
+
+/-- `all f n = true` iff every `i in [0, n-1]` satisfies `f i = true` -/
+@[specialize] def all (f : Nat → Bool) : Nat → Bool
+  | 0      => true
+  | succ n => all f n && f n
+
+/-- Tail-recursive version of `Nat.all`. -/
+@[inline] def allTR (f : Nat → Bool) (n : Nat) : Bool :=
+  let rec @[specialize] loop : Nat → Bool
+    | 0      => true
+    | succ m => f (n - succ m) && loop m
+  loop n

 /--
 `Nat.repeat f n a` is `f^(n) a`; that is, it iterates `f` `n` times on `a`.
@@ -789,7 +835,7 @@ theorem pred_lt_of_lt {n m : Nat} (h : m < n) : pred n < n :=
  pred_lt (not_eq_zero_of_lt h)

 set_option linter.missingDocs false in
-@[deprecated pred_lt_of_lt (since := "2024-06-01")] abbrev pred_lt' := @pred_lt_of_lt
+@[deprecated (since := "2024-06-01")] abbrev pred_lt' := @pred_lt_of_lt

 theorem sub_one_lt_of_lt {n m : Nat} (h : m < n) : n - 1 < n :=
  sub_one_lt (not_eq_zero_of_lt h)
@@ -1075,7 +1121,7 @@ theorem pred_mul (n m : Nat) : pred n * m = n * m - m := by
  | succ n => rw [Nat.pred_succ, succ_mul, Nat.add_sub_cancel]

 set_option linter.missingDocs false in
-@[deprecated pred_mul (since := "2024-06-01")] abbrev mul_pred_left := @pred_mul
+@[deprecated (since := "2024-06-01")] abbrev mul_pred_left := @pred_mul

 protected theorem sub_one_mul  (n m : Nat) : (n - 1) * m = n * m - m := by
  cases n with
@@ -1087,7 +1133,7 @@ theorem mul_pred (n m : Nat) : n * pred m = n * m - n := by
  rw [Nat.mul_comm, pred_mul, Nat.mul_comm]

 set_option linter.missingDocs false in
-@[deprecated mul_pred (since := "2024-06-01")] abbrev mul_pred_right := @mul_pred
+@[deprecated (since := "2024-06-01")] abbrev mul_pred_right := @mul_pred

 theorem mul_sub_one (n m : Nat) : n * (m - 1) = n * m - n := by
  rw [Nat.mul_comm, Nat.sub_one_mul , Nat.mul_comm]
@@ -1112,6 +1158,33 @@ theorem not_lt_eq (a b : Nat) : (¬ (a < b)) = (b ≤ a) :=
 theorem not_gt_eq (a b : Nat) : (¬ (a > b)) = (a ≤ b) :=
  not_lt_eq b a

+/-! # csimp theorems -/
+
+@[csimp] theorem fold_eq_foldTR : @fold = @foldTR :=
+  funext fun α => funext fun f => funext fun n => funext fun init =>
+  let rec go : ∀ m n, foldTR.loop f (m + n) m (fold f n init) = fold f (m + n) init
+    | 0,      n => by simp [foldTR.loop]
+    | succ m, n => by rw [foldTR.loop, add_sub_self_left, succ_add]; exact go m (succ n)
+  (go n 0).symm
+
+@[csimp] theorem any_eq_anyTR : @any = @anyTR :=
+  funext fun f => funext fun n =>
+  let rec go : ∀ m n,  (any f n || anyTR.loop f (m + n) m) = any f (m + n)
+    | 0,      n => by simp [anyTR.loop]
+    | succ m, n => by
+      rw [anyTR.loop, add_sub_self_left, ← Bool.or_assoc, succ_add]
+      exact go m (succ n)
+  (go n 0).symm
+
+@[csimp] theorem all_eq_allTR : @all = @allTR :=
+  funext fun f => funext fun n =>
+  let rec go : ∀ m n,  (all f n && allTR.loop f (m + n) m) = all f (m + n)
+    | 0,      n => by simp [allTR.loop]
+    | succ m, n => by
+      rw [allTR.loop, add_sub_self_left, ← Bool.and_assoc, succ_add]
+      exact go m (succ n)
+  (go n 0).symm
+
@[csimp] theorem repeat_eq_repeatTR : @repeat = @repeatTR :=
  funext fun α => funext fun f => funext fun n => funext fun init =>
  let rec go : ∀ m n, repeatTR.loop f m (repeat f n init) = repeat f (m + n) init
@@ -1120,3 +1193,31 @@ theorem not_gt_eq (a b : Nat) : (¬ (a > b)) = (a ≤ b) :=
  (go n 0).symm

 end Nat
+
+namespace Prod
+
+/--
+`(start, stop).foldI f a` evaluates `f` on all the numbers
+from `start` (inclusive) to `stop` (exclusive) in increasing order:
+* `(5, 8).foldI f init = init |> f 5 |> f 6 |> f 7`
+-/
+@[inline] def foldI {α : Type u} (f : Nat → α → α) (i : Nat × Nat) (a : α) : α :=
+  Nat.foldTR.loop f i.2 (i.2 - i.1) a
+
+/--
+`(start, stop).anyI f a` returns true if `f` is true for some natural number
+from `start` (inclusive) to `stop` (exclusive):
+* `(5, 8).anyI f = f 5 || f 6 || f 7`
+-/
+@[inline] def anyI (f : Nat → Bool) (i : Nat × Nat) : Bool :=
+  Nat.anyTR.loop f i.2 (i.2 - i.1)
+
+/--
+`(start, stop).allI f a` returns true if `f` is true for all natural numbers
+from `start` (inclusive) to `stop` (exclusive):
+* `(5, 8).anyI f = f 5 && f 6 && f 7`
+-/
+@[inline] def allI (f : Nat → Bool) (i : Nat × Nat) : Bool :=
+  Nat.allTR.loop f i.2 (i.2 - i.1)
+
+end Prod
--- a/src/Init/Data/Nat/Bitwise/Lemmas.lean
+++ b/src/Init/Data/Nat/Bitwise/Lemmas.lean
@@ -357,7 +357,7 @@ theorem testBit_two_pow_of_ne {n m : Nat} (hm : n ≠ m) : testBit (2 ^ n) m = f
  | zero => simp
  | succ n =>
    rw [mod_eq_of_lt (a := 1) (Nat.one_lt_two_pow (by omega)), mod_two_eq_one_iff_testBit_zero, testBit_two_pow_sub_one ]
-    simp only [zero_lt_succ, decide_true]
+    simp only [zero_lt_succ, decide_True]

@[simp] theorem mod_two_pos_mod_two_eq_one : x % 2 ^ j % 2 = 1 ↔ (0 < j) ∧ x % 2 = 1 := by
  rw [mod_two_eq_one_iff_testBit_zero, testBit_mod_two_pow]
--- a/src/Init/Data/Nat/Control.lean
+++ b/src/Init/Data/Nat/Control.lean
@@ -6,51 +6,50 @@ Author: Leonardo de Moura
 prelude
 import Init.Control.Basic
 import Init.Data.Nat.Basic
-import Init.Omega

 namespace Nat
 universe u v

-@[inline] def forM {m} [Monad m] (n : Nat) (f : (i : Nat) → i < n → m Unit) : m Unit :=
-  let rec @[specialize] loop : ∀ i, i ≤ n → m Unit
-    | 0,   _ => pure ()
-    | i+1, h => do f (n-i-1) (by omega); loop i (Nat.le_of_succ_le h)
-  loop n (by simp)
+@[inline] def forM {m} [Monad m] (n : Nat) (f : Nat → m Unit) : m Unit :=
+  let rec @[specialize] loop
+    | 0   => pure ()
+    | i+1 => do f (n-i-1); loop i
+  loop n

-@[inline] def forRevM {m} [Monad m] (n : Nat) (f : (i : Nat) → i < n → m Unit) : m Unit :=
-  let rec @[specialize] loop : ∀ i, i ≤ n → m Unit
-    | 0,   _ => pure ()
-    | i+1, h => do f i (by omega); loop i (Nat.le_of_succ_le h)
-  loop n (by simp)
+@[inline] def forRevM {m} [Monad m] (n : Nat) (f : Nat → m Unit) : m Unit :=
+  let rec @[specialize] loop
+    | 0   => pure ()
+    | i+1 => do f i; loop i
+  loop n

-@[inline] def foldM {α : Type u} {m : Type u → Type v} [Monad m] (n : Nat) (f : (i : Nat) → i < n → α → m α) (init : α) : m α :=
-  let rec @[specialize] loop : ∀ i, i ≤ n → α → m α
-    | 0,   h, a => pure a
-    | i+1, h, a => f (n-i-1) (by omega) a >>= loop i (Nat.le_of_succ_le h)
-  loop n (by omega) init
+@[inline] def foldM {α : Type u} {m : Type u → Type v} [Monad m] (f : Nat → α → m α) (init : α) (n : Nat) : m α :=
+  let rec @[specialize] loop
+    | 0,   a => pure a
+    | i+1, a => f (n-i-1) a >>= loop i
+  loop n init

-@[inline] def foldRevM {α : Type u} {m : Type u → Type v} [Monad m] (n : Nat) (f : (i : Nat) → i < n → α → m α) (init : α) : m α :=
-  let rec @[specialize] loop : ∀ i, i ≤ n → α → m α
-    | 0,   h, a => pure a
-    | i+1, h, a => f i (by omega) a >>= loop i (Nat.le_of_succ_le h)
-  loop n (by omega) init
+@[inline] def foldRevM {α : Type u} {m : Type u → Type v} [Monad m] (f : Nat → α → m α) (init : α) (n : Nat) : m α :=
+  let rec @[specialize] loop
+    | 0,   a => pure a
+    | i+1, a => f i a >>= loop i
+  loop n init

-@[inline] def allM {m} [Monad m] (n : Nat) (p : (i : Nat) → i < n → m Bool) : m Bool :=
-  let rec @[specialize] loop : ∀ i, i ≤ n → m Bool
-    | 0,   _ => pure true
-    | i+1 , h => do
-      match (← p (n-i-1) (by omega)) with
-      | true  => loop i (by omega)
+@[inline] def allM {m} [Monad m] (n : Nat) (p : Nat → m Bool) : m Bool :=
+  let rec @[specialize] loop
+    | 0   => pure true
+    | i+1 => do
+      match (← p (n-i-1)) with
+      | true  => loop i
      | false => pure false
-  loop n (by simp)
+  loop n

-@[inline] def anyM {m} [Monad m] (n : Nat) (p : (i : Nat) → i < n → m Bool) : m Bool :=
-  let rec @[specialize] loop : ∀ i, i ≤ n → m Bool
-    | 0,   _ => pure false
-    | i+1, h => do
-      match (← p (n-i-1) (by omega)) with
+@[inline] def anyM {m} [Monad m] (n : Nat) (p : Nat → m Bool) : m Bool :=
+  let rec @[specialize] loop
+    | 0   => pure false
+    | i+1 => do
+      match (← p (n-i-1)) with
      | true  => pure true
-      | false => loop i (Nat.le_of_succ_le h)
-  loop n (by simp)
+      | false => loop i
+  loop n

 end Nat
--- a/src/Init/Data/Nat/Dvd.lean
+++ b/src/Init/Data/Nat/Dvd.lean
@@ -92,7 +92,7 @@ protected theorem div_mul_cancel {n m : Nat} (H : n ∣ m) : m / n * n = m := by
  rw [Nat.mul_comm, Nat.mul_div_cancel' H]

@[simp] theorem mod_mod_of_dvd (a : Nat) (h : c ∣ b) : a % b % c = a % c := by
-  rw (occs := [2]) [← mod_add_div a b]
+  rw (config := {occs := .pos [2]}) [← mod_add_div a b]
  have ⟨x, h⟩ := h
  subst h
  rw [Nat.mul_assoc, add_mul_mod_self_left]
--- a/src/Init/Data/Nat/Fold.lean
+++ b/src/Init/Data/Nat/Fold.lean
@@ -1,217 +0,0 @@
-/-
-Copyright (c) 2014 Microsoft Corporation. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Floris van Doorn, Leonardo de Moura, Kim Morrison
-/
-prelude
-import Init.Omega
-import Init.Data.List.FinRange
-
-set_option linter.missingDocs true -- keep it documented
-universe u
-
-namespace Nat
-
-/--
-`Nat.fold` evaluates `f` on the numbers up to `n` exclusive, in increasing order:
-* `Nat.fold f 3 init = init |> f 0 |> f 1 |> f 2`
-/
-@[specialize] def fold {α : Type u} : (n : Nat) → (f : (i : Nat) → i < n → α → α) → (init : α) → α
-  | 0,      f, a => a
-  | succ n, f, a => f n (by omega) (fold n (fun i h => f i (by omega)) a)
-
-/-- Tail-recursive version of `Nat.fold`. -/
-@[inline] def foldTR {α : Type u} (n : Nat) (f : (i : Nat) → i < n → α → α) (init : α) : α :=
-  let rec @[specialize] loop : ∀ j, j ≤ n → α → α
-    | 0,      h, a => a
-    | succ m, h, a => loop m (by omega) (f (n - succ m) (by omega) a)
-  loop n (by omega) init
-
-/--
-`Nat.foldRev` evaluates `f` on the numbers up to `n` exclusive, in decreasing order:
-* `Nat.foldRev f 3 init = f 0 <| f 1 <| f 2 <| init`
-/
-@[specialize] def foldRev {α : Type u} : (n : Nat) → (f : (i : Nat) → i < n → α → α) → (init : α) → α
-  | 0,      f, a => a
-  | succ n, f, a => foldRev n (fun i h => f i (by omega)) (f n (by omega) a)
-
-/-- `any f n = true` iff there is `i in [0, n-1]` s.t. `f i = true` -/
-@[specialize] def any : (n : Nat) → (f : (i : Nat) → i < n → Bool) → Bool
-  | 0,      f => false
-  | succ n, f => any n (fun i h => f i (by omega)) || f n (by omega)
-
-/-- Tail-recursive version of `Nat.any`. -/
-@[inline] def anyTR (n : Nat) (f : (i : Nat) → i < n → Bool) : Bool :=
-  let rec @[specialize] loop : (i : Nat) → i ≤ n → Bool
-    | 0,      h => false
-    | succ m, h => f (n - succ m) (by omega) || loop m (by omega)
-  loop n (by omega)
-
-/-- `all f n = true` iff every `i in [0, n-1]` satisfies `f i = true` -/
-@[specialize] def all : (n : Nat) → (f : (i : Nat) → i < n → Bool) → Bool
-  | 0,      f => true
-  | succ n, f => all n (fun i h => f i (by omega)) && f n (by omega)
-
-/-- Tail-recursive version of `Nat.all`. -/
-@[inline] def allTR (n : Nat) (f : (i : Nat) → i < n → Bool) : Bool :=
-  let rec @[specialize] loop : (i : Nat) → i ≤ n   → Bool
-    | 0,      h => true
-    | succ m, h => f (n - succ m) (by omega) && loop m (by omega)
-  loop n (by omega)
-
-/-! # csimp theorems -/
-
-theorem fold_congr {α : Type u} {n m : Nat} (w : n = m)
-     (f : (i : Nat) → i < n → α → α) (init : α) :
-     fold n f init = fold m (fun i h => f i (by omega)) init := by
-  subst m
-  rfl
-
-theorem foldTR_loop_congr {α : Type u} {n m : Nat} (w : n = m)
-     (f : (i : Nat) → i < n → α → α) (j : Nat) (h : j ≤ n) (init : α) :
-     foldTR.loop n f j h init = foldTR.loop m (fun i h => f i (by omega)) j (by omega) init := by
-  subst m
-  rfl
-
-@[csimp] theorem fold_eq_foldTR : @fold = @foldTR :=
-  funext fun α => funext fun n => funext fun f => funext fun init =>
-  let rec go : ∀ m n f, fold (m + n) f init = foldTR.loop (m + n) f m (by omega) (fold n (fun i h => f i (by omega)) init)
-    | 0,      n, f => by
-      simp only [foldTR.loop]
-      have t : 0 + n = n := by omega
-      rw [fold_congr t]
-    | succ m, n, f => by
-      have t : (m + 1) + n = m + (n + 1) := by omega
-      rw [foldTR.loop]
-      simp only [succ_eq_add_one, Nat.add_sub_cancel]
-      rw [fold_congr t, foldTR_loop_congr t, go, fold]
-      congr
-      omega
-  go n 0 f
-
-theorem any_congr {n m : Nat} (w : n = m) (f : (i : Nat) → i < n → Bool) : any n f = any m (fun i h => f i (by omega)) := by
-  subst m
-  rfl
-
-theorem anyTR_loop_congr {n m : Nat} (w : n = m) (f : (i : Nat) → i < n → Bool) (j : Nat) (h : j ≤ n) :
-    anyTR.loop n f j h = anyTR.loop m (fun i h => f i (by omega)) j (by omega) := by
-  subst m
-  rfl
-
-@[csimp] theorem any_eq_anyTR : @any = @anyTR :=
-  funext fun n => funext fun f =>
-  let rec go : ∀ m n f, any (m + n) f = (any n (fun i h => f i (by omega)) || anyTR.loop (m + n) f m (by omega))
-    | 0,      n, f => by
-      simp [anyTR.loop]
-      have t : 0 + n = n := by omega
-      rw [any_congr t]
-    | succ m, n, f => by
-      have t : (m + 1) + n = m + (n + 1) := by omega
-      rw [anyTR.loop]
-      simp only [succ_eq_add_one]
-      rw [any_congr t, anyTR_loop_congr t, go, any, Bool.or_assoc]
-      congr
-      omega
-  go n 0 f
-
-theorem all_congr {n m : Nat} (w : n = m) (f : (i : Nat) → i < n → Bool) : all n f = all m (fun i h => f i (by omega)) := by
-  subst m
-  rfl
-
-theorem allTR_loop_congr {n m : Nat} (w : n = m) (f : (i : Nat) → i < n → Bool) (j : Nat) (h : j ≤ n) : allTR.loop n f j h = allTR.loop m (fun i h => f i (by omega)) j (by omega) := by
-  subst m
-  rfl
-
-@[csimp] theorem all_eq_allTR : @all = @allTR :=
-  funext fun n => funext fun f =>
-  let rec go : ∀ m n f, all (m + n) f = (all n (fun i h => f i (by omega)) && allTR.loop (m + n) f m (by omega))
-    | 0,      n, f => by
-      simp [allTR.loop]
-      have t : 0 + n = n := by omega
-      rw [all_congr t]
-    | succ m, n, f => by
-      have t : (m + 1) + n = m + (n + 1) := by omega
-      rw [allTR.loop]
-      simp only [succ_eq_add_one]
-      rw [all_congr t, allTR_loop_congr t, go, all, Bool.and_assoc]
-      congr
-      omega
-  go n 0 f
-
-@[simp] theorem fold_zero {α : Type u} (f : (i : Nat) → i < 0 → α → α) (init : α) :
-    fold 0 f init = init := by simp [fold]
-
-@[simp] theorem fold_succ {α : Type u} (n : Nat) (f : (i : Nat) → i < n + 1 → α → α) (init : α) :
-    fold (n + 1) f init = f n (by omega) (fold n (fun i h => f i (by omega)) init) := by simp [fold]
-
-theorem fold_eq_finRange_foldl {α : Type u} (n : Nat) (f : (i : Nat) → i < n → α → α) (init : α) :
-    fold n f init = (List.finRange n).foldl (fun acc ⟨i, h⟩ => f i h acc) init := by
-  induction n with
-  | zero => simp
-  | succ n ih =>
-    simp [ih, List.finRange_succ_last, List.foldl_map]
-
-@[simp] theorem foldRev_zero {α : Type u} (f : (i : Nat) → i < 0 → α → α) (init : α) :
-    foldRev 0 f init = init := by simp [foldRev]
-
-@[simp] theorem foldRev_succ {α : Type u} (n : Nat) (f : (i : Nat) → i < n + 1 → α → α) (init : α) :
-    foldRev (n + 1) f init = foldRev n (fun i h => f i (by omega)) (f n (by omega) init) := by
-  simp [foldRev]
-
-theorem foldRev_eq_finRange_foldr {α : Type u} (n : Nat) (f : (i : Nat) → i < n → α → α) (init : α) :
-    foldRev n f init = (List.finRange n).foldr (fun ⟨i, h⟩ acc => f i h acc) init := by
-  induction n generalizing init with
-  | zero => simp
-  | succ n ih => simp [ih, List.finRange_succ_last, List.foldr_map]
-
-@[simp] theorem any_zero {f : (i : Nat) → i < 0 → Bool} : any 0 f = false := by simp [any]
-
-@[simp] theorem any_succ {n : Nat} (f : (i : Nat) → i < n + 1 → Bool) :
-  any (n + 1) f = (any n (fun i h => f i (by omega)) || f n (by omega)) := by simp [any]
-
-theorem any_eq_finRange_any {n : Nat} (f : (i : Nat) → i < n → Bool) :
-    any n f = (List.finRange n).any (fun ⟨i, h⟩ => f i h) := by
-  induction n with
-  | zero => simp
-  | succ n ih => simp [ih, List.finRange_succ_last, List.any_map, Function.comp_def]
-
-@[simp] theorem all_zero {f : (i : Nat) → i < 0 → Bool} : all 0 f = true := by simp [all]
-
-@[simp] theorem all_succ {n : Nat} (f : (i : Nat) → i < n + 1 → Bool) :
-  all (n + 1) f = (all n (fun i h => f i (by omega)) && f n (by omega)) := by simp [all]
-
-theorem all_eq_finRange_all {n : Nat} (f : (i : Nat) → i < n → Bool) :
-    all n f = (List.finRange n).all (fun ⟨i, h⟩ => f i h) := by
-  induction n with
-  | zero => simp
-  | succ n ih => simp [ih, List.finRange_succ_last, List.all_map, Function.comp_def]
-
-end Nat
-
-namespace Prod
-
-/--
-`(start, stop).foldI f a` evaluates `f` on all the numbers
-from `start` (inclusive) to `stop` (exclusive) in increasing order:
-* `(5, 8).foldI f init = init |> f 5 |> f 6 |> f 7`
-/
-@[inline] def foldI {α : Type u} (i : Nat × Nat) (f : (j : Nat) → i.1 ≤ j → j < i.2 → α → α) (a : α) : α :=
-  (i.2 - i.1).fold (fun j _ => f (i.1 + j) (by omega) (by omega)) a
-
-/--
-`(start, stop).anyI f a` returns true if `f` is true for some natural number
-from `start` (inclusive) to `stop` (exclusive):
-* `(5, 8).anyI f = f 5 || f 6 || f 7`
-/
-@[inline] def anyI (i : Nat × Nat) (f : (j : Nat) → i.1 ≤ j → j < i.2 → Bool) : Bool :=
-  (i.2 - i.1).any (fun j _ => f (i.1 + j) (by omega) (by omega))
-
-/--
-`(start, stop).allI f a` returns true if `f` is true for all natural numbers
-from `start` (inclusive) to `stop` (exclusive):
-* `(5, 8).anyI f = f 5 && f 6 && f 7`
-/
-@[inline] def allI (i : Nat × Nat) (f : (j : Nat) → i.1 ≤ j → j < i.2 → Bool) : Bool :=
-  (i.2 - i.1).all (fun j _ => f (i.1 + j) (by omega) (by omega))
-
-end Prod
--- a/src/Init/Data/Nat/Lemmas.lean
+++ b/src/Init/Data/Nat/Lemmas.lean
@@ -651,8 +651,8 @@ theorem sub_mul_mod {x k n : Nat} (h₁ : n*k ≤ x) : (x - n*k) % n = x % n :=
  | .inr npos => Nat.mod_eq_of_lt (mod_lt _ npos)

 theorem mul_mod (a b n : Nat) : a * b % n = (a % n) * (b % n) % n := by
-  rw (occs := [1]) [← mod_add_div a n]
-  rw (occs := [1]) [← mod_add_div b n]
+  rw (config := {occs := .pos [1]}) [← mod_add_div a n]
+  rw (config := {occs := .pos [1]}) [← mod_add_div b n]
  rw [Nat.add_mul, Nat.mul_add, Nat.mul_add,
    Nat.mul_assoc, Nat.mul_assoc, ← Nat.mul_add n, add_mul_mod_self_left,
    Nat.mul_comm _ (n * (b / n)), Nat.mul_assoc, add_mul_mod_self_left]
@@ -679,10 +679,6 @@ theorem add_mod (a b n : Nat) : (a + b) % n = ((a % n) + (b % n)) % n := by
@[simp] theorem mod_mul_mod {a b c : Nat} : (a % c * b) % c = a * b % c := by
  rw [mul_mod, mod_mod, ← mul_mod]

-theorem mod_eq_sub (x w : Nat) : x % w = x - w * (x / w) := by
-  conv => rhs; congr; rw [← mod_add_div x w]
-  simp
-
 /-! ### pow -/

 theorem pow_succ' {m n : Nat} : m ^ n.succ = m * m ^ n := by
@@ -850,18 +846,6 @@ protected theorem pow_lt_pow_iff_pow_mul_le_pow {a n m : Nat} (h : 1 < a) :
  rw [←Nat.pow_add_one, Nat.pow_le_pow_iff_right (by omega), Nat.pow_lt_pow_iff_right (by omega)]
  omega

-protected theorem lt_pow_self {n a : Nat} (h : 1 < a) : n < a ^ n := by
-  induction n with
-  | zero => exact Nat.zero_lt_one
-  | succ _ ih => exact Nat.lt_of_lt_of_le (Nat.add_lt_add_right ih 1) (Nat.pow_lt_pow_succ h)
-
-protected theorem lt_two_pow_self : n < 2 ^ n :=
-  Nat.lt_pow_self Nat.one_lt_two
-
-@[simp]
-protected theorem mod_two_pow_self : n % 2 ^ n = n :=
-  Nat.mod_eq_of_lt Nat.lt_two_pow_self
-
@[simp]
 theorem two_pow_pred_mul_two (h : 0 < w) :
    2 ^ (w - 1) * 2 = 2 ^ w := by
@@ -1045,12 +1029,3 @@ instance decidableExistsLT [h : DecidablePred p] : DecidablePred fun n => ∃ m
 instance decidableExistsLE [DecidablePred p] : DecidablePred fun n => ∃ m : Nat, m ≤ n ∧ p m :=
  fun n => decidable_of_iff (∃ m, m < n + 1 ∧ p m)
    (exists_congr fun _ => and_congr_left' Nat.lt_succ_iff)
-
-/-! ### Results about `List.sum` specialized to `Nat` -/
-
-protected theorem sum_pos_iff_exists_pos {l : List Nat} : 0 < l.sum ↔ ∃ x ∈ l, 0 < x := by
-  induction l with
-  | nil => simp
-  | cons x xs ih =>
-    simp [← ih]
-    omega
--- a/src/Init/Data/Nat/Linear.lean
+++ b/src/Init/Data/Nat/Linear.lean
@@ -6,7 +6,6 @@ Authors: Leonardo de Moura
 prelude
 import Init.ByCases
 import Init.Data.Prod
-import Init.Data.RArray

 namespace Nat.Linear

@@ -16,7 +15,7 @@ namespace Nat.Linear

 abbrev Var := Nat

-abbrev Context := Lean.RArray Nat
+abbrev Context := List Nat

 /--
  When encoding polynomials. We use `fixedVar` for encoding numerals.
@@ -24,7 +23,12 @@ abbrev Context := Lean.RArray Nat
 def fixedVar := 100000000 -- Any big number should work here

 def Var.denote (ctx : Context) (v : Var) : Nat :=
-  bif v == fixedVar then 1 else ctx.get v
+  bif v == fixedVar then 1 else go ctx v
+where
+  go : List Nat → Nat → Nat
+   | [],    _   => 0
+   | a::_,  0   => a
+   | _::as, i+1 => go as i

 inductive Expr where
  | num  (v : Nat)
@@ -48,23 +52,25 @@ def Poly.denote (ctx : Context) (p : Poly) : Nat :=
  | [] => 0
  | (k, v) :: p => Nat.add (Nat.mul k (v.denote ctx)) (denote ctx p)

-def Poly.insert (k : Nat) (v : Var) (p : Poly) : Poly :=
+def Poly.insertSorted (k : Nat) (v : Var) (p : Poly) : Poly :=
  match p with
  | [] => [(k, v)]
-  | (k', v') :: p =>
-    bif Nat.blt v v' then
-      (k, v) :: (k', v') :: p
-    else bif Nat.beq v v' then
-      (k + k', v') :: p
-    else
-      (k', v') :: insert k v p
+  | (k', v') :: p => bif Nat.blt v v' then (k, v) :: (k', v') :: p else (k', v') :: insertSorted k v p

-def Poly.norm (p : Poly) : Poly := go p []
-where
-  go (p : Poly) (r : Poly) : Poly :=
+def Poly.sort (p : Poly) : Poly :=
+  let rec go (p : Poly) (r : Poly) : Poly :=
    match p with
    | [] => r
-    | (k, v) :: p => go p (r.insert k v)
+    | (k, v) :: p => go p (r.insertSorted k v)
+  go p []
+
+def Poly.fuse (p : Poly) : Poly :=
+  match p with
+  | []  => []
+  | (k, v) :: p =>
+    match fuse p with
+    | [] => [(k, v)]
+    | (k', v') :: p' => bif v == v' then (Nat.add k k', v)::p' else (k, v) :: (k', v') :: p'

 def Poly.mul (k : Nat) (p : Poly) : Poly :=
  bif k == 0 then
@@ -140,17 +146,15 @@ def Poly.combineAux (fuel : Nat) (p₁ p₂ : Poly) : Poly :=
 def Poly.combine (p₁ p₂ : Poly) : Poly :=
  combineAux hugeFuel p₁ p₂

-def Expr.toPoly (e : Expr) :=
-  go 1 e []
-where
-  -- Implementation note: This assembles the result using difference lists
-  -- to avoid `++` on lists.
-  go (coeff : Nat) : Expr → (Poly → Poly)
-    | Expr.num k    => bif k == 0 then id else ((coeff * k, fixedVar) :: ·)
-    | Expr.var i    => ((coeff, i) :: ·)
-    | Expr.add a b  => go coeff a ∘ go coeff b
-    | Expr.mulL k a
-    | Expr.mulR a k => bif k == 0 then id else go (coeff * k) a
+def Expr.toPoly : Expr → Poly
+  | Expr.num k    => bif k == 0 then [] else [ (k, fixedVar) ]
+  | Expr.var i    => [(1, i)]
+  | Expr.add a b  => a.toPoly ++ b.toPoly
+  | Expr.mulL k a => a.toPoly.mul k
+  | Expr.mulR a k => a.toPoly.mul k
+
+def Poly.norm (p : Poly) : Poly :=
+  p.sort.fuse

 def Expr.toNormPoly (e : Expr) : Poly :=
  e.toPoly.norm
@@ -197,7 +201,7 @@ def PolyCnstr.denote (ctx : Context) (c : PolyCnstr) : Prop :=
    Poly.denote_le ctx (c.lhs, c.rhs)

 def PolyCnstr.norm (c : PolyCnstr) : PolyCnstr :=
-  let (lhs, rhs) := Poly.cancel c.lhs.norm c.rhs.norm
+  let (lhs, rhs) := Poly.cancel c.lhs.sort.fuse c.rhs.sort.fuse
  { eq := c.eq, lhs, rhs }

 def PolyCnstr.isUnsat (c : PolyCnstr) : Bool :=
@@ -264,32 +268,24 @@ def PolyCnstr.toExpr (c : PolyCnstr) : ExprCnstr :=
  { c with lhs := c.lhs.toExpr, rhs := c.rhs.toExpr }

 attribute [local simp] Nat.add_comm Nat.add_assoc Nat.add_left_comm Nat.right_distrib Nat.left_distrib Nat.mul_assoc Nat.mul_comm
-attribute [local simp] Poly.denote Expr.denote Poly.insert Poly.norm Poly.norm.go Poly.cancelAux
+attribute [local simp] Poly.denote Expr.denote Poly.insertSorted Poly.sort Poly.sort.go Poly.fuse Poly.cancelAux
 attribute [local simp] Poly.mul Poly.mul.go

-theorem Poly.denote_insert (ctx : Context) (k : Nat) (v : Var) (p : Poly) :
-    (p.insert k v).denote ctx = p.denote ctx + k * v.denote ctx := by
+theorem Poly.denote_insertSorted (ctx : Context) (k : Nat) (v : Var) (p : Poly) : (p.insertSorted k v).denote ctx = p.denote ctx + k * v.denote ctx := by
  match p with
  | [] => simp
-  | (k', v') :: p =>
-    by_cases h₁ : Nat.blt v v'
-    · simp [h₁]
-    · by_cases h₂ : Nat.beq v v'
-      · simp only [insert, h₁, h₂, cond_false, cond_true]
-        simp [Nat.eq_of_beq_eq_true h₂]
-      · simp only [insert, h₁, h₂, cond_false, cond_true]
-        simp [denote_insert]
+  | (k', v') :: p => by_cases h : Nat.blt v v' <;> simp [h, denote_insertSorted]

-attribute [local simp] Poly.denote_insert
+attribute [local simp] Poly.denote_insertSorted

-theorem Poly.denote_norm_go (ctx : Context) (p : Poly) (r : Poly) : (norm.go p r).denote ctx = p.denote ctx + r.denote ctx := by
+theorem Poly.denote_sort_go (ctx : Context) (p : Poly) (r : Poly) : (sort.go p r).denote ctx = p.denote ctx + r.denote ctx := by
  match p with
  | [] => simp
-  | (k, v):: p => simp [denote_norm_go]
+  | (k, v):: p => simp [denote_sort_go]

-attribute [local simp] Poly.denote_norm_go
+attribute [local simp] Poly.denote_sort_go

-theorem Poly.denote_sort (ctx : Context) (m : Poly) : m.norm.denote ctx = m.denote ctx := by
+theorem Poly.denote_sort (ctx : Context) (m : Poly) : m.sort.denote ctx = m.denote ctx := by
  simp

 attribute [local simp] Poly.denote_sort
@@ -320,6 +316,18 @@ theorem Poly.denote_reverse (ctx : Context) (p : Poly) : denote ctx (List.revers

 attribute [local simp] Poly.denote_reverse

+theorem Poly.denote_fuse (ctx : Context) (p : Poly) : p.fuse.denote ctx = p.denote ctx := by
+  match p with
+  | [] => rfl
+  | (k, v) :: p =>
+    have ih := denote_fuse ctx p
+    simp
+    split
+    case _ h => simp [← ih, h]
+    case _ k' v' p' h => by_cases he : v == v' <;> simp [he, ← ih, h]; rw [eq_of_beq he]
+
+attribute [local simp] Poly.denote_fuse
+
 theorem Poly.denote_mul (ctx : Context) (k : Nat) (p : Poly) : (p.mul k).denote ctx = k * p.denote ctx := by
  simp
  by_cases h : k == 0 <;> simp [h]; simp [eq_of_beq h]
@@ -508,25 +516,13 @@ theorem Poly.denote_combine (ctx : Context) (p₁ p₂ : Poly) : (p₁.combine p

 attribute [local simp] Poly.denote_combine

-theorem Expr.denote_toPoly_go (ctx : Context) (e : Expr) :
-  (toPoly.go k e p).denote ctx = k * e.denote ctx + p.denote ctx := by
-  induction k, e using Expr.toPoly.go.induct generalizing p with
-  | case1 k k' =>
-    simp only [toPoly.go]
-    by_cases h : k' == 0
-    · simp [h, eq_of_beq h]
-    · simp [h, Var.denote]
-  | case2 k i => simp [toPoly.go]
-  | case3 k a b iha ihb => simp [toPoly.go, iha, ihb]
-  | case4 k k' a ih
-  | case5 k a k' ih =>
-    simp only [toPoly.go, denote, mul_eq]
-    by_cases h : k' == 0
-    · simp [h, eq_of_beq h]
-    · simp [h, cond_false, ih, Nat.mul_assoc]
-
 theorem Expr.denote_toPoly (ctx : Context) (e : Expr) : e.toPoly.denote ctx = e.denote ctx := by
-  simp [toPoly, Expr.denote_toPoly_go]
+  induction e with
+  | num k => by_cases h : k == 0 <;> simp [toPoly, h, Var.denote]; simp [eq_of_beq h]
+  | var i => simp [toPoly]
+  | add a b iha ihb => simp [toPoly, iha, ihb]
+  | mulL k a ih => simp [toPoly, ih, -Poly.mul]
+  | mulR k a ih => simp [toPoly, ih, -Poly.mul]

 attribute [local simp] Expr.denote_toPoly

@@ -558,8 +554,8 @@ theorem ExprCnstr.denote_toPoly (ctx : Context) (c : ExprCnstr) : c.toPoly.denot
  cases c; rename_i eq lhs rhs
  simp [ExprCnstr.denote, PolyCnstr.denote, ExprCnstr.toPoly];
  by_cases h : eq = true <;> simp [h]
-  · simp [Poly.denote_eq]
-  · simp [Poly.denote_le]
+  · simp [Poly.denote_eq, Expr.toPoly]
+  · simp [Poly.denote_le, Expr.toPoly]

 attribute [local simp] ExprCnstr.denote_toPoly

--- a/src/Init/Data/Option/Basic.lean
+++ b/src/Init/Data/Option/Basic.lean
@@ -16,22 +16,22 @@ def getM [Alternative m] : Option α → m α
  | none     => failure
  | some a   => pure a

+@[deprecated getM (since := "2024-04-17")]
+-- `[Monad m]` is not needed here.
+def toMonad [Monad m] [Alternative m] : Option α → m α := getM
+
 /-- Returns `true` on `some x` and `false` on `none`. -/
@[inline] def isSome : Option α → Bool
  | some _ => true
  | none   => false

-@[simp] theorem isSome_none : @isSome α none = false := rfl
-@[simp] theorem isSome_some : isSome (some a) = true := rfl
+@[deprecated isSome (since := "2024-04-17"), inline] def toBool : Option α → Bool := isSome

 /-- Returns `true` on `none` and `false` on `some x`. -/
@[inline] def isNone : Option α → Bool
  | some _ => false
  | none   => true

-@[simp] theorem isNone_none : @isNone α none = true := rfl
-@[simp] theorem isNone_some : isNone (some a) = false := rfl
-
 /--
 `x?.isEqSome y` is equivalent to `x? == some y`, but avoids an allocation.
 -/
@@ -134,10 +134,6 @@ def merge (fn : α → α → α) : Option α → Option α → Option α
@[inline] def get {α : Type u} : (o : Option α) → isSome o → α
  | some x, _ => x

-@[simp] theorem some_get : ∀ {x : Option α} (h : isSome x), some (x.get h) = x
-| some _, _ => rfl
-@[simp] theorem get_some (x : α) (h : isSome (some x)) : (some x).get h = x := rfl
-
 /-- `guard p a` returns `some a` if `p a` holds, otherwise `none`. -/
@[inline] def guard (p : α → Prop) [DecidablePred p] (a : α) : Option α :=
  if p a then some a else none
--- a/src/Init/Data/Option/Instances.lean
+++ b/src/Init/Data/Option/Instances.lean
@@ -86,6 +86,4 @@ instance : ForIn' m (Option α) α inferInstance where
      match ← f a rfl init with
      | .done r | .yield r => return r

-- No separate `ForIn` instance is required because it can be derived from `ForIn'`.
-
 end Option
--- a/src/Init/Data/Option/Lemmas.lean
+++ b/src/Init/Data/Option/Lemmas.lean
@@ -36,6 +36,11 @@ theorem get_of_mem : ∀ {o : Option α} (h : isSome o), a ∈ o → o.get h = a

 theorem not_mem_none (a : α) : a ∉ (none : Option α) := nofun

+@[simp] theorem some_get : ∀ {x : Option α} (h : isSome x), some (x.get h) = x
+| some _, _ => rfl
+
+@[simp] theorem get_some (x : α) (h : isSome (some x)) : (some x).get h = x := rfl
+
 theorem getD_of_ne_none {x : Option α} (hx : x ≠ none) (y : α) : some (x.getD y) = x := by
  cases x; {contradiction}; rw [getD_some]

@@ -55,9 +60,7 @@ theorem get_eq_getD {fallback : α} : (o : Option α) → {h : o.isSome} → o.g
 theorem some_get! [Inhabited α] : (o : Option α) → o.isSome → some (o.get!) = o
  | some _, _ => rfl

-theorem get!_eq_getD [Inhabited α] (o : Option α) : o.get! = o.getD default := rfl
-
-@[deprecated get!_eq_getD (since := "2024-11-18")] abbrev get!_eq_getD_default := @get!_eq_getD
+theorem get!_eq_getD_default [Inhabited α] (o : Option α) : o.get! = o.getD default := rfl

 theorem mem_unique {o : Option α} {a b : α} (ha : a ∈ o) (hb : b ∈ o) : a = b :=
  some.inj <| ha ▸ hb
@@ -70,11 +73,19 @@ theorem mem_unique {o : Option α} {a b : α} (ha : a ∈ o) (hb : b ∈ o) : a
 theorem eq_none_iff_forall_not_mem : o = none ↔ ∀ a, a ∉ o :=
  ⟨fun e a h => by rw [e] at h; (cases h), fun h => ext <| by simp; exact h⟩

+@[simp] theorem isSome_none : @isSome α none = false := rfl
+
+@[simp] theorem isSome_some : isSome (some a) = true := rfl
+
 theorem isSome_iff_exists : isSome x ↔ ∃ a, x = some a := by cases x <;> simp [isSome]

 theorem isSome_eq_isSome : (isSome x = isSome y) ↔ (x = none ↔ y = none) := by
  cases x <;> cases y <;> simp

+@[simp] theorem isNone_none : @isNone α none = true := rfl
+
+@[simp] theorem isNone_some : isNone (some a) = false := rfl
+
@[simp] theorem not_isSome : isSome a = false ↔ a.isNone = true := by
  cases a <;> simp

@@ -363,15 +374,9 @@ end choice

 -- See `Init.Data.Option.List` for lemmas about `toList`.

-@[simp] theorem some_or : (some a).or o = some a := rfl
+@[simp] theorem or_some : (some a).or o = some a := rfl
@[simp] theorem none_or : none.or o = o := rfl

-@[deprecated some_or (since := "2024-11-03")] theorem or_some : (some a).or o = some a := rfl
-
-/-- This will be renamed to `or_some` once the existing deprecated lemma is removed. -/
-@[simp] theorem or_some' {o : Option α} : o.or (some a) = o.getD a := by
-  cases o <;> rfl
-
 theorem or_eq_bif : or o o' = bif o.isSome then o else o' := by
  cases o <;> rfl

--- a/src/Init/Data/RArray.lean
+++ b/src/Init/Data/RArray.lean
@@ -1,69 +0,0 @@
-/-
-Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Joachim Breitner
-/
-
-prelude
-import Init.PropLemmas
-
-namespace Lean
-
-/--
-A `RArray` can model `Fin n → α` or `Array α`, but is optimized for a fast kernel-reducible `get`
-operation.
-
-The primary intended use case is the “denote” function of a typical proof by reflection proof, where
-only the `get` operation is necessary. It is not suitable as a general-purpose data structure.
-
-There is no well-formedness invariant attached to this data structure, to keep it concise; it's
-semantics is given through `RArray.get`. In that way one can also view an `RArray` as a decision
-tree implementing `Nat → α`.
-
-See `RArray.ofFn` and `RArray.ofArray` in module `Lean.Data.RArray` for functions that construct an
-`RArray`.
-
-It is not universe-polymorphic. ; smaller proof objects and no complication with the `ToExpr` type
-class.
-/
-inductive RArray (α : Type) : Type where
-  | leaf : α → RArray α
-  | branch : Nat → RArray α → RArray α → RArray α
-
-variable {α : Type}
-
-/-- The crucial operation, written with very little abstractional overhead -/
-noncomputable def RArray.get (a : RArray α) (n : Nat) : α :=
-  RArray.rec (fun x => x) (fun p _ _ l r => (Nat.ble p n).rec l r) a
-
-private theorem RArray.get_eq_def (a : RArray α) (n : Nat) :
-  a.get n = match a with
-    | .leaf x => x
-    | .branch p l r => (Nat.ble p n).rec (l.get n) (r.get n) := by
-  conv => lhs; unfold RArray.get
-  split <;> rfl
-
-/-- `RArray.get`, implemented conventionally -/
-def RArray.getImpl (a : RArray α) (n : Nat) : α :=
-  match a with
-  | .leaf x => x
-  | .branch p l r => if n < p then l.getImpl n else r.getImpl n
-
-@[csimp]
-theorem RArray.get_eq_getImpl : @RArray.get = @RArray.getImpl := by
-  funext α a n
-  induction a with
-  | leaf _ => rfl
-  | branch p l r ihl ihr =>
-    rw [RArray.getImpl, RArray.get_eq_def]
-    simp only [ihl, ihr, ← Nat.not_le, ← Nat.ble_eq, ite_not]
-    cases hnp : Nat.ble p n <;> rfl
-
-instance : GetElem (RArray α) Nat α (fun _ _ => True) where
-  getElem a n _ := a.get n
-
-def RArray.size : RArray α → Nat
-  | leaf _ => 1
-  | branch _ l r => l.size + r.size
-
-end Lean
--- a/src/Init/Data/Random.lean
+++ b/src/Init/Data/Random.lean
@@ -113,10 +113,10 @@ initialize IO.stdGenRef : IO.Ref StdGen ←
  let seed := UInt64.toNat (ByteArray.toUInt64LE! (← IO.getRandomBytes 8))
  IO.mkRef (mkStdGen seed)

-def IO.setRandSeed (n : Nat) : BaseIO Unit :=
+def IO.setRandSeed (n : Nat) : IO Unit :=
  IO.stdGenRef.set (mkStdGen n)

-def IO.rand (lo hi : Nat) : BaseIO Nat := do
+def IO.rand (lo hi : Nat) : IO Nat := do
  let gen ← IO.stdGenRef.get
  let (r, gen) := randNat gen lo hi
  IO.stdGenRef.set gen
--- a/src/Init/Data/Range.lean
+++ b/src/Init/Data/Range.lean
@@ -20,6 +20,21 @@ instance : Membership Nat Range where
 namespace Range
 universe u v

+@[inline] protected def forIn {β : Type u} {m : Type u → Type v} [Monad m] (range : Range) (init : β) (f : Nat → β → m (ForInStep β)) : m β :=
+  -- pass `stop` and `step` separately so the `range` object can be eliminated through inlining
+  let rec @[specialize] loop (fuel i stop step : Nat) (b : β) : m β := do
+    if i ≥ stop then
+      return b
+    else match fuel with
+     | 0   => pure b
+     | fuel+1 => match (← f i b) with
+        | ForInStep.done b  => pure b
+        | ForInStep.yield b => loop fuel (i + step) stop step b
+  loop range.stop range.start range.stop range.step init
+
+instance : ForIn m Range Nat where
+  forIn := Range.forIn
+
@[inline] protected def forIn' {β : Type u} {m : Type u → Type v} [Monad m] (range : Range) (init : β) (f : (i : Nat) → i ∈ range → β → m (ForInStep β)) : m β :=
  let rec @[specialize] loop (start stop step : Nat) (f : (i : Nat) → start ≤ i ∧ i < stop → β → m (ForInStep β)) (fuel i : Nat) (hl : start ≤ i) (b : β) : m β := do
    if hu : i < stop then
@@ -35,8 +50,6 @@ universe u v
 instance : ForIn' m Range Nat inferInstance where
  forIn' := Range.forIn'

-- No separate `ForIn` instance is required because it can be derived from `ForIn'`.
-
@[inline] protected def forM {m : Type u → Type v} [Monad m] (range : Range) (f : Nat → m PUnit) : m PUnit :=
  let rec @[specialize] loop (fuel i stop step : Nat) : m PUnit := do
    if i ≥ stop then
--- a/src/Init/Data/Repr.lean
+++ b/src/Init/Data/Repr.lean
@@ -162,7 +162,7 @@ private def reprArray : Array String := Id.run do
  List.range 128 |>.map (·.toUSize.repr) |> Array.mk

 private def reprFast (n : Nat) : String :=
-  if h : n < 128 then Nat.reprArray.get n h else
+  if h : n < 128 then Nat.reprArray.get ⟨n, h⟩ else
  if h : n < USize.size then (USize.ofNatCore n h).repr
  else (toDigits 10 n).asString

--- a/src/Init/Data/SInt/Basic.lean
+++ b/src/Init/Data/SInt/Basic.lean
@@ -22,48 +22,6 @@ structure Int8 where
  -/
  toUInt8 : UInt8

-/--
-The type of signed 16-bit integers. This type has special support in the
-compiler to make it actually 16 bits rather than wrapping a `Nat`.
-/
-structure Int16 where
-  /--
-  Obtain the `UInt16` that is 2's complement equivalent to the `Int16`.
-  -/
-  toUInt16 : UInt16
-
-/--
-The type of signed 32-bit integers. This type has special support in the
-compiler to make it actually 32 bits rather than wrapping a `Nat`.
-/
-structure Int32 where
-  /--
-  Obtain the `UInt32` that is 2's complement equivalent to the `Int32`.
-  -/
-  toUInt32 : UInt32
-
-/--
-The type of signed 64-bit integers. This type has special support in the
-compiler to make it actually 64 bits rather than wrapping a `Nat`.
-/
-structure Int64 where
-  /--
-  Obtain the `UInt64` that is 2's complement equivalent to the `Int64`.
-  -/
-  toUInt64 : UInt64
-
-/--
-A `ISize` is a signed integer with the size of a word for the platform's architecture.
-
-For example, if running on a 32-bit machine, ISize is equivalent to `Int32`.
-Or on a 64-bit machine, `Int64`.
-/
-structure ISize where
-  /--
-  Obtain the `USize` that is 2's complement equivalent to the `ISize`.
-  -/
-  toUSize : USize
-
 /-- The size of type `Int8`, that is, `2^8 = 256`. -/
 abbrev Int8.size : Nat := 256

@@ -74,16 +32,12 @@ Obtain the `BitVec` that contains the 2's complement representation of the `Int8

@[extern "lean_int8_of_int"]
 def Int8.ofInt (i : @& Int) : Int8 := ⟨⟨BitVec.ofInt 8 i⟩⟩
-@[extern "lean_int8_of_nat"]
+@[extern "lean_int8_of_int"]
 def Int8.ofNat (n : @& Nat) : Int8 := ⟨⟨BitVec.ofNat 8 n⟩⟩
 abbrev Int.toInt8 := Int8.ofInt
 abbrev Nat.toInt8 := Int8.ofNat
@[extern "lean_int8_to_int"]
 def Int8.toInt (i : Int8) : Int := i.toBitVec.toInt
-/--
-This function has the same behavior as `Int.toNat` for negative numbers.
-If you want to obtain the 2's complement representation use `toBitVec`.
-/
@[inline] def Int8.toNat (i : Int8) : Nat := i.toInt.toNat
@[extern "lean_int8_neg"]
 def Int8.neg (i : Int8) : Int8 := ⟨⟨-i.toBitVec⟩⟩
@@ -104,7 +58,7 @@ def Int8.mul (a b : Int8) : Int8 := ⟨⟨a.toBitVec * b.toBitVec⟩⟩
@[extern "lean_int8_div"]
 def Int8.div (a b : Int8) : Int8 := ⟨⟨BitVec.sdiv a.toBitVec b.toBitVec⟩⟩
@[extern "lean_int8_mod"]
-def Int8.mod (a b : Int8) : Int8 := ⟨⟨BitVec.srem a.toBitVec b.toBitVec⟩⟩
+def Int8.mod (a b : Int8) : Int8 := ⟨⟨BitVec.smod a.toBitVec b.toBitVec⟩⟩
@[extern "lean_int8_land"]
 def Int8.land (a b : Int8) : Int8 := ⟨⟨a.toBitVec &&& b.toBitVec⟩⟩
@[extern "lean_int8_lor"]
@@ -112,9 +66,9 @@ def Int8.lor (a b : Int8) : Int8 := ⟨⟨a.toBitVec ||| b.toBitVec⟩⟩
@[extern "lean_int8_xor"]
 def Int8.xor (a b : Int8) : Int8 := ⟨⟨a.toBitVec ^^^ b.toBitVec⟩⟩
@[extern "lean_int8_shift_left"]
-def Int8.shiftLeft (a b : Int8) : Int8 := ⟨⟨a.toBitVec <<< (b.toBitVec.smod 8)⟩⟩
+def Int8.shiftLeft (a b : Int8) : Int8 := ⟨⟨a.toBitVec <<< (mod b 8).toBitVec⟩⟩
@[extern "lean_int8_shift_right"]
-def Int8.shiftRight (a b : Int8) : Int8 := ⟨⟨BitVec.sshiftRight' a.toBitVec (b.toBitVec.smod 8)⟩⟩
+def Int8.shiftRight (a b : Int8) : Int8 := ⟨⟨BitVec.sshiftRight' a.toBitVec (mod b 8).toBitVec⟩⟩
@[extern "lean_int8_complement"]
 def Int8.complement (a : Int8) : Int8 := ⟨⟨~~~a.toBitVec⟩⟩

@@ -148,9 +102,6 @@ instance : ShiftLeft Int8   := ⟨Int8.shiftLeft⟩
 instance : ShiftRight Int8  := ⟨Int8.shiftRight⟩
 instance : DecidableEq Int8 := Int8.decEq

-@[extern "lean_bool_to_int8"]
-def Bool.toInt8 (b : Bool) : Int8 := if b then 1 else 0
-
@[extern "lean_int8_dec_lt"]
 def Int8.decLt (a b : Int8) : Decidable (a < b) :=
  inferInstanceAs (Decidable (a.toBitVec.slt b.toBitVec))
@@ -163,441 +114,3 @@ instance (a b : Int8) : Decidable (a < b) := Int8.decLt a b
 instance (a b : Int8) : Decidable (a ≤ b) := Int8.decLe a b
 instance : Max Int8 := maxOfLe
 instance : Min Int8 := minOfLe
-
-/-- The size of type `Int16`, that is, `2^16 = 65536`. -/
-abbrev Int16.size : Nat := 65536
-
-/--
-Obtain the `BitVec` that contains the 2's complement representation of the `Int16`.
-/
-@[inline] def Int16.toBitVec (x : Int16) : BitVec 16 := x.toUInt16.toBitVec
-
-@[extern "lean_int16_of_int"]
-def Int16.ofInt (i : @& Int) : Int16 := ⟨⟨BitVec.ofInt 16 i⟩⟩
-@[extern "lean_int16_of_nat"]
-def Int16.ofNat (n : @& Nat) : Int16 := ⟨⟨BitVec.ofNat 16 n⟩⟩
-abbrev Int.toInt16 := Int16.ofInt
-abbrev Nat.toInt16 := Int16.ofNat
-@[extern "lean_int16_to_int"]
-def Int16.toInt (i : Int16) : Int := i.toBitVec.toInt
-/--
-This function has the same behavior as `Int.toNat` for negative numbers.
-If you want to obtain the 2's complement representation use `toBitVec`.
-/
-@[inline] def Int16.toNat (i : Int16) : Nat := i.toInt.toNat
-@[extern "lean_int16_to_int8"]
-def Int16.toInt8 (a : Int16) : Int8 := ⟨⟨a.toBitVec.signExtend 8⟩⟩
-@[extern "lean_int8_to_int16"]
-def Int8.toInt16 (a : Int8) : Int16 := ⟨⟨a.toBitVec.signExtend 16⟩⟩
-@[extern "lean_int16_neg"]
-def Int16.neg (i : Int16) : Int16 := ⟨⟨-i.toBitVec⟩⟩
-
-instance : ToString Int16 where
-  toString i := toString i.toInt
-
-instance : OfNat Int16 n := ⟨Int16.ofNat n⟩
-instance : Neg Int16 where
-  neg := Int16.neg
-
-@[extern "lean_int16_add"]
-def Int16.add (a b : Int16) : Int16 := ⟨⟨a.toBitVec + b.toBitVec⟩⟩
-@[extern "lean_int16_sub"]
-def Int16.sub (a b : Int16) : Int16 := ⟨⟨a.toBitVec - b.toBitVec⟩⟩
-@[extern "lean_int16_mul"]
-def Int16.mul (a b : Int16) : Int16 := ⟨⟨a.toBitVec * b.toBitVec⟩⟩
-@[extern "lean_int16_div"]
-def Int16.div (a b : Int16) : Int16 := ⟨⟨BitVec.sdiv a.toBitVec b.toBitVec⟩⟩
-@[extern "lean_int16_mod"]
-def Int16.mod (a b : Int16) : Int16 := ⟨⟨BitVec.srem a.toBitVec b.toBitVec⟩⟩
-@[extern "lean_int16_land"]
-def Int16.land (a b : Int16) : Int16 := ⟨⟨a.toBitVec &&& b.toBitVec⟩⟩
-@[extern "lean_int16_lor"]
-def Int16.lor (a b : Int16) : Int16 := ⟨⟨a.toBitVec ||| b.toBitVec⟩⟩
-@[extern "lean_int16_xor"]
-def Int16.xor (a b : Int16) : Int16 := ⟨⟨a.toBitVec ^^^ b.toBitVec⟩⟩
-@[extern "lean_int16_shift_left"]
-def Int16.shiftLeft (a b : Int16) : Int16 := ⟨⟨a.toBitVec <<< (b.toBitVec.smod 16)⟩⟩
-@[extern "lean_int16_shift_right"]
-def Int16.shiftRight (a b : Int16) : Int16 := ⟨⟨BitVec.sshiftRight' a.toBitVec (b.toBitVec.smod 16)⟩⟩
-@[extern "lean_int16_complement"]
-def Int16.complement (a : Int16) : Int16 := ⟨⟨~~~a.toBitVec⟩⟩
-
-@[extern "lean_int16_dec_eq"]
-def Int16.decEq (a b : Int16) : Decidable (a = b) :=
-  match a, b with
-  | ⟨n⟩, ⟨m⟩ =>
-    if h : n = m then
-      isTrue <| h ▸ rfl
-    else
-      isFalse (fun h' => Int16.noConfusion h' (fun h' => absurd h' h))
-
-def Int16.lt (a b : Int16) : Prop := a.toBitVec.slt b.toBitVec
-def Int16.le (a b : Int16) : Prop := a.toBitVec.sle b.toBitVec
-
-instance : Inhabited Int16 where
-  default := 0
-
-instance : Add Int16         := ⟨Int16.add⟩
-instance : Sub Int16         := ⟨Int16.sub⟩
-instance : Mul Int16         := ⟨Int16.mul⟩
-instance : Mod Int16         := ⟨Int16.mod⟩
-instance : Div Int16         := ⟨Int16.div⟩
-instance : LT Int16          := ⟨Int16.lt⟩
-instance : LE Int16          := ⟨Int16.le⟩
-instance : Complement Int16  := ⟨Int16.complement⟩
-instance : AndOp Int16       := ⟨Int16.land⟩
-instance : OrOp Int16        := ⟨Int16.lor⟩
-instance : Xor Int16         := ⟨Int16.xor⟩
-instance : ShiftLeft Int16   := ⟨Int16.shiftLeft⟩
-instance : ShiftRight Int16  := ⟨Int16.shiftRight⟩
-instance : DecidableEq Int16 := Int16.decEq
-
-@[extern "lean_bool_to_int16"]
-def Bool.toInt16 (b : Bool) : Int16 := if b then 1 else 0
-
-@[extern "lean_int16_dec_lt"]
-def Int16.decLt (a b : Int16) : Decidable (a < b) :=
-  inferInstanceAs (Decidable (a.toBitVec.slt b.toBitVec))
-
-@[extern "lean_int16_dec_le"]
-def Int16.decLe (a b : Int16) : Decidable (a ≤ b) :=
-  inferInstanceAs (Decidable (a.toBitVec.sle b.toBitVec))
-
-instance (a b : Int16) : Decidable (a < b) := Int16.decLt a b
-instance (a b : Int16) : Decidable (a ≤ b) := Int16.decLe a b
-instance : Max Int16 := maxOfLe
-instance : Min Int16 := minOfLe
-
-/-- The size of type `Int32`, that is, `2^32 = 4294967296`. -/
-abbrev Int32.size : Nat := 4294967296
-
-/--
-Obtain the `BitVec` that contains the 2's complement representation of the `Int32`.
-/
-@[inline] def Int32.toBitVec (x : Int32) : BitVec 32 := x.toUInt32.toBitVec
-
-@[extern "lean_int32_of_int"]
-def Int32.ofInt (i : @& Int) : Int32 := ⟨⟨BitVec.ofInt 32 i⟩⟩
-@[extern "lean_int32_of_nat"]
-def Int32.ofNat (n : @& Nat) : Int32 := ⟨⟨BitVec.ofNat 32 n⟩⟩
-abbrev Int.toInt32 := Int32.ofInt
-abbrev Nat.toInt32 := Int32.ofNat
-@[extern "lean_int32_to_int"]
-def Int32.toInt (i : Int32) : Int := i.toBitVec.toInt
-/--
-This function has the same behavior as `Int.toNat` for negative numbers.
-If you want to obtain the 2's complement representation use `toBitVec`.
-/
-@[inline] def Int32.toNat (i : Int32) : Nat := i.toInt.toNat
-@[extern "lean_int32_to_int8"]
-def Int32.toInt8 (a : Int32) : Int8 := ⟨⟨a.toBitVec.signExtend 8⟩⟩
-@[extern "lean_int32_to_int16"]
-def Int32.toInt16 (a : Int32) : Int16 := ⟨⟨a.toBitVec.signExtend 16⟩⟩
-@[extern "lean_int8_to_int32"]
-def Int8.toInt32 (a : Int8) : Int32 := ⟨⟨a.toBitVec.signExtend 32⟩⟩
-@[extern "lean_int16_to_int32"]
-def Int16.toInt32 (a : Int16) : Int32 := ⟨⟨a.toBitVec.signExtend 32⟩⟩
-@[extern "lean_int32_neg"]
-def Int32.neg (i : Int32) : Int32 := ⟨⟨-i.toBitVec⟩⟩
-
-instance : ToString Int32 where
-  toString i := toString i.toInt
-
-instance : OfNat Int32 n := ⟨Int32.ofNat n⟩
-instance : Neg Int32 where
-  neg := Int32.neg
-
-@[extern "lean_int32_add"]
-def Int32.add (a b : Int32) : Int32 := ⟨⟨a.toBitVec + b.toBitVec⟩⟩
-@[extern "lean_int32_sub"]
-def Int32.sub (a b : Int32) : Int32 := ⟨⟨a.toBitVec - b.toBitVec⟩⟩
-@[extern "lean_int32_mul"]
-def Int32.mul (a b : Int32) : Int32 := ⟨⟨a.toBitVec * b.toBitVec⟩⟩
-@[extern "lean_int32_div"]
-def Int32.div (a b : Int32) : Int32 := ⟨⟨BitVec.sdiv a.toBitVec b.toBitVec⟩⟩
-@[extern "lean_int32_mod"]
-def Int32.mod (a b : Int32) : Int32 := ⟨⟨BitVec.srem a.toBitVec b.toBitVec⟩⟩
-@[extern "lean_int32_land"]
-def Int32.land (a b : Int32) : Int32 := ⟨⟨a.toBitVec &&& b.toBitVec⟩⟩
-@[extern "lean_int32_lor"]
-def Int32.lor (a b : Int32) : Int32 := ⟨⟨a.toBitVec ||| b.toBitVec⟩⟩
-@[extern "lean_int32_xor"]
-def Int32.xor (a b : Int32) : Int32 := ⟨⟨a.toBitVec ^^^ b.toBitVec⟩⟩
-@[extern "lean_int32_shift_left"]
-def Int32.shiftLeft (a b : Int32) : Int32 := ⟨⟨a.toBitVec <<< (b.toBitVec.smod 32)⟩⟩
-@[extern "lean_int32_shift_right"]
-def Int32.shiftRight (a b : Int32) : Int32 := ⟨⟨BitVec.sshiftRight' a.toBitVec (b.toBitVec.smod 32)⟩⟩
-@[extern "lean_int32_complement"]
-def Int32.complement (a : Int32) : Int32 := ⟨⟨~~~a.toBitVec⟩⟩
-
-@[extern "lean_int32_dec_eq"]
-def Int32.decEq (a b : Int32) : Decidable (a = b) :=
-  match a, b with
-  | ⟨n⟩, ⟨m⟩ =>
-    if h : n = m then
-      isTrue <| h ▸ rfl
-    else
-      isFalse (fun h' => Int32.noConfusion h' (fun h' => absurd h' h))
-
-def Int32.lt (a b : Int32) : Prop := a.toBitVec.slt b.toBitVec
-def Int32.le (a b : Int32) : Prop := a.toBitVec.sle b.toBitVec
-
-instance : Inhabited Int32 where
-  default := 0
-
-instance : Add Int32         := ⟨Int32.add⟩
-instance : Sub Int32         := ⟨Int32.sub⟩
-instance : Mul Int32         := ⟨Int32.mul⟩
-instance : Mod Int32         := ⟨Int32.mod⟩
-instance : Div Int32         := ⟨Int32.div⟩
-instance : LT Int32          := ⟨Int32.lt⟩
-instance : LE Int32          := ⟨Int32.le⟩
-instance : Complement Int32  := ⟨Int32.complement⟩
-instance : AndOp Int32       := ⟨Int32.land⟩
-instance : OrOp Int32        := ⟨Int32.lor⟩
-instance : Xor Int32         := ⟨Int32.xor⟩
-instance : ShiftLeft Int32   := ⟨Int32.shiftLeft⟩
-instance : ShiftRight Int32  := ⟨Int32.shiftRight⟩
-instance : DecidableEq Int32 := Int32.decEq
-
-@[extern "lean_bool_to_int32"]
-def Bool.toInt32 (b : Bool) : Int32 := if b then 1 else 0
-
-@[extern "lean_int32_dec_lt"]
-def Int32.decLt (a b : Int32) : Decidable (a < b) :=
-  inferInstanceAs (Decidable (a.toBitVec.slt b.toBitVec))
-
-@[extern "lean_int32_dec_le"]
-def Int32.decLe (a b : Int32) : Decidable (a ≤ b) :=
-  inferInstanceAs (Decidable (a.toBitVec.sle b.toBitVec))
-
-instance (a b : Int32) : Decidable (a < b) := Int32.decLt a b
-instance (a b : Int32) : Decidable (a ≤ b) := Int32.decLe a b
-instance : Max Int32 := maxOfLe
-instance : Min Int32 := minOfLe
-
-/-- The size of type `Int64`, that is, `2^64 = 18446744073709551616`. -/
-abbrev Int64.size : Nat := 18446744073709551616
-
-/--
-Obtain the `BitVec` that contains the 2's complement representation of the `Int64`.
-/
-@[inline] def Int64.toBitVec (x : Int64) : BitVec 64 := x.toUInt64.toBitVec
-
-@[extern "lean_int64_of_int"]
-def Int64.ofInt (i : @& Int) : Int64 := ⟨⟨BitVec.ofInt 64 i⟩⟩
-@[extern "lean_int64_of_nat"]
-def Int64.ofNat (n : @& Nat) : Int64 := ⟨⟨BitVec.ofNat 64 n⟩⟩
-abbrev Int.toInt64 := Int64.ofInt
-abbrev Nat.toInt64 := Int64.ofNat
-@[extern "lean_int64_to_int_sint"]
-def Int64.toInt (i : Int64) : Int := i.toBitVec.toInt
-/--
-This function has the same behavior as `Int.toNat` for negative numbers.
-If you want to obtain the 2's complement representation use `toBitVec`.
-/
-@[inline] def Int64.toNat (i : Int64) : Nat := i.toInt.toNat
-@[extern "lean_int64_to_int8"]
-def Int64.toInt8 (a : Int64) : Int8 := ⟨⟨a.toBitVec.signExtend 8⟩⟩
-@[extern "lean_int64_to_int16"]
-def Int64.toInt16 (a : Int64) : Int16 := ⟨⟨a.toBitVec.signExtend 16⟩⟩
-@[extern "lean_int64_to_int32"]
-def Int64.toInt32 (a : Int64) : Int32 := ⟨⟨a.toBitVec.signExtend 32⟩⟩
-@[extern "lean_int8_to_int64"]
-def Int8.toInt64 (a : Int8) : Int64 := ⟨⟨a.toBitVec.signExtend 64⟩⟩
-@[extern "lean_int16_to_int64"]
-def Int16.toInt64 (a : Int16) : Int64 := ⟨⟨a.toBitVec.signExtend 64⟩⟩
-@[extern "lean_int32_to_int64"]
-def Int32.toInt64 (a : Int32) : Int64 := ⟨⟨a.toBitVec.signExtend 64⟩⟩
-@[extern "lean_int64_neg"]
-def Int64.neg (i : Int64) : Int64 := ⟨⟨-i.toBitVec⟩⟩
-
-instance : ToString Int64 where
-  toString i := toString i.toInt
-
-instance : OfNat Int64 n := ⟨Int64.ofNat n⟩
-instance : Neg Int64 where
-  neg := Int64.neg
-
-@[extern "lean_int64_add"]
-def Int64.add (a b : Int64) : Int64 := ⟨⟨a.toBitVec + b.toBitVec⟩⟩
-@[extern "lean_int64_sub"]
-def Int64.sub (a b : Int64) : Int64 := ⟨⟨a.toBitVec - b.toBitVec⟩⟩
-@[extern "lean_int64_mul"]
-def Int64.mul (a b : Int64) : Int64 := ⟨⟨a.toBitVec * b.toBitVec⟩⟩
-@[extern "lean_int64_div"]
-def Int64.div (a b : Int64) : Int64 := ⟨⟨BitVec.sdiv a.toBitVec b.toBitVec⟩⟩
-@[extern "lean_int64_mod"]
-def Int64.mod (a b : Int64) : Int64 := ⟨⟨BitVec.srem a.toBitVec b.toBitVec⟩⟩
-@[extern "lean_int64_land"]
-def Int64.land (a b : Int64) : Int64 := ⟨⟨a.toBitVec &&& b.toBitVec⟩⟩
-@[extern "lean_int64_lor"]
-def Int64.lor (a b : Int64) : Int64 := ⟨⟨a.toBitVec ||| b.toBitVec⟩⟩
-@[extern "lean_int64_xor"]
-def Int64.xor (a b : Int64) : Int64 := ⟨⟨a.toBitVec ^^^ b.toBitVec⟩⟩
-@[extern "lean_int64_shift_left"]
-def Int64.shiftLeft (a b : Int64) : Int64 := ⟨⟨a.toBitVec <<< (b.toBitVec.smod 64)⟩⟩
-@[extern "lean_int64_shift_right"]
-def Int64.shiftRight (a b : Int64) : Int64 := ⟨⟨BitVec.sshiftRight' a.toBitVec (b.toBitVec.smod 64)⟩⟩
-@[extern "lean_int64_complement"]
-def Int64.complement (a : Int64) : Int64 := ⟨⟨~~~a.toBitVec⟩⟩
-
-@[extern "lean_int64_dec_eq"]
-def Int64.decEq (a b : Int64) : Decidable (a = b) :=
-  match a, b with
-  | ⟨n⟩, ⟨m⟩ =>
-    if h : n = m then
-      isTrue <| h ▸ rfl
-    else
-      isFalse (fun h' => Int64.noConfusion h' (fun h' => absurd h' h))
-
-def Int64.lt (a b : Int64) : Prop := a.toBitVec.slt b.toBitVec
-def Int64.le (a b : Int64) : Prop := a.toBitVec.sle b.toBitVec
-
-instance : Inhabited Int64 where
-  default := 0
-
-instance : Add Int64         := ⟨Int64.add⟩
-instance : Sub Int64         := ⟨Int64.sub⟩
-instance : Mul Int64         := ⟨Int64.mul⟩
-instance : Mod Int64         := ⟨Int64.mod⟩
-instance : Div Int64         := ⟨Int64.div⟩
-instance : LT Int64          := ⟨Int64.lt⟩
-instance : LE Int64          := ⟨Int64.le⟩
-instance : Complement Int64  := ⟨Int64.complement⟩
-instance : AndOp Int64       := ⟨Int64.land⟩
-instance : OrOp Int64        := ⟨Int64.lor⟩
-instance : Xor Int64         := ⟨Int64.xor⟩
-instance : ShiftLeft Int64   := ⟨Int64.shiftLeft⟩
-instance : ShiftRight Int64  := ⟨Int64.shiftRight⟩
-instance : DecidableEq Int64 := Int64.decEq
-
-@[extern "lean_bool_to_int64"]
-def Bool.toInt64 (b : Bool) : Int64 := if b then 1 else 0
-
-@[extern "lean_int64_dec_lt"]
-def Int64.decLt (a b : Int64) : Decidable (a < b) :=
-  inferInstanceAs (Decidable (a.toBitVec.slt b.toBitVec))
-
-@[extern "lean_int64_dec_le"]
-def Int64.decLe (a b : Int64) : Decidable (a ≤ b) :=
-  inferInstanceAs (Decidable (a.toBitVec.sle b.toBitVec))
-
-instance (a b : Int64) : Decidable (a < b) := Int64.decLt a b
-instance (a b : Int64) : Decidable (a ≤ b) := Int64.decLe a b
-instance : Max Int64 := maxOfLe
-instance : Min Int64 := minOfLe
-
-/-- The size of type `ISize`, that is, `2^System.Platform.numBits`. -/
-abbrev ISize.size : Nat := 2^System.Platform.numBits
-
-/--
-Obtain the `BitVec` that contains the 2's complement representation of the `ISize`.
-/
-@[inline] def ISize.toBitVec (x : ISize) : BitVec System.Platform.numBits := x.toUSize.toBitVec
-
-@[extern "lean_isize_of_int"]
-def ISize.ofInt (i : @& Int) : ISize := ⟨⟨BitVec.ofInt System.Platform.numBits i⟩⟩
-@[extern "lean_isize_of_nat"]
-def ISize.ofNat (n : @& Nat) : ISize := ⟨⟨BitVec.ofNat System.Platform.numBits n⟩⟩
-abbrev Int.toISize := ISize.ofInt
-abbrev Nat.toISize := ISize.ofNat
-@[extern "lean_isize_to_int"]
-def ISize.toInt (i : ISize) : Int := i.toBitVec.toInt
-/--
-This function has the same behavior as `Int.toNat` for negative numbers.
-If you want to obtain the 2's complement representation use `toBitVec`.
-/
-@[inline] def ISize.toNat (i : ISize) : Nat := i.toInt.toNat
-@[extern "lean_isize_to_int32"]
-def ISize.toInt32 (a : ISize) : Int32 := ⟨⟨a.toBitVec.signExtend 32⟩⟩
-/--
-Upcast `ISize` to `Int64`. This function is losless as `ISize` is either `Int32` or `Int64`.
-/
-@[extern "lean_isize_to_int64"]
-def ISize.toInt64 (a : ISize) : Int64 := ⟨⟨a.toBitVec.signExtend 64⟩⟩
-/--
-Upcast `Int32` to `ISize`. This function is losless as `ISize` is either `Int32` or `Int64`.
-/
-@[extern "lean_int32_to_isize"]
-def Int32.toISize (a : Int32) : ISize := ⟨⟨a.toBitVec.signExtend System.Platform.numBits⟩⟩
-@[extern "lean_int64_to_isize"]
-def Int64.toISize (a : Int64) : ISize := ⟨⟨a.toBitVec.signExtend System.Platform.numBits⟩⟩
-@[extern "lean_isize_neg"]
-def ISize.neg (i : ISize) : ISize := ⟨⟨-i.toBitVec⟩⟩
-
-instance : ToString ISize where
-  toString i := toString i.toInt
-
-instance : OfNat ISize n := ⟨ISize.ofNat n⟩
-instance : Neg ISize where
-  neg := ISize.neg
-
-@[extern "lean_isize_add"]
-def ISize.add (a b : ISize) : ISize := ⟨⟨a.toBitVec + b.toBitVec⟩⟩
-@[extern "lean_isize_sub"]
-def ISize.sub (a b : ISize) : ISize := ⟨⟨a.toBitVec - b.toBitVec⟩⟩
-@[extern "lean_isize_mul"]
-def ISize.mul (a b : ISize) : ISize := ⟨⟨a.toBitVec * b.toBitVec⟩⟩
-@[extern "lean_isize_div"]
-def ISize.div (a b : ISize) : ISize := ⟨⟨BitVec.sdiv a.toBitVec b.toBitVec⟩⟩
-@[extern "lean_isize_mod"]
-def ISize.mod (a b : ISize) : ISize := ⟨⟨BitVec.srem a.toBitVec b.toBitVec⟩⟩
-@[extern "lean_isize_land"]
-def ISize.land (a b : ISize) : ISize := ⟨⟨a.toBitVec &&& b.toBitVec⟩⟩
-@[extern "lean_isize_lor"]
-def ISize.lor (a b : ISize) : ISize := ⟨⟨a.toBitVec ||| b.toBitVec⟩⟩
-@[extern "lean_isize_xor"]
-def ISize.xor (a b : ISize) : ISize := ⟨⟨a.toBitVec ^^^ b.toBitVec⟩⟩
-@[extern "lean_isize_shift_left"]
-def ISize.shiftLeft (a b : ISize) : ISize := ⟨⟨a.toBitVec <<< (b.toBitVec.smod System.Platform.numBits)⟩⟩
-@[extern "lean_isize_shift_right"]
-def ISize.shiftRight (a b : ISize) : ISize := ⟨⟨BitVec.sshiftRight' a.toBitVec (b.toBitVec.smod System.Platform.numBits)⟩⟩
-@[extern "lean_isize_complement"]
-def ISize.complement (a : ISize) : ISize := ⟨⟨~~~a.toBitVec⟩⟩
-
-@[extern "lean_isize_dec_eq"]
-def ISize.decEq (a b : ISize) : Decidable (a = b) :=
-  match a, b with
-  | ⟨n⟩, ⟨m⟩ =>
-    if h : n = m then
-      isTrue <| h ▸ rfl
-    else
-      isFalse (fun h' => ISize.noConfusion h' (fun h' => absurd h' h))
-
-def ISize.lt (a b : ISize) : Prop := a.toBitVec.slt b.toBitVec
-def ISize.le (a b : ISize) : Prop := a.toBitVec.sle b.toBitVec
-
-instance : Inhabited ISize where
-  default := 0
-
-instance : Add ISize         := ⟨ISize.add⟩
-instance : Sub ISize         := ⟨ISize.sub⟩
-instance : Mul ISize         := ⟨ISize.mul⟩
-instance : Mod ISize         := ⟨ISize.mod⟩
-instance : Div ISize         := ⟨ISize.div⟩
-instance : LT ISize          := ⟨ISize.lt⟩
-instance : LE ISize          := ⟨ISize.le⟩
-instance : Complement ISize  := ⟨ISize.complement⟩
-instance : AndOp ISize       := ⟨ISize.land⟩
-instance : OrOp ISize        := ⟨ISize.lor⟩
-instance : Xor ISize         := ⟨ISize.xor⟩
-instance : ShiftLeft ISize   := ⟨ISize.shiftLeft⟩
-instance : ShiftRight ISize  := ⟨ISize.shiftRight⟩
-instance : DecidableEq ISize := ISize.decEq
-
-@[extern "lean_bool_to_isize"]
-def Bool.toISize (b : Bool) : ISize := if b then 1 else 0
-
-@[extern "lean_isize_dec_lt"]
-def ISize.decLt (a b : ISize) : Decidable (a < b) :=
-  inferInstanceAs (Decidable (a.toBitVec.slt b.toBitVec))
-
-@[extern "lean_isize_dec_le"]
-def ISize.decLe (a b : ISize) : Decidable (a ≤ b) :=
-  inferInstanceAs (Decidable (a.toBitVec.sle b.toBitVec))
-
-instance (a b : ISize) : Decidable (a < b) := ISize.decLt a b
-instance (a b : ISize) : Decidable (a ≤ b) := ISize.decLe a b
-instance : Max ISize := maxOfLe
-instance : Min ISize := minOfLe
--- a/src/Init/Data/Stream.lean
+++ b/src/Init/Data/Stream.lean
@@ -94,7 +94,7 @@ instance : Stream (Subarray α) α where
  next? s :=
    if h : s.start < s.stop then
      have : s.start + 1 ≤ s.stop := Nat.succ_le_of_lt h
-      some (s.array[s.start]'(Nat.lt_of_lt_of_le h s.stop_le_array_size),
+      some (s.array.get ⟨s.start, Nat.lt_of_lt_of_le h s.stop_le_array_size⟩,
        { s with start := s.start + 1, start_le_stop := this })
    else
      none
--- a/Show More
+++ b/Show More
Author	SHA1	Message	Date
Kim Morrison	737a82fc30	chore: basic functionality tests for modify/alter	2024-10-31 10:41:46 +11:00
Kim Morrison	2a85401689	feat: interim implementation of HashMap.modify/alter	2024-10-30 12:05:28 +11:00