benchmark

This PR fixes:
- Problems in other linux distributions that the default `tzdata`
directory is not the same as previously defined by ensuring it with a
fallback behavior when directory is missing.
- Trim unnecessary characters from local time identifier.

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

@@ -1,7 +1,8 @@
 # This workflow allows any user to add one of the `awaiting-review`, `awaiting-author`, `WIP`,
-# or `release-ci` labels by commenting on the PR or issue.
+# `release-ci`, or a `changelog-XXX` label by commenting on the PR or issue.
 # If any labels from the set {`awaiting-review`, `awaiting-author`, `WIP`} are added, other labels
 # from that set are removed automatically at the same time.
+# Similarly, if any `changelog-XXX` label is added, other `changelog-YYY` labels are removed.
 
 name: Label PR based on Comment
 
@@ -11,7 +12,7 @@ on:
 
 jobs:
   update-label:
-    if: github.event.issue.pull_request != null && (contains(github.event.comment.body, 'awaiting-review') || contains(github.event.comment.body, 'awaiting-author') || contains(github.event.comment.body, 'WIP') || contains(github.event.comment.body, 'release-ci'))
+    if: github.event.issue.pull_request != null && (contains(github.event.comment.body, 'awaiting-review') || contains(github.event.comment.body, 'awaiting-author') || contains(github.event.comment.body, 'WIP') || contains(github.event.comment.body, 'release-ci') || contains(github.event.comment.body, 'changelog-'))
     runs-on: ubuntu-latest
 
     steps:
@@ -20,13 +21,14 @@ jobs:
       with:
         github-token: ${{ secrets.GITHUB_TOKEN }}
         script: |
-          const { owner, repo, number: issue_number  } = context.issue;
+          const { owner, repo, number: issue_number } = context.issue;
           const commentLines = context.payload.comment.body.split('\r\n');
 
           const awaitingReview = commentLines.includes('awaiting-review');
           const awaitingAuthor = commentLines.includes('awaiting-author');
           const wip = commentLines.includes('WIP');
           const releaseCI = commentLines.includes('release-ci');
+          const changelogMatch = commentLines.find(line => line.startsWith('changelog-'));
 
           if (awaitingReview || awaitingAuthor || wip) {
             await github.rest.issues.removeLabel({ owner, repo, issue_number, name: 'awaiting-review' }).catch(() => {});
@@ -47,3 +49,19 @@ jobs:
           if (releaseCI) {
             await github.rest.issues.addLabels({ owner, repo, issue_number, labels: ['release-ci'] });
           }
+
+          if (changelogMatch) {
+            const changelogLabel = changelogMatch.trim();
+            const { data: existingLabels } = await github.rest.issues.listLabelsOnIssue({ owner, repo, issue_number });
+            const changelogLabels = existingLabels.filter(label => label.name.startsWith('changelog-'));
+
+            // Remove all other changelog labels
+            for (const label of changelogLabels) {
+              if (label.name !== changelogLabel) {
+                await github.rest.issues.removeLabel({ owner, repo, issue_number, name: label.name }).catch(() => {});
+              }
+            }
+
+            // Add the new changelog label
+            await github.rest.issues.addLabels({ owner, repo, issue_number, labels: [changelogLabel] });
+          }

doc/dev/bootstrap.md

@@ -103,10 +103,21 @@ your PR using rebase merge, bypassing the merge queue.
 As written above, changes in meta code in the current stage usually will only
 affect later stages. This is an issue in two specific cases.
 
+* For the special case of *quotations*, it is desirable to have changes in builtin parsers affect them immediately: when the changes in the parser become active in the next stage, builtin macros implemented via quotations should generate syntax trees compatible with the new parser, and quotation patterns in builtin macros and elaborators should be able to match syntax created by the new parser and macros.
+  Since quotations capture the syntax tree structure during execution of the current stage and turn it into code for the next stage, we need to run the current stage's builtin parsers in quotations via the interpreter for this to work.
+  Caveats:
+  * We activate this behavior by default when building stage 1 by setting `-Dinternal.parseQuotWithCurrentStage=true`.
+    We force-disable it inside `macro/macro_rules/elab/elab_rules` via `suppressInsideQuot` as they are guaranteed not to run in the next stage and may need to be run in the current one, so the stage 0 parser is the correct one to use for them.
+    It may be necessary to extend this disabling to functions that contain quotations and are (exclusively) used by one of the mentioned commands. A function using quotations should never be used by both builtin and non-builtin macros/elaborators. Example: https://github.com/leanprover/lean4/blob/f70b7e5722da6101572869d87832494e2f8534b7/src/Lean/Elab/Tactic/Config.lean#L118-L122
+  * The parser needs to be reachable via an `import` statement, otherwise the version of the previous stage will silently be used.
+  * Only the parser code (`Parser.fn`) is affected; all metadata such as leading tokens is taken from the previous stage.
+
+  For an example, see https://github.com/leanprover/lean4/commit/f9dcbbddc48ccab22c7674ba20c5f409823b4cc1#diff-371387aed38bb02bf7761084fd9460e4168ae16d1ffe5de041b47d3ad2d22422R13
+
 * For *non-builtin* meta code such as `notation`s or `macro`s in
   `Notation.lean`, we expect changes to affect the current file and all later
   files of the same stage immediately, just like outside the stdlib. To ensure
-  this, we need to build the stage using `-Dinterpreter.prefer_native=false` -
+  this, we build stage 1 using `-Dinterpreter.prefer_native=false` -
   otherwise, when executing a macro, the interpreter would notice that there is
   already a native symbol available for this function and run it instead of the
   new IR, but the symbol is from the previous stage!
@@ -124,26 +135,11 @@ affect later stages. This is an issue in two specific cases.
   further stages (e.g. after an `update-stage0`) will then need to be compiled
   with the flag set to `false` again since they will expect the new signature.
 
-  For an example, see https://github.com/leanprover/lean4/commit/da4c46370d85add64ef7ca5e7cc4638b62823fbb.
+  When enabling `prefer_native`, we usually want to *disable* `parseQuotWithCurrentStage` as it would otherwise make quotations use the interpreter after all.
+  However, there is a specific case where we want to set both options to `true`: when we make changes to a non-builtin parser like `simp` that has a builtin elaborator, we cannot have the new parser be active outside of quotations in stage 1 as the builtin elaborator from stage 0 would not understand them; on the other hand, we need quotations in e.g. the builtin `simp` elaborator to produce the new syntax in the next stage.
+  As this issue usually affects only tactics, enabling `debug.byAsSorry` instead of `prefer_native` can be a simpler solution.
 
-* For the special case of *quotations*, it is desirable to have changes in
-  built-in parsers affect them immediately: when the changes in the parser
-  become active in the next stage, macros implemented via quotations should
-  generate syntax trees compatible with the new parser, and quotation patterns
-  in macro and elaborators should be able to match syntax created by the new
-  parser and macros. Since quotations capture the syntax tree structure during
-  execution of the current stage and turn it into code for the next stage, we
-  need to run the current stage's built-in parsers in quotation via the
-  interpreter for this to work. Caveats:
-  * Since interpreting full parsers is not nearly as cheap and we rarely change
-    built-in syntax, this needs to be opted in using `-Dinternal.parseQuotWithCurrentStage=true`.
-  * The parser needs to be reachable via an `import` statement, otherwise the
-    version of the previous stage will silently be used.
-  * Only the parser code (`Parser.fn`) is affected; all metadata such as leading
-    tokens is taken from the previous stage.
-
-  For an example, see https://github.com/leanprover/lean4/commit/f9dcbbddc48ccab22c7674ba20c5f409823b4cc1#diff-371387aed38bb02bf7761084fd9460e4168ae16d1ffe5de041b47d3ad2d22422
-  (from before the flag defaulted to `false`).
+  For a `prefer_native` example, see https://github.com/leanprover/lean4/commit/da4c46370d85add64ef7ca5e7cc4638b62823fbb.
 
 To modify either of these flags both for building and editing the stdlib, adjust
 the code in `stage0/src/stdlib_flags.h`. The flags will automatically be reset

doc/examples/interp.lean

@@ -12,17 +12,17 @@ Remark: this example is based on an example found in the Idris manual.
 Vectors
 --------
 
-A `Vector` is a list of size `n` whose elements belong to a type `α`.
+A `Vec` is a list of size `n` whose elements belong to a type `α`.
 -/
 
-inductive Vector (α : Type u) : Nat → Type u
-  | nil : Vector α 0
-  | cons : α → Vector α n → Vector α (n+1)
+inductive Vec (α : Type u) : Nat → Type u
+  | nil : Vec α 0
+  | cons : α → Vec α n → Vec α (n+1)
 
 /-!
-We can overload the `List.cons` notation `::` and use it to create `Vector`s.
+We can overload the `List.cons` notation `::` and use it to create `Vec`s.
 -/
-infix:67 " :: " => Vector.cons
+infix:67 " :: " => Vec.cons
 
 /-!
 Now, we define the types of our simple functional language.
@@ -50,11 +50,11 @@ the builtin instance for `Add Int` as the solution.
 /-!
 Expressions are indexed by the types of the local variables, and the type of the expression itself.
 -/
-inductive HasType : Fin n → Vector Ty n → Ty → Type where
+inductive HasType : Fin n → Vec Ty n → Ty → Type where
   | stop : HasType 0 (ty :: ctx) ty
   | pop  : HasType k ctx ty → HasType k.succ (u :: ctx) ty
 
-inductive Expr : Vector Ty n → Ty → Type where
+inductive Expr : Vec Ty n → Ty → Type where
   | var   : HasType i ctx ty → Expr ctx ty
   | val   : Int → Expr ctx Ty.int
   | lam   : Expr (a :: ctx) ty → Expr ctx (Ty.fn a ty)
@@ -102,8 +102,8 @@ indexed over the types in scope. Since an environment is just another form of li
 to the vector of local variable types, we overload again the notation `::` so that we can use the usual list syntax.
 Given a proof that a variable is defined in the context, we can then produce a value from the environment.
 -/
-inductive Env : Vector Ty n → Type where
-  | nil  : Env Vector.nil
+inductive Env : Vec Ty n → Type where
+  | nil  : Env Vec.nil
   | cons : Ty.interp a → Env ctx → Env (a :: ctx)
 
 infix:67 " :: " => Env.cons

doc/examples/tc.lean

@@ -82,9 +82,7 @@ theorem Expr.typeCheck_correct (h₁ : HasType e ty) (h₂ : e.typeCheck ≠ .un
 /-!
 Now, we prove that if `Expr.typeCheck e` returns `Maybe.unknown`, then forall `ty`, `HasType e ty` does not hold.
 The notation `e.typeCheck` is sugar for `Expr.typeCheck e`. Lean can infer this because we explicitly said that `e` has type `Expr`.
-The proof is by induction on `e` and case analysis. The tactic `rename_i` is used to rename "inaccessible" variables.
-We say a variable is inaccessible if it is introduced by a tactic (e.g., `cases`) or has been shadowed by another variable introduced
-by the user. Note that the tactic `simp [typeCheck]` is applied to all goal generated by the `induction` tactic, and closes
+The proof is by induction on `e` and case analysis. Note that the tactic `simp [typeCheck]` is applied to all goal generated by the `induction` tactic, and closes
 the cases corresponding to the constructors `Expr.nat` and `Expr.bool`.
 -/
 theorem Expr.typeCheck_complete {e : Expr} : e.typeCheck = .unknown → ¬ HasType e ty := by

src/CMakeLists.txt

@@ -51,6 +51,8 @@ option(LLVM               "LLVM"               OFF)
 option(USE_GITHASH        "GIT_HASH"           ON)
 # When ON we install LICENSE files to CMAKE_INSTALL_PREFIX
 option(INSTALL_LICENSE "INSTALL_LICENSE" ON)
+# When ON we install a copy of cadical
+option(INSTALL_CADICAL "Install a copy of cadical" ON)
 # When ON thread storage is automatically finalized, it assumes platform support pthreads.
 # This option is important when using Lean as library that is invoked from a different programming language (e.g., Haskell).
 option(AUTO_THREAD_FINALIZATION "AUTO_THREAD_FINALIZATION" ON)
@@ -616,7 +618,7 @@ else()
     OUTPUT_NAME leancpp)
 endif()
 
-if((${STAGE} GREATER 0) AND CADICAL)
+if((${STAGE} GREATER 0) AND CADICAL AND INSTALL_CADICAL)
   add_custom_target(copy-cadical
     COMMAND cmake -E copy_if_different "${CADICAL}" "${CMAKE_BINARY_DIR}/bin/cadical${CMAKE_EXECUTABLE_SUFFIX}")
   add_dependencies(leancpp copy-cadical)
@@ -738,7 +740,7 @@ file(COPY ${LEAN_SOURCE_DIR}/bin/leanmake DESTINATION ${CMAKE_BINARY_DIR}/bin)
 
 install(DIRECTORY "${CMAKE_BINARY_DIR}/bin/" USE_SOURCE_PERMISSIONS DESTINATION bin)
 
-if (${STAGE} GREATER 0 AND CADICAL)
+if (${STAGE} GREATER 0 AND CADICAL AND INSTALL_CADICAL)
   install(PROGRAMS "${CADICAL}" DESTINATION bin)
 endif()
 

src/Init/Data.lean

@@ -43,3 +43,4 @@ import Init.Data.Zero
 import Init.Data.NeZero
 import Init.Data.Function
 import Init.Data.RArray
+import Init.Data.Vector

src/Init/Data/Array.lean

@@ -19,3 +19,4 @@ import Init.Data.Array.GetLit
 import Init.Data.Array.MapIdx
 import Init.Data.Array.Set
 import Init.Data.Array.Monadic
+import Init.Data.Array.FinRange

src/Init/Data/Array/Attach.lean

@@ -10,12 +10,13 @@ import Init.Data.List.Attach
 
 namespace Array
 
-/-- `O(n)`. Partial map. If `f : Π a, P a → β` is a partial function defined on
-  `a : α` satisfying `P`, then `pmap f l h` is essentially the same as `map f l`
-  but is defined only when all members of `l` satisfy `P`, using the proof
-  to apply `f`.
+/--
+`O(n)`. Partial map. If `f : Π a, P a → β` is a partial function defined on
+`a : α` satisfying `P`, then `pmap f l h` is essentially the same as `map f l`
+but is defined only when all members of `l` satisfy `P`, using the proof
+to apply `f`.
 
-We replace this at runtime with a more efficient version via
+We replace this at runtime with a more efficient version via the `csimp` lemma `pmap_eq_pmapImpl`.
 -/
 def pmap {P : α → Prop} (f : ∀ a, P a → β) (l : Array α) (H : ∀ a ∈ l, P a) : Array β :=
   (l.toList.pmap f (fun a m => H a (mem_def.mpr m))).toArray
@@ -73,6 +74,17 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
   intro a m h₁ h₂
   congr
 
+@[simp] theorem pmap_empty {P : α → Prop} (f : ∀ a, P a → β) : pmap f #[] (by simp) = #[] := rfl
+
+@[simp] theorem pmap_push {P : α → Prop} (f : ∀ a, P a → β) (a : α) (l : Array α) (h : ∀ b ∈ l.push a, P b) :
+    pmap f (l.push a) h =
+      (pmap f l (fun a m => by simp at h; exact h a (.inl m))).push (f a (h a (by simp))) := by
+  simp [pmap]
+
+@[simp] theorem attach_empty : (#[] : Array α).attach = #[] := rfl
+
+@[simp] theorem attachWith_empty {P : α → Prop} (H : ∀ x ∈ #[], P x) : (#[] : Array α).attachWith P H = #[] := rfl
+
 @[simp] theorem _root_.List.attachWith_mem_toArray {l : List α} :
     l.attachWith (fun x => x ∈ l.toArray) (fun x h => by simpa using h) =
       l.attach.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
@@ -80,6 +92,353 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
   apply List.pmap_congr_left
   simp
 
+@[simp]
+theorem pmap_eq_map (p : α → Prop) (f : α → β) (l : Array α) (H) :
+    @pmap _ _ p (fun a _ => f a) l H = map f l := by
+  cases l; simp
+
+theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a, q a → β} (l : Array α) {H₁ H₂}
+    (h : ∀ a ∈ l, ∀ (h₁ h₂), f a h₁ = g a h₂) : pmap f l H₁ = pmap g l H₂ := by
+  cases l
+  simp only [mem_toArray] at h
+  simp only [List.pmap_toArray, mk.injEq]
+  rw [List.pmap_congr_left _ h]
+
+theorem map_pmap {p : α → Prop} (g : β → γ) (f : ∀ a, p a → β) (l H) :
+    map g (pmap f l H) = pmap (fun a h => g (f a h)) l H := by
+  cases l
+  simp [List.map_pmap]
+
+theorem pmap_map {p : β → Prop} (g : ∀ b, p b → γ) (f : α → β) (l H) :
+    pmap g (map f l) H = pmap (fun a h => g (f a) h) l fun _ h => H _ (mem_map_of_mem _ h) := by
+  cases l
+  simp [List.pmap_map]
+
+theorem attach_congr {l₁ l₂ : Array α} (h : l₁ = l₂) :
+    l₁.attach = l₂.attach.map (fun x => ⟨x.1, h ▸ x.2⟩) := by
+  subst h
+  simp
+
+theorem attachWith_congr {l₁ l₂ : Array α} (w : l₁ = l₂) {P : α → Prop} {H : ∀ x ∈ l₁, P x} :
+    l₁.attachWith P H = l₂.attachWith P fun _ h => H _ (w ▸ h) := by
+  subst w
+  simp
+
+@[simp] theorem attach_push {a : α} {l : Array α} :
+    (l.push a).attach =
+      (l.attach.map (fun ⟨x, h⟩ => ⟨x, mem_push_of_mem a h⟩)).push ⟨a, by simp⟩ := by
+  cases l
+  rw [attach_congr (List.push_toArray _ _)]
+  simp [Function.comp_def]
+
+@[simp] theorem attachWith_push {a : α} {l : Array α} {P : α → Prop} {H : ∀ x ∈ l.push a, P x} :
+    (l.push a).attachWith P H =
+      (l.attachWith P (fun x h => by simp at H; exact H x (.inl h))).push ⟨a, H a (by simp)⟩ := by
+  cases l
+  simp [attachWith_congr (List.push_toArray _ _)]
+
+theorem pmap_eq_map_attach {p : α → Prop} (f : ∀ a, p a → β) (l H) :
+    pmap f l H = l.attach.map fun x => f x.1 (H _ x.2) := by
+  cases l
+  simp [List.pmap_eq_map_attach]
+
+theorem attach_map_coe (l : Array α) (f : α → β) :
+    (l.attach.map fun (i : {i // i ∈ l}) => f i) = l.map f := by
+  cases l
+  simp [List.attach_map_coe]
+
+theorem attach_map_val (l : Array α) (f : α → β) : (l.attach.map fun i => f i.val) = l.map f :=
+  attach_map_coe _ _
+
+@[simp]
+theorem attach_map_subtype_val (l : Array α) : l.attach.map Subtype.val = l := by
+  cases l; simp
+
+theorem attachWith_map_coe {p : α → Prop} (f : α → β) (l : Array α) (H : ∀ a ∈ l, p a) :
+    ((l.attachWith p H).map fun (i : { i // p i}) => f i) = l.map f := by
+  cases l; simp
+
+theorem attachWith_map_val {p : α → Prop} (f : α → β) (l : Array α) (H : ∀ a ∈ l, p a) :
+    ((l.attachWith p H).map fun i => f i.val) = l.map f :=
+  attachWith_map_coe _ _ _
+
+@[simp]
+theorem attachWith_map_subtype_val {p : α → Prop} (l : Array α) (H : ∀ a ∈ l, p a) :
+    (l.attachWith p H).map Subtype.val = l := by
+  cases l; simp
+
+@[simp]
+theorem mem_attach (l : Array α) : ∀ x, x ∈ l.attach
+  | ⟨a, h⟩ => by
+    have := mem_map.1 (by rw [attach_map_subtype_val] <;> exact h)
+    rcases this with ⟨⟨_, _⟩, m, rfl⟩
+    exact m
+
+@[simp]
+theorem mem_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H b} :
+    b ∈ pmap f l H ↔ ∃ (a : _) (h : a ∈ l), f a (H a h) = b := by
+  simp only [pmap_eq_map_attach, mem_map, mem_attach, true_and, Subtype.exists, eq_comm]
+
+theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {l H} {a} (h : a ∈ l) :
+    f a (H a h) ∈ pmap f l H := by
+  rw [mem_pmap]
+  exact ⟨a, h, rfl⟩
+
+@[simp]
+theorem size_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H} : (pmap f l H).size = l.size := by
+  cases l; simp
+
+@[simp]
+theorem size_attach {L : Array α} : L.attach.size = L.size := by
+  cases L; simp
+
+@[simp]
+theorem size_attachWith {p : α → Prop} {l : Array α} {H} : (l.attachWith p H).size = l.size := by
+  cases l; simp
+
+@[simp]
+theorem pmap_eq_empty_iff {p : α → Prop} {f : ∀ a, p a → β} {l H} : pmap f l H = #[] ↔ l = #[] := by
+  cases l; simp
+
+theorem pmap_ne_empty_iff {P : α → Prop} (f : (a : α) → P a → β) {xs : Array α}
+    (H : ∀ (a : α), a ∈ xs → P a) : xs.pmap f H ≠ #[] ↔ xs ≠ #[] := by
+  cases xs; simp
+
+theorem pmap_eq_self {l : Array α} {p : α → Prop} (hp : ∀ (a : α), a ∈ l → p a)
+    (f : (a : α) → p a → α) : l.pmap f hp = l ↔ ∀ a (h : a ∈ l), f a (hp a h) = a := by
+  cases l; simp [List.pmap_eq_self]
+
+@[simp]
+theorem attach_eq_empty_iff {l : Array α} : l.attach = #[] ↔ l = #[] := by
+  cases l; simp
+
+theorem attach_ne_empty_iff {l : Array α} : l.attach ≠ #[] ↔ l ≠ #[] := by
+  cases l; simp
+
+@[simp]
+theorem attachWith_eq_empty_iff {l : Array α} {P : α → Prop} {H : ∀ a ∈ l, P a} :
+    l.attachWith P H = #[] ↔ l = #[] := by
+  cases l; simp
+
+theorem attachWith_ne_empty_iff {l : Array α} {P : α → Prop} {H : ∀ a ∈ l, P a} :
+    l.attachWith P H ≠ #[] ↔ l ≠ #[] := by
+  cases l; simp
+
+@[simp]
+theorem getElem?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : Array α} (h : ∀ a ∈ l, p a) (n : Nat) :
+    (pmap f l h)[n]? = Option.pmap f l[n]? fun x H => h x (mem_of_getElem? H) := by
+  cases l; simp
+
+@[simp]
+theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : Array α} (h : ∀ a ∈ l, p a) {n : Nat}
+    (hn : n < (pmap f l h).size) :
+    (pmap f l h)[n] =
+      f (l[n]'(@size_pmap _ _ p f l h ▸ hn))
+        (h _ (getElem_mem (@size_pmap _ _ p f l h ▸ hn))) := by
+  cases l; simp
+
+@[simp]
+theorem getElem?_attachWith {xs : Array α} {i : Nat} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
+    (xs.attachWith P H)[i]? = xs[i]?.pmap Subtype.mk (fun _ a => H _ (mem_of_getElem? a)) :=
+  getElem?_pmap ..
+
+@[simp]
+theorem getElem?_attach {xs : Array α} {i : Nat} :
+    xs.attach[i]? = xs[i]?.pmap Subtype.mk (fun _ a => mem_of_getElem? a) :=
+  getElem?_attachWith
+
+@[simp]
+theorem getElem_attachWith {xs : Array α} {P : α → Prop} {H : ∀ a ∈ xs, P a}
+    {i : Nat} (h : i < (xs.attachWith P H).size) :
+    (xs.attachWith P H)[i] = ⟨xs[i]'(by simpa using h), H _ (getElem_mem (by simpa using h))⟩ :=
+  getElem_pmap ..
+
+@[simp]
+theorem getElem_attach {xs : Array α} {i : Nat} (h : i < xs.attach.size) :
+    xs.attach[i] = ⟨xs[i]'(by simpa using h), getElem_mem (by simpa using h)⟩ :=
+  getElem_attachWith h
+
+theorem foldl_pmap (l : Array α) {P : α → Prop} (f : (a : α) → P a → β)
+  (H : ∀ (a : α), a ∈ l → P a) (g : γ → β → γ) (x : γ) :
+    (l.pmap f H).foldl g x = l.attach.foldl (fun acc a => g acc (f a.1 (H _ a.2))) x := by
+  rw [pmap_eq_map_attach, foldl_map]
+
+theorem foldr_pmap (l : Array α) {P : α → Prop} (f : (a : α) → P a → β)
+  (H : ∀ (a : α), a ∈ l → P a) (g : β → γ → γ) (x : γ) :
+    (l.pmap f H).foldr g x = l.attach.foldr (fun a acc => g (f a.1 (H _ a.2)) acc) x := by
+  rw [pmap_eq_map_attach, foldr_map]
+
+/--
+If we fold over `l.attach` with a function that ignores the membership predicate,
+we get the same results as folding over `l` directly.
+
+This is useful when we need to use `attach` to show termination.
+
+Unfortunately this can't be applied by `simp` because of the higher order unification problem,
+and even when rewriting we need to specify the function explicitly.
+See however `foldl_subtype` below.
+-/
+theorem foldl_attach (l : Array α) (f : β → α → β) (b : β) :
+    l.attach.foldl (fun acc t => f acc t.1) b = l.foldl f b := by
+  rcases l with ⟨l⟩
+  simp only [List.attach_toArray, List.attachWith_mem_toArray, List.map_attach, size_toArray,
+    List.length_pmap, List.foldl_toArray', mem_toArray, List.foldl_subtype]
+  congr
+  ext
+  simpa using fun a => List.mem_of_getElem? a
+
+/--
+If we fold over `l.attach` with a function that ignores the membership predicate,
+we get the same results as folding over `l` directly.
+
+This is useful when we need to use `attach` to show termination.
+
+Unfortunately this can't be applied by `simp` because of the higher order unification problem,
+and even when rewriting we need to specify the function explicitly.
+See however `foldr_subtype` below.
+-/
+theorem foldr_attach (l : Array α) (f : α → β → β) (b : β) :
+    l.attach.foldr (fun t acc => f t.1 acc) b = l.foldr f b := by
+  rcases l with ⟨l⟩
+  simp only [List.attach_toArray, List.attachWith_mem_toArray, List.map_attach, size_toArray,
+    List.length_pmap, List.foldr_toArray', mem_toArray, List.foldr_subtype]
+  congr
+  ext
+  simpa using fun a => List.mem_of_getElem? a
+
+theorem attach_map {l : Array α} (f : α → β) :
+    (l.map f).attach = l.attach.map (fun ⟨x, h⟩ => ⟨f x, mem_map_of_mem f h⟩) := by
+  cases l
+  ext <;> simp
+
+theorem attachWith_map {l : Array α} (f : α → β) {P : β → Prop} {H : ∀ (b : β), b ∈ l.map f → P b} :
+    (l.map f).attachWith P H = (l.attachWith (P ∘ f) (fun _ h => H _ (mem_map_of_mem f h))).map
+      fun ⟨x, h⟩ => ⟨f x, h⟩ := by
+  cases l
+  ext
+  · simp
+  · simp only [List.map_toArray, List.attachWith_toArray, List.getElem_toArray,
+      List.getElem_attachWith, List.getElem_map, Function.comp_apply]
+    erw [List.getElem_attachWith] -- Why is `erw` needed here?
+
+theorem map_attachWith {l : Array α} {P : α → Prop} {H : ∀ (a : α), a ∈ l → P a}
+    (f : { x // P x } → β) :
+    (l.attachWith P H).map f =
+      l.pmap (fun a (h : a ∈ l ∧ P a) => f ⟨a, H _ h.1⟩) (fun a h => ⟨h, H a h⟩) := by
+  cases l
+  ext <;> simp
+
+/-- See also `pmap_eq_map_attach` for writing `pmap` in terms of `map` and `attach`. -/
+theorem map_attach {l : Array α} (f : { x // x ∈ l } → β) :
+    l.attach.map f = l.pmap (fun a h => f ⟨a, h⟩) (fun _ => id) := by
+  cases l
+  ext <;> simp
+
+theorem attach_filterMap {l : Array α} {f : α → Option β} :
+    (l.filterMap f).attach = l.attach.filterMap
+      fun ⟨x, h⟩ => (f x).pbind (fun b m => some ⟨b, mem_filterMap.mpr ⟨x, h, m⟩⟩) := by
+  cases l
+  rw [attach_congr (List.filterMap_toArray f _)]
+  simp [List.attach_filterMap, List.map_filterMap, Function.comp_def]
+
+theorem attach_filter {l : Array α} (p : α → Bool) :
+    (l.filter p).attach = l.attach.filterMap
+      fun x => if w : p x.1 then some ⟨x.1, mem_filter.mpr ⟨x.2, w⟩⟩ else none := by
+  cases l
+  rw [attach_congr (List.filter_toArray p _)]
+  simp [List.attach_filter, List.map_filterMap, Function.comp_def]
+
+-- We are still missing here `attachWith_filterMap` and `attachWith_filter`.
+-- Also missing are `filterMap_attach`, `filter_attach`, `filterMap_attachWith` and `filter_attachWith`.
+
+theorem pmap_pmap {p : α → Prop} {q : β → Prop} (g : ∀ a, p a → β) (f : ∀ b, q b → γ) (l H₁ H₂) :
+    pmap f (pmap g l H₁) H₂ =
+      pmap (α := { x // x ∈ l }) (fun a h => f (g a h) (H₂ (g a h) (mem_pmap_of_mem a.2))) l.attach
+        (fun a _ => H₁ a a.2) := by
+  cases l
+  simp [List.pmap_pmap, List.pmap_map]
+
+@[simp] theorem pmap_append {p : ι → Prop} (f : ∀ a : ι, p a → α) (l₁ l₂ : Array ι)
+    (h : ∀ a ∈ l₁ ++ l₂, p a) :
+    (l₁ ++ l₂).pmap f h =
+      (l₁.pmap f fun a ha => h a (mem_append_left l₂ ha)) ++
+        l₂.pmap f fun a ha => h a (mem_append_right l₁ ha) := by
+  cases l₁
+  cases l₂
+  simp
+
+theorem pmap_append' {p : α → Prop} (f : ∀ a : α, p a → β) (l₁ l₂ : Array α)
+    (h₁ : ∀ a ∈ l₁, p a) (h₂ : ∀ a ∈ l₂, p a) :
+    ((l₁ ++ l₂).pmap f fun a ha => (mem_append.1 ha).elim (h₁ a) (h₂ a)) =
+      l₁.pmap f h₁ ++ l₂.pmap f h₂ :=
+  pmap_append f l₁ l₂ _
+
+@[simp] theorem attach_append (xs ys : Array α) :
+    (xs ++ ys).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_append_left ys h⟩) ++
+      ys.attach.map fun ⟨x, h⟩ => ⟨x, mem_append_right xs h⟩ := by
+  cases xs
+  cases ys
+  rw [attach_congr (List.append_toArray _ _)]
+  simp [List.attach_append, Function.comp_def]
+
+@[simp] theorem attachWith_append {P : α → Prop} {xs ys : Array α}
+    {H : ∀ (a : α), a ∈ xs ++ ys → P a} :
+    (xs ++ ys).attachWith P H = xs.attachWith P (fun a h => H a (mem_append_left ys h)) ++
+      ys.attachWith P (fun a h => H a (mem_append_right xs h)) := by
+  simp [attachWith, attach_append, map_pmap, pmap_append]
+
+@[simp] theorem pmap_reverse {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
+    (H : ∀ (a : α), a ∈ xs.reverse → P a) :
+    xs.reverse.pmap f H = (xs.pmap f (fun a h => H a (by simpa using h))).reverse := by
+  induction xs <;> simp_all
+
+theorem reverse_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
+    (H : ∀ (a : α), a ∈ xs → P a) :
+    (xs.pmap f H).reverse = xs.reverse.pmap f (fun a h => H a (by simpa using h)) := by
+  rw [pmap_reverse]
+
+@[simp] theorem attachWith_reverse {P : α → Prop} {xs : Array α}
+    {H : ∀ (a : α), a ∈ xs.reverse → P a} :
+    xs.reverse.attachWith P H =
+      (xs.attachWith P (fun a h => H a (by simpa using h))).reverse := by
+  cases xs
+  simp
+
+theorem reverse_attachWith {P : α → Prop} {xs : Array α}
+    {H : ∀ (a : α), a ∈ xs → P a} :
+    (xs.attachWith P H).reverse = (xs.reverse.attachWith P (fun a h => H a (by simpa using h))) := by
+  cases xs
+  simp
+
+@[simp] theorem attach_reverse (xs : Array α) :
+    xs.reverse.attach = xs.attach.reverse.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
+  cases xs
+  rw [attach_congr (List.reverse_toArray _)]
+  simp
+
+theorem reverse_attach (xs : Array α) :
+    xs.attach.reverse = xs.reverse.attach.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
+  cases xs
+  simp
+
+@[simp] theorem back?_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
+    (H : ∀ (a : α), a ∈ xs → P a) :
+    (xs.pmap f H).back? = xs.attach.back?.map fun ⟨a, m⟩ => f a (H a m) := by
+  cases xs
+  simp
+
+@[simp] theorem back?_attachWith {P : α → Prop} {xs : Array α}
+    {H : ∀ (a : α), a ∈ xs → P a} :
+    (xs.attachWith P H).back? = xs.back?.pbind (fun a h => some ⟨a, H _ (mem_of_back?_eq_some h)⟩) := by
+  cases xs
+  simp
+
+@[simp]
+theorem back?_attach {xs : Array α} :
+    xs.attach.back? = xs.back?.pbind fun a h => some ⟨a, mem_of_back?_eq_some h⟩ := by
+  cases xs
+  simp
+
 /-! ## unattach
 
 `Array.unattach` is the (one-sided) inverse of `Array.attach`. It is a synonym for `Array.map Subtype.val`.
@@ -128,6 +487,15 @@ def unattach {α : Type _} {p : α → Prop} (l : Array { x // p x }) := l.map (
   cases l
   simp
 
+@[simp] theorem getElem?_unattach {p : α → Prop} {l : Array { x // p x }} (i : Nat) :
+    l.unattach[i]? = l[i]?.map Subtype.val := by
+  simp [unattach]
+
+@[simp] theorem getElem_unattach
+    {p : α → Prop} {l : Array { x // p x }} (i : Nat) (h : i < l.unattach.size) :
+    l.unattach[i] = (l[i]'(by simpa using h)).1 := by
+  simp [unattach]
+
 /-! ### Recognizing higher order functions using a function that only depends on the value. -/
 
 /--

src/Init/Data/Array/Basic.lean

@@ -13,6 +13,7 @@ import Init.Data.ToString.Basic
 import Init.GetElem
 import Init.Data.List.ToArray
 import Init.Data.Array.Set
+
 universe u v w
 
 /-! ### Array literal syntax -/
@@ -165,15 +166,15 @@ This will perform the update destructively provided that `a` has a reference
 count of 1 when called.
 -/
 @[extern "lean_array_fswap"]
-def swap (a : Array α) (i j : @& Fin a.size) : Array α :=
+def swap (a : Array α) (i j : @& Nat) (hi : i < a.size := by get_elem_tactic) (hj : j < a.size := by get_elem_tactic) : Array α :=
   let v₁ := a[i]
   let v₂ := a[j]
   let a'  := a.set i v₂
-  a'.set j v₁ (Nat.lt_of_lt_of_eq j.isLt (size_set a i v₂ _).symm)
+  a'.set j v₁ (Nat.lt_of_lt_of_eq hj (size_set a i v₂ _).symm)
 
-@[simp] theorem size_swap (a : Array α) (i j : Fin a.size) : (a.swap i j).size = a.size := by
+@[simp] theorem size_swap (a : Array α) (i j : Nat) {hi hj} : (a.swap i j hi hj).size = a.size := by
   show ((a.set i a[j]).set j a[i]
-    (Nat.lt_of_lt_of_eq j.isLt (size_set a i a[j] _).symm)).size = a.size
+    (Nat.lt_of_lt_of_eq hj (size_set a i a[j] _).symm)).size = a.size
   rw [size_set, size_set]
 
 /--
@@ -183,12 +184,14 @@ This will perform the update destructively provided that `a` has a reference
 count of 1 when called.
 -/
 @[extern "lean_array_swap"]
-def swap! (a : Array α) (i j : @& Nat) : Array α :=
+def swapIfInBounds (a : Array α) (i j : @& Nat) : Array α :=
   if h₁ : i < a.size then
-  if h₂ : j < a.size then swap a ⟨i, h₁⟩ ⟨j, h₂⟩
+  if h₂ : j < a.size then swap a i j
   else a
   else a
 
+@[deprecated swapIfInBounds (since := "2024-11-24")] abbrev swap! := @swapIfInBounds
+
 /-! ### GetElem instance for `USize`, backed by `uget` -/
 
 instance : GetElem (Array α) USize α fun xs i => i.toNat < xs.size where
@@ -233,7 +236,7 @@ def ofFn {n} (f : Fin n → α) : Array α := go 0 (mkEmpty n) where
 
 /-- The array `#[0, 1, ..., n - 1]`. -/
 def range (n : Nat) : Array Nat :=
-  n.fold (flip Array.push) (mkEmpty n)
+  ofFn fun (i : Fin n) => i
 
 def singleton (v : α) : Array α :=
   mkArray 1 v
@@ -249,7 +252,7 @@ def get? (a : Array α) (i : Nat) : Option α :=
 def back? (a : Array α) : Option α :=
   a[a.size - 1]?
 
-@[inline] def swapAt (a : Array α) (i : Fin a.size) (v : α) : α × Array α :=
+@[inline] def swapAt (a : Array α) (i : Nat) (v : α) (hi : i < a.size := by get_elem_tactic) : α × Array α :=
   let e := a[i]
   let a := a.set i v
   (e, a)
@@ -257,7 +260,7 @@ def back? (a : Array α) : Option α :=
 @[inline]
 def swapAt! (a : Array α) (i : Nat) (v : α) : α × Array α :=
   if h : i < a.size then
-    swapAt a ⟨i, h⟩ v
+    swapAt a i v
   else
     have : Inhabited (α × Array α) := ⟨(v, a)⟩
     panic! ("index " ++ toString i ++ " out of bounds")
@@ -613,8 +616,15 @@ def findIdx? {α : Type u} (p : α → Bool) (as : Array α) : Option Nat :=
     decreasing_by simp_wf; decreasing_trivial_pre_omega
   loop 0
 
-def getIdx? [BEq α] (a : Array α) (v : α) : Option Nat :=
-  a.findIdx? fun a => a == v
+@[inline]
+def findFinIdx? {α : Type u} (p : α → Bool) (as : Array α) : Option (Fin as.size) :=
+  let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
+  loop (j : Nat) :=
+    if h : j < as.size then
+      if p as[j] then some ⟨j, h⟩ else loop (j + 1)
+    else none
+    decreasing_by simp_wf; decreasing_trivial_pre_omega
+  loop 0
 
 @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
 def indexOfAux [BEq α] (a : Array α) (v : α) (i : Nat) : Option (Fin a.size) :=
@@ -627,6 +637,10 @@ decreasing_by simp_wf; decreasing_trivial_pre_omega
 def indexOf? [BEq α] (a : Array α) (v : α) : Option (Fin a.size) :=
   indexOfAux a v 0
 
+@[deprecated indexOf? (since := "2024-11-20")]
+def getIdx? [BEq α] (a : Array α) (v : α) : Option Nat :=
+  a.findIdx? fun a => a == v
+
 @[inline]
 def any (as : Array α) (p : α → Bool) (start := 0) (stop := as.size) : Bool :=
   Id.run <| as.anyM p start stop
@@ -735,7 +749,7 @@ where
   loop (as : Array α) (i : Nat) (j : Fin as.size) :=
     if h : i < j then
       have := termination h
-      let as := as.swap ⟨i, Nat.lt_trans h j.2⟩ j
+      let as := as.swap i j (Nat.lt_trans h j.2)
       have : j-1 < as.size := by rw [size_swap]; exact Nat.lt_of_le_of_lt (Nat.pred_le _) j.2
       loop as (i+1) ⟨j-1, this⟩
     else
@@ -766,49 +780,63 @@ def takeWhile (p : α → Bool) (as : Array α) : Array α :=
     decreasing_by simp_wf; decreasing_trivial_pre_omega
   go 0 #[]
 
-/-- Remove the element at a given index from an array without bounds checks, using a `Fin` index.
+/--
+Remove the element at a given index from an array without a runtime bounds checks,
+using a `Nat` index and a tactic-provided bound.
 
-  This function takes worst case O(n) time because
-  it has to backshift all elements at positions greater than `i`.-/
+This function takes worst case O(n) time because
+it has to backshift all elements at positions greater than `i`.-/
 @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
-def feraseIdx (a : Array α) (i : Fin a.size) : Array α :=
-  if h : i.val + 1 < a.size then
-    let a' := a.swap ⟨i.val + 1, h⟩ i
-    let i' : Fin a'.size := ⟨i.val + 1, by simp [a', h]⟩
-    a'.feraseIdx i'
+def eraseIdx (a : Array α) (i : Nat) (h : i < a.size := by get_elem_tactic) : Array α :=
+  if h' : i + 1 < a.size then
+    let a' := a.swap (i + 1) i
+    a'.eraseIdx (i + 1) (by simp [a', h'])
   else
     a.pop
-termination_by a.size - i.val
-decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ i.isLt
+termination_by a.size - i
+decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ h
 
 -- This is required in `Lean.Data.PersistentHashMap`.
-@[simp] theorem size_feraseIdx (a : Array α) (i : Fin a.size) : (a.feraseIdx i).size = a.size - 1 := by
-  induction a, i using Array.feraseIdx.induct with
-  | @case1 a i h a' _ ih =>
-    unfold feraseIdx
-    simp [h, a', ih]
-  | case2 a i h =>
-    unfold feraseIdx
-    simp [h]
+@[simp] theorem size_eraseIdx (a : Array α) (i : Nat) (h) : (a.eraseIdx i h).size = a.size - 1 := by
+  induction a, i, h using Array.eraseIdx.induct with
+  | @case1 a i h h' a' ih =>
+    unfold eraseIdx
+    simp [h', a', ih]
+  | case2 a i h h' =>
+    unfold eraseIdx
+    simp [h']
 
 /-- Remove the element at a given index from an array, or do nothing if the index is out of bounds.
 
   This function takes worst case O(n) time because
   it has to backshift all elements at positions greater than `i`.-/
-def eraseIdx (a : Array α) (i : Nat) : Array α :=
-  if h : i < a.size then a.feraseIdx ⟨i, h⟩ else a
+def eraseIdxIfInBounds (a : Array α) (i : Nat) : Array α :=
+  if h : i < a.size then a.eraseIdx i h else a
+
+/-- Remove the element at a given index from an array, or panic if the index is out of bounds.
+
+This function takes worst case O(n) time because
+it has to backshift all elements at positions greater than `i`. -/
+def eraseIdx! (a : Array α) (i : Nat) : Array α :=
+  if h : i < a.size then a.eraseIdx i h else panic! "invalid index"
 
 def erase [BEq α] (as : Array α) (a : α) : Array α :=
   match as.indexOf? a with
   | none   => as
-  | some i => as.feraseIdx i
+  | some i => as.eraseIdx i
+
+/-- Erase the first element that satisfies the predicate `p`. -/
+def eraseP (as : Array α) (p : α → Bool) : Array α :=
+  match as.findIdx? p with
+  | none   => as
+  | some i => as.eraseIdxIfInBounds i
 
 /-- Insert element `a` at position `i`. -/
-@[inline] def insertAt (as : Array α) (i : Fin (as.size + 1)) (a : α) : Array α :=
+@[inline] def insertIdx (as : Array α) (i : Nat) (a : α) (_ : i ≤ as.size := by get_elem_tactic) : Array α :=
   let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
   loop (as : Array α) (j : Fin as.size) :=
-    if i.1 < j then
-      let j' := ⟨j-1, Nat.lt_of_le_of_lt (Nat.pred_le _) j.2⟩
+    if i < j then
+      let j' : Fin as.size := ⟨j-1, Nat.lt_of_le_of_lt (Nat.pred_le _) j.2⟩
       let as := as.swap j' j
       loop as ⟨j', by rw [size_swap]; exact j'.2⟩
     else
@@ -818,12 +846,23 @@ def erase [BEq α] (as : Array α) (a : α) : Array α :=
   let as := as.push a
   loop as ⟨j, size_push .. ▸ j.lt_succ_self⟩
 
+@[deprecated insertIdx (since := "2024-11-20")] abbrev insertAt := @insertIdx
+
 /-- Insert element `a` at position `i`. Panics if `i` is not `i ≤ as.size`. -/
-def insertAt! (as : Array α) (i : Nat) (a : α) : Array α :=
+def insertIdx! (as : Array α) (i : Nat) (a : α) : Array α :=
   if h : i ≤ as.size then
-    insertAt as ⟨i, Nat.lt_succ_of_le h⟩ a
+    insertIdx as i a
   else panic! "invalid index"
 
+@[deprecated insertIdx! (since := "2024-11-20")] abbrev insertAt! := @insertIdx!
+
+/-- Insert element `a` at position `i`, or do nothing if `as.size < i`. -/
+def insertIdxIfInBounds (as : Array α) (i : Nat) (a : α) : Array α :=
+  if h : i ≤ as.size then
+    insertIdx as i a
+  else
+    as
+
 @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
 def isPrefixOfAux [BEq α] (as bs : Array α) (hle : as.size ≤ bs.size) (i : Nat) : Bool :=
   if h : i < as.size then
@@ -847,12 +886,12 @@ def isPrefixOf [BEq α] (as bs : Array α) : Bool :=
     false
 
 @[semireducible, specialize] -- This is otherwise irreducible because it uses well-founded recursion.
-def zipWithAux (f : α → β → γ) (as : Array α) (bs : Array β) (i : Nat) (cs : Array γ) : Array γ :=
+def zipWithAux (as : Array α) (bs : Array β) (f : α → β → γ) (i : Nat) (cs : Array γ) : Array γ :=
   if h : i < as.size then
     let a := as[i]
     if h : i < bs.size then
       let b := bs[i]
-      zipWithAux f as bs (i+1) <| cs.push <| f a b
+      zipWithAux as bs f (i+1) <| cs.push <| f a b
     else
       cs
   else
@@ -860,11 +899,23 @@ def zipWithAux (f : α → β → γ) (as : Array α) (bs : Array β) (i : Nat)
 decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 @[inline] def zipWith (as : Array α) (bs : Array β) (f : α → β → γ) : Array γ :=
-  zipWithAux f as bs 0 #[]
+  zipWithAux as bs f 0 #[]
 
 def zip (as : Array α) (bs : Array β) : Array (α × β) :=
   zipWith as bs Prod.mk
 
+def zipWithAll (as : Array α) (bs : Array β) (f : Option α → Option β → γ) : Array γ :=
+  go as bs 0 #[]
+where go (as : Array α) (bs : Array β) (i : Nat) (cs : Array γ) :=
+  if i < max as.size bs.size then
+    let a := as[i]?
+    let b := bs[i]?
+    go as bs (i+1) (cs.push (f a b))
+  else
+    cs
+  termination_by max as.size bs.size - i
+  decreasing_by simp_wf; decreasing_trivial_pre_omega
+
 def unzip (as : Array (α × β)) : Array α × Array β :=
   as.foldl (init := (#[], #[])) fun (as, bs) (a, b) => (as.push a, bs.push b)
 

src/Init/Data/Array/BinSearch.lean

@@ -5,59 +5,64 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Init.Data.Array.Basic
+import Init.Omega
 universe u v
 
--- TODO: CLEANUP
-
 namespace Array
--- TODO: remove the [Inhabited α] parameters as soon as we have the tactic framework for automating proof generation and using Array.fget
--- TODO: remove `partial` using well-founded recursion
 
-@[specialize] partial def binSearchAux {α : Type u} {β : Type v} [Inhabited β] (lt : α → α → Bool) (found : Option α → β) (as : Array α) (k : α) : Nat → Nat → β
-  | lo, hi =>
-    if lo <= hi then
-      let _ := Inhabited.mk k
-      let m := (lo + hi)/2
-      let a := as.get! m
-      if lt a k then binSearchAux lt found as k (m+1) hi
-      else if lt k a then
-        if m == 0 then found none
-        else binSearchAux lt found as k lo (m-1)
-      else found (some a)
-    else found none
+@[specialize] def binSearchAux {α : Type u} {β : Type v} (lt : α → α → Bool) (found : Option α → β) (as : Array α) (k : α) :
+    (lo : Fin (as.size + 1)) → (hi : Fin as.size) → (lo.1 ≤ hi.1) → β
+  | lo, hi, h =>
+    let m := (lo.1 + hi.1)/2
+    let a := as[m]
+    if lt a k then
+      if h' : m + 1 ≤ hi.1 then
+        binSearchAux lt found as k ⟨m+1, by omega⟩ hi h'
+      else found none
+    else if lt k a then
+      if h' : m = 0 ∨ m - 1 < lo.1 then found none
+      else binSearchAux lt found as k lo ⟨m-1, by omega⟩ (by simp; omega)
+    else found (some a)
+termination_by lo hi => hi.1 - lo.1
 
 @[inline] def binSearch {α : Type} (as : Array α) (k : α) (lt : α → α → Bool) (lo := 0) (hi := as.size - 1) : Option α :=
-  if lo < as.size then
+  if h : lo < as.size then
     let hi := if hi < as.size then hi else as.size - 1
-    binSearchAux lt id as k lo hi
+    if w : lo ≤ hi then
+      binSearchAux lt id as k ⟨lo, by omega⟩ ⟨hi, by simp [hi]; split <;> omega⟩ (by simp [hi]; omega)
+    else
+      none
   else
     none
 
 @[inline] def binSearchContains {α : Type} (as : Array α) (k : α) (lt : α → α → Bool) (lo := 0) (hi := as.size - 1) : Bool :=
-  if lo < as.size then
+  if h : lo < as.size then
     let hi := if hi < as.size then hi else as.size - 1
-    binSearchAux lt Option.isSome as k lo hi
+    if w : lo ≤ hi then
+      binSearchAux lt Option.isSome as k ⟨lo, by omega⟩ ⟨hi, by simp [hi]; split <;> omega⟩ (by simp [hi]; omega)
+    else
+      false
   else
     false
 
-@[specialize] private partial def binInsertAux {α : Type u} {m : Type u → Type v} [Monad m]
+@[specialize] private def binInsertAux {α : Type u} {m : Type u → Type v} [Monad m]
     (lt : α → α → Bool)
     (merge : α → m α)
     (add : Unit → m α)
     (as : Array α)
-    (k : α) : Nat → Nat → m (Array α)
-  | lo, hi =>
-    let _ := Inhabited.mk k
-    -- as[lo] < k < as[hi]
-    let mid    := (lo + hi)/2
-    let midVal := as.get! mid
-    if lt midVal k then
-      if mid == lo then do let v ← add (); pure <| as.insertAt! (lo+1) v
-      else binInsertAux lt merge add as k mid hi
-    else if lt k midVal then
-      binInsertAux lt merge add as k lo mid
+    (k : α) : (lo : Fin as.size) → (hi : Fin as.size) → (lo.1 ≤ hi.1) → (lt as[lo] k) → m (Array α)
+  | lo, hi, h, w =>
+    let mid    := (lo.1 + hi.1)/2
+    let midVal := as[mid]
+    if w₁ : lt midVal k then
+      if h' : mid = lo then do let v ← add (); pure <| as.insertIdx (lo+1) v
+      else binInsertAux lt merge add as k ⟨mid, by omega⟩ hi (by simp; omega) w₁
+    else if w₂ : lt k midVal then
+      have : mid ≠ lo := fun z => by simp [midVal, z] at w₁; simp_all
+      binInsertAux lt merge add as k lo ⟨mid, by omega⟩ (by simp; omega) w
     else do
       as.modifyM mid <| fun v => merge v
+termination_by lo hi => hi.1 - lo.1
 
 @[specialize] def binInsertM {α : Type u} {m : Type u → Type v} [Monad m]
     (lt : α → α → Bool)
@@ -65,13 +70,12 @@ namespace Array
     (add : Unit → m α)
     (as : Array α)
     (k : α) : m (Array α) :=
-  let _ := Inhabited.mk k
-  if as.isEmpty then do let v ← add (); pure <| as.push v
-  else if lt k (as.get! 0) then do let v ← add (); pure <| as.insertAt! 0 v
-  else if !lt (as.get! 0) k then as.modifyM 0 <| merge
-  else if lt as.back! k then do let v ← add (); pure <| as.push v
-  else if !lt k as.back! then as.modifyM (as.size - 1) <| merge
-  else binInsertAux lt merge add as k 0 (as.size - 1)
+  if h : as.size = 0 then do let v ← add (); pure <| as.push v
+  else if lt k as[0] then do let v ← add (); pure <| as.insertIdx 0 v
+  else if h' : !lt as[0] k then as.modifyM 0 <| merge
+  else if lt as[as.size - 1] k then do let v ← add (); pure <| as.push v
+  else if !lt k as[as.size - 1] then as.modifyM (as.size - 1) <| merge
+  else binInsertAux lt merge add as k ⟨0, by omega⟩ ⟨as.size - 1, by omega⟩ (by simp) (by simpa using h')
 
 @[inline] def binInsert {α : Type u} (lt : α → α → Bool) (as : Array α) (k : α) : Array α :=
   Id.run <| binInsertM lt (fun _ => k) (fun _ => k) as k

src/Init/Data/Array/Bootstrap.lean

@@ -23,7 +23,7 @@ theorem foldlM_toList.aux [Monad m]
   · cases Nat.not_le_of_gt ‹_› (Nat.zero_add _ ▸ H)
   · rename_i i; rw [Nat.succ_add] at H
     simp [foldlM_toList.aux f arr i (j+1) H]
-    rw (occs := .pos [2]) [← List.getElem_cons_drop_succ_eq_drop ‹_›]
+    rw (occs := [2]) [← List.getElem_cons_drop_succ_eq_drop ‹_›]
     rfl
   · rw [List.drop_of_length_le (Nat.ge_of_not_lt ‹_›)]; rfl
 

src/Init/Data/Array/DecidableEq.lean

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

src/Init/Data/Array/FinRange.lean

@@ -0,0 +1,14 @@
+/-
+Copyright (c) 2024 François G. Dorais. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: François G. Dorais
+-/
+prelude
+import Init.Data.List.FinRange
+
+namespace Array
+
+/-- `finRange n` is the array of all elements of `Fin n` in order. -/
+protected def finRange (n : Nat) : Array (Fin n) := ofFn fun i => i
+
+end Array

src/Init/Data/Array/Find.lean

@@ -272,4 +272,10 @@ theorem find?_mkArray_eq_none {n : Nat} {a : α} {p : α → Bool} :
     ((mkArray n a).find? p).get h = a := by
   simp [mkArray_eq_toArray_replicate]
 
+theorem find?_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
+    (H : ∀ (a : α), a ∈ xs → P a) (p : β → Bool) :
+    (xs.pmap f H).find? p = (xs.attach.find? (fun ⟨a, m⟩ => p (f a (H a m)))).map fun ⟨a, m⟩ => f a (H a m) := by
+  simp only [pmap_eq_map_attach, find?_map]
+  rfl
+
 end Array

src/Init/Data/Array/InsertionSort.lean

@@ -5,24 +5,91 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Init.Data.Array.Basic
+import Init.Data.Nat.Fold
+import Init.Data.Vector.Lemmas
 
-@[inline] def Array.insertionSort (a : Array α) (lt : α → α → Bool) : Array α :=
-  traverse a 0 a.size
-where
-  @[specialize] traverse (a : Array α) (i : Nat) (fuel : Nat) : Array α :=
-    match fuel with
-    | 0      => a
-    | fuel+1 =>
-      if h : i < a.size then
-        traverse (swapLoop a i h) (i+1) fuel
-      else
-        a
-  @[specialize] swapLoop (a : Array α) (j : Nat) (h : j < a.size) : Array α :=
-    match (generalizing := false) he:j with -- using `generalizing` because we don't want to refine the type of `h`
-    | 0    => a
-    | j'+1 =>
-      have h' : j' < a.size := by subst j; exact Nat.lt_trans (Nat.lt_succ_self _) h
-      if lt a[j] a[j'] then
-        swapLoop (a.swap ⟨j, h⟩ ⟨j', h'⟩) j' (by rw [size_swap]; assumption; done)
-      else
-        a
+namespace Vector
+
+/-- Swap the `i`-th element repeatedly to the left, while the element to its left is not `lt` it. -/
+@[specialize, inline] def swapLeftWhileLT {n} (a : Vector α n) (i : Nat) (h : i < n)
+    (lt : α → α → Bool := by exact (· < ·)) : Vector α n :=
+  match h' : i with
+  | 0 => a
+  | i'+1 =>
+    if lt a[i] a[i'] then
+      swapLeftWhileLT (a.swap i' i) i' (by omega) lt
+    else
+      a
+
+end Vector
+
+open Vector
+namespace Array
+
+/-- Sort an array in place using insertion sort. -/
+@[inline] def insertionSort (a : Array α) (lt : α → α → Bool := by exact (· < ·)) : Array α :=
+  a.size.fold (init := ⟨a, rfl⟩) (fun i h acc => swapLeftWhileLT acc i h lt) |>.toArray
+
+/-- Insert an element into an array, after the last element which is not `lt` the inserted element. -/
+def orderedInsert (a : Array α) (x : α) (lt : α → α → Bool := by exact (· < ·)) : Array α :=
+ swapLeftWhileLT ⟨a.push x, rfl⟩ a.size (by simp) lt |>.toArray
+
+end Array
+
+/-! ### Verification -/
+
+namespace Vector
+
+theorem swapLeftWhileLT_push {n} (a : Vector α n) (x : α) (j : Nat) (h : j < n) :
+    swapLeftWhileLT (a.push x) j (by omega) lt = (swapLeftWhileLT a j h lt).push x := by
+  induction j generalizing a with
+  | zero => simp [swapLeftWhileLT]
+  | succ j ih =>
+    simp [swapLeftWhileLT]
+    split <;> rename_i h
+    · rw [Vector.getElem_push_lt (by omega), Vector.getElem_push_lt (by omega)] at h
+      rw [← Vector.push_swap, ih, if_pos h]
+    · rw [Vector.getElem_push_lt (by omega), Vector.getElem_push_lt (by omega)] at h
+      rw [if_neg h]
+
+theorem swapLeftWhileLT_cast {n m} (a : Vector α n) (j : Nat) (h : j < n) (h' : n = m) :
+    swapLeftWhileLT (a.cast h') j (by omega) lt = (swapLeftWhileLT a j h lt).cast h' := by
+  subst h'
+  simp
+
+end Vector
+
+namespace Array
+
+@[simp] theorem size_insertionSort (a : Array α) : (a.insertionSort lt).size = a.size := by
+  simp [insertionSort]
+
+private theorem insertionSort_push' (a : Array α) (x : α) :
+    (a.push x).insertionSort lt =
+      (swapLeftWhileLT ⟨(a.insertionSort lt).push x, rfl⟩ a.size (by simp) lt).toArray := by
+  rw [insertionSort, Nat.fold_congr (size_push a x), Nat.fold]
+  have : (a.size.fold (fun i h acc => swapLeftWhileLT acc i (by simp; omega) lt) ⟨a.push x, rfl⟩) =
+      ((a.size.fold (fun i h acc => swapLeftWhileLT acc i h lt) ⟨a, rfl⟩).push x).cast (by simp) := by
+    rw [Vector.eq_cast_iff]
+    simp only [Nat.fold_eq_finRange_foldl]
+    rw [← List.foldl_hom (fun a => (Vector.push x a)) _ (fun v ⟨i, h⟩ => swapLeftWhileLT v i (by omega) lt)]
+    rw [Vector.push_mk]
+    rw [← List.foldl_hom (Vector.cast _) _ (fun v ⟨i, h⟩ => swapLeftWhileLT v i (by omega) lt)]
+    · simp
+    · intro v i
+      simp only
+      rw [swapLeftWhileLT_cast]
+    · simp [swapLeftWhileLT_push]
+  rw [this]
+  simp only [Nat.lt_add_one, swapLeftWhileLT_cast, Vector.toArray_cast]
+  unfold insertionSort
+  simp only [Vector.push]
+  congr
+  all_goals simp
+
+theorem insertionSort_push (a : Array α) (x : α) :
+    (a.push x).insertionSort lt = (a.insertionSort lt).orderedInsert x lt := by
+  rw [insertionSort_push', orderedInsert]
+  simp
+
+end Array

src/Init/Data/Array/Lemmas.lean

@@ -23,6 +23,9 @@ import Init.TacticsExtra
 
 namespace Array
 
+@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l := by
+  simp [mem_def]
+
 @[simp] theorem getElem_mk {xs : List α} {i : Nat} (h : i < xs.length) : (Array.mk xs)[i] = xs[i] := rfl
 
 theorem getElem_eq_getElem_toList {a : Array α} (h : i < a.size) : a[i] = a.toList[i] := rfl
@@ -36,12 +39,21 @@ theorem getElem?_eq_getElem {a : Array α} {i : Nat} (h : i < a.size) : a[i]? =
   · rw [getElem?_neg a i h]
     simp_all
 
+@[simp] theorem none_eq_getElem?_iff {a : Array α} {i : Nat} : none = a[i]? ↔ a.size ≤ i := by
+  simp [eq_comm (a := none)]
+
 theorem getElem?_eq {a : Array α} {i : Nat} :
     a[i]? = if h : i < a.size then some a[i] else none := by
   split
   · simp_all [getElem?_eq_getElem]
   · simp_all
 
+theorem getElem?_eq_some_iff {a : Array α} : a[i]? = some b ↔ ∃ h : i < a.size, a[i] = b := by
+  simp [getElem?_eq]
+
+theorem some_eq_getElem?_iff {a : Array α} : some b = a[i]? ↔ ∃ h : i < a.size, a[i] = b := by
+  rw [eq_comm, getElem?_eq_some_iff]
+
 theorem getElem?_eq_getElem?_toList (a : Array α) (i : Nat) : a[i]? = a.toList[i]? := by
   rw [getElem?_eq]
   split <;> simp_all
@@ -66,6 +78,35 @@ theorem getElem_push (a : Array α) (x : α) (i : Nat) (h : i < (a.push x).size)
 @[deprecated getElem_push_lt (since := "2024-10-21")] abbrev get_push_lt := @getElem_push_lt
 @[deprecated getElem_push_eq (since := "2024-10-21")] abbrev get_push_eq := @getElem_push_eq
 
+@[simp] theorem mem_push {a : Array α} {x y : α} : x ∈ a.push y ↔ x ∈ a ∨ x = y := by
+  simp [mem_def]
+
+theorem mem_push_self {a : Array α} {x : α} : x ∈ a.push x :=
+  mem_push.2 (Or.inr rfl)
+
+theorem mem_push_of_mem {a : Array α} {x : α} (y : α) (h : x ∈ a) : x ∈ a.push y :=
+  mem_push.2 (Or.inl h)
+
+theorem getElem_of_mem {a} {l : Array α} (h : a ∈ l) : ∃ (n : Nat) (h : n < l.size), l[n]'h = a := by
+  cases l
+  simp [List.getElem_of_mem (by simpa using h)]
+
+theorem getElem?_of_mem {a} {l : Array α} (h : a ∈ l) : ∃ n : Nat, l[n]? = some a :=
+  let ⟨n, _, e⟩ := getElem_of_mem h; ⟨n, e ▸ getElem?_eq_getElem _⟩
+
+theorem mem_of_getElem? {l : Array α} {n : Nat} {a : α} (e : l[n]? = some a) : a ∈ l :=
+  let ⟨_, e⟩ := getElem?_eq_some_iff.1 e; e ▸ getElem_mem ..
+
+theorem mem_iff_getElem {a} {l : Array α} : a ∈ l ↔ ∃ (n : Nat) (h : n < l.size), l[n]'h = a :=
+  ⟨getElem_of_mem, fun ⟨_, _, e⟩ => e ▸ getElem_mem ..⟩
+
+theorem mem_iff_getElem? {a} {l : Array α} : a ∈ l ↔ ∃ n : Nat, l[n]? = some a := by
+  simp [getElem?_eq_some_iff, mem_iff_getElem]
+
+theorem forall_getElem {l : Array α} {p : α → Prop} :
+    (∀ (n : Nat) h, p (l[n]'h)) ↔ ∀ a, a ∈ l → p a := by
+  cases l; simp [List.forall_getElem]
+
 @[simp] theorem get!_eq_getElem! [Inhabited α] (a : Array α) (i : Nat) : a.get! i = a[i]! := by
   simp [getElem!_def, get!, getD]
   split <;> rename_i h
@@ -93,9 +134,6 @@ We prefer to pull `List.toArray` outwards.
     (a.toArrayAux b).size = b.size + a.length := by
   simp [size]
 
-@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l := by
-  simp [mem_def]
-
 @[simp] theorem push_toArray (l : List α) (a : α) : l.toArray.push a = (l ++ [a]).toArray := by
   apply ext'
   simp
@@ -305,8 +343,8 @@ theorem isPrefixOfAux_toArray_zero [BEq α] (l₁ l₂ : List α) (hle : l₁.le
         rw [ih]
         simp_all
 
-theorem zipWithAux_toArray_succ (f : α → β → γ) (as : List α) (bs : List β) (i : Nat) (cs : Array γ) :
-    zipWithAux f as.toArray bs.toArray (i + 1) cs = zipWithAux f as.tail.toArray bs.tail.toArray i cs := by
+theorem zipWithAux_toArray_succ (as : List α) (bs : List β) (f : α → β → γ) (i : Nat) (cs : Array γ) :
+    zipWithAux as.toArray bs.toArray f (i + 1) cs = zipWithAux as.tail.toArray bs.tail.toArray f i cs := by
   rw [zipWithAux]
   conv => rhs; rw [zipWithAux]
   simp only [size_toArray, getElem_toArray, length_tail, getElem_tail]
@@ -317,8 +355,8 @@ theorem zipWithAux_toArray_succ (f : α → β → γ) (as : List α) (bs : List
       rw [dif_neg (by omega)]
   · rw [dif_neg (by omega)]
 
-theorem zipWithAux_toArray_succ' (f : α → β → γ) (as : List α) (bs : List β) (i : Nat) (cs : Array γ) :
-    zipWithAux f as.toArray bs.toArray (i + 1) cs = zipWithAux f (as.drop (i+1)).toArray (bs.drop (i+1)).toArray 0 cs := by
+theorem zipWithAux_toArray_succ' (as : List α) (bs : List β) (f : α → β → γ) (i : Nat) (cs : Array γ) :
+    zipWithAux as.toArray bs.toArray f (i + 1) cs = zipWithAux (as.drop (i+1)).toArray (bs.drop (i+1)).toArray f 0 cs := by
   induction i generalizing as bs cs with
   | zero => simp [zipWithAux_toArray_succ]
   | succ i ih =>
@@ -326,7 +364,7 @@ theorem zipWithAux_toArray_succ' (f : α → β → γ) (as : List α) (bs : Lis
     simp
 
 theorem zipWithAux_toArray_zero (f : α → β → γ) (as : List α) (bs : List β) (cs : Array γ) :
-    zipWithAux f as.toArray bs.toArray 0 cs = cs ++ (List.zipWith f as bs).toArray := by
+    zipWithAux as.toArray bs.toArray f 0 cs = cs ++ (List.zipWith f as bs).toArray := by
   rw [Array.zipWithAux]
   match as, bs with
   | [], _ => simp
@@ -334,7 +372,7 @@ theorem zipWithAux_toArray_zero (f : α → β → γ) (as : List α) (bs : List
   | a :: as, b :: bs =>
     simp [zipWith_cons_cons, zipWithAux_toArray_succ', zipWithAux_toArray_zero, push_append_toArray]
 
-@[simp] theorem zipWith_toArray (f : α → β → γ) (as : List α) (bs : List β) :
+@[simp] theorem zipWith_toArray (as : List α) (bs : List β) (f : α → β → γ) :
     Array.zipWith as.toArray bs.toArray f = (List.zipWith f as bs).toArray := by
   rw [Array.zipWith]
   simp [zipWithAux_toArray_zero]
@@ -343,6 +381,44 @@ theorem zipWithAux_toArray_zero (f : α → β → γ) (as : List α) (bs : List
     Array.zip as.toArray bs.toArray = (List.zip as bs).toArray := by
   simp [Array.zip, zipWith_toArray, zip]
 
+theorem zipWithAll_go_toArray (as : List α) (bs : List β) (f : Option α → Option β → γ) (i : Nat) (cs : Array γ) :
+    zipWithAll.go f as.toArray bs.toArray i cs = cs ++ (List.zipWithAll f (as.drop i) (bs.drop i)).toArray := by
+  unfold zipWithAll.go
+  split <;> rename_i h
+  · rw [zipWithAll_go_toArray]
+    simp at h
+    simp only [getElem?_toArray, push_append_toArray]
+    if ha : i < as.length then
+      if hb : i < bs.length then
+        rw [List.drop_eq_getElem_cons ha, List.drop_eq_getElem_cons hb]
+        simp only [ha, hb, getElem?_eq_getElem, zipWithAll_cons_cons]
+      else
+        simp only [Nat.not_lt] at hb
+        rw [List.drop_eq_getElem_cons ha]
+        rw [(drop_eq_nil_iff (l := bs)).mpr (by omega), (drop_eq_nil_iff (l := bs)).mpr (by omega)]
+        simp only [zipWithAll_nil, map_drop, map_cons]
+        rw [getElem?_eq_getElem ha]
+        rw [getElem?_eq_none hb]
+    else
+      if hb : i < bs.length then
+        simp only [Nat.not_lt] at ha
+        rw [List.drop_eq_getElem_cons hb]
+        rw [(drop_eq_nil_iff (l := as)).mpr (by omega), (drop_eq_nil_iff (l := as)).mpr (by omega)]
+        simp only [nil_zipWithAll, map_drop, map_cons]
+        rw [getElem?_eq_getElem hb]
+        rw [getElem?_eq_none ha]
+      else
+        omega
+  · simp only [size_toArray, Nat.not_lt] at h
+    rw [drop_eq_nil_of_le (by omega), drop_eq_nil_of_le (by omega)]
+    simp
+  termination_by max as.length bs.length - i
+  decreasing_by simp_wf; decreasing_trivial_pre_omega
+
+@[simp] theorem zipWithAll_toArray (f : Option α → Option β → γ) (as : List α) (bs : List β) :
+    Array.zipWithAll as.toArray bs.toArray f = (List.zipWithAll f as bs).toArray := by
+  simp [Array.zipWithAll, zipWithAll_go_toArray]
+
 end List
 
 namespace Array
@@ -420,6 +496,11 @@ where
   simp only [← length_toList]
   simp
 
+@[simp] theorem mapM_empty [Monad m] (f : α → m β) : mapM f #[] = pure #[] := by
+  rw [mapM, mapM.map]; rfl
+
+@[simp] theorem map_empty (f : α → β) : map f #[] = #[] := mapM_empty f
+
 @[simp] theorem appendList_nil (arr : Array α) : arr ++ ([] : List α) = arr := Array.ext' (by simp)
 
 @[simp] theorem appendList_cons (arr : Array α) (a : α) (l : List α) :
@@ -475,10 +556,10 @@ theorem getElem?_len_le (a : Array α) {i : Nat} (h : a.size ≤ i) : a[i]? = no
 theorem getD_get? (a : Array α) (i : Nat) (d : α) :
   Option.getD a[i]? d = if p : i < a.size then a[i]'p else d := by
   if h : i < a.size then
-    simp [setD, h, getElem?_def]
+    simp [setIfInBounds, h, getElem?_def]
   else
     have p : i ≥ a.size := Nat.le_of_not_gt h
-    simp [setD, getElem?_len_le _ p, h]
+    simp [setIfInBounds, getElem?_len_le _ p, h]
 
 @[simp] theorem getD_eq_get? (a : Array α) (n d) : a.getD n d = (a[n]?).getD d := by
   simp only [getD, get_eq_getElem, get?_eq_getElem?]; split <;> simp [getD_get?, *]
@@ -514,31 +595,46 @@ theorem getElem_set (a : Array α) (i : Nat) (h' : i < a.size) (v : α) (j : Nat
     (ne : i ≠ j) : (a.set i v)[j]? = a[j]? := by
   by_cases h : j < a.size <;> simp [getElem?_lt, getElem?_ge, Nat.ge_of_not_lt, ne, h]
 
-/-! # setD -/
+theorem push_set (a : Array α) (x y : α) {i : Nat} {hi} :
+    (a.set i x).push y = (a.push y).set i x (by simp; omega):= by
+  ext j h₁ h₂
+  · simp
+  · if h' : j = a.size then
+      rw [getElem_push, getElem_set_ne, dif_neg]
+      all_goals simp_all <;> omega
+    else
+      rw [getElem_push_lt, getElem_set, getElem_set]
+      split
+      · rfl
+      · rw [getElem_push_lt]
+      simp_all; omega
 
-@[simp] theorem set!_is_setD : @set! = @setD := rfl
+/-! # setIfInBounds -/
 
-@[simp] theorem size_setD (a : Array α) (index : Nat) (val : α) :
-    (Array.setD a index val).size = a.size := by
+@[simp] theorem set!_is_setIfInBounds : @set! = @setIfInBounds := rfl
+
+@[simp] theorem size_setIfInBounds (a : Array α) (index : Nat) (val : α) :
+    (Array.setIfInBounds a index val).size = a.size := by
   if h : index < a.size  then
-    simp [setD, h]
+    simp [setIfInBounds, h]
   else
-    simp [setD, h]
+    simp [setIfInBounds, h]
 
-@[simp] theorem getElem_setD_eq (a : Array α) {i : Nat} (v : α) (h : _) :
-    (setD a i v)[i]'h = v := by
+@[simp] theorem getElem_setIfInBounds_eq (a : Array α) {i : Nat} (v : α) (h : _) :
+    (setIfInBounds a i v)[i]'h = v := by
   simp at h
-  simp only [setD, h, ↓reduceDIte, getElem_set_eq]
+  simp only [setIfInBounds, h, ↓reduceDIte, getElem_set_eq]
 
 @[simp]
-theorem getElem?_setD_eq (a : Array α) {i : Nat} (p : i < a.size) (v : α) : (a.setD i v)[i]? = some v := by
+theorem getElem?_setIfInBounds_eq (a : Array α) {i : Nat} (p : i < a.size) (v : α) :
+    (a.setIfInBounds i v)[i]? = some v := by
   simp [getElem?_lt, p]
 
 /-- 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
+@[simp] theorem getD_get?_setIfInBounds (a : Array α) (i : Nat) (v d : α) :
+    Option.getD (setIfInBounds 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?]
+    simp [setIfInBounds, Nat.not_lt_of_le, h,  getD_get?]
 
 /-! # ofFn -/
 
@@ -583,7 +679,20 @@ theorem getElem?_ofFn (f : Fin n → α) (i : Nat) :
     (ofFn f)[i]? = if h : i < n then some (f ⟨i, h⟩) else none := by
   simp [getElem?_def]
 
-/-- # mkArray -/
+@[simp] theorem ofFn_zero (f : Fin 0 → α) : ofFn f = #[] := rfl
+
+theorem ofFn_succ (f : Fin (n+1) → α) :
+    ofFn f = (ofFn (fun (i : Fin n) => f i.castSucc)).push (f ⟨n, by omega⟩) := by
+  ext i h₁ h₂
+  · simp
+  · simp [getElem_push]
+    split <;> rename_i h₃
+    · rfl
+    · congr
+      simp at h₁ h₂
+      omega
+
+/-! # mkArray -/
 
 @[simp] theorem size_mkArray (n : Nat) (v : α) : (mkArray n v).size = n :=
   List.length_replicate ..
@@ -599,25 +708,12 @@ theorem getElem?_mkArray (n : Nat) (v : α) (i : Nat) :
     (mkArray n v)[i]? = if i < n then some v else none := by
   simp [getElem?_def]
 
-/-- # mem -/
+/-! # mem -/
 
 @[simp] theorem mem_toList {a : α} {l : Array α} : a ∈ l.toList ↔ a ∈ l := mem_def.symm
 
 theorem not_mem_nil (a : α) : ¬ a ∈ #[] := nofun
 
-theorem getElem_of_mem {a : α} {as : Array α} :
-    a ∈ as → (∃ (n : Nat) (h : n < as.size), as[n]'h = a) := by
-  intro ha
-  rcases List.getElem_of_mem ha.val with ⟨i, hbound, hi⟩
-  exists i
-  exists hbound
-
-theorem getElem?_of_mem {a : α} {as : Array α} :
-    a ∈ as → ∃ (n : Nat), as[n]? = some a := by
-  intro ha
-  rcases List.getElem?_of_mem ha.val with ⟨i, hi⟩
-  exists i
-
 @[simp] theorem mem_dite_empty_left {x : α} [Decidable p] {l : ¬ p → Array α} :
     (x ∈ if h : p then #[] else l h) ↔ ∃ h : ¬ p, x ∈ l h := by
   split <;> simp_all
@@ -634,7 +730,7 @@ theorem getElem?_of_mem {a : α} {as : Array α} :
     (x ∈ if p then l else #[]) ↔ p ∧ x ∈ l := by
   split <;> simp_all
 
-/-- # get lemmas -/
+/-! # get lemmas -/
 
 theorem lt_of_getElem {x : α} {a : Array α} {idx : Nat} {hidx : idx < a.size} (_ : a[idx] = x) :
     idx < a.size :=
@@ -659,10 +755,6 @@ theorem get?_eq_get?_toList (a : Array α) (i : Nat) : a.get? i = a.toList.get?
 theorem get!_eq_get? [Inhabited α] (a : Array α) : a.get! n = (a.get? n).getD default := by
   simp only [get!_eq_getElem?, get?_eq_getElem?]
 
-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]
-
 theorem back!_eq_back? [Inhabited α] (a : Array α) : a.back! = a.back?.getD default := by
   simp only [back!, get!_eq_getElem?, get?_eq_getElem?, back?]
 
@@ -672,6 +764,10 @@ theorem back!_eq_back? [Inhabited α] (a : Array α) : a.back! = a.back?.getD de
 @[simp] theorem back!_push [Inhabited α] (a : Array α) : (a.push x).back! = x := by
   simp [back!_eq_back?]
 
+theorem mem_of_back?_eq_some {xs : Array α} {a : α} (h : xs.back? = some a) : a ∈ xs := by
+  cases xs
+  simpa using List.mem_of_getLast?_eq_some (by simpa using h)
+
 theorem getElem?_push_lt (a : Array α) (x : α) (i : Nat) (h : i < a.size) :
     (a.push x)[i]? = some a[i] := by
   rw [getElem?_pos, getElem_push_lt]
@@ -730,32 +826,32 @@ theorem get_set (a : Array α) (i : Nat) (hi : i < a.size) (j : Nat) (hj : j < a
     (h : i ≠ j) : (a.set i v)[j]'(by simp [*]) = a[j] := by
   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
+theorem getElem_setIfInBounds (a : Array α) (i : Nat) (v : α) (h : i < (setIfInBounds a i v).size) :
+    (setIfInBounds a i v)[i] = v := by
   simp at h
-  simp only [setD, h, ↓reduceDIte, getElem_set_eq]
+  simp only [setIfInBounds, h, ↓reduceDIte, getElem_set_eq]
 
 theorem set_set (a : Array α) (i : Nat) (h) (v v' : α) :
     (a.set i v h).set i v' (by simp [h]) = a.set i v' := by simp [set, List.set_set]
 
 private theorem fin_cast_val (e : n = n') (i : Fin n) : e ▸ i = ⟨i.1, e ▸ i.2⟩ := by cases e; rfl
 
-theorem swap_def (a : Array α) (i j : Fin a.size) :
-    a.swap i j = (a.set i a[j]).set j a[i] := by
+theorem swap_def (a : Array α) (i j : Nat) (hi hj) :
+    a.swap i j hi hj = (a.set i a[j]).set j a[i] (by simpa using hj) := by
   simp [swap, fin_cast_val]
 
-@[simp] theorem toList_swap (a : Array α) (i j : Fin a.size) :
-    (a.swap i j).toList = (a.toList.set i a[j]).set j a[i] := by simp [swap_def]
+@[simp] theorem toList_swap (a : Array α) (i j : Nat) (hi hj) :
+    (a.swap i j hi hj).toList = (a.toList.set i a[j]).set j a[i] := by simp [swap_def]
 
-theorem getElem?_swap (a : Array α) (i j : Fin a.size) (k : Nat) : (a.swap i j)[k]? =
-    if j = k then some a[i.1] else if i = k then some a[j.1] else a[k]? := by
+theorem getElem?_swap (a : Array α) (i j : Nat) (hi hj) (k : Nat) : (a.swap i j hi hj)[k]? =
+    if j = k then some a[i] else if i = k then some a[j] else a[k]? := by
   simp [swap_def, get?_set, ← getElem_fin_eq_getElem_toList]
 
-@[simp] theorem swapAt_def (a : Array α) (i : Fin a.size) (v : α) :
-    a.swapAt i v = (a[i.1], a.set i v) := rfl
+@[simp] theorem swapAt_def (a : Array α) (i : Nat) (v : α) (hi) :
+    a.swapAt i v hi = (a[i], a.set i v) := rfl
 
-@[simp] theorem size_swapAt (a : Array α) (i : Fin a.size) (v : α) :
-    (a.swapAt i v).2.size = a.size := by simp [swapAt_def]
+@[simp] theorem size_swapAt (a : Array α) (i : Nat) (v : α) (hi) :
+    (a.swapAt i v hi).2.size = a.size := by simp [swapAt_def]
 
 @[simp]
 theorem swapAt!_def (a : Array α) (i : Nat) (v : α) (h : i < a.size) :
@@ -802,8 +898,10 @@ theorem eq_push_of_size_ne_zero {as : Array α} (h : as.size ≠ 0) :
 
 theorem size_eq_length_toList (as : Array α) : as.size = as.toList.length := rfl
 
-@[simp] theorem size_swap! (a : Array α) (i j) :
-    (a.swap! i j).size = a.size := by unfold swap!; split <;> (try split) <;> simp [size_swap]
+@[simp] theorem size_swapIfInBounds (a : Array α) (i j) :
+    (a.swapIfInBounds i j).size = a.size := by unfold swapIfInBounds; split <;> (try split) <;> simp [size_swap]
+
+@[deprecated size_swapIfInBounds (since := "2024-11-24")] abbrev size_swap! := @size_swapIfInBounds
 
 @[simp] theorem size_reverse (a : Array α) : a.reverse.size = a.size := by
   let rec go (as : Array α) (i j) : (reverse.loop as i j).size = as.size := by
@@ -815,16 +913,10 @@ theorem size_eq_length_toList (as : Array α) : as.size = as.toList.length := rf
   simp only [reverse]; split <;> simp [go]
 
 @[simp] theorem size_range {n : Nat} : (range n).size = n := by
-  unfold range
-  induction n with
-  | zero      => simp [Nat.fold]
-  | succ k ih =>
-    rw [Nat.fold, flip]
-    simp only [mkEmpty_eq, size_push] at *
-    omega
+  induction n <;> simp [range]
 
 @[simp] theorem toList_range (n : Nat) : (range n).toList = List.range n := by
-  induction n <;> simp_all [range, Nat.fold, flip, List.range_succ]
+  apply List.ext_getElem <;> simp [range]
 
 @[simp]
 theorem getElem_range {n : Nat} {x : Nat} (h : x < (Array.range n).size) : (Array.range n)[x] = x := by
@@ -1020,11 +1112,43 @@ theorem foldr_congr {as bs : Array α} (h₀ : as = bs) {f g : α → β → β}
     as.foldr f a start stop = bs.foldr g b start' stop' := by
   congr
 
+theorem foldl_eq_foldlM (f : β → α → β) (b) (l : Array α) :
+    l.foldl f b = l.foldlM (m := Id) f b := by
+  cases l
+  simp [List.foldl_eq_foldlM]
+
+theorem foldr_eq_foldrM (f : α → β → β) (b) (l : Array α) :
+    l.foldr f b = l.foldrM (m := Id) f b := by
+  cases l
+  simp [List.foldr_eq_foldrM]
+
+@[simp] theorem id_run_foldlM (f : β → α → Id β) (b) (l : Array α) :
+    Id.run (l.foldlM f b) = l.foldl f b := (foldl_eq_foldlM f b l).symm
+
+@[simp] theorem id_run_foldrM (f : α → β → Id β) (b) (l : Array α) :
+    Id.run (l.foldrM f b) = l.foldr f b := (foldr_eq_foldrM f b l).symm
+
+theorem foldl_hom (f : α₁ → α₂) (g₁ : α₁ → β → α₁) (g₂ : α₂ → β → α₂) (l : Array 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
+  cases l
+  simp
+  rw [List.foldl_hom _ _ _ _ _ H]
+
+theorem foldr_hom (f : β₁ → β₂) (g₁ : α → β₁ → β₁) (g₂ : α → β₂ → β₂) (l : Array α) (init : β₁)
+    (H : ∀ x y, g₂ x (f y) = f (g₁ x y)) : l.foldr g₂ (f init) = f (l.foldr g₁ init) := by
+  cases l
+  simp
+  rw [List.foldr_hom _ _ _ _ _ H]
+
 /-! ### 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, toList_map, List.mem_map]
 
+theorem exists_of_mem_map (h : b ∈ map f l) : ∃ a, a ∈ l ∧ f a = b := mem_map.1 h
+
+theorem mem_map_of_mem (f : α → β) (h : a ∈ l) : f a ∈ map f l := mem_map.2 ⟨_, h, rfl⟩
+
 theorem mapM_eq_mapM_toList [Monad m] [LawfulMonad m] (f : α → m β) (arr : Array α) :
     arr.mapM f = List.toArray <$> (arr.toList.mapM f) := by
   rw [mapM_eq_foldlM, ← foldlM_toList, ← List.foldrM_reverse]
@@ -1215,6 +1339,12 @@ theorem push_eq_append_singleton (as : Array α) (x) : as.push x = as ++ #[x] :=
 @[simp] theorem mem_append {a : α} {s t : Array α} : a ∈ s ++ t ↔ a ∈ s ∨ a ∈ t := by
   simp only [mem_def, toList_append, List.mem_append]
 
+theorem mem_append_left {a : α} {l₁ : Array α} (l₂ : Array α) (h : a ∈ l₁) : a ∈ l₁ ++ l₂ :=
+  mem_append.2 (Or.inl h)
+
+theorem mem_append_right {a : α} (l₁ : Array α) {l₂ : Array α} (h : a ∈ l₂) : a ∈ l₁ ++ l₂ :=
+  mem_append.2 (Or.inr h)
+
 @[simp] theorem size_append (as bs : Array α) : (as ++ bs).size = as.size + bs.size := by
   simp only [size, toList_append, List.length_append]
 
@@ -1561,28 +1691,30 @@ instance [DecidableEq α] (a : α) (as : Array α) : Decidable (a ∈ as) :=
 
 open Fin
 
-@[simp] theorem getElem_swap_right (a : Array α) {i j : Fin a.size} : (a.swap i j)[j.1] = a[i] := by
+@[simp] theorem getElem_swap_right (a : Array α) {i j : Nat} {hi hj} :
+    (a.swap i j hi hj)[j]'(by simpa using hj) = a[i] := by
   simp [swap_def, getElem_set]
 
-@[simp] theorem getElem_swap_left (a : Array α) {i j : Fin a.size} : (a.swap i j)[i.1] = a[j] := by
+@[simp] theorem getElem_swap_left (a : Array α) {i j : Nat} {hi hj} :
+    (a.swap i j hi hj)[i]'(by simpa using hi) = a[j] := by
   simp +contextual [swap_def, getElem_set]
 
-@[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
-  simp [swap_def, getElem_set, hi.symm, hj.symm]
+@[simp] theorem getElem_swap_of_ne (a : Array α) {i j : Nat} {hi hj} (hp : p < a.size)
+    (hi' : p ≠ i) (hj' : p ≠ j) : (a.swap i j hi hj)[p]'(a.size_swap .. |>.symm ▸ hp) = a[p] := by
+  simp [swap_def, getElem_set, hi'.symm, hj'.symm]
 
-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
+theorem getElem_swap' (a : Array α) (i j : Nat) {hi hj} (k : Nat) (hk : k < a.size) :
+    (a.swap i j hi hj)[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 [getElem_swap_left]
   · split <;> simp_all
 
-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
+theorem getElem_swap (a : Array α) (i j : Nat) {hi hj}(k : Nat) (hk : k < (a.swap i j).size) :
+    (a.swap i j hi hj)[k] = if k = i then a[j] else if k = j then a[i] else a[k]'(by simp_all) := by
   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
+@[simp] theorem swap_swap (a : Array α) {i j : Nat} (hi hj) :
+    (a.swap i j hi hj).swap i j ((a.size_swap ..).symm ▸ hi) ((a.size_swap ..).symm ▸ hj) = a := by
   apply ext
   · simp only [size_swap]
   · intros
@@ -1591,7 +1723,7 @@ theorem getElem_swap (a : Array α) (i j : Fin a.size) (k : Nat) (hk : k < (a.sw
     · simp_all
     · split <;> simp_all
 
-theorem swap_comm (a : Array α) {i j : Fin a.size} : a.swap i j = a.swap j i := by
+theorem swap_comm (a : Array α) {i j : Nat} {hi hj} : a.swap i j hi hj = a.swap j i hj hi := by
   apply ext
   · simp only [size_swap]
   · intros
@@ -1600,11 +1732,16 @@ theorem swap_comm (a : Array α) {i j : Fin a.size} : a.swap i j = a.swap j i :=
     · split <;> simp_all
     · split <;> simp_all
 
+theorem push_swap (a : Array α) (x : α) {i j : Nat} {hi hj} :
+    (a.swap i j hi hj).push x = (a.push x).swap i j (by simp; omega) (by simp; omega) := by
+  rw [swap_def, swap_def]
+  simp [push_set, getElem_push_lt, hi, hj]
+
 /-! ### eraseIdx -/
 
-theorem feraseIdx_eq_eraseIdx {a : Array α} {i : Fin a.size} :
-    a.feraseIdx i = a.eraseIdx i.1 := by
-  simp [eraseIdx]
+theorem eraseIdx_eq_eraseIdxIfInBounds {a : Array α} {i : Nat} (h : i < a.size) :
+    a.eraseIdx i h = a.eraseIdxIfInBounds i := by
+  simp [eraseIdxIfInBounds, h]
 
 /-! ### isPrefixOf -/
 
@@ -1626,6 +1763,20 @@ theorem feraseIdx_eq_eraseIdx {a : Array α} {i : Fin a.size} :
     (Array.zip as bs).toList = List.zip as.toList bs.toList := by
   simp [zip, toList_zipWith, List.zip]
 
+@[simp] theorem toList_zipWithAll (f : Option α → Option β → γ) (as : Array α) (bs : Array β) :
+    (Array.zipWithAll as bs f).toList = List.zipWithAll f as.toList bs.toList := by
+  cases as
+  cases bs
+  simp
+
+@[simp] theorem size_zipWith (as : Array α) (bs : Array β) (f : α → β → γ) :
+    (as.zipWith bs f).size = min as.size bs.size := by
+  rw [size_eq_length_toList, toList_zipWith, List.length_zipWith]
+
+@[simp] theorem size_zip (as : Array α) (bs : Array β) :
+    (as.zip bs).size = min as.size bs.size :=
+  as.size_zipWith bs Prod.mk
+
 /-! ### findSomeM?, findM?, findSome?, find? -/
 
 @[simp] theorem findSomeM?_toList [Monad m] [LawfulMonad m] (p : α → m (Option β)) (as : Array α) :
@@ -1700,10 +1851,10 @@ Our goal is to have `simp` "pull `List.toArray` outwards" as much as possible.
   apply ext'
   simp
 
-@[simp] theorem setD_toArray (l : List α) (i : Nat) (a : α) :
-    l.toArray.setD i a  = (l.set i a).toArray := by
+@[simp] theorem setIfInBounds_toArray (l : List α) (i : Nat) (a : α) :
+    l.toArray.setIfInBounds i a  = (l.set i a).toArray := by
   apply ext'
-  simp only [setD]
+  simp only [setIfInBounds]
   split
   · simp
   · simp_all [List.set_eq_of_length_le]
@@ -1748,8 +1899,8 @@ theorem all_toArray (p : α → Bool) (l : List α) : l.toArray.all p = l.all p
   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
+@[simp] theorem swap_toArray (l : List α) (i j : Nat) {hi hj}:
+    l.toArray.swap i j hi hj = ((l.set i l[j]).set j l[i]).toArray := by
   apply ext'
   simp
 
@@ -1834,16 +1985,15 @@ theorem takeWhile_go_toArray (p : α → Bool) (l : List α) (i : Nat) :
     l.toArray.takeWhile p = (l.takeWhile p).toArray := by
   simp [Array.takeWhile, takeWhile_go_toArray]
 
-@[simp] theorem feraseIdx_toArray (l : List α) (i : Fin l.toArray.size) :
-    l.toArray.feraseIdx i = (l.eraseIdx i).toArray := by
-  rw [feraseIdx]
-  split <;> rename_i h
-  · rw [feraseIdx_toArray]
+@[simp] theorem eraseIdx_toArray (l : List α) (i : Nat) (h : i < l.toArray.size) :
+    l.toArray.eraseIdx i h = (l.eraseIdx i).toArray := by
+  rw [Array.eraseIdx]
+  split <;> rename_i h'
+  · rw [eraseIdx_toArray]
     simp only [swap_toArray, Fin.getElem_fin, toList_toArray, mk.injEq]
     rw [eraseIdx_set_gt (by simp), eraseIdx_set_eq]
     simp
-  · rcases i with ⟨i, w⟩
-    simp at h w
+  · simp at h h'
     have t : i = l.length - 1 := by omega
     simp [t]
 termination_by l.length - i
@@ -1853,9 +2003,9 @@ decreasing_by
   simp
   omega
 
-@[simp] theorem eraseIdx_toArray (l : List α) (i : Nat) :
-    l.toArray.eraseIdx i = (l.eraseIdx i).toArray := by
-  rw [Array.eraseIdx]
+@[simp] theorem eraseIdxIfInBounds_toArray (l : List α) (i : Nat) :
+    l.toArray.eraseIdxIfInBounds i = (l.eraseIdx i).toArray := by
+  rw [Array.eraseIdxIfInBounds]
   split
   · simp
   · simp_all [eraseIdx_eq_self.2]
@@ -1874,13 +2024,13 @@ namespace Array
     (as.takeWhile p).toList = as.toList.takeWhile p := by
   induction as; simp
 
-@[simp] theorem toList_feraseIdx (as : Array α) (i : Fin as.size) :
-    (as.feraseIdx i).toList = as.toList.eraseIdx i.1 := by
+@[simp] theorem toList_eraseIdx (as : Array α) (i : Nat) (h : i < as.size) :
+    (as.eraseIdx i h).toList = as.toList.eraseIdx i := by
   induction as
   simp
 
-@[simp] theorem toList_eraseIdx (as : Array α) (i : Nat) :
-    (as.eraseIdx i).toList = as.toList.eraseIdx i := by
+@[simp] theorem toList_eraseIdxIfInBounds (as : Array α) (i : Nat) :
+    (as.eraseIdxIfInBounds i).toList = as.toList.eraseIdx i := by
   induction as
   simp
 
@@ -1914,6 +2064,40 @@ theorem array_array_induction (P : Array (Array α) → Prop) (h : ∀ (xss : Li
   specialize h (ass.toList.map toList)
   simpa [← toList_map, Function.comp_def, map_id] using h
 
+theorem foldl_map (f : β₁ → β₂) (g : α → β₂ → α) (l : Array β₁) (init : α) :
+    (l.map f).foldl g init = l.foldl (fun x y => g x (f y)) init := by
+  cases l; simp [List.foldl_map]
+
+theorem foldr_map (f : α₁ → α₂) (g : α₂ → β → β) (l : Array α₁) (init : β) :
+    (l.map f).foldr g init = l.foldr (fun x y => g (f x) y) init := by
+  cases l; simp [List.foldr_map]
+
+theorem foldl_filterMap (f : α → Option β) (g : γ → β → γ) (l : Array α) (init : γ) :
+    (l.filterMap f).foldl g init = l.foldl (fun x y => match f y with | some b => g x b | none => x) init := by
+  cases l
+  simp [List.foldl_filterMap]
+  rfl
+
+theorem foldr_filterMap (f : α → Option β) (g : β → γ → γ) (l : Array α) (init : γ) :
+    (l.filterMap f).foldr g init = l.foldr (fun x y => match f x with | some b => g b y | none => y) init := by
+  cases l
+  simp [List.foldr_filterMap]
+  rfl
+
+theorem foldl_map' (g : α → β) (f : α → α → α) (f' : β → β → β) (a : α) (l : Array α)
+    (h : ∀ x y, f' (g x) (g y) = g (f x y)) :
+    (l.map g).foldl f' (g a) = g (l.foldl f a) := by
+  cases l
+  simp
+  rw [List.foldl_map' _ _ _ _ _ h]
+
+theorem foldr_map' (g : α → β) (f : α → α → α) (f' : β → β → β) (a : α) (l : List α)
+    (h : ∀ x y, f' (g x) (g y) = g (f x y)) :
+    (l.map g).foldr f' (g a) = g (l.foldr f a) := by
+  cases l
+  simp
+  rw [List.foldr_map' _ _ _ _ _ h]
+
 /-! ### flatten -/
 
 @[simp] theorem flatten_empty : flatten (#[] : Array (Array α)) = #[] := rfl
@@ -1928,6 +2112,12 @@ theorem array_array_induction (P : Array (Array α) → Prop) (h : ∀ (xss : Li
   | nil => simp
   | cons xs xss ih => simp [ih]
 
+/-! ### reverse -/
+
+@[simp] theorem mem_reverse {x : α} {as : Array α} : x ∈ as.reverse ↔ x ∈ as := by
+  cases as
+  simp
+
 /-! ### findSomeRevM?, findRevM?, findSomeRev?, findRev? -/
 
 @[simp] theorem findSomeRevM?_eq_findSomeM?_reverse
@@ -2030,6 +2220,8 @@ theorem toArray_concat {as : List α} {x : α} :
 
 @[deprecated back!_toArray (since := "2024-10-31")] abbrev back_toArray := @back!_toArray
 
+@[deprecated setIfInBounds_toArray (since := "2024-11-24")] abbrev setD_toArray := @setIfInBounds_toArray
+
 end List
 
 namespace Array
@@ -2175,4 +2367,11 @@ abbrev get_swap' := @getElem_swap'
 @[deprecated eq_push_pop_back!_of_size_ne_zero (since := "2024-10-31")]
 abbrev eq_push_pop_back_of_size_ne_zero := @eq_push_pop_back!_of_size_ne_zero
 
+@[deprecated set!_is_setIfInBounds (since := "2024-11-24")] abbrev set_is_setIfInBounds := @set!_is_setIfInBounds
+@[deprecated size_setIfInBounds (since := "2024-11-24")] abbrev size_setD := @size_setIfInBounds
+@[deprecated getElem_setIfInBounds_eq (since := "2024-11-24")] abbrev getElem_setD_eq := @getElem_setIfInBounds_eq
+@[deprecated getElem?_setIfInBounds_eq (since := "2024-11-24")] abbrev get?_setD_eq := @getElem?_setIfInBounds_eq
+@[deprecated getD_get?_setIfInBounds (since := "2024-11-24")] abbrev getD_setD := @getD_get?_setIfInBounds
+@[deprecated getElem_setIfInBounds (since := "2024-11-24")] abbrev getElem_setD := @getElem_setIfInBounds
+
 end Array

src/Init/Data/Array/QSort.lean

@@ -13,19 +13,19 @@ namespace Array
 def qpartition (as : Array α) (lt : α → α → Bool) (lo hi : Nat) : Nat × Array α :=
   if h : as.size = 0 then (0, as) else have : Inhabited α := ⟨as[0]'(by revert h; cases as.size <;> simp)⟩ -- TODO: remove
   let mid := (lo + hi) / 2
-  let as  := if lt (as.get! mid) (as.get! lo) then as.swap! lo mid else as
-  let as  := if lt (as.get! hi)  (as.get! lo) then as.swap! lo hi  else as
-  let as  := if lt (as.get! mid) (as.get! hi) then as.swap! mid hi else as
+  let as  := if lt (as.get! mid) (as.get! lo) then as.swapIfInBounds lo mid else as
+  let as  := if lt (as.get! hi)  (as.get! lo) then as.swapIfInBounds lo hi  else as
+  let as  := if lt (as.get! mid) (as.get! hi) then as.swapIfInBounds mid hi else as
   let pivot := as.get! hi
   let rec loop (as : Array α) (i j : Nat) :=
     if h : j < hi then
       if lt (as.get! j) pivot then
-        let as := as.swap! i j
+        let as := as.swapIfInBounds i j
         loop as (i+1) (j+1)
       else
         loop as i (j+1)
     else
-      let as := as.swap! i hi
+      let as := as.swapIfInBounds i hi
       (i, as)
     termination_by hi - j
     decreasing_by all_goals simp_wf; decreasing_trivial_pre_omega

src/Init/Data/Array/Set.lean

@@ -25,9 +25,11 @@ Set an element in an array, or do nothing if the index is out of bounds.
 This will perform the update destructively provided that `a` has a reference
 count of 1 when called.
 -/
-@[inline] def Array.setD (a : Array α) (i : Nat) (v : α) : Array α :=
+@[inline] def Array.setIfInBounds (a : Array α) (i : Nat) (v : α) : Array α :=
   dite (LT.lt i a.size) (fun h => a.set i v h) (fun _ => a)
 
+@[deprecated Array.setIfInBounds (since := "2024-11-24")] abbrev Array.setD := @Array.setIfInBounds
+
 /--
 Set an element in an array, or panic if the index is out of bounds.
 
@@ -36,4 +38,4 @@ count of 1 when called.
 -/
 @[extern "lean_array_set"]
 def Array.set! (a : Array α) (i : @& Nat) (v : α) : Array α :=
-  Array.setD a i v
+  Array.setIfInBounds a i v

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

@@ -23,16 +23,13 @@ def split (s : Subarray α) (i : Fin s.size.succ) : (Subarray α × Subarray α)
   let ⟨i', isLt⟩ := i
   have := s.start_le_stop
   have := s.stop_le_array_size
-  have : i' ≤ s.stop - s.start := Nat.lt_succ.mp isLt
-  have : s.start + i' ≤ s.stop := by omega
-  have : s.start + i' ≤ s.array.size := by omega
   have : s.start + i' ≤ s.stop := by
     simp only [size] at isLt
     omega
   let pre := {s with
     stop := s.start + i',
     start_le_stop := by omega,
-    stop_le_array_size := by assumption
+    stop_le_array_size := by omega
   }
   let post := {s with
     start := s.start + i'
@@ -48,9 +45,7 @@ def drop (arr : Subarray α) (i : Nat) : Subarray α where
   array := arr.array
   start := min (arr.start + i) arr.stop
   stop := arr.stop
-  start_le_stop := by
-    rw [Nat.min_def]
-    split <;> simp only [Nat.le_refl, *]
+  start_le_stop := by omega
   stop_le_array_size := arr.stop_le_array_size
 
 /--
@@ -63,9 +58,7 @@ def take (arr : Subarray α) (i : Nat) : Subarray α where
   stop := min (arr.start + i) arr.stop
   start_le_stop := by
     have := arr.start_le_stop
-    rw [Nat.min_def]
-    split <;> omega
+    omega
   stop_le_array_size := by
     have := arr.stop_le_array_size
-    rw [Nat.min_def]
-    split <;> omega
+    omega

src/Init/Data/BitVec/Bitblast.lean

@@ -346,6 +346,10 @@ theorem getMsbD_sub {i : Nat} {i_lt : i < w} {x y : BitVec w} :
   · rfl
   · omega
 
+theorem getElem_sub {i : Nat} {x y : BitVec w} (h : i < w) :
+    (x - y)[i] = (x[i] ^^ ((~~~y + 1#w)[i] ^^ carry i x (~~~y + 1#w) false)) := by
+  simp [← getLsbD_eq_getElem, getLsbD_sub, h]
+
 theorem msb_sub {x y: BitVec w} :
     (x - y).msb
       = (x.msb ^^ ((~~~y + 1#w).msb ^^ carry (w - 1 - 0) x (~~~y + 1#w) false)) := by
@@ -410,6 +414,10 @@ theorem getLsbD_neg {i : Nat} {x : BitVec w} :
   · have h_ge : w ≤ i := by omega
     simp [getLsbD_ge _ _ h_ge, h_ge, hi]
 
+theorem getElem_neg {i : Nat} {x : BitVec w} (h : i < w) :
+    (-x)[i] = (x[i] ^^ decide (∃ j < i, x.getLsbD j = true)) := by
+  simp [← getLsbD_eq_getElem, getLsbD_neg, h]
+
 theorem getMsbD_neg {i : Nat} {x : BitVec w} :
     getMsbD (-x) i =
       (getMsbD x i ^^ decide (∃ j < w, i < j ∧ getMsbD x j = true)) := by

src/Init/Data/BitVec/Lemmas.lean

@@ -269,6 +269,10 @@ theorem ofBool_eq_iff_eq : ∀ {b b' : Bool}, BitVec.ofBool b = BitVec.ofBool b'
   getLsbD (x#'lt) i = x.testBit i := by
   simp [getLsbD, BitVec.ofNatLt]
 
+@[simp] theorem getMsbD_ofNatLt {n x i : Nat} (h : x < 2^n) :
+    getMsbD (x#'h) i = (decide (i < n) && x.testBit (n - 1 - i)) := by
+  simp [getMsbD, getLsbD]
+
 @[simp, bv_toNat] theorem toNat_ofNat (x w : Nat) : (BitVec.ofNat w x).toNat = x % 2^w := by
   simp [BitVec.toNat, BitVec.ofNat, Fin.ofNat']
 
@@ -561,6 +565,10 @@ theorem zeroExtend_eq_setWidth {v : Nat} {x : BitVec w} :
   else
     simp [n_le_i, toNat_ofNat]
 
+@[simp] theorem toInt_setWidth (x : BitVec w) :
+    (x.setWidth v).toInt = Int.bmod x.toNat (2^v) := by
+  simp [toInt_eq_toNat_bmod, toNat_setWidth, Int.emod_bmod]
+
 theorem setWidth'_eq {x : BitVec w} (h : w ≤ v) : x.setWidth' h = x.setWidth v := by
   apply eq_of_toNat_eq
   rw [toNat_setWidth, toNat_setWidth']
@@ -755,6 +763,10 @@ theorem extractLsb'_eq_extractLsb {w : Nat} (x : BitVec w) (start len : Nat) (h
 @[simp] theorem getLsbD_allOnes : (allOnes v).getLsbD i = decide (i < v) := by
   simp [allOnes]
 
+@[simp] theorem getMsbD_allOnes : (allOnes v).getMsbD i = decide (i < v) := by
+  simp [allOnes]
+  omega
+
 @[simp] theorem getElem_allOnes (i : Nat) (h : i < v) : (allOnes v)[i] = true := by
   simp [getElem_eq_testBit_toNat, h]
 
@@ -772,6 +784,12 @@ theorem extractLsb'_eq_extractLsb {w : Nat} (x : BitVec w) (start len : Nat) (h
 @[simp] theorem toNat_or (x y : BitVec v) :
     BitVec.toNat (x ||| y) = BitVec.toNat x ||| BitVec.toNat y := rfl
 
+@[simp] theorem toInt_or (x y : BitVec w) :
+    BitVec.toInt (x ||| y) = Int.bmod (BitVec.toNat x ||| BitVec.toNat y) (2^w) := by
+  rw_mod_cast [Int.bmod_def, BitVec.toInt, toNat_or, Nat.mod_eq_of_lt
+    (Nat.or_lt_two_pow (BitVec.isLt x) (BitVec.isLt y))]
+  omega
+
 @[simp] theorem toFin_or (x y : BitVec v) :
     BitVec.toFin (x ||| y) = BitVec.toFin x ||| BitVec.toFin y := by
   apply Fin.eq_of_val_eq
@@ -839,6 +857,12 @@ instance : Std.LawfulCommIdentity (α := BitVec n) (· ||| · ) (0#n) where
 @[simp] theorem toNat_and (x y : BitVec v) :
     BitVec.toNat (x &&& y) = BitVec.toNat x &&& BitVec.toNat y := rfl
 
+@[simp] theorem toInt_and (x y : BitVec w) :
+    BitVec.toInt (x &&& y) = Int.bmod (BitVec.toNat x &&& BitVec.toNat y) (2^w) := by
+  rw_mod_cast [Int.bmod_def, BitVec.toInt, toNat_and, Nat.mod_eq_of_lt
+    (Nat.and_lt_two_pow x.toNat (BitVec.isLt y))]
+  omega
+
 @[simp] theorem toFin_and (x y : BitVec v) :
     BitVec.toFin (x &&& y) = BitVec.toFin x &&& BitVec.toFin y := by
   apply Fin.eq_of_val_eq
@@ -906,6 +930,12 @@ instance : Std.LawfulCommIdentity (α := BitVec n) (· &&& · ) (allOnes n) wher
 @[simp] theorem toNat_xor (x y : BitVec v) :
     BitVec.toNat (x ^^^ y) = BitVec.toNat x ^^^ BitVec.toNat y := rfl
 
+@[simp] theorem toInt_xor (x y : BitVec w) :
+    BitVec.toInt (x ^^^ y) = Int.bmod (BitVec.toNat x ^^^ BitVec.toNat y) (2^w) := by
+  rw_mod_cast [Int.bmod_def, BitVec.toInt, toNat_xor, Nat.mod_eq_of_lt
+    (Nat.xor_lt_two_pow (BitVec.isLt x) (BitVec.isLt y))]
+  omega
+
 @[simp] theorem toFin_xor (x y : BitVec v) :
     BitVec.toFin (x ^^^ y) = BitVec.toFin x ^^^ BitVec.toFin y := by
   apply Fin.eq_of_val_eq
@@ -983,6 +1013,13 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
           _ ≤ 2 ^ i := Nat.pow_le_pow_of_le_right Nat.zero_lt_two w
       · simp
 
+@[simp] theorem toInt_not {x : BitVec w} :
+    (~~~x).toInt = Int.bmod (2^w - 1 - x.toNat) (2^w) := by
+  rw_mod_cast [BitVec.toInt, BitVec.toNat_not, Int.bmod_def]
+  simp [show ((2^w : Nat) : Int) - 1 - x.toNat = ((2^w - 1 - x.toNat) : Nat) by omega]
+  rw_mod_cast [Nat.mod_eq_of_lt (by omega)]
+  omega
+
 @[simp] theorem ofInt_negSucc_eq_not_ofNat {w n : Nat} :
     BitVec.ofInt w (Int.negSucc n) = ~~~.ofNat w n := by
   simp only [BitVec.ofInt, Int.toNat, Int.ofNat_eq_coe, toNat_eq, toNat_ofNatLt, toNat_not,
@@ -1007,6 +1044,10 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
 @[simp] theorem getLsbD_not {x : BitVec v} : (~~~x).getLsbD i = (decide (i < v) && ! x.getLsbD i) := by
   by_cases h' : i < v <;> simp_all [not_def]
 
+@[simp] theorem getMsbD_not {x : BitVec v} :
+    (~~~x).getMsbD i = (decide (i < v) && ! x.getMsbD i) := by
+  by_cases h' : i < v <;> simp_all [not_def]
+
 @[simp] theorem getElem_not {x : BitVec w} {i : Nat} (h : i < w) : (~~~x)[i] = !x[i] := by
   simp only [getElem_eq_testBit_toNat, toNat_not]
   rw [← Nat.sub_add_eq, Nat.add_comm 1]
@@ -1480,6 +1521,12 @@ theorem getLsbD_sshiftRight' {x y: BitVec w} {i : Nat} :
       (!decide (w ≤ i) && if y.toNat + i < w then x.getLsbD (y.toNat + i) else x.msb) := by
   simp only [BitVec.sshiftRight', BitVec.getLsbD_sshiftRight]
 
+@[simp]
+theorem getElem_sshiftRight' {x y : BitVec w} {i : Nat} (h : i < w) :
+    (x.sshiftRight' y)[i] =
+      (!decide (w ≤ i) && if y.toNat + i < w then x.getLsbD (y.toNat + i) else x.msb) := by
+  simp only [← getLsbD_eq_getElem, BitVec.sshiftRight', BitVec.getLsbD_sshiftRight]
+
 @[simp]
 theorem getMsbD_sshiftRight' {x y: BitVec w} {i : Nat} :
     (x.sshiftRight y.toNat).getMsbD i = (decide (i < w) && if i < y.toNat then x.msb else x.getMsbD (i - y.toNat)) := by
@@ -1572,6 +1619,82 @@ theorem signExtend_eq_setWidth_of_lt (x : BitVec w) {v : Nat} (hv : v ≤ w):
 theorem signExtend_eq (x : BitVec w) : x.signExtend w = x := by
   rw [signExtend_eq_setWidth_of_lt _ (Nat.le_refl _), setWidth_eq]
 
+/-- Sign extending to a larger bitwidth depends on the msb.
+If the msb is false, then the result equals the original value.
+If the msb is true, then we add a value of `(2^v - 2^w)`, which arises from the sign extension. -/
+private theorem toNat_signExtend_of_le (x : BitVec w) {v : Nat} (hv : w ≤ v) :
+    (x.signExtend v).toNat = x.toNat + if x.msb then 2^v - 2^w else 0 := by
+  apply Nat.eq_of_testBit_eq
+  intro i
+  have ⟨k, hk⟩ := Nat.exists_eq_add_of_le hv
+  rw [hk, testBit_toNat, getLsbD_signExtend, Nat.pow_add, ← Nat.mul_sub_one, Nat.add_comm (x.toNat)]
+  by_cases hx : x.msb
+  · simp only [hx, Bool.if_true_right, ↓reduceIte,
+      Nat.testBit_mul_pow_two_add _ x.isLt,
+      testBit_toNat, Nat.testBit_two_pow_sub_one]
+    -- Case analysis on i being in the intervals [0..w), [w..w + k), [w+k..∞)
+    have hi : i < w ∨ (w ≤ i ∧ i < w + k) ∨ w + k ≤ i := by omega
+    rcases hi with hi | hi | hi
+    · simp [hi]; omega
+    · simp [hi]; omega
+    · simp [hi, show ¬ (i < w + k) by omega, show ¬ (i < w) by omega]
+      omega
+  · simp only [hx, Bool.if_false_right,
+      Bool.false_eq_true, ↓reduceIte, Nat.zero_add, testBit_toNat]
+    have hi : i < w ∨ (w ≤ i ∧ i < w + k) ∨ w + k ≤ i := by omega
+    rcases hi with hi | hi | hi
+    · simp [hi]; omega
+    · simp [hi]
+    · simp [hi, show ¬ (i < w + k) by omega, show ¬ (i < w) by omega, getLsbD_ge x i (by omega)]
+
+/-- Sign extending to a larger bitwidth depends on the msb.
+If the msb is false, then the result equals the original value.
+If the msb is true, then we add a value of `(2^v - 2^w)`, which arises from the sign extension. -/
+theorem toNat_signExtend (x : BitVec w) {v : Nat} :
+    (x.signExtend v).toNat = (x.setWidth v).toNat + if x.msb then 2^v - 2^w else 0 := by
+  by_cases h : v ≤ w
+  · have : 2^v ≤ 2^w := Nat.pow_le_pow_of_le_right Nat.two_pos h
+    simp [signExtend_eq_setWidth_of_lt x h, toNat_setWidth, Nat.sub_eq_zero_of_le this]
+  · have : 2^w ≤ 2^v := Nat.pow_le_pow_of_le_right Nat.two_pos (by omega)
+    rw [toNat_signExtend_of_le x (by omega), toNat_setWidth, Nat.mod_eq_of_lt (by omega)]
+
+/-
+If the current width `w` is smaller than the extended width `v`,
+then the value when interpreted as an integer does not change.
+-/
+theorem toInt_signExtend_of_lt {x : BitVec w} (hv : w < v):
+    (x.signExtend v).toInt = x.toInt := by
+  simp only [toInt_eq_msb_cond, toNat_signExtend]
+  have : (x.signExtend v).msb = x.msb := by
+    rw [msb_eq_getLsbD_last, getLsbD_eq_getElem (Nat.sub_one_lt_of_lt hv)]
+    simp [getElem_signExtend, Nat.le_sub_one_of_lt hv]
+  have H : 2^w ≤ 2^v := Nat.pow_le_pow_of_le_right (by omega) (by omega)
+  simp only [this, toNat_setWidth, Int.natCast_add, Int.ofNat_emod, Int.natCast_mul]
+  by_cases h : x.msb
+  <;> norm_cast
+  <;> simp [h, Nat.mod_eq_of_lt (Nat.lt_of_lt_of_le x.isLt H)]
+  omega
+
+/-
+If the current width `w` is larger than the extended width `v`,
+then the value when interpreted as an integer is truncated,
+and we compute a modulo by `2^v`.
+-/
+theorem toInt_signExtend_of_le {x : BitVec w} (hv : v ≤ w) :
+    (x.signExtend v).toInt = Int.bmod x.toNat (2^v) := by
+  simp [signExtend_eq_setWidth_of_lt _ hv]
+
+/-
+Interpreting the sign extension of `(x : BitVec w)` to width `v`
+computes `x % 2^v` (where `%` is the balanced mod).
+-/
+theorem toInt_signExtend (x : BitVec w) :
+    (x.signExtend v).toInt = Int.bmod x.toNat (2^(min v w)) := by
+  by_cases hv : v ≤ w
+  · simp [toInt_signExtend_of_le hv, Nat.min_eq_left hv]
+  · simp only [Nat.not_le] at hv
+    rw [toInt_signExtend_of_lt hv, Nat.min_eq_right (by omega), toInt_eq_toNat_bmod]
+
 /-! ### append -/
 
 theorem append_def (x : BitVec v) (y : BitVec w) :
@@ -2611,7 +2734,7 @@ theorem getLsbD_rotateLeftAux_of_geq {x : BitVec w} {r : Nat} {i : Nat} (hi : i
   apply getLsbD_ge
   omega
 
-/-- When `r < w`, we give a formula for `(x.rotateRight r).getLsbD i`. -/
+/-- When `r < w`, we give a formula for `(x.rotateLeft r).getLsbD i`. -/
 theorem getLsbD_rotateLeft_of_le {x : BitVec w} {r i : Nat} (hr: r < w) :
     (x.rotateLeft r).getLsbD i =
       cond (i < r)
@@ -2638,6 +2761,64 @@ theorem getElem_rotateLeft {x : BitVec w} {r i : Nat} (h : i < w) :
       if h' : i < r % w then x[(w - (r % w) + i)] else x[i - (r % w)] := by
   simp [← BitVec.getLsbD_eq_getElem, h]
 
+theorem getMsbD_rotateLeftAux_of_lt {x : BitVec w} {r : Nat} {i : Nat} (hi : i < w - r) :
+    (x.rotateLeftAux r).getMsbD i = x.getMsbD (r + i) := by
+  rw [rotateLeftAux, getMsbD_or]
+  simp [show i < w - r by omega, Nat.add_comm]
+
+theorem getMsbD_rotateLeftAux_of_ge {x : BitVec w} {r : Nat} {i : Nat} (hi : i ≥ w - r) :
+    (x.rotateLeftAux r).getMsbD i = (decide (i < w) && x.getMsbD (i - (w - r))) := by
+  simp [rotateLeftAux, getMsbD_or, show i + r ≥ w by omega, show ¬i < w - r by omega]
+
+/--
+If a number `w * n ≤ i < w * (n + 1)`, then `i - w * n` equals `i % w`.
+This is true by subtracting `w * n` from the inequality, giving
+`0 ≤ i - w * n < w`, which uniquely identifies `i % w`.
+-/
+private theorem Nat.sub_mul_eq_mod_of_lt_of_le (hlo : w * n ≤ i) (hhi : i < w * (n + 1)) :
+    i - w * n = i % w := by
+  rw [Nat.mod_def]
+  congr
+  symm
+  apply Nat.div_eq_of_lt_le
+    (by rw [Nat.mul_comm]; omega)
+    (by rw [Nat.mul_comm]; omega)
+
+/-- When `r < w`, we give a formula for `(x.rotateLeft r).getMsbD i`. -/
+theorem getMsbD_rotateLeft_of_lt {n w : Nat} {x : BitVec w} (hi : r < w):
+    (x.rotateLeft r).getMsbD n = (decide (n < w) && x.getMsbD ((r + n) % w)) := by
+  rcases w with rfl | w
+  · simp
+  · rw [BitVec.rotateLeft_eq_rotateLeftAux_of_lt (by omega)]
+    by_cases h : n < (w + 1) - r
+    · simp [getMsbD_rotateLeftAux_of_lt h, Nat.mod_eq_of_lt, show r + n < (w + 1) by omega, show n < w + 1 by omega]
+    · simp [getMsbD_rotateLeftAux_of_ge <| Nat.ge_of_not_lt h]
+      by_cases h₁ : n < w + 1
+      · simp only [h₁, decide_true, Bool.true_and]
+        have h₂ : (r + n) < 2 * (w + 1) := by omega
+        congr 1
+        rw [← Nat.sub_mul_eq_mod_of_lt_of_le (n := 1) (by omega) (by omega), Nat.mul_one]
+        omega
+      · simp [h₁]
+
+theorem getMsbD_rotateLeft {r n w : Nat} {x : BitVec w} :
+    (x.rotateLeft r).getMsbD n = (decide (n < w) && x.getMsbD ((r + n) % w)) := by
+  rcases w with rfl | w
+  · simp
+  · by_cases h : r < w
+    · rw [getMsbD_rotateLeft_of_lt (by omega)]
+    · rw [← rotateLeft_mod_eq_rotateLeft, getMsbD_rotateLeft_of_lt (by apply Nat.mod_lt; simp)]
+      simp
+
+@[simp]
+theorem msb_rotateLeft {m w : Nat} {x : BitVec w} :
+    (x.rotateLeft m).msb = x.getMsbD (m % w) := by
+  simp only [BitVec.msb, getMsbD_rotateLeft]
+  by_cases h : w = 0
+  · simp [h]
+  · simp
+    omega
+
 /-! ## Rotate Right -/
 
 /--
@@ -2699,7 +2880,7 @@ theorem rotateRight_mod_eq_rotateRight {x : BitVec w} {r : Nat} :
   simp only [rotateRight, Nat.mod_mod]
 
 /-- When `r < w`, we give a formula for `(x.rotateRight r).getLsb i`. -/
-theorem getLsbD_rotateRight_of_le {x : BitVec w} {r i : Nat} (hr: r < w) :
+theorem getLsbD_rotateRight_of_lt {x : BitVec w} {r i : Nat} (hr: r < w) :
     (x.rotateRight r).getLsbD i =
       cond (i < w - r)
       (x.getLsbD (r + i))
@@ -2717,7 +2898,7 @@ theorem getLsbD_rotateRight {x : BitVec w} {r i : Nat} :
       (decide (i < w) && x.getLsbD (i - (w - (r % w)))) := by
   rcases w with ⟨rfl, w⟩
   · simp
-  · rw [← rotateRight_mod_eq_rotateRight, getLsbD_rotateRight_of_le (Nat.mod_lt _ (by omega))]
+  · rw [← rotateRight_mod_eq_rotateRight, getLsbD_rotateRight_of_lt (Nat.mod_lt _ (by omega))]
 
 @[simp]
 theorem getElem_rotateRight {x : BitVec w} {r i : Nat} (h : i < w) :
@@ -2725,6 +2906,56 @@ theorem getElem_rotateRight {x : BitVec w} {r i : Nat} (h : i < w) :
   simp only [← BitVec.getLsbD_eq_getElem]
   simp [getLsbD_rotateRight, h]
 
+theorem getMsbD_rotateRightAux_of_lt {x : BitVec w} {r : Nat} {i : Nat} (hi : i < r) :
+    (x.rotateRightAux r).getMsbD i = x.getMsbD (i + (w - r)) := by
+  rw [rotateRightAux, getMsbD_or, getMsbD_ushiftRight]
+  simp [show i < r by omega]
+
+theorem getMsbD_rotateRightAux_of_ge {x : BitVec w} {r : Nat} {i : Nat} (hi : i ≥ r) :
+    (x.rotateRightAux r).getMsbD i = (decide (i < w) && x.getMsbD (i - r)) := by
+  simp [rotateRightAux, show ¬ i < r by omega, show i + (w - r) ≥ w by omega]
+
+/-- When `m < w`, we give a formula for `(x.rotateLeft m).getMsbD i`. -/
+@[simp]
+theorem getMsbD_rotateRight_of_lt {w n m : Nat} {x : BitVec w} (hr : m < w):
+    (x.rotateRight m).getMsbD n = (decide (n < w) && (if (n < m % w)
+    then x.getMsbD ((w + n - m % w) % w) else x.getMsbD (n - m % w))):= by
+  rcases w with rfl | w
+  · simp
+  · rw [rotateRight_eq_rotateRightAux_of_lt (by omega)]
+    by_cases h : n < m
+    · simp only [getMsbD_rotateRightAux_of_lt h, show n < w + 1 by omega, decide_true,
+        show m % (w + 1) = m by rw [Nat.mod_eq_of_lt hr], h, ↓reduceIte,
+        show (w + 1 + n - m) < (w + 1) by omega, Nat.mod_eq_of_lt, Bool.true_and]
+      congr 1
+      omega
+    · simp [h, getMsbD_rotateRightAux_of_ge <| Nat.ge_of_not_lt h]
+      by_cases h₁ : n < w + 1
+      · simp [h, h₁, decide_true, Bool.true_and, Nat.mod_eq_of_lt hr]
+      · simp [h₁]
+
+@[simp]
+theorem getMsbD_rotateRight {w n m : Nat} {x : BitVec w} :
+    (x.rotateRight m).getMsbD n = (decide (n < w) && (if (n < m % w)
+    then x.getMsbD ((w + n - m % w) % w) else x.getMsbD (n - m % w))):= by
+  rcases w with rfl | w
+  · simp
+  · by_cases h₀ : m < w
+    · rw [getMsbD_rotateRight_of_lt (by omega)]
+    · rw [← rotateRight_mod_eq_rotateRight, getMsbD_rotateRight_of_lt (by apply Nat.mod_lt; simp)]
+      simp
+
+@[simp]
+theorem msb_rotateRight {r w : Nat} {x : BitVec w} :
+    (x.rotateRight r).msb = x.getMsbD ((w - r % w) % w) := by
+  simp only [BitVec.msb, getMsbD_rotateRight]
+  by_cases h₀ : 0 < w
+  · simp only [h₀, decide_true, Nat.add_zero, Nat.zero_le, Nat.sub_eq_zero_of_le, Bool.true_and,
+    ite_eq_left_iff, Nat.not_lt, Nat.le_zero_eq]
+    intro h₁
+    simp [h₁]
+  · simp [show w = 0 by omega]
+
 /- ## twoPow -/
 
 theorem twoPow_eq (w : Nat) (i : Nat) : twoPow w i = 1#w <<< i := by
@@ -2883,20 +3114,6 @@ theorem replicate_succ_eq {x : BitVec w} :
     (x ++ replicate n x).cast (by rw [Nat.mul_succ]; omega) := by
   simp [replicate]
 
-/--
-If a number `w * n ≤ i < w * (n + 1)`, then `i - w * n` equals `i % w`.
-This is true by subtracting `w * n` from the inequality, giving
-`0 ≤ i - w * n < w`, which uniquely identifies `i % w`.
--/
-private theorem Nat.sub_mul_eq_mod_of_lt_of_le (hlo : w * n ≤ i) (hhi : i < w * (n + 1)) :
-    i - w * n = i % w := by
-  rw [Nat.mod_def]
-  congr
-  symm
-  apply Nat.div_eq_of_lt_le
-    (by rw [Nat.mul_comm]; omega)
-    (by rw [Nat.mul_comm]; omega)
-
 @[simp]
 theorem getLsbD_replicate {n w : Nat} (x : BitVec w) :
     (x.replicate n).getLsbD i =
@@ -3002,6 +3219,11 @@ theorem toInt_neg_of_ne_intMin {x : BitVec w} (rs : x ≠ intMin w) :
   have := @Nat.two_pow_pred_mul_two w (by omega)
   split <;> split <;> omega
 
+theorem toInt_neg_eq_ite {x : BitVec w} :
+    (-x).toInt = if x = intMin w then x.toInt else -(x.toInt) := by
+  by_cases hx : x = intMin w <;>
+    simp [hx, neg_intMin, toInt_neg_of_ne_intMin]
+
 theorem msb_intMin {w : Nat} : (intMin w).msb = decide (0 < w) := by
   simp only [msb_eq_decide, toNat_intMin, decide_eq_decide]
   by_cases h : 0 < w <;> simp_all
@@ -3124,13 +3346,84 @@ theorem toNat_abs {x : BitVec w} : x.abs.toNat = if x.msb then 2^w - x.toNat els
   · simp [h]
 
 theorem getLsbD_abs {i : Nat} {x : BitVec w} :
-   getLsbD x.abs i = if x.msb then getLsbD (-x) i else getLsbD x i := by
+    getLsbD x.abs i = if x.msb then getLsbD (-x) i else getLsbD x i := by
+  by_cases h : x.msb <;> simp [BitVec.abs, h]
+
+theorem getElem_abs {i : Nat} {x : BitVec w} (h : i < w) :
+    x.abs[i] = if x.msb then (-x)[i] else x[i] := by
   by_cases h : x.msb <;> simp [BitVec.abs, h]
 
 theorem getMsbD_abs {i : Nat} {x : BitVec w} :
     getMsbD (x.abs) i = if x.msb then getMsbD (-x) i else getMsbD x i := by
   by_cases h : x.msb <;> simp [BitVec.abs, h]
 
+/-
+The absolute value of `x : BitVec w` is naively a case split on the sign of `x`.
+However, recall that when `x = intMin w`, `-x = x`.
+Thus, the full value of `abs x` is computed by the case split:
+- If `x : BitVec w` is `intMin`, then its absolute value is also `intMin w`, and
+  thus `toInt` will equal `intMin.toInt`.
+- Otherwise, if `x` is negative, then `x.abs.toInt = (-x).toInt`.
+- If `x` is positive, then it is equal to `x.abs.toInt = x.toInt`.
+-/
+theorem toInt_abs_eq_ite {x : BitVec w} :
+  x.abs.toInt =
+    if x = intMin w then (intMin w).toInt
+    else if x.msb then -x.toInt
+    else x.toInt := by
+  by_cases hx : x = intMin w
+  · simp [hx]
+  · simp [hx]
+    by_cases hx₂ : x.msb
+    · simp [hx₂, abs_eq, toInt_neg_of_ne_intMin hx]
+    · simp [hx₂, abs_eq]
+
+
+
+/-
+The absolute value of `x : BitVec w` is a case split on the sign of `x`, when `x ≠ intMin w`.
+This is a variant of `toInt_abs_eq_ite`.
+-/
+theorem toInt_abs_eq_ite_of_ne_intMin {x : BitVec w} (hx : x ≠ intMin w) :
+  x.abs.toInt = if x.msb then -x.toInt else x.toInt := by
+  simp [toInt_abs_eq_ite, hx]
+
+
+/--
+The absolute value of `x : BitVec w`, interpreted as an integer, is a case split:
+- When `x = intMin w`, then `x.abs = intMin w`
+- Otherwise, `x.abs.toInt` equals the absolute value (`x.toInt.natAbs`).
+
+This is a simpler version of `BitVec.toInt_abs_eq_ite`, which hides a case split on `x.msb`.
+-/
+theorem toInt_abs_eq_natAbs {x : BitVec w} : x.abs.toInt =
+    if x = intMin w then (intMin w).toInt else x.toInt.natAbs := by
+  rw [toInt_abs_eq_ite]
+  by_cases hx : x = intMin w
+  · simp [hx]
+  · simp [hx]
+    by_cases h : x.msb
+    · simp only [h, ↓reduceIte]
+      have : x.toInt < 0 := by
+        rw [toInt_neg_iff]
+        have := msb_eq_true_iff_two_mul_ge.mp h
+        omega
+      omega
+    · simp only [h, Bool.false_eq_true, ↓reduceIte]
+      have : 0 ≤ x.toInt := by
+        rw [toInt_pos_iff]
+        exact msb_eq_false_iff_two_mul_lt.mp (by simp [h])
+      omega
+
+/-
+The absolute value of `(x : BitVec w)`, when interpreted as an integer,
+is the absolute value of `x.toInt` when `(x ≠ intMin)`.
+-/
+theorem toInt_abs_eq_natAbs_of_ne_intMin {x : BitVec w} (hx : x ≠ intMin w) :
+    x.abs.toInt = x.toInt.natAbs := by
+  simp [toInt_abs_eq_natAbs, hx]
+
+
 /-! ### Decidable quantifiers -/
 
 theorem forall_zero_iff {P : BitVec 0 → Prop} :

src/Init/Data/ByteArray/Basic.lean

@@ -108,8 +108,18 @@ def toList (bs : ByteArray) : List UInt8 :=
 
 @[inline] def findIdx? (a : ByteArray) (p : UInt8 → Bool) (start := 0) : Option Nat :=
   let rec @[specialize] loop (i : Nat) :=
-    if i < a.size then
-      if p (a.get! i) then some i else loop (i+1)
+    if h : i < a.size then
+      if p a[i] then some i else loop (i+1)
+    else
+      none
+    termination_by a.size - i
+    decreasing_by decreasing_trivial_pre_omega
+  loop start
+
+@[inline] def findFinIdx? (a : ByteArray) (p : UInt8 → Bool) (start := 0) : Option (Fin a.size) :=
+  let rec @[specialize] loop (i : Nat) :=
+    if h : i < a.size then
+      if p a[i] then some ⟨i, h⟩ else loop (i+1)
     else
       none
     termination_by a.size - i

src/Init/Data/Fin/Fold.lean

@@ -13,17 +13,17 @@ namespace Fin
 /-- Folds over `Fin n` from the left: `foldl 3 f x = f (f (f x 0) 1) 2`. -/
 @[inline] def foldl (n) (f : α → Fin n → α) (init : α) : α := loop init 0 where
   /-- Inner loop for `Fin.foldl`. `Fin.foldl.loop n f x i = f (f (f x i) ...) (n-1)`  -/
-  loop (x : α) (i : Nat) : α :=
+  @[semireducible] loop (x : α) (i : Nat) : α :=
     if h : i < n then loop (f x ⟨i, h⟩) (i+1) else x
   termination_by n - i
-  decreasing_by decreasing_trivial_pre_omega
 
 /-- Folds over `Fin n` from the right: `foldr 3 f x = f 0 (f 1 (f 2 x))`. -/
-@[inline] def foldr (n) (f : Fin n → α → α) (init : α) : α := loop ⟨n, Nat.le_refl n⟩ init where
+@[inline] def foldr (n) (f : Fin n → α → α) (init : α) : α := loop n (Nat.le_refl n) init where
   /-- Inner loop for `Fin.foldr`. `Fin.foldr.loop n f i x = f 0 (f ... (f (i-1) x))`  -/
-  loop : {i // i ≤ n} → α → α
-  | ⟨0, _⟩, x => x
-  | ⟨i+1, h⟩, x => loop ⟨i, Nat.le_of_lt h⟩ (f ⟨i, h⟩ x)
+  loop : (i : _) → i ≤ n → α → α
+  | 0, _, x => x
+  | i+1, h, x => loop i (Nat.le_of_lt h) (f ⟨i, h⟩ x)
+  termination_by structural i => i
 
 /--
 Folds a monadic function over `Fin n` from left to right:
@@ -176,17 +176,19 @@ theorem foldl_eq_foldlM (f : α → Fin n → α) (x) :
 /-! ### foldr -/
 
 theorem foldr_loop_zero (f : Fin n → α → α) (x) :
-    foldr.loop n f ⟨0, Nat.zero_le _⟩ x = x := by
+    foldr.loop n f 0 (Nat.zero_le _) x = x := by
   rw [foldr.loop]
 
 theorem foldr_loop_succ (f : Fin n → α → α) (x) (h : i < n) :
-    foldr.loop n f ⟨i+1, h⟩ x = foldr.loop n f ⟨i, Nat.le_of_lt h⟩ (f ⟨i, h⟩ x) := by
+    foldr.loop n f (i+1) h x = foldr.loop n f i (Nat.le_of_lt h) (f ⟨i, h⟩ x) := by
   rw [foldr.loop]
 
 theorem foldr_loop (f : Fin (n+1) → α → α) (x) (h : i+1 ≤ n+1) :
-    foldr.loop (n+1) f ⟨i+1, h⟩ x =
-      f 0 (foldr.loop n (fun j => f j.succ) ⟨i, Nat.le_of_succ_le_succ h⟩ x) := by
-  induction i generalizing x <;> simp [foldr_loop_zero, foldr_loop_succ, *]
+    foldr.loop (n+1) f (i+1) h x =
+      f 0 (foldr.loop n (fun j => f j.succ) i (Nat.le_of_succ_le_succ h) x) := by
+  induction i generalizing x with
+  | zero => simp [foldr_loop_succ, foldr_loop_zero]
+  | succ i ih => rw [foldr_loop_succ, ih]; rfl
 
 @[simp] theorem foldr_zero (f : Fin 0 → α → α) (x) : foldr 0 f x = x :=
   foldr_loop_zero ..

src/Init/Data/Float.lean

@@ -31,7 +31,7 @@ opaque floatSpec : FloatSpec := {
 structure Float where
   val : floatSpec.float
 
-instance : Inhabited Float := ⟨{ val := floatSpec.val }⟩
+instance : Nonempty Float := ⟨{ val := floatSpec.val }⟩
 
 @[extern "lean_float_add"] opaque Float.add : Float → Float → Float
 @[extern "lean_float_sub"] opaque Float.sub : Float → Float → Float
@@ -136,6 +136,9 @@ instance : ToString Float where
 
 @[extern "lean_uint64_to_float"] opaque UInt64.toFloat (n : UInt64) : Float
 
+instance : Inhabited Float where
+  default := UInt64.toFloat 0
+
 instance : Repr Float where
   reprPrec n prec := if n < UInt64.toFloat 0 then Repr.addAppParen (toString n) prec else toString n
 

src/Init/Data/List.lean

@@ -26,3 +26,4 @@ import Init.Data.List.Sort
 import Init.Data.List.ToArray
 import Init.Data.List.MapIdx
 import Init.Data.List.OfFn
+import Init.Data.List.FinRange

src/Init/Data/List/Attach.lean

@@ -13,7 +13,7 @@ namespace List
   `a : α` satisfying `P`, then `pmap f l h` is essentially the same as `map f l`
   but is defined only when all members of `l` satisfy `P`, using the proof
   to apply `f`. -/
-@[simp] def pmap {P : α → Prop} (f : ∀ a, P a → β) : ∀ l : List α, (H : ∀ a ∈ l, P a) → List β
+def pmap {P : α → Prop} (f : ∀ a, P a → β) : ∀ l : List α, (H : ∀ a ∈ l, P a) → List β
   | [], _ => []
   | a :: l, H => f a (forall_mem_cons.1 H).1 :: pmap f l (forall_mem_cons.1 H).2
 
@@ -46,6 +46,11 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
   | cons _ L', hL' => congrArg _ <| go L' fun _ hx => hL' (.tail _ hx)
   exact go L h'
 
+@[simp] theorem pmap_nil {P : α → Prop} (f : ∀ a, P a → β) : pmap f [] (by simp) = [] := rfl
+
+@[simp] theorem pmap_cons {P : α → Prop} (f : ∀ a, P a → β) (a : α) (l : List α) (h : ∀ b ∈ a :: l, P b) :
+    pmap f (a :: l) h = f a (forall_mem_cons.1 h).1 :: pmap f l (forall_mem_cons.1 h).2 := rfl
+
 @[simp] theorem attach_nil : ([] : List α).attach = [] := rfl
 
 @[simp] theorem attachWith_nil : ([] : List α).attachWith P H = [] := rfl
@@ -148,7 +153,7 @@ theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {l H} {a} (h :
   exact ⟨a, h, rfl⟩
 
 @[simp]
-theorem length_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H} : length (pmap f l H) = length l := by
+theorem length_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H} : (pmap f l H).length = l.length := by
   induction l
   · rfl
   · simp only [*, pmap, length]
@@ -199,7 +204,7 @@ theorem attachWith_ne_nil_iff {l : List α} {P : α → Prop} {H : ∀ a ∈ l,
 
 @[simp]
 theorem getElem?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h : ∀ a ∈ l, p a) (n : Nat) :
-    (pmap f l h)[n]? = Option.pmap f l[n]? fun x H => h x (getElem?_mem H) := by
+    (pmap f l h)[n]? = Option.pmap f l[n]? fun x H => h x (mem_of_getElem? H) := by
   induction l generalizing n with
   | nil => simp
   | cons hd tl hl =>
@@ -215,7 +220,7 @@ theorem getElem?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h
       · simp_all
 
 theorem get?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h : ∀ a ∈ l, p a) (n : Nat) :
-    get? (pmap f l h) n = Option.pmap f (get? l n) fun x H => h x (get?_mem H) := by
+    get? (pmap f l h) n = Option.pmap f (get? l n) fun x H => h x (mem_of_get? H) := by
   simp only [get?_eq_getElem?]
   simp [getElem?_pmap, h]
 
@@ -238,18 +243,18 @@ theorem get_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h :
     (hn : n < (pmap f l h).length) :
     get (pmap f l h) ⟨n, hn⟩ =
       f (get l ⟨n, @length_pmap _ _ p f l h ▸ hn⟩)
-        (h _ (get_mem l ⟨n, @length_pmap _ _ p f l h ▸ hn⟩)) := by
+        (h _ (getElem_mem (@length_pmap _ _ p f l h ▸ hn))) := by
   simp only [get_eq_getElem]
   simp [getElem_pmap]
 
 @[simp]
 theorem getElem?_attachWith {xs : List α} {i : Nat} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
-    (xs.attachWith P H)[i]? = xs[i]?.pmap Subtype.mk (fun _ a => H _ (getElem?_mem a)) :=
+    (xs.attachWith P H)[i]? = xs[i]?.pmap Subtype.mk (fun _ a => H _ (mem_of_getElem? a)) :=
   getElem?_pmap ..
 
 @[simp]
 theorem getElem?_attach {xs : List α} {i : Nat} :
-    xs.attach[i]? = xs[i]?.pmap Subtype.mk (fun _ a => getElem?_mem a) :=
+    xs.attach[i]? = xs[i]?.pmap Subtype.mk (fun _ a => mem_of_getElem? a) :=
   getElem?_attachWith
 
 @[simp]
@@ -333,6 +338,7 @@ This is useful when we need to use `attach` to show termination.
 
 Unfortunately this can't be applied by `simp` because of the higher order unification problem,
 and even when rewriting we need to specify the function explicitly.
+See however `foldl_subtype` below.
 -/
 theorem foldl_attach (l : List α) (f : β → α → β) (b : β) :
     l.attach.foldl (fun acc t => f acc t.1) b = l.foldl f b := by
@@ -348,6 +354,7 @@ This is useful when we need to use `attach` to show termination.
 
 Unfortunately this can't be applied by `simp` because of the higher order unification problem,
 and even when rewriting we need to specify the function explicitly.
+See however `foldr_subtype` below.
 -/
 theorem foldr_attach (l : List α) (f : α → β → β) (b : β) :
     l.attach.foldr (fun t acc => f t.1 acc) b = l.foldr f b := by
@@ -452,16 +459,16 @@ theorem pmap_append' {p : α → Prop} (f : ∀ a : α, p a → β) (l₁ l₂ :
   pmap_append f l₁ l₂ _
 
 @[simp] theorem attach_append (xs ys : List α) :
-    (xs ++ ys).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_append_of_mem_left ys h⟩) ++
-      ys.attach.map fun ⟨x, h⟩ => ⟨x, mem_append_of_mem_right xs h⟩ := by
+    (xs ++ ys).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_append_left ys h⟩) ++
+      ys.attach.map fun ⟨x, h⟩ => ⟨x, mem_append_right xs h⟩ := by
   simp only [attach, attachWith, pmap, map_pmap, pmap_append]
   congr 1 <;>
   exact pmap_congr_left _ fun _ _ _ _ => rfl
 
 @[simp] theorem attachWith_append {P : α → Prop} {xs ys : List α}
     {H : ∀ (a : α), a ∈ xs ++ ys → P a} :
-    (xs ++ ys).attachWith P H = xs.attachWith P (fun a h => H a (mem_append_of_mem_left ys h)) ++
-      ys.attachWith P (fun a h => H a (mem_append_of_mem_right xs h)) := by
+    (xs ++ ys).attachWith P H = xs.attachWith P (fun a h => H a (mem_append_left ys h)) ++
+      ys.attachWith P (fun a h => H a (mem_append_right xs h)) := by
   simp only [attachWith, attach_append, map_pmap, pmap_append]
 
 @[simp] theorem pmap_reverse {P : α → Prop} (f : (a : α) → P a → β) (xs : List α)
@@ -598,6 +605,15 @@ def unattach {α : Type _} {p : α → Prop} (l : List { x // p x }) := l.map (
   | nil => simp
   | cons a l ih => simp [ih, Function.comp_def]
 
+@[simp] theorem getElem?_unattach {p : α → Prop} {l : List { x // p x }} (i : Nat) :
+    l.unattach[i]? = l[i]?.map Subtype.val := by
+  simp [unattach]
+
+@[simp] theorem getElem_unattach
+    {p : α → Prop} {l : List { x // p x }} (i : Nat) (h : i < l.unattach.length) :
+    l.unattach[i] = (l[i]'(by simpa using h)).1 := by
+  simp [unattach]
+
 /-! ### Recognizing higher order functions on subtypes using a function that only depends on the value. -/
 
 /--

src/Init/Data/List/Basic.lean

@@ -231,7 +231,7 @@ theorem ext_get? : ∀ {l₁ l₂ : List α}, (∀ n, l₁.get? n = l₂.get? n)
     injection h0 with aa; simp only [aa, ext_get? fun n => h (n+1)]
 
 /-- Deprecated alias for `ext_get?`. The preferred extensionality theorem is now `ext_getElem?`. -/
-@[deprecated (since := "2024-06-07")] abbrev ext := @ext_get?
+@[deprecated ext_get? (since := "2024-06-07")] abbrev ext := @ext_get?
 
 /-! ### getD -/
 
@@ -682,7 +682,7 @@ theorem elem_cons [BEq α] {a : α} :
     (b::bs).elem a = match a == b with | true => true | false => bs.elem a := rfl
 
 /-- `notElem a l` is `!(elem a l)`. -/
-@[deprecated (since := "2024-06-15")]
+@[deprecated "Use `!(elem a l)` instead."(since := "2024-06-15")]
 def notElem [BEq α] (a : α) (as : List α) : Bool :=
   !(as.elem a)
 
@@ -726,13 +726,13 @@ theorem elem_eq_true_of_mem [BEq α] [LawfulBEq α] {a : α} {as : List α} (h :
 instance [BEq α] [LawfulBEq α] (a : α) (as : List α) : Decidable (a ∈ as) :=
   decidable_of_decidable_of_iff (Iff.intro mem_of_elem_eq_true elem_eq_true_of_mem)
 
-theorem mem_append_of_mem_left {a : α} {as : List α} (bs : List α) : a ∈ as → a ∈ as ++ bs := by
+theorem mem_append_left {a : α} {as : List α} (bs : List α) : a ∈ as → a ∈ as ++ bs := by
   intro h
   induction h with
   | head => apply Mem.head
   | tail => apply Mem.tail; assumption
 
-theorem mem_append_of_mem_right {b : α} {bs : List α} (as : List α) : b ∈ bs → b ∈ as ++ bs := by
+theorem mem_append_right {b : α} {bs : List α} (as : List α) : b ∈ bs → b ∈ as ++ bs := by
   intro h
   induction as with
   | nil  => simp [h]
@@ -1427,10 +1427,10 @@ def zipWithAll (f : Option α → Option β → γ) : List α → List β → Li
   | a :: as, [] => (a :: as).map fun a => f (some a) none
   | a :: as, b :: bs => f a b :: zipWithAll f as bs
 
-@[simp] theorem zipWithAll_nil_right :
+@[simp] theorem zipWithAll_nil :
     zipWithAll f as [] = as.map fun a => f (some a) none := by
   cases as <;> rfl
-@[simp] theorem zipWithAll_nil_left :
+@[simp] theorem nil_zipWithAll :
     zipWithAll f [] bs = bs.map fun b => f none (some b) := rfl
 @[simp] theorem zipWithAll_cons_cons :
     zipWithAll f (a :: as) (b :: bs) = f (some a) (some b) :: zipWithAll f as bs := rfl

src/Init/Data/List/Control.lean

@@ -256,7 +256,7 @@ theorem findM?_eq_findSomeM? [Monad m] [LawfulMonad m] (p : α → m Bool) (as :
       have : a ∈ as := by
         have ⟨bs, h⟩ := h
         subst h
-        exact mem_append_of_mem_right _ (Mem.head ..)
+        exact mem_append_right _ (Mem.head ..)
       match (← f a this b) with
       | ForInStep.done b  => pure b
       | ForInStep.yield b =>

src/Init/Data/List/FinRange.lean

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

src/Init/Data/List/Lemmas.lean

@@ -101,7 +101,7 @@ theorem tail_eq_of_cons_eq (H : h₁ :: t₁ = h₂ :: t₂) : t₁ = t₂ := (c
 theorem cons_inj_right (a : α) {l l' : List α} : a :: l = a :: l' ↔ l = l' :=
   ⟨tail_eq_of_cons_eq, congrArg _⟩
 
-@[deprecated (since := "2024-06-15")] abbrev cons_inj := @cons_inj_right
+@[deprecated cons_inj_right (since := "2024-06-15")] abbrev cons_inj := @cons_inj_right
 
 theorem cons_eq_cons {a b : α} {l l' : List α} : a :: l = b :: l' ↔ a = b ∧ l = l' :=
   List.cons.injEq .. ▸ .rfl
@@ -171,7 +171,7 @@ theorem get_cons_succ {as : List α} {h : i + 1 < (a :: as).length} :
 theorem get_cons_succ' {as : List α} {i : Fin as.length} :
   (a :: as).get i.succ = as.get i := rfl
 
-@[deprecated (since := "2024-07-09")]
+@[deprecated "Deprecated without replacement." (since := "2024-07-09")]
 theorem get_cons_cons_one : (a₁ :: a₂ :: as).get (1 : Fin (as.length + 2)) = a₂ := rfl
 
 theorem get_mk_zero : ∀ {l : List α} (h : 0 < l.length), l.get ⟨0, h⟩ = l.head (length_pos.mp h)
@@ -394,9 +394,9 @@ theorem get?_concat_length (l : List α) (a : α) : (l ++ [a]).get? l.length = s
 theorem mem_cons_self (a : α) (l : List α) : a ∈ a :: l := .head ..
 
 theorem mem_concat_self (xs : List α) (a : α) : a ∈ xs ++ [a] :=
-  mem_append_of_mem_right xs (mem_cons_self a _)
+  mem_append_right xs (mem_cons_self a _)
 
-theorem mem_append_cons_self : a ∈ xs ++ a :: ys := mem_append_of_mem_right _ (mem_cons_self _ _)
+theorem mem_append_cons_self : a ∈ xs ++ a :: ys := mem_append_right _ (mem_cons_self _ _)
 
 theorem eq_append_cons_of_mem {a : α} {xs : List α} (h : a ∈ xs) :
     ∃ as bs, xs = as ++ a :: bs ∧ a ∉ as := by
@@ -507,12 +507,16 @@ theorem get_mem : ∀ (l : List α) n, get l n ∈ l
   | _ :: _, ⟨0, _⟩ => .head ..
   | _ :: l, ⟨_+1, _⟩ => .tail _ (get_mem l ..)
 
-theorem getElem?_mem {l : List α} {n : Nat} {a : α} (e : l[n]? = some a) : a ∈ l :=
+theorem mem_of_getElem? {l : List α} {n : Nat} {a : α} (e : l[n]? = some a) : a ∈ l :=
   let ⟨_, e⟩ := getElem?_eq_some_iff.1 e; e ▸ getElem_mem ..
 
-theorem get?_mem {l : List α} {n a} (e : l.get? n = some a) : a ∈ l :=
+@[deprecated mem_of_getElem? (since := "2024-09-06")] abbrev getElem?_mem := @mem_of_getElem?
+
+theorem mem_of_get? {l : List α} {n a} (e : l.get? n = some a) : a ∈ l :=
   let ⟨_, e⟩ := get?_eq_some.1 e; e ▸ get_mem ..
 
+@[deprecated mem_of_get? (since := "2024-09-06")] abbrev get?_mem := @mem_of_get?
+
 theorem mem_iff_getElem {a} {l : List α} : a ∈ l ↔ ∃ (n : Nat) (h : n < l.length), l[n]'h = a :=
   ⟨getElem_of_mem, fun ⟨_, _, e⟩ => e ▸ getElem_mem ..⟩
 
@@ -787,6 +791,24 @@ theorem mem_or_eq_of_mem_set : ∀ {l : List α} {n : Nat} {a b : α}, a ∈ l.s
     · intro a
       simp
 
+@[simp] theorem beq_nil_iff [BEq α] {l : List α} : (l == []) = l.isEmpty := by
+  cases l <;> rfl
+
+@[simp] theorem nil_beq_iff [BEq α] {l : List α} : ([] == l) = l.isEmpty := by
+  cases l <;> rfl
+
+@[simp] theorem cons_beq_cons [BEq α] {a b : α} {l₁ l₂ : List α} :
+    (a :: l₁ == b :: l₂) = (a == b && l₁ == l₂) := rfl
+
+theorem length_eq_of_beq [BEq α] {l₁ l₂ : List α} (h : l₁ == l₂) : l₁.length = l₂.length :=
+  match l₁, l₂ with
+  | [], [] => rfl
+  | [], _ :: _ => by simp [beq_nil_iff] at h
+  | _ :: _, [] => by simp [nil_beq_iff] at h
+  | a :: l₁, b :: l₂ => by
+    simp at h
+    simpa [Nat.add_one_inj]using length_eq_of_beq h.2
+
 /-! ### Lexicographic ordering -/
 
 protected theorem lt_irrefl [LT α] (lt_irrefl : ∀ x : α, ¬x < x) (l : List α) : ¬l < l := by
@@ -852,6 +874,12 @@ theorem foldr_eq_foldrM (f : α → β → β) (b) (l : List α) :
     l.foldr f b = l.foldrM (m := Id) f b := by
   induction l <;> simp [*, foldr]
 
+@[simp] theorem id_run_foldlM (f : β → α → Id β) (b) (l : List α) :
+    Id.run (l.foldlM f b) = l.foldl f b := (foldl_eq_foldlM f b l).symm
+
+@[simp] theorem id_run_foldrM (f : α → β → Id β) (b) (l : List α) :
+    Id.run (l.foldrM f b) = l.foldr f b := (foldr_eq_foldrM f b l).symm
+
 /-! ### foldl and foldr -/
 
 @[simp] theorem foldr_cons_eq_append (l : List α) : l.foldr cons l' = l ++ l' := by
@@ -1796,7 +1824,7 @@ theorem getElem_append_right' (l₁ : List α) {l₂ : List α} {n : Nat} (hn :
     l₂[n] = (l₁ ++ l₂)[n + l₁.length]'(by simpa [Nat.add_comm] using Nat.add_lt_add_left hn _) := by
   rw [getElem_append_right] <;> simp [*, le_add_left]
 
-@[deprecated (since := "2024-06-12")]
+@[deprecated "Deprecated without replacement." (since := "2024-06-12")]
 theorem get_append_right_aux {l₁ l₂ : List α} {n : Nat}
   (h₁ : l₁.length ≤ n) (h₂ : n < (l₁ ++ l₂).length) : n - l₁.length < l₂.length := by
   rw [length_append] at h₂
@@ -1813,7 +1841,7 @@ theorem getElem_of_append {l : List α} (eq : l = l₁ ++ a :: l₂) (h : l₁.l
   rw [← getElem?_eq_getElem, eq, getElem?_append_right (h ▸ Nat.le_refl _), h]
   simp
 
-@[deprecated (since := "2024-06-12")]
+@[deprecated "Deprecated without replacement." (since := "2024-06-12")]
 theorem get_of_append_proof {l : List α}
     (eq : l = l₁ ++ a :: l₂) (h : l₁.length = n) : n < length l := eq ▸ h ▸ by simp_arith
 
@@ -1997,11 +2025,8 @@ theorem not_mem_append {a : α} {s t : List α} (h₁ : a ∉ s) (h₂ : a ∉ t
 theorem mem_append_eq (a : α) (s t : List α) : (a ∈ s ++ t) = (a ∈ s ∨ a ∈ t) :=
   propext mem_append
 
-theorem mem_append_left {a : α} {l₁ : List α} (l₂ : List α) (h : a ∈ l₁) : a ∈ l₁ ++ l₂ :=
-  mem_append.2 (Or.inl h)
-
-theorem mem_append_right {a : α} (l₁ : List α) {l₂ : List α} (h : a ∈ l₂) : a ∈ l₁ ++ l₂ :=
-  mem_append.2 (Or.inr h)
+@[deprecated mem_append_left (since := "2024-11-20")] abbrev mem_append_of_mem_left := @mem_append_left
+@[deprecated mem_append_right (since := "2024-11-20")] abbrev mem_append_of_mem_right := @mem_append_right
 
 theorem mem_iff_append {a : α} {l : List α} : a ∈ l ↔ ∃ s t : List α, l = s ++ a :: t :=
   ⟨append_of_mem, fun ⟨s, t, e⟩ => e ▸ by simp⟩
@@ -3332,10 +3357,10 @@ theorem any_eq_not_all_not (l : List α) (p : α → Bool) : l.any p = !l.all (!
 theorem all_eq_not_any_not (l : List α) (p : α → Bool) : l.all p = !l.any (!p .) := by
   simp only [not_any_eq_all_not, Bool.not_not]
 
-@[simp] theorem any_map {l : List α} {p : α → Bool} : (l.map f).any p = l.any (p ∘ f) := by
+@[simp] theorem any_map {l : List α} {p : β → Bool} : (l.map f).any p = l.any (p ∘ f) := by
   induction l with simp | cons _ _ ih => rw [ih]
 
-@[simp] theorem all_map {l : List α} {p : α → Bool} : (l.map f).all p = l.all (p ∘ f) := by
+@[simp] theorem all_map {l : List α} {p : β → Bool} : (l.map f).all p = l.all (p ∘ f) := by
   induction l with simp | cons _ _ ih => rw [ih]
 
 @[simp] theorem any_filter {l : List α} {p q : α → Bool} :

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

@@ -9,7 +9,7 @@ import Init.Data.List.Basic
 
 namespace List
 
-/-! ### isEqv-/
+/-! ### isEqv -/
 
 theorem isEqv_eq_decide (a b : List α) (r) :
     isEqv a b r = if h : a.length = b.length then

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

@@ -293,7 +293,7 @@ theorem sorted_mergeSort
     apply sorted_mergeSort trans total
 termination_by l => l.length
 
-@[deprecated (since := "2024-09-02")] abbrev mergeSort_sorted := @sorted_mergeSort
+@[deprecated sorted_mergeSort (since := "2024-09-02")] abbrev mergeSort_sorted := @sorted_mergeSort
 
 /--
 If the input list is already sorted, then `mergeSort` does not change the list.
@@ -429,7 +429,8 @@ theorem sublist_mergeSort
         ((fun w => Sublist.of_sublist_append_right w h') fun b m₁ m₃ =>
           (Bool.eq_not_self true).mp ((rel_of_pairwise_cons hc m₁).symm.trans (h₃ b m₃))))
 
-@[deprecated (since := "2024-09-02")] abbrev mergeSort_stable := @sublist_mergeSort
+@[deprecated sublist_mergeSort (since := "2024-09-02")]
+abbrev mergeSort_stable := @sublist_mergeSort
 
 /--
 Another statement of stability of merge sort.
@@ -442,7 +443,8 @@ theorem pair_sublist_mergeSort
     (hab : le a b) (h : [a, b] <+ l) : [a, b] <+ mergeSort l le :=
   sublist_mergeSort trans total (pairwise_pair.mpr hab) h
 
-@[deprecated (since := "2024-09-02")] abbrev mergeSort_stable_pair := @pair_sublist_mergeSort
+@[deprecated pair_sublist_mergeSort(since := "2024-09-02")]
+abbrev mergeSort_stable_pair := @pair_sublist_mergeSort
 
 theorem map_merge {f : α → β} {r : α → α → Bool} {s : β → β → Bool} {l l' : List α}
     (hl : ∀ a ∈ l, ∀ b ∈ l', r a b = s (f a) (f b)) :

src/Init/Data/List/Sublist.lean

@@ -417,7 +417,7 @@ theorem Sublist.of_sublist_append_left (w : ∀ a, a ∈ l → a ∉ l₂) (h :
   obtain ⟨l₁', l₂', rfl, h₁, h₂⟩ := h
   have : l₂' = [] := by
     rw [eq_nil_iff_forall_not_mem]
-    exact fun x m => w x (mem_append_of_mem_right l₁' m) (h₂.mem m)
+    exact fun x m => w x (mem_append_right l₁' m) (h₂.mem m)
   simp_all
 
 theorem Sublist.of_sublist_append_right (w : ∀ a, a ∈ l → a ∉ l₁) (h : l <+ l₁ ++ l₂) : l <+ l₂ := by
@@ -425,7 +425,7 @@ theorem Sublist.of_sublist_append_right (w : ∀ a, a ∈ l → a ∉ l₁) (h :
   obtain ⟨l₁', l₂', rfl, h₁, h₂⟩ := h
   have : l₁' = [] := by
     rw [eq_nil_iff_forall_not_mem]
-    exact fun x m => w x (mem_append_of_mem_left l₂' m) (h₁.mem m)
+    exact fun x m => w x (mem_append_left l₂' m) (h₁.mem m)
   simp_all
 
 theorem Sublist.middle {l : List α} (h : l <+ l₁ ++ l₂) (a : α) : l <+ l₁ ++ a :: l₂ := by
@@ -835,7 +835,7 @@ theorem isPrefix_iff : l₁ <+: l₂ ↔ ∀ i (h : i < l₁.length), l₂[i]? =
       simpa using ⟨0, by simp⟩
     | cons b l₂ =>
       simp only [cons_append, cons_prefix_cons, ih]
-      rw (occs := .pos [2]) [← Nat.and_forall_add_one]
+      rw (occs := [2]) [← Nat.and_forall_add_one]
       simp [Nat.succ_lt_succ_iff, eq_comm]
 
 theorem isPrefix_iff_getElem {l₁ l₂ : List α} :

src/Init/Data/List/TakeDrop.lean

@@ -224,7 +224,7 @@ theorem take_succ {l : List α} {n : Nat} : l.take (n + 1) = l.take n ++ l[n]?.t
     · simp only [take, Option.toList, getElem?_cons_zero, nil_append]
     · simp only [take, hl, getElem?_cons_succ, cons_append]
 
-@[deprecated (since := "2024-07-25")]
+@[deprecated "Deprecated without replacement." (since := "2024-07-25")]
 theorem drop_sizeOf_le [SizeOf α] (l : List α) (n : Nat) : sizeOf (l.drop n) ≤ sizeOf l := by
   induction l generalizing n with
   | nil => rw [drop_nil]; apply Nat.le_refl

src/Init/Data/Nat.lean

@@ -20,3 +20,4 @@ import Init.Data.Nat.Mod
 import Init.Data.Nat.Lcm
 import Init.Data.Nat.Compare
 import Init.Data.Nat.Simproc
+import Init.Data.Nat.Fold

src/Init/Data/Nat/Basic.lean

@@ -35,52 +35,6 @@ Used as the default `Nat` eliminator by the `cases` tactic. -/
 protected abbrev casesAuxOn {motive : Nat → Sort u} (t : Nat) (zero : motive 0) (succ : (n : Nat) → motive (n + 1)) : motive t :=
   Nat.casesOn t zero succ
 
-/--
-`Nat.fold` evaluates `f` on the numbers up to `n` exclusive, in increasing order:
-* `Nat.fold f 3 init = init |> f 0 |> f 1 |> f 2`
--/
-@[specialize] def fold {α : Type u} (f : Nat → α → α) : (n : Nat) → (init : α) → α
-  | 0,      a => a
-  | succ n, a => f n (fold f n a)
-
-/-- Tail-recursive version of `Nat.fold`. -/
-@[inline] def foldTR {α : Type u} (f : Nat → α → α) (n : Nat) (init : α) : α :=
-  let rec @[specialize] loop
-    | 0,      a => a
-    | succ m, a => loop m (f (n - succ m) a)
-  loop n init
-
-/--
-`Nat.foldRev` evaluates `f` on the numbers up to `n` exclusive, in decreasing order:
-* `Nat.foldRev f 3 init = f 0 <| f 1 <| f 2 <| init`
--/
-@[specialize] def foldRev {α : Type u} (f : Nat → α → α) : (n : Nat) → (init : α) → α
-  | 0,      a => a
-  | succ n, a => foldRev f n (f n a)
-
-/-- `any f n = true` iff there is `i in [0, n-1]` s.t. `f i = true` -/
-@[specialize] def any (f : Nat → Bool) : Nat → Bool
-  | 0      => false
-  | succ n => any f n || f n
-
-/-- Tail-recursive version of `Nat.any`. -/
-@[inline] def anyTR (f : Nat → Bool) (n : Nat) : Bool :=
-  let rec @[specialize] loop : Nat → Bool
-    | 0      => false
-    | succ m => f (n - succ m) || loop m
-  loop n
-
-/-- `all f n = true` iff every `i in [0, n-1]` satisfies `f i = true` -/
-@[specialize] def all (f : Nat → Bool) : Nat → Bool
-  | 0      => true
-  | succ n => all f n && f n
-
-/-- Tail-recursive version of `Nat.all`. -/
-@[inline] def allTR (f : Nat → Bool) (n : Nat) : Bool :=
-  let rec @[specialize] loop : Nat → Bool
-    | 0      => true
-    | succ m => f (n - succ m) && loop m
-  loop n
 
 /--
 `Nat.repeat f n a` is `f^(n) a`; that is, it iterates `f` `n` times on `a`.
@@ -835,7 +789,7 @@ theorem pred_lt_of_lt {n m : Nat} (h : m < n) : pred n < n :=
   pred_lt (not_eq_zero_of_lt h)
 
 set_option linter.missingDocs false in
-@[deprecated (since := "2024-06-01")] abbrev pred_lt' := @pred_lt_of_lt
+@[deprecated pred_lt_of_lt (since := "2024-06-01")] abbrev pred_lt' := @pred_lt_of_lt
 
 theorem sub_one_lt_of_lt {n m : Nat} (h : m < n) : n - 1 < n :=
   sub_one_lt (not_eq_zero_of_lt h)
@@ -1121,7 +1075,7 @@ theorem pred_mul (n m : Nat) : pred n * m = n * m - m := by
   | succ n => rw [Nat.pred_succ, succ_mul, Nat.add_sub_cancel]
 
 set_option linter.missingDocs false in
-@[deprecated (since := "2024-06-01")] abbrev mul_pred_left := @pred_mul
+@[deprecated pred_mul (since := "2024-06-01")] abbrev mul_pred_left := @pred_mul
 
 protected theorem sub_one_mul  (n m : Nat) : (n - 1) * m = n * m - m := by
   cases n with
@@ -1133,7 +1087,7 @@ theorem mul_pred (n m : Nat) : n * pred m = n * m - n := by
   rw [Nat.mul_comm, pred_mul, Nat.mul_comm]
 
 set_option linter.missingDocs false in
-@[deprecated (since := "2024-06-01")] abbrev mul_pred_right := @mul_pred
+@[deprecated mul_pred (since := "2024-06-01")] abbrev mul_pred_right := @mul_pred
 
 theorem mul_sub_one (n m : Nat) : n * (m - 1) = n * m - n := by
   rw [Nat.mul_comm, Nat.sub_one_mul , Nat.mul_comm]
@@ -1158,33 +1112,6 @@ theorem not_lt_eq (a b : Nat) : (¬ (a < b)) = (b ≤ a) :=
 theorem not_gt_eq (a b : Nat) : (¬ (a > b)) = (a ≤ b) :=
   not_lt_eq b a
 
-/-! # csimp theorems -/
-
-@[csimp] theorem fold_eq_foldTR : @fold = @foldTR :=
-  funext fun α => funext fun f => funext fun n => funext fun init =>
-  let rec go : ∀ m n, foldTR.loop f (m + n) m (fold f n init) = fold f (m + n) init
-    | 0,      n => by simp [foldTR.loop]
-    | succ m, n => by rw [foldTR.loop, add_sub_self_left, succ_add]; exact go m (succ n)
-  (go n 0).symm
-
-@[csimp] theorem any_eq_anyTR : @any = @anyTR :=
-  funext fun f => funext fun n =>
-  let rec go : ∀ m n,  (any f n || anyTR.loop f (m + n) m) = any f (m + n)
-    | 0,      n => by simp [anyTR.loop]
-    | succ m, n => by
-      rw [anyTR.loop, add_sub_self_left, ← Bool.or_assoc, succ_add]
-      exact go m (succ n)
-  (go n 0).symm
-
-@[csimp] theorem all_eq_allTR : @all = @allTR :=
-  funext fun f => funext fun n =>
-  let rec go : ∀ m n,  (all f n && allTR.loop f (m + n) m) = all f (m + n)
-    | 0,      n => by simp [allTR.loop]
-    | succ m, n => by
-      rw [allTR.loop, add_sub_self_left, ← Bool.and_assoc, succ_add]
-      exact go m (succ n)
-  (go n 0).symm
-
 @[csimp] theorem repeat_eq_repeatTR : @repeat = @repeatTR :=
   funext fun α => funext fun f => funext fun n => funext fun init =>
   let rec go : ∀ m n, repeatTR.loop f m (repeat f n init) = repeat f (m + n) init
@@ -1193,31 +1120,3 @@ theorem not_gt_eq (a b : Nat) : (¬ (a > b)) = (a ≤ b) :=
   (go n 0).symm
 
 end Nat
-
-namespace Prod
-
-/--
-`(start, stop).foldI f a` evaluates `f` on all the numbers
-from `start` (inclusive) to `stop` (exclusive) in increasing order:
-* `(5, 8).foldI f init = init |> f 5 |> f 6 |> f 7`
--/
-@[inline] def foldI {α : Type u} (f : Nat → α → α) (i : Nat × Nat) (a : α) : α :=
-  Nat.foldTR.loop f i.2 (i.2 - i.1) a
-
-/--
-`(start, stop).anyI f a` returns true if `f` is true for some natural number
-from `start` (inclusive) to `stop` (exclusive):
-* `(5, 8).anyI f = f 5 || f 6 || f 7`
--/
-@[inline] def anyI (f : Nat → Bool) (i : Nat × Nat) : Bool :=
-  Nat.anyTR.loop f i.2 (i.2 - i.1)
-
-/--
-`(start, stop).allI f a` returns true if `f` is true for all natural numbers
-from `start` (inclusive) to `stop` (exclusive):
-* `(5, 8).anyI f = f 5 && f 6 && f 7`
--/
-@[inline] def allI (f : Nat → Bool) (i : Nat × Nat) : Bool :=
-  Nat.allTR.loop f i.2 (i.2 - i.1)
-
-end Prod

src/Init/Data/Nat/Control.lean

@@ -6,50 +6,51 @@ Author: Leonardo de Moura
 prelude
 import Init.Control.Basic
 import Init.Data.Nat.Basic
+import Init.Omega
 
 namespace Nat
 universe u v
 
-@[inline] def forM {m} [Monad m] (n : Nat) (f : Nat → m Unit) : m Unit :=
-  let rec @[specialize] loop
-    | 0   => pure ()
-    | i+1 => do f (n-i-1); loop i
-  loop n
+@[inline] def forM {m} [Monad m] (n : Nat) (f : (i : Nat) → i < n → m Unit) : m Unit :=
+  let rec @[specialize] loop : ∀ i, i ≤ n → m Unit
+    | 0,   _ => pure ()
+    | i+1, h => do f (n-i-1) (by omega); loop i (Nat.le_of_succ_le h)
+  loop n (by simp)
 
-@[inline] def forRevM {m} [Monad m] (n : Nat) (f : Nat → m Unit) : m Unit :=
-  let rec @[specialize] loop
-    | 0   => pure ()
-    | i+1 => do f i; loop i
-  loop n
+@[inline] def forRevM {m} [Monad m] (n : Nat) (f : (i : Nat) → i < n → m Unit) : m Unit :=
+  let rec @[specialize] loop : ∀ i, i ≤ n → m Unit
+    | 0,   _ => pure ()
+    | i+1, h => do f i (by omega); loop i (Nat.le_of_succ_le h)
+  loop n (by simp)
 
-@[inline] def foldM {α : Type u} {m : Type u → Type v} [Monad m] (f : Nat → α → m α) (init : α) (n : Nat) : m α :=
-  let rec @[specialize] loop
-    | 0,   a => pure a
-    | i+1, a => f (n-i-1) a >>= loop i
-  loop n init
+@[inline] def foldM {α : Type u} {m : Type u → Type v} [Monad m] (n : Nat) (f : (i : Nat) → i < n → α → m α) (init : α) : m α :=
+  let rec @[specialize] loop : ∀ i, i ≤ n → α → m α
+    | 0,   h, a => pure a
+    | i+1, h, a => f (n-i-1) (by omega) a >>= loop i (Nat.le_of_succ_le h)
+  loop n (by omega) init
 
-@[inline] def foldRevM {α : Type u} {m : Type u → Type v} [Monad m] (f : Nat → α → m α) (init : α) (n : Nat) : m α :=
-  let rec @[specialize] loop
-    | 0,   a => pure a
-    | i+1, a => f i a >>= loop i
-  loop n init
+@[inline] def foldRevM {α : Type u} {m : Type u → Type v} [Monad m] (n : Nat) (f : (i : Nat) → i < n → α → m α) (init : α) : m α :=
+  let rec @[specialize] loop : ∀ i, i ≤ n → α → m α
+    | 0,   h, a => pure a
+    | i+1, h, a => f i (by omega) a >>= loop i (Nat.le_of_succ_le h)
+  loop n (by omega) init
 
-@[inline] def allM {m} [Monad m] (n : Nat) (p : Nat → m Bool) : m Bool :=
-  let rec @[specialize] loop
-    | 0   => pure true
-    | i+1 => do
-      match (← p (n-i-1)) with
-      | true  => loop i
+@[inline] def allM {m} [Monad m] (n : Nat) (p : (i : Nat) → i < n → m Bool) : m Bool :=
+  let rec @[specialize] loop : ∀ i, i ≤ n → m Bool
+    | 0,   _ => pure true
+    | i+1 , h => do
+      match (← p (n-i-1) (by omega)) with
+      | true  => loop i (by omega)
       | false => pure false
-  loop n
+  loop n (by simp)
 
-@[inline] def anyM {m} [Monad m] (n : Nat) (p : Nat → m Bool) : m Bool :=
-  let rec @[specialize] loop
-    | 0   => pure false
-    | i+1 => do
-      match (← p (n-i-1)) with
+@[inline] def anyM {m} [Monad m] (n : Nat) (p : (i : Nat) → i < n → m Bool) : m Bool :=
+  let rec @[specialize] loop : ∀ i, i ≤ n → m Bool
+    | 0,   _ => pure false
+    | i+1, h => do
+      match (← p (n-i-1) (by omega)) with
       | true  => pure true
-      | false => loop i
-  loop n
+      | false => loop i (Nat.le_of_succ_le h)
+  loop n (by simp)
 
 end Nat

src/Init/Data/Nat/Dvd.lean

@@ -92,7 +92,7 @@ protected theorem div_mul_cancel {n m : Nat} (H : n ∣ m) : m / n * n = m := by
   rw [Nat.mul_comm, Nat.mul_div_cancel' H]
 
 @[simp] theorem mod_mod_of_dvd (a : Nat) (h : c ∣ b) : a % b % c = a % c := by
-  rw (occs := .pos [2]) [← mod_add_div a b]
+  rw (occs := [2]) [← mod_add_div a b]
   have ⟨x, h⟩ := h
   subst h
   rw [Nat.mul_assoc, add_mul_mod_self_left]

src/Init/Data/Nat/Fold.lean

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

src/Init/Data/Nat/Lemmas.lean

@@ -651,8 +651,8 @@ theorem sub_mul_mod {x k n : Nat} (h₁ : n*k ≤ x) : (x - n*k) % n = x % n :=
   | .inr npos => Nat.mod_eq_of_lt (mod_lt _ npos)
 
 theorem mul_mod (a b n : Nat) : a * b % n = (a % n) * (b % n) % n := by
-  rw (occs := .pos [1]) [← mod_add_div a n]
-  rw (occs := .pos [1]) [← mod_add_div b n]
+  rw (occs := [1]) [← mod_add_div a n]
+  rw (occs := [1]) [← mod_add_div b n]
   rw [Nat.add_mul, Nat.mul_add, Nat.mul_add,
     Nat.mul_assoc, Nat.mul_assoc, ← Nat.mul_add n, add_mul_mod_self_left,
     Nat.mul_comm _ (n * (b / n)), Nat.mul_assoc, add_mul_mod_self_left]
@@ -679,6 +679,10 @@ theorem add_mod (a b n : Nat) : (a + b) % n = ((a % n) + (b % n)) % n := by
 @[simp] theorem mod_mul_mod {a b c : Nat} : (a % c * b) % c = a * b % c := by
   rw [mul_mod, mod_mod, ← mul_mod]
 
+theorem mod_eq_sub (x w : Nat) : x % w = x - w * (x / w) := by
+  conv => rhs; congr; rw [← mod_add_div x w]
+  simp
+
 /-! ### pow -/
 
 theorem pow_succ' {m n : Nat} : m ^ n.succ = m * m ^ n := by
@@ -846,6 +850,18 @@ protected theorem pow_lt_pow_iff_pow_mul_le_pow {a n m : Nat} (h : 1 < a) :
   rw [←Nat.pow_add_one, Nat.pow_le_pow_iff_right (by omega), Nat.pow_lt_pow_iff_right (by omega)]
   omega
 
+protected theorem lt_pow_self {n a : Nat} (h : 1 < a) : n < a ^ n := by
+  induction n with
+  | zero => exact Nat.zero_lt_one
+  | succ _ ih => exact Nat.lt_of_lt_of_le (Nat.add_lt_add_right ih 1) (Nat.pow_lt_pow_succ h)
+
+protected theorem lt_two_pow_self : n < 2 ^ n :=
+  Nat.lt_pow_self Nat.one_lt_two
+
+@[simp]
+protected theorem mod_two_pow_self : n % 2 ^ n = n :=
+  Nat.mod_eq_of_lt Nat.lt_two_pow_self
+
 @[simp]
 theorem two_pow_pred_mul_two (h : 0 < w) :
     2 ^ (w - 1) * 2 = 2 ^ w := by

src/Init/Data/Sum/Basic.lean

@@ -31,7 +31,7 @@ This file defines basic operations on the the sum type `α ⊕ β`.
 
 ## Further material
 
-See `Batteries.Data.Sum.Lemmas` for theorems about these definitions.
+See `Init.Data.Sum.Lemmas` for theorems about these definitions.
 
 ## Notes
 

src/Init/Data/UInt/Basic.lean

@@ -246,6 +246,12 @@ instance (a b : UInt64) : Decidable (a ≤ b) := UInt64.decLe a b
 instance : Max UInt64 := maxOfLe
 instance : Min UInt64 := minOfLe
 
+theorem usize_size_le : USize.size ≤ 18446744073709551616 := by
+  cases usize_size_eq <;> next h => rw [h]; decide
+
+theorem le_usize_size : 4294967296 ≤ USize.size := by
+  cases usize_size_eq <;> next h => rw [h]; decide
+
 @[extern "lean_usize_mul"]
 def USize.mul (a b : USize) : USize := ⟨a.toBitVec * b.toBitVec⟩
 @[extern "lean_usize_div"]
@@ -264,10 +270,29 @@ def USize.xor (a b : USize) : USize := ⟨a.toBitVec ^^^ b.toBitVec⟩
 def USize.shiftLeft (a b : USize) : USize := ⟨a.toBitVec <<< (mod b (USize.ofNat System.Platform.numBits)).toBitVec⟩
 @[extern "lean_usize_shift_right"]
 def USize.shiftRight (a b : USize) : USize := ⟨a.toBitVec >>> (mod b (USize.ofNat System.Platform.numBits)).toBitVec⟩
+/--
+Upcast a `Nat` less than `2^32` to a `USize`.
+This is lossless because `USize.size` is either `2^32` or `2^64`.
+This function is overridden with a native implementation.
+-/
+@[extern "lean_usize_of_nat"]
+def USize.ofNat32 (n : @& Nat) (h : n < 4294967296) : USize :=
+  USize.ofNatCore n (Nat.lt_of_lt_of_le h le_usize_size)
 @[extern "lean_uint32_to_usize"]
 def UInt32.toUSize (a : UInt32) : USize := USize.ofNat32 a.toBitVec.toNat a.toBitVec.isLt
 @[extern "lean_usize_to_uint32"]
 def USize.toUInt32 (a : USize) : UInt32 := a.toNat.toUInt32
+/-- Converts a `UInt64` to a `USize` by reducing modulo `USize.size`. -/
+@[extern "lean_uint64_to_usize"]
+def UInt64.toUSize (a : UInt64) : USize := a.toNat.toUSize
+/--
+Upcast a `USize` to a `UInt64`.
+This is lossless because `USize.size` is either `2^32` or `2^64`.
+This function is overridden with a native implementation.
+-/
+@[extern "lean_usize_to_uint64"]
+def USize.toUInt64 (a : USize) : UInt64 :=
+  UInt64.ofNatCore a.toBitVec.toNat (Nat.lt_of_lt_of_le a.toBitVec.isLt usize_size_le)
 
 instance : Mul USize       := ⟨USize.mul⟩
 instance : Mod USize       := ⟨USize.mod⟩

src/Init/Data/UInt/BasicAux.lean

@@ -94,10 +94,8 @@ def UInt32.toUInt64 (a : UInt32) : UInt64 := ⟨⟨a.toNat, Nat.lt_trans a.toBit
 
 instance UInt64.instOfNat : OfNat UInt64 n := ⟨UInt64.ofNat n⟩
 
-theorem usize_size_gt_zero : USize.size > 0 := by
-  cases usize_size_eq with
-  | inl h => rw [h]; decide
-  | inr h => rw [h]; decide
+@[deprecated usize_size_pos (since := "2024-11-24")] theorem usize_size_gt_zero : USize.size > 0 :=
+  usize_size_pos
 
 def USize.val (x : USize) : Fin USize.size := x.toBitVec.toFin
 @[extern "lean_usize_of_nat"]

src/Init/Data/UInt/Lemmas.lean

@@ -133,6 +133,9 @@ declare_uint_theorems UInt32
 declare_uint_theorems UInt64
 declare_uint_theorems USize
 
+theorem USize.toNat_ofNat_of_lt_32 {n : Nat} (h : n < 4294967296) : toNat (ofNat n) = n :=
+  toNat_ofNat_of_lt (Nat.lt_of_lt_of_le h le_usize_size)
+
 theorem UInt32.toNat_lt_of_lt {n : UInt32} {m : Nat} (h : m < size) : n < ofNat m → n.toNat < m := by
   simp [lt_def, BitVec.lt_def, UInt32.toNat, toBitVec_eq_of_lt h]
 
@@ -145,22 +148,22 @@ theorem UInt32.toNat_le_of_le {n : UInt32} {m : Nat} (h : m < size) : n ≤ ofNa
 theorem UInt32.le_toNat_of_le {n : UInt32} {m : Nat} (h : m < size) : ofNat m ≤ n → m ≤ n.toNat := by
   simp [le_def, BitVec.le_def, UInt32.toNat, toBitVec_eq_of_lt h]
 
-@[deprecated (since := "2024-06-23")] protected abbrev UInt8.zero_toNat := @UInt8.toNat_zero
-@[deprecated (since := "2024-06-23")] protected abbrev UInt8.div_toNat := @UInt8.toNat_div
-@[deprecated (since := "2024-06-23")] protected abbrev UInt8.mod_toNat := @UInt8.toNat_mod
+@[deprecated UInt8.toNat_zero (since := "2024-06-23")] protected abbrev UInt8.zero_toNat := @UInt8.toNat_zero
+@[deprecated UInt8.toNat_div (since := "2024-06-23")] protected abbrev UInt8.div_toNat := @UInt8.toNat_div
+@[deprecated UInt8.toNat_mod (since := "2024-06-23")] protected abbrev UInt8.mod_toNat := @UInt8.toNat_mod
 
-@[deprecated (since := "2024-06-23")] protected abbrev UInt16.zero_toNat := @UInt16.toNat_zero
-@[deprecated (since := "2024-06-23")] protected abbrev UInt16.div_toNat := @UInt16.toNat_div
-@[deprecated (since := "2024-06-23")] protected abbrev UInt16.mod_toNat := @UInt16.toNat_mod
+@[deprecated UInt16.toNat_zero (since := "2024-06-23")] protected abbrev UInt16.zero_toNat := @UInt16.toNat_zero
+@[deprecated UInt16.toNat_div (since := "2024-06-23")] protected abbrev UInt16.div_toNat := @UInt16.toNat_div
+@[deprecated UInt16.toNat_mod (since := "2024-06-23")] protected abbrev UInt16.mod_toNat := @UInt16.toNat_mod
 
-@[deprecated (since := "2024-06-23")] protected abbrev UInt32.zero_toNat := @UInt32.toNat_zero
-@[deprecated (since := "2024-06-23")] protected abbrev UInt32.div_toNat := @UInt32.toNat_div
-@[deprecated (since := "2024-06-23")] protected abbrev UInt32.mod_toNat := @UInt32.toNat_mod
+@[deprecated UInt32.toNat_zero (since := "2024-06-23")] protected abbrev UInt32.zero_toNat := @UInt32.toNat_zero
+@[deprecated UInt32.toNat_div (since := "2024-06-23")] protected abbrev UInt32.div_toNat := @UInt32.toNat_div
+@[deprecated UInt32.toNat_mod (since := "2024-06-23")] protected abbrev UInt32.mod_toNat := @UInt32.toNat_mod
 
-@[deprecated (since := "2024-06-23")] protected abbrev UInt64.zero_toNat := @UInt64.toNat_zero
-@[deprecated (since := "2024-06-23")] protected abbrev UInt64.div_toNat := @UInt64.toNat_div
-@[deprecated (since := "2024-06-23")] protected abbrev UInt64.mod_toNat := @UInt64.toNat_mod
+@[deprecated UInt64.toNat_zero (since := "2024-06-23")] protected abbrev UInt64.zero_toNat := @UInt64.toNat_zero
+@[deprecated UInt64.toNat_div (since := "2024-06-23")] protected abbrev UInt64.div_toNat := @UInt64.toNat_div
+@[deprecated UInt64.toNat_mod (since := "2024-06-23")] protected abbrev UInt64.mod_toNat := @UInt64.toNat_mod
 
-@[deprecated (since := "2024-06-23")] protected abbrev USize.zero_toNat := @USize.toNat_zero
-@[deprecated (since := "2024-06-23")] protected abbrev USize.div_toNat := @USize.toNat_div
-@[deprecated (since := "2024-06-23")] protected abbrev USize.mod_toNat := @USize.toNat_mod
+@[deprecated USize.toNat_zero (since := "2024-06-23")] protected abbrev USize.zero_toNat := @USize.toNat_zero
+@[deprecated USize.toNat_div (since := "2024-06-23")] protected abbrev USize.div_toNat := @USize.toNat_div
+@[deprecated USize.toNat_mod (since := "2024-06-23")] protected abbrev USize.mod_toNat := @USize.toNat_mod

src/Init/Data/Vector.lean

@@ -0,0 +1,7 @@
+/-
+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.Vector.Basic

src/Init/Data/Vector/Basic.lean

@@ -0,0 +1,253 @@
+/-
+Copyright (c) 2024 Shreyas Srinivas. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Shreyas Srinivas, François G. Dorais, Kim Morrison
+-/
+
+prelude
+import Init.Data.Array.Lemmas
+
+/-!
+# Vectors
+
+`Vector α n` is a thin wrapper around `Array α` for arrays of fixed size `n`.
+-/
+
+/-- `Vector α n` is an `Array α` with size `n`. -/
+structure Vector (α : Type u) (n : Nat) extends Array α where
+  /-- Array size. -/
+  size_toArray : toArray.size = n
+deriving Repr, DecidableEq
+
+attribute [simp] Vector.size_toArray
+
+namespace Vector
+
+/-- Syntax for `Vector α n` -/
+syntax "#v[" withoutPosition(sepBy(term, ", ")) "]" : term
+
+open Lean in
+macro_rules
+  | `(#v[ $elems,* ]) => `(Vector.mk (n := $(quote elems.getElems.size)) #[$elems,*] rfl)
+
+/-- Custom eliminator for `Vector α n` through `Array α` -/
+@[elab_as_elim]
+def elimAsArray {motive : Vector α n → Sort u}
+    (mk : ∀ (a : Array α) (ha : a.size = n), motive ⟨a, ha⟩) :
+    (v : Vector α n) → motive v
+  | ⟨a, ha⟩ => mk a ha
+
+/-- Custom eliminator for `Vector α n` through `List α` -/
+@[elab_as_elim]
+def elimAsList {motive : Vector α n → Sort u}
+    (mk : ∀ (a : List α) (ha : a.length = n), motive ⟨⟨a⟩, ha⟩) :
+    (v : Vector α n) → motive v
+  | ⟨⟨a⟩, ha⟩ => mk a ha
+
+/-- Make an empty vector with pre-allocated capacity. -/
+@[inline] def mkEmpty (capacity : Nat) : Vector α 0 := ⟨.mkEmpty capacity, rfl⟩
+
+/-- Makes a vector of size `n` with all cells containing `v`. -/
+@[inline] def mkVector (n) (v : α) : Vector α n := ⟨mkArray n v, by simp⟩
+
+/-- Returns a vector of size `1` with element `v`. -/
+@[inline] def singleton (v : α) : Vector α 1 := ⟨#[v], rfl⟩
+
+instance [Inhabited α] : Inhabited (Vector α n) where
+  default := mkVector n default
+
+/-- Get an element of a vector using a `Fin` index. -/
+@[inline] def get (v : Vector α n) (i : Fin n) : α :=
+  v.toArray[(i.cast v.size_toArray.symm).1]
+
+/-- Get an element of a vector using a `USize` index and a proof that the index is within bounds. -/
+@[inline] def uget (v : Vector α n) (i : USize) (h : i.toNat < n) : α :=
+  v.toArray.uget i (v.size_toArray.symm ▸ h)
+
+instance : GetElem (Vector α n) Nat α fun _ i => i < n where
+  getElem x i h := get x ⟨i, h⟩
+
+/--
+Get an element of a vector using a `Nat` index. Returns the given default value if the index is out
+of bounds.
+-/
+@[inline] def getD (v : Vector α n) (i : Nat) (default : α) : α := v.toArray.getD i default
+
+/-- The last element of a vector. Panics if the vector is empty. -/
+@[inline] def back! [Inhabited α] (v : Vector α n) : α := v.toArray.back!
+
+/-- The last element of a vector, or `none` if the array is empty. -/
+@[inline] def back? (v : Vector α n) : Option α := v.toArray.back?
+
+/-- The last element of a non-empty vector. -/
+@[inline] def back [NeZero n] (v : Vector α n) : α :=
+  -- TODO: change to just `v[n]`
+  have : Inhabited α := ⟨v[0]'(Nat.pos_of_neZero n)⟩
+  v.back!
+
+/-- The first element of a non-empty vector.  -/
+@[inline] def head [NeZero n] (v : Vector α n) := v[0]'(Nat.pos_of_neZero n)
+
+/-- Push an element `x` to the end of a vector. -/
+@[inline] def push (x : α) (v : Vector α n)  : Vector α (n + 1) :=
+  ⟨v.toArray.push x, by simp⟩
+
+/-- Remove the last element of a vector. -/
+@[inline] def pop (v : Vector α n) : Vector α (n - 1) :=
+  ⟨Array.pop v.toArray, by simp⟩
+
+/--
+Set an element in a vector using a `Nat` index, with a tactic provided proof that the index is in
+bounds.
+
+This will perform the update destructively provided that the vector has a reference count of 1.
+-/
+@[inline] def set (v : Vector α n) (i : Nat) (x : α) (h : i < n := by get_elem_tactic): Vector α n :=
+  ⟨v.toArray.set i x (by simp [*]), by simp⟩
+
+/--
+Set an element in a vector using a `Nat` index. Returns the vector unchanged if the index is out of
+bounds.
+
+This will perform the update destructively provided that the vector has a reference count of 1.
+-/
+@[inline] def setIfInBounds (v : Vector α n) (i : Nat) (x : α) : Vector α n :=
+  ⟨v.toArray.setIfInBounds i x, by simp⟩
+
+/--
+Set an element in a vector using a `Nat` index. Panics if the index is out of bounds.
+
+This will perform the update destructively provided that the vector has a reference count of 1.
+-/
+@[inline] def set! (v : Vector α n) (i : Nat) (x : α) : Vector α n :=
+  ⟨v.toArray.set! i x, by simp⟩
+
+/-- Append two vectors. -/
+@[inline] def append (v : Vector α n) (w : Vector α m) : Vector α (n + m) :=
+  ⟨v.toArray ++ w.toArray, by simp⟩
+
+instance : HAppend (Vector α n) (Vector α m) (Vector α (n + m)) where
+  hAppend := append
+
+/-- Creates a vector from another with a provably equal length. -/
+@[inline] protected def cast (h : n = m) (v : Vector α n) : Vector α m :=
+  ⟨v.toArray, by simp [*]⟩
+
+/--
+Extracts the slice of a vector from indices `start` to `stop` (exclusive). If `start ≥ stop`, the
+result is empty. If `stop` is greater than the size of the vector, the size is used instead.
+-/
+@[inline] def extract (v : Vector α n) (start stop : Nat) : Vector α (min stop n - start) :=
+  ⟨v.toArray.extract start stop, by simp⟩
+
+/-- Maps elements of a vector using the function `f`. -/
+@[inline] def map (f : α → β) (v : Vector α n) : Vector β n :=
+  ⟨v.toArray.map f, by simp⟩
+
+/-- Maps corresponding elements of two vectors of equal size using the function `f`. -/
+@[inline] def zipWith (a : Vector α n) (b : Vector β n) (f : α → β → φ) : Vector φ n :=
+  ⟨Array.zipWith a.toArray b.toArray f, by simp⟩
+
+/-- The vector of length `n` whose `i`-th element is `f i`. -/
+@[inline] def ofFn (f : Fin n → α) : Vector α n :=
+  ⟨Array.ofFn f, by simp⟩
+
+/--
+Swap two elements of a vector using `Fin` indices.
+
+This will perform the update destructively provided that the vector has a reference count of 1.
+-/
+@[inline] def swap (v : Vector α n) (i j : Nat)
+    (hi : i < n := by get_elem_tactic) (hj : j < n := by get_elem_tactic) : Vector α n :=
+  ⟨v.toArray.swap i j (by simpa using hi) (by simpa using hj), by simp⟩
+
+/--
+Swap two elements of a vector using `Nat` indices. Panics if either index is out of bounds.
+
+This will perform the update destructively provided that the vector has a reference count of 1.
+-/
+@[inline] def swapIfInBounds (v : Vector α n) (i j : Nat) : Vector α n :=
+  ⟨v.toArray.swapIfInBounds i j, by simp⟩
+
+/--
+Swaps an element of a vector with a given value using a `Fin` index. The original value is returned
+along with the updated vector.
+
+This will perform the update destructively provided that the vector has a reference count of 1.
+-/
+@[inline] def swapAt (v : Vector α n) (i : Nat) (x : α) (hi : i < n := by get_elem_tactic) :
+    α × Vector α n :=
+  let a := v.toArray.swapAt i x (by simpa using hi)
+  ⟨a.fst, a.snd, by simp [a]⟩
+
+/--
+Swaps an element of a vector with a given value using a `Nat` index. Panics if the index is out of
+bounds. The original value is returned along with the updated vector.
+
+This will perform the update destructively provided that the vector has a reference count of 1.
+-/
+@[inline] def swapAt! (v : Vector α n) (i : Nat) (x : α) : α × Vector α n :=
+  let a := v.toArray.swapAt! i x
+  ⟨a.fst, a.snd, by simp [a]⟩
+
+/-- The vector `#v[0,1,2,...,n-1]`. -/
+@[inline] def range (n : Nat) : Vector Nat n := ⟨Array.range n, by simp⟩
+
+/--
+Extract the first `m` elements of a vector. If `m` is greater than or equal to the size of the
+vector then the vector is returned unchanged.
+-/
+@[inline] def take (v : Vector α n) (m : Nat) : Vector α (min m n) :=
+  ⟨v.toArray.take m, by simp⟩
+
+/--
+Deletes the first `m` elements of a vector. If `m` is greater than or equal to the size of the
+vector then the empty vector is returned.
+-/
+@[inline] def drop (v : Vector α n) (m : Nat) : Vector α (n - m) :=
+  ⟨v.toArray.extract m v.size, by simp⟩
+
+/--
+Compares two vectors of the same size using a given boolean relation `r`. `isEqv v w r` returns
+`true` if and only if `r v[i] w[i]` is true for all indices `i`.
+-/
+@[inline] def isEqv (v w : Vector α n) (r : α → α → Bool) : Bool :=
+  Array.isEqvAux v.toArray w.toArray (by simp) r n (by simp)
+
+instance [BEq α] : BEq (Vector α n) where
+  beq a b := isEqv a b (· == ·)
+
+/-- Reverse the elements of a vector. -/
+@[inline] def reverse (v : Vector α n) : Vector α n :=
+  ⟨v.toArray.reverse, by simp⟩
+
+/-- Delete an element of a vector using a `Nat` index and a tactic provided proof. -/
+@[inline] def eraseIdx (v : Vector α n) (i : Nat) (h : i < n := by get_elem_tactic) :
+    Vector α (n-1) :=
+  ⟨v.toArray.eraseIdx i (v.size_toArray.symm ▸ h), by simp [Array.size_eraseIdx]⟩
+
+/-- Delete an element of a vector using a `Nat` index. Panics if the index is out of bounds. -/
+@[inline] def eraseIdx! (v : Vector α n) (i : Nat) : Vector α (n-1) :=
+  if _ : i < n then
+    v.eraseIdx i
+  else
+    have : Inhabited (Vector α (n-1)) := ⟨v.pop⟩
+    panic! "index out of bounds"
+
+/-- Delete the first element of a vector. Returns the empty vector if the input vector is empty. -/
+@[inline] def tail (v : Vector α n) : Vector α (n-1) :=
+  if _ : 0 < n then
+    v.eraseIdx 0
+  else
+    v.cast (by omega)
+
+/--
+Finds the first index of a given value in a vector using `==` for comparison. Returns `none` if the
+no element of the index matches the given value.
+-/
+@[inline] def indexOf? [BEq α] (v : Vector α n) (x : α) : Option (Fin n) :=
+  (v.toArray.indexOf? x).map (Fin.cast v.size_toArray)
+
+/-- Returns `true` when `v` is a prefix of the vector `w`. -/
+@[inline] def isPrefixOf [BEq α] (v : Vector α m) (w : Vector α n) : Bool :=
+  v.toArray.isPrefixOf w.toArray

src/Init/Data/Vector/Lemmas.lean

@@ -0,0 +1,172 @@
+/-
+Copyright (c) 2024 Shreyas Srinivas. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Shreyas Srinivas, Francois Dorais
+-/
+prelude
+import Init.Data.Vector.Basic
+
+/-!
+## Vectors
+Lemmas about `Vector α n`
+-/
+
+namespace Vector
+
+theorem length_toList {α n} (xs : Vector α n) : xs.toList.length = n := by simp
+
+@[simp] theorem getElem_mk {data : Array α} {size : data.size = n} {i : Nat} (h : i < n) :
+    (Vector.mk data size)[i] = data[i] := rfl
+
+@[simp] theorem getElem_toArray {α n} (xs : Vector α n) (i : Nat) (h : i < xs.toArray.size) :
+    xs.toArray[i] = xs[i]'(by simpa using h) := by
+  cases xs
+  simp
+
+theorem getElem_toList {α n} (xs : Vector α n) (i : Nat) (h : i < xs.toList.length) :
+    xs.toList[i] = xs[i]'(by simpa using h) := by simp
+
+@[simp] theorem getElem_ofFn {α n} (f : Fin n → α) (i : Nat) (h : i < n) :
+    (Vector.ofFn f)[i] = f ⟨i, by simpa using h⟩ := by
+  simp [ofFn]
+
+/-- The empty vector maps to the empty vector. -/
+@[simp]
+theorem map_empty (f : α → β) : map f #v[] = #v[] := by
+  rw [map, mk.injEq]
+  exact Array.map_empty f
+
+theorem toArray_inj : ∀ {v w : Vector α n}, v.toArray = w.toArray → v = w
+  | {..}, {..}, rfl => rfl
+
+/-- A vector of length `0` is the empty vector. -/
+protected theorem eq_empty (v : Vector α 0) : v = #v[] := by
+  apply Vector.toArray_inj
+  apply Array.eq_empty_of_size_eq_zero v.2
+
+/--
+`Vector.ext` is an extensionality theorem.
+Vectors `a` and `b` are equal to each other if their elements are equal for each valid index.
+-/
+@[ext]
+protected theorem ext {a b : Vector α n} (h : (i : Nat) → (_ : i < n) → a[i] = b[i]) : a = b := by
+  apply Vector.toArray_inj
+  apply Array.ext
+  · rw [a.size_toArray, b.size_toArray]
+  · intro i hi _
+    rw [a.size_toArray] at hi
+    exact h i hi
+
+@[simp] theorem push_mk {data : Array α} {size : data.size = n} {x : α} :
+    (Vector.mk data size).push x =
+      Vector.mk (data.push x) (by simp [size, Nat.succ_eq_add_one]) := rfl
+
+@[simp] theorem pop_mk {data : Array α} {size : data.size = n} :
+    (Vector.mk data size).pop = Vector.mk data.pop (by simp [size]) := rfl
+
+@[simp] theorem swap_mk {data : Array α} {size : data.size = n} {i j : Nat} {hi hj} :
+    (Vector.mk data size).swap i j hi hj = Vector.mk (data.swap i j) (by simp_all) := rfl
+
+@[simp] theorem getElem_push_last {v : Vector α n} {x : α} : (v.push x)[n] = x := by
+  rcases v with ⟨data, rfl⟩
+  simp
+
+@[simp] theorem getElem_push_lt {v : Vector α n} {x : α} {i : Nat} (h : i < n) :
+    (v.push x)[i] = v[i] := by
+  rcases v with ⟨data, rfl⟩
+  simp [Array.getElem_push_lt, h]
+
+@[simp] theorem getElem_pop {v : Vector α n} {i : Nat} (h : i < n - 1) : (v.pop)[i] = v[i] := by
+  rcases v with ⟨data, rfl⟩
+  simp
+
+/--
+Variant of `getElem_pop` that will sometimes fire when `getElem_pop` gets stuck because of
+defeq issues in the implicit size argument.
+-/
+@[simp] theorem getElem_pop' (v : Vector α (n + 1)) (i : Nat) (h : i < n + 1 - 1) :
+    @getElem (Vector α n) Nat α (fun _ i => i < n) instGetElemNatLt v.pop i h = v[i] :=
+  getElem_pop h
+
+@[simp] theorem push_pop_back (v : Vector α (n + 1)) : v.pop.push v.back = v := by
+  ext i
+  by_cases h : i < n
+  · simp [h]
+  · replace h : i = v.size - 1 := by rw [size_toArray]; omega
+    subst h
+    simp [pop, back, back!, ← Array.eq_push_pop_back!_of_size_ne_zero]
+
+theorem push_swap (a : Vector α n) (x : α) {i j : Nat} {hi hj} :
+    (a.swap i j hi hj).push x = (a.push x).swap i j := by
+  cases a
+  simp [Array.push_swap]
+
+/-! ### cast -/
+
+@[simp] theorem cast_mk {n m} (a : Array α) (w : a.size = n) (h : n = m) :
+    (Vector.mk a w).cast h = ⟨a, h ▸ w⟩ := by
+  simp [Vector.cast]
+
+@[simp] theorem cast_refl {n} (a : Vector α n) : a.cast rfl = a := by
+  cases a
+  simp
+
+@[simp] theorem toArray_cast {n m} (a : Vector α n) (h : n = m) :
+    (a.cast h).toArray = a.toArray := by
+  subst h
+  simp
+
+theorem cast_inj {n m} (a : Vector α n) (b : Vector α n) (h : n = m) :
+    a.cast h = b.cast h ↔ a = b := by
+  cases h
+  simp
+
+theorem cast_eq_iff {n m} (a : Vector α n) (b : Vector α m) (h : n = m) :
+    a.cast h = b ↔ a = b.cast h.symm := by
+  cases h
+  simp
+
+theorem eq_cast_iff {n m} (a : Vector α n) (b : Vector α m) (h : m = n) :
+    a = b.cast h ↔ a.cast h.symm = b := by
+  cases h
+  simp
+
+/-! ### Decidable quantifiers. -/
+
+theorem forall_zero_iff {P : Vector α 0 → Prop} :
+    (∀ v, P v) ↔ P #v[] := by
+  constructor
+  · intro h
+    apply h
+  · intro h v
+    obtain (rfl : v = #v[]) := (by ext i h; simp at h)
+    apply h
+
+theorem forall_cons_iff {P : Vector α (n + 1) → Prop} :
+    (∀ v : Vector α (n + 1), P v) ↔ (∀ (x : α) (v : Vector α n), P (v.push x)) := by
+  constructor
+  · intro h _ _
+    apply h
+  · intro h v
+    have w : v = v.pop.push v.back := by simp
+    rw [w]
+    apply h
+
+instance instDecidableForallVectorZero (P : Vector α 0 → Prop) :
+    ∀ [Decidable (P #v[])], Decidable (∀ v, P v)
+  | .isTrue h => .isTrue fun ⟨v, s⟩ => by
+    obtain (rfl : v = .empty) := (by ext i h₁ h₂; exact s; cases h₂)
+    exact h
+  | .isFalse h => .isFalse (fun w => h (w _))
+
+instance instDecidableForallVectorSucc (P : Vector α (n+1) → Prop)
+    [Decidable (∀ (x : α) (v : Vector α n), P (v.push x))] : Decidable (∀ v, P v) :=
+  decidable_of_iff' (∀ x (v : Vector α n), P (v.push x)) forall_cons_iff
+
+instance instDecidableExistsVectorZero (P : Vector α 0 → Prop) [Decidable (P #v[])] :
+    Decidable (∃ v, P v) :=
+  decidable_of_iff (¬ ∀ v, ¬ P v) Classical.not_forall_not
+
+instance instDecidableExistsVectorSucc (P : Vector α (n+1) → Prop)
+    [Decidable (∀ (x : α) (v : Vector α n), ¬ P (v.push x))] : Decidable (∃ v, P v) :=
+  decidable_of_iff (¬ ∀ v, ¬ P v) Classical.not_forall_not

src/Init/GetElem.lean

@@ -206,12 +206,12 @@ instance : GetElem (List α) Nat α fun as i => i < as.length where
 @[simp] theorem getElem_cons_zero (a : α) (as : List α) (h : 0 < (a :: as).length) : getElem (a :: as) 0 h = a := by
   rfl
 
-@[deprecated (since := "2024-06-12")] abbrev cons_getElem_zero := @getElem_cons_zero
+@[deprecated getElem_cons_zero (since := "2024-06-12")] abbrev cons_getElem_zero := @getElem_cons_zero
 
 @[simp] theorem getElem_cons_succ (a : α) (as : List α) (i : Nat) (h : i + 1 < (a :: as).length) : getElem (a :: as) (i+1) h = getElem as i (Nat.lt_of_succ_lt_succ h) := by
   rfl
 
-@[deprecated (since := "2024-06-12")] abbrev cons_getElem_succ := @getElem_cons_succ
+@[deprecated getElem_cons_succ (since := "2024-06-12")] abbrev cons_getElem_succ := @getElem_cons_succ
 
 @[simp] theorem getElem_mem : ∀ {l : List α} {n} (h : n < l.length), l[n]'h ∈ l
   | _ :: _, 0, _ => .head ..
@@ -223,7 +223,8 @@ theorem getElem_cons_drop_succ_eq_drop {as : List α} {i : Nat} (h : i < as.leng
   | _::_, 0   => rfl
   | _::_, i+1 => getElem_cons_drop_succ_eq_drop (i := i) _
 
-@[deprecated (since := "2024-11-05")] abbrev get_drop_eq_drop := @getElem_cons_drop_succ_eq_drop
+@[deprecated getElem_cons_drop_succ_eq_drop (since := "2024-11-05")]
+abbrev get_drop_eq_drop := @getElem_cons_drop_succ_eq_drop
 
 end List
 

src/Init/Meta.lean

@@ -431,21 +431,20 @@ def getSubstring? (stx : Syntax) (withLeading := true) (withTrailing := true) :
     }
   | _, _ => none
 
-@[specialize] private partial def updateLast {α} [Inhabited α] (a : Array α) (f : α → Option α) (i : Nat) : Option (Array α) :=
-  if i == 0 then
-    none
-  else
-    let i := i - 1
-    let v := a[i]!
+@[specialize] private partial def updateLast {α} (a : Array α) (f : α → Option α) (i : Fin (a.size + 1)) : Option (Array α) :=
+  match i with
+  | 0 => none
+  | ⟨i + 1, h⟩ =>
+    let v := a[i]'(Nat.succ_lt_succ_iff.mp h)
     match f v with
-    | some v => some <| a.set! i v
-    | none   => updateLast a f i
+    | some v => some <| a.set i v (Nat.succ_lt_succ_iff.mp h)
+    | none   => updateLast a f ⟨i, Nat.lt_of_succ_lt h⟩
 
 partial def setTailInfoAux (info : SourceInfo) : Syntax → Option Syntax
   | atom _ val             => some <| atom info val
   | ident _ rawVal val pre => some <| ident info rawVal val pre
   | node info' k args      =>
-    match updateLast args (setTailInfoAux info) args.size with
+    match updateLast args (setTailInfoAux info) ⟨args.size, by simp⟩ with
     | some args => some <| node info' k args
     | none      => none
   | _                      => none

src/Init/MetaTypes.lean

@@ -251,10 +251,16 @@ def neutralConfig : Simp.Config := {
 
 end Simp
 
+/-- Configuration for which occurrences that match an expression should be rewritten. -/
 inductive Occurrences where
+  /-- All occurrences should be rewritten. -/
   | all
+  /-- A list of indices for which occurrences should be rewritten. -/
   | pos (idxs : List Nat)
+  /-- A list of indices for which occurrences should not be rewritten. -/
   | neg (idxs : List Nat)
   deriving Inhabited, BEq
 
+instance : Coe (List Nat) Occurrences := ⟨.pos⟩
+
 end Lean.Meta

src/Init/Notation.lean

@@ -71,9 +71,9 @@ def prio : Category := {}
 
 /-- `prec` is a builtin syntax category for precedences. A precedence is a value
 that expresses how tightly a piece of syntax binds: for example `1 + 2 * 3` is
-parsed as `1 + (2 * 3)` because `*` has a higher pr0ecedence than `+`.
+parsed as `1 + (2 * 3)` because `*` has a higher precedence than `+`.
 Higher numbers denote higher precedence.
-In addition to literals like `37`, there are some special named priorities:
+In addition to literals like `37`, there are some special named precedence levels:
 * `arg` for the precedence of function arguments
 * `max` for the highest precedence used in term parsers (not actually the maximum possible value)
 * `lead` for the precedence of terms not supposed to be used as arguments

src/Init/NotationExtra.lean

@@ -22,28 +22,28 @@ syntax explicitBinders            := (ppSpace bracketedExplicitBinders)+ <|> unb
 
 open TSyntax.Compat in
 def expandExplicitBindersAux (combinator : Syntax) (idents : Array Syntax) (type? : Option Syntax) (body : Syntax) : MacroM Syntax :=
-  let rec loop (i : Nat) (acc : Syntax) := do
+  let rec loop (i : Nat) (h : i ≤ idents.size) (acc : Syntax) := do
     match i with
     | 0   => pure acc
-    | i+1 =>
-      let ident := idents[i]![0]
+    | i + 1 =>
+      let ident := idents[i][0]
       let acc ← match ident.isIdent, type? with
         | true,  none      => `($combinator fun $ident => $acc)
         | true,  some type => `($combinator fun $ident : $type => $acc)
         | false, none      => `($combinator fun _ => $acc)
         | false, some type => `($combinator fun _ : $type => $acc)
-      loop i acc
-  loop idents.size body
+      loop i (Nat.le_of_succ_le h) acc
+  loop idents.size (by simp) body
 
 def expandBrackedBindersAux (combinator : Syntax) (binders : Array Syntax) (body : Syntax) : MacroM Syntax :=
-  let rec loop (i : Nat) (acc : Syntax) := do
+  let rec loop (i : Nat) (h : i ≤ binders.size) (acc : Syntax) := do
     match i with
     | 0   => pure acc
     | i+1 =>
-      let idents := binders[i]![1].getArgs
-      let type   := binders[i]![3]
-      loop i (← expandExplicitBindersAux combinator idents (some type) acc)
-  loop binders.size body
+      let idents := binders[i][1].getArgs
+      let type   := binders[i][3]
+      loop i (Nat.le_of_succ_le h) (← expandExplicitBindersAux combinator idents (some type) acc)
+  loop binders.size (by simp) body
 
 def expandExplicitBinders (combinatorDeclName : Name) (explicitBinders : Syntax) (body : Syntax) : MacroM Syntax := do
   let combinator := mkCIdentFrom (← getRef) combinatorDeclName

src/Init/Prelude.lean

@@ -2116,6 +2116,11 @@ theorem usize_size_eq : Or (Eq USize.size 4294967296) (Eq USize.size 18446744073
   | _, Or.inl rfl => Or.inl (of_decide_eq_true rfl)
   | _, Or.inr rfl => Or.inr (of_decide_eq_true rfl)
 
+theorem usize_size_pos : LT.lt 0 USize.size :=
+  match USize.size, usize_size_eq with
+  | _, Or.inl rfl => of_decide_eq_true rfl
+  | _, Or.inr rfl => of_decide_eq_true rfl
+
 /--
 A `USize` is an unsigned integer with the size of a word
 for the platform's architecture.
@@ -2155,24 +2160,7 @@ def USize.decEq (a b : USize) : Decidable (Eq a b) :=
 instance : DecidableEq USize := USize.decEq
 
 instance : Inhabited USize where
-  default := USize.ofNatCore 0 (match USize.size, usize_size_eq with
-    | _, Or.inl rfl => of_decide_eq_true rfl
-    | _, Or.inr rfl => of_decide_eq_true rfl)
-
-/--
-Upcast a `Nat` less than `2^32` to a `USize`.
-This is lossless because `USize.size` is either `2^32` or `2^64`.
-This function is overridden with a native implementation.
--/
-@[extern "lean_usize_of_nat"]
-def USize.ofNat32 (n : @& Nat) (h : LT.lt n 4294967296) : USize where
-  toBitVec :=
-    BitVec.ofNatLt n (
-      match System.Platform.numBits, System.Platform.numBits_eq with
-      | _, Or.inl rfl => h
-      | _, Or.inr rfl => Nat.lt_trans h (of_decide_eq_true rfl)
-    )
-
+  default := USize.ofNatCore 0 usize_size_pos
 /--
 A `Nat` denotes a valid unicode codepoint if it is less than `0x110000`, and
 it is also not a "surrogate" character (the range `0xd800` to `0xdfff` inclusive).
@@ -3432,25 +3420,6 @@ class Hashable (α : Sort u) where
 
 export Hashable (hash)
 
-/-- Converts a `UInt64` to a `USize` by reducing modulo `USize.size`. -/
-@[extern "lean_uint64_to_usize"]
-opaque UInt64.toUSize (u : UInt64) : USize
-
-/--
-Upcast a `USize` to a `UInt64`.
-This is lossless because `USize.size` is either `2^32` or `2^64`.
-This function is overridden with a native implementation.
--/
-@[extern "lean_usize_to_uint64"]
-def USize.toUInt64 (u : USize) : UInt64 where
-  toBitVec := BitVec.ofNatLt u.toBitVec.toNat (
-        let ⟨⟨n, h⟩⟩ := u
-        show LT.lt n _ from
-        match System.Platform.numBits, System.Platform.numBits_eq, h with
-        | _, Or.inl rfl, h => Nat.lt_trans h (of_decide_eq_true rfl)
-        | _, Or.inr rfl, h => h
-      )
-
 /-- An opaque hash mixing operation, used to implement hashing for tuples. -/
 @[extern "lean_uint64_mix_hash"]
 opaque mixHash (u₁ u₂ : UInt64) : UInt64

src/Init/ShareCommon.lean

@@ -5,6 +5,7 @@ Authors: Leonardo de Moura, Mario Carneiro
 -/
 prelude
 import Init.Util
+import Init.Data.UInt.Basic
 
 namespace ShareCommon
 /-

src/Init/SimpLemmas.lean

@@ -72,6 +72,21 @@ theorem let_body_congr {α : Sort u} {β : α → Sort v} {b b' : (a : α) →
     (a : α) (h : ∀ x, b x = b' x) : (let x := a; b x) = (let x := a; b' x) :=
   (funext h : b = b') ▸ rfl
 
+theorem letFun_unused {α : Sort u} {β : Sort v} (a : α) {b b' : β} (h : b = b') : @letFun α (fun _ => β) a (fun _ => b) = b' :=
+  h
+
+theorem letFun_congr {α : Sort u} {β : Sort v}  {a a' : α} {f f' : α → β} (h₁ : a = a') (h₂ : ∀ x, f x = f' x)
+    : @letFun α (fun _ => β) a f = @letFun α (fun _ => β) a' f' := by
+  rw [h₁, funext h₂]
+
+theorem letFun_body_congr {α : Sort u} {β : Sort v}  (a : α) {f f' : α → β} (h : ∀ x, f x = f' x)
+    : @letFun α (fun _ => β) a f = @letFun α (fun _ => β) a f' := by
+  rw [funext h]
+
+theorem letFun_val_congr {α : Sort u} {β : Sort v} {a a' : α} {f : α → β} (h : a = a')
+    : @letFun α (fun _ => β) a f = @letFun α (fun _ => β) a' f := by
+  rw [h]
+
 @[congr]
 theorem ite_congr {x y u v : α} {s : Decidable b} [Decidable c]
     (h₁ : b = c) (h₂ : c → x = u) (h₃ : ¬ c → y = v) : ite b x y = ite c u v := by

src/Init/Syntax.lean

@@ -30,7 +30,7 @@ Does nothing for non-`node` nodes, or if `i` is out of bounds of the node list.
 -/
 def setArg (stx : Syntax) (i : Nat) (arg : Syntax) : Syntax :=
   match stx with
-  | node info k args => node info k (args.setD i arg)
+  | node info k args => node info k (args.setIfInBounds i arg)
   | stx              => stx
 
 end Lean.Syntax

src/Init/System/IO.lean

@@ -462,6 +462,16 @@ Note that it is the caller's job to remove the file after use.
 -/
 @[extern "lean_io_create_tempfile"] opaque createTempFile : IO (Handle × FilePath)
 
+/--
+Creates a temporary directory in the most secure manner possible. There are no race conditions in the
+directory’s creation. The directory is readable and writable only by the creating user ID.
+
+Returns the new directory's path.
+
+It is the caller's job to remove the directory after use.
+-/
+@[extern "lean_io_create_tempdir"] opaque createTempDir : IO FilePath
+
 end FS
 
 @[extern "lean_io_getenv"] opaque getEnv (var : @& String) : BaseIO (Option String)
@@ -474,17 +484,6 @@ namespace FS
 def withFile (fn : FilePath) (mode : Mode) (f : Handle → IO α) : IO α :=
   Handle.mk fn mode >>= f
 
-/--
-Like `createTempFile` but also takes care of removing the file after usage.
--/
-def withTempFile [Monad m] [MonadFinally m] [MonadLiftT IO m] (f : Handle → FilePath → m α) :
-    m α := do
-  let (handle, path) ← createTempFile
-  try
-    f handle path
-  finally
-    removeFile path
-
 def Handle.putStrLn (h : Handle) (s : String) : IO Unit :=
   h.putStr (s.push '\n')
 
@@ -675,8 +674,10 @@ def appDir : IO FilePath := do
     | throw <| IO.userError s!"System.IO.appDir: unexpected filename '{p}'"
   FS.realPath p
 
+namespace FS
+
 /-- Create given path and all missing parents as directories. -/
-partial def FS.createDirAll (p : FilePath) : IO Unit := do
+partial def createDirAll (p : FilePath) : IO Unit := do
   if ← p.isDir then
     return ()
   if let some parent := p.parent then
@@ -693,7 +694,7 @@ partial def FS.createDirAll (p : FilePath) : IO Unit := do
 /--
   Fully remove given directory by deleting all contained files and directories in an unspecified order.
   Fails if any contained entry cannot be deleted or was newly created during execution. -/
-partial def FS.removeDirAll (p : FilePath) : IO Unit := do
+partial def removeDirAll (p : FilePath) : IO Unit := do
   for ent in (← p.readDir) do
     if (← ent.path.isDir : Bool) then
       removeDirAll ent.path
@@ -701,6 +702,32 @@ partial def FS.removeDirAll (p : FilePath) : IO Unit := do
       removeFile ent.path
   removeDir p
 
+/--
+Like `createTempFile`, but also takes care of removing the file after usage.
+-/
+def withTempFile [Monad m] [MonadFinally m] [MonadLiftT IO m] (f : Handle → FilePath → m α) :
+    m α := do
+  let (handle, path) ← createTempFile
+  try
+    f handle path
+  finally
+    removeFile path
+
+/--
+Like `createTempDir`, but also takes care of removing the directory after usage.
+
+All files in the directory are recursively deleted, regardless of how or when they were created.
+-/
+def withTempDir [Monad m] [MonadFinally m] [MonadLiftT IO m] (f : FilePath → m α) :
+    m α := do
+  let path ← createTempDir
+  try
+    f path
+  finally
+    removeDirAll path
+
+end FS
+
 namespace Process
 
 /-- Returns the current working directory of the calling process. -/

src/Init/System/Uri.lean

@@ -29,13 +29,13 @@ def decodeUri (uri : String) : String := Id.run do
   let len := rawBytes.size
   let mut i := 0
   let percent := '%'.toNat.toUInt8
-  while i < len do
-    let c := rawBytes[i]!
-    (decoded, i) := if c == percent && i + 1 < len then
-      let h1 := rawBytes[i + 1]!
+  while h : i < len do
+    let c := rawBytes[i]
+    (decoded, i) := if h₁ : c == percent ∧ i + 1 < len then
+      let h1 := rawBytes[i + 1]
       if let some hd1 := hexDigitToUInt8? h1 then
-        if i + 2 < len then
-          let h2 := rawBytes[i + 2]!
+        if h₂ : i + 2 < len then
+          let h2 := rawBytes[i + 2]
           if let some hd2 := hexDigitToUInt8? h2 then
             -- decode the hex digits into a byte.
             (decoded.push (hd1 * 16 + hd2), i + 3)

src/Init/Tactics.lean

@@ -428,11 +428,11 @@ macro "infer_instance" : tactic => `(tactic| exact inferInstance)
 /--
 `+opt` is short for `(opt := true)`. It sets the `opt` configuration option to `true`.
 -/
-syntax posConfigItem := "+" noWs ident
+syntax posConfigItem := " +" noWs ident
 /--
 `-opt` is short for `(opt := false)`. It sets the `opt` configuration option to `false`.
 -/
-syntax negConfigItem := "-" noWs ident
+syntax negConfigItem := " -" noWs ident
 /--
 `(opt := val)` sets the `opt` configuration option to `val`.
 

src/Init/Util.lean

@@ -90,10 +90,14 @@ def withPtrAddr {α : Type u} {β : Type v} (a : α) (k : USize → β) (h : ∀
 def Runtime.markMultiThreaded (a : α) : α := a
 
 /--
-  Marks given value and its object graph closure as persistent. This will remove
-  reference counter updates but prevent the closure from being deallocated until
-  the end of the process! It can still be useful to do eagerly when the value
-  will be marked persistent later anyway and there is available time budget to
-  mark it now or it would be unnecessarily marked multi-threaded in between. -/
+Marks given value and its object graph closure as persistent. This will remove
+reference counter updates but prevent the closure from being deallocated until
+the end of the process! It can still be useful to do eagerly when the value
+will be marked persistent later anyway and there is available time budget to
+mark it now or it would be unnecessarily marked multi-threaded in between.
+
+This function is only safe to use on objects (in the full closure) which are
+not used concurrently or which are already persistent.
+-/
 @[extern "lean_runtime_mark_persistent"]
-def Runtime.markPersistent (a : α) : α := a
+unsafe def Runtime.markPersistent (a : α) : α := a

src/Lean/Compiler/IR/Borrow.lean

@@ -205,8 +205,8 @@ def getParamInfo (k : ParamMap.Key) : M (Array Param) := do
 
 /-- For each ps[i], if ps[i] is owned, then mark xs[i] as owned. -/
 def ownArgsUsingParams (xs : Array Arg) (ps : Array Param) : M Unit :=
-  xs.size.forM fun i => do
-    let x := xs[i]!
+  xs.size.forM fun i _ => do
+    let x := xs[i]
     let p := ps[i]!
     unless p.borrow do ownArg x
 
@@ -216,8 +216,8 @@ def ownArgsUsingParams (xs : Array Arg) (ps : Array Param) : M Unit :=
    we would have to insert a `dec xs[i]` after `f xs` and consequently
    "break" the tail call. -/
 def ownParamsUsingArgs (xs : Array Arg) (ps : Array Param) : M Unit :=
-  xs.size.forM fun i => do
-    let x := xs[i]!
+  xs.size.forM fun i _ => do
+    let x := xs[i]
     let p := ps[i]!
     match x with
     | Arg.var x => if (← isOwned x) then ownVar p.x

src/Lean/Compiler/IR/Boxing.lean

@@ -48,9 +48,9 @@ def requiresBoxedVersion (env : Environment) (decl : Decl) : Bool :=
 def mkBoxedVersionAux (decl : Decl) : N Decl := do
   let ps := decl.params
   let qs ← ps.mapM fun _ => do let x ← N.mkFresh; pure { x := x, ty := IRType.object, borrow := false : Param }
-  let (newVDecls, xs) ← qs.size.foldM (init := (#[], #[])) fun i (newVDecls, xs) => do
+  let (newVDecls, xs) ← qs.size.foldM (init := (#[], #[])) fun i _ (newVDecls, xs) => do
     let p := ps[i]!
-    let q := qs[i]!
+    let q := qs[i]
     if !p.ty.isScalar then
       pure (newVDecls, xs.push (Arg.var q.x))
     else

src/Lean/Compiler/IR/ElimDeadBranches.lean

@@ -63,7 +63,7 @@ partial def merge (v₁ v₂ : Value) : Value :=
   | top, _ => top
   | _, top => top
   | v₁@(ctor i₁ vs₁), v₂@(ctor i₂ vs₂) =>
-    if i₁ == i₂ then ctor i₁ <| vs₁.size.fold (init := #[]) fun i r => r.push (merge vs₁[i]! vs₂[i]!)
+    if i₁ == i₂ then ctor i₁ <| vs₁.size.fold (init := #[]) fun i _ r => r.push (merge vs₁[i] vs₂[i]!)
     else choice [v₁, v₂]
   | choice vs₁, choice vs₂ => choice <| vs₁.foldl (addChoice merge) vs₂
   | choice vs, v => choice <| addChoice merge vs v
@@ -225,8 +225,8 @@ def updateCurrFnSummary (v : Value) : M Unit := do
 def updateJPParamsAssignment (ys : Array Param) (xs : Array Arg) : M Bool := do
   let ctx ← read
   let currFnIdx := ctx.currFnIdx
-  ys.size.foldM (init := false) fun i r => do
-    let y := ys[i]!
+  ys.size.foldM (init := false) fun i _ r => do
+    let y := ys[i]
     let x := xs[i]!
     let yVal ← findVarValue y.x
     let xVal ← findArgValue x
@@ -282,8 +282,8 @@ partial def interpFnBody : FnBody → M Unit
 def inferStep : M Bool := do
   let ctx ← read
   modify fun s => { s with assignments := ctx.decls.map fun _ => {} }
-  ctx.decls.size.foldM (init := false) fun idx modified => do
-    match ctx.decls[idx]! with
+  ctx.decls.size.foldM (init := false) fun idx _ modified => do
+    match ctx.decls[idx] with
     | .fdecl (xs := ys) (body := b) .. => do
       let s ← get
       let currVals := s.funVals[idx]!
@@ -336,8 +336,8 @@ def elimDeadBranches (decls : Array Decl) : CompilerM (Array Decl) := do
   let funVals := s.funVals
   let assignments := s.assignments
   modify fun s =>
-    let env := decls.size.fold (init := s.env) fun i env =>
-      addFunctionSummary env decls[i]!.name funVals[i]!
+    let env := decls.size.fold (init := s.env) fun i _ env =>
+      addFunctionSummary env decls[i].name funVals[i]!
     { s with env := env }
   return decls.mapIdx fun i decl => elimDead assignments[i]! decl
 

src/Lean/Compiler/IR/EmitC.lean

@@ -108,9 +108,9 @@ def emitFnDeclAux (decl : Decl) (cppBaseName : String) (isExternal : Bool) : M U
     if ps.size > closureMaxArgs && isBoxedName decl.name then
       emit "lean_object**"
     else
-      ps.size.forM fun i => do
+      ps.size.forM fun i _ => do
         if i > 0 then emit ", "
-        emit (toCType ps[i]!.ty)
+        emit (toCType ps[i].ty)
     emit ")"
   emitLn ";"
 
@@ -271,9 +271,9 @@ def emitTag (x : VarId) (xType : IRType) : M Unit := do
     emit x
 
 def isIf (alts : Array Alt) : Option (Nat × FnBody × FnBody) :=
-  if alts.size != 2 then none
-  else match alts[0]! with
-    | Alt.ctor c b => some (c.cidx, b, alts[1]!.body)
+  if h : alts.size ≠ 2 then none
+  else match alts[0] with
+    | Alt.ctor c b => some (c.cidx, b, alts[1].body)
     | _            => none
 
 def emitInc (x : VarId) (n : Nat) (checkRef : Bool) : M Unit := do
@@ -321,20 +321,22 @@ def emitSSet (x : VarId) (n : Nat) (offset : Nat) (y : VarId) (t : IRType) : M U
 
 def emitJmp (j : JoinPointId) (xs : Array Arg) : M Unit := do
   let ps ← getJPParams j
-  unless xs.size == ps.size do throw "invalid goto"
-  xs.size.forM fun i => do
-    let p := ps[i]!
-    let x := xs[i]!
-    emit p.x; emit " = "; emitArg x; emitLn ";"
-  emit "goto "; emit j; emitLn ";"
+  if h : xs.size = ps.size then
+    xs.size.forM fun i _ => do
+      let p := ps[i]
+      let x := xs[i]
+      emit p.x; emit " = "; emitArg x; emitLn ";"
+    emit "goto "; emit j; emitLn ";"
+  else
+    do throw "invalid goto"
 
 def emitLhs (z : VarId) : M Unit := do
   emit z; emit " = "
 
 def emitArgs (ys : Array Arg) : M Unit :=
-  ys.size.forM fun i => do
+  ys.size.forM fun i _ => do
     if i > 0 then emit ", "
-    emitArg ys[i]!
+    emitArg ys[i]
 
 def emitCtorScalarSize (usize : Nat) (ssize : Nat) : M Unit := do
   if usize == 0 then emit ssize
@@ -346,8 +348,8 @@ def emitAllocCtor (c : CtorInfo) : M Unit := do
   emitCtorScalarSize c.usize c.ssize; emitLn ");"
 
 def emitCtorSetArgs (z : VarId) (ys : Array Arg) : M Unit :=
-  ys.size.forM fun i => do
-    emit "lean_ctor_set("; emit z; emit ", "; emit i; emit ", "; emitArg ys[i]!; emitLn ");"
+  ys.size.forM fun i _ => do
+    emit "lean_ctor_set("; emit z; emit ", "; emit i; emit ", "; emitArg ys[i]; emitLn ");"
 
 def emitCtor (z : VarId) (c : CtorInfo) (ys : Array Arg) : M Unit := do
   emitLhs z;
@@ -358,7 +360,7 @@ def emitCtor (z : VarId) (c : CtorInfo) (ys : Array Arg) : M Unit := do
 
 def emitReset (z : VarId) (n : Nat) (x : VarId) : M Unit := do
   emit "if (lean_is_exclusive("; emit x; emitLn ")) {";
-  n.forM fun i => do
+  n.forM fun i _ => do
     emit " lean_ctor_release("; emit x; emit ", "; emit i; emitLn ");"
   emit " "; emitLhs z; emit x; emitLn ";";
   emitLn "} else {";
@@ -399,12 +401,12 @@ def emitSimpleExternalCall (f : String) (ps : Array Param) (ys : Array Arg) : M
   emit f; emit "("
   -- We must remove irrelevant arguments to extern calls.
   discard <| ys.size.foldM
-    (fun i (first : Bool) =>
+    (fun i _ (first : Bool) =>
       if ps[i]!.ty.isIrrelevant then
         pure first
       else do
         unless first do emit ", "
-        emitArg ys[i]!
+        emitArg ys[i]
         pure false)
     true
   emitLn ");"
@@ -431,8 +433,8 @@ def emitPartialApp (z : VarId) (f : FunId) (ys : Array Arg) : M Unit := do
   let decl ← getDecl f
   let arity := decl.params.size;
   emitLhs z; emit "lean_alloc_closure((void*)("; emitCName f; emit "), "; emit arity; emit ", "; emit ys.size; emitLn ");";
-  ys.size.forM fun i => do
-    let y := ys[i]!
+  ys.size.forM fun i _ => do
+    let y := ys[i]
     emit "lean_closure_set("; emit z; emit ", "; emit i; emit ", "; emitArg y; emitLn ");"
 
 def emitApp (z : VarId) (f : VarId) (ys : Array Arg) : M Unit :=
@@ -544,34 +546,36 @@ That is, we have
 -/
 def overwriteParam (ps : Array Param) (ys : Array Arg) : Bool :=
   let n := ps.size;
-  n.any fun i =>
-    let p := ps[i]!
-    (i+1, n).anyI fun j => paramEqArg p ys[j]!
+  n.any fun i _ =>
+    let p := ps[i]
+    (i+1, n).anyI fun j _ _ => paramEqArg p ys[j]!
 
 def emitTailCall (v : Expr) : M Unit :=
   match v with
   | Expr.fap _ ys => do
     let ctx ← read
     let ps := ctx.mainParams
-    unless ps.size == ys.size do throw "invalid tail call"
-    if overwriteParam ps ys then
-      emitLn "{"
-      ps.size.forM fun i => do
-        let p := ps[i]!
-        let y := ys[i]!
-        unless paramEqArg p y do
-          emit (toCType p.ty); emit " _tmp_"; emit i; emit " = "; emitArg y; emitLn ";"
-      ps.size.forM fun i => do
-        let p := ps[i]!
-        let y := ys[i]!
-        unless paramEqArg p y do emit p.x; emit " = _tmp_"; emit i; emitLn ";"
-      emitLn "}"
+    if h : ps.size = ys.size then
+      if overwriteParam ps ys then
+        emitLn "{"
+        ps.size.forM fun i _ => do
+          let p := ps[i]
+          let y := ys[i]
+          unless paramEqArg p y do
+            emit (toCType p.ty); emit " _tmp_"; emit i; emit " = "; emitArg y; emitLn ";"
+        ps.size.forM fun i _ => do
+          let p := ps[i]
+          let y := ys[i]
+          unless paramEqArg p y do emit p.x; emit " = _tmp_"; emit i; emitLn ";"
+        emitLn "}"
+      else
+        ys.size.forM fun i _ => do
+          let p := ps[i]
+          let y := ys[i]
+          unless paramEqArg p y do emit p.x; emit " = "; emitArg y; emitLn ";"
+      emitLn "goto _start;"
     else
-      ys.size.forM fun i => do
-        let p := ps[i]!
-        let y := ys[i]!
-        unless paramEqArg p y do emit p.x; emit " = "; emitArg y; emitLn ";"
-    emitLn "goto _start;"
+      throw "invalid tail call"
   | _ => throw "bug at emitTailCall"
 
 mutual
@@ -654,16 +658,16 @@ def emitDeclAux (d : Decl) : M Unit := do
         if xs.size > closureMaxArgs && isBoxedName d.name then
           emit "lean_object** _args"
         else
-          xs.size.forM fun i => do
+          xs.size.forM fun i _ => do
             if i > 0 then emit ", "
-            let x := xs[i]!
+            let x := xs[i]
             emit (toCType x.ty); emit " "; emit x.x
         emit ")"
       else
         emit ("_init_" ++ baseName ++ "()")
       emitLn " {";
       if xs.size > closureMaxArgs && isBoxedName d.name then
-        xs.size.forM fun i => do
+        xs.size.forM fun i _ => do
           let x := xs[i]!
           emit "lean_object* "; emit x.x; emit " = _args["; emit i; emitLn "];"
       emitLn "_start:";

src/Lean/Compiler/IR/EmitLLVM.lean

@@ -571,9 +571,9 @@ def emitAllocCtor (builder : LLVM.Builder llvmctx)
 
 def emitCtorSetArgs (builder : LLVM.Builder llvmctx)
     (z : VarId) (ys : Array Arg) : M llvmctx Unit := do
-  ys.size.forM fun i => do
+  ys.size.forM fun i _ => do
     let zv ← emitLhsVal builder z
-    let (_yty, yv) ← emitArgVal builder ys[i]!
+    let (_yty, yv) ← emitArgVal builder ys[i]
     let iv ← constIntUnsigned i
     callLeanCtorSet builder zv iv yv
     emitLhsSlotStore builder z zv
@@ -702,8 +702,8 @@ def emitPartialApp (builder : LLVM.Builder llvmctx) (z : VarId) (f : FunId) (ys
                                     (← constIntUnsigned arity)
                                     (← constIntUnsigned ys.size)
   LLVM.buildStore builder zval zslot
-  ys.size.forM fun i => do
-    let (yty, yslot) ← emitArgSlot_ builder ys[i]!
+  ys.size.forM fun i _ => do
+    let (yty, yslot) ← emitArgSlot_ builder ys[i]
     let yval ← LLVM.buildLoad2 builder yty yslot
     callLeanClosureSetFn builder zval (← constIntUnsigned i) yval
 
@@ -922,7 +922,7 @@ def emitReset (builder : LLVM.Builder llvmctx) (z : VarId) (n : Nat) (x : VarId)
   buildIfThenElse_ builder "isExclusive" isExclusive
    (fun builder => do
      let xv ← emitLhsVal builder x
-     n.forM fun i => do
+     n.forM fun i _ => do
          callLeanCtorRelease builder xv (← constIntUnsigned i)
      emitLhsSlotStore builder z xv
      return ShouldForwardControlFlow.yes
@@ -1172,8 +1172,8 @@ def emitFnArgs (builder : LLVM.Builder llvmctx)
     (needsPackedArgs? : Bool)  (llvmfn : LLVM.Value llvmctx) (params : Array Param) : M llvmctx Unit := do
   if needsPackedArgs? then do
       let argsp ← LLVM.getParam llvmfn 0 -- lean_object **args
-      for i in List.range params.size do
-          let param := params[i]!
+      for h : i in [:params.size] do
+          let param := params[i]
           -- argsi := (args + i)
           let argsi ← LLVM.buildGEP2 builder (← LLVM.voidPtrType llvmctx) argsp #[← constIntUnsigned i] s!"packed_arg_{i}_slot"
           let llvmty ← toLLVMType param.ty
@@ -1182,15 +1182,16 @@ def emitFnArgs (builder : LLVM.Builder llvmctx)
           -- slot for arg[i] which is always void* ?
           let alloca ← buildPrologueAlloca builder llvmty s!"arg_{i}"
           LLVM.buildStore builder pv alloca
-          addVartoState params[i]!.x alloca llvmty
+          addVartoState param.x alloca llvmty
   else
       let n ← LLVM.countParams llvmfn
-      for i in (List.range n.toNat) do
-        let llvmty ← toLLVMType params[i]!.ty
+      for i in [:n.toNat] do
+        let param := params[i]!
+        let llvmty ← toLLVMType param.ty
         let alloca ← buildPrologueAlloca builder  llvmty s!"arg_{i}"
         let arg ← LLVM.getParam llvmfn (UInt64.ofNat i)
         let _ ← LLVM.buildStore builder arg alloca
-        addVartoState params[i]!.x alloca llvmty
+        addVartoState param.x alloca llvmty
 
 def emitDeclAux (mod : LLVM.Module llvmctx) (builder : LLVM.Builder llvmctx) (d : Decl) : M llvmctx Unit := do
   let env ← getEnv

src/Lean/Compiler/IR/ExpandResetReuse.lean

@@ -54,7 +54,7 @@ abbrev Mask := Array (Option VarId)
 partial def eraseProjIncForAux (y : VarId) (bs : Array FnBody) (mask : Mask) (keep : Array FnBody) : Array FnBody × Mask :=
   let done (_ : Unit)        := (bs ++ keep.reverse, mask)
   let keepInstr (b : FnBody) := eraseProjIncForAux y bs.pop mask (keep.push b)
-  if bs.size < 2 then done ()
+  if h : bs.size < 2 then done ()
   else
     let b := bs.back!
     match b with
@@ -62,7 +62,7 @@ partial def eraseProjIncForAux (y : VarId) (bs : Array FnBody) (mask : Mask) (ke
     | .vdecl _ _ (.uproj _ _) _   => keepInstr b
     | .inc z n c p _ =>
       if n == 0 then done () else
-      let b' := bs[bs.size - 2]!
+      let b' := bs[bs.size - 2]
       match b' with
       | .vdecl w _ (.proj i x) _ =>
         if w == z && y == x then
@@ -134,15 +134,15 @@ abbrev M := ReaderT Context (StateM Nat)
   modifyGet fun n => ({ idx := n }, n + 1)
 
 def releaseUnreadFields (y : VarId) (mask : Mask) (b : FnBody) : M FnBody :=
-  mask.size.foldM (init := b) fun i b =>
-    match mask.get! i with
+  mask.size.foldM (init := b) fun i _ b =>
+    match mask[i] with
     | some _ => pure b -- code took ownership of this field
     | none   => do
       let fld ← mkFresh
       pure (FnBody.vdecl fld IRType.object (Expr.proj i y) (FnBody.dec fld 1 true false b))
 
 def setFields (y : VarId) (zs : Array Arg) (b : FnBody) : FnBody :=
-  zs.size.fold (init := b) fun i b => FnBody.set y i (zs.get! i) b
+  zs.size.fold (init := b) fun i _ b => FnBody.set y i zs[i] b
 
 /-- Given `set x[i] := y`, return true iff `y := proj[i] x` -/
 def isSelfSet (ctx : Context) (x : VarId) (i : Nat) (y : Arg) : Bool :=

src/Lean/Compiler/IR/RC.lean

@@ -79,13 +79,13 @@ private def addDecForAlt (ctx : Context) (caseLiveVars altLiveVars : LiveVarSet)
 /-- `isFirstOcc xs x i = true` if `xs[i]` is the first occurrence of `xs[i]` in `xs` -/
 private def isFirstOcc (xs : Array Arg) (i : Nat) : Bool :=
   let x := xs[i]!
-  i.all fun j => xs[j]! != x
+  i.all fun j _ => xs[j]! != x
 
 /-- Return true if `x` also occurs in `ys` in a position that is not consumed.
    That is, it is also passed as a borrow reference. -/
 private def isBorrowParamAux (x : VarId) (ys : Array Arg) (consumeParamPred : Nat → Bool) : Bool :=
-  ys.size.any fun i =>
-    let y := ys[i]!
+  ys.size.any fun i _ =>
+    let y := ys[i]
     match y with
     | Arg.irrelevant => false
     | Arg.var y      => x == y && !consumeParamPred i
@@ -99,15 +99,15 @@ Return `n`, the number of times `x` is consumed.
 - `consumeParamPred i = true` if parameter `i` is consumed.
 -/
 private def getNumConsumptions (x : VarId) (ys : Array Arg) (consumeParamPred : Nat → Bool) : Nat :=
-  ys.size.fold (init := 0) fun i n =>
-    let y := ys[i]!
+  ys.size.fold (init := 0) fun i _ n =>
+    let y := ys[i]
     match y with
     | Arg.irrelevant => n
     | Arg.var y      => if x == y && consumeParamPred i then n+1 else n
 
 private def addIncBeforeAux (ctx : Context) (xs : Array Arg) (consumeParamPred : Nat → Bool) (b : FnBody) (liveVarsAfter : LiveVarSet) : FnBody :=
-  xs.size.fold (init := b) fun i b =>
-    let x := xs[i]!
+  xs.size.fold (init := b) fun i _ b =>
+    let x := xs[i]
     match x with
     | Arg.irrelevant => b
     | Arg.var x =>
@@ -128,8 +128,8 @@ private def addIncBefore (ctx : Context) (xs : Array Arg) (ps : Array Param) (b
 
 /-- See `addIncBeforeAux`/`addIncBefore` for the procedure that inserts `inc` operations before an application.  -/
 private def addDecAfterFullApp (ctx : Context) (xs : Array Arg) (ps : Array Param) (b : FnBody) (bLiveVars : LiveVarSet) : FnBody :=
-xs.size.fold (init := b) fun i b =>
-  match xs[i]! with
+xs.size.fold (init := b) fun i _ b =>
+  match xs[i] with
   | Arg.irrelevant => b
   | Arg.var x      =>
     /- We must add a `dec` if `x` must be consumed, it is alive after the application,

src/Lean/Compiler/LCNF/Basic.lean

@@ -366,10 +366,10 @@ to be updated.
 @[implemented_by updateFunDeclCoreImp] opaque FunDeclCore.updateCore (decl: FunDecl) (type : Expr) (params : Array Param) (value : Code) : FunDecl
 
 def CasesCore.extractAlt! (cases : Cases) (ctorName : Name) : Alt × Cases :=
-  let found (i : Nat) := (cases.alts[i]!, { cases with alts := cases.alts.eraseIdx i })
-  if let some i := cases.alts.findIdx? fun | .alt ctorName' .. => ctorName == ctorName' | _ => false then
+  let found i := (cases.alts[i], { cases with alts := cases.alts.eraseIdx i })
+  if let some i := cases.alts.findFinIdx? fun | .alt ctorName' .. => ctorName == ctorName' | _ => false then
     found i
-  else if let some i := cases.alts.findIdx? fun | .default _ => true | _ => false then
+  else if let some i := cases.alts.findFinIdx? fun | .default _ => true | _ => false then
     found i
   else
     unreachable!

src/Lean/Compiler/LCNF/ElimDeadBranches.lean

@@ -587,15 +587,15 @@ def Decl.elimDeadBranches (decls : Array Decl) : CompilerM (Array Decl) := do
     refer to the docstring of `Decl.safe`.
     -/
     if decls[i]!.safe then .bot else .top
-  let mut funVals := decls.size.fold (init := .empty) fun i p => p.push (initialVal i)
+  let mut funVals := decls.size.fold (init := .empty) fun i _ p => p.push (initialVal i)
   let ctx := { decls }
   let mut state := { assignments, funVals }
   (_, state) ← inferMain |>.run ctx |>.run state
   funVals := state.funVals
   assignments := state.assignments
   modifyEnv fun e =>
-    decls.size.fold (init := e) fun i env =>
-      addFunctionSummary env decls[i]!.name funVals[i]!
+    decls.size.fold (init := e) fun i _ env =>
+      addFunctionSummary env decls[i].name funVals[i]!
 
   decls.mapIdxM fun i decl => if decl.safe then elimDead assignments[i]! decl else return decl
 

src/Lean/Compiler/LCNF/InferType.lean

@@ -76,8 +76,8 @@ def getType (fvarId : FVarId) : InferTypeM Expr := do
 
 def mkForallFVars (xs : Array Expr) (type : Expr) : InferTypeM Expr :=
   let b := type.abstract xs
-  xs.size.foldRevM (init := b) fun i b => do
-    let x := xs[i]!
+  xs.size.foldRevM (init := b) fun i _ b => do
+    let x := xs[i]
     let n ← InferType.getBinderName x.fvarId!
     let ty ← InferType.getType x.fvarId!
     let ty := ty.abstractRange i xs;

src/Lean/Compiler/LCNF/PassManager.lean

@@ -134,9 +134,9 @@ def withEachOccurrence (targetName : Name) (f : Nat → PassInstaller) : PassIns
 
 def installAfter (targetName : Name) (p : Pass → Pass) (occurrence : Nat := 0) : PassInstaller where
   install passes :=
-    if let some idx := passes.findIdx? (fun p => p.name == targetName && p.occurrence == occurrence) then
-      let passUnderTest := passes[idx]!
-      return passes.insertAt! (idx + 1) (p passUnderTest)
+    if let some idx := passes.findFinIdx? (fun p => p.name == targetName && p.occurrence == occurrence) then
+      let passUnderTest := passes[idx]
+      return passes.insertIdx (idx + 1) (p passUnderTest)
     else
       throwError s!"Tried to insert pass after {targetName}, occurrence {occurrence} but {targetName} is not in the pass list"
 
@@ -145,9 +145,9 @@ def installAfterEach (targetName : Name) (p : Pass → Pass) : PassInstaller :=
 
 def installBefore (targetName : Name) (p : Pass → Pass) (occurrence : Nat := 0): PassInstaller where
   install passes :=
-    if let some idx := passes.findIdx? (fun p => p.name == targetName && p.occurrence == occurrence) then
-      let passUnderTest := passes[idx]!
-      return passes.insertAt! idx (p passUnderTest)
+    if let some idx := passes.findFinIdx? (fun p => p.name == targetName && p.occurrence == occurrence) then
+      let passUnderTest := passes[idx]
+      return passes.insertIdx idx (p passUnderTest)
     else
       throwError s!"Tried to insert pass after {targetName}, occurrence {occurrence} but {targetName} is not in the pass list"
 
@@ -157,9 +157,7 @@ def installBeforeEachOccurrence (targetName : Name) (p : Pass → Pass) : PassIn
 def replacePass (targetName : Name) (p : Pass → Pass) (occurrence : Nat := 0) : PassInstaller where
   install passes := do
     let some idx := passes.findIdx? (fun p => p.name == targetName && p.occurrence == occurrence) | throwError s!"Tried to replace {targetName}, occurrence {occurrence} but {targetName} is not in the pass list"
-    let target := passes[idx]!
-    let replacement := p target
-    return passes.set! idx replacement
+    return passes.modify idx p
 
 def replaceEachOccurrence (targetName : Name) (p : Pass → Pass) : PassInstaller :=
     withEachOccurrence targetName (replacePass targetName p ·)

src/Lean/Compiler/LCNF/SpecInfo.lean

@@ -152,8 +152,8 @@ def saveSpecParamInfo (decls : Array Decl) : CompilerM Unit := do
       let specArgs? := getSpecializationArgs? (← getEnv) decl.name
       let contains (i : Nat) : Bool := specArgs?.getD #[] |>.contains i
       let mut paramsInfo : Array SpecParamInfo := #[]
-      for i in [:decl.params.size] do
-        let param := decl.params[i]!
+      for h :i in [:decl.params.size] do
+        let param := decl.params[i]
         let info ←
           if contains i then
             pure .user
@@ -181,14 +181,14 @@ def saveSpecParamInfo (decls : Array Decl) : CompilerM Unit := do
       declsInfo := declsInfo.push paramsInfo
   if declsInfo.any fun paramsInfo => paramsInfo.any (· matches .user | .fixedInst | .fixedHO) then
     let m := mkFixedParamsMap decls
-    for i in [:decls.size] do
-      let decl := decls[i]!
+    for hi : i in [:decls.size] do
+      let decl := decls[i]
       let mut paramsInfo := declsInfo[i]!
       let some mask := m.find? decl.name | unreachable!
       trace[Compiler.specialize.info] "{decl.name} {mask}"
       paramsInfo := paramsInfo.zipWith mask fun info fixed => if fixed || info matches .user then info else .other
       for j in [:paramsInfo.size] do
-        let mut info  := paramsInfo[j]!
+        let mut info := paramsInfo[j]!
         if info matches .fixedNeutral && !hasFwdDeps decl paramsInfo j then
           paramsInfo := paramsInfo.set! j .other
       if paramsInfo.any fun info => info matches .fixedInst | .fixedHO | .user then

src/Lean/Compiler/LCNF/ToLCNF.lean

@@ -499,8 +499,8 @@ where
       match app with
       | .fvar f =>
         let mut argsNew := #[]
-        for i in [arity : args.size] do
-          argsNew := argsNew.push (← visitAppArg args[i]!)
+        for h :i in [arity : args.size] do
+          argsNew := argsNew.push (← visitAppArg args[i])
         letValueToArg <| .fvar f argsNew
       | .erased | .type .. => return .erased
 

src/Lean/Compiler/Specialize.lean

@@ -26,13 +26,14 @@ private def elabSpecArgs (declName : Name) (args : Array Syntax) : MetaM (Array
       if let some idx := arg.isNatLit? then
         if idx == 0 then throwErrorAt arg "invalid specialization argument index, index must be greater than 0"
         let idx := idx - 1
-        if idx >= argNames.size then
+        if h : idx >= argNames.size then
           throwErrorAt arg "invalid argument index, `{declName}` has #{argNames.size} arguments"
-        if result.contains idx then throwErrorAt arg "invalid specialization argument index, `{argNames[idx]!}` has already been specified as a specialization candidate"
-        result := result.push idx
+        else
+          if result.contains idx then throwErrorAt arg "invalid specialization argument index, `{argNames[idx]}` has already been specified as a specialization candidate"
+          result := result.push idx
       else
         let argName := arg.getId
-        if let some idx := argNames.getIdx? argName then
+        if let some idx := argNames.indexOf? argName then
           if result.contains idx then throwErrorAt arg "invalid specialization argument name `{argName}`, it has already been specified as a specialization candidate"
           result := result.push idx
         else

src/Lean/CoreM.lean

@@ -11,6 +11,7 @@ import Lean.ResolveName
 import Lean.Elab.InfoTree.Types
 import Lean.MonadEnv
 import Lean.Elab.Exception
+import Lean.Language.Basic
 
 namespace Lean
 register_builtin_option diagnostics : Bool := {
@@ -30,6 +31,11 @@ register_builtin_option maxHeartbeats : Nat := {
   descr := "maximum amount of heartbeats per command. A heartbeat is number of (small) memory allocations (in thousands), 0 means no limit"
 }
 
+register_builtin_option Elab.async : Bool := {
+  defValue := false
+  descr := "perform elaboration using multiple threads where possible"
+}
+
 /--
 If the `diagnostics` option is not already set, gives a message explaining this option.
 Begins with a `\n`, so an error message can look like `m!"some error occurred{useDiagnosticMsg}"`.
@@ -72,6 +78,13 @@ structure State where
   messages        : MessageLog     := {}
   /-- Info tree. We have the info tree here because we want to update it while adding attributes. -/
   infoState       : Elab.InfoState := {}
+  /--
+  Snapshot trees of asynchronous subtasks. As these are untyped and reported only at the end of the
+  command's main elaboration thread, they are only useful for basic message log reporting; for
+  incremental reporting and reuse within a long-running elaboration thread, types rooted in
+  `CommandParsedSnapshot` need to be adjusted.
+  -/
+  snapshotTasks : Array (Language.SnapshotTask Language.SnapshotTree) := #[]
   deriving Nonempty
 
 /-- Context for the CoreM monad. -/
@@ -180,7 +193,8 @@ instance : Elab.MonadInfoTree CoreM where
   modifyInfoState f := modify fun s => { s with infoState := f s.infoState }
 
 @[inline] def modifyCache (f : Cache → Cache) : CoreM Unit :=
-  modify fun ⟨env, next, ngen, trace, cache, messages, infoState⟩ => ⟨env, next, ngen, trace, f cache, messages, infoState⟩
+  modify fun ⟨env, next, ngen, trace, cache, messages, infoState, snaps⟩ =>
+   ⟨env, next, ngen, trace, f cache, messages, infoState, snaps⟩
 
 @[inline] def modifyInstLevelTypeCache (f : InstantiateLevelCache → InstantiateLevelCache) : CoreM Unit :=
   modifyCache fun ⟨c₁, c₂⟩ => ⟨f c₁, c₂⟩
@@ -355,13 +369,83 @@ instance : MonadLog CoreM where
     if (← read).suppressElabErrors then
       -- discard elaboration errors, except for a few important and unlikely misleading ones, on
       -- parse error
-      unless msg.data.hasTag (· matches `Elab.synthPlaceholder | `Tactic.unsolvedGoals) do
+      unless msg.data.hasTag (· matches `Elab.synthPlaceholder | `Tactic.unsolvedGoals | `trace) do
         return
 
     let ctx ← read
     let msg := { msg with data := MessageData.withNamingContext { currNamespace := ctx.currNamespace, openDecls := ctx.openDecls } msg.data };
     modify fun s => { s with messages := s.messages.add msg }
 
+/--
+Includes a given task (such as from `wrapAsyncAsSnapshot`) in the overall snapshot tree for this
+command's elaboration, making its result available to reporting and the language server. The
+reporter will not know about this snapshot tree node until the main elaboration thread for this
+command has finished so this function is not useful for incremental reporting within a longer
+elaboration thread but only for tasks that outlive it such as background kernel checking or proof
+elaboration.
+-/
+def logSnapshotTask (task : Language.SnapshotTask Language.SnapshotTree) : CoreM Unit :=
+  modify fun s => { s with snapshotTasks := s.snapshotTasks.push task }
+
+/-- Wraps the given action for use in `EIO.asTask` etc., discarding its final monadic state. -/
+def wrapAsync (act : Unit → CoreM α) : CoreM (EIO Exception α) := do
+  let st ← get
+  let ctx ← read
+  let heartbeats := (← IO.getNumHeartbeats) - ctx.initHeartbeats
+  return withCurrHeartbeats (do
+      -- include heartbeats since start of elaboration in new thread as well such that forking off
+      -- an action doesn't suddenly allow it to succeed from a lower heartbeat count
+      IO.addHeartbeats heartbeats.toUInt64
+      act () : CoreM _)
+    |>.run' ctx st
+
+/-- Option for capturing output to stderr during elaboration. -/
+register_builtin_option stderrAsMessages : Bool := {
+  defValue := true
+  group    := "server"
+  descr    := "(server) capture output to the Lean stderr channel (such as from `dbg_trace`) during elaboration of a command as a diagnostic message"
+}
+
+open Language in
+/--
+Wraps the given action for use in `BaseIO.asTask` etc., discarding its final state except for
+`logSnapshotTask` tasks, which are reported as part of the returned tree.
+-/
+def wrapAsyncAsSnapshot (act : Unit → CoreM Unit) (desc : String := by exact decl_name%.toString) :
+    CoreM (BaseIO SnapshotTree) := do
+  let t ← wrapAsync fun _ => do
+    IO.FS.withIsolatedStreams (isolateStderr := stderrAsMessages.get (← getOptions)) do
+      let tid ← IO.getTID
+      -- reset trace state and message log so as not to report them twice
+      modify ({ · with messages := {}, traceState := { tid } })
+      try
+        withTraceNode `Elab.async (fun _ => return desc) do
+          act ()
+      catch e =>
+        logError e.toMessageData
+      finally
+        addTraceAsMessages
+      get
+  let ctx ← readThe Core.Context
+  return do
+    match (← t.toBaseIO) with
+    | .ok (output, st) =>
+      let mut msgs := st.messages
+      if !output.isEmpty then
+        msgs := msgs.add {
+          fileName := ctx.fileName
+          severity := MessageSeverity.information
+          pos      := ctx.fileMap.toPosition <| ctx.ref.getPos?.getD 0
+          data     := output
+        }
+      return .mk {
+        desc
+        diagnostics := (← Language.Snapshot.Diagnostics.ofMessageLog msgs)
+        traces := st.traceState
+      } st.snapshotTasks
+    -- interrupt or abort exception as `try catch` above should have caught any others
+    | .error _ => default
+
 end Core
 
 export Core (CoreM mkFreshUserName checkSystem withCurrHeartbeats)

src/Lean/Data/HashMap.lean

@@ -277,4 +277,23 @@ attribute [deprecated Std.HashMap.empty (since := "2024-08-08")] mkHashMap
 attribute [deprecated Std.HashMap.empty (since := "2024-08-08")] HashMap.empty
 attribute [deprecated Std.HashMap.ofList (since := "2024-08-08")] HashMap.ofList
 
+attribute [deprecated Std.HashMap.insert (since := "2024-08-08")] HashMap.insert
+attribute [deprecated Std.HashMap.containsThenInsert (since := "2024-08-08")] HashMap.insert'
+attribute [deprecated Std.HashMap.insertIfNew (since := "2024-08-08")] HashMap.insertIfNew
+attribute [deprecated Std.HashMap.erase (since := "2024-08-08")] HashMap.erase
+attribute [deprecated "Use `m[k]?` instead." (since := "2024-08-08")] HashMap.findEntry?
+attribute [deprecated "Use `m[k]?` instead." (since := "2024-08-08")] HashMap.find?
+attribute [deprecated "Use `m[k]?.getD` instead." (since := "2024-08-08")] HashMap.findD
+attribute [deprecated "Use `m[k]!` instead." (since := "2024-08-08")] HashMap.find!
+attribute [deprecated Std.HashMap.contains (since := "2024-08-08")] HashMap.contains
+attribute [deprecated Std.HashMap.foldM (since := "2024-08-08")] HashMap.foldM
+attribute [deprecated Std.HashMap.fold (since := "2024-08-08")] HashMap.fold
+attribute [deprecated Std.HashMap.forM (since := "2024-08-08")] HashMap.forM
+attribute [deprecated Std.HashMap.size (since := "2024-08-08")] HashMap.size
+attribute [deprecated Std.HashMap.isEmpty (since := "2024-08-08")] HashMap.isEmpty
+attribute [deprecated Std.HashMap.toList (since := "2024-08-08")] HashMap.toList
+attribute [deprecated Std.HashMap.toArray (since := "2024-08-08")] HashMap.toArray
+attribute [deprecated "Deprecateed without a replacement." (since := "2024-08-08")] HashMap.numBuckets
+attribute [deprecated "Deprecateed without a replacement." (since := "2024-08-08")] HashMap.ofListWith
+
 end Lean.HashMap

src/Lean/Data/PersistentArray.lean

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura
 -/
 prelude
+import Init.Data.Nat.Fold
 import Init.Data.Array.Basic
 import Init.NotationExtra
 import Init.Data.ToString.Macro
@@ -371,7 +372,7 @@ instance : ToString Stats := ⟨Stats.toString⟩
 end PersistentArray
 
 def mkPersistentArray {α : Type u} (n : Nat) (v : α) : PArray α :=
-  n.fold (init := PersistentArray.empty) fun _ p => p.push v
+  n.fold (init := PersistentArray.empty) fun _ _ p => p.push v
 
 @[inline] def mkPArray {α : Type u} (n : Nat) (v : α) : PArray α :=
   mkPersistentArray n v

src/Lean/Data/PersistentHashMap.lean

@@ -233,10 +233,10 @@ partial def eraseAux [BEq α] : Node α β → USize → α → Node α β
   | n@(Node.collision keys vals heq), _, k =>
     match keys.indexOf? k with
     | some idx =>
-      let keys' := keys.feraseIdx idx
-      have keq := keys.size_feraseIdx idx
-      let vals' := vals.feraseIdx (Eq.ndrec idx heq)
-      have veq := vals.size_feraseIdx (Eq.ndrec idx heq)
+      let keys' := keys.eraseIdx idx
+      have keq := keys.size_eraseIdx idx _
+      let vals' := vals.eraseIdx (Eq.ndrec idx heq)
+      have veq := vals.size_eraseIdx (Eq.ndrec idx heq) _
       have : keys.size - 1 = vals.size - 1 := by rw [heq]
       Node.collision keys' vals' (keq.trans (this.trans veq.symm))
     | none     => n

src/Lean/Elab.lean

@@ -23,6 +23,7 @@ import Lean.Elab.Quotation
 import Lean.Elab.Syntax
 import Lean.Elab.Do
 import Lean.Elab.StructInst
+import Lean.Elab.MutualInductive
 import Lean.Elab.Inductive
 import Lean.Elab.Structure
 import Lean.Elab.Print

src/Lean/Elab/App.lean

@@ -807,8 +807,8 @@ def getElabElimExprInfo (elimExpr : Expr) : MetaM ElabElimInfo := do
     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]!
+    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
@@ -1150,48 +1150,33 @@ private def throwLValError (e : Expr) (eType : Expr) (msg : MessageData) : TermE
   throwError "{msg}{indentExpr e}\nhas type{indentExpr eType}"
 
 /--
-`findMethod? S fName` tries the following for each namespace `S'` in the resolution order for `S`:
-- If `env` contains `S' ++ fName`, returns `(S', S' ++ fName)`
-- Otherwise if `env` contains private name `prv` for `S' ++ fName`, returns `(S', prv)`
+`findMethod? S fName` tries the for each namespace `S'` in the resolution order for `S` to resolve the name `S'.fname`.
+If it resolves to `name`, returns `(S', name)`.
 -/
 private partial def findMethod? (structName fieldName : Name) : MetaM (Option (Name × Name)) := do
   let env ← getEnv
   let find? structName' : MetaM (Option (Name × Name)) := do
     let fullName := structName' ++ fieldName
-    if env.contains fullName then
-      return some (structName', fullName)
-    let fullNamePrv := mkPrivateName env fullName
-    if env.contains fullNamePrv then
-      return some (structName', fullNamePrv)
-    return none
+    -- We do not want to make use of the current namespace for resolution.
+    let candidates := ResolveName.resolveGlobalName (← getEnv) Name.anonymous (← getOpenDecls) fullName
+      |>.filter (fun (_, fieldList) => fieldList.isEmpty)
+      |>.map Prod.fst
+    match candidates with
+    | []          => return none
+    | [fullName'] => return some (structName', fullName')
+    | _ => throwError "\
+      invalid field notation '{fieldName}', the name '{fullName}' is ambiguous, possible interpretations: \
+      {MessageData.joinSep (candidates.map (m!"'{.ofConstName ·}'")) ", "}"
   -- Optimization: the first element of the resolution order is `structName`,
   -- so we can skip computing the resolution order in the common case
   -- of the name resolving in the `structName` namespace.
   find? structName <||> do
     let resolutionOrder ← if isStructure env structName then getStructureResolutionOrder structName else pure #[structName]
-    for h : i in [1:resolutionOrder.size] do
-      if let some res ← find? resolutionOrder[i] then
+    for ns in resolutionOrder[1:resolutionOrder.size] do
+      if let some res ← find? ns then
         return res
     return none
 
-/--
-  Return `some (structName', fullName)` if `structName ++ fieldName` is an alias for `fullName`, and
-  `fullName` is of the form `structName' ++ fieldName`.
-
-  TODO: if there is more than one applicable alias, it returns `none`. We should consider throwing an error or
-  warning.
--/
-private def findMethodAlias? (env : Environment) (structName fieldName : Name) : Option (Name × Name) :=
-  let fullName := structName ++ fieldName
-  -- We never skip `protected` aliases when resolving dot-notation.
-  let aliasesCandidates := getAliases env fullName (skipProtected := false) |>.filterMap fun alias =>
-    match alias.eraseSuffix? fieldName with
-    | none => none
-    | some structName' => some (structName', alias)
-  match aliasesCandidates with
-  | [r] => some r
-  | _   => none
-
 private def throwInvalidFieldNotation (e eType : Expr) : TermElabM α :=
   throwLValError e eType "invalid field notation, type is not of the form (C ...) where C is a constant"
 
@@ -1223,30 +1208,22 @@ private def resolveLValAux (e : Expr) (eType : Expr) (lval : LVal) : TermElabM L
         throwLValError e eType m!"invalid projection, structure has only {numFields} field(s)"
   | some structName, LVal.fieldName _ fieldName _ _ =>
     let env ← getEnv
-    let searchEnv : Unit → TermElabM LValResolution := fun _ => do
-      if let some (baseStructName, fullName) ← findMethod? structName (.mkSimple fieldName) then
-        return LValResolution.const baseStructName structName fullName
-      else if let some (structName', fullName) := findMethodAlias? env structName (.mkSimple fieldName) then
-        return LValResolution.const structName' structName' fullName
-      else
-        throwLValError e eType
-          m!"invalid field '{fieldName}', the environment does not contain '{Name.mkStr structName fieldName}'"
-    -- search local context first, then environment
-    let searchCtx : Unit → TermElabM LValResolution := fun _ => do
-      let fullName := Name.mkStr structName fieldName
-      for localDecl in (← getLCtx) do
-        if localDecl.isAuxDecl then
-          if let some localDeclFullName := (← read).auxDeclToFullName.find? localDecl.fvarId then
-            if fullName == (privateToUserName? localDeclFullName).getD localDeclFullName then
-              /- LVal notation is being used to make a "local" recursive call. -/
-              return LValResolution.localRec structName fullName localDecl.toExpr
-      searchEnv ()
     if isStructure env structName then
-      match findField? env structName (Name.mkSimple fieldName) with
-      | some baseStructName => return LValResolution.projFn baseStructName structName (Name.mkSimple fieldName)
-      | none                => searchCtx ()
-    else
-      searchCtx ()
+      if let some baseStructName := findField? env structName (Name.mkSimple fieldName) then
+        return LValResolution.projFn baseStructName structName (Name.mkSimple fieldName)
+    -- Search the local context first
+    let fullName := Name.mkStr structName fieldName
+    for localDecl in (← getLCtx) do
+      if localDecl.isAuxDecl then
+        if let some localDeclFullName := (← read).auxDeclToFullName.find? localDecl.fvarId then
+          if fullName == (privateToUserName? localDeclFullName).getD localDeclFullName then
+            /- LVal notation is being used to make a "local" recursive call. -/
+            return LValResolution.localRec structName fullName localDecl.toExpr
+    -- Then search the environment
+    if let some (baseStructName, fullName) ← findMethod? structName (.mkSimple fieldName) then
+      return LValResolution.const baseStructName structName fullName
+    throwLValError e eType
+      m!"invalid field '{fieldName}', the environment does not contain '{Name.mkStr structName fieldName}'"
   | none, LVal.fieldName _ _ (some suffix) _ =>
     if e.isConst then
       throwUnknownConstant (e.constName! ++ suffix)
@@ -1326,7 +1303,7 @@ Otherwise, if there isn't another parameter with the same name, we add `e` to `n
 
 Remark: `fullName` is the name of the resolved "field" access function. It is used for reporting errors
 -/
-private partial def addLValArg (baseName : Name) (fullName : Name) (e : Expr) (args : Array Arg) (namedArgs : Array NamedArg) (f : Expr) :
+private partial def addLValArg (baseName : Name) (fullName : Name) (e : Expr) (args : Array Arg) (namedArgs : Array NamedArg) (f : Expr) (explicit : Bool) :
     MetaM (Array Arg × Array NamedArg) := do
   withoutModifyingState <| go f (← inferType f) 0 namedArgs (namedArgs.map (·.name)) true
 where
@@ -1347,29 +1324,29 @@ where
     let mut unusableNamedArgs := unusableNamedArgs
     for x in xs, bInfo in bInfos do
       let xDecl ← x.mvarId!.getDecl
-      if let some idx := remainingNamedArgs.findIdx? (·.name == xDecl.userName) then
+      if let some idx := remainingNamedArgs.findFinIdx? (·.name == xDecl.userName) then
         /- If there is named argument with name `xDecl.userName`, then it is accounted for and we can't make use of it. -/
         remainingNamedArgs := remainingNamedArgs.eraseIdx idx
       else
-        if (← typeMatchesBaseName xDecl.type baseName) then
-          /- We found a type of the form (baseName ...).
-             First, we check if the current argument is an explicit one,
+        if ← typeMatchesBaseName xDecl.type baseName then
+          /- We found a type of the form (baseName ...), or we found the first explicit argument in useFirstExplicit mode.
+             First, we check if the current argument is one that can be used positionally,
              and if the current explicit position "fits" at `args` (i.e., it must be ≤ arg.size) -/
-          if argIdx ≤ args.size && bInfo.isExplicit then
+          if h : argIdx ≤ args.size ∧ (explicit || bInfo.isExplicit) then
             /- We can insert `e` as an explicit argument -/
-            return (args.insertAt! argIdx (Arg.expr e), namedArgs)
+            return (args.insertIdx argIdx (Arg.expr e), namedArgs)
           else
             /- If we can't add `e` to `args`, we try to add it using a named argument, but this is only possible
                if there isn't an argument with the same name occurring before it. -/
             if !allowNamed || unusableNamedArgs.contains xDecl.userName then
               throwError "\
-                invalid field notation, function '{fullName}' has argument with the expected type\
+                invalid field notation, function '{.ofConstName fullName}' has argument with the expected type\
                 {indentExpr xDecl.type}\n\
                 but it cannot be used"
             else
               return (args, namedArgs.push { name := xDecl.userName, val := Arg.expr e })
         /- Advance `argIdx` and update seen named arguments. -/
-        if bInfo.isExplicit then
+        if explicit || bInfo.isExplicit then
           argIdx := argIdx + 1
         unusableNamedArgs := unusableNamedArgs.push xDecl.userName
     /- If named arguments aren't allowed, then it must still be possible to pass the value as an explicit argument.
@@ -1380,7 +1357,7 @@ where
       if let some f' ← coerceToFunction? (mkAppN f xs) then
         return ← go f' (← inferType f') argIdx remainingNamedArgs unusableNamedArgs false
     throwError "\
-      invalid field notation, function '{fullName}' does not have argument with type ({baseName} ...) that can be used, \
+      invalid field notation, function '{.ofConstName fullName}' does not have argument with type ({.ofConstName baseName} ...) that can be used, \
       it must be explicit or implicit with a unique name"
 
 /-- Adds the `TermInfo` for the field of a projection. See `Lean.Parser.Term.identProjKind`. -/
@@ -1426,7 +1403,7 @@ private def elabAppLValsAux (namedArgs : Array NamedArg) (args : Array Arg) (exp
       let projFn ← mkConst constName
       let projFn ← addProjTermInfo lval.getRef projFn
       if lvals.isEmpty then
-        let (args, namedArgs) ← addLValArg baseStructName constName f args namedArgs projFn
+        let (args, namedArgs) ← addLValArg baseStructName constName f args namedArgs projFn explicit
         elabAppArgs projFn namedArgs args expectedType? explicit ellipsis
       else
         let f ← elabAppArgs projFn #[] #[Arg.expr f] (expectedType? := none) (explicit := false) (ellipsis := false)
@@ -1434,7 +1411,7 @@ private def elabAppLValsAux (namedArgs : Array NamedArg) (args : Array Arg) (exp
     | LValResolution.localRec baseName fullName fvar =>
       let fvar ← addProjTermInfo lval.getRef fvar
       if lvals.isEmpty then
-        let (args, namedArgs) ← addLValArg baseName fullName f args namedArgs fvar
+        let (args, namedArgs) ← addLValArg baseName fullName f args namedArgs fvar explicit
         elabAppArgs fvar namedArgs args expectedType? explicit ellipsis
       else
         let f ← elabAppArgs fvar #[] #[Arg.expr f] (expectedType? := none) (explicit := false) (ellipsis := false)

src/Lean/Elab/BuiltinCommand.lean

@@ -211,7 +211,7 @@ private def replaceBinderAnnotation (binder : TSyntax ``Parser.Term.bracketedBin
         else
           `(bracketedBinderF| {$id $[: $ty?]?})
       for id in ids.reverse do
-        if let some idx := binderIds.findIdx? fun binderId => binderId.raw.isIdent && binderId.raw.getId == id.raw.getId then
+        if let some idx := binderIds.findFinIdx? fun binderId => binderId.raw.isIdent && binderId.raw.getId == id.raw.getId then
           binderIds := binderIds.eraseIdx idx
           modifiedVarDecls := true
           varDeclsNew := varDeclsNew.push (← mkBinder id explicit)

src/Lean/Elab/Command.lean

@@ -84,6 +84,7 @@ structure State where
   ngen           : NameGenerator := {}
   infoState      : InfoState := {}
   traceState     : TraceState := {}
+  snapshotTasks  : Array (Language.SnapshotTask Language.SnapshotTree) := #[]
   deriving Nonempty
 
 structure Context where
@@ -114,8 +115,7 @@ structure Context where
   -/
   suppressElabErrors : Bool := false
 
-abbrev CommandElabCoreM (ε) := ReaderT Context $ StateRefT State $ EIO ε
-abbrev CommandElabM := CommandElabCoreM Exception
+abbrev CommandElabM := ReaderT Context $ StateRefT State $ EIO Exception
 abbrev CommandElab  := Syntax → CommandElabM Unit
 structure Linter where
   run : Syntax → CommandElabM Unit
@@ -198,36 +198,6 @@ instance : AddErrorMessageContext CommandElabM where
     let msg ← addMacroStack msg ctx.macroStack
     return (ref, msg)
 
-def mkMessageAux (ctx : Context) (ref : Syntax) (msgData : MessageData) (severity : MessageSeverity) : Message :=
-  let pos := ref.getPos?.getD ctx.cmdPos
-  let endPos := ref.getTailPos?.getD pos
-  mkMessageCore ctx.fileName ctx.fileMap msgData severity pos endPos
-
-private def addTraceAsMessagesCore (ctx : Context) (log : MessageLog) (traceState : TraceState) : MessageLog := Id.run do
-  if traceState.traces.isEmpty then return log
-  let mut traces : Std.HashMap (String.Pos × String.Pos) (Array MessageData) := ∅
-  for traceElem in traceState.traces do
-    let ref := replaceRef traceElem.ref ctx.ref
-    let pos := ref.getPos?.getD 0
-    let endPos := ref.getTailPos?.getD pos
-    traces := traces.insert (pos, endPos) <| traces.getD (pos, endPos) #[] |>.push traceElem.msg
-  let mut log := log
-  let traces' := traces.toArray.qsort fun ((a, _), _) ((b, _), _) => a < b
-  for ((pos, endPos), traceMsg) in traces' do
-    let data := .tagged `trace <| .joinSep traceMsg.toList "\n"
-    log := log.add <| mkMessageCore ctx.fileName ctx.fileMap data .information pos endPos
-  return log
-
-private def addTraceAsMessages : CommandElabM Unit := do
-  let ctx ← read
-  -- do not add trace messages if `trace.profiler.output` is set as it would be redundant and
-  -- pretty printing the trace messages is expensive
-  if trace.profiler.output.get? (← getOptions) |>.isNone then
-    modify fun s => { s with
-      messages          := addTraceAsMessagesCore ctx s.messages s.traceState
-      traceState.traces := {}
-    }
-
 private def runCore (x : CoreM α) : CommandElabM α := do
   let s ← get
   let ctx ← read
@@ -253,6 +223,7 @@ private def runCore (x : CoreM α) : CommandElabM α := do
     nextMacroScope := s.nextMacroScope
     infoState.enabled := s.infoState.enabled
     traceState := s.traceState
+    snapshotTasks := s.snapshotTasks
   }
   let (ea, coreS) ← liftM x
   modify fun s => { s with
@@ -261,6 +232,7 @@ private def runCore (x : CoreM α) : CommandElabM α := do
     ngen              := coreS.ngen
     infoState.trees   := s.infoState.trees.append coreS.infoState.trees
     traceState.traces := coreS.traceState.traces.map fun t => { t with ref := replaceRef t.ref ctx.ref }
+    snapshotTasks     := coreS.snapshotTasks
     messages          := s.messages ++ coreS.messages
   }
   return ea
@@ -268,10 +240,6 @@ private def runCore (x : CoreM α) : CommandElabM α := do
 def liftCoreM (x : CoreM α) : CommandElabM α := do
   MonadExcept.ofExcept (← runCore (observing x))
 
-private def ioErrorToMessage (ctx : Context) (ref : Syntax) (err : IO.Error) : Message :=
-  let ref := getBetterRef ref ctx.macroStack
-  mkMessageAux ctx ref (toString err) MessageSeverity.error
-
 @[inline] def liftIO {α} (x : IO α) : CommandElabM α := do
   let ctx ← read
   IO.toEIO (fun (ex : IO.Error) => Exception.error ctx.ref ex.toString) x
@@ -294,9 +262,8 @@ instance : MonadLog CommandElabM where
   logMessage msg := do
     if (← read).suppressElabErrors then
       -- discard elaboration errors on parse error
-      -- NOTE: unlike `CoreM`'s `logMessage`, we do not currently have any command-level errors that
-      -- we want to allowlist
-      return
+      unless msg.data.hasTag (· matches `trace) do
+        return
     let currNamespace ← getCurrNamespace
     let openDecls ← getOpenDecls
     let msg := { msg with data := MessageData.withNamingContext { currNamespace := currNamespace, openDecls := openDecls } msg.data }
@@ -322,6 +289,61 @@ def runLinters (stx : Syntax) : CommandElabM Unit := do
             finally
               modify fun s => { savedState with messages := s.messages }
 
+/--
+Catches and logs exceptions occurring in `x`. Unlike `try catch` in `CommandElabM`, this function
+catches interrupt exceptions as well and thus is intended for use at the top level of elaboration.
+Interrupt and abort exceptions are caught but not logged.
+-/
+@[inline] def withLoggingExceptions (x : CommandElabM Unit) : CommandElabM Unit := fun ctx ref =>
+  EIO.catchExceptions (withLogging x ctx ref) (fun _ => pure ())
+
+@[inherit_doc Core.wrapAsync]
+def wrapAsync (act : Unit → CommandElabM α) : CommandElabM (EIO Exception α) := do
+  return act () |>.run (← read) |>.run' (← get)
+
+open Language in
+@[inherit_doc Core.wrapAsyncAsSnapshot]
+-- `CoreM` and `CommandElabM` are too different to meaningfully share this code
+def wrapAsyncAsSnapshot (act : Unit → CommandElabM Unit)
+    (desc : String := by exact decl_name%.toString) :
+    CommandElabM (BaseIO SnapshotTree) := do
+  let t ← wrapAsync fun _ => do
+    IO.FS.withIsolatedStreams (isolateStderr := Core.stderrAsMessages.get (← getOptions)) do
+      let tid ← IO.getTID
+      -- reset trace state and message log so as not to report them twice
+      modify ({ · with messages := {}, traceState := { tid } })
+      try
+        withTraceNode `Elab.async (fun _ => return desc) do
+          act ()
+      catch e =>
+        logError e.toMessageData
+      finally
+        addTraceAsMessages
+      get
+  let ctx ← read
+  return do
+    match (← t.toBaseIO) with
+    | .ok (output, st) =>
+      let mut msgs := st.messages
+      if !output.isEmpty then
+        msgs := msgs.add {
+          fileName := ctx.fileName
+          severity := MessageSeverity.information
+          pos      := ctx.fileMap.toPosition <| ctx.ref.getPos?.getD 0
+          data     := output
+        }
+      return .mk {
+        desc
+        diagnostics := (← Language.Snapshot.Diagnostics.ofMessageLog msgs)
+        traces := st.traceState
+      } st.snapshotTasks
+    -- interrupt or abort exception as `try catch` above should have caught any others
+    | .error _ => default
+
+@[inherit_doc Core.logSnapshotTask]
+def logSnapshotTask (task : Language.SnapshotTask Language.SnapshotTree) : CommandElabM Unit :=
+  modify fun s => { s with snapshotTasks := s.snapshotTasks.push task }
+
 protected def getCurrMacroScope : CommandElabM Nat  := do pure (← read).currMacroScope
 protected def getMainModule     : CommandElabM Name := do pure (← getEnv).mainModule
 
@@ -532,12 +554,6 @@ def elabCommandTopLevel (stx : Syntax) : CommandElabM Unit := withRef stx do pro
     let mut msgs := (← get).messages
     for tree in (← getInfoTrees) do
       trace[Elab.info] (← tree.format)
-    if (← isTracingEnabledFor `Elab.snapshotTree) then
-      if let some snap := (← read).snap? then
-        -- We can assume that the root command snapshot is not involved in parallelism yet, so this
-        -- should be true iff the command supports incrementality
-        if (← IO.hasFinished snap.new.result) then
-          liftCoreM <| Language.ToSnapshotTree.toSnapshotTree snap.new.result.get |>.trace
     modify fun st => { st with
       messages := initMsgs ++ msgs
       infoState := { st.infoState with trees := initInfoTrees ++ st.infoState.trees }
@@ -668,14 +684,6 @@ def runTermElabM (elabFn : Array Expr → TermElabM α) : CommandElabM α := do
           Term.addAutoBoundImplicits' xs someType fun xs _ =>
             Term.withoutAutoBoundImplicit <| elabFn xs
 
-/--
-Catches and logs exceptions occurring in `x`. Unlike `try catch` in `CommandElabM`, this function
-catches interrupt exceptions as well and thus is intended for use at the top level of elaboration.
-Interrupt and abort exceptions are caught but not logged.
--/
-@[inline] def withLoggingExceptions (x : CommandElabM Unit) : CommandElabCoreM Empty Unit := fun ctx ref =>
-  EIO.catchExceptions (withLogging x ctx ref) (fun _ => pure ())
-
 private def liftAttrM {α} (x : AttrM α) : CommandElabM α := do
   liftCoreM x
 

src/Lean/Elab/Declaration.lean

@@ -7,9 +7,8 @@ prelude
 import Lean.Util.CollectLevelParams
 import Lean.Elab.DeclUtil
 import Lean.Elab.DefView
-import Lean.Elab.Inductive
-import Lean.Elab.Structure
 import Lean.Elab.MutualDef
+import Lean.Elab.MutualInductive
 import Lean.Elab.DeclarationRange
 namespace Lean.Elab.Command
 
@@ -163,15 +162,11 @@ def elabDeclaration : CommandElab := fun stx => do
     if declKind == ``Lean.Parser.Command.«axiom» then
       let modifiers ← elabModifiers modifiers
       elabAxiom modifiers decl
-    else if declKind == ``Lean.Parser.Command.«inductive» then
+    else if declKind == ``Lean.Parser.Command.«inductive»
+        || declKind == ``Lean.Parser.Command.classInductive
+        || declKind == ``Lean.Parser.Command.«structure» then
       let modifiers ← elabModifiers modifiers
       elabInductive modifiers decl
-    else if declKind == ``Lean.Parser.Command.classInductive then
-      let modifiers ← elabModifiers modifiers
-      elabClassInductive modifiers decl
-    else if declKind == ``Lean.Parser.Command.«structure» then
-      let modifiers ← elabModifiers modifiers
-      elabStructure modifiers decl
     else
       throwError "unexpected declaration"
 
@@ -278,10 +273,10 @@ def elabMutual : CommandElab := fun stx => do
     -- only case implementing incrementality currently
     elabMutualDef stx[1].getArgs
   else withoutCommandIncrementality true do
-    if isMutualInductive stx then
+    if ← isMutualInductive stx then
       elabMutualInductive stx[1].getArgs
     else
-      throwError "invalid mutual block: either all elements of the block must be inductive declarations, or they must all be definitions/theorems/abbrevs"
+      throwError "invalid mutual block: either all elements of the block must be inductive/structure declarations, or they must all be definitions/theorems/abbrevs"
 
 /- leading_parser "attribute " >> "[" >> sepBy1 (eraseAttr <|> Term.attrInstance) ", " >> "]" >> many1 ident -/
 @[builtin_command_elab «attribute»] def elabAttr : CommandElab := fun stx => do

src/Lean/Elab/Deriving/Util.lean

@@ -49,9 +49,9 @@ invoking ``mkInstImplicitBinders `BarClass foo #[`α, `n, `β]`` gives `` `([Bar
 def mkInstImplicitBinders (className : Name) (indVal : InductiveVal) (argNames : Array Name) : TermElabM (Array Syntax) :=
   forallBoundedTelescope indVal.type indVal.numParams fun xs _ => do
     let mut binders := #[]
-    for i in [:xs.size] do
+    for h : i in [:xs.size] do
       try
-        let x := xs[i]!
+        let x := xs[i]
         let c ← mkAppM className #[x]
         if (← isTypeCorrect c) then
           let argName := argNames[i]!
@@ -86,8 +86,8 @@ def mkContext (fnPrefix : String) (typeName : Name) : TermElabM Context := do
 
 def mkLocalInstanceLetDecls (ctx : Context) (className : Name) (argNames : Array Name) : TermElabM (Array (TSyntax ``Parser.Term.letDecl)) := do
   let mut letDecls := #[]
-  for i in [:ctx.typeInfos.size] do
-    let indVal       := ctx.typeInfos[i]!
+  for h : i in [:ctx.typeInfos.size] do
+    let indVal       := ctx.typeInfos[i]
     let auxFunName   := ctx.auxFunNames[i]!
     let currArgNames ← mkInductArgNames indVal
     let numParams    := indVal.numParams

src/Lean/Elab/Do.lean

@@ -796,10 +796,10 @@ Note that we are not restricting the macro power since the
 actions to be in the same universe.
 -/
 private def mkTuple (elems : Array Syntax) : MacroM Syntax := do
-  if elems.size == 0 then
+  if elems.size = 0 then
     mkUnit
-  else if elems.size == 1 then
-    return elems[0]!
+  else if h : elems.size = 1 then
+    return elems[0]
   else
     elems.extract 0 (elems.size - 1) |>.foldrM (init := elems.back!) fun elem tuple =>
       ``(MProd.mk $elem $tuple)
@@ -831,10 +831,10 @@ def isDoExpr? (doElem : Syntax) : Option Syntax :=
   We use this method when expanding the `for-in` notation.
 -/
 private def destructTuple (uvars : Array Var) (x : Syntax) (body : Syntax) : MacroM Syntax := do
-  if uvars.size == 0 then
+  if uvars.size = 0 then
     return body
-  else if uvars.size == 1 then
-    `(let $(uvars[0]!):ident := $x; $body)
+  else if h : uvars.size = 1 then
+    `(let $(uvars[0]):ident := $x; $body)
   else
     destruct uvars.toList x body
 where
@@ -1314,9 +1314,9 @@ private partial def expandLiftMethodAux (inQuot : Bool) (inBinder : Bool) : Synt
     else if liftMethodDelimiter k then
       return stx
     -- For `pure` if-then-else, we only lift `(<- ...)` occurring in the condition.
-    else if args.size >= 2 && (k == ``termDepIfThenElse || k == ``termIfThenElse) then do
+    else if h : args.size >= 2 ∧ (k == ``termDepIfThenElse || k == ``termIfThenElse) then do
       let inAntiquot := stx.isAntiquot && !stx.isEscapedAntiquot
-      let arg1 ← expandLiftMethodAux (inQuot && !inAntiquot || stx.isQuot) inBinder args[1]!
+      let arg1 ← expandLiftMethodAux (inQuot && !inAntiquot || stx.isQuot) inBinder args[1]
       let args := args.set! 1 arg1
       return Syntax.node i k args
     else if k == ``Parser.Term.liftMethod && !inQuot then withFreshMacroScope do
@@ -1518,7 +1518,7 @@ mutual
   -/
   partial def doForToCode (doFor : Syntax) (doElems : List Syntax) : M CodeBlock := do
     let doForDecls := doFor[1].getSepArgs
-    if doForDecls.size > 1 then
+    if h : doForDecls.size > 1 then
       /-
         Expand
         ```

src/Lean/Elab/Frontend.lean

@@ -102,7 +102,7 @@ partial def IO.processCommandsIncrementally (inputCtx : Parser.InputContext)
 where
   go initialSnap t commands :=
     let snap := t.get
-    let commands := commands.push snap.data
+    let commands := commands.push snap
     if let some next := snap.nextCmdSnap? then
       go initialSnap next.task commands
     else
@@ -115,9 +115,9 @@ where
       -- snapshots as they subsume any info trees reported incrementally by their children.
       let trees := commands.map (·.finishedSnap.get.infoTree?) |>.filterMap id |>.toPArray'
       return {
-        commandState := { snap.data.finishedSnap.get.cmdState with messages, infoState.trees := trees }
-        parserState := snap.data.parserState
-        cmdPos := snap.data.parserState.pos
+        commandState := { snap.finishedSnap.get.cmdState with messages, infoState.trees := trees }
+        parserState := snap.parserState
+        cmdPos := snap.parserState.pos
         commands := commands.map (·.stx)
         inputCtx, initialSnap
       }
@@ -164,8 +164,8 @@ def runFrontend
     | return (← mkEmptyEnvironment, false)
 
   if let some out := trace.profiler.output.get? opts then
-    let traceState := cmdState.traceState
-    let profile ← Firefox.Profile.export mainModuleName.toString startTime traceState opts
+    let traceStates := snaps.getAll.map (·.traces)
+    let profile ← Firefox.Profile.export mainModuleName.toString startTime traceStates opts
     IO.FS.writeFile ⟨out⟩ <| Json.compress <| toJson profile
 
   let hasErrors := snaps.getAll.any (·.diagnostics.msgLog.hasErrors)

src/Lean/Elab/LetRec.lean

@@ -87,8 +87,8 @@ private def elabLetRecDeclValues (view : LetRecView) : TermElabM (Array Expr) :=
   view.decls.mapM fun view => do
     forallBoundedTelescope view.type view.binderIds.size 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:view.binderIds.size] do
-        addLocalVarInfo view.binderIds[i]! xs[i]!
+      for h : i in [0:view.binderIds.size] do
+        addLocalVarInfo view.binderIds[i] xs[i]!
       withDeclName view.declName do
         withInfoContext' view.valStx
           (mkInfo := (pure <| .inl <| mkBodyInfo view.valStx ·))

src/Lean/Elab/Match.lean

@@ -282,8 +282,8 @@ where
         let dArg := dArgs[i]!
         unless (← isDefEq tArg dArg) do
           return i :: (← goType tArg dArg)
-      for i in [info.numParams : tArgs.size] do
-        let tArg := tArgs[i]!
+      for h : i in [info.numParams : tArgs.size] do
+        let tArg := tArgs[i]
         let dArg := dArgs[i]!
         unless (← isDefEq tArg dArg) do
           return i :: (← goIndex tArg dArg)

src/Lean/Elab/MutualDef.lean

@@ -840,8 +840,8 @@ private def mkLetRecClosures (sectionVars : Array Expr) (mainFVarIds : Array FVa
 abbrev Replacement := FVarIdMap Expr
 
 def insertReplacementForMainFns (r : Replacement) (sectionVars : Array Expr) (mainHeaders : Array DefViewElabHeader) (mainFVars : Array Expr) : Replacement :=
-  mainFVars.size.fold (init := r) fun i r =>
-    r.insert mainFVars[i]!.fvarId! (mkAppN (Lean.mkConst mainHeaders[i]!.declName) sectionVars)
+  mainFVars.size.fold (init := r) fun i _ r =>
+    r.insert mainFVars[i].fvarId! (mkAppN (Lean.mkConst mainHeaders[i]!.declName) sectionVars)
 
 
 def insertReplacementForLetRecs (r : Replacement) (letRecClosures : List LetRecClosure) : Replacement :=
@@ -871,8 +871,8 @@ def Replacement.apply (r : Replacement) (e : Expr) : Expr :=
 
 def pushMain (preDefs : Array PreDefinition) (sectionVars : Array Expr) (mainHeaders : Array DefViewElabHeader) (mainVals : Array Expr)
     : TermElabM (Array PreDefinition) :=
-  mainHeaders.size.foldM (init := preDefs) fun i preDefs => do
-    let header := mainHeaders[i]!
+  mainHeaders.size.foldM (init := preDefs) fun i _ preDefs => do
+    let header := mainHeaders[i]
     let termination ← declValToTerminationHint header.value
     let termination := termination.rememberExtraParams header.numParams mainVals[i]!
     let value ← mkLambdaFVars sectionVars mainVals[i]!

src/Lean/Elab/Notation.lean

@@ -17,7 +17,7 @@ open Lean.Parser.Command
 private partial def antiquote (vars : Array Syntax) : Syntax → Syntax
   | stx => match stx with
   | `($id:ident) =>
-    if (vars.findIdx? (fun var => var.getId == id.getId)).isSome then
+    if vars.any (fun var => var.getId == id.getId) then
       mkAntiquotNode id (kind := `term) (isPseudoKind := true)
     else
       stx

src/Lean/Elab/Open.lean

@@ -49,12 +49,12 @@ private def resolveNameUsingNamespacesCore (nss : List Name) (idStx : Syntax) :
       exs := exs.push ex
   if exs.size == nss.length then
     withRef idStx do
-      if exs.size == 1 then
-        throw exs[0]!
+      if h : exs.size = 1 then
+        throw exs[0]
       else
         throwErrorWithNestedErrors "failed to open" exs
-  if result.size == 1 then
-    return result[0]!
+  if h : result.size = 1 then
+    return result[0]
   else
     withRef idStx do throwError "ambiguous identifier '{idStx.getId}', possible interpretations: {result.map mkConst}"
 

src/Lean/Elab/PatternVar.lean

@@ -332,9 +332,9 @@ where
     else
       let accessible := isNextArgAccessible ctx
       let (d, ctx)   := getNextParam ctx
-      match ctx.namedArgs.findIdx? fun namedArg => namedArg.name == d.1 with
+      match ctx.namedArgs.findFinIdx? fun namedArg => namedArg.name == d.1 with
       | some idx =>
-        let arg := ctx.namedArgs[idx]!
+        let arg := ctx.namedArgs[idx]
         let ctx := { ctx with namedArgs := ctx.namedArgs.eraseIdx idx }
         let ctx ← pushNewArg accessible ctx arg.val
         processCtorAppContext ctx

src/Lean/Elab/PreDefinition/Basic.lean

@@ -244,8 +244,8 @@ def checkCodomainsLevel (preDefs : Array PreDefinition) : MetaM Unit := do
     lambdaTelescope preDef.value fun xs _ => return xs.size
   forallBoundedTelescope preDefs[0]!.type arities[0]!  fun _ type₀ => do
     let u₀ ← getLevel type₀
-    for i in [1:preDefs.size] do
-      forallBoundedTelescope preDefs[i]!.type arities[i]! fun _ typeᵢ =>
+    for h : i in [1:preDefs.size] do
+      forallBoundedTelescope preDefs[i].type arities[i]! fun _ typeᵢ =>
       unless ← isLevelDefEq u₀ (← getLevel typeᵢ) do
         withOptions (fun o => pp.sanitizeNames.set o false) do
           throwError m!"invalid mutual definition, result types must be in the same universe " ++

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

@@ -145,8 +145,8 @@ private partial def replaceRecApps (recArgInfos : Array RecArgInfo) (positions :
     | Expr.app _ _ =>
       let processApp (e : Expr) : StateRefT (HasConstCache recFnNames) M Expr :=
         e.withApp fun f args => do
-          if let .some fnIdx := recArgInfos.findIdx? (f.isConstOf ·.fnName) then
-            let recArgInfo := recArgInfos[fnIdx]!
+          if let .some fnIdx := recArgInfos.findFinIdx? (f.isConstOf ·.fnName) then
+            let recArgInfo := recArgInfos[fnIdx]
             let some recArg := args[recArgInfo.recArgPos]?
               | throwError "insufficient number of parameters at recursive application {indentExpr e}"
             -- For reflexive type, we may have nested recursive applications in recArg
@@ -292,9 +292,9 @@ def mkBrecOnApp (positions : Positions) (fnIdx : Nat) (brecOnConst : Nat → Exp
     let packedFTypes ← inferArgumentTypesN positions.size brecOn
     let packedFArgs ← positions.mapMwith PProdN.mkLambdas packedFTypes FArgs
     let brecOn := mkAppN brecOn packedFArgs
-    let some poss := positions.find? (·.contains fnIdx)
+    let some (size, idx) := positions.findSome? fun pos => (pos.size, ·) <$> pos.indexOf? fnIdx
       | throwError "mkBrecOnApp: Could not find {fnIdx} in {positions}"
-    let brecOn ← PProdN.proj poss.size (poss.getIdx? fnIdx).get! brecOn
+    let brecOn ← PProdN.proj size idx brecOn
     mkLambdaFVars ys (mkAppN brecOn otherArgs)
 
 end Lean.Elab.Structural

src/Lean/Elab/PreDefinition/TerminationArgument.lean

@@ -53,10 +53,10 @@ def TerminationArgument.elab (funName : Name) (type : Expr) (arity extraParams :
     (hint : TerminationBy) : TermElabM TerminationArgument := withDeclName funName do
   assert! extraParams ≤ arity
 
-  if hint.vars.size > extraParams then
+  if h : hint.vars.size > extraParams then
     let mut msg := m!"{parameters hint.vars.size} bound in `termination_by`, but the body of " ++
       m!"{funName} only binds {parameters extraParams}."
-    if let `($ident:ident) := hint.vars[0]! then
+    if let `($ident:ident) := hint.vars[0] then
       if ident.getId.isSuffixOf funName then
           msg := msg ++ m!" (Since Lean v4.6.0, the `termination_by` clause no longer " ++
             "expects the function name here.)"

src/Lean/Elab/PreDefinition/TerminationHint.lean

@@ -90,10 +90,10 @@ lambda of `value`, and throws appropriate errors.
 -/
 def TerminationBy.checkVars (funName : Name) (extraParams : Nat) (tb : TerminationBy) : MetaM Unit := do
   unless tb.synthetic do
-    if tb.vars.size > extraParams then
+    if h : tb.vars.size > extraParams then
       let mut msg := m!"{parameters tb.vars.size} bound in `termination_by`, but the body of " ++
         m!"{funName} only binds {parameters extraParams}."
-      if let `($ident:ident) := tb.vars[0]! then
+      if let `($ident:ident) := tb.vars[0] then
         if ident.getId.isSuffixOf funName then
             msg := msg ++ m!" (Since Lean v4.6.0, the `termination_by` clause no longer " ++
               "expects the function name here.)"

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

@@ -21,8 +21,8 @@ open Meta
 private partial def addNonRecPreDefs (fixedPrefixSize : Nat) (argsPacker : ArgsPacker) (preDefs : Array PreDefinition) (preDefNonRec : PreDefinition)  : TermElabM Unit := do
   let us := preDefNonRec.levelParams.map mkLevelParam
   let all := preDefs.toList.map (·.declName)
-  for fidx in [:preDefs.size] do
-    let preDef := preDefs[fidx]!
+  for h : fidx in [:preDefs.size] do
+    let preDef := preDefs[fidx]
     let value ← forallBoundedTelescope preDef.type (some fixedPrefixSize) fun xs _ => do
       let value := mkAppN (mkConst preDefNonRec.declName us) xs
       let value ← argsPacker.curryProj value fidx

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

@@ -40,7 +40,7 @@ private partial def post (fixedPrefix : Nat) (argsPacker : ArgsPacker) (funNames
     return TransformStep.done e
   let declName := f.constName!
   let us       := f.constLevels!
-  if let some fidx := funNames.getIdx? declName then
+  if let some fidx := funNames.indexOf? declName then
     let arity := fixedPrefix + argsPacker.varNamess[fidx]!.size
     let e' ← withAppN arity e fun args => do
       let fixedArgs := args[:fixedPrefix]