cleanup test

Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>

.github/workflows/pr-release.yml

@@ -164,10 +164,10 @@ jobs:
 
             # Use GitHub API to check if a comment already exists
             existing_comment="$(curl --retry 3 --location --silent \
-                                    -H "Authorization: token ${{ secrets.MATHLIB4_BOT }}" \
+                                    -H "Authorization: token ${{ secrets.MATHLIB4_COMMENT_BOT }}" \
                                     -H "Accept: application/vnd.github.v3+json" \
                                     "https://api.github.com/repos/leanprover/lean4/issues/${{ steps.workflow-info.outputs.pullRequestNumber }}/comments" \
-                                    | jq 'first(.[] | select(.body | test("^- . Mathlib") or startswith("Mathlib CI status")) | select(.user.login == "leanprover-community-mathlib4-bot"))')"
+                                    | jq 'first(.[] | select(.body | test("^- . Mathlib") or startswith("Mathlib CI status")) | select(.user.login == "leanprover-community-bot"))')"
             existing_comment_id="$(echo "$existing_comment" | jq -r .id)"
             existing_comment_body="$(echo "$existing_comment" | jq -r .body)"
 
@@ -177,14 +177,14 @@ jobs:
               echo "Posting message to the comments: $MESSAGE"
 
               # Append new result to the existing comment or post a new comment
-              # It's essential we use the MATHLIB4_BOT token here, so that Mathlib CI can subsequently edit the comment.
+              # It's essential we use the MATHLIB4_COMMENT_BOT token here, so that Mathlib CI can subsequently edit the comment.
               if [ -z "$existing_comment_id" ]; then
                 INTRO="Mathlib CI status ([docs](https://leanprover-community.github.io/contribute/tags_and_branches.html)):"
                 # Post new comment with a bullet point
                 echo "Posting as new comment at leanprover/lean4/issues/${{ steps.workflow-info.outputs.pullRequestNumber }}/comments"
                 curl -L -s \
                   -X POST \
-                  -H "Authorization: token ${{ secrets.MATHLIB4_BOT }}" \
+                  -H "Authorization: token ${{ secrets.MATHLIB4_COMMENT_BOT }}" \
                   -H "Accept: application/vnd.github.v3+json" \
                   -d "$(jq --null-input --arg intro "$INTRO" --arg val "$MESSAGE" '{"body":($intro + "\n" + $val)}')" \
                   "https://api.github.com/repos/leanprover/lean4/issues/${{ steps.workflow-info.outputs.pullRequestNumber }}/comments"
@@ -193,7 +193,7 @@ jobs:
                 echo "Appending to existing comment at leanprover/lean4/issues/${{ steps.workflow-info.outputs.pullRequestNumber }}/comments"
                 curl -L -s \
                   -X PATCH \
-                  -H "Authorization: token ${{ secrets.MATHLIB4_BOT }}" \
+                  -H "Authorization: token ${{ secrets.MATHLIB4_COMMENT_BOT }}" \
                   -H "Accept: application/vnd.github.v3+json" \
                   -d "$(jq --null-input --arg existing "$existing_comment_body" --arg message "$MESSAGE" '{"body":($existing + "\n" + $message)}')" \
                   "https://api.github.com/repos/leanprover/lean4/issues/comments/$existing_comment_id"
@@ -340,6 +340,7 @@ jobs:
             # (This should no longer be possible once `nightly-testing-YYYY-MM-DD` is a tag, but it is still safe to merge.)
             git merge "$BASE" --strategy-option ours --no-commit --allow-unrelated-histories
             lake update batteries
+            get add lake-manifest.json
             git commit --allow-empty -m "Trigger CI for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
           fi
 

RELEASES.md

@@ -10,7 +10,317 @@ of each version.
 
 v4.12.0
 ----------
-Development in progress.
+
+### Language features, tactics, and metaprograms
+
+* `bv_decide` tactic. This release introduces a new tactic for proving goals involving `BitVec` and `Bool`. It reduces the goal to a SAT instance that is refuted by an external solver, and the resulting LRAT proof is checked in Lean. This is used to synthesize a proof of the goal by reflection. As this process uses verified algorithms, proofs generated by this tactic use `Lean.ofReduceBool`, so this tactic includes the Lean compiler as part of the trusted code base. The external solver CaDiCaL is included with Lean and does not need to be installed separately to make use of `bv_decide`.
+
+  For example, we can use `bv_decide` to verify that a bit twiddling formula leaves at most one bit set:
+  ```lean
+  def popcount (x : BitVec 64) : BitVec 64 :=
+    let rec go (x pop : BitVec 64) : Nat → BitVec 64
+      | 0 => pop
+      | n + 1 => go (x >>> 2) (pop + (x &&& 1)) n
+    go x 0 64
+
+  example (x : BitVec 64) : popcount ((x &&& (x - 1)) ^^^ x) ≤ 1 := by
+    simp only [popcount, popcount.go]
+    bv_decide
+  ```
+  When the external solver fails to refute the SAT instance generated by `bv_decide`, it can report a counterexample:
+  ```lean
+  /--
+  error: The prover found a counterexample, consider the following assignment:
+  x = 0xffffffffffffffff#64
+  -/
+  #guard_msgs in
+  example (x : BitVec 64) : x < x + 1 := by
+    bv_decide
+  ```
+
+  See `Lean.Elab.Tactic.BVDecide` for a more detailed overview, and look in `tests/lean/run/bv_*` for examples.
+
+  [#5013](https://github.com/leanprover/lean4/pull/5013), [#5074](https://github.com/leanprover/lean4/pull/5074), [#5100](https://github.com/leanprover/lean4/pull/5100), [#5113](https://github.com/leanprover/lean4/pull/5113), [#5137](https://github.com/leanprover/lean4/pull/5137), [#5203](https://github.com/leanprover/lean4/pull/5203), [#5212](https://github.com/leanprover/lean4/pull/5212), [#5220](https://github.com/leanprover/lean4/pull/5220).
+
+* `simp` tactic
+  * [#4988](https://github.com/leanprover/lean4/pull/4988) fixes a panic in the `reducePow` simproc.
+  * [#5071](https://github.com/leanprover/lean4/pull/5071) exposes the `index` option to the `dsimp` tactic, introduced to `simp` in [#4202](https://github.com/leanprover/lean4/pull/4202).
+  * [#5159](https://github.com/leanprover/lean4/pull/5159) fixes a panic at `Fin.isValue` simproc.
+  * [#5167](https://github.com/leanprover/lean4/pull/5167) and [#5175](https://github.com/leanprover/lean4/pull/5175) rename the `simpCtorEq` simproc to `reduceCtorEq` and makes it optional. (See breaking changes.)
+  * [#5187](https://github.com/leanprover/lean4/pull/5187) ensures `reduceCtorEq` is enabled in the `norm_cast` tactic.
+  * [#5073](https://github.com/leanprover/lean4/pull/5073) modifies the simp debug trace messages to tag with "dpre" and "dpost" instead of "pre" and "post" when in definitional rewrite mode. [#5054](https://github.com/leanprover/lean4/pull/5054) explains the `reduce` steps for `trace.Debug.Meta.Tactic.simp` trace messages.
+* `ext` tactic
+  * [#4996](https://github.com/leanprover/lean4/pull/4996) reduces default maximum iteration depth from 1000000 to 100.
+* `induction` tactic
+  * [#5117](https://github.com/leanprover/lean4/pull/5117) fixes a bug where `let` bindings in minor premises wouldn't be counted correctly.
+
+* `omega` tactic
+  * [#5157](https://github.com/leanprover/lean4/pull/5157) fixes a panic.
+
+* `conv` tactic
+  * [#5149](https://github.com/leanprover/lean4/pull/5149) improves `arg n` to handle subsingleton instance arguments.
+
+* [#5044](https://github.com/leanprover/lean4/pull/5044) upstreams the `#time` command.
+* [#5079](https://github.com/leanprover/lean4/pull/5079) makes `#check` and `#reduce` typecheck the elaborated terms.
+
+* **Incrementality**
+  * [#4974](https://github.com/leanprover/lean4/pull/4974) fixes regression where we would not interrupt elaboration of previous document versions.
+  * [#5004](https://github.com/leanprover/lean4/pull/5004) fixes a performance regression.
+  * [#5001](https://github.com/leanprover/lean4/pull/5001) disables incremental body elaboration in presence of `where` clauses in declarations.
+  * [#5018](https://github.com/leanprover/lean4/pull/5018) enables infotrees on the command line for ilean generation.
+  * [#5040](https://github.com/leanprover/lean4/pull/5040) and [#5056](https://github.com/leanprover/lean4/pull/5056) improve performance of info trees.
+  * [#5090](https://github.com/leanprover/lean4/pull/5090) disables incrementality in the `case .. | ..` tactic.
+  * [#5312](https://github.com/leanprover/lean4/pull/5312) fixes a bug where changing whitespace after the module header could break subsequent commands.
+
+* **Definitions**
+  * [#5016](https://github.com/leanprover/lean4/pull/5016) and [#5066](https://github.com/leanprover/lean4/pull/5066) add `clean_wf` tactic to clean up tactic state in `decreasing_by`. This can be disabled with `set_option debug.rawDecreasingByGoal false`.
+  * [#5055](https://github.com/leanprover/lean4/pull/5055) unifies equational theorems between structural and well-founded recursion.
+  * [#5041](https://github.com/leanprover/lean4/pull/5041) allows mutually recursive functions to use different parameter names among the “fixed parameter prefix”
+  * [#4154](https://github.com/leanprover/lean4/pull/4154) and [#5109](https://github.com/leanprover/lean4/pull/5109) add fine-grained equational lemmas for non-recursive functions. See breaking changes.
+  * [#5129](https://github.com/leanprover/lean4/pull/5129) unifies equation lemmas for recursive and non-recursive definitions. The `backward.eqns.deepRecursiveSplit` option can be set to `false` to get the old behavior. See breaking changes.
+  * [#5141](https://github.com/leanprover/lean4/pull/5141) adds `f.eq_unfold` lemmas. Now Lean produces the following zoo of rewrite rules:
+    ```
+    Option.map.eq_1      : Option.map f none = none
+    Option.map.eq_2      : Option.map f (some x) = some (f x)
+    Option.map.eq_def    : Option.map f p = match o with | none => none | (some x) => some (f x)
+    Option.map.eq_unfold : Option.map = fun f p => match o with | none => none | (some x) => some (f x)
+    ```
+    The `f.eq_unfold` variant is especially useful to rewrite with `rw` under binders.
+  * [#5136](https://github.com/leanprover/lean4/pull/5136) fixes bugs in recursion over predicates.
+
+* **Variable inclusion**
+  * [#5206](https://github.com/leanprover/lean4/pull/5206) documents that `include` currently only applies to theorems.
+
+* **Elaboration**
+  * [#4926](https://github.com/leanprover/lean4/pull/4926) fixes a bug where autoparam errors were associated to an incorrect source position.
+  * [#4833](https://github.com/leanprover/lean4/pull/4833) fixes an issue where cdot anonymous functions (e.g. `(· + ·)`) would not handle ambiguous notation correctly. Numbers the parameters, making this example expand as `fun x1 x2 => x1 + x2` rather than `fun x x_1 => x + x_1`.
+  * [#5037](https://github.com/leanprover/lean4/pull/5037) improves strength of the tactic that proves array indexing is in bounds.
+  * [#5119](https://github.com/leanprover/lean4/pull/5119) fixes a bug in the tactic that proves indexing is in bounds where it could loop in the presence of mvars.
+  * [#5072](https://github.com/leanprover/lean4/pull/5072) makes the structure type clickable in "not a field of structure" errors for structure instance notation.
+  * [#4717](https://github.com/leanprover/lean4/pull/4717) fixes a bug where mutual `inductive` commands could create terms that the kernel rejects.
+  * [#5142](https://github.com/leanprover/lean4/pull/5142) fixes a bug where `variable` could fail when mixing binder updates and declarations.
+
+* **Other fixes or improvements**
+  * [#5118](https://github.com/leanprover/lean4/pull/5118) changes the definition of the `syntheticHole` parser so that hovering over `_` in `?_` gives the docstring for synthetic holes.
+  * [#5173](https://github.com/leanprover/lean4/pull/5173) uses the emoji variant selector for ✅️,❌️,💥️ in messages, improving fonts selection.
+  * [#5183](https://github.com/leanprover/lean4/pull/5183) fixes a bug in `rename_i` where implementation detail hypotheses could be renamed.
+
+### Language server, widgets, and IDE extensions
+
+* [#4821](https://github.com/leanprover/lean4/pull/4821) resolves two language server bugs that especially affect Windows users. (1) Editing the header could result in the watchdog not correctly restarting the file worker, which would lead to the file seemingly being processed forever. (2) On an especially slow Windows machine, we found that starting the language server would sometimes not succeed at all. This PR also resolves an issue where we would not correctly emit messages that we received while the file worker is being restarted to the corresponding file worker after the restart.
+* [#5006](https://github.com/leanprover/lean4/pull/5006) updates the user widget manual.
+* [#5193](https://github.com/leanprover/lean4/pull/5193) updates the quickstart guide with the new display name for the Lean 4 extension ("Lean 4").
+* [#5185](https://github.com/leanprover/lean4/pull/5185) fixes a bug where over time "import out of date" messages would accumulate.
+* [#4900](https://github.com/leanprover/lean4/pull/4900) improves ilean loading performance by about a factor of two. Optimizes the JSON parser and the conversion from JSON to Lean data structures; see PR description for details.
+* **Other fixes or improvements**
+  * [#5031](https://github.com/leanprover/lean4/pull/5031) localizes an instance in `Lsp.Diagnostics`.
+
+### Pretty printing
+
+* [#4976](https://github.com/leanprover/lean4/pull/4976) introduces `@[app_delab]`, a macro for creating delaborators for particular constants. The `@[app_delab ident]` syntax resolves `ident` to its constant name `name` and then expands to `@[delab app.name]`.
+* [#4982](https://github.com/leanprover/lean4/pull/4982) fixes a bug where the pretty printer assumed structure projections were type correct (such terms can appear in type mismatch errors). Improves hoverability of `#print` output for structures.
+* [#5218](https://github.com/leanprover/lean4/pull/5218) and [#5239](https://github.com/leanprover/lean4/pull/5239) add `pp.exprSizes` debugging option. When true, each pretty printed expression is prefixed with `[size a/b/c]`, where `a` is the size without sharing, `b` is the actual size, and `c` is the size with the maximum possible sharing.
+
+### Library
+
+* [#5020](https://github.com/leanprover/lean4/pull/5020) swaps the parameters to `Membership.mem`. A purpose of this change is to make set-like `CoeSort` coercions to refer to the eta-expanded function `fun x => Membership.mem s x`, which can reduce in many computations. Another is that having the `s` argument first leads to better discrimination tree keys. (See breaking changes.)
+* `Array`
+  * [#4970](https://github.com/leanprover/lean4/pull/4970) adds `@[ext]` attribute to `Array.ext`.
+  * [#4957](https://github.com/leanprover/lean4/pull/4957) deprecates `Array.get_modify`.
+* `List`
+  * [#4995](https://github.com/leanprover/lean4/pull/4995) upstreams `List.findIdx` lemmas.
+  * [#5029](https://github.com/leanprover/lean4/pull/5029), [#5048](https://github.com/leanprover/lean4/pull/5048) and [#5132](https://github.com/leanprover/lean4/pull/5132) add `List.Sublist` lemmas, some upstreamed. [#5077](https://github.com/leanprover/lean4/pull/5077) fixes implicitness in refl/rfl lemma binders.  add `List.Sublist` theorems.
+  * [#5047](https://github.com/leanprover/lean4/pull/5047) upstreams `List.Pairwise` lemmas.
+  * [#5053](https://github.com/leanprover/lean4/pull/5053), [#5124](https://github.com/leanprover/lean4/pull/5124), and [#5161](https://github.com/leanprover/lean4/pull/5161) add `List.find?/findSome?/findIdx?` theorems.
+  * [#5039](https://github.com/leanprover/lean4/pull/5039) adds `List.foldlRecOn` and `List.foldrRecOn` recursion principles to prove things about `List.foldl` and `List.foldr`.
+  * [#5069](https://github.com/leanprover/lean4/pull/5069) upstreams `List.Perm`.
+  * [#5092](https://github.com/leanprover/lean4/pull/5092) and [#5107](https://github.com/leanprover/lean4/pull/5107) add `List.mergeSort` and a fast `@[csimp]` implementation.
+  * [#5103](https://github.com/leanprover/lean4/pull/5103) makes the simp lemmas for `List.subset` more aggressive.
+  * [#5106](https://github.com/leanprover/lean4/pull/5106) changes the statement of `List.getLast?_cons`.
+  * [#5123](https://github.com/leanprover/lean4/pull/5123) and [#5158](https://github.com/leanprover/lean4/pull/5158) add `List.range` and `List.iota` lemmas.
+  * [#5130](https://github.com/leanprover/lean4/pull/5130) adds `List.join` lemmas.
+  * [#5131](https://github.com/leanprover/lean4/pull/5131) adds `List.append` lemmas.
+  * [#5152](https://github.com/leanprover/lean4/pull/5152) adds `List.erase(|P|Idx)` lemmas.
+  * [#5127](https://github.com/leanprover/lean4/pull/5127) makes miscellaneous lemma updates.
+  * [#5153](https://github.com/leanprover/lean4/pull/5153) and [#5160](https://github.com/leanprover/lean4/pull/5160) add lemmas about `List.attach` and `List.pmap`.
+  * [#5164](https://github.com/leanprover/lean4/pull/5164), [#5177](https://github.com/leanprover/lean4/pull/5177), and [#5215](https://github.com/leanprover/lean4/pull/5215) add `List.find?` and `List.range'/range/iota` lemmas.
+  * [#5196](https://github.com/leanprover/lean4/pull/5196) adds `List.Pairwise_erase` and related lemmas.
+  * [#5151](https://github.com/leanprover/lean4/pull/5151) and [#5163](https://github.com/leanprover/lean4/pull/5163) improve confluence of `List` simp lemmas. [#5105](https://github.com/leanprover/lean4/pull/5105) and [#5102](https://github.com/leanprover/lean4/pull/5102) adjust `List` simp lemmas.
+  * [#5178](https://github.com/leanprover/lean4/pull/5178) removes `List.getLast_eq_iff_getLast_eq_some` as a simp lemma.
+  * [#5210](https://github.com/leanprover/lean4/pull/5210) reverses the meaning of `List.getElem_drop` and `List.getElem_drop'`.
+  * [#5214](https://github.com/leanprover/lean4/pull/5214) moves `@[csimp]` lemmas earlier where possible.
+* `Nat` and `Int`
+  * [#5104](https://github.com/leanprover/lean4/pull/5104) adds `Nat.add_left_eq_self` and relatives.
+  * [#5146](https://github.com/leanprover/lean4/pull/5146) adds missing `Nat.and_xor_distrib_(left|right)`.
+  * [#5148](https://github.com/leanprover/lean4/pull/5148) and [#5190](https://github.com/leanprover/lean4/pull/5190) improve `Nat` and `Int` simp lemma confluence.
+  * [#5165](https://github.com/leanprover/lean4/pull/5165) adjusts `Int` simp lemmas.
+  * [#5166](https://github.com/leanprover/lean4/pull/5166) adds `Int` lemmas relating `neg` and `emod`/`mod`.
+  * [#5208](https://github.com/leanprover/lean4/pull/5208) reverses the direction of the `Int.toNat_sub` simp lemma.
+  * [#5209](https://github.com/leanprover/lean4/pull/5209) adds `Nat.bitwise` lemmas.
+  * [#5230](https://github.com/leanprover/lean4/pull/5230) corrects the docstrings for integer division and modulus.
+* `Option`
+  * [#5128](https://github.com/leanprover/lean4/pull/5128) and [#5154](https://github.com/leanprover/lean4/pull/5154) add `Option` lemmas.
+* `BitVec`
+  * [#4889](https://github.com/leanprover/lean4/pull/4889) adds `sshiftRight` bitblasting.
+  * [#4981](https://github.com/leanprover/lean4/pull/4981) adds `Std.Associative` and `Std.Commutative` instances for `BitVec.[and|or|xor]`.
+  * [#4913](https://github.com/leanprover/lean4/pull/4913) enables `missingDocs` error for `BitVec` modules.
+  * [#4930](https://github.com/leanprover/lean4/pull/4930) makes parameter names for `BitVec` more consistent.
+  * [#5098](https://github.com/leanprover/lean4/pull/5098) adds `BitVec.intMin`. Introduces `boolToPropSimps` simp set for converting from boolean to propositional expressions.
+  * [#5200](https://github.com/leanprover/lean4/pull/5200) and [#5217](https://github.com/leanprover/lean4/pull/5217) rename `BitVec.getLsb` to `BitVec.getLsbD`, etc., to bring naming in line with `List`/`Array`/etc.
+  * **Theorems:** [#4977](https://github.com/leanprover/lean4/pull/4977), [#4951](https://github.com/leanprover/lean4/pull/4951), [#4667](https://github.com/leanprover/lean4/pull/4667), [#5007](https://github.com/leanprover/lean4/pull/5007), [#4997](https://github.com/leanprover/lean4/pull/4997), [#5083](https://github.com/leanprover/lean4/pull/5083), [#5081](https://github.com/leanprover/lean4/pull/5081), [#4392](https://github.com/leanprover/lean4/pull/4392)
+* `UInt`
+  * [#4514](https://github.com/leanprover/lean4/pull/4514) fixes naming convention for `UInt` lemmas.
+* `Std.HashMap` and `Std.HashSet`
+  * [#4943](https://github.com/leanprover/lean4/pull/4943) deprecates variants of hash map query methods. (See breaking changes.)
+  * [#4917](https://github.com/leanprover/lean4/pull/4917) switches the library and Lean to `Std.HashMap` and `Std.HashSet` almost everywhere.
+  * [#4954](https://github.com/leanprover/lean4/pull/4954) deprecates `Lean.HashMap` and `Lean.HashSet`.
+  * [#5023](https://github.com/leanprover/lean4/pull/5023) cleans up lemma parameters.
+
+* `Std.Sat` (for `bv_decide`)
+  * [#4933](https://github.com/leanprover/lean4/pull/4933) adds definitions of SAT and CNF.
+  * [#4953](https://github.com/leanprover/lean4/pull/4953) defines "and-inverter graphs" (AIGs) as described in section 3 of [Davis-Swords 2013](https://arxiv.org/pdf/1304.7861.pdf).
+
+* **Parsec**
+  * [#4774](https://github.com/leanprover/lean4/pull/4774) generalizes the `Parsec` library, allowing parsing of iterable data beyong `String` such as `ByteArray`. (See breaking changes.)
+  * [#5115](https://github.com/leanprover/lean4/pull/5115) moves `Lean.Data.Parsec` to `Std.Internal.Parsec` for bootstrappng reasons.
+
+* `Thunk`
+  * [#4969](https://github.com/leanprover/lean4/pull/4969) upstreams `Thunk.ext`.
+
+* **IO**
+  * [#4973](https://github.com/leanprover/lean4/pull/4973) modifies `IO.FS.lines` to handle `\r\n` on all operating systems instead of just on Windows.
+  * [#5125](https://github.com/leanprover/lean4/pull/5125) adds `createTempFile` and `withTempFile` for creating temporary files that can only be read and written by the current user.
+
+* **Other fixes or improvements**
+  * [#4945](https://github.com/leanprover/lean4/pull/4945) adds `Array`, `Bool` and `Prod` utilities from LeanSAT.
+  * [#4960](https://github.com/leanprover/lean4/pull/4960) adds `Relation.TransGen.trans`.
+  * [#5012](https://github.com/leanprover/lean4/pull/5012) states `WellFoundedRelation Nat` using `<`, not `Nat.lt`.
+  * [#5011](https://github.com/leanprover/lean4/pull/5011) uses `≠` instead of `Not (Eq ...)` in `Fin.ne_of_val_ne`.
+  * [#5197](https://github.com/leanprover/lean4/pull/5197) upstreams `Fin.le_antisymm`.
+  * [#5042](https://github.com/leanprover/lean4/pull/5042) reduces usage of `refine'`.
+  * [#5101](https://github.com/leanprover/lean4/pull/5101) adds about `if-then-else` and `Option`.
+  * [#5112](https://github.com/leanprover/lean4/pull/5112) adds basic instances for `ULift` and `PLift`.
+  * [#5133](https://github.com/leanprover/lean4/pull/5133) and [#5168](https://github.com/leanprover/lean4/pull/5168) make fixes from running the simpNF linter over Lean.
+  * [#5156](https://github.com/leanprover/lean4/pull/5156) removes a bad simp lemma in `omega` theory.
+  * [#5155](https://github.com/leanprover/lean4/pull/5155) improves confluence of `Bool` simp lemmas.
+  * [#5162](https://github.com/leanprover/lean4/pull/5162) improves confluence of `Function.comp` simp lemmas.
+  * [#5191](https://github.com/leanprover/lean4/pull/5191) improves confluence of `if-then-else` simp lemmas.
+  * [#5147](https://github.com/leanprover/lean4/pull/5147) adds `@[elab_as_elim]` to `Quot.rec`, `Nat.strongInductionOn` and `Nat.casesStrongInductionOn`, and also renames the latter two to `Nat.strongRecOn` and `Nat.casesStrongRecOn` (deprecated in [#5179](https://github.com/leanprover/lean4/pull/5179)).
+  * [#5180](https://github.com/leanprover/lean4/pull/5180) disables some simp lemmas with bad discrimination tree keys.
+  * [#5189](https://github.com/leanprover/lean4/pull/5189) cleans up internal simp lemmas that had leaked.
+  * [#5198](https://github.com/leanprover/lean4/pull/5198) cleans up `allowUnsafeReducibility`.
+  * [#5229](https://github.com/leanprover/lean4/pull/5229) removes unused lemmas from some `simp` tactics.
+  * [#5199](https://github.com/leanprover/lean4/pull/5199) removes >6 month deprecations.
+
+### Lean internals
+
+* **Performance**
+  * Some core algorithms have been rewritten in C++ for performance.
+    * [#4910](https://github.com/leanprover/lean4/pull/4910) and [#4912](https://github.com/leanprover/lean4/pull/4912) reimplement `instantiateLevelMVars`.
+    * [#4915](https://github.com/leanprover/lean4/pull/4915), [#4922](https://github.com/leanprover/lean4/pull/4922), and [#4931](https://github.com/leanprover/lean4/pull/4931) reimplement `instantiateExprMVars`, 30% faster on a benchmark.
+  * [#4934](https://github.com/leanprover/lean4/pull/4934) has optimizations for the kernel's `Expr` equality test.
+  * [#4990](https://github.com/leanprover/lean4/pull/4990) fixes bug in hashing for the kernel's `Expr` equality test.
+  * [#4935](https://github.com/leanprover/lean4/pull/4935) and [#4936](https://github.com/leanprover/lean4/pull/4936) skip some `PreDefinition` transformations if they are not needed.
+  * [#5225](https://github.com/leanprover/lean4/pull/5225) adds caching for visited exprs at `CheckAssignmentQuick` in `ExprDefEq`.
+  * [#5226](https://github.com/leanprover/lean4/pull/5226) maximizes term sharing at `instantiateMVarDeclMVars`, used by `runTactic`.
+* **Diagnostics and profiling**
+  * [#4923](https://github.com/leanprover/lean4/pull/4923) adds profiling for `instantiateMVars` in `Lean.Elab.MutualDef`, which can be a bottleneck there.
+  * [#4924](https://github.com/leanprover/lean4/pull/4924) adds diagnostics for large theorems, controlled by the `diagnostics.threshold.proofSize` option.
+  * [#4897](https://github.com/leanprover/lean4/pull/4897) improves display of diagnostic results.
+* **Other fixes or improvements**
+  * [#4921](https://github.com/leanprover/lean4/pull/4921) cleans up `Expr.betaRev`.
+  * [#4940](https://github.com/leanprover/lean4/pull/4940) fixes tests by not writing directly to stdout, which is unreliable now that elaboration and reporting are executed in separate threads.
+  * [#4955](https://github.com/leanprover/lean4/pull/4955) documents that `stderrAsMessages` is now the default on the command line as well.
+  * [#4647](https://github.com/leanprover/lean4/pull/4647) adjusts documentation for building on macOS.
+  * [#4987](https://github.com/leanprover/lean4/pull/4987) makes regular mvar assignments take precedence over delayed ones in `instantiateMVars`. Normally delayed assignment metavariables are never directly assigned, but on errors Lean assigns `sorry` to unassigned metavariables.
+  * [#4967](https://github.com/leanprover/lean4/pull/4967) adds linter name to errors when a linter crashes.
+  * [#5043](https://github.com/leanprover/lean4/pull/5043) cleans up command line snapshots logic.
+  * [#5067](https://github.com/leanprover/lean4/pull/5067) minimizes some imports.
+  * [#5068](https://github.com/leanprover/lean4/pull/5068) generalizes the monad for `addMatcherInfo`.
+  * [f71a1f](https://github.com/leanprover/lean4/commit/f71a1fb4ae958fccb3ad4d48786a8f47ced05c15) adds missing test for [#5126](https://github.com/leanprover/lean4/issues/5126).
+  * [#5201](https://github.com/leanprover/lean4/pull/5201) restores a test.
+  * [#3698](https://github.com/leanprover/lean4/pull/3698) fixes a bug where label attributes did not pass on the attribute kind.
+  * Typos: [#5080](https://github.com/leanprover/lean4/pull/5080), [#5150](https://github.com/leanprover/lean4/pull/5150), [#5202](https://github.com/leanprover/lean4/pull/5202)
+
+### Compiler, runtime, and FFI
+
+* [#3106](https://github.com/leanprover/lean4/pull/3106) moves frontend to new snapshot architecture. Note that `Frontend.processCommand` and `FrontendM` are no longer used by Lean core, but they will be preserved.
+* [#4919](https://github.com/leanprover/lean4/pull/4919) adds missing include in runtime for `AUTO_THREAD_FINALIZATION` feature on Windows.
+* [#4941](https://github.com/leanprover/lean4/pull/4941) adds more `LEAN_EXPORT`s for Windows.
+* [#4911](https://github.com/leanprover/lean4/pull/4911) improves formatting of CLI help text for the frontend.
+* [#4950](https://github.com/leanprover/lean4/pull/4950) improves file reading and writing.
+  * `readBinFile` and `readFile` now only require two system calls (`stat` + `read`) instead of one `read` per 1024 byte chunk.
+  * `Handle.getLine` and `Handle.putStr` no longer get tripped up by NUL characters.
+* [#4971](https://github.com/leanprover/lean4/pull/4971) handles the SIGBUS signal when detecting stack overflows.
+* [#5062](https://github.com/leanprover/lean4/pull/5062) avoids overwriting existing signal handlers, like in [rust-lang/rust#69685](https://github.com/rust-lang/rust/pull/69685).
+* [#4860](https://github.com/leanprover/lean4/pull/4860) improves workarounds for building on Windows. Splits `libleanshared` on Windows to avoid symbol limit, removes the `LEAN_EXPORT` denylist workaround, adds missing `LEAN_EXPORT`s.
+* [#4952](https://github.com/leanprover/lean4/pull/4952) output panics into Lean's redirected stderr, ensuring panics ARE visible as regular messages in the language server and properly ordered in relation to other messages on the command line.
+* [#4963](https://github.com/leanprover/lean4/pull/4963) links LibUV.
+
+### Lake
+
+* [#5030](https://github.com/leanprover/lean4/pull/5030) removes dead code.
+* [#4770](https://github.com/leanprover/lean4/pull/4770) adds additional fields to the package configuration which will be used by Reservoir. See the PR description for details.
+
+
+### DevOps/CI
+* [#4914](https://github.com/leanprover/lean4/pull/4914) and [#4937](https://github.com/leanprover/lean4/pull/4937) improve the release checklist.
+* [#4925](https://github.com/leanprover/lean4/pull/4925) ignores stale leanpkg tests.
+* [#5003](https://github.com/leanprover/lean4/pull/5003) upgrades `actions/cache` in CI.
+* [#5010](https://github.com/leanprover/lean4/pull/5010) sets `save-always` in cache actions in CI.
+* [#5008](https://github.com/leanprover/lean4/pull/5008) adds more libuv search patterns for the speedcenter.
+* [#5009](https://github.com/leanprover/lean4/pull/5009) reduce number of runs in the speedcenter for "fast" benchmarks from 10 to 3.
+* [#5014](https://github.com/leanprover/lean4/pull/5014) adjusts lakefile editing to use new `git` syntax in `pr-release` workflow.
+* [#5025](https://github.com/leanprover/lean4/pull/5025) has `pr-release` workflow pass `--retry` to `curl`.
+* [#5022](https://github.com/leanprover/lean4/pull/5022) builds MacOS Aarch64 release for PRs by default.
+* [#5045](https://github.com/leanprover/lean4/pull/5045) adds libuv to the required packages heading in macos docs.
+* [#5034](https://github.com/leanprover/lean4/pull/5034) fixes the install name of `libleanshared_1` on macOS.
+* [#5051](https://github.com/leanprover/lean4/pull/5051) fixes Windows stage 0.
+* [#5052](https://github.com/leanprover/lean4/pull/5052) fixes 32bit stage 0 builds in CI.
+* [#5057](https://github.com/leanprover/lean4/pull/5057) avoids rebuilding `leanmanifest` in each build.
+* [#5099](https://github.com/leanprover/lean4/pull/5099) makes `restart-on-label` workflow also filter by commit SHA.
+* [#4325](https://github.com/leanprover/lean4/pull/4325) adds CaDiCaL.
+
+### Breaking changes
+
+* [LibUV](https://libuv.org/) is now required to build Lean. This change only affects developers who compile Lean themselves instead of obtaining toolchains via `elan`. We have updated the official build instructions with information on how to obtain LibUV on our supported platforms. ([#4963](https://github.com/leanprover/lean4/pull/4963))
+
+* Recursive definitions with a `decreasing_by` clause that begins with `simp_wf` may break. Try removing `simp_wf` or replacing it with `simp`. ([#5016](https://github.com/leanprover/lean4/pull/5016))
+
+* The behavior of `rw [f]` where `f` is a non-recursive function defined by pattern matching changed.
+
+  For example, preciously, `rw [Option.map]` would rewrite `Option.map f o` to `match o with … `. Now this rewrite fails because it will use the equational lemmas, and these require constructors – just like for `List.map`.
+
+  Remedies:
+  * Split on `o` before rewriting.
+  * Use `rw [Option.map.eq_def]`, which rewrites any (saturated) application of `Option.map`.
+  * Use `set_option backward.eqns.nonrecursive false` when *defining* the function in question.
+  ([#4154](https://github.com/leanprover/lean4/pull/4154))
+
+* The unified handling of equation lemmas for recursive and non-recursive functions can break existing code, as there now can be extra equational lemmas:
+
+  * Explicit uses of `f.eq_2` might have to be adjusted if the numbering changed.
+
+  * Uses of `rw [f]` or `simp [f]` may no longer apply if they previously matched (and introduced a `match` statement), when the equational lemmas got more fine-grained.
+
+    In this case either case analysis on the parameters before rewriting helps, or setting the option `backward.eqns.deepRecursiveSplit false` while *defining* the function.
+
+  ([#5129](https://github.com/leanprover/lean4/pull/5129), [#5207](https://github.com/leanprover/lean4/pull/5207))
+
+* The `reduceCtorEq` simproc is now optional, and it might need to be included in lists of simp lemmas, like `simp only [reduceCtorEq]`. This simproc is responsible for reducing equalities of constructors. ([#5167](https://github.com/leanprover/lean4/pull/5167))
+
+* `Nat.strongInductionOn` is now `Nat.strongRecOn` and `Nat.caseStrongInductionOn` to `Nat.caseStrongRecOn`. ([#5147](https://github.com/leanprover/lean4/pull/5147))
+
+* The parameters to `Membership.mem` have been swapped, which affects all `Membership` instances. ([#5020](https://github.com/leanprover/lean4/pull/5020))
+
+* The meanings of `List.getElem_drop` and `List.getElem_drop'` have been reversed and the first is now a simp lemma. ([#5210](https://github.com/leanprover/lean4/pull/5210))
+
+* The `Parsec` library has moved from `Lean.Data.Parsec` to `Std.Internal.Parsec`. The `Parsec` type is now more general with a parameter for an iterable. Users parsing strings can migrate to `Parser` in the `Std.Internal.Parsec.String` namespace, which also includes string-focused parsing combinators. ([#4774](https://github.com/leanprover/lean4/pull/4774))
+
+* The `Lean` module has switched from `Lean.HashMap` and `Lean.HashSet` to `Std.HashMap` and `Std.HashSet` ([#4943](https://github.com/leanprover/lean4/pull/4943)). `Lean.HashMap` and `Lean.HashSet` are now deprecated ([#4954](https://github.com/leanprover/lean4/pull/4954)) and will be removed in a future release. Users of `Lean` APIs that interact with hash maps, for example `Lean.Environment.const2ModIdx`, might encounter minor breakage due to the following changes from `Lean.HashMap` to `Std.HashMap`:
+  * query functions use the term `get` instead of `find`, ([#4943](https://github.com/leanprover/lean4/pull/4943))
+  * the notation `map[key]` no longer returns an optional value but instead expects a proof that the key is present in the map. The previous behavior is available via the `map[key]?` notation.
+
 
 v4.11.0
 ----------
@@ -21,7 +331,7 @@ v4.11.0
 
   See breaking changes below.
 
-  PRs: [#4883](https://github.com/leanprover/lean4/pull/4883), [1242ff](https://github.com/leanprover/lean4/commit/1242ffbfb5a79296041683682268e770fc3cf820), [#5000](https://github.com/leanprover/lean4/pull/5000), [#5036](https://github.com/leanprover/lean4/pull/5036), [#5138](https://github.com/leanprover/lean4/pull/5138), [0edf1b](https://github.com/leanprover/lean4/commit/0edf1bac392f7e2fe0266b28b51c498306363a84).
+  PRs: [#4883](https://github.com/leanprover/lean4/pull/4883), [#4814](https://github.com/leanprover/lean4/pull/4814), [#5000](https://github.com/leanprover/lean4/pull/5000), [#5036](https://github.com/leanprover/lean4/pull/5036), [#5138](https://github.com/leanprover/lean4/pull/5138), [0edf1b](https://github.com/leanprover/lean4/commit/0edf1bac392f7e2fe0266b28b51c498306363a84).
 
 * **Recursive definitions**
   * Structural recursion can now be explicitly requested using

releases_drafts/hashmap.md

@@ -1,3 +0,0 @@
-* The `Lean` module has switched from `Lean.HashMap` and `Lean.HashSet` to `Std.HashMap` and `Std.HashSet`. `Lean.HashMap` and `Lean.HashSet` are now deprecated and will be removed in a future release. Users of `Lean` APIs that interact with hash maps, for example `Lean.Environment.const2ModIdx`, might encounter minor breakage due to the following breaking changes from `Lean.HashMap` to `Std.HashMap`:
-    * query functions use the term `get` instead of `find`,
-    * the notation `map[key]` no longer returns an optional value but expects a proof that the key is present in the map instead. The previous behavior is available via the `map[key]?` notation.

releases_drafts/libuv.md

@@ -1 +0,0 @@
-* #4963 [LibUV](https://libuv.org/) is now required to build Lean. This change only affects developers who compile Lean themselves instead of obtaining toolchains via `elan`. We have updated the official build instructions with information on how to obtain LibUV on our supported platforms.

src/Init/Classical.lean

@@ -80,6 +80,8 @@ noncomputable scoped instance (priority := low) propDecidable (a : Prop) : Decid
 noncomputable def decidableInhabited (a : Prop) : Inhabited (Decidable a) where
   default := inferInstance
 
+instance (a : Prop) : Nonempty (Decidable a) := ⟨propDecidable a⟩
+
 noncomputable def typeDecidableEq (α : Sort u) : DecidableEq α :=
   fun _ _ => inferInstance
 

src/Init/Control/Lawful/Basic.lean

@@ -133,6 +133,9 @@ theorem seqLeft_eq_bind [Monad m] [LawfulMonad m] (x : m α) (y : m β) : x <* y
   rw [← bind_pure_comp]
   simp only [bind_assoc, pure_bind]
 
+@[simp] theorem Functor.map_unit [Monad m] [LawfulMonad m] {a : m PUnit} : (fun _ => PUnit.unit) <$> a = a := by
+  simp [map]
+
 /--
 An alternative constructor for `LawfulMonad` which has more
 defaultable fields in the common case.
@@ -180,9 +183,9 @@ end Id
 
 instance : LawfulMonad Option := LawfulMonad.mk'
   (id_map := fun x => by cases x <;> rfl)
-  (pure_bind := fun x f => rfl)
-  (bind_assoc := fun x f g => by cases x <;> rfl)
-  (bind_pure_comp := fun f x => by cases x <;> rfl)
+  (pure_bind := fun _ _ => rfl)
+  (bind_assoc := fun x _ _ => by cases x <;> rfl)
+  (bind_pure_comp := fun _ x => by cases x <;> rfl)
 
 instance : LawfulApplicative Option := inferInstance
 instance : LawfulFunctor Option := inferInstance

src/Init/Control/Lawful/Instances.lean

@@ -84,14 +84,19 @@ instance [Monad m] [LawfulMonad m] : LawfulMonad (ExceptT ε m) where
   pure_bind      := by intros; apply ext; simp [run_bind]
   bind_assoc     := by intros; apply ext; simp [run_bind]; apply bind_congr; intro a; cases a <;> simp
 
+@[simp] theorem map_throw [Monad m] [LawfulMonad m] {α β : Type _} (f : α → β) (e : ε) :
+    f <$> (throw e : ExceptT ε m α) = (throw e : ExceptT ε m β) := by
+  simp only [ExceptT.instMonad, ExceptT.map, ExceptT.mk, throw, throwThe, MonadExceptOf.throw,
+    pure_bind]
+
 end ExceptT
 
 /-! # Except -/
 
 instance : LawfulMonad (Except ε) := LawfulMonad.mk'
   (id_map := fun x => by cases x <;> rfl)
-  (pure_bind := fun a f => rfl)
-  (bind_assoc := fun a f g => by cases a <;> rfl)
+  (pure_bind := fun _ _ => rfl)
+  (bind_assoc := fun a _ _ => by cases a <;> rfl)
 
 instance : LawfulApplicative (Except ε) := inferInstance
 instance : LawfulFunctor (Except ε) := inferInstance

src/Init/Data/Array/Attach.lean

@@ -5,6 +5,7 @@ Authors: Joachim Breitner, Mario Carneiro
 -/
 prelude
 import Init.Data.Array.Mem
+import Init.Data.Array.Lemmas
 import Init.Data.List.Attach
 
 namespace Array
@@ -26,4 +27,154 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
   with the same elements but in the type `{x // x ∈ xs}`. -/
 @[inline] def attach (xs : Array α) : Array {x // x ∈ xs} := xs.attachWith _ fun _ => id
 
+@[simp] theorem _root_.List.attachWith_toArray {l : List α} {P : α → Prop} {H : ∀ x ∈ l.toArray, P x} :
+    l.toArray.attachWith P H = (l.attachWith P (by simpa using H)).toArray := by
+  simp [attachWith]
+
+@[simp] theorem _root_.List.attach_toArray {l : List α} :
+    l.toArray.attach = (l.attachWith (· ∈ l.toArray) (by simp)).toArray := by
+  simp [attach]
+
+@[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]
+
+@[simp] theorem toList_attach {α : Type _} {l : Array α} :
+    l.attach.toList = l.toList.attachWith (· ∈ l) (by simp [mem_toList]) := by
+  simp [attach]
+
+/-! ## unattach
+
+`Array.unattach` is the (one-sided) inverse of `Array.attach`. It is a synonym for `Array.map Subtype.val`.
+
+We use it by providing a simp lemma `l.attach.unattach = l`, and simp lemmas which recognize higher order
+functions applied to `l : Array { x // p x }` which only depend on the value, not the predicate, and rewrite these
+in terms of a simpler function applied to `l.unattach`.
+
+Further, we provide simp lemmas that push `unattach` inwards.
+-/
+
+/--
+A synonym for `l.map (·.val)`. Mostly this should not be needed by users.
+It is introduced as in intermediate step by lemmas such as `map_subtype`,
+and is ideally subsequently simplified away by `unattach_attach`.
+
+If not, usually the right approach is `simp [Array.unattach, -Array.map_subtype]` to unfold.
+-/
+def unattach {α : Type _} {p : α → Prop} (l : Array { x // p x }) := l.map (·.val)
+
+@[simp] theorem unattach_nil {α : Type _} {p : α → Prop} : (#[] : Array { x // p x }).unattach = #[] := rfl
+@[simp] theorem unattach_push {α : Type _} {p : α → Prop} {a : { x // p x }} {l : Array { x // p x }} :
+    (l.push a).unattach = l.unattach.push a.1 := by
+  simp [unattach]
+
+@[simp] theorem size_unattach {α : Type _} {p : α → Prop} {l : Array { x // p x }} :
+    l.unattach.size = l.size := by
+  unfold unattach
+  simp
+
+@[simp] theorem _root_.List.unattach_toArray {α : Type _} {p : α → Prop} {l : List { x // p x }} :
+    l.toArray.unattach = l.unattach.toArray := by
+  simp [unattach, List.unattach]
+
+@[simp] theorem toList_unattach {α : Type _} {p : α → Prop} {l : Array { x // p x }} :
+    l.unattach.toList = l.toList.unattach := by
+  simp [unattach, List.unattach]
+
+@[simp] theorem unattach_attach {α : Type _} (l : Array α) : l.attach.unattach = l := by
+  cases l
+  simp
+
+@[simp] theorem unattach_attachWith {α : Type _} {p : α → Prop} {l : Array α}
+    {H : ∀ a ∈ l, p a} :
+    (l.attachWith p H).unattach = l := by
+  cases l
+  simp
+
+/-! ### Recognizing higher order functions using a function that only depends on the value. -/
+
+/--
+This lemma identifies folds over arrays of subtypes, where the function only depends on the value, not the proposition,
+and simplifies these to the function directly taking the value.
+-/
+theorem foldl_subtype {p : α → Prop} {l : Array { x // p x }}
+    {f : β → { x // p x } → β} {g : β → α → β} {x : β}
+    {hf : ∀ b x h, f b ⟨x, h⟩ = g b x} :
+    l.foldl f x = l.unattach.foldl g x := by
+  cases l
+  simp only [List.foldl_toArray', List.unattach_toArray]
+  rw [List.foldl_subtype] -- Why can't simp do this?
+  simp [hf]
+
+/-- Variant of `foldl_subtype` with side condition to check `stop = l.size`. -/
+@[simp] theorem foldl_subtype' {p : α → Prop} {l : Array { x // p x }}
+    {f : β → { x // p x } → β} {g : β → α → β} {x : β}
+    {hf : ∀ b x h, f b ⟨x, h⟩ = g b x} (h : stop = l.size) :
+    l.foldl f x 0 stop = l.unattach.foldl g x := by
+  subst h
+  rwa [foldl_subtype]
+
+/--
+This lemma identifies folds over arrays of subtypes, where the function only depends on the value, not the proposition,
+and simplifies these to the function directly taking the value.
+-/
+theorem foldr_subtype {p : α → Prop} {l : Array { x // p x }}
+    {f : { x // p x } → β → β} {g : α → β → β} {x : β}
+    {hf : ∀ x h b, f ⟨x, h⟩ b = g x b} :
+    l.foldr f x = l.unattach.foldr g x := by
+  cases l
+  simp only [List.foldr_toArray', List.unattach_toArray]
+  rw [List.foldr_subtype]
+  simp [hf]
+
+/-- Variant of `foldr_subtype` with side condition to check `stop = l.size`. -/
+@[simp] theorem foldr_subtype' {p : α → Prop} {l : Array { x // p x }}
+    {f : { x // p x } → β → β} {g : α → β → β} {x : β}
+    {hf : ∀ x h b, f ⟨x, h⟩ b = g x b} (h : start = l.size) :
+    l.foldr f x start 0 = l.unattach.foldr g x := by
+  subst h
+  rwa [foldr_subtype]
+
+/--
+This lemma identifies maps over arrays of subtypes, where the function only depends on the value, not the proposition,
+and simplifies these to the function directly taking the value.
+-/
+@[simp] theorem map_subtype {p : α → Prop} {l : Array { x // p x }}
+    {f : { x // p x } → β} {g : α → β} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
+    l.map f = l.unattach.map g := by
+  cases l
+  simp only [List.map_toArray, List.unattach_toArray]
+  rw [List.map_subtype]
+  simp [hf]
+
+@[simp] theorem filterMap_subtype {p : α → Prop} {l : Array { x // p x }}
+    {f : { x // p x } → Option β} {g : α → Option β} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
+    l.filterMap f = l.unattach.filterMap g := by
+  cases l
+  simp only [size_toArray, List.filterMap_toArray', List.unattach_toArray, List.length_unattach,
+    mk.injEq]
+  rw [List.filterMap_subtype]
+  simp [hf]
+
+@[simp] theorem unattach_filter {p : α → Prop} {l : Array { x // p x }}
+    {f : { x // p x } → Bool} {g : α → Bool} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
+    (l.filter f).unattach = l.unattach.filter g := by
+  cases l
+  simp [hf]
+  rw [List.unattach_filter]
+  simp [hf]
+
+/-! ### Simp lemmas pushing `unattach` inwards. -/
+
+@[simp] theorem unattach_reverse {p : α → Prop} {l : Array { x // p x }} :
+    l.reverse.unattach = l.unattach.reverse := by
+  cases l
+  simp
+
+@[simp] theorem unattach_append {p : α → Prop} {l₁ l₂ : Array { x // p x }} :
+    (l₁ ++ l₂).unattach = l₁.unattach ++ l₂.unattach := by
+  cases l₁
+  cases l₂
+  simp
+
 end Array

src/Init/Data/Array/Basic.lean

@@ -617,7 +617,7 @@ def concatMap (f : α → Array β) (as : Array α) : Array β :=
 
 `flatten #[#[a₁, a₂, ⋯], #[b₁, b₂, ⋯], ⋯]` = `#[a₁, a₂, ⋯, b₁, b₂, ⋯]`
 -/
-def flatten (as : Array (Array α)) : Array α :=
+@[inline] def flatten (as : Array (Array α)) : Array α :=
   as.foldl (init := empty) fun r a => r ++ a
 
 @[inline]
@@ -720,7 +720,7 @@ 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`.
-theorem size_feraseIdx (a : Array α) (i : Fin a.size) : (a.feraseIdx i).size = a.size - 1 := by
+@[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
@@ -810,11 +810,27 @@ 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)
 
-/-! ### Auxiliary functions used in metaprogramming.
+/-! ## Auxiliary functions used in metaprogramming.
 
 We do not intend to provide verification theorems for these functions.
 -/
 
+/-! ### eraseReps -/
+
+/--
+`O(|l|)`. Erase repeated adjacent elements. Keeps the first occurrence of each run.
+* `eraseReps #[1, 3, 2, 2, 2, 3, 5] = #[1, 3, 2, 3, 5]`
+-/
+def eraseReps {α} [BEq α] (as : Array α) : Array α :=
+  if h : 0 < as.size then
+    let ⟨last, r⟩ := as.foldl (init := (as[0], #[])) fun ⟨last, r⟩ a =>
+      if a == last then ⟨last, r⟩ else ⟨a, r.push last⟩
+    r.push last
+  else
+    #[]
+
+/-! ### allDiff -/
+
 private def allDiffAuxAux [BEq α] (as : Array α) (a : α) : forall (i : Nat), i < as.size → Bool
   | 0,   _ => true
   | i+1, h =>
@@ -832,6 +848,8 @@ decreasing_by simp_wf; decreasing_trivial_pre_omega
 def allDiff [BEq α] (as : Array α) : Bool :=
   allDiffAux as 0
 
+/-! ### getEvenElems -/
+
 @[inline] def getEvenElems (as : Array α) : Array α :=
   (·.2) <| as.foldl (init := (true, Array.empty)) fun (even, r) a =>
     if even then

src/Init/Data/Array/Bootstrap.lean

@@ -73,7 +73,7 @@ theorem foldr_eq_foldr_toList (f : α → β → β) (init : β) (arr : Array α
 
 @[simp] theorem append_eq_append (arr arr' : Array α) : arr.append arr' = arr ++ arr' := rfl
 
-@[simp] theorem append_toList (arr arr' : Array α) :
+@[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_eq_foldl_toList]
@@ -111,8 +111,8 @@ abbrev toList_eq := @toListImpl_eq
 @[deprecated pop_toList (since := "2024-09-09")]
 abbrev pop_data := @pop_toList
 
-@[deprecated append_toList (since := "2024-09-09")]
-abbrev append_data := @append_toList
+@[deprecated toList_append (since := "2024-09-09")]
+abbrev append_data := @toList_append
 
 @[deprecated appendList_toList (since := "2024-09-09")]
 abbrev appendList_data := @appendList_toList

src/Init/Data/Array/Lemmas.lean

@@ -91,28 +91,74 @@ abbrev toArray_data := @toArray_toList
 @[simp] theorem getElem_toArray {a : List α} {i : Nat} (h : i < a.toArray.size) :
     a.toArray[i] = a[i]'(by simpa using h) := rfl
 
-@[simp] theorem toArray_concat {as : List α} {x : α} :
+@[simp] theorem getElem?_toArray {a : List α} {i : Nat} : a.toArray[i]? = a[i]? := rfl
+
+@[deprecated "Use the reverse direction of `List.push_toArray`." (since := "2024-09-27")]
+theorem toArray_concat {as : List α} {x : α} :
     (as ++ [x]).toArray = as.toArray.push x := by
   apply ext'
   simp
 
-@[simp] theorem foldrM_toArray [Monad m] (f : α → β → m β) (init : β) (l : List α) :
+@[simp] theorem push_toArray (l : List α) (a : α) : l.toArray.push a = (l ++ [a]).toArray := by
+  apply ext'
+  simp
+
+/-- Unapplied variant of `push_toArray`, useful for monadic reasoning. -/
+@[simp] theorem push_toArray_fun (l : List α) : l.toArray.push = fun a => (l ++ [a]).toArray := by
+  funext a
+  simp
+
+theorem foldrM_toArray [Monad m] (f : α → β → m β) (init : β) (l : List α) :
     l.toArray.foldrM f init = l.foldrM f init := by
   rw [foldrM_eq_reverse_foldlM_toList]
   simp
 
-@[simp] theorem foldlM_toArray [Monad m] (f : β → α → m β) (init : β) (l : List α) :
+theorem foldlM_toArray [Monad m] (f : β → α → m β) (init : β) (l : List α) :
     l.toArray.foldlM f init = l.foldlM f init := by
   rw [foldlM_eq_foldlM_toList]
 
-@[simp] theorem foldr_toArray (f : α → β → β) (init : β) (l : List α) :
+theorem foldr_toArray (f : α → β → β) (init : β) (l : List α) :
     l.toArray.foldr f init = l.foldr f init := by
   rw [foldr_eq_foldr_toList]
 
-@[simp] theorem foldl_toArray (f : β → α → β) (init : β) (l : List α) :
+theorem foldl_toArray (f : β → α → β) (init : β) (l : List α) :
     l.toArray.foldl f init = l.foldl f init := by
   rw [foldl_eq_foldl_toList]
 
+/-- Variant of `foldrM_toArray` with a side condition for the `start` argument. -/
+@[simp] theorem foldrM_toArray' [Monad m] (f : α → β → m β) (init : β) (l : List α)
+    (h : start = l.toArray.size) :
+    l.toArray.foldrM f init start 0 = l.foldrM f init := by
+  subst h
+  rw [foldrM_eq_reverse_foldlM_toList]
+  simp
+
+/-- Variant of `foldlM_toArray` with a side condition for the `stop` argument. -/
+@[simp] theorem foldlM_toArray' [Monad m] (f : β → α → m β) (init : β) (l : List α)
+    (h : stop = l.toArray.size) :
+    l.toArray.foldlM f init 0 stop = l.foldlM f init := by
+  subst h
+  rw [foldlM_eq_foldlM_toList]
+
+/-- Variant of `foldr_toArray` with a side condition for the `start` argument. -/
+@[simp] theorem foldr_toArray' (f : α → β → β) (init : β) (l : List α)
+    (h : start = l.toArray.size) :
+    l.toArray.foldr f init start 0 = l.foldr f init := by
+  subst h
+  rw [foldr_eq_foldr_toList]
+
+/-- Variant of `foldl_toArray` with a side condition for the `stop` argument. -/
+@[simp] theorem foldl_toArray' (f : β → α → β) (init : β) (l : List α)
+    (h : stop = l.toArray.size) :
+    l.toArray.foldl f init 0 stop = l.foldl f init := by
+  subst h
+  rw [foldl_eq_foldl_toList]
+
+@[simp] theorem append_toArray (l₁ l₂ : List α) :
+    l₁.toArray ++ l₂.toArray = (l₁ ++ l₂).toArray := by
+  apply ext'
+  simp
+
 end List
 
 namespace Array
@@ -126,10 +172,10 @@ attribute [simp] uset
 @[deprecated toArray_toList (since := "2024-09-09")]
 abbrev toArray_data := @toArray_toList
 
-@[simp] theorem toList_length {l : Array α} : l.toList.length = l.size := rfl
+@[simp] theorem length_toList {l : Array α} : l.toList.length = l.size := rfl
 
-@[deprecated toList_length (since := "2024-09-09")]
-abbrev data_length := @toList_length
+@[deprecated length_toList (since := "2024-09-09")]
+abbrev data_length := @length_toList
 
 @[simp] theorem mkEmpty_eq (α n) : @mkEmpty α n = #[] := rfl
 
@@ -165,25 +211,25 @@ where
       mapM.map f arr i r = (arr.toList.drop i).foldlM (fun bs a => bs.push <$> f a) r := by
     unfold mapM.map; split
     · rw [← List.get_drop_eq_drop _ i ‹_›]
-      simp only [aux (i + 1), map_eq_pure_bind, toList_length, List.foldlM_cons, bind_assoc,
+      simp only [aux (i + 1), map_eq_pure_bind, length_toList, List.foldlM_cons, bind_assoc,
         pure_bind]
       rfl
     · rw [List.drop_of_length_le (Nat.ge_of_not_lt ‹_›)]; rfl
   termination_by arr.size - i
   decreasing_by decreasing_trivial_pre_omega
 
-@[simp] theorem map_toList (f : α → β) (arr : Array α) : (arr.map f).toList = arr.toList.map f := by
+@[simp] theorem toList_map (f : α → β) (arr : Array α) : (arr.map f).toList = arr.toList.map f := by
   rw [map, mapM_eq_foldlM]
   apply congrArg toList (foldl_eq_foldl_toList (fun bs a => push bs (f a)) #[] arr) |>.trans
   have H (l arr) : List.foldl (fun bs a => push bs (f a)) arr l = ⟨arr.toList ++ l.map f⟩ := by
     induction l generalizing arr <;> simp [*]
   simp [H]
 
-@[deprecated map_toList (since := "2024-09-09")]
-abbrev map_data := @map_toList
+@[deprecated toList_map (since := "2024-09-09")]
+abbrev map_data := @toList_map
 
 @[simp] theorem size_map (f : α → β) (arr : Array α) : (arr.map f).size = arr.size := by
-  simp only [← toList_length]
+  simp only [← length_toList]
   simp
 
 @[simp] theorem appendList_nil (arr : Array α) : arr ++ ([] : List α) = arr := Array.ext' (by simp)
@@ -191,6 +237,11 @@ abbrev map_data := @map_toList
 @[simp] theorem appendList_cons (arr : Array α) (a : α) (l : List α) :
     arr ++ (a :: l) = arr.push a ++ l := Array.ext' (by simp)
 
+@[simp] theorem toList_appendList (arr : Array α) (l : List α) :
+    (arr ++ l).toList = arr.toList ++ l := by
+  cases arr
+  simp
+
 theorem foldl_toList_eq_bind (l : List α) (acc : Array β)
     (F : Array β → α → Array β) (G : α → List β)
     (H : ∀ acc a, (F acc a).toList = acc.toList ++ G a) :
@@ -282,14 +333,14 @@ theorem getElem_set (a : Array α) (i : Fin a.size) (v : α) (j : Nat)
 @[simp] theorem set!_is_setD : @set! = @setD := rfl
 
 @[simp] theorem size_setD (a : Array α) (index : Nat) (val : α) :
-  (Array.setD a index val).size = a.size := by
+    (Array.setD a index val).size = a.size := by
   if h : index < a.size  then
     simp [setD, h]
   else
     simp [setD, h]
 
 @[simp] theorem getElem_setD_eq (a : Array α) {i : Nat} (v : α) (h : _) :
-  (setD a i v)[i]'h = v := by
+    (setD a i v)[i]'h = v := by
   simp at h
   simp only [setD, h, dite_true, getElem_set, ite_true]
 
@@ -299,7 +350,7 @@ theorem getElem?_setD_eq (a : Array α) {i : Nat} (p : i < a.size) (v : α) : (a
 
 /-- Simplifies a normal form from `get!` -/
 @[simp] theorem getD_get?_setD (a : Array α) (i : Nat) (v d : α) :
-  Option.getD (setD a i v)[i]? d = if i < a.size then v else d := by
+    Option.getD (setD a i v)[i]? d = if i < a.size then v else d := by
   by_cases h : i < a.size <;>
     simp [setD, Nat.not_lt_of_le, h,  getD_get?]
 
@@ -414,12 +465,18 @@ theorem getElem_mem_toList (a : Array α) (h : i < a.size) : a[i] ∈ a.toList :
 @[deprecated getElem_mem_toList (since := "2024-09-09")]
 abbrev getElem_mem_data := @getElem_mem_toList
 
+theorem getElem?_eq_toList_getElem? (a : Array α) (i : Nat) : a[i]? = a.toList[i]? := by
+  by_cases i < a.size <;> simp_all [getElem?_pos, getElem?_neg]
+
+@[deprecated getElem?_eq_toList_getElem? (since := "2024-09-30")]
 theorem getElem?_eq_toList_get? (a : Array α) (i : Nat) : a[i]? = a.toList.get? i := by
   by_cases i < a.size <;> simp_all [getElem?_pos, getElem?_neg, List.get?_eq_get, eq_comm]
 
-@[deprecated getElem?_eq_toList_get? (since := "2024-09-09")]
+set_option linter.deprecated false in
+@[deprecated getElem?_eq_toList_getElem? (since := "2024-09-09")]
 abbrev getElem?_eq_data_get? := @getElem?_eq_toList_get?
 
+set_option linter.deprecated false in
 theorem get?_eq_toList_get? (a : Array α) (i : Nat) : a.get? i = a.toList.get? i :=
   getElem?_eq_toList_get? ..
 
@@ -429,11 +486,15 @@ abbrev get?_eq_data_get? := @get?_eq_toList_get?
 theorem get!_eq_get? [Inhabited α] (a : Array α) : a.get! n = (a.get? n).getD default := by
   simp [get!_eq_getD]
 
+theorem getElem?_eq_some_iff {as : Array α} : as[n]? = some a ↔ ∃ h : n < as.size, as[n] = a := by
+  cases as
+  simp [List.getElem?_eq_some_iff]
+
 @[simp] theorem back_eq_back? [Inhabited α] (a : Array α) : a.back = a.back?.getD default := by
   simp [back, back?]
 
 @[simp] theorem back?_push (a : Array α) : (a.push x).back? = some x := by
-  simp [back?, getElem?_eq_toList_get?]
+  simp [back?, getElem?_eq_toList_getElem?]
 
 theorem back_push [Inhabited α] (a : Array α) : (a.push x).back = x := by simp
 
@@ -491,7 +552,7 @@ theorem get_set (a : Array α) (i : Fin a.size) (j : Nat) (hj : j < a.size) (v :
   simp only [set, getElem_eq_getElem_toList, List.getElem_set_ne h]
 
 theorem getElem_setD (a : Array α) (i : Nat) (v : α) (h : i < (setD a i v).size) :
-  (setD a i v)[i] = v := by
+    (setD a i v)[i] = v := by
   simp at h
   simp only [setD, h, dite_true, get_set, ite_true]
 
@@ -593,11 +654,11 @@ theorem getElem_range {n : Nat} {x : Nat} (h : x < (Array.range n).size) : (Arra
   simp [getElem_eq_getElem_toList]
 
 set_option linter.deprecated false in
-@[simp] theorem reverse_toList (a : Array α) : a.reverse.toList = a.toList.reverse := by
+@[simp] theorem toList_reverse (a : Array α) : a.reverse.toList = a.toList.reverse := by
   let rec go (as : Array α) (i j hj)
       (h : i + j + 1 = a.size) (h₂ : as.size = a.size)
-      (H : ∀ k, as.toList.get? k = if i ≤ k ∧ k ≤ j then a.toList.get? k else a.toList.reverse.get? k)
-      (k) : (reverse.loop as i ⟨j, hj⟩).toList.get? k = a.toList.reverse.get? k := by
+      (H : ∀ k, as.toList[k]? = if i ≤ k ∧ k ≤ j then a.toList[k]? else a.toList.reverse[k]?)
+      (k : Nat) : (reverse.loop as i ⟨j, hj⟩).toList[k]? = a.toList.reverse[k]? := by
     rw [reverse.loop]; dsimp; split <;> rename_i h₁
     · match j with | j+1 => ?_
       simp only [Nat.add_sub_cancel]
@@ -605,34 +666,37 @@ set_option linter.deprecated false in
       · rwa [Nat.add_right_comm i]
       · simp [size_swap, h₂]
       · intro k
-        rw [← getElem?_eq_toList_get?, get?_swap]
-        simp only [H, getElem_eq_toList_get, ← List.get?_eq_get, Nat.le_of_lt h₁,
-          getElem?_eq_toList_get?]
+        rw [← getElem?_eq_toList_getElem?, get?_swap]
+        simp only [H, getElem_eq_getElem_toList, ← List.getElem?_eq_getElem, Nat.le_of_lt h₁,
+          getElem?_eq_toList_getElem?]
         split <;> rename_i h₂
         · simp only [← h₂, Nat.not_le.2 (Nat.lt_succ_self _), Nat.le_refl, and_false]
-          exact (List.get?_reverse' (j+1) i (Eq.trans (by simp_arith) h)).symm
+          exact (List.getElem?_reverse' (j+1) i (Eq.trans (by simp_arith) h)).symm
         split <;> rename_i h₃
         · simp only [← h₃, Nat.not_le.2 (Nat.lt_succ_self _), Nat.le_refl, false_and]
-          exact (List.get?_reverse' i (j+1) (Eq.trans (by simp_arith) h)).symm
+          exact (List.getElem?_reverse' i (j+1) (Eq.trans (by simp_arith) h)).symm
         simp only [Nat.succ_le, Nat.lt_iff_le_and_ne.trans (and_iff_left h₃),
           Nat.lt_succ.symm.trans (Nat.lt_iff_le_and_ne.trans (and_iff_left (Ne.symm h₂)))]
     · rw [H]; split <;> rename_i h₂
       · cases Nat.le_antisymm (Nat.not_lt.1 h₁) (Nat.le_trans h₂.1 h₂.2)
         cases Nat.le_antisymm h₂.1 h₂.2
-        exact (List.get?_reverse' _ _ h).symm
+        exact (List.getElem?_reverse' _ _ h).symm
       · rfl
     termination_by j - i
   simp only [reverse]
   split
   · match a with | ⟨[]⟩ | ⟨[_]⟩ => rfl
   · have := Nat.sub_add_cancel (Nat.le_of_not_le ‹_›)
-    refine List.ext_get? <| go _ _ _ _ (by simp [this]) rfl fun k => ?_
+    refine List.ext_getElem? <| go _ _ _ _ (by simp [this]) rfl fun k => ?_
     split
     · rfl
     · rename_i h
       simp only [← show k < _ + 1 ↔ _ from Nat.lt_succ (n := a.size - 1), this, Nat.zero_le,
         true_and, Nat.not_lt] at h
-      rw [List.get?_eq_none.2 ‹_›, List.get?_eq_none.2 (a.toList.length_reverse ▸ ‹_›)]
+      rw [List.getElem?_eq_none_iff.2 ‹_›, List.getElem?_eq_none_iff.2 (a.toList.length_reverse ▸ ‹_›)]
+
+@[deprecated toList_reverse (since := "2024-09-30")]
+abbrev reverse_toList := @toList_reverse
 
 /-! ### foldl / foldr -/
 
@@ -695,19 +759,35 @@ theorem foldr_induction
   simp [foldr, foldrM]; split; {exact go _ h0}
   · next h => exact (Nat.eq_zero_of_not_pos h ▸ h0)
 
+@[congr]
+theorem foldl_congr {as bs : Array α} (h₀ : as = bs) {f g : β → α → β} (h₁ : f = g)
+     {a b : β} (h₂ : a = b) {start start' stop stop' : Nat} (h₃ : start = start') (h₄ : stop = stop') :
+    as.foldl f a start stop = bs.foldl g b start' stop' := by
+  congr
+
+@[congr]
+theorem foldr_congr {as bs : Array α} (h₀ : as = bs) {f g : α → β → β} (h₁ : f = g)
+     {a b : β} (h₂ : a = b) {start start' stop stop' : Nat} (h₃ : start = start') (h₄ : stop = stop') :
+    as.foldr f a start stop = bs.foldr g b start' stop' := by
+  congr
+
 /-! ### map -/
 
 @[simp] theorem mem_map {f : α → β} {l : Array α} : b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b := by
-  simp only [mem_def, map_toList, List.mem_map]
+  simp only [mem_def, toList_map, List.mem_map]
 
 theorem mapM_eq_mapM_toList [Monad m] [LawfulMonad m] (f : α → m β) (arr : Array α) :
-    arr.mapM f = return mk (← arr.toList.mapM f) := by
+    arr.mapM f = List.toArray <$> (arr.toList.mapM f) := by
   rw [mapM_eq_foldlM, foldlM_eq_foldlM_toList, ← List.foldrM_reverse]
   conv => rhs; rw [← List.reverse_reverse arr.toList]
   induction arr.toList.reverse with
   | nil => simp
   | cons a l ih => simp [ih]
 
+@[simp] theorem toList_mapM [Monad m] [LawfulMonad m] (f : α → m β) (arr : Array α) :
+    toList <$> arr.mapM f = arr.toList.mapM f := by
+  simp [mapM_eq_mapM_toList]
+
 @[deprecated mapM_eq_mapM_toList (since := "2024-09-09")]
 abbrev mapM_eq_mapM_data := @mapM_eq_mapM_toList
 
@@ -764,16 +844,27 @@ theorem map_spec (as : Array α) (f : α → β) (p : Fin as.size → β → Pro
   simpa using map_induction as f (fun _ => True) trivial p (by simp_all)
 
 @[simp] theorem getElem_map (f : α → β) (as : Array α) (i : Nat) (h) :
-    ((as.map f)[i]) = f (as[i]'(size_map .. ▸ h)) := by
+    (as.map f)[i] = f (as[i]'(size_map .. ▸ h)) := by
   have := map_spec as f (fun i b => b = f (as[i]))
   simp only [implies_true, true_implies] at this
   obtain ⟨eq, w⟩ := this
   apply w
   simp_all
 
+@[simp] theorem getElem?_map (f : α → β) (as : Array α) (i : Nat) :
+    (as.map f)[i]? = as[i]?.map f := by
+  simp [getElem?_def]
+
+@[simp] theorem map_push {f : α → β} {as : Array α} {x : α} :
+    (as.push x).map f = (as.map f).push (f x) := by
+  ext
+  · simp
+  · simp only [getElem_map, get_push, size_map]
+    split <;> rfl
+
 /-! ### mapIdx -/
 
--- This could also be prove from `SatisfiesM_mapIdxM`.
+-- This could also be proved from `SatisfiesM_mapIdxM` in Batteries.
 theorem mapIdx_induction (as : Array α) (f : Fin as.size → α → β)
     (motive : Nat → Prop) (h0 : motive 0)
     (p : Fin as.size → β → Prop)
@@ -813,36 +904,41 @@ theorem mapIdx_spec (as : Array α) (f : Fin as.size → α → β)
 
 @[simp] theorem getElem_mapIdx (a : Array α) (f : Fin a.size → α → β) (i : Nat)
     (h : i < (mapIdx a f).size) :
-    haveI : i < a.size := by simp_all
-    (a.mapIdx f)[i] = f ⟨i, this⟩ a[i] :=
+    (a.mapIdx f)[i] = f ⟨i, by simp_all⟩ (a[i]'(by simp_all)) :=
   (mapIdx_spec _ _ (fun i b => b = f i a[i]) fun _ => rfl).2 i _
 
+@[simp] theorem getElem?_mapIdx (a : Array α) (f : Fin a.size → α → β) (i : Nat) :
+    (a.mapIdx f)[i]? =
+      a[i]?.pbind fun b h => f ⟨i, (getElem?_eq_some_iff.1 h).1⟩ b := by
+  simp only [getElem?_def, size_mapIdx, getElem_mapIdx]
+  split <;> simp_all
+
 /-! ### modify -/
 
 @[simp] theorem size_modify (a : Array α) (i : Nat) (f : α → α) : (a.modify i f).size = a.size := by
   unfold modify modifyM Id.run
   split <;> simp
 
-theorem getElem_modify {as : Array α} {x i} (h : i < as.size) :
-    (as.modify x f)[i]'(by simp [h]) = if x = i then f as[i] else as[i] := by
+theorem getElem_modify {as : Array α} {x i} (h : i < (as.modify x f).size) :
+    (as.modify x f)[i] = if x = i then f (as[i]'(by simpa using h)) else as[i]'(by simpa using h) := by
   simp only [modify, modifyM, get_eq_getElem, Id.run, Id.pure_eq]
   split
-  · simp only [Id.bind_eq, get_set _ _ _ h]; split <;> simp [*]
-  · rw [if_neg (mt (by rintro rfl; exact h) ‹_›)]
+  · simp only [Id.bind_eq, get_set _ _ _ (by simpa using h)]; split <;> simp [*]
+  · rw [if_neg (mt (by rintro rfl; exact h) (by simp_all))]
 
-theorem getElem_modify_self {as : Array α} {i : Nat} (h : i < as.size) (f : α → α) :
-    (as.modify i f)[i]'(by simp [h]) = f as[i] := by
+theorem getElem_modify_self {as : Array α} {i : Nat} (f : α → α) (h : i < (as.modify i f).size) :
+    (as.modify i f)[i] = f (as[i]'(by simpa using h)) := by
   simp [getElem_modify h]
 
-theorem getElem_modify_of_ne {as : Array α} {i : Nat} (hj : j < as.size)
-    (f : α → α) (h : i ≠ j) :
-    (as.modify i f)[j]'(by rwa [size_modify]) = as[j] := by
+theorem getElem_modify_of_ne {as : Array α} {i : Nat} (h : i ≠ j)
+    (f : α → α) (hj : j < (as.modify i f).size) :
+    (as.modify i f)[j] = as[j]'(by simpa using hj) := by
   simp [getElem_modify hj, h]
 
 @[deprecated getElem_modify (since := "2024-08-08")]
-theorem get_modify {arr : Array α} {x i} (h : i < arr.size) :
-    (arr.modify x f).get ⟨i, by simp [h]⟩ =
-    if x = i then f (arr.get ⟨i, h⟩) else arr.get ⟨i, h⟩ := by
+theorem get_modify {arr : Array α} {x i} (h : i < (arr.modify x f).size) :
+    (arr.modify x f).get ⟨i, h⟩ =
+    if x = i then f (arr.get ⟨i, by simpa using h⟩) else arr.get ⟨i, by simpa using h⟩ := by
   simp [getElem_modify h]
 
 /-! ### filter -/
@@ -872,6 +968,13 @@ abbrev filter_data := @toList_filter
 theorem mem_of_mem_filter {a : α} {l} (h : a ∈ filter p l) : a ∈ l :=
   (mem_filter.mp h).1
 
+@[congr]
+theorem filter_congr {as bs : Array α} (h : as = bs)
+    {f : α → Bool} {g : α → Bool} (h' : f = g) {start stop start' stop' : Nat}
+    (h₁ : start = start') (h₂ : stop = stop') :
+    filter f as start stop = filter g bs start' stop' := by
+  congr
+
 /-! ### filterMap -/
 
 @[simp] theorem toList_filterMap (f : α → Option β) (l : Array α) :
@@ -894,6 +997,13 @@ abbrev filterMap_data := @toList_filterMap
     b ∈ filterMap f l ↔ ∃ a, a ∈ l ∧ f a = some b := by
   simp only [mem_def, toList_filterMap, List.mem_filterMap]
 
+@[congr]
+theorem filterMap_congr {as bs : Array α} (h : as = bs)
+    {f : α → Option β} {g : α → Option β} (h' : f = g) {start stop start' stop' : Nat}
+    (h₁ : start = start') (h₂ : stop = stop') :
+    filterMap f as start stop = filterMap g bs start' stop' := by
+  congr
+
 /-! ### empty -/
 
 theorem size_empty : (#[] : Array α).size = 0 := rfl
@@ -908,34 +1018,66 @@ abbrev empty_data := @toList_empty
 theorem push_eq_append_singleton (as : Array α) (x) : as.push x = as ++ #[x] := rfl
 
 @[simp] theorem mem_append {a : α} {s t : Array α} : a ∈ s ++ t ↔ a ∈ s ∨ a ∈ t := by
-  simp only [mem_def, append_toList, List.mem_append]
+  simp only [mem_def, toList_append, List.mem_append]
 
-theorem size_append (as bs : Array α) : (as ++ bs).size = as.size + bs.size := by
-  simp only [size, append_toList, List.length_append]
+@[simp] theorem size_append (as bs : Array α) : (as ++ bs).size = as.size + bs.size := by
+  simp only [size, toList_append, List.length_append]
 
-theorem get_append_left {as bs : Array α} {h : i < (as ++ bs).size} (hlt : i < as.size) :
+theorem getElem_append {as bs : Array α} (h : i < (as ++ bs).size) :
+    (as ++ bs)[i] = if h' : i < as.size then as[i] else bs[i - as.size]'(by simp at h; omega) := by
+  cases as; cases bs
+  simp [List.getElem_append]
+
+theorem getElem_append_left {as bs : Array α} {h : i < (as ++ bs).size} (hlt : i < as.size) :
     (as ++ bs)[i] = as[i] := by
   simp only [getElem_eq_getElem_toList]
-  have h' : i < (as.toList ++ bs.toList).length := by rwa [← toList_length, append_toList] at h
+  have h' : i < (as.toList ++ bs.toList).length := by rwa [← length_toList, toList_append] at h
   conv => rhs; rw [← List.getElem_append_left (bs := bs.toList) (h' := h')]
-  apply List.get_of_eq; rw [append_toList]
+  apply List.get_of_eq; rw [toList_append]
 
-theorem get_append_right {as bs : Array α} {h : i < (as ++ bs).size} (hle : as.size ≤ i)
+@[deprecated getElem_append_left (since := "2024-09-30")]
+abbrev get_append_left := @getElem_append_left
+
+theorem getElem_append_right {as bs : Array α} {h : i < (as ++ bs).size} (hle : as.size ≤ i)
     (hlt : i - as.size < bs.size := Nat.sub_lt_left_of_lt_add hle (size_append .. ▸ h)) :
     (as ++ bs)[i] = bs[i - as.size] := by
   simp only [getElem_eq_getElem_toList]
-  have h' : i < (as.toList ++ bs.toList).length := by rwa [← toList_length, append_toList] at h
+  have h' : i < (as.toList ++ bs.toList).length := by rwa [← length_toList, toList_append] at h
   conv => rhs; rw [← List.getElem_append_right (h₁ := hle) (h₂ := h')]
-  apply List.get_of_eq; rw [append_toList]
+  apply List.get_of_eq; rw [toList_append]
+
+@[deprecated getElem_append_right (since := "2024-09-30")]
+abbrev get_append_right := @getElem_append_right
 
 @[simp] theorem append_nil (as : Array α) : as ++ #[] = as := by
-  apply ext'; simp only [append_toList, toList_empty, List.append_nil]
+  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 [append_toList, toList_empty, List.nil_append]
+  apply ext'; simp only [toList_append, toList_empty, List.nil_append]
 
 theorem append_assoc (as bs cs : Array α) : as ++ bs ++ cs = as ++ (bs ++ cs) := by
-  apply ext'; simp only [append_toList, List.append_assoc]
+  apply ext'; simp only [toList_append, List.append_assoc]
+
+/-! ### flatten -/
+
+@[simp] theorem toList_flatten {l : Array (Array α)} : l.flatten.toList = (l.toList.map toList).join := by
+  dsimp [flatten]
+  simp only [foldl_eq_foldl_toList]
+  generalize l.toList = l
+  have : ∀ a : Array α, (List.foldl ?_ a l).toList = a.toList ++ ?_ := ?_
+  exact this #[]
+  induction l with
+  | nil => simp
+  | cons h => induction h.toList <;> simp [*]
+
+theorem mem_flatten : ∀ {L : Array (Array α)}, a ∈ L.flatten ↔ ∃ l, l ∈ L ∧ a ∈ l := by
+  simp only [mem_def, toList_flatten, List.mem_join, List.mem_map]
+  intro l
+  constructor
+  · rintro ⟨_, ⟨s, m, rfl⟩, h⟩
+    exact ⟨s, m, h⟩
+  · rintro ⟨s, h₁, h₂⟩
+    refine ⟨s.toList, ⟨⟨s, h₁, rfl⟩, h₂⟩⟩
 
 /-! ### extract -/
 
@@ -985,20 +1127,20 @@ theorem size_extract_loop (as bs : Array α) (size start : Nat) :
   simp [extract]; rw [size_extract_loop, size_empty, Nat.zero_add, Nat.sub_min_sub_right,
     Nat.min_assoc, Nat.min_self]
 
-theorem get_extract_loop_lt_aux (as bs : Array α) (size start : Nat) (hlt : i < bs.size) :
+theorem getElem_extract_loop_lt_aux (as bs : Array α) (size start : Nat) (hlt : i < bs.size) :
     i < (extract.loop as size start bs).size := by
   rw [size_extract_loop]
   apply Nat.lt_of_lt_of_le hlt
   exact Nat.le_add_right ..
 
-theorem get_extract_loop_lt (as bs : Array α) (size start : Nat) (hlt : i < bs.size)
-    (h := get_extract_loop_lt_aux as bs size start hlt) :
+theorem getElem_extract_loop_lt (as bs : Array α) (size start : Nat) (hlt : i < bs.size)
+    (h := getElem_extract_loop_lt_aux as bs size start hlt) :
     (extract.loop as size start bs)[i] = bs[i] := by
-  apply Eq.trans _ (get_append_left (bs:=extract.loop as size start #[]) hlt)
+  apply Eq.trans _ (getElem_append_left (bs:=extract.loop as size start #[]) hlt)
   · rw [size_append]; exact Nat.lt_of_lt_of_le hlt (Nat.le_add_right ..)
   · congr; rw [extract_loop_eq_aux]
 
-theorem get_extract_loop_ge_aux (as bs : Array α) (size start : Nat) (hge : i ≥ bs.size)
+theorem getElem_extract_loop_ge_aux (as bs : Array α) (size start : Nat) (hge : i ≥ bs.size)
     (h : i < (extract.loop as size start bs).size) : start + i - bs.size < as.size := by
   have h : i < bs.size + (as.size - start) := by
       apply Nat.lt_of_lt_of_le h
@@ -1009,9 +1151,9 @@ theorem get_extract_loop_ge_aux (as bs : Array α) (size start : Nat) (hge : i
   apply Nat.add_lt_of_lt_sub'
   exact Nat.sub_lt_left_of_lt_add hge h
 
-theorem get_extract_loop_ge (as bs : Array α) (size start : Nat) (hge : i ≥ bs.size)
+theorem getElem_extract_loop_ge (as bs : Array α) (size start : Nat) (hge : i ≥ bs.size)
     (h : i < (extract.loop as size start bs).size)
-    (h' := get_extract_loop_ge_aux as bs size start hge h) :
+    (h' := getElem_extract_loop_ge_aux as bs size start hge h) :
     (extract.loop as size start bs)[i] = as[start + i - bs.size] := by
   induction size using Nat.recAux generalizing start bs with
   | zero =>
@@ -1033,28 +1175,37 @@ theorem get_extract_loop_ge (as bs : Array α) (size start : Nat) (hge : i ≥ b
       have h₂ : bs.size < (extract.loop as size (start+1) (bs.push as[start])).size := by
         rw [size_extract_loop]; apply Nat.lt_of_lt_of_le h₁; exact Nat.le_add_right ..
       have h : (extract.loop as size (start + 1) (push bs as[start]))[bs.size] = as[start] := by
-        rw [get_extract_loop_lt as (bs.push as[start]) size (start+1) h₁ h₂, get_push_eq]
+        rw [getElem_extract_loop_lt as (bs.push as[start]) size (start+1) h₁ h₂, get_push_eq]
       rw [h]; congr; rw [Nat.add_sub_cancel]
     else
       have hge : bs.size + 1 ≤ i := Nat.lt_of_le_of_ne hge hi
       rw [ih (bs.push as[start]) (start+1) ((size_push ..).symm ▸ hge)]
       congr 1; rw [size_push, Nat.add_right_comm, Nat.add_sub_add_right]
 
-theorem get_extract_aux {as : Array α} {start stop : Nat} (h : i < (as.extract start stop).size) :
+theorem getElem_extract_aux {as : Array α} {start stop : Nat} (h : i < (as.extract start stop).size) :
     start + i < as.size := by
   rw [size_extract] at h; apply Nat.add_lt_of_lt_sub'; apply Nat.lt_of_lt_of_le h
   apply Nat.sub_le_sub_right; apply Nat.min_le_right
 
-@[simp] theorem get_extract {as : Array α} {start stop : Nat}
+@[simp] theorem getElem_extract {as : Array α} {start stop : Nat}
     (h : i < (as.extract start stop).size) :
-    (as.extract start stop)[i] = as[start + i]'(get_extract_aux h) :=
+    (as.extract start stop)[i] = as[start + i]'(getElem_extract_aux h) :=
   show (extract.loop as (min stop as.size - start) start #[])[i]
-    = as[start + i]'(get_extract_aux h) by rw [get_extract_loop_ge]; rfl; exact Nat.zero_le _
+    = as[start + i]'(getElem_extract_aux h) by rw [getElem_extract_loop_ge]; rfl; exact Nat.zero_le _
+
+theorem getElem?_extract {as : Array α} {start stop : Nat} :
+    (as.extract start stop)[i]? = if i < min stop as.size - start then as[start + i]? else none := by
+  simp only [getElem?_def, size_extract, getElem_extract]
+  split
+  · split
+    · rfl
+    · omega
+  · rfl
 
 @[simp] theorem extract_all (as : Array α) : as.extract 0 as.size = as := by
   apply ext
   · rw [size_extract, Nat.min_self, Nat.sub_zero]
-  · intros; rw [get_extract]; congr; rw [Nat.zero_add]
+  · intros; rw [getElem_extract]; congr; rw [Nat.zero_add]
 
 theorem extract_empty_of_stop_le_start (as : Array α) {start stop : Nat} (h : stop ≤ start) :
     as.extract start stop = #[] := by
@@ -1136,9 +1287,12 @@ theorem any_iff_exists {p : α → Bool} {as : Array α} {start stop} :
 theorem any_eq_true {p : α → Bool} {as : Array α} :
     any as p ↔ ∃ i : Fin as.size, p as[i] := by simp [any_iff_exists, Fin.isLt]
 
-theorem any_def {p : α → Bool} (as : Array α) : as.any p = as.toList.any p := by
+theorem any_toList {p : α → Bool} (as : Array α) : as.toList.any p = as.any p := by
   rw [Bool.eq_iff_iff, any_eq_true, List.any_eq_true]; simp only [List.mem_iff_get]
-  exact ⟨fun ⟨i, h⟩ => ⟨_, ⟨i, rfl⟩, h⟩, fun ⟨_, ⟨i, rfl⟩, h⟩ => ⟨i, h⟩⟩
+  exact ⟨fun ⟨_, ⟨i, rfl⟩, h⟩ => ⟨i, h⟩, fun ⟨i, h⟩ => ⟨_, ⟨i, rfl⟩, h⟩⟩
+
+@[deprecated "Use the reverse direction of `Array.any_toList`" (since := "2024-09-30")]
+abbrev any_def := @any_toList
 
 /-! ### all -/
 
@@ -1170,22 +1324,25 @@ theorem all_iff_forall {p : α → Bool} {as : Array α} {start stop} :
 theorem all_eq_true {p : α → Bool} {as : Array α} : all as p ↔ ∀ i : Fin as.size, p as[i] := by
   simp [all_iff_forall, Fin.isLt]
 
-theorem all_def {p : α → Bool} (as : Array α) : as.all p = as.toList.all p := by
+theorem all_toList {p : α → Bool} (as : Array α) : as.toList.all p = as.all p := by
   rw [Bool.eq_iff_iff, all_eq_true, List.all_eq_true]; simp only [List.mem_iff_getElem]
   constructor
+  · intro w i
+    exact w as[i] ⟨i, i.2, (getElem_eq_getElem_toList i.2).symm⟩
   · rintro w x ⟨r, h, rfl⟩
     rw [← getElem_eq_getElem_toList]
     exact w ⟨r, h⟩
-  · intro w i
-    exact w as[i] ⟨i, i.2, (getElem_eq_getElem_toList i.2).symm⟩
+
+@[deprecated "Use the reverse direction of `Array.all_toList`" (since := "2024-09-30")]
+abbrev all_def := @all_toList
 
 theorem all_eq_true_iff_forall_mem {l : Array α} : l.all p ↔ ∀ x, x ∈ l → p x := by
-  simp only [all_def, List.all_eq_true, mem_def]
+  simp only [← all_toList, List.all_eq_true, mem_def]
 
 /-! ### contains -/
 
 theorem contains_def [DecidableEq α] {a : α} {as : Array α} : as.contains a ↔ a ∈ as := by
-  rw [mem_def, contains, any_def, List.any_eq_true]; simp [and_comm]
+  rw [mem_def, contains, ← any_toList, List.any_eq_true]; simp [and_comm]
 
 instance [DecidableEq α] (a : α) (as : Array α) : Decidable (a ∈ as) :=
   decidable_of_iff _ contains_def
@@ -1194,12 +1351,12 @@ instance [DecidableEq α] (a : α) (as : Array α) : Decidable (a ∈ as) :=
 
 open Fin
 
-@[simp] theorem get_swap_right (a : Array α) {i j : Fin a.size} : (a.swap i j)[j.val] = a[i] :=
+@[simp] theorem getElem_swap_right (a : Array α) {i j : Fin a.size} : (a.swap i j)[j.val] = a[i] :=
   by simp only [swap, fin_cast_val, get_eq_getElem, getElem_set_eq, getElem_fin]
 
-@[simp] theorem get_swap_left (a : Array α) {i j : Fin a.size} : (a.swap i j)[i.val] = a[j] :=
+@[simp] theorem getElem_swap_left (a : Array α) {i j : Fin a.size} : (a.swap i j)[i.val] = a[j] :=
   if he : ((Array.size_set _ _ _).symm ▸ j).val = i.val then by
-    simp only [←he, fin_cast_val, get_swap_right, getElem_fin]
+    simp only [←he, fin_cast_val, getElem_swap_right, getElem_fin]
   else by
     apply Eq.trans
     · apply Array.get_set_ne
@@ -1207,7 +1364,7 @@ open Fin
       · assumption
     · simp [get_set_ne]
 
-@[simp] theorem get_swap_of_ne (a : Array α) {i j : Fin a.size} (hp : p < a.size)
+@[simp] theorem getElem_swap_of_ne (a : Array α) {i j : Fin a.size} (hp : p < a.size)
     (hi : p ≠ i) (hj : p ≠ j) : (a.swap i j)[p]'(a.size_swap .. |>.symm ▸ hp) = a[p] := by
   apply Eq.trans
   · have : ((a.size_set i (a.get j)).symm ▸ j).val = j.val := by simp only [fin_cast_val]
@@ -1219,22 +1376,22 @@ open Fin
     · apply Ne.symm
       · assumption
 
-theorem get_swap (a : Array α) (i j : Fin a.size) (k : Nat) (hk: k < a.size) :
+theorem getElem_swap' (a : Array α) (i j : Fin a.size) (k : Nat) (hk : k < a.size) :
     (a.swap i j)[k]'(by simp_all) = if k = i then a[j] else if k = j then a[i]  else a[k] := by
   split
-  · simp_all only [get_swap_left]
+  · simp_all only [getElem_swap_left]
   · split <;> simp_all
 
-theorem get_swap' (a : Array α) (i j : Fin a.size) (k : Nat) (hk' : k < (a.swap i j).size) :
+theorem getElem_swap (a : Array α) (i j : Fin a.size) (k : Nat) (hk : k < (a.swap i j).size) :
     (a.swap i j)[k] = if k = i then a[j] else if k = j then a[i] else a[k]'(by simp_all) := by
-  apply get_swap
+  apply getElem_swap'
 
 @[simp] theorem swap_swap (a : Array α) {i j : Fin a.size} :
     (a.swap i j).swap ⟨i.1, (a.size_swap ..).symm ▸i.2⟩ ⟨j.1, (a.size_swap ..).symm ▸j.2⟩ = a := by
   apply ext
   · simp only [size_swap]
   · intros
-    simp only [get_swap']
+    simp only [getElem_swap]
     split
     · simp_all
     · split <;> simp_all
@@ -1243,11 +1400,35 @@ theorem swap_comm (a : Array α) {i j : Fin a.size} : a.swap i j = a.swap j i :=
   apply ext
   · simp only [size_swap]
   · intros
-    simp only [get_swap']
+    simp only [getElem_swap]
     split
     · split <;> simp_all
     · split <;> simp_all
 
+@[deprecated getElem_extract_loop_lt_aux (since := "2024-09-30")]
+abbrev get_extract_loop_lt_aux := @getElem_extract_loop_lt_aux
+@[deprecated getElem_extract_loop_lt (since := "2024-09-30")]
+abbrev get_extract_loop_lt := @getElem_extract_loop_lt
+@[deprecated getElem_extract_loop_ge_aux (since := "2024-09-30")]
+abbrev get_extract_loop_ge_aux := @getElem_extract_loop_ge_aux
+@[deprecated getElem_extract_loop_ge (since := "2024-09-30")]
+abbrev get_extract_loop_ge := @getElem_extract_loop_ge
+@[deprecated getElem_extract_aux (since := "2024-09-30")]
+abbrev get_extract_aux := @getElem_extract_aux
+@[deprecated getElem_extract (since := "2024-09-30")]
+abbrev get_extract := @getElem_extract
+
+@[deprecated getElem_swap_right (since := "2024-09-30")]
+abbrev get_swap_right := @getElem_swap_right
+@[deprecated getElem_swap_left (since := "2024-09-30")]
+abbrev get_swap_left := @getElem_swap_left
+@[deprecated getElem_swap_of_ne (since := "2024-09-30")]
+abbrev get_swap_of_ne := @getElem_swap_of_ne
+@[deprecated getElem_swap (since := "2024-09-30")]
+abbrev get_swap := @getElem_swap
+@[deprecated getElem_swap' (since := "2024-09-30")]
+abbrev get_swap' := @getElem_swap'
+
 end Array
 
 
@@ -1264,9 +1445,6 @@ Our goal is to have `simp` "pull `List.toArray` outwards" as much as possible.
 @[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l := by
   simp [mem_def]
 
-@[simp] theorem getElem?_toArray (l : List α) (i : Nat) : l.toArray[i]? = l[i]? := by
-  simp [getElem?_eq_getElem?_toList]
-
 @[simp] theorem toListRev_toArray (l : List α) : l.toArray.toListRev = l.reverse := by
   simp
 
@@ -1316,19 +1494,45 @@ Our goal is to have `simp` "pull `List.toArray` outwards" as much as possible.
   · simp
   · simp_all [List.set_eq_of_length_le]
 
-@[simp] theorem anyM_toArray [Monad m] [LawfulMonad m] (p : α → m Bool) (l : List α) :
+theorem anyM_toArray [Monad m] [LawfulMonad m] (p : α → m Bool) (l : List α) :
     l.toArray.anyM p = l.anyM p := by
   rw [← anyM_toList]
 
-@[simp] theorem any_toArray (p : α → Bool) (l : List α) : l.toArray.any p = l.any p := by
-  rw [Array.any_def]
+theorem any_toArray (p : α → Bool) (l : List α) : l.toArray.any p = l.any p := by
+  rw [any_toList]
 
-@[simp] theorem allM_toArray [Monad m] [LawfulMonad m] (p : α → m Bool) (l : List α) :
+theorem allM_toArray [Monad m] [LawfulMonad m] (p : α → m Bool) (l : List α) :
     l.toArray.allM p = l.allM p := by
   rw [← allM_toList]
 
-@[simp] theorem all_toArray (p : α → Bool) (l : List α) : l.toArray.all p = l.all p := by
-  rw [Array.all_def]
+theorem all_toArray (p : α → Bool) (l : List α) : l.toArray.all p = l.all p := by
+  rw [all_toList]
+
+/-- Variant of `anyM_toArray` with a side condition on `stop`. -/
+@[simp] theorem anyM_toArray' [Monad m] [LawfulMonad m] (p : α → m Bool) (l : List α)
+    (h : stop = l.toArray.size) :
+    l.toArray.anyM p 0 stop = l.anyM p := by
+  subst h
+  rw [← anyM_toList]
+
+/-- Variant of `any_toArray` with a side condition on `stop`. -/
+@[simp] theorem any_toArray' (p : α → Bool) (l : List α) (h : stop = l.toArray.size) :
+    l.toArray.any p 0 stop = l.any p := by
+  subst h
+  rw [any_toList]
+
+/-- Variant of `allM_toArray` with a side condition on `stop`. -/
+@[simp] theorem allM_toArray' [Monad m] [LawfulMonad m] (p : α → m Bool) (l : List α)
+    (h : stop = l.toArray.size) :
+    l.toArray.allM p 0 stop = l.allM p := by
+  subst h
+  rw [← allM_toList]
+
+/-- Variant of `all_toArray` with a side condition on `stop`. -/
+@[simp] theorem all_toArray' (p : α → Bool) (l : List α) (h : stop = l.toArray.size) :
+    l.toArray.all p 0 stop = l.all p := by
+  subst h
+  rw [all_toList]
 
 @[simp] theorem swap_toArray (l : List α) (i j : Fin l.toArray.size) :
     l.toArray.swap i j = ((l.set i l[j]).set j l[i]).toArray := by
@@ -1343,21 +1547,30 @@ Our goal is to have `simp` "pull `List.toArray` outwards" as much as possible.
   apply ext'
   simp
 
-@[simp] theorem filter_toArray (p : α → Bool) (l : List α) :
+@[simp] theorem filter_toArray' (p : α → Bool) (l : List α) (h : stop = l.toArray.size) :
+    l.toArray.filter p 0 stop = (l.filter p).toArray := by
+  subst h
+  apply ext'
+  rw [toList_filter]
+
+@[simp] theorem filterMap_toArray' (f : α → Option β) (l : List α) (h : stop = l.toArray.size) :
+    l.toArray.filterMap f 0 stop = (l.filterMap f).toArray := by
+  subst h
+  apply ext'
+  rw [toList_filterMap]
+
+theorem filter_toArray (p : α → Bool) (l : List α) :
     l.toArray.filter p = (l.filter p).toArray := by
-  apply ext'
-  erw [toList_filter] -- `erw` required to unify `l.length` with `l.toArray.size`.
-
-@[simp] theorem filterMap_toArray (f : α → Option β) (l : List α) :
-    l.toArray.filterMap f = (l.filterMap f).toArray := by
-  apply ext'
-  erw [toList_filterMap] -- `erw` required to unify `l.length` with `l.toArray.size`.
-
-@[simp] theorem append_toArray (l₁ l₂ : List α) :
-    l₁.toArray ++ l₂.toArray = (l₁ ++ l₂).toArray := by
-  apply ext'
   simp
 
+theorem filterMap_toArray (f : α → Option β) (l : List α) :
+    l.toArray.filterMap f = (l.filterMap f).toArray := by
+  simp
+
+@[simp] theorem flatten_toArray (l : List (List α)) : (l.toArray.map List.toArray).flatten = l.join.toArray := by
+  apply ext'
+  simp [Function.comp_def]
+
 @[simp] theorem toArray_range (n : Nat) : (range n).toArray = Array.range n := by
   apply ext'
   simp

src/Init/Data/Array/QSort.lean

@@ -5,6 +5,7 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Init.Data.Array.Basic
+import Init.Data.Ord
 
 namespace Array
 -- TODO: remove the [Inhabited α] parameters as soon as we have the tactic framework for automating proof generation and using Array.fget
@@ -44,4 +45,11 @@ def qpartition (as : Array α) (lt : α → α → Bool) (lo hi : Nat) : Nat ×
     else as
   sort as low high
 
+set_option linter.unusedVariables.funArgs false in
+/--
+Sort an array using `compare` to compare elements.
+-/
+def qsortOrd [ord : Ord α] (xs : Array α) : Array α :=
+  xs.qsort fun x y => compare x y |>.isLT
+
 end Array

src/Init/Data/Array/Subarray.lean

@@ -59,6 +59,22 @@ def popFront (s : Subarray α) : Subarray α :=
   else
     s
 
+/--
+The empty subarray.
+-/
+protected def empty : Subarray α where
+  array := #[]
+  start := 0
+  stop := 0
+  start_le_stop := Nat.le_refl 0
+  stop_le_array_size := Nat.le_refl 0
+
+instance : EmptyCollection (Subarray α) :=
+  ⟨Subarray.empty⟩
+
+instance : Inhabited (Subarray α) :=
+  ⟨{}⟩
+
 @[inline] unsafe def forInUnsafe {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (s : Subarray α) (b : β) (f : α → β → m (ForInStep β)) : m β :=
   let sz := USize.ofNat s.stop
   let rec @[specialize] loop (i : USize) (b : β) : m β := do

src/Init/Data/BitVec/Basic.lean

@@ -269,8 +269,8 @@ Return the absolute value of a signed bitvector.
 protected def abs (x : BitVec n) : BitVec n := if x.msb then .neg x else x
 
 /--
-Multiplication for bit vectors. This can be interpreted as either signed or unsigned negation
-modulo `2^n`.
+Multiplication for bit vectors. This can be interpreted as either signed or unsigned
+multiplication modulo `2^n`.
 
 SMT-Lib name: `bvmul`.
 -/
@@ -676,6 +676,13 @@ result of appending a single bit to the front in the naive implementation).
     That is, the new bit is the least significant bit. -/
 def concat {n} (msbs : BitVec n) (lsb : Bool) : BitVec (n+1) := msbs ++ (ofBool lsb)
 
+/--
+`x.shiftConcat b` shifts all bits of `x` to the left by `1` and sets the least significant bit to `b`.
+It is a non-dependent version of `concat` that does not change the total bitwidth.
+-/
+def shiftConcat (x : BitVec n) (b : Bool) : BitVec n :=
+  (x.concat b).truncate n
+
 /-- Prepend a single bit to the front of a bitvector, using big endian order (see `append`).
     That is, the new bit is the most significant bit. -/
 def cons {n} (msb : Bool) (lsbs : BitVec n) : BitVec (n+1) :=

src/Init/Data/BitVec/Bitblast.lean

@@ -164,6 +164,17 @@ theorem getLsbD_add {i : Nat} (i_lt : i < w) (x y : BitVec w) :
       (getLsbD x i ^^ (getLsbD y i ^^ carry i x y false)) := by
   simpa using getLsbD_add_add_bool i_lt x y false
 
+theorem getElem_add_add_bool {i : Nat} (i_lt : i < w) (x y : BitVec w) (c : Bool) :
+    (x + y + setWidth w (ofBool c))[i] =
+      (x[i] ^^ (y[i] ^^ carry i x y c)) := by
+  simp only [← getLsbD_eq_getElem]
+  rw [getLsbD_add_add_bool]
+  omega
+
+theorem getElem_add {i : Nat} (i_lt : i < w) (x y : BitVec w) :
+    (x + y)[i] = (x[i] ^^ (y[i] ^^ carry i x y false)) := by
+  simpa using getElem_add_add_bool i_lt x y false
+
 theorem adc_spec (x y : BitVec w) (c : Bool) :
     adc x y c = (carry w x y c, x + y + setWidth w (ofBool c)) := by
   simp only [adc]
@@ -368,6 +379,10 @@ theorem getLsbD_mul (x y : BitVec w) (i : Nat) :
   · simp
   · omega
 
+theorem getElem_mul {x y : BitVec w} {i : Nat} (h : i < w) :
+    (x * y)[i] = (mulRec x y w)[i] := by
+  simp [mulRec_eq_mul_signExtend_setWidth]
+
 /-! ## shiftLeft recurrence for bitblasting -/
 
 /--
@@ -438,6 +453,385 @@ theorem shiftLeft_eq_shiftLeftRec (x : BitVec w₁) (y : BitVec w₂) :
   · simp [of_length_zero]
   · simp [shiftLeftRec_eq]
 
+/-! # udiv/urem recurrence for bitblasting
+
+In order to prove the correctness of the division algorithm on the integers,
+one shows that `n.div d = q` and `n.mod d = r` iff `n = d * q + r` and `0 ≤ r < d`.
+Mnemonic: `n` is the numerator, `d` is the denominator, `q` is the quotient, and `r` the remainder.
+
+This *uniqueness of decomposition* is not true for bitvectors.
+For `n = 0, d = 3, w = 3`, we can write:
+- `0 = 0 * 3 + 0` (`q = 0`, `r = 0 < 3`.)
+- `0 = 2 * 3 + 2 = 6 + 2 ≃ 0 (mod 8)` (`q = 2`, `r = 2 < 3`).
+
+Such examples can be created by choosing different `(q, r)` for a fixed `(d, n)`
+such that `(d * q + r)` overflows and wraps around to equal `n`.
+
+This tells us that the division algorithm must have more restrictions than just the ones
+we have for integers. These restrictions are captured in `DivModState.Lawful`.
+The key idea is to state the relationship in terms of the toNat values of {n, d, q, r}.
+If the division equation `d.toNat * q.toNat + r.toNat = n.toNat` holds,
+then `n.udiv d = q` and `n.umod d = r`.
+
+Following this, we implement the division algorithm by repeated shift-subtract.
+
+References:
+- Fast 32-bit Division on the DSP56800E: Minimized nonrestoring division algorithm by David Baca
+- Bitwuzla sources for bitblasting.h
+-/
+
+private theorem Nat.div_add_eq_left_of_lt {x y z : Nat} (hx : z ∣ x) (hy : y < z) (hz : 0 < z) :
+    (x + y) / z = x / z := by
+  refine Nat.div_eq_of_lt_le ?lo ?hi
+  · apply Nat.le_trans
+    · exact div_mul_le_self x z
+    · omega
+  · simp only [succ_eq_add_one, Nat.add_mul, Nat.one_mul]
+    apply Nat.add_lt_add_of_le_of_lt
+    · apply Nat.le_of_eq
+      exact (Nat.div_eq_iff_eq_mul_left hz hx).mp rfl
+    · exact hy
+
+/-- If the division equation `d.toNat * q.toNat + r.toNat = n.toNat` holds,
+then `n.udiv d = q`. -/
+theorem udiv_eq_of_mul_add_toNat {d n q r : BitVec w} (hd : 0 < d)
+    (hrd : r < d)
+    (hdqnr : d.toNat * q.toNat + r.toNat = n.toNat) :
+    n.udiv d = q := by
+  apply BitVec.eq_of_toNat_eq
+  rw [toNat_udiv]
+  replace hdqnr : (d.toNat * q.toNat + r.toNat) / d.toNat = n.toNat / d.toNat := by
+    simp [hdqnr]
+  rw [Nat.div_add_eq_left_of_lt] at hdqnr
+  · rw [← hdqnr]
+    exact mul_div_right q.toNat hd
+  · exact Nat.dvd_mul_right d.toNat q.toNat
+  · exact hrd
+  · exact hd
+
+/-- If the division equation `d.toNat * q.toNat + r.toNat = n.toNat` holds,
+then `n.umod d = r`. -/
+theorem umod_eq_of_mul_add_toNat {d n q r : BitVec w} (hrd : r < d)
+    (hdqnr : d.toNat * q.toNat + r.toNat = n.toNat) :
+    n.umod d = r := by
+  apply BitVec.eq_of_toNat_eq
+  rw [toNat_umod]
+  replace hdqnr : (d.toNat * q.toNat + r.toNat) % d.toNat = n.toNat % d.toNat := by
+    simp [hdqnr]
+  rw [Nat.add_mod, Nat.mul_mod_right] at hdqnr
+  simp only [Nat.zero_add, mod_mod] at hdqnr
+  replace hrd : r.toNat < d.toNat := by
+    simpa [BitVec.lt_def] using hrd
+  rw [Nat.mod_eq_of_lt hrd] at hdqnr
+  simp [hdqnr]
+
+/-! ### DivModState -/
+
+/-- `DivModState` is a structure that maintains the state of recursive `divrem` calls. -/
+structure DivModState (w : Nat) : Type where
+  /-- The number of bits in the numerator that are not yet processed -/
+  wn : Nat
+  /-- The number of bits in the remainder (and quotient) -/
+  wr : Nat
+  /-- The current quotient. -/
+  q : BitVec w
+  /-- The current remainder. -/
+  r : BitVec w
+
+
+/-- `DivModArgs` contains the arguments to a `divrem` call which remain constant throughout
+execution. -/
+structure DivModArgs (w : Nat) where
+  /-- the numerator (aka, dividend) -/
+  n : BitVec w
+  /-- the denumerator (aka, divisor)-/
+  d : BitVec w
+
+/-- A `DivModState` is lawful if the remainder width `wr` plus the numerator width `wn` equals `w`,
+and the bitvectors `r` and `n` have values in the bounds given by bitwidths `wr`, resp. `wn`.
+
+This is a proof engineering choice: an alternative world could have been
+`r : BitVec wr` and `n : BitVec wn`, but this required much more dependent typing coercions.
+
+Instead, we choose to declare all involved bitvectors as length `w`, and then prove that
+the values are within their respective bounds.
+
+We start with `wn = w` and `wr = 0`, and then in each step, we decrement `wn` and increment `wr`.
+In this way, we grow a legal remainder in each loop iteration.
+-/
+structure DivModState.Lawful {w : Nat} (args : DivModArgs w) (qr : DivModState w) : Prop where
+  /-- The sum of widths of the dividend and remainder is `w`. -/
+  hwrn : qr.wr + qr.wn = w
+  /-- The denominator is positive. -/
+  hdPos : 0 < args.d
+  /-- The remainder is strictly less than the denominator. -/
+  hrLtDivisor : qr.r.toNat < args.d.toNat
+  /-- The remainder is morally a `Bitvec wr`, and so has value less than `2^wr`. -/
+  hrWidth : qr.r.toNat < 2^qr.wr
+  /-- The quotient is morally a `Bitvec wr`, and so has value less than `2^wr`. -/
+  hqWidth : qr.q.toNat < 2^qr.wr
+  /-- The low `(w - wn)` bits of `n` obey the invariant for division. -/
+  hdiv : args.n.toNat >>> qr.wn = args.d.toNat * qr.q.toNat + qr.r.toNat
+
+/-- A lawful DivModState implies `w > 0`. -/
+def DivModState.Lawful.hw {args : DivModArgs w} {qr : DivModState w}
+    {h : DivModState.Lawful args qr} : 0 < w := by
+  have hd := h.hdPos
+  rcases w with rfl | w
+  · have hcontra : args.d = 0#0 := by apply Subsingleton.elim
+    rw [hcontra] at hd
+    simp at hd
+  · omega
+
+/-- An initial value with both `q, r = 0`. -/
+def DivModState.init (w : Nat) : DivModState w := {
+  wn := w
+  wr := 0
+  q := 0#w
+  r := 0#w
+}
+
+/-- The initial state is lawful. -/
+def DivModState.lawful_init {w : Nat} (args : DivModArgs w) (hd : 0#w < args.d) :
+    DivModState.Lawful args (DivModState.init w) := by
+  simp only [BitVec.DivModState.init]
+  exact {
+    hwrn := by simp only; omega,
+    hdPos := by assumption
+    hrLtDivisor := by simp [BitVec.lt_def] at hd ⊢; assumption
+    hrWidth := by simp [DivModState.init],
+    hqWidth := by simp [DivModState.init],
+    hdiv := by
+      simp only [DivModState.init, toNat_ofNat, zero_mod, Nat.mul_zero, Nat.add_zero];
+      rw [Nat.shiftRight_eq_div_pow]
+      apply Nat.div_eq_of_lt args.n.isLt
+  }
+
+/--
+A lawful DivModState with a fully consumed dividend (`wn = 0`) witnesses that the
+quotient has been correctly computed.
+-/
+theorem DivModState.udiv_eq_of_lawful {n d : BitVec w} {qr : DivModState w}
+    (h_lawful : DivModState.Lawful {n, d} qr)
+    (h_final  : qr.wn = 0) :
+    n.udiv d = qr.q := by
+  apply udiv_eq_of_mul_add_toNat h_lawful.hdPos h_lawful.hrLtDivisor
+  have hdiv := h_lawful.hdiv
+  simp only [h_final] at *
+  omega
+
+/--
+A lawful DivModState with a fully consumed dividend (`wn = 0`) witnesses that the
+remainder has been correctly computed.
+-/
+theorem DivModState.umod_eq_of_lawful {qr : DivModState w}
+    (h : DivModState.Lawful {n, d} qr)
+    (h_final  : qr.wn = 0) :
+    n.umod d = qr.r := by
+  apply umod_eq_of_mul_add_toNat h.hrLtDivisor
+  have hdiv := h.hdiv
+  simp only [shiftRight_zero] at hdiv
+  simp only [h_final] at *
+  exact hdiv.symm
+
+/-! ### DivModState.Poised -/
+
+/--
+A `Poised` DivModState is a state which is `Lawful` and furthermore, has at least
+one numerator bit left to process `(0 < wn)`
+
+The input to the shift subtractor is a legal input to `divrem`, and we also need to have an
+input bit to perform shift subtraction on, and thus we need `0 < wn`.
+-/
+structure DivModState.Poised {w : Nat} (args : DivModArgs w) (qr : DivModState w)
+  extends DivModState.Lawful args qr : Type where
+  /-- Only perform a round of shift-subtract if we have dividend bits. -/
+  hwn_lt : 0 < qr.wn
+
+/--
+In the shift subtract input, the dividend is at least one bit long (`wn > 0`), so
+the remainder has bits to be computed (`wr < w`).
+-/
+def DivModState.wr_lt_w {qr : DivModState w} (h : qr.Poised args) : qr.wr < w := by
+  have hwrn := h.hwrn
+  have hwn_lt := h.hwn_lt
+  omega
+
+/-! ### Division shift subtractor -/
+
+/--
+One round of the division algorithm, that tries to perform a subtract shift.
+Note that this should only be called when `r.msb = false`, so we will not overflow.
+-/
+def divSubtractShift (args : DivModArgs w) (qr : DivModState w) : DivModState w :=
+  let {n, d} := args
+  let wn := qr.wn - 1
+  let wr := qr.wr + 1
+  let r' := shiftConcat qr.r (n.getLsbD wn)
+  if r' < d then {
+    q := qr.q.shiftConcat false, -- If `r' < d`, then we do not have a quotient bit.
+    r := r'
+    wn, wr
+  } else {
+    q := qr.q.shiftConcat true, -- Otherwise, `r' ≥ d`, and we have a quotient bit.
+    r := r' - d -- we subtract to maintain the invariant that `r < d`.
+    wn, wr
+  }
+
+/-- The value of shifting right by `wn - 1` equals shifting by `wn` and grabbing the lsb at `(wn - 1)`. -/
+theorem DivModState.toNat_shiftRight_sub_one_eq
+    {args : DivModArgs w} {qr : DivModState w} (h : qr.Poised args) :
+    args.n.toNat >>> (qr.wn - 1)
+    = (args.n.toNat >>> qr.wn) * 2 + (args.n.getLsbD (qr.wn - 1)).toNat := by
+  show BitVec.toNat (args.n >>> (qr.wn - 1)) = _
+  have {..} := h -- break the structure down for `omega`
+  rw [shiftRight_sub_one_eq_shiftConcat args.n h.hwn_lt]
+  rw [toNat_shiftConcat_eq_of_lt (k := w - qr.wn)]
+  · simp
+  · omega
+  · apply BitVec.toNat_ushiftRight_lt
+    omega
+
+/--
+This is used when proving the correctness of the divison algorithm,
+where we know that `r < d`.
+We then want to show that `((r.shiftConcat b) - d) < d` as the loop invariant.
+In arithmetic, this is the same as showing that
+`r * 2 + 1 - d < d`, which this theorem establishes.
+-/
+private theorem two_mul_add_sub_lt_of_lt_of_lt_two (h : a < x) (hy : y < 2) :
+    2 * a + y - x < x := by omega
+
+/-- We show that the output of `divSubtractShift` is lawful, which tells us that it
+obeys the division equation. -/
+theorem lawful_divSubtractShift (qr : DivModState w) (h : qr.Poised args) :
+    DivModState.Lawful args (divSubtractShift args qr) := by
+  rcases args with ⟨n, d⟩
+  simp only [divSubtractShift, decide_eq_true_eq]
+  -- We add these hypotheses for `omega` to find them later.
+  have ⟨⟨hrwn, hd, hrd, hr, hn, hrnd⟩, hwn_lt⟩ := h
+  have : d.toNat * (qr.q.toNat * 2) = d.toNat * qr.q.toNat * 2 := by rw [Nat.mul_assoc]
+  by_cases rltd : shiftConcat qr.r (n.getLsbD (qr.wn - 1)) < d
+  · simp only [rltd, ↓reduceIte]
+    constructor <;> try bv_omega
+    case pos.hrWidth => apply toNat_shiftConcat_lt_of_lt <;> omega
+    case pos.hqWidth => apply toNat_shiftConcat_lt_of_lt <;> omega
+    case pos.hdiv =>
+      simp [qr.toNat_shiftRight_sub_one_eq h, h.hdiv, this,
+        toNat_shiftConcat_eq_of_lt (qr.wr_lt_w h) h.hrWidth,
+        toNat_shiftConcat_eq_of_lt (qr.wr_lt_w h) h.hqWidth]
+      omega
+  · simp only [rltd, ↓reduceIte]
+    constructor <;> try bv_omega
+    case neg.hrLtDivisor =>
+      simp only [lt_def, Nat.not_lt] at rltd
+      rw [BitVec.toNat_sub_of_le rltd,
+        toNat_shiftConcat_eq_of_lt (hk := qr.wr_lt_w h) (hx := h.hrWidth),
+        Nat.mul_comm]
+      apply two_mul_add_sub_lt_of_lt_of_lt_two <;> bv_omega
+    case neg.hrWidth =>
+      simp only
+      have hdr' : d ≤ (qr.r.shiftConcat (n.getLsbD (qr.wn - 1))) :=
+        BitVec.not_lt_iff_le.mp rltd
+      have hr' : ((qr.r.shiftConcat (n.getLsbD (qr.wn - 1)))).toNat < 2 ^ (qr.wr + 1) := by
+        apply toNat_shiftConcat_lt_of_lt <;> bv_omega
+      rw [BitVec.toNat_sub_of_le hdr']
+      omega
+    case neg.hqWidth =>
+      apply toNat_shiftConcat_lt_of_lt <;> omega
+    case neg.hdiv =>
+      have rltd' := (BitVec.not_lt_iff_le.mp rltd)
+      simp only [qr.toNat_shiftRight_sub_one_eq h,
+        BitVec.toNat_sub_of_le rltd',
+        toNat_shiftConcat_eq_of_lt (qr.wr_lt_w h) h.hrWidth]
+      simp only [BitVec.le_def,
+        toNat_shiftConcat_eq_of_lt (qr.wr_lt_w h) h.hrWidth] at rltd'
+      simp only [toNat_shiftConcat_eq_of_lt (qr.wr_lt_w h) h.hqWidth, h.hdiv, Nat.mul_add]
+      bv_omega
+
+/-! ### Core division algorithm circuit -/
+
+/-- A recursive definition of division for bitblasting, in terms of a shift-subtraction circuit. -/
+def divRec {w : Nat} (m : Nat) (args : DivModArgs w) (qr : DivModState w) :
+    DivModState w :=
+  match m with
+  | 0 => qr
+  | m + 1 => divRec m args <| divSubtractShift args qr
+
+@[simp]
+theorem divRec_zero (qr : DivModState w) :
+    divRec 0 args qr = qr := rfl
+
+@[simp]
+theorem divRec_succ (m : Nat) (args : DivModArgs w) (qr : DivModState w) :
+    divRec (m + 1) args qr =
+      divRec m args (divSubtractShift args qr) := rfl
+
+/-- The output of `divRec` is a lawful state -/
+theorem lawful_divRec {args : DivModArgs w} {qr : DivModState w}
+    (h : DivModState.Lawful args qr) :
+    DivModState.Lawful args (divRec qr.wn args qr) := by
+  generalize hm : qr.wn = m
+  induction m generalizing qr
+  case zero =>
+    exact h
+  case succ wn' ih =>
+    simp only [divRec_succ]
+    apply ih
+    · apply lawful_divSubtractShift
+      constructor
+      · assumption
+      · omega
+    · simp only [divSubtractShift, hm]
+      split <;> rfl
+
+/-- The output of `divRec` has no more bits left to process (i.e., `wn = 0`) -/
+@[simp]
+theorem wn_divRec (args : DivModArgs w) (qr : DivModState w) :
+    (divRec qr.wn args qr).wn = 0 := by
+  generalize hm : qr.wn = m
+  induction m generalizing qr
+  case zero =>
+    assumption
+  case succ wn' ih =>
+    apply ih
+    simp only [divSubtractShift, hm]
+    split <;> rfl
+
+/-- The result of `udiv` agrees with the result of the division recurrence. -/
+theorem udiv_eq_divRec (hd : 0#w < d) :
+    let out := divRec w {n, d} (DivModState.init w)
+    n.udiv d = out.q := by
+  have := DivModState.lawful_init {n, d} hd
+  have := lawful_divRec this
+  apply DivModState.udiv_eq_of_lawful this (wn_divRec ..)
+
+/-- The result of `umod` agrees with the result of the division recurrence. -/
+theorem umod_eq_divRec (hd : 0#w < d) :
+    let out := divRec w {n, d} (DivModState.init w)
+    n.umod d = out.r := by
+  have := DivModState.lawful_init {n, d} hd
+  have := lawful_divRec this
+  apply DivModState.umod_eq_of_lawful this (wn_divRec ..)
+
+theorem divRec_succ' (m : Nat) (args : DivModArgs w) (qr : DivModState w) :
+    divRec (m+1) args qr =
+    let wn := qr.wn - 1
+    let wr := qr.wr + 1
+    let r' := shiftConcat qr.r (args.n.getLsbD wn)
+    let input : DivModState _ :=
+      if r' < args.d then {
+        q := qr.q.shiftConcat false,
+        r := r'
+        wn, wr
+      } else {
+        q := qr.q.shiftConcat true,
+        r := r' - args.d
+        wn, wr
+      }
+    divRec m args input := by
+  simp [divRec_succ, divSubtractShift]
+
 /- ### Arithmetic shift right (sshiftRight) recurrence -/
 
 /--

src/Init/Data/BitVec/Lemmas.lean

@@ -165,7 +165,8 @@ theorem getMsbD_eq_getMsb?_getD (x : BitVec w) (i : Nat) :
   · simp [getMsb?, h]
   · rw [getLsbD_eq_getElem?_getD, getMsb?_eq_getLsb?]
     split <;>
-    · simp
+    · simp only [getLsb?_eq_getElem?, Bool.and_iff_right_iff_imp, decide_eq_true_eq,
+        Option.getD_none, Bool.and_eq_false_imp]
       intros
       omega
 
@@ -303,7 +304,7 @@ theorem getElem?_zero_ofNat_one : (BitVec.ofNat (w+1) 1)[0]? = some true := by
 
 -- This does not need to be a `@[simp]` theorem as it is already handled by `getElem?_eq_getElem`.
 theorem getElem?_zero_ofBool (b : Bool) : (ofBool b)[0]? = some b := by
-  simp [ofBool, cond_eq_if]
+  simp only [ofBool, ofNat_eq_ofNat, cond_eq_if]
   split <;> simp_all
 
 @[simp] theorem getElem_zero_ofBool (b : Bool) : (ofBool b)[0] = b := by
@@ -332,7 +333,7 @@ theorem getElem_ofBool {b : Bool} {i : Nat} : (ofBool b)[0] = b := by
 
 theorem msb_eq_getLsbD_last (x : BitVec w) :
     x.msb = x.getLsbD (w - 1) := by
-  simp [BitVec.msb, getMsbD, getLsbD]
+  simp only [BitVec.msb, getMsbD]
   rcases w  with rfl | w
   · simp [BitVec.eq_nil x]
   · simp
@@ -360,7 +361,7 @@ theorem toNat_ge_of_msb_true {x : BitVec n} (p : BitVec.msb x = true) : x.toNat
   | 0 =>
     simp [BitVec.msb, BitVec.getMsbD] at p
   | n + 1 =>
-    simp [BitVec.msb_eq_decide] at p
+    simp only [msb_eq_decide, Nat.add_one_sub_one, decide_eq_true_eq] at p
     simp only [Nat.add_sub_cancel]
     exact p
 
@@ -420,7 +421,7 @@ theorem toInt_eq_toNat_bmod (x : BitVec n) : x.toInt = Int.bmod x.toNat (2^n) :=
 /-- Prove equality of bitvectors in terms of nat operations. -/
 theorem eq_of_toInt_eq {x y : BitVec n} : x.toInt = y.toInt → x = y := by
   intro eq
-  simp [toInt_eq_toNat_cond] at eq
+  simp only [toInt_eq_toNat_cond] at eq
   apply eq_of_toNat_eq
   revert eq
   have _xlt := x.isLt
@@ -462,6 +463,16 @@ theorem toInt_pos_iff {w : Nat} {x : BitVec w} :
     0 ≤ BitVec.toInt x ↔ 2 * x.toNat < 2 ^ w := by
   simp [toInt_eq_toNat_cond]; omega
 
+theorem eq_zero_or_eq_one (a : BitVec 1) : a = 0#1 ∨ a = 1#1 := by
+  obtain ⟨a, ha⟩ := a
+  simp only [Nat.reducePow]
+  have acases : a = 0 ∨ a = 1 := by omega
+  rcases acases with ⟨rfl | rfl⟩
+  · simp
+  · case inr h =>
+    subst h
+    simp
+
 /-! ### setWidth, zeroExtend and truncate -/
 
 @[simp]
@@ -524,6 +535,7 @@ theorem getElem_setWidth' (x : BitVec w) (i : Nat) (h : w ≤ v) (hi : i < v) :
     (setWidth' h x)[i] = x.getLsbD i := by
   rw [getElem_eq_testBit_toNat, toNat_setWidth', getLsbD]
 
+@[simp]
 theorem getElem_setWidth (m : Nat) (x : BitVec n) (i : Nat) (h : i < m) :
     (setWidth m x)[i] = x.getLsbD i := by
   rw [setWidth]
@@ -900,8 +912,8 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
     rw [← h]
     rw [Nat.testBit_two_pow_sub_succ (isLt _)]
     · cases w : decide (i < v)
-      · simp at w
-        simp [w]
+      · simp only [decide_eq_false_iff_not, Nat.not_lt] at w
+        simp only [Bool.false_bne, Bool.false_and]
         rw [Nat.testBit_lt_two_pow]
         calc BitVec.toNat x < 2 ^ v := isLt _
           _ ≤ 2 ^ i := Nat.pow_le_pow_of_le_right Nat.zero_lt_two w
@@ -949,6 +961,16 @@ theorem not_not {b : BitVec w} : ~~~(~~~b) = b := by
   ext i
   simp
 
+@[simp] theorem getMsb_not {x : BitVec w} :
+    (~~~x).getMsbD i = (decide (i < w) && !(x.getMsbD i)) := by
+  simp only [getMsbD]
+  by_cases h : i < w
+  · simp [h]; omega
+  · simp [h];
+
+@[simp] theorem msb_not {x : BitVec w} : (~~~x).msb = (decide (0 < w) && !x.msb) := by
+  simp [BitVec.msb]
+
 /-! ### cast -/
 
 @[simp] theorem not_cast {x : BitVec w} (h : w = w') : ~~~(cast h x) = cast h (~~~x) := by
@@ -1031,7 +1053,8 @@ theorem shiftLeft_or_distrib (x y : BitVec w) (n : Nat) :
   simp only [t]
   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 [h₁, h₂, h₃]
+    <;> 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
 
@@ -1149,6 +1172,17 @@ theorem ushiftRight_or_distrib (x y : BitVec w)  (n : Nat) :
 theorem ushiftRight_zero_eq (x : BitVec w) : x >>> 0 = x := by
   simp [bv_toNat]
 
+/--
+Shifting right by `n < w` yields a bitvector whose value is less than `2 ^ (w - n)`.
+-/
+theorem toNat_ushiftRight_lt (x : BitVec w) (n : Nat) (hn : n ≤ w) :
+    (x >>> n).toNat < 2 ^ (w - n) := by
+  rw [toNat_ushiftRight, Nat.shiftRight_eq_div_pow, Nat.div_lt_iff_lt_mul]
+  · rw [Nat.pow_sub_mul_pow]
+    · apply x.isLt
+    · apply hn
+  · apply Nat.pow_pos (by decide)
+
 /-! ### ushiftRight reductions from BitVec to Nat -/
 
 @[simp]
@@ -1282,6 +1316,22 @@ theorem sshiftRight_add {x : BitVec w} {m n : Nat} :
         omega
       · simp [h₃, sshiftRight_msb_eq_msb]
 
+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,
+    Bool.true_and, msb_not]
+  by_cases h : w ≤ i
+  <;> by_cases h' : n + i < w
+  <;> by_cases h'' : 0 < w
+  <;> simp [h, h', h'']
+  <;> omega
+
+@[simp]
+theorem not_sshiftRight_not {x : BitVec w} {n : Nat} :
+    ~~~((~~~x).sshiftRight n) = x.sshiftRight n := by
+  simp [not_sshiftRight]
+
 /-! ### sshiftRight reductions from BitVec to Nat -/
 
 @[simp]
@@ -1312,6 +1362,69 @@ theorem umod_eq {x y : BitVec n} :
 theorem toNat_umod {x y : BitVec n} :
     (x.umod y).toNat = x.toNat % y.toNat := rfl
 
+/-! ### sdiv -/
+
+/-- Equation theorem for `sdiv` in terms of `udiv`. -/
+theorem sdiv_eq (x y : BitVec w) : x.sdiv y =
+  match x.msb, y.msb with
+  | false, false => udiv x y
+  | false, true  =>  - (x.udiv (- y))
+  | true,  false => - ((- x).udiv y)
+  | true,  true  => (- x).udiv (- y) := by
+  rw [BitVec.sdiv]
+  rcases x.msb <;> rcases y.msb <;> simp
+
+@[bv_toNat]
+theorem toNat_sdiv {x y : BitVec w} : (x.sdiv y).toNat =
+    match x.msb, y.msb with
+    | false, false => (udiv x y).toNat
+    | false, true  =>  (- (x.udiv (- y))).toNat
+    | true,  false => (- ((- x).udiv y)).toNat
+    | true,  true  => ((- x).udiv (- y)).toNat := by
+  simp only [sdiv_eq, toNat_udiv]
+  by_cases h : x.msb <;> by_cases h' : y.msb <;> simp [h, h']
+
+theorem sdiv_eq_and (x y : BitVec 1) : x.sdiv y = x &&& y := by
+  have hx : x = 0#1 ∨ x = 1#1 := by bv_omega
+  have hy : y = 0#1 ∨ y = 1#1 := by bv_omega
+  rcases hx with rfl | rfl <;>
+    rcases hy with rfl | rfl <;>
+      rfl
+
+/-! ### smod -/
+
+/-- Equation theorem for `smod` in terms of `umod`. -/
+theorem smod_eq (x y : BitVec w) : x.smod y =
+  match x.msb, y.msb with
+  | false, false => x.umod y
+  | false, true =>
+    let u := x.umod (- y)
+    (if u = 0#w then u else u + y)
+  | true, false =>
+    let u := umod (- x) y
+    (if u = 0#w then u else y - u)
+  | true, true => - ((- x).umod (- y)) := by
+  rw [BitVec.smod]
+  rcases x.msb <;> rcases y.msb <;> simp
+
+@[bv_toNat]
+theorem toNat_smod {x y : BitVec w} : (x.smod y).toNat =
+    match x.msb, y.msb with
+    | false, false => (x.umod y).toNat
+    | false, true =>
+      let u := x.umod (- y)
+      (if u = 0#w then u.toNat else (u + y).toNat)
+    | true, false =>
+      let u := (-x).umod y
+      (if u = 0#w then u.toNat else (y - u).toNat)
+    | true, true => (- ((- x).umod (- y))).toNat := by
+  simp only [smod_eq, toNat_umod]
+  by_cases h : x.msb <;> by_cases h' : y.msb
+  <;> by_cases h'' : (-x).umod y = 0#w <;> by_cases h''' : x.umod (-y) = 0#w
+  <;> simp only [h, h', h'', h''']
+  <;> simp only [umod, toNat_eq, toNat_ofNatLt, toNat_ofNat, Nat.zero_mod] at h'' h'''
+  <;> simp [h'', h''']
+
 /-! ### signExtend -/
 
 /-- Equation theorem for `Int.sub` when both arguments are `Int.ofNat` -/
@@ -1396,18 +1509,18 @@ theorem getLsbD_append {x : BitVec n} {y : BitVec m} :
   simp only [append_def, getLsbD_or, getLsbD_shiftLeftZeroExtend, getLsbD_setWidth']
   by_cases h : i < m
   · simp [h]
-  · simp [h]; simp_all
+  · simp_all [h]
 
 theorem getElem_append {x : BitVec n} {y : BitVec m} (h : i < n + m) :
     (x ++ y)[i] = bif i < m then getLsbD y i else getLsbD x (i - m) := by
   simp only [append_def, getElem_or, getElem_shiftLeftZeroExtend, getElem_setWidth']
   by_cases h' : i < m
   · simp [h']
-  · simp [h']; simp_all
+  · simp_all [h']
 
 @[simp] theorem getMsbD_append {x : BitVec n} {y : BitVec m} :
     getMsbD (x ++ y) i = bif n ≤ i then getMsbD y (i - n) else getMsbD x i := by
-  simp [append_def]
+  simp only [append_def]
   by_cases h : n ≤ i
   · simp [h]
   · simp [h]
@@ -1415,7 +1528,7 @@ theorem getElem_append {x : BitVec n} {y : BitVec m} (h : i < n + m) :
 theorem msb_append {x : BitVec w} {y : BitVec v} :
     (x ++ y).msb = bif (w == 0) then (y.msb) else (x.msb) := by
   rw [← append_eq, append]
-  simp [msb_setWidth']
+  simp only [msb_or, msb_shiftLeftZeroExtend, msb_setWidth']
   by_cases h : w = 0
   · subst h
     simp [BitVec.msb, getMsbD]
@@ -1512,6 +1625,21 @@ theorem shiftRight_add {w : Nat} (x : BitVec w) (n m : Nat) :
   ext i
   simp [Nat.add_assoc n m i]
 
+theorem shiftLeft_ushiftRight {x : BitVec w} {n : Nat}:
+    x >>> n <<< n = x &&& BitVec.allOnes w <<< n := by
+  induction n generalizing x
+  case zero =>
+    ext; simp
+  case succ n ih =>
+    rw [BitVec.shiftLeft_add, Nat.add_comm, BitVec.shiftRight_add, ih,
+       Nat.add_comm, BitVec.shiftLeft_add, BitVec.shiftLeft_and_distrib]
+    ext i
+    by_cases hw : w = 0
+    · simp [hw]
+    · by_cases hi₂ : i.val = 0
+      · simp [hi₂]
+      · simp [Nat.lt_one_iff, hi₂, show 1 + (i.val - 1) = i by omega]
+
 @[deprecated shiftRight_add (since := "2024-06-02")]
 theorem shiftRight_shiftRight {w : Nat} (x : BitVec w) (n m : Nat) :
     (x >>> n) >>> m = x >>> (n + m) := by
@@ -1521,13 +1649,13 @@ 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 [getLsbD, getMsbD]
+  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 [getMsbD]
+  simp only [Fin.getElem_fin, Fin.val_rev, getMsbD, Fin.is_lt, decide_True, Bool.true_and]
   congr 1
   omega
 
@@ -1552,13 +1680,13 @@ theorem toNat_cons' {x : BitVec w} :
 
 theorem getLsbD_cons (b : Bool) {n} (x : BitVec n) (i : Nat) :
     getLsbD (cons b x) i = if i = n then b else getLsbD x i := by
-  simp only [getLsbD, toNat_cons, Nat.testBit_or]
-  rw [Nat.testBit_shiftLeft]
+  simp only [getLsbD, toNat_cons, Nat.testBit_or, Nat.testBit_shiftLeft, ge_iff_le]
   rcases Nat.lt_trichotomy i n with i_lt_n | i_eq_n | n_lt_i
   · have p1 : ¬(n ≤ i) := by omega
     have p2 : i ≠ n := by omega
     simp [p1, p2]
-  · simp [i_eq_n, testBit_toNat]
+  · 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
     have p2 : i - n ≠ 0 := by omega
@@ -1572,7 +1700,8 @@ 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 [i_eq_n, testBit_toNat]
+  · 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
     have p2 : i - n ≠ 0 := by omega
@@ -1683,6 +1812,51 @@ theorem getElem_concat (x : BitVec w) (b : Bool) (i : Nat) (h : i < w + 1) :
     (concat x a) ^^^ (concat y b) = concat (x ^^^ y) (a ^^ b) := by
   ext i; cases i using Fin.succRecOn <;> simp
 
+/-! ### shiftConcat -/
+
+theorem getLsbD_shiftConcat (x : BitVec w) (b : Bool) (i : Nat) :
+    (shiftConcat x b).getLsbD i
+    = (decide (i < w) && (if (i = 0) then b else x.getLsbD (i - 1))) := by
+  simp only [shiftConcat, getLsbD_setWidth, getLsbD_concat]
+
+theorem getLsbD_shiftConcat_eq_decide (x : BitVec w) (b : Bool) (i : Nat) :
+    (shiftConcat x b).getLsbD i
+    = (decide (i < w) && ((decide (i = 0) && b) || (decide (0 < i) && x.getLsbD (i - 1)))) := by
+  simp only [getLsbD_shiftConcat]
+  split <;> simp [*, show ((0 < i) ↔ ¬(i = 0)) by omega]
+
+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]
+  split
+  · simp [*]
+  · congr 1; omega
+
+@[simp, bv_toNat]
+theorem toNat_shiftConcat {x : BitVec w} {b : Bool} :
+    (x.shiftConcat b).toNat
+    = (x.toNat <<< 1 + b.toNat) % 2 ^ w  := by
+  simp [shiftConcat, Nat.shiftLeft_eq]
+
+/-- `x.shiftConcat b` does not overflow if `x < 2^k` for `k < w`, and so
+`x.shiftConcat b |>.toNat = x.toNat * 2 + b.toNat`. -/
+theorem toNat_shiftConcat_eq_of_lt {x : BitVec w} {b : Bool} {k : Nat}
+    (hk : k < w) (hx : x.toNat < 2 ^ k) :
+    (x.shiftConcat b).toNat = x.toNat * 2 + b.toNat := by
+  simp only [toNat_shiftConcat, Nat.shiftLeft_eq, Nat.pow_one]
+  have : 2 ^ k < 2 ^ w := Nat.pow_lt_pow_of_lt (by omega) (by omega)
+  have : 2 ^ k * 2 ≤ 2 ^ w := (Nat.pow_lt_pow_iff_pow_mul_le_pow (by omega)).mp this
+  rw [Nat.mod_eq_of_lt (by cases b <;> simp [bv_toNat] <;> omega)]
+
+theorem toNat_shiftConcat_lt_of_lt {x : BitVec w} {b : Bool} {k : Nat}
+    (hk : k < w) (hx : x.toNat < 2 ^ k) :
+    (x.shiftConcat b).toNat < 2 ^ (k + 1) := by
+  rw [toNat_shiftConcat_eq_of_lt hk hx]
+  have : 2 ^ (k + 1) ≤ 2 ^ w := Nat.pow_le_pow_of_le_right (by decide) (by assumption)
+  have := Bool.toNat_lt b
+  omega
+
 @[simp] theorem zero_concat_false : concat 0#w false = 0#(w + 1) := by
   ext
   simp [getLsbD_concat]
@@ -1737,6 +1911,20 @@ theorem ofInt_add {n} (x y : Int) : BitVec.ofInt n (x + y) =
   apply eq_of_toInt_eq
   simp
 
+@[simp]
+theorem shiftLeft_add_distrib {x y : BitVec w} {n : Nat} :
+    (x + y) <<< n = x <<< n + y <<< n := by
+  induction n
+  case zero =>
+    simp
+  case succ n ih =>
+    simp [ih, toNat_eq, Nat.shiftLeft_eq, ← Nat.add_mul]
+
+theorem add_eq_xor {a b : BitVec 1} : a + b = a ^^^ b := by
+  have ha : a = 0 ∨ a = 1 := eq_zero_or_eq_one _
+  have hb : b = 0 ∨ b = 1 := eq_zero_or_eq_one _
+  rcases ha with h | h <;> (rcases hb with h' | h' <;> (simp [h, h']))
+
 /-! ### sub/neg -/
 
 theorem sub_def {n} (x y : BitVec n) : x - y = .ofNat n ((2^n - y.toNat) + x.toNat) := by rfl
@@ -1783,7 +1971,7 @@ theorem toInt_neg {x : BitVec w} :
     Int.bmod_add_cancel]
   by_cases h : x.toNat < ((2 ^ w) + 1) / 2
   · rw [Int.bmod_pos (x := x.toNat)]
-    all_goals simp [toNat_mod_cancel', h]
+    all_goals simp only [toNat_mod_cancel']
     norm_cast
   · rw [Int.bmod_neg (x := x.toNat)]
     · simp only [toNat_mod_cancel']
@@ -1797,7 +1985,7 @@ theorem toInt_neg {x : BitVec w} :
 
 theorem sub_toAdd {n} (x y : BitVec n) : x - y = x + - y := by
   apply eq_of_toNat_eq
-  simp
+  simp only [toNat_sub, toNat_add, toNat_neg, Nat.add_mod_mod]
   rw [Nat.add_comm]
 
 @[simp] theorem neg_zero (n:Nat) : -BitVec.ofNat n 0 = BitVec.ofNat n 0 := by apply eq_of_toNat_eq ; simp
@@ -1846,6 +2034,22 @@ theorem neg_ne_iff_ne_neg {x y : BitVec w} : -x ≠ y ↔ x ≠ -y := by
     subst h'
     simp at h
 
+theorem sub_eq_xor {a b : BitVec 1} : a - b = a ^^^ b := by
+  have ha : a = 0 ∨ a = 1 := eq_zero_or_eq_one _
+  have hb : b = 0 ∨ b = 1 := eq_zero_or_eq_one _
+  rcases ha with h | h <;> (rcases hb with h' | h' <;> (simp [h, h']))
+
+/-! ### abs -/
+
+@[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
@@ -1902,6 +2106,11 @@ theorem ofInt_mul {n} (x y : Int) : BitVec.ofInt n (x * y) =
   apply eq_of_toInt_eq
   simp
 
+theorem mul_eq_and {a b : BitVec 1} : a * b = a &&& b := by
+  have ha : a = 0 ∨ a = 1 := eq_zero_or_eq_one _
+  have hb : b = 0 ∨ b = 1 := eq_zero_or_eq_one _
+  rcases ha with h | h <;> (rcases hb with h' | h' <;> (simp [h, h']))
+
 /-! ### le and lt -/
 
 @[bv_toNat] theorem le_def {x y : BitVec n} :
@@ -1968,6 +2177,10 @@ protected theorem umod_lt (x : BitVec n) {y : BitVec n} : 0 < y → x.umod y < y
   simp only [ofNat_eq_ofNat, lt_def, toNat_ofNat, Nat.zero_mod, umod, toNat_ofNatLt]
   apply Nat.mod_lt
 
+theorem not_lt_iff_le {x y : BitVec w} : (¬ x < y) ↔ y ≤ x := by
+  constructor <;>
+    (intro h; simp only [lt_def, Nat.not_lt, le_def] at h ⊢; omega)
+
 /-! ### ofBoolList -/
 
 @[simp] theorem getMsbD_ofBoolListBE : (ofBoolListBE bs).getMsbD i = bs.getD i false := by
@@ -2073,6 +2286,12 @@ theorem getLsbD_rotateLeft {x : BitVec w} {r i : Nat}  :
   · simp
   · rw [← rotateLeft_mod_eq_rotateLeft, getLsbD_rotateLeft_of_le (Nat.mod_lt _ (by omega))]
 
+@[simp]
+theorem getElem_rotateLeft {x : BitVec w} {r i : Nat} (h : i < w) :
+    (x.rotateLeft r)[i] =
+      if h' : i < r % w then x[(w - (r % w) + i)] else x[i - (r % w)] := by
+  simp [← BitVec.getLsbD_eq_getElem, h]
+
 /-! ## Rotate Right -/
 
 /--
@@ -2154,6 +2373,12 @@ theorem getLsbD_rotateRight {x : BitVec w} {r i : Nat} :
   · simp
   · 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) :
+    (x.rotateRight r)[i] = if h' : i < w - (r % w) then x[(r % w) + i] else x[(i - (w - (r % w)))] := by
+  simp only [← BitVec.getLsbD_eq_getElem]
+  simp [getLsbD_rotateRight, h]
+
 /- ## twoPow -/
 
 @[simp, bv_toNat]
@@ -2182,6 +2407,12 @@ theorem getLsbD_twoPow (i j : Nat) : (twoPow w i).getLsbD j = ((i < w) && (i = j
           simp at hi
         simp_all
 
+@[simp]
+theorem getElem_twoPow {i j : Nat} (h : j < w) : (twoPow w i)[j] = decide (j = i) := by
+  rw [←getLsbD_eq_getElem, getLsbD_twoPow]
+  simp [eq_comm]
+  omega
+
 theorem and_twoPow (x : BitVec w) (i : Nat) :
     x &&& (twoPow w i) = if x.getLsbD i then twoPow w i else 0#w := by
   ext j
@@ -2213,6 +2444,17 @@ theorem twoPow_zero {w : Nat} : twoPow w 0 = 1#w := by
 theorem getLsbD_one {w i : Nat} : (1#w).getLsbD i = (decide (0 < w) && decide (0 = i)) := by
   rw [← twoPow_zero, getLsbD_twoPow]
 
+@[simp]
+theorem getElem_one {w i : Nat} (h : i < w) : (1#w)[i] = decide (i = 0) := by
+  rw [← twoPow_zero, getElem_twoPow]
+
+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]
+
+/- ### cons -/
+
 @[simp] theorem true_cons_zero : cons true 0#w = twoPow (w + 1) w := by
   ext
   simp [getLsbD_cons]
@@ -2310,6 +2552,12 @@ theorem getLsbD_replicate {n w : Nat} (x : BitVec w) :
       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]
+theorem getElem_replicate {n w : Nat} (x : BitVec w) (h : i < w * n) :
+    (x.replicate n)[i] = if h' : w = 0 then false else x[i % w]'(@Nat.mod_lt i w (by omega)) := by
+  simp only [← getLsbD_eq_getElem, getLsbD_replicate]
+  by_cases h' : w = 0 <;> simp [h'] <;> omega
+
 /-! ### intMin -/
 
 /-- The bitvector of width `w` that has the smallest value when interpreted as an integer. -/

src/Init/Data/Bool.lean

@@ -368,13 +368,14 @@ theorem and_or_inj_left_iff :
 /-- convert a `Bool` to a `Nat`, `false -> 0`, `true -> 1` -/
 def toNat (b : Bool) : Nat := cond b 1 0
 
-@[simp] theorem toNat_false : false.toNat = 0 := rfl
+@[simp, bv_toNat] theorem toNat_false : false.toNat = 0 := rfl
 
-@[simp] theorem toNat_true : true.toNat = 1 := rfl
+@[simp, bv_toNat] theorem toNat_true : true.toNat = 1 := rfl
 
 theorem toNat_le (c : Bool) : c.toNat ≤ 1 := by
   cases c <;> trivial
 
+@[bv_toNat]
 theorem toNat_lt (b : Bool) : b.toNat < 2 :=
   Nat.lt_succ_of_le (toNat_le _)
 

src/Init/Data/ByteArray/Basic.lean

@@ -245,7 +245,7 @@ On an invalid position, returns `(default : UInt8)`. -/
 @[inline]
 def curr : Iterator → UInt8
   | ⟨arr, i⟩ =>
-    if h:i < arr.size then
+    if h : i < arr.size then
       arr[i]'h
     else
       default

src/Init/Data/Fin/Lemmas.lean

@@ -582,8 +582,8 @@ theorem rev_succ (k : Fin n) : rev (succ k) = castSucc (rev k) := k.rev_addNat 1
 @[simp] theorem coe_pred (j : Fin (n + 1)) (h : j ≠ 0) : (j.pred h : Nat) = j - 1 := rfl
 
 @[simp] theorem succ_pred : ∀ (i : Fin (n + 1)) (h : i ≠ 0), (i.pred h).succ = i
-  | ⟨0, h⟩, hi => by simp only [mk_zero, ne_eq, not_true] at hi
-  | ⟨n + 1, h⟩, hi => rfl
+  | ⟨0, _⟩, hi => by simp only [mk_zero, ne_eq, not_true] at hi
+  | ⟨_ + 1, _⟩, _ => rfl
 
 @[simp]
 theorem pred_succ (i : Fin n) {h : i.succ ≠ 0} : i.succ.pred h = i := by

src/Init/Data/Float.lean

@@ -72,21 +72,35 @@ instance floatDecLt (a b : Float) : Decidable (a < b) := Float.decLt a b
 instance floatDecLe (a b : Float) : Decidable (a ≤ b) := Float.decLe a b
 
 @[extern "lean_float_to_string"] opaque Float.toString : Float → String
-
-/-- If the given float is positive, truncates the value to the nearest positive integer.
-If negative or larger than the maximum value for UInt8, returns 0. -/
+/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
+If negative or NaN, returns `0`.
+If larger than the maximum value for `UInt8` (including Inf), returns the maximum value of `UInt8`
+(i.e. `UInt8.size - 1`).
+-/
 @[extern "lean_float_to_uint8"] opaque Float.toUInt8 : Float → UInt8
-/-- If the given float is positive, truncates the value to the nearest positive integer.
-If negative or larger than the maximum value for UInt16, returns 0. -/
+/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
+If negative or NaN, returns `0`.
+If larger than the maximum value for `UInt16` (including Inf), returns the maximum value of `UInt16`
+(i.e. `UInt16.size - 1`).
+-/
 @[extern "lean_float_to_uint16"] opaque Float.toUInt16 : Float → UInt16
-/-- If the given float is positive, truncates the value to the nearest positive integer.
-If negative or larger than the maximum value for UInt32, returns 0. -/
+/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
+If negative or NaN, returns `0`.
+If larger than the maximum value for `UInt32` (including Inf), returns the maximum value of `UInt32`
+(i.e. `UInt32.size - 1`).
+-/
 @[extern "lean_float_to_uint32"] opaque Float.toUInt32 : Float → UInt32
-/-- If the given float is positive, truncates the value to the nearest positive integer.
-If negative or larger than the maximum value for UInt64, returns 0. -/
+/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
+If negative or NaN, returns `0`.
+If larger than the maximum value for `UInt64` (including Inf), returns the maximum value of `UInt64`
+(i.e. `UInt64.size - 1`).
+-/
 @[extern "lean_float_to_uint64"] opaque Float.toUInt64 : Float → UInt64
-/-- If the given float is positive, truncates the value to the nearest positive integer.
-If negative or larger than the maximum value for USize, returns 0. -/
+/-- If the given float is non-negative, truncates the value to the nearest non-negative integer.
+If negative or NaN, returns `0`.
+If larger than the maximum value for `USize` (including Inf), returns the maximum value of `USize`
+(i.e. `USize.size - 1`). This value is platform dependent).
+-/
 @[extern "lean_float_to_usize"] opaque Float.toUSize : Float → USize
 
 @[extern "lean_float_isnan"] opaque Float.isNaN : Float → Bool

src/Init/Data/Int/DivModLemmas.lean

@@ -253,7 +253,7 @@ theorem tmod_def (a b : Int) : tmod a b = a - b * a.tdiv b := by
 
 theorem fmod_add_fdiv : ∀ a b : Int, a.fmod b + b * a.fdiv b = a
   | 0, ofNat _ | 0, -[_+1] => congrArg ofNat <| by simp
-  | succ m, ofNat n => congrArg ofNat <| Nat.mod_add_div ..
+  | succ _, ofNat _ => congrArg ofNat <| Nat.mod_add_div ..
   | succ m, -[n+1] => by
     show subNatNat (m % succ n) n + (↑(succ n * (m / succ n)) + n + 1) = (m + 1)
     rw [Int.add_comm _ n, ← Int.add_assoc, ← Int.add_assoc,
@@ -289,8 +289,8 @@ theorem fmod_eq_tmod {a b : Int} (Ha : 0 ≤ a) (Hb : 0 ≤ b) : fmod a b = tmod
 
 @[simp] protected theorem ediv_neg : ∀ a b : Int, a / (-b) = -(a / b)
   | ofNat m, 0 => show ofNat (m / 0) = -↑(m / 0) by rw [Nat.div_zero]; rfl
-  | ofNat m, -[n+1] => (Int.neg_neg _).symm
-  | ofNat m, succ n | -[m+1], 0 | -[m+1], succ n | -[m+1], -[n+1] => rfl
+  | ofNat _, -[_+1] => (Int.neg_neg _).symm
+  | ofNat _, succ _ | -[_+1], 0 | -[_+1], succ _ | -[_+1], -[_+1] => rfl
 
 theorem ediv_neg' {a b : Int} (Ha : a < 0) (Hb : 0 < b) : a / b < 0 :=
   match a, b, eq_negSucc_of_lt_zero Ha, eq_succ_of_zero_lt Hb with
@@ -339,7 +339,7 @@ theorem add_mul_ediv_right (a b : Int) {c : Int} (H : c ≠ 0) : (a + b * c) / c
       | _, ⟨k, rfl⟩, -[n+1] => show (a - n.succ * k.succ).ediv k.succ = a.ediv k.succ - n.succ by
         rw [← Int.add_sub_cancel (ediv ..), ← this, Int.sub_add_cancel]
   fun {k n} => @fun
-  | ofNat m => congrArg ofNat <| Nat.add_mul_div_right _ _ k.succ_pos
+  | ofNat _ => congrArg ofNat <| Nat.add_mul_div_right _ _ k.succ_pos
   | -[m+1] => by
     show ((n * k.succ : Nat) - m.succ : Int).ediv k.succ = n - (m / k.succ + 1 : Nat)
     by_cases h : m < n * k.succ
@@ -396,7 +396,7 @@ theorem add_mul_ediv_left (a : Int) {b : Int}
       rw [Int.mul_neg, Int.ediv_neg, Int.ediv_neg]; apply congrArg Neg.neg; apply this
   fun m k b =>
   match b, k with
-  | ofNat n, k => congrArg ofNat (Nat.mul_div_mul_left _ _ m.succ_pos)
+  | ofNat _, _ => congrArg ofNat (Nat.mul_div_mul_left _ _ m.succ_pos)
   | -[n+1], 0 => by
     rw [Int.ofNat_zero, Int.mul_zero, Int.ediv_zero, Int.ediv_zero]
   | -[n+1], succ k => congrArg negSucc <|
@@ -822,14 +822,14 @@ theorem ediv_eq_ediv_of_mul_eq_mul {a b c d : Int}
 unseal Nat.div in
 @[simp] protected theorem tdiv_neg : ∀ a b : Int, a.tdiv (-b) = -(a.tdiv b)
   | ofNat m, 0 => show ofNat (m / 0) = -↑(m / 0) by rw [Nat.div_zero]; rfl
-  | ofNat m, -[n+1] | -[m+1], succ n => (Int.neg_neg _).symm
-  | ofNat m, succ n | -[m+1], 0 | -[m+1], -[n+1] => rfl
+  | ofNat _, -[_+1] | -[_+1], succ _ => (Int.neg_neg _).symm
+  | ofNat _, succ _ | -[_+1], 0 | -[_+1], -[_+1] => rfl
 
 unseal Nat.div in
 @[simp] protected theorem neg_tdiv : ∀ a b : Int, (-a).tdiv b = -(a.tdiv b)
   | 0, n => by simp [Int.neg_zero]
-  | succ m, (n:Nat) | -[m+1], 0 | -[m+1], -[n+1] => rfl
-  | succ m, -[n+1] | -[m+1], succ n => (Int.neg_neg _).symm
+  | succ _, (n:Nat) | -[_+1], 0 | -[_+1], -[_+1] => rfl
+  | succ _, -[_+1] | -[_+1], succ _ => (Int.neg_neg _).symm
 
 protected theorem neg_tdiv_neg (a b : Int) : (-a).tdiv (-b) = a.tdiv b := by
   simp [Int.tdiv_neg, Int.neg_tdiv, Int.neg_neg]

src/Init/Data/Int/Lemmas.lean

@@ -181,12 +181,12 @@ theorem subNatNat_add_negSucc (m n k : Nat) :
       Nat.add_comm]
 
 protected theorem add_assoc : ∀ a b c : Int, a + b + c = a + (b + c)
-  | (m:Nat), (n:Nat), c => aux1 ..
+  | (m:Nat), (n:Nat), _ => aux1 ..
   | Nat.cast m, b, Nat.cast k => by
     rw [Int.add_comm, ← aux1, Int.add_comm k, aux1, Int.add_comm b]
   | a, (n:Nat), (k:Nat) => by
     rw [Int.add_comm, Int.add_comm a, ← aux1, Int.add_comm a, Int.add_comm k]
-  | -[m+1], -[n+1], (k:Nat) => aux2 ..
+  | -[_+1], -[_+1], (k:Nat) => aux2 ..
   | -[m+1], (n:Nat), -[k+1] => by
     rw [Int.add_comm, ← aux2, Int.add_comm n, ← aux2, Int.add_comm -[m+1]]
   | (m:Nat), -[n+1], -[k+1] => by

src/Init/Data/Int/Order.lean

@@ -512,8 +512,8 @@ theorem toNat_add_nat {a : Int} (ha : 0 ≤ a) (n : Nat) : (a + n).toNat = a.toN
 
 @[simp] theorem pred_toNat : ∀ i : Int, (i - 1).toNat = i.toNat - 1
   | 0 => rfl
-  | (n+1:Nat) => by simp [ofNat_add]
-  | -[n+1] => rfl
+  | (_+1:Nat) => by simp [ofNat_add]
+  | -[_+1] => rfl
 
 theorem toNat_sub_toNat_neg : ∀ n : Int, ↑n.toNat - ↑(-n).toNat = n
   | 0 => rfl

src/Init/Data/List/Attach.lean

@@ -73,7 +73,7 @@ theorem map_pmap {p : α → Prop} (g : β → γ) (f : ∀ a, p a → β) (l H)
   · simp only [*, pmap, map]
 
 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 a h => H _ (mem_map_of_mem _ h) := by
+    pmap g (map f l) H = pmap (fun a h => g (f a) h) l fun _ h => H _ (mem_map_of_mem _ h) := by
   induction l
   · rfl
   · simp only [*, pmap, map]
@@ -84,7 +84,7 @@ theorem attach_congr {l₁ l₂ : List α} (h : l₁ = l₂) :
   simp
 
 theorem attachWith_congr {l₁ l₂ : List α} (w : l₁ = l₂) {P : α → Prop} {H : ∀ x ∈ l₁, P x} :
-    l₁.attachWith P H = l₂.attachWith P fun x h => H _ (w ▸ h) := by
+    l₁.attachWith P H = l₂.attachWith P fun _ h => H _ (w ▸ h) := by
   subst w
   simp
 
@@ -353,7 +353,7 @@ theorem attach_map {l : List α} (f : α → β) :
   induction l <;> simp [*]
 
 theorem attachWith_map {l : List 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 a h => H _ (mem_map_of_mem f h))).map
+    (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
   induction l <;> simp [*]
 
@@ -548,4 +548,131 @@ theorem count_attachWith [DecidableEq α] {p : α → Prop} (l : List α) (H :
     (l.attachWith p H).count a = l.count ↑a :=
   Eq.trans (countP_congr fun _ _ => by simp [Subtype.ext_iff]) <| countP_attachWith _ _ _
 
+/-! ## unattach
+
+`List.unattach` is the (one-sided) inverse of `List.attach`. It is a synonym for `List.map Subtype.val`.
+
+We use it by providing a simp lemma `l.attach.unattach = l`, and simp lemmas which recognize higher order
+functions applied to `l : List { x // p x }` which only depend on the value, not the predicate, and rewrite these
+in terms of a simpler function applied to `l.unattach`.
+
+Further, we provide simp lemmas that push `unattach` inwards.
+-/
+
+/--
+A synonym for `l.map (·.val)`. Mostly this should not be needed by users.
+It is introduced as an intermediate step by lemmas such as `map_subtype`,
+and is ideally subsequently simplified away by `unattach_attach`.
+
+If not, usually the right approach is `simp [List.unattach, -List.map_subtype]` to unfold.
+-/
+def unattach {α : Type _} {p : α → Prop} (l : List { x // p x }) := l.map (·.val)
+
+@[simp] theorem unattach_nil {α : Type _} {p : α → Prop} : ([] : List { x // p x }).unattach = [] := rfl
+@[simp] theorem unattach_cons {α : Type _} {p : α → Prop} {a : { x // p x }} {l : List { x // p x }} :
+  (a :: l).unattach = a.val :: l.unattach := rfl
+
+@[simp] theorem length_unattach {α : Type _} {p : α → Prop} {l : List { x // p x }} :
+    l.unattach.length = l.length := by
+  unfold unattach
+  simp
+
+@[simp] theorem unattach_attach {α : Type _} (l : List α) : l.attach.unattach = l := by
+  unfold unattach
+  induction l with
+  | nil => simp
+  | cons a l ih => simp [ih, Function.comp_def]
+
+@[simp] theorem unattach_attachWith {α : Type _} {p : α → Prop} {l : List α}
+    {H : ∀ a ∈ l, p a} :
+    (l.attachWith p H).unattach = l := by
+  unfold unattach
+  induction l with
+  | nil => simp
+  | cons a l ih => simp [ih, Function.comp_def]
+
+/-! ### Recognizing higher order functions on subtypes using a function that only depends on the value. -/
+
+/--
+This lemma identifies folds over lists of subtypes, where the function only depends on the value, not the proposition,
+and simplifies these to the function directly taking the value.
+-/
+@[simp] theorem foldl_subtype {p : α → Prop} {l : List { x // p x }}
+    {f : β → { x // p x } → β} {g : β → α → β} {x : β}
+    {hf : ∀ b x h, f b ⟨x, h⟩ = g b x} :
+    l.foldl f x = l.unattach.foldl g x := by
+  unfold unattach
+  induction l generalizing x with
+  | nil => simp
+  | cons a l ih => simp [ih, hf]
+
+/--
+This lemma identifies folds over lists of subtypes, where the function only depends on the value, not the proposition,
+and simplifies these to the function directly taking the value.
+-/
+@[simp] theorem foldr_subtype {p : α → Prop} {l : List { x // p x }}
+    {f : { x // p x } → β → β} {g : α → β → β} {x : β}
+    {hf : ∀ x h b, f ⟨x, h⟩ b = g x b} :
+    l.foldr f x = l.unattach.foldr g x := by
+  unfold unattach
+  induction l generalizing x with
+  | nil => simp
+  | cons a l ih => simp [ih, hf]
+
+/--
+This lemma identifies maps over lists of subtypes, where the function only depends on the value, not the proposition,
+and simplifies these to the function directly taking the value.
+-/
+@[simp] theorem map_subtype {p : α → Prop} {l : List { x // p x }}
+    {f : { x // p x } → β} {g : α → β} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
+    l.map f = l.unattach.map g := by
+  unfold unattach
+  induction l with
+  | nil => simp
+  | cons a l ih => simp [ih, hf]
+
+@[simp] theorem filterMap_subtype {p : α → Prop} {l : List { x // p x }}
+    {f : { x // p x } → Option β} {g : α → Option β} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
+    l.filterMap f = l.unattach.filterMap g := by
+  unfold unattach
+  induction l with
+  | nil => simp
+  | cons a l ih => simp [ih, hf, filterMap_cons]
+
+@[simp] theorem bind_subtype {p : α → Prop} {l : List { x // p x }}
+    {f : { x // p x } → List β} {g : α → List β} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
+    (l.bind f) = l.unattach.bind g := by
+  unfold unattach
+  induction l with
+  | nil => simp
+  | cons a l ih => simp [ih, hf]
+
+@[simp] theorem unattach_filter {p : α → Prop} {l : List { x // p x }}
+    {f : { x // p x } → Bool} {g : α → Bool} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
+    (l.filter f).unattach = l.unattach.filter g := by
+  induction l with
+  | nil => simp
+  | cons a l ih =>
+    simp only [filter_cons, hf, unattach_cons]
+    split <;> simp [ih]
+
+/-! ### Simp lemmas pushing `unattach` inwards. -/
+
+@[simp] theorem unattach_reverse {p : α → Prop} {l : List { x // p x }} :
+    l.reverse.unattach = l.unattach.reverse := by
+  simp [unattach, -map_subtype]
+
+@[simp] theorem unattach_append {p : α → Prop} {l₁ l₂ : List { x // p x }} :
+    (l₁ ++ l₂).unattach = l₁.unattach ++ l₂.unattach := by
+  simp [unattach, -map_subtype]
+
+@[simp] theorem unattach_join {p : α → Prop} {l : List (List { x // p x })} :
+    l.join.unattach = (l.map unattach).join := by
+  unfold unattach
+  induction l <;> simp_all
+
+@[simp] theorem unattach_replicate {p : α → Prop} {n : Nat} {x : { x // p x }} :
+    (List.replicate n x).unattach = List.replicate n x.1 := by
+  simp [unattach, -map_subtype]
+
 end List

src/Init/Data/List/Basic.lean

@@ -43,7 +43,7 @@ The operations are organized as follow:
 * Logic: `any`, `all`, `or`, and `and`.
 * Zippers: `zipWith`, `zip`, `zipWithAll`, and `unzip`.
 * Ranges and enumeration: `range`, `iota`, `enumFrom`, and `enum`.
-* Minima and maxima: `minimum?` and `maximum?`.
+* Minima and maxima: `min?` and `max?`.
 * Other functions: `intersperse`, `intercalate`, `eraseDups`, `eraseReps`, `span`, `groupBy`,
   `removeAll`
   (currently these functions are mostly only used in meta code,
@@ -218,8 +218,8 @@ def get? : (as : List α) → (i : Nat) → Option α
 
 theorem ext_get? : ∀ {l₁ l₂ : List α}, (∀ n, l₁.get? n = l₂.get? n) → l₁ = l₂
   | [], [], _ => rfl
-  | a :: l₁, [], h => nomatch h 0
-  | [], a' :: l₂, h => nomatch h 0
+  | _ :: _, [], h => nomatch h 0
+  | [], _ :: _, h => nomatch h 0
   | a :: l₁, a' :: l₂, h => by
     have h0 : some a = some a' := h 0
     injection h0 with aa; simp only [aa, ext_get? fun n => h (n+1)]
@@ -1464,30 +1464,34 @@ def enum : List α → List (Nat × α) := enumFrom 0
 
 /-! ## Minima and maxima -/
 
-/-! ### minimum? -/
+/-! ### min? -/
 
 /--
 Returns the smallest element of the list, if it is not empty.
-* `[].minimum? = none`
-* `[4].minimum? = some 4`
-* `[1, 4, 2, 10, 6].minimum? = some 1`
+* `[].min? = none`
+* `[4].min? = some 4`
+* `[1, 4, 2, 10, 6].min? = some 1`
 -/
-def minimum? [Min α] : List α → Option α
+def min? [Min α] : List α → Option α
   | []    => none
   | a::as => some <| as.foldl min a
 
-/-! ### maximum? -/
+@[inherit_doc min?, deprecated min? (since := "2024-09-29")] abbrev minimum? := @min?
+
+/-! ### max? -/
 
 /--
 Returns the largest element of the list, if it is not empty.
-* `[].maximum? = none`
-* `[4].maximum? = some 4`
-* `[1, 4, 2, 10, 6].maximum? = some 10`
+* `[].max? = none`
+* `[4].max? = some 4`
+* `[1, 4, 2, 10, 6].max? = some 10`
 -/
-def maximum? [Max α] : List α → Option α
+def max? [Max α] : List α → Option α
   | []    => none
   | a::as => some <| as.foldl max a
 
+@[inherit_doc max?, deprecated max? (since := "2024-09-29")] abbrev maximum? := @max?
+
 /-! ## Other list operations
 
 The functions are currently mostly used in meta code,

src/Init/Data/List/BasicAux.lean

@@ -235,8 +235,8 @@ theorem sizeOf_get [SizeOf α] (as : List α) (i : Fin as.length) : sizeOf (as.g
 theorem le_antisymm [LT α] [s : Antisymm (¬ · < · : α → α → Prop)] {as bs : List α} (h₁ : as ≤ bs) (h₂ : bs ≤ as) : as = bs :=
   match as, bs with
   | [],    []    => rfl
-  | [],    b::bs => False.elim <| h₂ (List.lt.nil ..)
-  | a::as, []    => False.elim <| h₁ (List.lt.nil ..)
+  | [],    _::_ => False.elim <| h₂ (List.lt.nil ..)
+  | _::_, []    => False.elim <| h₁ (List.lt.nil ..)
   | a::as, b::bs => by
     by_cases hab : a < b
     · exact False.elim <| h₂ (List.lt.head _ _ hab)

src/Init/Data/List/Erase.lean

@@ -52,9 +52,9 @@ theorem eraseP_of_forall_not {l : List α} (h : ∀ a, a ∈ l → ¬p a) : l.er
 theorem eraseP_ne_nil {xs : List α} {p : α → Bool} : xs.eraseP p ≠ [] ↔ xs ≠ [] ∧ ∀ x, p x → xs ≠ [x] := by
   simp
 
-theorem exists_of_eraseP : ∀ {l : List α} {a} (al : a ∈ l) (pa : p a),
+theorem exists_of_eraseP : ∀ {l : List α} {a} (_ : a ∈ l) (_ : p a),
     ∃ a l₁ l₂, (∀ b ∈ l₁, ¬p b) ∧ p a ∧ l = l₁ ++ a :: l₂ ∧ l.eraseP p = l₁ ++ l₂
-  | b :: l, a, al, pa =>
+  | b :: l, _, al, pa =>
     if pb : p b then
       ⟨b, [], l, forall_mem_nil _, pb, by simp [pb]⟩
     else
@@ -168,8 +168,8 @@ theorem eraseP_append_left {a : α} (pa : p a) :
 
 theorem eraseP_append_right :
     ∀ {l₁ : List α} l₂, (∀ b ∈ l₁, ¬p b) → eraseP p (l₁++l₂) = l₁ ++ l₂.eraseP p
-  | [],      l₂, _ => rfl
-  | x :: xs, l₂, h => by
+  | [],     _, _ => rfl
+  | _ :: _, _, h => by
     simp [(forall_mem_cons.1 h).1, eraseP_append_right _ (forall_mem_cons.1 h).2]
 
 theorem eraseP_append (l₁ l₂ : List α) :

src/Init/Data/List/Impl.lean

@@ -31,7 +31,7 @@ The following operations are still missing `@[csimp]` replacements:
 The following operations are not recursive to begin with
 (or are defined in terms of recursive primitives):
 `isEmpty`, `isSuffixOf`, `isSuffixOf?`, `rotateLeft`, `rotateRight`, `insert`, `zip`, `enum`,
-`minimum?`, `maximum?`, and `removeAll`.
+`min?`, `max?`, and `removeAll`.
 
 The following operations were already given `@[csimp]` replacements in `Init/Data/List/Basic.lean`:
 `length`, `map`, `filter`, `replicate`, `leftPad`, `unzip`, `range'`, `iota`, `intersperse`.

src/Init/Data/List/Lemmas.lean

@@ -55,7 +55,7 @@ See also
 * `Init.Data.List.Erase` for lemmas about `List.eraseP` and `List.erase`.
 * `Init.Data.List.Find` for lemmas about `List.find?`, `List.findSome?`, `List.findIdx`,
   `List.findIdx?`, and `List.indexOf`
-* `Init.Data.List.MinMax` for lemmas about `List.minimum?` and `List.maximum?`.
+* `Init.Data.List.MinMax` for lemmas about `List.min?` and `List.max?`.
 * `Init.Data.List.Pairwise` for lemmas about `List.Pairwise` and `List.Nodup`.
 * `Init.Data.List.Sublist` for lemmas about `List.Subset`, `List.Sublist`, `List.IsPrefix`,
   `List.IsSuffix`, and `List.IsInfix`.
@@ -191,7 +191,7 @@ theorem get?_eq_some : l.get? n = some a ↔ ∃ h, get l ⟨n, h⟩ = a :=
   ⟨fun e =>
     have : n < length l := Nat.gt_of_not_le fun hn => by cases get?_len_le hn ▸ e
     ⟨this, by rwa [get?_eq_get this, Option.some.injEq] at e⟩,
-  fun ⟨h, e⟩ => e ▸ get?_eq_get _⟩
+  fun ⟨_, e⟩ => e ▸ get?_eq_get _⟩
 
 theorem get?_eq_none : l.get? n = none ↔ length l ≤ n :=
   ⟨fun e => Nat.ge_of_not_lt (fun h' => by cases e ▸ get?_eq_some.2 ⟨h', rfl⟩), get?_len_le⟩
@@ -203,6 +203,9 @@ theorem get?_eq_none : l.get? n = none ↔ length l ≤ n :=
 
 @[simp] theorem get_eq_getElem (l : List α) (i : Fin l.length) : l.get i = l[i.1]'i.2 := rfl
 
+theorem getElem?_eq_some {l : List α} : l[i]? = some a ↔ ∃ h : i < l.length, l[i]'h = a := by
+  simpa using get?_eq_some
+
 /--
 If one has `l.get i` in an expression (with `i : Fin l.length`) and `h : l = l'`,
 `rw [h]` will give a "motive it not type correct" error, as it cannot rewrite the
@@ -489,7 +492,7 @@ 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 getElem_mem : ∀ {l : List α} {n} (h : n < l.length), l[n]'h ∈ l
+@[simp] theorem getElem_mem : ∀ {l : List α} {n} (h : n < l.length), l[n]'h ∈ l
   | _ :: _, 0, _ => .head ..
   | _ :: l, _+1, _ => .tail _ (getElem_mem (l := l) ..)
 
@@ -715,9 +718,9 @@ theorem set_eq_of_length_le {l : List α} {n : Nat} (h : l.length ≤ n) {a : α
 theorem set_comm (a b : α) : ∀ {n m : Nat} (l : List α), n ≠ m →
     (l.set n a).set m b = (l.set m b).set n a
   | _, _, [], _ => by simp
-  | n+1, 0, _ :: _, _ => by simp [set]
-  | 0, m+1, _ :: _, _ => by simp [set]
-  | n+1, m+1, x :: t, h =>
+  | _+1, 0, _ :: _, _ => by simp [set]
+  | 0, _+1, _ :: _, _ => by simp [set]
+  | _+1, _+1, _ :: t, h =>
     congrArg _ <| set_comm a b t fun h' => h <| Nat.succ_inj'.mpr h'
 
 @[simp]
@@ -878,6 +881,20 @@ theorem foldr_map' {α β : Type u} (g : α → β) (f : α → α → α) (f' :
   · simp
   · simp [*, h]
 
+theorem foldl_assoc {op : α → α → α} [ha : Std.Associative op] :
+    ∀ {l : List α} {a₁ a₂}, l.foldl op (op a₁ a₂) = op a₁ (l.foldl op a₂)
+  | [], a₁, a₂ => rfl
+  | a :: l, a₁, a₂ => by
+    simp only [foldl_cons, ha.assoc]
+    rw [foldl_assoc]
+
+theorem foldr_assoc {op : α → α → α} [ha : Std.Associative op] :
+    ∀ {l : List α} {a₁ a₂}, l.foldr op (op a₁ a₂) = op (l.foldr op a₁) a₂
+  | [], a₁, a₂ => rfl
+  | a :: l, a₁, a₂ => by
+    simp only [foldr_cons, ha.assoc]
+    rw [foldr_assoc]
+
 theorem foldl_hom (f : α₁ → α₂) (g₁ : α₁ → β → α₁) (g₂ : α₂ → β → α₂) (l : List β) (init : α₁)
     (H : ∀ x y, g₂ (f x) y = f (g₁ x y)) : l.foldl g₂ (f init) = f (l.foldl g₁ init) := by
   induction l generalizing init <;> simp [*, H]
@@ -977,8 +994,8 @@ theorem getLast_eq_getElem : ∀ (l : List α) (h : l ≠ []),
       match l with
       | [] => contradiction
       | a :: l => exact Nat.le_refl _)
-  | [a], h => rfl
-  | a :: b :: l, h => by
+  | [_], _ => rfl
+  | _ :: _ :: _, _ => by
     simp [getLast, get, Nat.succ_sub_succ, getLast_eq_getElem]
 
 @[deprecated getLast_eq_getElem (since := "2024-07-15")]
@@ -1004,14 +1021,14 @@ theorem getLast_eq_getLastD (a l h) : @getLast α (a::l) h = getLastD l a := by
 theorem getLast!_cons [Inhabited α] : @getLast! α _ (a::l) = getLastD l a := by
   simp [getLast!, getLast_eq_getLastD]
 
-theorem getLast_mem : ∀ {l : List α} (h : l ≠ []), getLast l h ∈ l
+@[simp] theorem getLast_mem : ∀ {l : List α} (h : l ≠ []), getLast l h ∈ l
   | [], h => absurd rfl h
   | [_], _ => .head ..
   | _::a::l, _ => .tail _ <| getLast_mem (cons_ne_nil a l)
 
 theorem getLast_mem_getLast? : ∀ {l : List α} (h : l ≠ []), getLast l h ∈ getLast? l
   | [], h => by contradiction
-  | a :: l, _ => rfl
+  | _ :: _, _ => rfl
 
 theorem getLastD_mem_cons : ∀ (l : List α) (a : α), getLastD l a ∈ a::l
   | [], _ => .head ..
@@ -1102,7 +1119,7 @@ theorem head?_eq_some_iff {xs : List α} {a : α} : xs.head? = some a ↔ ∃ ys
 @[simp] theorem head?_isSome : l.head?.isSome ↔ l ≠ [] := by
   cases l <;> simp
 
-theorem head_mem : ∀ {l : List α} (h : l ≠ []), head l h ∈ l
+@[simp] theorem head_mem : ∀ {l : List α} (h : l ≠ []), head l h ∈ l
   | [], h => absurd rfl h
   | _::_, _ => .head ..
 
@@ -1117,7 +1134,7 @@ theorem mem_of_mem_head? : ∀ {l : List α} {a : α}, a ∈ l.head? → a ∈ l
 
 theorem head_mem_head? : ∀ {l : List α} (h : l ≠ []), head l h ∈ head? l
   | [], h => by contradiction
-  | a :: l, _ => rfl
+  | _ :: _, _ => rfl
 
 theorem head?_concat {a : α} : (l ++ [a]).head? = l.head?.getD a := by
   cases l <;> simp
@@ -1449,7 +1466,7 @@ theorem map_filter_eq_foldr (f : α → β) (p : α → Bool) (as : List α) :
 
 @[simp] theorem filter_append {p : α → Bool} :
     ∀ (l₁ l₂ : List α), filter p (l₁ ++ l₂) = filter p l₁ ++ filter p l₂
-  | [], l₂ => rfl
+  | [], _ => rfl
   | a :: l₁, l₂ => by simp [filter]; split <;> simp [filter_append l₁]
 
 theorem filter_eq_cons_iff {l} {a} {as} :
@@ -1673,7 +1690,7 @@ theorem getElem?_append_left {l₁ l₂ : List α} {n : Nat} (hn : n < l₁.leng
 
 theorem getElem?_append_right : ∀ {l₁ l₂ : List α} {n : Nat}, l₁.length ≤ n →
   (l₁ ++ l₂)[n]? = l₂[n - l₁.length]?
-| [], _, n, _ => rfl
+| [], _, _, _ => rfl
 | a :: l, _, n+1, h₁ => by
   rw [cons_append]
   simp [Nat.succ_sub_succ_eq_sub, getElem?_append_right (Nat.lt_succ.1 h₁)]
@@ -1738,8 +1755,8 @@ theorem append_of_mem {a : α} {l : List α} : a ∈ l → ∃ s t : List α, l
 
 theorem append_inj :
     ∀ {s₁ s₂ t₁ t₂ : List α}, s₁ ++ t₁ = s₂ ++ t₂ → length s₁ = length s₂ → s₁ = s₂ ∧ t₁ = t₂
-  | [], [], t₁, t₂, h, _ => ⟨rfl, h⟩
-  | a :: s₁, b :: s₂, t₁, t₂, h, hl => by
+  | [], [], _, _, h, _ => ⟨rfl, h⟩
+  | _ :: _, _ :: _, _, _, h, hl => by
     simp [append_inj (cons.inj h).2 (Nat.succ.inj hl)] at h ⊢; exact h
 
 theorem append_inj_right (h : s₁ ++ t₁ = s₂ ++ t₂) (hl : length s₁ = length s₂) : t₁ = t₂ :=
@@ -2392,6 +2409,10 @@ theorem map_eq_replicate_iff {l : List α} {f : α → β} {b : β} :
 @[simp] theorem map_const (l : List α) (b : β) : map (Function.const α b) l = replicate l.length b :=
   map_eq_replicate_iff.mpr fun _ _ => rfl
 
+@[simp] theorem map_const_fun (x : β) : map (Function.const α x) = (replicate ·.length x) := by
+  funext l
+  simp
+
 /-- Variant of `map_const` using a lambda rather than `Function.const`. -/
 -- This can not be a `@[simp]` lemma because it would fire on every `List.map`.
 theorem map_const' (l : List α) (b : β) : map (fun _ => b) l = replicate l.length b :=
@@ -2686,7 +2707,7 @@ theorem bind_reverse {β} (l : List α) (f : α → List β) : (l.reverse.bind f
 @[simp] theorem reverse_replicate (n) (a : α) : reverse (replicate n a) = replicate n a :=
   eq_replicate_iff.2
     ⟨by rw [length_reverse, length_replicate],
-     fun b h => eq_of_mem_replicate (mem_reverse.1 h)⟩
+     fun _ h => eq_of_mem_replicate (mem_reverse.1 h)⟩
 
 /-! #### Further results about `getLast` and `getLast?` -/
 
@@ -2891,7 +2912,7 @@ theorem head?_dropLast (xs : List α) : xs.dropLast.head? = if 1 < xs.length the
 
 theorem getLast_dropLast {xs : List α} (h) :
    xs.dropLast.getLast h =
-     xs[xs.length - 2]'(match xs, h with | (a :: b :: xs), _ => Nat.lt_trans (Nat.lt_add_one _) (Nat.lt_add_one _)) := by
+     xs[xs.length - 2]'(match xs, h with | (_ :: _ :: _), _ => Nat.lt_trans (Nat.lt_add_one _) (Nat.lt_add_one _)) := by
   rw [getLast_eq_getElem, getElem_dropLast]
   congr 1
   simp; rfl
@@ -2915,8 +2936,8 @@ theorem dropLast_cons_of_ne_nil {α : Type u} {x : α}
 
 theorem dropLast_concat_getLast : ∀ {l : List α} (h : l ≠ []), dropLast l ++ [getLast l h] = l
   | [], h => absurd rfl h
-  | [a], h => rfl
-  | a :: b :: l, h => by
+  | [_], _ => rfl
+  | _ :: b :: l, _ => by
     rw [dropLast_cons₂, cons_append, getLast_cons (cons_ne_nil _ _)]
     congr
     exact dropLast_concat_getLast (cons_ne_nil b l)

src/Init/Data/List/MinMax.lean

@@ -7,7 +7,7 @@ prelude
 import Init.Data.List.Lemmas
 
 /-!
-# Lemmas about `List.minimum?` and `List.maximum?.
+# Lemmas about `List.min?` and `List.max?.
 -/
 
 namespace List
@@ -16,24 +16,24 @@ open Nat
 
 /-! ## Minima and maxima -/
 
-/-! ### minimum? -/
+/-! ### min? -/
 
-@[simp] theorem minimum?_nil [Min α] : ([] : List α).minimum? = none := rfl
+@[simp] theorem min?_nil [Min α] : ([] : List α).min? = none := rfl
 
--- We don't put `@[simp]` on `minimum?_cons`,
+-- We don't put `@[simp]` on `min?_cons`,
 -- because the definition in terms of `foldl` is not useful for proofs.
-theorem minimum?_cons [Min α] {xs : List α} : (x :: xs).minimum? = foldl min x xs := rfl
+theorem min?_cons [Min α] {xs : List α} : (x :: xs).min? = foldl min x xs := rfl
 
-@[simp] theorem minimum?_eq_none_iff {xs : List α} [Min α] : xs.minimum? = none ↔ xs = [] := by
-  cases xs <;> simp [minimum?]
+@[simp] theorem min?_eq_none_iff {xs : List α} [Min α] : xs.min? = none ↔ xs = [] := by
+  cases xs <;> simp [min?]
 
-theorem minimum?_mem [Min α] (min_eq_or : ∀ a b : α, min a b = a ∨ min a b = b) :
-    {xs : List α} → xs.minimum? = some a → a ∈ xs := by
+theorem min?_mem [Min α] (min_eq_or : ∀ a b : α, min a b = a ∨ min a b = b) :
+    {xs : List α} → xs.min? = some a → a ∈ xs := by
   intro xs
   match xs with
   | nil => simp
   | x :: xs =>
-    simp only [minimum?_cons, Option.some.injEq, List.mem_cons]
+    simp only [min?_cons, Option.some.injEq, List.mem_cons]
     intro eq
     induction xs generalizing x with
     | nil =>
@@ -49,12 +49,12 @@ theorem minimum?_mem [Min α] (min_eq_or : ∀ a b : α, min a b = a ∨ min a b
 
 -- See also `Init.Data.List.Nat.Basic` for specialisations of the next two results to `Nat`.
 
-theorem le_minimum?_iff [Min α] [LE α]
+theorem le_min?_iff [Min α] [LE α]
     (le_min_iff : ∀ a b c : α, a ≤ min b c ↔ a ≤ b ∧ a ≤ c) :
-    {xs : List α} → xs.minimum? = some a → ∀ {x}, x ≤ a ↔ ∀ b, b ∈ xs → x ≤ b
+    {xs : List α} → xs.min? = some a → ∀ {x}, x ≤ a ↔ ∀ b, b ∈ xs → x ≤ b
   | nil => by simp
   | cons x xs => by
-    rw [minimum?]
+    rw [min?]
     intro eq y
     simp only [Option.some.injEq] at eq
     induction xs generalizing x with
@@ -67,46 +67,46 @@ theorem le_minimum?_iff [Min α] [LE α]
 
 -- This could be refactored by designing appropriate typeclasses to replace `le_refl`, `min_eq_or`,
 -- and `le_min_iff`.
-theorem minimum?_eq_some_iff [Min α] [LE α] [anti : Antisymm ((· : α) ≤ ·)]
+theorem min?_eq_some_iff [Min α] [LE α] [anti : Antisymm ((· : α) ≤ ·)]
     (le_refl : ∀ a : α, a ≤ a)
     (min_eq_or : ∀ a b : α, min a b = a ∨ min a b = b)
     (le_min_iff : ∀ a b c : α, a ≤ min b c ↔ a ≤ b ∧ a ≤ c) {xs : List α} :
-    xs.minimum? = some a ↔ a ∈ xs ∧ ∀ b, b ∈ xs → a ≤ b := by
-  refine ⟨fun h => ⟨minimum?_mem min_eq_or h, (le_minimum?_iff le_min_iff h).1 (le_refl _)⟩, ?_⟩
+    xs.min? = some a ↔ a ∈ xs ∧ ∀ b, b ∈ xs → a ≤ b := by
+  refine ⟨fun h => ⟨min?_mem min_eq_or h, (le_min?_iff le_min_iff h).1 (le_refl _)⟩, ?_⟩
   intro ⟨h₁, h₂⟩
   cases xs with
   | nil => simp at h₁
   | cons x xs =>
     exact congrArg some <| anti.1
-      ((le_minimum?_iff le_min_iff (xs := x::xs) rfl).1 (le_refl _) _ h₁)
-      (h₂ _ (minimum?_mem min_eq_or (xs := x::xs) rfl))
+      ((le_min?_iff le_min_iff (xs := x::xs) rfl).1 (le_refl _) _ h₁)
+      (h₂ _ (min?_mem min_eq_or (xs := x::xs) rfl))
 
-theorem minimum?_replicate [Min α] {n : Nat} {a : α} (w : min a a = a) :
-    (replicate n a).minimum? = if n = 0 then none else some a := by
+theorem min?_replicate [Min α] {n : Nat} {a : α} (w : min a a = a) :
+    (replicate n a).min? = if n = 0 then none else some a := by
   induction n with
   | zero => rfl
-  | succ n ih => cases n <;> simp_all [replicate_succ, minimum?_cons]
+  | succ n ih => cases n <;> simp_all [replicate_succ, min?_cons]
 
-@[simp] theorem minimum?_replicate_of_pos [Min α] {n : Nat} {a : α} (w : min a a = a) (h : 0 < n) :
-    (replicate n a).minimum? = some a := by
-  simp [minimum?_replicate, Nat.ne_of_gt h, w]
+@[simp] theorem min?_replicate_of_pos [Min α] {n : Nat} {a : α} (w : min a a = a) (h : 0 < n) :
+    (replicate n a).min? = some a := by
+  simp [min?_replicate, Nat.ne_of_gt h, w]
 
-/-! ### maximum? -/
+/-! ### max? -/
 
-@[simp] theorem maximum?_nil [Max α] : ([] : List α).maximum? = none := rfl
+@[simp] theorem max?_nil [Max α] : ([] : List α).max? = none := rfl
 
--- We don't put `@[simp]` on `maximum?_cons`,
+-- We don't put `@[simp]` on `max?_cons`,
 -- because the definition in terms of `foldl` is not useful for proofs.
-theorem maximum?_cons [Max α] {xs : List α} : (x :: xs).maximum? = foldl max x xs := rfl
+theorem max?_cons [Max α] {xs : List α} : (x :: xs).max? = foldl max x xs := rfl
 
-@[simp] theorem maximum?_eq_none_iff {xs : List α} [Max α] : xs.maximum? = none ↔ xs = [] := by
-  cases xs <;> simp [maximum?]
+@[simp] theorem max?_eq_none_iff {xs : List α} [Max α] : xs.max? = none ↔ xs = [] := by
+  cases xs <;> simp [max?]
 
-theorem maximum?_mem [Max α] (min_eq_or : ∀ a b : α, max a b = a ∨ max a b = b) :
-    {xs : List α} → xs.maximum? = some a → a ∈ xs
+theorem max?_mem [Max α] (min_eq_or : ∀ a b : α, max a b = a ∨ max a b = b) :
+    {xs : List α} → xs.max? = some a → a ∈ xs
   | nil => by simp
   | cons x xs => by
-    rw [maximum?]; rintro ⟨⟩
+    rw [max?]; rintro ⟨⟩
     induction xs generalizing x with simp at *
     | cons y xs ih =>
       rcases ih (max x y) with h | h <;> simp [h]
@@ -114,40 +114,57 @@ theorem maximum?_mem [Max α] (min_eq_or : ∀ a b : α, max a b = a ∨ max a b
 
 -- See also `Init.Data.List.Nat.Basic` for specialisations of the next two results to `Nat`.
 
-theorem maximum?_le_iff [Max α] [LE α]
+theorem max?_le_iff [Max α] [LE α]
     (max_le_iff : ∀ a b c : α, max b c ≤ a ↔ b ≤ a ∧ c ≤ a) :
-    {xs : List α} → xs.maximum? = some a → ∀ {x}, a ≤ x ↔ ∀ b ∈ xs, b ≤ x
+    {xs : List α} → xs.max? = some a → ∀ {x}, a ≤ x ↔ ∀ b ∈ xs, b ≤ x
   | nil => by simp
   | cons x xs => by
-    rw [maximum?]; rintro ⟨⟩ y
+    rw [max?]; rintro ⟨⟩ y
     induction xs generalizing x with
     | nil => simp
     | cons y xs ih => simp [ih, max_le_iff, and_assoc]
 
 -- This could be refactored by designing appropriate typeclasses to replace `le_refl`, `max_eq_or`,
 -- and `le_min_iff`.
-theorem maximum?_eq_some_iff [Max α] [LE α] [anti : Antisymm ((· : α) ≤ ·)]
+theorem max?_eq_some_iff [Max α] [LE α] [anti : Antisymm ((· : α) ≤ ·)]
     (le_refl : ∀ a : α, a ≤ a)
     (max_eq_or : ∀ a b : α, max a b = a ∨ max a b = b)
     (max_le_iff : ∀ a b c : α, max b c ≤ a ↔ b ≤ a ∧ c ≤ a) {xs : List α} :
-    xs.maximum? = some a ↔ a ∈ xs ∧ ∀ b ∈ xs, b ≤ a := by
-  refine ⟨fun h => ⟨maximum?_mem max_eq_or h, (maximum?_le_iff max_le_iff h).1 (le_refl _)⟩, ?_⟩
+    xs.max? = some a ↔ a ∈ xs ∧ ∀ b ∈ xs, b ≤ a := by
+  refine ⟨fun h => ⟨max?_mem max_eq_or h, (max?_le_iff max_le_iff h).1 (le_refl _)⟩, ?_⟩
   intro ⟨h₁, h₂⟩
   cases xs with
   | nil => simp at h₁
   | cons x xs =>
     exact congrArg some <| anti.1
-      (h₂ _ (maximum?_mem max_eq_or (xs := x::xs) rfl))
-      ((maximum?_le_iff max_le_iff (xs := x::xs) rfl).1 (le_refl _) _ h₁)
+      (h₂ _ (max?_mem max_eq_or (xs := x::xs) rfl))
+      ((max?_le_iff max_le_iff (xs := x::xs) rfl).1 (le_refl _) _ h₁)
 
-theorem maximum?_replicate [Max α] {n : Nat} {a : α} (w : max a a = a) :
-    (replicate n a).maximum? = if n = 0 then none else some a := by
+theorem max?_replicate [Max α] {n : Nat} {a : α} (w : max a a = a) :
+    (replicate n a).max? = if n = 0 then none else some a := by
   induction n with
   | zero => rfl
-  | succ n ih => cases n <;> simp_all [replicate_succ, maximum?_cons]
+  | succ n ih => cases n <;> simp_all [replicate_succ, max?_cons]
 
-@[simp] theorem maximum?_replicate_of_pos [Max α] {n : Nat} {a : α} (w : max a a = a) (h : 0 < n) :
-    (replicate n a).maximum? = some a := by
-  simp [maximum?_replicate, Nat.ne_of_gt h, w]
+@[simp] theorem max?_replicate_of_pos [Max α] {n : Nat} {a : α} (w : max a a = a) (h : 0 < n) :
+    (replicate n a).max? = some a := by
+  simp [max?_replicate, Nat.ne_of_gt h, w]
+
+@[deprecated min?_nil (since := "2024-09-29")] abbrev minimum?_nil := @min?_nil
+@[deprecated min?_cons (since := "2024-09-29")] abbrev minimum?_cons := @min?_cons
+@[deprecated min?_eq_none_iff (since := "2024-09-29")] abbrev mininmum?_eq_none_iff := @min?_eq_none_iff
+@[deprecated min?_mem (since := "2024-09-29")] abbrev minimum?_mem := @min?_mem
+@[deprecated le_min?_iff (since := "2024-09-29")] abbrev le_minimum?_iff := @le_min?_iff
+@[deprecated min?_eq_some_iff (since := "2024-09-29")] abbrev minimum?_eq_some_iff := @min?_eq_some_iff
+@[deprecated min?_replicate (since := "2024-09-29")] abbrev minimum?_replicate := @min?_replicate
+@[deprecated min?_replicate_of_pos (since := "2024-09-29")] abbrev minimum?_replicate_of_pos := @min?_replicate_of_pos
+@[deprecated max?_nil (since := "2024-09-29")] abbrev maximum?_nil := @max?_nil
+@[deprecated max?_cons (since := "2024-09-29")] abbrev maximum?_cons := @max?_cons
+@[deprecated max?_eq_none_iff (since := "2024-09-29")] abbrev maximum?_eq_none_iff := @max?_eq_none_iff
+@[deprecated max?_mem (since := "2024-09-29")] abbrev maximum?_mem := @max?_mem
+@[deprecated max?_le_iff (since := "2024-09-29")] abbrev maximum?_le_iff := @max?_le_iff
+@[deprecated max?_eq_some_iff (since := "2024-09-29")] abbrev maximum?_eq_some_iff := @max?_eq_some_iff
+@[deprecated max?_replicate (since := "2024-09-29")] abbrev maximum?_replicate := @max?_replicate
+@[deprecated max?_replicate_of_pos (since := "2024-09-29")] abbrev maximum?_replicate_of_pos := @max?_replicate_of_pos
 
 end List

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

@@ -86,26 +86,26 @@ theorem mem_eraseIdx_iff_getElem? {x : α} {l} {k} : x ∈ eraseIdx l k ↔ ∃
     obtain ⟨h', -⟩ := getElem?_eq_some_iff.1 h
     exact ⟨h', h⟩
 
-/-! ### minimum? -/
+/-! ### min? -/
 
--- A specialization of `minimum?_eq_some_iff` to Nat.
-theorem minimum?_eq_some_iff' {xs : List Nat} :
-    xs.minimum? = some a ↔ (a ∈ xs ∧ ∀ b ∈ xs, a ≤ b) :=
-  minimum?_eq_some_iff
+-- A specialization of `min?_eq_some_iff` to Nat.
+theorem min?_eq_some_iff' {xs : List Nat} :
+    xs.min? = some a ↔ (a ∈ xs ∧ ∀ b ∈ xs, a ≤ b) :=
+  min?_eq_some_iff
     (le_refl := Nat.le_refl)
-    (min_eq_or := fun _ _ => by omega)
-    (le_min_iff := fun _ _ _ => by omega)
+    (min_eq_or := fun _ _ => Nat.min_def .. ▸ by split <;> simp)
+    (le_min_iff := fun _ _ _ => Nat.le_min)
 
 -- This could be generalized,
 -- but will first require further work on order typeclasses in the core repository.
-theorem minimum?_cons' {a : Nat} {l : List Nat} :
-    (a :: l).minimum? = some (match l.minimum? with
+theorem min?_cons' {a : Nat} {l : List Nat} :
+    (a :: l).min? = some (match l.min? with
     | none => a
     | some m => min a m) := by
-  rw [minimum?_eq_some_iff']
+  rw [min?_eq_some_iff']
   split <;> rename_i h m
   · simp_all
-  · rw [minimum?_eq_some_iff'] at m
+  · rw [min?_eq_some_iff'] at m
     obtain ⟨m, le⟩ := m
     rw [Nat.min_def]
     constructor
@@ -122,11 +122,11 @@ theorem minimum?_cons' {a : Nat} {l : List Nat} :
 theorem foldl_min
     {α : Type _} [Min α] [Std.IdempotentOp (min : α → α → α)] [Std.Associative (min : α → α → α)]
     {l : List α} {a : α} :
-    l.foldl (init := a) min = min a (l.minimum?.getD a) := by
+    l.foldl (init := a) min = min a (l.min?.getD a) := by
   cases l with
   | nil => simp [Std.IdempotentOp.idempotent]
   | cons b l =>
-    simp only [minimum?]
+    simp only [min?]
     induction l generalizing a b with
     | nil => simp
     | cons c l ih => simp [ih, Std.Associative.assoc]
@@ -134,7 +134,7 @@ theorem foldl_min
 theorem foldl_min_right {α β : Type _}
     [Min β] [Std.IdempotentOp (min : β → β → β)] [Std.Associative (min : β → β → β)]
     {l : List α} {b : β} {f : α → β} :
-    (l.foldl (init := b) fun acc a => min acc (f a)) = min b ((l.map f).minimum?.getD b) := by
+    (l.foldl (init := b) fun acc a => min acc (f a)) = min b ((l.map f).min?.getD b) := by
   rw [← foldl_map, foldl_min]
 
 theorem foldl_min_le {l : List Nat} {a : Nat} : l.foldl (init := a) min ≤ a := by
@@ -148,12 +148,12 @@ theorem foldl_min_min_of_le {l : List Nat} {a b : Nat} (h : a ≤ b) :
     l.foldl (init := a) min ≤ b :=
   Nat.le_trans (foldl_min_le) h
 
-theorem minimum?_getD_le_of_mem {l : List Nat} {a k : Nat} (h : a ∈ l) :
-    l.minimum?.getD k ≤ a := by
+theorem min?_getD_le_of_mem {l : List Nat} {a k : Nat} (h : a ∈ l) :
+    l.min?.getD k ≤ a := by
   cases l with
   | nil => simp at h
   | cons b l =>
-    simp [minimum?_cons]
+    simp [min?_cons]
     simp at h
     rcases h with (rfl | h)
     · exact foldl_min_le
@@ -166,26 +166,26 @@ theorem minimum?_getD_le_of_mem {l : List Nat} {a k : Nat} (h : a ∈ l) :
         · exact foldl_min_min_of_le (Nat.min_le_right _ _)
         · exact ih _ h
 
-/-! ### maximum? -/
+/-! ### max? -/
 
--- A specialization of `maximum?_eq_some_iff` to Nat.
-theorem maximum?_eq_some_iff' {xs : List Nat} :
-    xs.maximum? = some a ↔ (a ∈ xs ∧ ∀ b ∈ xs, b ≤ a) :=
-  maximum?_eq_some_iff
+-- A specialization of `max?_eq_some_iff` to Nat.
+theorem max?_eq_some_iff' {xs : List Nat} :
+    xs.max? = some a ↔ (a ∈ xs ∧ ∀ b ∈ xs, b ≤ a) :=
+  max?_eq_some_iff
     (le_refl := Nat.le_refl)
-    (max_eq_or := fun _ _ => by omega)
-    (max_le_iff := fun _ _ _ => by omega)
+    (max_eq_or := fun _ _ => Nat.max_def .. ▸ by split <;> simp)
+    (max_le_iff := fun _ _ _ => Nat.max_le)
 
 -- This could be generalized,
 -- but will first require further work on order typeclasses in the core repository.
-theorem maximum?_cons' {a : Nat} {l : List Nat} :
-    (a :: l).maximum? = some (match l.maximum? with
+theorem max?_cons' {a : Nat} {l : List Nat} :
+    (a :: l).max? = some (match l.max? with
     | none => a
     | some m => max a m) := by
-  rw [maximum?_eq_some_iff']
+  rw [max?_eq_some_iff']
   split <;> rename_i h m
   · simp_all
-  · rw [maximum?_eq_some_iff'] at m
+  · rw [max?_eq_some_iff'] at m
     obtain ⟨m, le⟩ := m
     rw [Nat.max_def]
     constructor
@@ -202,11 +202,11 @@ theorem maximum?_cons' {a : Nat} {l : List Nat} :
 theorem foldl_max
     {α : Type _} [Max α] [Std.IdempotentOp (max : α → α → α)] [Std.Associative (max : α → α → α)]
     {l : List α} {a : α} :
-    l.foldl (init := a) max = max a (l.maximum?.getD a) := by
+    l.foldl (init := a) max = max a (l.max?.getD a) := by
   cases l with
   | nil => simp [Std.IdempotentOp.idempotent]
   | cons b l =>
-    simp only [maximum?]
+    simp only [max?]
     induction l generalizing a b with
     | nil => simp
     | cons c l ih => simp [ih, Std.Associative.assoc]
@@ -214,7 +214,7 @@ theorem foldl_max
 theorem foldl_max_right {α β : Type _}
     [Max β] [Std.IdempotentOp (max : β → β → β)] [Std.Associative (max : β → β → β)]
     {l : List α} {b : β} {f : α → β} :
-    (l.foldl (init := b) fun acc a => max acc (f a)) = max b ((l.map f).maximum?.getD b) := by
+    (l.foldl (init := b) fun acc a => max acc (f a)) = max b ((l.map f).max?.getD b) := by
   rw [← foldl_map, foldl_max]
 
 theorem le_foldl_max {l : List Nat} {a : Nat} : a ≤ l.foldl (init := a) max := by
@@ -228,12 +228,12 @@ theorem le_foldl_max_of_le {l : List Nat} {a b : Nat} (h : a ≤ b) :
     a ≤ l.foldl (init := b) max :=
   Nat.le_trans h (le_foldl_max)
 
-theorem le_maximum?_getD_of_mem {l : List Nat} {a k : Nat} (h : a ∈ l) :
-    a ≤ l.maximum?.getD k := by
+theorem le_max?_getD_of_mem {l : List Nat} {a k : Nat} (h : a ∈ l) :
+    a ≤ l.max?.getD k := by
   cases l with
   | nil => simp at h
   | cons b l =>
-    simp [maximum?_cons]
+    simp [max?_cons]
     simp at h
     rcases h with (rfl | h)
     · exact le_foldl_max
@@ -246,4 +246,11 @@ theorem le_maximum?_getD_of_mem {l : List Nat} {a k : Nat} (h : a ∈ l) :
         · exact le_foldl_max_of_le (Nat.le_max_right b a)
         · exact ih _ h
 
+@[deprecated min?_eq_some_iff' (since := "2024-09-29")] abbrev minimum?_eq_some_iff' := @min?_eq_some_iff'
+@[deprecated min?_cons' (since := "2024-09-29")] abbrev minimum?_cons' := @min?_cons'
+@[deprecated min?_getD_le_of_mem (since := "2024-09-29")] abbrev minimum?_getD_le_of_mem := @min?_getD_le_of_mem
+@[deprecated max?_eq_some_iff' (since := "2024-09-29")] abbrev maximum?_eq_some_iff' := @max?_eq_some_iff'
+@[deprecated max?_cons' (since := "2024-09-29")] abbrev maximum?_cons' := @max?_cons'
+@[deprecated le_max?_getD_of_mem (since := "2024-09-29")] abbrev le_maximum?_getD_of_mem := @le_max?_getD_of_mem
+
 end List

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

@@ -10,7 +10,7 @@ import Init.Data.List.Erase
 namespace List
 
 theorem getElem?_eraseIdx (l : List α) (i : Nat) (j : Nat) :
-    (l.eraseIdx i)[j]? = if h : j < i then l[j]? else l[j + 1]? := by
+    (l.eraseIdx i)[j]? = if j < i then l[j]? else l[j + 1]? := by
   rw [eraseIdx_eq_take_drop_succ, getElem?_append]
   split <;> rename_i h
   · rw [getElem?_take]

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

@@ -154,7 +154,7 @@ theorem erase_range' :
 /-! ### range -/
 
 theorem reverse_range' : ∀ s n : Nat, reverse (range' s n) = map (s + n - 1 - ·) (range n)
-  | s, 0 => rfl
+  | _, 0 => rfl
   | s, n + 1 => by
     rw [range'_1_concat, reverse_append, range_succ_eq_map,
       show s + (n + 1) - 1 = s + n from rfl, map, map_map]

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

@@ -42,7 +42,7 @@ theorem getElem_take' (L : List α) {i j : Nat} (hi : i < L.length) (hj : i < j)
 
 /-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
 length `> i`. Version designed to rewrite from the small list to the big list. -/
-theorem getElem_take (L : List α) {j i : Nat} {h : i < (L.take j).length} :
+@[simp] theorem getElem_take (L : List α) {j i : Nat} {h : i < (L.take j).length} :
     (L.take j)[i] =
     L[i]'(Nat.lt_of_lt_of_le h (length_take_le' _ _)) := by
   rw [length_take, Nat.lt_min] at h; rw [getElem_take' L _ h.1]
@@ -52,7 +52,7 @@ length `> i`. Version designed to rewrite from the big list to the small list. -
 @[deprecated getElem_take' (since := "2024-06-12")]
 theorem get_take (L : List α) {i j : Nat} (hi : i < L.length) (hj : i < j) :
     get L ⟨i, hi⟩ = get (L.take j) ⟨i, length_take .. ▸ Nat.lt_min.mpr ⟨hj, hi⟩⟩ := by
-  simp [getElem_take' _ hi hj]
+  simp
 
 /-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
 length `> i`. Version designed to rewrite from the small list to the big list. -/

src/Init/Data/List/Perm.lean

@@ -98,8 +98,8 @@ theorem Perm.append_cons (a : α) {h₁ h₂ t₁ t₂ : List α} (p₁ : h₁ ~
   perm_middle.trans <| by rw [append_nil]
 
 theorem perm_append_comm : ∀ {l₁ l₂ : List α}, l₁ ++ l₂ ~ l₂ ++ l₁
-  | [], l₂ => by simp
-  | a :: t, l₂ => (perm_append_comm.cons _).trans perm_middle.symm
+  | [], _ => by simp
+  | _ :: _, _ => (perm_append_comm.cons _).trans perm_middle.symm
 
 theorem perm_append_comm_assoc (l₁ l₂ l₃ : List α) :
     Perm (l₁ ++ (l₂ ++ l₃)) (l₂ ++ (l₁ ++ l₃)) := by
@@ -248,6 +248,10 @@ theorem countP_eq_countP_filter_add (l : List α) (p q : α → Bool) :
 theorem Perm.count_eq [DecidableEq α] {l₁ l₂ : List α} (p : l₁ ~ l₂) (a) :
     count a l₁ = count a l₂ := p.countP_eq _
 
+/-
+This theorem is a variant of `Perm.foldl_eq` defined in Mathlib which uses typeclasses rather
+than the explicit `comm` argument.
+-/
 theorem Perm.foldl_eq' {f : β → α → β} {l₁ l₂ : List α} (p : l₁ ~ l₂)
     (comm : ∀ x ∈ l₁, ∀ y ∈ l₁, ∀ (z), f (f z x) y = f (f z y) x)
     (init) : foldl f init l₁ = foldl f init l₂ := by
@@ -264,6 +268,28 @@ theorem Perm.foldl_eq' {f : β → α → β} {l₁ l₂ : List α} (p : l₁ ~
     refine (IH₁ comm init).trans (IH₂ ?_ _)
     intros; apply comm <;> apply p₁.symm.subset <;> assumption
 
+/-
+This theorem is a variant of `Perm.foldr_eq` defined in Mathlib which uses typeclasses rather
+than the explicit `comm` argument.
+-/
+theorem Perm.foldr_eq' {f : α → β → β} {l₁ l₂ : List α} (p : l₁ ~ l₂)
+    (comm : ∀ x ∈ l₁, ∀ y ∈ l₁, ∀ (z), f y (f x z) = f x (f y z))
+    (init) : foldr f init l₁ = foldr f init l₂ := by
+  induction p using recOnSwap' generalizing init with
+  | nil => simp
+  | cons x _p IH =>
+    simp only [foldr]
+    congr 1
+    apply IH; intros; apply comm <;> exact .tail _ ‹_›
+  | swap' x y _p IH =>
+    simp only [foldr]
+    rw [comm x (.tail _ <| .head _) y (.head _)]
+    congr 2
+    apply IH; intros; apply comm <;> exact .tail _ (.tail _ ‹_›)
+  | trans p₁ _p₂ IH₁ IH₂ =>
+    refine (IH₁ comm init).trans (IH₂ ?_ _)
+    intros; apply comm <;> apply p₁.symm.subset <;> assumption
+
 theorem Perm.rec_heq {β : List α → Sort _} {f : ∀ a l, β l → β (a :: l)} {b : β []} {l l' : List α}
     (hl : l ~ l') (f_congr : ∀ {a l l' b b'}, l ~ l' → HEq b b' → HEq (f a l b) (f a l' b'))
     (f_swap : ∀ {a a' l b}, HEq (f a (a' :: l) (f a' l b)) (f a' (a :: l) (f a l b))) :

src/Init/Data/List/Range.lean

@@ -92,7 +92,7 @@ theorem map_add_range' (a) : ∀ s n step, map (a + ·) (range' s n step) = rang
 
 theorem range'_append : ∀ s m n step : Nat,
     range' s m step ++ range' (s + step * m) n step = range' s (n + m) step
-  | s, 0, n, step => rfl
+  | _, 0, _, _ => rfl
   | s, m + 1, n, step => by
     simpa [range', Nat.mul_succ, Nat.add_assoc, Nat.add_comm]
       using range'_append (s + step) m n step
@@ -131,7 +131,7 @@ theorem range'_eq_cons_iff : range' s n = a :: xs ↔ s = a ∧ 0 < n ∧ xs = r
 /-! ### range -/
 
 theorem range_loop_range' : ∀ s n : Nat, range.loop s (range' s n) = range' 0 (n + s)
-  | 0, n => rfl
+  | 0, _ => rfl
   | s + 1, n => by rw [← Nat.add_assoc, Nat.add_right_comm n s 1]; exact range_loop_range' s (n + 1)
 
 theorem range_eq_range' (n : Nat) : range n = range' 0 n :=
@@ -214,9 +214,9 @@ theorem enumFrom_eq_nil {n : Nat} {l : List α} : List.enumFrom n l = [] ↔ l =
 @[simp]
 theorem getElem?_enumFrom :
     ∀ n (l : List α) m, (enumFrom n l)[m]? = l[m]?.map fun a => (n + m, a)
-  | n, [], m => rfl
-  | n, a :: l, 0 => by simp
-  | n, a :: l, m + 1 => by
+  | _, [], _ => rfl
+  | _, _ :: _, 0 => by simp
+  | n, _ :: l, m + 1 => by
     simp only [enumFrom_cons, getElem?_cons_succ]
     exact (getElem?_enumFrom (n + 1) l m).trans <| by rw [Nat.add_right_comm]; rfl
 

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

@@ -102,7 +102,7 @@ def mergeSortTR (l : List α) (le : α → α → Bool := by exact fun a b => a
 where run : {n : Nat} → { l : List α // l.length = n } → List α
   | 0, ⟨[], _⟩ => []
   | 1, ⟨[a], _⟩ => [a]
-  | n+2, xs =>
+  | _+2, xs =>
     let (l, r) := splitInTwo xs
     mergeTR (run l) (run r) le
 
@@ -136,13 +136,13 @@ where
   run : {n : Nat} → { l : List α // l.length = n } → List α
   | 0, ⟨[], _⟩ => []
   | 1, ⟨[a], _⟩ => [a]
-  | n+2, xs =>
+  | _+2, xs =>
     let (l, r) := splitRevInTwo xs
     mergeTR (run' l) (run r) le
   run' : {n : Nat} → { l : List α // l.length = n } → List α
   | 0, ⟨[], _⟩ => []
   | 1, ⟨[a], _⟩ => [a]
-  | n+2, xs =>
+  | _+2, xs =>
     let (l, r) := splitRevInTwo' xs
     mergeTR (run' r) (run l) le
 

src/Init/Data/List/Sublist.lean

@@ -725,16 +725,25 @@ theorem infix_iff_suffix_prefix {l₁ l₂ : List α} : l₁ <:+: l₂ ↔ ∃ t
 theorem IsInfix.eq_of_length (h : l₁ <:+: l₂) : l₁.length = l₂.length → l₁ = l₂ :=
   h.sublist.eq_of_length
 
+theorem IsInfix.eq_of_length_le (h : l₁ <:+: l₂) : l₂.length ≤ l₁.length → l₁ = l₂ :=
+  h.sublist.eq_of_length_le
+
 theorem IsPrefix.eq_of_length (h : l₁ <+: l₂) : l₁.length = l₂.length → l₁ = l₂ :=
   h.sublist.eq_of_length
 
+theorem IsPrefix.eq_of_length_le (h : l₁ <+: l₂) : l₂.length ≤ l₁.length → l₁ = l₂ :=
+  h.sublist.eq_of_length_le
+
 theorem IsSuffix.eq_of_length (h : l₁ <:+ l₂) : l₁.length = l₂.length → l₁ = l₂ :=
   h.sublist.eq_of_length
 
+theorem IsSuffix.eq_of_length_le (h : l₁ <:+ l₂) : l₂.length ≤ l₁.length → l₁ = l₂ :=
+  h.sublist.eq_of_length_le
+
 theorem prefix_of_prefix_length_le :
     ∀ {l₁ l₂ l₃ : List α}, l₁ <+: l₃ → l₂ <+: l₃ → length l₁ ≤ length l₂ → l₁ <+: l₂
-  | [], l₂, _, _, _, _ => nil_prefix
-  | a :: l₁, b :: l₂, _, ⟨r₁, rfl⟩, ⟨r₂, e⟩, ll => by
+  | [], _, _, _, _, _ => nil_prefix
+  | _ :: _, b :: _, _, ⟨_, rfl⟩, ⟨_, e⟩, ll => by
     injection e with _ e'; subst b
     rcases prefix_of_prefix_length_le ⟨_, rfl⟩ ⟨_, e'⟩ (le_of_succ_le_succ ll) with ⟨r₃, rfl⟩
     exact ⟨r₃, rfl⟩
@@ -829,6 +838,24 @@ theorem isPrefix_iff : l₁ <+: l₂ ↔ ∀ i (h : i < l₁.length), l₂[i]? =
       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} :
+    l₁ <+: l₂ ↔ ∃ (h : l₁.length ≤ l₂.length), ∀ x (hx : x < l₁.length),
+      l₁[x] = l₂[x]'(Nat.lt_of_lt_of_le hx h) where
+  mp h := ⟨h.length_le, fun _ _ ↦ h.getElem _⟩
+  mpr h := by
+    obtain ⟨hl, h⟩ := h
+    induction l₂ generalizing l₁ with
+    | nil =>
+      simpa using hl
+    | cons _ _ tail_ih =>
+      cases l₁ with
+      | nil =>
+        exact nil_prefix
+      | cons _ _ =>
+        simp only [length_cons, Nat.add_le_add_iff_right, Fin.getElem_fin] at hl h
+        simp only [cons_prefix_cons]
+        exact ⟨h 0 (zero_lt_succ _), tail_ih hl fun a ha ↦ h a.succ (succ_lt_succ ha)⟩
+
 -- See `Init.Data.List.Nat.Sublist` for `isSuffix_iff` and `ifInfix_iff`.
 
 theorem isPrefix_filterMap_iff {β} {f : α → Option β} {l₁ : List α} {l₂ : List β} :

src/Init/Data/List/Zip.lean

@@ -247,9 +247,9 @@ theorem zip_eq_zipWith : ∀ (l₁ : List α) (l₂ : List β), zip l₁ l₂ =
 
 theorem zip_map (f : α → γ) (g : β → δ) :
     ∀ (l₁ : List α) (l₂ : List β), zip (l₁.map f) (l₂.map g) = (zip l₁ l₂).map (Prod.map f g)
-  | [], l₂ => rfl
-  | l₁, [] => by simp only [map, zip_nil_right]
-  | a :: l₁, b :: l₂ => by
+  | [], _ => rfl
+  | _, [] => by simp only [map, zip_nil_right]
+  | _ :: _, _ :: _ => by
     simp only [map, zip_cons_cons, zip_map, Prod.map]; constructor
 
 theorem zip_map_left (f : α → γ) (l₁ : List α) (l₂ : List β) :
@@ -287,12 +287,12 @@ theorem of_mem_zip {a b} : ∀ {l₁ : List α} {l₂ : List β}, (a, b) ∈ zip
 
 theorem map_fst_zip :
     ∀ (l₁ : List α) (l₂ : List β), l₁.length ≤ l₂.length → map Prod.fst (zip l₁ l₂) = l₁
-  | [], bs, _ => rfl
+  | [], _, _ => rfl
   | _ :: as, _ :: bs, h => by
     simp [Nat.succ_le_succ_iff] at h
     show _ :: map Prod.fst (zip as bs) = _ :: as
     rw [map_fst_zip as bs h]
-  | a :: as, [], h => by simp at h
+  | _ :: _, [], h => by simp at h
 
 theorem map_snd_zip :
     ∀ (l₁ : List α) (l₂ : List β), l₂.length ≤ l₁.length → map Prod.snd (zip l₁ l₂) = l₂
@@ -430,9 +430,9 @@ theorem zip_unzip : ∀ l : List (α × β), zip (unzip l).1 (unzip l).2 = l
 
 theorem unzip_zip_left :
     ∀ {l₁ : List α} {l₂ : List β}, length l₁ ≤ length l₂ → (unzip (zip l₁ l₂)).1 = l₁
-  | [], l₂, _ => rfl
-  | l₁, [], h => by rw [eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero h)]; rfl
-  | a :: l₁, b :: l₂, h => by
+  | [], _, _ => rfl
+  | _, [], h => by rw [eq_nil_of_length_eq_zero (Nat.eq_zero_of_le_zero h)]; rfl
+  | _ :: _, _ :: _, h => by
     simp only [zip_cons_cons, unzip_cons, unzip_zip_left (le_of_succ_le_succ h)]
 
 theorem unzip_zip_right :

src/Init/Data/Nat/Basic.lean

@@ -248,7 +248,7 @@ protected theorem add_mul (n m k : Nat) : (n + m) * k = n * k + m * k :=
   Nat.right_distrib n m k
 
 protected theorem mul_assoc : ∀ (n m k : Nat), (n * m) * k = n * (m * k)
-  | n, m, 0      => rfl
+  | _, _, 0      => rfl
   | n, m, succ k => by simp [mul_succ, Nat.mul_assoc n m k, Nat.left_distrib]
 instance : Std.Associative (α := Nat) (· * ·) := ⟨Nat.mul_assoc⟩
 
@@ -634,6 +634,8 @@ theorem lt_succ_of_lt (h : a < b) : a < succ b := le_succ_of_le h
 
 theorem lt_add_one_of_lt (h : a < b) : a < b + 1 := le_succ_of_le h
 
+@[simp] theorem lt_one_iff : n < 1 ↔ n = 0 := Nat.lt_succ_iff.trans <| by rw [le_zero_eq]
+
 theorem succ_pred_eq_of_ne_zero : ∀ {n}, n ≠ 0 → succ (pred n) = n
   | _+1, _ => rfl
 

src/Init/Data/Nat/Div.lean

@@ -269,7 +269,7 @@ protected theorem div_div_eq_div_mul (m n k : Nat) : m / n / k = m / (n * k) :=
 
 theorem div_mul_le_self : ∀ (m n : Nat), m / n * n ≤ m
   | m, 0   => by simp
-  | m, n+1 => (le_div_iff_mul_le (Nat.succ_pos _)).1 (Nat.le_refl _)
+  | _, _+1 => (le_div_iff_mul_le (Nat.succ_pos _)).1 (Nat.le_refl _)
 
 theorem div_lt_iff_lt_mul (Hk : 0 < k) : x / k < y ↔ x < y * k := by
   rw [← Nat.not_le, ← Nat.not_le]; exact not_congr (le_div_iff_mul_le Hk)

src/Init/Data/Nat/Lemmas.lean

@@ -605,6 +605,9 @@ theorem add_mod (a b n : Nat) : (a + b) % n = ((a % n) + (b % n)) % n := by
     | zero => simp_all
     | succ k => omega
 
+@[simp] theorem mod_mul_mod {a b c : Nat} : (a % c * b) % c = a * b % c := by
+  rw [mul_mod, mod_mod, ← mul_mod]
+
 /-! ### pow -/
 
 theorem pow_succ' {m n : Nat} : m ^ n.succ = m * m ^ n := by
@@ -767,6 +770,11 @@ protected theorem two_pow_pred_mod_two_pow (h : 0 < w) :
   rw [mod_eq_of_lt]
   apply Nat.pow_pred_lt_pow (by omega) h
 
+protected theorem pow_lt_pow_iff_pow_mul_le_pow {a n m : Nat} (h : 1 < a) :
+    a ^ n < a ^ m ↔ a ^ n * a ≤ a ^ m := by
+  rw [←Nat.pow_add_one, Nat.pow_le_pow_iff_right (by omega), Nat.pow_lt_pow_iff_right (by omega)]
+  omega
+
 @[simp]
 theorem two_pow_pred_mul_two (h : 0 < w) :
     2 ^ (w - 1) * 2 = 2 ^ w := by
@@ -866,15 +874,15 @@ theorem shiftLeft_succ_inside (m n : Nat) : m <<< (n+1) = (2*m) <<< n := rfl
 
 /-- Shiftleft on successor with multiple moved to outside. -/
 theorem shiftLeft_succ : ∀(m n), m <<< (n + 1) = 2 * (m <<< n)
-| m, 0 => rfl
-| m, k + 1 => by
+| _, 0 => rfl
+| _, k + 1 => by
   rw [shiftLeft_succ_inside _ (k+1)]
   rw [shiftLeft_succ _ k, shiftLeft_succ_inside]
 
 /-- Shiftright on successor with division moved inside. -/
 theorem shiftRight_succ_inside : ∀m n, m >>> (n+1) = (m/2) >>> n
-| m, 0 => rfl
-| m, k + 1 => by
+| _, 0 => rfl
+| _, k + 1 => by
   rw [shiftRight_succ _ (k+1)]
   rw [shiftRight_succ_inside _ k, shiftRight_succ]
 

src/Init/Data/NeZero.lean

@@ -35,4 +35,4 @@ theorem neZero_iff {n : R} : NeZero n ↔ n ≠ 0 :=
   ⟨fun h ↦ h.out, NeZero.mk⟩
 
 @[simp] theorem neZero_zero_iff_false {α : Type _} [Zero α] : NeZero (0 : α) ↔ False :=
-  ⟨fun h ↦ h.ne rfl, fun h ↦ h.elim⟩
+  ⟨fun _ ↦ NeZero.ne (0 : α) rfl, fun h ↦ h.elim⟩

src/Init/Data/Option.lean

@@ -8,3 +8,5 @@ import Init.Data.Option.Basic
 import Init.Data.Option.BasicAux
 import Init.Data.Option.Instances
 import Init.Data.Option.Lemmas
+import Init.Data.Option.Attach
+import Init.Data.Option.List

src/Init/Data/Option/Attach.lean

@@ -0,0 +1,178 @@
+/-
+Copyright (c) 2024 Lean FRO. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Kim Morrison
+-/
+prelude
+import Init.Data.Option.Basic
+import Init.Data.Option.List
+import Init.Data.List.Attach
+import Init.BinderPredicates
+
+namespace Option
+
+/--
+Unsafe implementation of `attachWith`, taking advantage of the fact that the representation of
+`Option {x // P x}` is the same as the input `Option α`.
+-/
+@[inline] private unsafe def attachWithImpl
+    (o : Option α) (P : α → Prop) (_ : ∀ x ∈ o, P x) : Option {x // P x} := unsafeCast o
+
+/-- "Attach" a proof `P x` that holds for the element of `o`, if present,
+to produce a new option with the same element but in the type `{x // P x}`. -/
+@[implemented_by attachWithImpl] def attachWith
+    (xs : Option α) (P : α → Prop) (H : ∀ x ∈ xs, P x) : Option {x // P x} :=
+  match xs with
+  | none => none
+  | some x => some ⟨x, H x (mem_some_self x)⟩
+
+/-- "Attach" the proof that the element of `xs`, if present, is in `xs`
+to produce a new option with the same elements but in the type `{x // x ∈ xs}`. -/
+@[inline] def attach (xs : Option α) : Option {x // x ∈ xs} := xs.attachWith _ fun _ => id
+
+@[simp] theorem attach_none : (none : Option α).attach = none := rfl
+@[simp] theorem attachWith_none : (none : Option α).attachWith P H = none := rfl
+
+@[simp] theorem attach_some {x : α} :
+    (some x).attach = some ⟨x, rfl⟩ := rfl
+@[simp] theorem attachWith_some {x : α} {P : α → Prop} (h : ∀ (b : α), b ∈ some x → P b) :
+    (some x).attachWith P h = some ⟨x, by simpa using h⟩ := rfl
+
+theorem attach_congr {o₁ o₂ : Option α} (h : o₁ = o₂) :
+    o₁.attach = o₂.attach.map (fun x => ⟨x.1, h ▸ x.2⟩) := by
+  subst h
+  simp
+
+theorem attachWith_congr {o₁ o₂ : Option α} (w : o₁ = o₂) {P : α → Prop} {H : ∀ x ∈ o₁, P x} :
+    o₁.attachWith P H = o₂.attachWith P fun x h => H _ (w ▸ h) := by
+  subst w
+  simp
+
+theorem attach_map_coe (o : Option α) (f : α → β) :
+    (o.attach.map fun (i : {i // i ∈ o}) => f i) = o.map f := by
+  cases o <;> simp
+
+theorem attach_map_val (o : Option α) (f : α → β) :
+    (o.attach.map fun i => f i.val) = o.map f :=
+  attach_map_coe _ _
+
+@[simp]
+theorem attach_map_subtype_val (o : Option α) :
+    o.attach.map Subtype.val = o :=
+  (attach_map_coe _ _).trans (congrFun Option.map_id _)
+
+theorem attachWith_map_coe {p : α → Prop} (f : α → β) (o : Option α) (H : ∀ a ∈ o, p a) :
+    ((o.attachWith p H).map fun (i : { i // p i}) => f i.val) = o.map f := by
+  cases o <;> simp [H]
+
+theorem attachWith_map_val {p : α → Prop} (f : α → β) (o : Option α) (H : ∀ a ∈ o, p a) :
+    ((o.attachWith p H).map fun i => f i.val) = o.map f :=
+  attachWith_map_coe _ _ _
+
+@[simp]
+theorem attachWith_map_subtype_val {p : α → Prop} (o : Option α) (H : ∀ a ∈ o, p a) :
+    (o.attachWith p H).map Subtype.val = o :=
+  (attachWith_map_coe _ _ _).trans (congrFun Option.map_id _)
+
+@[simp] theorem mem_attach : ∀ (o : Option α) (x : {x // x ∈ o}), x ∈ o.attach
+  | none, ⟨x, h⟩ => by simp at h
+  | some a, ⟨x, h⟩ => by simpa using h
+
+@[simp] theorem isNone_attach (o : Option α) : o.attach.isNone = o.isNone := by
+  cases o <;> simp
+
+@[simp] theorem isNone_attachWith {p : α → Prop} (o : Option α) (H : ∀ a ∈ o, p a) :
+    (o.attachWith p H).isNone = o.isNone := by
+  cases o <;> simp
+
+@[simp] theorem isSome_attach (o : Option α) : o.attach.isSome = o.isSome := by
+  cases o <;> simp
+
+@[simp] theorem isSome_attachWith {p : α → Prop} (o : Option α) (H : ∀ a ∈ o, p a) :
+    (o.attachWith p H).isSome = o.isSome := by
+  cases o <;> simp
+
+@[simp] theorem attach_eq_none_iff (o : Option α) : o.attach = none ↔ o = none := by
+  cases o <;> simp
+
+@[simp] theorem attach_eq_some_iff {o : Option α} {x : {x // x ∈ o}} :
+    o.attach = some x ↔ o = some x.val := by
+  cases o <;> cases x <;> simp
+
+@[simp] theorem attachWith_eq_none_iff {p : α → Prop} (o : Option α) (H : ∀ a ∈ o, p a) :
+    o.attachWith p H = none ↔ o = none := by
+  cases o <;> simp
+
+@[simp] theorem attachWith_eq_some_iff {p : α → Prop} {o : Option α} (H : ∀ a ∈ o, p a) {x : {x // p x}} :
+    o.attachWith p H = some x ↔ o = some x.val := by
+  cases o <;> cases x <;> simp
+
+@[simp] theorem get_attach {o : Option α} (h : o.attach.isSome = true) :
+    o.attach.get h = ⟨o.get (by simpa using h), by simp⟩ := by
+  cases o
+  · simp at h
+  · simp [get_some]
+
+@[simp] theorem get_attachWith {p : α → Prop} {o : Option α} (H : ∀ a ∈ o, p a) (h : (o.attachWith p H).isSome) :
+    (o.attachWith p H).get h = ⟨o.get (by simpa using h), H _ (by simp)⟩ := by
+  cases o
+  · simp at h
+  · simp [get_some]
+
+@[simp] theorem toList_attach (o : Option α) :
+    o.attach.toList = o.toList.attach.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
+  cases o <;> simp
+
+theorem attach_map {o : Option α} (f : α → β) :
+    (o.map f).attach = o.attach.map (fun ⟨x, h⟩ => ⟨f x, mem_map_of_mem f h⟩) := by
+  cases o <;> simp
+
+theorem attachWith_map {o : Option α} (f : α → β) {P : β → Prop} {H : ∀ (b : β), b ∈ o.map f → P b} :
+    (o.map f).attachWith P H = (o.attachWith (P ∘ f) (fun a h => H _ (mem_map_of_mem f h))).map
+      fun ⟨x, h⟩ => ⟨f x, h⟩ := by
+  cases o <;> simp
+
+theorem map_attach {o : Option α} (f : { x // x ∈ o } → β) :
+    o.attach.map f = o.pmap (fun a (h : a ∈ o) => f ⟨a, h⟩) (fun a h => h) := by
+  cases o <;> simp
+
+theorem map_attachWith {o : Option α} {P : α → Prop} {H : ∀ (a : α), a ∈ o → P a}
+    (f : { x // P x } → β) :
+    (o.attachWith P H).map f =
+      o.pmap (fun a (h : a ∈ o ∧ P a) => f ⟨a, h.2⟩) (fun a h => ⟨h, H a h⟩) := by
+  cases o <;> simp
+
+theorem attach_bind {o : Option α} {f : α → Option β} :
+    (o.bind f).attach =
+      o.attach.bind fun ⟨x, h⟩ => (f x).attach.map fun ⟨y, h'⟩ => ⟨y, mem_bind_iff.mpr ⟨x, h, h'⟩⟩ := by
+  cases o <;> simp
+
+theorem bind_attach {o : Option α} {f : {x // x ∈ o} → Option β} :
+    o.attach.bind f = o.pbind fun a h => f ⟨a, h⟩ := by
+  cases o <;> simp
+
+theorem pbind_eq_bind_attach {o : Option α} {f : (a : α) → a ∈ o → Option β} :
+    o.pbind f = o.attach.bind fun ⟨x, h⟩ => f x h := by
+  cases o <;> simp
+
+theorem attach_filter {o : Option α} {p : α → Bool} :
+    (o.filter p).attach =
+      o.attach.bind fun ⟨x, h⟩ => if h' : p x then some ⟨x, by simp_all⟩ else none := by
+  cases o with
+  | none => simp
+  | some a =>
+    simp only [filter_some, attach_some]
+    ext
+    simp only [mem_def, attach_eq_some_iff, ite_none_right_eq_some, some.injEq, some_bind,
+      dite_none_right_eq_some]
+    constructor
+    · rintro ⟨h, w⟩
+      refine ⟨h, by ext; simpa using w⟩
+    · rintro ⟨h, rfl⟩
+      simp [h]
+
+theorem filter_attach {o : Option α} {p : {x // x ∈ o} → Bool} :
+    o.attach.filter p = o.pbind fun a h => if p ⟨a, h⟩ then some ⟨a, h⟩ else none := by
+  cases o <;> simp [filter_some]
+
+end Option

src/Init/Data/Option/Basic.lean

@@ -202,7 +202,7 @@ result.
 instance (α) [BEq α] [LawfulBEq α] : LawfulBEq (Option α) where
   rfl {x} :=
     match x with
-    | some x => LawfulBEq.rfl (α := α)
+    | some _ => LawfulBEq.rfl (α := α)
     | none => rfl
   eq_of_beq {x y h} := by
     match x, y with

src/Init/Data/Option/Lemmas.lean

@@ -138,6 +138,10 @@ theorem bind_eq_none' {o : Option α} {f : α → Option β} :
     o.bind f = none ↔ ∀ b a, a ∈ o → b ∉ f a := by
   simp only [eq_none_iff_forall_not_mem, not_exists, not_and, mem_def, bind_eq_some]
 
+theorem mem_bind_iff {o : Option α} {f : α → Option β} :
+    b ∈ o.bind f ↔ ∃ a, a ∈ o ∧ b ∈ f a := by
+  cases o <;> simp
+
 theorem bind_comm {f : α → β → Option γ} (a : Option α) (b : Option β) :
     (a.bind fun x => b.bind (f x)) = b.bind fun y => a.bind fun x => f x y := by
   cases a <;> cases b <;> rfl
@@ -232,9 +236,27 @@ theorem isSome_filter_of_isSome (p : α → Bool) (o : Option α) (h : (o.filter
   cases o <;> simp at h ⊢
 
 @[simp] theorem filter_eq_none {p : α → Bool} :
-    Option.filter p o = none ↔ o = none ∨ ∀ a, a ∈ o → ¬ p a := by
+    o.filter p = none ↔ o = none ∨ ∀ a, a ∈ o → ¬ p a := by
   cases o <;> simp [filter_some]
 
+@[simp] theorem filter_eq_some {o : Option α} {p : α → Bool} :
+    o.filter p = some a ↔ a ∈ o ∧ p a := by
+  cases o with
+  | none => simp
+  | some a =>
+    simp [filter_some]
+    split <;> rename_i h
+    · simp only [some.injEq, iff_self_and]
+      rintro rfl
+      exact h
+    · simp only [reduceCtorEq, false_iff, not_and, Bool.not_eq_true]
+      rintro rfl
+      simpa using h
+
+theorem mem_filter_iff {p : α → Bool} {a : α} {o : Option α} :
+    a ∈ o.filter p ↔ a ∈ o ∧ p a := by
+  simp
+
 @[simp] theorem all_guard (p : α → Prop) [DecidablePred p] (a : α) :
     Option.all q (guard p a) = (!p a || q a) := by
   simp only [guard]
@@ -308,8 +330,8 @@ theorem guard_comp {p : α → Prop} [DecidablePred p] {f : β → α} :
 theorem liftOrGet_eq_or_eq {f : α → α → α} (h : ∀ a b, f a b = a ∨ f a b = b) :
     ∀ o₁ o₂, liftOrGet f o₁ o₂ = o₁ ∨ liftOrGet f o₁ o₂ = o₂
   | none, none => .inl rfl
-  | some a, none => .inl rfl
-  | none, some b => .inr rfl
+  | some _, none => .inl rfl
+  | none, some _ => .inr rfl
   | some a, some b => by have := h a b; simp [liftOrGet] at this ⊢; exact this
 
 @[simp] theorem liftOrGet_none_left {f} {b : Option α} : liftOrGet f none b = b := by
@@ -350,6 +372,8 @@ end choice
 
 @[simp] theorem toList_none (α : Type _) : (none : Option α).toList = [] := rfl
 
+-- See `Init.Data.Option.List` for lemmas about `toList`.
+
 @[simp] theorem or_some : (some a).or o = some a := rfl
 @[simp] theorem none_or : none.or o = o := rfl
 

src/Init/Data/Option/List.lean

@@ -0,0 +1,14 @@
+/-
+Copyright (c) 2024 Lean FRO. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Kim Morrison
+-/
+prelude
+import Init.Data.List.Lemmas
+
+namespace Option
+
+@[simp] theorem mem_toList {a : α} {o : Option α} : a ∈ o.toList ↔ a ∈ o := by
+  cases o <;> simp [eq_comm]
+
+end Option

src/Init/Data/String/Basic.lean

@@ -322,7 +322,7 @@ theorem lt_next (s : String) (i : Pos) : i.1 < (s.next i).1 :=
 
 theorem utf8PrevAux_lt_of_pos : ∀ (cs : List Char) (i p : Pos), p ≠ 0 →
     (utf8PrevAux cs i p).1 < p.1
-  | [], i, p, h =>
+  | [], _, _, h =>
     Nat.lt_of_le_of_lt (Nat.zero_le _)
       (Nat.zero_lt_of_ne_zero (mt (congrArg Pos.mk) h))
   | c::cs, i, p, h => by

src/Init/PropLemmas.lean

@@ -352,10 +352,10 @@ theorem not_forall_of_exists_not {p : α → Prop} : (∃ x, ¬p x) → ¬∀ x,
 @[simp] theorem exists_or_eq_left' (y : α) (p : α → Prop) : ∃ x : α, y = x ∨ p x := ⟨y, .inl rfl⟩
 @[simp] theorem exists_or_eq_right' (y : α) (p : α → Prop) : ∃ x : α, p x ∨ y = x := ⟨y, .inr rfl⟩
 
-@[simp] theorem exists_prop' {p : Prop} : (∃ _ : α, p) ↔ Nonempty α ∧ p :=
+theorem exists_prop' {p : Prop} : (∃ _ : α, p) ↔ Nonempty α ∧ p :=
   ⟨fun ⟨a, h⟩ => ⟨⟨a⟩, h⟩, fun ⟨⟨a⟩, h⟩ => ⟨a, h⟩⟩
 
-theorem exists_prop : (∃ _h : a, b) ↔ a ∧ b :=
+@[simp] theorem exists_prop : (∃ _h : a, b) ↔ a ∧ b :=
   ⟨fun ⟨hp, hq⟩ => ⟨hp, hq⟩, fun ⟨hp, hq⟩ => ⟨hp, hq⟩⟩
 
 @[simp] theorem exists_apply_eq_apply (f : α → β) (a' : α) : ∃ a, f a = f a' := ⟨a', rfl⟩
@@ -458,7 +458,7 @@ theorem Decidable.imp_iff_not_or [Decidable a] : (a → b) ↔ (¬a ∨ b) :=
 theorem Decidable.imp_iff_or_not [Decidable b] : b → a ↔ a ∨ ¬b :=
   Decidable.imp_iff_not_or.trans or_comm
 
-theorem Decidable.imp_or [h : Decidable a] : (a → b ∨ c) ↔ (a → b) ∨ (a → c) :=
+theorem Decidable.imp_or [Decidable a] : (a → b ∨ c) ↔ (a → b) ∨ (a → c) :=
   if h : a then by
     rw [imp_iff_right h, imp_iff_right h, imp_iff_right h]
   else by

src/Init/Tactics.lean

@@ -399,6 +399,19 @@ example (a b c d : Nat) : a + b + c + d = d + (b + c) + a := by ac_rfl
 -/
 syntax (name := acRfl) "ac_rfl" : tactic
 
+/--
+`ac_nf` normalizes equalities up to application of an associative and commutative operator.
+```
+instance : Associative (α := Nat) (.+.) := ⟨Nat.add_assoc⟩
+instance : Commutative (α := Nat) (.+.) := ⟨Nat.add_comm⟩
+
+example (a b c d : Nat) : a + b + c + d = d + (b + c) + a := by
+ ac_nf
+ -- goal: a + (b + (c + d)) = a + (b + (c + d))
+```
+-/
+syntax (name := acNf) "ac_nf" : tactic
+
 /--
 The `sorry` tactic closes the goal using `sorryAx`. This is intended for stubbing out incomplete
 parts of a proof while still having a syntactically correct proof skeleton. Lean will give
@@ -788,7 +801,7 @@ syntax inductionAlt  := ppDedent(ppLine) inductionAltLHS+ " => " (hole <|> synth
 After `with`, there is an optional tactic that runs on all branches, and
 then a list of alternatives.
 -/
-syntax inductionAlts := " with" (ppSpace tactic)? withPosition((colGe inductionAlt)+)
+syntax inductionAlts := " with" (ppSpace colGt tactic)? withPosition((colGe inductionAlt)+)
 
 /--
 Assuming `x` is a variable in the local context with an inductive type,

src/Init/WF.lean

@@ -249,8 +249,8 @@ theorem lex_def {r : α → α → Prop} {s : β → β → Prop} {p q : α ×
     Prod.Lex r s p q ↔ r p.1 q.1 ∨ p.1 = q.1 ∧ s p.2 q.2 :=
   ⟨fun h => by cases h <;> simp [*], fun h =>
     match p, q, h with
-    | (a, b), (c, d), Or.inl h => Lex.left _ _ h
-    | (a, b), (c, d), Or.inr ⟨e, h⟩ => by subst e; exact Lex.right _ h⟩
+    | _, _, Or.inl h => Lex.left _ _ h
+    | (_, _), (_, _), Or.inr ⟨e, h⟩ => by subst e; exact Lex.right _ h⟩
 
 namespace Lex
 

src/Lean/Attributes.lean

@@ -305,15 +305,16 @@ def registerAttributeImplBuilder (builderId : Name) (builder : AttributeImplBuil
   if table.contains builderId then throw (IO.userError ("attribute implementation builder '" ++ toString builderId ++ "' has already been declared"))
   attributeImplBuilderTableRef.modify fun table => table.insert builderId builder
 
-def mkAttributeImplOfBuilder (builderId ref : Name) (args : List DataValue) : IO AttributeImpl := do
-  let table ← attributeImplBuilderTableRef.get
-  match table[builderId]? with
-  | none         => throw (IO.userError ("unknown attribute implementation builder '" ++ toString builderId ++ "'"))
-  | some builder => IO.ofExcept <| builder ref args
+structure AttributeExtensionOLeanEntry where
+  builderId : Name
+  ref : Name
+  args : List DataValue
 
-inductive AttributeExtensionOLeanEntry where
-  | decl (declName : Name) -- `declName` has type `AttributeImpl`
-  | builder (builderId ref : Name) (args : List DataValue)
+def mkAttributeImplOfEntry (e : AttributeExtensionOLeanEntry) : IO AttributeImpl := do
+  let table ← attributeImplBuilderTableRef.get
+  match table[e.builderId]? with
+  | none         => throw (IO.userError ("unknown attribute implementation builder '" ++ toString e.builderId ++ "'"))
+  | some builder => IO.ofExcept <| builder e.ref e.args
 
 structure AttributeExtensionState where
   newEntries : List AttributeExtensionOLeanEntry := []
@@ -337,19 +338,13 @@ unsafe def mkAttributeImplOfConstantUnsafe (env : Environment) (opts : Options)
 @[implemented_by mkAttributeImplOfConstantUnsafe]
 opaque mkAttributeImplOfConstant (env : Environment) (opts : Options) (declName : Name) : Except String AttributeImpl
 
-def mkAttributeImplOfEntry (env : Environment) (opts : Options) (e : AttributeExtensionOLeanEntry) : IO AttributeImpl :=
-  match e with
-  | .decl declName              => IO.ofExcept <| mkAttributeImplOfConstant env opts declName
-  | .builder builderId ref args => mkAttributeImplOfBuilder builderId ref args
-
 private def AttributeExtension.addImported (es : Array (Array AttributeExtensionOLeanEntry)) : ImportM AttributeExtensionState := do
-  let ctx ← read
   let map ← attributeMapRef.get
   let map ← es.foldlM
     (fun map entries =>
       entries.foldlM
         (fun (map : Std.HashMap Name AttributeImpl) entry => do
-          let attrImpl ← mkAttributeImplOfEntry ctx.env ctx.opts entry
+          let attrImpl ← mkAttributeImplOfEntry entry
           return map.insert attrImpl.name attrImpl)
         map)
     map
@@ -400,19 +395,13 @@ def getAttributeImpl (env : Environment) (attrName : Name) : Except String Attri
   | some attr => pure attr
   | none      => throw ("unknown attribute '" ++ toString attrName ++ "'")
 
-def registerAttributeOfDecl (env : Environment) (opts : Options) (attrDeclName : Name) : Except String Environment := do
-  let attrImpl ← mkAttributeImplOfConstant env opts attrDeclName
-  if isAttribute env attrImpl.name then
-    throw ("invalid builtin attribute declaration, '" ++ toString attrImpl.name ++ "' has already been used")
-  else
-    return attributeExtension.addEntry env (.decl attrDeclName, attrImpl)
-
 def registerAttributeOfBuilder (env : Environment) (builderId ref : Name) (args : List DataValue) : IO Environment := do
-  let attrImpl ← mkAttributeImplOfBuilder builderId ref args
+  let entry := {builderId, ref, args}
+  let attrImpl ← mkAttributeImplOfEntry entry
   if isAttribute env attrImpl.name then
     throw (IO.userError ("invalid builtin attribute declaration, '" ++ toString attrImpl.name ++ "' has already been used"))
   else
-    return attributeExtension.addEntry env (.builder builderId ref args, attrImpl)
+    return attributeExtension.addEntry env (entry, attrImpl)
 
 def Attribute.add (declName : Name) (attrName : Name) (stx : Syntax) (kind := AttributeKind.global) : AttrM Unit := do
   let attr ← ofExcept <| getAttributeImpl (← getEnv) attrName

src/Lean/Compiler/IR/SimpCase.lean

@@ -20,18 +20,18 @@ def ensureHasDefault (alts : Array Alt) : Array Alt :=
 private def getOccsOf (alts : Array Alt) (i : Nat) : Nat := Id.run do
   let aBody := (alts.get! i).body
   let mut n := 1
-  for j in [i+1:alts.size] do
-    if alts[j]!.body == aBody then
+  for h : j in [i+1:alts.size] do
+    if alts[j].body == aBody then
       n := n+1
   return n
 
 private def maxOccs (alts : Array Alt) : Alt × Nat := Id.run do
   let mut maxAlt := alts[0]!
   let mut max    := getOccsOf alts 0
-  for i in [1:alts.size] do
+  for h : i in [1:alts.size] do
     let curr := getOccsOf alts i
     if curr > max then
-       maxAlt := alts[i]!
+       maxAlt := alts[i]
        max    := curr
   return (maxAlt, max)
 

src/Lean/Compiler/LCNF/Check.lean

@@ -110,8 +110,8 @@ def isCtorParam (f : Expr) (i : Nat) : CoreM Bool := do
 def checkAppArgs (f : Expr) (args : Array Arg) : CheckM Unit := do
   let mut fType ← inferType f
   let mut j := 0
-  for i in [:args.size] do
-    let arg := args[i]!
+  for h : i in [:args.size] do
+    let arg := args[i]
     if fType.isErased then
       return ()
     fType := fType.headBeta

src/Lean/Compiler/LCNF/ElimDeadBranches.lean

@@ -505,8 +505,8 @@ ones. Return whether any `Value` got updated in the process.
 -/
 def inferStep : InterpM Bool := do
   let ctx ← read
-  for idx in [0:ctx.decls.size] do
-    let decl := ctx.decls[idx]!
+  for h : idx in [0:ctx.decls.size] do
+    let decl := ctx.decls[idx]
     if !decl.safe then
       continue
 

src/Lean/Compiler/LCNF/MonoTypes.lean

@@ -48,8 +48,8 @@ def hasTrivialStructure? (declName : Name) : CoreM (Option TrivialStructureInfo)
   let [ctorName] := info.ctors | return none
   let mask ← getRelevantCtorFields ctorName
   let mut result := none
-  for i in [:mask.size] do
-    if mask[i]! then
+  for h : i in [:mask.size] do
+    if mask[i] then
       if result.isSome then return none
       result := some { ctorName, fieldIdx := i, numParams := info.numParams }
   return result
@@ -129,4 +129,4 @@ def getOtherDeclMonoType (declName : Name) : CoreM Expr := do
     modifyEnv fun env => monoTypeExt.modifyState env fun s => { s with mono := s.mono.insert declName type }
     return type
 
-end Lean.Compiler.LCNF
+end Lean.Compiler.LCNF

src/Lean/Compiler/LCNF/PullFunDecls.lean

@@ -96,9 +96,9 @@ where
     unless (← visited i) do
       modify fun (k, visited) => (k, visited.set! i true)
       let pi := ps[i]!
-      for j in [:ps.size] do
+      for h : j in [:ps.size] do
         unless (← visited j) do
-          let pj := ps[j]!
+          let pj := ps[j]
           if pj.used.contains pi.decl.fvarId then
             visit j
       modify fun (k, visited) => (pi.attach k, visited)

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

@@ -18,10 +18,10 @@ or not.
 private def getMaxOccs (alts : Array Alt) : Alt × Nat := Id.run do
   let mut maxAlt := alts[0]!
   let mut max    := getNumOccsOf alts 0
-  for i in [1:alts.size] do
+  for h : i in [1:alts.size] do
     let curr := getNumOccsOf alts i
     if curr > max then
-       maxAlt := alts[i]!
+       maxAlt := alts[i]
        max    := curr
   return (maxAlt, max)
 where
@@ -34,8 +34,8 @@ where
   getNumOccsOf (alts : Array Alt) (i : Nat) : Nat := Id.run do
     let code := alts[i]!.getCode
     let mut n := 1
-    for j in [i+1:alts.size] do
-      if Code.alphaEqv alts[j]!.getCode code then
+    for h : j in [i+1:alts.size] do
+      if Code.alphaEqv alts[j].getCode code then
         n := n+1
     return n
 

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

@@ -121,8 +121,8 @@ where
     let mut paramsNew := #[]
     let singleton : FVarIdSet := ({} : FVarIdSet).insert params[targetParamIdx]!.fvarId
     let dependsOnDiscr := k.dependsOn singleton || decls.any (·.dependsOn singleton)
-    for i in [:params.size] do
-      let param := params[i]!
+    for h : i in [:params.size] do
+      let param := params[i]
       if targetParamIdx == i then
         if dependsOnDiscr then
           paramsNew := paramsNew.push (← internalizeParam param)
@@ -300,4 +300,3 @@ builtin_initialize
   registerTraceClass `Compiler.simp.jpCases
 
 end Lean.Compiler.LCNF
-

src/Lean/Compiler/LCNF/SpecInfo.lean

@@ -129,9 +129,9 @@ See comment at `.fixedNeutral`.
 -/
 private def hasFwdDeps (decl : Decl) (paramsInfo : Array SpecParamInfo) (j : Nat) : Bool := Id.run do
   let param := decl.params[j]!
-  for k in [j+1 : decl.params.size] do
+  for h : k in [j+1 : decl.params.size] do
     if paramsInfo[k]! matches .user | .fixedHO | .fixedInst then
-      let param' := decl.params[k]!
+      let param' := decl.params[k]
       if param'.type.containsFVar param.fvarId then
         return true
   return false
@@ -214,4 +214,3 @@ builtin_initialize
   registerTraceClass `Compiler.specialize.info
 
 end Lean.Compiler.LCNF
-

src/Lean/Compiler/LCNF/ToDecl.lean

@@ -50,9 +50,9 @@ partial def inlineMatchers (e : Expr) : CoreM Expr :=
       let numAlts := info.numAlts
       let altNumParams := info.altNumParams
       let rec inlineMatcher (i : Nat) (args : Array Expr) (letFVars : Array Expr) : MetaM Expr := do
-        if i < numAlts then
+        if h : i < numAlts then
           let altIdx := i + info.getFirstAltPos
-          let numParams := altNumParams[i]!
+          let numParams := altNumParams[i]
           let alt ← normalizeAlt args[altIdx]! numParams
           Meta.withLetDecl (← mkFreshUserName `_alt) (← Meta.inferType alt) alt fun altFVar =>
             inlineMatcher (i+1) (args.set! altIdx altFVar) (letFVars.push altFVar)

src/Lean/Elab/App.lean

@@ -411,21 +411,23 @@ private def finalize : M Expr := do
   synthesizeAppInstMVars
   return e
 
-/-- Return `true` if there is a named argument that depends on the next argument. -/
-private def anyNamedArgDependsOnCurrent : M Bool := do
+/--
+Returns a named argument that depends on the next argument, otherwise `none`.
+-/
+private def findNamedArgDependsOnCurrent? : M (Option NamedArg) := do
   let s ← get
   if s.namedArgs.isEmpty then
-    return false
+    return none
   else
     forallTelescopeReducing s.fType fun xs _ => do
       let curr := xs[0]!
-      for i in [1:xs.size] do
-        let xDecl ← xs[i]!.fvarId!.getDecl
-        if s.namedArgs.any fun arg => arg.name == xDecl.userName then
+      for h : i in [1:xs.size] do
+        let xDecl ← xs[i].fvarId!.getDecl
+        if let some arg := s.namedArgs.find? fun arg => arg.name == xDecl.userName then
           /- Remark: a default value at `optParam` does not count as a dependency -/
           if (← exprDependsOn xDecl.type.cleanupAnnotations curr.fvarId!) then
-            return true
-      return false
+            return arg
+      return none
 
 
 /-- Return `true` if there are regular or named arguments to be processed. -/
@@ -433,11 +435,13 @@ private def hasArgsToProcess : M Bool := do
   let s ← get
   return !s.args.isEmpty || !s.namedArgs.isEmpty
 
-/-- Return `true` if the next argument at `args` is of the form `_` -/
-private def isNextArgHole : M Bool := do
+/--
+Returns the argument syntax if the next argument at `args` is of the form `_`.
+-/
+private def nextArgHole? : M (Option Syntax) := do
   match (← get).args with
-  | Arg.stx (Syntax.node _ ``Lean.Parser.Term.hole _) :: _ => pure true
-  | _ => pure false
+  | Arg.stx stx@(Syntax.node _ ``Lean.Parser.Term.hole _) :: _ => pure stx
+  | _ => pure none
 
 /--
   Return `true` if the next argument to be processed is the outparam of a local instance, and it the result type
@@ -512,8 +516,9 @@ where
 
 mutual
   /--
-    Create a fresh local variable with the current binder name and argument type, add it to `etaArgs` and `f`,
-    and then execute the main loop.-/
+  Create a fresh local variable with the current binder name and argument type, add it to `etaArgs` and `f`,
+  and then execute the main loop.
+  -/
   private partial def addEtaArg (argName : Name) : M Expr := do
     let n    ← getBindingName
     let type ← getArgExpectedType
@@ -522,6 +527,9 @@ mutual
       addNewArg argName x
       main
 
+  /--
+  Create a fresh metavariable for the implicit argument, add it to `f`, and thn execute the main loop.
+  -/
   private partial def addImplicitArg (argName : Name) : M Expr := do
     let argType ← getArgExpectedType
     let arg ← if (← isNextOutParamOfLocalInstanceAndResult) then
@@ -539,35 +547,47 @@ mutual
     main
 
   /--
-    Process a `fType` of the form `(x : A) → B x`.
-    This method assume `fType` is a function type -/
+  Process a `fType` of the form `(x : A) → B x`.
+  This method assume `fType` is a function type.
+  -/
   private partial def processExplicitArg (argName : Name) : M Expr := do
     match (← get).args with
     | arg::args =>
-      if (← anyNamedArgDependsOnCurrent) then
+      -- Note: currently the following test never succeeds in explicit mode since `@x.f` notation does not exist.
+      if let some true := NamedArg.suppressDeps <$> (← findNamedArgDependsOnCurrent?) then
         /-
-        We treat the explicit argument `argName` as implicit if we have named arguments that depend on it.
-        The idea is that this explicit argument can be inferred using the type of the named argument one.
-        Note that we also use this approach in the branch where there are no explicit arguments left.
-        This is important to make sure the system behaves in a uniform way.
-        Moreover, users rely on this behavior. For example, consider the example on issue #1851
+        We treat the explicit argument `argName` as implicit
+        if we have a named arguments that depends on it whose `suppressDeps` flag set to `true`.
+        The motivation for this is class projections (issue #1851).
+        In some cases, class projections can have explicit parameters. For example, in
         ```
         class Approx {α : Type} (a : α) (X : Type) : Type where
           val : X
-
-        variable {α β X Y : Type} {f' : α → β} {x' : α} [f : Approx f' (X → Y)] [x : Approx x' X]
-
-        #check f.val
-        #check f.val x.val
         ```
-        The type of `Approx.val` is `{α : Type} → (a : α) → {X : Type} → [self : Approx a X] → X`
-        Note that the argument `a` is explicit since there is no way to infer it from the expected
-        type or the type of other explicit arguments.
-        Recall that `f.val` is sugar for `Approx.val (self := f)`. In both `#check` commands above
-        the user assumed that `a` does not need to be provided since it can be inferred from the type
-        of `self`.
-        We used to that only in the branch where `(← get).args` was empty, but it created an asymmetry
-        because `#check f.val` worked as expected, but one would have to write `#check f.val _ x.val`
+        the type of `Approx.val` is `{α : Type} → (a : α) → {X : Type} → [self : Approx a X] → X`.
+        Note that the parameter `a` is explicit since there is no way to infer it from the expected
+        type or from the types of other explicit parameters.
+        Being a parameter of the class, `a` is determined by the type of `self`.
+
+        Consider
+        ```
+        variable {α β X Y : Type} {f' : α → β} {x' : α} [f : Approx f' (X → Y)]
+        ```
+        Recall that `f.val` is, to first approximation, sugar for `Approx.val (self := f)`.
+        Without further refinement, this would expand to `fun f'' : α → β => Approx.val f'' f`,
+        which is a type error, since `f''` must be defeq to `f'`.
+        Furthermore, with projection notation, users expect all structure parameters
+        to be uniformly implicit; after all, they are determined by `self`.
+        To handle this, the `(self := f)` named argument is annotated with the `suppressDeps` flag.
+        This causes the `a` parameter to become implicit, and `f.val` instead expands to `Approx.val f' f`.
+
+        This feature previously was enabled for *all* explicit arguments, which confused users
+        and was frequently reported as a bug (issue #1867).
+        Now it is only enabled for the `self` argument in structure projections.
+
+        We used to do this only when `(← get).args` was empty,
+        but it created an asymmetry because `f.val` worked as expected,
+        yet one would have to write `f.val _ x` when there are further arguments.
         -/
         return (← addImplicitArg argName)
       propagateExpectedType arg
@@ -584,7 +604,6 @@ mutual
         match evalSyntaxConstant env opts tacticDecl with
         | Except.error err       => throwError err
         | Except.ok tacticSyntax =>
-          -- TODO(Leo): does this work correctly for tactic sequences?
           let tacticBlock ← `(by $(⟨tacticSyntax⟩))
           /-
           We insert position information from the current ref into `stx` everywhere, simulating this being
@@ -596,24 +615,32 @@ mutual
           -/
           let info := (← getRef).getHeadInfo
           let tacticBlock := tacticBlock.raw.rewriteBottomUp (·.setInfo info)
-          let argNew := Arg.stx tacticBlock
+          let mvar ← mkTacticMVar argType.consumeTypeAnnotations tacticBlock (.autoParam argName)
+          -- Note(kmill): We are adding terminfo to simulate a previous implementation that elaborated `tacticBlock`.
+          -- We should look into removing this since terminfo for synthetic syntax is suspect,
+          -- but we noted it was necessary to preserve the behavior of the unused variable linter.
+          addTermInfo' tacticBlock mvar
+          let argNew := Arg.expr mvar
           propagateExpectedType argNew
           elabAndAddNewArg argName argNew
           main
       | false, _, some _ =>
         throwError "invalid autoParam, argument must be a constant"
       | _, _, _ =>
-        if !(← get).namedArgs.isEmpty then
-          if (← anyNamedArgDependsOnCurrent) then
-            addImplicitArg argName
-          else if (← read).ellipsis then
+        if (← read).ellipsis then
+          addImplicitArg argName
+        else if !(← get).namedArgs.isEmpty then
+          if let some _ ← findNamedArgDependsOnCurrent? then
+            /-
+            Dependencies of named arguments cannot be turned into eta arguments
+            since they are determined by the named arguments.
+            Instead we can turn them into implicit arguments.
+            -/
             addImplicitArg argName
           else
             addEtaArg argName
         else if !(← read).explicit then
-          if (← read).ellipsis then
-            addImplicitArg argName
-          else if (← fTypeHasOptAutoParams) then
+          if (← fTypeHasOptAutoParams) then
             addEtaArg argName
           else
             finalize
@@ -641,24 +668,30 @@ mutual
       finalize
 
   /--
-    Process a `fType` of the form `[x : A] → B x`.
-    This method assume `fType` is a function type -/
+  Process a `fType` of the form `[x : A] → B x`.
+  This method assume `fType` is a function type.
+  -/
   private partial def processInstImplicitArg (argName : Name) : M Expr := do
     if (← read).explicit then
-      if (← isNextArgHole) then
-        /- Recall that if '@' has been used, and the argument is '_', then we still use type class resolution -/
-        let arg ← mkFreshExprMVar (← getArgExpectedType) MetavarKind.synthetic
+      if let some stx ← nextArgHole? then
+        -- We still use typeclass resolution for `_` arguments.
+        -- This behavior can be suppressed with `(_)`.
+        let ty ← getArgExpectedType
+        let arg ← mkInstMVar ty
+        addTermInfo' stx arg ty
         modify fun s => { s with args := s.args.tail! }
-        addInstMVar arg.mvarId!
-        addNewArg argName arg
         main
       else
         processExplicitArg argName
     else
-      let arg ← mkFreshExprMVar (← getArgExpectedType) MetavarKind.synthetic
+      discard <| mkInstMVar (← getArgExpectedType)
+      main
+  where
+    mkInstMVar (ty : Expr) : M Expr := do
+      let arg ← mkFreshExprMVar ty MetavarKind.synthetic
       addInstMVar arg.mvarId!
       addNewArg argName arg
-      main
+      return arg
 
   /-- Elaborate function application arguments. -/
   partial def main : M Expr := do
@@ -689,6 +722,104 @@ end
 
 end ElabAppArgs
 
+
+/-! # Eliminator-like function application elaborator -/
+
+/--
+Information about an eliminator used by the elab-as-elim elaborator.
+This is not to be confused with `Lean.Meta.ElimInfo`, which is for `induction` and `cases`.
+The elab-as-elim routine is less restrictive in what counts as an eliminator, and it doesn't need
+to have a strict notion of what is a "target" — all it cares about are
+1. that the return type of a function is of the form `m ...` where `m` is a parameter
+   (unlike `induction` and `cases` eliminators, the arguments to `m`, known as "discriminants",
+   can be any expressions, not just parameters), and
+2. which arguments should be eagerly elaborated, to make discriminants be as elaborated as
+   possible for the expected type generalization procedure,
+   and which should be postponed (since they are the "minor premises").
+
+Note that the routine isn't doing induction/cases *on* particular expressions.
+The purpose of elab-as-elim is to successfully solve the higher-order unification problem
+between the return type of the function and the expected type.
+-/
+structure ElabElimInfo where
+  /-- The eliminator. -/
+  elimExpr   : Expr
+  /-- The type of the eliminator. -/
+  elimType   : Expr
+  /-- The position of the motive parameter. -/
+  motivePos  : Nat
+  /--
+  Positions of "major" parameters (those that should be eagerly elaborated
+  because they can contribute to the motive inference procedure).
+  All parameters that are neither the motive nor a major parameter are "minor" parameters.
+  The major parameters include all of the parameters that transitively appear in the motive's arguments,
+  as well as "first-order" arguments that include such parameters,
+  since they too can help with elaborating discriminants.
+
+  For example, in the following theorem the argument `h : a = b`
+  should be elaborated eagerly because it contains `b`, which occurs in `motive b`.
+  ```
+  theorem Eq.subst' {α} {motive : α → Prop} {a b : α} (h : a = b) : motive a → motive b
+  ```
+  For another example, the term `isEmptyElim (α := α)` is an underapplied eliminator, and it needs
+  argument `α` to be elaborated eagerly to create a type-correct motive.
+  ```
+  def isEmptyElim [IsEmpty α] {p : α → Sort _} (a : α) : p a := ...
+  example {α : Type _} [IsEmpty α] : id (α → False) := isEmptyElim (α := α)
+  ```
+  -/
+  majorsPos : Array Nat := #[]
+  deriving Repr, Inhabited
+
+def getElabElimExprInfo (elimExpr : Expr) : MetaM ElabElimInfo := do
+  let elimType ← inferType elimExpr
+  trace[Elab.app.elab_as_elim] "eliminator {indentExpr elimExpr}\nhas type{indentExpr elimType}"
+  forallTelescopeReducing elimType fun xs type => do
+    let motive  := type.getAppFn
+    let motiveArgs := type.getAppArgs
+    unless motive.isFVar do
+      throwError "unexpected eliminator resulting type{indentExpr type}"
+    let motiveType ← inferType motive
+    forallTelescopeReducing motiveType fun motiveParams motiveResultType => do
+      unless motiveParams.size == motiveArgs.size do
+        throwError "unexpected number of arguments at motive type{indentExpr motiveType}"
+      unless motiveResultType.isSort do
+        throwError "motive result type must be a sort{indentExpr motiveType}"
+    let some motivePos ← pure (xs.indexOf? motive) |
+      throwError "unexpected eliminator type{indentExpr elimType}"
+    /-
+    Compute transitive closure of fvars appearing in arguments to the motive.
+    These are the primary set of major parameters.
+    -/
+    let initMotiveFVars : CollectFVars.State := motiveArgs.foldl (init := {}) collectFVars
+    let motiveFVars ← xs.size.foldRevM (init := initMotiveFVars) fun i s => do
+      let x := xs[i]!
+      if s.fvarSet.contains x.fvarId! then
+        return collectFVars s (← inferType x)
+      else
+        return s
+    /- Collect the major parameter positions -/
+    let mut majorsPos := #[]
+    for h : i in [:xs.size] do
+      let x := xs[i]
+      unless motivePos == i do
+        let xType ← x.fvarId!.getType
+        /-
+        We also consider "first-order" types because we can reliably "extract" information from them.
+        We say a term is "first-order" if all applications are of the form `f ...` where `f` is a constant.
+        -/
+        let isFirstOrder (e : Expr) : Bool := Option.isNone <| e.find? fun e => e.isApp && !e.getAppFn.isConst
+        if motiveFVars.fvarSet.contains x.fvarId!
+            || (isFirstOrder xType
+                && Option.isSome (xType.find? fun e => e.isFVar && motiveFVars.fvarSet.contains e.fvarId!)) then
+          majorsPos := majorsPos.push i
+    trace[Elab.app.elab_as_elim] "motivePos: {motivePos}"
+    trace[Elab.app.elab_as_elim] "majorsPos: {majorsPos}"
+    return { elimExpr, elimType,  motivePos, majorsPos }
+
+def getElabElimInfo (elimName : Name) : MetaM ElabElimInfo := do
+  getElabElimExprInfo (← mkConstWithFreshMVarLevels elimName)
+
 builtin_initialize elabAsElim : TagAttribute ←
   registerTagAttribute `elab_as_elim
     "instructs elaborator that the arguments of the function application should be elaborated as were an eliminator"
@@ -703,33 +834,15 @@ builtin_initialize elabAsElim : TagAttribute ←
         let info ← getConstInfo declName
         if (← hasOptAutoParams info.type) then
           throwError "[elab_as_elim] attribute cannot be used in declarations containing optional and auto parameters"
-        discard <| getElimInfo declName
+        discard <| getElabElimInfo declName
       go.run' {} {}
 
-/-! # Eliminator-like function application elaborator -/
 namespace ElabElim
 
 /-- Context of the `elab_as_elim` elaboration procedure. -/
 structure Context where
-  elimInfo : ElimInfo
+  elimInfo : ElabElimInfo
   expectedType : Expr
-  /--
-  Position of additional arguments that should be elaborated eagerly
-  because they can contribute to the motive inference procedure.
-  For example, in the following theorem the argument `h : a = b`
-  should be elaborated eagerly because it contains `b` which occurs
-  in `motive b`.
-  ```
-  theorem Eq.subst' {α} {motive : α → Prop} {a b : α} (h : a = b) : motive a → motive b
-  ```
-  For another example, the term `isEmptyElim (α := α)` is an underapplied eliminator, and it needs
-  argument `α` to be elaborated eagerly to create a type-correct motive.
-  ```
-  def isEmptyElim [IsEmpty α] {p : α → Sort _} (a : α) : p a := ...
-  example {α : Type _} [IsEmpty α] : id (α → False) := isEmptyElim (α := α)
-  ```
-  -/
-  extraArgsPos : Array Nat
 
 /-- State of the `elab_as_elim` elaboration procedure. -/
 structure State where
@@ -741,8 +854,6 @@ structure State where
   namedArgs    : List NamedArg
   /-- User-provided arguments that still have to be processed. -/
   args         : List Arg
-  /-- Discriminants (targets) processed so far. -/
-  discrs       : Array (Option Expr)
   /-- Instance implicit arguments collected so far. -/
   instMVars    : Array MVarId := #[]
   /-- Position of the next argument to be processed. We use it to decide whether the argument is the motive or a discriminant. -/
@@ -788,7 +899,7 @@ def finalize : M Expr := do
   let some motive := (← get).motive?
     | throwError "failed to elaborate eliminator, insufficient number of arguments"
   trace[Elab.app.elab_as_elim] "motive: {motive}"
-  forallTelescope (← get).fType fun xs _ => do
+  forallTelescope (← get).fType fun xs fType => do
     trace[Elab.app.elab_as_elim] "xs: {xs}"
     let mut expectedType := (← read).expectedType
     trace[Elab.app.elab_as_elim] "expectedType:{indentD expectedType}"
@@ -797,6 +908,7 @@ def finalize : M Expr := do
     let mut f := (← get).f
     if xs.size > 0 then
       -- under-application, specialize the expected type using `xs`
+      -- Note: if we ever wanted to support optParams and autoParams, this is where it could be.
       assert! (← get).args.isEmpty
       for x in xs do
         let .forallE _ t b _ ← whnf expectedType | throwInsufficient
@@ -813,18 +925,11 @@ def finalize : M Expr := do
     trace[Elab.app.elab_as_elim] "expectedType after processing:{indentD expectedType}"
     let result := mkAppN f xs
     trace[Elab.app.elab_as_elim] "result:{indentD result}"
-    let mut discrs := (← get).discrs
-    let idx := (← get).idx
-    if discrs.any Option.isNone then
-      for i in [idx:idx + xs.size], x in xs do
-        if let some tidx := (← read).elimInfo.targetsPos.indexOf? i then
-          discrs := discrs.set! tidx x
-    if let some idx := discrs.findIdx? Option.isNone then
-      -- This should not happen.
-      trace[Elab.app.elab_as_elim] "Internal error, missing target with index {idx}"
-      throwError "failed to elaborate eliminator, insufficient number of arguments"
-    trace[Elab.app.elab_as_elim] "discrs: {discrs.map Option.get!}"
-    let motiveVal ← mkMotive (discrs.map Option.get!) expectedType
+    unless fType.getAppFn == (← get).motive? do
+      throwError "Internal error, eliminator target type isn't an application of the motive"
+    let discrs := fType.getAppArgs
+    trace[Elab.app.elab_as_elim] "discrs: {discrs}"
+    let motiveVal ← mkMotive discrs expectedType
     unless (← isTypeCorrect motiveVal) do
       throwError "failed to elaborate eliminator, motive is not type correct:{indentD motiveVal}"
     unless (← isDefEq motive motiveVal) do
@@ -858,10 +963,6 @@ def getNextArg? (binderName : Name) (binderInfo : BinderInfo) : M (LOption Arg)
 def setMotive (motive : Expr) : M Unit :=
   modify fun s => { s with motive? := motive }
 
-/-- Push the given expression into the `discrs` field in the state, where `i` is which target it is for. -/
-def addDiscr (i : Nat) (discr : Expr) : M Unit :=
-  modify fun s => { s with discrs := s.discrs.set! i discr }
-
 /-- Elaborate the given argument with the given expected type. -/
 private def elabArg (arg : Arg) (argExpectedType : Expr) : M Expr := do
   match arg with
@@ -904,18 +1005,13 @@ partial def main : M Expr := do
         mkImplicitArg binderType binderInfo
     setMotive motive
     addArgAndContinue motive
-  else if let some tidx := (← read).elimInfo.targetsPos.indexOf? idx then
+  else if (← read).elimInfo.majorsPos.contains idx then
     match (← getNextArg? binderName binderInfo) with
-    | .some arg => let discr ← elabArg arg binderType; addDiscr tidx discr; addArgAndContinue discr
+    | .some arg => let discr ← elabArg arg binderType; addArgAndContinue discr
     | .undef => finalize
-    | .none => let discr ← mkImplicitArg binderType binderInfo; addDiscr tidx discr; addArgAndContinue discr
+    | .none => let discr ← mkImplicitArg binderType binderInfo; addArgAndContinue discr
   else match (← getNextArg? binderName binderInfo) with
-    | .some (.stx stx) =>
-      if (← read).extraArgsPos.contains idx then
-        let arg ← elabArg (.stx stx) binderType
-        addArgAndContinue arg
-      else
-        addArgAndContinue (← postponeElabTerm stx binderType)
+    | .some (.stx stx) => addArgAndContinue (← postponeElabTerm stx binderType)
     | .some (.expr val) => addArgAndContinue (← ensureArgType (← get).f val binderType)
     | .undef => finalize
     | .none => addArgAndContinue (← mkImplicitArg binderType binderInfo)
@@ -969,13 +1065,10 @@ def elabAppArgs (f : Expr) (namedArgs : Array NamedArg) (args : Array Arg)
     let some expectedType := expectedType? | throwError "failed to elaborate eliminator, expected type is not available"
     let expectedType ← instantiateMVars expectedType
     if expectedType.getAppFn.isMVar then throwError "failed to elaborate eliminator, expected type is not available"
-    let extraArgsPos ← getElabAsElimExtraArgsPos elimInfo
-    trace[Elab.app.elab_as_elim] "extraArgsPos: {extraArgsPos}"
-    ElabElim.main.run { elimInfo, expectedType, extraArgsPos } |>.run' {
+    ElabElim.main.run { elimInfo, expectedType } |>.run' {
       f, fType
       args := args.toList
       namedArgs := namedArgs.toList
-      discrs := mkArray elimInfo.targetsPos.size none
     }
   else
     ElabAppArgs.main.run { explicit, ellipsis, resultIsOutParamSupport } |>.run' {
@@ -986,12 +1079,12 @@ def elabAppArgs (f : Expr) (namedArgs : Array NamedArg) (args : Array Arg)
     }
 where
   /-- Return `some info` if we should elaborate as an eliminator. -/
-  elabAsElim? : TermElabM (Option ElimInfo) := do
+  elabAsElim? : TermElabM (Option ElabElimInfo) := do
     unless (← read).heedElabAsElim do return none
     if explicit || ellipsis then return none
     let .const declName _ := f | return none
     unless (← shouldElabAsElim declName) do return none
-    let elimInfo ← getElimInfo declName
+    let elimInfo ← getElabElimInfo declName
     forallTelescopeReducing (← inferType f) fun xs _ => do
       /- Process arguments similar to `Lean.Elab.Term.ElabElim.main` to see if the motive has been
          provided, in which case we use the standard app elaborator.
@@ -1022,41 +1115,6 @@ where
             return none
         | _, _ => return some elimInfo
 
-  /--
-  Collect extra argument positions that must be elaborated eagerly when using `elab_as_elim`.
-  The idea is that they contribute to motive inference. See comment at `ElamElim.Context.extraArgsPos`.
-  -/
-  getElabAsElimExtraArgsPos (elimInfo : ElimInfo) : MetaM (Array Nat) := do
-    forallTelescope elimInfo.elimType fun xs type => do
-      let targets := type.getAppArgs
-      /- Compute transitive closure of fvars appearing in the motive and the targets. -/
-      let initMotiveFVars : CollectFVars.State := targets.foldl (init := {}) collectFVars
-      let motiveFVars ← xs.size.foldRevM (init := initMotiveFVars) fun i s => do
-        let x := xs[i]!
-        if elimInfo.motivePos == i || elimInfo.targetsPos.contains i || s.fvarSet.contains x.fvarId! then
-          return collectFVars s (← inferType x)
-        else
-          return s
-      /- Collect the extra argument positions -/
-      let mut extraArgsPos := #[]
-      for i in [:xs.size] do
-        let x := xs[i]!
-        unless elimInfo.motivePos == i || elimInfo.targetsPos.contains i do
-          let xType ← x.fvarId!.getType
-          /- We only consider "first-order" types because we can reliably "extract" information from them. -/
-          if motiveFVars.fvarSet.contains x.fvarId!
-             || (isFirstOrder xType
-                 && Option.isSome (xType.find? fun e => e.isFVar && motiveFVars.fvarSet.contains e.fvarId!)) then
-            extraArgsPos := extraArgsPos.push i
-      return extraArgsPos
-
-  /-
-  Helper function for implementing `elab_as_elim`.
-  We say a term is "first-order" if all applications are of the form `f ...` where `f` is a constant.
-  -/
-  isFirstOrder (e : Expr) : Bool :=
-    Option.isNone <| e.find? fun e =>
-      e.isApp && !e.getAppFn.isConst
 
 /-- Auxiliary inductive datatype that represents the resolution of an `LVal`. -/
 inductive LValResolution where
@@ -1221,7 +1279,7 @@ private partial def mkBaseProjections (baseStructName : Name) (structName : Name
     let mut e := e
     for projFunName in path do
       let projFn ← mkConst projFunName
-      e ← elabAppArgs projFn #[{ name := `self, val := Arg.expr e }] (args := #[]) (expectedType? := none) (explicit := false) (ellipsis := false)
+      e ← elabAppArgs projFn #[{ name := `self, val := Arg.expr e, suppressDeps := true }] (args := #[]) (expectedType? := none) (explicit := false) (ellipsis := false)
     return e
 
 private def typeMatchesBaseName (type : Expr) (baseName : Name) : MetaM Bool := do
@@ -1243,8 +1301,8 @@ private def addLValArg (baseName : Name) (fullName : Name) (e : Expr) (args : Ar
   forallTelescopeReducing fType fun xs _ => do
     let mut argIdx := 0 -- position of the next explicit argument
     let mut remainingNamedArgs := namedArgs
-    for i in [:xs.size] do
-      let x := xs[i]!
+    for h : i in [:xs.size] do
+      let x := xs[i]
       let xDecl ← x.fvarId!.getDecl
       /- If there is named argument with name `xDecl.userName`, then we skip it. -/
       match remainingNamedArgs.findIdx? (fun namedArg => namedArg.name == xDecl.userName) with
@@ -1305,10 +1363,10 @@ private def elabAppLValsAux (namedArgs : Array NamedArg) (args : Array Arg) (exp
         let projFn ← mkConst info.projFn
         let projFn ← addProjTermInfo lval.getRef projFn
         if lvals.isEmpty then
-          let namedArgs ← addNamedArg namedArgs { name := `self, val := Arg.expr f }
+          let namedArgs ← addNamedArg namedArgs { name := `self, val := Arg.expr f, suppressDeps := true }
           elabAppArgs projFn namedArgs args expectedType? explicit ellipsis
         else
-          let f ← elabAppArgs projFn #[{ name := `self, val := Arg.expr f }] #[] (expectedType? := none) (explicit := false) (ellipsis := false)
+          let f ← elabAppArgs projFn #[{ name := `self, val := Arg.expr f, suppressDeps := true }] #[] (expectedType? := none) (explicit := false) (ellipsis := false)
           loop f lvals
       else
         unreachable!

src/Lean/Elab/Arg.lean

@@ -9,18 +9,22 @@ import Lean.Elab.Term
 namespace Lean.Elab.Term
 
 /--
-  Auxiliary inductive datatype for combining unelaborated syntax
-  and already elaborated expressions. It is used to elaborate applications. -/
+Auxiliary inductive datatype for combining unelaborated syntax
+and already elaborated expressions. It is used to elaborate applications.
+-/
 inductive Arg where
   | stx  (val : Syntax)
   | expr (val : Expr)
   deriving Inhabited
 
-/-- Named arguments created using the notation `(x := val)` -/
+/-- Named arguments created using the notation `(x := val)`. -/
 structure NamedArg where
   ref  : Syntax := Syntax.missing
   name : Name
   val  : Arg
+  /-- If `true`, then make all parameters that depend on this one become implicit.
+  This is used for projection notation, since structure parameters might be explicit for classes. -/
+  suppressDeps : Bool := false
   deriving Inhabited
 
 /--

src/Lean/Elab/BuiltinNotation.lean

@@ -55,8 +55,8 @@ open Meta
             let cinfo ← getConstInfoCtor ctor
             let numExplicitFields ← forallTelescopeReducing cinfo.type fun xs _ => do
               let mut n := 0
-              for i in [cinfo.numParams:xs.size] do
-                if (← getFVarLocalDecl xs[i]!).binderInfo.isExplicit then
+              for h : i in [cinfo.numParams:xs.size] do
+                if (← getFVarLocalDecl xs[i]).binderInfo.isExplicit then
                   n := n + 1
               return n
             let args := args.getElems

src/Lean/Elab/BuiltinTerm.lean

@@ -150,26 +150,10 @@ private def getMVarFromUserName (ident : Syntax) : MetaM Expr := do
     elabTerm b expectedType?
   | _ => throwUnsupportedSyntax
 
-private def mkTacticMVar (type : Expr) (tacticCode : Syntax) : TermElabM Expr := do
-  let mvar ← mkFreshExprMVar type MetavarKind.syntheticOpaque
-  let mvarId := mvar.mvarId!
-  let ref ← getRef
-  registerSyntheticMVar ref mvarId <| SyntheticMVarKind.tactic tacticCode (← saveContext)
-  return mvar
-
-register_builtin_option debug.byAsSorry : Bool := {
-  defValue := false
-  group    := "debug"
-  descr    := "replace `by ..` blocks with `sorry` IF the expected type is a proposition"
-}
-
 @[builtin_term_elab byTactic] def elabByTactic : TermElab := fun stx expectedType? => do
   match expectedType? with
   | some expectedType =>
-    if ← pure (debug.byAsSorry.get (← getOptions)) <&&> isProp expectedType then
-      mkSorry expectedType false
-    else
-      mkTacticMVar expectedType stx
+    mkTacticMVar expectedType stx .term
   | none =>
     tryPostpone
     throwError ("invalid 'by' tactic, expected type has not been provided")

src/Lean/Elab/DeclNameGen.lean

@@ -64,13 +64,13 @@ private partial def winnowExpr (e : Expr) : MetaM Expr := do
         let mut fty ← inferType f
         let mut j := 0
         let mut e' ← visit f
-        for i in [0:args.size] do
+        for h : i in [0:args.size] do
           unless fty.isForall do
             fty ← withTransparency .all <| whnf <| fty.instantiateRevRange j i args
             j := i
           let .forallE _ _ fty' bi := fty | failure
           fty := fty'
-          let arg := args[i]!
+          let arg := args[i]
           if ← pure bi.isExplicit <||> (pure !arg.isSort <&&> isTypeFormer arg) then
             unless (← isProof arg) do
               e' := .app e' (← visit arg)
@@ -206,8 +206,11 @@ Uses heuristics to generate an informative but terse base name for a term of the
 Makes use of the current namespace.
 It tries to make these names relatively unique ecosystem-wide,
 and it adds suffixes using the current module if the resulting name doesn't refer to anything defined in this module.
+
+If any constant in `type` has a name with macro scopes, then the result will be a name with fresh macro scopes.
+While in this case we could skip the naming heuristics, we still want informative names for debugging purposes.
 -/
-def mkBaseNameWithSuffix (pre : String) (type : Expr) : MetaM String := do
+def mkBaseNameWithSuffix (pre : String) (type : Expr) : MetaM Name := do
   let (name, st) ← mkBaseName type |>.run {}
   let name := pre ++ name
   let project := (← getMainModule).getRoot
@@ -217,8 +220,13 @@ def mkBaseNameWithSuffix (pre : String) (type : Expr) : MetaM String := do
   let isModuleLocal := modules.any Option.isNone
   -- We can also avoid adding the full module suffix if the instance refers to "project"-local names.
   let isProjectLocal := isModuleLocal || modules.any fun mod? => mod?.map (·.getRoot) == project
-  if !isProjectLocal then
-    return s!"{name}{moduleToSuffix project}"
+  let name := Name.mkSimple <|
+    if !isProjectLocal then
+      s!"{name}{moduleToSuffix project}"
+    else
+      name
+  if Option.isSome <| type.find? (fun e => if let .const n _ := e then n.hasMacroScopes else false) then
+    mkFreshUserName name
   else
     return name
 
@@ -233,8 +241,8 @@ def mkBaseNameWithSuffix' (pre : String) (binders : Array Syntax) (type : Syntax
         let ty ← mkForallFVars binds (← Term.elabType type)
         mkBaseNameWithSuffix pre ty
     catch _ =>
-      pure pre
-  liftMacroM <| mkUnusedBaseName <| Name.mkSimple name
+      mkFreshUserName <| Name.mkSimple pre
+  liftMacroM <| mkUnusedBaseName name
 
 end NameGen
 

src/Lean/Elab/Deriving/Inhabited.lean

@@ -86,8 +86,8 @@ where
       addLocalInstancesForParams xs[:ctorVal.numParams] fun localInst2Index => do
         let mut usedInstIdxs := {}
         let mut ok := true
-        for i in [ctorVal.numParams:xs.size] do
-          let x := xs[i]!
+        for h : i in [ctorVal.numParams:xs.size] do
+          let x := xs[i]
           let instType ← mkAppM `Inhabited #[(← inferType x)]
           trace[Elab.Deriving.inhabited] "checking {instType} for '{ctorName}'"
           match (← trySynthInstance instType) with

src/Lean/Elab/Deriving/Repr.lean

@@ -29,8 +29,8 @@ def mkBodyForStruct (header : Header) (indVal : InductiveVal) : TermElabM Term :
     let mut fields ← `(Format.nil)
     if xs.size != numParams + fieldNames.size then
       throwError "'deriving Repr' failed, unexpected number of fields in structure"
-    for i in [:fieldNames.size] do
-      let fieldName := fieldNames[i]!
+    for h : i in [:fieldNames.size] do
+      let fieldName := fieldNames[i]
       let fieldNameLit := Syntax.mkStrLit (toString fieldName)
       let x := xs[numParams + i]!
       if i != 0 then
@@ -59,10 +59,10 @@ where
         let mut ctorArgs := #[]
         let mut rhs : Term := Syntax.mkStrLit (toString ctorInfo.name)
         rhs ← `(Format.text $rhs)
-        for i in [:xs.size] do
+        for h : i in [:xs.size] do
           -- Note: some inductive parameters are explicit if they were promoted from indices,
           -- so we process all constructor arguments in the same loop.
-          let x := xs[i]!
+          let x := xs[i]
           let a ← mkIdent <$> if i < indVal.numParams then pure header.argNames[i]! else mkFreshUserName `a
           if i < indVal.numParams then
             -- add `_` for inductive parameters, they are inaccessible

src/Lean/Elab/Do.lean

@@ -513,7 +513,7 @@ partial def extendUpdatedVarsAux (c : Code) (ws : VarSet) : TermElabM Code :=
     | .ite ref none o c t e => return .ite ref none o c (← update t) (← update e)
     | .ite ref (some h) o cond t e =>
       if ws.contains h.getId then
-        -- if the `h` at `if h:c then t else e` shadows a variable in `ws`, we `pullExitPoints`
+        -- if the `h` at `if h : c then t else e` shadows a variable in `ws`, we `pullExitPoints`
         pullExitPoints c
       else
         return Code.ite ref (some h) o cond (← update t) (← update e)

src/Lean/Elab/Inductive.lean

@@ -168,8 +168,8 @@ private def checkHeader (r : ElabHeaderResult) (numParams : Nat) (firstType? : O
 
 -- Auxiliary function for checking whether the types in mutually inductive declaration are compatible.
 private partial def checkHeaders (rs : Array ElabHeaderResult) (numParams : Nat) (i : Nat) (firstType? : Option Expr) : TermElabM Unit := do
-  if i < rs.size then
-    let type ← checkHeader rs[i]! numParams firstType?
+  if h : i < rs.size then
+    let type ← checkHeader rs[i] numParams firstType?
     checkHeaders rs numParams (i+1) type
 
 private def elabHeader (views : Array InductiveView) : TermElabM (Array ElabHeaderResult) := do
@@ -222,11 +222,11 @@ private def replaceArrowBinderNames (type : Expr) (newNames : Array Name) : Expr
   go type 0
 where
   go (type : Expr) (i : Nat) : Expr :=
-    if i < newNames.size then
+    if h : i < newNames.size then
       match type with
       | .forallE n d b bi =>
         if n.hasMacroScopes then
-          mkForall newNames[i]! bi d (go b (i+1))
+          mkForall newNames[i] bi d (go b (i+1))
         else
           mkForall n bi d (go b (i+1))
       | _ => type

src/Lean/Elab/Match.lean

@@ -330,8 +330,8 @@ private def elabPatterns (patternStxs : Array Syntax) (matchType : Expr) : Excep
   withReader (fun ctx => { ctx with implicitLambda := false }) do
     let mut patterns  := #[]
     let mut matchType := matchType
-    for idx in [:patternStxs.size] do
-      let patternStx := patternStxs[idx]!
+    for h : idx in [:patternStxs.size] do
+      let patternStx := patternStxs[idx]
       matchType ← whnf matchType
       match matchType with
       | Expr.forallE _ d b _ =>

src/Lean/Elab/MutualDef.lean

@@ -406,9 +406,9 @@ private def elabFunValues (headers : Array DefViewElabHeader) (vars : Array Expr
       (if header.kind.isTheorem && !deprecated.oldSectionVars.get (← getOptions) then withHeaderSecVars vars sc #[header] else fun x => x #[]) fun vars => do
       forallBoundedTelescope header.type header.numParams fun xs type => do
         -- Add new info nodes for new fvars. The server will detect all fvars of a binder by the binder's source location.
-        for i in [0:header.binderIds.size] do
+        for h : i in [0:header.binderIds.size] do
           -- skip auto-bound prefix in `xs`
-          addLocalVarInfo header.binderIds[i]! xs[header.numParams - header.binderIds.size + i]!
+          addLocalVarInfo header.binderIds[i] xs[header.numParams - header.binderIds.size + i]!
         let val ← withReader ({ · with tacSnap? := header.tacSnap? }) do
           -- synthesize mvars here to force the top-level tactic block (if any) to run
           elabTermEnsuringType valStx type <* synthesizeSyntheticMVarsNoPostponing

src/Lean/Elab/PreDefinition/Nonrec/Eqns.lean

@@ -77,9 +77,9 @@ def mkEqns (declName : Name) (info : DefinitionVal) : MetaM (Array Name) :=
     withReducible do
       mkEqnTypes #[] goal.mvarId!
   let mut thmNames := #[]
-  for i in [: eqnTypes.size] do
-    let type := eqnTypes[i]!
-    trace[Elab.definition.eqns] "eqnType[{i}]: {eqnTypes[i]!}"
+  for h : i in [: eqnTypes.size] do
+    let type := eqnTypes[i]
+    trace[Elab.definition.eqns] "eqnType[{i}]: {eqnTypes[i]}"
     let name := (Name.str baseName eqnThmSuffixBase).appendIndexAfter (i+1)
     thmNames := thmNames.push name
     let value ← mkProof declName type

src/Lean/Elab/PreDefinition/Structural/Eqns.lean

@@ -67,8 +67,8 @@ def mkEqns (info : EqnInfo) : MetaM (Array Name) :=
     mkEqnTypes info.declNames goal.mvarId!
   let baseName := info.declName
   let mut thmNames := #[]
-  for i in [: eqnTypes.size] do
-    let type := eqnTypes[i]!
+  for h : i in [: eqnTypes.size] do
+    let type := eqnTypes[i]
     trace[Elab.definition.structural.eqns] "eqnType {i}: {type}"
     let name := (Name.str baseName eqnThmSuffixBase).appendIndexAfter (i+1)
     thmNames := thmNames.push name

src/Lean/Elab/PreDefinition/WF/Eqns.lean

@@ -83,9 +83,9 @@ def mkEqns (declName : Name) (info : EqnInfo) : MetaM (Array Name) :=
     withReducible do
       mkEqnTypes info.declNames goal.mvarId!
   let mut thmNames := #[]
-  for i in [: eqnTypes.size] do
-    let type := eqnTypes[i]!
-    trace[Elab.definition.wf.eqns] "{eqnTypes[i]!}"
+  for h : i in [: eqnTypes.size] do
+    let type := eqnTypes[i]
+    trace[Elab.definition.wf.eqns] "{eqnTypes[i]}"
     let name := (Name.str baseName eqnThmSuffixBase).appendIndexAfter (i+1)
     thmNames := thmNames.push name
     let value ← mkProof declName type

src/Lean/Elab/Quotation.lean

@@ -655,9 +655,9 @@ The parameter `alts` provides position information for alternatives.
 -/
 private def checkUnusedAlts (stx : Syntax) (alts : Array Syntax) (altIdxMap : NameMap Nat) (ignoreIfUnused : IdxSet) : TermElabM Syntax := do
   let (stx, used) ← findUsedAlts stx altIdxMap
-  for i in [:alts.size] do
+  for h : i in [:alts.size] do
     unless used.contains i || ignoreIfUnused.contains i do
-      logErrorAt alts[i]! s!"redundant alternative #{i+1}"
+      logErrorAt alts[i] s!"redundant alternative #{i+1}"
   return stx
 
 def match_syntax.expand (stx : Syntax) : TermElabM Syntax := do

src/Lean/Elab/StructInst.lean

@@ -682,7 +682,12 @@ private partial def elabStruct (s : Struct) (expectedType? : Option Expr) : Term
               -- We add info to get reliable positions for messages from evaluating the tactic script.
               let info := field.ref.getHeadInfo
               let stx := stx.raw.rewriteBottomUp (·.setInfo info)
-              cont (← elabTermEnsuringType stx (d.getArg! 0).consumeTypeAnnotations) field
+              let type := (d.getArg! 0).consumeTypeAnnotations
+              let mvar ← mkTacticMVar type stx (.fieldAutoParam fieldName s.structName)
+              -- Note(kmill): We are adding terminfo to simulate a previous implementation that elaborated `tacticBlock`.
+              -- (See the aformentioned `processExplicitArg` for a comment about this.)
+              addTermInfo' stx mvar
+              cont mvar field
           | _ =>
             if bi == .instImplicit then
               let val ← withRef field.ref <| mkFreshExprMVar d .synthetic

src/Lean/Elab/Structure.lean

@@ -468,7 +468,8 @@ where
     if h : i < view.parents.size then
       let parentStx := view.parents.get ⟨i, h⟩
       withRef parentStx do
-      let parentType ← Term.elabType parentStx
+      let parentType ← Term.withSynthesize <| Term.elabType parentStx
+      let parentType ← whnf parentType
       let parentStructName ← getStructureName parentType
       if let some existingFieldName ← findExistingField? infos parentStructName then
         if structureDiamondWarning.get (← getOptions) then
@@ -732,7 +733,8 @@ private def addDefaults (lctx : LocalContext) (defaultAuxDecls : Array (Name ×
         throwError "invalid default value for field, it contains metavariables{indentExpr value}"
       /- The identity function is used as "marker". -/
       let value ← mkId value
-      discard <| mkAuxDefinition declName type value (zetaDelta := true)
+      -- No need to compile the definition, since it is only used during elaboration.
+      discard <| mkAuxDefinition declName type value (zetaDelta := true) (compile := false)
       setReducibleAttribute declName
 
 /--

src/Lean/Elab/SyntheticMVars.lean

@@ -257,8 +257,8 @@ private def throwStuckAtUniverseCnstr : TermElabM Unit := do
     unless found.contains (lhs, rhs) do
       found := found.insert (lhs, rhs)
       uniqueEntries := uniqueEntries.push entry
-  for i in [1:uniqueEntries.size] do
-    logErrorAt uniqueEntries[i]!.ref (← mkLevelStuckErrorMessage uniqueEntries[i]!)
+  for h : i in [1:uniqueEntries.size] do
+    logErrorAt uniqueEntries[i].ref (← mkLevelStuckErrorMessage uniqueEntries[i]!)
   throwErrorAt uniqueEntries[0]!.ref (← mkLevelStuckErrorMessage uniqueEntries[0]!)
 
 /--
@@ -316,6 +316,18 @@ def PostponeBehavior.ofBool : Bool → PostponeBehavior
   | true  => .yes
   | false => .no
 
+private def TacticMVarKind.logError (tacticCode : Syntax) (kind : TacticMVarKind) : TermElabM Unit := do
+  match kind with
+  | term => pure ()
+  | autoParam argName => logErrorAt tacticCode m!"could not synthesize default value for parameter '{argName}' using tactics"
+  | fieldAutoParam fieldName structName => logErrorAt tacticCode m!"could not synthesize default value for field '{fieldName}' of '{structName}' using tactics"
+
+private def TacticMVarKind.maybeWithoutRecovery (kind : TacticMVarKind) (m : TacticM α) : TacticM α := do
+  if kind matches .autoParam .. | .fieldAutoParam .. then
+    withoutErrToSorry <| Tactic.withoutRecover <| m
+  else
+    m
+
 mutual
 
   /--
@@ -325,7 +337,7 @@ mutual
 
   If `report := false`, then `runTactic` will not capture exceptions nor will report unsolved goals. Unsolved goals become exceptions.
   -/
-  partial def runTactic (mvarId : MVarId) (tacticCode : Syntax) (report := true) : TermElabM Unit := withoutAutoBoundImplicit do
+  partial def runTactic (mvarId : MVarId) (tacticCode : Syntax) (kind : TacticMVarKind) (report := true) : TermElabM Unit := withoutAutoBoundImplicit do
     instantiateMVarDeclMVars mvarId
     /-
     TODO: consider using `runPendingTacticsAt` at `mvarId` local context and target type.
@@ -342,7 +354,7 @@ mutual
     in more complicated scenarios.
     -/
     tryCatchRuntimeEx
-      (do let remainingGoals ← withInfoHole mvarId <| Tactic.run mvarId do
+      (do let remainingGoals ← withInfoHole mvarId <| Tactic.run mvarId <| kind.maybeWithoutRecovery do
             withTacticInfoContext tacticCode do
               -- also put an info node on the `by` keyword specifically -- the token may be `canonical` and thus shown in the info
               -- view even though it is synthetic while a node like `tacticCode` never is (#1990)
@@ -354,10 +366,13 @@ mutual
               synthesizeSyntheticMVars (postpone := .no)
           unless remainingGoals.isEmpty do
             if report then
+              kind.logError tacticCode
               reportUnsolvedGoals remainingGoals
             else
               throwError "unsolved goals\n{goalsToMessageData remainingGoals}")
       fun ex => do
+        if report then
+          kind.logError tacticCode
         if report && (← read).errToSorry then
           for mvarId in (← getMVars (mkMVar mvarId)) do
             mvarId.admit
@@ -385,10 +400,10 @@ mutual
       return false
     -- NOTE: actual processing at `synthesizeSyntheticMVarsAux`
     | .postponed savedContext => resumePostponed savedContext mvarSyntheticDecl.stx mvarId postponeOnError
-    | .tactic tacticCode savedContext =>
+    | .tactic tacticCode savedContext kind =>
       withSavedContext savedContext do
         if runTactics then
-          runTactic mvarId tacticCode
+          runTactic mvarId tacticCode kind
           return true
         else
           return false
@@ -529,9 +544,9 @@ the result of a tactic block.
 def runPendingTacticsAt (e : Expr) : TermElabM Unit := do
   for mvarId in (← getMVars e) do
     let mvarId ← getDelayedMVarRoot mvarId
-    if let some { kind := .tactic tacticCode savedContext, .. } ← getSyntheticMVarDecl? mvarId then
+    if let some { kind := .tactic tacticCode savedContext kind, .. } ← getSyntheticMVarDecl? mvarId then
       withSavedContext savedContext do
-        runTactic mvarId tacticCode
+        runTactic mvarId tacticCode kind
         markAsResolved mvarId
 
 builtin_initialize

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

@@ -55,9 +55,9 @@ def evalBvCheck : Tactic := fun
   | `(tactic| bv_check%$tk $path:str) => do
     let cfg ← BVDecide.Frontend.BVCheck.mkContext path.getString
     liftMetaFinishingTactic fun g => do
-      let res ← Normalize.bvNormalize g
-      match res.goal with
-      | some g => bvCheck g cfg
+      let g'? ← Normalize.bvNormalize g
+      match g'? with
+      | some g' => bvCheck g' cfg
       | none =>
         let bvNormalizeStx ← `(tactic| bv_normalize)
         TryThis.addSuggestion tk bvNormalizeStx (origSpan? := ← getRef)

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

@@ -265,10 +265,6 @@ def bvUnsat (g : MVarId) (cfg : TacticContext) : MetaM (Except CounterExample Lr
 The result of calling `bv_decide`.
 -/
 structure Result where
-  /--
-  Trace of the `simp` used in `bv_decide`'s normalization procedure.
-  -/
-  simpTrace : Simp.Stats
   /--
   If the normalization step was not enough to solve the goal this contains the LRAT proof
   certificate.
@@ -280,10 +276,10 @@ Try to close `g` using a bitblaster. Return either a `CounterExample` if one is
 if `g` is proven.
 -/
 def bvDecide' (g : MVarId) (cfg : TacticContext) : MetaM (Except CounterExample Result) := do
-  let ⟨g?, simpTrace⟩ ← Normalize.bvNormalize g
-  let some g := g? | return .ok ⟨simpTrace, none⟩
+  let g? ← Normalize.bvNormalize g
+  let some g := g? | return .ok ⟨none⟩
   match ← bvUnsat g cfg with
-  | .ok lratCert => return .ok ⟨simpTrace, some lratCert⟩
+  | .ok lratCert => return .ok ⟨some lratCert⟩
   | .error counterExample => return .error counterExample
 
 /--

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

@@ -75,9 +75,7 @@ instance : ToExpr Gate where
   toExpr x :=
     match x with
     | .and => mkConst ``Gate.and
-    | .or => mkConst ``Gate.or
     | .xor => mkConst ``Gate.xor
-    | .imp => mkConst ``Gate.imp
     | .beq => mkConst ``Gate.beq
   toTypeExpr := mkConst ``Gate
 

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

@@ -343,7 +343,7 @@ where
     return mkApp4 congrProof (toExpr inner.width) innerExpr innerEval innerProof
 
   goBvLit (x : Expr) : M (Option ReifiedBVExpr) := do
-    let some ⟨width, bvVal⟩ ← getBitVecValue? x | return none
+    let some ⟨width, bvVal⟩ ← getBitVecValue? x | return ← ofAtom x
     let bvExpr : BVExpr width := .const bvVal
     let expr := mkApp2 (mkConst ``BVExpr.const) (toExpr width) (toExpr bvVal)
     let proof := do

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

@@ -65,7 +65,6 @@ partial def of (t : Expr) : M (Option ReifiedBVLogical) := do
       let subProof ← sub.evalsAtAtoms
       return mkApp3 (mkConst ``Std.Tactic.BVDecide.Reflect.Bool.not_congr) subExpr subEvalExpr subProof
     return some ⟨boolExpr, proof, expr⟩
-  | Bool.or lhsExpr rhsExpr => gateReflection lhsExpr rhsExpr .or ``Std.Tactic.BVDecide.Reflect.Bool.or_congr
   | Bool.and lhsExpr rhsExpr => gateReflection lhsExpr rhsExpr .and ``Std.Tactic.BVDecide.Reflect.Bool.and_congr
   | Bool.xor lhsExpr rhsExpr => gateReflection lhsExpr rhsExpr .xor ``Std.Tactic.BVDecide.Reflect.Bool.xor_congr
   | BEq.beq α _ lhsExpr rhsExpr =>

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

@@ -89,7 +89,7 @@ where
       M (Option ReifiedBVPred) := do
     let some lhs ← ReifiedBVExpr.of lhsExpr | return none
     let some rhs ← ReifiedBVExpr.of rhsExpr | return none
-    if h:lhs.width = rhs.width then
+    if h : lhs.width = rhs.width then
       let bvExpr : BVPred := .bin (w := lhs.width) lhs.bvExpr pred (h ▸ rhs.bvExpr)
       let expr :=
         mkApp4

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

@@ -37,40 +37,102 @@ builtin_simproc [bv_normalize] eqToBEq (((_ : Bool) = (_ : Bool))) := fun e => d
     let proof := mkApp2 (mkConst ``Bool.eq_to_beq) lhs rhs
     return .done { expr := new, proof? := some proof }
 
-structure Result where
-  goal : Option MVarId := none
-  stats : Simp.Stats := {}
+builtin_simproc [bv_normalize] andOnes ((_ : BitVec _) &&& (_ : BitVec _)) := fun e => do
+  let_expr HAnd.hAnd _ _ _ _ lhs rhs := e | return .continue
+  let some ⟨w, rhsValue⟩ ← getBitVecValue? rhs | return .continue
+  if rhsValue == -1#w then
+    let proof := mkApp2 (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.and_ones) (toExpr w) lhs
+    return .visit { expr := lhs, proof? := some proof }
+  else
+    return .continue
 
-def bvNormalize (g : MVarId) : MetaM Result := do
+builtin_simproc [bv_normalize] onesAnd ((_ : BitVec _) &&& (_ : BitVec _)) := fun e => do
+  let_expr HAnd.hAnd _ _ _ _ lhs rhs := e | return .continue
+  let some ⟨w, lhsValue⟩ ← getBitVecValue? lhs | return .continue
+  if lhsValue == -1#w then
+    let proof := mkApp2 (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.ones_and) (toExpr w) rhs
+    return .visit { expr := rhs, proof? := some proof }
+  else
+    return .continue
+
+builtin_simproc [bv_normalize] maxUlt (BitVec.ult (_ : BitVec _) (_ : BitVec _)) := fun e => do
+  let_expr BitVec.ult _ lhs rhs := e | return .continue
+  let some ⟨w, lhsValue⟩ ← getBitVecValue? lhs | return .continue
+  if lhsValue == -1#w then
+    let proof := mkApp2 (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.max_ult') (toExpr w) rhs
+    return .visit { expr := toExpr Bool.false, proof? := some proof }
+  else
+    return .continue
+
+/--
+A pass in the normalization pipeline. Takes the current goal and produces a refined one or closes
+the goal fully, indicated by returning `none`.
+-/
+abbrev Pass := MVarId → MetaM (Option MVarId)
+
+namespace Pass
+
+/--
+Repeatedly run a list of `Pass` until they either close the goal or an iteration doesn't change
+the goal anymore.
+-/
+partial def fixpointPipeline (passes : List Pass) (goal : MVarId) : MetaM (Option MVarId) := do
+  let runPass (goal? : Option MVarId) (pass : Pass) : MetaM (Option MVarId) := do
+    let some goal := goal? | return none
+    pass goal
+
+  let some newGoal := ← passes.foldlM (init := some goal) runPass | return none
+  if goal != newGoal then
+    trace[Meta.Tactic.bv] m!"Rerunning pipeline on:\n{newGoal}"
+    fixpointPipeline passes newGoal
+  else
+    trace[Meta.Tactic.bv] "Pipeline reached a fixpoint"
+    return newGoal
+
+/--
+Responsible for applying the Bitwuzla style rewrite rules.
+-/
+def rewriteRulesPass : Pass := fun goal => do
+  let bvThms ← bvNormalizeExt.getTheorems
+  let bvSimprocs ← bvNormalizeSimprocExt.getSimprocs
+  let sevalThms ← getSEvalTheorems
+  let sevalSimprocs ← Simp.getSEvalSimprocs
+
+  let simpCtx : Simp.Context := {
+    config := { failIfUnchanged := false, zetaDelta := true }
+    simpTheorems := #[bvThms, sevalThms]
+    congrTheorems := (← getSimpCongrTheorems)
+  }
+
+  let hyps ← goal.getNondepPropHyps
+  let ⟨result?, _⟩ ← simpGoal goal
+    (ctx := simpCtx)
+    (simprocs := #[bvSimprocs, sevalSimprocs])
+    (fvarIdsToSimp := hyps)
+  let some (_, newGoal) := result? | return none
+  return newGoal
+
+/--
+The normalization passes used by `bv_normalize` and thus `bv_decide`.
+-/
+def defaultPipeline : List Pass := [rewriteRulesPass]
+
+end Pass
+
+def bvNormalize (g : MVarId) : MetaM (Option MVarId) := do
   withTraceNode `bv (fun _ => return "Normalizing goal") do
     -- Contradiction proof
-    let some g ← g.falseOrByContra | return {}
-
-    -- Normalization by simp
-    let bvThms ← bvNormalizeExt.getTheorems
-    let bvSimprocs ← bvNormalizeSimprocExt.getSimprocs
-    let sevalThms ← getSEvalTheorems
-    let sevalSimprocs ← Simp.getSEvalSimprocs
-
-    let simpCtx : Simp.Context := {
-      config := { failIfUnchanged := false, zetaDelta := true }
-      simpTheorems := #[bvThms, sevalThms]
-      congrTheorems := (← getSimpCongrTheorems)
-    }
-
-    let hyps ← g.getNondepPropHyps
-    let ⟨result?, stats⟩ ← simpGoal g
-      (ctx := simpCtx)
-      (simprocs := #[bvSimprocs, sevalSimprocs])
-      (fvarIdsToSimp := hyps)
-    let some (_, g) := result? | return ⟨none, stats⟩
-    return ⟨some g, stats⟩
+    let some g ← g.falseOrByContra | return none
+    trace[Meta.Tactic.bv] m!"Running preprocessing pipeline on:\n{g}"
+    Pass.fixpointPipeline Pass.defaultPipeline g
 
 @[builtin_tactic Lean.Parser.Tactic.bvNormalize]
 def evalBVNormalize : Tactic := fun
   | `(tactic| bv_normalize) => do
-    liftMetaFinishingTactic fun g => do
-      discard <| bvNormalize g
+    let g ← getMainGoal
+    match ← bvNormalize g with
+    | some newGoal => setGoals [newGoal]
+    | none => setGoals []
   | _ => throwUnsupportedSyntax
 
 end Frontend.Normalize

src/Lean/Elab/Tactic/Induction.lean

@@ -205,8 +205,8 @@ private def isWildcard (altStx : Syntax) : Bool :=
   getAltName altStx == `_
 
 private def checkAltNames (alts : Array Alt) (altsSyntax : Array Syntax) : TacticM Unit :=
-  for i in [:altsSyntax.size] do
-    let altStx := altsSyntax[i]!
+  for h : i in [:altsSyntax.size] do
+    let altStx := altsSyntax[i]
     if getAltName altStx == `_ && i != altsSyntax.size - 1 then
       withRef altStx <| throwError "invalid occurrence of wildcard alternative, it must be the last alternative"
     let altName := getAltName altStx
@@ -236,8 +236,8 @@ private def saveAltVarsInfo (altMVarId : MVarId) (altStx : Syntax) (fvarIds : Ar
     let altVars := getAltVars altStx
     for fvarId in fvarIds do
       if !useNamesForExplicitOnly || (← fvarId.getDecl).binderInfo.isExplicit then
-        if i < altVars.size then
-          Term.addLocalVarInfo altVars[i]! (mkFVar fvarId)
+        if h : i < altVars.size then
+          Term.addLocalVarInfo altVars[i] (mkFVar fvarId)
           i := i + 1
 
 open Language in
@@ -320,8 +320,8 @@ where
     2- The errors are produced in the same order the appear in the code above. This is not super
     important when using IDEs.
     -/
-    for altStxIdx in [0:altStxs.size] do
-      let altStx := altStxs[altStxIdx]!
+    for h : altStxIdx in [0:altStxs.size] do
+      let altStx := altStxs[altStxIdx]
       let altName := getAltName altStx
       if let some i := alts.findIdx? (·.1 == altName) then
         -- cover named alternative

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

@@ -513,13 +513,13 @@ def fourierMotzkinSelect (data : Array FourierMotzkinData) : MetaM FourierMotzki
   if bestSize = 0 then
     trace[omega] "Selected variable {data[0]!.var}."
     return data[0]!
-  for i in [1:data.size] do
-    let exact := data[i]!.exact
-    let size := data[i]!.size
+  for h : i in [1:data.size] do
+    let exact := data[i].exact
+    let size := data[i].size
     if size = 0 || !bestExact && exact || (bestExact == exact) && size < bestSize then
       if size = 0 then
-        trace[omega] "Selected variable {data[i]!.var}"
-        return data[i]!
+        trace[omega] "Selected variable {data[i].var}"
+        return data[i]
       bestIdx := i
       bestExact := exact
       bestSize := size

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

@@ -277,6 +277,7 @@ where
       | _ => mkAtomLinearCombo e
     | (``Min.min, #[_, _, a, b]) => rewrite e (mkApp2 (.const ``Int.ofNat_min []) a b)
     | (``Max.max, #[_, _, a, b]) => rewrite e (mkApp2 (.const ``Int.ofNat_max []) a b)
+    | (``Int.toNat, #[n]) => rewrite e (mkApp (.const ``Int.toNat_eq_max []) n)
     | (``HShiftLeft.hShiftLeft, #[_, _, _, _, a, b]) =>
       rewrite e (mkApp2 (.const ``Int.ofNat_shiftLeft_eq []) a b)
     | (``HShiftRight.hShiftRight, #[_, _, _, _, a, b]) =>

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

@@ -29,12 +29,14 @@ The minimum non-zero entry in a list of natural numbers, or zero if all entries
 We completely characterize the function via
 `nonzeroMinimum_eq_zero_iff` and `nonzeroMinimum_eq_nonzero_iff` below.
 -/
-def nonzeroMinimum (xs : List Nat) : Nat := xs.filter (· ≠ 0) |>.minimum? |>.getD 0
+def nonzeroMinimum (xs : List Nat) : Nat := xs.filter (· ≠ 0) |>.min? |>.getD 0
 
 -- A specialization of `minimum?_eq_some_iff` to Nat.
-theorem minimum?_eq_some_iff' {xs : List Nat} :
-    xs.minimum? = some a ↔ (a ∈ xs ∧ ∀ b ∈ xs, a ≤ b) :=
-  minimum?_eq_some_iff
+-- This is a duplicate `min?_eq_some_iff'` proved in `Init.Data.List.Nat.Basic`,
+-- and could be deduplicated but the import hierarchy is awkward.
+theorem min?_eq_some_iff'' {xs : List Nat} :
+    xs.min? = some a ↔ (a ∈ xs ∧ ∀ b ∈ xs, a ≤ b) :=
+  min?_eq_some_iff
     (le_refl := Nat.le_refl)
     (min_eq_or := fun _ _ => Nat.min_def .. ▸ by split <;> simp)
     (le_min_iff := fun _ _ _ => Nat.le_min)
@@ -42,27 +44,27 @@ theorem minimum?_eq_some_iff' {xs : List Nat} :
 open Classical in
 @[simp] theorem nonzeroMinimum_eq_zero_iff {xs : List Nat} :
     xs.nonzeroMinimum = 0 ↔ ∀ x ∈ xs, x = 0 := by
-  simp [nonzeroMinimum, Option.getD_eq_iff, minimum?_eq_none_iff, minimum?_eq_some_iff',
+  simp [nonzeroMinimum, Option.getD_eq_iff, min?_eq_none_iff, min?_eq_some_iff'',
     filter_eq_nil_iff, mem_filter]
 
 theorem nonzeroMinimum_mem {xs : List Nat} (w : xs.nonzeroMinimum ≠ 0) :
     xs.nonzeroMinimum ∈ xs := by
   dsimp [nonzeroMinimum] at *
-  generalize h : (xs.filter (· ≠ 0) |>.minimum?) = m at *
+  generalize h : (xs.filter (· ≠ 0) |>.min?) = m at *
   match m, w with
-  | some (m+1), _ => simp_all [minimum?_eq_some_iff', mem_filter]
+  | some (m+1), _ => simp_all [min?_eq_some_iff'', mem_filter]
 
 theorem nonzeroMinimum_pos {xs : List Nat} (m : a ∈ xs) (h : a ≠ 0) : 0 < xs.nonzeroMinimum :=
   Nat.pos_iff_ne_zero.mpr fun w => h (nonzeroMinimum_eq_zero_iff.mp w _ m)
 
 theorem nonzeroMinimum_le {xs : List Nat} (m : a ∈ xs) (h : a ≠ 0) : xs.nonzeroMinimum ≤ a := by
-  have : (xs.filter (· ≠ 0) |>.minimum?) = some xs.nonzeroMinimum := by
+  have : (xs.filter (· ≠ 0) |>.min?) = some xs.nonzeroMinimum := by
     have w := nonzeroMinimum_pos m h
     dsimp [nonzeroMinimum] at *
-    generalize h : (xs.filter (· ≠ 0) |>.minimum?) = m? at *
+    generalize h : (xs.filter (· ≠ 0) |>.min?) = m? at *
     match m?, w with
     | some m?, _ => rfl
-  rw [minimum?_eq_some_iff'] at this
+  rw [min?_eq_some_iff''] at this
   apply this.2
   simp [List.mem_filter]
   exact ⟨m, h⟩
@@ -142,4 +144,4 @@ theorem minNatAbs_eq_nonzero_iff (xs : List Int) (w : z ≠ 0) :
 @[simp] theorem minNatAbs_nil : ([] : List Int).minNatAbs = 0 := rfl
 
 /-- The maximum absolute value in a list of integers. -/
-def maxNatAbs (xs : List Int) : Nat := xs.map Int.natAbs |>.maximum? |>.getD 0
+def maxNatAbs (xs : List Int) : Nat := xs.map Int.natAbs |>.max? |>.getD 0

src/Lean/Elab/Tactic/Simp.lean

@@ -47,7 +47,7 @@ def tacticToDischarge (tacticCode : Syntax) : TacticM (IO.Ref Term.State × Simp
         -/
         withoutModifyingStateWithInfoAndMessages do
           Term.withSynthesize (postpone := .no) do
-            Term.runTactic (report := false) mvar.mvarId! tacticCode
+            Term.runTactic (report := false) mvar.mvarId! tacticCode .term
           let result ← instantiateMVars mvar
           if result.hasExprMVar then
             return none

src/Lean/Elab/Term.lean

@@ -29,6 +29,15 @@ structure SavedContext where
   errToSorry : Bool
   levelNames : List Name
 
+/-- The kind of a tactic metavariable, used for additional error reporting. -/
+inductive TacticMVarKind
+  /-- Standard tactic metavariable, arising from `by ...` syntax. -/
+  | term
+  /-- Tactic metavariable arising from an autoparam for a function application. -/
+  | autoParam (argName : Name)
+  /-- Tactic metavariable arising from an autoparam for a structure field. -/
+  | fieldAutoParam (fieldName structName : Name)
+
 /-- We use synthetic metavariables as placeholders for pending elaboration steps. -/
 inductive SyntheticMVarKind where
   /--
@@ -43,7 +52,7 @@ inductive SyntheticMVarKind where
   Otherwise, we generate the error `("type mismatch" ++ e ++ "has type" ++ eType ++ "but it is expected to have type" ++ expectedType)` -/
   | coe (header? : Option String) (expectedType : Expr) (e : Expr) (f? : Option Expr)
   /-- Use tactic to synthesize value for metavariable. -/
-  | tactic (tacticCode : Syntax) (ctx : SavedContext)
+  | tactic (tacticCode : Syntax) (ctx : SavedContext) (kind : TacticMVarKind)
   /-- Metavariable represents a hole whose elaboration has been postponed. -/
   | postponed (ctx : SavedContext)
   deriving Inhabited
@@ -1191,6 +1200,26 @@ private def postponeElabTermCore (stx : Syntax) (expectedType? : Option Expr) :
 def getSyntheticMVarDecl? (mvarId : MVarId) : TermElabM (Option SyntheticMVarDecl) :=
   return (← get).syntheticMVars.find? mvarId
 
+register_builtin_option debug.byAsSorry : Bool := {
+  defValue := false
+  group    := "debug"
+  descr    := "replace `by ..` blocks with `sorry` IF the expected type is a proposition"
+}
+
+/--
+Creates a new metavariable of type `type` that will be synthesized using the tactic code.
+The `tacticCode` syntax is the full `by ..` syntax.
+-/
+def mkTacticMVar (type : Expr) (tacticCode : Syntax) (kind : TacticMVarKind) : TermElabM Expr := do
+  if ← pure (debug.byAsSorry.get (← getOptions)) <&&> isProp type then
+    mkSorry type false
+  else
+    let mvar ← mkFreshExprMVar type MetavarKind.syntheticOpaque
+    let mvarId := mvar.mvarId!
+    let ref ← getRef
+    registerSyntheticMVar ref mvarId <| SyntheticMVarKind.tactic tacticCode (← saveContext) kind
+    return mvar
+
 /--
   Create an auxiliary annotation to make sure we create an `Info` even if `e` is a metavariable.
   See `mkTermInfo`.

src/Lean/Environment.lean

@@ -515,11 +515,11 @@ def addEntry {α β σ : Type} (ext : PersistentEnvExtension α β σ) (env : En
 def getState {α β σ : Type} [Inhabited σ] (ext : PersistentEnvExtension α β σ) (env : Environment) : σ :=
   (ext.toEnvExtension.getState env).state
 
-/-- Set the current state of the given extension in the given environment. This change is *not* persisted across files. -/
+/-- Set the current state of the given extension in the given environment. -/
 def setState {α β σ : Type} (ext : PersistentEnvExtension α β σ) (env : Environment) (s : σ) : Environment :=
   ext.toEnvExtension.modifyState env fun ps => { ps with  state := s }
 
-/-- Modify the state of the given extension in the given environment by applying the given function. This change is *not* persisted across files. -/
+/-- Modify the state of the given extension in the given environment by applying the given function. -/
 def modifyState {α β σ : Type} (ext : PersistentEnvExtension α β σ) (env : Environment) (f : σ → σ) : Environment :=
   ext.toEnvExtension.modifyState env fun ps => { ps with state := f (ps.state) }
 
@@ -765,8 +765,8 @@ where
   loop (i : Nat) (env : Environment) : IO Environment := do
     -- Recall that the size of the array stored `persistentEnvExtensionRef` may increase when we import user-defined environment extensions.
     let pExtDescrs ← persistentEnvExtensionsRef.get
-    if i < pExtDescrs.size then
-      let extDescr := pExtDescrs[i]!
+    if h : i < pExtDescrs.size then
+      let extDescr := pExtDescrs[i]
       let s := extDescr.toEnvExtension.getState env
       let prevSize := (← persistentEnvExtensionsRef.get).size
       let prevAttrSize ← getNumBuiltinAttributes
@@ -858,7 +858,7 @@ def finalizeImport (s : ImportState) (imports : Array Import) (opts : Options) (
     numConsts + mod.constants.size + mod.extraConstNames.size
   let mut const2ModIdx : Std.HashMap Name ModuleIdx := Std.HashMap.empty (capacity := numConsts)
   let mut constantMap : Std.HashMap Name ConstantInfo := Std.HashMap.empty (capacity := numConsts)
-  for h:modIdx in [0:s.moduleData.size] do
+  for h : modIdx in [0:s.moduleData.size] do
     let mod := s.moduleData[modIdx]'h.upper
     for cname in mod.constNames, cinfo in mod.constants do
       match constantMap.getThenInsertIfNew? cname cinfo with
@@ -1096,6 +1096,13 @@ def isDefEqGuarded (env : Environment) (lctx : LocalContext) (a b : Expr) : Bool
 @[extern "lean_kernel_whnf"]
 opaque whnf (env : Environment) (lctx : LocalContext) (a : Expr) : Except KernelException Expr
 
+/--
+  Kernel typecheck function. We use it mainly for debugging purposes.
+  Recall that the Kernel type checker does not support metavariables.
+  When implementing automation, consider using the `MetaM` methods. -/
+@[extern "lean_kernel_check"]
+opaque check (env : Environment) (lctx : LocalContext) (a : Expr) : Except KernelException Expr
+
 end Kernel
 
 class MonadEnv (m : Type → Type) where

src/Lean/LocalContext.lean

@@ -385,14 +385,14 @@ def size (lctx : LocalContext) : Nat :=
   Id.run <| lctx.findDeclRevM? f
 
 partial def isSubPrefixOfAux (a₁ a₂ : PArray (Option LocalDecl)) (exceptFVars : Array Expr) (i j : Nat) : Bool :=
-  if i < a₁.size then
-    match a₁[i]! with
+  if h : i < a₁.size then
+    match a₁[i] with
     | none       => isSubPrefixOfAux a₁ a₂ exceptFVars (i+1) j
     | some decl₁ =>
       if exceptFVars.any fun fvar => fvar.fvarId! == decl₁.fvarId then
         isSubPrefixOfAux a₁ a₂ exceptFVars (i+1) j
-      else if j < a₂.size then
-        match a₂[j]! with
+      else if h2 : j < a₂.size then
+        match a₂[j] with
         | none       => isSubPrefixOfAux a₁ a₂ exceptFVars i (j+1)
         | some decl₂ => if decl₁.fvarId == decl₂.fvarId then isSubPrefixOfAux a₁ a₂ exceptFVars (i+1) (j+1) else isSubPrefixOfAux a₁ a₂ exceptFVars i (j+1)
       else false

src/Lean/Meta/ACLt.lean

@@ -155,8 +155,8 @@ where
           if !infos[i]!.isInstImplicit then
             if !(← lt args[i]! b) then
               return false
-        for i in [infos.size:args.size] do
-          if !(← lt args[i]! b) then
+        for h : i in [infos.size:args.size] do
+          if !(← lt args[i] b) then
             return false
         return true
     | .lam _ d e ..     => lt d b <&&> lt e b

src/Lean/Meta/AppBuilder.lean

@@ -277,7 +277,7 @@ private def mkAppMFinal (methodName : Name) (f : Expr) (args : Array Expr) (inst
 
 private partial def mkAppMArgs (f : Expr) (fType : Expr) (xs : Array Expr) : MetaM Expr :=
   let rec loop (type : Expr) (i : Nat) (j : Nat) (args : Array Expr) (instMVars : Array MVarId) : MetaM Expr := do
-    if i >= xs.size then
+    if h : i >= xs.size then
       mkAppMFinal `mkAppM f args instMVars
     else match type with
       | Expr.forallE n d b bi =>
@@ -293,7 +293,7 @@ private partial def mkAppMArgs (f : Expr) (fType : Expr) (xs : Array Expr) : Met
           let mvar ← mkFreshExprMVar d MetavarKind.synthetic n
           loop b i j (args.push mvar) (instMVars.push mvar.mvarId!)
         | _ =>
-          let x := xs[i]!
+          let x := xs[i]
           let xType ← inferType x
           if (← isDefEq d xType) then
             loop b (i+1) j (args.push x) instMVars

src/Lean/Meta/ArgsPacker.lean

@@ -69,8 +69,8 @@ The `type` should be the expected type of the packed argument, as created with `
 partial def pack (type : Expr) (args : Array Expr) : Expr := go 0 type
 where
   go (i : Nat) (type : Expr) : Expr :=
-    if i < args.size - 1 then
-      let arg := args[i]!
+    if h : i < args.size - 1 then
+      let arg := args[i]
       assert! type.isAppOfArity ``PSigma 2
       let us := type.getAppFn.constLevels!
       let α := type.appFn!.appArg!

src/Lean/Meta/CongrTheorems.lean

@@ -77,7 +77,7 @@ partial def mkHCongrWithArity (f : Expr) (numArgs : Nat) : MetaM CongrTheorem :=
 where
   withNewEqs {α} (xs ys : Array Expr) (k : Array Expr → Array CongrArgKind → MetaM α) : MetaM α :=
     let rec loop (i : Nat) (eqs : Array Expr) (kinds : Array CongrArgKind) := do
-      if  i < xs.size then
+      if i < xs.size then
         let x := xs[i]!
         let y := ys[i]!
         let xType := (← inferType x).cleanupAnnotations
@@ -185,11 +185,11 @@ private def getClassSubobjectMask? (f : Expr) : MetaM (Option (Array Bool)) := d
   forallTelescopeReducing val.type (cleanupAnnotations := true) fun xs _ => do
     let env ← getEnv
     let mut mask := #[]
-    for i in [:xs.size] do
+    for h : i in [:xs.size] do
       if i < val.numParams then
         mask := mask.push false
       else
-        let localDecl ← xs[i]!.fvarId!.getDecl
+        let localDecl ← xs[i].fvarId!.getDecl
         mask := mask.push (isSubobjectField? env val.induct localDecl.userName).isSome
     return some mask
 
@@ -211,14 +211,14 @@ def getCongrSimpKinds (f : Expr) (info : FunInfo) : MetaM (Array CongrArgKind) :
   -/
   let mut result := #[]
   let mask? ← getClassSubobjectMask? f
-  for i in [:info.paramInfo.size] do
+  for h : i in [:info.paramInfo.size] do
     if info.resultDeps.contains i then
       result := result.push .fixed
-    else if info.paramInfo[i]!.isProp then
+    else if info.paramInfo[i].isProp then
       result := result.push .cast
-    else if info.paramInfo[i]!.isInstImplicit then
+    else if info.paramInfo[i].isInstImplicit then
       if let some mask := mask? then
-        if h : i < mask.size then
+        if h2 : i < mask.size then
           if mask[i] then
             -- Parameter is a subobect field of a class constructor. See comment above.
             result := result.push .eq

src/Lean/Meta/Eval.lean

@@ -6,6 +6,7 @@ Authors: Sebastian Ullrich, Leonardo de Moura
 prelude
 import Lean.AddDecl
 import Lean.Meta.Check
+import Lean.Util.CollectLevelParams
 
 namespace Lean.Meta
 
@@ -13,12 +14,13 @@ unsafe def evalExprCore (α) (value : Expr) (checkType : Expr → MetaM Unit) (s
   withoutModifyingEnv do
     let name ← mkFreshUserName `_tmp
     let value ← instantiateMVars value
+    let us := collectLevelParams {} value |>.params
     if value.hasMVar then
       throwError "failed to evaluate expression, it contains metavariables{indentExpr value}"
     let type ← inferType value
     checkType type
     let decl := Declaration.defnDecl {
-       name, levelParams := [], type
+       name, levelParams := us.toList, type
        value, hints := ReducibilityHints.opaque,
        safety
     }