doc-string

This PR refactors the `NoNatZeroDivisors` to make sure it will work with
the new `Semiring` support.

.github/workflows/build-template.yml

@@ -104,7 +104,7 @@ jobs:
           # NOTE: must be in sync with `save` below
           path: |
             .ccache
-            ${{ matrix.name == 'Linux Lake' && 'build/stage1/**/*.trace
+            ${{ matrix.name == 'Linux Lake' && false && 'build/stage1/**/*.trace
             build/stage1/**/*.olean*
             build/stage1/**/*.ilean
             build/stage1/**/*.c
@@ -245,7 +245,7 @@ jobs:
           # NOTE: must be in sync with `restore` above
           path: |
             .ccache
-            ${{ matrix.name == 'Linux Lake' && 'build/stage1/**/*.trace
+            ${{ matrix.name == 'Linux Lake' && false && 'build/stage1/**/*.trace
             build/stage1/**/*.olean*
             build/stage1/**/*.ilean
             build/stage1/**/*.c

.github/workflows/ci.yml

@@ -164,9 +164,15 @@ jobs:
               {
                 // portable release build: use channel with older glibc (2.26)
                 "name": "Linux release",
-                "os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
+                "os": large && level < 2 ? "nscloud-ubuntu-22.04-amd64-4x16" : "ubuntu-latest",
                 "release": true,
-                "check-level": 2,
+                // Special handling for release jobs. We want:
+                // 1. To run it in PRs so developrs get PR toolchains (so secondary is sufficient)
+                // 2. To skip it in merge queues as it takes longer than the
+                //    Linux lake build and adds little value in the merge queue
+                // 3. To run it in release (obviously)
+                "check-level": isPr ? 0 : 2,
+                "secondary": isPr,
                 "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
                 "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-linux-gnu.tar.zst",
                 "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
@@ -176,12 +182,13 @@ jobs:
               },
               {
                 "name": "Linux Lake",
-                "os": large ? "nscloud-ubuntu-22.04-amd64-8x8" : "ubuntu-latest",
+                "os": large ? "nscloud-ubuntu-22.04-amd64-8x16" : "ubuntu-latest",
                 "check-level": 0,
                 "test": true,
                 "check-rebootstrap": level >= 1,
                 "check-stage3": level >= 2,
-                "test-speedcenter": level >= 2,
+                // NOTE: `test-speedcenter` currently seems to be broken on `ubuntu-latest`
+                "test-speedcenter": large && level >= 2,
                 "CMAKE_OPTIONS": "-DUSE_LAKE=ON",
               },
               {
@@ -215,7 +222,8 @@ jobs:
               },
               {
                 "name": "macOS aarch64",
-                "os": "macos-14",
+                // standard GH runner only comes with 7GB so use large runner if possible
+                "os": large ? "nscloud-macos-sonoma-arm64-6x14" : "macos-14",
                 "CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
                 "release": true,
                 "shell": "bash -euxo pipefail {0}",
@@ -223,11 +231,7 @@ jobs:
                 "prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm*",
                 "binary-check": "otool -L",
                 "tar": "gtar", // https://github.com/actions/runner-images/issues/2619
-                // Special handling for MacOS aarch64, we want:
-                // 1. To run it in PRs so Mac devs get PR toolchains (so secondary is sufficient)
-                // 2. To skip it in merge queues as it takes longer than the Linux build and adds
-                //    little value in the merge queue
-                // 3. To run it in release (obviously)
+                // See above for release job levels
                 "check-level": isPr ? 0 : 2,
                 "secondary": isPr,
               },
@@ -246,7 +250,7 @@ jobs:
               },
               {
                 "name": "Linux aarch64",
-                "os": "nscloud-ubuntu-22.04-arm64-4x8",
+                "os": "nscloud-ubuntu-22.04-arm64-4x16",
                 "CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-linux_aarch64",
                 "release": true,
                 "check-level": 2,

.gitignore

@@ -6,7 +6,6 @@
 lake-manifest.json
 /build
 /src/lakefile.toml
-/tests/lakefile.toml
 /lakefile.toml
 GPATH
 GRTAGS

script/prepare-llvm-mingw.sh

@@ -50,5 +50,4 @@ echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='--sysroot ROOT -L ROOT/lib -Wl,-Bstatic
 # when not using the above flags, link GMP dynamically/as usual. Always link ICU dynamically.
 echo -n " -DLEAN_EXTRA_LINKER_FLAGS='-lgmp $(pkg-config --libs libuv) -lucrtbase'"
 # do not set `LEAN_CC` for tests
-echo -n " -DAUTO_THREAD_FINALIZATION=OFF -DSTAGE0_AUTO_THREAD_FINALIZATION=OFF"
 echo -n " -DLEAN_TEST_VARS=''"

src/CMakeLists.txt

@@ -58,9 +58,6 @@ option(USE_GITHASH        "GIT_HASH"           ON)
 option(INSTALL_LICENSE "INSTALL_LICENSE" ON)
 # When ON we install a copy of cadical
 option(INSTALL_CADICAL "Install a copy of cadical" ON)
-# When ON 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)
 
 # FLAGS for disabling optimizations and debugging
 option(FREE_VAR_RANGE_OPT  "FREE_VAR_RANGE_OPT"   ON)
@@ -182,10 +179,6 @@ else()
   string(APPEND LEAN_EXTRA_CXX_FLAGS " -D LEAN_MULTI_THREAD")
 endif()
 
-if(AUTO_THREAD_FINALIZATION AND NOT MSVC)
-  string(APPEND LEAN_EXTRA_CXX_FLAGS " -D LEAN_AUTO_THREAD_FINALIZATION")
-endif()
-
 # Set Module Path
 set(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} "${CMAKE_SOURCE_DIR}/cmake/Modules")
 

src/Init.lean

@@ -37,6 +37,7 @@ import Init.Ext
 import Init.Omega
 import Init.MacroTrace
 import Init.Grind
+import Init.GrindInstances
 import Init.While
 import Init.Syntax
 import Init.Internal

src/Init/Classical.lean

@@ -45,7 +45,7 @@ theorem em (p : Prop) : p ∨ ¬p :=
     | Or.inr h, _ => Or.inr h
     | _, Or.inr h => Or.inr h
     | Or.inl hut, Or.inl hvf =>
-      have hne : u ≠ v := by simp [hvf, hut, true_ne_false]
+      have hne : u ≠ v := by simp [hvf, hut]
       Or.inl hne
   have p_implies_uv : p → u = v :=
     fun hp =>

src/Init/Control/Lawful/Basic.lean

@@ -50,7 +50,7 @@ attribute [simp] id_map
   (comp_map _ _ _).symm
 
 theorem Functor.map_unit [Functor f] [LawfulFunctor f] {a : f PUnit} : (fun _ => PUnit.unit) <$> a = a := by
-  simp [map]
+  simp
 
 /--
 An applicative functor satisfies the laws of an applicative functor.

src/Init/Control/Lawful/Instances.lean

@@ -67,7 +67,7 @@ protected theorem seqLeft_eq {α β ε : Type u} {m : Type u → Type v} [Monad
   | Except.error _ => simp
   | Except.ok _ =>
     simp [←bind_pure_comp]; apply bind_congr; intro b;
-    cases b <;> simp [comp, Except.map, const]
+    cases b <;> simp [Except.map, const]
 
 protected theorem seqRight_eq [Monad m] [LawfulMonad m] (x : ExceptT ε m α) (y : ExceptT ε m β) : x *> y = const α id <$> x <*> y := by
   change (x >>= fun _ => y) = (const α id <$> x) >>= fun f => f <$> y

src/Init/Data.lean

@@ -46,3 +46,4 @@ import Init.Data.NeZero
 import Init.Data.Function
 import Init.Data.RArray
 import Init.Data.Vector
+import Init.Data.Iterators

src/Init/Data/AC.lean

@@ -209,7 +209,7 @@ theorem Context.evalList_sort_congr
   induction c generalizing a b with
   | nil => simp [sort.loop, h₂]
   | cons c _  ih =>
-    simp [sort.loop]; apply ih; simp [evalList_insert ctx h, evalList]
+    simp [sort.loop]; apply ih; simp [evalList_insert ctx h]
     cases a with
     | nil => apply absurd h₃; simp
     | cons a as =>
@@ -282,7 +282,7 @@ theorem Context.toList_nonEmpty (e : Expr) : e.toList ≠ [] := by
     simp [Expr.toList]
     cases h : l.toList with
     | nil => contradiction
-    | cons => simp [List.append]
+    | cons => simp
 
 theorem Context.unwrap_isNeutral
   {ctx : Context α}
@@ -328,13 +328,13 @@ theorem Context.eval_toList (ctx : Context α) (e : Expr) : evalList α ctx e.to
   induction e with
   | var x => rfl
   | op l r ih₁ ih₂ =>
-    simp [evalList, Expr.toList, eval, ←ih₁, ←ih₂]
+    simp [Expr.toList, eval, ←ih₁, ←ih₂]
     apply evalList_append <;> apply toList_nonEmpty
 
 theorem Context.eval_norm (ctx : Context α) (e : Expr) : evalList α ctx (norm ctx e) = eval α ctx e := by
   simp [norm]
   cases h₁ : ContextInformation.isIdem ctx <;> cases h₂ : ContextInformation.isComm ctx <;>
-  simp_all [evalList_removeNeutrals, eval_toList, toList_nonEmpty, evalList_mergeIdem, evalList_sort]
+  simp_all [evalList_removeNeutrals, eval_toList, evalList_mergeIdem, evalList_sort]
 
 theorem Context.eq_of_norm (ctx : Context α) (a b : Expr) (h : norm ctx a == norm ctx b) : eval α ctx a = eval α ctx b := by
   have h := congrArg (evalList α ctx) (eq_of_beq h)

src/Init/Data/Array/Attach.lean

@@ -68,15 +68,15 @@ well-founded recursion mechanism to prove that the function terminates.
     l.toArray.pmap f H = (l.pmap f (by simpa using H)).toArray := by
   simp [pmap]
 
-@[simp] theorem toList_attachWith {xs : Array α} {P : α → Prop} {H : ∀ x ∈ xs, P x} :
+@[simp, grind =] theorem toList_attachWith {xs : Array α} {P : α → Prop} {H : ∀ x ∈ xs, P x} :
    (xs.attachWith P H).toList = xs.toList.attachWith P (by simpa [mem_toList_iff] using H) := by
   simp [attachWith]
 
-@[simp] theorem toList_attach {xs : Array α} :
+@[simp, grind =] theorem toList_attach {xs : Array α} :
     xs.attach.toList = xs.toList.attachWith (· ∈ xs) (by simp [mem_toList_iff]) := by
   simp [attach]
 
-@[simp] theorem toList_pmap {xs : Array α} {P : α → Prop} {f : ∀ a, P a → β} {H : ∀ a ∈ xs, P a} :
+@[simp, grind =] theorem toList_pmap {xs : Array α} {P : α → Prop} {f : ∀ a, P a → β} {H : ∀ a ∈ xs, P a} :
     (xs.pmap f H).toList = xs.toList.pmap f (fun a m => H a (mem_def.mpr m)) := by
   simp [pmap]
 
@@ -92,16 +92,16 @@ well-founded recursion mechanism to prove that the function terminates.
   intro a m h₁ h₂
   congr
 
-@[simp] theorem pmap_empty {P : α → Prop} (f : ∀ a, P a → β) : pmap f #[] (by simp) = #[] := rfl
+@[simp, grind =] 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) (xs : Array α) (h : ∀ b ∈ xs.push a, P b) :
+@[simp, grind =] theorem pmap_push {P : α → Prop} (f : ∀ a, P a → β) (a : α) (xs : Array α) (h : ∀ b ∈ xs.push a, P b) :
     pmap f (xs.push a) h =
       (pmap f xs (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, grind =] 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, grind =] 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) =
@@ -122,11 +122,13 @@ theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a,
   simp only [List.pmap_toArray, mk.injEq]
   rw [List.pmap_congr_left _ h]
 
+@[grind =]
 theorem map_pmap {p : α → Prop} {g : β → γ} {f : ∀ a, p a → β} {xs : Array α} (H) :
     map g (pmap f xs H) = pmap (fun a h => g (f a h)) xs H := by
   cases xs
   simp [List.map_pmap]
 
+@[grind =]
 theorem pmap_map {p : β → Prop} {g : ∀ b, p b → γ} {f : α → β} {xs : Array α} (H) :
     pmap g (map f xs) H = pmap (fun a h => g (f a) h) xs fun _ h => H _ (mem_map_of_mem h) := by
   cases xs
@@ -142,18 +144,18 @@ theorem attachWith_congr {xs ys : Array α} (w : xs = ys) {P : α → Prop} {H :
   subst w
   simp
 
-@[simp] theorem attach_push {a : α} {xs : Array α} :
+@[simp, grind =] theorem attach_push {a : α} {xs : Array α} :
     (xs.push a).attach =
       (xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_push_of_mem a h⟩)).push ⟨a, by simp⟩ := by
   cases xs
   rw [attach_congr (List.push_toArray _ _)]
   simp [Function.comp_def]
 
-@[simp] theorem attachWith_push {a : α} {xs : Array α} {P : α → Prop} {H : ∀ x ∈ xs.push a, P x} :
+@[simp, grind =] theorem attachWith_push {a : α} {xs : Array α} {P : α → Prop} {H : ∀ x ∈ xs.push a, P x} :
     (xs.push a).attachWith P H =
       (xs.attachWith P (fun x h => by simp at H; exact H x (.inl h))).push ⟨a, H a (by simp)⟩ := by
   cases xs
-  simp [attachWith_congr (List.push_toArray _ _)]
+  simp
 
 theorem pmap_eq_map_attach {p : α → Prop} {f : ∀ a, p a → β} {xs : Array α} (H) :
     pmap f xs H = xs.attach.map fun x => f x.1 (H _ x.2) := by
@@ -189,38 +191,39 @@ theorem attachWith_map_subtype_val {p : α → Prop} {xs : Array α} (H : ∀ a
     (xs.attachWith p H).map Subtype.val = xs := by
   cases xs; simp
 
-@[simp]
+@[simp, grind]
 theorem mem_attach (xs : Array α) : ∀ x, x ∈ xs.attach
   | ⟨a, h⟩ => by
     have := mem_map.1 (by rw [attach_map_subtype_val] <;> exact h)
     rcases this with ⟨⟨_, _⟩, m, rfl⟩
     exact m
 
-@[simp]
+@[simp, grind]
 theorem mem_attachWith {xs : Array α} {q : α → Prop} (H) (x : {x // q x}) :
     x ∈ xs.attachWith q H ↔ x.1 ∈ xs := by
   cases xs
   simp
 
-@[simp]
+@[simp, grind =]
 theorem mem_pmap {p : α → Prop} {f : ∀ a, p a → β} {xs H b} :
     b ∈ pmap f xs H ↔ ∃ (a : _) (h : a ∈ xs), f a (H a h) = b := by
   simp only [pmap_eq_map_attach, mem_map, mem_attach, true_and, Subtype.exists, eq_comm]
 
+@[grind]
 theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {xs H} {a} (h : a ∈ xs) :
     f a (H a h) ∈ pmap f xs H := by
   rw [mem_pmap]
   exact ⟨a, h, rfl⟩
 
-@[simp]
+@[simp, grind =]
 theorem size_pmap {p : α → Prop} {f : ∀ a, p a → β} {xs H} : (pmap f xs H).size = xs.size := by
   cases xs; simp
 
-@[simp]
+@[simp, grind =]
 theorem size_attach {xs : Array α} : xs.attach.size = xs.size := by
   cases xs; simp
 
-@[simp]
+@[simp, grind =]
 theorem size_attachWith {p : α → Prop} {xs : Array α} {H} : (xs.attachWith p H).size = xs.size := by
   cases xs; simp
 
@@ -252,13 +255,13 @@ theorem attachWith_ne_empty_iff {xs : Array α} {P : α → Prop} {H : ∀ a ∈
     xs.attachWith P H ≠ #[] ↔ xs ≠ #[] := by
   cases xs; simp
 
-@[simp]
+@[simp, grind =]
 theorem getElem?_pmap {p : α → Prop} {f : ∀ a, p a → β} {xs : Array α} (h : ∀ a ∈ xs, p a) (i : Nat) :
     (pmap f xs h)[i]? = Option.pmap f xs[i]? fun x H => h x (mem_of_getElem? H) := by
   cases xs; simp
 
 -- The argument `f` is explicit to allow rewriting from right to left.
-@[simp]
+@[simp, grind =]
 theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {xs : Array α} (h : ∀ a ∈ xs, p a) {i : Nat}
     (hi : i < (pmap f xs h).size) :
     (pmap f xs h)[i] =
@@ -266,57 +269,59 @@ theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {xs : Array α} (
         (h _ (getElem_mem (@size_pmap _ _ p f xs h ▸ hi))) := by
   cases xs; simp
 
-@[simp]
+@[simp, grind =]
 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]
+@[simp, grind =]
 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]
+@[simp, grind =]
 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 _ _ h
 
-@[simp]
+@[simp, grind =]
 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
 
-@[simp] theorem pmap_attach {xs : Array α} {p : {x // x ∈ xs} → Prop} {f : ∀ a, p a → β} (H) :
+@[simp, grind =] theorem pmap_attach {xs : Array α} {p : {x // x ∈ xs} → Prop} {f : ∀ a, p a → β} (H) :
     pmap f xs.attach H =
       xs.pmap (P := fun a => ∃ h : a ∈ xs, p ⟨a, h⟩)
         (fun a h => f ⟨a, h.1⟩ h.2) (fun a h => ⟨h, H ⟨a, h⟩ (by simp)⟩) := by
   ext <;> simp
 
-@[simp] theorem pmap_attachWith {xs : Array α} {p : {x // q x} → Prop} {f : ∀ a, p a → β} (H₁ H₂) :
+@[simp, grind =] theorem pmap_attachWith {xs : Array α} {p : {x // q x} → Prop} {f : ∀ a, p a → β} (H₁ H₂) :
     pmap f (xs.attachWith q H₁) H₂ =
       xs.pmap (P := fun a => ∃ h : q a, p ⟨a, h⟩)
         (fun a h => f ⟨a, h.1⟩ h.2) (fun a h => ⟨H₁ _ h, H₂ ⟨a, H₁ _ h⟩ (by simpa)⟩) := by
   ext <;> simp
 
+@[grind =]
 theorem foldl_pmap {xs : Array α} {P : α → Prop} {f : (a : α) → P a → β}
     (H : ∀ (a : α), a ∈ xs → P a) (g : γ → β → γ) (x : γ) :
     (xs.pmap f H).foldl g x = xs.attach.foldl (fun acc a => g acc (f a.1 (H _ a.2))) x := by
   rw [pmap_eq_map_attach, foldl_map]
 
+@[grind =]
 theorem foldr_pmap {xs : Array α} {P : α → Prop} {f : (a : α) → P a → β}
     (H : ∀ (a : α), a ∈ xs → P a) (g : β → γ → γ) (x : γ) :
     (xs.pmap f H).foldr g x = xs.attach.foldr (fun a acc => g (f a.1 (H _ a.2)) acc) x := by
   rw [pmap_eq_map_attach, foldr_map]
 
-@[simp] theorem foldl_attachWith
+@[simp, grind =] theorem foldl_attachWith
     {xs : Array α} {q : α → Prop} (H : ∀ a, a ∈ xs → q a) {f : β → { x // q x} → β} {b} (w : stop = xs.size) :
     (xs.attachWith q H).foldl f b 0 stop = xs.attach.foldl (fun b ⟨a, h⟩ => f b ⟨a, H _ h⟩) b := by
   subst w
   rcases xs with ⟨xs⟩
   simp [List.foldl_attachWith, List.foldl_map]
 
-@[simp] theorem foldr_attachWith
+@[simp, grind =] theorem foldr_attachWith
     {xs : Array α} {q : α → Prop} (H : ∀ a, a ∈ xs → q a) {f : { x // q x} → β → β} {b} (w : start = xs.size) :
     (xs.attachWith q H).foldr f b start 0 = xs.attach.foldr (fun a acc => f ⟨a.1, H _ a.2⟩ acc) b := by
   subst w
@@ -337,7 +342,7 @@ theorem foldl_attach {xs : Array α} {f : β → α → β} {b : β} :
     xs.attach.foldl (fun acc t => f acc t.1) b = xs.foldl f b := by
   rcases xs with ⟨xs⟩
   simp only [List.attach_toArray, List.attachWith_mem_toArray, List.size_toArray,
-    List.length_pmap, List.foldl_toArray', mem_toArray, List.foldl_subtype]
+    List.foldl_toArray', mem_toArray, List.foldl_subtype]
   congr
   ext
   simpa using fun a => List.mem_of_getElem? a
@@ -356,23 +361,25 @@ theorem foldr_attach {xs : Array α} {f : α → β → β} {b : β} :
     xs.attach.foldr (fun t acc => f t.1 acc) b = xs.foldr f b := by
   rcases xs with ⟨xs⟩
   simp only [List.attach_toArray, List.attachWith_mem_toArray, List.size_toArray,
-    List.length_pmap, List.foldr_toArray', mem_toArray, List.foldr_subtype]
+    List.foldr_toArray', mem_toArray, List.foldr_subtype]
   congr
   ext
   simpa using fun a => List.mem_of_getElem? a
 
+@[grind =]
 theorem attach_map {xs : Array α} {f : α → β} :
     (xs.map f).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨f x, mem_map_of_mem h⟩) := by
   cases xs
   ext <;> simp
 
+@[grind =]
 theorem attachWith_map {xs : Array α} {f : α → β} {P : β → Prop} (H : ∀ (b : β), b ∈ xs.map f → P b) :
     (xs.map f).attachWith P H = (xs.attachWith (P ∘ f) (fun _ h => H _ (mem_map_of_mem h))).map
       fun ⟨x, h⟩ => ⟨f x, h⟩ := by
   cases xs
   simp [List.attachWith_map]
 
-@[simp] theorem map_attachWith {xs : Array α} {P : α → Prop} {H : ∀ (a : α), a ∈ xs → P a}
+@[simp, grind =] theorem map_attachWith {xs : Array α} {P : α → Prop} {H : ∀ (a : α), a ∈ xs → P a}
     {f : { x // P x } → β} :
     (xs.attachWith P H).map f = xs.attach.map fun ⟨x, h⟩ => f ⟨x, H _ h⟩ := by
   cases xs <;> simp_all
@@ -393,6 +400,7 @@ theorem map_attach_eq_pmap {xs : Array α} {f : { x // x ∈ xs } → β} :
 @[deprecated map_attach_eq_pmap (since := "2025-02-09")]
 abbrev map_attach := @map_attach_eq_pmap
 
+@[grind =]
 theorem attach_filterMap {xs : Array α} {f : α → Option β} :
     (xs.filterMap f).attach = xs.attach.filterMap
       fun ⟨x, h⟩ => (f x).pbind (fun b m => some ⟨b, mem_filterMap.mpr ⟨x, h, m⟩⟩) := by
@@ -400,6 +408,7 @@ theorem attach_filterMap {xs : Array α} {f : α → Option β} :
   rw [attach_congr List.filterMap_toArray]
   simp [List.attach_filterMap, List.map_filterMap, Function.comp_def]
 
+@[grind =]
 theorem attach_filter {xs : Array α} (p : α → Bool) :
     (xs.filter p).attach = xs.attach.filterMap
       fun x => if w : p x.1 then some ⟨x.1, mem_filter.mpr ⟨x.2, w⟩⟩ else none := by
@@ -409,7 +418,7 @@ theorem attach_filter {xs : Array α} (p : α → Bool) :
 
 -- We are still missing here `attachWith_filterMap` and `attachWith_filter`.
 
-@[simp]
+@[simp, grind =]
 theorem filterMap_attachWith {q : α → Prop} {xs : Array α} {f : {x // q x} → Option β} (H)
     (w : stop = (xs.attachWith q H).size) :
     (xs.attachWith q H).filterMap f 0 stop = xs.attach.filterMap (fun ⟨x, h⟩ => f ⟨x, H _ h⟩) := by
@@ -417,7 +426,7 @@ theorem filterMap_attachWith {q : α → Prop} {xs : Array α} {f : {x // q x}
   cases xs
   simp [Function.comp_def]
 
-@[simp]
+@[simp, grind =]
 theorem filter_attachWith {q : α → Prop} {xs : Array α} {p : {x // q x} → Bool} (H)
     (w : stop = (xs.attachWith q H).size) :
     (xs.attachWith q H).filter p 0 stop =
@@ -426,6 +435,7 @@ theorem filter_attachWith {q : α → Prop} {xs : Array α} {p : {x // q x} →
   cases xs
   simp [Function.comp_def, List.filter_map]
 
+@[grind =]
 theorem pmap_pmap {p : α → Prop} {q : β → Prop} {g : ∀ a, p a → β} {f : ∀ b, q b → γ} {xs} (H₁ H₂) :
     pmap f (pmap g xs H₁) H₂ =
       pmap (α := { x // x ∈ xs }) (fun a h => f (g a h) (H₂ (g a h) (mem_pmap_of_mem a.2))) xs.attach
@@ -433,7 +443,7 @@ theorem pmap_pmap {p : α → Prop} {q : β → Prop} {g : ∀ a, p a → β} {f
   cases xs
   simp [List.pmap_pmap, List.pmap_map]
 
-@[simp] theorem pmap_append {p : ι → Prop} {f : ∀ a : ι, p a → α} {xs ys : Array ι}
+@[simp, grind =] theorem pmap_append {p : ι → Prop} {f : ∀ a : ι, p a → α} {xs ys : Array ι}
     (h : ∀ a ∈ xs ++ ys, p a) :
     (xs ++ ys).pmap f h =
       (xs.pmap f fun a ha => h a (mem_append_left ys ha)) ++
@@ -448,7 +458,7 @@ theorem pmap_append' {p : α → Prop} {f : ∀ a : α, p a → β} {xs ys : Arr
       xs.pmap f h₁ ++ ys.pmap f h₂ :=
   pmap_append _
 
-@[simp] theorem attach_append {xs ys : Array α} :
+@[simp, grind =] 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
@@ -456,59 +466,62 @@ theorem pmap_append' {p : α → Prop} {f : ∀ a : α, p a → β} {xs ys : Arr
   rw [attach_congr (List.append_toArray _ _)]
   simp [List.attach_append, Function.comp_def]
 
-@[simp] theorem attachWith_append {P : α → Prop} {xs ys : Array α}
+@[simp, grind =] 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 [attachWith]
 
-@[simp] theorem pmap_reverse {P : α → Prop} {f : (a : α) → P a → β} {xs : Array α}
+@[simp, grind =] 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
 
+@[grind =]
 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}
+@[simp, grind =] 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
 
+@[grind =]
 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} :
+@[simp, grind =] 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
 
+@[grind =]
 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}
+@[simp, grind =] 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}
+@[simp, grind =] 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? h)⟩) := by
   cases xs
   simp
 
-@[simp]
+@[simp, grind =]
 theorem back?_attach {xs : Array α} :
     xs.attach.back? = xs.back?.pbind fun a h => some ⟨a, mem_of_back? h⟩ := by
   cases xs
@@ -526,7 +539,7 @@ theorem countP_attachWith {p : α → Prop} {q : α → Bool} {xs : Array α} {H
   cases xs
   simp
 
-@[simp]
+@[simp, grind =]
 theorem count_attach [BEq α] {xs : Array α} {a : {x // x ∈ xs}} :
     xs.attach.count a = xs.count ↑a := by
   rcases xs with ⟨xs⟩
@@ -535,13 +548,13 @@ theorem count_attach [BEq α] {xs : Array α} {a : {x // x ∈ xs}} :
   simp only [Subtype.beq_iff]
   rw [List.countP_pmap, List.countP_attach (p := (fun x => x == a.1)), List.count]
 
-@[simp]
+@[simp, grind =]
 theorem count_attachWith [BEq α] {p : α → Prop} {xs : Array α} (H : ∀ a ∈ xs, p a) {a : {x // p x}} :
     (xs.attachWith p H).count a = xs.count ↑a := by
   cases xs
   simp
 
-@[simp] theorem countP_pmap {p : α → Prop} {g : ∀ a, p a → β} {f : β → Bool} {xs : Array α} (H₁) :
+@[simp, grind =] theorem countP_pmap {p : α → Prop} {g : ∀ a, p a → β} {f : β → Bool} {xs : Array α} (H₁) :
     (xs.pmap g H₁).countP f =
       xs.attach.countP (fun ⟨a, m⟩ => f (g a (H₁ a m))) := by
   simp [pmap_eq_map_attach, countP_map, Function.comp_def]
@@ -690,7 +703,7 @@ and simplifies these to the function directly taking the value.
     {f : { x // p x } → Array β} {g : α → Array β} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
     (xs.flatMap f) = xs.unattach.flatMap g := by
   cases xs
-  simp only [List.size_toArray, List.flatMap_toArray, List.unattach_toArray, List.length_unattach,
+  simp only [List.flatMap_toArray, List.unattach_toArray, 
     mk.injEq]
   rw [List.flatMap_subtype]
   simp [hf]

src/Init/Data/Array/Basic.lean

@@ -1788,7 +1788,7 @@ decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ h
   induction xs, i, h using Array.eraseIdx.induct with
   | @case1 xs i h h' xs' ih =>
     unfold eraseIdx
-    simp +zetaDelta [h', xs', ih]
+    simp +zetaDelta [h', ih]
   | case2 xs i h h' =>
     unfold eraseIdx
     simp [h']

src/Init/Data/Array/Bootstrap.lean

@@ -119,13 +119,13 @@ abbrev pop_toList := @Array.toList_pop
 @[simp] theorem toList_empty : (#[] : Array α).toList = [] := rfl
 
 @[simp, grind =] theorem append_empty {xs : Array α} : xs ++ #[] = xs := by
-  apply ext'; simp only [toList_append, toList_empty, List.append_nil]
+  apply ext'; simp only [toList_append, List.append_nil]
 
 @[deprecated append_empty (since := "2025-01-13")]
 abbrev append_nil := @append_empty
 
 @[simp, grind =] theorem empty_append {xs : Array α} : #[] ++ xs = xs := by
-  apply ext'; simp only [toList_append, toList_empty, List.nil_append]
+  apply ext'; simp only [toList_append, List.nil_append]
 
 @[deprecated empty_append (since := "2025-01-13")]
 abbrev nil_append := @empty_append

src/Init/Data/Array/Count.lean

@@ -105,6 +105,7 @@ theorem boole_getElem_le_countP {xs : Array α} {i : Nat} (h : i < xs.size) :
   rcases xs with ⟨xs⟩
   simp [List.boole_getElem_le_countP]
 
+@[grind =]
 theorem countP_set {xs : Array α} {i : Nat} {a : α} (h : i < xs.size) :
     (xs.set i a).countP p = xs.countP p - (if p xs[i] then 1 else 0) + (if p a then 1 else 0) := by
   rcases xs with ⟨xs⟩
@@ -219,9 +220,10 @@ theorem boole_getElem_le_count {xs : Array α} {i : Nat} {a : α} (h : i < xs.si
   rw [count_eq_countP]
   apply boole_getElem_le_countP (p := (· == a))
 
+@[grind =]
 theorem count_set {xs : Array α} {i : Nat} {a b : α} (h : i < xs.size) :
     (xs.set i a).count b = xs.count b - (if xs[i] == b then 1 else 0) + (if a == b then 1 else 0) := by
-  simp [count_eq_countP, countP_set, h]
+  simp [count_eq_countP, countP_set]
 
 variable [LawfulBEq α]
 
@@ -229,7 +231,7 @@ variable [LawfulBEq α]
   simp [count_push]
 
 @[simp] theorem count_push_of_ne {xs : Array α} (h : b ≠ a) : count a (xs.push b) = count a xs := by
-  simp_all [count_push, h]
+  simp_all [count_push]
 
 theorem count_singleton_self {a : α} : count a #[a] = 1 := by simp
 
@@ -290,17 +292,17 @@ abbrev mkArray_count_eq_of_count_eq_size := @replicate_count_eq_of_count_eq_size
 theorem count_le_count_map [BEq β] [LawfulBEq β] {xs : Array α} {f : α → β} {x : α} :
     count x xs ≤ count (f x) (map f xs) := by
   rcases xs with ⟨xs⟩
-  simp [List.count_le_count_map, countP_map]
+  simp [List.count_le_count_map]
 
 theorem count_filterMap {α} [BEq β] {b : β} {f : α → Option β} {xs : Array α} :
     count b (filterMap f xs) = countP (fun a => f a == some b) xs := by
   rcases xs with ⟨xs⟩
-  simp [List.count_filterMap, countP_filterMap]
+  simp [List.count_filterMap]
 
 theorem count_flatMap {α} [BEq β] {xs : Array α} {f : α → Array β} {x : β} :
     count x (xs.flatMap f) = sum (map (count x ∘ f) xs) := by
   rcases xs with ⟨xs⟩
-  simp [List.count_flatMap, countP_flatMap, Function.comp_def]
+  simp [List.count_flatMap, Function.comp_def]
 
 theorem countP_replace {a b : α} {xs : Array α} {p : α → Bool} :
     (xs.replace a b).countP p =

src/Init/Data/Array/DecidableEq.lean

@@ -23,7 +23,7 @@ private theorem rel_of_isEqvAux
   induction i with
   | zero => contradiction
   | succ i ih =>
-    simp only [Array.isEqvAux, Bool.and_eq_true, decide_eq_true_eq] at heqv
+    simp only [Array.isEqvAux, Bool.and_eq_true] at heqv
     by_cases hj' : j < i
     next =>
       exact ih _ heqv.right hj'

src/Init/Data/Array/Erase.lean

@@ -206,7 +206,7 @@ theorem erase_eq_eraseP [LawfulBEq α] (a : α) (xs : Array α) : xs.erase a = x
 theorem erase_ne_empty_iff [LawfulBEq α] {xs : Array α} {a : α} :
     xs.erase a ≠ #[] ↔ xs ≠ #[] ∧ xs ≠ #[a] := by
   rcases xs with ⟨xs⟩
-  simp [List.erase_ne_nil_iff]
+  simp
 
 theorem exists_erase_eq [LawfulBEq α] {a : α} {xs : Array α} (h : a ∈ xs) :
     ∃ ys zs, a ∉ ys ∧ xs = ys.push a ++ zs ∧ xs.erase a = ys ++ zs := by
@@ -306,7 +306,7 @@ theorem erase_eq_iff [LawfulBEq α] {a : α} {xs : Array α} :
 @[simp] theorem erase_replicate_self [LawfulBEq α] {a : α} :
     (replicate n a).erase a = replicate (n - 1) a := by
   simp only [← List.toArray_replicate, List.erase_toArray]
-  simp [List.erase_replicate]
+  simp
 
 @[deprecated erase_replicate_self (since := "2025-03-18")]
 abbrev erase_mkArray_self := @erase_replicate_self
@@ -352,7 +352,7 @@ theorem getElem?_eraseIdx_of_lt {xs : Array α} {i : Nat} (h : i < xs.size) {j :
 theorem getElem?_eraseIdx_of_ge {xs : Array α} {i : Nat} (h : i < xs.size) {j : Nat} (h' : i ≤ j) :
     (xs.eraseIdx i)[j]? = xs[j + 1]? := by
   rw [getElem?_eraseIdx]
-  simp only [dite_eq_ite, ite_eq_right_iff]
+  simp only [ite_eq_right_iff]
   intro h'
   omega
 

src/Init/Data/Array/Extract.lean

@@ -29,7 +29,7 @@ namespace Array
   · simp
     omega
   · simp only [size_extract] at h₁ h₂
-    simp [h]
+    simp
 
 theorem size_extract_le {as : Array α} {i j : Nat} :
     (as.extract i j).size ≤ j - i := by
@@ -46,7 +46,7 @@ theorem size_extract_of_le {as : Array α} {i j : Nat} (h : j ≤ as.size) :
   simp
   omega
 
-@[simp]
+@[simp, grind =]
 theorem extract_push {as : Array α} {b : α} {start stop : Nat} (h : stop ≤ as.size) :
     (as.push b).extract start stop = as.extract start stop := by
   ext i h₁ h₂
@@ -56,7 +56,7 @@ theorem extract_push {as : Array α} {b : α} {start stop : Nat} (h : stop ≤ a
     simp only [getElem_extract, getElem_push]
     rw [dif_pos (by omega)]
 
-@[simp]
+@[simp, grind =]
 theorem extract_eq_pop {as : Array α} {stop : Nat} (h : stop = as.size - 1) :
     as.extract 0 stop = as.pop := by
   ext i h₁ h₂
@@ -65,7 +65,7 @@ theorem extract_eq_pop {as : Array α} {stop : Nat} (h : stop = as.size - 1) :
   · simp only [size_extract, size_pop] at h₁ h₂
     simp [getElem_extract, getElem_pop]
 
-@[simp]
+@[simp, grind _=_]
 theorem extract_append_extract {as : Array α} {i j k : Nat} :
     as.extract i j ++ as.extract j k = as.extract (min i j) (max j k) := by
   ext l h₁ h₂
@@ -162,14 +162,14 @@ theorem extract_sub_one {as : Array α} {i j : Nat} (h : j < as.size) :
 @[simp]
 theorem getElem?_extract_of_lt {as : Array α} {i j k : Nat} (h : k < min j as.size - i) :
     (as.extract i j)[k]? = some (as[i + k]'(by omega)) := by
-  simp [getElem?_extract, h]
+  simp [h]
 
 theorem getElem?_extract_of_succ {as : Array α} {j : Nat} :
     (as.extract 0 (j + 1))[j]? = as[j]? := by
   simp [getElem?_extract]
   omega
 
-@[simp] theorem extract_extract {as : Array α} {i j k l : Nat} :
+@[simp, grind =] theorem extract_extract {as : Array α} {i j k l : Nat} :
     (as.extract i j).extract k l = as.extract (i + k) (min (i + l) j) := by
   ext m h₁ h₂
   · simp
@@ -185,6 +185,7 @@ theorem ne_empty_of_extract_ne_empty {as : Array α} {i j : Nat} (h : as.extract
     as ≠ #[] :=
   mt extract_eq_empty_of_eq_empty h
 
+@[grind =]
 theorem extract_set {as : Array α} {i j k : Nat} (h : k < as.size) {a : α} :
     (as.set k a).extract i j =
       if _ : k < i then
@@ -211,13 +212,14 @@ theorem extract_set {as : Array α} {i j k : Nat} (h : k < as.size) {a : α} :
         simp [getElem_set]
         omega
 
+@[grind =]
 theorem set_extract {as : Array α} {i j k : Nat} (h : k < (as.extract i j).size) {a : α} :
     (as.extract i j).set k a = (as.set (i + k) a (by simp at h; omega)).extract i j := by
   ext l h₁ h₂
   · simp
   · simp_all [getElem_set]
 
-@[simp]
+@[simp, grind =]
 theorem extract_append {as bs : Array α} {i j : Nat} :
     (as ++ bs).extract i j = as.extract i j ++ bs.extract (i - as.size) (j - as.size) := by
   ext l h₁ h₂
@@ -242,14 +244,14 @@ theorem extract_append_right {as bs : Array α} :
     (as ++ bs).extract as.size (as.size + i) = bs.extract 0 i := by
   simp
 
-@[simp] theorem map_extract {as : Array α} {i j : Nat} :
+@[simp, grind =] theorem map_extract {as : Array α} {i j : Nat} :
     (as.extract i j).map f = (as.map f).extract i j := by
   ext l h₁ h₂
   · simp
   · simp only [size_map, size_extract] at h₁ h₂
     simp only [getElem_map, getElem_extract]
 
-@[simp] theorem extract_replicate {a : α} {n i j : Nat} :
+@[simp, grind =] theorem extract_replicate {a : α} {n i j : Nat} :
     (replicate n a).extract i j = replicate (min j n - i) a := by
   ext l h₁ h₂
   · simp
@@ -297,6 +299,7 @@ theorem set_eq_push_extract_append_extract {as : Array α} {i : Nat} (h : i < as
   simp at h
   simp [List.set_eq_take_append_cons_drop, h, List.take_of_length_le]
 
+@[grind =]
 theorem extract_reverse {as : Array α} {i j : Nat} :
     as.reverse.extract i j = (as.extract (as.size - j) (as.size - i)).reverse := by
   ext l h₁ h₂
@@ -307,6 +310,7 @@ theorem extract_reverse {as : Array α} {i j : Nat} :
     congr 1
     omega
 
+@[grind =]
 theorem reverse_extract {as : Array α} {i j : Nat} :
     (as.extract i j).reverse = as.reverse.extract (as.size - j) (as.size - i) := by
   rw [extract_reverse]

src/Init/Data/Array/Find.lean

@@ -81,7 +81,7 @@ theorem find?_eq_findSome?_guard {xs : Array α} : find? p xs = findSome? (Optio
 
 @[simp, grind =] theorem getElem_zero_filterMap {f : α → Option β} {xs : Array α} (h) :
     (xs.filterMap f)[0] = (xs.findSome? f).get (by cases xs; simpa [List.length_filterMap_eq_countP] using h) := by
-  cases xs; simp [← List.head_eq_getElem, ← getElem?_zero_filterMap]
+  cases xs; simp [← getElem?_zero_filterMap]
 
 @[simp, grind =] theorem back?_filterMap {f : α → Option β} {xs : Array α} : (xs.filterMap f).back? = xs.findSomeRev? f := by
   cases xs; simp
@@ -122,7 +122,7 @@ theorem getElem_zero_flatten.proof {xss : Array (Array α)} (h : 0 < xss.flatten
 theorem getElem_zero_flatten {xss : Array (Array α)} (h) :
     (flatten xss)[0] = (xss.findSome? fun xs => xs[0]?).get (getElem_zero_flatten.proof h) := by
   have t := getElem?_zero_flatten xss
-  simp [getElem?_eq_getElem, h] at t
+  simp at t
   simp [← t]
 
 @[grind =]
@@ -308,7 +308,7 @@ abbrev find?_flatten_eq_some := @find?_flatten_eq_some_iff
 @[simp, grind =] theorem find?_flatMap {xs : Array α} {f : α → Array β} {p : β → Bool} :
     (xs.flatMap f).find? p = xs.findSome? (fun x => (f x).find? p) := by
   cases xs
-  simp [List.find?_flatMap, Array.flatMap_toArray]
+  simp [List.find?_flatMap]
 
 theorem find?_flatMap_eq_none_iff {xs : Array α} {f : α → Array β} {p : β → Bool} :
     (xs.flatMap f).find? p = none ↔ ∀ x ∈ xs, ∀ y ∈ f x, !p y := by
@@ -348,7 +348,7 @@ abbrev find?_mkArray_of_neg := @find?_replicate_of_neg
 -- This isn't a `@[simp]` lemma since there is already a lemma for `l.find? p = none` for any `l`.
 theorem find?_replicate_eq_none_iff {n : Nat} {a : α} {p : α → Bool} :
     (replicate n a).find? p = none ↔ n = 0 ∨ !p a := by
-  simp [← List.toArray_replicate, List.find?_replicate_eq_none_iff, Classical.or_iff_not_imp_left]
+  simp [← List.toArray_replicate, Classical.or_iff_not_imp_left]
 
 @[deprecated find?_replicate_eq_none_iff (since := "2025-03-18")]
 abbrev find?_mkArray_eq_none_iff := @find?_replicate_eq_none_iff
@@ -488,7 +488,7 @@ theorem findIdx_push {xs : Array α} {a : α} {p : α → Bool} :
   simp only [push_eq_append, findIdx_append]
   split <;> rename_i h
   · rfl
-  · simp [findIdx_singleton, Nat.add_comm]
+  · simp [Nat.add_comm]
 
 theorem findIdx_le_findIdx {xs : Array α} {p q : α → Bool} (h : ∀ x ∈ xs, p x → q x) : xs.findIdx q ≤ xs.findIdx p := by
   rcases xs with ⟨xs⟩
@@ -553,7 +553,7 @@ theorem findIdx?_eq_some_of_exists {xs : Array α} {p : α → Bool} (h : ∃ x,
 theorem findIdx?_eq_none_iff_findIdx_eq {xs : Array α} {p : α → Bool} :
     xs.findIdx? p = none ↔ xs.findIdx p = xs.size := by
   rcases xs with ⟨xs⟩
-  simp [List.findIdx?_eq_none_iff_findIdx_eq]
+  simp
 
 theorem findIdx?_eq_guard_findIdx_lt {xs : Array α} {p : α → Bool} :
     xs.findIdx? p = Option.guard (fun i => i < xs.size) (xs.findIdx p) := by
@@ -798,7 +798,7 @@ The lemmas below should be made consistent with those for `findFinIdx?` (and pro
 
 theorem idxOf?_eq_map_finIdxOf?_val [BEq α] {xs : Array α} {a : α} :
     xs.idxOf? a = (xs.finIdxOf? a).map (·.val) := by
-  simp [idxOf?, finIdxOf?, findIdx?_eq_map_findFinIdx?_val]
+  simp [idxOf?, finIdxOf?]
 
 @[grind =] theorem finIdxOf?_empty [BEq α] : (#[] : Array α).finIdxOf? a = none := by simp
 

src/Init/Data/Array/InsertIdx.lean

@@ -47,11 +47,16 @@ theorem insertIdx_zero {xs : Array α} {x : α} : xs.insertIdx 0 x = #[x] ++ xs
   simp at h
   simp [List.length_insertIdx, h]
 
-theorem eraseIdx_insertIdx {i : Nat} {xs : Array α} (h : i ≤ xs.size) :
+theorem eraseIdx_insertIdx_self {i : Nat} {xs : Array α} (h : i ≤ xs.size) :
     (xs.insertIdx i a).eraseIdx i (by simp; omega) = xs := by
   rcases xs with ⟨xs⟩
   simp_all
 
+@[deprecated eraseIdx_insertIdx_self (since := "2025-06-15")]
+theorem eraseIdx_insertIdx {i : Nat} {xs : Array α} (h : i ≤ xs.size) :
+    (xs.insertIdx i a).eraseIdx i (by simp; omega) = xs := by
+  simp [eraseIdx_insertIdx_self]
+
 theorem insertIdx_eraseIdx_of_ge {as : Array α}
     (w₁ : i < as.size) (w₂ : j ≤ (as.eraseIdx i).size) (h : i ≤ j) :
     (as.eraseIdx i).insertIdx j a =
@@ -66,6 +71,18 @@ theorem insertIdx_eraseIdx_of_le {as : Array α}
   cases as
   simpa using List.insertIdx_eraseIdx_of_le (by simpa) (by simpa)
 
+@[grind =]
+theorem insertIdx_eraseIdx {as : Array α} (h₁ : i < as.size) (h₂ : j ≤ (as.eraseIdx i).size) :
+    (as.eraseIdx i).insertIdx j a =
+      if h : i ≤ j then
+        (as.insertIdx (j + 1) a (by simp_all; omega)).eraseIdx i (by simp_all; omega)
+      else
+        (as.insertIdx j a).eraseIdx (i + 1) (by simp_all) := by
+  split <;> rename_i h'
+  · rw [insertIdx_eraseIdx_of_ge] <;> omega
+  · rw [insertIdx_eraseIdx_of_le] <;> omega
+
+@[grind =]
 theorem insertIdx_comm (a b : α) {i j : Nat} {xs : Array α} (_ : i ≤ j) (_ : j ≤ xs.size) :
     (xs.insertIdx i a).insertIdx (j + 1) b (by simpa) =
       (xs.insertIdx j b).insertIdx i a (by simp; omega) := by
@@ -81,6 +98,7 @@ theorem insertIdx_size_self {xs : Array α} {x : α} : xs.insertIdx xs.size x =
   rcases xs with ⟨xs⟩
   simp
 
+@[grind =]
 theorem getElem_insertIdx {xs : Array α} {x : α} {i k : Nat} (w : i ≤ xs.size) (h : k < (xs.insertIdx i x).size) :
     (xs.insertIdx i x)[k] =
       if h₁ : k < i then
@@ -91,21 +109,22 @@ theorem getElem_insertIdx {xs : Array α} {x : α} {i k : Nat} (w : i ≤ xs.siz
         else
           xs[k-1]'(by simp [size_insertIdx] at h; omega) := by
   cases xs
-  simp [List.getElem_insertIdx, w]
+  simp [List.getElem_insertIdx]
 
 theorem getElem_insertIdx_of_lt {xs : Array α} {x : α} {i k : Nat} (w : i ≤ xs.size) (h : k < i) :
     (xs.insertIdx i x)[k]'(by simp; omega) = xs[k] := by
-  simp [getElem_insertIdx, w, h]
+  simp [getElem_insertIdx, h]
 
 theorem getElem_insertIdx_self {xs : Array α} {x : α} {i : Nat} (w : i ≤ xs.size) :
     (xs.insertIdx i x)[i]'(by simp; omega) = x := by
-  simp [getElem_insertIdx, w]
+  simp [getElem_insertIdx]
 
 theorem getElem_insertIdx_of_gt {xs : Array α} {x : α} {i k : Nat} (w : k ≤ xs.size) (h : k > i) :
     (xs.insertIdx i x)[k]'(by simp; omega) = xs[k - 1]'(by omega) := by
-  simp [getElem_insertIdx, w, h]
+  simp [getElem_insertIdx]
   rw [dif_neg (by omega), dif_neg (by omega)]
 
+@[grind =]
 theorem getElem?_insertIdx {xs : Array α} {x : α} {i k : Nat} (h : i ≤ xs.size) :
     (xs.insertIdx i x)[k]? =
       if k < i then
@@ -116,7 +135,7 @@ theorem getElem?_insertIdx {xs : Array α} {x : α} {i k : Nat} (h : i ≤ xs.si
         else
           xs[k-1]? := by
   cases xs
-  simp [List.getElem?_insertIdx, h]
+  simp [List.getElem?_insertIdx]
 
 theorem getElem?_insertIdx_of_lt {xs : Array α} {x : α} {i k : Nat} (w : i ≤ xs.size) (h : k < i) :
     (xs.insertIdx i x)[k]? = xs[k]? := by

src/Init/Data/Array/Lemmas.lean

@@ -125,7 +125,7 @@ theorem none_eq_getElem?_iff {xs : Array α} {i : Nat} : none = xs[i]? ↔ xs.si
   simp
 
 theorem getElem?_eq_none {xs : Array α} (h : xs.size ≤ i) : xs[i]? = none := by
-  simp [getElem?_eq_none_iff, h]
+  simp [h]
 
 grind_pattern Array.getElem?_eq_none => xs.size ≤ i, xs[i]?
 
@@ -154,16 +154,16 @@ theorem getElem_eq_iff {xs : Array α} {i : Nat} {h : i < xs.size} : xs[i] = x
   exact ⟨fun w => ⟨h, w⟩, fun h => h.2⟩
 
 theorem getElem_eq_getElem?_get {xs : Array α} {i : Nat} (h : i < xs.size) :
-    xs[i] = xs[i]?.get (by simp [getElem?_eq_getElem, h]) := by
-  simp [getElem_eq_iff]
+    xs[i] = xs[i]?.get (by simp [h]) := by
+  simp
 
 theorem getD_getElem? {xs : Array α} {i : Nat} {d : α} :
     xs[i]?.getD d = if p : i < xs.size then xs[i]'p else d := by
   if h : i < xs.size then
-    simp [h, getElem?_def]
+    simp [h]
   else
     have p : i ≥ xs.size := Nat.le_of_not_gt h
-    simp [getElem?_eq_none p, h]
+    simp [h]
 
 @[simp] theorem getElem?_empty {i : Nat} : (#[] : Array α)[i]? = none := rfl
 
@@ -175,14 +175,14 @@ theorem getElem_push_lt {xs : Array α} {x : α} {i : Nat} (h : i < xs.size) :
 
 @[simp] theorem getElem_push_eq {xs : Array α} {x : α} : (xs.push x)[xs.size] = x := by
   simp only [push, ← getElem_toList, List.concat_eq_append]
-  rw [List.getElem_append_right] <;> simp [← getElem_toList, Nat.zero_lt_one]
+  rw [List.getElem_append_right] <;> simp
 
 @[grind =] theorem getElem_push {xs : Array α} {x : α} {i : Nat} (h : i < (xs.push x).size) :
     (xs.push x)[i] = if h : i < xs.size then xs[i] else x := by
   by_cases h' : i < xs.size
   · simp [getElem_push_lt, h']
   · simp at h
-    simp [getElem_push_lt, Nat.le_antisymm (Nat.le_of_lt_succ h) (Nat.ge_of_not_lt h')]
+    simp [Nat.le_antisymm (Nat.le_of_lt_succ h) (Nat.ge_of_not_lt h')]
 
 @[grind =] theorem getElem?_push {xs : Array α} {x} : (xs.push x)[i]? = if i = xs.size then some x else xs[i]? := by
   simp [getElem?_def, getElem_push]
@@ -906,7 +906,7 @@ theorem all_push [BEq α] {xs : Array α} {a : α} {p : α → Bool} :
 abbrev getElem_set_eq := @getElem_set_self
 
 @[simp] theorem getElem?_set_self {xs : Array α} {i : Nat} (h : i < xs.size) {v : α} :
-    (xs.set i v)[i]? = some v := by simp [getElem?_eq_getElem, h]
+    (xs.set i v)[i]? = some v := by simp [h]
 
 @[deprecated getElem?_set_self (since := "2024-12-11")]
 abbrev getElem?_set_eq := @getElem?_set_self
@@ -918,7 +918,7 @@ abbrev getElem?_set_eq := @getElem?_set_self
 
 @[simp] theorem getElem?_set_ne {xs : Array α} {i : Nat} (h : i < xs.size) {v : α} {j : Nat}
     (ne : i ≠ j) : (xs.set i v)[j]? = xs[j]? := by
-  by_cases h : j < xs.size <;> simp [getElem?_eq_getElem, getElem?_eq_none, Nat.ge_of_not_lt, ne, h]
+  by_cases h : j < xs.size <;> simp [ne, h]
 
 @[grind] theorem getElem_set {xs : Array α} {i : Nat} (h' : i < xs.size) {v : α} {j : Nat}
     (h : j < (xs.set i v).size) :
@@ -1044,7 +1044,7 @@ theorem getElem?_setIfInBounds_self {xs : Array α} {i : Nat} {a : α} :
 @[simp]
 theorem getElem?_setIfInBounds_self_of_lt {xs : Array α} {i : Nat} {a : α} (h : i < xs.size) :
     (xs.setIfInBounds i a)[i]? = some a := by
-  simp [getElem?_setIfInBounds, h]
+  simp [h]
 
 @[deprecated getElem?_setIfInBounds_self (since := "2024-12-11")]
 abbrev getElem?_setIfInBounds_eq := @getElem?_setIfInBounds_self
@@ -1088,7 +1088,7 @@ theorem mem_or_eq_of_mem_setIfInBounds
 @[simp] theorem getD_getElem?_setIfInBounds {xs : Array α} {i : Nat} {v d : α} :
     (xs.setIfInBounds i v)[i]?.getD d = if i < xs.size then v else d := by
   by_cases h : i < xs.size <;>
-    simp [setIfInBounds, Nat.not_lt_of_le, h,  getD_getElem?]
+    simp [setIfInBounds, h,  ]
 
 @[simp, grind =] theorem toList_setIfInBounds {xs : Array α} {i : Nat} {x : α} :
     (xs.setIfInBounds i x).toList = xs.toList.set i x := by
@@ -1200,7 +1200,7 @@ where
       mapM.map f xs i bs = (xs.toList.drop i).foldlM (fun bs a => bs.push <$> f a) bs := by
     unfold mapM.map; split
     · rw [← List.getElem_cons_drop_succ_eq_drop ‹_›]
-      simp only [aux (i + 1), map_eq_pure_bind, length_toList, List.foldlM_cons, bind_assoc,
+      simp only [aux (i + 1), map_eq_pure_bind, List.foldlM_cons, bind_assoc,
         pure_bind]
       rfl
     · rw [List.drop_of_length_le (Nat.ge_of_not_lt ‹_›)]; rfl
@@ -1755,7 +1755,7 @@ theorem forall_mem_filterMap {f : α → Option β} {xs : Array α} {P : β →
 
 theorem map_filterMap_of_inv {f : α → Option β} {g : β → α} (H : ∀ x : α, (f x).map g = some x) {xs : Array α} :
     map g (filterMap f xs) = xs := by
-  simp only [map_filterMap, H, filterMap_some, id]
+  simp only [map_filterMap, H, filterMap_some]
 
 @[grind →]
 theorem forall_none_of_filterMap_eq_empty (h : filterMap f xs = #[]) : ∀ x ∈ xs, f x = none := by
@@ -1894,7 +1894,7 @@ theorem getElem?_append_left {xs ys : Array α} {i : Nat} (hn : i < xs.size) :
     (xs ++ ys)[i]? = xs[i]? := by
   have hn' : i < (xs ++ ys).size := Nat.lt_of_lt_of_le hn <|
     size_append .. ▸ Nat.le_add_right ..
-  simp_all [getElem?_eq_getElem, getElem_append]
+  simp_all
 
 theorem getElem?_append_right {xs ys : Array α} {i : Nat} (h : xs.size ≤ i) :
     (xs ++ ys)[i]? = ys[i - xs.size]? := by
@@ -2025,7 +2025,7 @@ theorem append_eq_singleton_iff {xs ys : Array α} {x : α} :
     xs ++ ys = #[x] ↔ (xs = #[] ∧ ys = #[x]) ∨ (xs = #[x] ∧ ys = #[]) := by
   rcases xs with ⟨xs⟩
   rcases ys with ⟨ys⟩
-  simp only [List.append_toArray, mk.injEq, List.append_eq_singleton_iff, toArray_eq_append_iff]
+  simp only [List.append_toArray, mk.injEq, List.append_eq_singleton_iff]
 
 theorem singleton_eq_append_iff {xs ys : Array α} {x : α} :
     #[x] = xs ++ ys ↔ (xs = #[] ∧ ys = #[x]) ∨ (xs = #[x] ∧ ys = #[]) := by
@@ -2351,7 +2351,7 @@ theorem flatMap_toArray {β} {f : α → Array β} {as : List α} :
 theorem size_flatMap {xs : Array α} {f : α → Array β} :
     (xs.flatMap f).size = sum (map (fun a => (f a).size) xs) := by
   rcases xs with ⟨l⟩
-  simp [Function.comp_def]
+  simp
 
 @[simp, grind] theorem mem_flatMap {f : α → Array β} {b} {xs : Array α} : b ∈ xs.flatMap f ↔ ∃ a, a ∈ xs ∧ b ∈ f a := by
   simp [flatMap_def, mem_flatten]
@@ -2569,7 +2569,7 @@ abbrev map_mkArray := @map_replicate
 @[grind] theorem filter_replicate (w : stop = n) :
     (replicate n a).filter p 0 stop = if p a then replicate n a else #[] := by
   apply Array.ext'
-  simp only [w, toList_filter', toList_replicate, List.filter_replicate]
+  simp only [w]
   split <;> simp_all
 
 @[deprecated filter_replicate (since := "2025-03-18")]
@@ -2609,7 +2609,7 @@ abbrev filterMap_mkArray_of_some := @filterMap_replicate_of_some
 @[simp] theorem filterMap_replicate_of_isSome {f : α → Option β} (h : (f a).isSome) :
     (replicate n a).filterMap f = replicate n (Option.get _ h) := by
   match w : f a, h with
-  | some b, _ => simp [filterMap_replicate, h, w]
+  | some b, _ => simp [filterMap_replicate, w]
 
 @[deprecated filterMap_replicate_of_isSome (since := "2025-03-18")]
 abbrev filterMap_mkArray_of_isSome := @filterMap_replicate_of_isSome
@@ -2644,7 +2644,7 @@ abbrev flatten_mkArray_replicate := @flatten_replicate_replicate
 
 theorem flatMap_replicate {f : α → Array β} : (replicate n a).flatMap f = (replicate n (f a)).flatten := by
   rw [← toList_inj]
-  simp [flatMap_toList, List.flatMap_replicate]
+  simp [List.flatMap_replicate]
 
 @[deprecated flatMap_replicate (since := "2025-03-18")]
 abbrev flatMap_mkArray := @flatMap_replicate
@@ -4142,7 +4142,7 @@ theorem getElem_modify_of_ne {xs : Array α} {i : Nat} (h : i ≠ j)
 
 @[simp] theorem getElem_swap_right {xs : Array α} {i j : Nat} {hi hj} :
     (xs.swap i j hi hj)[j]'(by simpa using hj) = xs[i] := by
-  simp [swap_def, getElem_set]
+  simp [swap_def]
 
 @[simp] theorem getElem_swap_left {xs : Array α} {i j : Nat} {hi hj} :
     (xs.swap i j hi hj)[i]'(by simpa using hi) = xs[j] := by
@@ -4439,7 +4439,7 @@ theorem size_uset {xs : Array α} {v : α} {i : USize} (h : i.toNat < xs.size) :
 
 @[simp] theorem getD_eq_getD_getElem? {xs : Array α} {i : Nat} {d : α} :
     xs.getD i d = xs[i]?.getD d := by
-  simp only [getD]; split <;> simp [getD_getElem?, *]
+  simp only [getD]; split <;> simp [*]
 
 theorem getElem!_eq_getD [Inhabited α] {xs : Array α} {i} : xs[i]! = xs.getD i default := by
   rfl
@@ -4467,13 +4467,13 @@ theorem getElem?_size_le {xs : Array α} {i : Nat} (h : xs.size ≤ i) : xs[i]?
   simp [getElem?_neg, h]
 
 theorem getElem_mem_toList {xs : Array α} {i : Nat} (h : i < xs.size) : xs[i] ∈ xs.toList := by
-  simp only [← getElem_toList, List.getElem_mem, ugetElem_eq_getElem]
+  simp only [← getElem_toList, List.getElem_mem]
 
 theorem back!_eq_back? [Inhabited α] {xs : Array α} : xs.back! = xs.back?.getD default := by
   simp [back!, back?, getElem!_def, Option.getD]; rfl
 
 @[simp, grind] theorem back?_push {xs : Array α} {x : α} : (xs.push x).back? = some x := by
-  simp [back?, ← getElem?_toList]
+  simp [back?]
 
 @[simp] theorem back!_push [Inhabited α] {xs : Array α} {x : α} : (xs.push x).back! = x := by
   simp [back!_eq_back?]
@@ -4622,7 +4622,7 @@ theorem uset_toArray {l : List α} {i : USize} {a : α} {h : i.toNat < l.toArray
 @[simp, grind =] theorem flatten_toArray {L : List (List α)} :
     (L.toArray.map List.toArray).flatten = L.flatten.toArray := by
   apply ext'
-  simp [Function.comp_def]
+  simp
 
 end List
 
@@ -4714,7 +4714,7 @@ namespace List
       intro h'
       specialize ih (by omega)
       have : as.length - (i + 1) + 1 = as.length - i := by omega
-      simp_all [ih]
+      simp_all
     · simp only [size_toArray, Nat.not_lt] at h
       have : as.length = 0 := by omega
       simp_all
@@ -4725,7 +4725,7 @@ end List
 namespace Array
 
 @[deprecated size_toArray (since := "2024-12-11")]
-theorem size_mk (as : List α) : (Array.mk as).size = as.length := by simp [size]
+theorem size_mk (as : List α) : (Array.mk as).size = as.length := by simp
 
 @[deprecated getElem?_eq_getElem (since := "2024-12-11")]
 theorem getElem?_lt
@@ -4741,7 +4741,7 @@ theorem get?_eq_getElem? (xs : Array α) (i : Nat) : xs.get? i = xs[i]? := rfl
 
 @[deprecated getElem?_eq_none (since := "2024-12-11")]
 theorem getElem?_len_le (xs : Array α) {i : Nat} (h : xs.size ≤ i) : xs[i]? = none := by
-  simp [getElem?_eq_none, h]
+  simp [h]
 
 @[deprecated getD_getElem? (since := "2024-12-11")] abbrev getD_get? := @getD_getElem?
 
@@ -4756,7 +4756,7 @@ set_option linter.deprecated false in
 theorem get!_eq_getD_getElem? [Inhabited α] (xs : Array α) (i : Nat) :
     xs.get! i = xs[i]?.getD default := by
   by_cases p : i < xs.size <;>
-  simp [get!, getElem!_eq_getD, getD_eq_getD_getElem?, getD_getElem?, p]
+  simp [get!, getD_eq_getD_getElem?, p]
 
 set_option linter.deprecated false in
 @[deprecated get!_eq_getD_getElem? (since := "2025-02-12")] abbrev get!_eq_getElem? := @get!_eq_getD_getElem?

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

@@ -162,7 +162,7 @@ instance [DecidableEq α] [LT α] [DecidableLT α]
     {xs ys : Array α} : lex xs ys = false ↔ ys ≤ xs := by
   cases xs
   cases ys
-  simp [List.not_lt_iff_ge]
+  simp
 
 instance [DecidableEq α] [LT α] [DecidableLT α] : DecidableLT (Array α) :=
   fun xs ys => decidable_of_iff (lex xs ys = true) lex_eq_true_iff_lt

src/Init/Data/Array/MapIdx.lean

@@ -135,7 +135,7 @@ abbrev getElem_zipWithIndex := @getElem_zipIdx
 
 @[simp, grind =] theorem zipIdx_toArray {l : List α} {k : Nat} :
     l.toArray.zipIdx k = (l.zipIdx k).toArray := by
-  ext i hi₁ hi₂ <;> simp [Nat.add_comm]
+  ext i hi₁ hi₂ <;> simp
 
 @[deprecated zipIdx_toArray (since := "2025-01-21")]
 abbrev zipWithIndex_toArray := @zipIdx_toArray

src/Init/Data/Array/Monadic.lean

@@ -36,19 +36,19 @@ theorem map_toList_inj [Monad m] [LawfulMonad m]
     xs.mapM (m := m) (pure <| f ·) = pure (xs.map f) := by
   induction xs; simp_all
 
-@[simp] theorem idRun_mapM {xs : Array α} {f : α → Id β} : (xs.mapM f).run = xs.map (f · |>.run) :=
+@[simp, grind =] theorem idRun_mapM {xs : Array α} {f : α → Id β} : (xs.mapM f).run = xs.map (f · |>.run) :=
   mapM_pure
 
 @[deprecated idRun_mapM (since := "2025-05-21")]
 theorem mapM_id {xs : Array α} {f : α → Id β} : xs.mapM f = xs.map f :=
   mapM_pure
 
-@[simp] theorem mapM_map [Monad m] [LawfulMonad m] {f : α → β} {g : β → m γ} {xs : Array α} :
+@[simp, grind =] theorem mapM_map [Monad m] [LawfulMonad m] {f : α → β} {g : β → m γ} {xs : Array α} :
     (xs.map f).mapM g = xs.mapM (g ∘ f) := by
   rcases xs with ⟨xs⟩
   simp
 
-@[simp] theorem mapM_append [Monad m] [LawfulMonad m] {f : α → m β} {xs ys : Array α} :
+@[simp, grind =] theorem mapM_append [Monad m] [LawfulMonad m] {f : α → m β} {xs ys : Array α} :
     (xs ++ ys).mapM f = (return (← xs.mapM f) ++ (← ys.mapM f)) := by
   rcases xs with ⟨xs⟩
   rcases ys with ⟨ys⟩
@@ -59,7 +59,7 @@ theorem mapM_eq_foldlM_push [Monad m] [LawfulMonad m] {f : α → m β} {xs : Ar
   rcases xs with ⟨xs⟩
   simp only [List.mapM_toArray, bind_pure_comp, List.size_toArray, List.foldlM_toArray']
   rw [List.mapM_eq_reverse_foldlM_cons]
-  simp only [bind_pure_comp, Functor.map_map]
+  simp only [Functor.map_map]
   suffices ∀ (l), (fun l' => l'.reverse.toArray) <$> List.foldlM (fun acc a => (fun a => a :: acc) <$> f a) l xs =
       List.foldlM (fun acc a => acc.push <$> f a) l.reverse.toArray xs by
     exact this []
@@ -143,13 +143,13 @@ theorem foldrM_filter [Monad m] [LawfulMonad m] {p : α → Bool} {g : α → β
   cases as <;> cases bs
   simp_all
 
-@[simp] theorem forM_append [Monad m] [LawfulMonad m] {xs ys : Array α} {f : α → m PUnit} :
+@[simp, grind =] theorem forM_append [Monad m] [LawfulMonad m] {xs ys : Array α} {f : α → m PUnit} :
     forM (xs ++ ys) f = (do forM xs f; forM ys f) := by
   rcases xs with ⟨xs⟩
   rcases ys with ⟨ys⟩
   simp
 
-@[simp] theorem forM_map [Monad m] [LawfulMonad m] {xs : Array α} {g : α → β} {f : β → m PUnit} :
+@[simp, grind =] theorem forM_map [Monad m] [LawfulMonad m] {xs : Array α} {g : α → β} {f : β → m PUnit} :
     forM (xs.map g) f = forM xs (fun a => f (g a)) := by
   rcases xs with ⟨xs⟩
   simp
@@ -208,7 +208,7 @@ theorem forIn'_yield_eq_foldl
       xs.attach.foldl (fun b ⟨a, h⟩ => f a h b) init :=
   forIn'_pure_yield_eq_foldl _ _
 
-@[simp] theorem forIn'_map [Monad m] [LawfulMonad m]
+@[simp, grind =] theorem forIn'_map [Monad m] [LawfulMonad m]
     {xs : Array α} (g : α → β) (f : (b : β) → b ∈ xs.map g → γ → m (ForInStep γ)) :
     forIn' (xs.map g) init f = forIn' xs init fun a h y => f (g a) (mem_map_of_mem h) y := by
   rcases xs with ⟨xs⟩
@@ -234,14 +234,14 @@ theorem forIn_eq_foldlM [Monad m] [LawfulMonad m]
     forIn xs init (fun a b => (fun c => .yield (g a b c)) <$> f a b) =
       xs.foldlM (fun b a => g a b <$> f a b) init := by
   rcases xs with ⟨xs⟩
-  simp [List.foldlM_map]
+  simp
 
 @[simp] theorem forIn_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
     {xs : Array α} (f : α → β → β) (init : β) :
     forIn xs init (fun a b => pure (.yield (f a b))) =
       pure (f := m) (xs.foldl (fun b a => f a b) init) := by
   rcases xs with ⟨xs⟩
-  simp [List.forIn_pure_yield_eq_foldl, List.foldl_map]
+  simp [List.forIn_pure_yield_eq_foldl]
 
 theorem idRun_forIn_yield_eq_foldl
     {xs : Array α} (f : α → β → Id β) (init : β) :
@@ -256,7 +256,7 @@ theorem forIn_yield_eq_foldl
       xs.foldl (fun b a => f a b) init :=
   forIn_pure_yield_eq_foldl _ _
 
-@[simp] theorem forIn_map [Monad m] [LawfulMonad m]
+@[simp, grind =] theorem forIn_map [Monad m] [LawfulMonad m]
     {xs : Array α} {g : α → β} {f : β → γ → m (ForInStep γ)} :
     forIn (xs.map g) init f = forIn xs init fun a y => f (g a) y := by
   rcases xs with ⟨xs⟩

src/Init/Data/Array/Range.lean

@@ -189,11 +189,11 @@ theorem self_mem_range_succ {n : Nat} : n ∈ range (n + 1) := by simp
 @[simp, grind =] theorem take_range {i n : Nat} : take (range n) i = range (min i n) := by
   ext <;> simp
 
-@[simp] theorem find?_range_eq_some {n : Nat} {i : Nat} {p : Nat → Bool} :
+@[simp, grind =] theorem find?_range_eq_some {n : Nat} {i : Nat} {p : Nat → Bool} :
     (range n).find? p = some i ↔ p i ∧ i ∈ range n ∧ ∀ j, j < i → !p j := by
   simp [range_eq_range']
 
-@[simp] theorem find?_range_eq_none {n : Nat} {p : Nat → Bool} :
+@[simp, grind =] theorem find?_range_eq_none {n : Nat} {p : Nat → Bool} :
     (range n).find? p = none ↔ ∀ i, i < n → !p i := by
   simp only [← List.toArray_range, List.find?_toArray, List.find?_range_eq_none]
 
@@ -213,13 +213,13 @@ theorem zipIdx_eq_empty_iff {xs : Array α} {i : Nat} : xs.zipIdx i = #[] ↔ xs
   cases xs
   simp
 
-@[simp]
+@[simp, grind =]
 theorem getElem?_zipIdx {xs : Array α} {i j} : (zipIdx xs i)[j]? = xs[j]?.map fun a => (a, i + j) := by
   simp [getElem?_def]
 
 theorem map_snd_add_zipIdx_eq_zipIdx {xs : Array α} {n k : Nat} :
     map (Prod.map id (· + n)) (zipIdx xs k) = zipIdx xs (n + k) :=
-  ext_getElem? fun i ↦ by simp [(· ∘ ·), Nat.add_comm, Nat.add_left_comm]; rfl
+  ext_getElem? fun i ↦ by simp [Nat.add_comm, Nat.add_left_comm]; rfl
 
 -- Arguments are explicit for parity with `zipIdx_map_fst`.
 @[simp]
@@ -256,7 +256,7 @@ theorem zipIdx_eq_map_add {xs : Array α} {i : Nat} :
   simp only [zipIdx_toArray, List.map_toArray, mk.injEq]
   rw [List.zipIdx_eq_map_add]
 
-@[simp]
+@[simp, grind =]
 theorem zipIdx_singleton {x : α} {k : Nat} : zipIdx #[x] k = #[(x, k)] :=
   rfl
 
@@ -304,6 +304,7 @@ theorem zipIdx_map {xs : Array α} {k : Nat} {f : α → β} :
   cases xs
   simp [List.zipIdx_map]
 
+@[grind =]
 theorem zipIdx_append {xs ys : Array α} {k : Nat} :
     zipIdx (xs ++ ys) k = zipIdx xs k ++ zipIdx ys (k + xs.size) := by
   cases xs

src/Init/Data/BitVec.lean

@@ -6,7 +6,10 @@ Authors: Kim Morrison
 module
 
 prelude
+import Init.Data.BitVec.BasicAux
 import Init.Data.BitVec.Basic
+import Init.Data.BitVec.Bootstrap
 import Init.Data.BitVec.Bitblast
-import Init.Data.BitVec.Folds
+import Init.Data.BitVec.Decidable
 import Init.Data.BitVec.Lemmas
+import Init.Data.BitVec.Folds

src/Init/Data/BitVec/Basic.lean

@@ -74,25 +74,27 @@ section getXsb
 
 /--
 Returns the `i`th least significant bit.
-
-This will be renamed `getLsb` after the existing deprecated alias is removed.
 -/
-@[inline, expose] def getLsb' (x : BitVec w) (i : Fin w) : Bool := x.toNat.testBit i
+@[inline, expose] def getLsb (x : BitVec w) (i : Fin w) : Bool := x.toNat.testBit i
+
+@[deprecated getLsb (since := "2025-06-17"), inherit_doc getLsb]
+abbrev getLsb' := @getLsb
 
 /-- Returns the `i`th least significant bit, or `none` if `i ≥ w`. -/
 @[inline, expose] def getLsb? (x : BitVec w) (i : Nat) : Option Bool :=
-  if h : i < w then some (getLsb' x ⟨i, h⟩) else none
+  if h : i < w then some (getLsb x ⟨i, h⟩) else none
 
 /--
 Returns the `i`th most significant bit.
-
-This will be renamed `BitVec.getMsb` after the existing deprecated alias is removed.
 -/
-@[inline] def getMsb' (x : BitVec w) (i : Fin w) : Bool := x.getLsb' ⟨w-1-i, by omega⟩
+@[inline] def getMsb (x : BitVec w) (i : Fin w) : Bool := x.getLsb ⟨w-1-i, by omega⟩
+
+@[deprecated getMsb (since := "2025-06-17"), inherit_doc getMsb]
+abbrev getMsb' := @getMsb
 
 /-- Returns the `i`th most significant bit or `none` if `i ≥ w`. -/
 @[inline] def getMsb? (x : BitVec w) (i : Nat) : Option Bool :=
-  if h : i < w then some (getMsb' x ⟨i, h⟩) else none
+  if h : i < w then some (getMsb x ⟨i, h⟩) else none
 
 /-- Returns the `i`th least significant bit or `false` if `i ≥ w`. -/
 @[inline, expose] def getLsbD (x : BitVec w) (i : Nat) : Bool :=
@@ -110,11 +112,11 @@ end getXsb
 section getElem
 
 instance : GetElem (BitVec w) Nat Bool fun _ i => i < w where
-  getElem xs i h := xs.getLsb' ⟨i, h⟩
+  getElem xs i h := xs.getLsb ⟨i, h⟩
 
 /-- We prefer `x[i]` as the simp normal form for `getLsb'` -/
-@[simp] theorem getLsb'_eq_getElem (x : BitVec w) (i : Fin w) :
-    x.getLsb' i = x[i] := rfl
+@[simp] theorem getLsb_eq_getElem (x : BitVec w) (i : Fin w) :
+    x.getLsb i = x[i] := rfl
 
 /-- We prefer `x[i]?` as the simp normal form for `getLsb?` -/
 @[simp] theorem getLsb?_eq_getElem? (x : BitVec w) (i : Nat) :
@@ -723,6 +725,12 @@ def twoPow (w : Nat) (i : Nat) : BitVec w := 1#w <<< i
 
 end bitwise
 
+/-- The bitvector of width `w` that has the smallest value when interpreted as an integer. -/
+def intMin (w : Nat) := twoPow w (w - 1)
+
+/-- The bitvector of width `w` that has the largest value when interpreted as an integer. -/
+def intMax (w : Nat) := (twoPow w (w - 1)) - 1
+
 /--
 Computes a hash of a bitvector, combining 64-bit words using `mixHash`.
 -/
@@ -842,4 +850,15 @@ treating `x` and `y` as 2's complement signed bitvectors.
 def smulOverflow {w : Nat} (x y : BitVec w) : Bool :=
   (x.toInt * y.toInt ≥ 2 ^ (w - 1)) || (x.toInt * y.toInt < - 2 ^ (w - 1))
 
+/-- Count the number of leading zeros downward from the `n`-th bit to the `0`-th bit for the bitblaster.
+  This builds a tree of `if-then-else` lookups whose length is linear in the bitwidth,
+  and an efficient circuit for bitblasting `clz`. -/
+def clzAuxRec {w : Nat} (x : BitVec w) (n : Nat) : BitVec w :=
+  match n with
+  | 0 => if x.getLsbD 0 then BitVec.ofNat w (w - 1) else BitVec.ofNat w w
+  | n' + 1 => if x.getLsbD n then BitVec.ofNat w (w - 1 - n) else clzAuxRec x n'
+
+/-- Count the number of leading zeros. -/
+def clz (x : BitVec w) : BitVec w := clzAuxRec x (w - 1)
+
 end BitVec

src/Init/Data/BitVec/Bitblast.lean

@@ -6,12 +6,14 @@ Authors: Harun Khan, Abdalrhman M Mohamed, Joe Hendrix, Siddharth Bhat
 module
 
 prelude
-import Init.Data.BitVec.Folds
 import all Init.Data.Nat.Bitwise.Basic
 import Init.Data.Nat.Mod
 import all Init.Data.Int.DivMod
 import Init.Data.Int.LemmasAux
-import all Init.Data.BitVec.Lemmas
+import all Init.Data.BitVec.Basic
+import Init.Data.BitVec.Decidable
+import Init.Data.BitVec.Lemmas
+import Init.Data.BitVec.Folds
 
 /-!
 # Bit blasting of bitvectors
@@ -238,7 +240,7 @@ theorem toNat_add_of_and_eq_zero {x y : BitVec w} (h : x &&& y = 0#w) :
     simp only [decide_eq_true_eq] at this
     omega
   rw [← carry_width]
-  simp [not_eq_true, carry_of_and_eq_zero h]
+  simp [carry_of_and_eq_zero h]
 
 /-- Carry function for bitwise addition. -/
 def adcb (x y c : Bool) : Bool × Bool := (atLeastTwo x y c, x ^^ (y ^^ c))
@@ -252,7 +254,7 @@ theorem getLsbD_add_add_bool {i : Nat} (i_lt : i < w) (x y : BitVec w) (c : Bool
       (getLsbD x i ^^ (getLsbD y i ^^ carry i x y c)) := by
   let ⟨x, x_lt⟩ := x
   let ⟨y, y_lt⟩ := y
-  simp only [getLsbD, toNat_add, toNat_setWidth, i_lt, toNat_ofFin, toNat_ofBool,
+  simp only [getLsbD, toNat_add, toNat_setWidth, toNat_ofFin, toNat_ofBool,
     Nat.mod_add_mod, Nat.add_mod_mod]
   apply Eq.trans
   rw [← Nat.div_add_mod x (2^i), ← Nat.div_add_mod y (2^i)]
@@ -295,7 +297,7 @@ theorem adc_spec (x y : BitVec w) (c : Bool) :
     simp [carry, Nat.mod_one]
     cases c <;> rfl
   case step =>
-    simp [adcb, Prod.mk.injEq, carry_succ, getElem_add_add_bool]
+    simp [adcb, carry_succ, getElem_add_add_bool]
 
 theorem add_eq_adc (w : Nat) (x y : BitVec w) : x + y = (adc x y false).snd := by
   simp [adc_spec]
@@ -312,7 +314,7 @@ theorem msb_add {w : Nat} {x y: BitVec w} :
       Bool.xor x.msb (Bool.xor y.msb (carry (w - 1) x y false)) := by
   simp only [BitVec.msb, BitVec.getMsbD]
   by_cases h : w ≤ 0
-  · simp [h, show w = 0 by omega]
+  · simp [show w = 0 by omega]
   · rw [getLsbD_add (x := x)]
     simp [show w > 0 by omega]
     omega
@@ -332,15 +334,15 @@ theorem add_eq_or_of_and_eq_zero {w : Nat} (x y : BitVec w)
     (h : x &&& y = 0#w) : x + y = x ||| y := by
   rw [add_eq_adc, adc, iunfoldr_replace (fun _ => false) (x ||| y)]
   · rfl
-  · simp only [adcb, atLeastTwo, Bool.and_false, Bool.or_false, bne_false, getLsbD_or,
+  · simp only [adcb, atLeastTwo, Bool.and_false, Bool.or_false, bne_false, 
     Prod.mk.injEq, and_eq_false_imp]
     intros i
     replace h : (x &&& y).getLsbD i = (0#w).getLsbD i := by rw [h]
     simp only [getLsbD_and, getLsbD_zero, and_eq_false_imp] at h
     constructor
     · intros hx
-      simp_all [hx]
-    · by_cases hx : x.getLsbD i <;> simp_all [hx]
+      simp_all
+    · by_cases hx : x.getLsbD i <;> simp_all
 
 /-! ### Sub-/
 
@@ -377,7 +379,7 @@ theorem bit_not_add_self (x : BitVec w) :
   simp only [add_eq_adc]
   apply iunfoldr_replace_snd (fun _ => false) (-1) false rfl
   intro i; simp only [adcb, Fin.is_lt, getLsbD_eq_getElem, atLeastTwo_false_right, bne_false,
-    ofNat_eq_ofNat, Fin.getElem_fin, Prod.mk.injEq, and_eq_false_imp]
+    ofNat_eq_ofNat, Prod.mk.injEq, and_eq_false_imp]
   rw [iunfoldr_replace_snd (fun _ => ()) (((iunfoldr (fun i c => (c, !(x[i.val])))) ()).snd)]
   <;> simp [bit_not_testBit, neg_one_eq_allOnes, getElem_allOnes]
 
@@ -409,7 +411,7 @@ theorem getLsbD_neg {i : Nat} {x : BitVec w} :
   · rw [getLsbD_add hi]
     have : 0 < w := by omega
     simp only [getLsbD_not, hi, decide_true, Bool.true_and, getLsbD_one, this, not_bne,
-      _root_.true_and, not_eq_eq_eq_not]
+      not_eq_eq_eq_not]
     cases i with
     | zero =>
       have carry_zero : carry 0 ?x ?y false = false := by
@@ -424,7 +426,7 @@ theorem getLsbD_neg {i : Nat} {x : BitVec w} :
       · rintro h j hj; exact And.right <| h j (by omega)
       · rintro h j hj; exact ⟨by omega, h j (by omega)⟩
   · have h_ge : w ≤ i := by omega
-    simp [getLsbD_of_ge _ _ h_ge, h_ge, hi]
+    simp [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
@@ -433,7 +435,7 @@ theorem getElem_neg {i : Nat} {x : BitVec w} (h : i < w) :
 theorem getMsbD_neg {i : Nat} {x : BitVec w} :
     getMsbD (-x) i =
       (getMsbD x i ^^ decide (∃ j < w, i < j ∧ getMsbD x j = true)) := by
-  simp only [getMsbD, getLsbD_neg, Bool.decide_and, Bool.and_eq_true, decide_eq_true_eq]
+  simp only [getMsbD, getLsbD_neg, Bool.and_eq_true, decide_eq_true_eq]
   by_cases hi : i < w
   case neg =>
     simp [hi]; omega
@@ -518,14 +520,11 @@ theorem msb_neg {w : Nat} {x : BitVec w} :
   rw [(show w = w - 1 + 1 by omega), Int.pow_succ] at this
   omega
 
-@[simp] theorem setWidth_neg_of_le {x : BitVec v} (h : w ≤ v) : BitVec.setWidth w (-x) = -BitVec.setWidth w x := by
-  simp [← BitVec.signExtend_eq_setWidth_of_le _ h, BitVec.signExtend_neg_of_le h]
-
 /-! ### abs -/
 
 theorem msb_abs {w : Nat} {x : BitVec w} :
     x.abs.msb = (decide (x = intMin w) && decide (0 < w)) := by
-  simp only [BitVec.abs, getMsbD_neg, ne_eq, decide_not, Bool.not_bne]
+  simp only [BitVec.abs]
   by_cases h₀ : 0 < w
   · by_cases h₁ : x = intMin w
     · simp [h₁, msb_intMin]
@@ -548,54 +547,14 @@ theorem ult_eq_not_carry (x y : BitVec w) : x.ult y = !carry w x (~~~y) true :=
   rw [Nat.mod_eq_of_lt (by omega)]
   omega
 
-theorem ule_eq_not_ult (x y : BitVec w) : x.ule y = !y.ult x := by
-  simp [BitVec.ule, BitVec.ult, ← decide_not]
-
 theorem ule_eq_carry (x y : BitVec w) : x.ule y = carry w y (~~~x) true := by
   simp [ule_eq_not_ult, ult_eq_not_carry]
 
-/-- If two bitvectors have the same `msb`, then signed and unsigned comparisons coincide -/
-theorem slt_eq_ult_of_msb_eq {x y : BitVec w} (h : x.msb = y.msb) :
-    x.slt y = x.ult y := by
-  simp only [BitVec.slt, toInt_eq_msb_cond, BitVec.ult, decide_eq_decide, h]
-  cases y.msb <;> simp
-
-/-- If two bitvectors have different `msb`s, then unsigned comparison is determined by this bit -/
-theorem ult_eq_msb_of_msb_neq {x y : BitVec w} (h : x.msb ≠ y.msb) :
-    x.ult y = y.msb := by
-  simp only [BitVec.ult, msb_eq_decide, ne_eq, decide_eq_decide] at *
-  omega
-
-/-- If two bitvectors have different `msb`s, then signed and unsigned comparisons are opposites -/
-theorem slt_eq_not_ult_of_msb_neq {x y : BitVec w} (h : x.msb ≠ y.msb) :
-    x.slt y = !x.ult y := by
-  simp only [BitVec.slt, toInt_eq_msb_cond, Bool.eq_not_of_ne h, ult_eq_msb_of_msb_neq h]
-  cases y.msb <;> (simp [-Int.natCast_pow]; omega)
-
-theorem slt_eq_ult {x y : BitVec w} :
-    x.slt y = (x.msb != y.msb).xor (x.ult y) := by
-  by_cases h : x.msb = y.msb
-  · simp [h, slt_eq_ult_of_msb_eq]
-  · have h' : x.msb != y.msb := by simp_all
-    simp [slt_eq_not_ult_of_msb_neq h, h']
-
 theorem slt_eq_not_carry {x y : BitVec w} :
     x.slt y = (x.msb == y.msb).xor (carry w x (~~~y) true) := by
   simp only [slt_eq_ult, bne, ult_eq_not_carry]
   cases x.msb == y.msb <;> simp
 
-theorem sle_eq_not_slt {x y : BitVec w} : x.sle y = !y.slt x := by
-  simp only [BitVec.sle, BitVec.slt, ← decide_not, decide_eq_decide]; omega
-
-theorem zero_sle_eq_not_msb {w : Nat} {x : BitVec w} : BitVec.sle 0#w x = !x.msb := by
-  rw [sle_eq_not_slt, BitVec.slt_zero_eq_msb]
-
-theorem zero_sle_iff_msb_eq_false {w : Nat} {x : BitVec w} : BitVec.sle 0#w x ↔ x.msb = false := by
-  simp [zero_sle_eq_not_msb]
-
-theorem toNat_toInt_of_sle {w : Nat} {x : BitVec w} (hx : BitVec.sle 0#w x) : x.toInt.toNat = x.toNat :=
-  toNat_toInt_of_msb x (zero_sle_iff_msb_eq_false.1 hx)
-
 theorem sle_eq_carry {x y : BitVec w} :
     x.sle y = !((x.msb == y.msb).xor (carry w y (~~~x) true)) := by
   rw [sle_eq_not_slt, slt_eq_not_carry, beq_comm]
@@ -618,12 +577,6 @@ theorem neg_sle_zero (h : 0 < w) {x : BitVec w} :
   rw [sle_eq_slt_or_eq, neg_slt_zero h, sle_eq_slt_or_eq]
   simp [Bool.beq_eq_decide_eq (-x), Bool.beq_eq_decide_eq _ x, Eq.comm (a := x), Bool.or_assoc]
 
-theorem sle_eq_ule {x y : BitVec w} : x.sle y = (x.msb != y.msb ^^ x.ule y) := by
-  rw [sle_eq_not_slt, slt_eq_ult, ← Bool.xor_not, ← ule_eq_not_ult, bne_comm]
-
-theorem sle_eq_ule_of_msb_eq {x y : BitVec w} (h : x.msb = y.msb) : x.sle y = x.ule y := by
-  simp [BitVec.sle_eq_ule, h]
-
 /-! ### mul recurrence for bit blasting -/
 
 /--
@@ -658,7 +611,7 @@ theorem setWidth_setWidth_succ_eq_setWidth_setWidth_add_twoPow (x : BitVec w) (i
       getElem_twoPow]
     by_cases hik : i = k
     · subst hik
-      simp [h]
+      simp
     · by_cases hik' : k < (i + 1)
       · have hik'' : k < i := by omega
         simp [hik', hik'']
@@ -667,8 +620,8 @@ theorem setWidth_setWidth_succ_eq_setWidth_setWidth_add_twoPow (x : BitVec w) (i
         simp [hik', hik'']
         omega
   · ext k
-    simp only [and_twoPow, getLsbD_and, getLsbD_setWidth, Fin.is_lt, decide_true, Bool.true_and,
-      getLsbD_zero, and_eq_false_imp, and_eq_true, decide_eq_true_eq, and_imp]
+    simp only [and_twoPow, 
+      ]
     by_cases hi : x.getLsbD i <;> simp [hi] <;> omega
 
 /--
@@ -825,7 +778,7 @@ private theorem Nat.div_add_eq_left_of_lt {x y z : Nat} (hx : z ∣ x) (hy : y <
   · apply Nat.le_trans
     · exact div_mul_le_self x z
     · omega
-  · simp only [succ_eq_add_one, Nat.add_mul, Nat.one_mul]
+  · simp only [Nat.add_mul, Nat.one_mul]
     apply Nat.add_lt_add_of_le_of_lt
     · apply Nat.le_of_eq
       exact (Nat.div_eq_iff_eq_mul_left hz hx).mp rfl
@@ -938,10 +891,10 @@ def DivModState.lawful_init {w : Nat} (args : DivModArgs w) (hd : 0#w < args.d)
     hwrn := by simp only; omega,
     hdPos := by assumption
     hrLtDivisor := by simp [BitVec.lt_def] at hd ⊢; assumption
-    hrWidth := by simp [DivModState.init],
-    hqWidth := by simp [DivModState.init],
+    hrWidth := by simp,
+    hqWidth := by simp,
     hdiv := by
-      simp only [DivModState.init, toNat_ofNat, zero_mod, Nat.mul_zero, Nat.add_zero];
+      simp only [toNat_ofNat, zero_mod, Nat.mul_zero, Nat.add_zero];
       rw [Nat.shiftRight_eq_div_pow]
       apply Nat.div_eq_of_lt args.n.isLt
   }
@@ -969,7 +922,7 @@ theorem DivModState.umod_eq_of_lawful {qr : DivModState w}
     n % d = qr.r := by
   apply umod_eq_of_mul_add_toNat h.hrLtDivisor
   have hdiv := h.hdiv
-  simp only [shiftRight_zero] at hdiv
+  simp only at hdiv
   simp only [h_final] at *
   exact hdiv.symm
 
@@ -1047,7 +1000,7 @@ obeys the division equation. -/
 theorem lawful_divSubtractShift (qr : DivModState w) (h : qr.Poised args) :
     DivModState.Lawful args (divSubtractShift args qr) := by
   rcases args with ⟨n, d⟩
-  simp only [divSubtractShift, decide_eq_true_eq]
+  simp only [divSubtractShift]
   -- We add these hypotheses for `omega` to find them later.
   have ⟨⟨hrwn, hd, hrd, hr, hn, hrnd⟩, hwn_lt⟩ := h
   have : d.toNat * (qr.q.toNat * 2) = d.toNat * qr.q.toNat * 2 := by rw [Nat.mul_assoc]
@@ -1184,7 +1137,7 @@ theorem getLsbD_udiv (n d : BitVec w) (hy : 0#w < d)  (i : Nat) :
 
 theorem getMsbD_udiv (n d : BitVec w) (hd : 0#w < d)  (i : Nat) :
     (n / d).getMsbD i = (decide (i < w) && (divRec w {n, d} (DivModState.init w)).q.getMsbD i) := by
-  simp [getMsbD_eq_getLsbD, getLsbD_udiv, udiv_eq_divRec (by assumption)]
+  simp [getMsbD_eq_getLsbD, udiv_eq_divRec (by assumption)]
 
 /- ### Arithmetic shift right (sshiftRight) recurrence -/
 
@@ -1351,7 +1304,7 @@ theorem negOverflow_eq {w : Nat} (x : BitVec w) :
     (negOverflow x) = (decide (0 < w) && (x == intMin w)) := by
   simp only [negOverflow]
   rcases w with _|w
-  · simp [toInt_of_zero_length, Int.min_eq_right]
+  · simp [toInt_of_zero_length]
   · suffices - 2 ^ w = (intMin (w + 1)).toInt by simp [beq_eq_decide_eq, ← toInt_inj, this]
     simp only [toInt_intMin, Nat.add_one_sub_one, Int.natCast_emod, Int.neg_inj]
     rw_mod_cast [Nat.mod_eq_of_lt (by simp [Nat.pow_lt_pow_succ])]
@@ -1393,7 +1346,7 @@ theorem umulOverflow_eq {w : Nat} (x y : BitVec w) :
       (0 < w && BitVec.twoPow (w * 2) w ≤ x.zeroExtend (w * 2) * y.zeroExtend (w * 2)) := by
   simp only [umulOverflow, toNat_twoPow, le_def, toNat_mul, toNat_setWidth, mod_mul_mod]
   rcases w with _|w
-  · simp [of_length_zero, toInt_zero, mul_mod_mod]
+  · simp [of_length_zero]
   · simp only [ge_iff_le, show 0 < w + 1 by omega, decide_true, mul_mod_mod, Bool.true_and,
       decide_eq_decide]
     rw [Nat.mod_eq_of_lt BitVec.toNat_mul_toNat_lt, Nat.mod_eq_of_lt]
@@ -1629,11 +1582,11 @@ theorem toInt_sdiv_of_ne_or_ne (a b : BitVec w) (h : a ≠ intMin w ∨ b ≠ -1
   have := Nat.two_pow_pos (w - 1)
 
   by_cases hbintMin : b = intMin w
-  · simp only [ne_eq, Decidable.not_not] at hbintMin
+  · simp only at hbintMin
     subst hbintMin
     have toIntA_lt := @BitVec.toInt_lt w a; norm_cast at toIntA_lt
     have le_toIntA := @BitVec.le_toInt w a; norm_cast at le_toIntA
-    simp only [sdiv_intMin, h, ↓reduceIte, toInt_zero, toInt_intMin, wpos,
+    simp only [sdiv_intMin, toInt_intMin, wpos,
       Nat.two_pow_pred_mod_two_pow, Int.tdiv_neg]
     · by_cases ha_intMin : a = intMin w
       · simp only [ha_intMin, ↓reduceIte, show 1 < w by omega, toInt_one, toInt_intMin, wpos,
@@ -1709,6 +1662,88 @@ theorem toInt_sdiv (a b : BitVec w) : (a.sdiv b).toInt = (a.toInt.tdiv b.toInt).
   · rw [← toInt_bmod_cancel]
     rw [BitVec.toInt_sdiv_of_ne_or_ne _ _ (by simpa only [Decidable.not_and_iff_not_or_not] using h)]
 
+private theorem neg_udiv_eq_intMin_iff_eq_intMin_eq_one_of_msb_eq_true
+    {x y : BitVec w} (hx : x.msb = true) (hy : y.msb = false) :
+    -x / y = intMin w ↔ (x = intMin w ∧ y = 1#w) := by
+  constructor
+  · intros h
+    rcases w with _ | w; decide +revert
+    have : (-x / y).msb = true := by simp [h, msb_intMin]
+    rw [msb_udiv] at this
+    simp only [bool_to_prop] at this
+    obtain ⟨hx, hy⟩ := this
+    simp only [beq_iff_eq] at hy
+    subst hy
+    simp only [udiv_one, zero_lt_succ, neg_eq_intMin] at h
+    simp [h]
+  · rintro ⟨hx, hy⟩
+    subst hx hy
+    simp
+
+/--
+the most significant bit of the signed division `x.sdiv y` can be computed
+by the following cases:
+(1) x nonneg, y nonneg: never neg.
+(2) x nonneg, y neg: neg when result nonzero.
+   We know that y is nonzero since it is negative, so we only check `|x| ≥ |y|`.
+(3) x neg, y nonneg: neg when result nonzero.
+  We check that `y ≠ 0` and `|x| ≥ |y|`.
+(4) x neg, y neg: neg when `x = intMin, `y = -1`, since `intMin / -1 = intMin`.
+
+The proof strategy is to perform a case analysis on the sign of `x` and `y`,
+followed by unfolding the `sdiv` into `udiv`.
+-/
+theorem msb_sdiv_eq_decide {x y : BitVec w} :
+    (x.sdiv y).msb = (decide (0 < w) &&
+      (!x.msb && y.msb && decide (-y ≤ x)) ||
+      (x.msb && !y.msb && decide (y ≤ -x) && !decide (y = 0#w)) ||
+      (x.msb && y.msb && decide (x = intMin w) && decide (y = -1#w)))
+     := by
+  rcases w; decide +revert
+  case succ w =>
+    simp only [decide_true, ne_eq, decide_and, decide_not, Bool.true_and,
+      sdiv_eq, udiv_eq]
+    rcases hxmsb : x.msb <;> rcases hymsb : y.msb
+    · simp [hxmsb, hymsb, msb_udiv_eq_false_of, Bool.not_false, Bool.and_false, Bool.false_and,
+        Bool.and_true, Bool.or_self, Bool.and_self]
+    · simp only [hxmsb, hymsb, msb_neg, msb_udiv_eq_false_of, bne_false, Bool.not_false,
+        Bool.and_self, ne_zero_of_msb_true, decide_false, Bool.and_true, Bool.true_and, Bool.not_true,
+        Bool.false_and, Bool.or_false, bool_to_prop]
+      have : x / -y ≠ intMin (w + 1) := by
+        intros h
+        have : (x / -y).msb = (intMin (w + 1)).msb := by simp only [h]
+        simp only [msb_udiv, msb_intMin, show 0 < w + 1 by omega, decide_true, and_eq_true, beq_iff_eq] at this
+        obtain ⟨hcontra, _⟩ := this
+        simp only [hcontra, true_eq_false] at hxmsb
+      simp [this, hymsb, udiv_ne_zero_iff_ne_zero_and_le]
+    · simp only [hxmsb, hymsb, Bool.not_true, Bool.and_self, Bool.false_and, Bool.not_false,
+        Bool.true_and, Bool.false_or, Bool.and_false, Bool.or_false]
+      by_cases hx₁ : x = 0#(w + 1)
+      · simp [hx₁, neg_zero, zero_udiv, msb_zero, le_zero_iff, Bool.and_not_self]
+      · by_cases hy₁ : y = 0#(w + 1)
+        · simp [hy₁, udiv_zero, neg_zero, msb_zero, decide_true, Bool.not_true, Bool.and_false]
+        · simp only [hy₁, decide_false, Bool.not_false, Bool.and_true]
+          by_cases hxy₁ : (- x / y) = 0#(w + 1)
+          · simp only [hxy₁, neg_zero, msb_zero, false_eq_decide_iff, BitVec.not_le,
+              decide_eq_true_eq, BitVec.not_le]
+            simp only [udiv_eq_zero_iff_eq_zero_or_lt, hy₁, _root_.false_or] at hxy₁
+            bv_omega
+          · simp only [udiv_eq_zero_iff_eq_zero_or_lt, _root_.not_or, BitVec.not_lt,
+              hy₁, not_false_eq_true, _root_.true_and] at hxy₁
+            simp only [hxy₁, decide_true, msb_neg, bne_iff_ne, ne_eq,
+              bool_to_prop,
+              bne_iff_ne, ne_eq, udiv_eq_zero_iff_eq_zero_or_lt, hy₁, _root_.false_or,
+              BitVec.not_lt, hxy₁, _root_.true_and, decide_not, not_eq_eq_eq_not, not_eq_not,
+              msb_udiv, msb_neg]
+            simp only [hx₁, not_false_eq_true, _root_.true_and, decide_not, hxmsb, not_eq_eq_eq_not,
+              Bool.not_true, decide_eq_false_iff_not, Decidable.not_not, beq_iff_eq]
+            rw [neg_udiv_eq_intMin_iff_eq_intMin_eq_one_of_msb_eq_true hxmsb hymsb]
+    · simp only [msb_udiv, msb_neg, hxmsb, bne_true, Bool.not_and, Bool.not_true, Bool.and_true,
+        Bool.false_and, Bool.and_false, hymsb, ne_zero_of_msb_true, decide_false, Bool.not_false,
+        Bool.or_self, Bool.and_self, Bool.true_and, Bool.false_or]
+      simp only [bool_to_prop]
+      simp [BitVec.ne_zero_of_msb_true (x := x) hxmsb, neg_eq_iff_eq_neg]
+
 theorem msb_umod_eq_false_of_left {x : BitVec w} (hx : x.msb = false) (y : BitVec w) : (x % y).msb = false := by
   rw [msb_eq_false_iff_two_mul_lt] at hx ⊢
   rw [toNat_umod]
@@ -1728,7 +1763,7 @@ theorem msb_umod_of_le_of_ne_zero_of_le {x y : BitVec w}
 theorem toInt_srem (x y : BitVec w) : (x.srem y).toInt = x.toInt.tmod y.toInt := by
   rw [srem_eq]
   by_cases hyz : y = 0#w
-  · simp only [hyz, ofNat_eq_ofNat, msb_zero, umod_zero, neg_zero, neg_neg, toInt_zero, Int.tmod_zero]
+  · simp only [hyz, msb_zero, umod_zero, neg_zero, neg_neg, toInt_zero, Int.tmod_zero]
     cases x.msb <;> rfl
   cases h : x.msb
   · cases h' : y.msb
@@ -1807,7 +1842,7 @@ theorem toInt_umod_neg_add {x y : BitVec w} (hymsb : y.msb = true) (hxmsb : x.ms
   have hylt : (-y).toNat ≤ 2 ^ (w) := toNat_neg_lt_of_msb y hymsb
   have hmodlt := Nat.mod_lt x.toNat (y := (-y).toNat)
       (by rw [toNat_neg, Nat.mod_eq_of_lt (by omega)]; omega)
-  simp only [hdvd, reduceIte, toInt_add, hxnonneg, show ¬0 ≤ y.toInt by omega]
+  simp only [toInt_add]
   rw [toInt_umod, toInt_eq_neg_toNat_neg_of_msb_true hymsb, Int.bmod_add_bmod,
     Int.bmod_eq_of_le (by omega) (by omega),
     toInt_eq_toNat_of_msb hxmsb, Int.emod_neg]
@@ -1822,7 +1857,7 @@ theorem toInt_sub_neg_umod {x y : BitVec w} (hxmsb : x.msb = true) (hymsb : y.ms
     · subst hyzero; simp
     · simp only [toNat_eq, toNat_ofNat, zero_mod] at hyzero
       have hypos : 0 < y.toNat := by omega
-      simp only [reduceIte, toInt_sub, toInt_eq_toNat_of_msb hymsb, toInt_umod,
+      simp only [toInt_sub, toInt_eq_toNat_of_msb hymsb, toInt_umod,
         Int.sub_bmod_bmod, toInt_eq_neg_toNat_neg_of_msb_true hxmsb, Int.neg_emod]
       have hmodlt := Nat.mod_lt (x := (-x).toNat) (y := y.toNat) hypos
       rw [Int.bmod_eq_of_le (by omega) (by omega)]
@@ -1860,7 +1895,7 @@ theorem toInt_smod {x y : BitVec w} :
         · simp [show ¬-x % y = 0#(w + 1) by simp_all, toInt_sub_neg_umod hxmsb hymsb hx_dvd_y]
       · rw [←Int.neg_inj, neg_toInt_neg_umod_eq_of_msb_true_msb_true hxmsb hymsb]
         simp [BitVec.toInt_eq_neg_toNat_neg_of_msb_true, hxmsb, hymsb,
-          Int.fmod_eq_emod_of_nonneg _, show 0 ≤ (-y).toNat by omega]
+          Int.fmod_eq_emod_of_nonneg _]
 
 /-! ### Lemmas that use bit blasting circuits -/
 
@@ -1894,7 +1929,7 @@ theorem carry_extractLsb'_eq_carry {w i len : Nat} (hi : i < len)
     {x y : BitVec w} {b : Bool}:
     (carry i (extractLsb' 0 len x) (extractLsb' 0 len y) b)
     = (carry i x y b) := by
-  simp only [carry, extractLsb'_toNat, shiftRight_zero, toNat_false, Nat.add_zero, ge_iff_le,
+  simp only [carry, extractLsb'_toNat, shiftRight_zero, ge_iff_le,
     decide_eq_decide]
   have : 2 ^ i ∣ 2^len := by
     apply Nat.pow_dvd_pow

src/Init/Data/BitVec/Bootstrap.lean

@@ -0,0 +1,146 @@
+/-
+Copyright (c) 2023 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Joe Hendrix, Harun Khan, Alex Keizer, Abdalrhman M Mohamed, Siddharth Bhat
+-/
+module
+
+prelude
+import all Init.Data.BitVec.Basic
+
+namespace BitVec
+
+theorem testBit_toNat (x : BitVec w) : x.toNat.testBit i = x.getLsbD i := rfl
+
+@[simp] theorem getLsbD_ofFin (x : Fin (2^n)) (i : Nat) :
+    getLsbD (BitVec.ofFin x) i = x.val.testBit i := rfl
+
+@[simp] theorem getLsbD_of_ge (x : BitVec w) (i : Nat) (ge : w ≤ i) : getLsbD x i = false := by
+  let ⟨x, x_lt⟩ := x
+  simp only [getLsbD_ofFin]
+  apply Nat.testBit_lt_two_pow
+  have p : 2^w ≤ 2^i := Nat.pow_le_pow_right (by omega) ge
+  omega
+
+/-- Prove equality of bitvectors in terms of nat operations. -/
+theorem eq_of_toNat_eq {n} : ∀ {x y : BitVec n}, x.toNat = y.toNat → x = y
+  | ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
+
+theorem eq_of_getLsbD_eq {x y : BitVec w}
+    (pred : ∀ i, i < w → x.getLsbD i = y.getLsbD i) : x = y := by
+  apply eq_of_toNat_eq
+  apply Nat.eq_of_testBit_eq
+  intro i
+  if i_lt : i < w then
+    exact pred i i_lt
+  else
+    have p : i ≥ w := Nat.le_of_not_gt i_lt
+    simp [testBit_toNat, getLsbD_of_ge _ _ p]
+
+@[simp, bitvec_to_nat] theorem toNat_ofNat (x w : Nat) : (BitVec.ofNat w x).toNat = x % 2^w := by
+  simp [BitVec.toNat, BitVec.ofNat, Fin.ofNat]
+
+@[ext] theorem eq_of_getElem_eq {x y : BitVec n} :
+        (∀ i (hi : i < n), x[i] = y[i]) → x = y :=
+  fun h => BitVec.eq_of_getLsbD_eq (h ↑·)
+
+@[simp] theorem toNat_append (x : BitVec m) (y : BitVec n) :
+    (x ++ y).toNat = x.toNat <<< n ||| y.toNat :=
+  rfl
+
+@[simp] theorem toNat_ofBool (b : Bool) : (ofBool b).toNat = b.toNat := by
+  cases b <;> rfl
+
+@[simp, bitvec_to_nat] theorem toNat_cast (h : w = v) (x : BitVec w) : (x.cast h).toNat = x.toNat := rfl
+
+@[simp, bitvec_to_nat] theorem toNat_ofFin (x : Fin (2^n)) : (BitVec.ofFin x).toNat = x.val := rfl
+
+@[simp] theorem toNat_ofNatLT (x : Nat) (p : x < 2^w) : (x#'p).toNat = x := rfl
+
+@[simp] theorem toNat_cons (b : Bool) (x : BitVec w) :
+    (cons b x).toNat = (b.toNat <<< w) ||| x.toNat := by
+  let ⟨x, _⟩ := x
+  simp only [cons, toNat_cast, toNat_append, toNat_ofBool, toNat_ofFin]
+
+theorem getElem_cons {b : Bool} {n} {x : BitVec n} {i : Nat} (h : i < n + 1) :
+    (cons b x)[i] = if h : i = n then b else x[i] := by
+  simp only [getElem_eq_testBit_toNat, toNat_cons, Nat.testBit_or]
+  rw [Nat.testBit_shiftLeft]
+  rcases Nat.lt_trichotomy i n with i_lt_n | i_eq_n | n_lt_i
+  · have p1 : ¬(n ≤ i) := by omega
+    have p2 : i ≠ n := by omega
+    simp [p1, p2]
+  · simp only [i_eq_n, ge_iff_le, Nat.le_refl, decide_true, Nat.sub_self, Nat.testBit_zero,
+    Bool.true_and, testBit_toNat, getLsbD_of_ge, Bool.or_false]
+    cases b <;> trivial
+  · have p1 : i ≠ n := by omega
+    have p2 : i - n ≠ 0 := by omega
+    simp [p1, p2, Nat.testBit_bool_to_nat]
+
+private theorem lt_two_pow_of_le {x m n : Nat} (lt : x < 2 ^ m) (le : m ≤ n) : x < 2 ^ n :=
+  Nat.lt_of_lt_of_le lt (Nat.pow_le_pow_right (by trivial : 0 < 2) le)
+
+@[simp, bitvec_to_nat] theorem toNat_setWidth' {m n : Nat} (p : m ≤ n) (x : BitVec m) :
+    (setWidth' p x).toNat = x.toNat := by
+  simp only [setWidth', toNat_ofNatLT]
+
+@[simp, bitvec_to_nat] theorem toNat_setWidth (i : Nat) (x : BitVec n) :
+    BitVec.toNat (setWidth i x) = x.toNat % 2^i := by
+  let ⟨x, lt_n⟩ := x
+  simp only [setWidth]
+  if n_le_i : n ≤ i then
+    have x_lt_two_i : x < 2 ^ i := lt_two_pow_of_le lt_n n_le_i
+    simp [n_le_i, Nat.mod_eq_of_lt, x_lt_two_i]
+  else
+    simp [n_le_i, toNat_ofNat]
+
+@[simp] theorem ofNat_toNat (m : Nat) (x : BitVec n) : BitVec.ofNat m x.toNat = setWidth m x := by
+  apply eq_of_toNat_eq
+  simp only [toNat_ofNat, toNat_setWidth]
+
+theorem getElem_setWidth' (x : BitVec w) (i : Nat) (h : w ≤ v) (hi : i < v) :
+    (setWidth' h x)[i] = x.getLsbD i := by
+  rw [getElem_eq_testBit_toNat, toNat_setWidth', getLsbD]
+
+@[simp]
+theorem getElem_setWidth (m : Nat) (x : BitVec n) (i : Nat) (h : i < m) :
+    (setWidth m x)[i] = x.getLsbD i := by
+  rw [setWidth]
+  split
+  · rw [getElem_setWidth']
+  · simp only [ofNat_toNat, getElem_eq_testBit_toNat, toNat_setWidth, Nat.testBit_mod_two_pow,
+      getLsbD, Bool.and_eq_right_iff_imp, decide_eq_true_eq]
+    omega
+
+@[simp] theorem cons_msb_setWidth (x : BitVec (w+1)) : (cons x.msb (x.setWidth w)) = x := by
+  ext i
+  simp only [getElem_cons]
+  split <;> rename_i h
+  · simp [BitVec.msb, getMsbD, h]
+  · by_cases h' : i < w
+    · simp_all only [getElem_setWidth, getLsbD_eq_getElem]
+    · omega
+
+@[simp, bitvec_to_nat] theorem toNat_neg (x : BitVec n) : (- x).toNat = (2^n - x.toNat) % 2^n := by
+  simp [Neg.neg, BitVec.neg]
+
+@[simp] theorem setWidth_neg_of_le {x : BitVec v} (h : w ≤ v) : BitVec.setWidth w (-x) = -BitVec.setWidth w x := by
+  apply BitVec.eq_of_toNat_eq
+  simp only [toNat_setWidth, toNat_neg]
+  rw [Nat.mod_mod_of_dvd _ (Nat.pow_dvd_pow 2 h)]
+  rw [Nat.mod_eq_mod_iff]
+  rw [Nat.mod_def]
+  refine ⟨1 + x.toNat / 2^w, 2^(v-w), ?_⟩
+  rw [← Nat.pow_add]
+  have : v - w + w = v := by omega
+  rw [this]
+  rw [Nat.add_mul, Nat.one_mul, Nat.mul_comm (2^w)]
+  have sub_sub : ∀ (a : Nat) {b c : Nat} (h : c ≤ b), a - (b - c) = a + c - b := by omega
+  rw [sub_sub _ (Nat.div_mul_le_self x.toNat (2 ^ w))]
+  have : x.toNat / 2 ^ w * 2 ^ w ≤ x.toNat := Nat.div_mul_le_self x.toNat (2 ^ w)
+  have : x.toNat < 2 ^w ∨ x.toNat - 2 ^ w < x.toNat / 2 ^ w * 2 ^ w := by
+    have := Nat.lt_div_mul_add (a := x.toNat) (b := 2 ^ w) (Nat.two_pow_pos w)
+    omega
+  omega
+
+end BitVec

src/Init/Data/BitVec/Decidable.lean

@@ -0,0 +1,79 @@
+/-
+Copyright (c) 2023 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Joe Hendrix, Harun Khan, Alex Keizer, Abdalrhman M Mohamed, Siddharth Bhat
+
+-/
+module
+
+prelude
+import Init.Data.BitVec.Bootstrap
+
+set_option linter.missingDocs true
+
+namespace BitVec
+
+/-! ### Decidable quantifiers -/
+
+theorem forall_zero_iff {P : BitVec 0 → Prop} :
+    (∀ v, P v) ↔ P 0#0 := by
+  constructor
+  · intro h
+    apply h
+  · intro h v
+    obtain (rfl : v = 0#0) := (by ext i ⟨⟩)
+    apply h
+
+theorem forall_cons_iff {P : BitVec (n + 1) → Prop} :
+    (∀ v : BitVec (n + 1), P v) ↔ (∀ (x : Bool) (v : BitVec n), P (v.cons x)) := by
+  constructor
+  · intro h _ _
+    apply h
+  · intro h v
+    have w : v = (v.setWidth n).cons v.msb := by simp only [cons_msb_setWidth]
+    rw [w]
+    apply h
+
+instance instDecidableForallBitVecZero (P : BitVec 0 → Prop) :
+    ∀ [Decidable (P 0#0)], Decidable (∀ v, P v)
+  | .isTrue h => .isTrue fun v => by
+    obtain (rfl : v = 0#0) := (by ext i ⟨⟩)
+    exact h
+  | .isFalse h => .isFalse (fun w => h (w _))
+
+instance instDecidableForallBitVecSucc (P : BitVec (n+1) → Prop) [DecidablePred P]
+    [Decidable (∀ (x : Bool) (v : BitVec n), P (v.cons x))] : Decidable (∀ v, P v) :=
+  decidable_of_iff' (∀ x (v : BitVec n), P (v.cons x)) forall_cons_iff
+
+instance instDecidableExistsBitVecZero (P : BitVec 0 → Prop) [Decidable (P 0#0)] :
+    Decidable (∃ v, P v) :=
+  decidable_of_iff (¬ ∀ v, ¬ P v) Classical.not_forall_not
+
+instance instDecidableExistsBitVecSucc (P : BitVec (n+1) → Prop) [DecidablePred P]
+    [Decidable (∀ (x : Bool) (v : BitVec n), ¬ P (v.cons x))] : Decidable (∃ v, P v) :=
+  decidable_of_iff (¬ ∀ v, ¬ P v) Classical.not_forall_not
+
+/--
+For small numerals this isn't necessary (as typeclass search can use the above two instances),
+but for large numerals this provides a shortcut.
+Note, however, that for large numerals the decision procedure may be very slow,
+and you should use `bv_decide` if possible.
+-/
+instance instDecidableForallBitVec :
+    ∀ (n : Nat) (P : BitVec n → Prop) [DecidablePred P], Decidable (∀ v, P v)
+  | 0, _, _ => inferInstance
+  | n + 1, _, _ =>
+    have := instDecidableForallBitVec n
+    inferInstance
+
+/--
+For small numerals this isn't necessary (as typeclass search can use the above two instances),
+but for large numerals this provides a shortcut.
+Note, however, that for large numerals the decision procedure may be very slow.
+-/
+instance instDecidableExistsBitVec :
+    ∀ (n : Nat) (P : BitVec n → Prop) [DecidablePred P], Decidable (∃ v, P v)
+  | 0, _, _ => inferInstance
+  | _ + 1, _, _ => inferInstance
+
+end BitVec

src/Init/Data/BitVec/Folds.lean

@@ -82,9 +82,9 @@ theorem iunfoldr_getLsbD' {f : Fin w → α → α × Bool} (state : Nat → α)
       simp only [getLsbD_cons]
       have hj2 : j.val ≤ w := by simp
       cases (Nat.lt_or_eq_of_le (Nat.lt_succ.mp i.isLt)) with
-      | inl h3 => simp [if_neg, (Nat.ne_of_lt h3)]
+      | inl h3 => simp [(Nat.ne_of_lt h3)]
                   exact (ih hj2).1 ⟨i.val, h3⟩
-      | inr h3 => simp [h3, if_pos]
+      | inr h3 => simp [h3]
                   cases (Nat.eq_zero_or_pos j.val) with
                   | inl hj3 => congr
                                rw [← (ih hj2).2]

src/Init/Data/Bool.lean

@@ -488,7 +488,7 @@ Converts `true` to `1` and `false` to `0`.
 
 @[simp] theorem ite_eq_true_else_eq_false {q : Prop} :
     (if b = true then q else b = false) ↔ (b = true → q) := by
-  cases b <;> simp [not_eq_self]
+  cases b <;> simp
 
 /-
 `not_ite_eq_true_eq_true` and related theorems below are added for

src/Init/Data/Fin/Fold.lean

@@ -252,7 +252,7 @@ theorem foldl_succ_last (f : α → Fin (n+1) → α) (x) :
     foldl (n+1) f x = f (foldl n (f · ·.castSucc) x) (last n) := by
   rw [foldl_succ]
   induction n generalizing x with
-  | zero => simp [foldl_succ, Fin.last]
+  | zero => simp [Fin.last]
   | succ n ih => rw [foldl_succ, ih (f · ·.succ), foldl_succ]; simp
 
 theorem foldl_add (f : α → Fin (n + m) → α) (x) :

src/Init/Data/Fin/Lemmas.lean

@@ -381,7 +381,7 @@ theorem zero_ne_one : (0 : Fin (n + 2)) ≠ 1 := Fin.ne_of_lt one_pos
 @[simp] theorem val_succ (j : Fin n) : (j.succ : Nat) = j + 1 := rfl
 
 @[simp] theorem succ_pos (a : Fin n) : (0 : Fin (n + 1)) < a.succ := by
-  simp [Fin.lt_def, Nat.succ_pos]
+  simp [Fin.lt_def]
 
 @[simp] theorem succ_le_succ_iff {a b : Fin n} : a.succ ≤ b.succ ↔ a ≤ b := Nat.succ_le_succ_iff
 
@@ -414,7 +414,7 @@ theorem one_lt_succ_succ (a : Fin n) : (1 : Fin (n + 2)) < a.succ.succ := by
   simp only [lt_def, val_add, val_last, Fin.ext_iff]
   let ⟨k, hk⟩ := k
   match Nat.eq_or_lt_of_le (Nat.le_of_lt_succ hk) with
-  | .inl h => cases h; simp [Nat.succ_pos]
+  | .inl h => cases h; simp
   | .inr hk' => simp [Nat.ne_of_lt hk', Nat.mod_eq_of_lt (Nat.succ_lt_succ hk'), Nat.le_succ]
 
 @[simp] theorem add_one_le_iff {n : Nat} : ∀ {k : Fin (n + 1)}, k + 1 ≤ k ↔ k = last _ := by
@@ -426,7 +426,7 @@ theorem one_lt_succ_succ (a : Fin n) : (1 : Fin (n + 2)) < a.succ.succ := by
     intro (k : Fin (n+2))
     rw [← add_one_lt_iff, lt_def, le_def, Nat.lt_iff_le_and_ne, and_iff_left]
     rw [val_add_one]
-    split <;> simp [*, (Nat.succ_ne_zero _).symm, Nat.ne_of_gt (Nat.lt_succ_self _)]
+    split <;> simp [*, Nat.ne_of_gt (Nat.lt_succ_self _)]
 
 @[simp] theorem last_le_iff {n : Nat} {k : Fin (n + 1)} : last n ≤ k ↔ k = last n := by
   rw [Fin.ext_iff, Nat.le_antisymm_iff, le_def, and_iff_right (by apply le_last)]
@@ -738,7 +738,7 @@ theorem pred_mk {n : Nat} (i : Nat) (h : i < n + 1) (w) : Fin.pred ⟨i, h⟩ w
     ∀ {a b : Fin (n + 1)} {ha : a ≠ 0} {hb : b ≠ 0}, a.pred ha = b.pred hb ↔ a = b
   | ⟨0, _⟩, _, ha, _ => by simp only [mk_zero, ne_eq, not_true] at ha
   | ⟨i + 1, _⟩, ⟨0, _⟩, _, hb => by simp only [mk_zero, ne_eq, not_true] at hb
-  | ⟨i + 1, hi⟩, ⟨j + 1, hj⟩, ha, hb => by simp [Fin.ext_iff, Nat.succ.injEq]
+  | ⟨i + 1, hi⟩, ⟨j + 1, hj⟩, ha, hb => by simp [Fin.ext_iff]
 
 @[simp] theorem pred_one {n : Nat} :
     Fin.pred (1 : Fin (n + 2)) (Ne.symm (Fin.ne_of_lt one_pos)) = 0 := rfl
@@ -1117,7 +1117,7 @@ protected theorem mul_one [i : NeZero n] (k : Fin n) : k * 1 = k := by
   | n + 1, _ =>
     match n with
     | 0 => exact Subsingleton.elim (α := Fin 1) ..
-    | n+1 => simp [Fin.ext_iff, mul_def, Nat.mod_eq_of_lt (is_lt k)]
+    | n+1 => simp [mul_def, Nat.mod_eq_of_lt (is_lt k)]
 
 protected theorem mul_comm (a b : Fin n) : a * b = b * a :=
   Fin.ext <| by rw [mul_def, mul_def, Nat.mul_comm]

src/Init/Data/Function.lean

@@ -31,19 +31,19 @@ Examples:
 @[inline, expose]
 def uncurry : (α → β → φ) → α × β → φ := fun f a => f a.1 a.2
 
-@[simp]
+@[simp, grind]
 theorem curry_uncurry (f : α → β → φ) : curry (uncurry f) = f :=
   rfl
 
-@[simp]
+@[simp, grind]
 theorem uncurry_curry (f : α × β → φ) : uncurry (curry f) = f :=
   funext fun ⟨_a, _b⟩ => rfl
 
-@[simp]
+@[simp, grind]
 theorem uncurry_apply_pair {α β γ} (f : α → β → γ) (x : α) (y : β) : uncurry f (x, y) = f x y :=
   rfl
 
-@[simp]
+@[simp, grind]
 theorem curry_apply {α β γ} (f : α × β → γ) (x : α) (y : β) : curry f x y = f (x, y) :=
   rfl
 

src/Init/Data/Int/Compare.lean

@@ -37,7 +37,7 @@ theorem compare_eq_ite_le (a b : Int) :
   · next hlt => simp [Int.le_of_lt hlt, Int.not_le.2 hlt]
   · next hge =>
     split
-    · next hgt => simp [Int.le_of_lt hgt, Int.not_le.2 hgt]
+    · next hgt => simp [Int.not_le.2 hgt]
     · next hle => simp [Int.not_lt.1 hge, Int.not_lt.1 hle]
 
 protected theorem compare_swap (a b : Int) : (compare a b).swap = compare b a := by

src/Init/Data/Int/DivMod/Bootstrap.lean

@@ -56,7 +56,7 @@ protected theorem dvd_trans : ∀ {a b c : Int}, a ∣ b → b ∣ c → a ∣ c
 
 @[simp] protected theorem dvd_neg {a b : Int} : a ∣ -b ↔ a ∣ b := by
   constructor <;> exact fun ⟨k, e⟩ =>
-    ⟨-k, by simp [← e, Int.neg_mul, Int.mul_neg, Int.neg_neg]⟩
+    ⟨-k, by simp [← e, Int.mul_neg, Int.neg_neg]⟩
 
 @[simp] theorem natAbs_dvd_natAbs {a b : Int} : natAbs a ∣ natAbs b ↔ a ∣ b := by
   refine ⟨fun ⟨k, hk⟩ => ?_, fun ⟨k, hk⟩ => ⟨natAbs k, hk.symm ▸ natAbs_mul a k⟩⟩

src/Init/Data/Int/DivMod/Lemmas.lean

@@ -217,7 +217,7 @@ theorem tdiv_eq_ediv {a b : Int} :
       negSucc_not_nonneg, sign_of_add_one]
     simp only [negSucc_emod_ofNat_succ_eq_zero_iff]
     norm_cast
-    simp only [subNat_eq_zero_iff, Nat.succ_eq_add_one, sign_negSucc, Int.sub_neg, false_or]
+    simp only [Nat.succ_eq_add_one, false_or]
     split <;> rename_i h
     · rw [Int.add_zero, neg_ofNat_eq_negSucc_iff]
       exact Nat.succ_div_of_mod_eq_zero h
@@ -1317,7 +1317,7 @@ protected theorem eq_tdiv_of_mul_eq_left {a b c : Int}
   | 0, n => by simp [Int.neg_zero]
   | succ _, (n:Nat) => by simp [tdiv, ← Int.negSucc_eq]
   | -[_+1], 0 | -[_+1], -[_+1] => by
-    simp only [tdiv, neg_negSucc, ← Int.natCast_succ, Int.neg_neg]
+    simp only [tdiv, neg_negSucc, Int.neg_neg]
   | succ _, -[_+1] | -[_+1], succ _ => (Int.neg_neg _).symm
 
 protected theorem neg_tdiv_neg (a b : Int) : (-a).tdiv (-b) = a.tdiv b := by
@@ -1408,7 +1408,7 @@ theorem mul_tmod (a b n : Int) : (a * b).tmod n = (a.tmod n * b.tmod n).tmod n :
   case inv => simp [Int.dvd_neg]
   induction m using wlog_sign
   case inv => simp
-  simp only [← Int.natCast_mul, ← ofNat_tmod]
+  simp only [← ofNat_tmod]
   norm_cast at h
   rw [Nat.mod_mod_of_dvd _ h]
 
@@ -1576,7 +1576,7 @@ theorem neg_mul_tmod_left (a b : Int) : (-(a * b)).tmod b = 0 := by
 
 @[simp] protected theorem tdiv_one : ∀ a : Int, a.tdiv 1 = a
   | (n:Nat) => congrArg ofNat (Nat.div_one _)
-  | -[n+1] => by simp [Int.tdiv, neg_ofNat_succ]; rfl
+  | -[n+1] => by simp [Int.tdiv]; rfl
 
 @[simp] theorem tmod_one (a : Int) : tmod a 1 = 0 := by
   simp [tmod_def, Int.tdiv_one, Int.one_mul, Int.sub_self]
@@ -1698,7 +1698,7 @@ theorem lt_ediv_iff_of_dvd_of_neg {a b c : Int} (hc : c < 0) (hcb : c ∣ b) :
 theorem ediv_le_ediv_iff_of_dvd_of_pos_of_pos {a b c d : Int} (hb : 0 < b) (hd : 0 < d)
     (hba : b ∣ a) (hdc : d ∣ c) : a / b ≤ c / d ↔ d * a ≤ c * b := by
   obtain ⟨⟨x, rfl⟩, y, rfl⟩ := hba, hdc
-  simp [*, Int.ne_of_lt, Int.ne_of_gt, d.mul_assoc, b.mul_comm]
+  simp [*, Int.ne_of_gt, d.mul_assoc, b.mul_comm]
 
 theorem ediv_le_ediv_iff_of_dvd_of_pos_of_neg {a b c d : Int} (hb : 0 < b) (hd : d < 0)
     (hba : b ∣ a) (hdc : d ∣ c) : a / b ≤ c / d ↔ c * b ≤ d * a := by
@@ -1713,12 +1713,12 @@ theorem ediv_le_ediv_iff_of_dvd_of_neg_of_pos {a b c d : Int} (hb : b < 0) (hd :
 theorem ediv_le_ediv_iff_of_dvd_of_neg_of_neg {a b c d : Int} (hb : b < 0) (hd : d < 0)
     (hba : b ∣ a) (hdc : d ∣ c) : a / b ≤ c / d ↔ d * a ≤ c * b := by
   obtain ⟨⟨x, rfl⟩, y, rfl⟩ := hba, hdc
-  simp [*, Int.ne_of_lt, Int.ne_of_gt, d.mul_assoc, b.mul_comm]
+  simp [*, Int.ne_of_lt, d.mul_assoc, b.mul_comm]
 
 theorem ediv_lt_ediv_iff_of_dvd_of_pos {a b c d : Int} (hb : 0 < b) (hd : 0 < d) (hba : b ∣ a)
     (hdc : d ∣ c) : a / b < c / d ↔ d * a < c * b := by
   obtain ⟨⟨x, rfl⟩, y, rfl⟩ := hba, hdc
-  simp [*, Int.ne_of_lt, Int.ne_of_gt, d.mul_assoc, b.mul_comm]
+  simp [*, Int.ne_of_gt, d.mul_assoc, b.mul_comm]
 
 theorem ediv_lt_ediv_iff_of_dvd_of_pos_of_neg {a b c d : Int} (hb : 0 < b) (hd : d < 0)
     (hba : b ∣ a) (hdc : d ∣ c) : a / b < c / d ↔ c * b < d * a := by
@@ -1733,7 +1733,7 @@ theorem ediv_lt_ediv_iff_of_dvd_of_neg_of_pos {a b c d : Int} (hb : b < 0) (hd :
 theorem ediv_lt_ediv_iff_of_dvd_of_neg_of_neg {a b c d : Int} (hb : b < 0) (hd : d < 0)
     (hba : b ∣ a) (hdc : d ∣ c) : a / b < c / d ↔ d * a < c * b := by
   obtain ⟨⟨x, rfl⟩, y, rfl⟩ := hba, hdc
-  simp [*, Int.ne_of_lt, Int.ne_of_gt, d.mul_assoc, b.mul_comm]
+  simp [*, Int.ne_of_lt, d.mul_assoc, b.mul_comm]
 
 /-! ### `tdiv` and ordering -/
 
@@ -2446,7 +2446,7 @@ theorem lt_mul_fdiv_self_add {x k : Int} (h : 0 < k) : x < k * (x.fdiv k) + k :=
 
 @[simp]
 theorem emod_bmod (x : Int) (n : Nat) : Int.bmod (x%n) n = Int.bmod x n := by
-  simp [bmod, Int.emod_emod]
+  simp [bmod]
 
 @[deprecated emod_bmod (since := "2025-04-11")]
 theorem emod_bmod_congr (x : Int) (n : Nat) : Int.bmod (x%n) n = Int.bmod x n :=
@@ -2987,7 +2987,7 @@ theorem self_le_ediv_of_nonpos_of_nonneg {x y : Int} (hx : x ≤ 0) (hy : 0 ≤
   · simp [hx', zero_ediv]
   · by_cases hy : y = 0
     · simp [hy]; omega
-    · simp only [ge_iff_le, Int.le_ediv_iff_mul_le (c := y) (a := x) (b := x) (by omega),
+    · simp only [Int.le_ediv_iff_mul_le (c := y) (a := x) (b := x) (by omega),
         show (x * y ≤ x) = (x * y ≤ x * 1) by rw [Int.mul_one], Int.mul_one]
       apply Int.mul_le_mul_of_nonpos_left (a := x) (b := y) (c  := (1 : Int)) (by omega) (by omega)
 

src/Init/Data/Int/Gcd.lean

@@ -631,7 +631,7 @@ theorem lcm_mul_left_dvd_mul_lcm (k m n : Nat) : lcm (m * n) k ∣ lcm m k * lcm
   simpa [lcm_comm, Nat.mul_comm] using lcm_mul_right_dvd_mul_lcm _ _ _
 
 theorem lcm_dvd_mul_self_left_iff_dvd_mul {k n m : Nat} : lcm k n ∣ k * m ↔ n ∣ k * m := by
-  simp [← natAbs_dvd_natAbs, natAbs_mul, Nat.lcm_dvd_mul_self_left_iff_dvd_mul,
+  simp [Nat.lcm_dvd_mul_self_left_iff_dvd_mul,
     lcm_eq_natAbs_lcm_natAbs]
 
 theorem lcm_dvd_mul_self_right_iff_dvd_mul {k m n : Nat} : lcm n k ∣ m * k ↔ n ∣ m * k := by

src/Init/Data/Int/Lemmas.lean

@@ -454,7 +454,7 @@ theorem negOfNat_eq_subNatNat_zero (n) : negOfNat n = subNatNat 0 n := by cases
 theorem ofNat_mul_subNatNat (m n k : Nat) :
     m * subNatNat n k = subNatNat (m * n) (m * k) := by
   cases m with
-  | zero => simp [ofNat_zero, Int.zero_mul, Nat.zero_mul, subNatNat_self]
+  | zero => simp [Int.zero_mul, Nat.zero_mul, subNatNat_self]
   | succ m => cases n.lt_or_ge k with
     | inl h =>
       have h' : succ m * n < succ m * k := Nat.mul_lt_mul_of_pos_left h (Nat.succ_pos m)

src/Init/Data/Int/Linear.lean

@@ -23,6 +23,7 @@ namespace Int.Linear
 abbrev Var := Nat
 abbrev Context := Lean.RArray Int
 
+@[expose]
 def Var.denote (ctx : Context) (v : Var) : Int :=
   ctx.get v
 
@@ -36,6 +37,7 @@ inductive Expr where
   | mulR (a : Expr) (k : Int)
   deriving Inhabited, BEq
 
+@[expose]
 def Expr.denote (ctx : Context) : Expr → Int
   | .add a b  => Int.add (denote ctx a) (denote ctx b)
   | .sub a b  => Int.sub (denote ctx a) (denote ctx b)
@@ -50,6 +52,7 @@ inductive Poly where
   | add (k : Int) (v : Var) (p : Poly)
   deriving BEq
 
+@[expose]
 def Poly.denote (ctx : Context) (p : Poly) : Int :=
   match p with
   | .num k => k
@@ -59,6 +62,7 @@ def Poly.denote (ctx : Context) (p : Poly) : Int :=
 Similar to `Poly.denote`, but produces a denotation better for `simp +arith`.
 Remark: we used to convert `Poly` back into `Expr` to achieve that.
 -/
+@[expose]
 def Poly.denote' (ctx : Context) (p : Poly) : Int :=
   match p with
   | .num k => k
@@ -75,8 +79,8 @@ where
 theorem Poly.denote'_go_eq_denote (ctx : Context) (p : Poly) (r : Int) : denote'.go ctx r p = p.denote ctx + r := by
   induction r, p using denote'.go.induct ctx <;> simp [denote'.go, denote]
   next => rw [Int.add_comm]
-  next ih => simp [denote'.go] at ih; rw [ih]; ac_rfl
-  next ih => simp [denote'.go] at ih; rw [ih]; ac_rfl
+  next ih => simp at ih; rw [ih]; ac_rfl
+  next ih => simp at ih; rw [ih]; ac_rfl
 
 theorem Poly.denote'_eq_denote (ctx : Context) (p : Poly) : p.denote' ctx = p.denote ctx := by
   unfold denote' <;> split <;> simp [denote, denote'_go_eq_denote] <;> ac_rfl
@@ -84,11 +88,13 @@ theorem Poly.denote'_eq_denote (ctx : Context) (p : Poly) : p.denote' ctx = p.de
 theorem Poly.denote'_add (ctx : Context) (a : Int) (x : Var) (p : Poly) : (Poly.add a x p).denote' ctx = a * x.denote ctx + p.denote ctx := by
   simp [Poly.denote'_eq_denote, denote]
 
+@[expose]
 def Poly.addConst (p : Poly) (k : Int) : Poly :=
   match p with
   | .num k' => .num (k+k')
   | .add k' v' p => .add k' v' (addConst p k)
 
+@[expose]
 def Poly.insert (k : Int) (v : Var) (p : Poly) : Poly :=
   match p with
   | .num k' => .add k v (.num k')
@@ -104,16 +110,19 @@ def Poly.insert (k : Int) (v : Var) (p : Poly) : Poly :=
       .add k' v' (insert k v p)
 
 /-- Normalizes the given polynomial by fusing monomial and constants. -/
+@[expose]
 def Poly.norm (p : Poly) : Poly :=
   match p with
   | .num k => .num k
   | .add k v p => (norm p).insert k v
 
+@[expose]
 def Poly.append (p₁ p₂ : Poly) : Poly :=
   match p₁ with
   | .num k₁ => p₂.addConst k₁
   | .add k x p₁ => .add k x (append p₁ p₂)
 
+@[expose]
 def Poly.combine' (fuel : Nat) (p₁ p₂ : Poly) : Poly :=
   match fuel with
   | 0 => p₁.append p₂
@@ -133,10 +142,12 @@ def Poly.combine' (fuel : Nat) (p₁ p₂ : Poly) : Poly :=
     else
       .add a₂ x₂ (combine' fuel (.add a₁ x₁ p₁) p₂)
 
+@[expose]
 def Poly.combine (p₁ p₂ : Poly) : Poly :=
   combine' 100000000 p₁ p₂
 
 /-- Converts the given expression into a polynomial. -/
+@[expose]
 def Expr.toPoly' (e : Expr) : Poly :=
   go 1 e (.num 0)
 where
@@ -150,6 +161,7 @@ where
     | .neg a    => go (-coeff) a
 
 /-- Converts the given expression into a polynomial, and then normalizes it. -/
+@[expose]
 def Expr.norm (e : Expr) : Poly :=
   e.toPoly'.norm
 
@@ -159,6 +171,7 @@ Examples:
 - `cdiv 7 3` returns `3`
 - `cdiv (-7) 3` returns `-2`.
 -/
+@[expose]
 def cdiv (a b : Int) : Int :=
   -((-a)/b)
 
@@ -173,6 +186,7 @@ See theorem `cdiv_add_cmod`. We also have
 -b < cmod a b ≤ 0
 ```
 -/
+@[expose]
 def cmod (a b : Int) : Int :=
   -((-a)%b)
 
@@ -219,6 +233,7 @@ theorem cdiv_eq_div_of_divides {a b : Int} (h : a % b = 0) : a/b = cdiv a b := b
   next => rw [Int.mul_eq_mul_right_iff h] at this; assumption
 
 /-- Returns the constant of the given linear polynomial. -/
+@[expose]
 def Poly.getConst : Poly → Int
   | .num k => k
   | .add _ _ p => getConst p
@@ -230,6 +245,7 @@ Notes:
 - We only use this function with `k`s that divides all coefficients.
 - We use `cdiv` for the constant to implement the inequality tightening rule.
 -/
+@[expose]
 def Poly.div (k : Int) : Poly → Poly
   | .num k' => .num (cdiv k' k)
   | .add k' x p => .add (k'/k) x (div k p)
@@ -238,6 +254,7 @@ def Poly.div (k : Int) : Poly → Poly
 Returns `true` if `k` divides all coefficients and the constant of the given
 linear polynomial.
 -/
+@[expose]
 def Poly.divAll (k : Int) : Poly → Bool
   | .num k' => k' % k == 0
   | .add k' _ p => k' % k == 0 && divAll k p
@@ -245,6 +262,7 @@ def Poly.divAll (k : Int) : Poly → Bool
 /--
 Returns `true` if `k` divides all coefficients of the given linear polynomial.
 -/
+@[expose]
 def Poly.divCoeffs (k : Int) : Poly → Bool
   | .num _ => true
   | .add k' _ p => k' % k == 0 && divCoeffs k p
@@ -252,11 +270,13 @@ def Poly.divCoeffs (k : Int) : Poly → Bool
 /--
 `p.mul k` multiplies all coefficients and constant of the polynomial `p` by `k`.
 -/
+@[expose]
 def Poly.mul' (p : Poly) (k : Int) : Poly :=
   match p with
   | .num k' => .num (k*k')
   | .add k' v p => .add (k*k') v (mul' p k)
 
+@[expose]
 def Poly.mul (p : Poly) (k : Int) : Poly :=
   if k == 0 then
     .num 0
@@ -343,7 +363,7 @@ theorem Expr.denote_toPoly'_go (ctx : Context) (e : Expr) :
     simp [eq_of_beq h]
   | case2 k k' h =>
     simp only [toPoly'.go, h, cond_false]
-    simp [Var.denote]
+    simp
   | case3 k i => simp [toPoly'.go]
   | case4 k a b iha ihb => simp [toPoly'.go, iha, ihb]
   | case5 k a b iha ihb =>
@@ -351,7 +371,7 @@ theorem Expr.denote_toPoly'_go (ctx : Context) (e : Expr) :
     rw [Int.sub_eq_add_neg, ←Int.neg_mul, Int.add_assoc]
   | case6 k k' a h
   | case8 k a k' h =>
-    simp only [toPoly'.go, h, cond_false]
+    simp only [toPoly'.go, h]
     simp [eq_of_beq h]
   | case7 k a k' h ih =>
     simp only [toPoly'.go, h, cond_false]
@@ -383,9 +403,10 @@ attribute [local simp] Poly.denote'_eq_denote
 
 theorem Expr.eq_of_norm_eq (ctx : Context) (e : Expr) (p : Poly) (h : e.norm == p) : e.denote ctx = p.denote' ctx := by
   have h := congrArg (Poly.denote ctx) (eq_of_beq h)
-  simp [Poly.norm] at h
+  simp at h
   simp [*]
 
+@[expose]
 def norm_eq_cert (lhs rhs : Expr) (p : Poly) : Bool :=
   p == (lhs.sub rhs).norm
 
@@ -401,6 +422,7 @@ theorem norm_le (ctx : Context) (lhs rhs : Expr) (p : Poly) (h : norm_eq_cert lh
   · exact Int.sub_nonpos_of_le
   · exact Int.le_of_sub_nonpos
 
+@[expose]
 def norm_eq_var_cert (lhs rhs : Expr) (x y : Var) : Bool :=
   (lhs.sub rhs).norm == .add 1 x (.add (-1) y (.num 0))
 
@@ -411,6 +433,7 @@ theorem norm_eq_var (ctx : Context) (lhs rhs : Expr) (x y : Var) (h : norm_eq_va
   simp at h
   rw [←Int.sub_eq_zero, h, ← @Int.sub_eq_zero (Var.denote ctx x), Int.sub_eq_add_neg]
 
+@[expose]
 def norm_eq_var_const_cert (lhs rhs : Expr) (x : Var) (k : Int) : Bool :=
   (lhs.sub rhs).norm == .add 1 x (.num (-k))
 
@@ -429,6 +452,7 @@ private theorem mul_eq_zero_iff (a k : Int) (h₁ : k > 0) : k * a = 0 ↔ a = 0
 theorem norm_eq_coeff' (ctx : Context) (p p' : Poly) (k : Int) : p = p'.mul k → k > 0 → (p.denote ctx = 0 ↔ p'.denote ctx = 0) := by
   intro; subst p; intro h; simp [mul_eq_zero_iff, *]
 
+@[expose]
 def norm_eq_coeff_cert (lhs rhs : Expr) (p : Poly) (k : Int) : Bool :=
   (lhs.sub rhs).norm == p.mul k && k > 0
 
@@ -448,7 +472,7 @@ private theorem mul_le_zero_iff (a k : Int) (h₁ : k > 0) : k * a ≤ 0 ↔ a
     simp at h; assumption
 
 private theorem norm_le_coeff' (ctx : Context) (p p' : Poly) (k : Int) : p = p'.mul k → k > 0 → (p.denote ctx ≤ 0 ↔ p'.denote ctx ≤ 0) := by
-  simp [norm_eq_coeff_cert]
+  simp
   intro; subst p; intro h; simp [mul_le_zero_iff, *]
 
 theorem norm_le_coeff (ctx : Context) (lhs rhs : Expr) (p : Poly) (k : Int)
@@ -492,6 +516,7 @@ private theorem eq_of_norm_eq_of_divCoeffs {ctx : Context} {p₁ p₂ : Poly} {k
   apply mul_add_cmod_le_iff
   assumption
 
+@[expose]
 def norm_le_coeff_tight_cert (lhs rhs : Expr) (p : Poly) (k : Int) : Bool :=
   let p' := lhs.sub rhs |>.norm
   k > 0 && (p'.divCoeffs k && p == p'.div k)
@@ -502,11 +527,13 @@ theorem norm_le_coeff_tight (ctx : Context) (lhs rhs : Expr) (p : Poly) (k : Int
   rw [norm_le ctx lhs rhs (lhs.sub rhs).norm BEq.rfl, Poly.denote'_eq_denote]
   apply eq_of_norm_eq_of_divCoeffs
 
+@[expose]
 def Poly.isUnsatEq (p : Poly) : Bool :=
   match p with
   | .num k => k != 0
   | _ => false
 
+@[expose]
 def Poly.isValidEq (p : Poly) : Bool :=
   match p with
   | .num k => k == 0
@@ -530,11 +557,13 @@ theorem eq_eq_true (ctx : Context) (lhs rhs : Expr) : (lhs.sub rhs).norm.isValid
     rw [← Int.sub_eq_zero, h]
     assumption
 
+@[expose]
 def Poly.isUnsatLe (p : Poly) : Bool :=
   match p with
   | .num k => k > 0
   | _ => false
 
+@[expose]
 def Poly.isValidLe (p : Poly) : Bool :=
   match p with
   | .num k => k ≤ 0
@@ -595,6 +624,7 @@ private theorem poly_eq_zero_eq_false (ctx : Context) {p : Poly} {k : Int} : p.d
   have high := h₃
   exact contra h₂ low high this
 
+@[expose]
 def unsatEqDivCoeffCert (lhs rhs : Expr) (k : Int) : Bool :=
   let p := (lhs.sub rhs).norm
   p.divCoeffs k && k > 0 && cmod p.getConst k < 0
@@ -621,6 +651,7 @@ private theorem gcd_dvd_step {k a b x : Int} (h : k ∣ a*x + b) : gcd a k ∣ b
   have h₂ : gcd a k ∣ a*x := Int.dvd_trans (gcd_dvd_left a k) (Int.dvd_mul_right a x)
   exact Int.dvd_iff_dvd_of_dvd_add h₁ |>.mp h₂
 
+@[expose]
 def Poly.gcdCoeffs : Poly → Int → Int
   | .num _, k => k
   | .add k' _ p, k => gcdCoeffs p (gcd k' k)
@@ -631,6 +662,7 @@ theorem Poly.gcd_dvd_const {ctx : Context} {p : Poly} {k : Int} (h : k ∣ p.den
     rw [Int.add_comm] at h
     exact ih (gcd_dvd_step h)
 
+@[expose]
 def Poly.isUnsatDvd (k : Int) (p : Poly) : Bool :=
   p.getConst % p.gcdCoeffs k != 0
 
@@ -668,9 +700,11 @@ theorem dvd_eq_false (ctx : Context) (k : Int) (e : Expr) (h : e.norm.isUnsatDvd
   rw [norm_dvd ctx k e e.norm BEq.rfl]
   apply dvd_eq_false' ctx k e.norm h
 
+@[expose]
 def dvd_coeff_cert (k₁ : Int) (p₁ : Poly) (k₂ : Int) (p₂ : Poly) (k : Int) : Bool :=
   k != 0 && (k₁ == k*k₂ && p₁ == p₂.mul k)
 
+@[expose]
 def norm_dvd_gcd_cert (k₁ : Int) (e₁ : Expr) (k₂ : Int) (p₂ : Poly) (k : Int) : Bool :=
   dvd_coeff_cert k₁ e₁.norm k₂ p₂ k
 
@@ -702,6 +736,7 @@ private theorem dvd_gcd_of_dvd (d a x p : Int) (h : d ∣ a * x + p) : gcd d a
   rw [Int.mul_assoc, Int.mul_assoc, ← Int.mul_sub] at h
   exists k₁ * k - k₂ * x
 
+@[expose]
 def dvd_elim_cert (k₁ : Int) (p₁ : Poly) (k₂ : Int) (p₂ : Poly) : Bool :=
   match p₁ with
   | .add a _ p => k₂ == gcd k₁ a && p₂ == p
@@ -764,6 +799,7 @@ private theorem dvd_solve_elim' {x : Int} {d₁ a₁ p₁ : Int} {d₂ a₂ p₂
  rw [h₃, h₄, Int.mul_assoc, Int.mul_assoc, ←Int.mul_sub] at this
  exact ⟨k₄ * k₁ - k₃ * k₂, this⟩
 
+@[expose]
 def dvd_solve_combine_cert (d₁ : Int) (p₁ : Poly) (d₂ : Int) (p₂ : Poly) (d : Int) (p : Poly) (g α β : Int) : Bool :=
   match p₁, p₂ with
   | .add a₁ x₁ p₁, .add a₂ x₂ p₂ =>
@@ -779,12 +815,13 @@ theorem dvd_solve_combine (ctx : Context) (d₁ : Int) (p₁ : Poly) (d₂ : Int
   split <;> simp
   next a₁ x₁ p₁ a₂ x₂ p₂ =>
   intro _ hg hd hp; subst x₁ p
-  simp [Poly.denote'_add]
+  simp
   intro h₁ h₂
   rw [Int.add_comm] at h₁ h₂
   rw [Int.add_comm _ (g * x₂.denote ctx), Int.add_left_comm, ← Int.add_assoc, hd]
   exact dvd_solve_combine' hg.symm h₁ h₂
 
+@[expose]
 def dvd_solve_elim_cert (d₁ : Int) (p₁ : Poly) (d₂ : Int) (p₂ : Poly) (d : Int) (p : Poly) : Bool :=
   match p₁, p₂ with
   | .add a₁ x₁ p₁, .add a₂ x₂ p₂ =>
@@ -816,6 +853,7 @@ theorem le_norm (ctx : Context) (p₁ p₂ : Poly) (h : p₁.norm == p₂) : p
   simp at h
   simp [*]
 
+@[expose]
 def le_coeff_cert (p₁ p₂ : Poly) (k : Int) : Bool :=
   k > 0 && (p₁.divCoeffs k && p₂ == p₁.div k)
 
@@ -824,6 +862,7 @@ theorem le_coeff (ctx : Context) (p₁ p₂ : Poly) (k : Int) : le_coeff_cert p
   intro h₁ h₂ h₃
   exact eq_of_norm_eq_of_divCoeffs h₁ h₂ h₃ |>.mp
 
+@[expose]
 def le_neg_cert (p₁ p₂ : Poly) : Bool :=
   p₂ == (p₁.mul (-1) |>.addConst 1)
 
@@ -834,11 +873,13 @@ theorem le_neg (ctx : Context) (p₁ p₂ : Poly) : le_neg_cert p₁ p₂ → ¬
   simp at h
   exact h
 
+@[expose]
 def Poly.leadCoeff (p : Poly) : Int :=
   match p with
   | .add a _ _ => a
   | _ => 1
 
+@[expose]
 def le_combine_cert (p₁ p₂ p₃ : Poly) : Bool :=
   let a₁ := p₁.leadCoeff.natAbs
   let a₂ := p₂.leadCoeff.natAbs
@@ -854,6 +895,7 @@ theorem le_combine (ctx : Context) (p₁ p₂ p₃ : Poly)
   · rw [← Int.zero_mul (Poly.denote ctx p₂)]; apply Int.mul_le_mul_of_nonpos_right <;> simp [*]
   · rw [← Int.zero_mul (Poly.denote ctx p₁)]; apply Int.mul_le_mul_of_nonpos_right <;> simp [*]
 
+@[expose]
 def le_combine_coeff_cert (p₁ p₂ p₃ : Poly) (k : Int) : Bool :=
   let a₁ := p₁.leadCoeff.natAbs
   let a₂ := p₂.leadCoeff.natAbs
@@ -883,6 +925,7 @@ theorem eq_norm (ctx : Context) (p₁ p₂ : Poly) (h : p₁.norm == p₂) : p
   simp at h
   simp [*]
 
+@[expose]
 def eq_coeff_cert (p p' : Poly) (k : Int) : Bool :=
   p == p'.mul k && k > 0
 
@@ -893,6 +936,7 @@ theorem eq_coeff (ctx : Context) (p p' : Poly) (k : Int) : eq_coeff_cert p p' k
 theorem eq_unsat (ctx : Context) (p : Poly) : p.isUnsatEq → p.denote' ctx = 0 → False := by
   simp [Poly.isUnsatEq] <;> split <;> simp
 
+@[expose]
 def eq_unsat_coeff_cert (p : Poly) (k : Int) : Bool :=
   p.divCoeffs k && k > 0 && cmod p.getConst k < 0
 
@@ -902,6 +946,7 @@ theorem eq_unsat_coeff (ctx : Context) (p : Poly) (k : Int) : eq_unsat_coeff_cer
   have h := poly_eq_zero_eq_false ctx h₁ h₂ h₃; clear h₁ h₂ h₃
   simp [h]
 
+@[expose]
 def Poly.coeff (p : Poly) (x : Var) : Int :=
   match p with
   | .add a y p => bif x == y then a else coeff p x
@@ -916,7 +961,8 @@ private theorem dvd_of_eq' {a x p : Int} : a*x + p = 0 → a ∣ p := by
   rw [Int.mul_comm, ← Int.neg_mul, Eq.comm, Int.mul_comm] at h
   exact ⟨-x, h⟩
 
-private def abs (x : Int) : Int :=
+@[expose]
+def abs (x : Int) : Int :=
   Int.ofNat x.natAbs
 
 private theorem abs_dvd {a p : Int} (h : a ∣ p) : abs a ∣ p := by
@@ -924,6 +970,7 @@ private theorem abs_dvd {a p : Int} (h : a ∣ p) : abs a ∣ p := by
   · simp at h; assumption
   · simp [Int.negSucc_eq] at h; assumption
 
+@[expose]
 def dvd_of_eq_cert (x : Var) (p₁ : Poly) (d₂ : Int) (p₂ : Poly) : Bool :=
   let a := p₁.coeff x
   d₂ == abs a && p₂ == p₁.insert (-a) x
@@ -950,6 +997,7 @@ private theorem eq_dvd_subst' {a x p d b q : Int} : a*x + p = 0 → d ∣ b*x +
   rw [← Int.mul_assoc] at h
   exact ⟨z, h⟩
 
+@[expose]
 def eq_dvd_subst_cert (x : Var) (p₁ : Poly) (d₂ : Int) (p₂ : Poly) (d₃ : Int) (p₃ : Poly) : Bool :=
   let a := p₁.coeff x
   let b := p₂.coeff x
@@ -979,6 +1027,7 @@ theorem eq_dvd_subst (ctx : Context) (x : Var) (p₁ : Poly) (d₂ : Int) (p₂
   apply abs_dvd
   simp [this, Int.neg_mul]
 
+@[expose]
 def eq_eq_subst_cert (x : Var) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly) : Bool :=
   let a := p₁.coeff x
   let b := p₂.coeff x
@@ -991,6 +1040,7 @@ theorem eq_eq_subst (ctx : Context) (x : Var) (p₁ : Poly) (p₂ : Poly) (p₃
   intro h₁ h₂
   simp [*]
 
+@[expose]
 def eq_le_subst_nonneg_cert (x : Var) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly) : Bool :=
   let a := p₁.coeff x
   let b := p₂.coeff x
@@ -1006,6 +1056,7 @@ theorem eq_le_subst_nonneg (ctx : Context) (x : Var) (p₁ : Poly) (p₂ : Poly)
   simp at h₂
   simp [*]
 
+@[expose]
 def eq_le_subst_nonpos_cert (x : Var) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly) : Bool :=
   let a := p₁.coeff x
   let b := p₂.coeff x
@@ -1022,6 +1073,7 @@ theorem eq_le_subst_nonpos (ctx : Context) (x : Var) (p₁ : Poly) (p₂ : Poly)
   rw [Int.mul_comm]
   assumption
 
+@[expose]
 def eq_of_core_cert (p₁ : Poly) (p₂ : Poly) (p₃ : Poly) : Bool :=
   p₃ == p₁.combine (p₂.mul (-1))
 
@@ -1031,6 +1083,7 @@ theorem eq_of_core (ctx : Context) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly)
   intro; subst p₃; simp
   intro h; rw [h, Int.add_neg_eq_sub, Int.sub_self]
 
+@[expose]
 def Poly.isUnsatDiseq (p : Poly) : Bool :=
   match p with
   | .num 0 => true
@@ -1047,11 +1100,12 @@ theorem diseq_coeff (ctx : Context) (p p' : Poly) (k : Int) : eq_coeff_cert p p'
   intro _ _; simp [mul_eq_zero_iff, *]
 
 theorem diseq_neg (ctx : Context) (p p' : Poly) : p' == p.mul (-1) → p.denote' ctx ≠ 0 → p'.denote' ctx ≠ 0 := by
-  simp; intro _ _; simp [mul_eq_zero_iff, *]
+  simp; intro _ _; simp [*]
 
 theorem diseq_unsat (ctx : Context) (p : Poly) : p.isUnsatDiseq → p.denote' ctx ≠ 0 → False := by
   simp [Poly.isUnsatDiseq] <;> split <;> simp
 
+@[expose]
 def diseq_eq_subst_cert (x : Var) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly) : Bool :=
   let a := p₁.coeff x
   let b := p₂.coeff x
@@ -1071,6 +1125,7 @@ theorem diseq_of_core (ctx : Context) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly)
   intro h; rw [← Int.sub_eq_zero] at h
   rw [Int.add_neg_eq_sub]; assumption
 
+@[expose]
 def eq_of_le_ge_cert (p₁ p₂ : Poly) : Bool :=
   p₂ == p₁.mul (-1)
 
@@ -1081,6 +1136,7 @@ theorem eq_of_le_ge (ctx : Context) (p₁ : Poly) (p₂ : Poly)
   intro h₁ h₂
   simp [Int.eq_iff_le_and_ge, *]
 
+@[expose]
 def le_of_le_diseq_cert (p₁ : Poly) (p₂ : Poly) (p₃ : Poly) : Bool :=
   -- Remark: we can generate two different certificates in the future, and avoid the `||` in the certificate.
   (p₂ == p₁ || p₂ == p₁.mul (-1)) &&
@@ -1095,6 +1151,7 @@ theorem le_of_le_diseq (ctx : Context) (p₁ : Poly) (p₂ : Poly) (p₃ : Poly)
     next h => have := Int.lt_of_le_of_lt h₁ h; simp at this
   intro h; cases h <;> intro <;> subst p₂ p₃ <;> simp <;> apply this
 
+@[expose]
 def diseq_split_cert (p₁ p₂ p₃ : Poly) : Bool :=
   p₂ == p₁.addConst 1 &&
   p₃ == (p₁.mul (-1)).addConst 1
@@ -1113,6 +1170,7 @@ theorem diseq_split_resolve (ctx : Context) (p₁ p₂ p₃ : Poly)
   intro h₁ h₂ h₃
   exact (diseq_split ctx p₁ p₂ p₃ h₁ h₂).resolve_left h₃
 
+@[expose]
 def OrOver (n : Nat) (p : Nat → Prop) : Prop :=
   match n with
   | 0 => False
@@ -1127,6 +1185,7 @@ theorem orOver_resolve {n p} : OrOver (n+1) p → ¬ p n → OrOver n p := by
   · contradiction
   · assumption
 
+@[expose]
 def OrOver_cases_type (n : Nat) (p : Nat → Prop) : Prop :=
   match n with
   | 0 => p 0
@@ -1186,6 +1245,7 @@ private theorem cooper_dvd_left_core
   rw [this] at h₃
   exists k.toNat
 
+@[expose]
 def cooper_dvd_left_cert (p₁ p₂ p₃ : Poly) (d : Int) (n : Nat) : Bool :=
   p₁.casesOn (fun _ => false) fun a x _ =>
   p₂.casesOn (fun _ => false) fun b y _ =>
@@ -1194,11 +1254,13 @@ def cooper_dvd_left_cert (p₁ p₂ p₃ : Poly) (d : Int) (n : Nat) : Bool :=
    .and (a < 0)  <| .and (b > 0)  <|
    .and (d > 0)  <| n == Int.lcm a (a * d / Int.gcd (a * d) c)
 
+@[expose]
 def Poly.tail (p : Poly) : Poly :=
   match p with
   | .add _ _ p => p
   | _ => p
 
+@[expose]
 def cooper_dvd_left_split (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (k : Nat) : Prop :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1238,6 +1300,7 @@ theorem cooper_dvd_left (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (n : N
  simp only [denote'_addConst_eq]
  exact cooper_dvd_left_core ha hb hd h₁ h₂ h₃
 
+@[expose]
 def cooper_dvd_left_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (b : Int) (p' : Poly) : Bool :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1248,8 +1311,9 @@ def cooper_dvd_left_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (b : Int) (p' :
 theorem cooper_dvd_left_split_ineq (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (k : Nat) (b : Int) (p' : Poly)
     : cooper_dvd_left_split ctx p₁ p₂ p₃ d k → cooper_dvd_left_split_ineq_cert p₁ p₂ k b p' → p'.denote' ctx ≤ 0 := by
   simp [cooper_dvd_left_split_ineq_cert, cooper_dvd_left_split]
-  intros; subst p' b; simp [denote'_mul_combine_mul_addConst_eq]; assumption
+  intros; subst p' b; simp; assumption
 
+@[expose]
 def cooper_dvd_left_split_dvd1_cert (p₁ p' : Poly) (a : Int) (k : Int) : Bool :=
   a == p₁.leadCoeff && p' == p₁.tail.addConst k
 
@@ -1258,6 +1322,7 @@ theorem cooper_dvd_left_split_dvd1 (ctx : Context) (p₁ p₂ p₃ : Poly) (d :
   simp [cooper_dvd_left_split_dvd1_cert, cooper_dvd_left_split]
   intros; subst a p'; simp; assumption
 
+@[expose]
 def cooper_dvd_left_split_dvd2_cert (p₁ p₃ : Poly) (d : Int) (k : Nat) (d' : Int) (p' : Poly): Bool :=
   let p  := p₁.tail
   let s  := p₃.tail
@@ -1283,16 +1348,18 @@ private theorem cooper_left_core
   have h := cooper_dvd_left_core a_neg b_pos d_pos h₁ h₂ h₃
   simp only [Int.mul_one, gcd_zero, ofNat_natAbs_of_nonpos (Int.le_of_lt a_neg), Int.ediv_neg,
     Int.ediv_self (Int.ne_of_lt a_neg), Int.reduceNeg, lcm_neg_right, lcm_one,
-    Int.add_left_comm, Int.zero_mul, Int.mul_zero, Int.add_zero, Int.dvd_zero,
+    Int.zero_mul, Int.mul_zero, Int.add_zero, Int.dvd_zero,
     and_true] at h
   assumption
 
+@[expose]
 def cooper_left_cert (p₁ p₂ : Poly) (n : Nat) : Bool :=
   p₁.casesOn (fun _ => false) fun a x _ =>
   p₂.casesOn (fun _ => false) fun b y _ =>
    .and (x == y) <| .and (a < 0)  <| .and (b > 0)  <|
    n == a.natAbs
 
+@[expose]
 def cooper_left_split (ctx : Context) (p₁ p₂ : Poly) (k : Nat) : Prop :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1320,6 +1387,7 @@ theorem cooper_left (ctx : Context) (p₁ p₂ : Poly) (n : Nat)
  simp only [denote'_addConst_eq]
  assumption
 
+@[expose]
 def cooper_left_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (b : Int) (p' : Poly) : Bool :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1330,8 +1398,9 @@ def cooper_left_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (b : Int) (p' : Pol
 theorem cooper_left_split_ineq (ctx : Context) (p₁ p₂ : Poly) (k : Nat) (b : Int) (p' : Poly)
     : cooper_left_split ctx p₁ p₂ k → cooper_left_split_ineq_cert p₁ p₂ k b p' → p'.denote' ctx ≤ 0 := by
   simp [cooper_left_split_ineq_cert, cooper_left_split]
-  intros; subst p' b; simp [denote'_mul_combine_mul_addConst_eq]; assumption
+  intros; subst p' b; simp; assumption
 
+@[expose]
 def cooper_left_split_dvd_cert (p₁ p' : Poly) (a : Int) (k : Int) : Bool :=
   a == p₁.leadCoeff && p' == p₁.tail.addConst k
 
@@ -1353,7 +1422,7 @@ private theorem cooper_dvd_right_core
   have h₁'    : p ≤ (-a)*x := by rw [Int.neg_mul, ← Lean.Omega.Int.add_le_zero_iff_le_neg']; assumption
   have h₂'    : b * x ≤ -q := by rw [← Lean.Omega.Int.add_le_zero_iff_le_neg', Int.add_comm]; assumption
   have ⟨k, h₁, h₂, h₃, h₄, h₅⟩ := Int.cooper_resolution_dvd_right a_pos' b_pos d_pos |>.mp ⟨x, h₁', h₂', h₃⟩
-  simp only [Int.neg_mul, neg_gcd, lcm_neg_left, Int.mul_neg, Int.neg_neg, Int.neg_dvd] at *
+  simp only [Int.neg_mul, Int.mul_neg, Int.neg_neg] at *
   apply orOver_of_exists
   have hlt := ofNat_lt h₁ h₂
   replace h₃ := Int.add_le_add_right h₃ (-(a*q)); rw [Int.add_right_neg] at h₃
@@ -1363,8 +1432,9 @@ private theorem cooper_dvd_right_core
   have : -(c * k) + -(c * q) + b * s = -(c * q) + b * s + -(c * k) := by ac_rfl
   rw [this] at h₅; clear this
   exists k.toNat
-  simp only [hlt, true_and, and_true, cast_toNat h₁, h₃, h₄, h₅]
+  simp only [hlt, and_true, cast_toNat h₁, h₃, h₄, h₅]
 
+@[expose]
 def cooper_dvd_right_cert (p₁ p₂ p₃ : Poly) (d : Int) (n : Nat) : Bool :=
   p₁.casesOn (fun _ => false) fun a x _ =>
   p₂.casesOn (fun _ => false) fun b y _ =>
@@ -1373,6 +1443,7 @@ def cooper_dvd_right_cert (p₁ p₂ p₃ : Poly) (d : Int) (n : Nat) : Bool :=
    .and (a < 0)  <| .and (b > 0)  <|
    .and (d > 0)  <| n == Int.lcm b (b * d / Int.gcd (b * d) c)
 
+@[expose]
 def cooper_dvd_right_split (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (k : Nat) : Prop :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1402,9 +1473,10 @@ theorem cooper_dvd_right (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (n :
  intro h₁ h₂ h₃
  have := cooper_dvd_right_core ha hb hd h₁ h₂ h₃
  simp only [denote'_mul_combine_mul_addConst_eq]
- simp only [denote'_addConst_eq, ←Int.neg_mul]
+ simp only [denote'_addConst_eq]
  exact cooper_dvd_right_core ha hb hd h₁ h₂ h₃
 
+@[expose]
 def cooper_dvd_right_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (a : Int) (p' : Poly) : Bool :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1415,8 +1487,9 @@ def cooper_dvd_right_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (a : Int) (p'
 theorem cooper_dvd_right_split_ineq (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (k : Nat) (a : Int) (p' : Poly)
     : cooper_dvd_right_split ctx p₁ p₂ p₃ d k → cooper_dvd_right_split_ineq_cert p₁ p₂ k a p' → p'.denote' ctx ≤ 0 := by
   simp [cooper_dvd_right_split_ineq_cert, cooper_dvd_right_split]
-  intros; subst a p'; simp [denote'_mul_combine_mul_addConst_eq]; assumption
+  intros; subst a p'; simp; assumption
 
+@[expose]
 def cooper_dvd_right_split_dvd1_cert (p₂ p' : Poly) (b : Int) (k : Int) : Bool :=
   b == p₂.leadCoeff && p' == p₂.tail.addConst k
 
@@ -1425,6 +1498,7 @@ theorem cooper_dvd_right_split_dvd1 (ctx : Context) (p₁ p₂ p₃ : Poly) (d :
   simp [cooper_dvd_right_split_dvd1_cert, cooper_dvd_right_split]
   intros; subst b p'; simp; assumption
 
+@[expose]
 def cooper_dvd_right_split_dvd2_cert (p₂ p₃ : Poly) (d : Int) (k : Nat) (d' : Int) (p' : Poly): Bool :=
   let q  := p₂.tail
   let s  := p₃.tail
@@ -1448,17 +1522,19 @@ private theorem cooper_right_core
   have d_pos : (0 : Int) < 1 := by decide
   have h₃ : 1 ∣ 0*x + 0 := Int.one_dvd _
   have h := cooper_dvd_right_core a_neg b_pos d_pos h₁ h₂ h₃
-  simp only [Int.mul_one, gcd_zero, Int.natAbs_of_nonneg (Int.le_of_lt b_pos), Int.ediv_neg,
-    Int.ediv_self (Int.ne_of_gt b_pos), Int.reduceNeg, lcm_neg_right, lcm_one,
-    Int.add_left_comm, Int.zero_mul, Int.mul_zero, Int.add_zero, Int.dvd_zero,
+  simp only [Int.mul_one, gcd_zero, Int.natAbs_of_nonneg (Int.le_of_lt b_pos), 
+    Int.ediv_self (Int.ne_of_gt b_pos), lcm_one,
+    Int.zero_mul, Int.mul_zero, Int.add_zero, Int.dvd_zero,
     and_true, Int.neg_zero] at h
   assumption
 
+@[expose]
 def cooper_right_cert (p₁ p₂ : Poly) (n : Nat) : Bool :=
   p₁.casesOn (fun _ => false) fun a x _ =>
   p₂.casesOn (fun _ => false) fun b y _ =>
   .and (x == y) <| .and (a < 0)  <| .and (b > 0) <| n == b.natAbs
 
+@[expose]
 def cooper_right_split (ctx : Context) (p₁ p₂ : Poly) (k : Nat) : Prop :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1483,9 +1559,10 @@ theorem cooper_right (ctx : Context) (p₁ p₂ : Poly) (n : Nat)
  intro h₁ h₂
  have := cooper_right_core ha hb h₁ h₂
  simp only [denote'_mul_combine_mul_addConst_eq]
- simp only [denote'_addConst_eq, ←Int.neg_mul]
+ simp only [denote'_addConst_eq]
  assumption
 
+@[expose]
 def cooper_right_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (a : Int) (p' : Poly) : Bool :=
   let p  := p₁.tail
   let q  := p₂.tail
@@ -1496,8 +1573,9 @@ def cooper_right_split_ineq_cert (p₁ p₂ : Poly) (k : Int) (a : Int) (p' : Po
 theorem cooper_right_split_ineq (ctx : Context) (p₁ p₂ : Poly) (k : Nat) (a : Int) (p' : Poly)
     : cooper_right_split ctx p₁ p₂ k → cooper_right_split_ineq_cert p₁ p₂ k a p' → p'.denote' ctx ≤ 0 := by
   simp [cooper_right_split_ineq_cert, cooper_right_split]
-  intros; subst a p'; simp [denote'_mul_combine_mul_addConst_eq]; assumption
+  intros; subst a p'; simp; assumption
 
+@[expose]
 def cooper_right_split_dvd_cert (p₂ p' : Poly) (b : Int) (k : Int) : Bool :=
   b == p₂.leadCoeff && p' == p₂.tail.addConst k
 
@@ -1587,6 +1665,7 @@ abbrev Poly.casesOnAdd (p : Poly) (k : Int → Var → Poly → Bool) : Bool :=
 abbrev Poly.casesOnNum (p : Poly) (k : Int → Bool) : Bool :=
   p.casesOn k (fun _ _ _ => false)
 
+@[expose]
 def cooper_unsat_cert (p₁ p₂ p₃ : Poly) (d : Int) (α β : Int) : Bool :=
   p₁.casesOnAdd fun k₁ x p₁ =>
   p₂.casesOnAdd fun k₂ y p₂ =>
@@ -1603,7 +1682,7 @@ theorem cooper_unsat (ctx : Context) (p₁ p₂ p₃ : Poly) (d : Int) (α β :
    : cooper_unsat_cert p₁ p₂ p₃ d α β →
      p₁.denote' ctx ≤ 0 → p₂.denote' ctx ≤ 0 → d ∣ p₃.denote' ctx → False := by
   unfold cooper_unsat_cert <;> cases p₁ <;> cases p₂ <;> cases p₃ <;> simp only [Poly.casesOnAdd,
-    Bool.false_eq_true, Poly.denote'_add, mul_def, add_def, false_implies]
+    Bool.false_eq_true, Poly.denote'_add, false_implies]
   next k₁ x p₁ k₂ y p₂ c z p₃ =>
   cases p₁ <;> cases p₂ <;> cases p₃ <;> simp only [Poly.casesOnNum, Int.reduceNeg,
     Bool.and_eq_true, beq_iff_eq, decide_eq_true_eq, and_imp, Bool.false_eq_true,
@@ -1626,6 +1705,7 @@ theorem emod_nonneg (x y : Int) : y != 0 → -1 * (x % y) ≤ 0 := by
   simp at this
   assumption
 
+@[expose]
 def emod_le_cert (y n : Int) : Bool :=
   y != 0 && n == 1 - y.natAbs
 
@@ -1708,6 +1788,7 @@ private theorem eq_neg_addConst_add (ctx : Context) (p : Poly)
   rw [Int.add_right_neg]
   simp
 
+@[expose]
 def dvd_le_tight_cert (d : Int) (p₁ p₂ p₃ : Poly) : Bool :=
   let b₁ := p₁.getConst
   let b₂ := p₂.getConst
@@ -1728,6 +1809,7 @@ theorem dvd_le_tight (ctx : Context) (d : Int) (p₁ p₂ p₃ : Poly)
   simp only [Poly.denote'_eq_denote]
   exact dvd_le_tight' hd
 
+@[expose]
 def dvd_neg_le_tight_cert (d : Int) (p₁ p₂ p₃ : Poly) : Bool :=
   let b₁ := p₁.getConst
   let b₂ := p₂.getConst
@@ -1737,7 +1819,7 @@ def dvd_neg_le_tight_cert (d : Int) (p₁ p₂ p₃ : Poly) : Bool :=
   d > 0 && (p₂ == p.addConst b₂ && p₃ == p.addConst (b₁ - d*((b₁ - b₂)/d)))
 
 theorem Poly.mul_minus_one_getConst_eq (p : Poly) : (p.mul (-1)).getConst = -p.getConst := by
-  simp [Poly.mul, Poly.getConst]
+  simp [Poly.mul]
   induction p <;> simp [Poly.mul', Poly.getConst, *]
 
 theorem dvd_neg_le_tight (ctx : Context) (d : Int) (p₁ p₂ p₃ : Poly)
@@ -1764,6 +1846,7 @@ theorem le_norm_expr (ctx : Context) (lhs rhs : Expr) (p : Poly)
     : norm_eq_cert lhs rhs p → lhs.denote ctx ≤ rhs.denote ctx → p.denote' ctx ≤ 0 := by
   intro h₁ h₂; rwa [norm_le ctx lhs rhs p h₁] at h₂
 
+@[expose]
 def not_le_norm_expr_cert (lhs rhs : Expr) (p : Poly) : Bool :=
   p == (((lhs.sub rhs).norm).mul (-1)).addConst 1
 
@@ -1796,6 +1879,7 @@ theorem of_not_dvd (a b : Int) : a != 0 → ¬ (a ∣ b) → b % a > 0 := by
   simp [h₁] at h₂
   assumption
 
+@[expose]
 def le_of_le_cert (p q : Poly) (k : Nat) : Bool :=
   q == p.addConst (- k)
 
@@ -1806,6 +1890,7 @@ theorem le_of_le (ctx : Context) (p q : Poly) (k : Nat)
   simp [Lean.Omega.Int.add_le_zero_iff_le_neg']
   exact Int.le_trans h (Int.ofNat_zero_le _)
 
+@[expose]
 def not_le_of_le_cert (p q : Poly) (k : Nat) : Bool :=
   q == (p.mul (-1)).addConst (1 + k)
 
@@ -1815,10 +1900,11 @@ theorem not_le_of_le (ctx : Context) (p q : Poly) (k : Nat)
   intro h
   apply Int.pos_of_neg_neg
   apply Int.lt_of_add_one_le
-  simp [Int.neg_add, Int.neg_sub]
+  simp [Int.neg_add]
   rw [← Int.add_assoc, ← Int.add_assoc, Int.add_neg_cancel_right, Lean.Omega.Int.add_le_zero_iff_le_neg']
   simp; exact Int.le_trans h (Int.ofNat_zero_le _)
 
+@[expose]
 def eq_def_cert (x : Var) (xPoly : Poly) (p : Poly) : Bool :=
   p == .add (-1) x xPoly
 
@@ -1827,6 +1913,7 @@ theorem eq_def (ctx : Context) (x : Var) (xPoly : Poly) (p : Poly)
   simp [eq_def_cert]; intro _ h; subst p; simp [h]
   rw [← Int.sub_eq_add_neg, Int.sub_self]
 
+@[expose]
 def eq_def'_cert (x : Var) (e : Expr) (p : Poly) : Bool :=
   p == .add (-1) x e.norm
 

src/Init/Data/Int/OfNat.lean

@@ -19,6 +19,7 @@ We use them to implement the arithmetic theories in `grind`
 
 abbrev Var := Nat
 abbrev Context := Lean.RArray Nat
+@[expose]
 def Var.denote (ctx : Context) (v : Var) : Nat :=
   ctx.get v
 
@@ -31,6 +32,7 @@ inductive Expr where
   | mod  (a b : Expr)
   deriving BEq
 
+@[expose]
 def Expr.denote (ctx : Context) : Expr → Nat
   | .num k    => k
   | .var v    => v.denote ctx
@@ -39,6 +41,7 @@ def Expr.denote (ctx : Context) : Expr → Nat
   | .div a b  => Nat.div (denote ctx a) (denote ctx b)
   | .mod a b  => Nat.mod (denote ctx a) (denote ctx b)
 
+@[expose]
 def Expr.denoteAsInt (ctx : Context) : Expr → Int
   | .num k    => Int.ofNat k
   | .var v    => Int.ofNat (v.denote ctx)
@@ -48,7 +51,7 @@ def Expr.denoteAsInt (ctx : Context) : Expr → Int
   | .mod a b  => Int.emod (denoteAsInt ctx a) (denoteAsInt ctx b)
 
 theorem Expr.denoteAsInt_eq (ctx : Context) (e : Expr) : e.denoteAsInt ctx = e.denote ctx := by
-  induction e <;> simp [denote, denoteAsInt, Int.natCast_ediv, *] <;> rfl
+  induction e <;> simp [denote, denoteAsInt, *] <;> rfl
 
 theorem Expr.eq_denoteAsInt (ctx : Context) (e : Expr) : e.denote ctx = e.denoteAsInt ctx := by
   apply Eq.symm; apply denoteAsInt_eq

src/Init/Data/Int/Order.lean

@@ -448,7 +448,7 @@ protected theorem le_max_left (a b : Int) : a ≤ max a b := by rw [Int.max_def]
 protected theorem le_max_right (a b : Int) : b ≤ max a b := Int.max_comm .. ▸ Int.le_max_left ..
 
 protected theorem max_eq_right {a b : Int} (h : a ≤ b) : max a b = b := by
-  simp [Int.max_def, h, Int.not_lt.2 h]
+  simp [Int.max_def, h]
 
 protected theorem max_eq_left {a b : Int} (h : b ≤ a) : max a b = a := by
   rw [← Int.max_comm b a]; exact Int.max_eq_right h

src/Init/Data/Iterators.lean

@@ -0,0 +1,19 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Basic
+import Init.Data.Iterators.PostconditionMonad
+import Init.Data.Iterators.Consumers
+import Init.Data.Iterators.Lemmas
+import Init.Data.Iterators.Internal
+
+/-!
+# Iterators
+
+See `Std.Data.Iterators` for an overview over the iterator API.
+-/

src/Init/Data/Iterators/Basic.lean

@@ -3,6 +3,8 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
 import Init.Core
 import Init.Classical
@@ -31,7 +33,7 @@ See `Std.Data.Iterators.Producers` for ways to iterate over common data structur
 By convention, the monadic iterator associated with an object can be obtained via dot notation.
 For example, `List.iterM IO` creates an iterator over a list in the monad `IO`.
 
-See `Std.Data.Iterators.Consumers` for ways to use an iterator. For example, `it.toList` will
+See `Init.Data.Iterators.Consumers` for ways to use an iterator. For example, `it.toList` will
 convert a provably finite iterator `it` into a list and `it.allowNontermination.toList` will
 do so even if finiteness cannot be proved. It is also always possible to manually iterate using
 `it.step`, relying on the termination measures `it.finitelyManySteps` and `it.finitelyManySkips`.
@@ -75,7 +77,7 @@ See `Std.Data.Iterators.Producers` for ways to iterate over common data structur
 By convention, the monadic iterator associated with an object can be obtained via dot notation.
 For example, `List.iterM IO` creates an iterator over a list in the monad `IO`.
 
-See `Std.Data.Iterators.Consumers` for ways to use an iterator. For example, `it.toList` will
+See `Init.Data.Iterators.Consumers` for ways to use an iterator. For example, `it.toList` will
 convert a provably finite iterator `it` into a list and `it.allowNontermination.toList` will
 do so even if finiteness cannot be proved. It is also always possible to manually iterate using
 `it.step`, relying on the termination measures `it.finitelyManySteps` and `it.finitelyManySkips`.
@@ -111,12 +113,14 @@ structure Iter {α : Type w} (β : Type w) where
 Converts a pure iterator (`Iter β`) into a monadic iterator (`IterM Id β`) in the
 identity monad `Id`.
 -/
+@[expose]
 def Iter.toIterM {α : Type w} {β : Type w} (it : Iter (α := α) β) : IterM (α := α) Id β :=
   ⟨it.internalState⟩
 
 /--
 Converts a monadic iterator (`IterM Id β`) over `Id` into a pure iterator (`Iter β`).
 -/
+@[expose]
 def IterM.toIter {α : Type w} {β : Type w} (it : IterM (α := α) Id β) : Iter (α := α) β :=
   ⟨it.internalState⟩
 
@@ -170,6 +174,7 @@ inductive IterStep (α β) where
 Returns the succeeding iterator stored in an iterator step or `none` if the step is `.done`
 and the iterator has finished.
 -/
+@[expose]
 def IterStep.successor : IterStep α β → Option α
   | .yield it _ => some it
   | .skip it => some it
@@ -179,7 +184,7 @@ def IterStep.successor : IterStep α β → Option α
 If present, applies `f` to the iterator of an `IterStep` and replaces the iterator
 with the result of the application of `f`.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def IterStep.mapIterator {α' : Type u'} (f : α → α') : IterStep α β → IterStep α' β
   | .yield it out => .yield (f it) out
   | .skip it => .skip (f it)
@@ -224,12 +229,13 @@ of another state. Having this proof bundled up with the step is important for te
 
 See `IterM.Step` and `Iter.Step` for the concrete choice of the plausibility predicate.
 -/
+@[expose]
 def PlausibleIterStep (IsPlausibleStep : IterStep α β → Prop) := Subtype IsPlausibleStep
 
 /--
 Match pattern for the `yield` case. See also `IterStep.yield`.
 -/
-@[match_pattern, simp]
+@[match_pattern, simp, expose]
 def PlausibleIterStep.yield {IsPlausibleStep : IterStep α β → Prop}
     (it' : α) (out : β) (h : IsPlausibleStep (.yield it' out)) :
     PlausibleIterStep IsPlausibleStep :=
@@ -238,7 +244,7 @@ def PlausibleIterStep.yield {IsPlausibleStep : IterStep α β → Prop}
 /--
 Match pattern for the `skip` case. See also `IterStep.skip`.
 -/
-@[match_pattern, simp]
+@[match_pattern, simp, expose]
 def PlausibleIterStep.skip {IsPlausibleStep : IterStep α β → Prop}
     (it' : α) (h : IsPlausibleStep (.skip it')) : PlausibleIterStep IsPlausibleStep :=
   ⟨.skip it', h⟩
@@ -246,7 +252,7 @@ def PlausibleIterStep.skip {IsPlausibleStep : IterStep α β → Prop}
 /--
 Match pattern for the `done` case. See also `IterStep.done`.
 -/
-@[match_pattern, simp]
+@[match_pattern, simp, expose]
 def PlausibleIterStep.done {IsPlausibleStep : IterStep α β → Prop}
     (h : IsPlausibleStep .done) : PlausibleIterStep IsPlausibleStep :=
   ⟨.done, h⟩
@@ -283,7 +289,7 @@ section Monadic
 /--
 Converts wraps the state of an iterator into an `IterM` object.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def toIterM {α : Type w} (it : α) (m : Type w → Type w') (β : Type w) :
     IterM (α := α) m β :=
   ⟨it⟩
@@ -302,6 +308,7 @@ theorem internalState_toIterM {α m β} (it : α) :
 Asserts that certain step is plausibly the successor of a given iterator. What "plausible" means
 is up to the `Iterator` instance but it should be strong enough to allow termination proofs.
 -/
+@[expose]
 abbrev IterM.IsPlausibleStep {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β] :
     IterM (α := α) m β → IterStep (IterM (α := α) m β) β → Prop :=
   Iterator.IsPlausibleStep (α := α) (m := m)
@@ -310,6 +317,7 @@ abbrev IterM.IsPlausibleStep {α : Type w} {m : Type w → Type w'} {β : Type w
 The type of the step object returned by `IterM.step`, containing an `IterStep`
 and a proof that this is a plausible step for the given iterator.
 -/
+@[expose]
 abbrev IterM.Step {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     (it : IterM (α := α) m β) :=
   PlausibleIterStep it.IsPlausibleStep
@@ -318,6 +326,7 @@ abbrev IterM.Step {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator
 Asserts that a certain output value could plausibly be emitted by the given iterator in its next
 step.
 -/
+@[expose]
 def IterM.IsPlausibleOutput {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     (it : IterM (α := α) m β) (out : β) : Prop :=
   ∃ it', it.IsPlausibleStep (.yield it' out)
@@ -326,6 +335,7 @@ def IterM.IsPlausibleOutput {α : Type w} {m : Type w → Type w'} {β : Type w}
 Asserts that a certain iterator `it'` could plausibly be the directly succeeding iterator of another
 given iterator `it`.
 -/
+@[expose]
 def IterM.IsPlausibleSuccessorOf {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     (it' it : IterM (α := α) m β) : Prop :=
   ∃ step, step.successor = some it' ∧ it.IsPlausibleStep step
@@ -334,6 +344,7 @@ def IterM.IsPlausibleSuccessorOf {α : Type w} {m : Type w → Type w'} {β : Ty
 Asserts that a certain iterator `it'` could plausibly be the directly succeeding iterator of another
 given iterator `it` while no value is emitted (see `IterStep.skip`).
 -/
+@[expose]
 def IterM.IsPlausibleSkipSuccessorOf {α : Type w} {m : Type w → Type w'} {β : Type w}
     [Iterator α m β] (it' it : IterM (α := α) m β) : Prop :=
   it.IsPlausibleStep (.skip it')
@@ -356,14 +367,27 @@ section Pure
 Asserts that certain step is plausibly the successor of a given iterator. What "plausible" means
 is up to the `Iterator` instance but it should be strong enough to allow termination proofs.
 -/
+@[expose]
 def Iter.IsPlausibleStep {α : Type w} {β : Type w} [Iterator α Id β]
     (it : Iter (α := α) β) (step : IterStep (Iter (α := α) β) β) : Prop :=
   it.toIterM.IsPlausibleStep (step.mapIterator Iter.toIterM)
 
+/--
+Asserts that a certain iterator `it` could plausibly yield the value `out` after an arbitrary
+number of steps.
+-/
+inductive IterM.IsPlausibleIndirectOutput {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    : IterM (α := α) m β → β → Prop where
+  | direct {it : IterM (α := α) m β} {out : β} : it.IsPlausibleOutput out →
+      it.IsPlausibleIndirectOutput out
+  | indirect {it it' : IterM (α := α) m β} {out : β} : it'.IsPlausibleSuccessorOf it →
+      it'.IsPlausibleIndirectOutput out → it.IsPlausibleIndirectOutput out
+
 /--
 The type of the step object returned by `Iter.step`, containing an `IterStep`
 and a proof that this is a plausible step for the given iterator.
 -/
+@[expose]
 def Iter.Step {α : Type w} {β : Type w} [Iterator α Id β] (it : Iter (α := α) β) :=
   PlausibleIterStep (Iter.IsPlausibleStep it)
 
@@ -378,7 +402,7 @@ def Iter.Step.toMonadic {α : Type w} {β : Type w} [Iterator α Id β] {it : It
 /--
 Converts an `IterM.Step` into an `Iter.Step`.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def IterM.Step.toPure {α : Type w} {β : Type w} [Iterator α Id β] {it : IterM (α := α) Id β}
     (step : it.Step) : it.toIter.Step :=
   ⟨step.val.mapIterator IterM.toIter, (by simp [Iter.IsPlausibleStep, step.property])⟩
@@ -402,6 +426,7 @@ theorem IterM.Step.toPure_done {α β : Type w} [Iterator α Id β] {it : IterM
 Asserts that a certain output value could plausibly be emitted by the given iterator in its next
 step.
 -/
+@[expose]
 def Iter.IsPlausibleOutput {α : Type w} {β : Type w} [Iterator α Id β]
     (it : Iter (α := α) β) (out : β) : Prop :=
   it.toIterM.IsPlausibleOutput out
@@ -410,10 +435,43 @@ def Iter.IsPlausibleOutput {α : Type w} {β : Type w} [Iterator α Id β]
 Asserts that a certain iterator `it'` could plausibly be the directly succeeding iterator of another
 given iterator `it`.
 -/
+@[expose]
 def Iter.IsPlausibleSuccessorOf {α : Type w} {β : Type w} [Iterator α Id β]
     (it' it : Iter (α := α) β) : Prop :=
   it'.toIterM.IsPlausibleSuccessorOf it.toIterM
 
+/--
+Asserts that a certain iterator `it` could plausibly yield the value `out` after an arbitrary
+number of steps.
+-/
+inductive Iter.IsPlausibleIndirectOutput {α β : Type w} [Iterator α Id β] :
+    Iter (α := α) β → β → Prop where
+  | direct {it : Iter (α := α) β} {out : β} : it.IsPlausibleOutput out →
+      it.IsPlausibleIndirectOutput out
+  | indirect {it it' : Iter (α := α) β} {out : β} : it'.IsPlausibleSuccessorOf it →
+      it'.IsPlausibleIndirectOutput out → it.IsPlausibleIndirectOutput out
+
+theorem Iter.isPlausibleIndirectOutput_iff_isPlausibleIndirectOutput_toIterM {α β : Type w}
+    [Iterator α Id β] {it : Iter (α := α) β} {out : β} :
+    it.IsPlausibleIndirectOutput out ↔ it.toIterM.IsPlausibleIndirectOutput out := by
+  constructor
+  · intro h
+    induction h with
+    | direct h =>
+      exact .direct h
+    | indirect h _ ih =>
+      exact .indirect h ih
+  · intro h
+    rw [← Iter.toIter_toIterM (it := it)]
+    generalize it.toIterM = it at ⊢ h
+    induction h with
+    | direct h =>
+      exact .direct h
+    | indirect h h' ih =>
+      rename_i it it' out
+      replace h : it'.toIter.IsPlausibleSuccessorOf it.toIter := h
+      exact .indirect (α := α) h ih
+
 /--
 Asserts that a certain iterator `it'` could plausibly be the directly succeeding iterator of another
 given iterator `it` while no value is emitted (see `IterStep.skip`).
@@ -427,7 +485,7 @@ Makes a single step with the given iterator `it`, potentially emitting a value a
 succeeding iterator. If this function is used recursively, termination can sometimes be proved with
 the termination measures `it.finitelyManySteps` and `it.finitelyManySkips`.
 -/
-@[always_inline, inline]
+@[always_inline, inline, expose]
 def Iter.step {α β : Type w} [Iterator α Id β] (it : Iter (α := α) β) : it.Step :=
   it.toIterM.step.run.toPure
 
@@ -456,6 +514,7 @@ structure IterM.TerminationMeasures.Finite
 The relation of plausible successors on `IterM.TerminationMeasures.Finite`. It is well-founded
 if there is a `Finite` instance.
 -/
+@[expose]
 def IterM.TerminationMeasures.Finite.Rel
     {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β] :
     TerminationMeasures.Finite α m → TerminationMeasures.Finite α m → Prop :=
@@ -464,12 +523,13 @@ def IterM.TerminationMeasures.Finite.Rel
 instance {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     [Finite α m] : WellFoundedRelation (IterM.TerminationMeasures.Finite α m) where
   rel := IterM.TerminationMeasures.Finite.Rel
-  wf := (InvImage.wf _ Finite.wf).transGen
+  wf := by exact (InvImage.wf _ Finite.wf).transGen
 
 /--
 Termination measure to be used in well-founded recursive functions recursing over a finite iterator
 (see also `Finite`).
 -/
+@[expose]
 def IterM.finitelyManySteps {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     [Finite α m] (it : IterM (α := α) m β) : IterM.TerminationMeasures.Finite α m :=
   ⟨it⟩
@@ -494,9 +554,10 @@ theorem IterM.TerminationMeasures.Finite.rel_of_skip
 macro_rules | `(tactic| decreasing_trivial) => `(tactic|
   first
   | exact IterM.TerminationMeasures.Finite.rel_of_yield ‹_›
-  | exact IterM.TerminationMeasures.Finite.rel_of_skip ‹_›)
+  | exact IterM.TerminationMeasures.Finite.rel_of_skip ‹_›
+  | fail)
 
-@[inherit_doc IterM.finitelyManySteps]
+@[inherit_doc IterM.finitelyManySteps, expose]
 def Iter.finitelyManySteps {α : Type w} {β : Type w} [Iterator α Id β] [Finite α Id]
     (it : Iter (α := α) β) : IterM.TerminationMeasures.Finite α Id :=
   it.toIterM.finitelyManySteps
@@ -521,7 +582,8 @@ theorem Iter.TerminationMeasures.Finite.rel_of_skip
 macro_rules | `(tactic| decreasing_trivial) => `(tactic|
   first
   | exact Iter.TerminationMeasures.Finite.rel_of_yield ‹_›
-  | exact Iter.TerminationMeasures.Finite.rel_of_skip ‹_›)
+  | exact Iter.TerminationMeasures.Finite.rel_of_skip ‹_›
+  | fail)
 
 theorem IterM.isPlausibleSuccessorOf_of_yield
     {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
@@ -561,6 +623,7 @@ structure IterM.TerminationMeasures.Productive
 The relation of plausible successors while skipping on `IterM.TerminationMeasures.Productive`.
 It is well-founded if there is a `Productive` instance.
 -/
+@[expose]
 def IterM.TerminationMeasures.Productive.Rel
     {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β] :
     TerminationMeasures.Productive α m → TerminationMeasures.Productive α m → Prop :=
@@ -569,12 +632,13 @@ def IterM.TerminationMeasures.Productive.Rel
 instance {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     [Productive α m] : WellFoundedRelation (IterM.TerminationMeasures.Productive α m) where
   rel := IterM.TerminationMeasures.Productive.Rel
-  wf := (InvImage.wf _ Productive.wf).transGen
+  wf := by exact (InvImage.wf _ Productive.wf).transGen
 
 /--
 Termination measure to be used in well-founded recursive functions recursing over a productive
 iterator (see also `Productive`).
 -/
+@[expose]
 def IterM.finitelyManySkips {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     [Productive α m] (it : IterM (α := α) m β) : IterM.TerminationMeasures.Productive α m :=
   ⟨it⟩
@@ -590,9 +654,11 @@ theorem IterM.TerminationMeasures.Productive.rel_of_skip
   .single h
 
 macro_rules | `(tactic| decreasing_trivial) => `(tactic|
-  exact IterM.TerminationMeasures.Productive.rel_of_skip ‹_›)
+  first
+    | exact IterM.TerminationMeasures.Productive.rel_of_skip ‹_›
+    | fail)
 
-@[inherit_doc IterM.finitelyManySkips]
+@[inherit_doc IterM.finitelyManySkips, expose]
 def Iter.finitelyManySkips {α : Type w} {β : Type w} [Iterator α Id β] [Productive α Id]
     (it : Iter (α := α) β) : IterM.TerminationMeasures.Productive α Id :=
   it.toIterM.finitelyManySkips
@@ -608,7 +674,9 @@ theorem Iter.TerminationMeasures.Productive.rel_of_skip
   IterM.TerminationMeasures.Productive.rel_of_skip h
 
 macro_rules | `(tactic| decreasing_trivial) => `(tactic|
-  exact Iter.TerminationMeasures.Productive.rel_of_skip ‹_›)
+  first
+    | exact Iter.TerminationMeasures.Productive.rel_of_skip ‹_›
+    | fail)
 
 instance [Iterator α m β] [Finite α m] : Productive α m where
   wf := by

src/Init/Data/Iterators/Consumers.lean

@@ -0,0 +1,13 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Consumers.Monadic
+import Init.Data.Iterators.Consumers.Access
+import Init.Data.Iterators.Consumers.Collect
+import Init.Data.Iterators.Consumers.Loop
+import Init.Data.Iterators.Consumers.Partial

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

@@ -3,8 +3,10 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Consumers.Partial
+import Init.Data.Iterators.Consumers.Partial
 
 namespace Std.Iterators
 

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

@@ -3,10 +3,12 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Basic
-import Std.Data.Iterators.Consumers.Partial
-import Std.Data.Iterators.Consumers.Monadic.Collect
+import Init.Data.Iterators.Basic
+import Init.Data.Iterators.Consumers.Partial
+import Init.Data.Iterators.Consumers.Monadic.Collect
 
 /-!
 # Collectors
@@ -54,4 +56,18 @@ def Iter.Partial.toList {α : Type w} {β : Type w}
     [Iterator α Id β] [IteratorCollectPartial α Id Id] (it : Iter.Partial (α := α) β) : List β :=
   it.it.toIterM.allowNontermination.toList.run
 
+/--
+This class charaterizes how the plausibility behavior (`IsPlausibleStep`) and the actual iteration
+behavior (`it.step`) should relate to each other for pure iterators. Intuitively, a step should
+only be plausible if it is possible. For simplicity's sake, the actual definition is weaker but
+presupposes that the iterator is finite.
+
+This is an experimental instance and it should not be explicitly used downstream of the standard
+library.
+-/
+class LawfulPureIterator (α : Type w) [Iterator α Id β]
+    [Finite α Id] [IteratorCollect α Id Id] where
+  mem_toList_iff_isPlausibleIndirectOutput {it : Iter (α := α) β} {out : β} :
+    out ∈ it.toList ↔ it.IsPlausibleIndirectOutput out
+
 end Std.Iterators

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

@@ -3,9 +3,11 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Consumers.Monadic.Loop
-import Std.Data.Iterators.Consumers.Partial
+import Init.Data.Iterators.Consumers.Monadic.Loop
+import Init.Data.Iterators.Consumers.Partial
 
 /-!
 # Loop consumers
@@ -22,11 +24,24 @@ These operations are implemented using the `IteratorLoop` and `IteratorLoopParti
 
 namespace Std.Iterators
 
+/--
+A `ForIn'` instance for iterators. Its generic membership relation is not easy to use,
+so this is not marked as `instance`. This way, more convenient instances can be built on top of it
+or future library improvements will make it more comfortable.
+-/
+def Iter.instForIn' {α : Type w} {β : Type w} {n : Type w → Type w'} [Monad n]
+    [Iterator α Id β] [Finite α Id] [IteratorLoop α Id n] :
+    ForIn' n (Iter (α := α) β) β ⟨fun it out => it.IsPlausibleIndirectOutput out⟩ where
+  forIn' it init f :=
+    IteratorLoop.finiteForIn' (fun δ (c : Id δ) => pure c.run) |>.forIn' it.toIterM init
+        fun out h acc =>
+          f out (Iter.isPlausibleIndirectOutput_iff_isPlausibleIndirectOutput_toIterM.mpr h) acc
+
 instance (α : Type w) (β : Type w) (n : Type w → Type w') [Monad n]
     [Iterator α Id β] [Finite α Id] [IteratorLoop α Id n] :
-    ForIn n (Iter (α := α) β) β where
-  forIn it init f :=
-    IteratorLoop.finiteForIn (fun δ (c : Id δ) => pure c.run) |>.forIn it.toIterM init f
+    ForIn n (Iter (α := α) β) β :=
+  haveI : ForIn' n (Iter (α := α) β) β _ := Iter.instForIn'
+  instForInOfForIn'
 
 instance (α : Type w) (β : Type w) (n : Type w → Type w') [Monad n]
     [Iterator α Id β] [IteratorLoopPartial α Id n] :
@@ -111,4 +126,14 @@ def Iter.Partial.fold {α : Type w} {β : Type w} {γ : Type w} [Iterator α Id
     (init : γ) (it : Iter.Partial (α := α) β) : γ :=
   ForIn.forIn (m := Id) it init (fun x acc => ForInStep.yield (f acc x))
 
+@[always_inline, inline, inherit_doc IterM.size]
+def Iter.size {α : Type w} {β : Type w} [Iterator α Id β] [IteratorSize α Id]
+    (it : Iter (α := α) β) : Nat :=
+  (IteratorSize.size it.toIterM).run.down
+
+@[always_inline, inline, inherit_doc IterM.Partial.size]
+def Iter.Partial.size {α : Type w} {β : Type w} [Iterator α Id β] [IteratorSizePartial α Id]
+    (it : Iter (α := α) β) : Nat :=
+  (IteratorSizePartial.size it.toIterM).run.down
+
 end Std.Iterators

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

@@ -0,0 +1,11 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Consumers.Monadic.Collect
+import Init.Data.Iterators.Consumers.Monadic.Loop
+import Init.Data.Iterators.Consumers.Monadic.Partial

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

@@ -3,9 +3,11 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Consumers.Monadic.Partial
-import Std.Data.Internal.LawfulMonadLiftFunction
+import Init.Data.Iterators.Consumers.Monadic.Partial
+import Init.Data.Iterators.Internal.LawfulMonadLiftFunction
 
 /-!
 # Collectors

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

@@ -3,10 +3,12 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
 import Init.RCases
-import Std.Data.Iterators.Basic
-import Std.Data.Iterators.Consumers.Monadic.Partial
+import Init.Data.Iterators.Basic
+import Init.Data.Iterators.Consumers.Monadic.Partial
 
 /-!
 # Loop-based consumers
@@ -62,8 +64,9 @@ class IteratorLoop (α : Type w) (m : Type w → Type w') {β : Type w} [Iterato
   forIn : ∀ (_lift : (γ : Type w) → m γ → n γ) (γ : Type w),
       (plausible_forInStep : β → γ → ForInStep γ → Prop) →
       IteratorLoop.WellFounded α m plausible_forInStep →
-      IterM (α := α) m β → γ →
-      ((b : β) → (c : γ) → n (Subtype (plausible_forInStep b c))) → n γ
+      (it : IterM (α := α) m β) → γ →
+      ((b : β) → it.IsPlausibleIndirectOutput b → (c : γ) → n (Subtype (plausible_forInStep b c))) →
+      n γ
 
 /--
 `IteratorLoopPartial α m` provides efficient implementations of loop-based consumers for `α`-based
@@ -76,7 +79,29 @@ provided by the standard library.
 class IteratorLoopPartial (α : Type w) (m : Type w → Type w') {β : Type w} [Iterator α m β]
     (n : Type w → Type w'') where
   forInPartial : ∀ (_lift : (γ : Type w) → m γ → n γ) {γ : Type w},
-      IterM (α := α) m β → γ → ((b : β) → (c : γ) → n (ForInStep γ)) → n γ
+      (it : IterM (α := α) m β) → γ →
+      ((b : β) → it.IsPlausibleIndirectOutput b → (c : γ) → n (ForInStep γ)) → n γ
+
+/--
+`IteratorSize α m` provides an implementation of the `IterM.size` function.
+
+This class is experimental and users of the iterator API should not explicitly depend on it.
+They can, however, assume that consumers that require an instance will work for all iterators
+provided by the standard library.
+-/
+class IteratorSize (α : Type w) (m : Type w → Type w') {β : Type w} [Iterator α m β] where
+  size : IterM (α := α) m β → m (ULift Nat)
+
+/--
+`IteratorSizePartial α m` provides an implementation of the `IterM.Partial.size` function that
+can be used as `it.allowTermination.size`.
+
+This class is experimental and users of the iterator API should not explicitly depend on it.
+They can, however, assume that consumers that require an instance will work for all iterators
+provided by the standard library.
+-/
+class IteratorSizePartial (α : Type w) (m : Type w → Type w') {β : Type w} [Iterator α m β] where
+  size : IterM (α := α) m β → m (ULift Nat)
 
 end Typeclasses
 
@@ -91,7 +116,7 @@ private def IteratorLoop.WFRel.mk {α : Type w} {m : Type w → Type w'} {β : T
     IteratorLoop.WFRel wf :=
   (it, c)
 
-instance {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
+private instance {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
     {γ : Type x} {plausible_forInStep : β → γ → ForInStep γ → Prop}
     (wf : IteratorLoop.WellFounded α m plausible_forInStep) :
     WellFoundedRelation (IteratorLoop.WFRel wf) where
@@ -102,23 +127,27 @@ instance {α : Type w} {m : Type w → Type w'} {β : Type w} [Iterator α m β]
 This is the loop implementation of the default instance `IteratorLoop.defaultImplementation`.
 -/
 @[specialize]
-def IterM.DefaultConsumers.forIn {m : Type w → Type w'} {α : Type w} {β : Type w}
+def IterM.DefaultConsumers.forIn' {m : Type w → Type w'} {α : Type w} {β : Type w}
     [Iterator α m β]
     {n : Type w → Type w''} [Monad n]
     (lift : ∀ γ, m γ → n γ) (γ : Type w)
     (plausible_forInStep : β → γ → ForInStep γ → Prop)
     (wf : IteratorLoop.WellFounded α m plausible_forInStep)
     (it : IterM (α := α) m β) (init : γ)
-    (f : (b : β) → (c : γ) → n (Subtype (plausible_forInStep b c))) : n γ :=
+    (f : (b : β) → it.IsPlausibleIndirectOutput b → (c : γ) → n (Subtype (plausible_forInStep b c))) : n γ :=
   haveI : WellFounded _ := wf
   letI : MonadLift m n := ⟨fun {γ} => lift γ⟩
   do
     match ← it.step with
-    | .yield it' out _ =>
-      match ← f out init with
-      | ⟨.yield c, _⟩ => IterM.DefaultConsumers.forIn lift _ plausible_forInStep wf it' c f
+    | .yield it' out h =>
+      match ← f out (.direct ⟨_, h⟩) init with
+      | ⟨.yield c, _⟩ =>
+        IterM.DefaultConsumers.forIn' lift _ plausible_forInStep wf it' c
+          (fun out h' acc => f out (.indirect ⟨_, rfl, h⟩ h') acc)
       | ⟨.done c, _⟩ => return c
-    | .skip it' _ => IterM.DefaultConsumers.forIn lift _ plausible_forInStep wf it' init f
+    | .skip it' h =>
+      IterM.DefaultConsumers.forIn' lift _ plausible_forInStep wf it' init
+        (fun out h' acc => f out (.indirect ⟨_, rfl, h⟩ h') acc)
     | .done _ => return init
 termination_by IteratorLoop.WFRel.mk wf it init
 decreasing_by
@@ -134,7 +163,7 @@ implementations are possible and should be used instead.
 def IteratorLoop.defaultImplementation {α : Type w} {m : Type w → Type w'} {n : Type w → Type w''}
     [Monad n] [Iterator α m β] :
     IteratorLoop α m n where
-  forIn lift := IterM.DefaultConsumers.forIn lift
+  forIn lift := IterM.DefaultConsumers.forIn' lift
 
 /--
 Asserts that a given `IteratorLoop` instance is equal to `IteratorLoop.defaultImplementation`.
@@ -153,15 +182,19 @@ partial def IterM.DefaultConsumers.forInPartial {m : Type w → Type w'} {α : T
     {n : Type w → Type w''} [Monad n]
     (lift : ∀ γ, m γ → n γ) (γ : Type w)
     (it : IterM (α := α) m β) (init : γ)
-    (f : (b : β) → (c : γ) → n (ForInStep γ)) : n γ :=
+    (f : (b : β) → it.IsPlausibleIndirectOutput b → (c : γ) → n (ForInStep γ)) : n γ :=
   letI : MonadLift m n := ⟨fun {γ} => lift γ⟩
   do
     match ← it.step with
-    | .yield it' out _ =>
-      match ← f out init with
-      | .yield c => IterM.DefaultConsumers.forInPartial lift _ it' c f
+    | .yield it' out h =>
+      match ← f out (.direct ⟨_, h⟩) init with
+      | .yield c =>
+        IterM.DefaultConsumers.forInPartial lift _ it' c
+          fun out h' acc => f out (.indirect ⟨_, rfl, h⟩ h') acc
       | .done c => return c
-    | .skip it' _ => IterM.DefaultConsumers.forInPartial lift _ it' init f
+    | .skip it' h =>
+      IterM.DefaultConsumers.forInPartial lift _ it' init
+        fun out h' acc => f out (.indirect ⟨_, rfl, h⟩ h') acc
     | .done _ => return init
 
 /--
@@ -196,27 +229,40 @@ theorem IteratorLoop.wellFounded_of_finite {m : Type w → Type w'}
     exact WellFoundedRelation.wf
 
 /--
-This `ForIn`-style loop construct traverses a finite iterator using an `IteratorLoop` instance.
+This `ForIn'`-style loop construct traverses a finite iterator using an `IteratorLoop` instance.
 -/
 @[always_inline, inline]
-def IteratorLoop.finiteForIn {m : Type w → Type w'} {n : Type w → Type w''}
+def IteratorLoop.finiteForIn' {m : Type w → Type w'} {n : Type w → Type w''}
     {α : Type w} {β : Type w} [Iterator α m β] [Finite α m] [IteratorLoop α m n]
     (lift : ∀ γ, m γ → n γ) :
-    ForIn n (IterM (α := α) m β) β where
-  forIn {γ} [Monad n] it init f :=
+    ForIn' n (IterM (α := α) m β) β ⟨fun it out => it.IsPlausibleIndirectOutput out⟩ where
+  forIn' {γ} [Monad n] it init f :=
     IteratorLoop.forIn (α := α) (m := m) lift γ (fun _ _ _ => True)
       wellFounded_of_finite
-      it init ((⟨·, .intro⟩) <$> f · ·)
+      it init (fun out h acc => (⟨·, .intro⟩) <$> f out h acc)
+
+/--
+A `ForIn'` instance for iterators. Its generic membership relation is not easy to use,
+so this is not marked as `instance`. This way, more convenient instances can be built on top of it
+or future library improvements will make it more comfortable.
+-/
+def IterM.instForIn' {m : Type w → Type w'} {n : Type w → Type w''}
+    {α : Type w} {β : Type w} [Iterator α m β] [Finite α m] [IteratorLoop α m n]
+    [MonadLiftT m n] :
+    ForIn' n (IterM (α := α) m β) β ⟨fun it out => it.IsPlausibleIndirectOutput out⟩ :=
+  IteratorLoop.finiteForIn' (fun _ => monadLift)
 
 instance {m : Type w → Type w'} {n : Type w → Type w''}
     {α : Type w} {β : Type w} [Iterator α m β] [Finite α m] [IteratorLoop α m n]
     [MonadLiftT m n] :
-    ForIn n (IterM (α := α) m β) β := IteratorLoop.finiteForIn (fun _ => monadLift)
+    ForIn n (IterM (α := α) m β) β :=
+  haveI : ForIn' n (IterM (α := α) m β) β _ := IterM.instForIn'
+  instForInOfForIn'
 
 instance {m : Type w → Type w'} {n : Type w → Type w''}
     {α : Type w} {β : Type w} [Iterator α m β] [IteratorLoopPartial α m n] [MonadLiftT m n] :
-    ForIn n (IterM.Partial (α := α) m β) β where
-  forIn it init f :=
+    ForIn' n (IterM.Partial (α := α) m β) β ⟨fun it out => it.it.IsPlausibleIndirectOutput out⟩ where
+  forIn' it init f :=
     IteratorLoopPartial.forInPartial (α := α) (m := m) (fun _ => monadLift) it.it init f
 
 instance {m : Type w → Type w'} {n : Type w → Type w''}
@@ -327,4 +373,86 @@ def IterM.Partial.drain {α : Type w} {m : Type w → Type w'} [Monad m] {β : T
     m PUnit :=
   it.fold (γ := PUnit) (fun _ _ => .unit) .unit
 
+section Size
+
+/--
+This is the implementation of the default instance `IteratorSize.defaultImplementation`.
+-/
+@[always_inline, inline]
+def IterM.DefaultConsumers.size {α : Type w} {m : Type w → Type w'} [Monad m] {β : Type w}
+    [Iterator α m β] [IteratorLoop α m m] [Finite α m] (it : IterM (α := α) m β) :
+    m (ULift Nat) :=
+  it.fold (init := .up 0) fun acc _ => .up (acc.down + 1)
+
+/--
+This is the implementation of the default instance `IteratorSizePartial.defaultImplementation`.
+-/
+@[always_inline, inline]
+def IterM.DefaultConsumers.sizePartial {α : Type w} {m : Type w → Type w'} [Monad m] {β : Type w}
+    [Iterator α m β] [IteratorLoopPartial α m m] (it : IterM (α := α) m β) :
+    m (ULift Nat) :=
+  it.allowNontermination.fold (init := .up 0) fun acc _ => .up (acc.down + 1)
+
+/--
+This is the default implementation of the `IteratorSize` class.
+It simply iterates using `IteratorLoop` and counts the elements.
+For certain iterators, more efficient implementations are possible and should be used instead.
+-/
+@[always_inline, inline]
+def IteratorSize.defaultImplementation {α β : Type w} {m : Type w → Type w'} [Monad m]
+    [Iterator α m β] [Finite α m] [IteratorLoop α m m] :
+    IteratorSize α m where
+  size := IterM.DefaultConsumers.size
+
+
+/--
+This is the default implementation of the `IteratorSizePartial` class.
+It simply iterates using `IteratorLoopPartial` and counts the elements.
+For certain iterators, more efficient implementations are possible and should be used instead.
+-/
+@[always_inline, inline]
+instance IteratorSizePartial.defaultImplementation {α β : Type w} {m : Type w → Type w'} [Monad m]
+    [Iterator α m β] [IteratorLoopPartial α m m] :
+    IteratorSizePartial α m where
+  size := IterM.DefaultConsumers.sizePartial
+
+/--
+Computes how many elements the iterator returns. In monadic situations, it is unclear which effects
+are caused by calling `size`, and if the monad is nondeterministic, it is also unclear what the
+returned value should be. The reference implementation, `IteratorSize.defaultImplementation`,
+simply iterates over the whole iterator monadically, counting the number of emitted values.
+An `IteratorSize` instance is considered lawful if it is equal to the reference implementation.
+
+**Performance**:
+
+Default performance is linear in the number of steps taken by the iterator.
+-/
+@[always_inline, inline]
+def IterM.size {α : Type} {m : Type → Type w'} {β : Type} [Iterator α m β] [Monad m]
+    (it : IterM (α := α) m β) [IteratorSize α m] : m Nat :=
+  ULift.down <$> IteratorSize.size it
+
+/--
+Computes how many elements the iterator emits.
+
+With monadic iterators (`IterM`), it is unclear which effects
+are caused by calling `size`, and if the monad is nondeterministic, it is also unclear what the
+returned value should be. The reference implementation, `IteratorSize.defaultImplementation`,
+simply iterates over the whole iterator monadically, counting the number of emitted values.
+An `IteratorSize` instance is considered lawful if it is equal to the reference implementation.
+
+This is the partial version of `size`. It does not require a proof of finiteness and might loop
+forever. It is not possible to verify the behavior in Lean because it uses `partial`.
+
+**Performance**:
+
+Default performance is linear in the number of steps taken by the iterator.
+-/
+@[always_inline, inline]
+def IterM.Partial.size {α : Type} {m : Type → Type w'} {β : Type} [Iterator α m β] [Monad m]
+    (it : IterM.Partial (α := α) m β) [IteratorSizePartial α m] : m Nat :=
+  ULift.down <$> IteratorSizePartial.size it.it
+
+end Size
+
 end Std.Iterators

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

@@ -3,8 +3,10 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Basic
+import Init.Data.Iterators.Basic
 
 namespace Std.Iterators
 

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

@@ -3,8 +3,10 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Basic
+import Init.Data.Iterators.Basic
 
 namespace Std.Iterators
 

src/Init/Data/Iterators/Internal.lean

@@ -0,0 +1,10 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Internal.LawfulMonadLiftFunction
+import Init.Data.Iterators.Internal.Termination

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

@@ -3,6 +3,8 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
 import Init.Control.Basic
 import Init.Control.Lawful.Basic

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

@@ -3,8 +3,10 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Basic
+import Init.Data.Iterators.Basic
 
 /-!
 This is an internal module used by iterator implementations.

src/Init/Data/Iterators/Lemmas.lean

@@ -3,5 +3,7 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Internal.Termination
+import Init.Data.Iterators.Lemmas.Consumers

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

@@ -3,8 +3,10 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Basic
+import Init.Data.Iterators.Basic
 
 namespace Std.Iterators
 

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

@@ -0,0 +1,11 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Lemmas.Consumers.Monadic
+import Init.Data.Iterators.Lemmas.Consumers.Collect
+import Init.Data.Iterators.Lemmas.Consumers.Loop

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

@@ -0,0 +1,114 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Lemmas.Basic
+import Init.Data.Iterators.Lemmas.Consumers.Monadic.Collect
+import all Init.Data.Iterators.Consumers.Access
+import all Init.Data.Iterators.Consumers.Collect
+
+namespace Std.Iterators
+
+theorem Iter.toArray_eq_toArray_toIterM {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
+    it.toArray = it.toIterM.toArray.run :=
+  (rfl)
+
+theorem Iter.toList_eq_toList_toIterM {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
+    it.toList = it.toIterM.toList.run :=
+  (rfl)
+
+theorem Iter.toListRev_eq_toListRev_toIterM {α β} [Iterator α Id β] [Finite α Id]
+    {it : Iter (α := α) β} :
+    it.toListRev = it.toIterM.toListRev.run :=
+  (rfl)
+
+@[simp]
+theorem IterM.toList_toIter {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    {it : IterM (α := α) Id β} :
+    it.toIter.toList = it.toList.run :=
+  (rfl)
+
+@[simp]
+theorem IterM.toListRev_toIter {α β} [Iterator α Id β] [Finite α Id]
+    {it : IterM (α := α) Id β} :
+    it.toIter.toListRev = it.toListRev.run :=
+  (rfl)
+
+theorem Iter.toList_toArray {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
+    it.toArray.toList = it.toList := by
+  simp [toArray_eq_toArray_toIterM, toList_eq_toList_toIterM, ← IterM.toList_toArray]
+
+theorem Iter.toArray_toList {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
+    it.toList.toArray = it.toArray := by
+  simp [toArray_eq_toArray_toIterM, toList_eq_toList_toIterM, ← IterM.toArray_toList]
+
+@[simp]
+theorem Iter.reverse_toListRev [Iterator α Id β] [Finite α Id]
+    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    {it : Iter (α := α) β} :
+    it.toListRev.reverse = it.toList := by
+  simp [toListRev_eq_toListRev_toIterM, toList_eq_toList_toIterM, ← IterM.reverse_toListRev]
+
+theorem Iter.toListRev_eq {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
+    it.toListRev = it.toList.reverse := by
+  simp [Iter.toListRev_eq_toListRev_toIterM, Iter.toList_eq_toList_toIterM, IterM.toListRev_eq]
+
+theorem Iter.toArray_eq_match_step {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
+    it.toArray = match it.step with
+      | .yield it' out _ => #[out] ++ it'.toArray
+      | .skip it' _ => it'.toArray
+      | .done _ => #[] := by
+  simp only [Iter.toArray_eq_toArray_toIterM, Iter.step]
+  rw [IterM.toArray_eq_match_step, Id.run_bind]
+  generalize it.toIterM.step.run = step
+  cases step using PlausibleIterStep.casesOn <;> simp
+
+theorem Iter.toList_eq_match_step {α β} [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id]
+    [LawfulIteratorCollect α Id Id] {it : Iter (α := α) β} :
+    it.toList = match it.step with
+      | .yield it' out _ => out :: it'.toList
+      | .skip it' _ => it'.toList
+      | .done _ => [] := by
+  rw [← Iter.toList_toArray, Iter.toArray_eq_match_step]
+  split <;> simp [Iter.toList_toArray]
+
+theorem Iter.toListRev_eq_match_step {α β} [Iterator α Id β] [Finite α Id] {it : Iter (α := α) β} :
+    it.toListRev = match it.step with
+      | .yield it' out _ => it'.toListRev ++ [out]
+      | .skip it' _ => it'.toListRev
+      | .done _ => [] := by
+  rw [Iter.toListRev_eq_toListRev_toIterM, IterM.toListRev_eq_match_step, Iter.step, Id.run_bind]
+  generalize it.toIterM.step.run = step
+  cases step using PlausibleIterStep.casesOn <;> simp
+
+theorem Iter.getElem?_toList_eq_atIdxSlow? {α β}
+    [Iterator α Id β] [Finite α Id] [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    {it : Iter (α := α) β} {k : Nat} :
+    it.toList[k]? = it.atIdxSlow? k := by
+  induction it using Iter.inductSteps generalizing k with | step it ihy ihs =>
+  rw [toList_eq_match_step, atIdxSlow?]
+  obtain ⟨step, h⟩ := it.step
+  cases step
+  · cases k <;> simp [ihy h]
+  · simp [ihs h]
+  · simp
+
+theorem Iter.toList_eq_of_atIdxSlow?_eq {α₁ α₂ β}
+    [Iterator α₁ Id β] [Finite α₁ Id] [IteratorCollect α₁ Id Id] [LawfulIteratorCollect α₁ Id Id]
+    [Iterator α₂ Id β] [Finite α₂ Id] [IteratorCollect α₂ Id Id] [LawfulIteratorCollect α₂ Id Id]
+    {it₁ : Iter (α := α₁) β} {it₂ : Iter (α := α₂) β}
+    (h : ∀ k, it₁.atIdxSlow? k = it₂.atIdxSlow? k) :
+    it₁.toList = it₂.toList := by
+  ext; simp [getElem?_toList_eq_atIdxSlow?, h]
+
+end Std.Iterators

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

@@ -0,0 +1,285 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Lemmas.Consumers.Collect
+import all Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop
+import all Init.Data.Iterators.Consumers.Loop
+
+namespace Std.Iterators
+
+theorem Iter.forIn'_eq {α β : Type w} [Iterator α Id β] [Finite α Id]
+    {m : Type w → Type w''} [Monad m] [IteratorLoop α Id m] [hl : LawfulIteratorLoop α Id m]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : (b : β) → it.IsPlausibleIndirectOutput b → γ → m (ForInStep γ)} :
+    letI : ForIn' m (Iter (α := α) β) β _ := Iter.instForIn'
+    ForIn'.forIn' it init f =
+      IterM.DefaultConsumers.forIn' (fun _ c => pure c.run) γ (fun _ _ _ => True)
+        IteratorLoop.wellFounded_of_finite it.toIterM init
+          (fun out h acc => (⟨·, .intro⟩) <$>
+            f out (Iter.isPlausibleIndirectOutput_iff_isPlausibleIndirectOutput_toIterM.mpr h) acc) := by
+  cases hl.lawful; rfl
+
+theorem Iter.forIn_eq {α β : Type w} [Iterator α Id β] [Finite α Id]
+    {m : Type w → Type w''} [Monad m] [IteratorLoop α Id m] [hl : LawfulIteratorLoop α Id m]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : (b : β) → γ → m (ForInStep γ)} :
+    ForIn.forIn it init f =
+      IterM.DefaultConsumers.forIn' (fun _ c => pure c.run) γ (fun _ _ _ => True)
+        IteratorLoop.wellFounded_of_finite it.toIterM init
+          (fun out _ acc => (⟨·, .intro⟩) <$>
+            f out acc) := by
+  cases hl.lawful; rfl
+
+theorem Iter.forIn'_eq_forIn'_toIterM {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : (out : β) → _ → γ → m (ForInStep γ)} :
+    letI : ForIn' m (Iter (α := α) β) β _ := Iter.instForIn'
+    ForIn'.forIn' it init f =
+      letI : MonadLift Id m := ⟨Std.Internal.idToMonad (α := _)⟩
+      letI : ForIn' m (IterM (α := α) Id β) β _ := IterM.instForIn'
+      ForIn'.forIn' it.toIterM init
+        (fun out h acc => f out (isPlausibleIndirectOutput_iff_isPlausibleIndirectOutput_toIterM.mpr h) acc) := by
+  rfl
+
+theorem Iter.forIn_eq_forIn_toIterM {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : β → γ → m (ForInStep γ)} :
+    ForIn.forIn it init f =
+      letI : MonadLift Id m := ⟨Std.Internal.idToMonad (α := _)⟩
+      ForIn.forIn it.toIterM init f := by
+  rfl
+
+theorem Iter.forIn'_eq_match_step {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : (out : β) → _ → γ → m (ForInStep γ)} :
+    letI : ForIn' m (Iter (α := α) β) β _ := Iter.instForIn'
+    ForIn'.forIn' it init f = (do
+      match it.step with
+      | .yield it' out h =>
+        match ← f out (.direct ⟨_, h⟩) init with
+        | .yield c =>
+          ForIn'.forIn' it' c
+            fun out h'' acc => f out (.indirect ⟨_, rfl, h⟩ h'') acc
+        | .done c => return c
+      | .skip it' h =>
+          ForIn'.forIn' it' init
+            fun out h' acc => f out (.indirect ⟨_, rfl, h⟩ h') acc
+      | .done _ => return init) := by
+  rw [Iter.forIn'_eq_forIn'_toIterM, @IterM.forIn'_eq_match_step, Iter.step]
+  simp only [liftM, monadLift, pure_bind]
+  generalize it.toIterM.step = step
+  cases step using PlausibleIterStep.casesOn
+  · apply bind_congr
+    intro forInStep
+    rfl
+  · rfl
+  · rfl
+
+theorem Iter.forIn_eq_match_step {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : β → γ → m (ForInStep γ)} :
+    ForIn.forIn it init f = (do
+      match it.step with
+      | .yield it' out _ =>
+        match ← f out init with
+        | .yield c => ForIn.forIn it' c f
+        | .done c => return c
+      | .skip it' _ => ForIn.forIn it' init f
+      | .done _ => return init) := by
+  rw [Iter.forIn_eq_forIn_toIterM, @IterM.forIn_eq_match_step, Iter.step]
+  simp only [liftM, monadLift, pure_bind]
+  generalize it.toIterM.step = step
+  cases step using PlausibleIterStep.casesOn
+  · apply bind_congr
+    intro forInStep
+    rfl
+  · rfl
+  · rfl
+
+private theorem Iter.forIn'_toList.aux {ρ : Type u} {α : Type v} {γ : Type w} {m : Type w → Type w'}
+    [Monad m] {_ : Membership α ρ} [ForIn' m ρ α inferInstance]
+    {r s : ρ} {init : γ} {f : (a : α) → _ → γ → m (ForInStep γ)} (h : r = s) :
+    forIn' r init f = forIn' s init (fun a h' acc => f a (h ▸ h') acc) := by
+  cases h; rfl
+
+theorem Iter.forIn'_toList {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    [LawfulPureIterator α]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : (out : β) → _ → γ → m (ForInStep γ)} :
+    letI : ForIn' m (Iter (α := α) β) β _ := Iter.instForIn'
+    ForIn'.forIn' it.toList init f = ForIn'.forIn' it init (fun out h acc => f out (LawfulPureIterator.mem_toList_iff_isPlausibleIndirectOutput.mpr h) acc) := by
+  induction it using Iter.inductSteps generalizing init with case step it ihy ihs =>
+  have := it.toList_eq_match_step
+  generalize hs : it.step = step at this
+  rw [forIn'_toList.aux this]
+  rw [forIn'_eq_match_step]
+  rw [List.forIn'_eq_foldlM] at *
+  simp only [map_eq_pure_bind, List.foldlM_map, hs]
+  cases step using PlausibleIterStep.casesOn
+  · rename_i it' out h
+    simp only [List.attach_cons, List.foldlM_cons, bind_pure_comp, map_bind]
+    apply bind_congr
+    intro forInStep
+    cases forInStep
+    · induction it'.toList.attach <;> simp [*]
+    · simp only [List.foldlM_map]
+      simp only [List.forIn'_eq_foldlM] at ihy
+      simp only at this
+      simp only [ihy h (f := fun out h acc => f out (by rw [this]; exact List.mem_cons_of_mem _ h) acc)]
+  · rename_i it' h
+    simp only [bind_pure_comp]
+    simp only [List.forIn'_eq_foldlM] at ihs
+    simp only at this
+    simp only [ihs h (f := fun out h acc => f out (this ▸ h) acc)]
+  · simp
+
+theorem Iter.forIn'_eq_forIn'_toList {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    [LawfulPureIterator α]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : (out : β) → _ → γ → m (ForInStep γ)} :
+    letI : ForIn' m (Iter (α := α) β) β _ := Iter.instForIn'
+    ForIn'.forIn' it init f = ForIn'.forIn' it.toList init (fun out h acc => f out (LawfulPureIterator.mem_toList_iff_isPlausibleIndirectOutput.mp h) acc) := by
+  simp only [forIn'_toList]
+  congr
+
+theorem Iter.forIn_toList {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : β → γ → m (ForInStep γ)} :
+    ForIn.forIn it.toList init f = ForIn.forIn it init f := by
+  rw [List.forIn_eq_foldlM]
+  induction it using Iter.inductSteps generalizing init with case step it ihy ihs =>
+  rw [forIn_eq_match_step, Iter.toList_eq_match_step]
+  simp only [map_eq_pure_bind]
+  generalize it.step = step
+  cases step using PlausibleIterStep.casesOn
+  · rename_i it' out h
+    simp only [List.foldlM_cons, bind_pure_comp, map_bind]
+    apply bind_congr
+    intro forInStep
+    cases forInStep
+    · induction it'.toList <;> simp [*]
+    · simp only [ForIn.forIn, forIn', List.forIn'] at ihy
+      simp [ihy h, forIn_eq_forIn_toIterM]
+  · rename_i it' h
+    simp only [bind_pure_comp]
+    rw [ihs h]
+  · simp
+
+theorem Iter.foldM_eq_forIn {α β γ : Type w} [Iterator α Id β] [Finite α Id] {m : Type w → Type w'}
+    [Monad m] [IteratorLoop α Id m] {f : γ → β → m γ}
+    {init : γ} {it : Iter (α := α) β} :
+    it.foldM (init := init) f = ForIn.forIn it init (fun x acc => ForInStep.yield <$> f acc x) :=
+  (rfl)
+
+theorem Iter.foldM_eq_foldM_toIterM {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ} {f : γ → β → m γ} :
+    it.foldM (init := init) f = letI : MonadLift Id m := ⟨pure⟩; it.toIterM.foldM (init := init) f :=
+  (rfl)
+
+theorem Iter.forIn_yield_eq_foldM {α β γ δ : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m] [IteratorLoop α Id m]
+    [LawfulIteratorLoop α Id m] {f : β → γ → m δ} {g : β → γ → δ → γ} {init : γ}
+    {it : Iter (α := α) β} :
+    ForIn.forIn it init (fun c b => (fun d => .yield (g c b d)) <$> f c b) =
+      it.foldM (fun b c => g c b <$> f c b) init := by
+  simp [Iter.foldM_eq_forIn]
+
+theorem Iter.foldM_eq_match_step {α β γ : Type w} [Iterator α Id β] [Finite α Id]
+    {m : Type w → Type w'} [Monad m] [LawfulMonad m] [IteratorLoop α Id m]
+    [LawfulIteratorLoop α Id m] {f : γ → β → m γ} {init : γ} {it : Iter (α := α) β} :
+    it.foldM (init := init) f = (do
+      match it.step with
+      | .yield it' out _ => it'.foldM (init := ← f init out) f
+      | .skip it' _ => it'.foldM (init := init) f
+      | .done _ => return init) := by
+  rw [Iter.foldM_eq_forIn, Iter.forIn_eq_match_step]
+  generalize it.step = step
+  cases step using PlausibleIterStep.casesOn <;> simp [foldM_eq_forIn]
+
+theorem Iter.foldlM_toList {α β γ : Type w} [Iterator α Id β] [Finite α Id] {m : Type w → Type w'}
+    [Monad m] [LawfulMonad m] [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    {f : γ → β → m γ}
+    {init : γ} {it : Iter (α := α) β} :
+    it.toList.foldlM (init := init) f = it.foldM (init := init) f := by
+  rw [Iter.foldM_eq_forIn, ← Iter.forIn_toList]
+  simp only [List.forIn_yield_eq_foldlM, id_map']
+
+theorem IterM.forIn_eq_foldM {α β : Type w} [Iterator α Id β]
+    [Finite α Id] {m : Type w → Type w''} [Monad m] [LawfulMonad m]
+    [IteratorLoop α Id m] [LawfulIteratorLoop α Id m]
+    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    {γ : Type w} {it : Iter (α := α) β} {init : γ}
+    {f : β → γ → m (ForInStep γ)} :
+    forIn it init f = ForInStep.value <$>
+      it.foldM (fun c b => match c with
+        | .yield c => f b c
+        | .done c => pure (.done c)) (ForInStep.yield init) := by
+  simp only [← Iter.forIn_toList, List.forIn_eq_foldlM, ← Iter.foldlM_toList]; rfl
+
+theorem Iter.fold_eq_forIn {α β γ : Type w} [Iterator α Id β]
+    [Finite α Id] [IteratorLoop α Id Id] {f : γ → β → γ} {init : γ} {it : Iter (α := α) β} :
+    it.fold (init := init) f =
+      (ForIn.forIn (m := Id) it init (fun x acc => pure (ForInStep.yield (f acc x)))).run := by
+  rfl
+
+theorem Iter.fold_eq_foldM {α β γ : Type w} [Iterator α Id β]
+    [Finite α Id] [IteratorLoop α Id Id] {f : γ → β → γ} {init : γ}
+    {it : Iter (α := α) β} :
+    it.fold (init := init) f = (it.foldM (m := Id) (init := init) (pure <| f · ·)).run := by
+  simp [foldM_eq_forIn, fold_eq_forIn]
+
+@[simp]
+theorem Iter.forIn_pure_yield_eq_fold {α β γ : Type w} [Iterator α Id β]
+    [Finite α Id] [IteratorLoop α Id Id]
+    [LawfulIteratorLoop α Id Id] {f : β → γ → γ} {init : γ}
+    {it : Iter (α := α) β} :
+    ForIn.forIn (m := Id) it init (fun c b => pure (.yield (f c b))) =
+      pure (it.fold (fun b c => f c b) init) := by
+  simp only [fold_eq_forIn]
+  rfl
+
+theorem Iter.fold_eq_match_step {α β γ : Type w} [Iterator α Id β] [Finite α Id]
+    [IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
+    {f : γ → β → γ} {init : γ} {it : Iter (α := α) β} :
+    it.fold (init := init) f = (match it.step with
+      | .yield it' out _ => it'.fold (init := f init out) f
+      | .skip it' _ => it'.fold (init := init) f
+      | .done _ => init) := by
+  rw [fold_eq_foldM, foldM_eq_match_step]
+  simp only [fold_eq_foldM]
+  generalize it.step = step
+  cases step using PlausibleIterStep.casesOn <;> simp
+
+theorem Iter.foldl_toList {α β γ : Type w} [Iterator α Id β] [Finite α Id]
+    [IteratorLoop α Id Id] [LawfulIteratorLoop α Id Id]
+    [IteratorCollect α Id Id] [LawfulIteratorCollect α Id Id]
+    {f : γ → β → γ} {init : γ} {it : Iter (α := α) β} :
+    it.toList.foldl (init := init) f = it.fold (init := init) f := by
+  rw [fold_eq_foldM, List.foldl_eq_foldlM, ← Iter.foldlM_toList]
+
+end Std.Iterators

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

@@ -3,7 +3,8 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Consumers.Monadic.Collect
-import Std.Data.Iterators.Consumers.Monadic.Loop
-import Std.Data.Iterators.Consumers.Monadic.Partial
+import Init.Data.Iterators.Lemmas.Consumers.Monadic.Collect
+import Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop

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

@@ -0,0 +1,157 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Array.Lemmas
+import Init.Data.Iterators.Lemmas.Monadic.Basic
+import all Init.Data.Iterators.Consumers.Monadic.Collect
+
+namespace Std.Iterators
+
+variable {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''}
+  {lift : ⦃δ : Type w⦄ → m δ → n δ} {f : β → n γ} {it : IterM (α := α) m β}
+
+theorem IterM.DefaultConsumers.toArrayMapped.go.aux₁ [Monad n] [LawfulMonad n] [Iterator α m β]
+    [Finite α m] {b : γ} {bs : Array γ} :
+    IterM.DefaultConsumers.toArrayMapped.go lift f it (#[b] ++ bs) (m := m) =
+      (#[b] ++ ·) <$> IterM.DefaultConsumers.toArrayMapped.go lift f it bs (m := m) := by
+  induction it, bs using IterM.DefaultConsumers.toArrayMapped.go.induct
+  next it bs ih₁ ih₂ =>
+  rw [go, map_eq_pure_bind, go, bind_assoc]
+  apply bind_congr
+  intro step
+  split
+  · simp [ih₁ _ _ ‹_›]
+  · simp [ih₂ _ ‹_›]
+  · simp
+
+theorem IterM.DefaultConsumers.toArrayMapped.go.aux₂ [Monad n] [LawfulMonad n] [Iterator α m β]
+    [Finite α m] {acc : Array γ} :
+    IterM.DefaultConsumers.toArrayMapped.go lift f it acc (m := m) =
+      (acc ++ ·) <$> IterM.DefaultConsumers.toArrayMapped lift f it (m := m) := by
+  rw [← Array.toArray_toList (xs := acc)]
+  generalize acc.toList = acc
+  induction acc with
+  | nil => simp [toArrayMapped]
+  | cons x xs ih =>
+    rw [List.toArray_cons, IterM.DefaultConsumers.toArrayMapped.go.aux₁, ih]
+    simp only [Functor.map_map, Array.append_assoc]
+
+theorem IterM.DefaultConsumers.toArrayMapped_eq_match_step [Monad n] [LawfulMonad n]
+    [Iterator α m β] [Finite α m] :
+    IterM.DefaultConsumers.toArrayMapped lift f it (m := m) = letI : MonadLift m n := ⟨lift (δ := _)⟩; (do
+      match ← it.step with
+      | .yield it' out _ =>
+        return #[← f out] ++ (← IterM.DefaultConsumers.toArrayMapped lift f it' (m := m))
+      | .skip it' _ => IterM.DefaultConsumers.toArrayMapped lift f it' (m := m)
+      | .done _ => return #[]) := by
+  rw [IterM.DefaultConsumers.toArrayMapped, IterM.DefaultConsumers.toArrayMapped.go]
+  apply bind_congr
+  intro step
+  split <;> simp [IterM.DefaultConsumers.toArrayMapped.go.aux₂]
+
+theorem IterM.toArray_eq_match_step [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m] :
+    it.toArray = (do
+      match ← it.step with
+      | .yield it' out _ => return #[out] ++ (← it'.toArray)
+      | .skip it' _ => it'.toArray
+      | .done _ => return #[]) := by
+  simp only [IterM.toArray, LawfulIteratorCollect.toArrayMapped_eq]
+  rw [IterM.DefaultConsumers.toArrayMapped_eq_match_step]
+  simp [bind_pure_comp, pure_bind, toArray]
+
+theorem IterM.toList_toArray [Monad m] [Iterator α m β] [Finite α m] [IteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    Array.toList <$> it.toArray = it.toList := by
+  simp [IterM.toList]
+
+theorem IterM.toArray_toList [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    [IteratorCollect α m m] {it : IterM (α := α) m β} :
+    List.toArray <$> it.toList = it.toArray := by
+  simp [IterM.toList]
+
+theorem IterM.toList_eq_match_step [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m] {it : IterM (α := α) m β} :
+    it.toList = (do
+      match ← it.step with
+      | .yield it' out _ => return out :: (← it'.toList)
+      | .skip it' _ => it'.toList
+      | .done _ => return []) := by
+  simp [← IterM.toList_toArray]
+  rw [IterM.toArray_eq_match_step, map_eq_pure_bind, bind_assoc]
+  apply bind_congr
+  intro step
+  split <;> simp
+
+theorem IterM.toListRev.go.aux₁ [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    {it : IterM (α := α) m β} {b : β} {bs : List β} :
+    IterM.toListRev.go it (bs ++ [b]) = (· ++ [b]) <$> IterM.toListRev.go it bs:= by
+  induction it, bs using IterM.toListRev.go.induct
+  next it bs ih₁ ih₂ =>
+  rw [go, go, map_eq_pure_bind, bind_assoc]
+  apply bind_congr
+  intro step
+  simp only [List.cons_append] at ih₁
+  split <;> simp [*]
+
+theorem IterM.toListRev.go.aux₂ [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    {it : IterM (α := α) m β} {acc : List β} :
+    IterM.toListRev.go it acc = (· ++ acc) <$> it.toListRev := by
+  rw [← List.reverse_reverse (as := acc)]
+  generalize acc.reverse = acc
+  induction acc with
+  | nil => simp [toListRev]
+  | cons x xs ih => simp [IterM.toListRev.go.aux₁, ih]
+
+theorem IterM.toListRev_eq_match_step [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    {it : IterM (α := α) m β} :
+    it.toListRev = (do
+      match ← it.step with
+      | .yield it' out _ => return (← it'.toListRev) ++ [out]
+      | .skip it' _ => it'.toListRev
+      | .done _ => return []) := by
+  simp [IterM.toListRev]
+  rw [toListRev.go]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn <;> simp [IterM.toListRev.go.aux₂]
+
+theorem IterM.reverse_toListRev [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    List.reverse <$> it.toListRev = it.toList := by
+  apply Eq.symm
+  induction it using IterM.inductSteps
+  rename_i it ihy ihs
+  rw [toListRev_eq_match_step, toList_eq_match_step, map_eq_pure_bind, bind_assoc]
+  apply bind_congr
+  intro step
+  split <;> simp (discharger := assumption) [ihy, ihs]
+
+theorem IterM.toListRev_eq [Monad m] [LawfulMonad m] [Iterator α m β] [Finite α m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    it.toListRev = List.reverse <$> it.toList := by
+  rw [← IterM.reverse_toListRev]
+  simp
+
+theorem LawfulIteratorCollect.toArray_eq {α β : Type w} {m : Type w → Type w'}
+    [Monad m] [Iterator α m β] [Finite α m] [IteratorCollect α m m]
+    [hl : LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    it.toArray = (letI : IteratorCollect α m m := .defaultImplementation; it.toArray) := by
+  simp only [IterM.toArray, toArrayMapped_eq]
+
+theorem LawfulIteratorCollect.toList_eq {α β : Type w} {m : Type w → Type w'}
+    [Monad m] [Iterator α m β] [Finite α m] [IteratorCollect α m m]
+    [hl : LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    it.toList = (letI : IteratorCollect α m m := .defaultImplementation; it.toList) := by
+  simp [IterM.toList, toArray_eq]
+
+end Std.Iterators

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

@@ -0,0 +1,277 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Paul Reichert
+-/
+module
+
+prelude
+import Init.Data.Iterators.Lemmas.Consumers.Monadic.Collect
+import all Init.Data.Iterators.Consumers.Monadic.Loop
+
+namespace Std.Iterators
+
+theorem IterM.DefaultConsumers.forIn'_eq_match_step {α β : Type w} {m : Type w → Type w'}
+    [Iterator α m β]
+    {n : Type w → Type w''} [Monad n]
+    {lift : ∀ γ, m γ → n γ} {γ : Type w}
+    {plausible_forInStep : β → γ → ForInStep γ → Prop}
+    {wf : IteratorLoop.WellFounded α m plausible_forInStep}
+    {it : IterM (α := α) m β} {init : γ}
+    {f : (b : β) → it.IsPlausibleIndirectOutput b → (c : γ) → n (Subtype (plausible_forInStep b c))} :
+    IterM.DefaultConsumers.forIn' lift γ plausible_forInStep wf it init f = (do
+      match ← lift _ it.step with
+      | .yield it' out h =>
+        match ← f out (.direct ⟨_, h⟩) init with
+        | ⟨.yield c, _⟩ =>
+          IterM.DefaultConsumers.forIn' lift _ plausible_forInStep wf it' c
+            fun out h'' acc => f out (.indirect ⟨_, rfl, h⟩ h'') acc
+        | ⟨.done c, _⟩ => return c
+      | .skip it' h =>
+        IterM.DefaultConsumers.forIn' lift _ plausible_forInStep wf it' init
+          fun out h' acc => f out (.indirect ⟨_, rfl, h⟩ h') acc
+      | .done _ => return init) := by
+  rw [forIn']
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn <;> rfl
+
+theorem IterM.forIn'_eq {α β : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    {n : Type w → Type w''} [Monad n] [IteratorLoop α m n] [hl : LawfulIteratorLoop α m n]
+    [MonadLiftT m n] {γ : Type w} {it : IterM (α := α) m β} {init : γ}
+    {f : (b : β) → it.IsPlausibleIndirectOutput b → γ → n (ForInStep γ)} :
+    letI : ForIn' n (IterM (α := α) m β) β _ := IterM.instForIn'
+    ForIn'.forIn' it init f = IterM.DefaultConsumers.forIn' (fun _ => monadLift) γ (fun _ _ _ => True)
+        IteratorLoop.wellFounded_of_finite it init ((⟨·, .intro⟩) <$> f · · ·) := by
+  cases hl.lawful; rfl
+
+theorem IterM.forIn_eq {α β : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    {n : Type w → Type w''} [Monad n] [IteratorLoop α m n] [hl : LawfulIteratorLoop α m n]
+    [MonadLiftT m n] {γ : Type w} {it : IterM (α := α) m β} {init : γ}
+    {f : β → γ → n (ForInStep γ)} :
+    ForIn.forIn it init f = IterM.DefaultConsumers.forIn' (fun _ => monadLift) γ (fun _ _ _ => True)
+        IteratorLoop.wellFounded_of_finite it init (fun out _ acc => (⟨·, .intro⟩) <$> f out acc) := by
+  cases hl.lawful; rfl
+
+theorem IterM.forIn'_eq_match_step {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] {n : Type w → Type w''} [Monad n] [LawfulMonad n]
+    [IteratorLoop α m n] [LawfulIteratorLoop α m n]
+    [MonadLiftT m n] {γ : Type w} {it : IterM (α := α) m β} {init : γ}
+    {f : (out : β) → _ → γ → n (ForInStep γ)} :
+    letI : ForIn' n (IterM (α := α) m β) β _ := IterM.instForIn'
+    ForIn'.forIn' it init f = (do
+      match ← it.step with
+      | .yield it' out h =>
+        match ← f out (.direct ⟨_, h⟩) init with
+        | .yield c =>
+          ForIn'.forIn' it' c
+            fun out h'' acc => f out (.indirect ⟨_, rfl, h⟩ h'') acc
+        | .done c => return c
+      | .skip it' h =>
+        ForIn'.forIn' it' init
+          fun out h' acc => f out (.indirect ⟨_, rfl, h⟩ h') acc
+      | .done _ => return init) := by
+  rw [IterM.forIn'_eq, DefaultConsumers.forIn'_eq_match_step]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn
+  · simp only [map_eq_pure_bind, bind_assoc]
+    apply bind_congr
+    intro forInStep
+    cases forInStep <;> simp [IterM.forIn'_eq]
+  · simp [IterM.forIn'_eq]
+  · simp
+
+theorem IterM.forIn_eq_match_step {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] {n : Type w → Type w''} [Monad n] [LawfulMonad n]
+    [IteratorLoop α m n] [LawfulIteratorLoop α m n]
+    [MonadLiftT m n] {γ : Type w} {it : IterM (α := α) m β} {init : γ}
+    {f : β → γ → n (ForInStep γ)} :
+    ForIn.forIn it init f = (do
+      match ← it.step with
+      | .yield it' out _ =>
+        match ← f out init with
+        | .yield c => ForIn.forIn it' c f
+        | .done c => return c
+      | .skip it' _ => ForIn.forIn it' init f
+      | .done _ => return init) := by
+  rw [IterM.forIn_eq, DefaultConsumers.forIn'_eq_match_step]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn
+  · simp only [map_eq_pure_bind, bind_assoc]
+    apply bind_congr
+    intro forInStep
+    cases forInStep <;> simp [IterM.forIn_eq]
+  · simp [IterM.forIn_eq]
+  · simp
+
+theorem IterM.forM_eq_forIn {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] {n : Type w → Type w''} [Monad n] [LawfulMonad n]
+    [IteratorLoop α m n] [LawfulIteratorLoop α m n]
+    [MonadLiftT m n] {it : IterM (α := α) m β}
+    {f : β → n PUnit} :
+    ForM.forM it f = ForIn.forIn it PUnit.unit (fun out _ => do f out; return .yield .unit) :=
+  rfl
+
+theorem IterM.forM_eq_match_step {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] {n : Type w → Type w''} [Monad n] [LawfulMonad n]
+    [IteratorLoop α m n] [LawfulIteratorLoop α m n]
+    [MonadLiftT m n] {it : IterM (α := α) m β}
+    {f : β → n PUnit} :
+    ForM.forM it f = (do
+      match ← it.step with
+      | .yield it' out _ =>
+        f out
+        ForM.forM it' f
+      | .skip it' _ => ForM.forM it' f
+      | .done _ => return) := by
+  rw [forM_eq_forIn, forIn_eq_match_step]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn <;> simp [forM_eq_forIn]
+
+theorem IterM.foldM_eq_forIn {α β γ : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    {n : Type w → Type w''} [Monad n] [IteratorLoop α m n] [MonadLiftT m n] {f : γ → β → n γ}
+    {init : γ} {it : IterM (α := α) m β} :
+    it.foldM (init := init) f = ForIn.forIn it init (fun x acc => ForInStep.yield <$> f acc x) :=
+  (rfl)
+
+theorem IterM.forIn_yield_eq_foldM {α β γ δ : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] {n : Type w → Type w''} [Monad n] [LawfulMonad n] [IteratorLoop α m n]
+    [LawfulIteratorLoop α m n] [MonadLiftT m n] {f : β → γ → n δ} {g : β → γ → δ → γ} {init : γ}
+    {it : IterM (α := α) m β} :
+    ForIn.forIn it init (fun c b => (fun d => .yield (g c b d)) <$> f c b) =
+      it.foldM (fun b c => g c b <$> f c b) init := by
+  simp [IterM.foldM_eq_forIn]
+
+theorem IterM.foldM_eq_match_step {α β γ : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    {n : Type w → Type w''} [Monad n] [LawfulMonad n] [IteratorLoop α m n] [LawfulIteratorLoop α m n]
+    [MonadLiftT m n] {f : γ → β → n γ} {init : γ} {it : IterM (α := α) m β} :
+    it.foldM (init := init) f = (do
+      match ← it.step with
+      | .yield it' out _ => it'.foldM (init := ← f init out) f
+      | .skip it' _ => it'.foldM (init := init) f
+      | .done _ => return init) := by
+  rw [IterM.foldM_eq_forIn, IterM.forIn_eq_match_step]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn <;> simp [foldM_eq_forIn]
+
+theorem IterM.fold_eq_forIn {α β γ : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] [Monad m]
+    [IteratorLoop α m m] {f : γ → β → γ} {init : γ} {it : IterM (α := α) m β} :
+    it.fold (init := init) f =
+      ForIn.forIn (m := m) it init (fun x acc => pure (ForInStep.yield (f acc x))) := by
+  rfl
+
+theorem IterM.fold_eq_foldM {α β γ : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] [Monad m] [LawfulMonad m] [IteratorLoop α m m] {f : γ → β → γ} {init : γ}
+    {it : IterM (α := α) m β} :
+    it.fold (init := init) f = it.foldM (init := init) (pure <| f · ·) := by
+  simp [foldM_eq_forIn, fold_eq_forIn]
+
+@[simp]
+theorem IterM.forIn_pure_yield_eq_fold {α β γ : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] [Monad m] [LawfulMonad m] [IteratorLoop α m m]
+    [LawfulIteratorLoop α m m] {f : β → γ → γ} {init : γ}
+    {it : IterM (α := α) m β} :
+    ForIn.forIn it init (fun c b => pure (.yield (f c b))) =
+      it.fold (fun b c => f c b) init := by
+  simp [IterM.fold_eq_forIn]
+
+theorem IterM.fold_eq_match_step {α β γ : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    [Monad m] [LawfulMonad m] [IteratorLoop α m m] [LawfulIteratorLoop α m m]
+    {f : γ → β → γ} {init : γ} {it : IterM (α := α) m β} :
+    it.fold (init := init) f = (do
+      match ← it.step with
+      | .yield it' out _ => it'.fold (init := f init out) f
+      | .skip it' _ => it'.fold (init := init) f
+      | .done _ => return init) := by
+  rw [fold_eq_foldM, foldM_eq_match_step]
+  simp only [fold_eq_foldM]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn <;> simp
+
+theorem IterM.toList_eq_fold {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] [Monad m] [LawfulMonad m] [IteratorLoop α m m] [LawfulIteratorLoop α m m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    it.toList = it.fold (init := []) (fun l out => l ++ [out]) := by
+  suffices h : ∀ l' : List β, (l' ++ ·) <$> it.toList =
+      it.fold (init := l') (fun l out => l ++ [out]) by
+    specialize h []
+    simpa using h
+  induction it using IterM.inductSteps with | step it ihy ihs =>
+  intro l'
+  rw [IterM.toList_eq_match_step, IterM.fold_eq_match_step]
+  simp only [map_eq_pure_bind, bind_assoc]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn
+  · rename_i it' out h
+    specialize ihy h (l' ++ [out])
+    simpa using ihy
+  · rename_i it' h
+    simp [ihs h]
+  · simp
+
+theorem IterM.drain_eq_fold {α β : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    [Monad m] [IteratorLoop α m m] {it : IterM (α := α) m β} :
+    it.drain = it.fold (init := PUnit.unit) (fun _ _ => .unit) :=
+  (rfl)
+
+theorem IterM.drain_eq_foldM {α β : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    [Monad m] [LawfulMonad m] [IteratorLoop α m m] {it : IterM (α := α) m β} :
+    it.drain = it.foldM (init := PUnit.unit) (fun _ _ => pure .unit) := by
+  simp [IterM.drain_eq_fold, IterM.fold_eq_foldM]
+
+theorem IterM.drain_eq_forIn {α β : Type w} {m : Type w → Type w'}  [Iterator α m β] [Finite α m]
+    [Monad m] [IteratorLoop α m m] {it : IterM (α := α) m β} :
+    it.drain = ForIn.forIn (m := m) it PUnit.unit (fun _ _ => pure (ForInStep.yield .unit)) := by
+  simp [IterM.drain_eq_fold, IterM.fold_eq_forIn]
+
+theorem IterM.drain_eq_match_step {α β : Type w} {m : Type w → Type w'} [Iterator α m β] [Finite α m]
+    [Monad m] [LawfulMonad m] [IteratorLoop α m m] [LawfulIteratorLoop α m m]
+    {it : IterM (α := α) m β} :
+    it.drain = (do
+      match ← it.step with
+      | .yield it' _ _ => it'.drain
+      | .skip it' _ => it'.drain
+      | .done _ => return .unit) := by
+  rw [IterM.drain_eq_fold, IterM.fold_eq_match_step]
+  simp [IterM.drain_eq_fold]
+
+theorem IterM.drain_eq_map_toList {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] [Monad m] [LawfulMonad m] [IteratorLoop α m m] [LawfulIteratorLoop α m m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    it.drain = (fun _ => .unit) <$> it.toList := by
+  induction it using IterM.inductSteps with | step it ihy ihs =>
+  rw [IterM.drain_eq_match_step, IterM.toList_eq_match_step]
+  simp only [map_eq_pure_bind, bind_assoc]
+  apply bind_congr
+  intro step
+  cases step using PlausibleIterStep.casesOn
+  · rename_i it' out h
+    simp [ihy h]
+  · rename_i it' h
+    simp [ihs h]
+  · simp
+
+theorem IterM.drain_eq_map_toListRev {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] [Monad m] [LawfulMonad m] [IteratorLoop α m m] [LawfulIteratorLoop α m m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    it.drain = (fun _ => .unit) <$> it.toListRev := by
+  simp [IterM.drain_eq_map_toList, IterM.toListRev_eq]
+
+theorem IterM.drain_eq_map_toArray {α β : Type w} {m : Type w → Type w'} [Iterator α m β]
+    [Finite α m] [Monad m] [LawfulMonad m] [IteratorLoop α m m] [LawfulIteratorLoop α m m]
+    [IteratorCollect α m m] [LawfulIteratorCollect α m m]
+    {it : IterM (α := α) m β} :
+    it.drain = (fun _ => .unit) <$> it.toList := by
+  simp [IterM.drain_eq_map_toList]
+
+end Std.Iterators

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

@@ -3,8 +3,10 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
-import Std.Data.Iterators.Basic
+import Init.Data.Iterators.Basic
 
 namespace Std.Iterators
 

src/Init/Data/Iterators/PostconditionMonad.lean

@@ -3,6 +3,8 @@ Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul Reichert
 -/
+module
+
 prelude
 import Init.Control.Lawful.Basic
 import Init.Data.Subtype
@@ -48,6 +50,7 @@ def PostconditionT.lift {α : Type w} {m : Type w → Type w'} [Functor m] (x :
     PostconditionT m α :=
   ⟨fun _ => True, (⟨·, .intro⟩) <$> x⟩
 
+@[always_inline, inline]
 protected def PostconditionT.pure {m : Type w → Type w'} [Pure m] {α : Type w}
     (a : α) : PostconditionT m α :=
   ⟨fun y => a = y, pure <| ⟨a, rfl⟩⟩
@@ -117,16 +120,20 @@ instance {m : Type w → Type w'} [Monad m] : Monad (PostconditionT m) where
   pure := PostconditionT.pure
   bind := PostconditionT.bind
 
-@[simp]
-theorem PostconditionT.computation_pure {m : Type w → Type w'} [Monad m] {α : Type w}
-    {x : α} :
-    (pure x : PostconditionT m α).operation = pure ⟨x, rfl⟩ :=
+theorem PostconditionT.pure_eq_pure {m : Type w → Type w'} [Monad m] {α} {a : α} :
+    pure a = PostconditionT.pure (m := m) a :=
   rfl
 
 @[simp]
 theorem PostconditionT.property_pure {m : Type w → Type w'} [Monad m] {α : Type w}
     {x : α} :
-    (pure x : PostconditionT m α).Property = (x = ·) :=
+    (pure x : PostconditionT m α).Property = (x = ·) := by
+  rfl
+
+@[simp]
+theorem PostconditionT.operation_pure {m : Type w → Type w'} [Monad m] {α : Type w}
+    {x : α} :
+    (pure x : PostconditionT m α).operation = pure ⟨x, property_pure (m := m) ▸ rfl⟩ := by
   rfl
 
 theorem PostconditionT.ext {m : Type w → Type w'} [Monad m] [LawfulMonad m]
@@ -181,10 +188,10 @@ protected theorem PostconditionT.bind_assoc {m : Type w → Type w'} [Monad m] [
 protected theorem PostconditionT.map_pure {m : Type w → Type w'} [Monad m] [LawfulMonad m]
     {α : Type w} {β : Type w} {f : α → β} {a : α} :
     (pure a : PostconditionT m α).map f = pure (f a) := by
-  apply PostconditionT.ext <;> simp [pure, Functor.map, PostconditionT.map, PostconditionT.pure]
+  apply PostconditionT.ext <;> simp [pure, PostconditionT.map, PostconditionT.pure]
 
 instance [Monad m] [LawfulMonad m] : LawfulMonad (PostconditionT m) where
-  map_const {α β} := by ext a x; simp [Functor.mapConst, Function.const_apply, Functor.map]
+  map_const {α β} := by ext a x; simp [Functor.mapConst, Functor.map]
   id_map {α} x := by simp [Functor.map]
   comp_map {α β γ} g h := by intro x; simp [Functor.map]; rfl
   seqLeft_eq {α β} x y := by simp [SeqLeft.seqLeft, Functor.map, Seq.seq]; rfl
@@ -209,12 +216,19 @@ theorem PostconditionT.property_map {m : Type w → Type w'} [Functor m] {α : T
 @[simp]
 theorem PostconditionT.operation_map {m : Type w → Type w'} [Functor m] {α : Type w} {β : Type w}
     {x : PostconditionT m α} {f : α → β} :
-    (x.map f).operation = (fun a => ⟨_, a, rfl⟩) <$> x.operation :=
+    (x.map f).operation =
+      (fun a => ⟨_, (property_map (m := m)).mpr ⟨a.1, rfl, a.2⟩⟩) <$> x.operation := by
   rfl
 
 @[simp]
-theorem PostconditionT.operation_lift {m : Type w →Type w'} [Functor m] {α : Type w}
-    {x : m α} : (lift x : PostconditionT m α).operation = (⟨·, True.intro⟩) <$> x :=
+theorem PostconditionT.property_lift {m : Type w → Type w'} [Functor m] {α : Type w}
+    {x : m α} : (lift x : PostconditionT m α).Property = (fun _ => True) := by
+  rfl
+
+@[simp]
+theorem PostconditionT.operation_lift {m : Type w → Type w'} [Functor m] {α : Type w}
+    {x : m α} : (lift x : PostconditionT m α).operation =
+      (⟨·, property_lift (m := m) ▸ True.intro⟩) <$> x := by
   rfl
 
 end Std.Iterators

src/Init/Data/List/Attach.lean

@@ -69,14 +69,14 @@ well-founded recursion mechanism to prove that the function terminates.
   | 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, grind =] 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) :
+@[simp, grind =] 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, grind =] theorem attach_nil : ([] : List α).attach = [] := rfl
 
-@[simp] theorem attachWith_nil : ([] : List α).attachWith P H = [] := rfl
+@[simp, grind =] theorem attachWith_nil : ([] : List α).attachWith P H = [] := rfl
 
 @[simp]
 theorem pmap_eq_map {p : α → Prop} {f : α → β} {l : List α} (H) :
@@ -92,12 +92,14 @@ theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a,
   | cons x l ih =>
     rw [pmap, pmap, h _ mem_cons_self, ih fun a ha => h a (mem_cons_of_mem _ ha)]
 
+@[grind =]
 theorem map_pmap {p : α → Prop} {g : β → γ} {f : ∀ a, p a → β} {l : List α} (H) :
     map g (pmap f l H) = pmap (fun a h => g (f a h)) l H := by
   induction l
   · rfl
   · simp only [*, pmap, map]
 
+@[grind =]
 theorem pmap_map {p : β → Prop} {g : ∀ b, p b → γ} {f : α → β} {l : List α} (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
   induction l
@@ -114,7 +116,7 @@ theorem attachWith_congr {l₁ l₂ : List α} (w : l₁ = l₂) {P : α → Pro
   subst w
   simp
 
-@[simp] theorem attach_cons {x : α} {xs : List α} :
+@[simp, grind =] theorem attach_cons {x : α} {xs : List α} :
     (x :: xs).attach =
       ⟨x, mem_cons_self⟩ :: xs.attach.map fun ⟨y, h⟩ => ⟨y, mem_cons_of_mem x h⟩ := by
   simp only [attach, attachWith, pmap, map_pmap, cons.injEq, true_and]
@@ -122,7 +124,7 @@ theorem attachWith_congr {l₁ l₂ : List α} (w : l₁ = l₂) {P : α → Pro
   intros a _ m' _
   rfl
 
-@[simp]
+@[simp, grind =]
 theorem attachWith_cons {x : α} {xs : List α} {p : α → Prop} (h : ∀ a ∈ x :: xs, p a) :
     (x :: xs).attachWith p h = ⟨x, h x (mem_cons_self)⟩ ::
       xs.attachWith p (fun a ha ↦ h a (mem_cons_of_mem x ha)) :=
@@ -162,14 +164,14 @@ theorem attachWith_map_subtype_val {p : α → Prop} {l : List α} (H : ∀ a
     (l.attachWith p H).map Subtype.val = l :=
   (attachWith_map_val _).trans (List.map_id _)
 
-@[simp]
+@[simp, grind]
 theorem mem_attach (l : List 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]
+@[simp, grind]
 theorem mem_attachWith {l : List α} {q : α → Prop} (H) (x : {x // q x}) :
     x ∈ l.attachWith q H ↔ x.1 ∈ l := by
   induction l with
@@ -182,27 +184,28 @@ theorem mem_attachWith {l : List α} {q : α → Prop} (H) (x : {x // q x}) :
       · simp [← h]
       · simp_all
 
-@[simp]
+@[simp, grind =]
 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]
 
+@[grind]
 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]
+@[simp, grind =]
 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]
 
-@[simp]
+@[simp, grind =]
 theorem length_attach {l : List α} : l.attach.length = l.length :=
   length_pmap
 
-@[simp]
+@[simp, grind =]
 theorem length_attachWith {p : α → Prop} {l H} : length (l.attachWith p H) = length l :=
   length_pmap
 
@@ -237,7 +240,7 @@ theorem attachWith_ne_nil_iff {l : List α} {P : α → Prop} {H : ∀ a ∈ l,
     l.attachWith P H ≠ [] ↔ l ≠ [] :=
   pmap_ne_nil_iff _ _
 
-@[simp]
+@[simp, grind =]
 theorem getElem?_pmap {p : α → Prop} {f : ∀ a, p a → β} {l : List α} (h : ∀ a ∈ l, p a) (i : Nat) :
     (pmap f l h)[i]? = Option.pmap f l[i]? fun x H => h x (mem_of_getElem? H) := by
   induction l generalizing i with
@@ -252,10 +255,10 @@ set_option linter.deprecated false in
 theorem get?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h : ∀ a ∈ l, p a) (n : Nat) :
     get? (pmap f l h) n = Option.pmap f (get? l n) fun x H => h x (mem_of_get? H) := by
   simp only [get?_eq_getElem?]
-  simp [getElem?_pmap, h]
+  simp [getElem?_pmap]
 
 -- The argument `f` is explicit to allow rewriting from right to left.
-@[simp]
+@[simp, grind =]
 theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h : ∀ a ∈ l, p a) {i : Nat}
     (hn : i < (pmap f l h).length) :
     (pmap f l h)[i] =
@@ -279,109 +282,111 @@ theorem get_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h :
   simp only [get_eq_getElem]
   simp [getElem_pmap]
 
-@[simp]
+@[simp, grind =]
 theorem getElem?_attachWith {xs : List α} {i : Nat} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
     (xs.attachWith P H)[i]? = xs[i]?.pmap Subtype.mk (fun _ a => H _ (mem_of_getElem? a)) :=
   getElem?_pmap ..
 
-@[simp]
+@[simp, grind =]
 theorem getElem?_attach {xs : List α} {i : Nat} :
     xs.attach[i]? = xs[i]?.pmap Subtype.mk (fun _ a => mem_of_getElem? a) :=
   getElem?_attachWith
 
-@[simp]
+@[simp, grind =]
 theorem getElem_attachWith {xs : List α} {P : α → Prop} {H : ∀ a ∈ xs, P a}
     {i : Nat} (h : i < (xs.attachWith P H).length) :
     (xs.attachWith P H)[i] = ⟨xs[i]'(by simpa using h), H _ (getElem_mem (by simpa using h))⟩ :=
   getElem_pmap ..
 
-@[simp]
+@[simp, grind =]
 theorem getElem_attach {xs : List α} {i : Nat} (h : i < xs.attach.length) :
     xs.attach[i] = ⟨xs[i]'(by simpa using h), getElem_mem (by simpa using h)⟩ :=
   getElem_attachWith h
 
-@[simp] theorem pmap_attach {l : List α} {p : {x // x ∈ l} → Prop} {f : ∀ a, p a → β} (H) :
+@[simp, grind =] theorem pmap_attach {l : List α} {p : {x // x ∈ l} → Prop} {f : ∀ a, p a → β} (H) :
     pmap f l.attach H =
       l.pmap (P := fun a => ∃ h : a ∈ l, p ⟨a, h⟩)
         (fun a h => f ⟨a, h.1⟩ h.2) (fun a h => ⟨h, H ⟨a, h⟩ (by simp)⟩) := by
   apply ext_getElem <;> simp
 
-@[simp] theorem pmap_attachWith {l : List α} {p : {x // q x} → Prop} {f : ∀ a, p a → β} (H₁ H₂) :
+@[simp, grind =] theorem pmap_attachWith {l : List α} {p : {x // q x} → Prop} {f : ∀ a, p a → β} (H₁ H₂) :
     pmap f (l.attachWith q H₁) H₂ =
       l.pmap (P := fun a => ∃ h : q a, p ⟨a, h⟩)
         (fun a h => f ⟨a, h.1⟩ h.2) (fun a h => ⟨H₁ _ h, H₂ ⟨a, H₁ _ h⟩ (by simpa)⟩) := by
   apply ext_getElem <;> simp
 
-@[simp] theorem head?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp, grind =] theorem head?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.pmap f H).head? = xs.attach.head?.map fun ⟨a, m⟩ => f a (H a m) := by
   induction xs with
   | nil => simp
   | cons x xs ih =>
     simp at ih
-    simp [head?_pmap, ih]
+    simp
 
-@[simp] theorem head_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp, grind =] theorem head_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
     (H : ∀ (a : α), a ∈ xs → P a) (h : xs.pmap f H ≠ []) :
     (xs.pmap f H).head h = f (xs.head (by simpa using h)) (H _ (head_mem _)) := by
   induction xs with
   | nil => simp at h
-  | cons x xs ih => simp [head_pmap, ih]
+  | cons x xs ih => simp
 
-@[simp] theorem head?_attachWith {P : α → Prop} {xs : List α}
+@[simp, grind =] theorem head?_attachWith {P : α → Prop} {xs : List α}
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.attachWith P H).head? = xs.head?.pbind (fun a h => some ⟨a, H _ (mem_of_head? h)⟩) := by
   cases xs <;> simp_all
 
-@[simp] theorem head_attachWith {P : α → Prop} {xs : List α}
+@[simp, grind =] theorem head_attachWith {P : α → Prop} {xs : List α}
     {H : ∀ (a : α), a ∈ xs → P a} (h : xs.attachWith P H ≠ []) :
     (xs.attachWith P H).head h = ⟨xs.head (by simpa using h), H _ (head_mem _)⟩ := by
   cases xs with
   | nil => simp at h
-  | cons x xs => simp [head_attachWith, h]
+  | cons x xs => simp
 
-@[simp] theorem head?_attach {xs : List α} :
+@[simp, grind =] theorem head?_attach {xs : List α} :
     xs.attach.head? = xs.head?.pbind (fun a h => some ⟨a, mem_of_head? h⟩) := by
   cases xs <;> simp_all
 
-@[simp] theorem head_attach {xs : List α} (h) :
+@[simp, grind =] theorem head_attach {xs : List α} (h) :
     xs.attach.head h = ⟨xs.head (by simpa using h), head_mem (by simpa using h)⟩ := by
   cases xs with
   | nil => simp at h
-  | cons x xs => simp [head_attach, h]
+  | cons x xs => simp
 
-@[simp] theorem tail_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp, grind =] theorem tail_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.pmap f H).tail = xs.tail.pmap f (fun a h => H a (mem_of_mem_tail h)) := by
   cases xs <;> simp
 
-@[simp] theorem tail_attachWith {P : α → Prop} {xs : List α}
+@[simp, grind =] theorem tail_attachWith {P : α → Prop} {xs : List α}
     {H : ∀ (a : α), a ∈ xs → P a} :
     (xs.attachWith P H).tail = xs.tail.attachWith P (fun a h => H a (mem_of_mem_tail h)) := by
   cases xs <;> simp
 
-@[simp] theorem tail_attach {xs : List α} :
+@[simp, grind =] theorem tail_attach {xs : List α} :
     xs.attach.tail = xs.tail.attach.map (fun ⟨x, h⟩ => ⟨x, mem_of_mem_tail h⟩) := by
   cases xs <;> simp
 
+@[grind]
 theorem foldl_pmap {l : List 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]
 
+@[grind]
 theorem foldr_pmap {l : List 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]
 
-@[simp] theorem foldl_attachWith
+@[simp, grind =] theorem foldl_attachWith
     {l : List α} {q : α → Prop} (H : ∀ a, a ∈ l → q a) {f : β → { x // q x } → β} {b} :
     (l.attachWith q H).foldl f b = l.attach.foldl (fun b ⟨a, h⟩ => f b ⟨a, H _ h⟩) b := by
   induction l generalizing b with
   | nil => simp
   | cons a l ih => simp [ih, foldl_map]
 
-@[simp] theorem foldr_attachWith
+@[simp, grind =] theorem foldr_attachWith
     {l : List α} {q : α → Prop} (H : ∀ a, a ∈ l → q a) {f : { x // q x } → β → β} {b} :
     (l.attachWith q H).foldr f b = l.attach.foldr (fun a acc => f ⟨a.1, H _ a.2⟩ acc) b := by
   induction l generalizing b with
@@ -420,16 +425,18 @@ theorem foldr_attach {l : List α} {f : α → β → β} {b : β} :
   | nil => simp
   | cons a l ih => rw [foldr_cons, attach_cons, foldr_cons, foldr_map, ih]
 
+@[grind =]
 theorem attach_map {l : List α} {f : α → β} :
     (l.map f).attach = l.attach.map (fun ⟨x, h⟩ => ⟨f x, mem_map_of_mem h⟩) := by
   induction l <;> simp [*]
 
+@[grind =]
 theorem attachWith_map {l : List α} {f : α → β} {P : β → Prop} (H : ∀ (b : β), b ∈ l.map f → P b) :
     (l.map f).attachWith P H = (l.attachWith (P ∘ f) (fun _ h => H _ (mem_map_of_mem h))).map
       fun ⟨x, h⟩ => ⟨f x, h⟩ := by
   induction l <;> simp [*]
 
-@[simp] theorem map_attachWith {l : List α} {P : α → Prop} {H : ∀ (a : α), a ∈ l → P a}
+@[simp, grind =] theorem map_attachWith {l : List α} {P : α → Prop} {H : ∀ (a : α), a ∈ l → P a}
     {f : { x // P x } → β} :
     (l.attachWith P H).map f = l.attach.map fun ⟨x, h⟩ => f ⟨x, H _ h⟩ := by
   induction l <;> simp_all
@@ -458,13 +465,14 @@ theorem map_attach_eq_pmap {l : List α} {f : { x // x ∈ l } → β} :
 @[deprecated map_attach_eq_pmap (since := "2025-02-09")]
 abbrev map_attach := @map_attach_eq_pmap
 
+@[grind =]
 theorem attach_filterMap {l : List 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
   induction l with
   | nil => rfl
   | cons x xs ih =>
-    simp only [filterMap_cons, attach_cons, ih, filterMap_map]
+    simp only [filterMap_cons, attach_cons, filterMap_map]
     split <;> rename_i h
     · simp only [Option.pbind_eq_none_iff, reduceCtorEq, exists_false,
         or_false] at h
@@ -488,6 +496,7 @@ theorem attach_filterMap {l : List α} {f : α → Option β} :
       ext
       simp
 
+@[grind =]
 theorem attach_filter {l : List 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
@@ -499,7 +508,7 @@ theorem attach_filter {l : List α} (p : α → Bool) :
 
 -- We are still missing here `attachWith_filterMap` and `attachWith_filter`.
 
-@[simp]
+@[simp, grind =]
 theorem filterMap_attachWith {q : α → Prop} {l : List α} {f : {x // q x} → Option β} (H) :
     (l.attachWith q H).filterMap f = l.attach.filterMap (fun ⟨x, h⟩ => f ⟨x, H _ h⟩) := by
   induction l with
@@ -508,7 +517,7 @@ theorem filterMap_attachWith {q : α → Prop} {l : List α} {f : {x // q x} →
     simp only [attachWith_cons, filterMap_cons]
     split <;> simp_all [Function.comp_def]
 
-@[simp]
+@[simp, grind =]
 theorem filter_attachWith {q : α → Prop} {l : List α} {p : {x // q x} → Bool} (H) :
     (l.attachWith q H).filter p =
       (l.attach.filter (fun ⟨x, h⟩ => p ⟨x, H _ h⟩)).map (fun ⟨x, h⟩ => ⟨x, H _ h⟩) := by
@@ -518,13 +527,14 @@ theorem filter_attachWith {q : α → Prop} {l : List α} {p : {x // q x} → Bo
     simp only [attachWith_cons, filter_cons]
     split <;> simp_all [Function.comp_def, filter_map]
 
+@[grind =]
 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
   simp [pmap_eq_map_attach, attach_map]
 
-@[simp] theorem pmap_append {p : ι → Prop} {f : ∀ a : ι, p a → α} {l₁ l₂ : List ι}
+@[simp, grind =] theorem pmap_append {p : ι → Prop} {f : ∀ a : ι, p a → α} {l₁ l₂ : List 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)) ++
@@ -541,47 +551,50 @@ theorem pmap_append' {p : α → Prop} {f : ∀ a : α, p a → β} {l₁ l₂ :
       l₁.pmap f h₁ ++ l₂.pmap f h₂ :=
   pmap_append _
 
-@[simp] theorem attach_append {xs ys : List α} :
+@[simp, grind =] theorem attach_append {xs ys : List α} :
     (xs ++ ys).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_append_left ys h⟩) ++
       ys.attach.map fun ⟨x, h⟩ => ⟨x, mem_append_right xs h⟩ := by
-  simp only [attach, attachWith, pmap, map_pmap, pmap_append]
+  simp only [attach, attachWith, map_pmap, pmap_append]
   congr 1 <;>
   exact pmap_congr_left _ fun _ _ _ _ => rfl
 
-@[simp] theorem attachWith_append {P : α → Prop} {xs ys : List α}
+@[simp, grind =] theorem attachWith_append {P : α → Prop} {xs ys : List α}
     {H : ∀ (a : α), a ∈ xs ++ ys → P a} :
     (xs ++ ys).attachWith P H = xs.attachWith P (fun a h => H a (mem_append_left ys h)) ++
       ys.attachWith P (fun a h => H a (mem_append_right xs h)) := by
-  simp only [attachWith, attach_append, map_pmap, pmap_append]
+  simp only [attachWith, pmap_append]
 
-@[simp] theorem pmap_reverse {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp, grind =] theorem pmap_reverse {P : α → Prop} {f : (a : α) → P a → β} {xs : List 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
 
+@[grind =]
 theorem reverse_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List 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 : List α}
+@[simp, grind =] theorem attachWith_reverse {P : α → Prop} {xs : List 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 :=
   pmap_reverse ..
 
+@[grind =]
 theorem reverse_attachWith {P : α → Prop} {xs : List 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))) :=
   reverse_pmap ..
 
-@[simp] theorem attach_reverse {xs : List α} :
+@[simp, grind =] theorem attach_reverse {xs : List α} :
     xs.reverse.attach = xs.attach.reverse.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
   simp only [attach, attachWith, reverse_pmap, map_pmap]
   apply pmap_congr_left
   intros
   rfl
 
+@[grind =]
 theorem reverse_attach {xs : List α} :
     xs.attach.reverse = xs.reverse.attach.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
   simp only [attach, attachWith, reverse_pmap, map_pmap]
@@ -589,7 +602,7 @@ theorem reverse_attach {xs : List α} :
   intros
   rfl
 
-@[simp] theorem getLast?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp, grind =] theorem getLast?_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
     (H : ∀ (a : α), a ∈ xs → P a) :
     (xs.pmap f H).getLast? = xs.attach.getLast?.map fun ⟨a, m⟩ => f a (H a m) := by
   simp only [getLast?_eq_head?_reverse]
@@ -597,30 +610,30 @@ theorem reverse_attach {xs : List α} :
   simp only [Option.map_map]
   congr
 
-@[simp] theorem getLast_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
+@[simp, grind =] theorem getLast_pmap {P : α → Prop} {f : (a : α) → P a → β} {xs : List α}
     (H : ∀ (a : α), a ∈ xs → P a) (h : xs.pmap f H ≠ []) :
     (xs.pmap f H).getLast h = f (xs.getLast (by simpa using h)) (H _ (getLast_mem _)) := by
   simp only [getLast_eq_head_reverse]
   simp only [reverse_pmap, head_pmap, head_reverse]
 
-@[simp] theorem getLast?_attachWith {P : α → Prop} {xs : List α}
+@[simp, grind =] theorem getLast?_attachWith {P : α → Prop} {xs : List α}
     {H : ∀ (a : α), a ∈ xs → P a} :
     (xs.attachWith P H).getLast? = xs.getLast?.pbind (fun a h => some ⟨a, H _ (mem_of_getLast? h)⟩) := by
   rw [getLast?_eq_head?_reverse, reverse_attachWith, head?_attachWith]
   simp
 
-@[simp] theorem getLast_attachWith {P : α → Prop} {xs : List α}
+@[simp, grind =] theorem getLast_attachWith {P : α → Prop} {xs : List α}
     {H : ∀ (a : α), a ∈ xs → P a} (h : xs.attachWith P H ≠ []) :
     (xs.attachWith P H).getLast h = ⟨xs.getLast (by simpa using h), H _ (getLast_mem _)⟩ := by
-  simp only [getLast_eq_head_reverse, reverse_attachWith, head_attachWith, head_map]
+  simp only [getLast_eq_head_reverse, reverse_attachWith, head_attachWith]
 
-@[simp]
+@[simp, grind =]
 theorem getLast?_attach {xs : List α} :
     xs.attach.getLast? = xs.getLast?.pbind fun a h => some ⟨a, mem_of_getLast? h⟩ := by
   rw [getLast?_eq_head?_reverse, reverse_attach, head?_map, head?_attach]
   simp
 
-@[simp]
+@[simp, grind =]
 theorem getLast_attach {xs : List α} (h : xs.attach ≠ []) :
     xs.attach.getLast h = ⟨xs.getLast (by simpa using h), getLast_mem (by simpa using h)⟩ := by
   simp only [getLast_eq_head_reverse, reverse_attach, head_map, head_attach]
@@ -638,14 +651,14 @@ theorem countP_attachWith {p : α → Prop} {q : α → Bool} {l : List α} (H :
 @[simp]
 theorem count_attach [BEq α] {l : List α} {a : {x // x ∈ l}} :
     l.attach.count a = l.count ↑a :=
-  Eq.trans (countP_congr fun _ _ => by simp [Subtype.ext_iff]) <| countP_attach
+  Eq.trans (countP_congr fun _ _ => by simp) <| countP_attach
 
-@[simp]
+@[simp, grind =]
 theorem count_attachWith [BEq α] {p : α → Prop} {l : List α} (H : ∀ a ∈ l, p a) {a : {x // p x}} :
     (l.attachWith p H).count a = l.count ↑a :=
-  Eq.trans (countP_congr fun _ _ => by simp [Subtype.ext_iff]) <| countP_attachWith _
+  Eq.trans (countP_congr fun _ _ => by simp) <| countP_attachWith _
 
-@[simp] theorem countP_pmap {p : α → Prop} {g : ∀ a, p a → β} {f : β → Bool} {l : List α} (H₁) :
+@[simp, grind =] theorem countP_pmap {p : α → Prop} {g : ∀ a, p a → β} {f : β → Bool} {l : List α} (H₁) :
     (l.pmap g H₁).countP f =
       l.attach.countP (fun ⟨a, m⟩ => f (g a (H₁ a m))) := by
   simp [pmap_eq_map_attach, countP_map, Function.comp_def]
@@ -704,7 +717,7 @@ def unattach {α : Type _} {p : α → Prop} (l : List { x // p x }) : List α :
   unfold unattach
   induction l with
   | nil => simp
-  | cons a l ih => simp [ih, Function.comp_def]
+  | cons a l ih => simp [ih]
 
 @[simp] theorem getElem?_unattach {p : α → Prop} {l : List { x // p x }} (i : Nat) :
     l.unattach[i]? = l[i]?.map Subtype.val := by

src/Init/Data/List/Basic.lean

@@ -673,7 +673,7 @@ instance : Std.Associative (α := List α) (· ++ ·) := ⟨append_assoc⟩
 theorem append_cons (as : List α) (b : α) (bs : List α) : as ++ b :: bs = as ++ [b] ++ bs := by
   simp
 
-@[simp] theorem concat_eq_append {as : List α} {a : α} : as.concat a = as ++ [a] := by
+@[simp, grind =] theorem concat_eq_append {as : List α} {a : α} : as.concat a = as ++ [a] := by
   induction as <;> simp [concat, *]
 
 theorem reverseAux_eq_append {as bs : List α} : reverseAux as bs = reverseAux as [] ++ bs := by
@@ -730,9 +730,9 @@ Examples:
 -/
 @[inline] def flatMap {α : Type u} {β : Type v} (b : α → List β) (as : List α) : List β := flatten (map b as)
 
-@[simp, grind] theorem flatMap_nil {f : α → List β} : List.flatMap f [] = [] := by simp [flatten, List.flatMap]
+@[simp, grind] theorem flatMap_nil {f : α → List β} : List.flatMap f [] = [] := by simp [List.flatMap]
 @[simp, grind] theorem flatMap_cons {x : α} {xs : List α} {f : α → List β} :
-  List.flatMap f (x :: xs) = f x ++ List.flatMap f xs := by simp [flatten, List.flatMap]
+  List.flatMap f (x :: xs) = f x ++ List.flatMap f xs := by simp [List.flatMap]
 
 /-! ### replicate -/
 
@@ -753,7 +753,7 @@ def replicate : (n : Nat) → (a : α) → List α
 @[simp, grind] theorem length_replicate {n : Nat} {a : α} : (replicate n a).length = n := by
   induction n with
   | zero => simp
-  | succ n ih => simp only [ih, replicate_succ, length_cons, Nat.succ_eq_add_one]
+  | succ n ih => simp only [ih, replicate_succ, length_cons]
 
 /-! ## Additional functions -/
 
@@ -892,7 +892,7 @@ theorem mem_of_elem_eq_true [BEq α] [LawfulBEq α] {a : α} {as : List α} : el
   | a'::as =>
     simp [elem]
     split
-    next h => intros; simp [BEq.beq] at h; subst h; apply Mem.head
+    next h => intros; simp at h; subst h; apply Mem.head
     next _ => intro h; exact Mem.tail _ (mem_of_elem_eq_true h)
 
 theorem elem_eq_true_of_mem [BEq α] [ReflBEq α] {a : α} {as : List α} (h : a ∈ as) : elem a as = true := by
@@ -1780,7 +1780,7 @@ where
   | a :: l, i, h =>
     if p a then
       some ⟨i, by
-        simp only [Nat.add_comm _ i, ← Nat.add_assoc] at h
+        simp only [Nat.add_comm _ i] at h
         exact Nat.lt_of_add_right_lt (Nat.lt_of_succ_le (Nat.le_of_eq h))⟩
     else
       go l (i + 1) (by simp at h; simpa [← Nat.add_assoc, Nat.add_right_comm] using h)
@@ -2015,7 +2015,7 @@ def zip : List α → List β → List (Prod α β) :=
   zipWith Prod.mk
 
 @[simp] theorem zip_nil_left : zip ([] : List α) (l : List β)  = [] := rfl
-@[simp] theorem zip_nil_right : zip (l : List α) ([] : List β)  = [] := by simp [zip, zipWith]
+@[simp] theorem zip_nil_right : zip (l : List α) ([] : List β)  = [] := by simp [zip]
 @[simp] theorem zip_cons_cons : zip (a :: as) (b :: bs) = (a, b) :: zip as bs := rfl
 
 /-! ### zipWithAll -/

src/Init/Data/List/BasicAux.lean

@@ -276,7 +276,7 @@ theorem getElem_append_right {as bs : List α} {i : Nat} (h₁ : as.length ≤ i
   induction as generalizing i with
   | nil => trivial
   | cons a as ih =>
-    cases i with simp [Nat.succ_sub_succ] <;> simp [Nat.succ_sub_succ] at h₁
+    cases i with simp [Nat.succ_sub_succ] <;> simp at h₁
     | succ i => apply ih; simp [h₁]
 
 @[deprecated "Deprecated without replacement." (since := "2025-02-13")]

src/Init/Data/List/Control.lean

@@ -237,8 +237,8 @@ def foldlM {m : Type u → Type v} [Monad m] {s : Type u} {α : Type w} : (f : s
     let s' ← f s a
     List.foldlM f s' as
 
-@[simp, grind] theorem foldlM_nil [Monad m] {f : β → α → m β} {b : β} : [].foldlM f b = pure b := rfl
-@[simp, grind] theorem foldlM_cons [Monad m] {f : β → α → m β} {b : β} {a : α} {l : List α} :
+@[simp, grind =] theorem foldlM_nil [Monad m] {f : β → α → m β} {b : β} : [].foldlM f b = pure b := rfl
+@[simp, grind =] theorem foldlM_cons [Monad m] {f : β → α → m β} {b : β} {a : α} {l : List α} :
     (a :: l).foldlM f b = f b a >>= l.foldlM f := by
   simp [List.foldlM]
 
@@ -261,7 +261,7 @@ example [Monad m] (f : α → β → m β) :
 def foldrM {m : Type u → Type v} [Monad m] {s : Type u} {α : Type w} (f : α → s → m s) (init : s) (l : List α) : m s :=
   l.reverse.foldlM (fun s a => f a s) init
 
-@[simp, grind] theorem foldrM_nil [Monad m] {f : α → β → m β} {b : β} : [].foldrM f b = pure b := rfl
+@[simp, grind =] theorem foldrM_nil [Monad m] {f : α → β → m β} {b : β} : [].foldrM f b = pure b := rfl
 
 /--
 Maps `f` over the list and collects the results with `<|>`. The result for the end of the list is
@@ -347,7 +347,7 @@ theorem findM?_pure {m} [Monad m] [LawfulMonad m] (p : α → Bool) (as : List
     | true  => simp
     | false => simp [ih]
 
-@[simp]
+@[simp, grind =]
 theorem idRun_findM? (p : α → Id Bool) (as : List α) :
     (findM? p as).run = as.find? (p · |>.run) :=
   findM?_pure _ _
@@ -400,7 +400,7 @@ theorem findSomeM?_pure [Monad m] [LawfulMonad m] {f : α → Option β} {as : L
     | some b => simp
     | none   => simp [ih]
 
-@[simp]
+@[simp, grind =]
 theorem idRun_findSomeM? (f : α → Id (Option β)) (as : List α) :
     (findSomeM? f as).run = as.findSome? (f · |>.run) :=
   findSomeM?_pure
@@ -444,23 +444,23 @@ instance : ForIn' m (List α) α inferInstance where
 -- No separate `ForIn` instance is required because it can be derived from `ForIn'`.
 
 -- We simplify `List.forIn'` to `forIn'`.
-@[simp] theorem forIn'_eq_forIn' [Monad m] : @List.forIn' α β m _ = forIn' := rfl
+@[simp, grind =] theorem forIn'_eq_forIn' [Monad m] : @List.forIn' α β m _ = forIn' := rfl
 
-@[simp] theorem forIn'_nil [Monad m] {f : (a : α) → a ∈ [] → β → m (ForInStep β)} {b : β} : forIn' [] b f = pure b :=
+@[simp, grind =] theorem forIn'_nil [Monad m] {f : (a : α) → a ∈ [] → β → m (ForInStep β)} {b : β} : forIn' [] b f = pure b :=
   rfl
 
-@[simp] theorem forIn_nil [Monad m] {f : α → β → m (ForInStep β)} {b : β} : forIn [] b f = pure b :=
+@[simp, grind =] theorem forIn_nil [Monad m] {f : α → β → m (ForInStep β)} {b : β} : forIn [] b f = pure b :=
   rfl
 
 instance : ForM m (List α) α where
   forM := List.forM
 
 -- We simplify `List.forM` to `forM`.
-@[simp] theorem forM_eq_forM [Monad m] : @List.forM m _ α = forM := rfl
+@[simp, grind =] theorem forM_eq_forM [Monad m] : @List.forM m _ α = forM := rfl
 
-@[simp] theorem forM_nil [Monad m] {f : α → m PUnit} : forM [] f = pure ⟨⟩ :=
+@[simp, grind =] theorem forM_nil [Monad m] {f : α → m PUnit} : forM [] f = pure ⟨⟩ :=
   rfl
-@[simp] theorem forM_cons [Monad m] {f : α → m PUnit} {a : α} {as : List α} : forM (a::as) f = f a >>= fun _ => forM as f :=
+@[simp, grind =] theorem forM_cons [Monad m] {f : α → m PUnit} {a : α} {as : List α} : forM (a::as) f = f a >>= fun _ => forM as f :=
   rfl
 
 instance : Functor List where

src/Init/Data/List/Count.lean

@@ -86,7 +86,7 @@ theorem countP_le_length : countP p l ≤ l.length := by
   simp only [countP_eq_length_filter, filter_append, length_append]
 
 @[simp] theorem countP_pos_iff {p} : 0 < countP p l ↔ ∃ a ∈ l, p a := by
-  simp only [countP_eq_length_filter, length_pos_iff_exists_mem, mem_filter, exists_prop]
+  simp only [countP_eq_length_filter, length_pos_iff_exists_mem, mem_filter]
 
 @[simp] theorem one_le_countP_iff {p} : 1 ≤ countP p l ↔ ∃ a ∈ l, p a :=
   countP_pos_iff
@@ -169,7 +169,7 @@ theorem length_filterMap_eq_countP {f : α → Option β} {l : List α} :
   | nil => rfl
   | cons x l ih =>
     simp only [filterMap_cons, countP_cons]
-    split <;> simp [ih, *]
+    split <;> simp [*]
 
 theorem countP_filterMap {p : β → Bool} {f : α → Option β} {l : List α} :
     countP p (filterMap f l) = countP (fun a => ((f a).map p).getD false) l := by

src/Init/Data/List/Erase.lean

@@ -146,7 +146,7 @@ theorem mem_of_mem_eraseP {l : List α} : a ∈ l.eraseP p → a ∈ l := (erase
 @[simp] theorem eraseP_eq_self_iff {p} {l : List α} : l.eraseP p = l ↔ ∀ a ∈ l, ¬ p a := by
   rw [← Sublist.length_eq eraseP_sublist, length_eraseP]
   split <;> rename_i h
-  · simp only [any_eq_true, length_eq_zero_iff] at h
+  · simp only [any_eq_true] at h
     constructor
     · intro; simp_all [Nat.sub_one_eq_self]
     · intro; obtain ⟨x, m, h⟩ := h; simp_all
@@ -287,9 +287,9 @@ theorem eraseP_comm {l : List α} (h : ∀ a ∈ l, ¬ p a ∨ ¬ q a) :
     by_cases h₁ : p a
     · by_cases h₂ : q a
       · simp_all
-      · simp [h₁, h₂, ih (fun b m => h b (mem_cons_of_mem _ m))]
+      · simp [h₁, h₂]
     · by_cases h₂ : q a
-      · simp [h₁, h₂, ih (fun b m => h b (mem_cons_of_mem _ m))]
+      · simp [h₁, h₂]
       · simp [h₁, h₂, ih (fun b m => h b (mem_cons_of_mem _ m))]
 
 theorem head_eraseP_mem {xs : List α} {p : α → Bool} (h) : (xs.eraseP p).head h ∈ xs :=
@@ -578,7 +578,7 @@ theorem eraseIdx_eq_take_drop_succ :
   match l, i with
   | [], _
   | a::l, 0
-  | a::l, i + 1 => simp [Nat.succ_inj]
+  | a::l, i + 1 => simp
 
 @[deprecated eraseIdx_eq_nil_iff (since := "2025-01-30")]
 abbrev eraseIdx_eq_nil := @eraseIdx_eq_nil_iff
@@ -587,7 +587,7 @@ theorem eraseIdx_ne_nil_iff {l : List α} {i : Nat} : eraseIdx l i ≠ [] ↔ 2
   match l with
   | []
   | [a]
-  | a::b::l => simp [Nat.succ_inj]
+  | a::b::l => simp
 
 @[deprecated eraseIdx_ne_nil_iff (since := "2025-01-30")]
 abbrev eraseIdx_ne_nil := @eraseIdx_ne_nil_iff

src/Init/Data/List/FinRange.lean

@@ -62,7 +62,7 @@ end List
 
 namespace Fin
 
-theorem foldlM_eq_foldlM_finRange [Monad m] (f : α → Fin n → m α) (x : α) :
+@[grind =] theorem foldlM_eq_foldlM_finRange [Monad m] (f : α → Fin n → m α) (x : α) :
     foldlM n f x = (List.finRange n).foldlM f x := by
   induction n generalizing x with
   | zero => simp
@@ -72,21 +72,21 @@ theorem foldlM_eq_foldlM_finRange [Monad m] (f : α → Fin n → m α) (x : α)
     funext y
     simp [ih, List.foldlM_map]
 
-theorem foldrM_eq_foldrM_finRange [Monad m] [LawfulMonad m] (f : Fin n → α → m α) (x : α) :
+@[grind =] theorem foldrM_eq_foldrM_finRange [Monad m] [LawfulMonad m] (f : Fin n → α → m α) (x : α) :
     foldrM n f x = (List.finRange n).foldrM f x := by
   induction n generalizing x with
   | zero => simp
   | succ n ih =>
     simp [foldrM_succ, List.finRange_succ, ih, List.foldrM_map]
 
-theorem foldl_eq_finRange_foldl (f : α → Fin n → α) (x : α) :
+@[grind =] theorem foldl_eq_finRange_foldl (f : α → Fin n → α) (x : α) :
     foldl n f x = (List.finRange n).foldl f x := by
   induction n generalizing x with
   | zero => simp
   | succ n ih =>
     simp [foldl_succ, List.finRange_succ, ih, List.foldl_map]
 
-theorem foldr_eq_finRange_foldr (f : Fin n → α → α) (x : α) :
+@[grind =] theorem foldr_eq_finRange_foldr (f : Fin n → α → α) (x : α) :
     foldr n f x = (List.finRange n).foldr f x := by
   induction n generalizing x with
   | zero => simp

src/Init/Data/List/Find.lean

@@ -183,7 +183,7 @@ grind_pattern Sublist.findSome?_isSome => l₁ <+ l₂, l₂.findSome? f
 
 theorem Sublist.findSome?_eq_none {l₁ l₂ : List α} (h : l₁ <+ l₂) :
     l₂.findSome? f = none → l₁.findSome? f = none := by
-  simp only [List.findSome?_eq_none_iff, Bool.not_eq_true]
+  simp only [List.findSome?_eq_none_iff]
   exact fun w x m => w x (Sublist.mem m h)
 
 theorem IsPrefix.findSome?_eq_some {l₁ l₂ : List α} {f : α → Option β} (h : l₁ <+: l₂) :
@@ -383,7 +383,7 @@ theorem find?_flatten_eq_some_iff {xs : List (List α)} {p : α → Bool} {a :
       · simpa using h₂ x (by simpa using ⟨l, ma, m⟩)
       · specialize h₁ _ mb
         simp_all
-    · simp [h₁]
+    · simp
       refine ⟨as, bs, ?_⟩
       refine ⟨?_, ?_, ?_⟩
       · simp_all
@@ -592,7 +592,7 @@ theorem findIdx_eq_length {p : α → Bool} {xs : List α} :
   | cons x xs ih =>
     rw [findIdx_cons, length_cons]
     simp only [cond_eq_if]
-    split <;> simp_all [Nat.succ.injEq]
+    split <;> simp_all
 
 theorem findIdx_eq_length_of_false {p : α → Bool} {xs : List α} (h : ∀ x ∈ xs, p x = false) :
     xs.findIdx p = xs.length := by
@@ -737,7 +737,7 @@ theorem findIdx?_eq_none_iff {xs : List α} {p : α → Bool} :
   | nil => simp_all
   | cons x xs ih =>
     simp only [findIdx?_cons]
-    split <;> simp_all [cond_eq_if]
+    split <;> simp_all
 
 @[simp, grind =]
 theorem findIdx?_isSome {xs : List α} {p : α → Bool} :
@@ -799,13 +799,13 @@ theorem findIdx?_eq_some_iff_getElem {xs : List α} {p : α → Bool} {i : Nat}
   induction xs generalizing i with
   | nil => simp
   | cons x xs ih =>
-    simp only [findIdx?_cons, Nat.zero_add]
+    simp only [findIdx?_cons]
     split
     · simp only [Option.some.injEq, Bool.not_eq_true, length_cons]
       cases i with
       | zero => simp_all
       | succ i =>
-        simp only [Bool.not_eq_true, zero_ne_add_one, getElem_cons_succ, false_iff, not_exists,
+        simp only [zero_ne_add_one, getElem_cons_succ, false_iff, not_exists,
           not_and, Classical.not_forall, Bool.not_eq_false]
         intros
         refine ⟨0, zero_lt_succ i, ‹_›⟩
@@ -830,8 +830,8 @@ theorem of_findIdx?_eq_some {xs : List α} {p : α → Bool} (w : xs.findIdx? p
   induction xs generalizing i with
   | nil => simp_all
   | cons x xs ih =>
-    simp_all only [findIdx?_cons, Nat.zero_add]
-    split at w <;> cases i <;> simp_all [succ_inj]
+    simp_all only [findIdx?_cons]
+    split at w <;> cases i <;> simp_all
 
 @[deprecated of_findIdx?_eq_some (since := "2025-02-02")]
 abbrev findIdx?_of_eq_some := @of_findIdx?_eq_some
@@ -842,7 +842,7 @@ theorem of_findIdx?_eq_none {xs : List α} {p : α → Bool} (w : xs.findIdx? p
   induction xs generalizing i with
   | nil => simp_all
   | cons x xs ih =>
-    simp_all only [Bool.not_eq_true, findIdx?_cons, Nat.zero_add]
+    simp_all only [Bool.not_eq_true, findIdx?_cons]
     cases i with
     | zero =>
       split at w <;> simp_all
@@ -888,7 +888,7 @@ theorem findIdx?_flatten {l : List (List α)} {p : α → Bool} :
   cases n with
   | zero => simp
   | succ n =>
-    simp only [replicate, findIdx?_cons, Nat.zero_add, zero_lt_succ, true_and]
+    simp only [replicate, findIdx?_cons, zero_lt_succ, true_and]
     split <;> simp_all
 
 theorem findIdx?_eq_findSome?_zipIdx {xs : List α} {p : α → Bool} :
@@ -899,7 +899,7 @@ theorem findIdx?_eq_findSome?_zipIdx {xs : List α} {p : α → Bool} :
     simp only [findIdx?_cons, Nat.zero_add, zipIdx]
     split
     · simp_all
-    · simp_all only [zipIdx_cons, ite_false, Option.isNone_none, findSome?_cons_of_isNone, reduceCtorEq]
+    · simp_all only [ite_false, Option.isNone_none, findSome?_cons_of_isNone, reduceCtorEq]
       rw [← map_snd_add_zipIdx_eq_zipIdx (n := 1) (k := 0)]
       simp [Function.comp_def, findSome?_map]
 
@@ -975,7 +975,7 @@ theorem findIdx_eq_getD_findIdx? {xs : List α} {p : α → Bool} :
   | nil => simp
   | cons x xs ih =>
     simp only [findIdx_cons, findIdx?_cons]
-    split <;> simp_all [ih]
+    split <;> simp_all
 
 @[simp] theorem findIdx?_subtype {p : α → Prop} {l : List { x // p x }}
     {f : { x // p x } → Bool} {g : α → Bool} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
@@ -985,7 +985,7 @@ theorem findIdx_eq_getD_findIdx? {xs : List α} {p : α → Bool} :
   | nil => simp
   | cons a l ih =>
     simp [hf, findIdx?_cons]
-    split <;> simp [ih, Function.comp_def]
+    split <;> simp [ih]
 
 /-! ### findFinIdx? -/
 
@@ -1078,7 +1078,7 @@ theorem isNone_findFinIdx? {l : List α} {p : α → Bool} :
     {f : { x // p x } → Bool} {g : α → Bool} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
     l.findFinIdx? f = (l.unattach.findFinIdx? g).map (fun i => i.cast (by simp)) := by
   induction l with
-  | nil => simp [unattach]
+  | nil => simp
   | cons a l ih =>
     simp [hf, findFinIdx?_cons]
     split <;> simp [ih, Function.comp_def]
@@ -1136,7 +1136,7 @@ theorem idxOf_lt_length_of_mem [BEq α] [EquivBEq α] {l : List α} (h : a ∈ l
     simp only [mem_cons] at h
     obtain rfl | h := h
     · simp
-    · simp only [idxOf_cons, cond_eq_if, beq_iff_eq, length_cons]
+    · simp only [idxOf_cons, cond_eq_if, length_cons]
       specialize ih h
       split
       · exact zero_lt_succ xs.length

src/Init/Data/List/Impl.lean

@@ -234,7 +234,7 @@ Examples:
   intro xs; induction xs with intro acc
   | nil => simp [takeWhile, takeWhileTR.go]
   | cons x xs IH =>
-    simp only [takeWhileTR.go, Array.toListImpl_eq, takeWhile]
+    simp only [takeWhileTR.go, takeWhile]
     split
     · intro h; rw [IH] <;> simp_all
     · simp [*]

src/Init/Data/List/Lemmas.lean

@@ -255,7 +255,7 @@ theorem getElem?_cons_zero {l : List α} : (a::l)[0]? = some a := rfl
 
 @[grind =]
 theorem getElem?_cons : (a :: l)[i]? = if i = 0 then some a else l[i-1]? := by
-  cases i <;> simp [getElem?_cons_zero]
+  cases i <;> simp
 
 theorem getElem?_eq_some_iff {l : List α} : l[i]? = some a ↔ ∃ h : i < l.length, l[i] = a :=
   match l with
@@ -287,16 +287,16 @@ theorem getElem_eq_iff {l : List α} {i : Nat} (h : i < l.length) : l[i] = x ↔
   exact ⟨fun w => ⟨h, w⟩, fun h => h.2⟩
 
 theorem getElem_eq_getElem?_get {l : List α} {i : Nat} (h : i < l.length) :
-    l[i] = l[i]?.get (by simp [getElem?_eq_getElem, h]) := by
-  simp [getElem_eq_iff]
+    l[i] = l[i]?.get (by simp [h]) := by
+  simp
 
 theorem getD_getElem? {l : List α} {i : Nat} {d : α} :
     l[i]?.getD d = if p : i < l.length then l[i]'p else d := by
   if h : i < l.length then
-    simp [h, getElem?_def]
+    simp [h]
   else
     have p : i ≥ l.length := Nat.le_of_not_gt h
-    simp [getElem?_eq_none p, h]
+    simp [h]
 
 @[simp] theorem getElem_singleton {a : α} {i : Nat} (h : i < 1) : [a][i] = a := by
   match i, h with
@@ -332,7 +332,7 @@ theorem ext_getElem {l₁ l₂ : List α} (hl : length l₁ = length l₂)
     (h : ∀ (i : Nat) (h₁ : i < l₁.length) (h₂ : i < l₂.length), l₁[i]'h₁ = l₂[i]'h₂) : l₁ = l₂ :=
   ext_getElem? fun n =>
     if h₁ : n < length l₁ then by
-      simp_all [getElem?_eq_getElem]
+      simp_all
     else by
       have h₁ := Nat.le_of_not_lt h₁
       rw [getElem?_eq_none h₁, getElem?_eq_none]; rwa [← hl]
@@ -636,7 +636,7 @@ theorem all_bne' [BEq α] [PartialEquivBEq α] {l : List α} :
 
 @[simp] theorem getElem?_set_self {l : List α} {i : Nat} {a : α} (h : i < l.length) :
     (l.set i a)[i]? = some a := by
-  simp_all [getElem?_eq_some_iff]
+  simp_all
 
 /-- This differs from `getElem?_set_self` by monadically mapping `Function.const _ a` over the `Option`
 returned by `l[i]?`. -/
@@ -679,7 +679,7 @@ theorem getElem?_set_self' {l : List α} {i : Nat} {a : α} :
     subst h
     rw [if_pos rfl]
     split <;> rename_i h
-    · simp only [getElem?_set_self (by simpa), h]
+    · simp only [getElem?_set_self (by simpa)]
     · simp_all
   else
     simp [h]
@@ -1276,9 +1276,9 @@ theorem length_filter_le (p : α → Bool) (l : List α) :
   induction l with
   | nil => simp
   | cons a l ih =>
-    simp only [filter_cons, length_cons, succ_eq_add_one]
+    simp only [filter_cons, length_cons]
     split
-    · simp only [length_cons, succ_eq_add_one]
+    · simp only [length_cons]
       exact Nat.succ_le_succ ih
     · exact Nat.le_trans ih (Nat.le_add_right _ _)
 
@@ -1296,7 +1296,7 @@ theorem length_filter_eq_length_iff {l} : (filter p l).length = l.length ↔ ∀
   induction l with
   | nil => simp
   | cons a l ih =>
-    simp only [filter_cons, length_cons, succ_eq_add_one, mem_cons, forall_eq_or_imp]
+    simp only [filter_cons, length_cons, mem_cons, forall_eq_or_imp]
     split <;> rename_i h
     · simp_all [Nat.add_one_inj] -- Why does the simproc not fire here?
     · have := Nat.ne_of_lt (Nat.lt_succ.mpr (length_filter_le p l))
@@ -1388,7 +1388,7 @@ theorem filter_eq_cons_iff {l} {a} {as} :
       · obtain ⟨l₁, l₂, rfl, w₁, w₂, w₃⟩ := ih h
         exact ⟨x :: l₁, l₂, by simp_all⟩
   · rintro ⟨l₁, l₂, rfl, h₁, h, h₂⟩
-    simp [h₂, filter_cons, filter_eq_nil_iff.mpr h₁, h]
+    simp [h₂, filter_eq_nil_iff.mpr h₁, h]
 
 theorem filter_congr {p q : α → Bool} :
     ∀ {l : List α}, (∀ x ∈ l, p x = q x) → filter p l = filter q l
@@ -1404,7 +1404,7 @@ theorem head_filter_of_pos {p : α → Bool} {l : List α} (w : l ≠ []) (h : p
   | nil => simp
   | cons =>
     simp only [head_cons] at h
-    simp [filter_cons, h]
+    simp [h]
 
 @[simp] theorem filter_sublist {p : α → Bool} : ∀ {l : List α}, filter p l <+ l
   | [] => .slnil
@@ -1420,7 +1420,7 @@ theorem head_filter_of_pos {p : α → Bool} {l : List α} (w : l ≠ []) (h : p
 
 @[simp]
 theorem filterMap_eq_map {f : α → β} : filterMap (some ∘ f) = map f := by
-  funext l; induction l <;> simp [*, filterMap_cons]
+  funext l; induction l <;> simp [*]
 
 /-- Variant of `filterMap_eq_map` with `some ∘ f` expanded out to a lambda. -/
 @[simp]
@@ -1453,7 +1453,7 @@ theorem filterMap_length_eq_length {l} :
   induction l with
   | nil => simp
   | cons a l ih =>
-    simp only [filterMap_cons, length_cons, succ_eq_add_one, mem_cons, forall_eq_or_imp]
+    simp only [filterMap_cons, length_cons, mem_cons, forall_eq_or_imp]
     split <;> rename_i h
     · have := Nat.ne_of_lt (Nat.lt_succ.mpr (length_filterMap_le f l))
       simp_all
@@ -1465,7 +1465,7 @@ theorem filterMap_eq_filter {p : α → Bool} :
   funext l
   induction l with
   | nil => rfl
-  | cons a l IH => by_cases pa : p a <;> simp [filterMap_cons, Option.guard, pa, ← IH]
+  | cons a l IH => by_cases pa : p a <;> simp [Option.guard, pa, ← IH]
 
 @[grind]
 theorem filterMap_filterMap {f : α → Option β} {g : β → Option γ} {l : List α} :
@@ -1512,7 +1512,7 @@ theorem forall_mem_filterMap {f : α → Option β} {l : List α} {P : β → Pr
 
 theorem map_filterMap_of_inv
     {f : α → Option β} {g : β → α} (H : ∀ x : α, (f x).map g = some x) {l : List α} :
-    map g (filterMap f l) = l := by simp only [map_filterMap, H, filterMap_some, id]
+    map g (filterMap f l) = l := by simp only [map_filterMap, H, filterMap_some]
 
 theorem head_filterMap_of_eq_some {f : α → Option β} {l : List α} (w : l ≠ []) {b : β} (h : f (l.head w) = some b) :
     (filterMap f l).head ((ne_nil_of_mem (mem_filterMap.2 ⟨_, head_mem w, h⟩))) =
@@ -1521,7 +1521,7 @@ theorem head_filterMap_of_eq_some {f : α → Option β} {l : List α} (w : l
   | nil => simp at w
   | cons a l =>
     simp only [head_cons] at h
-    simp [filterMap_cons, h]
+    simp [h]
 
 @[grind →]
 theorem forall_none_of_filterMap_eq_nil (h : filterMap f xs = []) : ∀ x ∈ xs, f x = none := by
@@ -1613,7 +1613,7 @@ theorem getElem?_append_left {l₁ l₂ : List α} {i : Nat} (hn : i < l₁.leng
     (l₁ ++ l₂)[i]? = l₁[i]? := by
   have hn' : i < (l₁ ++ l₂).length := Nat.lt_of_lt_of_le hn <|
     length_append .. ▸ Nat.le_add_right ..
-  simp_all [getElem?_eq_getElem, getElem_append]
+  simp_all
 
 theorem getElem?_append_right : ∀ {l₁ l₂ : List α} {i : Nat}, l₁.length ≤ i →
   (l₁ ++ l₂)[i]? = l₂[i - l₁.length]?
@@ -1817,10 +1817,10 @@ theorem filterMap_eq_append_iff {f : α → Option β} :
         intro h
         rcases cons_eq_append_iff.mp h with (⟨rfl, rfl⟩ | ⟨_, ⟨rfl, h⟩⟩)
         · refine ⟨[], x :: l, ?_⟩
-          simp [filterMap_cons, w]
+          simp [w]
         · obtain ⟨l₁, l₂, rfl, rfl, rfl⟩ := ih ‹_›
           refine ⟨x :: l₁, l₂, ?_⟩
-          simp [filterMap_cons, w]
+          simp [w]
   · rintro ⟨l₁, l₂, rfl, rfl, rfl⟩
     simp
 
@@ -1885,7 +1885,7 @@ theorem append_concat {a : α} {l₁ l₂ : List α} : l₁ ++ concat l₂ a = c
 theorem map_concat {f : α → β} {a : α} {l : List α} : map f (concat l a) = concat (map f l) (f a) := by
   induction l with
   | nil => rfl
-  | cons x xs ih => simp [ih]
+  | cons x xs ih => simp
 
 theorem eq_nil_or_concat : ∀ l : List α, l = [] ∨ ∃ l' b, l = concat l' b
   | [] => .inl rfl
@@ -2191,7 +2191,7 @@ theorem forall_mem_replicate {p : α → Prop} {a : α} {n} :
   · rw [getElem?_eq_none (by simpa using h), if_neg h]
 
 @[simp] theorem getElem?_replicate_of_lt {n : Nat} {i : Nat} (h : i < n) : (replicate n a)[i]? = some a := by
-  simp [getElem?_replicate, h]
+  simp [h]
 
 @[grind] theorem head?_replicate {a : α} {n : Nat} : (replicate n a).head? = if n = 0 then none else some a := by
   cases n <;> simp [replicate_succ]
@@ -2329,8 +2329,8 @@ theorem filterMap_replicate_of_some {f : α → Option β} (h : f a = some b) :
   induction n with
   | zero => simp
   | succ n ih =>
-    simp only [replicate_succ, flatten_cons, ih, replicate_append_replicate, replicate_inj, or_true,
-      and_true, add_one_mul, Nat.add_comm]
+    simp only [replicate_succ, flatten_cons, ih, replicate_append_replicate, 
+      add_one_mul, Nat.add_comm]
 
 theorem flatMap_replicate {β} {f : α → List β} : (replicate n a).flatMap f = (replicate n (f a)).flatten := by
   induction n with
@@ -2413,7 +2413,7 @@ theorem reverse_ne_nil_iff {xs : List α} : xs.reverse ≠ [] ↔ xs ≠ [] :=
 theorem getElem?_reverse' : ∀ {l : List α} {i j}, i + j + 1 = length l →
     l.reverse[i]? = l[j]?
   | [], _, _, _ => rfl
-  | a::l, i, 0, h => by simp [Nat.succ.injEq] at h; simp [h, getElem?_append_right, Nat.succ.injEq]
+  | a::l, i, 0, h => by simp [Nat.succ.injEq] at h; simp [h]
   | a::l, i, j+1, h => by
     have := Nat.succ.inj h; simp at this ⊢
     rw [getElem?_append_left, getElem?_reverse' this]
@@ -2649,7 +2649,7 @@ theorem foldl_map_hom {g : α → β} {f : α → α → α} {f' : β → β →
     (l.map g).foldl f' (g a) = g (l.foldl f a) := by
   induction l generalizing a
   · simp
-  · simp [*, h]
+  · simp [*]
 
 @[deprecated foldl_map_hom (since := "2025-01-20")] abbrev foldl_map' := @foldl_map_hom
 
@@ -2658,7 +2658,7 @@ theorem foldr_map_hom {g : α → β} {f : α → α → α} {f' : β → β →
     (l.map g).foldr f' (g a) = g (l.foldr f a) := by
   induction l generalizing a
   · simp
-  · simp [*, h]
+  · simp [*]
 
 @[deprecated foldr_map_hom (since := "2025-01-20")] abbrev foldr_map' := @foldr_map_hom
 
@@ -2742,11 +2742,11 @@ def foldlRecOn {motive : β → Sort _} : ∀ (l : List α) (op : β → α →
     foldlRecOn tl op (hl b hb hd mem_cons_self)
       fun y hy x hx => hl y hy x (mem_cons_of_mem hd hx)
 
-@[simp] theorem foldlRecOn_nil {motive : β → Sort _} {op : β → α → β} (hb : motive b)
+@[simp, grind =] theorem foldlRecOn_nil {motive : β → Sort _} {op : β → α → β} (hb : motive b)
     (hl : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ []), motive (op b a)) :
     foldlRecOn [] op hb hl = hb := rfl
 
-@[simp] theorem foldlRecOn_cons {motive : β → Sort _} {op : β → α → β} (hb : motive b)
+@[simp, grind =] theorem foldlRecOn_cons {motive : β → Sort _} {op : β → α → β} (hb : motive b)
     (hl : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ x :: l), motive (op b a)) :
     foldlRecOn (x :: l) op hb hl =
       foldlRecOn l op (hl b hb x mem_cons_self)
@@ -2777,11 +2777,11 @@ def foldrRecOn {motive : β → Sort _} : ∀ (l : List α) (op : α → β →
     hl (foldr op b l)
       (foldrRecOn l op hb fun b c a m => hl b c a (mem_cons_of_mem x m)) x mem_cons_self
 
-@[simp] theorem foldrRecOn_nil {motive : β → Sort _} {op : α → β → β} (hb : motive b)
+@[simp, grind =] theorem foldrRecOn_nil {motive : β → Sort _} {op : α → β → β} (hb : motive b)
     (hl : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ []), motive (op a b)) :
     foldrRecOn [] op hb hl = hb := rfl
 
-@[simp] theorem foldrRecOn_cons {motive : β → Sort _} {op : α → β → β} (hb : motive b)
+@[simp, grind =] theorem foldrRecOn_cons {motive : β → Sort _} {op : α → β → β} (hb : motive b)
     (hl : ∀ (b : β) (_ : motive b) (a : α) (_ : a ∈ x :: l), motive (op a b)) :
     foldrRecOn (x :: l) op hb hl =
       hl _ (foldrRecOn l op hb fun b c a m => hl b c a (mem_cons_of_mem x m))
@@ -2847,7 +2847,7 @@ theorem foldr_rel {l : List α} {f : α → β → β} {g : α → γ → γ} {a
     by_cases h' : l = []
     · simp_all
     · simp only [head_eq_iff_head?_eq_some, head?_reverse] at ih
-      simp [ih, h, h', getLast_cons, head_eq_iff_head?_eq_some]
+      simp [ih, h', getLast_cons, head_eq_iff_head?_eq_some]
 
 theorem getLast_eq_head_reverse {l : List α} (h : l ≠ []) :
     l.getLast h = l.reverse.head (by simp_all) := by
@@ -2917,13 +2917,13 @@ theorem getLast_filterMap_of_eq_some {f : α → Option β} {l : List α} (w : l
   rw [head_filterMap_of_eq_some (by simp_all)]
   simp_all
 
-theorem getLast?_flatMap {l : List α} {f : α → List β} :
+@[grind =] theorem getLast?_flatMap {l : List α} {f : α → List β} :
     (l.flatMap f).getLast? = l.reverse.findSome? fun a => (f a).getLast? := by
   simp only [← head?_reverse, reverse_flatMap]
   rw [head?_flatMap]
   rfl
 
-theorem getLast?_flatten {L : List (List α)} :
+@[grind =] theorem getLast?_flatten {L : List (List α)} :
     (flatten L).getLast? = L.reverse.findSome? fun l => l.getLast? := by
   simp [← flatMap_id, getLast?_flatMap]
 
@@ -2938,7 +2938,7 @@ theorem getLast?_replicate {a : α} {n : Nat} : (replicate n a).getLast? = if n
 /-! ### leftpad -/
 
 -- We unfold `leftpad` and `rightpad` for verification purposes.
-attribute [simp] leftpad rightpad
+attribute [simp, grind] leftpad rightpad
 
 -- `length_leftpad` and `length_rightpad` are in `Init.Data.List.Nat.Basic`.
 
@@ -3042,6 +3042,9 @@ we do not separately develop much theory about it.
 theorem mem_partition : a ∈ l ↔ a ∈ (partition p l).1 ∨ a ∈ (partition p l).2 := by
   by_cases p a <;> simp_all
 
+grind_pattern mem_partition => a ∈ (partition p l).1
+grind_pattern mem_partition => a ∈ (partition p l).2
+
 /-! ### dropLast
 
 `dropLast` is the specification for `Array.pop`, so theorems about `List.dropLast`
@@ -3113,7 +3116,7 @@ theorem dropLast_concat_getLast : ∀ {l : List α} (h : l ≠ []), dropLast l +
     congr
     exact dropLast_concat_getLast (cons_ne_nil b l)
 
-@[simp] theorem map_dropLast {f : α → β} {l : List α} : l.dropLast.map f = (l.map f).dropLast := by
+@[simp, grind _=_] theorem map_dropLast {f : α → β} {l : List α} : l.dropLast.map f = (l.map f).dropLast := by
   induction l with
   | nil => rfl
   | cons x xs ih => cases xs <;> simp [ih]
@@ -3125,6 +3128,7 @@ theorem dropLast_concat_getLast : ∀ {l : List α} (h : l ≠ []), dropLast l +
     rw [cons_append, dropLast, dropLast_append_of_ne_nil h, cons_append]
     simp [h]
 
+@[grind =]
 theorem dropLast_append {l₁ l₂ : List α} :
     (l₁ ++ l₂).dropLast = if l₂.isEmpty then l₁.dropLast else l₁ ++ l₂.dropLast := by
   split <;> simp_all
@@ -3132,9 +3136,9 @@ theorem dropLast_append {l₁ l₂ : List α} :
 theorem dropLast_append_cons : dropLast (l₁ ++ b :: l₂) = l₁ ++ dropLast (b :: l₂) := by
   simp
 
-@[simp] theorem dropLast_concat : dropLast (l₁ ++ [b]) = l₁ := by simp
+@[simp, grind =] theorem dropLast_concat : dropLast (l₁ ++ [b]) = l₁ := by simp
 
-@[simp] theorem dropLast_replicate {n : Nat} {a : α} : dropLast (replicate n a) = replicate (n - 1) a := by
+@[simp, grind =] theorem dropLast_replicate {n : Nat} {a : α} : dropLast (replicate n a) = replicate (n - 1) a := by
   match n with
   | 0 => simp
   | 1 => simp [replicate_succ]
@@ -3147,7 +3151,7 @@ theorem dropLast_append_cons : dropLast (l₁ ++ b :: l₂) = l₁ ++ dropLast (
     dropLast (a :: replicate n a) = replicate n a := by
   rw [← replicate_succ, dropLast_replicate, Nat.add_sub_cancel]
 
-@[simp] theorem tail_reverse {l : List α} : l.reverse.tail = l.dropLast.reverse := by
+@[simp, grind _=_] theorem tail_reverse {l : List α} : l.reverse.tail = l.dropLast.reverse := by
   apply ext_getElem
   · simp
   · intro i h₁ h₂
@@ -3387,20 +3391,21 @@ theorem replace_append_right [LawfulBEq α] {l₁ l₂ : List α} (h : ¬ a ∈
     (l₁ ++ l₂).replace a b = l₁ ++ l₂.replace a b := by
   simp [replace_append, h]
 
+@[grind _=_]
 theorem replace_take {l : List α} {i : Nat} :
     (l.take i).replace a b = (l.replace a b).take i := by
   induction l generalizing i with
   | nil => simp
   | cons x xs ih =>
     cases i with
-    | zero => simp [ih]
+    | zero => simp
     | succ i =>
       simp only [replace_cons, take_succ_cons]
       split <;> simp_all
 
 @[simp] theorem replace_replicate_self [LawfulBEq α] {a : α} (h : 0 < n) :
     (replicate n a).replace a b = b :: replicate (n - 1) a := by
-  cases n <;> simp_all [replicate_succ, replace_cons]
+  cases n <;> simp_all [replicate_succ]
 
 @[simp] theorem replace_replicate_ne [LawfulBEq α] {a b c : α} (h : !b == a) :
     (replicate n a).replace b c = replicate n a := by
@@ -3502,11 +3507,11 @@ theorem getElem?_insert_succ {l : List α} {a : α} {i : Nat} :
   apply Option.some.inj
   rw [← getElem?_eq_getElem, getElem?_insert]
   split
-  · simp [getElem?_eq_getElem, h]
+  · simp [h]
   · split
     · rfl
     · have h' : i - 1 < l.length := Nat.lt_of_le_of_lt (Nat.pred_le _) h
-      simp [getElem?_eq_getElem, h']
+      simp [h']
 
 theorem head?_insert {l : List α} {a : α} :
     (l.insert a).head? = some (if h : a ∈ l then l.head (ne_nil_of_mem h) else a) := by
@@ -3527,7 +3532,7 @@ theorem head_insert {l : List α} {a : α} (w) :
 
 theorem insert_append_of_mem_left {l₁ l₂ : List α} (h : a ∈ l₂) :
     (l₁ ++ l₂).insert a = l₁ ++ l₂ := by
-  simp [insert_append, h]
+  simp [h]
 
 theorem insert_append_of_not_mem_left {l₁ l₂ : List α} (h : ¬ a ∈ l₂) :
     (l₁ ++ l₂).insert a = l₁.insert a ++ l₂ := by
@@ -3553,10 +3558,10 @@ end insert
 
 /-! ### `removeAll` -/
 
-@[simp] theorem removeAll_nil [BEq α] {xs : List α} : xs.removeAll [] = xs := by
+@[simp, grind =] theorem removeAll_nil [BEq α] {xs : List α} : xs.removeAll [] = xs := by
   simp [removeAll]
 
-theorem cons_removeAll [BEq α] {x : α} {xs ys : List α} :
+@[grind =] theorem cons_removeAll [BEq α] {x : α} {xs ys : List α} :
     (x :: xs).removeAll ys =
       if ys.contains x = false then
         x :: xs.removeAll ys
@@ -3564,6 +3569,7 @@ theorem cons_removeAll [BEq α] {x : α} {xs ys : List α} :
         xs.removeAll ys := by
   simp [removeAll, filter_cons]
 
+@[grind =]
 theorem removeAll_cons [BEq α] {xs : List α} {y : α} {ys : List α} :
     xs.removeAll (y :: ys) = (xs.filter fun x => !x == y).removeAll ys := by
   simp [removeAll, Bool.and_comm]
@@ -3583,7 +3589,7 @@ theorem removeAll_cons [BEq α] {xs : List α} {y : α} {ys : List α} :
 
 /-! ### `eraseDupsBy` and `eraseDups` -/
 
-@[simp] theorem eraseDupsBy_nil : ([] : List α).eraseDupsBy r = [] := rfl
+@[simp, grind =] theorem eraseDupsBy_nil : ([] : List α).eraseDupsBy r = [] := rfl
 
 private theorem eraseDupsBy_loop_cons {as bs : List α} {r : α → α → Bool} :
     eraseDupsBy.loop r as bs = bs.reverse ++ eraseDupsBy.loop r (as.filter fun a => !bs.any (r a)) [] := by
@@ -3603,17 +3609,19 @@ private theorem eraseDupsBy_loop_cons {as bs : List α} {r : α → α → Bool}
       simp
 termination_by as.length
 
+@[grind =]
 theorem eraseDupsBy_cons :
     (a :: as).eraseDupsBy r = a :: (as.filter fun b => r b a = false).eraseDupsBy r := by
   simp only [eraseDupsBy, eraseDupsBy.loop, any_nil]
   rw [eraseDupsBy_loop_cons]
   simp
 
-@[simp] theorem eraseDups_nil [BEq α] : ([] : List α).eraseDups = [] := rfl
-theorem eraseDups_cons [BEq α] {a : α} {as : List α} :
+@[simp, grind =] theorem eraseDups_nil [BEq α] : ([] : List α).eraseDups = [] := rfl
+@[grind =] theorem eraseDups_cons [BEq α] {a : α} {as : List α} :
     (a :: as).eraseDups = a :: (as.filter fun b => !b == a).eraseDups := by
   simp [eraseDups, eraseDupsBy_cons]
 
+@[grind =]
 theorem eraseDups_append [BEq α] [LawfulBEq α] {as bs : List α} :
     (as ++ bs).eraseDups = as.eraseDups ++ (bs.removeAll as).eraseDups := by
   match as with
@@ -3685,7 +3693,7 @@ theorem getElem!_of_getElem? [Inhabited α] : ∀ {l : List α} {i : Nat}, l[i]?
     rw [getElem!_pos] <;> simp_all
   | _::l, _+1, e => by
     simp at e
-    simp_all [getElem!_of_getElem? (l := l) e]
+    simp_all
 
 theorem ext_get {l₁ l₂ : List α} (hl : length l₁ = length l₂)
     (h : ∀ n h₁ h₂, get l₁ ⟨n, h₁⟩ = get l₂ ⟨n, h₂⟩) : l₁ = l₂ :=

src/Init/Data/List/MapIdx.lean

@@ -218,8 +218,8 @@ theorem mapFinIdx_eq_cons_iff {l : List α} {b : β} {f : (i : Nat) → α → (
   cases l with
   | nil => simp
   | cons x l' =>
-    simp only [mapFinIdx_cons, cons.injEq, length_cons, Fin.zero_eta, Fin.cast_succ_eq,
-      exists_and_left]
+    simp only [mapFinIdx_cons, cons.injEq, 
+      ]
     constructor
     · rintro ⟨rfl, rfl⟩
       refine ⟨x, l', ⟨rfl, rfl⟩, by simp⟩
@@ -267,7 +267,7 @@ theorem mapFinIdx_eq_append_iff {l : List α} {f : (i : Nat) → α → (h : i <
       · simp
         omega
       · intro i hi₁ hi₂
-        simp only [getElem_mapFinIdx, getElem_take]
+        simp only [getElem_mapFinIdx]
         simp only [length_take, getElem_drop]
         have : l₁.length ≤ l.length := by omega
         simp only [Nat.min_eq_left this, Nat.add_comm]
@@ -286,7 +286,7 @@ theorem mapFinIdx_eq_append_iff {l : List α} {f : (i : Nat) → α → (h : i <
 theorem mapFinIdx_eq_mapFinIdx_iff {l : List α} {f g : (i : Nat) → α → (h : i < l.length) → β} :
     l.mapFinIdx f = l.mapFinIdx g ↔ ∀ (i : Nat) (h : i < l.length), f i l[i] h = g i l[i] h := by
   rw [eq_comm, mapFinIdx_eq_iff]
-  simp [Fin.forall_iff]
+  simp
 
 @[simp, grind =] theorem mapFinIdx_mapFinIdx {l : List α}
     {f : (i : Nat) → α → (h : i < l.length) → β}
@@ -341,7 +341,7 @@ theorem getElem?_mapIdx_go : ∀ {l : List α} {acc : Array β} {i : Nat},
     (mapIdx.go f l acc)[i]? =
       if h : i < acc.size then some acc[i] else Option.map (f i) l[i - acc.size]?
   | [], acc, i => by
-    simp only [mapIdx.go, Array.toListImpl_eq, getElem?_def, Array.length_toList,
+    simp only [mapIdx.go, getElem?_def, Array.length_toList,
       ← Array.getElem_toList, length_nil, Nat.not_lt_zero, ↓reduceDIte, Option.map_none]
   | a :: l, acc, i => by
     rw [mapIdx.go, getElem?_mapIdx_go]
@@ -524,7 +524,7 @@ theorem mapIdx_eq_replicate_iff {l : List α} {f : Nat → α → β} {b : β} :
   simp [mapIdx_eq_iff]
   intro i
   by_cases h : i < l.length
-  · simp [getElem?_reverse, h]
+  · simp [h]
     congr
     omega
   · simp at h

src/Init/Data/List/Monadic.lean

@@ -60,27 +60,27 @@ theorem mapM'_eq_mapM [Monad m] [LawfulMonad m] {f : α → m β} {l : List α}
     | [], acc => by simp [mapM.loop, mapM']
     | a::l, acc => by simp [go l, mapM.loop, mapM']
 
-@[simp] theorem mapM_nil [Monad m] {f : α → m β} : [].mapM f = pure [] := rfl
+@[simp, grind =] theorem mapM_nil [Monad m] {f : α → m β} : [].mapM f = pure [] := rfl
 
-@[simp] theorem mapM_cons [Monad m] [LawfulMonad m] {f : α → m β} :
+@[simp, grind =] theorem mapM_cons [Monad m] [LawfulMonad m] {f : α → m β} :
     (a :: l).mapM f = (return (← f a) :: (← l.mapM f)) := by simp [← mapM'_eq_mapM, mapM']
 
 @[simp] theorem mapM_pure [Monad m] [LawfulMonad m] {l : List α} {f : α → β} :
     l.mapM (m := m) (pure <| f ·) = pure (l.map f) := by
   induction l <;> simp_all
 
-@[simp] theorem idRun_mapM {l : List α} {f : α → Id β} : (l.mapM f).run = l.map (f · |>.run) :=
+@[simp, grind =] theorem idRun_mapM {l : List α} {f : α → Id β} : (l.mapM f).run = l.map (f · |>.run) :=
   mapM_pure
 
 @[deprecated idRun_mapM (since := "2025-05-21")]
 theorem mapM_id {l : List α} {f : α → Id β} : (l.mapM f).run = l.map (f · |>.run) :=
   mapM_pure
 
-@[simp] theorem mapM_map [Monad m] [LawfulMonad m] {f : α → β} {g : β → m γ} {l : List α} :
+@[simp, grind =] theorem mapM_map [Monad m] [LawfulMonad m] {f : α → β} {g : β → m γ} {l : List α} :
     (l.map f).mapM g = l.mapM (g ∘ f) := by
   induction l <;> simp_all
 
-@[simp] theorem mapM_append [Monad m] [LawfulMonad m] {f : α → m β} {l₁ l₂ : List α} :
+@[simp, grind =] theorem mapM_append [Monad m] [LawfulMonad m] {f : α → m β} {l₁ l₂ : List α} :
     (l₁ ++ l₂).mapM f = (return (← l₁.mapM f) ++ (← l₂.mapM f)) := by induction l₁ <;> simp [*]
 
 /-- Auxiliary lemma for `mapM_eq_reverse_foldlM_cons`. -/
@@ -90,8 +90,8 @@ theorem foldlM_cons_eq_append [Monad m] [LawfulMonad m] {f : α → m β} {as :
   induction as generalizing b bs with
   | nil => simp
   | cons a as ih =>
-    simp only [bind_pure_comp] at ih
-    simp [ih, _root_.map_bind, Functor.map_map, Function.comp_def]
+    simp only at ih
+    simp [ih, _root_.map_bind, Functor.map_map]
 
 theorem mapM_eq_reverse_foldlM_cons [Monad m] [LawfulMonad m] {f : α → m β} {l : List α} :
     mapM f l = reverse <$> (l.foldlM (fun acc a => (· :: acc) <$> f a) []) := by
@@ -99,14 +99,14 @@ theorem mapM_eq_reverse_foldlM_cons [Monad m] [LawfulMonad m] {f : α → m β}
   induction l with
   | nil => simp
   | cons a as ih =>
-    simp only [mapM'_cons, ih, bind_map_left, foldlM_cons, LawfulMonad.bind_assoc, pure_bind,
-      foldlM_cons_eq_append, _root_.map_bind, Functor.map_map, Function.comp_def, reverse_append,
+    simp only [mapM'_cons, ih, bind_map_left, foldlM_cons, 
+      foldlM_cons_eq_append, _root_.map_bind, Functor.map_map, reverse_append,
       reverse_cons, reverse_nil, nil_append, singleton_append]
     simp [bind_pure_comp]
 
 /-! ### filterMapM -/
 
-@[simp] theorem filterMapM_nil [Monad m] {f : α → m (Option β)} : [].filterMapM f = pure [] := rfl
+@[simp, grind =] theorem filterMapM_nil [Monad m] {f : α → m (Option β)} : [].filterMapM f = pure [] := rfl
 
 theorem filterMapM_loop_eq [Monad m] [LawfulMonad m] {f : α → m (Option β)} {l : List α} {acc : List β} :
     filterMapM.loop f l acc = (acc.reverse ++ ·) <$> filterMapM.loop f l [] := by
@@ -121,7 +121,7 @@ theorem filterMapM_loop_eq [Monad m] [LawfulMonad m] {f : α → m (Option β)}
     · rw [ih, ih (acc := [b])]
       simp
 
-@[simp] theorem filterMapM_cons [Monad m] [LawfulMonad m] {f : α → m (Option β)} :
+@[simp, grind =] theorem filterMapM_cons [Monad m] [LawfulMonad m] {f : α → m (Option β)} :
     (a :: l).filterMapM f = do
       match (← f a) with
       | none => filterMapM f l
@@ -137,20 +137,20 @@ theorem filterMapM_loop_eq [Monad m] [LawfulMonad m] {f : α → m (Option β)}
 
 /-! ### flatMapM -/
 
-@[simp] theorem flatMapM_nil [Monad m] {f : α → m (List β)} : [].flatMapM f = pure [] := rfl
+@[simp, grind =] theorem flatMapM_nil [Monad m] {f : α → m (List β)} : [].flatMapM f = pure [] := rfl
 
 theorem flatMapM_loop_eq [Monad m] [LawfulMonad m] {f : α → m (List β)} {l : List α} {acc : List (List β)} :
     flatMapM.loop f l acc = (acc.reverse.flatten ++ ·) <$> flatMapM.loop f l [] := by
   induction l generalizing acc with
   | nil => simp [flatMapM.loop]
   | cons a l ih =>
-    simp only [flatMapM.loop, append_nil, _root_.map_bind]
+    simp only [flatMapM.loop, _root_.map_bind]
     congr
     funext bs
     rw [ih, ih (acc := [bs])]
     simp
 
-@[simp] theorem flatMapM_cons [Monad m] [LawfulMonad m] {f : α → m (List β)} :
+@[simp, grind =] theorem flatMapM_cons [Monad m] [LawfulMonad m] {f : α → m (List β)} :
     (a :: l).flatMapM f = do
       let bs ← f a
       return (bs ++ (← l.flatMapM f)) := by
@@ -230,11 +230,11 @@ theorem forM_cons' [Monad m] :
     (a::as).forM f = (f a >>= fun _ => as.forM f : m PUnit) :=
   List.forM_cons
 
-@[simp] theorem forM_append [Monad m] [LawfulMonad m] {l₁ l₂ : List α} {f : α → m PUnit} :
+@[simp, grind =] theorem forM_append [Monad m] [LawfulMonad m] {l₁ l₂ : List α} {f : α → m PUnit} :
     forM (l₁ ++ l₂) f = (do forM l₁ f; forM l₂ f) := by
   induction l₁ <;> simp [*]
 
-@[simp] theorem forM_map [Monad m] [LawfulMonad m] {l : List α} {g : α → β} {f : β → m PUnit} :
+@[simp, grind =] theorem forM_map [Monad m] [LawfulMonad m] {l : List α} {g : α → β} {f : β → m PUnit} :
     forM (l.map g) f = forM l (fun a => f (g a)) := by
   induction l <;> simp [*]
 
@@ -257,7 +257,7 @@ theorem forIn'_loop_congr [Monad m] {as bs : List α}
       · simp
         rw [ih]
 
-@[simp] theorem forIn'_cons [Monad m] {a : α} {as : List α}
+@[simp, grind =] theorem forIn'_cons [Monad m] {a : α} {as : List α}
     (f : (a' : α) → a' ∈ a :: as → β → m (ForInStep β)) (b : β) :
     forIn' (a::as) b f = f a mem_cons_self b >>=
       fun | ForInStep.done b => pure b | ForInStep.yield b => forIn' as b fun a' m b => f a' (mem_cons_of_mem a m) b := by
@@ -270,7 +270,7 @@ theorem forIn'_loop_congr [Monad m] {as bs : List α}
     intros
     rfl
 
-@[simp] theorem forIn_cons [Monad m] (f : α → β → m (ForInStep β)) (a : α) (as : List α) (b : β) :
+@[simp, grind =] theorem forIn_cons [Monad m] (f : α → β → m (ForInStep β)) (a : α) (as : List α) (b : β) :
     forIn (a::as) b f = f a b >>= fun | ForInStep.done b => pure b | ForInStep.yield b => forIn as b f := by
   have := forIn'_cons (a := a) (as := as) (fun a' _ b => f a' b) b
   simpa only [forIn'_eq_forIn]
@@ -363,7 +363,7 @@ theorem forIn'_yield_eq_foldl
       l.attach.foldl (fun b ⟨a, h⟩ => f a h b) init :=
   forIn'_pure_yield_eq_foldl _ _
 
-@[simp] theorem forIn'_map [Monad m] [LawfulMonad m]
+@[simp, grind =] theorem forIn'_map [Monad m] [LawfulMonad m]
     {l : List α} (g : α → β) (f : (b : β) → b ∈ l.map g → γ → m (ForInStep γ)) :
     forIn' (l.map g) init f = forIn' l init fun a h y => f (g a) (mem_map_of_mem h) y := by
   induction l generalizing init <;> simp_all
@@ -381,7 +381,7 @@ theorem forIn_eq_foldlM [Monad m] [LawfulMonad m]
   induction l generalizing init with
   | nil => simp
   | cons a as ih =>
-    simp only [foldlM_cons, bind_pure_comp, forIn_cons, _root_.map_bind]
+    simp only [foldlM_cons, forIn_cons, _root_.map_bind]
     congr 1
     funext x
     match x with
@@ -422,7 +422,7 @@ theorem forIn_yield_eq_foldl
       l.foldl (fun b a => f a b) init :=
   forIn_pure_yield_eq_foldl _ _
 
-@[simp] theorem forIn_map [Monad m] [LawfulMonad m]
+@[simp, grind =] theorem forIn_map [Monad m] [LawfulMonad m]
     {l : List α} {g : α → β} {f : β → γ → m (ForInStep γ)} :
     forIn (l.map g) init f = forIn l init fun a y => f (g a) y := by
   induction l generalizing init <;> simp_all
@@ -444,7 +444,7 @@ theorem allM_eq_not_anyM_not [Monad m] [LawfulMonad m] {p : α → m Bool} {as :
   induction as with
   | nil => simp
   | cons a as ih =>
-    simp only [anyM, ih, pure_bind, all_cons]
+    simp only [anyM, ih, pure_bind]
     split <;> simp_all
 
 @[simp] theorem allM_pure [Monad m] [LawfulMonad m] {p : α → Bool} {as : List α} :
@@ -486,7 +486,7 @@ and simplifies these to the function directly taking the value.
   induction l generalizing x with
   | nil => simp
   | cons a l ih =>
-    simp [ih, hf, foldrM_cons]
+    simp [ih, foldrM_cons]
     congr
     funext b
     simp [hf]

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

@@ -26,6 +26,7 @@ namespace List
 
 /-! ### dropLast -/
 
+@[grind _=_]
 theorem tail_dropLast {l : List α} : tail (dropLast l) = dropLast (tail l) := by
   ext1
   simp only [getElem?_tail, getElem?_dropLast, length_tail]
@@ -35,7 +36,7 @@ theorem tail_dropLast {l : List α} : tail (dropLast l) = dropLast (tail l) := b
   · omega
   · rfl
 
-@[simp] theorem dropLast_reverse {l : List α} : l.reverse.dropLast = l.tail.reverse := by
+@[simp, grind _=_] theorem dropLast_reverse {l : List α} : l.reverse.dropLast = l.tail.reverse := by
   apply ext_getElem
   · simp
   · intro i h₁ h₂
@@ -67,7 +68,7 @@ theorem length_filterMap_pos_iff {xs : List α} {f : α → Option β} :
   | cons x xs ih =>
     simp only [filterMap, mem_cons, exists_prop, exists_eq_or_imp]
     split
-    · simp_all [ih]
+    · simp_all
     · simp_all
 
 @[simp]
@@ -114,8 +115,8 @@ section intersperse
 
 variable {l : List α} {sep : α} {i : Nat}
 
-@[simp] theorem length_intersperse : (l.intersperse sep).length = 2 * l.length - 1 := by
-  fun_induction intersperse <;> simp only [intersperse, length_cons, length_nil] at *
+@[simp, grind =] theorem length_intersperse : (l.intersperse sep).length = 2 * l.length - 1 := by
+  fun_induction intersperse <;> simp only [length_cons, length_nil] at *
   rename_i h _
   have := length_pos_iff.mpr h
   omega
@@ -193,7 +194,7 @@ theorem mem_eraseIdx_iff_getElem {x : α} :
   | a::l, 0 => by simp [mem_iff_getElem, Nat.succ_lt_succ_iff]
   | a::l, k+1 => by
     rw [← Nat.or_exists_add_one]
-    simp [mem_eraseIdx_iff_getElem, @eq_comm _ a, succ_inj, Nat.succ_lt_succ_iff]
+    simp [mem_eraseIdx_iff_getElem, @eq_comm _ a, Nat.succ_lt_succ_iff]
 
 theorem mem_eraseIdx_iff_getElem? {x : α} {l} {k} : x ∈ eraseIdx l k ↔ ∃ i ≠ k, l[i]? = some x := by
   simp only [mem_eraseIdx_iff_getElem, getElem_eq_iff, exists_and_left]

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

@@ -16,6 +16,7 @@ namespace List
 
 open Nat
 
+@[grind =]
 theorem countP_set {p : α → Bool} {l : List α} {i : Nat} {a : α} (h : i < l.length) :
     (l.set i a).countP p = l.countP p - (if p l[i] then 1 else 0) + (if p a then 1 else 0) := by
   induction l generalizing i with
@@ -29,10 +30,12 @@ theorem countP_set {p : α → Bool} {l : List α} {i : Nat} {a : α} (h : i < l
       have : (if p l[i] = true then 1 else 0) ≤ l.countP p := boole_getElem_le_countP (p := p) h
       omega
 
+@[grind =]
 theorem count_set [BEq α] {a b : α} {l : List α} {i : Nat} (h : i < l.length) :
     (l.set i a).count b = l.count b - (if l[i] == b then 1 else 0) + (if a == b then 1 else 0) := by
   simp [count_eq_countP, countP_set, h]
 
+@[grind =]
 theorem countP_replace [BEq α] [LawfulBEq α] {a b : α} {l : List α} {p : α → Bool} :
     (l.replace a b).countP p =
       if l.contains a then l.countP p + (if p b then 1 else 0) - (if p a then 1 else 0) else l.countP p := by
@@ -42,7 +45,7 @@ theorem countP_replace [BEq α] [LawfulBEq α] {a b : α} {l : List α} {p : α
     simp [replace_cons]
     split <;> rename_i h
     · simp at h
-      simp [h, ih, countP_cons]
+      simp [h, countP_cons]
       omega
     · simp only [beq_eq_false_iff_ne, ne_eq] at h
       simp only [countP_cons, ih, contains_eq_mem, decide_eq_true_eq, mem_cons, h, false_or]
@@ -55,6 +58,7 @@ theorem countP_replace [BEq α] [LawfulBEq α] {a b : α} {l : List α} {p : α
           omega
       · omega
 
+@[grind =]
 theorem count_replace [BEq α] [LawfulBEq α] {a b c : α} {l : List α} :
     (l.replace a b).count c =
       if l.contains a then l.count c + (if b == c then 1 else 0) - (if a == c then 1 else 0) else l.count c := by
@@ -71,12 +75,12 @@ theorem count_replace [BEq α] [LawfulBEq α] {a b c : α} {l : List α} :
       · have := List.count_pos_iff.mpr (h' ▸ h)
         omega
       · rfl
-    · simp [h']
+    · simp
   · rw [count_cons]
     split <;> rename_i h'
     · simp only [beq_iff_eq] at h'
       rw [count_eq_zero.mpr (h' ▸ h)]
-      simp [h']
+      simp
     · simp
 
 /--
@@ -117,6 +121,8 @@ theorem le_countP_tail {l} : countP p l - 1 ≤ countP p l.tail := by
   simp only [length_tail] at this
   omega
 
+grind_pattern le_countP_tail => countP p l.tail
+
 variable [BEq α]
 
 theorem Sublist.le_count (s : l₁ <+ l₂) (a : α) : count a l₂ - (l₂.length - l₁.length) ≤ count a l₁ :=
@@ -134,4 +140,6 @@ theorem IsInfix.le_count (s : l₁ <:+: l₂) (a : α) : count a l₂ - (l₂.le
 theorem le_count_tail {a : α} {l : List α} : count a l - 1 ≤ count a l.tail :=
   le_countP_tail
 
+grind_pattern le_count_tail => count a l.tail
+
 end List

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

@@ -29,7 +29,7 @@ theorem getElem?_eraseIdx {l : List α} {i : Nat} {j : Nat} :
     · simp only [length_take, Nat.min_def, Nat.not_lt] at h
       split at h
       · omega
-      · simp_all [getElem?_eq_none]
+      · simp_all
         omega
     · simp only [length_take]
       simp only [length_take, Nat.min_def, Nat.not_lt] at h
@@ -46,7 +46,7 @@ theorem getElem?_eraseIdx_of_lt {l : List α} {i : Nat} {j : Nat} (h : j < i) :
 theorem getElem?_eraseIdx_of_ge {l : List α} {i : Nat} {j : Nat} (h : i ≤ j) :
     (l.eraseIdx i)[j]? = l[j + 1]? := by
   rw [getElem?_eraseIdx]
-  simp only [dite_eq_ite, ite_eq_right_iff]
+  simp only [ite_eq_right_iff]
   intro h'
   omega
 
@@ -187,7 +187,7 @@ theorem set_eraseIdx {xs : List α} {i : Nat} {j : Nat} {a : α} :
       · have t : ¬ n < i := by omega
         simp [t]
 
-@[simp] theorem eraseIdx_length_sub_one {l : List α} :
+@[simp, grind =] theorem eraseIdx_length_sub_one {l : List α} :
     (l.eraseIdx (l.length - 1)) = l.dropLast := by
   apply ext_getElem
   · simp [length_eraseIdx]

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

@@ -15,8 +15,7 @@ Proves various lemmas about `List.insertIdx`.
 -/
 
 set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
--- TODO: restore after an update-stage0
--- set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
 
 open Function Nat
 
@@ -30,19 +29,20 @@ section InsertIdx
 
 variable {a : α}
 
-@[simp]
+@[simp, grind =]
 theorem insertIdx_zero {xs : List α} {x : α} : xs.insertIdx 0 x = x :: xs :=
   rfl
 
-@[simp]
+@[simp, grind =]
 theorem insertIdx_succ_nil {n : Nat} {a : α} : ([] : List α).insertIdx (n + 1) a = [] :=
   rfl
 
-@[simp]
+@[simp, grind =]
 theorem insertIdx_succ_cons {xs : List α} {hd x : α} {i : Nat} :
     (hd :: xs).insertIdx (i + 1) x = hd :: xs.insertIdx i x :=
   rfl
 
+@[grind =]
 theorem length_insertIdx : ∀ {i} {as : List α}, (as.insertIdx i a).length = if i ≤ as.length then as.length + 1 else as.length
   | 0, _ => by simp
   | n + 1, [] => by simp
@@ -56,14 +56,9 @@ theorem length_insertIdx_of_le_length (h : i ≤ length as) (a : α) : (as.inser
 theorem length_insertIdx_of_length_lt (h : length as < i) (a : α) : (as.insertIdx i a).length = as.length := by
   simp [length_insertIdx, h]
 
-@[simp]
-theorem eraseIdx_insertIdx {i : Nat} {l : List α} (a : α) : (l.insertIdx i a).eraseIdx i = l := by
-  rw [eraseIdx_eq_modifyTailIdx, insertIdx, modifyTailIdx_modifyTailIdx_self]
-  exact modifyTailIdx_id _ _
-
 theorem insertIdx_eraseIdx_of_ge :
-    ∀ {i m as},
-      i < length as → i ≤ m → (as.eraseIdx i).insertIdx m a = (as.insertIdx (m + 1) a).eraseIdx i
+    ∀ {i j as},
+      i < length as → i ≤ j → (as.eraseIdx i).insertIdx j a = (as.insertIdx (j + 1) a).eraseIdx i
   | 0, 0, [], has, _ => (Nat.lt_irrefl _ has).elim
   | 0, 0, _ :: as, _, _ => by simp [eraseIdx, insertIdx]
   | 0, _ + 1, _ :: _, _, _ => rfl
@@ -79,6 +74,15 @@ theorem insertIdx_eraseIdx_of_le :
     congrArg (cons a) <|
       insertIdx_eraseIdx_of_le (Nat.lt_of_succ_lt_succ has) (Nat.le_of_succ_le_succ hmn)
 
+@[grind =]
+theorem insertIdx_eraseIdx (h : i < length as) :
+    (as.eraseIdx i).insertIdx j a =
+      if i ≤ j then (as.insertIdx (j + 1) a).eraseIdx i else (as.insertIdx j a).eraseIdx (i + 1) := by
+  split <;> rename_i h'
+  · rw [insertIdx_eraseIdx_of_ge h h']
+  · rw [insertIdx_eraseIdx_of_le h (by omega)]
+
+@[grind =]
 theorem insertIdx_comm (a b : α) :
     ∀ {i j : Nat} {l : List α} (_ : i ≤ j) (_ : j ≤ length l),
       (l.insertIdx i a).insertIdx (j + 1) b = (l.insertIdx j b).insertIdx i a
@@ -110,6 +114,14 @@ theorem insertIdx_of_length_lt {l : List α} {x : α} {i : Nat} (h : l.length <
     · simp only [Nat.succ_lt_succ_iff, length] at h
       simpa using ih h
 
+@[simp, grind =]
+theorem eraseIdx_insertIdx_self {i : Nat} {l : List α} (a : α) : (l.insertIdx i a).eraseIdx i = l := by
+  rw [eraseIdx_eq_modifyTailIdx, insertIdx, modifyTailIdx_modifyTailIdx_self]
+  exact modifyTailIdx_id _ _
+
+@[deprecated eraseIdx_insertIdx_self (since := "2025-06-18")]
+abbrev eraseIdx_insertIdx := @eraseIdx_insertIdx_self
+
 @[simp]
 theorem insertIdx_length_self {l : List α} {x : α} : l.insertIdx l.length x = l ++ [x] := by
   induction l with
@@ -185,6 +197,7 @@ theorem getElem_insertIdx_of_gt {l : List α} {x : α} {i j : Nat} (hn : i < j)
 @[deprecated getElem_insertIdx_of_gt (since := "2025-02-04")]
 abbrev getElem_insertIdx_of_ge := @getElem_insertIdx_of_gt
 
+@[grind =]
 theorem getElem_insertIdx {l : List α} {x : α} {i j : Nat} (h : j < (l.insertIdx i x).length) :
     (l.insertIdx i x)[j] =
       if h₁ : j < i then
@@ -201,6 +214,7 @@ theorem getElem_insertIdx {l : List α} {x : α} {i j : Nat} (h : j < (l.insertI
       rw [getElem_insertIdx_self h]
     · rw [getElem_insertIdx_of_gt (by omega)]
 
+@[grind =]
 theorem getElem?_insertIdx {l : List α} {x : α} {i j : Nat} :
     (l.insertIdx i x)[j]? =
       if j < i then

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

@@ -17,7 +17,7 @@ namespace List
 
 /-! ### modifyHead -/
 
-@[simp] theorem length_modifyHead {f : α → α} {l : List α} : (l.modifyHead f).length = l.length := by
+@[simp, grind =] theorem length_modifyHead {f : α → α} {l : List α} : (l.modifyHead f).length = l.length := by
   cases l <;> simp [modifyHead]
 
 theorem modifyHead_eq_set [Inhabited α] (f : α → α) (l : List α) :
@@ -26,9 +26,10 @@ theorem modifyHead_eq_set [Inhabited α] (f : α → α) (l : List α) :
 @[simp] theorem modifyHead_eq_nil_iff {f : α → α} {l : List α} :
     l.modifyHead f = [] ↔ l = [] := by cases l <;> simp [modifyHead]
 
-@[simp] theorem modifyHead_modifyHead {l : List α} {f g : α → α} :
+@[simp, grind =] theorem modifyHead_modifyHead {l : List α} {f g : α → α} :
     (l.modifyHead f).modifyHead g = l.modifyHead (g ∘ f) := by cases l <;> simp [modifyHead]
 
+@[grind =]
 theorem getElem_modifyHead {l : List α} {f : α → α} {i} (h : i < (l.modifyHead f).length) :
     (l.modifyHead f)[i] = if h' : i = 0 then f (l[0]'(by simp at h; omega)) else l[i]'(by simpa using h) := by
   cases l with
@@ -41,6 +42,7 @@ theorem getElem_modifyHead {l : List α} {f : α → α} {i} (h : i < (l.modifyH
 @[simp] theorem getElem_modifyHead_succ {l : List α} {f : α → α} {n} (h : n + 1 < (l.modifyHead f).length) :
     (l.modifyHead f)[n + 1] = l[n + 1]'(by simpa using h) := by simp [getElem_modifyHead]
 
+@[grind =]
 theorem getElem?_modifyHead {l : List α} {f : α → α} {i} :
     (l.modifyHead f)[i]? = if i = 0 then l[i]?.map f else l[i]? := by
   cases l with
@@ -53,19 +55,19 @@ theorem getElem?_modifyHead {l : List α} {f : α → α} {i} :
 @[simp] theorem getElem?_modifyHead_succ {l : List α} {f : α → α} {n} :
     (l.modifyHead f)[n + 1]? = l[n + 1]? := by simp [getElem?_modifyHead]
 
-@[simp] theorem head_modifyHead (f : α → α) (l : List α) (h) :
+@[simp, grind =] theorem head_modifyHead (f : α → α) (l : List α) (h) :
     (l.modifyHead f).head h = f (l.head (by simpa using h)) := by
   cases l with
   | nil => simp at h
   | cons hd tl => simp
 
-@[simp] theorem head?_modifyHead {l : List α} {f : α → α} :
+@[simp, grind =] theorem head?_modifyHead {l : List α} {f : α → α} :
     (l.modifyHead f).head? = l.head?.map f := by cases l <;> simp
 
-@[simp] theorem tail_modifyHead {f : α → α} {l : List α} :
+@[simp, grind =] theorem tail_modifyHead {f : α → α} {l : List α} :
     (l.modifyHead f).tail = l.tail := by cases l <;> simp
 
-@[simp] theorem take_modifyHead {f : α → α} {l : List α} {i} :
+@[simp, grind =] theorem take_modifyHead {f : α → α} {l : List α} {i} :
     (l.modifyHead f).take i = (l.take i).modifyHead f := by
   cases l <;> cases i <;> simp
 
@@ -73,6 +75,7 @@ theorem getElem?_modifyHead {l : List α} {f : α → α} {i} :
     (l.modifyHead f).drop i = l.drop i := by
   cases l <;> cases i <;> simp_all
 
+@[grind =]
 theorem eraseIdx_modifyHead_zero {f : α → α} {l : List α} :
     (l.modifyHead f).eraseIdx 0 = l.eraseIdx 0 := by simp
 
@@ -81,7 +84,7 @@ theorem eraseIdx_modifyHead_zero {f : α → α} {l : List α} :
 
 @[simp] theorem modifyHead_id : modifyHead (id : α → α) = id := by funext l; cases l <;> simp
 
-@[simp] theorem modifyHead_dropLast {l : List α} {f : α → α} :
+@[simp, grind _=_] theorem modifyHead_dropLast {l : List α} {f : α → α} :
     l.dropLast.modifyHead f = (l.modifyHead f).dropLast := by
   rcases l with _|⟨a, l⟩
   · simp
@@ -99,7 +102,7 @@ theorem eraseIdx_eq_modifyTailIdx : ∀ i (l : List α), eraseIdx l i = l.modify
   | _+1, [] => rfl
   | _+1, _ :: _ => congrArg (cons _) (eraseIdx_eq_modifyTailIdx _ _)
 
-@[simp] theorem length_modifyTailIdx (f : List α → List α) (H : ∀ l, (f l).length = l.length) :
+@[simp, grind =] theorem length_modifyTailIdx (f : List α → List α) (H : ∀ l, (f l).length = l.length) :
     ∀ (l : List α) i, (l.modifyTailIdx i f).length = l.length
   | _, 0 => H _
   | [], _+1 => rfl
@@ -142,7 +145,7 @@ theorem modifyTailIdx_modifyTailIdx_self {f g : List α → List α} (i : Nat) (
 
 /-! ### modify -/
 
-@[simp] theorem modify_nil (f : α → α) (i) : [].modify i f = [] := by cases i <;> rfl
+@[simp, grind =] theorem modify_nil (f : α → α) (i) : [].modify i f = [] := by cases i <;> rfl
 
 @[simp] theorem modify_zero_cons (f : α → α) (a : α) (l : List α) :
     (a :: l).modify 0 f = f a :: l := rfl
@@ -150,6 +153,15 @@ theorem modifyTailIdx_modifyTailIdx_self {f g : List α → List α} (i : Nat) (
 @[simp] theorem modify_succ_cons (f : α → α) (a : α) (l : List α) (i) :
     (a :: l).modify (i + 1) f = a :: l.modify i f := rfl
 
+@[grind =]
+theorem modify_cons {f : α → α} {a : α} {l : List α} {i : Nat} :
+    (a :: l).modify i f =
+      if i = 0 then f a :: l else a :: l.modify (i - 1) f := by
+  split <;> rename_i h
+  · subst h
+    simp
+  · match i, h with | i + 1, _ => simp
+
 theorem modifyHead_eq_modify_zero (f : α → α) (l : List α) :
     l.modifyHead f = l.modify 0 f := by cases l <;> simp
 
@@ -160,12 +172,12 @@ theorem modifyHead_eq_modify_zero (f : α → α) (l : List α) :
     ∀ i (l : List α) j, (l.modify i f)[j]? = (fun a => if i = j then f a else a) <$> l[j]?
   | n, l, 0 => by cases l <;> cases n <;> simp
   | n, [], _+1 => by cases n <;> rfl
-  | 0, _ :: l, j+1 => by cases h : l[j]? <;> simp [h, modify, j.succ_ne_zero.symm]
+  | 0, _ :: l, j+1 => by cases h : l[j]? <;> simp [h, modify]
   | i+1, a :: l, j+1 => by
     simp only [modify_succ_cons, getElem?_cons_succ, Nat.reduceEqDiff, Option.map_eq_map]
     refine (getElem?_modify f i l j).trans ?_
     cases h' : l[j]? <;> by_cases h : i = j <;>
-      simp [h, if_pos, if_neg, Option.map, mt Nat.succ.inj, not_false_iff, h']
+      simp [h, Option.map]
 
 @[simp, grind =] theorem length_modify (f : α → α) : ∀ (l : List α) i, (l.modify i f).length = l.length :=
   length_modifyTailIdx _ fun l => by cases l <;> rfl
@@ -200,6 +212,7 @@ theorem modify_eq_self {f : α → α} {i} {l : List α} (h : l.length ≤ i) :
     intro h
     omega
 
+@[grind =]
 theorem modify_modify_eq (f g : α → α) (i) (l : List α) :
     (l.modify i f).modify i g = l.modify i (g ∘ f) := by
   apply ext_getElem
@@ -213,7 +226,7 @@ theorem modify_modify_ne (f g : α → α) {i j} (l : List α) (h : i ≠ j) :
   apply ext_getElem
   · simp
   · intro m' h₁ h₂
-    simp only [getElem_modify, getElem_modify_ne, h₂]
+    simp only [getElem_modify]
     split <;> split <;> first | rfl | omega
 
 theorem modify_eq_set [Inhabited α] (f : α → α) (i) (l : List α) :
@@ -221,7 +234,7 @@ theorem modify_eq_set [Inhabited α] (f : α → α) (i) (l : List α) :
   apply ext_getElem
   · simp
   · intro m h₁ h₂
-    simp [getElem_modify, getElem_set, h₂]
+    simp [getElem_modify, getElem_set]
     split <;> rename_i h
     · subst h
       simp only [length_modify] at h₁
@@ -245,7 +258,7 @@ theorem exists_of_modify (f : α → α) {i} {l : List α} (h : i < l.length) :
 @[simp] theorem modify_id (i) (l : List α) : l.modify i id = l := by
   simp [modify]
 
-@[grind =]
+@[grind _=_]
 theorem take_modify (f : α → α) (i j) (l : List α) :
     (l.modify i f).take j = (l.take j).modify i f := by
   induction j generalizing l i with
@@ -274,7 +287,7 @@ theorem drop_modify_of_ge (f : α → α) (i j) (l : List α) (h : i ≥ j) :
   apply ext_getElem
   · simp
   · intro m' h₁ h₂
-    simp [getElem_drop, getElem_modify, ite_eq_right_iff]
+    simp [getElem_drop, getElem_modify]
     split <;> split <;> first | rfl | omega
 
 theorem eraseIdx_modify_of_eq (f : α → α) (i) (l : List α) :

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

@@ -27,11 +27,12 @@ open Nat
 
 /-! ### range' -/
 
-@[simp] theorem mem_range'_1 : m ∈ range' s n ↔ s ≤ m ∧ m < s + n := by
+@[simp, grind =] theorem mem_range'_1 : m ∈ range' s n ↔ s ≤ m ∧ m < s + n := by
   simp [mem_range']; exact ⟨
     fun ⟨i, h, e⟩ => e ▸ ⟨Nat.le_add_right .., Nat.add_lt_add_left h _⟩,
     fun ⟨h₁, h₂⟩ => ⟨m - s, Nat.sub_lt_left_of_lt_add h₁ h₂, (Nat.add_sub_cancel' h₁).symm⟩⟩
 
+@[grind =]
 theorem getLast?_range' {n : Nat} : (range' s n).getLast? = if n = 0 then none else some (s + n - 1) := by
   induction n generalizing s with
   | zero => simp
@@ -43,7 +44,7 @@ theorem getLast?_range' {n : Nat} : (range' s n).getLast? = if n = 0 then none e
     · rw [if_neg h]
       simp
 
-@[simp] theorem getLast_range' {n : Nat} (h) : (range' s n).getLast h = s + n - 1 := by
+@[simp, grind =] theorem getLast_range' {n : Nat} (h) : (range' s n).getLast h = s + n - 1 := by
   cases n with
   | zero => simp at h
   | succ n => simp [getLast?_range', getLast_eq_iff_getLast?_eq_some]
@@ -187,7 +188,7 @@ theorem reverse_range' : ∀ {s n : Nat}, reverse (range' s n) = map (s + n - 1
       show s + (n + 1) - 1 = s + n from rfl, map, map_map]
     simp [reverse_range', Nat.sub_right_comm, Nat.sub_sub]
 
-@[simp]
+@[simp, grind =]
 theorem mem_range {m n : Nat} : m ∈ range n ↔ m < n := by
   simp only [range_eq_range', mem_range'_1, Nat.zero_le, true_and, Nat.zero_add]
 
@@ -201,7 +202,7 @@ theorem pairwise_lt_range {n : Nat} : Pairwise (· < ·) (range n) := by
 theorem pairwise_le_range {n : Nat} : Pairwise (· ≤ ·) (range n) :=
   Pairwise.imp Nat.le_of_lt pairwise_lt_range
 
-@[simp] theorem take_range {i n : Nat} : take i (range n) = range (min i n) := by
+@[simp, grind =] theorem take_range {i n : Nat} : take i (range n) = range (min i n) := by
   apply List.ext_getElem
   · simp
   · simp +contextual [getElem_take, Nat.lt_min]
@@ -209,10 +210,11 @@ theorem pairwise_le_range {n : Nat} : Pairwise (· ≤ ·) (range n) :=
 theorem nodup_range {n : Nat} : Nodup (range n) := by
   simp +decide only [range_eq_range', nodup_range']
 
-@[simp] theorem find?_range_eq_some {n : Nat} {i : Nat} {p : Nat → Bool} :
+@[simp, grind] theorem find?_range_eq_some {n : Nat} {i : Nat} {p : Nat → Bool} :
     (range n).find? p = some i ↔ p i ∧ i ∈ range n ∧ ∀ j, j < i → !p j := by
   simp [range_eq_range']
 
+@[grind]
 theorem find?_range_eq_none {n : Nat} {p : Nat → Bool} :
     (range n).find? p = none ↔ ∀ i, i < n → !p i := by
   simp
@@ -374,15 +376,15 @@ end
 
 /-! ### zipIdx -/
 
-@[simp]
+@[simp, grind =]
 theorem zipIdx_singleton {x : α} {k : Nat} : zipIdx [x] k = [(x, k)] :=
   rfl
 
-@[simp] theorem head?_zipIdx {l : List α} {k : Nat} :
+@[simp, grind =] theorem head?_zipIdx {l : List α} {k : Nat} :
     (zipIdx l k).head? = l.head?.map fun a => (a, k) := by
   simp [head?_eq_getElem?]
 
-@[simp] theorem getLast?_zipIdx {l : List α} {k : Nat} :
+@[simp, grind =] theorem getLast?_zipIdx {l : List α} {k : Nat} :
     (zipIdx l k).getLast? = l.getLast?.map fun a => (a, k + l.length - 1) := by
   simp [getLast?_eq_getElem?]
   cases l <;> simp
@@ -405,6 +407,7 @@ to avoid the inequality and the subtraction. -/
 theorem mk_mem_zipIdx_iff_getElem? {i : Nat} {x : α} {l : List α} : (x, i) ∈ zipIdx l ↔ l[i]? = some x := by
   simp [mk_mem_zipIdx_iff_le_and_getElem?_sub]
 
+@[grind =]
 theorem mem_zipIdx_iff_le_and_getElem?_sub {x : α × Nat} {l : List α} {k : Nat} :
     x ∈ zipIdx l k ↔ k ≤ x.2 ∧ l[x.2 - k]? = some x.1 := by
   cases x
@@ -467,6 +470,7 @@ theorem zipIdx_map {l : List α} {k : Nat} {f : α → β} :
     rw [map_cons, zipIdx_cons', zipIdx_cons', map_cons, map_map, IH, map_map]
     rfl
 
+@[grind =]
 theorem zipIdx_append {xs ys : List α} {k : Nat} :
     zipIdx (xs ++ ys) k = zipIdx xs k ++ zipIdx ys (k + xs.length) := by
   induction xs generalizing ys k with
@@ -504,7 +508,7 @@ theorem zipIdx_eq_append_iff {l : List α} {k : Nat} :
   · rintro ⟨l₁', l₂', rfl, rfl, rfl⟩
     simp only [zipIdx_eq_zip_range']
     refine ⟨l₁', l₂', range' k l₁'.length, range' (k + l₁'.length) l₂'.length, ?_⟩
-    simp [Nat.add_comm]
+    simp
 
 /-! ### enumFrom -/
 
@@ -631,7 +635,7 @@ theorem enumFrom_eq_append_iff {l : List α} {n : Nat} :
   · rintro ⟨l₁', l₂', rfl, rfl, rfl⟩
     simp only [enumFrom_eq_zip_range']
     refine ⟨range' n l₁'.length, range' (n + l₁'.length) l₂'.length, l₁', l₂', ?_⟩
-    simp [Nat.add_comm]
+    simp
 
 end
 

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

@@ -118,6 +118,7 @@ theorem suffix_iff_eq_append : l₁ <:+ l₂ ↔ take (length l₂ - length l₁
   ⟨by rintro ⟨r, rfl⟩; simp only [length_append, Nat.add_sub_cancel_right, take_left], fun e =>
     ⟨_, e⟩⟩
 
+@[grind =]
 theorem prefix_take_iff {xs ys : List α} {i : Nat} : xs <+: ys.take i ↔ xs <+: ys ∧ xs.length ≤ i := by
   constructor
   · intro h
@@ -140,7 +141,7 @@ theorem suffix_iff_eq_drop : l₁ <:+ l₂ ↔ l₁ = drop (length l₂ - length
     xs.take i <+: xs.take j ↔ i ≤ j := by
   simp only [prefix_iff_eq_take, length_take]
   induction i generalizing xs j with
-  | zero => simp [Nat.min_eq_left, eq_self_iff_true, Nat.zero_le, take]
+  | zero => simp [Nat.min_eq_left, Nat.zero_le, take]
   | succ i IH =>
     cases xs with
     | nil => simp_all
@@ -149,7 +150,7 @@ theorem suffix_iff_eq_drop : l₁ <:+ l₂ ↔ l₁ = drop (length l₂ - length
       | zero =>
         simp
       | succ j =>
-        simp only [length_cons, Nat.succ_eq_add_one, Nat.add_lt_add_iff_right] at hm
+        simp only [length_cons, Nat.add_lt_add_iff_right] at hm
         simp [← @IH j xs hm, Nat.min_eq_left, Nat.le_of_lt hm]
 
 @[simp] theorem append_left_sublist_self {xs : List α} (ys : List α) : xs ++ ys <+ ys ↔ xs = [] := by
@@ -192,7 +193,7 @@ theorem append_sublist_of_sublist_right {xs ys zs : List α} (h : zs <+ ys) :
     have hl' := h'.length_le
     simp only [length_append] at hl'
     have : xs.length = 0 := by omega
-    simp_all only [Nat.zero_add, length_eq_zero_iff, true_and, append_nil]
+    simp_all only [Nat.zero_add, length_eq_zero_iff, true_and]
     exact Sublist.eq_of_length_le h' hl
   · rintro ⟨rfl, rfl⟩
     simp

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

@@ -28,8 +28,8 @@ open Nat
 /-! ### take -/
 
 @[simp, grind =] theorem length_take : ∀ {i : Nat} {l : List α}, (take i l).length = min i l.length
-  | 0, l => by simp [Nat.zero_min]
-  | succ n, [] => by simp [Nat.min_zero]
+  | 0, l => by simp
+  | succ n, [] => by simp
   | succ n, _ :: l => by simp [Nat.succ_min_succ, length_take]
 
 theorem length_take_le (i) (l : List α) : length (take i l) ≤ i := by simp [Nat.min_le_left]
@@ -99,6 +99,7 @@ theorem getLast_take {l : List α} (h : l.take i ≠ []) :
   · rw [getElem?_eq_none (by omega), getLast_eq_getElem]
     simp
 
+@[grind =]
 theorem take_take : ∀ {i j} {l : List α}, take i (take j l) = take (min i j) l
   | n, 0, l => by rw [Nat.min_zero, take_zero, take_nil]
   | 0, m, l => by rw [Nat.zero_min, take_zero, take_zero]
@@ -117,56 +118,60 @@ theorem take_set_of_le {a : α} {i j : Nat} {l : List α} (h : j ≤ i) :
 @[deprecated take_set_of_le (since := "2025-02-04")]
 abbrev take_set_of_lt := @take_set_of_le
 
-@[simp] theorem take_replicate {a : α} : ∀ {i n : Nat}, take i (replicate n a) = replicate (min i n) a
-  | n, 0 => by simp [Nat.min_zero]
-  | 0, m => by simp [Nat.zero_min]
+@[simp, grind =] theorem take_replicate {a : α} : ∀ {i n : Nat}, take i (replicate n a) = replicate (min i n) a
+  | n, 0 => by simp
+  | 0, m => by simp
   | succ n, succ m => by simp [replicate_succ, succ_min_succ, take_replicate]
 
-@[simp] theorem drop_replicate {a : α} : ∀ {i n : Nat}, drop i (replicate n a) = replicate (n - i) a
+@[simp, grind =] theorem drop_replicate {a : α} : ∀ {i n : Nat}, drop i (replicate n a) = replicate (n - i) a
   | n, 0 => by simp
   | 0, m => by simp
   | succ n, succ m => by simp [replicate_succ, succ_sub_succ, drop_replicate]
 
 /-- Taking the first `i` elements in `l₁ ++ l₂` is the same as appending the first `i` elements
 of `l₁` to the first `n - l₁.length` elements of `l₂`. -/
-theorem take_append_eq_append_take {l₁ l₂ : List α} {i : Nat} :
+theorem take_append {l₁ l₂ : List α} {i : Nat} :
     take i (l₁ ++ l₂) = take i l₁ ++ take (i - l₁.length) l₂ := by
   induction l₁ generalizing i
   · simp
   · cases i
     · simp [*]
-    · simp only [cons_append, take_succ_cons, length_cons, succ_eq_add_one, cons.injEq,
+    · simp only [cons_append, take_succ_cons, length_cons, cons.injEq,
         append_cancel_left_eq, true_and, *]
       congr 1
       omega
 
+@[deprecated take_append (since := "2025-06-16")]
+abbrev take_append_eq_append_take := @take_append
+
 theorem take_append_of_le_length {l₁ l₂ : List α} {i : Nat} (h : i ≤ l₁.length) :
     (l₁ ++ l₂).take i = l₁.take i := by
-  simp [take_append_eq_append_take, Nat.sub_eq_zero_of_le h]
+  simp [take_append, Nat.sub_eq_zero_of_le h]
 
 /-- Taking the first `l₁.length + i` elements in `l₁ ++ l₂` is the same as appending the first
 `i` elements of `l₂` to `l₁`. -/
-theorem take_append {l₁ l₂ : List α} (i : Nat) :
+theorem take_length_add_append {l₁ l₂ : List α} (i : Nat) :
     take (l₁.length + i) (l₁ ++ l₂) = l₁ ++ take i l₂ := by
-  rw [take_append_eq_append_take, take_of_length_le (Nat.le_add_right _ _), Nat.add_sub_cancel_left]
+  rw [take_append, take_of_length_le (Nat.le_add_right _ _), Nat.add_sub_cancel_left]
 
 @[simp]
 theorem take_eq_take_iff :
     ∀ {l : List α} {i j : Nat}, l.take i = l.take j ↔ min i l.length = min j l.length
-  | [], i, j => by simp [Nat.min_zero]
+  | [], i, j => by simp
   | _ :: xs, 0, 0 => by simp
-  | x :: xs, i + 1, 0 => by simp [Nat.zero_min, succ_min_succ]
-  | x :: xs, 0, j + 1 => by simp [Nat.zero_min, succ_min_succ]
+  | x :: xs, i + 1, 0 => by simp [succ_min_succ]
+  | x :: xs, 0, j + 1 => by simp [succ_min_succ]
   | x :: xs, i + 1, j + 1 => by simp [succ_min_succ, take_eq_take_iff]
 
 @[deprecated take_eq_take_iff (since := "2025-02-16")]
 abbrev take_eq_take := @take_eq_take_iff
 
+@[grind =]
 theorem take_add {l : List α} {i j : Nat} : l.take (i + j) = l.take i ++ (l.drop i).take j := by
   suffices take (i + j) (take i l ++ drop i l) = take i l ++ take j (drop i l) by
     rw [take_append_drop] at this
     assumption
-  rw [take_append_eq_append_take, take_of_length_le, append_right_inj]
+  rw [take_append, take_of_length_le, append_right_inj]
   · simp only [take_eq_take_iff, length_take, length_drop]
     omega
   apply Nat.le_trans (m := i)
@@ -236,7 +241,7 @@ dropping the first `i` elements. Version designed to rewrite from the small list
       exact Nat.add_lt_of_lt_sub (length_drop ▸ h)) := by
   rw [getElem_drop']
 
-@[simp]
+@[simp, grind =]
 theorem getElem?_drop {xs : List α} {i j : Nat} : (xs.drop i)[j]? = xs[i + j]? := by
   ext
   simp only [getElem?_eq_some_iff, getElem_drop]
@@ -274,7 +279,7 @@ theorem mem_drop_iff_getElem {l : List α} {a : α} :
 @[simp] theorem head_drop {l : List α} {i : Nat} (h : l.drop i ≠ []) :
     (l.drop i).head h = l[i]'(by simp_all) := by
   have w : i < l.length := length_lt_of_drop_ne_nil h
-  simp [getElem?_eq_getElem, h, w, head_eq_iff_head?_eq_some]
+  simp [w, head_eq_iff_head?_eq_some]
 
 theorem getLast?_drop {l : List α} : (l.drop i).getLast? = if l.length ≤ i then none else l.getLast? := by
   rw [getLast?_eq_getElem?, getElem?_drop]
@@ -285,7 +290,7 @@ theorem getLast?_drop {l : List α} : (l.drop i).getLast? = if l.length ≤ i th
     congr
     omega
 
-@[simp] theorem getLast_drop {l : List α} (h : l.drop i ≠ []) :
+@[simp, grind =] theorem getLast_drop {l : List α} (h : l.drop i ≠ []) :
     (l.drop i).getLast h = l.getLast (ne_nil_of_length_pos (by simp at h; omega)) := by
   simp only [ne_eq, drop_eq_nil_iff] at h
   apply Option.some_inj.1
@@ -306,25 +311,29 @@ theorem drop_length_cons {l : List α} (h : l ≠ []) (a : α) :
 
 /-- Dropping the elements up to `i` in `l₁ ++ l₂` is the same as dropping the elements up to `i`
 in `l₁`, dropping the elements up to `i - l₁.length` in `l₂`, and appending them. -/
-theorem drop_append_eq_append_drop {l₁ l₂ : List α} {i : Nat} :
+@[grind =]
+theorem drop_append {l₁ l₂ : List α} {i : Nat} :
     drop i (l₁ ++ l₂) = drop i l₁ ++ drop (i - l₁.length) l₂ := by
   induction l₁ generalizing i
   · simp
   · cases i
     · simp [*]
-    · simp only [cons_append, drop_succ_cons, length_cons, succ_eq_add_one, append_cancel_left_eq, *]
+    · simp only [cons_append, drop_succ_cons, length_cons, append_cancel_left_eq, *]
       congr 1
       omega
 
+@[deprecated drop_append (since := "2025-06-16")]
+abbrev drop_append_eq_append_drop := @drop_append
+
 theorem drop_append_of_le_length {l₁ l₂ : List α} {i : Nat} (h : i ≤ l₁.length) :
     (l₁ ++ l₂).drop i = l₁.drop i ++ l₂ := by
-  simp [drop_append_eq_append_drop, Nat.sub_eq_zero_of_le h]
+  simp [drop_append, Nat.sub_eq_zero_of_le h]
 
 /-- Dropping the elements up to `l₁.length + i` in `l₁ + l₂` is the same as dropping the elements
 up to `i` in `l₂`. -/
 @[simp]
-theorem drop_append {l₁ l₂ : List α} (i : Nat) : drop (l₁.length + i) (l₁ ++ l₂) = drop i l₂ := by
-  rw [drop_append_eq_append_drop, drop_eq_nil_of_le] <;>
+theorem drop_length_add_append {l₁ l₂ : List α} (i : Nat) : drop (l₁.length + i) (l₁ ++ l₂) = drop i l₂ := by
+  rw [drop_append, drop_eq_nil_of_le] <;>
     simp [Nat.add_sub_cancel_left, Nat.le_add_right]
 
 theorem set_eq_take_append_cons_drop {l : List α} {i : Nat} {a : α} :
@@ -454,11 +463,11 @@ theorem drop_sub_one {l : List α} {i : Nat} (h : 0 < i) :
 
 theorem false_of_mem_take_findIdx {xs : List α} {p : α → Bool} (h : x ∈ xs.take (xs.findIdx p)) :
     p x = false := by
-  simp only [mem_take_iff_getElem, forall_exists_index] at h
+  simp only [mem_take_iff_getElem] at h
   obtain ⟨i, h, rfl⟩ := h
   exact not_of_lt_findIdx (by omega)
 
-@[simp] theorem findIdx_take {xs : List α} {i : Nat} {p : α → Bool} :
+@[simp, grind =] theorem findIdx_take {xs : List α} {i : Nat} {p : α → Bool} :
     (xs.take i).findIdx p = min i (xs.findIdx p) := by
   induction xs generalizing i with
   | nil => simp
@@ -470,12 +479,12 @@ theorem false_of_mem_take_findIdx {xs : List α} {p : α → Bool} (h : x ∈ xs
       · simp
       · rw [Nat.add_min_add_right]
 
-@[simp] theorem min_findIdx_findIdx {xs : List α} {p q : α → Bool} :
+@[simp, grind =] theorem min_findIdx_findIdx {xs : List α} {p q : α → Bool} :
     min (xs.findIdx p) (xs.findIdx q) = xs.findIdx (fun a => p a || q a) := by
   induction xs with
   | nil => simp
   | cons x xs ih =>
-    simp [findIdx_cons, cond_eq_if, Bool.not_eq_eq_eq_not, Bool.not_true]
+    simp [findIdx_cons, cond_eq_if]
     split <;> split <;> simp_all [Nat.add_min_add_right]
 
 /-! ### findIdx? -/
@@ -512,7 +521,7 @@ theorem dropWhile_eq_drop_findIdx_not {xs : List α} {p : α → Bool} :
 
 /-! ### rotateLeft -/
 
-@[simp] theorem rotateLeft_replicate {n} {a : α} : rotateLeft (replicate m a) n = replicate m a := by
+@[simp, grind =] theorem rotateLeft_replicate {n} {a : α} : rotateLeft (replicate m a) n = replicate m a := by
   cases n with
   | zero => simp
   | succ n =>
@@ -525,7 +534,7 @@ theorem dropWhile_eq_drop_findIdx_not {xs : List α} {p : α → Bool} :
 
 /-! ### rotateRight -/
 
-@[simp] theorem rotateRight_replicate {n} {a : α} : rotateRight (replicate m a) n = replicate m a := by
+@[simp, grind =] theorem rotateRight_replicate {n} {a : α} : rotateRight (replicate m a) n = replicate m a := by
   cases n with
   | zero => simp
   | succ n =>
@@ -541,7 +550,7 @@ theorem dropWhile_eq_drop_findIdx_not {xs : List α} {p : α → Bool} :
 @[simp, grind =] theorem length_zipWith {f : α → β → γ} {l₁ : List α} {l₂ : List β} :
     length (zipWith f l₁ l₂) = min (length l₁) (length l₂) := by
   induction l₁ generalizing l₂ <;> cases l₂ <;>
-    simp_all [succ_min_succ, Nat.zero_min, Nat.min_zero]
+    simp_all [succ_min_succ]
 
 theorem lt_length_left_of_zipWith {f : α → β → γ} {i : Nat} {l : List α} {l' : List β}
     (h : i < (zipWith f l l').length) : i < l.length := by rw [length_zipWith] at h; omega

src/Init/Data/List/OfFn.lean

@@ -96,7 +96,7 @@ theorem ofFn_add {n m} {f : Fin (n + m) → α} :
 
 @[simp]
 theorem ofFn_eq_nil_iff {f : Fin n → α} : ofFn f = [] ↔ n = 0 := by
-  cases n <;> simp only [ofFn_zero, ofFn_succ, eq_self_iff_true, Nat.succ_ne_zero, reduceCtorEq]
+  cases n <;> simp only [ofFn_zero, ofFn_succ, Nat.succ_ne_zero, reduceCtorEq]
 
 @[simp 500, grind =]
 theorem mem_ofFn {n} {f : Fin n → α} {a : α} : a ∈ ofFn f ↔ ∃ i, f i = a := by

src/Init/Data/List/Pairwise.lean

@@ -59,7 +59,7 @@ theorem Pairwise.and (hR : Pairwise R l) (hS : Pairwise S l) :
   induction hR with
   | nil => simp only [Pairwise.nil]
   | cons R1 _ IH =>
-    simp only [Pairwise.nil, pairwise_cons] at hS ⊢
+    simp only [pairwise_cons] at hS ⊢
     exact ⟨fun b bl => ⟨R1 b bl, hS.1 b bl⟩, IH hS.2⟩
 
 theorem pairwise_and_iff : l.Pairwise (fun a b => R a b ∧ S a b) ↔ Pairwise R l ∧ Pairwise S l :=

src/Init/Data/List/Perm.lean

@@ -198,8 +198,8 @@ theorem Perm.filterMap (f : α → Option β) {l₁ l₂ : List α} (p : l₁ ~
     filterMap f l₁ ~ filterMap f l₂ := by
   induction p with
   | nil => simp
-  | cons x _p IH => cases h : f x <;> simp [h, filterMap_cons, IH, Perm.cons]
-  | swap x y l₂ => cases hx : f x <;> cases hy : f y <;> simp [hx, hy, filterMap_cons, swap]
+  | cons x _p IH => cases h : f x <;> simp [h, IH, Perm.cons]
+  | swap x y l₂ => cases hx : f x <;> cases hy : f y <;> simp [hx, hy, swap]
   | trans _p₁ _p₂ IH₁ IH₂ => exact IH₁.trans IH₂
 
 grind_pattern Perm.filterMap => l₁ ~ l₂, filterMap f l₁
@@ -341,9 +341,9 @@ theorem Perm.foldr_eq' {f : α → β → β} {l₁ l₂ : List α} (p : l₁ ~
     intros; apply comm <;> apply p₁.symm.subset <;> assumption
 
 theorem Perm.rec_heq {β : List α → Sort _} {f : ∀ a l, β l → β (a :: l)} {b : β []} {l l' : List α}
-    (hl : l ~ l') (f_congr : ∀ {a l l' b b'}, l ~ l' → HEq b b' → HEq (f a l b) (f a l' b'))
-    (f_swap : ∀ {a a' l b}, HEq (f a (a' :: l) (f a' l b)) (f a' (a :: l) (f a l b))) :
-    HEq (@List.rec α β b f l) (@List.rec α β b f l') := by
+    (hl : l ~ l') (f_congr : ∀ {a l l' b b'}, l ~ l' → b ≍ b' → f a l b ≍ f a l' b')
+    (f_swap : ∀ {a a' l b}, f a (a' :: l) (f a' l b) ≍ f a' (a :: l) (f a l b)) :
+    @List.rec α β b f l ≍ @List.rec α β b f l' := by
   induction hl with
   | nil => rfl
   | cons a h ih => exact f_congr h ih
@@ -442,7 +442,7 @@ grind_pattern Perm.count => l₁ ~ l₂, count a l₂
 
 theorem isPerm_iff : ∀ {l₁ l₂ : List α}, l₁.isPerm l₂ ↔ l₁ ~ l₂
   | [], [] => by simp [isPerm, isEmpty]
-  | [], _ :: _ => by simp [isPerm, isEmpty, Perm.nil_eq]
+  | [], _ :: _ => by simp [isPerm, isEmpty]
   | a :: l₁, l₂ => by simp [isPerm, isPerm_iff, cons_perm_iff_perm_erase]
 
 instance decidablePerm {α} [DecidableEq α] (l₁ l₂ : List α) : Decidable (l₁ ~ l₂) := decidable_of_iff _ isPerm_iff

src/Init/Data/List/Range.lean

@@ -28,7 +28,7 @@ open Nat
 /-! ### range' -/
 
 theorem range'_succ {s n step} : range' s (n + 1) step = s :: range' (s + step) n step := by
-  simp [range', Nat.add_succ, Nat.mul_succ]
+  simp [range']
 
 @[simp] theorem length_range' {s step} : ∀ {n : Nat}, length (range' s n step) = n
   | 0 => rfl
@@ -88,7 +88,7 @@ theorem getElem?_range' {s step} :
   (getElem?_eq_some_iff.1 <| getElem?_range' (by simpa using H)).2
 
 theorem head?_range' : (range' s n).head? = if n = 0 then none else some s := by
-  induction n <;> simp_all [range'_succ, head?_append]
+  induction n <;> simp_all [range'_succ]
 
 @[simp] theorem head_range' (h) : (range' s n).head h = s := by
   repeat simp_all [head?_range', head_eq_iff_head?_eq_some]
@@ -246,11 +246,11 @@ theorem getElem_zipIdx {l : List α} (h : i < (l.zipIdx j).length) :
 theorem tail_zipIdx {l : List α} {i : Nat} : (zipIdx l i).tail = zipIdx l.tail (i + 1) := by
   induction l generalizing i with
   | nil => simp
-  | cons _ l ih => simp [ih, zipIdx_cons]
+  | cons _ l ih => simp [zipIdx_cons]
 
 theorem map_snd_add_zipIdx_eq_zipIdx {l : List α} {n k : Nat} :
     map (Prod.map id (· + n)) (zipIdx l k) = zipIdx l (n + k) :=
-  ext_getElem? fun i ↦ by simp [(· ∘ ·), Nat.add_comm, Nat.add_left_comm]; rfl
+  ext_getElem? fun i ↦ by simp [Nat.add_comm, Nat.add_left_comm]; rfl
 
 theorem zipIdx_cons' {i : Nat} {x : α} {xs : List α} :
     zipIdx (x :: xs) i = (x, i) :: (zipIdx xs i).map (Prod.map id (· + 1)) := by
@@ -328,12 +328,12 @@ theorem getElem_enumFrom (l : List α) (n) (i : Nat) (h : i < (l.enumFrom n).len
 theorem tail_enumFrom (l : List α) (n : Nat) : (enumFrom n l).tail = enumFrom (n + 1) l.tail := by
   induction l generalizing n with
   | nil => simp
-  | cons _ l ih => simp [ih, enumFrom_cons]
+  | cons _ l ih => simp [enumFrom_cons]
 
 @[deprecated map_snd_add_zipIdx_eq_zipIdx (since := "2025-01-21"), simp]
 theorem map_fst_add_enumFrom_eq_enumFrom (l : List α) (n k : Nat) :
     map (Prod.map (· + n) id) (enumFrom k l) = enumFrom (n + k) l :=
-  ext_getElem? fun i ↦ by simp [(· ∘ ·), Nat.add_comm, Nat.add_left_comm]; rfl
+  ext_getElem? fun i ↦ by simp [Nat.add_comm, Nat.add_left_comm]; rfl
 
 @[deprecated map_snd_add_zipIdx_eq_zipIdx (since := "2025-01-21"), simp]
 theorem map_fst_add_enum_eq_enumFrom (l : List α) (n : Nat) :

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

@@ -44,8 +44,8 @@ def merge (xs ys : List α) (le : α → α → Bool := by exact fun a b => a
 @[simp] theorem nil_merge (ys : List α) : merge [] ys le = ys := by simp [merge]
 @[simp] theorem merge_right (xs : List α) : merge xs [] le = xs := by
   induction xs with
-  | nil => simp [merge]
-  | cons x xs ih => simp [merge, ih]
+  | nil => simp
+  | cons x xs ih => simp [merge]
 
 /--
 Split a list in two equal parts. If the length is odd, the first part will be one element longer.

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

@@ -57,10 +57,10 @@ where go : List α → List α → List α → List α
 
 theorem mergeTR_go_eq : mergeTR.go le l₁ l₂ acc = acc.reverse ++ merge l₁ l₂ le := by
   induction l₁ generalizing l₂ acc with
-  | nil => simp [mergeTR.go, merge, reverseAux_eq]
+  | nil => simp [mergeTR.go, reverseAux_eq]
   | cons x l₁ ih₁ =>
     induction l₂ generalizing acc with
-    | nil => simp [mergeTR.go, merge, reverseAux_eq]
+    | nil => simp [mergeTR.go, reverseAux_eq]
     | cons y l₂ ih₂ =>
       simp [mergeTR.go, merge]
       split <;> simp [ih₁, ih₂]
@@ -172,7 +172,7 @@ theorem splitRevInTwo_snd (l : { l : List α // l.length = n }) :
 
 theorem mergeSortTR_run_eq_mergeSort : {n : Nat} → (l : { l : List α // l.length = n }) → mergeSortTR.run le l = mergeSort l.1 le
   | 0, ⟨[], _⟩
-  | 1, ⟨[a], _⟩ => by simp [mergeSortTR.run, mergeSort]
+  | 1, ⟨[a], _⟩ => by simp [mergeSortTR.run]
   | n+2, ⟨a :: b :: l, h⟩ => by
     cases h
     simp only [mergeSortTR.run, mergeSortTR.run, mergeSort]
@@ -189,7 +189,7 @@ set_option maxHeartbeats 400000 in
 mutual
 theorem mergeSortTR₂_run_eq_mergeSort : {n : Nat} → (l : { l : List α // l.length = n }) → mergeSortTR₂.run le l = mergeSort l.1 le
   | 0, ⟨[], _⟩
-  | 1, ⟨[a], _⟩ => by simp [mergeSortTR₂.run, mergeSort]
+  | 1, ⟨[a], _⟩ => by simp [mergeSortTR₂.run]
   | n+2, ⟨a :: b :: l, h⟩ => by
     cases h
     simp only [mergeSortTR₂.run, mergeSort]
@@ -201,10 +201,10 @@ termination_by n => n
 
 theorem mergeSortTR₂_run'_eq_mergeSort : {n : Nat} → (l : { l : List α // l.length = n }) → (w : l' = l.1.reverse) → mergeSortTR₂.run' le l = mergeSort l' le
   | 0, ⟨[], _⟩, w
-  | 1, ⟨[a], _⟩, w => by simp_all [mergeSortTR₂.run', mergeSort]
+  | 1, ⟨[a], _⟩, w => by simp_all [mergeSortTR₂.run']
   | n+2, ⟨a :: b :: l, h⟩, w => by
     cases h
-    simp only [mergeSortTR₂.run', mergeSort]
+    simp only [mergeSortTR₂.run']
     rw [splitRevInTwo'_fst, splitRevInTwo'_snd]
     rw [mergeSortTR₂_run_eq_mergeSort, mergeSortTR₂_run'_eq_mergeSort _ rfl]
     rw [← merge_eq_mergeTR]
@@ -220,7 +220,7 @@ theorem mergeSortTR₂_run'_eq_mergeSort : {n : Nat} → (l : { l : List α // l
         congr 2
         · dsimp at w
           simp only [w]
-          simp only [splitInTwo_fst, splitInTwo_snd, reverse_take, take_reverse]
+          simp only [splitInTwo_fst, take_reverse]
           congr 1
           rw [w, length_reverse]
           simp

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

@@ -33,11 +33,11 @@ namespace List
 namespace MergeSort.Internal
 
 @[simp] theorem splitInTwo_fst (l : { l : List α // l.length = n }) :
-    (splitInTwo l).1 = ⟨l.1.take ((n+1)/2), by simp [splitInTwo, splitAt_eq, l.2]; omega⟩ := by
+    (splitInTwo l).1 = ⟨l.1.take ((n+1)/2), by simp [l.2]; omega⟩ := by
   simp [splitInTwo, splitAt_eq]
 
 @[simp] theorem splitInTwo_snd (l : { l : List α // l.length = n }) :
-    (splitInTwo l).2 = ⟨l.1.drop ((n+1)/2), by simp [splitInTwo, splitAt_eq, l.2]; omega⟩ := by
+    (splitInTwo l).2 = ⟨l.1.drop ((n+1)/2), by simp [l.2]; omega⟩ := by
   simp [splitInTwo, splitAt_eq]
 
 theorem splitInTwo_fst_append_splitInTwo_snd (l : { l : List α // l.length = n }) : (splitInTwo l).1.1 ++ (splitInTwo l).2.1 = l.1 := by
@@ -166,15 +166,15 @@ The elements of `merge le xs ys` are exactly the elements of `xs` and `ys`.
 -- We subsequently prove that `mergeSort_perm : merge le xs ys ~ xs ++ ys`.
 theorem mem_merge {a : α} {xs ys : List α} : a ∈ merge xs ys le ↔ a ∈ xs ∨ a ∈ ys := by
   induction xs generalizing ys with
-  | nil => simp [merge]
+  | nil => simp
   | cons x xs ih =>
     induction ys with
-    | nil => simp [merge]
+    | nil => simp
     | cons y ys ih =>
       simp only [merge]
       split <;> rename_i h
       · simp_all [or_assoc]
-      · simp only [mem_cons, or_assoc, Bool.not_eq_true, ih, ← or_assoc]
+      · simp only [mem_cons, ih, ← or_assoc]
         apply or_congr_left
         simp only [or_comm (a := a = y), or_assoc]
 
@@ -186,8 +186,8 @@ theorem mem_merge_right (s : α → α → Bool) (h : x ∈ r) : x ∈ merge l r
 
 theorem merge_stable : ∀ (xs ys) (_ : ∀ x y, x ∈ xs → y ∈ ys → x.2 ≤ y.2),
     (merge xs ys (zipIdxLE le)).map (·.1) = merge (xs.map (·.1)) (ys.map (·.1)) le
-  | [], ys, _ => by simp [merge]
-  | xs, [], _ => by simp [merge]
+  | [], ys, _ => by simp
+  | xs, [], _ => by simp
   | (i, x) :: xs, (j, y) :: ys, h => by
     simp only [merge, zipIdxLE, map_cons]
     split <;> rename_i w
@@ -239,7 +239,7 @@ theorem sorted_merge
 theorem merge_of_le : ∀ {xs ys : List α} (_ : ∀ a b, a ∈ xs → b ∈ ys → le a b),
     merge xs ys le = xs ++ ys
   | [], ys, _
-  | xs, [], _ => by simp [merge]
+  | xs, [], _ => by simp
   | x :: xs, y :: ys, h => by
     simp only [merge, cons_append]
     rw [if_pos, merge_of_le]
@@ -249,8 +249,8 @@ theorem merge_of_le : ∀ {xs ys : List α} (_ : ∀ a b, a ∈ xs → b ∈ ys
 
 variable (le) in
 theorem merge_perm_append : ∀ {xs ys : List α}, merge xs ys le ~ xs ++ ys
-  | [], ys => by simp [merge]
-  | xs, [] => by simp [merge]
+  | [], ys => by simp
+  | xs, [] => by simp
   | x :: xs, y :: ys => by
     simp only [merge]
     split
@@ -269,8 +269,8 @@ theorem Perm.merge (s₁ s₂ : α → α → Bool) (hl : l₁ ~ l₂) (hr : r
 @[simp] theorem mergeSort_singleton (a : α) : [a].mergeSort r = [a] := by rw [List.mergeSort]
 
 theorem mergeSort_perm : ∀ (l : List α) (le), mergeSort l le ~ l
-  | [], _ => by simp [mergeSort]
-  | [a], _ => by simp [mergeSort]
+  | [], _ => by simp
+  | [a], _ => by simp
   | a :: b :: xs, le => by
     simp only [mergeSort]
     have : (splitInTwo ⟨a :: b :: xs, rfl⟩).1.1.length < xs.length + 1 + 1 := by simp [splitInTwo_fst]; omega
@@ -297,8 +297,8 @@ theorem sorted_mergeSort
     (trans : ∀ (a b c : α), le a b → le b c → le a c)
     (total : ∀ (a b : α), le a b || le b a) :
     (l : List α) → (mergeSort l le).Pairwise le
-  | [] => by simp [mergeSort]
-  | [a] => by simp [mergeSort]
+  | [] => by simp
+  | [a] => by simp
   | a :: b :: xs => by
     rw [mergeSort]
     apply sorted_merge @trans @total
@@ -310,8 +310,8 @@ termination_by l => l.length
 If the input list is already sorted, then `mergeSort` does not change the list.
 -/
 theorem mergeSort_of_sorted : ∀ {l : List α} (_ : Pairwise le l), mergeSort l le = l
-  | [], _ => by simp [mergeSort]
-  | [a], _ => by simp [mergeSort]
+  | [], _ => by simp
+  | [a], _ => by simp
   | a :: b :: xs, h => by
     have : (splitInTwo ⟨a :: b :: xs, rfl⟩).1.1.length < xs.length + 1 + 1 := by simp [splitInTwo_fst]; omega
     have : (splitInTwo ⟨a :: b :: xs, rfl⟩).2.1.length < xs.length + 1 + 1 := by simp [splitInTwo_snd]; omega
@@ -340,7 +340,7 @@ theorem mergeSort_zipIdx {l : List α} :
 where go : ∀ (i : Nat) (l : List α),
     (mergeSort (l.zipIdx i) (zipIdxLE le)).map (·.1) = mergeSort l le
   | _, []
-  | _, [a] => by simp [mergeSort]
+  | _, [a] => by simp
   | _, a :: b :: xs => by
     have : (splitInTwo ⟨a :: b :: xs, rfl⟩).1.1.length < xs.length + 1 + 1 := by simp [splitInTwo_fst]; omega
     have : (splitInTwo ⟨a :: b :: xs, rfl⟩).2.1.length < xs.length + 1 + 1 := by simp [splitInTwo_snd]; omega

src/Init/Data/List/Sublist.lean

@@ -276,7 +276,7 @@ grind_pattern Sublist.map => l₁ <+ l₂, map f l₂
 @[grind]
 protected theorem Sublist.filterMap (f : α → Option β) (s : l₁ <+ l₂) :
     filterMap f l₁ <+ filterMap f l₂ := by
-  induction s <;> simp [filterMap_cons] <;> split <;> simp [*, cons, cons₂]
+  induction s <;> simp [filterMap_cons] <;> split <;> simp [*, cons]
 
 grind_pattern Sublist.filterMap => l₁ <+ l₂, filterMap f l₁
 grind_pattern Sublist.filterMap => l₁ <+ l₂, filterMap f l₂
@@ -542,7 +542,7 @@ theorem sublist_flatten_of_mem {L : List (List α)} {l} (h : l ∈ L) : l <+ L.f
   | nil => cases h
   | cons l' L ih =>
     rcases mem_cons.1 h with (rfl | h)
-    · simp [h]
+    · simp
     · simp [ih h, flatten_cons, sublist_append_of_sublist_right]
 
 theorem sublist_flatten_iff {L : List (List α)} {l} :
@@ -914,7 +914,7 @@ theorem infix_cons_iff : l₁ <:+: a :: l₂ ↔ l₁ <+: a :: l₂ ∨ l₁ <:+
 theorem prefix_concat_iff {l₁ l₂ : List α} {a : α} :
     l₁ <+: l₂ ++ [a] ↔ l₁ = l₂ ++ [a] ∨ l₁ <+: l₂ := by
   simp only [← reverse_suffix, reverse_concat, suffix_cons_iff]
-  simp only [concat_eq_append, ← reverse_concat, reverse_eq_iff, reverse_reverse]
+  simp only [← reverse_concat, reverse_eq_iff, reverse_reverse]
 
 theorem suffix_concat_iff {l₁ l₂ : List α} {a : α} :
     l₁ <:+ l₂ ++ [a] ↔ l₁ = [] ∨ ∃ t, l₁ = t ++ [a] ∧ t <:+ l₂ := by
@@ -941,7 +941,7 @@ theorem prefix_iff_getElem? {l₁ l₂ : List α} :
     | nil =>
       simpa using ⟨0, by simp⟩
     | cons b l₂ =>
-      simp only [cons_append, cons_prefix_cons, ih]
+      simp only [cons_prefix_cons, ih]
       rw (occs := [2]) [← Nat.and_forall_add_one]
       simp [Nat.succ_lt_succ_iff, eq_comm]
 
@@ -964,7 +964,7 @@ theorem prefix_iff_getElem {l₁ l₂ : List α} :
       | nil =>
         exact nil_prefix
       | cons _ _ =>
-        simp only [length_cons, Nat.add_le_add_iff_right, Fin.getElem_fin] at hl h
+        simp only [length_cons, Nat.add_le_add_iff_right] at hl h
         simp only [cons_prefix_cons]
         exact ⟨h 0 (zero_lt_succ _), tail_ih hl fun a ha ↦ h a.succ (succ_lt_succ ha)⟩
 

src/Init/Data/List/TakeDrop.lean

@@ -350,7 +350,7 @@ theorem takeWhile_filterMap {f : α → Option β} {p : β → Bool} {l : List
     · simp only [takeWhile_cons, h]
       split <;> simp_all
     · simp [takeWhile_cons, h, ih]
-      split <;> simp_all [filterMap_cons]
+      split <;> simp_all
 
 theorem dropWhile_filterMap {f : α → Option β} {p : β → Bool} {l : List α} :
     (l.filterMap f).dropWhile p = (l.dropWhile fun a => (f a).all p).filterMap f := by
@@ -362,7 +362,7 @@ theorem dropWhile_filterMap {f : α → Option β} {p : β → Bool} {l : List
     · simp only [dropWhile_cons, h]
       split <;> simp_all
     · simp [dropWhile_cons, h, ih]
-      split <;> simp_all [filterMap_cons]
+      split <;> simp_all
 
 theorem takeWhile_filter {p q : α → Bool} {l : List α} :
     (l.filter p).takeWhile q = (l.takeWhile fun a => !p a || q a).filter p := by
@@ -393,7 +393,7 @@ theorem takeWhile_append {xs ys : List α} :
     (l₁ ++ l₂).takeWhile p = l₁ ++ l₂.takeWhile p := by
   induction l₁ with
   | nil => simp
-  | cons x xs ih => simp_all [takeWhile_cons]
+  | cons x xs ih => simp_all
 
 theorem dropWhile_append {xs ys : List α} :
     (xs ++ ys).dropWhile p =
@@ -408,7 +408,7 @@ theorem dropWhile_append {xs ys : List α} :
     (l₁ ++ l₂).dropWhile p = l₂.dropWhile p := by
   induction l₁ with
   | nil => simp
-  | cons x xs ih => simp_all [dropWhile_cons]
+  | cons x xs ih => simp_all
 
 @[simp] theorem takeWhile_replicate_eq_filter {p : α → Bool} :
     (replicate n a).takeWhile p = (replicate n a).filter p := by
@@ -440,7 +440,7 @@ theorem take_takeWhile {l : List α} {p : α → Bool} :
   induction l generalizing i with
   | nil => simp
   | cons x xs ih =>
-    by_cases h : p x <;> cases i <;> simp [takeWhile_cons, h, ih, take_succ_cons]
+    by_cases h : p x <;> cases i <;> simp [h, ih, take_succ_cons]
 
 @[simp] theorem all_takeWhile {l : List α} : (l.takeWhile p).all p = true := by
   induction l with
@@ -461,13 +461,13 @@ theorem replace_takeWhile [BEq α] [LawfulBEq α] {l : List α} {p : α → Bool
     simp only [takeWhile_cons, replace_cons]
     split <;> rename_i h₁ <;> split <;> rename_i h₂
     · simp_all
-    · simp [replace_cons, h₂, takeWhile_cons, h₁, ih]
+    · simp [replace_cons, h₂, h₁, ih]
     · simp_all
     · simp_all
 
 /-! ### splitAt -/
 
-@[simp] theorem splitAt_eq {i : Nat} {l : List α} : splitAt i l = (l.take i, l.drop i) := by
+@[simp, grind =] theorem splitAt_eq {i : Nat} {l : List α} : splitAt i l = (l.take i, l.drop i) := by
   rw [splitAt, splitAt_go, reverse_nil, nil_append]
   split <;> simp_all [take_of_length_le, drop_of_length_le]
 

src/Init/Data/List/ToArray.lean

@@ -21,8 +21,7 @@ We prefer to pull `List.toArray` outwards past `Array` operations.
 -/
 
 set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
--- TODO: restore after an update-stage0
--- set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
 
 namespace Array
 
@@ -577,7 +576,7 @@ theorem flatMap_toArray_cons {β} (f : α → Array β) (a : α) (as : List α)
   rw [Array.eraseIdx]
   split <;> rename_i h'
   · rw [eraseIdx_toArray]
-    simp only [swap_toArray, Fin.getElem_fin, toList_toArray, mk.injEq]
+    simp only [swap_toArray, toList_toArray, mk.injEq]
     rw [eraseIdx_set_gt (by simp), eraseIdx_set_eq]
     simp
   · simp at h h'
@@ -668,7 +667,7 @@ theorem replace_toArray [BEq α] [LawfulBEq α] (l : List α) (a b : α) :
     l.toArray.replace a b = (l.replace a b).toArray := by
   rw [Array.replace]
   split <;> rename_i i h
-  · simp only [finIdxOf?_toArray, finIdxOf?_eq_none_iff] at h
+  · simp only [finIdxOf?_toArray] at h
     rw [replace_of_not_mem]
     exact finIdxOf?_eq_none_iff.mp h
   · simp_all only [finIdxOf?_toArray, finIdxOf?_eq_some_iff, Fin.getElem_fin, set_toArray,

src/Init/Data/List/Zip.lean

@@ -184,7 +184,7 @@ theorem zipWith_eq_cons_iff {f : α → β → γ} {l₁ : List α} {l₂ : List
   | [], b :: l₂ => simp
   | a :: l₁, [] => simp
   | a' :: l₁, b' :: l₂ =>
-    simp only [zip_cons_cons, cons.injEq, Prod.mk.injEq]
+    simp only [cons.injEq]
     constructor
     · rintro ⟨⟨rfl, rfl⟩, rfl⟩
       refine ⟨a', l₁, b', l₂, by simp⟩

src/Init/Data/Nat/Basic.lean

@@ -406,6 +406,12 @@ theorem le_of_add_right_le {n m k : Nat} (h : n + k ≤ m) : n ≤ m :=
 theorem le_add_right_of_le {n m k : Nat} (h : n ≤ m) : n ≤ m + k :=
   Nat.le_trans h (le_add_right m k)
 
+theorem le_of_add_left_le {n m k : Nat} (h : k + n ≤ m) : n ≤ m :=
+  Nat.le_trans (le_add_left n k) h
+
+theorem le_add_left_of_le {n m k : Nat} (h : n ≤ m) : n ≤ k + m :=
+  Nat.le_trans h (le_add_left m k)
+
 theorem lt_of_add_one_le {n m : Nat} (h : n + 1 ≤ m) : n < m := h
 
 theorem add_one_le_of_lt {n m : Nat} (h : n < m) : n + 1 ≤ m := h
@@ -931,7 +937,7 @@ protected theorem pred_succ (n : Nat) : pred n.succ = n := rfl
 @[simp] protected theorem add_one_sub_one (n : Nat) : n + 1 - 1 = n := rfl
 
 theorem sub_one_eq_self {n : Nat} : n - 1 = n ↔ n = 0 := by cases n <;> simp [ne_add_one]
-theorem eq_self_sub_one {n : Nat} : n = n - 1 ↔ n = 0 := by cases n <;> simp [add_one_ne]
+theorem eq_self_sub_one {n : Nat} : n = n - 1 ↔ n = 0 := by cases n <;> simp
 
 theorem succ_pred {a : Nat} (h : a ≠ 0) : a.pred.succ = a := by
   induction a with
@@ -1092,13 +1098,13 @@ theorem add_le_of_le_sub {a b c : Nat} (hle : b ≤ c) (h : a ≤ c - b) : a + b
   | ⟨d, hd⟩ =>
     apply @le.intro _ _ d
     rw [Nat.eq_add_of_sub_eq hle hd.symm]
-    simp [Nat.add_comm, Nat.add_assoc, Nat.add_left_comm]
+    simp [Nat.add_comm, Nat.add_left_comm]
 
 theorem le_sub_of_add_le {a b c : Nat} (h : a + b ≤ c) : a ≤ c - b := by
   match le.dest h with
   | ⟨d, hd⟩ =>
     apply @le.intro _ _ d
-    have hd : a + d + b = c := by simp [← hd, Nat.add_comm, Nat.add_assoc, Nat.add_left_comm]
+    have hd : a + d + b = c := by simp [← hd, Nat.add_comm, Nat.add_left_comm]
     have hd := Nat.sub_eq_of_eq_add hd.symm
     exact hd.symm