sorting

.github/PULL_REQUEST_TEMPLATE.md

@@ -5,7 +5,6 @@
 * Include the link to your `RFC` or `bug` issue in the description.
 * If the issue does not already have approval from a developer, submit the PR as draft.
 * The PR title/description will become the commit message. Keep it up-to-date as the PR evolves.
-* A toolchain of the form `leanprover/lean4-pr-releases:pr-release-NNNN` for Linux and M-series Macs will be generated upon build. To generate binaries for Windows and Intel-based Macs as well, write a comment containing `release-ci` on its own line.
 * If you rebase your PR onto `nightly-with-mathlib` then CI will test Mathlib against your PR.
 * You can manage the `awaiting-review`, `awaiting-author`, and `WIP` labels yourself, by writing a comment containing one of these labels on its own line.
 * Remove this section, up to and including the `---` before submitting.

.github/workflows/ci.yml

@@ -114,7 +114,7 @@ jobs:
           elif [[ "${{ github.event_name }}" != "pull_request" ]]; then
             check_level=1
           else
-            labels="$(gh api repos/${{ github.repository_owner }}/${{ github.event.repository.name }}/pulls/${{ github.event.pull_request.number }} --jq '.labels')"
+            labels="$(gh api repos/${{ github.repository_owner }}/${{ github.event.repository.name }}/pulls/${{ github.event.pull_request.number }}) --jq '.labels'"
             if echo "$labels" | grep -q "release-ci"; then
               check_level=2
             elif echo "$labels" | grep -q "merge-ci"; then

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

@@ -1,7 +1,6 @@
-# This workflow allows any user to add one of the `awaiting-review`, `awaiting-author`, `WIP`,
-# or `release-ci` labels by commenting on the PR or issue.
-# If any labels from the set {`awaiting-review`, `awaiting-author`, `WIP`} are added, other labels
-# from that set are removed automatically at the same time.
+# This workflow allows any user to add one of the `awaiting-review`, `awaiting-author`, or `WIP` labels,
+# by commenting on the PR or issue.
+# Other labels from this set are removed automatically at the same time.
 
 name: Label PR based on Comment
 
@@ -11,7 +10,7 @@ on:
 
 jobs:
   update-label:
-    if: github.event.issue.pull_request != null && (contains(github.event.comment.body, 'awaiting-review') || contains(github.event.comment.body, 'awaiting-author') || contains(github.event.comment.body, 'WIP') || contains(github.event.comment.body, 'release-ci'))
+    if: github.event.issue.pull_request != null && (contains(github.event.comment.body, 'awaiting-review') || contains(github.event.comment.body, 'awaiting-author') || contains(github.event.comment.body, 'WIP'))
     runs-on: ubuntu-latest
 
     steps:
@@ -26,7 +25,6 @@ jobs:
           const awaitingReview = commentLines.includes('awaiting-review');
           const awaitingAuthor = commentLines.includes('awaiting-author');
           const wip = commentLines.includes('WIP');
-          const releaseCI = commentLines.includes('release-ci');
 
           if (awaitingReview || awaitingAuthor || wip) {
             await github.rest.issues.removeLabel({ owner, repo, issue_number, name: 'awaiting-review' }).catch(() => {});
@@ -43,7 +41,3 @@ jobs:
           if (wip) {
             await github.rest.issues.addLabels({ owner, repo, issue_number, labels: ['WIP'] });
           }
-
-          if (releaseCI) {
-            await github.rest.issues.addLabels({ owner, repo, issue_number, labels: ['release-ci'] });
-          }

nix/bootstrap.nix

@@ -95,13 +95,12 @@ lib.warn "The Nix-based build is deprecated" rec {
       Lean = attachSharedLib leanshared Lean' // { allExternalDeps = [ Std ]; };
       Lake = build {
         name = "Lake";
-        sharedLibName = "Lake_shared";
         src = src + "/src/lake";
         deps = [ Init Lean ];
       };
       Lake-Main = build {
-        name = "LakeMain";
-        roots = [{ glob = "one"; mod = "LakeMain"; }];
+        name = "Lake.Main";
+        roots = [ "Lake.Main" ];
         executableName = "lake";
         deps = [ Lake ];
         linkFlags = lib.optional stdenv.isLinux "-rdynamic";
@@ -134,7 +133,7 @@ lib.warn "The Nix-based build is deprecated" rec {
       mods = foldl' (mods: pkg: mods // pkg.mods) {} stdlib;
       print-paths = Lean.makePrintPathsFor [] mods;
       leanc = writeShellScriptBin "leanc" ''
-        LEAN_CC=${stdenv.cc}/bin/cc ${Leanc.executable}/bin/leanc -I${lean-bin-tools-unwrapped}/include ${stdlibLinkFlags} -L${libInit_shared} -L${leanshared_1} -L${leanshared} -L${Lake.sharedLib} "$@"
+        LEAN_CC=${stdenv.cc}/bin/cc ${Leanc.executable}/bin/leanc -I${lean-bin-tools-unwrapped}/include ${stdlibLinkFlags} -L${libInit_shared} -L${leanshared_1} -L${leanshared} "$@"
       '';
       lean = runCommand "lean" { buildInputs = lib.optional stdenv.isDarwin darwin.cctools; } ''
         mkdir -p $out/bin
@@ -145,7 +144,7 @@ lib.warn "The Nix-based build is deprecated" rec {
         name = "lean-${desc}";
         buildCommand = ''
           mkdir -p $out/bin $out/lib/lean
-          ln -sf ${leancpp}/lib/lean/* ${lib.concatMapStringsSep " " (l: "${l.modRoot}/* ${l.staticLib}/*") (lib.reverseList stdlib)} ${libInit_shared}/* ${leanshared_1}/* ${leanshared}/* ${Lake.sharedLib}/* $out/lib/lean/
+          ln -sf ${leancpp}/lib/lean/* ${lib.concatMapStringsSep " " (l: "${l.modRoot}/* ${l.staticLib}/*") (lib.reverseList stdlib)} ${libInit_shared}/* ${leanshared_1}/* ${leanshared}/* $out/lib/lean/
           # put everything in a single final derivation so `IO.appDir` references work
           cp ${lean}/bin/lean ${leanc}/bin/leanc ${Lake-Main.executable}/bin/lake $out/bin
           # NOTE: `lndir` will not override existing `bin/leanc`
@@ -178,7 +177,7 @@ lib.warn "The Nix-based build is deprecated" rec {
         '';
       };
       update-stage0 =
-        let cTree = symlinkJoin { name = "cs"; paths = map (lib: lib.cTree) (stdlib ++ [Lake-Main]); }; in
+        let cTree = symlinkJoin { name = "cs"; paths = map (lib: lib.cTree) stdlib; }; in
         writeShellScriptBin "update-stage0" ''
           CSRCS=${cTree} CP_C_PARAMS="--dereference --no-preserve=all" ${src + "/script/lib/update-stage0"}
         '';

nix/buildLeanPackage.nix

@@ -30,7 +30,7 @@ lib.makeOverridable (
   pluginDeps ? [],
   # `overrideAttrs` for `buildMod`
   overrideBuildModAttrs ? null,
-  debug ? false, leanFlags ? [], leancFlags ? [], linkFlags ? [], executableName ? lib.toLower name, libName ? name, sharedLibName ? libName,
+  debug ? false, leanFlags ? [], leancFlags ? [], linkFlags ? [], executableName ? lib.toLower name, libName ? name,
   srcTarget ? "..#stage0", srcArgs ? "(\${args[*]})", lean-final ? lean-final' }@args:
 with builtins; let
   # "Init.Core" ~> "Init/Core"
@@ -233,7 +233,7 @@ in rec {
   cTree     = symlinkJoin { name = "${name}-cTree"; paths = map (mod: mod.c) (attrValues mods); };
   oTree     = symlinkJoin { name = "${name}-oTree"; paths = (attrValues objects); };
   iTree     = symlinkJoin { name = "${name}-iTree"; paths = map (mod: mod.ilean) (attrValues mods); };
-  sharedLib = mkSharedLib "lib${sharedLibName}" ''
+  sharedLib = mkSharedLib "lib${libName}" ''
     ${if stdenv.isDarwin then "-Wl,-force_load,${staticLib}/lib${libName}.a" else "-Wl,--whole-archive ${staticLib}/lib${libName}.a -Wl,--no-whole-archive"} \
     ${lib.concatStringsSep " " (map (d: "${d.sharedLib}/*") deps)}'';
   executable = lib.makeOverridable ({ withSharedStdlib ? true }: let

script/lib/update-stage0

@@ -18,7 +18,7 @@ done
 
 # special handling for Lake files due to its nested directory
 # copy the README to ensure the `stage0/src/lake` directory is comitted
-for f in $(git ls-files 'src/lake/Lake/*' src/lake/Lake.lean src/lake/LakeMain.lean src/lake/README.md ':!:src/lakefile.toml'); do
+for f in $(git ls-files 'src/lake/Lake/*' src/lake/Lake.lean src/lake/README.md ':!:src/lakefile.toml'); do
     if [[ $f == *.lean ]]; then
         f=${f#src/lake}
         f=${f%.lean}.c

src/CMakeLists.txt

@@ -333,12 +333,7 @@ if(NOT LEAN_STANDALONE)
 endif()
 
 # flags for user binaries = flags for toolchain binaries + Lake
-set(LEANC_STATIC_LINKER_FLAGS " ${TOOLCHAIN_STATIC_LINKER_FLAGS} -lLake")
-if(${CMAKE_SYSTEM_NAME} MATCHES "Linux")
-  set(LEANC_SHARED_LINKER_FLAGS " ${TOOLCHAIN_SHARED_LINKER_FLAGS} -Wl,--as-needed -lLake_shared -Wl,--no-as-needed")
-else()
-  set(LEANC_SHARED_LINKER_FLAGS " ${TOOLCHAIN_SHARED_LINKER_FLAGS} -lLake_shared")
-endif()
+string(APPEND LEANC_STATIC_LINKER_FLAGS " ${TOOLCHAIN_STATIC_LINKER_FLAGS} -lLake")
 
 if (LLVM)
   string(APPEND LEANSHARED_LINKER_FLAGS " -L${LLVM_CONFIG_LIBDIR} ${LLVM_CONFIG_LDFLAGS} ${LLVM_CONFIG_LIBS} ${LLVM_CONFIG_SYSTEM_LIBS}")
@@ -383,20 +378,16 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Linux")
   string(APPEND CMAKE_CXX_FLAGS " -fPIC -ftls-model=initial-exec")
   string(APPEND LEANC_EXTRA_FLAGS " -fPIC")
   string(APPEND TOOLCHAIN_SHARED_LINKER_FLAGS " -Wl,-rpath=\\$$ORIGIN/..:\\$$ORIGIN")
-  string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libLake.a.export -Wl,--no-whole-archive")
   string(APPEND CMAKE_EXE_LINKER_FLAGS " -Wl,-rpath=\\\$ORIGIN/../lib:\\\$ORIGIN/../lib/lean")
 elseif(${CMAKE_SYSTEM_NAME} MATCHES "Darwin")
   string(APPEND CMAKE_CXX_FLAGS " -ftls-model=initial-exec")
   string(APPEND INIT_SHARED_LINKER_FLAGS " -install_name @rpath/libInit_shared.dylib")
   string(APPEND LEANSHARED_1_LINKER_FLAGS " -install_name @rpath/libleanshared_1.dylib")
   string(APPEND LEANSHARED_LINKER_FLAGS " -install_name @rpath/libleanshared.dylib")
-  string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/temp/libLake.a.export -install_name @rpath/libLake_shared.dylib")
   string(APPEND CMAKE_EXE_LINKER_FLAGS " -Wl,-rpath,@executable_path/../lib -Wl,-rpath,@executable_path/../lib/lean")
 elseif(${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
   string(APPEND CMAKE_CXX_FLAGS " -fPIC")
   string(APPEND LEANC_EXTRA_FLAGS " -fPIC")
-elseif(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
-  string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,--out-implib,${CMAKE_BINARY_DIR}/lib/lean/libLake_shared.dll.a -Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libLake.a.export -Wl,--no-whole-archive")
 endif()
 
 if(${CMAKE_SYSTEM_NAME} MATCHES "Linux")
@@ -596,13 +587,8 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
   )
   add_custom_target(leanshared ALL
     DEPENDS Init_shared leancpp
-    COMMAND touch ${CMAKE_LIBRARY_OUTPUT_DIRECTORY}/libleanshared_1${CMAKE_SHARED_LIBRARY_SUFFIX}
     COMMAND touch ${CMAKE_LIBRARY_OUTPUT_DIRECTORY}/libleanshared${CMAKE_SHARED_LIBRARY_SUFFIX}
   )
-  add_custom_target(lake_shared ALL
-    DEPENDS leanshared
-    COMMAND touch ${CMAKE_LIBRARY_OUTPUT_DIRECTORY}/libLake_shared${CMAKE_SHARED_LIBRARY_SUFFIX}
-  )
 else()
   add_custom_target(Init_shared ALL
     WORKING_DIRECTORY ${LEAN_SOURCE_DIR}
@@ -620,21 +606,11 @@ else()
 endif()
 
 if(NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
-  add_custom_target(lake_lib ALL
+  add_custom_target(lake ALL
     WORKING_DIRECTORY ${LEAN_SOURCE_DIR}
     DEPENDS leanshared
     COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make Lake
     VERBATIM)
-  add_custom_target(lake_shared ALL
-    WORKING_DIRECTORY ${LEAN_SOURCE_DIR}
-    DEPENDS lake_lib
-    COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make libLake_shared
-    VERBATIM)
-  add_custom_target(lake ALL
-    WORKING_DIRECTORY ${LEAN_SOURCE_DIR}
-    DEPENDS lake_shared
-    COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make lake
-    VERBATIM)
 endif()
 
 if(PREV_STAGE)

src/Init/ByCases.lean

@@ -40,23 +40,21 @@ theorem apply_ite (f : α → β) (P : Prop) [Decidable P] (x y : α) :
 /-- A `dite` whose results do not actually depend on the condition may be reduced to an `ite`. -/
 @[simp] theorem dite_eq_ite [Decidable P] : (dite P (fun _ => a) fun _ => b) = ite P a b := rfl
 
-@[deprecated "Use `ite_eq_right_iff`" (since := "2024-09-18")]
+-- We don't mark this as `simp` as it is already handled by `ite_eq_right_iff`.
 theorem ite_some_none_eq_none [Decidable P] :
     (if P then some x else none) = none ↔ ¬ P := by
   simp only [ite_eq_right_iff, reduceCtorEq]
   rfl
 
-@[deprecated "Use `Option.ite_none_right_eq_some`" (since := "2024-09-18")]
-theorem ite_some_none_eq_some [Decidable P] :
+@[simp] theorem ite_some_none_eq_some [Decidable P] :
     (if P then some x else none) = some y ↔ P ∧ x = y := by
   split <;> simp_all
 
-@[deprecated "Use `dite_eq_right_iff" (since := "2024-09-18")]
+-- This is not marked as `simp` as it is already handled by `dite_eq_right_iff`.
 theorem dite_some_none_eq_none [Decidable P] {x : P → α} :
     (if h : P then some (x h) else none) = none ↔ ¬P := by
   simp
 
-@[deprecated "Use `Option.dite_none_right_eq_some`" (since := "2024-09-18")]
-theorem dite_some_none_eq_some [Decidable P] {x : P → α} {y : α} :
+@[simp] theorem dite_some_none_eq_some [Decidable P] {x : P → α} {y : α} :
     (if h : P then some (x h) else none) = some y ↔ ∃ h : P, x h = y := by
   by_cases h : P <;> simp [h]

src/Init/Classical.lean

@@ -134,30 +134,6 @@ The left-to-right direction, double negation elimination (DNE),
 is classically true but not constructively. -/
 @[simp] theorem not_not : ¬¬a ↔ a := Decidable.not_not
 
-/-- Transfer decidability of `¬ p` to decidability of `p`. -/
--- This can not be an instance as it would be tried everywhere.
-def decidable_of_decidable_not (p : Prop) [h : Decidable (¬ p)] : Decidable p :=
-  match h with
-  | isFalse h => isTrue (Classical.not_not.mp h)
-  | isTrue h => isFalse h
-
-attribute [local instance] decidable_of_decidable_not in
-/-- Negation of the condition `P : Prop` in a `dite` is the same as swapping the branches. -/
-@[simp low] protected theorem dite_not [hn : Decidable (¬p)] (x : ¬p → α) (y : ¬¬p → α) :
-    dite (¬p) x y = dite p (fun h => y (not_not_intro h)) x := by
-  cases hn <;> rename_i g
-  · simp [not_not.mp g]
-  · simp [g]
-
-attribute [local instance] decidable_of_decidable_not in
-/-- Negation of the condition `P : Prop` in a `ite` is the same as swapping the branches. -/
-@[simp low] protected theorem ite_not (p : Prop) [Decidable (¬ p)] (x y : α) : ite (¬p) x y = ite p y x :=
-  dite_not (fun _ => x) (fun _ => y)
-
-attribute [local instance] decidable_of_decidable_not in
-@[simp low] protected theorem decide_not (p : Prop) [Decidable (¬ p)] : decide (¬p) = !decide p :=
-  byCases (fun h : p => by simp_all) (fun h => by simp_all)
-
 @[simp low] theorem not_forall {p : α → Prop} : (¬∀ x, p x) ↔ ∃ x, ¬p x := Decidable.not_forall
 
 theorem not_forall_not {p : α → Prop} : (¬∀ x, ¬p x) ↔ ∃ x, p x := Decidable.not_forall_not

src/Init/Control/Basic.lean

@@ -28,7 +28,7 @@ Important instances include
 * `Option`, where `failure := none` and `<|>` returns the left-most `some`.
 * Parser combinators typically provide an `Applicative` instance for error-handling and
   backtracking.
-
+  
 Error recovery and state can interact subtly. For example, the implementation of `Alternative` for `OptionT (StateT σ Id)` keeps modifications made to the state while recovering from failure, while `StateT σ (OptionT Id)` discards them.
 -/
 -- NB: List instance is in mathlib. Once upstreamed, add

src/Init/Conv.lean

@@ -97,18 +97,11 @@ Users should prefer `unfold` for unfolding definitions. -/
 syntax (name := delta) "delta" (ppSpace colGt ident)+ : conv
 
 /--
-* `unfold id` unfolds all occurrences of definition `id` in the target.
+* `unfold foo` unfolds all occurrences of `foo` in the target.
 * `unfold id1 id2 ...` is equivalent to `unfold id1; unfold id2; ...`.
-
-Definitions can be either global or local definitions.
-
-For non-recursive global definitions, this tactic is identical to `delta`.
-For recursive global definitions, it uses the "unfolding lemma" `id.eq_def`,
-which is generated for each recursive definition, to unfold according to the recursive definition given by the user.
-Only one level of unfolding is performed, in contrast to `simp only [id]`, which unfolds definition `id` recursively.
-
-This is the `conv` version of the `unfold` tactic.
--/
+Like the `unfold` tactic, this uses equational lemmas for the chosen definition
+to rewrite the target. For recursive definitions,
+only one layer of unfolding is performed. -/
 syntax (name := unfold) "unfold" (ppSpace colGt ident)+ : conv
 
 /--

src/Init/Core.lean

@@ -165,23 +165,9 @@ inductive PSum (α : Sort u) (β : Sort v) where
 
 @[inherit_doc] infixr:30 " ⊕' " => PSum
 
-/--
-`PSum α β` is inhabited if `α` is inhabited.
-This is not an instance to avoid non-canonical instances.
--/
-@[reducible] def  PSum.inhabitedLeft {α β} [Inhabited α] : Inhabited (PSum α β) := ⟨PSum.inl default⟩
+instance {α β} [Inhabited α] : Inhabited (PSum α β) := ⟨PSum.inl default⟩
 
-/--
-`PSum α β` is inhabited if `β` is inhabited.
-This is not an instance to avoid non-canonical instances.
--/
-@[reducible] def PSum.inhabitedRight {α β} [Inhabited β] : Inhabited (PSum α β) := ⟨PSum.inr default⟩
-
-instance PSum.nonemptyLeft [h : Nonempty α] : Nonempty (PSum α β) :=
-  Nonempty.elim h (fun a => ⟨PSum.inl a⟩)
-
-instance PSum.nonemptyRight [h : Nonempty β] : Nonempty (PSum α β) :=
-  Nonempty.elim h (fun b => ⟨PSum.inr b⟩)
+instance {α β} [Inhabited β] : Inhabited (PSum α β) := ⟨PSum.inr default⟩
 
 /--
 `Sigma β`, also denoted `Σ a : α, β a` or `(a : α) × β a`, is the type of dependent pairs
@@ -817,7 +803,7 @@ variable {a b c d : Prop}
 theorem iff_iff_implies_and_implies {a b : Prop} : (a ↔ b) ↔ (a → b) ∧ (b → a) :=
   Iff.intro (fun h => And.intro h.mp h.mpr) (fun h => Iff.intro h.left h.right)
 
-@[refl] theorem Iff.refl (a : Prop) : a ↔ a :=
+theorem Iff.refl (a : Prop) : a ↔ a :=
   Iff.intro (fun h => h) (fun h => h)
 
 protected theorem Iff.rfl {a : Prop} : a ↔ a :=
@@ -1164,20 +1150,12 @@ end Subtype
 section
 variable {α : Type u} {β : Type v}
 
-/-- This is not an instance to avoid non-canonical instances. -/
-@[reducible] def Sum.inhabitedLeft [Inhabited α] : Inhabited (Sum α β) where
+instance Sum.inhabitedLeft [Inhabited α] : Inhabited (Sum α β) where
   default := Sum.inl default
 
-/-- This is not an instance to avoid non-canonical instances. -/
-@[reducible] def Sum.inhabitedRight [Inhabited β] : Inhabited (Sum α β) where
+instance Sum.inhabitedRight [Inhabited β] : Inhabited (Sum α β) where
   default := Sum.inr default
 
-instance Sum.nonemptyLeft [h : Nonempty α] : Nonempty (Sum α β) :=
-  Nonempty.elim h (fun a => ⟨Sum.inl a⟩)
-
-instance Sum.nonemptyRight [h : Nonempty β] : Nonempty (Sum α β) :=
-  Nonempty.elim h (fun b => ⟨Sum.inr b⟩)
-
 instance {α : Type u} {β : Type v} [DecidableEq α] [DecidableEq β] : DecidableEq (Sum α β) := fun a b =>
   match a, b with
   | Sum.inl a, Sum.inl b =>
@@ -1193,21 +1171,6 @@ end
 
 /-! # Product -/
 
-instance [h1 : Nonempty α] [h2 : Nonempty β] : Nonempty (α × β) :=
-  Nonempty.elim h1 fun x =>
-    Nonempty.elim h2 fun y =>
-      ⟨(x, y)⟩
-
-instance [h1 : Nonempty α] [h2 : Nonempty β] : Nonempty (MProd α β) :=
-  Nonempty.elim h1 fun x =>
-    Nonempty.elim h2 fun y =>
-      ⟨⟨x, y⟩⟩
-
-instance [h1 : Nonempty α] [h2 : Nonempty β] : Nonempty (PProd α β) :=
-  Nonempty.elim h1 fun x =>
-    Nonempty.elim h2 fun y =>
-      ⟨⟨x, y⟩⟩
-
 instance [Inhabited α] [Inhabited β] : Inhabited (α × β) where
   default := (default, default)
 

src/Init/Data.lean

@@ -39,5 +39,3 @@ import Init.Data.BEq
 import Init.Data.Subtype
 import Init.Data.ULift
 import Init.Data.PLift
-import Init.Data.Zero
-import Init.Data.NeZero

src/Init/Data/Array.lean

@@ -15,4 +15,3 @@ import Init.Data.Array.BasicAux
 import Init.Data.Array.Lemmas
 import Init.Data.Array.TakeDrop
 import Init.Data.Array.Bootstrap
-import Init.Data.Array.GetLit

src/Init/Data/Array/Attach.lean

@@ -20,7 +20,7 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
   with the same elements but in the type `{x // P x}`. -/
 @[implemented_by attachWithImpl] def attachWith
     (xs : Array α) (P : α → Prop) (H : ∀ x ∈ xs, P x) : Array {x // P x} :=
-  ⟨xs.toList.attachWith P fun x h => H x (Array.Mem.mk h)⟩
+  ⟨xs.data.attachWith P fun x h => H x (Array.Mem.mk h)⟩
 
 /-- `O(1)`. "Attach" the proof that the elements of `xs` are in `xs` to produce a new array
   with the same elements but in the type `{x // x ∈ xs}`. -/

src/Init/Data/Array/Basic.lean

@@ -13,76 +13,42 @@ import Init.Data.ToString.Basic
 import Init.GetElem
 universe u v w
 
-/-! ### Array literal syntax -/
-
-syntax "#[" withoutPosition(sepBy(term, ", ")) "]" : term
-
-macro_rules
-  | `(#[ $elems,* ]) => `(List.toArray [ $elems,* ])
-
+namespace Array
 variable {α : Type u}
 
-namespace Array
+@[extern "lean_mk_array"]
+def mkArray {α : Type u} (n : Nat) (v : α) : Array α := {
+  data := List.replicate n v
+}
 
-/-! ### Preliminary theorems -/
+/--
+`ofFn f` with `f : Fin n → α` returns the list whose ith element is `f i`.
+```
+ofFn f = #[f 0, f 1, ... , f(n - 1)]
+``` -/
+def ofFn {n} (f : Fin n → α) : Array α := go 0 (mkEmpty n) where
+  /-- Auxiliary for `ofFn`. `ofFn.go f i acc = acc ++ #[f i, ..., f(n - 1)]` -/
+  go (i : Nat) (acc : Array α) : Array α :=
+    if h : i < n then go (i+1) (acc.push (f ⟨i, h⟩)) else acc
+termination_by n - i
+decreasing_by simp_wf; decreasing_trivial_pre_omega
 
-@[simp] theorem size_set (a : Array α) (i : Fin a.size) (v : α) : (set a i v).size = a.size :=
-  List.length_set ..
+/-- The array `#[0, 1, ..., n - 1]`. -/
+def range (n : Nat) : Array Nat :=
+  n.fold (flip Array.push) (mkEmpty n)
 
-@[simp] theorem size_push (a : Array α) (v : α) : (push a v).size = a.size + 1 :=
-  List.length_concat ..
+@[simp] theorem size_mkArray (n : Nat) (v : α) : (mkArray n v).size = n :=
+  List.length_replicate ..
 
-theorem ext (a b : Array α)
-    (h₁ : a.size = b.size)
-    (h₂ : (i : Nat) → (hi₁ : i < a.size) → (hi₂ : i < b.size) → a[i] = b[i])
-    : a = b := by
-  let rec extAux (a b : List α)
-      (h₁ : a.length = b.length)
-      (h₂ : (i : Nat) → (hi₁ : i < a.length) → (hi₂ : i < b.length) → a.get ⟨i, hi₁⟩ = b.get ⟨i, hi₂⟩)
-      : a = b := by
-    induction a generalizing b with
-    | nil =>
-      cases b with
-      | nil       => rfl
-      | cons b bs => rw [List.length_cons] at h₁; injection h₁
-    | cons a as ih =>
-      cases b with
-      | nil => rw [List.length_cons] at h₁; injection h₁
-      | cons b bs =>
-        have hz₁ : 0 < (a::as).length := by rw [List.length_cons]; apply Nat.zero_lt_succ
-        have hz₂ : 0 < (b::bs).length := by rw [List.length_cons]; apply Nat.zero_lt_succ
-        have headEq : a = b := h₂ 0 hz₁ hz₂
-        have h₁' : as.length = bs.length := by rw [List.length_cons, List.length_cons] at h₁; injection h₁
-        have h₂' : (i : Nat) → (hi₁ : i < as.length) → (hi₂ : i < bs.length) → as.get ⟨i, hi₁⟩ = bs.get ⟨i, hi₂⟩ := by
-          intro i hi₁ hi₂
-          have hi₁' : i+1 < (a::as).length := by rw [List.length_cons]; apply Nat.succ_lt_succ; assumption
-          have hi₂' : i+1 < (b::bs).length := by rw [List.length_cons]; apply Nat.succ_lt_succ; assumption
-          have : (a::as).get ⟨i+1, hi₁'⟩ = (b::bs).get ⟨i+1, hi₂'⟩ := h₂ (i+1) hi₁' hi₂'
-          apply this
-        have tailEq : as = bs := ih bs h₁' h₂'
-        rw [headEq, tailEq]
-  cases a; cases b
-  apply congrArg
-  apply extAux
-  assumption
-  assumption
+instance : EmptyCollection (Array α) := ⟨Array.empty⟩
+instance : Inhabited (Array α) where
+  default := Array.empty
 
-theorem ext' {as bs : Array α} (h : as.toList = bs.toList) : as = bs := by
-  cases as; cases bs; simp at h; rw [h]
+@[simp] def isEmpty (a : Array α) : Bool :=
+  a.size = 0
 
-@[simp] theorem toArrayAux_eq (as : List α) (acc : Array α) : (as.toArrayAux acc).toList = acc.toList ++ as := by
-  induction as generalizing acc <;> simp [*, List.toArrayAux, Array.push, List.append_assoc, List.concat_eq_append]
-
-@[simp] theorem toList_toArray (as : List α) : as.toArray.toList = as := by
-  simp [List.toArray, Array.mkEmpty]
-
-@[simp] theorem size_toArray (as : List α) : as.toArray.size = as.length := by simp [size]
-
-@[deprecated toList_toArray (since := "2024-09-09")] abbrev data_toArray := @toList_toArray
-
-@[deprecated Array.toList (since := "2024-09-10")] abbrev Array.data := @Array.toList
-
-/-! ### Externs -/
+def singleton (v : α) : Array α :=
+  mkArray 1 v
 
 /-- Low-level version of `size` that directly queries the C array object cached size.
     While this is not provable, `usize` always returns the exact size of the array since
@@ -98,6 +64,29 @@ def usize (a : @& Array α) : USize := a.size.toUSize
 def uget (a : @& Array α) (i : USize) (h : i.toNat < a.size) : α :=
   a[i.toNat]
 
+instance : GetElem (Array α) USize α fun xs i => i.toNat < xs.size where
+  getElem xs i h := xs.uget i h
+
+def back [Inhabited α] (a : Array α) : α :=
+  a.get! (a.size - 1)
+
+def get? (a : Array α) (i : Nat) : Option α :=
+  if h : i < a.size then some a[i] else none
+
+def back? (a : Array α) : Option α :=
+  a.get? (a.size - 1)
+
+-- auxiliary declaration used in the equation compiler when pattern matching array literals.
+abbrev getLit {α : Type u} {n : Nat} (a : Array α) (i : Nat) (h₁ : a.size = n) (h₂ : i < n) : α :=
+  have := h₁.symm ▸ h₂
+  a[i]
+
+@[simp] theorem size_set (a : Array α) (i : Fin a.size) (v : α) : (set a i v).size = a.size :=
+  List.length_set ..
+
+@[simp] theorem size_push (a : Array α) (v : α) : (push a v).size = a.size + 1 :=
+  List.length_concat ..
+
 /-- Low-level version of `fset` which is as fast as a C array fset.
    `Fin` values are represented as tag pointers in the Lean runtime. Thus,
    `fset` may be slightly slower than `uset`. -/
@@ -105,19 +94,6 @@ def uget (a : @& Array α) (i : USize) (h : i.toNat < a.size) : α :=
 def uset (a : Array α) (i : USize) (v : α) (h : i.toNat < a.size) : Array α :=
   a.set ⟨i.toNat, h⟩ v
 
-@[extern "lean_array_pop"]
-def pop (a : Array α) : Array α where
-  toList := a.toList.dropLast
-
-@[simp] theorem size_pop (a : Array α) : a.pop.size = a.size - 1 := by
-  match a with
-  | ⟨[]⟩ => rfl
-  | ⟨a::as⟩ => simp [pop, Nat.succ_sub_succ_eq_sub, size]
-
-@[extern "lean_mk_array"]
-def mkArray {α : Type u} (n : Nat) (v : α) : Array α where
-  toList := List.replicate n v
-
 /--
 Swaps two entries in an array.
 
@@ -131,10 +107,6 @@ def swap (a : Array α) (i j : @& Fin a.size) : Array α :=
   let a'  := a.set i v₂
   a'.set (size_set a i v₂ ▸ j) v₁
 
-@[simp] theorem size_swap (a : Array α) (i j : Fin a.size) : (a.swap i j).size = a.size := by
-  show ((a.set i (a.get j)).set (size_set a i _ ▸ j) (a.get i)).size = a.size
-  rw [size_set, size_set]
-
 /--
 Swaps two entries in an array, or returns the array unchanged if either index is out of bounds.
 
@@ -148,66 +120,6 @@ def swap! (a : Array α) (i j : @& Nat) : Array α :=
   else a
   else a
 
-/-! ### GetElem instance for `USize`, backed by `uget` -/
-
-instance : GetElem (Array α) USize α fun xs i => i.toNat < xs.size where
-  getElem xs i h := xs.uget i h
-
-/-! ### Definitions -/
-
-instance : EmptyCollection (Array α) := ⟨Array.empty⟩
-instance : Inhabited (Array α) where
-  default := Array.empty
-
-@[simp] def isEmpty (a : Array α) : Bool :=
-  a.size = 0
-
--- TODO(Leo): cleanup
-@[specialize]
-def isEqvAux (a b : Array α) (hsz : a.size = b.size) (p : α → α → Bool) (i : Nat) : Bool :=
-  if h : i < a.size then
-     have : i < b.size := hsz ▸ h
-     p a[i] b[i] && isEqvAux a b hsz p (i+1)
-  else
-    true
-decreasing_by simp_wf; decreasing_trivial_pre_omega
-
-@[inline] def isEqv (a b : Array α) (p : α → α → Bool) : Bool :=
-  if h : a.size = b.size then
-    isEqvAux a b h p 0
-  else
-    false
-
-instance [BEq α] : BEq (Array α) :=
-  ⟨fun a b => isEqv a b BEq.beq⟩
-
-/--
-`ofFn f` with `f : Fin n → α` returns the list whose ith element is `f i`.
-```
-ofFn f = #[f 0, f 1, ... , f(n - 1)]
-``` -/
-def ofFn {n} (f : Fin n → α) : Array α := go 0 (mkEmpty n) where
-  /-- Auxiliary for `ofFn`. `ofFn.go f i acc = acc ++ #[f i, ..., f(n - 1)]` -/
-  go (i : Nat) (acc : Array α) : Array α :=
-    if h : i < n then go (i+1) (acc.push (f ⟨i, h⟩)) else acc
-decreasing_by simp_wf; decreasing_trivial_pre_omega
-
-/-- The array `#[0, 1, ..., n - 1]`. -/
-def range (n : Nat) : Array Nat :=
-  n.fold (flip Array.push) (mkEmpty n)
-
-def singleton (v : α) : Array α :=
-  mkArray 1 v
-
-def back [Inhabited α] (a : Array α) : α :=
-  a.get! (a.size - 1)
-
-def get? (a : Array α) (i : Nat) : Option α :=
-  if h : i < a.size then some a[i] else none
-
-def back? (a : Array α) : Option α :=
-  a.get? (a.size - 1)
-
 @[inline] def swapAt (a : Array α) (i : Fin a.size) (v : α) : α × Array α :=
   let e := a.get i
   let a := a.set i v
@@ -221,6 +133,11 @@ def swapAt! (a : Array α) (i : Nat) (v : α) : α × Array α :=
     have : Inhabited α := ⟨v⟩
     panic! ("index " ++ toString i ++ " out of bounds")
 
+@[extern "lean_array_pop"]
+def pop (a : Array α) : Array α := {
+  data := a.data.dropLast
+}
+
 def shrink (a : Array α) (n : Nat) : Array α :=
   let rec loop
     | 0,   a => a
@@ -394,6 +311,7 @@ def mapM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α
       map (i+1) (r.push (← f as[i]))
     else
       pure r
+  termination_by as.size - i
   decreasing_by simp_wf; decreasing_trivial_pre_omega
   map 0 (mkEmpty as.size)
 
@@ -466,6 +384,7 @@ def anyM {α : Type u} {m : Type → Type w} [Monad m] (p : α → m Bool) (as :
           loop (j+1)
       else
         pure false
+      termination_by stop - j
       decreasing_by simp_wf; decreasing_trivial_pre_omega
     loop start
   if h : stop ≤ as.size then
@@ -551,22 +470,12 @@ def findIdx? {α : Type u} (as : Array α) (p : α → Bool) : Option Nat :=
     if h : j < as.size then
       if p as[j] then some j else loop (j + 1)
     else none
+    termination_by as.size - j
     decreasing_by simp_wf; decreasing_trivial_pre_omega
   loop 0
 
 def getIdx? [BEq α] (a : Array α) (v : α) : Option Nat :=
-  a.findIdx? fun a => a == v
-
-def indexOfAux [BEq α] (a : Array α) (v : α) (i : Nat) : Option (Fin a.size) :=
-  if h : i < a.size then
-    let idx : Fin a.size := ⟨i, h⟩;
-    if a.get idx == v then some idx
-    else indexOfAux a v (i+1)
-  else none
-decreasing_by simp_wf; decreasing_trivial_pre_omega
-
-def indexOf? [BEq α] (a : Array α) (v : α) : Option (Fin a.size) :=
-  indexOfAux a v 0
+a.findIdx? fun a => a == v
 
 @[inline]
 def any (as : Array α) (p : α → Bool) (start := 0) (stop := as.size) : Bool :=
@@ -582,11 +491,18 @@ def contains [BEq α] (as : Array α) (a : α) : Bool :=
 def elem [BEq α] (a : α) (as : Array α) : Bool :=
   as.contains a
 
+@[inline] def getEvenElems (as : Array α) : Array α :=
+  (·.2) <| as.foldl (init := (true, Array.empty)) fun (even, r) a =>
+    if even then
+      (false, r.push a)
+    else
+      (true, r)
+
 /-- Convert a `Array α` into an `List α`. This is O(n) in the size of the array.  -/
--- This function is exported to C, where it is called by `Array.toList`
+-- This function is exported to C, where it is called by `Array.data`
 -- (the projection) to implement this functionality.
-@[export lean_array_to_list_impl]
-def toListImpl (as : Array α) : List α :=
+@[export lean_array_to_list]
+def toList (as : Array α) : List α :=
   as.foldr List.cons []
 
 /-- Prepends an `Array α` onto the front of a list.  Equivalent to `as.toList ++ l`. -/
@@ -594,6 +510,17 @@ def toListImpl (as : Array α) : List α :=
 def toListAppend (as : Array α) (l : List α) : List α :=
   as.foldr List.cons l
 
+instance {α : Type u} [Repr α] : Repr (Array α) where
+  reprPrec a _ :=
+    let _ : Std.ToFormat α := ⟨repr⟩
+    if a.size == 0 then
+      "#[]"
+    else
+      Std.Format.bracketFill "#[" (Std.Format.joinSep (toList a) ("," ++ Std.Format.line)) "]"
+
+instance [ToString α] : ToString (Array α) where
+  toString a := "#" ++ toString a.toList
+
 protected def append (as : Array α) (bs : Array α) : Array α :=
   bs.foldl (init := as) fun r v => r.push v
 
@@ -619,13 +546,44 @@ def concatMap (f : α → Array β) (as : Array α) : Array β :=
 def flatten (as : Array (Array α)) : Array α :=
   as.foldl (init := empty) fun r a => r ++ a
 
+end Array
+
+export Array (mkArray)
+
+syntax "#[" withoutPosition(sepBy(term, ", ")) "]" : term
+
+macro_rules
+  | `(#[ $elems,* ]) => `(List.toArray [ $elems,* ])
+
+namespace Array
+
+-- TODO(Leo): cleanup
+@[specialize]
+def isEqvAux (a b : Array α) (hsz : a.size = b.size) (p : α → α → Bool) (i : Nat) : Bool :=
+  if h : i < a.size then
+     have : i < b.size := hsz ▸ h
+     p a[i] b[i] && isEqvAux a b hsz p (i+1)
+  else
+    true
+termination_by a.size - i
+decreasing_by simp_wf; decreasing_trivial_pre_omega
+
+@[inline] def isEqv (a b : Array α) (p : α → α → Bool) : Bool :=
+  if h : a.size = b.size then
+    isEqvAux a b h p 0
+  else
+    false
+
+instance [BEq α] : BEq (Array α) :=
+  ⟨fun a b => isEqv a b BEq.beq⟩
+
 @[inline]
 def filter (p : α → Bool) (as : Array α) (start := 0) (stop := as.size) : Array α :=
   as.foldl (init := #[]) (start := start) (stop := stop) fun r a =>
     if p a then r.push a else r
 
 @[inline]
-def filterM {α : Type} [Monad m] (p : α → m Bool) (as : Array α) (start := 0) (stop := as.size) : m (Array α) :=
+def filterM [Monad m] (p : α → m Bool) (as : Array α) (start := 0) (stop := as.size) : m (Array α) :=
   as.foldlM (init := #[]) (start := start) (stop := stop) fun r a => do
     if (← p a) then return r.push a else return r
 
@@ -660,23 +618,92 @@ def partition (p : α → Bool) (as : Array α) : Array α × Array α := Id.run
       cs := cs.push a
   return (bs, cs)
 
+theorem ext (a b : Array α)
+    (h₁ : a.size = b.size)
+    (h₂ : (i : Nat) → (hi₁ : i < a.size) → (hi₂ : i < b.size) → a[i] = b[i])
+    : a = b := by
+  let rec extAux (a b : List α)
+      (h₁ : a.length = b.length)
+      (h₂ : (i : Nat) → (hi₁ : i < a.length) → (hi₂ : i < b.length) → a.get ⟨i, hi₁⟩ = b.get ⟨i, hi₂⟩)
+      : a = b := by
+    induction a generalizing b with
+    | nil =>
+      cases b with
+      | nil       => rfl
+      | cons b bs => rw [List.length_cons] at h₁; injection h₁
+    | cons a as ih =>
+      cases b with
+      | nil => rw [List.length_cons] at h₁; injection h₁
+      | cons b bs =>
+        have hz₁ : 0 < (a::as).length := by rw [List.length_cons]; apply Nat.zero_lt_succ
+        have hz₂ : 0 < (b::bs).length := by rw [List.length_cons]; apply Nat.zero_lt_succ
+        have headEq : a = b := h₂ 0 hz₁ hz₂
+        have h₁' : as.length = bs.length := by rw [List.length_cons, List.length_cons] at h₁; injection h₁
+        have h₂' : (i : Nat) → (hi₁ : i < as.length) → (hi₂ : i < bs.length) → as.get ⟨i, hi₁⟩ = bs.get ⟨i, hi₂⟩ := by
+          intro i hi₁ hi₂
+          have hi₁' : i+1 < (a::as).length := by rw [List.length_cons]; apply Nat.succ_lt_succ; assumption
+          have hi₂' : i+1 < (b::bs).length := by rw [List.length_cons]; apply Nat.succ_lt_succ; assumption
+          have : (a::as).get ⟨i+1, hi₁'⟩ = (b::bs).get ⟨i+1, hi₂'⟩ := h₂ (i+1) hi₁' hi₂'
+          apply this
+        have tailEq : as = bs := ih bs h₁' h₂'
+        rw [headEq, tailEq]
+  cases a; cases b
+  apply congrArg
+  apply extAux
+  assumption
+  assumption
+
+theorem extLit {n : Nat}
+    (a b : Array α)
+    (hsz₁ : a.size = n) (hsz₂ : b.size = n)
+    (h : (i : Nat) → (hi : i < n) → a.getLit i hsz₁ hi = b.getLit i hsz₂ hi) : a = b :=
+  Array.ext a b (hsz₁.trans hsz₂.symm) fun i hi₁ _ => h i (hsz₁ ▸ hi₁)
+
+end Array
+
+-- CLEANUP the following code
+namespace Array
+
+def indexOfAux [BEq α] (a : Array α) (v : α) (i : Nat) : Option (Fin a.size) :=
+  if h : i < a.size then
+    let idx : Fin a.size := ⟨i, h⟩;
+    if a.get idx == v then some idx
+    else indexOfAux a v (i+1)
+  else none
+termination_by a.size - i
+decreasing_by simp_wf; decreasing_trivial_pre_omega
+
+def indexOf? [BEq α] (a : Array α) (v : α) : Option (Fin a.size) :=
+  indexOfAux a v 0
+
+@[simp] theorem size_swap (a : Array α) (i j : Fin a.size) : (a.swap i j).size = a.size := by
+  show ((a.set i (a.get j)).set (size_set a i _ ▸ j) (a.get i)).size = a.size
+  rw [size_set, size_set]
+
+@[simp] theorem size_pop (a : Array α) : a.pop.size = a.size - 1 := by
+  match a with
+  | ⟨[]⟩ => rfl
+  | ⟨a::as⟩ => simp [pop, Nat.succ_sub_succ_eq_sub, size]
+
+theorem reverse.termination {i j : Nat} (h : i < j) : j - 1 - (i + 1) < j - i := by
+  rw [Nat.sub_sub, Nat.add_comm]
+  exact Nat.lt_of_le_of_lt (Nat.pred_le _) (Nat.sub_succ_lt_self _ _ h)
+
 def reverse (as : Array α) : Array α :=
   if h : as.size ≤ 1 then
     as
   else
     loop as 0 ⟨as.size - 1, Nat.pred_lt (mt (fun h : as.size = 0 => h ▸ by decide) h)⟩
 where
-  termination {i j : Nat} (h : i < j) : j - 1 - (i + 1) < j - i := by
-    rw [Nat.sub_sub, Nat.add_comm]
-    exact Nat.lt_of_le_of_lt (Nat.pred_le _) (Nat.sub_succ_lt_self _ _ h)
   loop (as : Array α) (i : Nat) (j : Fin as.size) :=
     if h : i < j then
-      have := termination h
+      have := reverse.termination h
       let as := as.swap ⟨i, Nat.lt_trans h j.2⟩ j
       have : j-1 < as.size := by rw [size_swap]; exact Nat.lt_of_le_of_lt (Nat.pred_le _) j.2
       loop as (i+1) ⟨j-1, this⟩
     else
       as
+termination_by j - i
 
 def popWhile (p : α → Bool) (as : Array α) : Array α :=
   if h : as.size > 0 then
@@ -686,6 +713,7 @@ def popWhile (p : α → Bool) (as : Array α) : Array α :=
       as
   else
     as
+termination_by as.size
 decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 def takeWhile (p : α → Bool) (as : Array α) : Array α :=
@@ -698,6 +726,7 @@ def takeWhile (p : α → Bool) (as : Array α) : Array α :=
         r
     else
       r
+    termination_by as.size - i
     decreasing_by simp_wf; decreasing_trivial_pre_omega
   go 0 #[]
 
@@ -715,7 +744,6 @@ def feraseIdx (a : Array α) (i : Fin a.size) : Array α :=
 termination_by a.size - i.val
 decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ i.isLt
 
--- This is required in `Lean.Data.PersistentHashMap`.
 theorem size_feraseIdx (a : Array α) (i : Fin a.size) : (a.feraseIdx i).size = a.size - 1 := by
   induction a, i using Array.feraseIdx.induct with
   | @case1 a i h a' _ ih =>
@@ -746,6 +774,7 @@ def erase [BEq α] (as : Array α) (a : α) : Array α :=
       loop as ⟨j', by rw [size_swap]; exact j'.2⟩
     else
       as
+    termination_by j.1
     decreasing_by simp_wf; decreasing_trivial_pre_omega
   let j := as.size
   let as := as.push a
@@ -757,6 +786,39 @@ def insertAt! (as : Array α) (i : Nat) (a : α) : Array α :=
     insertAt as ⟨i, Nat.lt_succ_of_le h⟩ a
   else panic! "invalid index"
 
+def toListLitAux (a : Array α) (n : Nat) (hsz : a.size = n) : ∀ (i : Nat), i ≤ a.size → List α → List α
+  | 0,     _,  acc => acc
+  | (i+1), hi, acc => toListLitAux a n hsz i (Nat.le_of_succ_le hi) (a.getLit i hsz (Nat.lt_of_lt_of_eq (Nat.lt_of_lt_of_le (Nat.lt_succ_self i) hi) hsz) :: acc)
+
+def toArrayLit (a : Array α) (n : Nat) (hsz : a.size = n) : Array α :=
+  List.toArray <| toListLitAux a n hsz n (hsz ▸ Nat.le_refl _) []
+
+theorem ext' {as bs : Array α} (h : as.data = bs.data) : as = bs := by
+  cases as; cases bs; simp at h; rw [h]
+
+@[simp] theorem toArrayAux_eq (as : List α) (acc : Array α) : (as.toArrayAux acc).data = acc.data ++ as := by
+  induction as generalizing acc <;> simp [*, List.toArrayAux, Array.push, List.append_assoc, List.concat_eq_append]
+
+@[simp] theorem data_toArray (as : List α) : as.toArray.data = as := by
+  simp [List.toArray, Array.mkEmpty]
+
+@[simp] theorem size_toArray (as : List α) : as.toArray.size = as.length := by simp [size]
+
+theorem toArrayLit_eq (as : Array α) (n : Nat) (hsz : as.size = n) : as = toArrayLit as n hsz := by
+  apply ext'
+  simp [toArrayLit, data_toArray]
+  have hle : n ≤ as.size := hsz ▸ Nat.le_refl _
+  have hge : as.size ≤ n := hsz ▸ Nat.le_refl _
+  have := go n hle
+  rw [List.drop_eq_nil_of_le hge] at this
+  rw [this]
+where
+  getLit_eq (as : Array α) (i : Nat) (h₁ : as.size = n) (h₂ : i < n) : as.getLit i h₁ h₂ = getElem as.data i ((id (α := as.data.length = n) h₁) ▸ h₂) :=
+    rfl
+
+  go (i : Nat) (hi : i ≤ as.size) : toListLitAux as n hsz i hi (as.data.drop i) = as.data := by
+    induction i <;> simp [getLit_eq, List.get_drop_eq_drop, toListLitAux, List.drop, *]
+
 def isPrefixOfAux [BEq α] (as bs : Array α) (hle : as.size ≤ bs.size) (i : Nat) : Bool :=
   if h : i < as.size then
     let a := as[i]
@@ -768,6 +830,7 @@ def isPrefixOfAux [BEq α] (as bs : Array α) (hle : as.size ≤ bs.size) (i : N
       false
   else
     true
+termination_by as.size - i
 decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 /-- Return true iff `as` is a prefix of `bs`.
@@ -778,6 +841,23 @@ def isPrefixOf [BEq α] (as bs : Array α) : Bool :=
   else
     false
 
+private def allDiffAuxAux [BEq α] (as : Array α) (a : α) : forall (i : Nat), i < as.size → Bool
+  | 0,   _ => true
+  | i+1, h =>
+    have : i < as.size := Nat.lt_trans (Nat.lt_succ_self _) h;
+    a != as[i] && allDiffAuxAux as a i this
+
+private def allDiffAux [BEq α] (as : Array α) (i : Nat) : Bool :=
+  if h : i < as.size then
+    allDiffAuxAux as as[i] i h && allDiffAux as (i+1)
+  else
+    true
+termination_by as.size - i
+decreasing_by simp_wf; decreasing_trivial_pre_omega
+
+def allDiff [BEq α] (as : Array α) : Bool :=
+  allDiffAux as 0
+
 @[specialize] def zipWithAux (f : α → β → γ) (as : Array α) (bs : Array β) (i : Nat) (cs : Array γ) : Array γ :=
   if h : i < as.size then
     let a := as[i]
@@ -788,6 +868,7 @@ def isPrefixOf [BEq α] (as bs : Array α) : Bool :=
       cs
   else
     cs
+termination_by as.size - i
 decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 @[inline] def zipWith (as : Array α) (bs : Array β) (f : α → β → γ) : Array γ :=
@@ -803,47 +884,4 @@ def split (as : Array α) (p : α → Bool) : Array α × Array α :=
   as.foldl (init := (#[], #[])) fun (as, bs) a =>
     if p a then (as.push a, bs) else (as, bs.push a)
 
-/-! ### Auxiliary functions used in metaprogramming.
-
-We do not intend to provide verification theorems for these functions.
--/
-
-private def allDiffAuxAux [BEq α] (as : Array α) (a : α) : forall (i : Nat), i < as.size → Bool
-  | 0,   _ => true
-  | i+1, h =>
-    have : i < as.size := Nat.lt_trans (Nat.lt_succ_self _) h;
-    a != as[i] && allDiffAuxAux as a i this
-
-private def allDiffAux [BEq α] (as : Array α) (i : Nat) : Bool :=
-  if h : i < as.size then
-    allDiffAuxAux as as[i] i h && allDiffAux as (i+1)
-  else
-    true
-decreasing_by simp_wf; decreasing_trivial_pre_omega
-
-def allDiff [BEq α] (as : Array α) : Bool :=
-  allDiffAux as 0
-
-@[inline] def getEvenElems (as : Array α) : Array α :=
-  (·.2) <| as.foldl (init := (true, Array.empty)) fun (even, r) a =>
-    if even then
-      (false, r.push a)
-    else
-      (true, r)
-
-/-! ### Repr and ToString -/
-
-instance {α : Type u} [Repr α] : Repr (Array α) where
-  reprPrec a _ :=
-    let _ : Std.ToFormat α := ⟨repr⟩
-    if a.size == 0 then
-      "#[]"
-    else
-      Std.Format.bracketFill "#[" (Std.Format.joinSep (toList a) ("," ++ Std.Format.line)) "]"
-
-instance [ToString α] : ToString (Array α) where
-  toString a := "#" ++ toString a.toList
-
 end Array
-
-export Array (mkArray)

src/Init/Data/Array/Bootstrap.lean

@@ -15,106 +15,76 @@ This file contains some theorems about `Array` and `List` needed for `Init.Data.
 
 namespace Array
 
-theorem foldlM_eq_foldlM_toList.aux [Monad m]
+theorem foldlM_eq_foldlM_data.aux [Monad m]
     (f : β → α → m β) (arr : Array α) (i j) (H : arr.size ≤ i + j) (b) :
-    foldlM.loop f arr arr.size (Nat.le_refl _) i j b = (arr.toList.drop j).foldlM f b := by
+    foldlM.loop f arr arr.size (Nat.le_refl _) i j b = (arr.data.drop j).foldlM f b := by
   unfold foldlM.loop
   split; split
   · cases Nat.not_le_of_gt ‹_› (Nat.zero_add _ ▸ H)
   · rename_i i; rw [Nat.succ_add] at H
-    simp [foldlM_eq_foldlM_toList.aux f arr i (j+1) H]
+    simp [foldlM_eq_foldlM_data.aux f arr i (j+1) H]
     rw (config := {occs := .pos [2]}) [← List.get_drop_eq_drop _ _ ‹_›]
     rfl
   · rw [List.drop_of_length_le (Nat.ge_of_not_lt ‹_›)]; rfl
 
-theorem foldlM_eq_foldlM_toList [Monad m]
+theorem foldlM_eq_foldlM_data [Monad m]
     (f : β → α → m β) (init : β) (arr : Array α) :
-    arr.foldlM f init = arr.toList.foldlM f init := by
-  simp [foldlM, foldlM_eq_foldlM_toList.aux]
+    arr.foldlM f init = arr.data.foldlM f init := by
+  simp [foldlM, foldlM_eq_foldlM_data.aux]
 
-theorem foldl_eq_foldl_toList (f : β → α → β) (init : β) (arr : Array α) :
-    arr.foldl f init = arr.toList.foldl f init :=
-  List.foldl_eq_foldlM .. ▸ foldlM_eq_foldlM_toList ..
+theorem foldl_eq_foldl_data (f : β → α → β) (init : β) (arr : Array α) :
+    arr.foldl f init = arr.data.foldl f init :=
+  List.foldl_eq_foldlM .. ▸ foldlM_eq_foldlM_data ..
 
-theorem foldrM_eq_reverse_foldlM_toList.aux [Monad m]
+theorem foldrM_eq_reverse_foldlM_data.aux [Monad m]
     (f : α → β → m β) (arr : Array α) (init : β) (i h) :
-    (arr.toList.take i).reverse.foldlM (fun x y => f y x) init = foldrM.fold f arr 0 i h init := by
+    (arr.data.take i).reverse.foldlM (fun x y => f y x) init = foldrM.fold f arr 0 i h init := by
   unfold foldrM.fold
   match i with
   | 0 => simp [List.foldlM, List.take]
   | i+1 => rw [← List.take_concat_get _ _ h]; simp [← (aux f arr · i)]; rfl
 
-theorem foldrM_eq_reverse_foldlM_toList [Monad m] (f : α → β → m β) (init : β) (arr : Array α) :
-    arr.foldrM f init = arr.toList.reverse.foldlM (fun x y => f y x) init := by
+theorem foldrM_eq_reverse_foldlM_data [Monad m] (f : α → β → m β) (init : β) (arr : Array α) :
+    arr.foldrM f init = arr.data.reverse.foldlM (fun x y => f y x) init := by
   have : arr = #[] ∨ 0 < arr.size :=
     match arr with | ⟨[]⟩ => .inl rfl | ⟨a::l⟩ => .inr (Nat.zero_lt_succ _)
   match arr, this with | _, .inl rfl => rfl | arr, .inr h => ?_
-  simp [foldrM, h, ← foldrM_eq_reverse_foldlM_toList.aux, List.take_length]
+  simp [foldrM, h, ← foldrM_eq_reverse_foldlM_data.aux, List.take_length]
 
-theorem foldrM_eq_foldrM_toList [Monad m]
+theorem foldrM_eq_foldrM_data [Monad m]
     (f : α → β → m β) (init : β) (arr : Array α) :
-    arr.foldrM f init = arr.toList.foldrM f init := by
-  rw [foldrM_eq_reverse_foldlM_toList, List.foldlM_reverse]
+    arr.foldrM f init = arr.data.foldrM f init := by
+  rw [foldrM_eq_reverse_foldlM_data, List.foldlM_reverse]
 
-theorem foldr_eq_foldr_toList (f : α → β → β) (init : β) (arr : Array α) :
-    arr.foldr f init = arr.toList.foldr f init :=
-  List.foldr_eq_foldrM .. ▸ foldrM_eq_foldrM_toList ..
+theorem foldr_eq_foldr_data (f : α → β → β) (init : β) (arr : Array α) :
+    arr.foldr f init = arr.data.foldr f init :=
+  List.foldr_eq_foldrM .. ▸ foldrM_eq_foldrM_data ..
 
-@[simp] theorem push_toList (arr : Array α) (a : α) : (arr.push a).toList = arr.toList ++ [a] := by
+@[simp] theorem push_data (arr : Array α) (a : α) : (arr.push a).data = arr.data ++ [a] := by
   simp [push, List.concat_eq_append]
 
-@[simp] theorem toListAppend_eq (arr : Array α) (l) : arr.toListAppend l = arr.toList ++ l := by
-  simp [toListAppend, foldr_eq_foldr_toList]
+@[simp] theorem toListAppend_eq (arr : Array α) (l) : arr.toListAppend l = arr.data ++ l := by
+  simp [toListAppend, foldr_eq_foldr_data]
 
-@[simp] theorem toListImpl_eq (arr : Array α) : arr.toListImpl = arr.toList := by
-  simp [toListImpl, foldr_eq_foldr_toList]
+@[simp] theorem toList_eq (arr : Array α) : arr.toList = arr.data := by
+  simp [toList, foldr_eq_foldr_data]
 
-@[simp] theorem pop_toList (arr : Array α) : arr.pop.toList = arr.toList.dropLast := rfl
+@[simp] theorem pop_data (arr : Array α) : arr.pop.data = arr.data.dropLast := rfl
 
 @[simp] theorem append_eq_append (arr arr' : Array α) : arr.append arr' = arr ++ arr' := rfl
 
-@[simp] theorem append_toList (arr arr' : Array α) :
-    (arr ++ arr').toList = arr.toList ++ arr'.toList := by
+@[simp] theorem append_data (arr arr' : Array α) :
+    (arr ++ arr').data = arr.data ++ arr'.data := by
   rw [← append_eq_append]; unfold Array.append
-  rw [foldl_eq_foldl_toList]
-  induction arr'.toList generalizing arr <;> simp [*]
+  rw [foldl_eq_foldl_data]
+  induction arr'.data generalizing arr <;> simp [*]
 
 @[simp] theorem appendList_eq_append
     (arr : Array α) (l : List α) : arr.appendList l = arr ++ l := rfl
 
-@[simp] theorem appendList_toList (arr : Array α) (l : List α) :
-    (arr ++ l).toList = arr.toList ++ l := by
+@[simp] theorem appendList_data (arr : Array α) (l : List α) :
+    (arr ++ l).data = arr.data ++ l := by
   rw [← appendList_eq_append]; unfold Array.appendList
   induction l generalizing arr <;> simp [*]
 
-@[deprecated foldlM_eq_foldlM_toList (since := "2024-09-09")]
-abbrev foldlM_eq_foldlM_data := @foldlM_eq_foldlM_toList
-
-@[deprecated foldl_eq_foldl_toList (since := "2024-09-09")]
-abbrev foldl_eq_foldl_data := @foldl_eq_foldl_toList
-
-@[deprecated foldrM_eq_reverse_foldlM_toList (since := "2024-09-09")]
-abbrev foldrM_eq_reverse_foldlM_data := @foldrM_eq_reverse_foldlM_toList
-
-@[deprecated foldrM_eq_foldrM_toList (since := "2024-09-09")]
-abbrev foldrM_eq_foldrM_data := @foldrM_eq_foldrM_toList
-
-@[deprecated foldr_eq_foldr_toList (since := "2024-09-09")]
-abbrev foldr_eq_foldr_data := @foldr_eq_foldr_toList
-
-@[deprecated push_toList (since := "2024-09-09")]
-abbrev push_data := @push_toList
-
-@[deprecated toListImpl_eq (since := "2024-09-09")]
-abbrev toList_eq := @toListImpl_eq
-
-@[deprecated pop_toList (since := "2024-09-09")]
-abbrev pop_data := @pop_toList
-
-@[deprecated append_toList (since := "2024-09-09")]
-abbrev append_data := @append_toList
-
-@[deprecated appendList_toList (since := "2024-09-09")]
-abbrev appendList_data := @appendList_toList
-
 end Array

src/Init/Data/Array/GetLit.lean

@@ -1,46 +0,0 @@
-/-
-Copyright (c) 2018 Microsoft Corporation. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura
--/
-
-prelude
-import Init.Data.Array.Basic
-
-namespace Array
-
-/-! ### getLit -/
-
--- auxiliary declaration used in the equation compiler when pattern matching array literals.
-abbrev getLit {α : Type u} {n : Nat} (a : Array α) (i : Nat) (h₁ : a.size = n) (h₂ : i < n) : α :=
-  have := h₁.symm ▸ h₂
-  a[i]
-
-theorem extLit {n : Nat}
-    (a b : Array α)
-    (hsz₁ : a.size = n) (hsz₂ : b.size = n)
-    (h : (i : Nat) → (hi : i < n) → a.getLit i hsz₁ hi = b.getLit i hsz₂ hi) : a = b :=
-  Array.ext a b (hsz₁.trans hsz₂.symm) fun i hi₁ _ => h i (hsz₁ ▸ hi₁)
-
-def toListLitAux (a : Array α) (n : Nat) (hsz : a.size = n) : ∀ (i : Nat), i ≤ a.size → List α → List α
-  | 0,     _,  acc => acc
-  | (i+1), hi, acc => toListLitAux a n hsz i (Nat.le_of_succ_le hi) (a.getLit i hsz (Nat.lt_of_lt_of_eq (Nat.lt_of_lt_of_le (Nat.lt_succ_self i) hi) hsz) :: acc)
-
-def toArrayLit (a : Array α) (n : Nat) (hsz : a.size = n) : Array α :=
-  List.toArray <| toListLitAux a n hsz n (hsz ▸ Nat.le_refl _) []
-
-theorem toArrayLit_eq (as : Array α) (n : Nat) (hsz : as.size = n) : as = toArrayLit as n hsz := by
-  apply ext'
-  simp [toArrayLit, toList_toArray]
-  have hle : n ≤ as.size := hsz ▸ Nat.le_refl _
-  have hge : as.size ≤ n := hsz ▸ Nat.le_refl _
-  have := go n hle
-  rw [List.drop_eq_nil_of_le hge] at this
-  rw [this]
-where
-  getLit_eq (as : Array α) (i : Nat) (h₁ : as.size = n) (h₂ : i < n) : as.getLit i h₁ h₂ = getElem as.toList i ((id (α := as.toList.length = n) h₁) ▸ h₂) :=
-    rfl
-  go (i : Nat) (hi : i ≤ as.size) : toListLitAux as n hsz i hi (as.toList.drop i) = as.toList := by
-    induction i <;> simp [getLit_eq, List.get_drop_eq_drop, toListLitAux, List.drop, *]
-
-end Array

src/Init/Data/Array/Lemmas.lean

@@ -19,38 +19,29 @@ This file contains some theorems about `Array` and `List` needed for `Init.Data.
 
 namespace Array
 
-attribute [simp] uset
+attribute [simp] data_toArray uset
 
 @[simp] theorem singleton_def (v : α) : singleton v = #[v] := rfl
 
-@[simp] theorem toArray_toList : (a : Array α) → a.toList.toArray = a
-  | ⟨l⟩ => ext' (toList_toArray l)
+@[simp] theorem toArray_data : (a : Array α) → a.data.toArray = a
+  | ⟨l⟩ => ext' (data_toArray l)
 
-@[deprecated toArray_toList (since := "2024-09-09")]
-abbrev toArray_data := @toArray_toList
-
-@[simp] theorem toList_length {l : Array α} : l.toList.length = l.size := rfl
-
-@[deprecated toList_length (since := "2024-09-09")]
-abbrev data_length := @toList_length
+@[simp] theorem data_length {l : Array α} : l.data.length = l.size := rfl
 
 @[simp] theorem mkEmpty_eq (α n) : @mkEmpty α n = #[] := rfl
 
 @[simp] theorem size_mk (as : List α) : (Array.mk as).size = as.length := by simp [size]
 
-theorem getElem_eq_toList_getElem (a : Array α) (h : i < a.size) : a[i] = a.toList[i] := by
+theorem getElem_eq_data_getElem (a : Array α) (h : i < a.size) : a[i] = a.data[i] := by
   by_cases i < a.size <;> (try simp [*]) <;> rfl
 
-@[deprecated getElem_eq_toList_getElem (since := "2024-09-09")]
-abbrev getElem_eq_data_getElem := @getElem_eq_toList_getElem
-
-@[deprecated getElem_eq_toList_getElem (since := "2024-06-12")]
-theorem getElem_eq_toList_get (a : Array α) (h : i < a.size) : a[i] = a.toList.get ⟨i, h⟩ := by
-  simp [getElem_eq_toList_getElem]
+@[deprecated getElem_eq_data_getElem (since := "2024-06-12")]
+theorem getElem_eq_data_get (a : Array α) (h : i < a.size) : a[i] = a.data.get ⟨i, h⟩ := by
+  simp [getElem_eq_data_getElem]
 
 theorem foldrM_push [Monad m] (f : α → β → m β) (init : β) (arr : Array α) (a : α) :
     (arr.push a).foldrM f init = f a init >>= arr.foldrM f := by
-  simp [foldrM_eq_reverse_foldlM_toList, -size_push]
+  simp [foldrM_eq_reverse_foldlM_data, -size_push]
 
 @[simp] theorem foldrM_push' [Monad m] (f : α → β → m β) (init : β) (arr : Array α) (a : α) :
     (arr.push a).foldrM f init (start := arr.size + 1) = f a init >>= arr.foldrM f := by
@@ -65,17 +56,17 @@ theorem foldr_push (f : α → β → β) (init : β) (arr : Array α) (a : α)
 /-- A more efficient version of `arr.toList.reverse`. -/
 @[inline] def toListRev (arr : Array α) : List α := arr.foldl (fun l t => t :: l) []
 
-@[simp] theorem toListRev_eq (arr : Array α) : arr.toListRev = arr.toList.reverse := by
-  rw [toListRev, foldl_eq_foldl_toList, ← List.foldr_reverse, List.foldr_cons_nil]
+@[simp] theorem toListRev_eq (arr : Array α) : arr.toListRev = arr.data.reverse := by
+  rw [toListRev, foldl_eq_foldl_data, ← List.foldr_reverse, List.foldr_cons_nil]
 
 theorem get_push_lt (a : Array α) (x : α) (i : Nat) (h : i < a.size) :
     have : i < (a.push x).size := by simp [*, Nat.lt_succ_of_le, Nat.le_of_lt]
     (a.push x)[i] = a[i] := by
-  simp only [push, getElem_eq_toList_getElem, List.concat_eq_append, List.getElem_append_left, h]
+  simp only [push, getElem_eq_data_getElem, List.concat_eq_append, List.getElem_append_left, h]
 
 @[simp] theorem get_push_eq (a : Array α) (x : α) : (a.push x)[a.size] = x := by
-  simp only [push, getElem_eq_toList_getElem, List.concat_eq_append]
-  rw [List.getElem_append_right] <;> simp [getElem_eq_toList_getElem, Nat.zero_lt_one]
+  simp only [push, getElem_eq_data_getElem, List.concat_eq_append]
+  rw [List.getElem_append_right] <;> simp [getElem_eq_data_getElem, Nat.zero_lt_one]
 
 theorem get_push (a : Array α) (x : α) (i : Nat) (h : i < (a.push x).size) :
     (a.push x)[i] = if h : i < a.size then a[i] else x := by
@@ -86,31 +77,27 @@ theorem get_push (a : Array α) (x : α) (i : Nat) (h : i < (a.push x).size) :
 
 theorem mapM_eq_foldlM [Monad m] [LawfulMonad m] (f : α → m β) (arr : Array α) :
     arr.mapM f = arr.foldlM (fun bs a => bs.push <$> f a) #[] := by
-  rw [mapM, aux, foldlM_eq_foldlM_toList]; rfl
+  rw [mapM, aux, foldlM_eq_foldlM_data]; rfl
 where
   aux (i r) :
-      mapM.map f arr i r = (arr.toList.drop i).foldlM (fun bs a => bs.push <$> f a) r := by
+      mapM.map f arr i r = (arr.data.drop i).foldlM (fun bs a => bs.push <$> f a) r := by
     unfold mapM.map; split
     · rw [← List.get_drop_eq_drop _ i ‹_›]
-      simp only [aux (i + 1), map_eq_pure_bind, toList_length, List.foldlM_cons, bind_assoc,
-        pure_bind]
+      simp only [aux (i + 1), map_eq_pure_bind, data_length, List.foldlM_cons, bind_assoc, pure_bind]
       rfl
     · rw [List.drop_of_length_le (Nat.ge_of_not_lt ‹_›)]; rfl
   termination_by arr.size - i
   decreasing_by decreasing_trivial_pre_omega
 
-@[simp] theorem map_toList (f : α → β) (arr : Array α) : (arr.map f).toList = arr.toList.map f := by
+@[simp] theorem map_data (f : α → β) (arr : Array α) : (arr.map f).data = arr.data.map f := by
   rw [map, mapM_eq_foldlM]
-  apply congrArg toList (foldl_eq_foldl_toList (fun bs a => push bs (f a)) #[] arr) |>.trans
-  have H (l arr) : List.foldl (fun bs a => push bs (f a)) arr l = ⟨arr.toList ++ l.map f⟩ := by
+  apply congrArg data (foldl_eq_foldl_data (fun bs a => push bs (f a)) #[] arr) |>.trans
+  have H (l arr) : List.foldl (fun bs a => push bs (f a)) arr l = ⟨arr.data ++ l.map f⟩ := by
     induction l generalizing arr <;> simp [*]
   simp [H]
 
-@[deprecated map_toList (since := "2024-09-09")]
-abbrev map_data := @map_toList
-
 @[simp] theorem size_map (f : α → β) (arr : Array α) : (arr.map f).size = arr.size := by
-  simp only [← toList_length]
+  simp only [← data_length]
   simp
 
 @[simp] theorem appendList_nil (arr : Array α) : arr ++ ([] : List α) = arr := Array.ext' (by simp)
@@ -118,22 +105,16 @@ abbrev map_data := @map_toList
 @[simp] theorem appendList_cons (arr : Array α) (a : α) (l : List α) :
     arr ++ (a :: l) = arr.push a ++ l := Array.ext' (by simp)
 
-theorem foldl_toList_eq_bind (l : List α) (acc : Array β)
+theorem foldl_data_eq_bind (l : List α) (acc : Array β)
     (F : Array β → α → Array β) (G : α → List β)
-    (H : ∀ acc a, (F acc a).toList = acc.toList ++ G a) :
-    (l.foldl F acc).toList = acc.toList ++ l.bind G := by
+    (H : ∀ acc a, (F acc a).data = acc.data ++ G a) :
+    (l.foldl F acc).data = acc.data ++ l.bind G := by
   induction l generalizing acc <;> simp [*, List.bind]
 
-@[deprecated foldl_toList_eq_bind (since := "2024-09-09")]
-abbrev foldl_data_eq_bind := @foldl_toList_eq_bind
-
-theorem foldl_toList_eq_map (l : List α) (acc : Array β) (G : α → β) :
-    (l.foldl (fun acc a => acc.push (G a)) acc).toList = acc.toList ++ l.map G := by
+theorem foldl_data_eq_map (l : List α) (acc : Array β) (G : α → β) :
+    (l.foldl (fun acc a => acc.push (G a)) acc).data = acc.data ++ l.map G := by
   induction l generalizing acc <;> simp [*]
 
-@[deprecated foldl_toList_eq_map (since := "2024-09-09")]
-abbrev foldl_data_eq_map := @foldl_toList_eq_map
-
 theorem size_uset (a : Array α) (v i h) : (uset a i v h).size = a.size := by simp
 
 theorem anyM_eq_anyM_loop [Monad m] (p : α → m Bool) (as : Array α) (start stop) :
@@ -144,12 +125,9 @@ theorem anyM_stop_le_start [Monad m] (p : α → m Bool) (as : Array α) (start
     (h : min stop as.size ≤ start) : anyM p as start stop = pure false := by
   rw [anyM_eq_anyM_loop, anyM.loop, dif_neg (Nat.not_lt.2 h)]
 
-theorem mem_def {a : α} {as : Array α} : a ∈ as ↔ a ∈ as.toList :=
+theorem mem_def {a : α} {as : Array α} : a ∈ as ↔ a ∈ as.data :=
   ⟨fun | .mk h => h, Array.Mem.mk⟩
 
-@[simp] theorem not_mem_empty (a : α) : ¬(a ∈ #[]) := by
-  simp [mem_def]
-
 /-! # get -/
 
 @[simp] theorem get_eq_getElem (a : Array α) (i : Fin _) : a.get i = a[i.1] := rfl
@@ -186,11 +164,11 @@ theorem get!_eq_getD [Inhabited α] (a : Array α) : a.get! n = a.getD n default
 @[simp] theorem getElem_set_eq (a : Array α) (i : Fin a.size) (v : α) {j : Nat}
       (eq : i.val = j) (p : j < (a.set i v).size) :
     (a.set i v)[j]'p = v := by
-  simp [set, getElem_eq_toList_getElem, ←eq]
+  simp [set, getElem_eq_data_getElem, ←eq]
 
 @[simp] theorem getElem_set_ne (a : Array α) (i : Fin a.size) (v : α) {j : Nat} (pj : j < (a.set i v).size)
     (h : i.val ≠ j) : (a.set i v)[j]'pj = a[j]'(size_set a i v ▸ pj) := by
-  simp only [set, getElem_eq_toList_getElem, List.getElem_set_ne h]
+  simp only [set, getElem_eq_data_getElem, List.getElem_set_ne h]
 
 theorem getElem_set (a : Array α) (i : Fin a.size) (v : α) (j : Nat)
     (h : j < (a.set i v).size) :
@@ -271,23 +249,14 @@ termination_by n - i
 
 /-- # mkArray -/
 
-@[simp] theorem size_mkArray (n : Nat) (v : α) : (mkArray n v).size = n :=
-  List.length_replicate ..
-
-@[simp] theorem toList_mkArray (n : Nat) (v : α) : (mkArray n v).toList = List.replicate n v := rfl
-
-@[deprecated toList_mkArray (since := "2024-09-09")]
-abbrev mkArray_data := @toList_mkArray
+@[simp] theorem mkArray_data (n : Nat) (v : α) : (mkArray n v).data = List.replicate n v := rfl
 
 @[simp] theorem getElem_mkArray (n : Nat) (v : α) (h : i < (mkArray n v).size) :
-    (mkArray n v)[i] = v := by simp [Array.getElem_eq_toList_getElem]
+    (mkArray n v)[i] = v := by simp [Array.getElem_eq_data_getElem]
 
 /-- # mem -/
 
-theorem mem_toList {a : α} {l : Array α} : a ∈ l.toList ↔ a ∈ l := mem_def.symm
-
-@[deprecated mem_toList (since := "2024-09-09")]
-abbrev mem_data := @mem_toList
+theorem mem_data {a : α} {l : Array α} : a ∈ l.data ↔ a ∈ l := mem_def.symm
 
 theorem not_mem_nil (a : α) : ¬ a ∈ #[] := nofun
 
@@ -298,22 +267,6 @@ theorem getElem_of_mem {a : α} {as : Array α} :
   exists i
   exists hbound
 
-@[simp] theorem mem_dite_empty_left {x : α} [Decidable p] {l : ¬ p → Array α} :
-    (x ∈ if h : p then #[] else l h) ↔ ∃ h : ¬ p, x ∈ l h := by
-  split <;> simp_all [mem_def]
-
-@[simp] theorem mem_dite_empty_right {x : α} [Decidable p] {l : p → Array α} :
-    (x ∈ if h : p then l h else #[]) ↔ ∃ h : p, x ∈ l h := by
-  split <;> simp_all [mem_def]
-
-@[simp] theorem mem_ite_empty_left {x : α} [Decidable p] {l : Array α} :
-    (x ∈ if p then #[] else l) ↔ ¬ p ∧ x ∈ l := by
-  split <;> simp_all [mem_def]
-
-@[simp] theorem mem_ite_empty_right {x : α} [Decidable p] {l : Array α} :
-    (x ∈ if p then l else #[]) ↔ p ∧ x ∈ l := by
-  split <;> simp_all [mem_def]
-
 /-- # get lemmas -/
 
 theorem lt_of_getElem {x : α} {a : Array α} {idx : Nat} {hidx : idx < a.size} (_ : a[idx] = x) :
@@ -321,13 +274,10 @@ theorem lt_of_getElem {x : α} {a : Array α} {idx : Nat} {hidx : idx < a.size}
   hidx
 
 theorem getElem?_mem {l : Array α} {i : Fin l.size} : l[i] ∈ l := by
-  erw [Array.mem_def, getElem_eq_toList_getElem]
+  erw [Array.mem_def, getElem_eq_data_getElem]
   apply List.get_mem
 
-theorem getElem_fin_eq_toList_get (a : Array α) (i : Fin _) : a[i] = a.toList.get i := rfl
-
-@[deprecated getElem_fin_eq_toList_get (since := "2024-09-09")]
-abbrev getElem_fin_eq_data_get := @getElem_fin_eq_toList_get
+theorem getElem_fin_eq_data_get (a : Array α) (i : Fin _) : a[i] = a.data.get i := rfl
 
 @[simp] theorem ugetElem_eq_getElem (a : Array α) {i : USize} (h : i.toNat < a.size) :
   a[i] = a[i.toNat] := rfl
@@ -338,23 +288,14 @@ theorem getElem?_eq_getElem (a : Array α) (i : Nat) (h : i < a.size) : a[i]? =
 theorem get?_len_le (a : Array α) (i : Nat) (h : a.size ≤ i) : a[i]? = none := by
   simp [getElem?_neg, h]
 
-theorem getElem_mem_toList (a : Array α) (h : i < a.size) : a[i] ∈ a.toList := by
-  simp only [getElem_eq_toList_getElem, List.getElem_mem]
+theorem getElem_mem_data (a : Array α) (h : i < a.size) : a[i] ∈ a.data := by
+  simp only [getElem_eq_data_getElem, List.getElem_mem]
 
-@[deprecated getElem_mem_toList (since := "2024-09-09")]
-abbrev getElem_mem_data := @getElem_mem_toList
-
-theorem getElem?_eq_toList_get? (a : Array α) (i : Nat) : a[i]? = a.toList.get? i := by
+theorem getElem?_eq_data_get? (a : Array α) (i : Nat) : a[i]? = a.data.get? i := by
   by_cases i < a.size <;> simp_all [getElem?_pos, getElem?_neg, List.get?_eq_get, eq_comm]; rfl
 
-@[deprecated getElem?_eq_toList_get? (since := "2024-09-09")]
-abbrev getElem?_eq_data_get? := @getElem?_eq_toList_get?
-
-theorem get?_eq_toList_get? (a : Array α) (i : Nat) : a.get? i = a.toList.get? i :=
-  getElem?_eq_toList_get? ..
-
-@[deprecated get?_eq_toList_get? (since := "2024-09-09")]
-abbrev get?_eq_data_get? := @get?_eq_toList_get?
+theorem get?_eq_data_get? (a : Array α) (i : Nat) : a.get? i = a.data.get? i :=
+  getElem?_eq_data_get? ..
 
 theorem get!_eq_get? [Inhabited α] (a : Array α) : a.get! n = (a.get? n).getD default := by
   simp [get!_eq_getD]
@@ -363,7 +304,7 @@ theorem get!_eq_get? [Inhabited α] (a : Array α) : a.get! n = (a.get? n).getD
   simp [back, back?]
 
 @[simp] theorem back?_push (a : Array α) : (a.push x).back? = some x := by
-  simp [back?, getElem?_eq_toList_get?]
+  simp [back?, getElem?_eq_data_get?]
 
 theorem back_push [Inhabited α] (a : Array α) : (a.push x).back = x := by simp
 
@@ -392,14 +333,11 @@ theorem get?_push {a : Array α} : (a.push x)[i]? = if i = a.size then some x el
 @[simp] theorem get?_size {a : Array α} : a[a.size]? = none := by
   simp only [getElem?_def, Nat.lt_irrefl, dite_false]
 
-@[simp] theorem toList_set (a : Array α) (i v) : (a.set i v).toList = a.toList.set i.1 v := rfl
-
-@[deprecated toList_set (since := "2024-09-09")]
-abbrev data_set := @toList_set
+@[simp] theorem data_set (a : Array α) (i v) : (a.set i v).data = a.data.set i.1 v := rfl
 
 theorem get_set_eq (a : Array α) (i : Fin a.size) (v : α) :
     (a.set i v)[i.1] = v := by
-  simp only [set, getElem_eq_toList_getElem, List.getElem_set_self]
+  simp only [set, getElem_eq_data_getElem, List.getElem_set_self]
 
 theorem get?_set_eq (a : Array α) (i : Fin a.size) (v : α) :
     (a.set i v)[i.1]? = v := by simp [getElem?_pos, i.2]
@@ -418,7 +356,7 @@ theorem get_set (a : Array α) (i : Fin a.size) (j : Nat) (hj : j < a.size) (v :
 
 @[simp] theorem get_set_ne (a : Array α) (i : Fin a.size) {j : Nat} (v : α) (hj : j < a.size)
     (h : i.1 ≠ j) : (a.set i v)[j]'(by simp [*]) = a[j] := by
-  simp only [set, getElem_eq_toList_getElem, List.getElem_set_ne h]
+  simp only [set, getElem_eq_data_getElem, List.getElem_set_ne h]
 
 theorem getElem_setD (a : Array α) (i : Nat) (v : α) (h : i < (setD a i v).size) :
   (setD a i v)[i] = v := by
@@ -434,15 +372,12 @@ theorem swap_def (a : Array α) (i j : Fin a.size) :
     a.swap i j = (a.set i (a.get j)).set ⟨j.1, by simp [j.2]⟩ (a.get i) := by
   simp [swap, fin_cast_val]
 
-theorem toList_swap (a : Array α) (i j : Fin a.size) :
-    (a.swap i j).toList = (a.toList.set i (a.get j)).set j (a.get i) := by simp [swap_def]
-
-@[deprecated toList_swap (since := "2024-09-09")]
-abbrev data_swap := @toList_swap
+theorem data_swap (a : Array α) (i j : Fin a.size) :
+    (a.swap i j).data = (a.data.set i (a.get j)).set j (a.get i) := by simp [swap_def]
 
 theorem get?_swap (a : Array α) (i j : Fin a.size) (k : Nat) : (a.swap i j)[k]? =
     if j = k then some a[i.1] else if i = k then some a[j.1] else a[k]? := by
-  simp [swap_def, get?_set, ← getElem_fin_eq_toList_get]
+  simp [swap_def, get?_set, ← getElem_fin_eq_data_get]
 
 @[simp] theorem swapAt_def (a : Array α) (i : Fin a.size) (v : α) :
     a.swapAt i v = (a[i.1], a.set i v) := rfl
@@ -451,10 +386,7 @@ theorem get?_swap (a : Array α) (i j : Fin a.size) (k : Nat) : (a.swap i j)[k]?
 theorem swapAt!_def (a : Array α) (i : Nat) (v : α) (h : i < a.size) :
     a.swapAt! i v = (a[i], a.set ⟨i, h⟩ v) := by simp [swapAt!, h]
 
-@[simp] theorem toList_pop (a : Array α) : a.pop.toList = a.toList.dropLast := by simp [pop]
-
-@[deprecated toList_pop (since := "2024-09-09")]
-abbrev data_pop := @toList_pop
+@[simp] theorem data_pop (a : Array α) : a.pop.data = a.data.dropLast := by simp [pop]
 
 @[simp] theorem pop_empty : (#[] : Array α).pop = #[] := rfl
 
@@ -486,10 +418,7 @@ theorem eq_push_of_size_ne_zero {as : Array α} (h : as.size ≠ 0) :
   let _ : Inhabited α := ⟨as[0]⟩
   ⟨as.pop, as.back, eq_push_pop_back_of_size_ne_zero h⟩
 
-theorem size_eq_length_toList (as : Array α) : as.size = as.toList.length := rfl
-
-@[deprecated size_eq_length_toList (since := "2024-09-09")]
-abbrev size_eq_length_data := @size_eq_length_toList
+theorem size_eq_length_data (as : Array α) : as.size = as.data.length := rfl
 
 @[simp] theorem size_swap! (a : Array α) (i j) :
     (a.swap! i j).size = a.size := by unfold swap!; split <;> (try split) <;> simp [size_swap]
@@ -498,6 +427,7 @@ abbrev size_eq_length_data := @size_eq_length_toList
   let rec go (as : Array α) (i j) : (reverse.loop as i j).size = as.size := by
     rw [reverse.loop]
     if h : i < j then
+      have := reverse.termination h
       simp [(go · (i+1) ⟨j-1, ·⟩), h]
     else simp [h]
     termination_by j - i
@@ -512,32 +442,29 @@ abbrev size_eq_length_data := @size_eq_length_toList
     simp only [mkEmpty_eq, size_push] at *
     omega
 
-@[simp] theorem toList_range (n : Nat) : (range n).toList = List.range n := by
+@[simp] theorem data_range (n : Nat) : (range n).data = List.range n := by
   induction n <;> simp_all [range, Nat.fold, flip, List.range_succ]
 
-@[deprecated toList_range (since := "2024-09-09")]
-abbrev data_range := @toList_range
-
 @[simp]
 theorem getElem_range {n : Nat} {x : Nat} (h : x < (Array.range n).size) : (Array.range n)[x] = x := by
-  simp [getElem_eq_toList_getElem]
+  simp [getElem_eq_data_getElem]
 
 set_option linter.deprecated false in
-@[simp] theorem reverse_toList (a : Array α) : a.reverse.toList = a.toList.reverse := by
+@[simp] theorem reverse_data (a : Array α) : a.reverse.data = a.data.reverse := by
   let rec go (as : Array α) (i j hj)
       (h : i + j + 1 = a.size) (h₂ : as.size = a.size)
-      (H : ∀ k, as.toList.get? k = if i ≤ k ∧ k ≤ j then a.toList.get? k else a.toList.reverse.get? k)
-      (k) : (reverse.loop as i ⟨j, hj⟩).toList.get? k = a.toList.reverse.get? k := by
+      (H : ∀ k, as.data.get? k = if i ≤ k ∧ k ≤ j then a.data.get? k else a.data.reverse.get? k)
+      (k) : (reverse.loop as i ⟨j, hj⟩).data.get? k = a.data.reverse.get? k := by
     rw [reverse.loop]; dsimp; split <;> rename_i h₁
-    · match j with | j+1 => ?_
-      simp only [Nat.add_sub_cancel]
+    · have p := reverse.termination h₁
+      match j with | j+1 => ?_
+      simp only [Nat.add_sub_cancel] at p ⊢
       rw [(go · (i+1) j)]
       · rwa [Nat.add_right_comm i]
       · simp [size_swap, h₂]
       · intro k
-        rw [← getElem?_eq_toList_get?, get?_swap]
-        simp only [H, getElem_eq_toList_get, ← List.get?_eq_get, Nat.le_of_lt h₁,
-          getElem?_eq_toList_get?]
+        rw [← getElem?_eq_data_get?, get?_swap]
+        simp only [H, getElem_eq_data_get, ← List.get?_eq_get, Nat.le_of_lt h₁, getElem?_eq_data_get?]
         split <;> rename_i h₂
         · simp only [← h₂, Nat.not_le.2 (Nat.lt_succ_self _), Nat.le_refl, and_false]
           exact (List.get?_reverse' (j+1) i (Eq.trans (by simp_arith) h)).symm
@@ -562,7 +489,7 @@ set_option linter.deprecated false in
     · rename_i h
       simp only [← show k < _ + 1 ↔ _ from Nat.lt_succ (n := a.size - 1), this, Nat.zero_le,
         true_and, Nat.not_lt] at h
-      rw [List.get?_eq_none.2 ‹_›, List.get?_eq_none.2 (a.toList.length_reverse ▸ ‹_›)]
+      rw [List.get?_eq_none.2 ‹_›, List.get?_eq_none.2 (a.data.length_reverse ▸ ‹_›)]
 
 /-! ### foldl / foldr -/
 
@@ -602,19 +529,16 @@ theorem foldr_induction
 /-! ### map -/
 
 @[simp] theorem mem_map {f : α → β} {l : Array α} : b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b := by
-  simp only [mem_def, map_toList, List.mem_map]
+  simp only [mem_def, map_data, List.mem_map]
 
-theorem mapM_eq_mapM_toList [Monad m] [LawfulMonad m] (f : α → m β) (arr : Array α) :
-    arr.mapM f = return mk (← arr.toList.mapM f) := by
-  rw [mapM_eq_foldlM, foldlM_eq_foldlM_toList, ← List.foldrM_reverse]
-  conv => rhs; rw [← List.reverse_reverse arr.toList]
-  induction arr.toList.reverse with
+theorem mapM_eq_mapM_data [Monad m] [LawfulMonad m] (f : α → m β) (arr : Array α) :
+    arr.mapM f = return mk (← arr.data.mapM f) := by
+  rw [mapM_eq_foldlM, foldlM_eq_foldlM_data, ← List.foldrM_reverse]
+  conv => rhs; rw [← List.reverse_reverse arr.data]
+  induction arr.data.reverse with
   | nil => simp; rfl
   | cons a l ih => simp [ih]; simp [map_eq_pure_bind, push]
 
-@[deprecated mapM_eq_mapM_toList (since := "2024-09-09")]
-abbrev mapM_eq_mapM_data := @mapM_eq_mapM_toList
-
 theorem mapM_map_eq_foldl (as : Array α) (f : α → β) (i) :
     mapM.map (m := Id) f as i b = as.foldl (start := i) (fun r a => r.push (f a)) b := by
   unfold mapM.map
@@ -751,95 +675,86 @@ theorem get_modify {arr : Array α} {x i} (h : i < arr.size) :
 
 /-! ### filter -/
 
-@[simp] theorem filter_toList (p : α → Bool) (l : Array α) :
-    (l.filter p).toList = l.toList.filter p := by
+@[simp] theorem filter_data (p : α → Bool) (l : Array α) :
+    (l.filter p).data = l.data.filter p := by
   dsimp only [filter]
-  rw [foldl_eq_foldl_toList]
-  generalize l.toList = l
-  suffices ∀ a, (List.foldl (fun r a => if p a = true then push r a else r) a l).toList =
-      a.toList ++ List.filter p l by
+  rw [foldl_eq_foldl_data]
+  generalize l.data = l
+  suffices ∀ a, (List.foldl (fun r a => if p a = true then push r a else r) a l).data =
+      a.data ++ List.filter p l by
     simpa using this #[]
   induction l with simp
   | cons => split <;> simp [*]
 
-@[deprecated filter_toList (since := "2024-09-09")]
-abbrev filter_data := @filter_toList
-
 @[simp] theorem filter_filter (q) (l : Array α) :
-    filter p (filter q l) = filter (fun a => p a && q a) l := by
+    filter p (filter q l) = filter (fun a => p a ∧ q a) l := by
   apply ext'
-  simp only [filter_toList, List.filter_filter]
+  simp only [filter_data, List.filter_filter]
 
 @[simp] theorem mem_filter : x ∈ filter p as ↔ x ∈ as ∧ p x := by
-  simp only [mem_def, filter_toList, List.mem_filter]
+  simp only [mem_def, filter_data, List.mem_filter]
 
 theorem mem_of_mem_filter {a : α} {l} (h : a ∈ filter p l) : a ∈ l :=
   (mem_filter.mp h).1
 
 /-! ### filterMap -/
 
-@[simp] theorem filterMap_toList (f : α → Option β) (l : Array α) :
-    (l.filterMap f).toList = l.toList.filterMap f := by
+@[simp] theorem filterMap_data (f : α → Option β) (l : Array α) :
+    (l.filterMap f).data = l.data.filterMap f := by
   dsimp only [filterMap, filterMapM]
-  rw [foldlM_eq_foldlM_toList]
-  generalize l.toList = l
-  have this : ∀ a : Array β, (Id.run (List.foldlM (m := Id) ?_ a l)).toList =
-    a.toList ++ List.filterMap f l := ?_
+  rw [foldlM_eq_foldlM_data]
+  generalize l.data = l
+  have this : ∀ a : Array β, (Id.run (List.foldlM (m := Id) ?_ a l)).data =
+    a.data ++ List.filterMap f l := ?_
   exact this #[]
   induction l
   · simp_all [Id.run]
   · simp_all [Id.run, List.filterMap_cons]
     split <;> simp_all
 
-@[deprecated filterMap_toList (since := "2024-09-09")]
-abbrev filterMap_data := @filterMap_toList
-
 @[simp] theorem mem_filterMap {f : α → Option β} {l : Array α} {b : β} :
     b ∈ filterMap f l ↔ ∃ a, a ∈ l ∧ f a = some b := by
-  simp only [mem_def, filterMap_toList, List.mem_filterMap]
+  simp only [mem_def, filterMap_data, List.mem_filterMap]
 
 /-! ### empty -/
 
 theorem size_empty : (#[] : Array α).size = 0 := rfl
 
-theorem toList_empty : (#[] : Array α).toList = [] := rfl
-
-@[deprecated toList_empty (since := "2024-09-09")]
-abbrev empty_data := @toList_empty
+theorem empty_data : (#[] : Array α).data = [] := rfl
 
 /-! ### append -/
 
 theorem push_eq_append_singleton (as : Array α) (x) : as.push x = as ++ #[x] := rfl
 
 @[simp] theorem mem_append {a : α} {s t : Array α} : a ∈ s ++ t ↔ a ∈ s ∨ a ∈ t := by
-  simp only [mem_def, append_toList, List.mem_append]
+  simp only [mem_def, append_data, List.mem_append]
 
 theorem size_append (as bs : Array α) : (as ++ bs).size = as.size + bs.size := by
-  simp only [size, append_toList, List.length_append]
+  simp only [size, append_data, List.length_append]
 
 theorem get_append_left {as bs : Array α} {h : i < (as ++ bs).size} (hlt : i < as.size) :
     (as ++ bs)[i] = as[i] := by
-  simp only [getElem_eq_toList_getElem]
-  have h' : i < (as.toList ++ bs.toList).length := by rwa [← toList_length, append_toList] at h
-  conv => rhs; rw [← List.getElem_append_left (bs := bs.toList) (h' := h')]
-  apply List.get_of_eq; rw [append_toList]
+  simp only [getElem_eq_data_getElem]
+  have h' : i < (as.data ++ bs.data).length := by rwa [← data_length, append_data] at h
+  conv => rhs; rw [← List.getElem_append_left (bs := bs.data) (h' := h')]
+  apply List.get_of_eq; rw [append_data]
 
 theorem get_append_right {as bs : Array α} {h : i < (as ++ bs).size} (hle : as.size ≤ i)
     (hlt : i - as.size < bs.size := Nat.sub_lt_left_of_lt_add hle (size_append .. ▸ h)) :
     (as ++ bs)[i] = bs[i - as.size] := by
-  simp only [getElem_eq_toList_getElem]
-  have h' : i < (as.toList ++ bs.toList).length := by rwa [← toList_length, append_toList] at h
-  conv => rhs; rw [← List.getElem_append_right (h₁ := hle) (h₂ := h')]
-  apply List.get_of_eq; rw [append_toList]
+  simp only [getElem_eq_data_getElem]
+  have h' : i < (as.data ++ bs.data).length := by rwa [← data_length, append_data] at h
+  conv => rhs; rw [← List.getElem_append_right (h' := h') (h := Nat.not_lt_of_ge hle)]
+  apply List.get_of_eq; rw [append_data]
 
 @[simp] theorem append_nil (as : Array α) : as ++ #[] = as := by
-  apply ext'; simp only [append_toList, toList_empty, List.append_nil]
+  apply ext'; simp only [append_data, empty_data, List.append_nil]
 
 @[simp] theorem nil_append (as : Array α) : #[] ++ as = as := by
-  apply ext'; simp only [append_toList, toList_empty, List.nil_append]
+  apply ext'; simp only [append_data, empty_data, List.nil_append]
 
 theorem append_assoc (as bs cs : Array α) : as ++ bs ++ cs = as ++ (bs ++ cs) := by
-  apply ext'; simp only [append_toList, List.append_assoc]
+  apply ext'; simp only [append_data, List.append_assoc]
 
 /-! ### extract -/
 
@@ -1013,7 +928,7 @@ theorem any_iff_exists {p : α → Bool} {as : Array α} {start stop} :
 theorem any_eq_true {p : α → Bool} {as : Array α} :
     any as p ↔ ∃ i : Fin as.size, p as[i] := by simp [any_iff_exists, Fin.isLt]
 
-theorem any_def {p : α → Bool} (as : Array α) : as.any p = as.toList.any p := by
+theorem any_def {p : α → Bool} (as : Array α) : as.any p = as.data.any p := by
   rw [Bool.eq_iff_iff, any_eq_true, List.any_eq_true]; simp only [List.mem_iff_get]
   exact ⟨fun ⟨i, h⟩ => ⟨_, ⟨i, rfl⟩, h⟩, fun ⟨_, ⟨i, rfl⟩, h⟩ => ⟨i, h⟩⟩
 
@@ -1036,14 +951,14 @@ theorem all_iff_forall {p : α → Bool} {as : Array α} {start stop} :
 theorem all_eq_true {p : α → Bool} {as : Array α} : all as p ↔ ∀ i : Fin as.size, p as[i] := by
   simp [all_iff_forall, Fin.isLt]
 
-theorem all_def {p : α → Bool} (as : Array α) : as.all p = as.toList.all p := by
+theorem all_def {p : α → Bool} (as : Array α) : as.all p = as.data.all p := by
   rw [Bool.eq_iff_iff, all_eq_true, List.all_eq_true]; simp only [List.mem_iff_getElem]
   constructor
   · rintro w x ⟨r, h, rfl⟩
-    rw [← getElem_eq_toList_getElem]
+    rw [← getElem_eq_data_getElem]
     exact w ⟨r, h⟩
   · intro w i
-    exact w as[i] ⟨i, i.2, (getElem_eq_toList_getElem as i.2).symm⟩
+    exact w as[i] ⟨i, i.2, (getElem_eq_data_getElem as i.2).symm⟩
 
 theorem all_eq_true_iff_forall_mem {l : Array α} : l.all p ↔ ∀ x, x ∈ l → p x := by
   simp only [all_def, List.all_eq_true, mem_def]
@@ -1114,4 +1029,5 @@ theorem swap_comm (a : Array α) {i j : Fin a.size} : a.swap i j = a.swap j i :=
     · split <;> simp_all
     · split <;> simp_all
 
+
 end Array

src/Init/Data/Array/Mem.lean

@@ -14,7 +14,7 @@ namespace Array
 -- NB: This is defined as a structure rather than a plain def so that a lemma
 -- like `sizeOf_lt_of_mem` will not apply with no actual arrays around.
 structure Mem (as : Array α) (a : α) : Prop where
-  val : a ∈ as.toList
+  val : a ∈ as.data
 
 instance : Membership α (Array α) where
   mem := Mem

src/Init/Data/Array/TakeDrop.lean

@@ -10,8 +10,8 @@ import Init.Data.List.Nat.TakeDrop
 namespace Array
 
 theorem exists_of_uset (self : Array α) (i d h) :
-    ∃ l₁ l₂, self.toList = l₁ ++ self[i] :: l₂ ∧ List.length l₁ = i.toNat ∧
-      (self.uset i d h).toList = l₁ ++ d :: l₂ := by
-  simpa [Array.getElem_eq_toList_getElem] using List.exists_of_set _
+    ∃ l₁ l₂, self.data = l₁ ++ self[i] :: l₂ ∧ List.length l₁ = i.toNat ∧
+      (self.uset i d h).data = l₁ ++ d :: l₂ := by
+  simpa [Array.getElem_eq_data_getElem] using List.exists_of_set _
 
 end Array

src/Init/Data/BitVec/Basic.lean

@@ -64,7 +64,7 @@ protected def ofNatLt {n : Nat} (i : Nat) (p : i < 2^n) : BitVec n where
 /-- The `BitVec` with value `i mod 2^n`. -/
 @[match_pattern]
 protected def ofNat (n : Nat) (i : Nat) : BitVec n where
-  toFin := Fin.ofNat' (2^n) i
+  toFin := Fin.ofNat' i (Nat.two_pow_pos n)
 
 instance instOfNat : OfNat (BitVec n) i where ofNat := .ofNat n i
 instance natCastInst : NatCast (BitVec w) := ⟨BitVec.ofNat w⟩
@@ -173,9 +173,6 @@ instance : GetElem (BitVec w) Nat Bool fun _ i => i < w where
 theorem getElem_eq_testBit_toNat (x : BitVec w) (i : Nat) (h : i < w) :
   x[i] = x.toNat.testBit i := rfl
 
-theorem getLsbD_eq_getElem {x : BitVec w} {i : Nat} (h : i < w) :
-    x.getLsbD i = x[i] := rfl
-
 end getElem
 
 section Int
@@ -453,15 +450,13 @@ SMT-Lib name: `extract`.
 def extractLsb (hi lo : Nat) (x : BitVec n) : BitVec (hi - lo + 1) := extractLsb' lo _ x
 
 /--
-A version of `setWidth` that requires a proof, but is a noop.
+A version of `zeroExtend` that requires a proof, but is a noop.
 -/
-def setWidth' {n w : Nat} (le : n ≤ w) (x : BitVec n) : BitVec w :=
+def zeroExtend' {n w : Nat} (le : n ≤ w) (x : BitVec n) : BitVec w :=
   x.toNat#'(by
     apply Nat.lt_of_lt_of_le x.isLt
     exact Nat.pow_le_pow_of_le_right (by trivial) le)
 
-@[deprecated setWidth' (since := "2024-09-18"), inherit_doc setWidth'] abbrev zeroExtend' := @setWidth'
-
 /--
 `shiftLeftZeroExtend x n` returns `zeroExtend (w+n) x <<< n` without
 needing to compute `x % 2^(2+n)`.
@@ -474,35 +469,22 @@ def shiftLeftZeroExtend (msbs : BitVec w) (m : Nat) : BitVec (w + m) :=
   (msbs.toNat <<< m)#'(shiftLeftLt msbs.isLt m)
 
 /--
-Transform `x` of length `w` into a bitvector of length `v`, by either:
-- zero extending, that is, adding zeros in the high bits until it has length `v`, if `v > w`, or
-- truncating the high bits, if `v < w`.
+Zero extend vector `x` of length `w` by adding zeros in the high bits until it has length `v`.
+If `v < w` then it truncates the high bits instead.
 
 SMT-Lib name: `zero_extend`.
 -/
-def setWidth (v : Nat) (x : BitVec w) : BitVec v :=
+def zeroExtend (v : Nat) (x : BitVec w) : BitVec v :=
   if h : w ≤ v then
-    setWidth' h x
+    zeroExtend' h x
   else
     .ofNat v x.toNat
 
 /--
-Transform `x` of length `w` into a bitvector of length `v`, by either:
-- zero extending, that is, adding zeros in the high bits until it has length `v`, if `v > w`, or
-- truncating the high bits, if `v < w`.
-
-SMT-Lib name: `zero_extend`.
+Truncate the high bits of bitvector `x` of length `w`, resulting in a vector of length `v`.
+If `v > w` then it zero-extends the vector instead.
 -/
-abbrev zeroExtend := @setWidth
-
-/--
-Transform `x` of length `w` into a bitvector of length `v`, by either:
-- zero extending, that is, adding zeros in the high bits until it has length `v`, if `v > w`, or
-- truncating the high bits, if `v < w`.
-
-SMT-Lib name: `zero_extend`.
--/
-abbrev truncate := @setWidth
+abbrev truncate := @zeroExtend
 
 /--
 Sign extend a vector of length `w`, extending with `i` additional copies of the most significant
@@ -653,7 +635,7 @@ input is on the left, so `0xAB#8 ++ 0xCD#8 = 0xABCD#16`.
 SMT-Lib name: `concat`.
 -/
 def append (msbs : BitVec n) (lsbs : BitVec m) : BitVec (n+m) :=
-  shiftLeftZeroExtend msbs m ||| setWidth' (Nat.le_add_left m n) lsbs
+  shiftLeftZeroExtend msbs m ||| zeroExtend' (Nat.le_add_left m n) lsbs
 
 instance : HAppend (BitVec w) (BitVec v) (BitVec (w + v)) := ⟨.append⟩
 

src/Init/Data/BitVec/Bitblast.lean

@@ -132,18 +132,18 @@ theorem toNat_add_of_and_eq_zero {x y : BitVec w} (h : x &&& y = 0#w) :
   simp [not_eq_true, 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))
+def adcb (x y c : Bool) : Bool × Bool := (atLeastTwo x y c, Bool.xor x (Bool.xor y c))
 
 /-- Bitwise addition implemented via a ripple carry adder. -/
 def adc (x y : BitVec w) : Bool → Bool × BitVec w :=
   iunfoldr fun (i : Fin w) c => adcb (x.getLsbD i) (y.getLsbD i) c
 
 theorem getLsbD_add_add_bool {i : Nat} (i_lt : i < w) (x y : BitVec w) (c : Bool) :
-    getLsbD (x + y + setWidth w (ofBool c)) i =
-      (getLsbD x i ^^ (getLsbD y i ^^ carry i x y c)) := by
+    getLsbD (x + y + zeroExtend w (ofBool c)) i =
+      Bool.xor (getLsbD x i) (Bool.xor (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_zeroExtend, i_lt, 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)]
@@ -161,15 +161,15 @@ theorem getLsbD_add_add_bool {i : Nat} (i_lt : i < w) (x y : BitVec w) (c : Bool
 
 theorem getLsbD_add {i : Nat} (i_lt : i < w) (x y : BitVec w) :
     getLsbD (x + y) i =
-      (getLsbD x i ^^ (getLsbD y i ^^ carry i x y false)) := by
+      Bool.xor (getLsbD x i) (Bool.xor (getLsbD y i) (carry i x y false)) := by
   simpa using getLsbD_add_add_bool i_lt x y false
 
 theorem adc_spec (x y : BitVec w) (c : Bool) :
-    adc x y c = (carry w x y c, x + y + setWidth w (ofBool c)) := by
+    adc x y c = (carry w x y c, x + y + zeroExtend w (ofBool c)) := by
   simp only [adc]
   apply iunfoldr_replace
           (fun i => carry i x y c)
-          (x + y + setWidth w (ofBool c))
+          (x + y + zeroExtend w (ofBool c))
           c
   case init =>
     simp [carry, Nat.mod_one]
@@ -306,12 +306,12 @@ theorem mulRec_succ_eq (x y : BitVec w) (s : Nat) :
 Recurrence lemma: truncating to `i+1` bits and then zero extending to `w`
 equals truncating upto `i` bits `[0..i-1]`, and then adding the `i`th bit of `x`.
 -/
-theorem setWidth_setWidth_succ_eq_setWidth_setWidth_add_twoPow (x : BitVec w) (i : Nat) :
-    setWidth w (x.setWidth (i + 1)) =
-      setWidth w (x.setWidth i) + (x &&& twoPow w i) := by
+theorem zeroExtend_truncate_succ_eq_zeroExtend_truncate_add_twoPow (x : BitVec w) (i : Nat) :
+    zeroExtend w (x.truncate (i + 1)) =
+      zeroExtend w (x.truncate i) + (x &&& twoPow w i) := by
   rw [add_eq_or_of_and_eq_zero]
   · ext k
-    simp only [getLsbD_setWidth, Fin.is_lt, decide_True, Bool.true_and, getLsbD_or, getLsbD_and]
+    simp only [getLsbD_zeroExtend, Fin.is_lt, decide_True, Bool.true_and, getLsbD_or, getLsbD_and]
     by_cases hik : i = k
     · subst hik
       simp
@@ -322,32 +322,27 @@ theorem setWidth_setWidth_succ_eq_setWidth_setWidth_add_twoPow (x : BitVec w) (i
       · have hik'' : ¬ (k < i) := by omega
         simp [hik', hik'']
   · ext k
-    simp only [and_twoPow, getLsbD_and, getLsbD_setWidth, Fin.is_lt, decide_True, Bool.true_and,
+    simp only [and_twoPow, getLsbD_and, getLsbD_zeroExtend, Fin.is_lt, decide_True, Bool.true_and,
       getLsbD_zero, and_eq_false_imp, and_eq_true, decide_eq_true_eq, and_imp]
     by_cases hi : x.getLsbD i <;> simp [hi] <;> omega
 
-@[deprecated setWidth_setWidth_succ_eq_setWidth_setWidth_add_twoPow (since := "2024-09-18"),
-  inherit_doc setWidth_setWidth_succ_eq_setWidth_setWidth_add_twoPow]
-abbrev zeroExtend_truncate_succ_eq_zeroExtend_truncate_add_twoPow :=
-  @setWidth_setWidth_succ_eq_setWidth_setWidth_add_twoPow
-
 /--
 Recurrence lemma: multiplying `x` with the first `s` bits of `y` is the
 same as truncating `y` to `s` bits, then zero extending to the original length,
 and performing the multplication. -/
-theorem mulRec_eq_mul_signExtend_setWidth (x y : BitVec w) (s : Nat) :
-    mulRec x y s = x * ((y.setWidth (s + 1)).setWidth w) := by
+theorem mulRec_eq_mul_signExtend_truncate (x y : BitVec w) (s : Nat) :
+    mulRec x y s = x * ((y.truncate (s + 1)).zeroExtend w) := by
   induction s
   case zero =>
     simp only [mulRec_zero_eq, ofNat_eq_ofNat, Nat.reduceAdd]
     by_cases y.getLsbD 0
     case pos hy =>
-      simp only [hy, ↓reduceIte, setWidth_one_eq_ofBool_getLsb_zero,
+      simp only [hy, ↓reduceIte, truncate, zeroExtend_one_eq_ofBool_getLsb_zero,
         ofBool_true, ofNat_eq_ofNat]
-      rw [setWidth_ofNat_one_eq_ofNat_one_of_lt (by omega)]
+      rw [zeroExtend_ofNat_one_eq_ofNat_one_of_lt (by omega)]
       simp
     case neg hy =>
-      simp [hy, setWidth_one_eq_ofBool_getLsb_zero]
+      simp [hy, zeroExtend_one_eq_ofBool_getLsb_zero]
   case succ s' hs =>
     rw [mulRec_succ_eq, hs]
     have heq :
@@ -355,16 +350,13 @@ theorem mulRec_eq_mul_signExtend_setWidth (x y : BitVec w) (s : Nat) :
         (x * (y &&& (BitVec.twoPow w (s' + 1)))) := by
       simp only [ofNat_eq_ofNat, and_twoPow]
       by_cases hy : y.getLsbD (s' + 1) <;> simp [hy]
-    rw [heq, ← BitVec.mul_add, ← setWidth_setWidth_succ_eq_setWidth_setWidth_add_twoPow]
-
-@[deprecated mulRec_eq_mul_signExtend_setWidth (since := "2024-09-18"),
-  inherit_doc mulRec_eq_mul_signExtend_setWidth]
-abbrev mulRec_eq_mul_signExtend_truncate := @mulRec_eq_mul_signExtend_setWidth
+    rw [heq, ← BitVec.mul_add, ← zeroExtend_truncate_succ_eq_zeroExtend_truncate_add_twoPow]
 
 theorem getLsbD_mul (x y : BitVec w) (i : Nat) :
     (x * y).getLsbD i = (mulRec x y w).getLsbD i := by
-  simp only [mulRec_eq_mul_signExtend_setWidth]
-  rw [setWidth_setWidth_of_le]
+  simp only [mulRec_eq_mul_signExtend_truncate]
+  rw [truncate, ← truncate_eq_zeroExtend, ← truncate_eq_zeroExtend,
+    truncate_truncate_of_le]
   · simp
   · omega
 
@@ -410,22 +402,22 @@ theorem shiftLeft_or_of_and_eq_zero {x : BitVec w₁} {y z : BitVec w₂}
 `shiftLeftRec x y n` shifts `x` to the left by the first `n` bits of `y`.
 -/
 theorem shiftLeftRec_eq {x : BitVec w₁} {y : BitVec w₂} {n : Nat} :
-    shiftLeftRec x y n = x <<< (y.setWidth (n + 1)).setWidth w₂ := by
+    shiftLeftRec x y n = x <<< (y.truncate (n + 1)).zeroExtend w₂ := by
   induction n generalizing x y
   case zero =>
     ext i
-    simp only [shiftLeftRec_zero, twoPow_zero, Nat.reduceAdd, setWidth_one,
-      and_one_eq_setWidth_ofBool_getLsbD]
+    simp only [shiftLeftRec_zero, twoPow_zero, Nat.reduceAdd, truncate_one,
+      and_one_eq_zeroExtend_ofBool_getLsbD]
   case succ n ih =>
     simp only [shiftLeftRec_succ, and_twoPow]
     rw [ih]
     by_cases h : y.getLsbD (n + 1)
     · simp only [h, ↓reduceIte]
-      rw [setWidth_setWidth_succ_eq_setWidth_setWidth_or_twoPow_of_getLsbD_true h,
+      rw [zeroExtend_truncate_succ_eq_zeroExtend_truncate_or_twoPow_of_getLsbD_true h,
         shiftLeft_or_of_and_eq_zero]
       simp [and_twoPow]
     · simp only [h, false_eq_true, ↓reduceIte, shiftLeft_zero']
-      rw [setWidth_setWidth_succ_eq_setWidth_setWidth_of_getLsbD_false (i := n + 1)]
+      rw [zeroExtend_truncate_succ_eq_zeroExtend_truncate_of_getLsbD_false (i := n + 1)]
       simp [h]
 
 /--
@@ -474,18 +466,18 @@ theorem sshiftRight'_or_of_and_eq_zero {x : BitVec w₁} {y z : BitVec w₂}
     toNat_add_of_and_eq_zero h, sshiftRight_add]
 
 theorem sshiftRightRec_eq (x : BitVec w₁) (y : BitVec w₂) (n : Nat) :
-    sshiftRightRec x y n = x.sshiftRight' ((y.setWidth (n + 1)).setWidth w₂) := by
+    sshiftRightRec x y n = x.sshiftRight' ((y.truncate (n + 1)).zeroExtend w₂) := by
   induction n generalizing x y
   case zero =>
     ext i
-    simp [twoPow_zero, Nat.reduceAdd, and_one_eq_setWidth_ofBool_getLsbD, setWidth_one]
+    simp [twoPow_zero, Nat.reduceAdd, and_one_eq_zeroExtend_ofBool_getLsbD, truncate_one]
   case succ n ih =>
     simp only [sshiftRightRec_succ_eq, and_twoPow, ih]
     by_cases h : y.getLsbD (n + 1)
-    · rw [setWidth_setWidth_succ_eq_setWidth_setWidth_or_twoPow_of_getLsbD_true h,
+    · rw [zeroExtend_truncate_succ_eq_zeroExtend_truncate_or_twoPow_of_getLsbD_true h,
         sshiftRight'_or_of_and_eq_zero (by simp [and_twoPow]), h]
       simp
-    · rw [setWidth_setWidth_succ_eq_setWidth_setWidth_of_getLsbD_false (i := n + 1)
+    · rw [zeroExtend_truncate_succ_eq_zeroExtend_truncate_of_getLsbD_false (i := n + 1)
         (by simp [h])]
       simp [h]
 
@@ -537,20 +529,20 @@ theorem ushiftRight'_or_of_and_eq_zero {x : BitVec w₁} {y z : BitVec w₂}
   simp [← add_eq_or_of_and_eq_zero _ _ h, toNat_add_of_and_eq_zero h, shiftRight_add]
 
 theorem ushiftRightRec_eq (x : BitVec w₁) (y : BitVec w₂) (n : Nat) :
-    ushiftRightRec x y n = x >>> (y.setWidth (n + 1)).setWidth w₂ := by
+    ushiftRightRec x y n = x >>> (y.truncate (n + 1)).zeroExtend w₂ := by
   induction n generalizing x y
   case zero =>
     ext i
     simp only [ushiftRightRec_zero, twoPow_zero, Nat.reduceAdd,
-      and_one_eq_setWidth_ofBool_getLsbD, setWidth_one]
+      and_one_eq_zeroExtend_ofBool_getLsbD, truncate_one]
   case succ n ih =>
     simp only [ushiftRightRec_succ, and_twoPow]
     rw [ih]
     by_cases h : y.getLsbD (n + 1) <;> simp only [h, ↓reduceIte]
-    · rw [setWidth_setWidth_succ_eq_setWidth_setWidth_or_twoPow_of_getLsbD_true h,
+    · rw [zeroExtend_truncate_succ_eq_zeroExtend_truncate_or_twoPow_of_getLsbD_true h,
         ushiftRight'_or_of_and_eq_zero]
       simp [and_twoPow]
-    · simp [setWidth_setWidth_succ_eq_setWidth_setWidth_of_getLsbD_false, h]
+    · simp [zeroExtend_truncate_succ_eq_zeroExtend_truncate_of_getLsbD_false, h]
 
 /--
 Show that `x >>> y` can be written in terms of `ushiftRightRec`.

src/Init/Data/BitVec/Folds.lean

@@ -48,7 +48,7 @@ private theorem iunfoldr.eq_test
     simp only [init, eq_nil]
   case step =>
     intro i
-    simp_all [setWidth_succ]
+    simp_all [truncate_succ]
 
 theorem iunfoldr_getLsbD' {f : Fin w → α → α × Bool} (state : Nat → α)
     (ind : ∀(i : Fin w), (f i (state i.val)).fst = state (i.val+1)) :

src/Init/Data/BitVec/Lemmas.lean

@@ -31,13 +31,13 @@ namespace BitVec
   simp only [Bool.and_eq_false_imp, decide_eq_true_eq]
   omega
 
-theorem lt_of_getLsbD {x : BitVec w} {i : Nat} : getLsbD x i = true → i < w := by
+theorem lt_of_getLsbD (x : BitVec w) (i : Nat) : getLsbD x i = true → i < w := by
   if h : i < w then
     simp [h]
   else
     simp [Nat.ge_of_not_lt h]
 
-theorem lt_of_getMsbD {x : BitVec w} {i : Nat} : getMsbD x i = true → i < w := by
+theorem lt_of_getMsbD (x : BitVec w) (i : Nat) : getMsbD x i = true → i < w := by
   if h : i < w then
     simp [h]
   else
@@ -234,15 +234,6 @@ theorem ofBool_eq_iff_eq : ∀ {b b' : Bool}, BitVec.ofBool b = BitVec.ofBool b'
 
 @[simp] theorem not_ofBool : ~~~ (ofBool b) = ofBool (!b) := by cases b <;> rfl
 
-@[simp] theorem ofBool_and_ofBool : ofBool b &&& ofBool b' = ofBool (b && b') := by
-  cases b <;> cases b' <;> rfl
-
-@[simp] theorem ofBool_or_ofBool : ofBool b ||| ofBool b' = ofBool (b || b') := by
-  cases b <;> cases b' <;> rfl
-
-@[simp] theorem ofBool_xor_ofBool : ofBool b ^^^ ofBool b' = ofBool (b ^^ b') := by
-  cases b <;> cases b' <;> rfl
-
 @[simp, bv_toNat] 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
@@ -254,7 +245,7 @@ theorem ofBool_eq_iff_eq : ∀ {b b' : Bool}, BitVec.ofBool b = BitVec.ofBool b'
 @[simp, bv_toNat] theorem toNat_ofNat (x w : Nat) : (BitVec.ofNat w x).toNat = x % 2^w := by
   simp [BitVec.toNat, BitVec.ofNat, Fin.ofNat']
 
-@[simp] theorem toFin_ofNat (x : Nat) : toFin (BitVec.ofNat w x) = Fin.ofNat' (2^w) x := rfl
+@[simp] theorem toFin_ofNat (x : Nat) : toFin (BitVec.ofNat w x) = Fin.ofNat' x (Nat.two_pow_pos w) := rfl
 
 -- Remark: we don't use `[simp]` here because simproc` subsumes it for literals.
 -- If `x` and `n` are not literals, applying this theorem eagerly may not be a good idea.
@@ -282,31 +273,8 @@ theorem getLsbD_ofNat (n : Nat) (x : Nat) (i : 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_of_le_right (by trivial : 0 < 2) le)
 
-@[simp] theorem getElem_zero_ofNat_zero (i : Nat) (h : i < w) : (BitVec.ofNat w 0)[i] = false := by
-  simp [getElem_eq_testBit_toNat]
-
-@[simp] theorem getElem_zero_ofNat_one (h : 0 < w) : (BitVec.ofNat w 1)[0] = true := by
-  simp [getElem_eq_testBit_toNat, h]
-
-theorem getElem?_zero_ofNat_zero : (BitVec.ofNat (w+1) 0)[0]? = some false := by
-  simp
-
-theorem getElem?_zero_ofNat_one : (BitVec.ofNat (w+1) 1)[0]? = some true := by
-  simp
-
--- This does not need to be a `@[simp]` theorem as it is already handled by `getElem?_eq_getElem`.
-theorem getElem?_zero_ofBool (b : Bool) : (ofBool b)[0]? = some b := by
-  simp [ofBool, cond_eq_if]
-  split <;> simp_all
-
-@[simp] theorem getElem_zero_ofBool (b : Bool) : (ofBool b)[0] = b := by
-  rw [getElem_eq_iff, getElem?_zero_ofBool]
-
-theorem getElem?_succ_ofBool (b : Bool) (i : Nat) : (ofBool b)[i + 1]? = none := by
-  simp
-
 @[simp]
-theorem getLsbD_ofBool (b : Bool) (i : Nat) : (ofBool b).getLsbD i = ((i = 0) && b) := by
+theorem getLsbD_ofBool (b : Bool) (i : Nat) : (BitVec.ofBool b).getLsbD i = ((i = 0) && b) := by
   rcases b with rfl | rfl
   · simp [ofBool]
   · simp only [ofBool, ofNat_eq_ofNat, cond_true, getLsbD_ofNat, Bool.and_true]
@@ -362,10 +330,6 @@ theorem toNat_ge_of_msb_true {x : BitVec n} (p : BitVec.msb x = true) : x.toNat
 
 @[simp] theorem getMsbD_cast (h : w = v) (x : BitVec w) : (cast h x).getMsbD i = x.getMsbD i := by
   subst h; simp
-
-@[simp] theorem getElem_cast (h : w = v) (x : BitVec w) (p : i < v) : (cast h x)[i] = x[i] := by
-  subst h; simp
-
 @[simp] theorem msb_cast (h : w = v) (x : BitVec w) : (cast h x).msb = x.msb := by
   simp [BitVec.msb]
 
@@ -448,46 +412,46 @@ theorem toInt_pos_iff {w : Nat} {x : BitVec w} :
     0 ≤ BitVec.toInt x ↔ 2 * x.toNat < 2 ^ w := by
   simp [toInt_eq_toNat_cond]; omega
 
-/-! ### setWidth, zeroExtend and truncate -/
+/-! ### zeroExtend and truncate -/
 
-@[simp]
-theorem truncate_eq_setWidth {v : Nat} {x : BitVec w} :
-  truncate v x = setWidth v x := rfl
+theorem truncate_eq_zeroExtend {v : Nat} {x : BitVec w} :
+  truncate v x = zeroExtend v x := rfl
 
-@[simp]
-theorem zeroExtend_eq_setWidth {v : Nat} {x : BitVec w} :
-  zeroExtend v x = setWidth v x := rfl
+@[simp, bv_toNat] theorem toNat_zeroExtend' {m n : Nat} (p : m ≤ n) (x : BitVec m) :
+    (zeroExtend' p x).toNat = x.toNat := by
+  simp [zeroExtend']
 
-@[simp, bv_toNat] theorem toNat_setWidth' {m n : Nat} (p : m ≤ n) (x : BitVec m) :
-    (setWidth' p x).toNat = x.toNat := by
-  simp [setWidth']
-
-@[simp, bv_toNat] theorem toNat_setWidth (i : Nat) (x : BitVec n) :
-    BitVec.toNat (setWidth i x) = x.toNat % 2^i := by
+@[bv_toNat] theorem toNat_zeroExtend (i : Nat) (x : BitVec n) :
+    BitVec.toNat (zeroExtend i x) = x.toNat % 2^i := by
   let ⟨x, lt_n⟩ := x
-  simp only [setWidth]
+  simp only [zeroExtend]
   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]
 
-theorem setWidth'_eq {x : BitVec w} (h : w ≤ v) : x.setWidth' h = x.setWidth v := by
+theorem zeroExtend'_eq {x : BitVec w} (h : w ≤ v) : x.zeroExtend' h = x.zeroExtend v := by
   apply eq_of_toNat_eq
-  rw [toNat_setWidth, toNat_setWidth']
+  rw [toNat_zeroExtend, toNat_zeroExtend']
   rw [Nat.mod_eq_of_lt]
   exact Nat.lt_of_lt_of_le x.isLt (Nat.pow_le_pow_right (Nat.zero_lt_two) h)
 
-@[simp] theorem setWidth_eq (x : BitVec n) : setWidth n x = x := by
+@[simp, bv_toNat] theorem toNat_truncate (x : BitVec n) : (truncate i x).toNat = x.toNat % 2^i :=
+  toNat_zeroExtend i x
+
+@[simp] theorem zeroExtend_eq (x : BitVec n) : zeroExtend n x = x := by
   apply eq_of_toNat_eq
   let ⟨x, lt_n⟩ := x
-  simp [setWidth]
+  simp [truncate, zeroExtend]
 
-@[simp] theorem setWidth_zero (m n : Nat) : setWidth m 0#n = 0#m := by
+@[simp] theorem zeroExtend_zero (m n : Nat) : zeroExtend m 0#n = 0#m := by
   apply eq_of_toNat_eq
-  simp [toNat_setWidth]
+  simp [toNat_zeroExtend]
 
-@[simp] theorem ofNat_toNat (m : Nat) (x : BitVec n) : BitVec.ofNat m x.toNat = setWidth m x := by
+theorem truncate_eq (x : BitVec n) : truncate n x = x := zeroExtend_eq x
+
+@[simp] theorem ofNat_toNat (m : Nat) (x : BitVec n) : BitVec.ofNat m x.toNat = truncate m x := by
   apply eq_of_toNat_eq
   simp
 
@@ -506,33 +470,33 @@ theorem nat_eq_toNat {x : BitVec w} {y : Nat}
   rw [@eq_comm _ _ x.toNat]
   apply toNat_eq_nat
 
-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]
+theorem getElem_zeroExtend' (x : BitVec w) (i : Nat) (h : w ≤ v) (hi : i < v) :
+    (zeroExtend' h x)[i] = x.getLsbD i := by
+  rw [getElem_eq_testBit_toNat, toNat_zeroExtend', getLsbD]
 
-theorem getElem_setWidth (m : Nat) (x : BitVec n) (i : Nat) (h : i < m) :
-    (setWidth m x)[i] = x.getLsbD i := by
-  rw [setWidth]
+theorem getElem_zeroExtend (m : Nat) (x : BitVec n) (i : Nat) (h : i < m) :
+    (zeroExtend m x)[i] = x.getLsbD i := by
+  rw [zeroExtend]
   split
-  · rw [getElem_setWidth']
+  · rw [getElem_zeroExtend']
   · simp [getElem_eq_testBit_toNat, getLsbD]
     omega
 
-theorem getElem?_setWidth' (x : BitVec w) (i : Nat) (h : w ≤ v) :
-    (setWidth' h x)[i]? = if i < v then some (x.getLsbD i) else none := by
-  simp [getElem?_eq, getElem_setWidth']
+theorem getElem?_zeroExtend' (x : BitVec w) (i : Nat) (h : w ≤ v) :
+    (zeroExtend' h x)[i]? = if i < v then some (x.getLsbD i) else none := by
+  simp [getElem?_eq, getElem_zeroExtend']
 
-theorem getElem?_setWidth (m : Nat) (x : BitVec n) (i : Nat) :
-    (x.setWidth m)[i]? = if i < m then some (x.getLsbD i) else none := by
-  simp [getElem?_eq, getElem_setWidth]
+theorem getElem?_zeroExtend (m : Nat) (x : BitVec n) (i : Nat) :
+    (x.zeroExtend m)[i]? = if i < m then some (x.getLsbD i) else none := by
+  simp [getElem?_eq, getElem_zeroExtend]
 
-@[simp] theorem getLsbD_setWidth' (ge : m ≥ n) (x : BitVec n) (i : Nat) :
-    getLsbD (setWidth' ge x) i = getLsbD x i := by
-  simp [getLsbD, toNat_setWidth']
+@[simp] theorem getLsbD_zeroExtend' (ge : m ≥ n) (x : BitVec n) (i : Nat) :
+    getLsbD (zeroExtend' ge x) i = getLsbD x i := by
+  simp [getLsbD, toNat_zeroExtend']
 
-@[simp] theorem getMsbD_setWidth' (ge : m ≥ n) (x : BitVec n) (i : Nat) :
-    getMsbD (setWidth' ge x) i = (decide (i ≥ m - n) && getMsbD x (i - (m - n))) := by
-  simp only [getMsbD, getLsbD_setWidth', gt_iff_lt]
+@[simp] theorem getMsbD_zeroExtend' (ge : m ≥ n) (x : BitVec n) (i : Nat) :
+    getMsbD (zeroExtend' ge x) i = (decide (i ≥ m - n) && getMsbD x (i - (m - n))) := by
+  simp only [getMsbD, getLsbD_zeroExtend', gt_iff_lt]
   by_cases h₁ : decide (i < m) <;> by_cases h₂ : decide (i ≥ m - n) <;> by_cases h₃ : decide (i - (m - n) < n) <;>
     by_cases h₄ : n - 1 - (i - (m - n)) = m - 1 - i
   all_goals
@@ -543,15 +507,15 @@ theorem getElem?_setWidth (m : Nat) (x : BitVec n) (i : Nat) :
     (try apply (getLsbD_ge _ _ _).symm) <;>
     omega
 
-@[simp] theorem getLsbD_setWidth (m : Nat) (x : BitVec n) (i : Nat) :
-    getLsbD (setWidth m x) i = (decide (i < m) && getLsbD x i) := by
-  simp [getLsbD, toNat_setWidth, Nat.testBit_mod_two_pow]
+@[simp] theorem getLsbD_zeroExtend (m : Nat) (x : BitVec n) (i : Nat) :
+    getLsbD (zeroExtend m x) i = (decide (i < m) && getLsbD x i) := by
+  simp [getLsbD, toNat_zeroExtend, Nat.testBit_mod_two_pow]
 
-@[simp] theorem getMsbD_setWidth_add {x : BitVec w} (h : k ≤ i) :
-    (x.setWidth (w + k)).getMsbD i = x.getMsbD (i - k) := by
+@[simp] theorem getMsbD_zeroExtend_add {x : BitVec w} (h : k ≤ i) :
+    (x.zeroExtend (w + k)).getMsbD i = x.getMsbD (i - k) := by
   by_cases h : w = 0
   · subst h; simp [of_length_zero]
-  simp only [getMsbD, getLsbD_setWidth]
+  simp only [getMsbD, getLsbD_zeroExtend]
   by_cases h₁ : i < w + k <;> by_cases h₂ : i - k < w <;> by_cases h₃ : w + k - 1 - i < w + k
     <;> simp [h₁, h₂, h₃]
   · congr 1
@@ -559,63 +523,75 @@ theorem getElem?_setWidth (m : Nat) (x : BitVec n) (i : Nat) :
   all_goals (first | apply getLsbD_ge | apply Eq.symm; apply getLsbD_ge)
     <;> omega
 
-@[simp] theorem cast_setWidth (h : v = v') (x : BitVec w) :
-    cast h (setWidth v x) = setWidth v' x := by
+theorem getLsbD_truncate (m : Nat) (x : BitVec n) (i : Nat) :
+    getLsbD (truncate m x) i = (decide (i < m) && getLsbD x i) :=
+  getLsbD_zeroExtend m x i
+
+theorem msb_truncate (x : BitVec w) : (x.truncate (k + 1)).msb = x.getLsbD k := by
+  simp [BitVec.msb, getMsbD]
+
+@[simp] theorem cast_zeroExtend (h : v = v') (x : BitVec w) :
+    cast h (zeroExtend v x) = zeroExtend v' x := by
   subst h
   ext
   simp
 
-@[simp] theorem setWidth_setWidth_of_le (x : BitVec w) (h : k ≤ l) :
-    (x.setWidth l).setWidth k = x.setWidth k := by
+@[simp] theorem cast_truncate (h : v = v') (x : BitVec w) :
+    cast h (truncate v x) = truncate v' x := by
+  subst h
+  ext
+  simp
+
+@[simp] theorem zeroExtend_zeroExtend_of_le (x : BitVec w) (h : k ≤ l) :
+    (x.zeroExtend l).zeroExtend k = x.zeroExtend k := by
   ext i
-  simp only [getLsbD_setWidth, Fin.is_lt, decide_True, Bool.true_and]
-  have p := lt_of_getLsbD (x := x) (i := i)
+  simp only [getLsbD_zeroExtend, Fin.is_lt, decide_True, Bool.true_and]
+  have p := lt_of_getLsbD x i
   revert p
   cases getLsbD x i <;> simp; omega
 
-@[simp] theorem setWidth_cast {h : w = v} : (cast h x).setWidth k = x.setWidth k := by
+@[simp] theorem truncate_truncate_of_le (x : BitVec w) (h : k ≤ l) :
+    (x.truncate l).truncate k = x.truncate k :=
+  zeroExtend_zeroExtend_of_le x h
+
+/-- Truncating by the bitwidth has no effect. -/
+-- This doesn't need to be a `@[simp]` lemma, as `zeroExtend_eq` applies.
+theorem truncate_eq_self {x : BitVec w} : x.truncate w = x := zeroExtend_eq _
+
+@[simp] theorem truncate_cast {h : w = v} : (cast h x).truncate k = x.truncate k := by
   apply eq_of_getLsbD_eq
   simp
 
-theorem msb_setWidth (x : BitVec w) : (x.setWidth v).msb = (decide (0 < v) && x.getLsbD (v - 1)) := by
+theorem msb_zeroExtend (x : BitVec w) : (x.zeroExtend v).msb = (decide (0 < v) && x.getLsbD (v - 1)) := by
   rw [msb_eq_getLsbD_last]
-  simp only [getLsbD_setWidth]
+  simp only [getLsbD_zeroExtend]
   cases getLsbD x (v - 1) <;> simp; omega
 
-theorem msb_setWidth' (x : BitVec w) (h : w ≤ v) : (x.setWidth' h).msb = (decide (0 < v) && x.getLsbD (v - 1)) := by
-  rw [setWidth'_eq, msb_setWidth]
-
-theorem msb_setWidth'' (x : BitVec w) : (x.setWidth (k + 1)).msb = x.getLsbD k := by
-  simp [BitVec.msb, getMsbD]
+theorem msb_zeroExtend' (x : BitVec w) (h : w ≤ v) : (x.zeroExtend' h).msb = (decide (0 < v) && x.getLsbD (v - 1)) := by
+  rw [zeroExtend'_eq, msb_zeroExtend]
 
 /-- zero extending a bitvector to width 1 equals the boolean of the lsb. -/
-theorem setWidth_one_eq_ofBool_getLsb_zero (x : BitVec w) :
-    x.setWidth 1 = BitVec.ofBool (x.getLsbD 0) := by
+theorem zeroExtend_one_eq_ofBool_getLsb_zero (x : BitVec w) :
+    x.zeroExtend 1 = BitVec.ofBool (x.getLsbD 0) := by
   ext i
-  simp [getLsbD_setWidth, Fin.fin_one_eq_zero i]
+  simp [getLsbD_zeroExtend, Fin.fin_one_eq_zero i]
 
 /-- Zero extending `1#v` to `1#w` equals `1#w` when `v > 0`. -/
-theorem setWidth_ofNat_one_eq_ofNat_one_of_lt {v w : Nat} (hv : 0 < v) :
-    (BitVec.ofNat v 1).setWidth w = BitVec.ofNat w 1 := by
+theorem zeroExtend_ofNat_one_eq_ofNat_one_of_lt {v w : Nat} (hv : 0 < v) :
+    (BitVec.ofNat v 1).zeroExtend w = BitVec.ofNat w 1 := by
   ext ⟨i, hilt⟩
-  simp only [getLsbD_setWidth, hilt, decide_True, getLsbD_ofNat, Bool.true_and,
+  simp only [getLsbD_zeroExtend, hilt, decide_True, getLsbD_ofNat, Bool.true_and,
     Bool.and_iff_right_iff_imp, decide_eq_true_eq]
   intros hi₁
   have hv := Nat.testBit_one_eq_true_iff_self_eq_zero.mp hi₁
   omega
 
 /-- Truncating to width 1 produces a bitvector equal to the least significant bit. -/
-theorem setWidth_one {x : BitVec w} :
-    x.setWidth 1 = ofBool (x.getLsbD 0) := by
+theorem truncate_one {x : BitVec w} :
+    x.truncate 1 = ofBool (x.getLsbD 0) := by
   ext i
   simp [show i = 0 by omega]
 
-@[simp] theorem setWidth_ofNat_of_le (h : v ≤ w) (x : Nat) : setWidth v (BitVec.ofNat w x) = BitVec.ofNat v x := by
-  apply BitVec.eq_of_toNat_eq
-  simp only [toNat_setWidth, toNat_ofNat]
-  rw [Nat.mod_mod_of_dvd]
-  exact Nat.pow_dvd_pow_iff_le_right'.mpr h
-
 /-! ## extractLsb -/
 
 @[simp]
@@ -657,9 +633,6 @@ theorem extractLsb'_eq_extractLsb {w : Nat} (x : BitVec w) (start len : Nat) (h
 @[simp] theorem getLsbD_allOnes : (allOnes v).getLsbD i = decide (i < v) := by
   simp [allOnes]
 
-@[simp] theorem getElem_allOnes (i : Nat) (h : i < v) : (allOnes v)[i] = true := by
-  simp [getElem_eq_testBit_toNat, h]
-
 @[simp] theorem ofFin_add_rev (x : Fin (2^n)) : ofFin (x + x.rev) = allOnes n := by
   ext
   simp only [Fin.rev, getLsbD_ofFin, getLsbD_allOnes, Fin.is_lt, decide_True]
@@ -687,14 +660,11 @@ theorem extractLsb'_eq_extractLsb {w : Nat} (x : BitVec w) (start len : Nat) (h
   simp only [getMsbD]
   by_cases h : i < w <;> simp [h]
 
-@[simp] theorem getElem_or {x y : BitVec w} {i : Nat} (h : i < w) : (x ||| y)[i] = (x[i] || y[i]) := by
-  simp [getElem_eq_testBit_toNat]
-
 @[simp] theorem msb_or {x y : BitVec w} : (x ||| y).msb = (x.msb || y.msb) := by
   simp [BitVec.msb]
 
-@[simp] theorem setWidth_or {x y : BitVec w} :
-    (x ||| y).setWidth k = x.setWidth k ||| y.setWidth k := by
+@[simp] theorem truncate_or {x y : BitVec w} :
+    (x ||| y).truncate k = x.truncate k ||| y.truncate k := by
   ext
   simp
 
@@ -728,14 +698,11 @@ instance : Std.Commutative (fun (x y : BitVec w) => x ||| y) := ⟨BitVec.or_com
   simp only [getMsbD]
   by_cases h : i < w <;> simp [h]
 
-@[simp] theorem getElem_and {x y : BitVec w} {i : Nat} (h : i < w) : (x &&& y)[i] = (x[i] && y[i]) := by
-  simp [getElem_eq_testBit_toNat]
-
 @[simp] theorem msb_and {x y : BitVec w} : (x &&& y).msb = (x.msb && y.msb) := by
   simp [BitVec.msb]
 
-@[simp] theorem setWidth_and {x y : BitVec w} :
-    (x &&& y).setWidth k = x.setWidth k &&& y.setWidth k := by
+@[simp] theorem truncate_and {x y : BitVec w} :
+    (x &&& y).truncate k = x.truncate k &&& y.truncate k := by
   ext
   simp
 
@@ -762,24 +729,21 @@ instance : Std.Commutative (fun (x y : BitVec w) => x &&& y) := ⟨BitVec.and_co
   exact (Nat.mod_eq_of_lt <| Nat.xor_lt_two_pow x.isLt y.isLt).symm
 
 @[simp] theorem getLsbD_xor {x y : BitVec v} :
-    (x ^^^ y).getLsbD i = ((x.getLsbD i) ^^ (y.getLsbD i)) := by
+    (x ^^^ y).getLsbD i = (xor (x.getLsbD i) (y.getLsbD i)) := by
   rw [← testBit_toNat, getLsbD, getLsbD]
   simp
 
 @[simp] theorem getMsbD_xor {x y : BitVec w} :
-    (x ^^^ y).getMsbD i = (x.getMsbD i ^^ y.getMsbD i) := by
+    (x ^^^ y).getMsbD i = (xor (x.getMsbD i) (y.getMsbD i)) := by
   simp only [getMsbD]
   by_cases h : i < w <;> simp [h]
 
-@[simp] theorem getElem_xor {x y : BitVec w} {i : Nat} (h : i < w) : (x ^^^ y)[i] = (x[i] ^^ y[i]) := by
-  simp [getElem_eq_testBit_toNat]
-
 @[simp] theorem msb_xor {x y : BitVec w} :
-    (x ^^^ y).msb = (x.msb ^^ y.msb) := by
+    (x ^^^ y).msb = (xor x.msb y.msb) := by
   simp [BitVec.msb]
 
-@[simp] theorem setWidth_xor {x y : BitVec w} :
-    (x ^^^ y).setWidth k = x.setWidth k ^^^ y.setWidth k := by
+@[simp] theorem truncate_xor {x y : BitVec w} :
+    (x ^^^ y).truncate k = x.truncate k ^^^ y.truncate k := by
   ext
   simp
 
@@ -827,14 +791,8 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
 @[simp] theorem getLsbD_not {x : BitVec v} : (~~~x).getLsbD i = (decide (i < v) && ! x.getLsbD i) := by
   by_cases h' : i < v <;> simp_all [not_def]
 
-@[simp] theorem getElem_not {x : BitVec w} {i : Nat} (h : i < w) : (~~~x)[i] = !x[i] := by
-  simp only [getElem_eq_testBit_toNat, toNat_not]
-  rw [← Nat.sub_add_eq, Nat.add_comm 1]
-  rw [Nat.testBit_two_pow_sub_succ x.isLt]
-  simp [h]
-
-@[simp] theorem setWidth_not {x : BitVec w} (h : k ≤ w) :
-    (~~~x).setWidth k = ~~~(x.setWidth k) := by
+@[simp] theorem truncate_not {x : BitVec w} (h : k ≤ w) :
+    (~~~x).truncate k = ~~~(x.truncate k) := by
   ext
   simp [h]
   omega
@@ -868,7 +826,7 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
   BitVec.toNat_ofNat _ _
 
 @[simp] theorem toFin_shiftLeft {n : Nat} (x : BitVec w) :
-    BitVec.toFin (x <<< n) = Fin.ofNat' (2^w) (x.toNat <<< n) := rfl
+    BitVec.toFin (x <<< n) = Fin.ofNat' (x.toNat <<< n) (Nat.two_pow_pos w) := rfl
 
 @[simp]
 theorem shiftLeft_zero_eq (x : BitVec w) : x <<< 0 = x := by
@@ -922,9 +880,9 @@ theorem shiftLeft_or_distrib (x y : BitVec w) (n : Nat) :
     <;> omega
 
 theorem shiftLeftZeroExtend_eq {x : BitVec w} :
-    shiftLeftZeroExtend x n = setWidth (w+n) x <<< n := by
+    shiftLeftZeroExtend x n = zeroExtend (w+n) x <<< n := by
   apply eq_of_toNat_eq
-  rw [shiftLeftZeroExtend, setWidth]
+  rw [shiftLeftZeroExtend, zeroExtend]
   split
   · simp
     rw [Nat.mod_eq_of_lt]
@@ -935,7 +893,7 @@ theorem shiftLeftZeroExtend_eq {x : BitVec w} :
 @[simp] theorem getLsbD_shiftLeftZeroExtend (x : BitVec m) (n : Nat) :
     getLsbD (shiftLeftZeroExtend x n) i = ((! decide (i < n)) && getLsbD x (i - n)) := by
   rw [shiftLeftZeroExtend_eq]
-  simp only [getLsbD_shiftLeft, getLsbD_setWidth]
+  simp only [getLsbD_shiftLeft, getLsbD_zeroExtend]
   cases h₁ : decide (i < n) <;> cases h₂ : decide (i - n < m + n) <;> cases h₃ : decide (i < m + n)
     <;> simp_all
     <;> (rw [getLsbD_ge]; omega)
@@ -989,10 +947,6 @@ theorem getLsbD_shiftLeft' {x : BitVec w₁} {y : BitVec w₂} {i : Nat} :
     getLsbD (x >>> i) j = getLsbD x (i+j) := by
   unfold getLsbD ; simp
 
-@[simp] theorem getElem_ushiftRight (x : BitVec w) (i n : Nat) (h : i < w) :
-    (x >>> n)[i] = x.getLsbD (n + i) := by
-  simp [getElem_eq_testBit_toNat, toNat_ushiftRight, Nat.testBit_shiftRight, getLsbD]
-
 theorem ushiftRight_xor_distrib (x y : BitVec w) (n : Nat) :
     (x ^^^ y) >>> n = (x >>> n) ^^^ (y >>> n) := by
   ext
@@ -1073,7 +1027,7 @@ theorem sshiftRight_eq_of_msb_true {x : BitVec w} {s : Nat} (h : x.msb = true) :
     · simp only [hi, decide_False, Bool.not_false, Bool.true_and, Bool.iff_and_self,
         decide_eq_true_eq]
       intros hlsb
-      apply BitVec.lt_of_getLsbD hlsb
+      apply BitVec.lt_of_getLsbD _ _ hlsb
   · by_cases hi : i ≥ w
     · simp [hi]
     · simp only [sshiftRight_eq_of_msb_true hmsb, getLsbD_not, getLsbD_ushiftRight, Bool.not_and,
@@ -1178,15 +1132,15 @@ private theorem Int.negSucc_emod (m : Nat) (n : Int) :
     -(m + 1) % n = Int.subNatNat (Int.natAbs n) ((m % Int.natAbs n) + 1) := rfl
 
 /-- The sign extension is the same as zero extending when `msb = false`. -/
-theorem signExtend_eq_not_setWidth_not_of_msb_false {x : BitVec w} {v : Nat} (hmsb : x.msb = false) :
-    x.signExtend v = x.setWidth v := by
+theorem signExtend_eq_not_zeroExtend_not_of_msb_false {x : BitVec w} {v : Nat} (hmsb : x.msb = false) :
+    x.signExtend v = x.zeroExtend v := by
   ext i
   by_cases hv : i < v
-  · simp only [signExtend, getLsbD, getLsbD_setWidth, hv, decide_True, Bool.true_and, toNat_ofInt,
+  · simp only [signExtend, getLsbD, getLsbD_zeroExtend, hv, decide_True, Bool.true_and, toNat_ofInt,
       BitVec.toInt_eq_msb_cond, hmsb, ↓reduceIte, reduceCtorEq]
     rw [Int.ofNat_mod_ofNat, Int.toNat_ofNat, Nat.testBit_mod_two_pow]
     simp [BitVec.testBit_toNat]
-  · simp only [getLsbD_setWidth, hv, decide_False, Bool.false_and]
+  · simp only [getLsbD_zeroExtend, hv, decide_False, Bool.false_and]
     apply getLsbD_ge
     omega
 
@@ -1194,11 +1148,11 @@ theorem signExtend_eq_not_setWidth_not_of_msb_false {x : BitVec w} {v : Nat} (hm
 The sign extension is a bitwise not, followed by a zero extend, followed by another bitwise not
 when `msb = true`. The double bitwise not ensures that the high bits are '1',
 and the lower bits are preserved. -/
-theorem signExtend_eq_not_setWidth_not_of_msb_true {x : BitVec w} {v : Nat} (hmsb : x.msb = true) :
-    x.signExtend v = ~~~((~~~x).setWidth v) := by
+theorem signExtend_eq_not_zeroExtend_not_of_msb_true {x : BitVec w} {v : Nat} (hmsb : x.msb = true) :
+    x.signExtend v = ~~~((~~~x).zeroExtend v) := by
   apply BitVec.eq_of_toNat_eq
   simp only [signExtend, BitVec.toInt_eq_msb_cond, toNat_ofInt, toNat_not,
-    toNat_setWidth, hmsb, ↓reduceIte]
+    toNat_truncate, hmsb, ↓reduceIte]
   norm_cast
   rw [Int.ofNat_sub_ofNat_of_lt, Int.negSucc_emod]
   simp only [Int.natAbs_ofNat, Nat.succ_eq_add_one]
@@ -1214,27 +1168,27 @@ theorem signExtend_eq_not_setWidth_not_of_msb_true {x : BitVec w} {v : Nat} (hms
 @[simp] theorem getLsbD_signExtend (x  : BitVec w) {v i : Nat} :
     (x.signExtend v).getLsbD i = (decide (i < v) && if i < w then x.getLsbD i else x.msb) := by
   rcases hmsb : x.msb with rfl | rfl
-  · rw [signExtend_eq_not_setWidth_not_of_msb_false hmsb]
+  · rw [signExtend_eq_not_zeroExtend_not_of_msb_false hmsb]
     by_cases (i < v) <;> by_cases (i < w) <;> simp_all <;> omega
-  · rw [signExtend_eq_not_setWidth_not_of_msb_true hmsb]
+  · rw [signExtend_eq_not_zeroExtend_not_of_msb_true hmsb]
     by_cases (i < v) <;> by_cases (i < w) <;> simp_all <;> omega
 
 /-- Sign extending to a width smaller than the starting width is a truncation. -/
-theorem signExtend_eq_setWidth_of_lt (x : BitVec w) {v : Nat} (hv : v ≤ w):
-  x.signExtend v = x.setWidth v := by
+theorem signExtend_eq_truncate_of_lt (x : BitVec w) {v : Nat} (hv : v ≤ w):
+  x.signExtend v = x.truncate v := by
   ext i
-  simp only [getLsbD_signExtend, Fin.is_lt, decide_True, Bool.true_and, getLsbD_setWidth,
+  simp only [getLsbD_signExtend, Fin.is_lt, decide_True, Bool.true_and, getLsbD_zeroExtend,
     ite_eq_left_iff, Nat.not_lt]
   omega
 
 /-- Sign extending to the same bitwidth is a no op. -/
 theorem signExtend_eq (x : BitVec w) : x.signExtend w = x := by
-  rw [signExtend_eq_setWidth_of_lt _ (Nat.le_refl _), setWidth_eq]
+  rw [signExtend_eq_truncate_of_lt _ (Nat.le_refl _), truncate_eq]
 
 /-! ### append -/
 
 theorem append_def (x : BitVec v) (y : BitVec w) :
-    x ++ y = (shiftLeftZeroExtend x w ||| setWidth' (Nat.le_add_left w v) y) := rfl
+    x ++ y = (shiftLeftZeroExtend x w ||| zeroExtend' (Nat.le_add_left w v) y) := rfl
 
 @[simp] theorem toNat_append (x : BitVec m) (y : BitVec n) :
     (x ++ y).toNat = x.toNat <<< n ||| y.toNat :=
@@ -1242,7 +1196,7 @@ theorem append_def (x : BitVec v) (y : BitVec w) :
 
 @[simp] theorem getLsbD_append {x : BitVec n} {y : BitVec m} :
     getLsbD (x ++ y) i = bif i < m then getLsbD y i else getLsbD x (i - m) := by
-  simp only [append_def, getLsbD_or, getLsbD_shiftLeftZeroExtend, getLsbD_setWidth']
+  simp only [append_def, getLsbD_or, getLsbD_shiftLeftZeroExtend, getLsbD_zeroExtend']
   by_cases h : i < m
   · simp [h]
   · simp [h]; simp_all
@@ -1257,7 +1211,7 @@ theorem append_def (x : BitVec v) (y : BitVec w) :
 theorem msb_append {x : BitVec w} {y : BitVec v} :
     (x ++ y).msb = bif (w == 0) then (y.msb) else (x.msb) := by
   rw [← append_eq, append]
-  simp [msb_setWidth']
+  simp [msb_zeroExtend']
   by_cases h : w = 0
   · subst h
     simp [BitVec.msb, getMsbD]
@@ -1274,7 +1228,7 @@ theorem msb_append {x : BitVec w} {y : BitVec v} :
 @[simp] theorem zero_width_append (x : BitVec 0) (y : BitVec v) : x ++ y = cast (by omega) y := by
   ext
   rw [getLsbD_append]
-  simpa using lt_of_getLsbD
+  simpa using lt_of_getLsbD _ _
 
 @[simp] theorem cast_append_right (h : w + v = w + v') (x : BitVec w) (y : BitVec v) :
     cast h (x ++ y) = x ++ cast (by omega) y := by
@@ -1292,11 +1246,11 @@ theorem msb_append {x : BitVec w} {y : BitVec v} :
   ext
   simp
 
-theorem setWidth_append {x : BitVec w} {y : BitVec v} :
-    (x ++ y).setWidth k = if h : k ≤ v then y.setWidth k else (x.setWidth (k - v) ++ y).cast (by omega) := by
+theorem truncate_append {x : BitVec w} {y : BitVec v} :
+    (x ++ y).truncate k = if h : k ≤ v then y.truncate k else (x.truncate (k - v) ++ y).cast (by omega) := by
   apply eq_of_getLsbD_eq
   intro i
-  simp only [getLsbD_setWidth, Fin.is_lt, decide_True, getLsbD_append, Bool.true_and]
+  simp only [getLsbD_zeroExtend, Fin.is_lt, decide_True, getLsbD_append, Bool.true_and]
   split
   · have t : i < v := by omega
     simp [t]
@@ -1305,20 +1259,8 @@ theorem setWidth_append {x : BitVec w} {y : BitVec v} :
     · have t' : i - v < k - v := by omega
       simp [t, t']
 
-@[simp] theorem setWidth_append_of_eq {x : BitVec v} {y : BitVec w} (h : w' = w) : setWidth (v' + w') (x ++ y) = setWidth v' x ++ setWidth w' y := by
-  subst h
-  ext i
-  simp only [getLsbD_setWidth, Fin.is_lt, decide_True, getLsbD_append, cond_eq_if,
-    decide_eq_true_eq, Bool.true_and, setWidth_eq]
-  split
-  · simp_all
-  · simp_all only [Bool.iff_and_self, decide_eq_true_eq]
-    intro h
-    have := BitVec.lt_of_getLsbD h
-    omega
-
-@[simp] theorem setWidth_cons {x : BitVec w} : (cons a x).setWidth w = x := by
-  simp [cons, setWidth_append]
+@[simp] theorem truncate_cons {x : BitVec w} : (cons a x).truncate w = x := by
+  simp [cons, truncate_append]
 
 @[simp] theorem not_append {x : BitVec w} {y : BitVec v} : ~~~ (x ++ y) = (~~~ x) ++ (~~~ y) := by
   ext i
@@ -1405,18 +1347,18 @@ theorem toNat_cons' {x : BitVec w} :
 @[simp] theorem getMsbD_cons_succ : (cons a x).getMsbD (i + 1) = x.getMsbD i := by
   simp [cons, Nat.le_add_left 1 i]
 
-theorem setWidth_succ (x : BitVec w) :
-    setWidth (i+1) x = cons (getLsbD x i) (setWidth i x) := by
+theorem truncate_succ (x : BitVec w) :
+    truncate (i+1) x = cons (getLsbD x i) (truncate i x) := by
   apply eq_of_getLsbD_eq
   intro j
-  simp only [getLsbD_setWidth, getLsbD_cons, j.isLt, decide_True, Bool.true_and]
+  simp only [getLsbD_truncate, getLsbD_cons, j.isLt, decide_True, Bool.true_and]
   if j_eq : j.val = i then
     simp [j_eq]
   else
     have j_lt : j.val < i := Nat.lt_of_le_of_ne (Nat.le_of_succ_le_succ j.isLt) j_eq
     simp [j_eq, j_lt]
 
-theorem eq_msb_cons_setWidth (x : BitVec (w+1)) : x = (cons x.msb (x.setWidth w)) := by
+theorem eq_msb_cons_truncate (x : BitVec (w+1)) : x = (cons x.msb (x.truncate w)) := by
   ext i
   simp
   split <;> rename_i h
@@ -1430,18 +1372,15 @@ theorem eq_msb_cons_setWidth (x : BitVec (w+1)) : x = (cons x.msb (x.setWidth w)
 
 @[simp] theorem cons_or_cons (x y : BitVec w) (a b : Bool) :
     (cons a x) ||| (cons b y) = cons (a || b) (x ||| y) := by
-  ext i
-  simp [cons]
+  ext i; cases i using Fin.succRecOn <;> simp <;> split <;> rfl
 
 @[simp] theorem cons_and_cons (x y : BitVec w) (a b : Bool) :
     (cons a x) &&& (cons b y) = cons (a && b) (x &&& y) := by
-  ext i
-  simp [cons]
+  ext i; cases i using Fin.succRecOn <;> simp <;> split <;> rfl
 
 @[simp] theorem cons_xor_cons (x y : BitVec w) (a b : Bool) :
-    (cons a x) ^^^ (cons b y) = cons (a ^^ b) (x ^^^ y) := by
-  ext i
-  simp [cons]
+    (cons a x) ^^^ (cons b y) = cons (xor a b) (x ^^^ y) := by
+  ext i; cases i using Fin.succRecOn <;> simp <;> split <;> rfl
 
 /-! ### concat -/
 
@@ -1479,7 +1418,7 @@ theorem getLsbD_concat (x : BitVec w) (b : Bool) (i : Nat) :
   ext i; cases i using Fin.succRecOn <;> simp
 
 @[simp] theorem concat_xor_concat (x y : BitVec w) (a b : Bool) :
-    (concat x a) ^^^ (concat y b) = concat (x ^^^ y) (a ^^ b) := by
+    (concat x a) ^^^ (concat y b) = concat (x ^^^ y) (xor a b) := by
   ext i; cases i using Fin.succRecOn <;> simp
 
 /-! ### add -/
@@ -1497,8 +1436,7 @@ Definition of bitvector addition as a nat.
   x + .ofFin y = .ofFin (x.toFin + y) := rfl
 
 theorem ofNat_add {n} (x y : Nat) : BitVec.ofNat n (x + y) = BitVec.ofNat n x + BitVec.ofNat n y := by
-  apply eq_of_toNat_eq
-  simp [BitVec.ofNat, Fin.ofNat'_add]
+  apply eq_of_toNat_eq ; simp [BitVec.ofNat]
 
 theorem ofNat_add_ofNat {n} (x y : Nat) : BitVec.ofNat n x + BitVec.ofNat n y = BitVec.ofNat n (x + y) :=
   (ofNat_add x y).symm
@@ -1518,8 +1456,8 @@ instance : Std.LawfulIdentity (α := BitVec n) (· + ·) 0#n where
   left_id := BitVec.zero_add
   right_id := BitVec.add_zero
 
-theorem setWidth_add (x y : BitVec w) (h : i ≤ w) :
-    (x + y).setWidth i = x.setWidth i + y.setWidth i := by
+theorem truncate_add (x y : BitVec w) (h : i ≤ w) :
+    (x + y).truncate i = x.truncate i + y.truncate i := by
   have dvd : 2^i ∣ 2^w := Nat.pow_dvd_pow _ h
   simp [bv_toNat, h, Nat.mod_mod_of_dvd _ dvd]
 
@@ -1552,12 +1490,10 @@ theorem sub_def {n} (x y : BitVec n) : x - y = .ofNat n ((2^n - y.toNat) + x.toN
   rfl
 @[simp] theorem sub_ofFin (x : BitVec n) (y : Fin (2^n)) : x - .ofFin y = .ofFin (x.toFin - y) :=
   rfl
-
 -- Remark: we don't use `[simp]` here because simproc` subsumes it for literals.
 -- If `x` and `n` are not literals, applying this theorem eagerly may not be a good idea.
 theorem ofNat_sub_ofNat {n} (x y : Nat) : BitVec.ofNat n x - BitVec.ofNat n y = .ofNat n ((2^n - y % 2^n) + x) := by
-  apply eq_of_toNat_eq
-  simp [BitVec.ofNat, Fin.ofNat'_sub]
+  apply eq_of_toNat_eq ; simp [BitVec.ofNat]
 
 @[simp] protected theorem sub_zero (x : BitVec n) : x - 0#n = x := by apply eq_of_toNat_eq ; simp
 
@@ -1572,7 +1508,7 @@ theorem ofNat_sub_ofNat {n} (x y : Nat) : BitVec.ofNat n x - BitVec.ofNat n y =
   simp [Neg.neg, BitVec.neg]
 
 @[simp] theorem toFin_neg (x : BitVec n) :
-    (-x).toFin = Fin.ofNat' (2^n) (2^n - x.toNat) :=
+    (-x).toFin = Fin.ofNat' (2^n - x.toNat) (Nat.two_pow_pos _) :=
   rfl
 
 theorem sub_toAdd {n} (x y : BitVec n) : x - y = x + - y := by
@@ -1692,52 +1628,15 @@ theorem ofInt_mul {n} (x y : Int) : BitVec.ofInt n (x * y) =
   x < BitVec.ofFin y ↔ x.toFin < y := Iff.rfl
 @[simp] theorem ofFin_lt {x : Fin (2^n)} {y : BitVec n} :
   BitVec.ofFin x < y ↔ x < y.toFin := Iff.rfl
-@[simp] theorem ofNat_lt_ofNat {n} {x y : Nat} : BitVec.ofNat n x < BitVec.ofNat n y ↔ x % 2^n < y % 2^n := by
+@[simp] theorem ofNat_lt_ofNat {n} (x y : Nat) : BitVec.ofNat n x < BitVec.ofNat n y ↔ x % 2^n < y % 2^n := by
   simp [lt_def]
 
-@[simp] protected theorem not_le {x y : BitVec n} : ¬ x ≤ y ↔ y < x := by
-  simp [le_def, lt_def]
-
-@[simp] protected theorem not_lt {x y : BitVec n} : ¬ x < y ↔ y ≤ x := by
-  simp [le_def, lt_def]
-
-@[simp] protected theorem le_refl (x : BitVec n) : x ≤ x := by
-  simp [le_def]
-
-@[simp] protected theorem lt_irrefl (x : BitVec n) : ¬x < x := by
-  simp [lt_def]
-
-protected theorem le_trans {x y z : BitVec n} : x ≤ y → y ≤ z → x ≤ z := by
-  simp only [le_def]
-  apply Nat.le_trans
-
-protected theorem lt_trans {x y z : BitVec n} : x < y → y < z → x < z := by
-  simp only [lt_def]
-  apply Nat.lt_trans
-
-protected theorem le_total (x y : BitVec n) : x ≤ y ∨ y ≤ x := by
-  simp only [le_def]
-  apply Nat.le_total
-
-protected theorem le_antisymm {x y : BitVec n} : x ≤ y → y ≤ x → x = y := by
-  simp only [le_def, BitVec.toNat_eq]
-  apply Nat.le_antisymm
-
-protected theorem lt_asymm {x y : BitVec n} : x < y → ¬ y < x := by
-  simp only [lt_def]
-  apply Nat.lt_asymm
-
-protected theorem lt_of_le_ne {x y : BitVec n} : x ≤ y → ¬ x = y → x < y := by
-  simp only [lt_def, le_def, BitVec.toNat_eq]
-  apply Nat.lt_of_le_of_ne
-
-protected theorem ne_of_lt {x y : BitVec n} : x < y → x ≠ y := by
-  simp only [lt_def, ne_eq, toNat_eq]
-  apply Nat.ne_of_lt
-
-protected theorem umod_lt (x : BitVec n) {y : BitVec n} : 0 < y → x.umod y < y := by
-  simp only [ofNat_eq_ofNat, lt_def, toNat_ofNat, Nat.zero_mod, umod, toNat_ofNatLt]
-  apply Nat.mod_lt
+protected theorem lt_of_le_ne (x y : BitVec n) (h1 : x <= y) (h2 : ¬ x = y) : x < y := by
+  revert h1 h2
+  let ⟨x, lt⟩ := x
+  let ⟨y, lt⟩ := y
+  simp
+  exact Nat.lt_of_le_of_ne
 
 /-! ### ofBoolList -/
 
@@ -1977,18 +1876,18 @@ theorem twoPow_zero {w : Nat} : twoPow w 0 = 1#w := by
 theorem getLsbD_one {w i : Nat} : (1#w).getLsbD i = (decide (0 < w) && decide (0 = i)) := by
   rw [← twoPow_zero, getLsbD_twoPow]
 
-/- ### setWidth, setWidth, and bitwise operations -/
+/- ### zeroExtend, truncate, and bitwise operations -/
 
 /--
 When the `(i+1)`th bit of `x` is false,
 keeping the lower `(i + 1)` bits of `x` equals keeping the lower `i` bits.
 -/
-theorem setWidth_setWidth_succ_eq_setWidth_setWidth_of_getLsbD_false
+theorem zeroExtend_truncate_succ_eq_zeroExtend_truncate_of_getLsbD_false
   {x : BitVec w} {i : Nat} (hx : x.getLsbD i = false) :
-    setWidth w (x.setWidth (i + 1)) =
-      setWidth w (x.setWidth i) := by
+    zeroExtend w (x.truncate (i + 1)) =
+      zeroExtend w (x.truncate i) := by
   ext k
-  simp only [getLsbD_setWidth, Fin.is_lt, decide_True, Bool.true_and, getLsbD_or, getLsbD_and]
+  simp only [getLsbD_zeroExtend, Fin.is_lt, decide_True, Bool.true_and, getLsbD_or, getLsbD_and]
   by_cases hik : i = k
   · subst hik
     simp [hx]
@@ -1999,22 +1898,22 @@ When the `(i+1)`th bit of `x` is true,
 keeping the lower `(i + 1)` bits of `x` equalsk eeping the lower `i` bits
 and then performing bitwise-or with `twoPow i = (1 << i)`,
 -/
-theorem setWidth_setWidth_succ_eq_setWidth_setWidth_or_twoPow_of_getLsbD_true
+theorem zeroExtend_truncate_succ_eq_zeroExtend_truncate_or_twoPow_of_getLsbD_true
     {x : BitVec w} {i : Nat} (hx : x.getLsbD i = true) :
-    setWidth w (x.setWidth (i + 1)) =
-      setWidth w (x.setWidth i) ||| (twoPow w i) := by
+    zeroExtend w (x.truncate (i + 1)) =
+      zeroExtend w (x.truncate i) ||| (twoPow w i) := by
   ext k
-  simp only [getLsbD_setWidth, Fin.is_lt, decide_True, Bool.true_and, getLsbD_or, getLsbD_and]
+  simp only [getLsbD_zeroExtend, Fin.is_lt, decide_True, Bool.true_and, getLsbD_or, getLsbD_and]
   by_cases hik : i = k
   · subst hik
     simp [hx]
   · by_cases hik' : k < i + 1 <;> simp [hik, hik'] <;> omega
 
 /-- Bitwise and of `(x : BitVec w)` with `1#w` equals zero extending `x.lsb` to `w`. -/
-theorem and_one_eq_setWidth_ofBool_getLsbD {x : BitVec w} :
-    (x &&& 1#w) = setWidth w (ofBool (x.getLsbD 0)) := by
+theorem and_one_eq_zeroExtend_ofBool_getLsbD {x : BitVec w} :
+    (x &&& 1#w) = zeroExtend w (ofBool (x.getLsbD 0)) := by
   ext i
-  simp only [getLsbD_and, getLsbD_one, getLsbD_setWidth, Fin.is_lt, decide_True, getLsbD_ofBool,
+  simp only [getLsbD_and, getLsbD_one, getLsbD_zeroExtend, Fin.is_lt, decide_True, getLsbD_ofBool,
     Bool.true_and]
   by_cases h : (0 = (i : Nat)) <;> simp [h] <;> omega
 
@@ -2110,159 +2009,4 @@ theorem getLsbD_intMax (w : Nat) : (intMax w).getLsbD i = decide (i + 1 < w) :=
   · simp [h]
   · rw [Nat.sub_add_cancel (Nat.two_pow_pos (w - 1)), Nat.two_pow_pred_mod_two_pow (by omega)]
 
-
-/-! ### Non-overflow theorems -/
-
-/--
-If `y ≤ x`, then the subtraction `(x - y)` does not overflow.
-Thus, `(x - y).toNat = x.toNat - y.toNat`
--/
-theorem toNat_sub_of_le {x y : BitVec n} (h : y ≤ x) :
-    (x - y).toNat = x.toNat - y.toNat := by
-  simp only [toNat_sub]
-  rw [BitVec.le_def] at h
-  by_cases h' : x.toNat = y.toNat
-  · rw [h', Nat.sub_self, Nat.sub_add_cancel (by omega), Nat.mod_self]
-  · have : 2 ^ n - y.toNat + x.toNat = 2 ^ n + (x.toNat - y.toNat) := by omega
-    rw [this, Nat.add_mod_left, Nat.mod_eq_of_lt (by omega)]
-
-/-! ### Deprecations -/
-
-set_option linter.missingDocs false
-
-@[deprecated truncate_eq_setWidth (since := "2024-09-18")]
-abbrev truncate_eq_zeroExtend := @truncate_eq_setWidth
-
-@[deprecated toNat_setWidth' (since := "2024-09-18")]
-abbrev toNat_zeroExtend' := @toNat_setWidth'
-
-@[deprecated toNat_setWidth (since := "2024-09-18")]
-abbrev toNat_zeroExtend := @toNat_setWidth
-
-@[deprecated toNat_setWidth (since := "2024-09-18")]
-abbrev toNat_truncate := @toNat_setWidth
-
-@[deprecated setWidth_eq (since := "2024-09-18")]
-abbrev zeroExtend_eq := @setWidth_eq
-
-@[deprecated setWidth_eq (since := "2024-09-18")]
-abbrev truncate_eq := @setWidth_eq
-
-@[deprecated setWidth_zero (since := "2024-09-18")]
-abbrev zeroExtend_zero := @setWidth_zero
-
-@[deprecated getElem_setWidth (since := "2024-09-18")]
-abbrev getElem_zeroExtend := @getElem_setWidth
-
-@[deprecated getElem_setWidth' (since := "2024-09-18")]
-abbrev getElem_zeroExtend' := @getElem_setWidth'
-
-@[deprecated getElem?_setWidth (since := "2024-09-18")]
-abbrev getElem?_zeroExtend := @getElem?_setWidth
-
-@[deprecated getElem?_setWidth' (since := "2024-09-18")]
-abbrev getElem?_zeroExtend' := @getElem?_setWidth'
-
-@[deprecated getLsbD_setWidth (since := "2024-09-18")]
-abbrev getLsbD_zeroExtend := @getLsbD_setWidth
-
-@[deprecated getLsbD_setWidth' (since := "2024-09-18")]
-abbrev getLsbD_zeroExtend' := @getLsbD_setWidth'
-
-@[deprecated getMsbD_setWidth_add (since := "2024-09-18")]
-abbrev getMsbD_zeroExtend_add := @getMsbD_setWidth_add
-
-@[deprecated getMsbD_setWidth' (since := "2024-09-18")]
-abbrev getMsbD_zeroExtend' := @getMsbD_setWidth'
-
-@[deprecated getElem_setWidth (since := "2024-09-18")]
-abbrev getElem_truncate := @getElem_setWidth
-
-@[deprecated getElem?_setWidth (since := "2024-09-18")]
-abbrev getElem?_truncate := @getElem?_setWidth
-
-@[deprecated getLsbD_setWidth (since := "2024-09-18")]
-abbrev getLsbD_truncate := @getLsbD_setWidth
-
-@[deprecated msb_setWidth (since := "2024-09-18")]
-abbrev msb_truncate := @msb_setWidth
-
-@[deprecated cast_setWidth (since := "2024-09-18")]
-abbrev cast_zeroExtend := @cast_setWidth
-
-@[deprecated cast_setWidth (since := "2024-09-18")]
-abbrev cast_truncate := @cast_setWidth
-
-@[deprecated setWidth_setWidth_of_le (since := "2024-09-18")]
-abbrev zeroExtend_zeroExtend_of_le := @setWidth_setWidth_of_le
-
-@[deprecated setWidth_eq (since := "2024-09-18")]
-abbrev truncate_eq_self := @setWidth_eq
-
-@[deprecated setWidth_cast (since := "2024-09-18")]
-abbrev truncate_cast := @setWidth_cast
-
-@[deprecated msb_setWidth (since := "2024-09-18")]
-abbrev mbs_zeroExtend := @msb_setWidth
-
-@[deprecated msb_setWidth' (since := "2024-09-18")]
-abbrev mbs_zeroExtend' := @msb_setWidth'
-
-@[deprecated setWidth_one_eq_ofBool_getLsb_zero (since := "2024-09-18")]
-abbrev zeroExtend_one_eq_ofBool_getLsb_zero := @setWidth_one_eq_ofBool_getLsb_zero
-
-@[deprecated setWidth_ofNat_one_eq_ofNat_one_of_lt (since := "2024-09-18")]
-abbrev zeroExtend_ofNat_one_eq_ofNat_one_of_lt := @setWidth_ofNat_one_eq_ofNat_one_of_lt
-
-@[deprecated setWidth_one (since := "2024-09-18")]
-abbrev truncate_one := @setWidth_one
-
-@[deprecated setWidth_ofNat_of_le (since := "2024-09-18")]
-abbrev truncate_ofNat_of_le := @setWidth_ofNat_of_le
-
-@[deprecated setWidth_or (since := "2024-09-18")]
-abbrev truncate_or := @setWidth_or
-
-@[deprecated setWidth_and (since := "2024-09-18")]
-abbrev truncate_and := @setWidth_and
-
-@[deprecated setWidth_xor (since := "2024-09-18")]
-abbrev truncate_xor := @setWidth_xor
-
-@[deprecated setWidth_not (since := "2024-09-18")]
-abbrev truncate_not := @setWidth_not
-
-@[deprecated signExtend_eq_not_setWidth_not_of_msb_false  (since := "2024-09-18")]
-abbrev signExtend_eq_not_zeroExtend_not_of_msb_false  := @signExtend_eq_not_setWidth_not_of_msb_false
-
-@[deprecated signExtend_eq_not_setWidth_not_of_msb_true (since := "2024-09-18")]
-abbrev signExtend_eq_not_zeroExtend_not_of_msb_true := @signExtend_eq_not_setWidth_not_of_msb_true
-
-@[deprecated signExtend_eq_setWidth_of_lt (since := "2024-09-18")]
-abbrev signExtend_eq_truncate_of_lt := @signExtend_eq_setWidth_of_lt
-
-@[deprecated truncate_append (since := "2024-09-18")]
-abbrev truncate_append := @setWidth_append
-
-@[deprecated truncate_append_of_eq (since := "2024-09-18")]
-abbrev truncate_append_of_eq := @setWidth_append_of_eq
-
-@[deprecated truncate_cons (since := "2024-09-18")]
-abbrev truncate_cons := @setWidth_cons
-
-@[deprecated truncate_succ (since := "2024-09-18")]
-abbrev truncate_succ := @setWidth_succ
-
-@[deprecated truncate_add (since := "2024-09-18")]
-abbrev truncate_add := @setWidth_add
-
-@[deprecated setWidth_setWidth_succ_eq_setWidth_setWidth_of_getLsbD_false (since := "2024-09-18")]
-abbrev zeroExtend_truncate_succ_eq_zeroExtend_truncate_of_getLsbD_false := @setWidth_setWidth_succ_eq_setWidth_setWidth_of_getLsbD_false
-
-@[deprecated setWidth_setWidth_succ_eq_setWidth_setWidth_or_twoPow_of_getLsbD_true (since := "2024-09-18")]
-abbrev zeroExtend_truncate_succ_eq_zeroExtend_truncate_or_twoPow_of_getLsbD_true := @setWidth_setWidth_succ_eq_setWidth_setWidth_or_twoPow_of_getLsbD_true
-
-@[deprecated and_one_eq_setWidth_ofBool_getLsbD (since := "2024-09-18")]
-abbrev and_one_eq_zeroExtend_ofBool_getLsbD := @and_one_eq_setWidth_ofBool_getLsbD
-
 end BitVec

src/Init/Data/Bool.lean

@@ -6,13 +6,16 @@ Authors: F. G. Dorais
 prelude
 import Init.NotationExtra
 
-
-namespace Bool
-
 /-- Boolean exclusive or -/
 abbrev xor : Bool → Bool → Bool := bne
 
-@[inherit_doc] infixl:33 " ^^ " => xor
+namespace Bool
+
+/- Namespaced versions that can be used instead of prefixing `_root_` -/
+@[inherit_doc not] protected abbrev not := not
+@[inherit_doc or]  protected abbrev or  := or
+@[inherit_doc and] protected abbrev and := and
+@[inherit_doc xor] protected abbrev xor := xor
 
 instance (p : Bool → Prop) [inst : DecidablePred p] : Decidable (∀ x, p x) :=
   match inst true, inst false with
@@ -147,8 +150,8 @@ theorem and_or_distrib_right : ∀ (x y z : Bool), ((x || y) && z) = (x && z ||
 theorem or_and_distrib_left  : ∀ (x y z : Bool), (x || y && z) = ((x || y) && (x || z)) := by decide
 theorem or_and_distrib_right : ∀ (x y z : Bool), (x && y || z) = ((x || z) && (y || z)) := by decide
 
-theorem and_xor_distrib_left  : ∀ (x y z : Bool), (x && (y ^^ z)) = ((x && y) ^^ (x && z)) := by decide
-theorem and_xor_distrib_right : ∀ (x y z : Bool), ((x ^^ y) && z) = ((x && z) ^^ (y && z)) := by decide
+theorem and_xor_distrib_left  : ∀ (x y z : Bool), (x && xor y z) = xor (x && y) (x && z) := by decide
+theorem and_xor_distrib_right : ∀ (x y z : Bool), (xor x y && z) = xor (x && z) (y && z) := by decide
 
 /-- De Morgan's law for boolean and -/
 @[simp] theorem not_and : ∀ (x y : Bool), (!(x && y)) = (!x || !y) := by decide
@@ -254,6 +257,15 @@ theorem beq_eq_decide_eq [BEq α] [LawfulBEq α] [DecidableEq α] (a b : α) :
 theorem eq_not : ∀ {a b : Bool}, (a = (!b)) ↔ (a ≠ b) := by decide
 theorem not_eq : ∀ {a b : Bool}, ((!a) = b) ↔ (a ≠ b) := by decide
 
+@[simp] theorem not_eq_not : ∀ {a b : Bool}, ¬a = !b ↔ a = b := by decide
+@[simp] theorem not_not_eq : ∀ {a b : Bool}, ¬(!a) = b ↔ a = b := by decide
+
+/--
+We move `!` from the left hand side of an equality to the right hand side.
+This helps confluence, and also helps combining pairs of `!`s.
+-/
+@[simp] theorem not_eq_eq_eq_not : ∀ {a b : Bool}, ((!a) = b) ↔ (a = !b) := by decide
+
 @[simp] theorem coe_iff_coe : ∀{a b : Bool}, (a ↔ b) ↔ a = b := by decide
 
 @[simp] theorem coe_true_iff_false  : ∀{a b : Bool}, (a ↔ b = false) ↔ a = (!b) := by decide
@@ -267,37 +279,37 @@ theorem beq_comm {α} [BEq α] [LawfulBEq α] {a b : α} : (a == b) = (b == a) :
 
 /-! ### xor -/
 
-theorem false_xor : ∀ (x : Bool), (false ^^ x) = x := false_bne
+theorem false_xor : ∀ (x : Bool), xor false x = x := false_bne
 
-theorem xor_false : ∀ (x : Bool), (x ^^ false) = x := bne_false
+theorem xor_false : ∀ (x : Bool), xor x false = x := bne_false
 
-theorem true_xor : ∀ (x : Bool), (true ^^ x) = !x := true_bne
+theorem true_xor : ∀ (x : Bool), xor true x = !x := true_bne
 
-theorem xor_true : ∀ (x : Bool), (x ^^ true) = !x := bne_true
+theorem xor_true : ∀ (x : Bool), xor x true = !x := bne_true
 
-theorem not_xor_self : ∀ (x : Bool), (!x ^^ x) = true := not_bne_self
+theorem not_xor_self : ∀ (x : Bool), xor (!x) x = true := not_bne_self
 
-theorem xor_not_self : ∀ (x : Bool), (x ^^ !x) = true := bne_not_self
+theorem xor_not_self : ∀ (x : Bool), xor x (!x) = true := bne_not_self
 
-theorem not_xor : ∀ (x y : Bool), (!x ^^ y) = !(x ^^ y) := by decide
+theorem not_xor : ∀ (x y : Bool), xor (!x) y = !(xor x y) := by decide
 
-theorem xor_not : ∀ (x y : Bool), (x ^^ !y) = !(x ^^ y) := by decide
+theorem xor_not : ∀ (x y : Bool), xor x (!y) = !(xor x y) := by decide
 
-theorem not_xor_not : ∀ (x y : Bool), (!x ^^ !y) = (x ^^ y) := not_bne_not
+theorem not_xor_not : ∀ (x y : Bool), xor (!x) (!y) = (xor x y) := not_bne_not
 
-theorem xor_self : ∀ (x : Bool), (x ^^ x) = false := by decide
+theorem xor_self : ∀ (x : Bool), xor x x = false := by decide
 
-theorem xor_comm : ∀ (x y : Bool), (x ^^ y) = (y ^^ x) := by decide
+theorem xor_comm : ∀ (x y : Bool), xor x y = xor y x := by decide
 
-theorem xor_left_comm : ∀ (x y z : Bool), (x ^^ (y ^^ z)) = (y ^^ (x ^^ z)) := by decide
+theorem xor_left_comm : ∀ (x y z : Bool), xor x (xor y z) = xor y (xor x z) := by decide
 
-theorem xor_right_comm : ∀ (x y z : Bool), ((x ^^ y) ^^ z) = ((x ^^ z) ^^ y) := by decide
+theorem xor_right_comm : ∀ (x y z : Bool), xor (xor x y) z = xor (xor x z) y := by decide
 
-theorem xor_assoc : ∀ (x y z : Bool), ((x ^^ y) ^^ z) = (x ^^ (y ^^ z)) := bne_assoc
+theorem xor_assoc : ∀ (x y z : Bool), xor (xor x y) z = xor x (xor y z) := bne_assoc
 
-theorem xor_left_inj : ∀ {x y z : Bool}, (x ^^ y) = (x ^^ z) ↔ y = z := bne_left_inj
+theorem xor_left_inj : ∀ {x y z : Bool}, xor x y = xor x z ↔ y = z := bne_left_inj
 
-theorem xor_right_inj : ∀ {x y z : Bool}, (x ^^ z) = (y ^^ z) ↔ x = y := bne_right_inj
+theorem xor_right_inj : ∀ {x y z : Bool}, xor x z = xor y z ↔ x = y := bne_right_inj
 
 /-! ### le/lt -/
 
@@ -585,7 +597,7 @@ theorem decide_beq_decide (p q : Prop) [dpq : Decidable (p ↔ q)] [dp : Decidab
 
 end Bool
 
-export Bool (cond_eq_if xor and or not)
+export Bool (cond_eq_if)
 
 /-! ### decide -/
 

src/Init/Data/Fin/Basic.lean

@@ -31,7 +31,7 @@ This differs from addition, which wraps around:
 (2 : Fin 3) + 1 = (0 : Fin 3)
 ```
 -/
-def succ : Fin n → Fin (n + 1)
+def succ : Fin n → Fin n.succ
   | ⟨i, h⟩ => ⟨i+1, Nat.succ_lt_succ h⟩
 
 variable {n : Nat}
@@ -39,20 +39,16 @@ variable {n : Nat}
 /--
 Returns `a` modulo `n + 1` as a `Fin n.succ`.
 -/
-protected def ofNat {n : Nat} (a : Nat) : Fin (n + 1) :=
+protected def ofNat {n : Nat} (a : Nat) : Fin n.succ :=
   ⟨a % (n+1), Nat.mod_lt _ (Nat.zero_lt_succ _)⟩
 
 /--
 Returns `a` modulo `n` as a `Fin n`.
 
-The assumption `NeZero n` ensures that `Fin n` is nonempty.
+The assumption `n > 0` ensures that `Fin n` is nonempty.
 -/
-protected def ofNat' (n : Nat) [NeZero n] (a : Nat) : Fin n :=
-  ⟨a % n, Nat.mod_lt _ (pos_of_neZero n)⟩
-
--- We intend to deprecate `Fin.ofNat` in favor of `Fin.ofNat'` (and later rename).
--- This is waiting on https://github.com/leanprover/lean4/pull/5323
--- attribute [deprecated Fin.ofNat' (since := "2024-09-16")] Fin.ofNat
+protected def ofNat' {n : Nat} (a : Nat) (h : n > 0) : Fin n :=
+  ⟨a % n, Nat.mod_lt _ h⟩
 
 private theorem mlt {b : Nat} : {a : Nat} → a < n → b % n < n
   | 0,   h => Nat.mod_lt _ h
@@ -145,10 +141,10 @@ instance : ShiftLeft (Fin n) where
 instance : ShiftRight (Fin n) where
   shiftRight := Fin.shiftRight
 
-instance instOfNat {n : Nat} [NeZero n] {i : Nat} : OfNat (Fin n) i where
-  ofNat := Fin.ofNat' n i
+instance instOfNat : OfNat (Fin (no_index (n+1))) i where
+  ofNat := Fin.ofNat i
 
-instance instInhabited {n : Nat} [NeZero n] : Inhabited (Fin n) where
+instance : Inhabited (Fin (no_index (n+1))) where
   default := 0
 
 @[simp] theorem zero_eta : (⟨0, Nat.zero_lt_succ _⟩ : Fin (n + 1)) = 0 := rfl

src/Init/Data/Fin/Lemmas.lean

@@ -51,15 +51,10 @@ theorem eq_mk_iff_val_eq {a : Fin n} {k : Nat} {hk : k < n} :
 
 theorem mk_val (i : Fin n) : (⟨i, i.isLt⟩ : Fin n) = i := Fin.eta ..
 
-@[simp] theorem val_ofNat' (n : Nat) [NeZero n] (a : Nat) :
-  (Fin.ofNat' n a).val = a % n := rfl
+@[simp] theorem val_ofNat' (a : Nat) (is_pos : n > 0) :
+  (Fin.ofNat' a is_pos).val = a % n := rfl
 
-@[simp] theorem ofNat'_self {n : Nat} [NeZero n] : Fin.ofNat' n n = 0 := by
-  ext
-  simp
-  congr
-
-@[simp] theorem ofNat'_val_eq_self [NeZero n] (x : Fin n) : (Fin.ofNat' n x) = x := by
+@[simp] theorem ofNat'_val_eq_self (x : Fin n) (h) : (Fin.ofNat' x h) = x := by
   ext
   rw [val_ofNat', Nat.mod_eq_of_lt]
   exact x.2
@@ -73,9 +68,6 @@ theorem mk_val (i : Fin n) : (⟨i, i.isLt⟩ : Fin n) = i := Fin.eta ..
 @[simp] theorem modn_val (a : Fin n) (b : Nat) : (a.modn b).val = a.val % b :=
   rfl
 
-@[simp] theorem val_eq_zero (a : Fin 1) : a.val = 0 :=
-  Nat.eq_zero_of_le_zero <| Nat.le_of_lt_succ a.isLt
-
 theorem ite_val {n : Nat} {c : Prop} [Decidable c] {x : c → Fin n} (y : ¬c → Fin n) :
     (if h : c then x h else y h).val = if h : c then (x h).val else (y h).val := by
   by_cases c <;> simp [*]
@@ -128,7 +120,7 @@ theorem mk_le_of_le_val {b : Fin n} {a : Nat} (h : a ≤ b) :
 
 @[simp] theorem mk_lt_mk {x y : Nat} {hx hy} : (⟨x, hx⟩ : Fin n) < ⟨y, hy⟩ ↔ x < y := .rfl
 
-@[simp] theorem val_zero (n : Nat) [NeZero n] : ((0 : Fin n) : Nat) = 0 := rfl
+@[simp] theorem val_zero (n : Nat) : (0 : Fin (n + 1)).1 = 0 := rfl
 
 @[simp] theorem mk_zero : (⟨0, Nat.succ_pos n⟩ : Fin (n + 1)) = 0 := rfl
 
@@ -175,24 +167,8 @@ theorem rev_eq {n a : Nat} (i : Fin (n + 1)) (h : n = a + i) :
 @[simp] theorem rev_lt_rev {i j : Fin n} : rev i < rev j ↔ j < i := by
   rw [← Fin.not_le, ← Fin.not_le, rev_le_rev]
 
-/-! ### last -/
-
 @[simp] theorem val_last (n : Nat) : last n = n := rfl
 
-@[simp] theorem last_zero : (Fin.last 0 : Fin 1) = 0 := by
-  ext
-  simp
-
-@[simp] theorem zero_eq_last_iff {n : Nat} : (0 : Fin (n + 1)) = last n ↔ n = 0 := by
-  constructor
-  · intro h
-    simp_all [Fin.ext_iff]
-  · rintro rfl
-    simp
-
-@[simp] theorem last_eq_zero_iff {n : Nat} : Fin.last n = 0 ↔ n = 0 := by
-  simp [eq_comm (a := Fin.last n)]
-
 theorem le_last (i : Fin (n + 1)) : i ≤ last n := Nat.le_of_lt_succ i.is_lt
 
 theorem last_pos : (0 : Fin (n + 2)) < last (n + 1) := Nat.succ_pos _
@@ -226,28 +202,10 @@ instance subsingleton_one : Subsingleton (Fin 1) := subsingleton_iff_le_one.2 (b
 
 theorem fin_one_eq_zero (a : Fin 1) : a = 0 := Subsingleton.elim a 0
 
-@[simp] theorem zero_eq_one_iff {n : Nat} [NeZero n] : (0 : Fin n) = 1 ↔ n = 1 := by
-  constructor
-  · intro h
-    simp [Fin.ext_iff] at h
-    change 0 % n = 1 % n at h
-    rw [eq_comm] at h
-    simpa using h
-  · rintro rfl
-    simp
-
-@[simp] theorem one_eq_zero_iff {n : Nat} [NeZero n] : (1 : Fin n) = 0 ↔ n = 1 := by
-  rw [eq_comm]
-  simp
-
 theorem add_def (a b : Fin n) : a + b = Fin.mk ((a + b) % n) (Nat.mod_lt _ a.size_pos) := rfl
 
 theorem val_add (a b : Fin n) : (a + b).val = (a.val + b.val) % n := rfl
 
-@[simp] protected theorem zero_add {n : Nat} [NeZero n] (i : Fin n) : (0 : Fin n) + i = i := by
-  ext
-  simp [Fin.add_def, Nat.mod_eq_of_lt i.2]
-
 theorem val_add_one_of_lt {n : Nat} {i : Fin n.succ} (h : i < last _) : (i + 1).1 = i + 1 := by
   match n with
   | 0 => cases h
@@ -371,10 +329,6 @@ theorem succ_succ_ne_one (a : Fin n) : Fin.succ (Fin.succ a) ≠ 1 :=
 
 @[simp] theorem cast_mk (h : n = m) (i : Nat) (hn : i < n) : cast h ⟨i, hn⟩ = ⟨i, h ▸ hn⟩ := rfl
 
-@[simp] theorem cast_refl (n : Nat) (h : n = n) : cast h = id := by
-  ext
-  simp
-
 @[simp] theorem cast_trans {k : Nat} (h : n = m) (h' : m = k) {i : Fin n} :
     cast h' (cast h i) = cast (Eq.trans h h') i := rfl
 
@@ -483,10 +437,6 @@ theorem succ_castSucc {n : Nat} (i : Fin n) : i.castSucc.succ = castSucc i.succ
 
 @[simp] theorem coe_addNat (m : Nat) (i : Fin n) : (addNat i m : Nat) = i + m := rfl
 
-@[simp] theorem addNat_zero (n : Nat) (i : Fin n) : addNat i 0 = i := by
-  ext
-  simp
-
 @[simp] theorem addNat_one {i : Fin n} : addNat i 1 = i.succ := rfl
 
 theorem le_coe_addNat (m : Nat) (i : Fin n) : m ≤ addNat i m :=
@@ -516,7 +466,7 @@ theorem cast_addNat_left {n n' m : Nat} (i : Fin n') (h : n' + m = n + m) :
 
 theorem le_coe_natAdd (m : Nat) (i : Fin n) : m ≤ natAdd m i := Nat.le_add_right ..
 
-@[simp] theorem natAdd_zero {n : Nat} : natAdd 0 = cast (Nat.zero_add n).symm := by ext; simp
+theorem natAdd_zero {n : Nat} : natAdd 0 = cast (Nat.zero_add n).symm := by ext; simp
 
 /-- For rewriting in the reverse direction, see `Fin.cast_natAdd_right`. -/
 theorem natAdd_cast {n n' : Nat} (m : Nat) (i : Fin n') (h : n' = n) :
@@ -554,19 +504,9 @@ theorem cast_addNat {n : Nat} (m : Nat) (i : Fin n) :
 
 @[simp] theorem natAdd_last {m n : Nat} : natAdd n (last m) = last (n + m) := rfl
 
-@[simp] theorem addNat_last (n : Nat) :
-    addNat (last n) m = cast (by omega) (last (n + m)) := by
-  ext
-  simp
-
 theorem natAdd_castSucc {m n : Nat} {i : Fin m} : natAdd n (castSucc i) = castSucc (natAdd n i) :=
   rfl
 
-@[simp] theorem natAdd_eq_addNat (n : Nat) (i : Fin n) : Fin.natAdd n i = i.addNat n := by
-  ext
-  simp
-  omega
-
 theorem rev_castAdd (k : Fin n) (m : Nat) : rev (castAdd m k) = addNat (rev k) m := Fin.ext <| by
   rw [val_rev, coe_castAdd, coe_addNat, val_rev, Nat.sub_add_comm (Nat.succ_le_of_lt k.is_lt)]
 
@@ -632,15 +572,6 @@ theorem pred_add_one (i : Fin (n + 2)) (h : (i : Nat) < n + 1) :
 @[simp] theorem subNat_mk {i : Nat} (h₁ : i < n + m) (h₂ : m ≤ i) :
     subNat m ⟨i, h₁⟩ h₂ = ⟨i - m, Nat.sub_lt_right_of_lt_add h₂ h₁⟩ := rfl
 
-@[simp] theorem subNat_zero (i : Fin n) (h : 0 ≤ (i : Nat)): Fin.subNat 0 i h = i := by
-  ext
-  simp
-
-@[simp] theorem subNat_one_succ (i : Fin (n + 1)) (h : 1 ≤ ↑i) : (subNat 1 i h).succ = i := by
-  ext
-  simp
-  omega
-
 @[simp] theorem pred_castSucc_succ (i : Fin n) :
     pred (castSucc i.succ) (Fin.ne_of_gt (castSucc_pos i.succ_pos)) = castSucc i := rfl
 
@@ -651,7 +582,7 @@ theorem pred_add_one (i : Fin (n + 2)) (h : (i : Nat) < n + 1) :
     subNat m (addNat i m) h = i := Fin.ext <| Nat.add_sub_cancel i m
 
 @[simp] theorem natAdd_subNat_cast {i : Fin (n + m)} (h : n ≤ i) :
-    natAdd n (subNat n (cast (Nat.add_comm ..) i) h) = i := by simp [← cast_addNat]
+    natAdd n (subNat n (cast (Nat.add_comm ..) i) h) = i := by simp [← cast_addNat]; rfl
 
 /-! ### recursion and induction principles -/
 
@@ -819,13 +750,13 @@ theorem addCases_right {m n : Nat} {motive : Fin (m + n) → Sort _} {left right
 
 /-! ### add -/
 
-theorem ofNat'_add [NeZero n] (x : Nat) (y : Fin n) :
-    Fin.ofNat' n x + y = Fin.ofNat' n (x + y.val) := by
+@[simp] theorem ofNat'_add (x : Nat) (lt : 0 < n) (y : Fin n) :
+    Fin.ofNat' x lt + y = Fin.ofNat' (x + y.val) lt := by
   apply Fin.eq_of_val_eq
   simp [Fin.ofNat', Fin.add_def]
 
-theorem add_ofNat' [NeZero n] (x : Fin n) (y : Nat) :
-    x + Fin.ofNat' n y = Fin.ofNat' n (x.val + y) := by
+@[simp] theorem add_ofNat' (x : Fin n) (y : Nat) (lt : 0 < n) :
+    x + Fin.ofNat' y lt = Fin.ofNat' (x.val + y) lt := by
   apply Fin.eq_of_val_eq
   simp [Fin.ofNat', Fin.add_def]
 
@@ -834,21 +765,16 @@ theorem add_ofNat' [NeZero n] (x : Fin n) (y : Nat) :
 protected theorem coe_sub (a b : Fin n) : ((a - b : Fin n) : Nat) = ((n - b) + a) % n := by
   cases a; cases b; rfl
 
-theorem ofNat'_sub [NeZero n] (x : Nat) (y : Fin n) :
-    Fin.ofNat' n x - y = Fin.ofNat' n ((n - y.val) + x) := by
+@[simp] theorem ofNat'_sub (x : Nat) (lt : 0 < n) (y : Fin n) :
+    Fin.ofNat' x lt - y = Fin.ofNat' ((n - y.val) + x) lt := by
   apply Fin.eq_of_val_eq
   simp [Fin.ofNat', Fin.sub_def]
 
-theorem sub_ofNat' [NeZero n] (x : Fin n) (y : Nat) :
-    x - Fin.ofNat' n y = Fin.ofNat' n ((n - y % n) + x.val) := by
+@[simp] theorem sub_ofNat' (x : Fin n) (y : Nat) (lt : 0 < n) :
+    x - Fin.ofNat' y lt = Fin.ofNat' ((n - y % n) + x.val) lt := by
   apply Fin.eq_of_val_eq
   simp [Fin.ofNat', Fin.sub_def]
 
-@[simp] protected theorem sub_self [NeZero n] {x : Fin n} : x - x = 0 := by
-  ext
-  rw [Fin.sub_def]
-  simp
-
 private theorem _root_.Nat.mod_eq_sub_of_lt_two_mul {x n} (h₁ : n ≤ x) (h₂ : x < 2 * n) :
     x % n = x - n := by
   rw [Nat.mod_eq, if_pos (by omega), Nat.mod_eq_of_lt (by omega)]

src/Init/Data/Int/DivMod.lean

@@ -16,99 +16,83 @@ There are three main conventions for integer division,
 referred here as the E, F, T rounding conventions.
 All three pairs satisfy the identity `x % y + (x / y) * y = x` unconditionally,
 and satisfy `x / 0 = 0` and `x % 0 = x`.
-
-### Historical notes
-In early versions of Lean, the typeclasses provided by `/` and `%`
-were defined in terms of `tdiv` and `tmod`, and these were named simply as `div` and `mod`.
-
-However we decided it was better to use `ediv` and `emod`,
-as they are consistent with the conventions used in SMTLib, and Mathlib,
-and often mathematical reasoning is easier with these conventions.
-
-At that time, we did not rename `div` and `mod` to `tdiv` and `tmod` (along with all their lemma).
-In September 2024, we decided to do this rename (with deprecations in place),
-and later we intend to rename `ediv` and `emod` to `div` and `mod`, as nearly all users will only
-ever need to use these functions and their associated lemmas.
 -/
 
 /-! ### T-rounding division -/
 
 /--
-`tdiv` uses the [*"T-rounding"*][t-rounding]
+`div` uses the [*"T-rounding"*][t-rounding]
 (**T**runcation-rounding) convention, meaning that it rounds toward
 zero. Also note that division by zero is defined to equal zero.
 
   The relation between integer division and modulo is found in
-  `Int.tmod_add_tdiv` which states that
-  `tmod a b + b * (tdiv a b) = a`, unconditionally.
+  `Int.mod_add_div` which states that
+  `a % b + b * (a / b) = a`, unconditionally.
 
-  [t-rounding]: https://dl.acm.org/doi/pdf/10.1145/128861.128862
-  [theo tmod_add_tdiv]: https://leanprover-community.github.io/mathlib4_docs/find/?pattern=Int.tmod_add_tdiv#doc
+  [t-rounding]: https://dl.acm.org/doi/pdf/10.1145/128861.128862 [theo
+  mod_add_div]:
+  https://leanprover-community.github.io/mathlib4_docs/find/?pattern=Int.mod_add_div#doc
 
   Examples:
 
   ```
-  #eval (7 : Int).tdiv (0 : Int) -- 0
-  #eval (0 : Int).tdiv (7 : Int) -- 0
+  #eval (7 : Int).div (0 : Int) -- 0
+  #eval (0 : Int).div (7 : Int) -- 0
 
-  #eval (12 : Int).tdiv (6 : Int) -- 2
-  #eval (12 : Int).tdiv (-6 : Int) -- -2
-  #eval (-12 : Int).tdiv (6 : Int) -- -2
-  #eval (-12 : Int).tdiv (-6 : Int) -- 2
+  #eval (12 : Int).div (6 : Int) -- 2
+  #eval (12 : Int).div (-6 : Int) -- -2
+  #eval (-12 : Int).div (6 : Int) -- -2
+  #eval (-12 : Int).div (-6 : Int) -- 2
 
-  #eval (12 : Int).tdiv (7 : Int) -- 1
-  #eval (12 : Int).tdiv (-7 : Int) -- -1
-  #eval (-12 : Int).tdiv (7 : Int) -- -1
-  #eval (-12 : Int).tdiv (-7 : Int) -- 1
+  #eval (12 : Int).div (7 : Int) -- 1
+  #eval (12 : Int).div (-7 : Int) -- -1
+  #eval (-12 : Int).div (7 : Int) -- -1
+  #eval (-12 : Int).div (-7 : Int) -- 1
   ```
 
   Implemented by efficient native code.
 -/
 @[extern "lean_int_div"]
-def tdiv : (@& Int) → (@& Int) → Int
+def div : (@& Int) → (@& Int) → Int
   | ofNat m, ofNat n =>  ofNat (m / n)
   | ofNat m, -[n +1] => -ofNat (m / succ n)
   | -[m +1], ofNat n => -ofNat (succ m / n)
   | -[m +1], -[n +1] =>  ofNat (succ m / succ n)
 
-@[deprecated tdiv (since := "2024-09-11")] abbrev div := tdiv
-
 /-- Integer modulo. This function uses the
   [*"T-rounding"*][t-rounding] (**T**runcation-rounding) convention
-  to pair with `Int.tdiv`, meaning that `tmod a b + b * (tdiv a b) = a`
-  unconditionally (see [`Int.tmod_add_tdiv`][theo tmod_add_tdiv]). In
+  to pair with `Int.div`, meaning that `a % b + b * (a / b) = a`
+  unconditionally (see [`Int.mod_add_div`][theo mod_add_div]). In
   particular, `a % 0 = a`.
 
   [t-rounding]: https://dl.acm.org/doi/pdf/10.1145/128861.128862
-  [theo tmod_add_tdiv]: https://leanprover-community.github.io/mathlib4_docs/find/?pattern=Int.tmod_add_tdiv#doc
+  [theo mod_add_div]: https://leanprover-community.github.io/mathlib4_docs/find/?pattern=Int.mod_add_div#doc
 
   Examples:
 
   ```
-  #eval (7 : Int).tmod (0 : Int) -- 7
-  #eval (0 : Int).tmod (7 : Int) -- 0
+  #eval (7 : Int).mod (0 : Int) -- 7
+  #eval (0 : Int).mod (7 : Int) -- 0
 
-  #eval (12 : Int).tmod (6 : Int) -- 0
-  #eval (12 : Int).tmod (-6 : Int) -- 0
-  #eval (-12 : Int).tmod (6 : Int) -- 0
-  #eval (-12 : Int).tmod (-6 : Int) -- 0
+  #eval (12 : Int).mod (6 : Int) -- 0
+  #eval (12 : Int).mod (-6 : Int) -- 0
+  #eval (-12 : Int).mod (6 : Int) -- 0
+  #eval (-12 : Int).mod (-6 : Int) -- 0
 
-  #eval (12 : Int).tmod (7 : Int) -- 5
-  #eval (12 : Int).tmod (-7 : Int) -- 5
-  #eval (-12 : Int).tmod (7 : Int) -- -5
-  #eval (-12 : Int).tmod (-7 : Int) -- -5
+  #eval (12 : Int).mod (7 : Int) -- 5
+  #eval (12 : Int).mod (-7 : Int) -- 5
+  #eval (-12 : Int).mod (7 : Int) -- -5
+  #eval (-12 : Int).mod (-7 : Int) -- -5
   ```
 
   Implemented by efficient native code. -/
 @[extern "lean_int_mod"]
-def tmod : (@& Int) → (@& Int) → Int
+def mod : (@& Int) → (@& Int) → Int
   | ofNat m, ofNat n =>  ofNat (m % n)
   | ofNat m, -[n +1] =>  ofNat (m % succ n)
   | -[m +1], ofNat n => -ofNat (succ m % n)
   | -[m +1], -[n +1] => -ofNat (succ m % succ n)
 
-@[deprecated tmod (since := "2024-09-11")] abbrev mod := tmod
-
 /-! ### F-rounding division
 This pair satisfies `fdiv x y = floor (x / y)`.
 -/
@@ -249,9 +233,7 @@ instance : Mod Int where
 
 @[simp, norm_cast] theorem ofNat_ediv (m n : Nat) : (↑(m / n) : Int) = ↑m / ↑n := rfl
 
-theorem ofNat_tdiv (m n : Nat) : ↑(m / n) = tdiv ↑m ↑n := rfl
-
-@[deprecated ofNat_tdiv (since := "2024-09-11")] abbrev ofNat_div := ofNat_tdiv
+theorem ofNat_div (m n : Nat) : ↑(m / n) = div ↑m ↑n := rfl
 
 theorem ofNat_fdiv : ∀ m n : Nat, ↑(m / n) = fdiv ↑m ↑n
   | 0, _ => by simp [fdiv]

src/Init/Data/Int/DivModLemmas.lean

@@ -137,12 +137,12 @@ theorem eq_one_of_mul_eq_one_left {a b : Int} (H : 0 ≤ b) (H' : a * b = 1) : b
   | ofNat _ => show ofNat _ = _ by simp
   | -[_+1] => rfl
 
-@[simp] protected theorem zero_tdiv : ∀ b : Int, tdiv 0 b = 0
+@[simp] protected theorem zero_div : ∀ b : Int, div 0 b = 0
   | ofNat _ => show ofNat _ = _ by simp
   | -[_+1] => show -ofNat _ = _ by simp
 
 unseal Nat.div in
-@[simp] protected theorem tdiv_zero : ∀ a : Int, tdiv a 0 = 0
+@[simp] protected theorem div_zero : ∀ a : Int, div a 0 = 0
   | ofNat _ => show ofNat _ = _ by simp
   | -[_+1] => rfl
 
@@ -156,17 +156,16 @@ unseal Nat.div in
 
 /-! ### div equivalences  -/
 
-theorem tdiv_eq_ediv : ∀ {a b : Int}, 0 ≤ a → 0 ≤ b → a.tdiv b = a / b
+theorem div_eq_ediv : ∀ {a b : Int}, 0 ≤ a → 0 ≤ b → a.div b = a / b
   | 0, _, _, _ | _, 0, _, _ => by simp
   | succ _, succ _, _, _ => rfl
 
-
 theorem fdiv_eq_ediv : ∀ (a : Int) {b : Int}, 0 ≤ b → fdiv a b = a / b
   | 0, _, _ | -[_+1], 0, _ => by simp
   | succ _, ofNat _, _ | -[_+1], succ _, _ => rfl
 
-theorem fdiv_eq_tdiv {a b : Int} (Ha : 0 ≤ a) (Hb : 0 ≤ b) : fdiv a b = tdiv a b :=
-  tdiv_eq_ediv Ha Hb ▸ fdiv_eq_ediv _ Hb
+theorem fdiv_eq_div {a b : Int} (Ha : 0 ≤ a) (Hb : 0 ≤ b) : fdiv a b = div a b :=
+  div_eq_ediv Ha Hb ▸ fdiv_eq_ediv _ Hb
 
 /-! ### mod zero -/
 
@@ -176,9 +175,9 @@ theorem fdiv_eq_tdiv {a b : Int} (Ha : 0 ≤ a) (Hb : 0 ≤ b) : fdiv a b = tdiv
   | ofNat _ => congrArg ofNat <| Nat.mod_zero _
   | -[_+1]  => congrArg negSucc <| Nat.mod_zero _
 
-@[simp] theorem zero_tmod (b : Int) : tmod 0 b = 0 := by cases b <;> simp [tmod]
+@[simp] theorem zero_mod (b : Int) : mod 0 b = 0 := by cases b <;> simp [mod]
 
-@[simp] theorem tmod_zero : ∀ a : Int, tmod a 0 = a
+@[simp] theorem mod_zero : ∀ a : Int, mod a 0 = a
   | ofNat _ => congrArg ofNat <| Nat.mod_zero _
   | -[_+1] => congrArg (fun n => -ofNat n) <| Nat.mod_zero _
 
@@ -222,7 +221,7 @@ theorem ediv_add_emod' (a b : Int) : a / b * b + a % b = a := by
 theorem emod_def (a b : Int) : a % b = a - b * (a / b) := by
   rw [← Int.add_sub_cancel (a % b), emod_add_ediv]
 
-theorem tmod_add_tdiv : ∀ a b : Int, tmod a b + b * (a.tdiv b) = a
+theorem mod_add_div : ∀ a b : Int, mod a b + b * (a.div b) = a
   | ofNat _, ofNat _ => congrArg ofNat (Nat.mod_add_div ..)
   | ofNat m, -[n+1] => by
     show (m % succ n + -↑(succ n) * -↑(m / succ n) : Int) = m
@@ -239,17 +238,17 @@ theorem tmod_add_tdiv : ∀ a b : Int, tmod a b + b * (a.tdiv b) = a
     rw [Int.neg_mul, ← Int.neg_add]
     exact congrArg (-ofNat ·) (Nat.mod_add_div ..)
 
-theorem tdiv_add_tmod (a b : Int) : b * a.tdiv b + tmod a b = a := by
-  rw [Int.add_comm]; apply tmod_add_tdiv ..
+theorem div_add_mod (a b : Int) : b * a.div b + mod a b = a := by
+  rw [Int.add_comm]; apply mod_add_div ..
 
-theorem tmod_add_tdiv' (m k : Int) : tmod m k + m.tdiv k * k = m := by
-  rw [Int.mul_comm]; apply tmod_add_tdiv
+theorem mod_add_div' (m k : Int) : mod m k + m.div k * k = m := by
+  rw [Int.mul_comm]; apply mod_add_div
 
-theorem tdiv_add_tmod' (m k : Int) : m.tdiv k * k + tmod m k = m := by
-  rw [Int.mul_comm]; apply tdiv_add_tmod
+theorem div_add_mod' (m k : Int) : m.div k * k + mod m k = m := by
+  rw [Int.mul_comm]; apply div_add_mod
 
-theorem tmod_def (a b : Int) : tmod a b = a - b * a.tdiv b := by
-  rw [← Int.add_sub_cancel (tmod a b), tmod_add_tdiv]
+theorem mod_def (a b : Int) : mod a b = a - b * a.div b := by
+  rw [← Int.add_sub_cancel (mod a b), mod_add_div]
 
 theorem fmod_add_fdiv : ∀ a b : Int, a.fmod b + b * a.fdiv b = a
   | 0, ofNat _ | 0, -[_+1] => congrArg ofNat <| by simp
@@ -279,11 +278,11 @@ theorem fmod_def (a b : Int) : a.fmod b = a - b * a.fdiv b := by
 theorem fmod_eq_emod (a : Int) {b : Int} (hb : 0 ≤ b) : fmod a b = a % b := by
   simp [fmod_def, emod_def, fdiv_eq_ediv _ hb]
 
-theorem tmod_eq_emod {a b : Int} (ha : 0 ≤ a) (hb : 0 ≤ b) : tmod a b = a % b := by
-  simp [emod_def, tmod_def, tdiv_eq_ediv ha hb]
+theorem mod_eq_emod {a b : Int} (ha : 0 ≤ a) (hb : 0 ≤ b) : mod a b = a % b := by
+  simp [emod_def, mod_def, div_eq_ediv ha hb]
 
-theorem fmod_eq_tmod {a b : Int} (Ha : 0 ≤ a) (Hb : 0 ≤ b) : fmod a b = tmod a b :=
-  tmod_eq_emod Ha Hb ▸ fmod_eq_emod _ Hb
+theorem fmod_eq_mod {a b : Int} (Ha : 0 ≤ a) (Hb : 0 ≤ b) : fmod a b = mod a b :=
+  mod_eq_emod Ha Hb ▸ fmod_eq_emod _ Hb
 
 /-! ### `/` ediv -/
 
@@ -298,7 +297,7 @@ theorem ediv_neg' {a b : Int} (Ha : a < 0) (Hb : 0 < b) : a / b < 0 :=
 
 protected theorem div_def (a b : Int) : a / b = Int.ediv a b := rfl
 
-theorem negSucc_ediv (m : Nat) {b : Int} (H : 0 < b) : -[m+1] / b = -(ediv m b + 1) :=
+theorem negSucc_ediv (m : Nat) {b : Int} (H : 0 < b) : -[m+1] / b = -(div m b + 1) :=
   match b, eq_succ_of_zero_lt H with
   | _, ⟨_, rfl⟩ => rfl
 
@@ -306,22 +305,6 @@ theorem ediv_nonneg {a b : Int} (Ha : 0 ≤ a) (Hb : 0 ≤ b) : 0 ≤ a / b :=
   match a, b, eq_ofNat_of_zero_le Ha, eq_ofNat_of_zero_le Hb with
   | _, _, ⟨_, rfl⟩, ⟨_, rfl⟩ => ofNat_zero_le _
 
-theorem ediv_nonneg_of_nonpos_of_nonpos {a b : Int} (Ha : a ≤ 0) (Hb : b ≤ 0) : 0 ≤ a / b := by
-  match a, b with
-  | ofNat a, b =>
-    match Int.le_antisymm Ha (ofNat_zero_le a) with
-    | h1 =>
-      rw [h1, zero_ediv]
-      exact Int.le_refl 0
-  | a, ofNat b =>
-    match Int.le_antisymm Hb (ofNat_zero_le  b) with
-    | h1 =>
-      rw [h1, Int.ediv_zero]
-      exact Int.le_refl 0
-  | negSucc a, negSucc b =>
-    rw [Int.div_def, ediv]
-    exact le_add_one (ediv_nonneg (ofNat_zero_le a) (Int.le_trans (ofNat_zero_le b) (le.intro 1 rfl)))
-
 theorem ediv_nonpos {a b : Int} (Ha : 0 ≤ a) (Hb : b ≤ 0) : a / b ≤ 0 :=
   Int.nonpos_of_neg_nonneg <| Int.ediv_neg .. ▸ Int.ediv_nonneg Ha (Int.neg_nonneg_of_nonpos Hb)
 
@@ -813,191 +796,191 @@ theorem ediv_eq_ediv_of_mul_eq_mul {a b c d : Int}
   Int.ediv_eq_of_eq_mul_right H3 <| by
     rw [← Int.mul_ediv_assoc _ H2]; exact (Int.ediv_eq_of_eq_mul_left H4 H5.symm).symm
 
-/-! ### tdiv -/
+/-! ### div -/
 
-@[simp] protected theorem tdiv_one : ∀ a : Int, a.tdiv 1 = a
+@[simp] protected theorem div_one : ∀ a : Int, a.div 1 = a
   | (n:Nat) => congrArg ofNat (Nat.div_one _)
-  | -[n+1] => by simp [Int.tdiv, neg_ofNat_succ]; rfl
+  | -[n+1] => by simp [Int.div, neg_ofNat_succ]; rfl
 
 unseal Nat.div in
-@[simp] protected theorem tdiv_neg : ∀ a b : Int, a.tdiv (-b) = -(a.tdiv b)
+@[simp] protected theorem div_neg : ∀ a b : Int, a.div (-b) = -(a.div b)
   | ofNat m, 0 => show ofNat (m / 0) = -↑(m / 0) by rw [Nat.div_zero]; rfl
   | ofNat m, -[n+1] | -[m+1], succ n => (Int.neg_neg _).symm
   | ofNat m, succ n | -[m+1], 0 | -[m+1], -[n+1] => rfl
 
 unseal Nat.div in
-@[simp] protected theorem neg_tdiv : ∀ a b : Int, (-a).tdiv b = -(a.tdiv b)
+@[simp] protected theorem neg_div : ∀ a b : Int, (-a).div b = -(a.div b)
   | 0, n => by simp [Int.neg_zero]
   | succ m, (n:Nat) | -[m+1], 0 | -[m+1], -[n+1] => rfl
   | succ m, -[n+1] | -[m+1], succ n => (Int.neg_neg _).symm
 
-protected theorem neg_tdiv_neg (a b : Int) : (-a).tdiv (-b) = a.tdiv b := by
-  simp [Int.tdiv_neg, Int.neg_tdiv, Int.neg_neg]
+protected theorem neg_div_neg (a b : Int) : (-a).div (-b) = a.div b := by
+  simp [Int.div_neg, Int.neg_div, Int.neg_neg]
 
-protected theorem tdiv_nonneg {a b : Int} (Ha : 0 ≤ a) (Hb : 0 ≤ b) : 0 ≤ a.tdiv b :=
+protected theorem div_nonneg {a b : Int} (Ha : 0 ≤ a) (Hb : 0 ≤ b) : 0 ≤ a.div b :=
   match a, b, eq_ofNat_of_zero_le Ha, eq_ofNat_of_zero_le Hb with
   | _, _, ⟨_, rfl⟩, ⟨_, rfl⟩ => ofNat_zero_le _
 
-protected theorem tdiv_nonpos {a b : Int} (Ha : 0 ≤ a) (Hb : b ≤ 0) : a.tdiv b ≤ 0 :=
-  Int.nonpos_of_neg_nonneg <| Int.tdiv_neg .. ▸ Int.tdiv_nonneg Ha (Int.neg_nonneg_of_nonpos Hb)
+protected theorem div_nonpos {a b : Int} (Ha : 0 ≤ a) (Hb : b ≤ 0) : a.div b ≤ 0 :=
+  Int.nonpos_of_neg_nonneg <| Int.div_neg .. ▸ Int.div_nonneg Ha (Int.neg_nonneg_of_nonpos Hb)
 
-theorem tdiv_eq_zero_of_lt {a b : Int} (H1 : 0 ≤ a) (H2 : a < b) : a.tdiv b = 0 :=
+theorem div_eq_zero_of_lt {a b : Int} (H1 : 0 ≤ a) (H2 : a < b) : a.div b = 0 :=
   match a, b, eq_ofNat_of_zero_le H1, eq_succ_of_zero_lt (Int.lt_of_le_of_lt H1 H2) with
   | _, _, ⟨_, rfl⟩, ⟨_, rfl⟩ => congrArg Nat.cast <| Nat.div_eq_of_lt <| ofNat_lt.1 H2
 
-@[simp] protected theorem mul_tdiv_cancel (a : Int) {b : Int} (H : b ≠ 0) : (a * b).tdiv b = a :=
-  have : ∀ {a b : Nat}, (b : Int) ≠ 0 → (tdiv (a * b) b : Int) = a := fun H => by
-    rw [← ofNat_mul, ← ofNat_tdiv,
+@[simp] protected theorem mul_div_cancel (a : Int) {b : Int} (H : b ≠ 0) : (a * b).div b = a :=
+  have : ∀ {a b : Nat}, (b : Int) ≠ 0 → (div (a * b) b : Int) = a := fun H => by
+    rw [← ofNat_mul, ← ofNat_div,
       Nat.mul_div_cancel _ <| Nat.pos_of_ne_zero <| Int.ofNat_ne_zero.1 H]
   match a, b, a.eq_nat_or_neg, b.eq_nat_or_neg with
   | _, _, ⟨a, .inl rfl⟩, ⟨b, .inl rfl⟩ => this H
   | _, _, ⟨a, .inl rfl⟩, ⟨b, .inr rfl⟩ => by
-    rw [Int.mul_neg, Int.neg_tdiv, Int.tdiv_neg, Int.neg_neg,
+    rw [Int.mul_neg, Int.neg_div, Int.div_neg, Int.neg_neg,
       this (Int.neg_ne_zero.1 H)]
-  | _, _, ⟨a, .inr rfl⟩, ⟨b, .inl rfl⟩ => by rw [Int.neg_mul, Int.neg_tdiv, this H]
+  | _, _, ⟨a, .inr rfl⟩, ⟨b, .inl rfl⟩ => by rw [Int.neg_mul, Int.neg_div, this H]
   | _, _, ⟨a, .inr rfl⟩, ⟨b, .inr rfl⟩ => by
-    rw [Int.neg_mul_neg, Int.tdiv_neg, this (Int.neg_ne_zero.1 H)]
+    rw [Int.neg_mul_neg, Int.div_neg, this (Int.neg_ne_zero.1 H)]
 
-@[simp] protected theorem mul_tdiv_cancel_left (b : Int) (H : a ≠ 0) : (a * b).tdiv a = b :=
-  Int.mul_comm .. ▸ Int.mul_tdiv_cancel _ H
+@[simp] protected theorem mul_div_cancel_left (b : Int) (H : a ≠ 0) : (a * b).div a = b :=
+  Int.mul_comm .. ▸ Int.mul_div_cancel _ H
 
-@[simp] protected theorem tdiv_self {a : Int} (H : a ≠ 0) : a.tdiv a = 1 := by
-  have := Int.mul_tdiv_cancel 1 H; rwa [Int.one_mul] at this
+@[simp] protected theorem div_self {a : Int} (H : a ≠ 0) : a.div a = 1 := by
+  have := Int.mul_div_cancel 1 H; rwa [Int.one_mul] at this
 
-theorem mul_tdiv_cancel_of_tmod_eq_zero {a b : Int} (H : a.tmod b = 0) : b * (a.tdiv b) = a := by
-  have := tmod_add_tdiv a b; rwa [H, Int.zero_add] at this
+theorem mul_div_cancel_of_mod_eq_zero {a b : Int} (H : a.mod b = 0) : b * (a.div b) = a := by
+  have := mod_add_div a b; rwa [H, Int.zero_add] at this
 
-theorem tdiv_mul_cancel_of_tmod_eq_zero {a b : Int} (H : a.tmod b = 0) : a.tdiv b * b = a := by
-  rw [Int.mul_comm, mul_tdiv_cancel_of_tmod_eq_zero H]
+theorem div_mul_cancel_of_mod_eq_zero {a b : Int} (H : a.mod b = 0) : a.div b * b = a := by
+  rw [Int.mul_comm, mul_div_cancel_of_mod_eq_zero H]
 
-theorem dvd_of_tmod_eq_zero {a b : Int} (H : tmod b a = 0) : a ∣ b :=
-  ⟨b.tdiv a, (mul_tdiv_cancel_of_tmod_eq_zero H).symm⟩
+theorem dvd_of_mod_eq_zero {a b : Int} (H : mod b a = 0) : a ∣ b :=
+  ⟨b.div a, (mul_div_cancel_of_mod_eq_zero H).symm⟩
 
-protected theorem mul_tdiv_assoc (a : Int) : ∀ {b c : Int}, c ∣ b → (a * b).tdiv c = a * (b.tdiv c)
+protected theorem mul_div_assoc (a : Int) : ∀ {b c : Int}, c ∣ b → (a * b).div c = a * (b.div c)
   | _, c, ⟨d, rfl⟩ =>
     if cz : c = 0 then by simp [cz, Int.mul_zero] else by
-      rw [Int.mul_left_comm, Int.mul_tdiv_cancel_left _ cz, Int.mul_tdiv_cancel_left _ cz]
+      rw [Int.mul_left_comm, Int.mul_div_cancel_left _ cz, Int.mul_div_cancel_left _ cz]
 
-protected theorem mul_tdiv_assoc' (b : Int) {a c : Int} (h : c ∣ a) :
-    (a * b).tdiv c = a.tdiv c * b := by
-  rw [Int.mul_comm, Int.mul_tdiv_assoc _ h, Int.mul_comm]
+protected theorem mul_div_assoc' (b : Int) {a c : Int} (h : c ∣ a) :
+    (a * b).div c = a.div c * b := by
+  rw [Int.mul_comm, Int.mul_div_assoc _ h, Int.mul_comm]
 
-theorem tdiv_dvd_tdiv : ∀ {a b c : Int}, a ∣ b → b ∣ c → b.tdiv a ∣ c.tdiv a
+theorem div_dvd_div : ∀ {a b c : Int}, a ∣ b → b ∣ c → b.div a ∣ c.div a
   | a, _, _, ⟨b, rfl⟩, ⟨c, rfl⟩ => by
     by_cases az : a = 0
     · simp [az]
-    · rw [Int.mul_tdiv_cancel_left _ az, Int.mul_assoc, Int.mul_tdiv_cancel_left _ az]
+    · rw [Int.mul_div_cancel_left _ az, Int.mul_assoc, Int.mul_div_cancel_left _ az]
       apply Int.dvd_mul_right
 
-@[simp] theorem natAbs_tdiv (a b : Int) : natAbs (a.tdiv b) = (natAbs a).div (natAbs b) :=
+@[simp] theorem natAbs_div (a b : Int) : natAbs (a.div b) = (natAbs a).div (natAbs b) :=
   match a, b, eq_nat_or_neg a, eq_nat_or_neg b with
   | _, _, ⟨_, .inl rfl⟩, ⟨_, .inl rfl⟩ => rfl
-  | _, _, ⟨_, .inl rfl⟩, ⟨_, .inr rfl⟩ => by rw [Int.tdiv_neg, natAbs_neg, natAbs_neg]; rfl
-  | _, _, ⟨_, .inr rfl⟩, ⟨_, .inl rfl⟩ => by rw [Int.neg_tdiv, natAbs_neg, natAbs_neg]; rfl
-  | _, _, ⟨_, .inr rfl⟩, ⟨_, .inr rfl⟩ => by rw [Int.neg_tdiv_neg, natAbs_neg, natAbs_neg]; rfl
+  | _, _, ⟨_, .inl rfl⟩, ⟨_, .inr rfl⟩ => by rw [Int.div_neg, natAbs_neg, natAbs_neg]; rfl
+  | _, _, ⟨_, .inr rfl⟩, ⟨_, .inl rfl⟩ => by rw [Int.neg_div, natAbs_neg, natAbs_neg]; rfl
+  | _, _, ⟨_, .inr rfl⟩, ⟨_, .inr rfl⟩ => by rw [Int.neg_div_neg, natAbs_neg, natAbs_neg]; rfl
 
-protected theorem tdiv_eq_of_eq_mul_right {a b c : Int}
-    (H1 : b ≠ 0) (H2 : a = b * c) : a.tdiv b = c := by rw [H2, Int.mul_tdiv_cancel_left _ H1]
+protected theorem div_eq_of_eq_mul_right {a b c : Int}
+    (H1 : b ≠ 0) (H2 : a = b * c) : a.div b = c := by rw [H2, Int.mul_div_cancel_left _ H1]
 
-protected theorem eq_tdiv_of_mul_eq_right {a b c : Int}
-    (H1 : a ≠ 0) (H2 : a * b = c) : b = c.tdiv a :=
-  (Int.tdiv_eq_of_eq_mul_right H1 H2.symm).symm
+protected theorem eq_div_of_mul_eq_right {a b c : Int}
+    (H1 : a ≠ 0) (H2 : a * b = c) : b = c.div a :=
+  (Int.div_eq_of_eq_mul_right H1 H2.symm).symm
 
 /-! ### (t-)mod -/
 
-theorem ofNat_tmod (m n : Nat) : (↑(m % n) : Int) = tmod m n := rfl
+theorem ofNat_mod (m n : Nat) : (↑(m % n) : Int) = mod m n := rfl
 
-@[simp] theorem tmod_one (a : Int) : tmod a 1 = 0 := by
-  simp [tmod_def, Int.tdiv_one, Int.one_mul, Int.sub_self]
+@[simp] theorem mod_one (a : Int) : mod a 1 = 0 := by
+  simp [mod_def, Int.div_one, Int.one_mul, Int.sub_self]
 
-theorem tmod_eq_of_lt {a b : Int} (H1 : 0 ≤ a) (H2 : a < b) : tmod a b = a := by
-  rw [tmod_eq_emod H1 (Int.le_trans H1 (Int.le_of_lt H2)), emod_eq_of_lt H1 H2]
+theorem mod_eq_of_lt {a b : Int} (H1 : 0 ≤ a) (H2 : a < b) : mod a b = a := by
+  rw [mod_eq_emod H1 (Int.le_trans H1 (Int.le_of_lt H2)), emod_eq_of_lt H1 H2]
 
-theorem tmod_lt_of_pos (a : Int) {b : Int} (H : 0 < b) : tmod a b < b :=
+theorem mod_lt_of_pos (a : Int) {b : Int} (H : 0 < b) : mod a b < b :=
   match a, b, eq_succ_of_zero_lt H with
   | ofNat _, _, ⟨n, rfl⟩ => ofNat_lt.2 <| Nat.mod_lt _ n.succ_pos
   | -[_+1], _, ⟨n, rfl⟩ => Int.lt_of_le_of_lt
     (Int.neg_nonpos_of_nonneg <| Int.ofNat_nonneg _) (ofNat_pos.2 n.succ_pos)
 
-theorem tmod_nonneg : ∀ {a : Int} (b : Int), 0 ≤ a → 0 ≤ tmod a b
+theorem mod_nonneg : ∀ {a : Int} (b : Int), 0 ≤ a → 0 ≤ mod a b
   | ofNat _, -[_+1], _ | ofNat _, ofNat _, _ => ofNat_nonneg _
 
-@[simp] theorem tmod_neg (a b : Int) : tmod a (-b) = tmod a b := by
-  rw [tmod_def, tmod_def, Int.tdiv_neg, Int.neg_mul_neg]
+@[simp] theorem mod_neg (a b : Int) : mod a (-b) = mod a b := by
+  rw [mod_def, mod_def, Int.div_neg, Int.neg_mul_neg]
 
-@[simp] theorem mul_tmod_left (a b : Int) : (a * b).tmod b = 0 :=
+@[simp] theorem mul_mod_left (a b : Int) : (a * b).mod b = 0 :=
   if h : b = 0 then by simp [h, Int.mul_zero] else by
-    rw [Int.tmod_def, Int.mul_tdiv_cancel _ h, Int.mul_comm, Int.sub_self]
+    rw [Int.mod_def, Int.mul_div_cancel _ h, Int.mul_comm, Int.sub_self]
 
-@[simp] theorem mul_tmod_right (a b : Int) : (a * b).tmod a = 0 := by
-  rw [Int.mul_comm, mul_tmod_left]
+@[simp] theorem mul_mod_right (a b : Int) : (a * b).mod a = 0 := by
+  rw [Int.mul_comm, mul_mod_left]
 
-theorem tmod_eq_zero_of_dvd : ∀ {a b : Int}, a ∣ b → tmod b a = 0
-  | _, _, ⟨_, rfl⟩ => mul_tmod_right ..
+theorem mod_eq_zero_of_dvd : ∀ {a b : Int}, a ∣ b → mod b a = 0
+  | _, _, ⟨_, rfl⟩ => mul_mod_right ..
 
-theorem dvd_iff_tmod_eq_zero {a b : Int} : a ∣ b ↔ tmod b a = 0 :=
-  ⟨tmod_eq_zero_of_dvd, dvd_of_tmod_eq_zero⟩
+theorem dvd_iff_mod_eq_zero {a b : Int} : a ∣ b ↔ mod b a = 0 :=
+  ⟨mod_eq_zero_of_dvd, dvd_of_mod_eq_zero⟩
 
-@[simp] theorem neg_mul_tmod_right (a b : Int) : (-(a * b)).tmod a = 0 := by
-  rw [← dvd_iff_tmod_eq_zero, Int.dvd_neg]
+@[simp] theorem neg_mul_mod_right (a b : Int) : (-(a * b)).mod a = 0 := by
+  rw [← dvd_iff_mod_eq_zero, Int.dvd_neg]
   exact Int.dvd_mul_right a b
 
-@[simp] theorem neg_mul_tmod_left (a b : Int) : (-(a * b)).tmod b = 0 := by
-  rw [← dvd_iff_tmod_eq_zero, Int.dvd_neg]
+@[simp] theorem neg_mul_mod_left (a b : Int) : (-(a * b)).mod b = 0 := by
+  rw [← dvd_iff_mod_eq_zero, Int.dvd_neg]
   exact Int.dvd_mul_left a b
 
-protected theorem tdiv_mul_cancel {a b : Int} (H : b ∣ a) : a.tdiv b * b = a :=
-  tdiv_mul_cancel_of_tmod_eq_zero (tmod_eq_zero_of_dvd H)
+protected theorem div_mul_cancel {a b : Int} (H : b ∣ a) : a.div b * b = a :=
+  div_mul_cancel_of_mod_eq_zero (mod_eq_zero_of_dvd H)
 
-protected theorem mul_tdiv_cancel' {a b : Int} (H : a ∣ b) : a * b.tdiv a = b := by
-  rw [Int.mul_comm, Int.tdiv_mul_cancel H]
+protected theorem mul_div_cancel' {a b : Int} (H : a ∣ b) : a * b.div a = b := by
+  rw [Int.mul_comm, Int.div_mul_cancel H]
 
-protected theorem eq_mul_of_tdiv_eq_right {a b c : Int}
-    (H1 : b ∣ a) (H2 : a.tdiv b = c) : a = b * c := by rw [← H2, Int.mul_tdiv_cancel' H1]
+protected theorem eq_mul_of_div_eq_right {a b c : Int}
+    (H1 : b ∣ a) (H2 : a.div b = c) : a = b * c := by rw [← H2, Int.mul_div_cancel' H1]
 
-@[simp] theorem tmod_self {a : Int} : a.tmod a = 0 := by
-  have := mul_tmod_left 1 a; rwa [Int.one_mul] at this
+@[simp] theorem mod_self {a : Int} : a.mod a = 0 := by
+  have := mul_mod_left 1 a; rwa [Int.one_mul] at this
 
-@[simp] theorem neg_tmod_self (a : Int) : (-a).tmod a = 0 := by
-  rw [← dvd_iff_tmod_eq_zero, Int.dvd_neg]
+@[simp] theorem neg_mod_self (a : Int) : (-a).mod a = 0 := by
+  rw [← dvd_iff_mod_eq_zero, Int.dvd_neg]
   exact Int.dvd_refl a
 
-theorem lt_tdiv_add_one_mul_self (a : Int) {b : Int} (H : 0 < b) : a < (a.tdiv b + 1) * b := by
+theorem lt_div_add_one_mul_self (a : Int) {b : Int} (H : 0 < b) : a < (a.div b + 1) * b := by
   rw [Int.add_mul, Int.one_mul, Int.mul_comm]
-  exact Int.lt_add_of_sub_left_lt <| Int.tmod_def .. ▸ tmod_lt_of_pos _ H
+  exact Int.lt_add_of_sub_left_lt <| Int.mod_def .. ▸ mod_lt_of_pos _ H
 
-protected theorem tdiv_eq_iff_eq_mul_right {a b c : Int}
-    (H : b ≠ 0) (H' : b ∣ a) : a.tdiv b = c ↔ a = b * c :=
-  ⟨Int.eq_mul_of_tdiv_eq_right H', Int.tdiv_eq_of_eq_mul_right H⟩
+protected theorem div_eq_iff_eq_mul_right {a b c : Int}
+    (H : b ≠ 0) (H' : b ∣ a) : a.div b = c ↔ a = b * c :=
+  ⟨Int.eq_mul_of_div_eq_right H', Int.div_eq_of_eq_mul_right H⟩
 
-protected theorem tdiv_eq_iff_eq_mul_left {a b c : Int}
-    (H : b ≠ 0) (H' : b ∣ a) : a.tdiv b = c ↔ a = c * b := by
-  rw [Int.mul_comm]; exact Int.tdiv_eq_iff_eq_mul_right H H'
+protected theorem div_eq_iff_eq_mul_left {a b c : Int}
+    (H : b ≠ 0) (H' : b ∣ a) : a.div b = c ↔ a = c * b := by
+  rw [Int.mul_comm]; exact Int.div_eq_iff_eq_mul_right H H'
 
-protected theorem eq_mul_of_tdiv_eq_left {a b c : Int}
-    (H1 : b ∣ a) (H2 : a.tdiv b = c) : a = c * b := by
-  rw [Int.mul_comm, Int.eq_mul_of_tdiv_eq_right H1 H2]
+protected theorem eq_mul_of_div_eq_left {a b c : Int}
+    (H1 : b ∣ a) (H2 : a.div b = c) : a = c * b := by
+  rw [Int.mul_comm, Int.eq_mul_of_div_eq_right H1 H2]
 
-protected theorem tdiv_eq_of_eq_mul_left {a b c : Int}
-    (H1 : b ≠ 0) (H2 : a = c * b) : a.tdiv b = c :=
-  Int.tdiv_eq_of_eq_mul_right H1 (by rw [Int.mul_comm, H2])
+protected theorem div_eq_of_eq_mul_left {a b c : Int}
+    (H1 : b ≠ 0) (H2 : a = c * b) : a.div b = c :=
+  Int.div_eq_of_eq_mul_right H1 (by rw [Int.mul_comm, H2])
 
-protected theorem eq_zero_of_tdiv_eq_zero {d n : Int} (h : d ∣ n) (H : n.tdiv d = 0) : n = 0 := by
-  rw [← Int.mul_tdiv_cancel' h, H, Int.mul_zero]
+protected theorem eq_zero_of_div_eq_zero {d n : Int} (h : d ∣ n) (H : n.div d = 0) : n = 0 := by
+  rw [← Int.mul_div_cancel' h, H, Int.mul_zero]
 
-@[simp] protected theorem tdiv_left_inj {a b d : Int}
-    (hda : d ∣ a) (hdb : d ∣ b) : a.tdiv d = b.tdiv d ↔ a = b := by
-  refine ⟨fun h => ?_, congrArg (tdiv · d)⟩
-  rw [← Int.mul_tdiv_cancel' hda, ← Int.mul_tdiv_cancel' hdb, h]
+@[simp] protected theorem div_left_inj {a b d : Int}
+    (hda : d ∣ a) (hdb : d ∣ b) : a.div d = b.div d ↔ a = b := by
+  refine ⟨fun h => ?_, congrArg (div · d)⟩
+  rw [← Int.mul_div_cancel' hda, ← Int.mul_div_cancel' hdb, h]
 
-theorem tdiv_sign : ∀ a b, a.tdiv (sign b) = a * sign b
+theorem div_sign : ∀ a b, a.div (sign b) = a * sign b
   | _, succ _ => by simp [sign, Int.mul_one]
   | _, 0 => by simp [sign, Int.mul_zero]
   | _, -[_+1] => by simp [sign, Int.mul_neg, Int.mul_one]
 
-protected theorem sign_eq_tdiv_abs (a : Int) : sign a = a.tdiv (natAbs a) :=
+protected theorem sign_eq_div_abs (a : Int) : sign a = a.div (natAbs a) :=
   if az : a = 0 then by simp [az] else
-    (Int.tdiv_eq_of_eq_mul_left (ofNat_ne_zero.2 <| natAbs_ne_zero.2 az)
+    (Int.div_eq_of_eq_mul_left (ofNat_ne_zero.2 <| natAbs_ne_zero.2 az)
       (sign_mul_natAbs _).symm).symm
 
 /-! ### fdiv -/
@@ -1050,7 +1033,7 @@ theorem fmod_eq_of_lt {a b : Int} (H1 : 0 ≤ a) (H2 : a < b) : a.fmod b = a :=
   rw [fmod_eq_emod _ (Int.le_trans H1 (Int.le_of_lt H2)), emod_eq_of_lt H1 H2]
 
 theorem fmod_nonneg {a b : Int} (ha : 0 ≤ a) (hb : 0 ≤ b) : 0 ≤ a.fmod b :=
-  fmod_eq_tmod ha hb ▸ tmod_nonneg _ ha
+  fmod_eq_mod ha hb ▸ mod_nonneg _ ha
 
 theorem fmod_nonneg' (a : Int) {b : Int} (hb : 0 < b) : 0 ≤ a.fmod b :=
   fmod_eq_emod _ (Int.le_of_lt hb) ▸ emod_nonneg _ (Int.ne_of_lt hb).symm
@@ -1070,10 +1053,10 @@ theorem fmod_lt_of_pos (a : Int) {b : Int} (H : 0 < b) : a.fmod b < b :=
 
 /-! ### Theorems crossing div/mod versions -/
 
-theorem tdiv_eq_ediv_of_dvd {a b : Int} (h : b ∣ a) : a.tdiv b = a / b := by
+theorem div_eq_ediv_of_dvd {a b : Int} (h : b ∣ a) : a.div b = a / b := by
   by_cases b0 : b = 0
   · simp [b0]
-  · rw [Int.tdiv_eq_iff_eq_mul_left b0 h, ← Int.ediv_eq_iff_eq_mul_left b0 h]
+  · rw [Int.div_eq_iff_eq_mul_left b0 h, ← Int.ediv_eq_iff_eq_mul_left b0 h]
 
 theorem fdiv_eq_ediv_of_dvd : ∀ {a b : Int}, b ∣ a → a.fdiv b = a / b
   | _, b, ⟨c, rfl⟩ => by
@@ -1285,65 +1268,3 @@ theorem bmod_natAbs_plus_one (x : Int) (w : 1 < x.natAbs) : bmod x (x.natAbs + 1
           all_goals decide
     · exact ofNat_nonneg x
     · exact succ_ofNat_pos (x + 1)
-
-/-! ### Deprecations -/
-
-@[deprecated Int.zero_tdiv (since := "2024-09-11")] protected abbrev zero_div := @Int.zero_tdiv
-@[deprecated Int.tdiv_zero (since := "2024-09-11")] protected abbrev div_zero := @Int.tdiv_zero
-@[deprecated tdiv_eq_ediv (since := "2024-09-11")] abbrev div_eq_ediv := @tdiv_eq_ediv
-@[deprecated fdiv_eq_tdiv (since := "2024-09-11")] abbrev fdiv_eq_div := @fdiv_eq_tdiv
-@[deprecated zero_tmod (since := "2024-09-11")] abbrev zero_mod := @zero_tmod
-@[deprecated tmod_zero (since := "2024-09-11")] abbrev mod_zero := @tmod_zero
-@[deprecated tmod_add_tdiv (since := "2024-09-11")] abbrev mod_add_div := @tmod_add_tdiv
-@[deprecated tdiv_add_tmod (since := "2024-09-11")] abbrev div_add_mod := @tdiv_add_tmod
-@[deprecated tmod_add_tdiv' (since := "2024-09-11")] abbrev mod_add_div' := @tmod_add_tdiv'
-@[deprecated tdiv_add_tmod' (since := "2024-09-11")] abbrev div_add_mod' := @tdiv_add_tmod'
-@[deprecated tmod_def (since := "2024-09-11")] abbrev mod_def := @tmod_def
-@[deprecated tmod_eq_emod (since := "2024-09-11")] abbrev mod_eq_emod := @tmod_eq_emod
-@[deprecated fmod_eq_tmod (since := "2024-09-11")] abbrev fmod_eq_mod := @fmod_eq_tmod
-@[deprecated Int.tdiv_one (since := "2024-09-11")] protected abbrev div_one := @Int.tdiv_one
-@[deprecated Int.tdiv_neg (since := "2024-09-11")] protected abbrev div_neg := @Int.tdiv_neg
-@[deprecated Int.neg_tdiv (since := "2024-09-11")] protected abbrev neg_div := @Int.neg_tdiv
-@[deprecated Int.neg_tdiv_neg (since := "2024-09-11")] protected abbrev neg_div_neg := @Int.neg_tdiv_neg
-@[deprecated Int.tdiv_nonneg (since := "2024-09-11")] protected abbrev div_nonneg := @Int.tdiv_nonneg
-@[deprecated Int.tdiv_nonpos (since := "2024-09-11")] protected abbrev div_nonpos := @Int.tdiv_nonpos
-@[deprecated Int.tdiv_eq_zero_of_lt (since := "2024-09-11")] abbrev div_eq_zero_of_lt := @Int.tdiv_eq_zero_of_lt
-@[deprecated Int.mul_tdiv_cancel (since := "2024-09-11")] protected abbrev mul_div_cancel := @Int.mul_tdiv_cancel
-@[deprecated Int.mul_tdiv_cancel_left (since := "2024-09-11")] protected abbrev mul_div_cancel_left := @Int.mul_tdiv_cancel_left
-@[deprecated Int.tdiv_self (since := "2024-09-11")] protected abbrev div_self := @Int.tdiv_self
-@[deprecated Int.mul_tdiv_cancel_of_tmod_eq_zero (since := "2024-09-11")] abbrev mul_div_cancel_of_mod_eq_zero := @Int.mul_tdiv_cancel_of_tmod_eq_zero
-@[deprecated Int.tdiv_mul_cancel_of_tmod_eq_zero (since := "2024-09-11")] abbrev div_mul_cancel_of_mod_eq_zero := @Int.tdiv_mul_cancel_of_tmod_eq_zero
-@[deprecated Int.dvd_of_tmod_eq_zero (since := "2024-09-11")] abbrev dvd_of_mod_eq_zero := @Int.dvd_of_tmod_eq_zero
-@[deprecated Int.mul_tdiv_assoc (since := "2024-09-11")] protected abbrev mul_div_assoc := @Int.mul_tdiv_assoc
-@[deprecated Int.mul_tdiv_assoc' (since := "2024-09-11")] protected abbrev mul_div_assoc' := @Int.mul_tdiv_assoc'
-@[deprecated Int.tdiv_dvd_tdiv (since := "2024-09-11")] abbrev div_dvd_div := @Int.tdiv_dvd_tdiv
-@[deprecated Int.natAbs_tdiv (since := "2024-09-11")] abbrev natAbs_div := @Int.natAbs_tdiv
-@[deprecated Int.tdiv_eq_of_eq_mul_right (since := "2024-09-11")] protected abbrev div_eq_of_eq_mul_right := @Int.tdiv_eq_of_eq_mul_right
-@[deprecated Int.eq_tdiv_of_mul_eq_right (since := "2024-09-11")] protected abbrev eq_div_of_mul_eq_right := @Int.eq_tdiv_of_mul_eq_right
-@[deprecated Int.ofNat_tmod (since := "2024-09-11")] abbrev ofNat_mod := @Int.ofNat_tmod
-@[deprecated Int.tmod_one (since := "2024-09-11")] abbrev mod_one := @Int.tmod_one
-@[deprecated Int.tmod_eq_of_lt (since := "2024-09-11")] abbrev mod_eq_of_lt := @Int.tmod_eq_of_lt
-@[deprecated Int.tmod_lt_of_pos (since := "2024-09-11")] abbrev mod_lt_of_pos := @Int.tmod_lt_of_pos
-@[deprecated Int.tmod_nonneg (since := "2024-09-11")] abbrev mod_nonneg := @Int.tmod_nonneg
-@[deprecated Int.tmod_neg (since := "2024-09-11")] abbrev mod_neg := @Int.tmod_neg
-@[deprecated Int.mul_tmod_left (since := "2024-09-11")] abbrev mul_mod_left := @Int.mul_tmod_left
-@[deprecated Int.mul_tmod_right (since := "2024-09-11")] abbrev mul_mod_right := @Int.mul_tmod_right
-@[deprecated Int.tmod_eq_zero_of_dvd (since := "2024-09-11")] abbrev mod_eq_zero_of_dvd := @Int.tmod_eq_zero_of_dvd
-@[deprecated Int.dvd_iff_tmod_eq_zero (since := "2024-09-11")] abbrev dvd_iff_mod_eq_zero := @Int.dvd_iff_tmod_eq_zero
-@[deprecated Int.neg_mul_tmod_right (since := "2024-09-11")] abbrev neg_mul_mod_right := @Int.neg_mul_tmod_right
-@[deprecated Int.neg_mul_tmod_left (since := "2024-09-11")] abbrev neg_mul_mod_left := @Int.neg_mul_tmod_left
-@[deprecated Int.tdiv_mul_cancel (since := "2024-09-11")] protected abbrev div_mul_cancel := @Int.tdiv_mul_cancel
-@[deprecated Int.mul_tdiv_cancel' (since := "2024-09-11")] protected abbrev mul_div_cancel' := @Int.mul_tdiv_cancel'
-@[deprecated Int.eq_mul_of_tdiv_eq_right (since := "2024-09-11")] protected abbrev eq_mul_of_div_eq_right := @Int.eq_mul_of_tdiv_eq_right
-@[deprecated Int.tmod_self (since := "2024-09-11")] abbrev mod_self := @Int.tmod_self
-@[deprecated Int.neg_tmod_self (since := "2024-09-11")] abbrev neg_mod_self := @Int.neg_tmod_self
-@[deprecated Int.lt_tdiv_add_one_mul_self (since := "2024-09-11")] abbrev lt_div_add_one_mul_self := @Int.lt_tdiv_add_one_mul_self
-@[deprecated Int.tdiv_eq_iff_eq_mul_right (since := "2024-09-11")] protected abbrev div_eq_iff_eq_mul_right := @Int.tdiv_eq_iff_eq_mul_right
-@[deprecated Int.tdiv_eq_iff_eq_mul_left (since := "2024-09-11")] protected abbrev div_eq_iff_eq_mul_left := @Int.tdiv_eq_iff_eq_mul_left
-@[deprecated Int.eq_mul_of_tdiv_eq_left (since := "2024-09-11")] protected abbrev eq_mul_of_div_eq_left := @Int.eq_mul_of_tdiv_eq_left
-@[deprecated Int.tdiv_eq_of_eq_mul_left (since := "2024-09-11")] protected abbrev div_eq_of_eq_mul_left := @Int.tdiv_eq_of_eq_mul_left
-@[deprecated Int.eq_zero_of_tdiv_eq_zero (since := "2024-09-11")] protected abbrev eq_zero_of_div_eq_zero := @Int.eq_zero_of_tdiv_eq_zero
-@[deprecated Int.tdiv_left_inj (since := "2024-09-11")] protected abbrev div_left_inj := @Int.tdiv_left_inj
-@[deprecated Int.tdiv_sign (since := "2024-09-11")] abbrev div_sign := @Int.tdiv_sign
-@[deprecated Int.sign_eq_tdiv_abs (since := "2024-09-11")] protected abbrev sign_eq_div_abs := @Int.sign_eq_tdiv_abs
-@[deprecated Int.tdiv_eq_ediv_of_dvd (since := "2024-09-11")] abbrev div_eq_ediv_of_dvd := @Int.tdiv_eq_ediv_of_dvd

src/Init/Data/List/Attach.lean

@@ -48,8 +48,6 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
 
 @[simp] theorem attach_nil : ([] : List α).attach = [] := rfl
 
-@[simp] theorem attachWith_nil : ([] : List α).attachWith P H = [] := rfl
-
 @[simp]
 theorem pmap_eq_map (p : α → Prop) (f : α → β) (l : List α) (H) :
     @pmap _ _ p (fun a _ => f a) l H = map f l := by
@@ -57,14 +55,11 @@ theorem pmap_eq_map (p : α → Prop) (f : α → β) (l : List α) (H) :
   · rfl
   · simp only [*, pmap, map]
 
-theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a, q a → β} (l : List α) {H₁ H₂}
+theorem pmap_congr {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a, q a → β} (l : List α) {H₁ H₂}
     (h : ∀ a ∈ l, ∀ (h₁ h₂), f a h₁ = g a h₂) : pmap f l H₁ = pmap g l H₂ := by
   induction l with
   | nil => rfl
-  | cons x l ih =>
-    rw [pmap, pmap, h _ (mem_cons_self _ _), ih fun a ha => h a (mem_cons_of_mem _ ha)]
-
-@[deprecated pmap_congr_left (since := "2024-09-06")] abbrev pmap_congr := @pmap_congr_left
+  | cons x l ih => rw [pmap, pmap, h _ (mem_cons_self _ _), ih fun a ha => h a (mem_cons_of_mem _ ha)]
 
 theorem map_pmap {p : α → Prop} (g : β → γ) (f : ∀ a, p a → β) (l H) :
     map g (pmap f l H) = pmap (fun a h => g (f a h)) l H := by
@@ -78,33 +73,16 @@ theorem pmap_map {p : β → Prop} (g : ∀ b, p b → γ) (f : α → β) (l H)
   · rfl
   · simp only [*, pmap, map]
 
-theorem attach_congr {l₁ l₂ : List α} (h : l₁ = l₂) :
-    l₁.attach = l₂.attach.map (fun x => ⟨x.1, h ▸ x.2⟩) := by
-  subst h
-  simp
-
-theorem attachWith_congr {l₁ l₂ : List α} (w : l₁ = l₂) {P : α → Prop} {H : ∀ x ∈ l₁, P x} :
-    l₁.attachWith P H = l₂.attachWith P fun x h => H _ (w ▸ h) := by
-  subst w
-  simp
-
-@[simp] theorem attach_cons {x : α} {xs : List α} :
-    (x :: xs).attach =
-      ⟨x, mem_cons_self x xs⟩ :: xs.attach.map fun ⟨y, h⟩ => ⟨y, mem_cons_of_mem x h⟩ := by
+@[simp] theorem attach_cons (x : α) (xs : List α) :
+    (x :: xs).attach = ⟨x, mem_cons_self x xs⟩ :: 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]
-  apply pmap_congr_left
+  apply pmap_congr
   intros a _ m' _
   rfl
 
-@[simp]
-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 x xs)⟩ ::
-      xs.attachWith p (fun a ha ↦ h a (mem_cons_of_mem x ha)) :=
-  rfl
-
 theorem pmap_eq_map_attach {p : α → Prop} (f : ∀ a, p a → β) (l H) :
     pmap f l H = l.attach.map fun x => f x.1 (H _ x.2) := by
-  rw [attach, attachWith, map_pmap]; exact pmap_congr_left l fun _ _ _ _ => rfl
+  rw [attach, attachWith, map_pmap]; exact pmap_congr l fun _ _ _ _ => rfl
 
 theorem attach_map_coe (l : List α) (f : α → β) :
     (l.attach.map fun (i : {i // i ∈ l}) => f i) = l.map f := by
@@ -117,18 +95,12 @@ theorem attach_map_val (l : List α) (f : α → β) : (l.attach.map fun i => f
 theorem attach_map_subtype_val (l : List α) : l.attach.map Subtype.val = l :=
   (attach_map_coe _ _).trans (List.map_id _)
 
-theorem attachWith_map_coe {p : α → Prop} (f : α → β) (l : List α) (H : ∀ a ∈ l, p a) :
-    ((l.attachWith p H).map fun (i : { i // p i}) => f i) = l.map f := by
-  rw [attachWith, map_pmap]; exact pmap_eq_map _ _ _ _
-
-theorem attachWith_map_val {p : α → Prop} (f : α → β) (l : List α) (H : ∀ a ∈ l, p a) :
-    ((l.attachWith p H).map fun i => f i.val) = l.map f :=
-  attachWith_map_coe _ _ _
+theorem countP_attach (l : List α) (p : α → Bool) : l.attach.countP (fun a : {x // x ∈ l} => p a) = l.countP p := by
+  simp only [← Function.comp_apply (g := Subtype.val), ← countP_map, attach_map_subtype_val]
 
 @[simp]
-theorem attachWith_map_subtype_val {p : α → Prop} (l : List α) (H : ∀ a ∈ l, p a) :
-    (l.attachWith p H).map Subtype.val = l :=
-  (attachWith_map_coe _ _ _).trans (List.map_id _)
+theorem count_attach [DecidableEq 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 _ _
 
 @[simp]
 theorem mem_attach (l : List α) : ∀ x, x ∈ l.attach
@@ -142,11 +114,6 @@ theorem mem_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H b} :
     b ∈ pmap f l H ↔ ∃ (a : _) (h : a ∈ l), f a (H a h) = b := by
   simp only [pmap_eq_map_attach, mem_map, mem_attach, true_and, Subtype.exists, eq_comm]
 
-theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {l H} {a} (h : a ∈ l) :
-    f a (H a h) ∈ pmap f l H := by
-  rw [mem_pmap]
-  exact ⟨a, h, rfl⟩
-
 @[simp]
 theorem length_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H} : length (pmap f l H) = length l := by
   induction l
@@ -154,43 +121,21 @@ theorem length_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H} : length (pm
   · simp only [*, pmap, length]
 
 @[simp]
-theorem length_attach {L : List α} : L.attach.length = L.length :=
+theorem length_attach (L : List α) : L.attach.length = L.length :=
   length_pmap
 
 @[simp]
-theorem length_attachWith {p : α → Prop} {l H} : length (l.attachWith p H) = length l :=
-  length_pmap
-
-@[simp]
-theorem pmap_eq_nil_iff {p : α → Prop} {f : ∀ a, p a → β} {l H} : pmap f l H = [] ↔ l = [] := by
+theorem pmap_eq_nil {p : α → Prop} {f : ∀ a, p a → β} {l H} : pmap f l H = [] ↔ l = [] := by
   rw [← length_eq_zero, length_pmap, length_eq_zero]
 
-theorem pmap_ne_nil_iff {P : α → Prop} (f : (a : α) → P a → β) {xs : List α}
+theorem pmap_ne_nil {P : α → Prop} (f : (a : α) → P a → β) {xs : List α}
     (H : ∀ (a : α), a ∈ xs → P a) : xs.pmap f H ≠ [] ↔ xs ≠ [] := by
   simp
 
 @[simp]
-theorem attach_eq_nil_iff {l : List α} : l.attach = [] ↔ l = [] :=
-  pmap_eq_nil_iff
+theorem attach_eq_nil {l : List α} : l.attach = [] ↔ l = [] :=
+  pmap_eq_nil
 
-theorem attach_ne_nil_iff {l : List α} : l.attach ≠ [] ↔ l ≠ [] :=
-  pmap_ne_nil_iff _ _
-
-@[simp]
-theorem attachWith_eq_nil_iff {l : List α} {P : α → Prop} {H : ∀ a ∈ l, P a} :
-    l.attachWith P H = [] ↔ l = [] :=
-  pmap_eq_nil_iff
-
-theorem attachWith_ne_nil_iff {l : List α} {P : α → Prop} {H : ∀ a ∈ l, P a} :
-    l.attachWith P H ≠ [] ↔ l ≠ [] :=
-  pmap_ne_nil_iff _ _
-
-@[deprecated pmap_eq_nil_iff (since := "2024-09-06")] abbrev pmap_eq_nil := @pmap_eq_nil_iff
-@[deprecated pmap_ne_nil_iff (since := "2024-09-06")] abbrev pmap_ne_nil := @pmap_ne_nil_iff
-@[deprecated attach_eq_nil_iff (since := "2024-09-06")] abbrev attach_eq_nil := @attach_eq_nil_iff
-@[deprecated attach_ne_nil_iff (since := "2024-09-06")] abbrev attach_ne_nil := @attach_ne_nil_iff
-
-@[simp]
 theorem getElem?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h : ∀ a ∈ l, p a) (n : Nat) :
     (pmap f l h)[n]? = Option.pmap f l[n]? fun x H => h x (getElem?_mem H) := by
   induction l generalizing n with
@@ -212,12 +157,11 @@ theorem get?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h :
   simp only [get?_eq_getElem?]
   simp [getElem?_pmap, h]
 
-@[simp]
 theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h : ∀ a ∈ l, p a) {n : Nat}
     (hn : n < (pmap f l h).length) :
     (pmap f l h)[n] =
       f (l[n]'(@length_pmap _ _ p f l h ▸ hn))
-        (h _ (getElem_mem (@length_pmap _ _ p f l h ▸ hn))) := by
+        (h _ (getElem_mem l n (@length_pmap _ _ p f l h ▸ hn))) := by
   induction l generalizing n with
   | nil =>
     simp only [length, pmap] at hn
@@ -235,30 +179,8 @@ theorem get_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : List α} (h :
   simp only [get_eq_getElem]
   simp [getElem_pmap]
 
-@[simp]
-theorem getElem?_attachWith {xs : List α} {i : Nat} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
-    (xs.attachWith P H)[i]? = xs[i]?.pmap Subtype.mk (fun _ a => H _ (getElem?_mem a)) :=
-  getElem?_pmap ..
-
-@[simp]
-theorem getElem?_attach {xs : List α} {i : Nat} :
-    xs.attach[i]? = xs[i]?.pmap Subtype.mk (fun _ a => getElem?_mem a) :=
-  getElem?_attachWith
-
-@[simp]
-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]
-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 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
+    (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 =>
@@ -272,161 +194,6 @@ theorem getElem_attach {xs : List α} {i : Nat} (h : i < xs.attach.length) :
   | nil => simp at h
   | cons x xs ih => simp [head_pmap, ih]
 
-@[simp] 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_mem_head? h)⟩) := by
-  cases xs <;> simp_all
-
-@[simp] 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]
-
-@[simp] theorem head?_attach (xs : List α) :
-    xs.attach.head? = xs.head?.pbind (fun a h => some ⟨a, mem_of_mem_head? h⟩) := by
-  cases xs <;> simp_all
-
-@[simp] 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]
-
-@[simp] 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}
-    {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) :
-    xs.attach.tail = xs.tail.attach.map (fun ⟨x, h⟩ => ⟨x, mem_of_mem_tail h⟩) := by
-  cases xs <;> simp
-
-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]
-
-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]
-
-/--
-If we fold over `l.attach` with a function that ignores the membership predicate,
-we get the same results as folding over `l` directly.
-
-This is useful when we need to use `attach` to show termination.
-
-Unfortunately this can't be applied by `simp` because of the higher order unification problem,
-and even when rewriting we need to specify the function explicitly.
--/
-theorem foldl_attach (l : List α) (f : β → α → β) (b : β) :
-    l.attach.foldl (fun acc t => f acc t.1) b = l.foldl f b := by
-  induction l generalizing b with
-  | nil => simp
-  | cons a l ih => rw [foldl_cons, attach_cons, foldl_cons, foldl_map, ih]
-
-/--
-If we fold over `l.attach` with a function that ignores the membership predicate,
-we get the same results as folding over `l` directly.
-
-This is useful when we need to use `attach` to show termination.
-
-Unfortunately this can't be applied by `simp` because of the higher order unification problem,
-and even when rewriting we need to specify the function explicitly.
--/
-theorem foldr_attach (l : List α) (f : α → β → β) (b : β) :
-    l.attach.foldr (fun t acc => f t.1 acc) b = l.foldr f b := by
-  induction l generalizing b with
-  | nil => simp
-  | cons a l ih => rw [foldr_cons, attach_cons, foldr_cons, foldr_map, ih]
-
-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 f h⟩) := by
-  induction l <;> simp [*]
-
-theorem attachWith_map {l : List α} (f : α → β) {P : β → Prop} {H : ∀ (b : β), b ∈ l.map f → P b} :
-    (l.map f).attachWith P H = (l.attachWith (P ∘ f) (fun a h => H _ (mem_map_of_mem f h))).map
-      fun ⟨x, h⟩ => ⟨f x, h⟩ := by
-  induction l <;> simp [*]
-
-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.pmap (fun a (h : a ∈ l ∧ P a) => f ⟨a, H _ h.1⟩) (fun a h => ⟨h, H a h⟩) := by
-  induction l with
-  | nil => rfl
-  | cons x xs ih =>
-    simp only [attachWith_cons, map_cons, ih, pmap, cons.injEq, true_and]
-    apply pmap_congr_left
-    simp
-
-/-- See also `pmap_eq_map_attach` for writing `pmap` in terms of `map` and `attach`. -/
-theorem map_attach {l : List α} (f : { x // x ∈ l } → β) :
-    l.attach.map f = l.pmap (fun a h => f ⟨a, h⟩) (fun _ => id) := by
-  induction l with
-  | nil => rfl
-  | cons x xs ih =>
-    simp only [attach_cons, map_cons, map_map, Function.comp_apply, pmap, cons.injEq, true_and, ih]
-    apply pmap_congr_left
-    simp
-
-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]
-    split <;> rename_i h
-    · simp only [Option.pbind_eq_none_iff, reduceCtorEq, Option.mem_def, exists_false,
-        or_false] at h
-      rw [attach_congr]
-      rotate_left
-      · simp only [h]
-        rfl
-      rw [ih]
-      simp only [map_filterMap, Option.map_pbind, Option.map_some']
-      rfl
-    · simp only [Option.pbind_eq_some_iff] at h
-      obtain ⟨a, h, w⟩ := h
-      simp only [Option.some.injEq] at w
-      subst w
-      simp only [Option.mem_def] at h
-      rw [attach_congr]
-      rotate_left
-      · simp only [h]
-        rfl
-      rw [attach_cons, map_cons, map_map, ih, map_filterMap]
-      congr
-      ext
-      simp
-
-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
-  rw [attach_congr (congrFun (filterMap_eq_filter _).symm _), attach_filterMap, map_filterMap]
-  simp only [Option.guard]
-  congr
-  ext1
-  split <;> simp
-
--- We are still missing here `attachWith_filterMap` and `attachWith_filter`.
--- Also missing are `filterMap_attach`, `filter_attach`, `filterMap_attachWith` and `filter_attachWith`.
-
-theorem pmap_pmap {p : α → Prop} {q : β → Prop} (g : ∀ a, p a → β) (f : ∀ b, q b → γ) (l H₁ H₂) :
-    pmap f (pmap g l H₁) H₂ =
-      pmap (α := { x // x ∈ l }) (fun a h => f (g a h) (H₂ (g a h) (mem_pmap_of_mem a.2))) l.attach
-        (fun a _ => H₁ a a.2) := by
-  simp [pmap_eq_map_attach, attach_map]
-
 @[simp] 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 =
@@ -444,57 +211,46 @@ theorem pmap_append' {p : α → Prop} (f : ∀ a : α, p a → β) (l₁ l₂ :
       l₁.pmap f h₁ ++ l₂.pmap f h₂ :=
   pmap_append f l₁ l₂ _
 
+@[simp] 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
+
+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 attach_append (xs ys : List α) :
     (xs ++ ys).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_append_of_mem_left ys h⟩) ++
       ys.attach.map fun ⟨x, h⟩ => ⟨x, mem_append_of_mem_right xs h⟩ := by
   simp only [attach, attachWith, pmap, map_pmap, pmap_append]
   congr 1 <;>
-  exact pmap_congr_left _ fun _ _ _ _ => rfl
+  exact pmap_congr _ fun _ _ _ _ => rfl
 
-@[simp] theorem attachWith_append {P : α → Prop} {xs ys : List α}
-    {H : ∀ (a : α), a ∈ xs ++ ys → P a} :
-    (xs ++ ys).attachWith P H = xs.attachWith P (fun a h => H a (mem_append_of_mem_left ys h)) ++
-      ys.attachWith P (fun a h => H a (mem_append_of_mem_right xs h)) := by
-  simp only [attachWith, attach_append, map_pmap, pmap_append]
-
-@[simp] theorem pmap_reverse {P : α → Prop} (f : (a : α) → P a → β) (xs : List α)
-    (H : ∀ (a : α), a ∈ xs.reverse → P a) :
-    xs.reverse.pmap f H = (xs.pmap f (fun a h => H a (by simpa using h))).reverse := by
-  induction xs <;> simp_all
-
-theorem reverse_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : 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}
-    {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 ..
-
-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) :
-    xs.reverse.attach = xs.attach.reverse.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
+@[simp] 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
+  apply pmap_congr
   intros
   rfl
 
-theorem reverse_attach (xs : List α) :
-    xs.attach.reverse = xs.reverse.attach.map fun ⟨x, h⟩ => ⟨x, by simpa using h⟩ := by
+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]
-  apply pmap_congr_left
+  apply pmap_congr
   intros
   rfl
 
+
+theorem getLast?_attach {xs : List α} :
+    xs.attach.getLast? = match h : xs.getLast? with | none => none | some a => some ⟨a, mem_of_getLast?_eq_some h⟩ := by
+  rw [getLast?_eq_head?_reverse, reverse_attach, head?_map]
+  split <;> rename_i h
+  · simp only [getLast?_eq_none_iff] at h
+    subst h
+    simp
+  · obtain ⟨ys, rfl⟩ := getLast?_eq_some_iff.mp h
+    simp
+
 @[simp] 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
+    (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]
   rw [reverse_pmap, reverse_attach, head?_map, pmap_eq_map_attach, head?_map]
   simp only [Option.map_map]
@@ -503,49 +259,14 @@ theorem reverse_attach (xs : List α) :
 @[simp] 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}
-    {H : ∀ (a : α), a ∈ xs → P a} :
-    (xs.attachWith P H).getLast? = xs.getLast?.pbind (fun a h => some ⟨a, H _ (mem_of_getLast?_eq_some h)⟩) := by
-  rw [getLast?_eq_head?_reverse, reverse_attachWith, head?_attachWith]
-  simp
-
-@[simp] 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]
-theorem getLast?_attach {xs : List α} :
-    xs.attach.getLast? = xs.getLast?.pbind fun a h => some ⟨a, mem_of_getLast?_eq_some h⟩ := by
-  rw [getLast?_eq_head?_reverse, reverse_attach, head?_map, head?_attach]
-  simp
-
-@[simp]
-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]
-
-@[simp]
-theorem countP_attach (l : List α) (p : α → Bool) :
-    l.attach.countP (fun a : {x // x ∈ l} => p a) = l.countP p := by
-  simp only [← Function.comp_apply (g := Subtype.val), ← countP_map, attach_map_subtype_val]
-
-@[simp]
-theorem countP_attachWith {p : α → Prop} (l : List α) (H : ∀ a ∈ l, p a) (q : α → Bool) :
-    (l.attachWith p H).countP (fun a : {x // p x} => q a) = l.countP q := by
-  simp only [← Function.comp_apply (g := Subtype.val), ← countP_map, attachWith_map_subtype_val]
-
-@[simp]
-theorem count_attach [DecidableEq 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 _ _
-
-@[simp]
-theorem count_attachWith [DecidableEq 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 _ _ _
+  simp only [getLast_eq_iff_getLast_eq_some, getLast?_pmap, Option.map_eq_some', Subtype.exists]
+  refine ⟨xs.getLast (by simpa using h), by simp, ?_⟩
+  simp only [getLast?_attach, and_true]
+  split <;> rename_i h'
+  · simp only [getLast?_eq_none_iff] at h'
+    subst h'
+    simp at h
+  · symm
+    simpa [getLast_eq_iff_getLast_eq_some]
 
 end List

src/Init/Data/List/Basic.lean

@@ -1588,14 +1588,6 @@ such that adjacent elements are related by `R`.
   | []    => []
   | a::as => loop as a [] []
 where
-  /--
-  The arguments of `groupBy.loop l ag g gs` represent the following:
-
-  - `l : List α` are the elements which we still need to group.
-  - `ag : α` is the previous element for which a comparison was performed.
-  - `g : List α` is the group currently being assembled, in **reverse order**.
-  - `gs : List (List α)` is all of the groups that have been completed, in **reverse order**.
-  -/
   @[specialize] loop : List α → α → List α → List (List α) → List (List α)
   | a::as, ag, g, gs => match R ag a with
     | true  => loop as a (ag::g) gs

src/Init/Data/List/BasicAux.lean

@@ -155,7 +155,7 @@ def mapMono (as : List α) (f : α → α) : List α :=
 
 /-! ## Additional lemmas required for bootstrapping `Array`. -/
 
-theorem getElem_append_left {as bs : List α} (h : i < as.length) {h'} : (as ++ bs)[i] = as[i] := by
+theorem getElem_append_left (as bs : List α) (h : i < as.length) {h'} : (as ++ bs)[i] = as[i] := by
   induction as generalizing i with
   | nil => trivial
   | cons a as ih =>
@@ -163,14 +163,12 @@ theorem getElem_append_left {as bs : List α} (h : i < as.length) {h'} : (as ++
     | zero => rfl
     | succ i => apply ih
 
-theorem getElem_append_right {as bs : List α} {i : Nat} (h₁ : as.length ≤ i) {h₂} :
-    (as ++ bs)[i]'h₂ =
-      bs[i - as.length]'(by rw [length_append] at h₂; exact Nat.sub_lt_left_of_lt_add h₁ h₂) := by
+theorem getElem_append_right (as bs : List α) (h : ¬ i < as.length) {h' h''} : (as ++ bs)[i]'h' = bs[i - as.length]'h'' := by
   induction as generalizing i with
   | nil => trivial
   | cons a as ih =>
-    cases i with simp [get, Nat.succ_sub_succ] <;> simp [Nat.succ_sub_succ] at h₁
-    | succ i => apply ih; simp [h₁]
+    cases i with simp [get, Nat.succ_sub_succ] <;> simp [Nat.succ_sub_succ] at h
+    | succ i => apply ih; simp [h]
 
 theorem get_last {as : List α} {i : Fin (length (as ++ [a]))} (h : ¬ i.1 < as.length) : (as ++ [a] : List _).get i = a := by
   cases i; rename_i i h'

src/Init/Data/List/Count.lean

@@ -40,9 +40,6 @@ protected theorem countP_go_eq_add (l) : countP.go p l n = n + countP.go p l 0 :
 theorem countP_cons (a : α) (l) : countP p (a :: l) = countP p l + if p a then 1 else 0 := by
   by_cases h : p a <;> simp [h]
 
-theorem countP_singleton (a : α) : countP p [a] = if p a then 1 else 0 := by
-  simp [countP_cons]
-
 theorem length_eq_countP_add_countP (l) : length l = countP p l + countP (fun a => ¬p a) l := by
   induction l with
   | nil => rfl
@@ -64,10 +61,6 @@ theorem countP_eq_length_filter (l) : countP p l = length (filter p l) := by
     then rw [countP_cons_of_pos p l h, ih, filter_cons_of_pos h, length]
     else rw [countP_cons_of_neg p l h, ih, filter_cons_of_neg h]
 
-theorem countP_eq_length_filter' : countP p = length ∘ filter p := by
-  funext l
-  apply countP_eq_length_filter
-
 theorem countP_le_length : countP p l ≤ l.length := by
   simp only [countP_eq_length_filter]
   apply length_filter_le
@@ -75,38 +68,15 @@ theorem countP_le_length : countP p l ≤ l.length := by
 @[simp] theorem countP_append (l₁ l₂) : countP p (l₁ ++ l₂) = countP p l₁ + countP p l₂ := 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
+theorem countP_pos {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]
 
-@[deprecated countP_pos_iff (since := "2024-09-09")] abbrev countP_pos := @countP_pos_iff
-
-@[simp] theorem one_le_countP_iff {p} : 1 ≤ countP p l ↔ ∃ a ∈ l, p a :=
-  countP_pos_iff
-
-@[simp] theorem countP_eq_zero {p} : countP p l = 0 ↔ ∀ a ∈ l, ¬p a := by
+theorem countP_eq_zero {p} : countP p l = 0 ↔ ∀ a ∈ l, ¬p a := by
   simp only [countP_eq_length_filter, length_eq_zero, filter_eq_nil_iff]
 
-@[simp] theorem countP_eq_length {p} : countP p l = l.length ↔ ∀ a ∈ l, p a := by
+theorem countP_eq_length {p} : countP p l = l.length ↔ ∀ a ∈ l, p a := by
   rw [countP_eq_length_filter, filter_length_eq_length]
 
-theorem countP_replicate (p : α → Bool) (a : α) (n : Nat) :
-    countP p (replicate n a) = if p a then n else 0 := by
-  simp only [countP_eq_length_filter, filter_replicate]
-  split <;> simp
-
-theorem boole_getElem_le_countP (p : α → Bool) (l : List α) (i : Nat) (h : i < l.length) :
-    (if p l[i] then 1 else 0) ≤ l.countP p := by
-  induction l generalizing i with
-  | nil => simp at h
-  | cons x l ih =>
-    cases i with
-    | zero => simp [countP_cons]
-    | succ i =>
-      simp only [length_cons, add_one_lt_add_one_iff] at h
-      simp only [getElem_cons_succ, countP_cons]
-      specialize ih _ h
-      exact le_add_right_of_le ih
-
 theorem Sublist.countP_le (s : l₁ <+ l₂) : countP p l₁ ≤ countP p l₂ := by
   simp only [countP_eq_length_filter]
   apply s.filter _ |>.length_le
@@ -115,23 +85,16 @@ theorem IsPrefix.countP_le (s : l₁ <+: l₂) : countP p l₁ ≤ countP p l₂
 theorem IsSuffix.countP_le (s : l₁ <:+ l₂) : countP p l₁ ≤ countP p l₂ := s.sublist.countP_le _
 theorem IsInfix.countP_le (s : l₁ <:+: l₂) : countP p l₁ ≤ countP p l₂ := s.sublist.countP_le _
 
--- See `Init.Data.List.Nat.Count` for `Sublist.le_countP : countP p l₂ - (l₂.length - l₁.length) ≤ countP p l₁`.
-
-theorem countP_tail_le (l) : countP p l.tail ≤ countP p l :=
-  (tail_sublist l).countP_le _
-
--- See `Init.Data.List.Nat.Count` for `le_countP_tail : countP p l - 1 ≤ countP p l.tail`.
-
 theorem countP_filter (l : List α) :
-    countP p (filter q l) = countP (fun a => p a && q a) l := by
+    countP p (filter q l) = countP (fun a => p a ∧ q a) l := by
   simp only [countP_eq_length_filter, filter_filter]
 
-@[simp] theorem countP_true : (countP fun (_ : α) => true) = length := by
-  funext l
+@[simp] theorem countP_true {l : List α} : (l.countP fun _ => true) = l.length := by
+  rw [countP_eq_length]
   simp
 
-@[simp] theorem countP_false : (countP fun (_ : α) => false) = Function.const _ 0 := by
-  funext l
+@[simp] theorem countP_false {l : List α} : (l.countP fun _ => false) = 0 := by
+  rw [countP_eq_zero]
   simp
 
 @[simp] theorem countP_map (p : β → Bool) (f : α → β) :
@@ -139,30 +102,6 @@ theorem countP_filter (l : List α) :
   | [] => rfl
   | a :: l => by rw [map_cons, countP_cons, countP_cons, countP_map p f l]; rfl
 
-theorem length_filterMap_eq_countP (f : α → Option β) (l : List α) :
-    (filterMap f l).length = countP (fun a => (f a).isSome) l := by
-  induction l with
-  | nil => rfl
-  | cons x l ih =>
-    simp only [filterMap_cons, countP_cons]
-    split <;> simp [ih, *]
-
-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
-  simp only [countP_eq_length_filter, filter_filterMap, ← filterMap_eq_filter]
-  simp only [length_filterMap_eq_countP]
-  congr
-  ext a
-  simp (config := { contextual := true }) [Option.getD_eq_iff]
-
-@[simp] theorem countP_join (l : List (List α)) :
-    countP p l.join = Nat.sum (l.map (countP p)) := by
-  simp only [countP_eq_length_filter, filter_join]
-  simp [countP_eq_length_filter']
-
-@[simp] theorem countP_reverse (l : List α) : countP p l.reverse = countP p l := by
-  simp [countP_eq_length_filter, filter_reverse]
-
 variable {p q}
 
 theorem countP_mono_left (h : ∀ x ∈ l, p x → q x) : countP p l ≤ countP q l := by
@@ -197,11 +136,6 @@ theorem count_cons (a b : α) (l : List α) :
     count a (b :: l) = count a l + if b == a then 1 else 0 := by
   simp [count, countP_cons]
 
-theorem count_eq_countP (a : α) (l : List α) : count a l = countP (· == a) l := rfl
-theorem count_eq_countP' {a : α} : count a = countP (· == a) := by
-  funext l
-  apply count_eq_countP
-
 theorem count_tail : ∀ (l : List α) (a : α) (h : l ≠ []),
       l.tail.count a = l.count a - if l.head h == a then 1 else 0
   | head :: tail, a, _ => by simp [count_cons]
@@ -214,13 +148,6 @@ theorem IsPrefix.count_le (h : l₁ <+: l₂) (a : α) : count a l₁ ≤ count
 theorem IsSuffix.count_le (h : l₁ <:+ l₂) (a : α) : count a l₁ ≤ count a l₂ := h.sublist.count_le _
 theorem IsInfix.count_le (h : l₁ <:+: l₂) (a : α) : count a l₁ ≤ count a l₂ := h.sublist.count_le _
 
--- See `Init.Data.List.Nat.Count` for `Sublist.le_count : count a l₂ - (l₂.length - l₁.length) ≤ countP a l₁`.
-
-theorem count_tail_le (a : α) (l) : count a l.tail ≤ count a l :=
-  (tail_sublist l).count_le _
-
--- See `Init.Data.List.Nat.Count` for `le_count_tail : count a l - 1 ≤ count a l.tail`.
-
 theorem count_le_count_cons (a b : α) (l : List α) : count a l ≤ count a (b :: l) :=
   (sublist_cons_self _ _).count_le _
 
@@ -230,17 +157,6 @@ theorem count_singleton (a b : α) : count a [b] = if b == a then 1 else 0 := by
 @[simp] theorem count_append (a : α) : ∀ l₁ l₂, count a (l₁ ++ l₂) = count a l₁ + count a l₂ :=
   countP_append _
 
-theorem count_join (a : α) (l : List (List α)) : count a l.join = Nat.sum (l.map (count a)) := by
-  simp only [count_eq_countP, countP_join, count_eq_countP']
-
-@[simp] theorem count_reverse (a : α) (l : List α) : count a l.reverse = count a l := by
-  simp only [count_eq_countP, countP_eq_length_filter, filter_reverse, length_reverse]
-
-theorem boole_getElem_le_count (a : α) (l : List α) (i : Nat) (h : i < l.length) :
-    (if l[i] == a then 1 else 0) ≤ l.count a := by
-  rw [count_eq_countP]
-  apply boole_getElem_le_countP (· == a)
-
 variable [LawfulBEq α]
 
 @[simp] theorem count_cons_self (a : α) (l : List α) : count a (a :: l) = count a l + 1 := by
@@ -256,19 +172,14 @@ theorem count_concat_self (a : α) (l : List α) :
     count a (concat l a) = (count a l) + 1 := by simp
 
 @[simp]
-theorem count_pos_iff {a : α} {l : List α} : 0 < count a l ↔ a ∈ l := by
-  simp only [count, countP_pos_iff, beq_iff_eq, exists_eq_right]
-
-@[deprecated count_pos_iff (since := "2024-09-09")] abbrev count_pos_iff_mem := @count_pos_iff
-
-@[simp] theorem one_le_count_iff {a : α} {l : List α} : 1 ≤ count a l ↔ a ∈ l :=
-  count_pos_iff
+theorem count_pos_iff_mem {a : α} {l : List α} : 0 < count a l ↔ a ∈ l := by
+  simp only [count, countP_pos, beq_iff_eq, exists_eq_right]
 
 theorem count_eq_zero_of_not_mem {a : α} {l : List α} (h : a ∉ l) : count a l = 0 :=
-  Decidable.byContradiction fun h' => h <| count_pos_iff.1 (Nat.pos_of_ne_zero h')
+  Decidable.byContradiction fun h' => h <| count_pos_iff_mem.1 (Nat.pos_of_ne_zero h')
 
 theorem not_mem_of_count_eq_zero {a : α} {l : List α} (h : count a l = 0) : a ∉ l :=
-  fun h' => Nat.ne_of_lt (count_pos_iff.2 h') h.symm
+  fun h' => Nat.ne_of_lt (count_pos_iff_mem.2 h') h.symm
 
 theorem count_eq_zero {l : List α} : count a l = 0 ↔ a ∉ l :=
   ⟨not_mem_of_count_eq_zero, count_eq_zero_of_not_mem⟩
@@ -313,15 +224,6 @@ theorem count_le_count_map [DecidableEq β] (l : List α) (f : α → β) (x :
   rw [count, count, countP_map]
   apply countP_mono_left; simp (config := { contextual := true })
 
-theorem count_filterMap {α} [BEq β] (b : β) (f : α → Option β) (l : List α) :
-    count b (filterMap f l) = countP (fun a => f a == some b) l := by
-  rw [count_eq_countP, countP_filterMap]
-  congr
-  ext a
-  obtain _ | b := f a
-  · simp
-  · simp
-
 theorem count_erase (a b : α) :
     ∀ l : List α, count a (l.erase b) = count a l - if b == a then 1 else 0
   | [] => by simp

src/Init/Data/List/Erase.lean

@@ -109,10 +109,6 @@ protected theorem Sublist.eraseP : l₁ <+ l₂ → l₁.eraseP p <+ l₂.eraseP
 theorem length_eraseP_le (l : List α) : (l.eraseP p).length ≤ l.length :=
   l.eraseP_sublist.length_le
 
-theorem le_length_eraseP (l : List α) : l.length - 1 ≤ (l.eraseP p).length := by
-  rw [length_eraseP]
-  split <;> simp
-
 theorem mem_of_mem_eraseP {l : List α} : a ∈ l.eraseP p → a ∈ l := (eraseP_subset _ ·)
 
 @[simp] theorem mem_eraseP_of_neg {l : List α} (pa : ¬p a) : a ∈ l.eraseP p ↔ a ∈ l := by
@@ -336,10 +332,6 @@ theorem IsPrefix.erase (a : α) {l₁ l₂ : List α} (h : l₁ <+: l₂) : l₁
 theorem length_erase_le (a : α) (l : List α) : (l.erase a).length ≤ l.length :=
   (erase_sublist a l).length_le
 
-theorem le_length_erase [LawfulBEq α] (a : α) (l : List α) : l.length - 1 ≤ (l.erase a).length := by
-  rw [length_erase]
-  split <;> simp
-
 theorem mem_of_mem_erase {a b : α} {l : List α} (h : a ∈ l.erase b) : a ∈ l := erase_subset _ _ h
 
 @[simp] theorem mem_erase_of_ne [LawfulBEq α] {a b : α} {l : List α} (ab : a ≠ b) :
@@ -460,22 +452,13 @@ end erase
 
 /-! ### eraseIdx -/
 
-theorem length_eraseIdx (l : List α) (i : Nat) :
-    (l.eraseIdx i).length = if i < l.length then l.length - 1 else l.length := by
-  induction l generalizing i with
-  | nil => simp
-  | cons x l ih =>
-    cases i with
-    | zero => simp
-    | succ i =>
-      simp only [eraseIdx, length_cons, ih, add_one_lt_add_one_iff, Nat.add_one_sub_one]
-      split
-      · cases l <;> simp_all
-      · rfl
-
-theorem length_eraseIdx_of_lt {l : List α} {i} (h : i < length l) :
-    (l.eraseIdx i).length = length l - 1 := by
-  simp [length_eraseIdx, h]
+theorem length_eraseIdx : ∀ {l i}, i < length l → length (@eraseIdx α l i) = length l - 1
+  | [], _, _ => rfl
+  | _::_, 0, _ => by simp [eraseIdx]
+  | x::xs, i+1, h => by
+    have : i < length xs := Nat.lt_of_succ_lt_succ h
+    simp [eraseIdx, ← Nat.add_one]
+    rw [length_eraseIdx this, Nat.sub_add_cancel (Nat.lt_of_le_of_lt (Nat.zero_le _) this)]
 
 @[simp] theorem eraseIdx_zero (l : List α) : eraseIdx l 0 = tail l := by cases l <;> rfl
 
@@ -485,8 +468,6 @@ theorem eraseIdx_eq_take_drop_succ :
   | a::l, 0 => by simp
   | a::l, i + 1 => by simp [eraseIdx_eq_take_drop_succ l i]
 
--- See `Init.Data.List.Nat.Erase` for `getElem?_eraseIdx` and `getElem_eraseIdx`.
-
 @[simp] theorem eraseIdx_eq_nil {l : List α} {i : Nat} : eraseIdx l i = [] ↔ l = [] ∨ (length l = 1 ∧ i = 0) := by
   match l, i with
   | [], _
@@ -518,13 +499,6 @@ theorem eraseIdx_eq_self : ∀ {l : List α} {k : Nat}, eraseIdx l k = l ↔ len
 theorem eraseIdx_of_length_le {l : List α} {k : Nat} (h : length l ≤ k) : eraseIdx l k = l := by
   rw [eraseIdx_eq_self.2 h]
 
-theorem length_eraseIdx_le (l : List α) (i : Nat) : length (l.eraseIdx i) ≤ length l :=
-  (eraseIdx_sublist l i).length_le
-
-theorem le_length_eraseIdx (l : List α) (i : Nat) : length l - 1 ≤ length (l.eraseIdx i) := by
-  rw [length_eraseIdx]
-  split <;> simp
-
 theorem eraseIdx_append_of_lt_length {l : List α} {k : Nat} (hk : k < length l) (l' : List α) :
     eraseIdx (l ++ l') k = eraseIdx l k ++ l' := by
   induction l generalizing k with
@@ -546,7 +520,7 @@ theorem eraseIdx_append_of_length_le {l : List α} {k : Nat} (hk : length l ≤
 theorem eraseIdx_replicate {n : Nat} {a : α} {k : Nat} :
     (replicate n a).eraseIdx k = if k < n then replicate (n - 1) a else replicate n a := by
   split <;> rename_i h
-  · rw [eq_replicate_iff, length_eraseIdx_of_lt (by simpa using h)]
+  · rw [eq_replicate_iff, length_eraseIdx (by simpa using h)]
     simp only [length_replicate, true_and]
     intro b m
     replace m := mem_of_mem_eraseIdx m

src/Init/Data/List/Find.lean

@@ -224,7 +224,7 @@ theorem find?_eq_some : xs.find? p = some b ↔ p b ∧ ∃ as bs, xs = as ++ b
           simp only [cons_append] at h₁
           obtain ⟨rfl, -⟩ := h₁
           simp_all
-    · simp only [ih, Bool.not_eq_eq_eq_not, Bool.not_true, exists_and_right, and_congr_right_iff]
+    · simp only [ih, Bool.not_eq_true', exists_and_right, and_congr_right_iff]
       intro pb
       constructor
       · rintro ⟨as, ⟨⟨bs, rfl⟩, h₁⟩⟩
@@ -266,7 +266,7 @@ theorem mem_of_find?_eq_some : ∀ {l}, find? p l = some a → a ∈ l
     · exact H ▸ .head _
     · exact .tail _ (mem_of_find?_eq_some H)
 
-theorem get_find?_mem (xs : List α) (p : α → Bool) (h) : (xs.find? p).get h ∈ xs := by
+@[simp] theorem get_find?_mem (xs : List α) (p : α → Bool) (h) : (xs.find? p).get h ∈ xs := by
   induction xs with
   | nil => simp at h
   | cons x xs ih =>
@@ -539,7 +539,7 @@ theorem findIdx_lt_length {p : α → Bool} {xs : List α} :
 
 /-- `p` does not hold for elements with indices less than `xs.findIdx p`. -/
 theorem not_of_lt_findIdx {p : α → Bool} {xs : List α} {i : Nat} (h : i < xs.findIdx p) :
-    p (xs[i]'(Nat.le_trans h (findIdx_le_length p))) = false := by
+    ¬p (xs[i]'(Nat.le_trans h (findIdx_le_length p))) := by
   revert i
   induction xs with
   | nil => intro i h; rw [findIdx_nil] at h; simp at h
@@ -547,14 +547,10 @@ theorem not_of_lt_findIdx {p : α → Bool} {xs : List α} {i : Nat} (h : i < xs
     intro i h
     have ho := h
     rw [findIdx_cons] at h
-    have npx : p x = false := by
-      apply eq_false_of_ne_true
-      intro y
-      rw [y, cond_true] at h
-      simp at h
+    have npx : ¬p x := by intro y; rw [y, cond_true] at h; simp at h
     simp [npx, cond_false] at h
     cases i.eq_zero_or_pos with
-    | inl e => simpa [e, Fin.zero_eta, get_cons_zero]
+    | inl e => simpa only [e, Fin.zero_eta, get_cons_zero]
     | inr e =>
       have ipm := Nat.succ_pred_eq_of_pos e
       have ilt := Nat.le_trans ho (findIdx_le_length p)
@@ -564,11 +560,11 @@ theorem not_of_lt_findIdx {p : α → Bool} {xs : List α} {i : Nat} (h : i < xs
 
 /-- If `¬ p xs[j]` for all `j < i`, then `i ≤ xs.findIdx p`. -/
 theorem le_findIdx_of_not {p : α → Bool} {xs : List α} {i : Nat} (h : i < xs.length)
-    (h2 : ∀ j (hji : j < i), p (xs[j]'(Nat.lt_trans hji h)) = false) : i ≤ xs.findIdx p := by
+    (h2 : ∀ j (hji : j < i), ¬p (xs[j]'(Nat.lt_trans hji h))) : i ≤ xs.findIdx p := by
   apply Decidable.byContradiction
   intro f
   simp only [Nat.not_le] at f
-  exact absurd (@findIdx_getElem _ p xs (Nat.lt_trans f h)) (by simpa using h2 (xs.findIdx p) f)
+  exact absurd (@findIdx_getElem _ p xs (Nat.lt_trans f h)) (h2 (xs.findIdx p) f)
 
 /-- If `¬ p xs[j]` for all `j ≤ i`, then `i < xs.findIdx p`. -/
 theorem lt_findIdx_of_not {p : α → Bool} {xs : List α} {i : Nat} (h : i < xs.length)
@@ -580,18 +576,19 @@ theorem lt_findIdx_of_not {p : α → Bool} {xs : List α} {i : Nat} (h : i < xs
 
 /-- `xs.findIdx p = i` iff `p xs[i]` and `¬ p xs [j]` for all `j < i`. -/
 theorem findIdx_eq {p : α → Bool} {xs : List α} {i : Nat} (h : i < xs.length) :
-    xs.findIdx p = i ↔ p xs[i] ∧ ∀ j (hji : j < i), p (xs[j]'(Nat.lt_trans hji h)) = false := by
+    xs.findIdx p = i ↔ p xs[i] ∧ ∀ j (hji : j < i), ¬p (xs[j]'(Nat.lt_trans hji h)) := by
   refine ⟨fun f ↦ ⟨f ▸ (@findIdx_getElem _ p xs (f ▸ h)), fun _ hji ↦ not_of_lt_findIdx (f ▸ hji)⟩,
-    fun ⟨_, h2⟩ ↦ ?_⟩
+    fun ⟨h1, h2⟩ ↦ ?_⟩
   apply Nat.le_antisymm _ (le_findIdx_of_not h h2)
   apply Decidable.byContradiction
   intro h3
   simp at h3
-  simp_all [not_of_lt_findIdx h3]
+  exact not_of_lt_findIdx h3 h1
 
 theorem findIdx_append (p : α → Bool) (l₁ l₂ : List α) :
     (l₁ ++ l₂).findIdx p =
-      if ∃ x, x ∈ l₁ ∧ p x = true then l₁.findIdx p else l₂.findIdx p + l₁.length := by
+      if l₁.findIdx p < l₁.length then l₁.findIdx p else l₂.findIdx p + l₁.length := by
+  simp
   induction l₁ with
   | nil => simp
   | cons x xs ih =>
@@ -620,18 +617,6 @@ theorem IsPrefix.findIdx_eq_of_findIdx_lt_length {l₁ l₂ : List α} {p : α
   · rfl
   · simp_all
 
-theorem findIdx_le_findIdx {l : List α} {p q : α → Bool} (h : ∀ x ∈ l, p x → q x) : l.findIdx q ≤ l.findIdx p := by
-  induction l with
-  | nil => simp
-  | cons x xs ih =>
-    simp only [findIdx_cons, cond_eq_if]
-    split
-    · simp
-    · split
-      · simp_all
-      · simp only [Nat.add_le_add_iff_right]
-        exact ih fun _ m w => h _ (mem_cons_of_mem x m) w
-
 /-! ### findIdx? -/
 
 @[simp] theorem findIdx?_nil : ([] : List α).findIdx? p i = none := rfl
@@ -639,24 +624,11 @@ theorem findIdx_le_findIdx {l : List α} {p q : α → Bool} (h : ∀ x ∈ l, p
 @[simp] theorem findIdx?_cons :
     (x :: xs).findIdx? p i = if p x then some i else findIdx? p xs (i + 1) := rfl
 
-theorem findIdx?_succ :
+@[simp] theorem findIdx?_succ :
     (xs : List α).findIdx? p (i+1) = (xs.findIdx? p i).map fun i => i + 1 := by
   induction xs generalizing i with simp
   | cons _ _ _ => split <;> simp_all
 
-@[simp] theorem findIdx?_start_succ :
-    (xs : List α).findIdx? p (i+1) = (xs.findIdx? p 0).map fun k => k + (i + 1) := by
-  induction xs generalizing i with
-  | nil => simp
-  | cons _ _ _ =>
-    simp only [findIdx?_succ, findIdx?_cons, Nat.zero_add]
-    split
-    · simp_all
-    · simp_all only [findIdx?_succ, Bool.not_eq_true, Option.map_map, Nat.zero_add]
-      congr
-      ext
-      simp only [Nat.add_comm i, Function.comp_apply, Nat.add_assoc]
-
 @[simp]
 theorem findIdx?_eq_none_iff {xs : List α} {p : α → Bool} :
     xs.findIdx? p = none ↔ ∀ x, x ∈ xs → p x = false := by
@@ -708,16 +680,6 @@ theorem findIdx?_eq_none_iff_findIdx_eq {xs : List α} {p : α → Bool} :
     xs.findIdx? p = none ↔ xs.findIdx p = xs.length := by
   simp
 
-theorem findIdx?_eq_guard_findIdx_lt {xs : List α} {p : α → Bool} :
-    xs.findIdx? p = Option.guard (fun i => i < xs.length) (xs.findIdx p) := by
-  match h : xs.findIdx? p with
-  | none =>
-    simp only [findIdx?_eq_none_iff] at h
-    simp [findIdx_eq_length_of_false h, Option.guard]
-  | some i =>
-    simp only [findIdx?_eq_some_iff_findIdx_eq] at h
-    simp [h]
-
 theorem findIdx?_eq_some_iff_getElem {xs : List α} {p : α → Bool} {i : Nat} :
     xs.findIdx? p = some i ↔
       ∃ h : i < xs.length, p xs[i] ∧ ∀ j (hji : j < i), ¬p (xs[j]'(Nat.lt_trans hji h)) := by
@@ -815,7 +777,7 @@ theorem findIdx?_join {l : List (List α)} {p : α → Bool} :
     simp only [replicate, findIdx?_cons, Nat.zero_add, findIdx?_succ, zero_lt_succ, true_and]
     split <;> simp_all
 
-theorem findIdx?_eq_findSome?_enum {xs : List α} {p : α → Bool} :
+theorem findIdx?_eq_enum_findSome? {xs : List α} {p : α → Bool} :
     xs.findIdx? p = xs.enum.findSome? fun ⟨i, a⟩ => if p a then some i else none := by
   induction xs with
   | nil => simp
@@ -826,30 +788,6 @@ theorem findIdx?_eq_findSome?_enum {xs : List α} {p : α → Bool} :
     · simp_all only [enumFrom_cons, ite_false, Option.isNone_none, findSome?_cons_of_isNone, reduceCtorEq]
       simp [Function.comp_def, ← map_fst_add_enum_eq_enumFrom, findSome?_map]
 
-theorem findIdx?_eq_fst_find?_enum {xs : List α} {p : α → Bool} :
-    xs.findIdx? p = (xs.enum.find? fun ⟨_, x⟩ => p x).map (·.1) := by
-  induction xs with
-  | nil => simp
-  | cons x xs ih =>
-    simp only [findIdx?_cons, Nat.zero_add, findIdx?_start_succ, enum_cons]
-    split
-    · simp_all
-    · simp only [Option.map_map, enumFrom_eq_map_enum, Bool.false_eq_true, not_false_eq_true,
-        find?_cons_of_neg, find?_map, *]
-      congr
-
--- See also `findIdx_le_findIdx`.
-theorem findIdx?_eq_none_of_findIdx?_eq_none {xs : List α} {p q : α → Bool} (w : ∀ x ∈ xs, p x → q x) :
-    xs.findIdx? q = none → xs.findIdx? p = none := by
-  simp only [findIdx?_eq_none_iff]
-  intro h x m
-  cases z : p x
-  · rfl
-  · exfalso
-    specialize w x m z
-    specialize h x m
-    simp_all
-
 theorem Sublist.findIdx?_isSome {l₁ l₂ : List α} (h : l₁ <+ l₂) :
     (l₁.findIdx? p).isSome → (l₂.findIdx? p).isSome := by
   simp only [List.findIdx?_isSome, any_eq_true]
@@ -914,7 +852,7 @@ theorem lookup_eq_some_iff {l : List (α × β)} {k : α} {b : β} :
   simp only [lookup_eq_findSome?, findSome?_eq_some_iff]
   constructor
   · rintro ⟨l₁, a, l₂, rfl, h₁, h₂⟩
-    simp only [beq_iff_eq, Option.ite_none_right_eq_some, Option.some.injEq] at h₁
+    simp only [beq_iff_eq, ite_some_none_eq_some] at h₁
     obtain ⟨rfl, rfl⟩ := h₁
     simp at h₂
     exact ⟨l₁, l₂, rfl, by simpa using h₂⟩

src/Init/Data/List/Impl.lean

@@ -57,8 +57,8 @@ The following operations are given `@[csimp]` replacements below:
 
 @[csimp] theorem set_eq_setTR : @set = @setTR := by
   funext α l n a; simp [setTR]
-  let rec go (acc) : ∀ xs n, l = acc.toList ++ xs →
-    setTR.go l a xs n acc = acc.toList ++ xs.set n a
+  let rec go (acc) : ∀ xs n, l = acc.data ++ xs →
+    setTR.go l a xs n acc = acc.data ++ xs.set n a
   | [], _ => fun h => by simp [setTR.go, set, h]
   | x::xs, 0 => by simp [setTR.go, set]
   | x::xs, n+1 => fun h => by simp only [setTR.go, set]; rw [go _ xs] <;> simp [h]
@@ -77,11 +77,10 @@ The following operations are given `@[csimp]` replacements below:
 
 @[csimp] theorem filterMap_eq_filterMapTR : @List.filterMap = @filterMapTR := by
   funext α β f l
-  let rec go : ∀ as acc, filterMapTR.go f as acc = acc.toList ++ as.filterMap f
+  let rec go : ∀ as acc, filterMapTR.go f as acc = acc.data ++ as.filterMap f
     | [], acc => by simp [filterMapTR.go, filterMap]
     | a::as, acc => by
-      simp only [filterMapTR.go, go as, Array.push_toList, append_assoc, singleton_append,
-        filterMap]
+      simp only [filterMapTR.go, go as, Array.push_data, append_assoc, singleton_append, filterMap]
       split <;> simp [*]
   exact (go l #[]).symm
 
@@ -91,7 +90,7 @@ The following operations are given `@[csimp]` replacements below:
 @[specialize] def foldrTR (f : α → β → β) (init : β) (l : List α) : β := l.toArray.foldr f init
 
 @[csimp] theorem foldr_eq_foldrTR : @foldr = @foldrTR := by
-  funext α β f init l; simp [foldrTR, Array.foldr_eq_foldr_toList, -Array.size_toArray]
+  funext α β f init l; simp [foldrTR, Array.foldr_eq_foldr_data, -Array.size_toArray]
 
 /-! ### bind  -/
 
@@ -104,7 +103,7 @@ The following operations are given `@[csimp]` replacements below:
 
 @[csimp] theorem bind_eq_bindTR : @List.bind = @bindTR := by
   funext α β as f
-  let rec go : ∀ as acc, bindTR.go f as acc = acc.toList ++ as.bind f
+  let rec go : ∀ as acc, bindTR.go f as acc = acc.data ++ as.bind f
     | [], acc => by simp [bindTR.go, bind]
     | x::xs, acc => by simp [bindTR.go, bind, go xs]
   exact (go as #[]).symm
@@ -132,7 +131,7 @@ The following operations are given `@[csimp]` replacements below:
 
 @[csimp] theorem take_eq_takeTR : @take = @takeTR := by
   funext α n l; simp [takeTR]
-  suffices ∀ xs acc, l = acc.toList ++ xs → takeTR.go l xs n acc = acc.toList ++ xs.take n from
+  suffices ∀ xs acc, l = acc.data ++ xs → takeTR.go l xs n acc = acc.data ++ xs.take n from
     (this l #[] (by simp)).symm
   intro xs; induction xs generalizing n with intro acc
   | nil => cases n <;> simp [take, takeTR.go]
@@ -153,13 +152,13 @@ The following operations are given `@[csimp]` replacements below:
 
 @[csimp] theorem takeWhile_eq_takeWhileTR : @takeWhile = @takeWhileTR := by
   funext α p l; simp [takeWhileTR]
-  suffices ∀ xs acc, l = acc.toList ++ xs →
-      takeWhileTR.go p l xs acc = acc.toList ++ xs.takeWhile p from
+  suffices ∀ xs acc, l = acc.data ++ xs →
+      takeWhileTR.go p l xs acc = acc.data ++ xs.takeWhile p from
     (this l #[] (by simp)).symm
   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, Array.toList_eq, takeWhile]
     split
     · intro h; rw [IH] <;> simp_all
     · simp [*]
@@ -186,8 +185,8 @@ The following operations are given `@[csimp]` replacements below:
 
 @[csimp] theorem replace_eq_replaceTR : @List.replace = @replaceTR := by
   funext α _ l b c; simp [replaceTR]
-  suffices ∀ xs acc, l = acc.toList ++ xs →
-      replaceTR.go l b c xs acc = acc.toList ++ xs.replace b c from
+  suffices ∀ xs acc, l = acc.data ++ xs →
+      replaceTR.go l b c xs acc = acc.data ++ xs.replace b c from
     (this l #[] (by simp)).symm
   intro xs; induction xs with intro acc
   | nil => simp [replace, replaceTR.go]
@@ -209,7 +208,7 @@ The following operations are given `@[csimp]` replacements below:
 
 @[csimp] theorem erase_eq_eraseTR : @List.erase = @eraseTR := by
   funext α _ l a; simp [eraseTR]
-  suffices ∀ xs acc, l = acc.toList ++ xs → eraseTR.go l a xs acc = acc.toList ++ xs.erase a from
+  suffices ∀ xs acc, l = acc.data ++ xs → eraseTR.go l a xs acc = acc.data ++ xs.erase a from
     (this l #[] (by simp)).symm
   intro xs; induction xs with intro acc h
   | nil => simp [List.erase, eraseTR.go, h]
@@ -229,8 +228,8 @@ The following operations are given `@[csimp]` replacements below:
 
 @[csimp] theorem eraseP_eq_erasePTR : @eraseP = @erasePTR := by
   funext α p l; simp [erasePTR]
-  let rec go (acc) : ∀ xs, l = acc.toList ++ xs →
-    erasePTR.go p l xs acc = acc.toList ++ xs.eraseP p
+  let rec go (acc) : ∀ xs, l = acc.data ++ xs →
+    erasePTR.go p l xs acc = acc.data ++ xs.eraseP p
   | [] => fun h => by simp [erasePTR.go, eraseP, h]
   | x::xs => by
     simp [erasePTR.go, eraseP]; cases p x <;> simp
@@ -250,7 +249,7 @@ The following operations are given `@[csimp]` replacements below:
 
 @[csimp] theorem eraseIdx_eq_eraseIdxTR : @eraseIdx = @eraseIdxTR := by
   funext α l n; simp [eraseIdxTR]
-  suffices ∀ xs acc, l = acc.toList ++ xs → eraseIdxTR.go l xs n acc = acc.toList ++ xs.eraseIdx n from
+  suffices ∀ xs acc, l = acc.data ++ xs → eraseIdxTR.go l xs n acc = acc.data ++ xs.eraseIdx n from
     (this l #[] (by simp)).symm
   intro xs; induction xs generalizing n with intro acc h
   | nil => simp [eraseIdx, eraseIdxTR.go, h]
@@ -274,7 +273,7 @@ The following operations are given `@[csimp]` replacements below:
 
 @[csimp] theorem zipWith_eq_zipWithTR : @zipWith = @zipWithTR := by
   funext α β γ f as bs
-  let rec go : ∀ as bs acc, zipWithTR.go f as bs acc = acc.toList ++ as.zipWith f bs
+  let rec go : ∀ as bs acc, zipWithTR.go f as bs acc = acc.data ++ as.zipWith f bs
     | [], _, acc | _::_, [], acc => by simp [zipWithTR.go, zipWith]
     | a::as, b::bs, acc => by simp [zipWithTR.go, zipWith, go as bs]
   exact (go as bs #[]).symm
@@ -296,7 +295,7 @@ def enumFromTR (n : Nat) (l : List α) : List (Nat × α) :=
     | a::as, n => by
       rw [← show _ + as.length = n + (a::as).length from Nat.succ_add .., foldr, go as]
       simp [enumFrom, f]
-  rw [Array.foldr_eq_foldr_toList]
+  rw [Array.foldr_eq_foldr_data]
   simp [go]
 
 /-! ## Other list operations -/
@@ -322,7 +321,7 @@ where
   | [_] => simp
   | x::y::xs =>
     let rec go {acc x} : ∀ xs,
-      intercalateTR.go sep.toArray x xs acc = acc.toList ++ join (intersperse sep (x::xs))
+      intercalateTR.go sep.toArray x xs acc = acc.data ++ join (intersperse sep (x::xs))
     | [] => by simp [intercalateTR.go]
     | _::_ => by simp [intercalateTR.go, go]
     simp [intersperse, go]

src/Init/Data/List/Lemmas.lean

@@ -109,9 +109,6 @@ theorem cons_eq_cons {a b : α} {l l' : List α} : a :: l = b :: l' ↔ a = b
 theorem exists_cons_of_ne_nil : ∀ {l : List α}, l ≠ [] → ∃ b L, l = b :: L
   | c :: l', _ => ⟨c, l', rfl⟩
 
-theorem singleton_inj {α : Type _} {a b : α} : [a] = [b] ↔ a = b := by
-  simp
-
 /-! ### length -/
 
 theorem eq_nil_of_length_eq_zero (_ : length l = 0) : l = [] := match l with | [] => rfl
@@ -266,15 +263,9 @@ theorem get!_len_le [Inhabited α] : ∀ {l : List α} {n}, length l ≤ n → l
 theorem getElem?_eq_some_iff {l : List α} : l[n]? = some a ↔ ∃ h : n < l.length, l[n] = a := by
   simp only [← get?_eq_getElem?, get?_eq_some, get_eq_getElem]
 
-theorem some_eq_getElem?_iff {l : List α} : some a = l[n]? ↔ ∃ h : n < l.length, l[n] = a := by
-  rw [eq_comm, getElem?_eq_some_iff]
-
 @[simp] theorem getElem?_eq_none_iff : l[n]? = none ↔ length l ≤ n := by
   simp only [← get?_eq_getElem?, get?_eq_none]
 
-@[simp] theorem none_eq_getElem?_iff {l : List α} {n : Nat} : none = l[n]? ↔ length l ≤ n := by
-  simp [eq_comm (a := none)]
-
 theorem getElem?_eq_none (h : length l ≤ n) : l[n]? = none := getElem?_eq_none_iff.mpr h
 
 theorem getElem?_eq (l : List α) (i : Nat) :
@@ -407,22 +398,6 @@ theorem exists_mem_of_ne_nil (l : List α) (h : l ≠ []) : ∃ x, x ∈ l :=
 theorem eq_nil_iff_forall_not_mem {l : List α} : l = [] ↔ ∀ a, a ∉ l := by
   cases l <;> simp [-not_or]
 
-@[simp] theorem mem_dite_nil_left {x : α} [Decidable p] {l : ¬ p → List α} :
-    (x ∈ if h : p then [] else l h) ↔ ∃ h : ¬ p, x ∈ l h := by
-  split <;> simp_all
-
-@[simp] theorem mem_dite_nil_right {x : α} [Decidable p] {l : p → List α} :
-    (x ∈ if h : p then l h else []) ↔ ∃ h : p, x ∈ l h := by
-  split <;> simp_all
-
-@[simp] theorem mem_ite_nil_left {x : α} [Decidable p] {l : List α} :
-    (x ∈ if p then [] else l) ↔ ¬ p ∧ x ∈ l := by
-  split <;> simp_all
-
-@[simp] theorem mem_ite_nil_right {x : α} [Decidable p] {l : List α} :
-    (x ∈ if p then l else []) ↔ p ∧ x ∈ l := by
-  split <;> simp_all
-
 theorem eq_of_mem_singleton : a ∈ [b] → a = b
   | .head .. => rfl
 
@@ -489,9 +464,9 @@ theorem getElem?_of_mem {a} {l : List α} (h : a ∈ l) : ∃ n : Nat, l[n]? = s
 theorem get?_of_mem {a} {l : List α} (h : a ∈ l) : ∃ n, l.get? n = some a :=
   let ⟨⟨n, _⟩, e⟩ := get_of_mem h; ⟨n, e ▸ get?_eq_get _⟩
 
-theorem getElem_mem : ∀ {l : List α} {n} (h : n < l.length), l[n]'h ∈ l
+theorem getElem_mem : ∀ (l : List α) n (h : n < l.length), l[n]'h ∈ l
   | _ :: _, 0, _ => .head ..
-  | _ :: l, _+1, _ => .tail _ (getElem_mem (l := l) ..)
+  | _ :: l, _+1, _ => .tail _ (getElem_mem l ..)
 
 theorem get_mem : ∀ (l : List α) n h, get l ⟨n, h⟩ ∈ l
   | _ :: _, 0, _ => .head ..
@@ -533,7 +508,7 @@ theorem forall_getElem {l : List α} {p : α → Prop} :
       · simpa
       · apply w
         simp only [getElem_cons_succ]
-        exact getElem_mem (lt_of_succ_lt_succ h)
+        exact getElem_mem l n (lt_of_succ_lt_succ h)
 
 @[simp] theorem decide_mem_cons [BEq α] [LawfulBEq α] {l : List α} :
     decide (y ∈ a :: l) = (y == a || decide (y ∈ l)) := by
@@ -581,25 +556,17 @@ theorem any_eq {l : List α} : l.any p = decide (∃ x, x ∈ l ∧ p x) := by i
 
 theorem all_eq {l : List α} : l.all p = decide (∀ x, x ∈ l → p x) := by induction l <;> simp [*]
 
-theorem decide_exists_mem {l : List α} {p : α → Prop} [DecidablePred p] :
-    decide (∃ x, x ∈ l ∧ p x) = l.any p := by
+@[simp] theorem any_decide {l : List α} {p : α → Prop} [DecidablePred p] :
+    l.any p = decide (∃ x, x ∈ l ∧ p x) := by
   simp [any_eq]
 
-theorem decide_forall_mem {l : List α} {p : α → Prop} [DecidablePred p] :
-    decide (∀ x, x ∈ l → p x) = l.all p := by
+@[simp] theorem all_decide {l : List α} {p : α → Prop} [DecidablePred p] :
+    l.all p = decide (∀ x, x ∈ l → p x) := by
   simp [all_eq]
 
-@[simp] theorem any_eq_true {l : List α} : l.any p = true ↔ ∃ x, x ∈ l ∧ p x := by
-  simp only [any_eq, decide_eq_true_eq]
+@[simp] theorem any_eq_true {l : List α} : l.any p = true ↔ ∃ x, x ∈ l ∧ p x := by simp [any_eq]
 
-@[simp] theorem all_eq_true {l : List α} : l.all p = true ↔ ∀ x, x ∈ l → p x := by
-  simp only [all_eq, decide_eq_true_eq]
-
-@[simp] theorem any_eq_false {l : List α} : l.any p = false ↔ ∀ x, x ∈ l → ¬p x := by
-  simp [any_eq]
-
-@[simp] theorem all_eq_false {l : List α} : l.all p = false ↔ ∃ x, x ∈ l ∧ ¬p x := by
-  simp [all_eq]
+@[simp] theorem all_eq_true {l : List α} : l.all p = true ↔ ∀ x, x ∈ l → p x := by simp [all_eq]
 
 /-! ### set -/
 
@@ -738,45 +705,6 @@ theorem mem_or_eq_of_mem_set : ∀ {l : List α} {n : Nat} {a b : α}, a ∈ l.s
 
 -- See also `set_eq_take_append_cons_drop` in `Init.Data.List.TakeDrop`.
 
-/-! ### BEq -/
-
-@[simp] theorem reflBEq_iff [BEq α] : ReflBEq (List α) ↔ ReflBEq α := by
-  constructor
-  · intro h
-    constructor
-    intro a
-    suffices ([a] == [a]) = true by
-      simpa only [List.instBEq, List.beq, Bool.and_true]
-    simp
-  · intro h
-    constructor
-    intro a
-    induction a with
-    | nil => simp only [List.instBEq, List.beq]
-    | cons a as ih =>
-      simp [List.instBEq, List.beq]
-      exact ih
-
-@[simp] theorem lawfulBEq_iff [BEq α] : LawfulBEq (List α) ↔ LawfulBEq α := by
-  constructor
-  · intro h
-    constructor
-    · intro a b h
-      apply singleton_inj.1
-      apply eq_of_beq
-      simp only [List.instBEq, List.beq]
-      simpa
-    · intro a
-      suffices ([a] == [a]) = true by
-        simpa only [List.instBEq, List.beq, Bool.and_true]
-      simp
-  · intro h
-    constructor
-    · intro a b h
-      simpa using h
-    · intro a
-      simp
-
 /-! ### Lexicographic ordering -/
 
 protected theorem lt_irrefl [LT α] (lt_irrefl : ∀ x : α, ¬x < x) (l : List α) : ¬l < l := by
@@ -972,15 +900,11 @@ theorem getLast_eq_getLastD (a l h) : @getLast α (a::l) h = getLastD l a := by
 theorem getLast!_cons [Inhabited α] : @getLast! α _ (a::l) = getLastD l a := by
   simp [getLast!, getLast_eq_getLastD]
 
-theorem getLast_mem : ∀ {l : List α} (h : l ≠ []), getLast l h ∈ l
+@[simp] theorem getLast_mem : ∀ {l : List α} (h : l ≠ []), getLast l h ∈ l
   | [], h => absurd rfl h
   | [_], _ => .head ..
   | _::a::l, _ => .tail _ <| getLast_mem (cons_ne_nil a l)
 
-theorem getLast_mem_getLast? : ∀ {l : List α} (h : l ≠ []), getLast l h ∈ getLast? l
-  | [], h => by contradiction
-  | a :: l, _ => rfl
-
 theorem getLastD_mem_cons : ∀ (l : List α) (a : α), getLastD l a ∈ a::l
   | [], _ => .head ..
   | _::_, _ => .tail _ <| getLast_mem _
@@ -1051,11 +975,6 @@ theorem head?_eq_getElem? : ∀ l : List α, head? l = l[0]?
   | [] => rfl
   | a :: l => by simp
 
-theorem head_eq_getElem (l : List α) (h : l ≠ []) : head l h = l[0]'(length_pos.mpr h) := by
-  cases l with
-  | nil => simp at h
-  | cons _ _ => simp
-
 theorem head_eq_iff_head?_eq_some {xs : List α} (h) : xs.head h = a ↔ xs.head? = some a := by
   cases xs with
   | nil => simp at h
@@ -1070,23 +989,10 @@ theorem head?_eq_some_iff {xs : List α} {a : α} : xs.head? = some a ↔ ∃ ys
 @[simp] theorem head?_isSome : l.head?.isSome ↔ l ≠ [] := by
   cases l <;> simp
 
-theorem head_mem : ∀ {l : List α} (h : l ≠ []), head l h ∈ l
+@[simp] theorem head_mem : ∀ {l : List α} (h : l ≠ []), head l h ∈ l
   | [], h => absurd rfl h
   | _::_, _ => .head ..
 
-theorem mem_of_mem_head? : ∀ {l : List α} {a : α}, a ∈ l.head? → a ∈ l := by
-  intro l a h
-  cases l with
-  | nil => simp at h
-  | cons b l =>
-    simp at h
-    cases h
-    exact mem_cons_self a l
-
-theorem head_mem_head? : ∀ {l : List α} (h : l ≠ []), head l h ∈ head? l
-  | [], h => by contradiction
-  | a :: l, _ => rfl
-
 theorem head?_concat {a : α} : (l ++ [a]).head? = l.head?.getD a := by
   cases l <;> simp
 
@@ -1113,58 +1019,6 @@ theorem tail_eq_tailD (l) : @tail α l = tailD l [] := by cases l <;> rfl
 
 theorem tail_eq_tail? (l) : @tail α l = (tail? l).getD [] := by simp [tail_eq_tailD]
 
-theorem mem_of_mem_tail {a : α} {l : List α} (h : a ∈ tail l) : a ∈ l := by
-  induction l <;> simp_all
-
-theorem ne_nil_of_tail_ne_nil {l : List α} : l.tail ≠ [] → l ≠ [] := by
-  cases l <;> simp
-
-@[simp] theorem getElem_tail (l : List α) (i : Nat) (h : i < l.tail.length) :
-    (tail l)[i] = l[i + 1]'(add_lt_of_lt_sub (by simpa using h)) := by
-  cases l with
-  | nil => simp at h
-  | cons _ l => simp
-
-@[simp] theorem getElem?_tail (l : List α) (i : Nat) :
-    (tail l)[i]? = l[i + 1]? := by
-  cases l <;> simp
-
-@[simp] theorem set_tail (l : List α) (i : Nat) (a : α) :
-    l.tail.set i a = (l.set (i + 1) a).tail := by
-  cases l <;> simp
-
-theorem one_lt_length_of_tail_ne_nil {l : List α} (h : l.tail ≠ []) : 1 < l.length := by
-  cases l with
-  | nil => simp at h
-  | cons _ l =>
-    simp only [tail_cons, ne_eq] at h
-    exact Nat.lt_add_of_pos_left (length_pos.mpr h)
-
-@[simp] theorem head_tail (l : List α) (h : l.tail ≠ []) :
-    (tail l).head h = l[1]'(one_lt_length_of_tail_ne_nil h) := by
-  cases l with
-  | nil => simp at h
-  | cons _ l => simp [head_eq_getElem]
-
-@[simp] theorem head?_tail (l : List α) : (tail l).head? = l[1]? := by
-  simp [head?_eq_getElem?]
-
-@[simp] theorem getLast_tail (l : List α) (h : l.tail ≠ []) :
-    (tail l).getLast h = l.getLast (ne_nil_of_tail_ne_nil h) := by
-  simp only [getLast_eq_getElem, length_tail, getElem_tail]
-  congr
-  match l with
-  | _ :: _ :: l => simp
-
-theorem getLast?_tail (l : List α) : (tail l).getLast? = if l.length = 1 then none else l.getLast? := by
-  match l with
-  | [] => simp
-  | [a] => simp
-  | _ :: _ :: l =>
-    simp only [tail_cons, length_cons, getLast?_cons_cons]
-    rw [if_neg]
-    rintro ⟨⟩
-
 /-! ## Basic operations -/
 
 /-! ### map -/
@@ -1297,18 +1151,18 @@ theorem map_eq_foldr (f : α → β) (l : List α) : map f l = foldr (fun a bs =
 @[simp] theorem head?_map (f : α → β) (l : List α) : head? (map f l) = (head? l).map f := by
   cases l <;> rfl
 
-@[simp] theorem map_tail? (f : α → β) (l : List α) : (tail? l).map (map f) = tail? (map f l) := by
+@[simp] theorem tail?_map (f : α → β) (l : List α) : tail? (map f l) = (tail? l).map (map f) := by
   cases l <;> rfl
 
-@[simp] theorem map_tail (f : α → β) (l : List α) :
-    map f l.tail = (map f l).tail := by
+@[simp] theorem tail_map (f : α → β) (l : List α) :
+    (map f l).tail = map f l.tail := by
   cases l <;> simp_all
 
 theorem headD_map (f : α → β) (l : List α) (a : α) : headD (map f l) (f a) = f (headD l a) := by
   cases l <;> rfl
 
 theorem tailD_map (f : α → β) (l : List α) (l' : List α) :
-    tailD (map f l) (map f l') = map f (tailD l l') := by simp [← map_tail?]
+    tailD (map f l) (map f l') = map f (tailD l l') := by simp
 
 @[simp] theorem getLast_map (f : α → β) (l : List α) (h) :
     getLast (map f l) h = f (getLast l (by simpa using h)) := by
@@ -1391,7 +1245,7 @@ theorem forall_mem_filter {l : List α} {p : α → Bool} {P : α → Prop} :
 
 @[deprecated forall_mem_filter (since := "2024-07-25")] abbrev forall_mem_filter_iff := @forall_mem_filter
 
-@[simp] theorem filter_filter (q) : ∀ l, filter p (filter q l) = filter (fun a => p a && q a) l
+@[simp] theorem filter_filter (q) : ∀ l, filter p (filter q l) = filter (fun a => p a ∧ q a) l
   | [] => rfl
   | a :: l => by by_cases hp : p a <;> by_cases hq : q a <;> simp [hp, hq, filter_filter _ l]
 
@@ -1617,11 +1471,10 @@ theorem filterMap_eq_cons_iff {l} {b} {bs} :
 
 /-! ### append -/
 
-theorem getElem_append {l₁ l₂ : List α} (n : Nat) (h) :
-    (l₁ ++ l₂)[n] = if h' : n < l₁.length then l₁[n] else l₂[n - l₁.length]'(by simp at h h'; exact Nat.sub_lt_left_of_lt_add h' h) := by
-  split <;> rename_i h'
-  · rw [getElem_append_left h']
-  · rw [getElem_append_right (by simpa using h')]
+theorem getElem_append : ∀ {l₁ l₂ : List α} (n : Nat) (h : n < l₁.length),
+    (l₁ ++ l₂)[n]'(length_append .. ▸ Nat.lt_add_right _ h) = l₁[n]
+| a :: l, _, 0, h => rfl
+| a :: l, _, n+1, h => by simp only [get, cons_append]; apply getElem_append
 
 theorem getElem?_append_left {l₁ l₂ : List α} {n : Nat} (hn : n < l₁.length) :
     (l₁ ++ l₂)[n]? = l₁[n]? := by
@@ -1647,13 +1500,12 @@ theorem get?_append_right {l₁ l₂ : List α} {n : Nat} (h : l₁.length ≤ n
     (l₁ ++ l₂).get? n = l₂.get? (n - l₁.length) := by
   simp [getElem?_append_right, h]
 
-/-- Variant of `getElem_append_left` useful for rewriting from the small list to the big list. -/
-theorem getElem_append_left' (l₂ : List α) {l₁ : List α} {n : Nat} (hn : n < l₁.length) :
-    l₁[n] = (l₁ ++ l₂)[n]'(by simpa using Nat.lt_add_right l₂.length hn) := by
-  rw [getElem_append_left] <;> simp
+theorem getElem_append_right' {l₁ l₂ : List α} {n : Nat} (h₁ : l₁.length ≤ n) (h₂) :
+    (l₁ ++ l₂)[n]'h₂ =
+      l₂[n - l₁.length]'(by rw [length_append] at h₂; exact Nat.sub_lt_left_of_lt_add h₁ h₂) :=
+  Option.some.inj <| by rw [← getElem?_eq_getElem, ← getElem?_eq_getElem, getElem?_append_right h₁]
 
-/-- Variant of `getElem_append_right` useful for rewriting from the small list to the big list. -/
-theorem getElem_append_right' (l₁ : List α) {l₂ : List α} {n : Nat} (hn : n < l₂.length) :
+theorem getElem_append_right'' (l₁ : List α) {l₂ : List α} {n : Nat} (hn : n < l₂.length) :
     l₂[n] = (l₁ ++ l₂)[n + l₁.length]'(by simpa [Nat.add_comm] using Nat.add_lt_add_left hn _) := by
   rw [getElem_append_right] <;> simp [*, le_add_left]
 
@@ -1664,7 +1516,7 @@ theorem get_append_right_aux {l₁ l₂ : List α} {n : Nat}
   exact Nat.sub_lt_left_of_lt_add h₁ h₂
 
 set_option linter.deprecated false in
-@[deprecated getElem_append_right (since := "2024-06-12")]
+@[deprecated getElem_append_right' (since := "2024-06-12")]
 theorem get_append_right' {l₁ l₂ : List α} {n : Nat} (h₁ : l₁.length ≤ n) (h₂) :
     (l₁ ++ l₂).get ⟨n, h₂⟩ = l₂.get ⟨n - l₁.length, get_append_right_aux h₁ h₂⟩ :=
   Option.some.inj <| by rw [← get?_eq_get, ← get?_eq_get, get?_append_right h₁]
@@ -1756,7 +1608,7 @@ theorem get_append_left (as bs : List α) (h : i < as.length) {h'} :
   simp [getElem_append_left, h, h']
 
 @[deprecated getElem_append_right (since := "2024-06-12")]
-theorem get_append_right (as bs : List α) (h : as.length ≤ i) {h' h''} :
+theorem get_append_right (as bs : List α) (h : ¬ i < as.length) {h' h''} :
     (as ++ bs).get ⟨i, h'⟩ = bs.get ⟨i - as.length, h''⟩ := by
   simp [getElem_append_right, h, h', h'']
 
@@ -1952,7 +1804,7 @@ theorem map_eq_append_iff {f : α → β} :
     map f l = L₁ ++ L₂ ↔ ∃ l₁ l₂, l = l₁ ++ l₂ ∧ map f l₁ = L₁ ∧ map f l₂ = L₂ := by
   rw [← filterMap_eq_map, filterMap_eq_append_iff]
 
-theorem append_eq_map_iff {f : α → β} :
+theorem append_eq_map_iff (f : α → β) :
     L₁ ++ L₂ = map f l ↔ ∃ l₁ l₂, l = l₁ ++ l₂ ∧ map f l₁ = L₁ ∧ map f l₂ = L₂ := by
   rw [eq_comm, map_eq_append_iff]
 
@@ -2435,47 +2287,6 @@ theorem bind_replicate {β} (f : α → List β) : (replicate n a).bind f = (rep
 @[simp] theorem isEmpty_replicate : (replicate n a).isEmpty = decide (n = 0) := by
   cases n <;> simp [replicate_succ]
 
-/-- Every list is either empty, a non-empty `replicate`, or begins with a non-empty `replicate`
-followed by a different element. -/
-theorem eq_replicate_or_eq_replicate_append_cons {α : Type _} (l : List α) :
-    (l = []) ∨ (∃ n a, l = replicate n a ∧ 0 < n) ∨
-      (∃ n a b l', l = replicate n a ++ b :: l' ∧ 0 < n ∧ a ≠ b) := by
-  induction l with
-  | nil => simp
-  | cons x l ih =>
-    right
-    rcases ih with rfl | ⟨n, a, rfl, h⟩ | ⟨n, a, b, l', rfl, h⟩
-    · left
-      exact ⟨1, x, rfl, by decide⟩
-    · by_cases h' : x = a
-      · subst h'
-        left
-        exact ⟨n + 1, x, rfl, by simp⟩
-      · right
-        refine ⟨1, x, a, replicate (n - 1) a, ?_, by decide, h'⟩
-        match n with | n + 1 => simp [replicate_succ]
-    · right
-      by_cases h' : x = a
-      · subst h'
-        refine ⟨n + 1, x, b, l', by simp [replicate_succ], by simp, h.2⟩
-      · refine ⟨1, x, a, replicate (n - 1) a ++ b :: l', ?_, by decide, h'⟩
-        match n with | n + 1 => simp [replicate_succ]
-
-/-- An induction principle for lists based on contiguous runs of identical elements. -/
--- A `Sort _` valued version would require a different design. (And associated `@[simp]` lemmas.)
-theorem replicateRecOn {α : Type _} {p : List α → Prop} (m : List α)
-    (h0 : p []) (hr : ∀ a n, 0 < n → p (replicate n a))
-    (hi : ∀ a b n l, a ≠ b → 0 < n → p (b :: l) → p (replicate n a ++ b :: l)) : p m := by
-  rcases eq_replicate_or_eq_replicate_append_cons m with
-    rfl | ⟨n, a, rfl, hn⟩ | ⟨n, a, b, l', w, hn, h⟩
-  · exact h0
-  · exact hr _ _ hn
-  · have : (b :: l').length < m.length := by
-      simpa [w] using Nat.lt_add_of_pos_left hn
-    subst w
-    exact hi _ _ _ _ h hn (replicateRecOn (b :: l') h0 hr hi)
-termination_by m.length
-
 /-! ### reverse -/
 
 @[simp] theorem length_reverse (as : List α) : (as.reverse).length = as.length := by
@@ -2563,11 +2374,6 @@ theorem getLast?_eq_head?_reverse {xs : List α} : xs.getLast? = xs.reverse.head
 theorem head?_eq_getLast?_reverse {xs : List α} : xs.head? = xs.reverse.getLast? := by
   simp
 
-theorem mem_of_mem_getLast? {l : List α} {a : α} (h : a ∈ getLast? l) : a ∈ l := by
-  rw [getLast?_eq_head?_reverse] at h
-  rw [← mem_reverse]
-  exact mem_of_mem_head? h
-
 @[simp] theorem map_reverse (f : α → β) (l : List α) : l.reverse.map f = (l.map f).reverse := by
   induction l <;> simp [*]
 
@@ -2907,12 +2713,6 @@ 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
-  apply ext_getElem
-  · simp
-  · intro i h₁ h₂
-    simp [Nat.add_comm i, Nat.sub_add_eq]
-
 /-!
 ### splitAt
 

src/Init/Data/List/Nat.lean

@@ -9,6 +9,3 @@ import Init.Data.List.Nat.Pairwise
 import Init.Data.List.Nat.Range
 import Init.Data.List.Nat.Sublist
 import Init.Data.List.Nat.TakeDrop
-import Init.Data.List.Nat.Count
-import Init.Data.List.Nat.Erase
-import Init.Data.List.Nat.Find

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

@@ -5,7 +5,6 @@ Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, M
 -/
 prelude
 import Init.Data.List.Count
-import Init.Data.List.Find
 import Init.Data.List.MinMax
 import Init.Data.Nat.Lemmas
 
@@ -19,32 +18,12 @@ open Nat
 
 namespace List
 
-/-! ### dropLast -/
-
-theorem tail_dropLast (l : List α) : tail (dropLast l) = dropLast (tail l) := by
-  ext1
-  simp only [getElem?_tail, getElem?_dropLast, length_tail]
-  split <;> split
-  · rfl
-  · omega
-  · omega
-  · rfl
-
-@[simp] theorem dropLast_reverse (l : List α) : l.reverse.dropLast = l.tail.reverse := by
-  apply ext_getElem
-  · simp
-  · intro i h₁ h₂
-    simp only [getElem_dropLast, getElem_reverse, length_tail, getElem_tail]
-    congr
-    simp only [length_dropLast, length_reverse, length_tail] at h₁ h₂
-    omega
-
 /-! ### filter -/
 
 theorem length_filter_lt_length_iff_exists {l} :
     length (filter p l) < length l ↔ ∃ x ∈ l, ¬p x := by
   simpa [length_eq_countP_add_countP p l, countP_eq_length_filter] using
-    countP_pos_iff (p := fun x => ¬p x)
+    countP_pos (p := fun x => ¬p x)
 
 /-! ### reverse -/
 
@@ -58,8 +37,7 @@ theorem getElem_eq_getElem_reverse {l : List α} {i} (h : i < l.length) :
 
 /-- The length of the List returned by `List.leftpad n a l` is equal
   to the larger of `n` and `l.length` -/
--- We don't mark this as a `@[simp]` lemma since we allow `simp` to unfold `leftpad`,
--- so the left hand side simplifies directly to `n - l.length + l.length`.
+@[simp]
 theorem leftpad_length (n : Nat) (a : α) (l : List α) :
     (leftpad n a l).length = max n l.length := by
   simp only [leftpad, length_append, length_replicate, Nat.sub_add_eq_max]
@@ -119,53 +97,6 @@ theorem minimum?_cons' {a : Nat} {l : List Nat} :
         specialize le b h
         split <;> omega
 
-theorem foldl_min
-    {α : Type _} [Min α] [Std.IdempotentOp (min : α → α → α)] [Std.Associative (min : α → α → α)]
-    {l : List α} {a : α} :
-    l.foldl (init := a) min = min a (l.minimum?.getD a) := by
-  cases l with
-  | nil => simp [Std.IdempotentOp.idempotent]
-  | cons b l =>
-    simp only [minimum?]
-    induction l generalizing a b with
-    | nil => simp
-    | cons c l ih => simp [ih, Std.Associative.assoc]
-
-theorem foldl_min_right {α β : Type _}
-    [Min β] [Std.IdempotentOp (min : β → β → β)] [Std.Associative (min : β → β → β)]
-    {l : List α} {b : β} {f : α → β} :
-    (l.foldl (init := b) fun acc a => min acc (f a)) = min b ((l.map f).minimum?.getD b) := by
-  rw [← foldl_map, foldl_min]
-
-theorem foldl_min_le {l : List Nat} {a : Nat} : l.foldl (init := a) min ≤ a := by
-  induction l generalizing a with
-  | nil => simp
-  | cons c l ih =>
-    simp only [foldl_cons]
-    exact Nat.le_trans ih (Nat.min_le_left _ _)
-
-theorem foldl_min_min_of_le {l : List Nat} {a b : Nat} (h : a ≤ b) :
-    l.foldl (init := a) min ≤ b :=
-  Nat.le_trans (foldl_min_le) h
-
-theorem minimum?_getD_le_of_mem {l : List Nat} {a k : Nat} (h : a ∈ l) :
-    l.minimum?.getD k ≤ a := by
-  cases l with
-  | nil => simp at h
-  | cons b l =>
-    simp [minimum?_cons]
-    simp at h
-    rcases h with (rfl | h)
-    · exact foldl_min_le
-    · induction l generalizing b with
-      | nil => simp_all
-      | cons c l ih =>
-        simp only [foldl_cons]
-        simp at h
-        rcases h with (rfl | h)
-        · exact foldl_min_min_of_le (Nat.min_le_right _ _)
-        · exact ih _ h
-
 /-! ### maximum? -/
 
 -- A specialization of `maximum?_eq_some_iff` to Nat.
@@ -199,51 +130,4 @@ theorem maximum?_cons' {a : Nat} {l : List Nat} :
         specialize le b h
         split <;> omega
 
-theorem foldl_max
-    {α : Type _} [Max α] [Std.IdempotentOp (max : α → α → α)] [Std.Associative (max : α → α → α)]
-    {l : List α} {a : α} :
-    l.foldl (init := a) max = max a (l.maximum?.getD a) := by
-  cases l with
-  | nil => simp [Std.IdempotentOp.idempotent]
-  | cons b l =>
-    simp only [maximum?]
-    induction l generalizing a b with
-    | nil => simp
-    | cons c l ih => simp [ih, Std.Associative.assoc]
-
-theorem foldl_max_right {α β : Type _}
-    [Max β] [Std.IdempotentOp (max : β → β → β)] [Std.Associative (max : β → β → β)]
-    {l : List α} {b : β} {f : α → β} :
-    (l.foldl (init := b) fun acc a => max acc (f a)) = max b ((l.map f).maximum?.getD b) := by
-  rw [← foldl_map, foldl_max]
-
-theorem le_foldl_max {l : List Nat} {a : Nat} : a ≤ l.foldl (init := a) max := by
-  induction l generalizing a with
-  | nil => simp
-  | cons c l ih =>
-    simp only [foldl_cons]
-    exact Nat.le_trans (Nat.le_max_left _ _) ih
-
-theorem le_foldl_max_of_le {l : List Nat} {a b : Nat} (h : a ≤ b) :
-    a ≤ l.foldl (init := b) max :=
-  Nat.le_trans h (le_foldl_max)
-
-theorem le_maximum?_getD_of_mem {l : List Nat} {a k : Nat} (h : a ∈ l) :
-    a ≤ l.maximum?.getD k := by
-  cases l with
-  | nil => simp at h
-  | cons b l =>
-    simp [maximum?_cons]
-    simp at h
-    rcases h with (rfl | h)
-    · exact le_foldl_max
-    · induction l generalizing b with
-      | nil => simp_all
-      | cons c l ih =>
-        simp only [foldl_cons]
-        simp at h
-        rcases h with (rfl | h)
-        · exact le_foldl_max_of_le (Nat.le_max_right b a)
-        · exact ih _ h
-
 end List

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

@@ -1,86 +0,0 @@
-/-
-Copyright (c) 2024 Kim Morrison. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison
--/
-prelude
-import Init.Data.List.Count
-import Init.Data.Nat.Lemmas
-
-namespace List
-
-open Nat
-
-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
-  | nil => simp at h
-  | cons x l ih =>
-    cases i with
-    | zero => simp [countP_cons]
-    | succ i =>
-      simp [add_one_lt_add_one_iff] at h
-      simp [countP_cons, ih _ h]
-      have : (if p l[i] = true then 1 else 0) ≤ l.countP p := boole_getElem_le_countP p l i h
-      omega
-
-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]
-
-/--
-The number of elements satisfying a predicate in a sublist is at least the number of elements satisfying the predicate in the list,
-minus the difference in the lengths.
--/
-theorem Sublist.le_countP (s : l₁ <+ l₂) (p) : countP p l₂ - (l₂.length - l₁.length) ≤ countP p l₁ := by
-  match s with
-  | .slnil => simp
-  | .cons a s =>
-    rename_i l
-    simp only [countP_cons, length_cons]
-    have := s.le_countP p
-    have := s.length_le
-    split <;> omega
-  | .cons₂ a s =>
-    rename_i l₁ l₂
-    simp only [countP_cons, length_cons]
-    have := s.le_countP p
-    have := s.length_le
-    split <;> omega
-
-theorem IsPrefix.le_countP (s : l₁ <+: l₂) : countP p l₂ - (l₂.length - l₁.length) ≤ countP p l₁ :=
-  s.sublist.le_countP _
-
-theorem IsSuffix.le_countP (s : l₁ <:+ l₂) : countP p l₂ - (l₂.length - l₁.length) ≤ countP p l₁ :=
-  s.sublist.le_countP _
-
-theorem IsInfix.le_countP (s : l₁ <:+: l₂) : countP p l₂ - (l₂.length - l₁.length) ≤ countP p l₁ :=
-  s.sublist.le_countP _
-
-/--
-The number of elements satisfying a predicate in the tail of a list is
-at least one less than the number of elements satisfying the predicate in the list.
--/
-theorem le_countP_tail (l) : countP p l - 1 ≤ countP p l.tail := by
-  have := (tail_sublist l).le_countP p
-  simp only [length_tail] at this
-  omega
-
-variable [BEq α]
-
-theorem Sublist.le_count (s : l₁ <+ l₂) (a : α) : count a l₂ - (l₂.length - l₁.length) ≤ count a l₁ :=
-  s.le_countP _
-
-theorem IsPrefix.le_count (s : l₁ <+: l₂) (a : α) : count a l₂ - (l₂.length - l₁.length) ≤ count a l₁ :=
-  s.sublist.le_count _
-
-theorem IsSuffix.le_count (s : l₁ <:+ l₂) (a : α) : count a l₂ - (l₂.length - l₁.length) ≤ count a l₁ :=
-  s.sublist.le_count _
-
-theorem IsInfix.le_count (s : l₁ <:+: l₂) (a : α) : count a l₂ - (l₂.length - l₁.length) ≤ count a l₁ :=
-  s.sublist.le_count _
-
-theorem le_count_tail (a : α) (l) : count a l - 1 ≤ count a l.tail :=
-  le_countP_tail _
-
-end List

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

@@ -1,66 +0,0 @@
-/-
-Copyright (c) 2024 Kim Morrison. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison
--/
-prelude
-import Init.Data.List.Nat.TakeDrop
-import Init.Data.List.Erase
-
-namespace List
-
-theorem getElem?_eraseIdx (l : List α) (i : Nat) (j : Nat) :
-    (l.eraseIdx i)[j]? = if h : j < i then l[j]? else l[j + 1]? := by
-  rw [eraseIdx_eq_take_drop_succ, getElem?_append]
-  split <;> rename_i h
-  · rw [getElem?_take]
-    split
-    · rfl
-    · simp_all
-      omega
-  · rw [getElem?_drop]
-    split <;> rename_i h'
-    · simp only [length_take, Nat.min_def, Nat.not_lt] at h
-      split at h
-      · omega
-      · simp_all [getElem?_eq_none]
-        omega
-    · simp only [length_take]
-      simp only [length_take, Nat.min_def, Nat.not_lt] at h
-      split at h
-      · congr 1
-        omega
-      · rw [getElem?_eq_none, getElem?_eq_none] <;> omega
-
-theorem getElem?_eraseIdx_of_lt (l : List α) (i : Nat) (j : Nat) (h : j < i) :
-    (l.eraseIdx i)[j]? = l[j]? := by
-  rw [getElem?_eraseIdx]
-  simp [h]
-
-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]
-  intro h'
-  omega
-
-theorem getElem_eraseIdx (l : List α) (i : Nat) (j : Nat) (h : j < (l.eraseIdx i).length) :
-    (l.eraseIdx i)[j] = if h' : j < i then
-        l[j]'(by have := length_eraseIdx_le l i; omega)
-      else
-        l[j + 1]'(by rw [length_eraseIdx] at h; split at h <;> omega) := by
-  apply Option.some.inj
-  rw [← getElem?_eq_getElem, getElem?_eraseIdx]
-  split <;> simp
-
-theorem getElem_eraseIdx_of_lt (l : List α) (i : Nat) (j : Nat) (h : j < (l.eraseIdx i).length) (h' : j < i) :
-    (l.eraseIdx i)[j] = l[j]'(by have := length_eraseIdx_le l i; omega) := by
-  rw [getElem_eraseIdx]
-  simp only [dite_eq_left_iff, Nat.not_lt]
-  intro h'
-  omega
-
-theorem getElem_eraseIdx_of_ge (l : List α) (i : Nat) (j : Nat) (h : j < (l.eraseIdx i).length) (h' : i ≤ j) :
-    (l.eraseIdx i)[j] = l[j + 1]'(by rw [length_eraseIdx] at h; split at h <;> omega) := by
-  rw [getElem_eraseIdx, dif_neg]
-  omega

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

@@ -1,32 +0,0 @@
-/-
-Copyright (c) 2024 Kim Morrison. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison
--/
-prelude
-import Init.Data.List.Nat.Range
-import Init.Data.List.Find
-
-namespace List
-
-theorem findIdx?_eq_some_le_of_findIdx?_eq_some {xs : List α} {p q : α → Bool} (w : ∀ x ∈ xs, p x → q x) {i : Nat}
-    (h : xs.findIdx? p = some i) : ∃ j, j ≤ i ∧ xs.findIdx? q = some j := by
-  simp only [findIdx?_eq_findSome?_enum] at h
-  rw [findSome?_eq_some_iff] at h
-  simp only [Option.ite_none_right_eq_some, Option.some.injEq, ite_eq_right_iff, reduceCtorEq,
-    imp_false, Bool.not_eq_true, Prod.forall, exists_and_right, Prod.exists] at h
-  obtain ⟨h, h₁, b, ⟨es, h₂⟩, ⟨hb, rfl⟩, h₃⟩ := h
-  rw [enum_eq_enumFrom, enumFrom_eq_append_iff] at h₂
-  obtain ⟨l₁', l₂', rfl, rfl, h₂⟩ := h₂
-  rw [eq_comm, enumFrom_eq_cons_iff] at h₂
-  obtain ⟨a, as, rfl, h₂, rfl⟩ := h₂
-  simp only [Nat.zero_add, Prod.mk.injEq] at h₂
-  obtain ⟨rfl, rfl⟩ := h₂
-  simp only [findIdx?_append]
-  match h : findIdx? q l₁' with
-  | some j =>
-    refine ⟨j, ?_, by simp⟩
-    rw [findIdx?_eq_some_iff_findIdx_eq] at h
-    omega
-  | none =>
-    refine ⟨l₁'.length, by simp, by simp_all⟩

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

@@ -109,8 +109,7 @@ theorem range'_eq_append_iff : range' s n = xs ++ ys ↔ ∃ k, k ≤ n ∧ xs =
 @[simp] theorem find?_range'_eq_some {s n : Nat} {i : Nat} {p : Nat → Bool} :
     (range' s n).find? p = some i ↔ p i ∧ i ∈ range' s n ∧ ∀ j, s ≤ j → j < i → !p j := by
   rw [find?_eq_some]
-  simp only [Bool.not_eq_eq_eq_not, Bool.not_true, exists_and_right, mem_range'_1,
-    and_congr_right_iff]
+  simp only [Bool.not_eq_true', exists_and_right, mem_range'_1, and_congr_right_iff]
   simp only [range'_eq_append_iff, eq_comm (a := i :: _), range'_eq_cons_iff]
   intro h
   constructor
@@ -177,7 +176,7 @@ theorem pairwise_le_range (n : Nat) : Pairwise (· ≤ ·) (range n) :=
 theorem take_range (m n : Nat) : take m (range n) = range (min m n) := by
   apply List.ext_getElem
   · simp
-  · simp (config := { contextual := true }) [getElem_take, Nat.lt_min]
+  · simp (config := { contextual := true }) [← getElem_take, Nat.lt_min]
 
 theorem nodup_range (n : Nat) : Nodup (range n) := by
   simp (config := {decide := true}) only [range_eq_range', nodup_range']
@@ -259,9 +258,6 @@ theorem nodup_iota (n : Nat) : Nodup (iota n) :=
   | zero => simp at h
   | succ n => simp
 
-@[simp] theorem tail_iota (n : Nat) : (iota n).tail = iota (n - 1) := by
-  cases n <;> simp
-
 @[simp] theorem reverse_iota : reverse (iota n) = range' 1 n := by
   induction n with
   | zero => simp
@@ -276,15 +272,15 @@ theorem nodup_iota (n : Nat) : Nodup (iota n) :=
   rw [getLast_eq_head_reverse]
   simp
 
-theorem find?_iota_eq_none {n : Nat} {p : Nat → Bool} :
+theorem find?_iota_eq_none {n : Nat} (p : Nat → Bool) :
     (iota n).find? p = none ↔ ∀ i, 0 < i → i ≤ n → !p i := by
   simp
 
 @[simp] theorem find?_iota_eq_some {n : Nat} {i : Nat} {p : Nat → Bool} :
     (iota n).find? p = some i ↔ p i ∧ i ∈ iota n ∧ ∀ j, i < j → j ≤ n → !p j := by
   rw [find?_eq_some]
-  simp only [iota_eq_reverse_range', reverse_eq_append_iff, reverse_cons, append_assoc, cons_append,
-    nil_append, Bool.not_eq_eq_eq_not, Bool.not_true, exists_and_right, mem_reverse, mem_range'_1,
+  simp only [iota_eq_reverse_range', reverse_eq_append_iff, reverse_cons, append_assoc,
+    singleton_append, Bool.not_eq_true', exists_and_right, mem_reverse, mem_range'_1,
     and_congr_right_iff]
   intro h
   constructor
@@ -358,6 +354,17 @@ theorem map_enumFrom (f : α → β) (n : Nat) (l : List α) :
     map (Prod.map id f) (enumFrom n l) = enumFrom n (map f l) := by
   induction l generalizing n <;> simp_all
 
+@[simp]
+theorem enumFrom_map_fst (n) :
+    ∀ (l : List α), map Prod.fst (enumFrom n l) = range' n l.length
+  | [] => rfl
+  | _ :: _ => congrArg (cons _) (enumFrom_map_fst _ _)
+
+@[simp]
+theorem enumFrom_map_snd : ∀ (n) (l : List α), map Prod.snd (enumFrom n l) = l
+  | _, [] => rfl
+  | _, _ :: _ => congrArg (cons _) (enumFrom_map_snd _ _)
+
 theorem snd_mem_of_mem_enumFrom {x : Nat × α} {n : Nat} {l : List α} (h : x ∈ enumFrom n l) : x.2 ∈ l :=
   enumFrom_map_snd n l ▸ mem_map_of_mem _ h
 
@@ -380,6 +387,10 @@ theorem mem_enumFrom {x : α} {i j : Nat} {xs : List α} (h : (i, x) ∈ xs.enum
       x = xs[i - j]'(by have := le_fst_of_mem_enumFrom h; have := fst_lt_add_of_mem_enumFrom h; omega) :=
   ⟨le_fst_of_mem_enumFrom h, fst_lt_add_of_mem_enumFrom h, snd_eq_of_mem_enumFrom h⟩
 
+theorem enumFrom_cons' (n : Nat) (x : α) (xs : List α) :
+    enumFrom n (x :: xs) = (n, x) :: (enumFrom n xs).map (Prod.map (· + 1) id) := by
+  rw [enumFrom_cons, Nat.add_comm, ← map_fst_add_enumFrom_eq_enumFrom]
+
 theorem enumFrom_map (n : Nat) (l : List α) (f : α → β) :
     enumFrom n (l.map f) = (enumFrom n l).map (Prod.map id f) := by
   induction l with
@@ -396,39 +407,22 @@ theorem enumFrom_append (xs ys : List α) (n : Nat) :
     rw [cons_append, enumFrom_cons, IH, ← cons_append, ← enumFrom_cons, length, Nat.add_right_comm,
       Nat.add_assoc]
 
-theorem enumFrom_eq_cons_iff {l : List α} {n : Nat} :
-    l.enumFrom n = x :: l' ↔ ∃ a as, l = a :: as ∧ x = (n, a) ∧ l' = enumFrom (n + 1) as := by
-  rw [enumFrom_eq_zip_range', zip_eq_cons_iff]
-  constructor
-  · rintro ⟨l₁, l₂, h, rfl, rfl⟩
-    rw [range'_eq_cons_iff] at h
-    obtain ⟨rfl, -, rfl⟩ := h
-    exact ⟨x.2, l₂, by simp [enumFrom_eq_zip_range']⟩
-  · rintro ⟨a, as, rfl, rfl, rfl⟩
-    refine ⟨range' (n+1) as.length, as, ?_⟩
-    simp [enumFrom_eq_zip_range', range'_succ]
+theorem enumFrom_eq_zip_range' (l : List α) {n : Nat} : l.enumFrom n = (range' n l.length).zip l :=
+  zip_of_prod (enumFrom_map_fst _ _) (enumFrom_map_snd _ _)
 
-theorem enumFrom_eq_append_iff {l : List α} {n : Nat} :
-    l.enumFrom n = l₁ ++ l₂ ↔
-      ∃ l₁' l₂', l = l₁' ++ l₂' ∧ l₁ = l₁'.enumFrom n ∧ l₂ = l₂'.enumFrom (n + l₁'.length) := by
-  rw [enumFrom_eq_zip_range', zip_eq_append_iff]
-  constructor
-  · rintro ⟨w, x, y, z, h, h', rfl, rfl, rfl⟩
-    rw [range'_eq_append_iff] at h'
-    obtain ⟨k, -, rfl, rfl⟩ := h'
-    simp only [length_range'] at h
-    obtain rfl := h
-    refine ⟨y, z, rfl, ?_⟩
-    simp only [enumFrom_eq_zip_range', length_append, true_and]
-    congr
-    omega
-  · 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]
+theorem unzip_enumFrom_eq_prod (l : List α) {n : Nat} :
+    (l.enumFrom n).unzip = (range' n l.length, l) := by
+  simp only [enumFrom_eq_zip_range', unzip_zip, length_range']
 
 /-! ### enum -/
 
+theorem enum_cons : (a::as).enum = (0, a) :: as.enumFrom 1 := rfl
+
+theorem enum_cons' (x : α) (xs : List α) :
+    enum (x :: xs) = (0, x) :: (enum xs).map (Prod.map (· + 1) id) :=
+  enumFrom_cons' _ _ _
+
 @[simp]
 theorem enum_eq_nil {l : List α} : List.enum l = [] ↔ l = [] := enumFrom_eq_nil
 
@@ -454,9 +448,6 @@ theorem getElem_enum (l : List α) (i : Nat) (h : i < l.enum.length) :
     l.enum.getLast? = l.getLast?.map fun a => (l.length - 1, a) := by
   simp [getLast?_eq_getElem?]
 
-@[simp] theorem tail_enum (l : List α) : (enum l).tail = enumFrom 1 l.tail := by
-  simp [enum]
-
 theorem mk_mem_enum_iff_getElem? {i : Nat} {x : α} {l : List α} : (i, x) ∈ enum l ↔ l[i]? = x := by
   simp [enum, mk_mem_enumFrom_iff_le_and_getElem?_sub]
 

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

@@ -6,7 +6,6 @@ Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, M
 prelude
 import Init.Data.List.Zip
 import Init.Data.List.Sublist
-import Init.Data.List.Find
 import Init.Data.Nat.Lemmas
 
 /-!
@@ -36,23 +35,23 @@ theorem length_take_of_le (h : n ≤ length l) : length (take n l) = n := by sim
 
 /-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
 length `> i`. Version designed to rewrite from the big list to the small list. -/
-theorem getElem_take' (L : List α) {i j : Nat} (hi : i < L.length) (hj : i < j) :
+theorem getElem_take (L : List α) {i j : Nat} (hi : i < L.length) (hj : i < j) :
     L[i] = (L.take j)[i]'(length_take .. ▸ Nat.lt_min.mpr ⟨hj, hi⟩) :=
-  getElem_of_eq (take_append_drop j L).symm _ ▸ getElem_append_left ..
+  getElem_of_eq (take_append_drop j L).symm _ ▸ getElem_append ..
 
 /-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
 length `> i`. Version designed to rewrite from the small list to the big list. -/
-theorem getElem_take (L : List α) {j i : Nat} {h : i < (L.take j).length} :
+theorem getElem_take' (L : List α) {j i : Nat} {h : i < (L.take j).length} :
     (L.take j)[i] =
     L[i]'(Nat.lt_of_lt_of_le h (length_take_le' _ _)) := by
-  rw [length_take, Nat.lt_min] at h; rw [getElem_take' L _ h.1]
+  rw [length_take, Nat.lt_min] at h; rw [getElem_take L _ h.1]
 
 /-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
 length `> i`. Version designed to rewrite from the big list to the small list. -/
-@[deprecated getElem_take' (since := "2024-06-12")]
+@[deprecated getElem_take (since := "2024-06-12")]
 theorem get_take (L : List α) {i j : Nat} (hi : i < L.length) (hj : i < j) :
     get L ⟨i, hi⟩ = get (L.take j) ⟨i, length_take .. ▸ Nat.lt_min.mpr ⟨hj, hi⟩⟩ := by
-  simp [getElem_take' _ hi hj]
+  simp [getElem_take _ hi hj]
 
 /-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
 length `> i`. Version designed to rewrite from the small list to the big list. -/
@@ -60,7 +59,7 @@ length `> i`. Version designed to rewrite from the small list to the big list. -
 theorem get_take' (L : List α) {j i} :
     get (L.take j) i =
     get L ⟨i.1, Nat.lt_of_lt_of_le i.2 (length_take_le' _ _)⟩ := by
-  simp [getElem_take]
+  simp [getElem_take']
 
 theorem getElem?_take_eq_none {l : List α} {n m : Nat} (h : n ≤ m) :
     (l.take n)[m]? = none :=
@@ -110,7 +109,7 @@ theorem getLast?_take {l : List α} : (l.take n).getLast? = if n = 0 then none e
 
 theorem getLast_take {l : List α} (h : l.take n ≠ []) :
     (l.take n).getLast h = l[n - 1]?.getD (l.getLast (by simp_all)) := by
-  rw [getLast_eq_getElem, getElem_take]
+  rw [getLast_eq_getElem, getElem_take']
   simp [length_take, Nat.min_def]
   simp at h
   split
@@ -191,12 +190,20 @@ theorem dropLast_take {n : Nat} {l : List α} (h : n < l.length) :
     (l.take n).dropLast = l.take (n - 1) := by
   simp only [dropLast_eq_take, length_take, Nat.le_of_lt h, Nat.min_eq_left, take_take, sub_le]
 
-@[deprecated map_eq_append_iff (since := "2024-09-05")] abbrev map_eq_append_split := @map_eq_append_iff
+theorem map_eq_append_split {f : α → β} {l : List α} {s₁ s₂ : List β}
+    (h : map f l = s₁ ++ s₂) : ∃ l₁ l₂, l = l₁ ++ l₂ ∧ map f l₁ = s₁ ∧ map f l₂ = s₂ := by
+  have := h
+  rw [← take_append_drop (length s₁) l] at this ⊢
+  rw [map_append] at this
+  refine ⟨_, _, rfl, append_inj this ?_⟩
+  rw [length_map, length_take, Nat.min_eq_left]
+  rw [← length_map l f, h, length_append]
+  apply Nat.le_add_right
 
 theorem take_prefix_take_left (l : List α) {m n : Nat} (h : m ≤ n) : take m l <+: take n l := by
   rw [isPrefix_iff]
   intro i w
-  rw [getElem?_take_of_lt, getElem_take, getElem?_eq_getElem]
+  rw [getElem?_take_of_lt, getElem_take', getElem?_eq_getElem]
   simp only [length_take] at w
   exact Nat.lt_of_lt_of_le (Nat.lt_of_lt_of_le w (Nat.min_le_left _ _)) h
 
@@ -219,9 +226,8 @@ dropping the first `i` elements. Version designed to rewrite from the big list t
 theorem getElem_drop' (L : List α) {i j : Nat} (h : i + j < L.length) :
     L[i + j] = (L.drop i)[j]'(lt_length_drop L h) := by
   have : i ≤ L.length := Nat.le_trans (Nat.le_add_right _ _) (Nat.le_of_lt h)
-  rw [getElem_of_eq (take_append_drop i L).symm h, getElem_append_right]
-  · simp [Nat.min_eq_left this, Nat.add_sub_cancel_left]
-  · simp [Nat.min_eq_left this, Nat.le_add_right]
+  rw [getElem_of_eq (take_append_drop i L).symm h, getElem_append_right'] <;>
+    simp [Nat.min_eq_left this, Nat.add_sub_cancel_left, Nat.le_add_right]
 
 /-- The `i + j`-th element of a list coincides with the `j`-th element of the list obtained by
 dropping the first `i` elements. Version designed to rewrite from the big list to the small list. -/
@@ -262,26 +268,6 @@ theorem getElem?_drop (L : List α) (i j : Nat) : (L.drop i)[j]? = L[i + j]? :=
 theorem get?_drop (L : List α) (i j : Nat) : get? (L.drop i) j = get? L (i + j) := by
   simp
 
-theorem mem_take_iff_getElem {l : List α} {a : α} :
-    a ∈ l.take n ↔ ∃ (i : Nat) (hm : i < min n l.length), l[i] = a := by
-  rw [mem_iff_getElem]
-  constructor
-  · rintro ⟨i, hm, rfl⟩
-    simp at hm
-    refine ⟨i, by omega, by rw [getElem_take]⟩
-  · rintro ⟨i, hm, rfl⟩
-    refine ⟨i, by simpa, by rw [getElem_take]⟩
-
-theorem mem_drop_iff_getElem {l : List α} {a : α} :
-    a ∈ l.drop n ↔ ∃ (i : Nat) (hm : i + n < l.length), l[n + i] = a := by
-  rw [mem_iff_getElem]
-  constructor
-  · rintro ⟨i, hm, rfl⟩
-    simp at hm
-    refine ⟨i, by omega, by rw [getElem_drop]⟩
-  · rintro ⟨i, hm, rfl⟩
-    refine ⟨i, by simp; omega, by rw [getElem_drop]⟩
-
 theorem head?_drop (l : List α) (n : Nat) :
     (l.drop n).head? = l[n]? := by
   rw [head?_eq_getElem?, getElem?_drop, Nat.add_zero]
@@ -302,7 +288,7 @@ theorem getLast?_drop {l : List α} : (l.drop n).getLast? = if l.length ≤ n th
 
 theorem getLast_drop {l : List α} (h : l.drop n ≠ []) :
     (l.drop n).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
+  simp only [ne_eq, drop_eq_nil_iff_le] at h
   apply Option.some_inj.1
   simp only [← getLast?_eq_getLast, getLast?_drop, ite_eq_right_iff]
   omega
@@ -449,64 +435,6 @@ theorem reverse_drop {l : List α} {n : Nat} :
     rw [w, take_zero, drop_of_length_le, reverse_nil]
     omega
 
-/-! ### findIdx -/
-
-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
-  obtain ⟨i, h, rfl⟩ := h
-  exact not_of_lt_findIdx (by omega)
-
-@[simp] theorem findIdx_take {xs : List α} {n : Nat} {p : α → Bool} :
-    (xs.take n).findIdx p = min n (xs.findIdx p) := by
-  induction xs generalizing n with
-  | nil => simp
-  | cons x xs ih =>
-    cases n
-    · simp
-    · simp only [take_succ_cons, findIdx_cons, ih, cond_eq_if]
-      split
-      · simp
-      · rw [Nat.add_min_add_right]
-
-@[simp] theorem findIdx?_take {xs : List α} {n : Nat} {p : α → Bool} :
-    (xs.take n).findIdx? p = (xs.findIdx? p).bind (Option.guard (fun i => i < n)) := by
-  induction xs generalizing n with
-  | nil => simp
-  | cons x xs ih =>
-    cases n
-    · simp
-    · simp only [take_succ_cons, findIdx?_cons]
-      split
-      · simp
-      · simp [ih, Option.guard_comp, Option.bind_map]
-
-@[simp] 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]
-    split <;> split <;> simp_all [Nat.add_min_add_right]
-
-/-! ### takeWhile -/
-
-theorem takeWhile_eq_take_findIdx_not {xs : List α} {p : α → Bool} :
-    takeWhile p xs = take (xs.findIdx (fun a => !p a)) xs := by
-  induction xs with
-  | nil => simp
-  | cons x xs ih =>
-    simp only [takeWhile_cons, ih, findIdx_cons, cond_eq_if, Bool.not_eq_eq_eq_not, Bool.not_true]
-    split <;> simp_all
-
-theorem dropWhile_eq_drop_findIdx_not {xs : List α} {p : α → Bool} :
-    dropWhile p xs = drop (xs.findIdx (fun a => !p a)) xs := by
-  induction xs with
-  | nil => simp
-  | cons x xs ih =>
-    simp only [dropWhile_cons, ih, findIdx_cons, cond_eq_if, Bool.not_eq_eq_eq_not, Bool.not_true]
-    split <;> simp_all
-
 /-! ### rotateLeft -/
 
 @[simp] theorem rotateLeft_replicate (n) (a : α) : rotateLeft (replicate m a) n = replicate m a := by

src/Init/Data/List/Perm.lean

@@ -348,7 +348,7 @@ theorem perm_iff_count {l₁ l₂ : List α} : l₁ ~ l₂ ↔ ∀ a, count a l
       specialize H b
       simp at H
   | cons a l₁ IH =>
-    have : a ∈ l₂ := count_pos_iff.mp (by rw [← H]; simp)
+    have : a ∈ l₂ := count_pos_iff_mem.mp (by rw [← H]; simp)
     refine ((IH fun b => ?_).cons a).trans (perm_cons_erase this).symm
     specialize H b
     rw [(perm_cons_erase this).count_eq] at H

src/Init/Data/List/Range.lean

@@ -5,7 +5,6 @@ Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, M
 -/
 prelude
 import Init.Data.List.Pairwise
-import Init.Data.List.Zip
 
 /-!
 # Lemmas about `List.range` and `List.enum`
@@ -36,16 +35,11 @@ theorem range'_succ (s n step) : range' s (n + 1) step = s :: range' (s + step)
 theorem range'_ne_nil (s : Nat) {n : Nat} : range' s n ≠ [] ↔ n ≠ 0 := by
   cases n <;> simp
 
-@[simp] theorem range'_zero : range' s 0 step = [] := by
+@[simp] theorem range'_zero : range' s 0 = [] := by
   simp
 
 @[simp] theorem range'_one {s step : Nat} : range' s 1 step = [s] := rfl
 
-@[simp] theorem tail_range' (n : Nat) : (range' s n step).tail = range' (s + step) (n - 1) step := by
-  cases n with
-  | zero => simp
-  | succ n => simp [range'_succ]
-
 @[simp] theorem range'_inj : range' s n = range' s' n' ↔ n = n' ∧ (n = 0 ∨ s = s') := by
   constructor
   · intro h
@@ -159,9 +153,6 @@ theorem range'_eq_map_range (s n : Nat) : range' s n = map (s + ·) (range n) :=
 theorem range_ne_nil {n : Nat} : range n ≠ [] ↔ n ≠ 0 := by
   cases n <;> simp
 
-@[simp] theorem tail_range (n : Nat) : (range n).tail = range' 1 (n - 1) := by
-  rw [range_eq_range', tail_range']
-
 @[simp]
 theorem range_sublist {m n : Nat} : range m <+ range n ↔ m ≤ n := by
   simp only [range_eq_range', range'_sublist_right]
@@ -228,12 +219,6 @@ theorem getElem_enumFrom (l : List α) (n) (i : Nat) (h : i < (l.enumFrom n).len
   simp only [getElem?_enumFrom, getElem?_eq_getElem h]
   simp
 
-@[simp]
-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]
-
 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
@@ -242,47 +227,4 @@ theorem map_fst_add_enum_eq_enumFrom (l : List α) (n : Nat) :
     map (Prod.map (· + n) id) (enum l) = enumFrom n l :=
   map_fst_add_enumFrom_eq_enumFrom l _ _
 
-theorem enumFrom_cons' (n : Nat) (x : α) (xs : List α) :
-    enumFrom n (x :: xs) = (n, x) :: (enumFrom n xs).map (Prod.map (· + 1) id) := by
-  rw [enumFrom_cons, Nat.add_comm, ← map_fst_add_enumFrom_eq_enumFrom]
-
-@[simp]
-theorem enumFrom_map_fst (n) :
-    ∀ (l : List α), map Prod.fst (enumFrom n l) = range' n l.length
-  | [] => rfl
-  | _ :: _ => congrArg (cons _) (enumFrom_map_fst _ _)
-
-@[simp]
-theorem enumFrom_map_snd : ∀ (n) (l : List α), map Prod.snd (enumFrom n l) = l
-  | _, [] => rfl
-  | _, _ :: _ => congrArg (cons _) (enumFrom_map_snd _ _)
-
-theorem enumFrom_eq_zip_range' (l : List α) {n : Nat} : l.enumFrom n = (range' n l.length).zip l :=
-  zip_of_prod (enumFrom_map_fst _ _) (enumFrom_map_snd _ _)
-
-@[simp]
-theorem unzip_enumFrom_eq_prod (l : List α) {n : Nat} :
-    (l.enumFrom n).unzip = (range' n l.length, l) := by
-  simp only [enumFrom_eq_zip_range', unzip_zip, length_range']
-
-/-! ### enum -/
-
-theorem enum_cons : (a::as).enum = (0, a) :: as.enumFrom 1 := rfl
-
-theorem enum_cons' (x : α) (xs : List α) :
-    enum (x :: xs) = (0, x) :: (enum xs).map (Prod.map (· + 1) id) :=
-  enumFrom_cons' _ _ _
-
-theorem enum_eq_enumFrom {l : List α} : l.enum = l.enumFrom 0 := rfl
-
-theorem enumFrom_eq_map_enum (l : List α) (n : Nat) :
-    enumFrom n l = (enum l).map (Prod.map (· + n) id) := by
-  induction l generalizing n with
-  | nil => simp
-  | cons x xs ih =>
-    simp only [enumFrom_cons, ih, enum_cons, map_cons, Prod.map_apply, Nat.zero_add, id_eq, map_map,
-      cons.injEq, map_inj_left, Function.comp_apply, Prod.forall, Prod.mk.injEq, and_true, true_and]
-    intro a b _
-    exact (succ_add a n).symm
-
 end List

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

@@ -22,18 +22,17 @@ namespace List
 This version is not tail-recursive,
 but it is replaced at runtime by `mergeTR` using a `@[csimp]` lemma.
 -/
-def merge (xs ys : List α) (le : α → α → Bool := by exact fun a b => a ≤ b) : List α :=
-  match xs, ys with
+def merge (le : α → α → Bool) : List α → List α → List α
   | [], ys => ys
   | xs, [] => xs
   | x :: xs, y :: ys =>
     if le x y then
-      x :: merge xs (y :: ys) le
+      x :: merge le xs (y :: ys)
     else
-      y :: merge (x :: xs) ys le
+      y :: merge le (x :: xs) ys
 
-@[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
+@[simp] theorem nil_merge (ys : List α) : merge le [] ys = ys := by simp [merge]
+@[simp] theorem merge_right (xs : List α) : merge le xs [] = xs := by
   induction xs with
   | nil => simp [merge]
   | cons x xs ih => simp [merge, ih]
@@ -46,7 +45,6 @@ def splitInTwo (l : { l : List α // l.length = n }) :
   let r := splitAt ((n+1)/2) l.1
   (⟨r.1, by simp [r, splitAt_eq, l.2]; omega⟩, ⟨r.2, by simp [r, splitAt_eq, l.2]; omega⟩)
 
-set_option linter.unusedVariables false in
 /--
 Simplified implementation of stable merge sort.
 
@@ -58,15 +56,16 @@ It is replaced at runtime in the compiler by `mergeSortTR₂` using a `@[csimp]`
 Because we want the sort to be stable,
 it is essential that we split the list in two contiguous sublists.
 -/
-def mergeSort : ∀ (xs : List α) (le : α → α → Bool := by exact fun a b => a ≤ b), List α
-  | [], _ => []
-  | [a], _ => [a]
-  | a :: b :: xs, le =>
+def mergeSort (le : α → α → Bool) : List α → List α
+  | [] => []
+  | [a] => [a]
+  | a :: b :: xs =>
     let lr := splitInTwo ⟨a :: b :: xs, rfl⟩
     have := by simpa using lr.2.2
     have := by simpa using lr.1.2
-    merge (mergeSort lr.1 le) (mergeSort lr.2 le) le
-termination_by xs => xs.length
+    merge le (mergeSort le lr.1) (mergeSort le lr.2)
+termination_by l => l.length
+
 
 /--
 Given an ordering relation `le : α → α → Bool`,

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

@@ -38,7 +38,7 @@ namespace List.MergeSort.Internal
 /--
 `O(min |l| |r|)`. Merge two lists using `le` as a switch.
 -/
-def mergeTR (l₁ l₂ : List α) (le : α → α → Bool) : List α :=
+def mergeTR (le : α → α → Bool) (l₁ l₂ : List α) : List α :=
   go l₁ l₂ []
 where go : List α → List α → List α → List α
   | [], l₂, acc => reverseAux acc l₂
@@ -49,7 +49,7 @@ where go : List α → List α → List α → List α
     else
       go (x :: xs) ys (y :: acc)
 
-theorem mergeTR_go_eq : mergeTR.go le l₁ l₂ acc = acc.reverse ++ merge l₁ l₂ le := by
+theorem mergeTR_go_eq : mergeTR.go le l₁ l₂ acc = acc.reverse ++ merge le l₁ l₂ := by
   induction l₁ generalizing l₂ acc with
   | nil => simp [mergeTR.go, merge, reverseAux_eq]
   | cons x l₁ ih₁ =>
@@ -97,14 +97,14 @@ This version uses the tail-recurive `mergeTR` function as a subroutine.
 This is not the final version we use at runtime, as `mergeSortTR₂` is faster.
 This definition is useful as an intermediate step in proving the `@[csimp]` lemma for `mergeSortTR₂`.
 -/
-def mergeSortTR (l : List α) (le : α → α → Bool := by exact fun a b => a ≤ b) : List α :=
+def mergeSortTR (le : α → α → Bool) (l : List α) : List α :=
   run ⟨l, rfl⟩
 where run : {n : Nat} → { l : List α // l.length = n } → List α
   | 0, ⟨[], _⟩ => []
   | 1, ⟨[a], _⟩ => [a]
   | n+2, xs =>
     let (l, r) := splitInTwo xs
-    mergeTR (run l) (run r) le
+    mergeTR le (run l) (run r)
 
 /--
 Split a list in two equal parts, reversing the first part.
@@ -130,7 +130,7 @@ Faster version of `mergeSortTR`, which avoids unnecessary list reversals.
 -- Per the benchmark in `tests/bench/mergeSort/`
 -- (which averages over 4 use cases: already sorted lists, reverse sorted lists, almost sorted lists, and random lists),
 -- for lists of length 10^6, `mergeSortTR₂` is about 20% faster than `mergeSortTR`.
-def mergeSortTR₂ (l : List α) (le : α → α → Bool := by exact fun a b => a ≤ b) : List α :=
+def mergeSortTR₂ (le : α → α → Bool) (l : List α) : List α :=
   run ⟨l, rfl⟩
 where
   run : {n : Nat} → { l : List α // l.length = n } → List α
@@ -138,13 +138,13 @@ where
   | 1, ⟨[a], _⟩ => [a]
   | n+2, xs =>
     let (l, r) := splitRevInTwo xs
-    mergeTR (run' l) (run r) le
+    mergeTR le (run' l) (run r)
   run' : {n : Nat} → { l : List α // l.length = n } → List α
   | 0, ⟨[], _⟩ => []
   | 1, ⟨[a], _⟩ => [a]
   | n+2, xs =>
     let (l, r) := splitRevInTwo' xs
-    mergeTR (run' r) (run l) le
+    mergeTR le (run' r) (run l)
 
 theorem splitRevInTwo'_fst (l : { l : List α // l.length = n }) :
     (splitRevInTwo' l).1 = ⟨(splitInTwo ⟨l.1.reverse, by simpa using l.2⟩).2.1, by have := l.2; simp; omega⟩ := by
@@ -166,7 +166,7 @@ theorem splitRevInTwo_snd (l : { l : List α // l.length = n }) :
     (splitRevInTwo l).2 = ⟨(splitInTwo l).2.1, by have := l.2; simp; omega⟩ := by
   simp only [splitRevInTwo, splitRevAt_eq, reverse_take, splitInTwo_snd]
 
-theorem mergeSortTR_run_eq_mergeSort : {n : Nat} → (l : { l : List α // l.length = n }) → mergeSortTR.run le l = mergeSort l.1 le
+theorem mergeSortTR_run_eq_mergeSort : {n : Nat} → (l : { l : List α // l.length = n }) → mergeSortTR.run le l = mergeSort le l.1
   | 0, ⟨[], _⟩
   | 1, ⟨[a], _⟩ => by simp [mergeSortTR.run, mergeSort]
   | n+2, ⟨a :: b :: l, h⟩ => by
@@ -183,7 +183,7 @@ theorem mergeSort_eq_mergeSortTR : @mergeSort = @mergeSortTR := by
 -- This mutual block is unfortunately quite slow to elaborate.
 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
+theorem mergeSortTR₂_run_eq_mergeSort : {n : Nat} → (l : { l : List α // l.length = n }) → mergeSortTR₂.run le l = mergeSort le l.1
   | 0, ⟨[], _⟩
   | 1, ⟨[a], _⟩ => by simp [mergeSortTR₂.run, mergeSort]
   | n+2, ⟨a :: b :: l, h⟩ => by
@@ -195,7 +195,7 @@ theorem mergeSortTR₂_run_eq_mergeSort : {n : Nat} → (l : { l : List α // l.
     rw [reverse_reverse]
 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
+theorem mergeSortTR₂_run'_eq_mergeSort : {n : Nat} → (l : { l : List α // l.length = n }) → (w : l' = l.1.reverse) → mergeSortTR₂.run' le l = mergeSort le l'
   | 0, ⟨[], _⟩, w
   | 1, ⟨[a], _⟩, w => by simp_all [mergeSortTR₂.run', mergeSort]
   | n+2, ⟨a :: b :: l, h⟩, w => by

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

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2024 Lean FRO. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison, Eric Wieser, François G. Dorais
+Authors: Kim Morrison
 -/
 prelude
 import Init.Data.List.Perm
@@ -23,6 +23,11 @@ import Init.Data.Bool
 
 namespace List
 
+-- We enable this instance locally so we can write `Pairwise le` instead of `Pairwise (le · ·)` everywhere.
+attribute [local instance] boolRelToRel
+
+variable {le : α → α → Bool}
+
 /-! ### splitInTwo -/
 
 @[simp] theorem splitInTwo_fst (l : { l : List α // l.length = n }) :
@@ -84,8 +89,6 @@ theorem splitInTwo_fst_le_splitInTwo_snd {l : { l : List α // l.length = n }} (
 
 /-! ### enumLE -/
 
-variable {le : α → α → Bool}
-
 theorem enumLE_trans (trans : ∀ a b c, le a b → le b c → le a c)
     (a b c : Nat × α) : enumLE le a b → enumLE le b c → enumLE le a c := by
   simp only [enumLE]
@@ -114,67 +117,19 @@ theorem enumLE_trans (trans : ∀ a b c, le a b → le b c → le a c)
   · simp_all
   · simp_all
 
-theorem enumLE_total (total : ∀ a b, le a b || le b a)
-    (a b : Nat × α) : enumLE le a b || enumLE le b a := by
+theorem enumLE_total (total : ∀ a b, !le a b → le b a)
+    (a b : Nat × α) : !enumLE le a b → enumLE le b a := by
   simp only [enumLE]
   split <;> split
-  · simpa using Nat.le_total a.fst b.fst
+  · simpa using Nat.le_of_lt
   · simp
   · simp
-  · have := total a.2 b.2
-    simp_all
+  · simp_all [total a.2 b.2]
 
 /-! ### merge -/
 
-theorem cons_merge_cons (s : α → α → Bool) (a b l r) :
-    merge (a::l) (b::r) s = if s a b then a :: merge l (b::r) s else b :: merge (a::l) r s := by
-  simp only [merge]
-
-@[simp] theorem cons_merge_cons_pos (s : α → α → Bool) (l r) (h : s a b) :
-    merge (a::l) (b::r) s = a :: merge l (b::r) s := by
-  rw [cons_merge_cons, if_pos h]
-
-@[simp] theorem cons_merge_cons_neg (s : α → α → Bool) (l r) (h : ¬ s a b) :
-    merge (a::l) (b::r) s = b :: merge (a::l) r s := by
-  rw [cons_merge_cons, if_neg h]
-
-@[simp] theorem length_merge (s : α → α → Bool) (l r) :
-    (merge l r s).length = l.length + r.length := by
-  match l, r with
-  | [], r => simp
-  | l, [] => simp
-  | a::l, b::r =>
-    rw [cons_merge_cons]
-    split
-    · simp_arith [length_merge s l (b::r)]
-    · simp_arith [length_merge s (a::l) r]
-
-/--
-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]
-  | cons x xs ih =>
-    induction ys with
-    | nil => simp [merge]
-    | 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]
-        apply or_congr_left
-        simp only [or_comm (a := a = y), or_assoc]
-
-theorem mem_merge_left (s : α → α → Bool) (h : x ∈ l) : x ∈ merge l r s :=
-  mem_merge.2 <| .inl h
-
-theorem mem_merge_right (s : α → α → Bool) (h : x ∈ r) : x ∈ merge l r s :=
-  mem_merge.2 <| .inr h
-
 theorem merge_stable : ∀ (xs ys) (_ : ∀ x y, x ∈ xs → y ∈ ys → x.1 ≤ y.1),
-    (merge xs ys (enumLE le)).map (·.2) = merge (xs.map (·.2)) (ys.map (·.2)) le
+    (merge (enumLE le) xs ys).map (·.2) = merge le (xs.map (·.2)) (ys.map (·.2))
   | [], ys, _ => by simp [merge]
   | xs, [], _ => by simp [merge]
   | (i, x) :: xs, (j, y) :: ys, h => by
@@ -188,17 +143,32 @@ theorem merge_stable : ∀ (xs ys) (_ : ∀ x y, x ∈ xs → y ∈ ys → x.1
       rw [merge_stable, map_cons]
       exact fun x' y' mx my => h x' y' mx (mem_cons_of_mem (j, y) my)
 
--- We enable this instance locally so we can write `Pairwise le` instead of `Pairwise (le · ·)` everywhere.
-attribute [local instance] boolRelToRel
+/--
+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 le xs ys ↔ a ∈ xs ∨ a ∈ ys := by
+  induction xs generalizing ys with
+  | nil => simp [merge]
+  | cons x xs ih =>
+    induction ys with
+    | nil => simp [merge]
+    | 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]
+        apply or_congr_left
+        simp only [or_comm (a := a = y), or_assoc]
 
 /--
-If the ordering relation `le` is transitive and total (i.e. `le a b || le b a` for all `a, b`)
+If the ordering relation `le` is transitive and total (i.e. `le a b ∨ le b a` for all `a, b`)
 then the `merge` of two sorted lists is sorted.
 -/
 theorem sorted_merge
     (trans : ∀ (a b c : α), le a b → le b c → le a c)
-    (total : ∀ (a b : α), le a b || le b a)
-    (l₁ l₂ : List α) (h₁ : l₁.Pairwise le) (h₂ : l₂.Pairwise le) : (merge l₁ l₂ le).Pairwise le := by
+    (total : ∀ (a b : α), !le a b → le b a)
+    (l₁ l₂ : List α) (h₁ : l₁.Pairwise le) (h₂ : l₂.Pairwise le) : (merge le l₁ l₂).Pairwise le := by
   induction l₁ generalizing l₂ with
   | nil => simpa only [merge]
   | cons x l₁ ih₁ =>
@@ -218,15 +188,14 @@ theorem sorted_merge
       · apply Pairwise.cons
         · intro z m
           rw [mem_merge, mem_cons] at m
-          simp only [Bool.not_eq_true] at h
           rcases m with (⟨rfl|m⟩|m)
-          · simpa [h] using total y z
-          · exact trans _ _ _ (by simpa [h] using total x y) (rel_of_pairwise_cons h₁ m)
+          · exact total _ _ (by simpa using h)
+          · exact trans _ _ _ (total _ _ (by simpa using h)) (rel_of_pairwise_cons h₁ m)
           · exact rel_of_pairwise_cons h₂ m
         · exact ih₂ h₂.tail
 
 theorem merge_of_le : ∀ {xs ys : List α} (_ : ∀ a b, a ∈ xs → b ∈ ys → le a b),
-    merge xs ys le = xs ++ ys
+    merge le xs ys = xs ++ ys
   | [], ys, _
   | xs, [], _ => by simp [merge]
   | x :: xs, y :: ys, h => by
@@ -237,7 +206,7 @@ theorem merge_of_le : ∀ {xs ys : List α} (_ : ∀ a b, a ∈ xs → b ∈ ys
     · exact h x y (mem_cons_self _ _) (mem_cons_self _ _)
 
 variable (le) in
-theorem merge_perm_append : ∀ {xs ys : List α}, merge xs ys le ~ xs ++ ys
+theorem merge_perm_append : ∀ {xs ys : List α}, merge le xs ys ~ xs ++ ys
   | [], ys => by simp [merge]
   | xs, [] => by simp [merge]
   | x :: xs, y :: ys => by
@@ -253,35 +222,36 @@ theorem merge_perm_append : ∀ {xs ys : List α}, merge xs ys le ~ xs ++ ys
 
 @[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]
-  | a :: b :: xs, le => by
+variable (le) in
+theorem mergeSort_perm : ∀ (l : List α), mergeSort le l ~ l
+  | [] => by simp [mergeSort]
+  | [a] => by simp [mergeSort]
+  | a :: b :: xs => by
     simp only [mergeSort]
     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
     exact (merge_perm_append le).trans
-      (((mergeSort_perm _ _).append (mergeSort_perm _ _)).trans
+      (((mergeSort_perm _).append (mergeSort_perm _)).trans
         (Perm.of_eq (splitInTwo_fst_append_splitInTwo_snd _)))
 termination_by l => l.length
 
-@[simp] theorem length_mergeSort (l : List α) : (mergeSort l le).length = l.length :=
-  (mergeSort_perm l le).length_eq
+@[simp] theorem mergeSort_length (l : List α) : (mergeSort le l).length = l.length :=
+  (mergeSort_perm le l).length_eq
 
-@[simp] theorem mem_mergeSort {a : α} {l : List α} : a ∈ mergeSort l le ↔ a ∈ l :=
-  (mergeSort_perm l le).mem_iff
+@[simp] theorem mem_mergeSort {a : α} {l : List α} : a ∈ mergeSort le l ↔ a ∈ l :=
+  (mergeSort_perm le l).mem_iff
 
 /--
 The result of `mergeSort` is sorted,
 as long as the comparison function is transitive (`le a b → le b c → le a c`)
-and total in the sense that `le a b || le b a`.
+and total in the sense that `le a b ∨ le b a`.
 
 The comparison function need not be irreflexive, i.e. `le a b` and `le b a` is allowed even when `a ≠ b`.
 -/
 theorem 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
+    (total : ∀ (a b : α), !le a b → le b a) :
+    (l : List α) → (mergeSort le l).Pairwise le
   | [] => by simp [mergeSort]
   | [a] => by simp [mergeSort]
   | a :: b :: xs => by
@@ -298,7 +268,7 @@ 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
+theorem mergeSort_of_sorted : ∀ {l : List α} (_ : Pairwise le l), mergeSort le l = l
   | [], _ => by simp [mergeSort]
   | [a], _ => by simp [mergeSort]
   | a :: b :: xs, h => by
@@ -324,10 +294,10 @@ See also:
 * `pair_sublist_mergeSort`: if `[a, b] <+ l` and `le a b`, then `[a, b] <+ mergeSort le l`)
 -/
 theorem mergeSort_enum {l : List α} :
-    (mergeSort (l.enum) (enumLE le)).map (·.2) = mergeSort l le :=
+    (mergeSort (enumLE le) (l.enum)).map (·.2) = mergeSort le l :=
   go 0 l
 where go : ∀ (i : Nat) (l : List α),
-    (mergeSort (l.enumFrom i) (enumLE le)).map (·.2) = mergeSort l le
+    (mergeSort (enumLE le) (l.enumFrom i)).map (·.2) = mergeSort le l
   | _, []
   | _, [a] => by simp [mergeSort]
   | _, a :: b :: xs => by
@@ -348,26 +318,26 @@ termination_by _ l => l.length
 
 theorem mergeSort_cons {le : α → α → Bool}
     (trans : ∀ (a b c : α), le a b → le b c → le a c)
-    (total : ∀ (a b : α), le a b || le b a)
+    (total : ∀ (a b : α), !le a b → le b a)
     (a : α) (l : List α) :
-    ∃ l₁ l₂, mergeSort (a :: l) le = l₁ ++ a :: l₂ ∧ mergeSort l le = l₁ ++ l₂ ∧
+    ∃ l₁ l₂, mergeSort le (a :: l) = l₁ ++ a :: l₂ ∧ mergeSort le l = l₁ ++ l₂ ∧
       ∀ b, b ∈ l₁ → !le a b := by
   rw [← mergeSort_enum]
   rw [enum_cons]
   have nd : Nodup ((a :: l).enum.map (·.1)) := by rw [enum_map_fst]; exact nodup_range _
-  have m₁ : (0, a) ∈ mergeSort ((a :: l).enum) (enumLE le) :=
+  have m₁ : (0, a) ∈ mergeSort (enumLE le) ((a :: l).enum) :=
     mem_mergeSort.mpr (mem_cons_self _ _)
   obtain ⟨l₁, l₂, h⟩ := append_of_mem m₁
   have s := sorted_mergeSort (enumLE_trans trans) (enumLE_total total) ((a :: l).enum)
   rw [h] at s
-  have p := mergeSort_perm ((a :: l).enum) (enumLE le)
+  have p := mergeSort_perm (enumLE le) ((a :: l).enum)
   rw [h] at p
   refine ⟨l₁.map (·.2), l₂.map (·.2), ?_, ?_, ?_⟩
   · simpa using congrArg (·.map (·.2)) h
   · rw [← mergeSort_enum.go 1, ← map_append]
     congr 1
-    have q : mergeSort (enumFrom 1 l) (enumLE le) ~ l₁ ++ l₂ :=
-      (mergeSort_perm (enumFrom 1 l) (enumLE le)).trans
+    have q : mergeSort (enumLE le) (enumFrom 1 l) ~ l₁ ++ l₂ :=
+      (mergeSort_perm (enumLE le) (enumFrom 1 l)).trans
         (p.symm.trans perm_middle).cons_inv
     apply Perm.eq_of_sorted (le := enumLE le)
     · rintro ⟨i, a⟩ ⟨j, b⟩  ha hb
@@ -407,9 +377,9 @@ then `c` is still a sublist of `mergeSort le l`.
 -/
 theorem sublist_mergeSort
     (trans : ∀ (a b c : α), le a b → le b c → le a c)
-    (total : ∀ (a b : α), le a b || le b a) :
+    (total : ∀ (a b : α), !le a b → le b a) :
     ∀ {c : List α} (_ : c.Pairwise le) (_ : c <+ l),
-    c <+ mergeSort l le
+    c <+ mergeSort le l
   | _, _, .slnil => nil_sublist _
   | c, hc, @Sublist.cons _ _ l a h => by
     obtain ⟨l₁, l₂, h₁, h₂, -⟩ := mergeSort_cons trans total a l
@@ -438,45 +408,8 @@ then `[a, b]` is still a sublist of `mergeSort le l`.
 -/
 theorem pair_sublist_mergeSort
     (trans : ∀ (a b c : α), le a b → le b c → le a c)
-    (total : ∀ (a b : α), le a b || le b a)
-    (hab : le a b) (h : [a, b] <+ l) : [a, b] <+ mergeSort l le :=
+    (total : ∀ (a b : α), !le a b → le b a)
+    (hab : le a b) (h : [a, b] <+ l) : [a, b] <+ mergeSort le l :=
   sublist_mergeSort trans total (pairwise_pair.mpr hab) h
 
 @[deprecated (since := "2024-09-02")] abbrev mergeSort_stable_pair := @pair_sublist_mergeSort
-
-theorem map_merge {f : α → β} {r : α → α → Bool} {s : β → β → Bool} {l l' : List α}
-    (hl : ∀ a ∈ l, ∀ b ∈ l', r a b = s (f a) (f b)) :
-    (l.merge l' r).map f = (l.map f).merge (l'.map f) s := by
-  match l, l' with
-  | [], x' => simp
-  | x, [] => simp
-  | x :: xs, x' :: xs' =>
-    simp only [List.forall_mem_cons] at hl
-    simp only [forall_and] at hl
-    simp only [List.map, List.cons_merge_cons]
-    rw [← hl.1.1]
-    split
-    · rw [List.map, map_merge, List.map]
-      simp only [List.forall_mem_cons, forall_and]
-      exact ⟨hl.2.1, hl.2.2⟩
-    · rw [List.map, map_merge, List.map]
-      simp only [List.forall_mem_cons]
-      exact ⟨hl.1.2, hl.2.2⟩
-
-theorem map_mergeSort {r : α → α → Bool} {s : β → β → Bool} {f : α → β} {l : List α}
-    (hl : ∀ a ∈ l, ∀ b ∈ l, r a b = s (f a) (f b)) :
-    (l.mergeSort r).map f = (l.map f).mergeSort s :=
-  match l with
-  | [] => by simp
-  | [x] => by simp
-  | a :: b :: l => by
-    simp only [mergeSort, splitInTwo_fst, splitInTwo_snd, map_cons]
-    rw [map_merge (fun a am b bm => hl a (mem_of_mem_take (by simpa using am))
-      b (mem_of_mem_drop (by simpa using bm)))]
-    rw [map_mergeSort (s := s) (fun a am b bm => hl a (mem_of_mem_take (by simpa using am))
-      b (mem_of_mem_take (by simpa using bm)))]
-    rw [map_mergeSort (s := s) (fun a am b bm => hl a (mem_of_mem_drop (by simpa using am))
-      b (mem_of_mem_drop (by simpa using bm)))]
-    rw [map_take, map_drop]
-    simp
-  termination_by length l

src/Init/Data/List/Sublist.lean

@@ -667,7 +667,7 @@ theorem IsSuffix.length_le (h : l₁ <:+ l₂) : l₁.length ≤ l₂.length :=
 theorem IsPrefix.getElem {x y : List α} (h : x <+: y) {n} (hn : n < x.length) :
     x[n] = y[n]'(Nat.le_trans hn h.length_le) := by
   obtain ⟨_, rfl⟩ := h
-  exact (List.getElem_append_left hn).symm
+  exact (List.getElem_append n hn).symm
 
 -- See `Init.Data.List.Nat.Sublist` for `IsSuffix.getElem`.
 

src/Init/Data/List/TakeDrop.lean

@@ -7,7 +7,7 @@ prelude
 import Init.Data.List.Lemmas
 
 /-!
-# Lemmas about `List.take` and `List.drop`.
+# Lemmas about `List.zip`, `List.zipWith`, `List.zipWithAll`, and `List.unzip`.
 -/
 
 namespace List
@@ -129,7 +129,7 @@ theorem drop_tail (l : List α) (n : Nat) : l.tail.drop n = l.drop (n + 1) := by
   rw [← drop_drop, drop_one]
 
 @[simp]
-theorem drop_eq_nil_iff {l : List α} {k : Nat} : l.drop k = [] ↔ l.length ≤ k := by
+theorem drop_eq_nil_iff_le {l : List α} {k : Nat} : l.drop k = [] ↔ l.length ≤ k := by
   refine ⟨fun h => ?_, drop_eq_nil_of_le⟩
   induction k generalizing l with
   | zero =>
@@ -141,8 +141,6 @@ theorem drop_eq_nil_iff {l : List α} {k : Nat} : l.drop k = [] ↔ l.length ≤
     · simp only [drop] at h
       simpa [Nat.succ_le_succ_iff] using hk h
 
-@[deprecated drop_eq_nil_iff (since := "2024-09-10")] abbrev drop_eq_nil_iff_le := @drop_eq_nil_iff
-
 @[simp]
 theorem take_eq_nil_iff {l : List α} {k : Nat} : l.take k = [] ↔ k = 0 ∨ l = [] := by
   cases l <;> cases k <;> simp [Nat.succ_ne_zero]

src/Init/Data/List/Zip.lean

@@ -16,6 +16,83 @@ open Nat
 
 /-! ## Zippers -/
 
+/-! ### zip -/
+
+theorem zip_map (f : α → γ) (g : β → δ) :
+    ∀ (l₁ : List α) (l₂ : List β), zip (l₁.map f) (l₂.map g) = (zip l₁ l₂).map (Prod.map f g)
+  | [], l₂ => rfl
+  | l₁, [] => by simp only [map, zip_nil_right]
+  | a :: l₁, b :: l₂ => by
+    simp only [map, zip_cons_cons, zip_map, Prod.map]; constructor
+
+theorem zip_map_left (f : α → γ) (l₁ : List α) (l₂ : List β) :
+    zip (l₁.map f) l₂ = (zip l₁ l₂).map (Prod.map f id) := by rw [← zip_map, map_id]
+
+theorem zip_map_right (f : β → γ) (l₁ : List α) (l₂ : List β) :
+    zip l₁ (l₂.map f) = (zip l₁ l₂).map (Prod.map id f) := by rw [← zip_map, map_id]
+
+theorem zip_append :
+    ∀ {l₁ r₁ : List α} {l₂ r₂ : List β} (_h : length l₁ = length l₂),
+      zip (l₁ ++ r₁) (l₂ ++ r₂) = zip l₁ l₂ ++ zip r₁ r₂
+  | [], r₁, l₂, r₂, h => by simp only [eq_nil_of_length_eq_zero h.symm]; rfl
+  | l₁, r₁, [], r₂, h => by simp only [eq_nil_of_length_eq_zero h]; rfl
+  | a :: l₁, r₁, b :: l₂, r₂, h => by
+    simp only [cons_append, zip_cons_cons, zip_append (Nat.succ.inj h)]
+
+theorem zip_map' (f : α → β) (g : α → γ) :
+    ∀ l : List α, zip (l.map f) (l.map g) = l.map fun a => (f a, g a)
+  | [] => rfl
+  | a :: l => by simp only [map, zip_cons_cons, zip_map']
+
+theorem of_mem_zip {a b} : ∀ {l₁ : List α} {l₂ : List β}, (a, b) ∈ zip l₁ l₂ → a ∈ l₁ ∧ b ∈ l₂
+  | _ :: l₁, _ :: l₂, h => by
+    cases h
+    case head => simp
+    case tail h =>
+    · have := of_mem_zip h
+      exact ⟨Mem.tail _ this.1, Mem.tail _ this.2⟩
+
+@[deprecated of_mem_zip (since := "2024-07-28")] abbrev mem_zip := @of_mem_zip
+
+theorem map_fst_zip :
+    ∀ (l₁ : List α) (l₂ : List β), l₁.length ≤ l₂.length → map Prod.fst (zip l₁ l₂) = l₁
+  | [], bs, _ => rfl
+  | _ :: as, _ :: bs, h => by
+    simp [Nat.succ_le_succ_iff] at h
+    show _ :: map Prod.fst (zip as bs) = _ :: as
+    rw [map_fst_zip as bs h]
+  | a :: as, [], h => by simp at h
+
+theorem map_snd_zip :
+    ∀ (l₁ : List α) (l₂ : List β), l₂.length ≤ l₁.length → map Prod.snd (zip l₁ l₂) = l₂
+  | _, [], _ => by
+    rw [zip_nil_right]
+    rfl
+  | [], b :: bs, h => by simp at h
+  | a :: as, b :: bs, h => by
+    simp [Nat.succ_le_succ_iff] at h
+    show _ :: map Prod.snd (zip as bs) = _ :: bs
+    rw [map_snd_zip as bs h]
+
+theorem map_prod_left_eq_zip {l : List α} (f : α → β) :
+    (l.map fun x => (x, f x)) = l.zip (l.map f) := by
+  rw [← zip_map']
+  congr
+  simp
+
+theorem map_prod_right_eq_zip {l : List α} (f : α → β) :
+    (l.map fun x => (f x, x)) = (l.map f).zip l := by
+  rw [← zip_map']
+  congr
+  simp
+
+/-- See also `List.zip_replicate` in `Init.Data.List.TakeDrop` for a generalization with different lengths. -/
+@[simp] theorem zip_replicate' {a : α} {b : β} {n : Nat} :
+    zip (replicate n a) (replicate n b) = replicate n (a, b) := by
+  induction n with
+  | zero => rfl
+  | succ n ih => simp [replicate_succ, ih]
+
 /-! ### zipWith -/
 
 theorem zipWith_comm (f : α → β → γ) :
@@ -152,7 +229,6 @@ theorem drop_zipWith : (zipWith f l l').drop n = zipWith f (l.drop n) (l'.drop n
 
 @[deprecated drop_zipWith (since := "2024-07-26")] abbrev zipWith_distrib_drop := @drop_zipWith
 
-@[simp]
 theorem tail_zipWith : (zipWith f l l').tail = zipWith f l.tail l'.tail := by
   rw [← drop_one]; simp [drop_zipWith]
 
@@ -172,65 +248,6 @@ theorem zipWith_append (f : α → β → γ) (l la : List α) (l' lb : List β)
       simp only [length_cons, Nat.succ.injEq] at h
       simp [ih _ h]
 
-theorem zipWith_eq_cons_iff {f : α → β → γ} {l₁ : List α} {l₂ : List β} :
-    zipWith f l₁ l₂ = g :: l ↔
-      ∃ a l₁' b l₂', l₁ = a :: l₁' ∧ l₂ = b :: l₂' ∧ g = f a b ∧ l = zipWith f l₁' l₂' := by
-  match l₁, l₂ with
-  | [], [] => simp
-  | [], b :: l₂ => simp
-  | a :: l₁, [] => simp
-  | a' :: l₁, b' :: l₂ =>
-    simp only [zip_cons_cons, cons.injEq, Prod.mk.injEq]
-    constructor
-    · rintro ⟨⟨rfl, rfl⟩, rfl⟩
-      refine ⟨a', l₁, b', l₂, by simp⟩
-    · rintro ⟨a, l₁, b, l₂, ⟨rfl, rfl⟩, ⟨rfl, rfl⟩, rfl, rfl⟩
-      simp
-
-theorem zipWith_eq_append_iff {f : α → β → γ} {l₁ : List α} {l₂ : List β} :
-    zipWith f l₁ l₂ = l₁' ++ l₂' ↔
-      ∃ w x y z, w.length = y.length ∧ l₁ = w ++ x ∧ l₂ = y ++ z ∧ l₁' = zipWith f w y ∧ l₂' = zipWith f x z := by
-  induction l₁ generalizing l₂ l₁' with
-  | nil =>
-    simp
-    constructor
-    · rintro ⟨rfl, rfl⟩
-      exact ⟨[], [], [], by simp⟩
-    · rintro ⟨_, _, _, -, ⟨rfl, rfl⟩, _, rfl, rfl, rfl⟩
-      simp
-  | cons x₁ l₁ ih₁ =>
-    cases l₂ with
-    | nil =>
-      constructor
-      · simp only [zipWith_nil_right, nil_eq, append_eq_nil, exists_and_left, and_imp]
-        rintro rfl  rfl
-        exact ⟨[], x₁ :: l₁, [], by simp⟩
-      · rintro ⟨w, x, y, z, h₁, _, h₃, rfl, rfl⟩
-        simp only [nil_eq, append_eq_nil] at h₃
-        obtain ⟨rfl, rfl⟩ := h₃
-        simp
-    | cons x₂ l₂ =>
-      simp only [zipWith_cons_cons]
-      rw [cons_eq_append_iff]
-      constructor
-      · rintro (⟨rfl, rfl⟩ | ⟨l₁'', rfl, h⟩)
-        · exact ⟨[], x₁ :: l₁, [], x₂ :: l₂, by simp⟩
-        · rw [ih₁] at h
-          obtain ⟨w, x, y, z, h, rfl, rfl, h', rfl⟩ := h
-          refine ⟨x₁ :: w, x, x₂ :: y, z, by simp [h, h']⟩
-      · rintro ⟨w, x, y, z, h₁, h₂, h₃, rfl, rfl⟩
-        rw [cons_eq_append_iff] at h₂
-        rw [cons_eq_append_iff] at h₃
-        obtain (⟨rfl, rfl⟩ | ⟨w', rfl, rfl⟩) := h₂
-        · simp only [zipWith_nil_left, true_and, nil_eq, reduceCtorEq, false_and, exists_const,
-          or_false]
-          obtain (⟨rfl, rfl⟩ | ⟨y', rfl, rfl⟩) := h₃
-          · simp
-          · simp_all
-        · obtain (⟨rfl, rfl⟩ | ⟨y', rfl, rfl⟩) := h₃
-          · simp_all
-          · simp_all [zipWith_append, Nat.succ_inj']
-
 /-- See also `List.zipWith_replicate` in `Init.Data.List.TakeDrop` for a generalization with different lengths. -/
 @[simp] theorem zipWith_replicate' {a : α} {b : β} {n : Nat} :
     zipWith f (replicate n a) (replicate n b) = replicate n (f a b) := by
@@ -238,113 +255,6 @@ theorem zipWith_eq_append_iff {f : α → β → γ} {l₁ : List α} {l₂ : Li
   | zero => rfl
   | succ n ih => simp [replicate_succ, ih]
 
-/-! ### zip -/
-
-theorem zip_eq_zipWith : ∀ (l₁ : List α) (l₂ : List β), zip l₁ l₂ = zipWith Prod.mk l₁ l₂
-  | [], _ => rfl
-  | _, [] => rfl
-  | a :: l₁, b :: l₂ => by simp [zip_cons_cons, zip_eq_zipWith l₁ l₂]
-
-theorem zip_map (f : α → γ) (g : β → δ) :
-    ∀ (l₁ : List α) (l₂ : List β), zip (l₁.map f) (l₂.map g) = (zip l₁ l₂).map (Prod.map f g)
-  | [], l₂ => rfl
-  | l₁, [] => by simp only [map, zip_nil_right]
-  | a :: l₁, b :: l₂ => by
-    simp only [map, zip_cons_cons, zip_map, Prod.map]; constructor
-
-theorem zip_map_left (f : α → γ) (l₁ : List α) (l₂ : List β) :
-    zip (l₁.map f) l₂ = (zip l₁ l₂).map (Prod.map f id) := by rw [← zip_map, map_id]
-
-theorem zip_map_right (f : β → γ) (l₁ : List α) (l₂ : List β) :
-    zip l₁ (l₂.map f) = (zip l₁ l₂).map (Prod.map id f) := by rw [← zip_map, map_id]
-
-@[simp] theorem tail_zip (l₁ : List α) (l₂ : List β) :
-    (zip l₁ l₂).tail = zip l₁.tail l₂.tail := by
-  cases l₁ <;> cases l₂ <;> simp
-
-theorem zip_append :
-    ∀ {l₁ r₁ : List α} {l₂ r₂ : List β} (_h : length l₁ = length l₂),
-      zip (l₁ ++ r₁) (l₂ ++ r₂) = zip l₁ l₂ ++ zip r₁ r₂
-  | [], r₁, l₂, r₂, h => by simp only [eq_nil_of_length_eq_zero h.symm]; rfl
-  | l₁, r₁, [], r₂, h => by simp only [eq_nil_of_length_eq_zero h]; rfl
-  | a :: l₁, r₁, b :: l₂, r₂, h => by
-    simp only [cons_append, zip_cons_cons, zip_append (Nat.succ.inj h)]
-
-theorem zip_map' (f : α → β) (g : α → γ) :
-    ∀ l : List α, zip (l.map f) (l.map g) = l.map fun a => (f a, g a)
-  | [] => rfl
-  | a :: l => by simp only [map, zip_cons_cons, zip_map']
-
-theorem of_mem_zip {a b} : ∀ {l₁ : List α} {l₂ : List β}, (a, b) ∈ zip l₁ l₂ → a ∈ l₁ ∧ b ∈ l₂
-  | _ :: l₁, _ :: l₂, h => by
-    cases h
-    case head => simp
-    case tail h =>
-    · have := of_mem_zip h
-      exact ⟨Mem.tail _ this.1, Mem.tail _ this.2⟩
-
-@[deprecated of_mem_zip (since := "2024-07-28")] abbrev mem_zip := @of_mem_zip
-
-theorem map_fst_zip :
-    ∀ (l₁ : List α) (l₂ : List β), l₁.length ≤ l₂.length → map Prod.fst (zip l₁ l₂) = l₁
-  | [], bs, _ => rfl
-  | _ :: as, _ :: bs, h => by
-    simp [Nat.succ_le_succ_iff] at h
-    show _ :: map Prod.fst (zip as bs) = _ :: as
-    rw [map_fst_zip as bs h]
-  | a :: as, [], h => by simp at h
-
-theorem map_snd_zip :
-    ∀ (l₁ : List α) (l₂ : List β), l₂.length ≤ l₁.length → map Prod.snd (zip l₁ l₂) = l₂
-  | _, [], _ => by
-    rw [zip_nil_right]
-    rfl
-  | [], b :: bs, h => by simp at h
-  | a :: as, b :: bs, h => by
-    simp [Nat.succ_le_succ_iff] at h
-    show _ :: map Prod.snd (zip as bs) = _ :: bs
-    rw [map_snd_zip as bs h]
-
-theorem map_prod_left_eq_zip {l : List α} (f : α → β) :
-    (l.map fun x => (x, f x)) = l.zip (l.map f) := by
-  rw [← zip_map']
-  congr
-  simp
-
-theorem map_prod_right_eq_zip {l : List α} (f : α → β) :
-    (l.map fun x => (f x, x)) = (l.map f).zip l := by
-  rw [← zip_map']
-  congr
-  simp
-
-@[simp] theorem zip_eq_nil_iff {l₁ : List α} {l₂ : List β} :
-    zip l₁ l₂ = [] ↔ l₁ = [] ∨ l₂ = [] := by
-  simp [zip_eq_zipWith]
-
-theorem zip_eq_cons_iff {l₁ : List α} {l₂ : List β} :
-    zip l₁ l₂ = (a, b) :: l ↔
-      ∃ l₁' l₂', l₁ = a :: l₁' ∧ l₂ = b :: l₂' ∧ l = zip l₁' l₂' := by
-  simp only [zip_eq_zipWith, zipWith_eq_cons_iff]
-  constructor
-  · rintro ⟨a, l₁, b, l₂, rfl, rfl, h, rfl, rfl⟩
-    simp only [Prod.mk.injEq] at h
-    obtain ⟨rfl, rfl⟩ := h
-    simp
-  · rintro ⟨l₁', l₂', rfl, rfl, rfl⟩
-    refine ⟨a, l₁', b, l₂', by simp⟩
-
-theorem zip_eq_append_iff {l₁ : List α} {l₂ : List β} :
-    zip l₁ l₂ = l₁' ++ l₂' ↔
-      ∃ w x y z, w.length = y.length ∧ l₁ = w ++ x ∧ l₂ = y ++ z ∧ l₁' = zip w y ∧ l₂' = zip x z := by
-  simp [zip_eq_zipWith, zipWith_eq_append_iff]
-
-/-- See also `List.zip_replicate` in `Init.Data.List.TakeDrop` for a generalization with different lengths. -/
-@[simp] theorem zip_replicate' {a : α} {b : β} {n : Nat} :
-    zip (replicate n a) (replicate n b) = replicate n (a, b) := by
-  induction n with
-  | zero => rfl
-  | succ n ih => simp [replicate_succ, ih]
-
 /-! ### zipWithAll -/
 
 theorem getElem?_zipWithAll {f : Option α → Option β → γ} {i : Nat} :
@@ -374,16 +284,12 @@ theorem head?_zipWithAll {f : Option α → Option β → γ} :
       | none, none => .none | a?, b? => some (f a? b?) := by
   simp [head?_eq_getElem?, getElem?_zipWithAll]
 
-@[simp] theorem head_zipWithAll {f : Option α → Option β → γ} (h) :
+theorem head_zipWithAll {f : Option α → Option β → γ} (h) :
     (zipWithAll f as bs).head h = f as.head? bs.head? := by
   apply Option.some.inj
   rw [← head?_eq_head, head?_zipWithAll]
   split <;> simp_all
 
-@[simp] theorem tail_zipWithAll {f : Option α → Option β → γ} :
-    (zipWithAll f as bs).tail = zipWithAll f as.tail bs.tail := by
-  cases as <;> cases bs <;> simp
-
 theorem zipWithAll_map {μ} (f : Option γ → Option δ → μ) (g : α → γ) (h : β → δ) (l₁ : List α) (l₂ : List β) :
     zipWithAll f (l₁.map g) (l₂.map h) = zipWithAll (fun a b => f (g <$> a) (h <$> b)) l₁ l₂ := by
   induction l₁ generalizing l₂ <;> cases l₂ <;> simp_all
@@ -452,12 +358,6 @@ theorem zip_of_prod {l : List α} {l' : List β} {lp : List (α × β)} (hl : lp
     (hr : lp.map Prod.snd = l') : lp = l.zip l' := by
   rw [← hl, ← hr, ← zip_unzip lp, ← unzip_fst, ← unzip_snd, zip_unzip, zip_unzip]
 
-theorem tail_zip_fst {l : List (α × β)} : l.unzip.1.tail = l.tail.unzip.1 := by
-  simp
-
-theorem tail_zip_snd {l : List (α × β)} : l.unzip.2.tail = l.tail.unzip.2 := by
-  simp
-
 @[simp] theorem unzip_replicate {n : Nat} {a : α} {b : β} :
     unzip (replicate n (a, b)) = (replicate n a, replicate n b) := by
   ext1 <;> simp

src/Init/Data/Nat/Basic.lean

@@ -5,8 +5,6 @@ Authors: Floris van Doorn, Leonardo de Moura
 -/
 prelude
 import Init.SimpLemmas
-import Init.Data.NeZero
-
 set_option linter.missingDocs true -- keep it documented
 universe u
 
@@ -358,8 +356,6 @@ theorem eq_zero_or_pos : ∀ (n : Nat), n = 0 ∨ n > 0
 
 protected theorem pos_of_ne_zero {n : Nat} : n ≠ 0 → 0 < n := (eq_zero_or_pos n).resolve_left
 
-theorem pos_of_neZero (n : Nat) [NeZero n] : 0 < n := Nat.pos_of_ne_zero (NeZero.ne _)
-
 theorem lt.base (n : Nat) : n < succ n := Nat.le_refl (succ n)
 
 theorem lt_succ_self (n : Nat) : n < succ n := lt.base n
@@ -514,10 +510,6 @@ protected theorem add_lt_add_left {n m : Nat} (h : n < m) (k : Nat) : k + n < k
 protected theorem add_lt_add_right {n m : Nat} (h : n < m) (k : Nat) : n + k < m + k :=
   Nat.add_comm k m ▸ Nat.add_comm k n ▸ Nat.add_lt_add_left h k
 
-protected theorem lt_add_of_pos_left (h : 0 < k) : n < k + n := by
-  rw [Nat.add_comm]
-  exact Nat.add_lt_add_left h n
-
 protected theorem lt_add_of_pos_right (h : 0 < k) : n < n + k :=
   Nat.add_lt_add_left h n
 
@@ -722,8 +714,6 @@ protected theorem zero_ne_one : 0 ≠ (1 : Nat) :=
 
 theorem succ_ne_zero (n : Nat) : succ n ≠ 0 := by simp
 
-instance instNeZeroSucc {n : Nat} : NeZero (n + 1) := ⟨succ_ne_zero n⟩
-
 /-! # mul + order -/
 
 theorem mul_le_mul_left {n m : Nat} (k : Nat) (h : n ≤ m) : k * n ≤ k * m :=
@@ -794,9 +784,6 @@ theorem pos_pow_of_pos {n : Nat} (m : Nat) (h : 0 < n) : 0 < n^m :=
   | zero => cases h
   | succ n => simp [Nat.pow_succ]
 
-instance {n m : Nat} [NeZero n] : NeZero (n^m) :=
-  ⟨Nat.ne_zero_iff_zero_lt.mpr (Nat.pos_pow_of_pos m (pos_of_neZero _))⟩
-
 /-! # min/max -/
 
 /--

src/Init/Data/Nat/Bitwise/Lemmas.lean

@@ -226,18 +226,18 @@ private theorem succ_mod_two : succ x % 2 = 1 - x % 2 := by
     simp [Nat.mod_eq (x+2) 2, p, hyp]
     cases Nat.mod_two_eq_zero_or_one x with | _ p => simp [p]
 
-private theorem testBit_succ_zero : testBit (x + 1) 0 = !(testBit x 0) := by
+private theorem testBit_succ_zero : testBit (x + 1) 0 = not (testBit x 0) := by
   simp [testBit_to_div_mod, succ_mod_two]
   cases Nat.mod_two_eq_zero_or_one x with | _ p =>
     simp [p]
 
-theorem testBit_two_pow_add_eq (x i : Nat) : testBit (2^i + x) i = !(testBit x i) := by
+theorem testBit_two_pow_add_eq (x i : Nat) : testBit (2^i + x) i = not (testBit x i) := by
   simp [testBit_to_div_mod, add_div_left, Nat.two_pow_pos, succ_mod_two]
   cases mod_two_eq_zero_or_one (x / 2 ^ i) with
   | _ p => simp [p]
 
 theorem testBit_mul_two_pow_add_eq (a b i : Nat) :
-    testBit (2^i*a + b) i = (a%2 = 1 ^^ testBit b i) := by
+    testBit (2^i*a + b) i = Bool.xor (a%2 = 1) (testBit b i) := by
   match a with
   | 0 => simp
   | a+1 =>
@@ -476,20 +476,16 @@ theorem and_lt_two_pow (x : Nat) {y n : Nat} (right : y < 2^n) : (x &&& y) < 2^n
           exact pow_le_pow_of_le_right Nat.zero_lt_two i_ge_n
   simp [testBit_and, yf]
 
-@[simp] theorem and_pow_two_sub_one_eq_mod (x n : Nat) : x &&& 2^n - 1 = x % 2^n := by
+@[simp] theorem and_pow_two_is_mod (x n : Nat) : x &&& (2^n-1) = x % 2^n := by
   apply eq_of_testBit_eq
   intro i
   simp only [testBit_and, testBit_mod_two_pow]
   cases testBit x i <;> simp
 
-@[deprecated and_pow_two_sub_one_eq_mod (since := "2024-09-11")] abbrev and_pow_two_is_mod := @and_pow_two_sub_one_eq_mod
-
-theorem and_pow_two_sub_one_of_lt_two_pow {x : Nat} (lt : x < 2^n) : x &&& 2^n - 1 = x := by
-  rw [and_pow_two_sub_one_eq_mod]
+theorem and_pow_two_identity {x : Nat} (lt : x < 2^n) : x &&& 2^n-1 = x := by
+  rw [and_pow_two_is_mod]
   apply Nat.mod_eq_of_lt lt
 
-@[deprecated and_pow_two_sub_one_of_lt_two_pow (since := "2024-09-11")] abbrev and_two_pow_identity := @and_pow_two_sub_one_of_lt_two_pow
-
 @[simp] theorem and_mod_two_eq_one : (a &&& b) % 2 = 1 ↔ a % 2 = 1 ∧ b % 2 = 1 := by
   simp only [mod_two_eq_one_iff_testBit_zero]
   rw [testBit_and]
@@ -570,7 +566,7 @@ theorem or_div_two : (a ||| b) / 2 = a / 2 ||| b / 2 := by
 /-! ### xor -/
 
 @[simp] theorem testBit_xor (x y i : Nat) :
-    (x ^^^ y).testBit i = ((x.testBit i) ^^ (y.testBit i)) := by
+    (x ^^^ y).testBit i = Bool.xor (x.testBit i) (y.testBit i) := by
   simp [HXor.hXor, Xor.xor, xor, testBit_bitwise ]
 
 @[simp] theorem zero_xor (x : Nat) : 0 ^^^ x = x := by

src/Init/Data/Nat/Div.lean

@@ -134,19 +134,6 @@ theorem mod_eq_of_lt {a b : Nat} (h : a < b) : a % b = a :=
     if_neg h'
   (mod_eq a b).symm ▸ this
 
-@[simp] theorem one_mod_eq_zero_iff {n : Nat} : 1 % n = 0 ↔ n = 1 := by
-  match n with
-  | 0 => simp
-  | 1 => simp
-  | n + 2 =>
-    rw [mod_eq_of_lt (by exact Nat.lt_of_sub_eq_succ rfl)]
-    simp only [add_one_ne_zero, false_iff, ne_eq]
-    exact ne_of_beq_eq_false rfl
-
-@[simp] theorem Nat.zero_eq_one_mod_iff {n : Nat} : 0 = 1 % n ↔ n = 1 := by
-  rw [eq_comm]
-  simp
-
 theorem mod_eq_sub_mod {a b : Nat} (h : a ≥ b) : a % b = (a - b) % b :=
   match eq_zero_or_pos b with
   | Or.inl h₁ => h₁.symm ▸ (Nat.sub_zero a).symm ▸ rfl
@@ -170,13 +157,6 @@ theorem mod_lt (x : Nat) {y : Nat} : y > 0 → x % y < y := by
     rw [mod_eq_sub_mod h₁]
     exact h₂ h₃
 
-@[simp] protected theorem sub_mod_add_mod_cancel (a b : Nat) [NeZero a] : a - b % a + b % a = a := by
-  rw [Nat.sub_add_cancel]
-  cases a with
-  | zero => simp_all
-  | succ a =>
-    exact Nat.le_of_lt (mod_lt b (zero_lt_succ a))
-
 theorem mod_le (x y : Nat) : x % y ≤ x := by
   match Nat.lt_or_ge x y with
   | Or.inl h₁ => rw [mod_eq_of_lt h₁]; apply Nat.le_refl
@@ -217,6 +197,7 @@ decreasing_by apply div_rec_lemma; assumption
 theorem div_eq_sub_div (h₁ : 0 < b) (h₂ : b ≤ a) : a / b = (a - b) / b + 1 := by
  rw [div_eq a, if_pos]; constructor <;> assumption
 
+
 theorem mod_add_div (m k : Nat) : m % k + k * (m / k) = m := by
   induction m, k using mod.inductionOn with rw [div_eq, mod_eq]
   | base x y h => simp [h]

src/Init/Data/Nat/Lemmas.lean

@@ -84,6 +84,9 @@ protected theorem add_lt_add_of_lt_of_le {a b c d : Nat} (hlt : a < b) (hle : c
     a + c < b + d :=
   Nat.lt_of_le_of_lt (Nat.add_le_add_left hle _) (Nat.add_lt_add_right hlt _)
 
+protected theorem lt_add_of_pos_left : 0 < k → n < k + n := by
+  rw [Nat.add_comm]; exact Nat.lt_add_of_pos_right
+
 protected theorem pos_of_lt_add_right (h : n < n + k) : 0 < k :=
   Nat.lt_of_add_lt_add_left h
 
@@ -230,17 +233,6 @@ instance : Std.Associative (α := Nat) min := ⟨Nat.min_assoc⟩
 @[simp] protected theorem min_self_assoc' {m n : Nat} : min n (min m n) = min n m := by
   rw [Nat.min_comm m n, ← Nat.min_assoc, Nat.min_self]
 
-@[simp] theorem min_add_left {a b : Nat} : min a (b + a) = a := by
-  rw [Nat.min_def]
-  simp
-@[simp] theorem min_add_right {a b : Nat} : min a (a + b) = a := by
-  rw [Nat.min_def]
-  simp
-@[simp] theorem add_left_min {a b : Nat} : min (b + a) a = a := by
-  rw [Nat.min_comm, min_add_left]
-@[simp] theorem add_right_min {a b : Nat} : min (a + b) a = a := by
-  rw [Nat.min_comm, min_add_right]
-
 protected theorem sub_sub_eq_min : ∀ (a b : Nat), a - (a - b) = min a b
   | 0, _ => by rw [Nat.zero_sub, Nat.zero_min]
   | _, 0 => by rw [Nat.sub_zero, Nat.sub_self, Nat.min_zero]
@@ -295,17 +287,6 @@ protected theorem max_assoc : ∀ (a b c : Nat), max (max a b) c = max a (max b
   | _+1, _+1, _+1 => by simp only [Nat.succ_max_succ]; exact congrArg succ <| Nat.max_assoc ..
 instance : Std.Associative (α := Nat) max := ⟨Nat.max_assoc⟩
 
-@[simp] theorem max_add_left {a b : Nat} : max a (b + a) = b + a := by
-  rw [Nat.max_def]
-  simp
-@[simp] theorem max_add_right {a b : Nat} : max a (a + b) = a + b := by
-  rw [Nat.max_def]
-  simp
-@[simp] theorem add_left_max {a b : Nat} : max (b + a) a = b + a := by
-  rw [Nat.max_comm, max_add_left]
-@[simp] theorem add_right_max {a b : Nat} : max (a + b) a = a + b := by
-  rw [Nat.max_comm, max_add_right]
-
 protected theorem sub_add_eq_max (a b : Nat) : a - b + b = max a b := by
   match Nat.le_total a b with
   | .inl hl => rw [Nat.max_eq_right hl, Nat.sub_eq_zero_iff_le.mpr hl, Nat.zero_add]
@@ -596,15 +577,6 @@ theorem mul_mod (a b n : Nat) : a * b % n = (a % n) * (b % n) % n := by
 theorem add_mod (a b n : Nat) : (a + b) % n = ((a % n) + (b % n)) % n := by
   rw [add_mod_mod, mod_add_mod]
 
-@[simp] theorem self_sub_mod (n k : Nat) [NeZero k] : (n - k) % n = n - k := by
-  cases n with
-  | zero => simp
-  | succ n =>
-    rw [mod_eq_of_lt]
-    cases k with
-    | zero => simp_all
-    | succ k => omega
-
 /-! ### pow -/
 
 theorem pow_succ' {m n : Nat} : m ^ n.succ = m * m ^ n := by

src/Init/Data/NeZero.lean

@@ -1,38 +0,0 @@
-/-
-Copyright (c) 2021 Eric Rodriguez. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Eric Rodriguez
--/
-prelude
-import Init.Data.Zero
-
-
-/-!
-# `NeZero` typeclass
-
-We create a typeclass `NeZero n` which carries around the fact that `(n : R) ≠ 0`.
-
-## Main declarations
-
-* `NeZero`: `n ≠ 0` as a typeclass.
--/
-
-
-variable {R : Type _} [Zero R]
-
-/-- A type-class version of `n ≠ 0`.  -/
-class NeZero (n : R) : Prop where
-  /-- The proposition that `n` is not zero. -/
-  out : n ≠ 0
-
-theorem NeZero.ne (n : R) [h : NeZero n] : n ≠ 0 :=
-  h.out
-
-theorem NeZero.ne' (n : R) [h : NeZero n] : 0 ≠ n :=
-  h.out.symm
-
-theorem neZero_iff {n : R} : NeZero n ↔ n ≠ 0 :=
-  ⟨fun h ↦ h.out, NeZero.mk⟩
-
-@[simp] theorem neZero_zero_iff_false {α : Type _} [Zero α] : NeZero (0 : α) ↔ False :=
-  ⟨fun h ↦ h.ne rfl, fun h ↦ h.elim⟩

src/Init/Data/Option/Instances.lean

@@ -55,7 +55,7 @@ partial function defined on `a : α` giving an `Option β`, where `some a = x`,
 then `pbind x f h` is essentially the same as `bind x f`
 but is defined only when all `x = some a`, using the proof to apply `f`.
 -/
-@[inline]
+@[simp, inline]
 def pbind : ∀ x : Option α, (∀ a : α, a ∈ x → Option β) → Option β
   | none, _ => none
   | some a, f => f a rfl
@@ -65,7 +65,7 @@ Partial map. If `f : Π a, p a → β` is a partial function defined on `a : α`
 then `pmap f x h` is essentially the same as `map f x` but is defined only when all members of `x`
 satisfy `p`, using the proof to apply `f`.
 -/
-@[inline] def pmap {p : α → Prop} (f : ∀ a : α, p a → β) :
+@[simp, inline] def pmap {p : α → Prop} (f : ∀ a : α, p a → β) :
     ∀ x : Option α, (∀ a, a ∈ x → p a) → Option β
   | none, _ => none
   | some a, H => f a (H a rfl)

src/Init/Data/Option/Lemmas.lean

@@ -6,17 +6,12 @@ Authors: Mario Carneiro
 prelude
 import Init.Data.Option.BasicAux
 import Init.Data.Option.Instances
-import Init.Data.BEq
 import Init.Classical
 import Init.Ext
 
 namespace Option
 
-theorem mem_iff {a : α} {b : Option α} : a ∈ b ↔ b = some a := .rfl
-
-theorem mem_some {a b : α} : a ∈ some b ↔ b = a := by simp
-
-theorem mem_some_self (a : α) : a ∈ some a := mem_some.2 rfl
+theorem mem_iff {a : α} {b : Option α} : a ∈ b ↔ b = a := .rfl
 
 theorem some_ne_none (x : α) : some x ≠ none := nofun
 
@@ -79,9 +74,6 @@ theorem eq_none_iff_forall_not_mem : o = none ↔ ∀ a, a ∉ o :=
 
 theorem isSome_iff_exists : isSome x ↔ ∃ a, x = some a := by cases x <;> simp [isSome]
 
-@[simp] theorem isSome_eq_isSome : (isSome x = isSome y) ↔ (x = none ↔ y = none) := by
-  cases x <;> cases y <;> simp
-
 @[simp] theorem isNone_none : @isNone α none = true := rfl
 
 @[simp] theorem isNone_some : isNone (some a) = false := rfl
@@ -224,17 +216,8 @@ theorem mem_map_of_mem (g : α → β) (h : a ∈ x) : g a ∈ Option.map g x :=
   split <;> rfl
 
 @[simp] theorem filter_none (p : α → Bool) : none.filter p = none := rfl
-
 theorem filter_some : Option.filter p (some a) = if p a then some a else none := rfl
 
-theorem isSome_filter_of_isSome (p : α → Bool) (o : Option α) (h : (o.filter p).isSome) :
-    o.isSome := by
-  cases o <;> simp at h ⊢
-
-@[simp] theorem filter_eq_none {p : α → Bool} :
-    Option.filter p o = none ↔ o = none ∨ ∀ a, a ∈ o → ¬ p a := by
-  cases o <;> simp [filter_some]
-
 @[simp] theorem all_guard (p : α → Prop) [DecidablePred p] (a : α) :
     Option.all q (guard p a) = (!p a || q a) := by
   simp only [guard]
@@ -248,12 +231,6 @@ theorem isSome_filter_of_isSome (p : α → Bool) (o : Option α) (h : (o.filter
 theorem bind_map_comm {α β} {x : Option (Option α)} {f : α → β} :
     x.bind (Option.map f) = (x.map (Option.map f)).bind id := by cases x <;> simp
 
-theorem bind_map {f : α → β} {g : β → Option γ} {x : Option α} :
-    (x.map f).bind g = x.bind (g ∘ f) := by cases x <;> simp
-
-@[simp] theorem map_bind {f : α → Option β} {g : β → γ} {x : Option α} :
-    (x.bind f).map g = x.bind (Option.map g ∘ f) := by cases x <;> simp
-
 theorem join_map_eq_map_join {f : α → β} {x : Option (Option α)} :
     (x.map (Option.map f)).join = x.join.map f := by cases x <;> simp
 
@@ -284,27 +261,6 @@ theorem map_orElse {x y : Option α} : (x <|> y).map f = (x.map f <|> y.map f) :
 @[simp] theorem guard_pos [DecidablePred p] (h : p a) : Option.guard p a = some a := by
   simp [Option.guard, h]
 
-@[congr] theorem guard_congr {f g : α → Prop} [DecidablePred f] [DecidablePred g]
-    (h : ∀ a, f a ↔ g a):
-    guard f = guard g := by
-  funext a
-  simp [guard, h]
-
-@[simp] theorem guard_false {α} :
-    guard (fun (_ : α) => False) = fun _ => none := by
-  funext a
-  simp [guard]
-
-@[simp] theorem guard_true {α} :
-    guard (fun (_ : α) => True) = some := by
-  funext a
-  simp [guard]
-
-theorem guard_comp {p : α → Prop} [DecidablePred p] {f : β → α} :
-    guard p ∘ f = Option.map f ∘ guard (p ∘ f) := by
-  ext1 b
-  simp [guard]
-
 theorem liftOrGet_eq_or_eq {f : α → α → α} (h : ∀ a b, f a b = a ∨ f a b = b) :
     ∀ o₁ o₂, liftOrGet f o₁ o₂ = o₁ ∨ liftOrGet f o₁ o₂ = o₂
   | none, none => .inl rfl
@@ -401,101 +357,8 @@ theorem or_of_isNone {o o' : Option α} (h : o.isNone) : o.or o' = o' := by
   match o, h with
   | none, _ => simp
 
-/-! ### beq -/
-
-section beq
-
-variable [BEq α]
-
-@[simp] theorem none_beq_none : ((none : Option α) == none) = true := rfl
-@[simp] theorem none_beq_some (a : α) : ((none : Option α) == some a) = false := rfl
-@[simp] theorem some_beq_none (a : α) : ((some a : Option α) == none) = false := rfl
-@[simp] theorem some_beq_some {a b : α} : (some a == some b) = (a == b) := rfl
-
-@[simp] theorem reflBEq_iff : ReflBEq (Option α) ↔ ReflBEq α := by
-  constructor
-  · intro h
-    constructor
-    intro a
-    suffices (some a == some a) = true by
-      simpa only [some_beq_some]
-    simp
-  · intro h
-    constructor
-    · rintro (_ | a) <;> simp
-
-@[simp] theorem lawfulBEq_iff : LawfulBEq (Option α) ↔ LawfulBEq α := by
-  constructor
-  · intro h
-    constructor
-    · intro a b h
-      apply Option.some.inj
-      apply eq_of_beq
-      simpa
-    · intro a
-      suffices (some a == some a) = true by
-        simpa only [some_beq_some]
-      simp
-  · intro h
-    constructor
-    · intro a b h
-      simpa using h
-    · intro a
-      simp
-
-end beq
-
-/-! ### ite -/
 section ite
 
-@[simp] theorem dite_none_left_eq_some {p : Prop} [Decidable p] {b : ¬p → Option β} :
-    (if h : p then none else b h) = some a ↔ ∃ h, b h = some a := by
-  split <;> simp_all
-
-@[simp] theorem dite_none_right_eq_some {p : Prop} [Decidable p] {b : p → Option α} :
-    (if h : p then b h else none) = some a ↔ ∃ h, b h = some a := by
-  split <;> simp_all
-
-@[simp] theorem some_eq_dite_none_left {p : Prop} [Decidable p] {b : ¬p → Option β} :
-    some a = (if h : p then none else b h) ↔ ∃ h, some a = b h := by
-  split <;> simp_all
-
-@[simp] theorem some_eq_dite_none_right {p : Prop} [Decidable p] {b : p → Option α} :
-    some a = (if h : p then b h else none) ↔ ∃ h, some a = b h := by
-  split <;> simp_all
-
-@[simp] theorem ite_none_left_eq_some {p : Prop} [Decidable p] {b : Option β} :
-    (if p then none else b) = some a ↔ ¬ p ∧ b = some a := by
-  split <;> simp_all
-
-@[simp] theorem ite_none_right_eq_some {p : Prop} [Decidable p] {b : Option α} :
-    (if p then b else none) = some a ↔ p ∧ b = some a := by
-  split <;> simp_all
-
-@[simp] theorem some_eq_ite_none_left {p : Prop} [Decidable p] {b : Option β} :
-    some a = (if p then none else b) ↔ ¬ p ∧ some a = b := by
-  split <;> simp_all
-
-@[simp] theorem some_eq_ite_none_right {p : Prop} [Decidable p] {b : Option α} :
-    some a = (if p then b else none) ↔ p ∧ some a = b := by
-  split <;> simp_all
-
-theorem mem_dite_none_left {x : α} [Decidable p] {l : ¬ p → Option α} :
-    (x ∈ if h : p then none else l h) ↔ ∃ h : ¬ p, x ∈ l h := by
-  simp
-
-theorem mem_dite_none_right {x : α} [Decidable p] {l : p → Option α} :
-    (x ∈ if h : p then l h else none) ↔ ∃ h : p, x ∈ l h := by
-  simp
-
-theorem mem_ite_none_left {x : α} [Decidable p] {l : Option α} :
-    (x ∈ if p then none else l) ↔ ¬ p ∧ x ∈ l := by
-  simp
-
-theorem mem_ite_none_right {x : α} [Decidable p] {l : Option α} :
-    (x ∈ if p then l else none) ↔ p ∧ x ∈ l := by
-  simp
-
 @[simp] theorem isSome_dite {p : Prop} [Decidable p] {b : p → β} :
     (if h : p then some (b h) else none).isSome = true ↔ p := by
   split <;> simpa
@@ -532,82 +395,4 @@ theorem mem_ite_none_right {x : α} [Decidable p] {l : Option α} :
 
 end ite
 
-/-! ### pbind -/
-
-@[simp] theorem pbind_none : pbind none f = none := rfl
-@[simp] theorem pbind_some : pbind (some a) f = f a (mem_some_self a) := rfl
-
-@[simp] theorem map_pbind {o : Option α} {f : (a : α) → a ∈ o → Option β} {g : β → γ} :
-    (o.pbind f).map g = o.pbind (fun a h => (f a h).map g) := by
-  cases o <;> simp
-
-@[congr] theorem pbind_congr {o o' : Option α} (ho : o = o')
-    {f : (a : α) → a ∈ o → Option β} {g : (a : α) → a ∈ o' → Option β}
-    (hf : ∀ a h, f a (ho ▸ h) = g a h) : o.pbind f = o'.pbind g := by
-  subst ho
-  exact (funext fun a => funext fun h => hf a h) ▸ Eq.refl (o.pbind f)
-
-theorem pbind_eq_none_iff {o : Option α} {f : (a : α) → a ∈ o → Option β} :
-    o.pbind f = none ↔ o = none ∨ ∃ a h, f a h = none := by
-  cases o with
-  | none => simp
-  | some a =>
-    simp only [pbind_some, reduceCtorEq, mem_def, some.injEq, false_or]
-    constructor
-    · intro h
-      exact ⟨a, rfl, h⟩
-    · rintro ⟨a, rfl, h⟩
-      exact h
-
-theorem pbind_isSome {o : Option α} {f : (a : α) → a ∈ o → Option β} :
-    (o.pbind f).isSome = ∃ a h, (f a h).isSome := by
-  cases o with
-  | none => simp
-  | some a =>
-    simp only [pbind_some, mem_def, some.injEq, eq_iff_iff]
-    constructor
-    · intro h
-      exact ⟨a, rfl, h⟩
-    · rintro ⟨a, rfl, h⟩
-      exact h
-
-theorem pbind_eq_some_iff {o : Option α} {f : (a : α) → a ∈ o → Option β} {b : β} :
-    o.pbind f = some b ↔ ∃ a h, f a h = some b := by
-  cases o with
-  | none => simp
-  | some a =>
-    simp only [pbind_some, mem_def, some.injEq]
-    constructor
-    · intro h
-      exact ⟨a, rfl, h⟩
-    · rintro ⟨a, rfl, h⟩
-      exact h
-
-/-! ### pmap -/
-
-@[simp] theorem pmap_none {p : α → Prop} {f : ∀ (a : α), p a → β} {h} :
-    pmap f none h = none := rfl
-
-@[simp] theorem pmap_some {p : α → Prop} {f : ∀ (a : α), p a → β} {h}:
-    pmap f (some a) h = f a (h a (mem_some_self a)) := rfl
-
-@[simp] theorem pmap_eq_none_iff {p : α → Prop} {f : ∀ (a : α), p a → β} {h} :
-    pmap f o h = none ↔ o = none := by
-  cases o <;> simp
-
-@[simp] theorem pmap_isSome {p : α → Prop} {f : ∀ (a : α), p a → β} {o : Option α} {h} :
-    (pmap f o h).isSome = o.isSome := by
-  cases o <;> simp
-
-@[simp] theorem pmap_eq_some_iff {p : α → Prop} {f : ∀ (a : α), p a → β} {o : Option α} {h} :
-    pmap f o h = some b ↔ ∃ (a : α) (h : p a), o = some a ∧ b = f a h := by
-  cases o with
-  | none => simp
-  | some a =>
-    simp only [pmap, eq_comm, some.injEq, exists_and_left, exists_eq_left']
-    constructor
-    · exact fun w => ⟨h a rfl, w⟩
-    · rintro ⟨h, rfl⟩
-      rfl
-
 end Option

src/Init/Data/UInt/Basic.lean

@@ -290,17 +290,11 @@ instance (a b : UInt64) : Decidable (a ≤ b) := UInt64.decLe a b
 instance : Max UInt64 := maxOfLe
 instance : Min UInt64 := minOfLe
 
--- This instance would interfere with the global instance `NeZero (n + 1)`,
--- so we only enable it locally.
-@[local instance]
-private def instNeZeroUSizeSize : NeZero USize.size := ⟨add_one_ne_zero _⟩
-
-@[deprecated (since := "2024-09-16")]
 theorem usize_size_gt_zero : USize.size > 0 :=
   Nat.zero_lt_succ ..
 
 @[extern "lean_usize_of_nat"]
-def USize.ofNat (n : @& Nat) : USize := ⟨Fin.ofNat'  _ n⟩
+def USize.ofNat (n : @& Nat) : USize := ⟨Fin.ofNat' n usize_size_gt_zero⟩
 abbrev Nat.toUSize := USize.ofNat
 @[extern "lean_usize_to_nat"]
 def USize.toNat (n : USize) : Nat := n.val.val

src/Init/Data/Zero.lean

@@ -1,17 +0,0 @@
-/-
-Copyright (c) 2021 Gabriel Ebner. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Gabriel Ebner, Mario Carneiro
--/
-prelude
-import Init.Core
-
-/-!
-Instances converting between `Zero α` and `OfNat α (nat_lit 0)`.
--/
-
-instance (priority := 300) Zero.toOfNat0 {α} [Zero α] : OfNat α (nat_lit 0) where
-  ofNat := ‹Zero α›.1
-
-instance (priority := 200) Zero.ofOfNat0 {α} [OfNat α (nat_lit 0)] : Zero α where
-  zero := 0

src/Init/Meta.lean

@@ -7,7 +7,7 @@ Additional goodies for writing macros
 -/
 prelude
 import Init.MetaTypes
-import Init.Data.Array.GetLit
+import Init.Data.Array.Basic
 import Init.Data.Option.BasicAux
 
 namespace Lean
@@ -119,55 +119,28 @@ def isInaccessibleUserName : Name → Bool
   | Name.num p _   => isInaccessibleUserName p
   | _              => false
 
-/--
-Creates a round-trippable string name component if possible, otherwise returns `none`.
-Names that are valid identifiers are not escaped, and otherwise, if they do not contain `»`, they are escaped.
-- If `force` is `true`, then even valid identifiers are escaped.
--/
-def escapePart (s : String) (force : Bool := false) : Option String :=
-  if s.length > 0 && !force && isIdFirst (s.get 0) && (s.toSubstring.drop 1).all isIdRest then s
+def escapePart (s : String) : Option String :=
+  if s.length > 0 && isIdFirst (s.get 0) && (s.toSubstring.drop 1).all isIdRest then s
   else if s.any isIdEndEscape then none
   else some <| idBeginEscape.toString ++ s ++ idEndEscape.toString
 
-variable (sep : String) (escape : Bool) in
-/--
-Uses the separator `sep` (usually `"."`) to combine the components of the `Name` into a string.
-See the documentation for `Name.toString` for an explanation of `escape` and `isToken`.
--/
-def toStringWithSep (n : Name) (isToken : String → Bool := fun _ => false) : String :=
-  match n with
+-- NOTE: does not roundtrip even with `escape = true` if name is anonymous or contains numeric part or `idEndEscape`
+variable (sep : String) (escape : Bool)
+def toStringWithSep : Name → String
   | anonymous       => "[anonymous]"
-  | str anonymous s => maybeEscape s (isToken s)
+  | str anonymous s => maybeEscape s
   | num anonymous v => toString v
-  | str n s         =>
-    -- Escape the last component if the identifier would otherwise be a token
-    let r := toStringWithSep n isToken
-    let r' := r ++ sep ++ maybeEscape s false
-    if escape && isToken r' then r ++ sep ++ maybeEscape s true else r'
-  | num n v         => toStringWithSep n (isToken := fun _ => false) ++ sep ++ Nat.repr v
+  | str n s         => toStringWithSep n ++ sep ++ maybeEscape s
+  | num n v         => toStringWithSep n ++ sep ++ Nat.repr v
 where
-  maybeEscape s force := if escape then escapePart s force |>.getD s else s
+  maybeEscape s := if escape then escapePart s |>.getD s else s
 
-/--
-Converts a name to a string.
-
-- If `escape` is `true`, then escapes name components using `«` and `»` to ensure that
-  those names that can appear in source files round trip.
-  Names with number components, anonymous names, and names containing `»` might not round trip.
-  Furthermore, "pseudo-syntax" produced by the delaborator, such as `_`, `#0` or `?u`, is not escaped.
-- The optional `isToken` function is used when `escape` is `true` to determine whether more
-  escaping is necessary to avoid parser tokens.
-  The insertion algorithm works so long as parser tokens do not themselves contain `«` or `»`.
--/
-protected def toString (n : Name) (escape := true) (isToken : String → Bool := fun _ => false) : String :=
+protected def toString (n : Name) (escape := true) : String :=
   -- never escape "prettified" inaccessible names or macro scopes or pseudo-syntax introduced by the delaborator
-  toStringWithSep "." (escape && !n.isInaccessibleUserName && !n.hasMacroScopes && !maybePseudoSyntax) n isToken
+  toStringWithSep "." (escape && !n.isInaccessibleUserName && !n.hasMacroScopes && !maybePseudoSyntax) n
 where
   maybePseudoSyntax :=
-    if n == `_ then
-      -- output hole as is
-      true
-    else if let .str _ s := n.getRoot then
+    if let .str _ s := n.getRoot then
       -- could be pseudo-syntax for loose bvar or universe mvar, output as is
       "#".isPrefixOf s || "?".isPrefixOf s
     else

src/Init/Prelude.lean

@@ -1014,7 +1014,7 @@ with `Or : Prop → Prop → Prop`, which is the propositional connective).
 It is `@[macro_inline]` because it has C-like short-circuiting behavior:
 if `x` is true then `y` is not evaluated.
 -/
-@[macro_inline] def Bool.or (x y : Bool) : Bool :=
+@[macro_inline] def or (x y : Bool) : Bool :=
   match x with
   | true  => true
   | false => y
@@ -1025,7 +1025,7 @@ with `And : Prop → Prop → Prop`, which is the propositional connective).
 It is `@[macro_inline]` because it has C-like short-circuiting behavior:
 if `x` is false then `y` is not evaluated.
 -/
-@[macro_inline] def Bool.and (x y : Bool) : Bool :=
+@[macro_inline] def and (x y : Bool) : Bool :=
   match x with
   | false => false
   | true  => y
@@ -1034,12 +1034,10 @@ if `x` is false then `y` is not evaluated.
 `not x`, or `!x`, is the boolean "not" operation (not to be confused
 with `Not : Prop → Prop`, which is the propositional connective).
 -/
-@[inline] def Bool.not : Bool → Bool
+@[inline] def not : Bool → Bool
   | true  => false
   | false => true
 
-export Bool (or and not)
-
 /--
 The type of natural numbers, starting at zero. It is defined as an
 inductive type freely generated by "zero is a natural number" and
@@ -1306,11 +1304,6 @@ class HShiftRight (α : Type u) (β : Type v) (γ : outParam (Type w)) where
     this is equivalent to `a / 2 ^ b`. -/
   hShiftRight : α → β → γ
 
-/-- A type with a zero element. -/
-class Zero (α : Type u) where
-  /-- The zero element of the type. -/
-  zero : α
-
 /-- The homogeneous version of `HAdd`: `a + b : α` where `a b : α`. -/
 class Add (α : Type u) where
   /-- `a + b` computes the sum of `a` and `b`. See `HAdd`. -/
@@ -2575,17 +2568,17 @@ structure Array (α : Type u) where
   /--
   Converts a `Array α` into an `List α`.
 
-  At runtime, this projection is implemented by `Array.toListImpl` and is O(n) in the length of the
+  At runtime, this projection is implemented by `Array.toList` and is O(n) in the length of the
   array. -/
-  toList : List α
+  data : List α
 
-attribute [extern "lean_array_to_list"] Array.toList
+attribute [extern "lean_array_data"] Array.data
 attribute [extern "lean_array_mk"] Array.mk
 
 /-- Construct a new empty array with initial capacity `c`. -/
 @[extern "lean_mk_empty_array_with_capacity"]
 def Array.mkEmpty {α : Type u} (c : @& Nat) : Array α where
-  toList := List.nil
+  data := List.nil
 
 /-- Construct a new empty array. -/
 def Array.empty {α : Type u} : Array α := mkEmpty 0
@@ -2593,12 +2586,12 @@ def Array.empty {α : Type u} : Array α := mkEmpty 0
 /-- Get the size of an array. This is a cached value, so it is O(1) to access. -/
 @[reducible, extern "lean_array_get_size"]
 def Array.size {α : Type u} (a : @& Array α) : Nat :=
- a.toList.length
+ a.data.length
 
 /-- Access an element from an array without bounds checks, using a `Fin` index. -/
 @[extern "lean_array_fget"]
 def Array.get {α : Type u} (a : @& Array α) (i : @& Fin a.size) : α :=
-  a.toList.get i
+  a.data.get i
 
 /-- Access an element from an array, or return `v₀` if the index is out of bounds. -/
 @[inline] abbrev Array.getD (a : Array α) (i : Nat) (v₀ : α) : α :=
@@ -2615,7 +2608,7 @@ Push an element onto the end of an array. This is amortized O(1) because
 -/
 @[extern "lean_array_push"]
 def Array.push {α : Type u} (a : Array α) (v : α) : Array α where
-  toList := List.concat a.toList v
+  data := List.concat a.data v
 
 /-- Create array `#[]` -/
 def Array.mkArray0 {α : Type u} : Array α :=
@@ -2661,7 +2654,7 @@ count of 1 when called.
 -/
 @[extern "lean_array_fset"]
 def Array.set (a : Array α) (i : @& Fin a.size) (v : α) : Array α where
-  toList := a.toList.set i.val v
+  data := a.data.set i.val v
 
 /--
 Set an element in an array, or do nothing if the index is out of bounds.

src/Init/PropLemmas.lean

@@ -186,21 +186,6 @@ theorem ite_true_same {p q : Prop} [Decidable p] : (if p then p else q) ↔ (¬p
 @[deprecated ite_else_self (since := "2024-08-28")]
 theorem ite_false_same {p q : Prop} [Decidable p] : (if p then q else p) ↔ (p ∧ q) := ite_else_self
 
-/-- If two if-then-else statements only differ by the `Decidable` instances, they are equal. -/
--- This is useful for ensuring confluence, but rarely otherwise.
-@[simp] theorem ite_eq_ite (p : Prop) {h h' : Decidable p} (x y : α) :
-    (@ite _ p h x y = @ite _ p h' x y) ↔ True := by
-  simp
-  congr
-
-/-- If two if-then-else statements only differ by the `Decidable` instances, they are equal. -/
--- This is useful for ensuring confluence, but rarely otherwise.
-@[simp] theorem ite_iff_ite (p : Prop) {h h' : Decidable p} (x y : Prop) :
-    (@ite _ p h x y ↔ @ite _ p h' x y) ↔ True := by
-  rw [iff_true]
-  suffices @ite _ p h x y = @ite _ p h' x y by simp [this]
-  congr
-
 /-! ## exists and forall -/
 
 section quantifiers
@@ -556,9 +541,6 @@ This is the same as `decidable_of_iff` but the iff is flipped. -/
 instance Decidable.predToBool (p : α → Prop) [DecidablePred p] :
     CoeDep (α → Prop) p (α → Bool) := ⟨fun b => decide <| p b⟩
 
-instance [DecidablePred p] : DecidablePred (p ∘ f) :=
-  fun x => inferInstanceAs (Decidable (p (f x)))
-
 /-- Prove that `a` is decidable by constructing a boolean `b` and a proof that `b ↔ a`.
 (This is sometimes taken as an alternate definition of decidability.) -/
 def decidable_of_bool : ∀ (b : Bool), (b ↔ a) → Decidable a

src/Init/SimpLemmas.lean

@@ -231,21 +231,8 @@ instance : Std.Associative (· || ·) := ⟨Bool.or_assoc⟩
 @[simp] theorem Bool.not_false : (!false) = true := by decide
 @[simp] theorem beq_true  (b : Bool) : (b == true)  =  b := by cases b <;> rfl
 @[simp] theorem beq_false (b : Bool) : (b == false) = !b := by cases b <;> rfl
-
-
-/--
-We move `!` from the left hand side of an equality to the right hand side.
-This helps confluence, and also helps combining pairs of `!`s.
--/
-@[simp] theorem Bool.not_eq_eq_eq_not {a b : Bool} : ((!a) = b) ↔ (a = !b) := by
-  cases a <;> cases b <;> simp
-
-@[simp] theorem Bool.not_eq_not {a b : Bool} : ¬a = !b ↔ a = b := by
-  cases a <;> cases b <;> simp
-theorem Bool.not_not_eq {a b : Bool} : ¬(!a) = b ↔ a = b := by simp
-
-theorem Bool.not_eq_true'  (b : Bool) : ((!b) = true) = (b = false) := by simp
-theorem Bool.not_eq_false' (b : Bool) : ((!b) = false) = (b = true) := by simp
+@[simp] theorem Bool.not_eq_true'  (b : Bool) : ((!b) = true) = (b = false) := by cases b <;> simp
+@[simp] theorem Bool.not_eq_false' (b : Bool) : ((!b) = false) = (b = true) := by cases b <;> simp
 
 @[simp] theorem Bool.not_eq_true (b : Bool) : (¬(b = true)) = (b = false) := by cases b <;> decide
 @[simp] theorem Bool.not_eq_false (b : Bool) : (¬(b = false)) = (b = true) := by cases b <;> decide

src/Init/Tactics.lean

@@ -676,16 +676,12 @@ compiled by Lean.
 syntax (name := delta) "delta" (ppSpace colGt ident)+ (location)? : tactic
 
 /--
-* `unfold id` unfolds all occurrences of definition `id` in the target.
+* `unfold id` unfolds definition `id`.
 * `unfold id1 id2 ...` is equivalent to `unfold id1; unfold id2; ...`.
-* `unfold id at h` unfolds at the hypothesis `h`.
 
-Definitions can be either global or local definitions.
-
-For non-recursive global definitions, this tactic is identical to `delta`.
-For recursive global definitions, it uses the "unfolding lemma" `id.eq_def`,
-which is generated for each recursive definition, to unfold according to the recursive definition given by the user.
-Only one level of unfolding is performed, in contrast to `simp only [id]`, which unfolds definition `id` recursively.
+For non-recursive definitions, this tactic is identical to `delta`. For recursive definitions,
+it uses the "unfolding lemma" `id.eq_def`, which is generated for each recursive definition,
+to unfold according to the recursive definition given by the user.
 -/
 syntax (name := unfold) "unfold" (ppSpace colGt ident)+ (location)? : tactic
 
@@ -773,9 +769,8 @@ macro_rules
 macro "refine_lift' " e:term : tactic => `(tactic| focus (refine' no_implicit_lambda% $e; rotate_right))
 /-- Similar to `have`, but using `refine'` -/
 macro "have' " d:haveDecl : tactic => `(tactic| refine_lift' have $d:haveDecl; ?_)
-set_option linter.missingDocs false in -- OK, because `tactic_alt` causes inheritance of docs
+/-- Similar to `have`, but using `refine'` -/
 macro (priority := high) "have'" x:ident " := " p:term : tactic => `(tactic| have' $x:ident : _ := $p)
-attribute [tactic_alt tacticHave'_] «tacticHave'_:=_»
 /-- Similar to `let`, but using `refine'` -/
 macro "let' " d:letDecl : tactic => `(tactic| refine_lift' let $d:letDecl; ?_)
 

src/Lean/Compiler/IR/Borrow.lean

@@ -68,7 +68,7 @@ namespace InitParamMap
 def initBorrow (ps : Array Param) : Array Param :=
   ps.map fun p => { p with borrow := p.ty.isObj }
 
-/-- We do not perform borrow inference for constants marked as `export`.
+/-- We do perform borrow inference for constants marked as `export`.
    Reason: we current write wrappers in C++ for using exported functions.
    These wrappers use smart pointers such as `object_ref`.
    When writing a new wrapper we need to know whether an argument is a borrow

src/Lean/Compiler/IR/Checker.lean

@@ -50,7 +50,7 @@ def markJP (j : JoinPointId) : M Unit :=
 def getDecl (c : Name) : M Decl := do
   let ctx ← read
   match findEnvDecl' ctx.env c ctx.decls with
-  | none   => throw s!"depends on declaration '{c}', which has no executable code; consider marking definition as 'noncomputable'"
+  | none   => throw s!"unknown declaration '{c}'"
   | some d => pure d
 
 def checkVar (x : VarId) : M Unit := do
@@ -182,7 +182,7 @@ end Checker
 def checkDecl (decls : Array Decl) (decl : Decl) : CompilerM Unit := do
   let env ← getEnv
   match (Checker.checkDecl decl { env := env, decls := decls }).run' {} with
-  | .error msg => throw s!"failed to compile definition, compiler IR check failed at '{decl.name}'. Error: {msg}"
+  | .error msg => throw s!"compiler IR check failed at '{decl.name}', error: {msg}"
   | _ => pure ()
 
 def checkDecls (decls : Array Decl) : CompilerM Unit :=

src/Lean/Compiler/IR/RC.lean

@@ -91,7 +91,7 @@ private def isBorrowParamAux (x : VarId) (ys : Array Arg) (consumeParamPred : Na
     | Arg.var y      => x == y && !consumeParamPred i
 
 private def isBorrowParam (x : VarId) (ys : Array Arg) (ps : Array Param) : Bool :=
-  isBorrowParamAux x ys fun i => ! ps[i]!.borrow
+  isBorrowParamAux x ys fun i => not ps[i]!.borrow
 
 /--
 Return `n`, the number of times `x` is consumed.
@@ -124,7 +124,7 @@ private def addIncBeforeAux (ctx : Context) (xs : Array Arg) (consumeParamPred :
         addInc ctx x b numIncs
 
 private def addIncBefore (ctx : Context) (xs : Array Arg) (ps : Array Param) (b : FnBody) (liveVarsAfter : LiveVarSet) : FnBody :=
-  addIncBeforeAux ctx xs (fun i => ! ps[i]!.borrow) b liveVarsAfter
+  addIncBeforeAux ctx xs (fun i => not ps[i]!.borrow) b liveVarsAfter
 
 /-- See `addIncBeforeAux`/`addIncBefore` for the procedure that inserts `inc` operations before an application.  -/
 private def addDecAfterFullApp (ctx : Context) (xs : Array Arg) (ps : Array Param) (b : FnBody) (bLiveVars : LiveVarSet) : FnBody :=

src/Lean/Data/PersistentArray.lean

@@ -317,8 +317,8 @@ variable {m : Type → Type w} [Monad m]
   anyMAux p t.root <||> t.tail.anyM p
 
 @[inline] def allM (a : PersistentArray α) (p : α → m Bool) : m Bool := do
-  let b ← anyM a (fun v => do let b ← p v; pure (!b))
-  pure (!b)
+  let b ← anyM a (fun v => do let b ← p v; pure (not b))
+  pure (not b)
 
 end
 

src/Lean/Data/Rat.lean

@@ -29,7 +29,7 @@ instance : Repr Rat where
 
 @[inline] def Rat.normalize (a : Rat) : Rat :=
   let n := Nat.gcd a.num.natAbs a.den
-  if n == 1 then a else { num := a.num.tdiv n, den := a.den / n }
+  if n == 1 then a else { num := a.num.div n, den := a.den / n }
 
 def mkRat (num : Int) (den : Nat) : Rat :=
   if den == 0 then { num := 0 } else Rat.normalize { num, den }
@@ -53,7 +53,7 @@ protected def lt (a b : Rat) : Bool :=
 protected def mul (a b : Rat) : Rat :=
   let g1 := Nat.gcd a.den b.num.natAbs
   let g2 := Nat.gcd a.num.natAbs b.den
-  { num := (a.num.tdiv g2)*(b.num.tdiv g1)
+  { num := (a.num.div g2)*(b.num.div g1)
     den := (b.den / g2)*(a.den / g1) }
 
 protected def inv (a : Rat) : Rat :=
@@ -78,7 +78,7 @@ protected def add (a b : Rat) : Rat :=
     if g1 == 1 then
       { num, den }
     else
-      { num := num.tdiv g1, den := den / g1 }
+      { num := num.div g1, den := den / g1 }
 
 protected def sub (a b : Rat) : Rat :=
   let g := Nat.gcd a.den b.den
@@ -91,7 +91,7 @@ protected def sub (a b : Rat) : Rat :=
     if g1 == 1 then
       { num, den }
     else
-      { num := num.tdiv g1, den := den / g1 }
+      { num := num.div g1, den := den / g1 }
 
 protected def neg (a : Rat) : Rat :=
   { a with num := - a.num }
@@ -100,14 +100,14 @@ protected def floor (a : Rat) : Int :=
   if a.den == 1 then
     a.num
   else
-    let r := a.num.tmod a.den
+    let r := a.num.mod a.den
     if a.num < 0 then r - 1 else r
 
 protected def ceil (a : Rat) : Int :=
   if a.den == 1 then
     a.num
   else
-    let r := a.num.tmod a.den
+    let r := a.num.mod a.den
     if a.num > 0 then r + 1 else r
 
 instance : LT Rat where

src/Lean/Elab/App.lean

@@ -1594,13 +1594,10 @@ private def elabAtom : TermElab := fun stx expectedType? => do
 @[builtin_term_elab dotIdent] def elabDotIdent : TermElab := elabAtom
 @[builtin_term_elab explicitUniv] def elabExplicitUniv : TermElab := elabAtom
 @[builtin_term_elab pipeProj] def elabPipeProj : TermElab
-  | `($e |>.%$tk$f $args*), expectedType? =>
+  | `($e |>.$f $args*), expectedType? =>
     universeConstraintsCheckpoint do
       let (namedArgs, args, ellipsis) ← expandArgs args
-      let mut stx ← `($e |>.%$tk$f)
-      if let (some startPos, some stopPos) := (e.raw.getPos?, f.raw.getTailPos?) then
-        stx := ⟨stx.raw.setInfo <| .synthetic (canonical := true) startPos stopPos⟩
-      elabAppAux stx namedArgs args (ellipsis := ellipsis) expectedType?
+      elabAppAux (← `($e |>.$f)) namedArgs args (ellipsis := ellipsis) expectedType?
   | _, _ => throwUnsupportedSyntax
 
 @[builtin_term_elab explicit] def elabExplicit : TermElab := fun stx expectedType? =>

src/Lean/Elab/Deriving/FromToJson.lean

@@ -15,109 +15,145 @@ open Lean.Json
 open Lean.Parser.Term
 open Lean.Meta
 
-def mkToJsonHeader (indVal : InductiveVal) : TermElabM Header := do
-  mkHeader ``ToJson 1 indVal
-
-def mkFromJsonHeader (indVal : InductiveVal) : TermElabM Header := do
-  let header ← mkHeader ``FromJson 0 indVal
-  let jsonArg ← `(bracketedBinderF|(json : Json))
-  return {header with
-    binders := header.binders.push jsonArg}
-
 def mkJsonField (n : Name) : CoreM (Bool × Term) := do
   let .str .anonymous s := n | throwError "invalid json field name {n}"
   let s₁ := s.dropRightWhile (· == '?')
   return (s != s₁, Syntax.mkStrLit s₁)
 
-def mkToJsonBodyForStruct (header : Header) (indName : Name) : TermElabM Term := do
-  let fields := getStructureFieldsFlattened (← getEnv) indName (includeSubobjectFields := false)
-  let fields ← fields.mapM fun field => do
-    let (isOptField, nm) ← mkJsonField field
-    let target := mkIdent header.targetNames[0]!
-    if isOptField then ``(opt $nm $target.$(mkIdent field))
-    else ``([($nm, toJson ($target).$(mkIdent field))])
-  `(mkObj <| List.join [$fields,*])
-
-def mkToJsonBodyForInduct (ctx : Context) (header : Header) (indName : Name) : TermElabM Term := do
-  let indVal ← getConstInfoInduct indName
-  let toJsonFuncId := mkIdent ctx.auxFunNames[0]!
-  -- Return syntax to JSONify `id`, either via `ToJson` or recursively
-  -- if `id`'s type is the type we're deriving for.
-  let mkToJson (id : Ident) (type : Expr) : TermElabM Term := do
+def mkToJsonInstance (declName : Name) : CommandElabM Bool := do
+  if isStructure (← getEnv) declName then
+    let cmds ← liftTermElabM do
+      let ctx ← mkContext "toJson" declName
+      let header ← mkHeader ``ToJson 1 ctx.typeInfos[0]!
+      let fields := getStructureFieldsFlattened (← getEnv) declName (includeSubobjectFields := false)
+      let fields ← fields.mapM fun field => do
+        let (isOptField, nm) ← mkJsonField field
+        let target := mkIdent header.targetNames[0]!
+        if isOptField then ``(opt $nm ($target).$(mkIdent field))
+        else ``([($nm, toJson ($target).$(mkIdent field))])
+      let cmd ← `(private def $(mkIdent ctx.auxFunNames[0]!):ident $header.binders:bracketedBinder* : Json :=
+        mkObj <| List.join [$fields,*])
+      return #[cmd] ++ (← mkInstanceCmds ctx ``ToJson #[declName])
+    cmds.forM elabCommand
+    return true
+  else
+    let indVal ← getConstInfoInduct declName
+    let cmds ← liftTermElabM do
+      let ctx ← mkContext "toJson" declName
+      let toJsonFuncId := mkIdent ctx.auxFunNames[0]!
+      -- Return syntax to JSONify `id`, either via `ToJson` or recursively
+      -- if `id`'s type is the type we're deriving for.
+      let mkToJson (id : Ident) (type : Expr) : TermElabM Term := do
         if type.isAppOf indVal.name then `($toJsonFuncId:ident $id:ident)
         else ``(toJson $id:ident)
-  let discrs ← mkDiscrs header indVal
-  let alts ← mkAlts indVal fun ctor args userNames => do
-    let ctorStr := ctor.name.eraseMacroScopes.getString!
-    match args, userNames with
-    | #[], _ => ``(toJson $(quote ctorStr))
-    | #[(x, t)], none => ``(mkObj [($(quote ctorStr), $(← mkToJson x t))])
-    | xs, none =>
-      let xs ← xs.mapM fun (x, t) => mkToJson x t
-      ``(mkObj [($(quote ctorStr), Json.arr #[$[$xs:term],*])])
-    | xs, some userNames =>
-      let xs ← xs.mapIdxM fun idx (x, t) => do
-        `(($(quote userNames[idx]!.eraseMacroScopes.getString!), $(← mkToJson x t)))
-      ``(mkObj [($(quote ctorStr), mkObj [$[$xs:term],*])])
-  `(match $[$discrs],* with $alts:matchAlt*)
+      let header ← mkHeader ``ToJson 1 ctx.typeInfos[0]!
+      let discrs ← mkDiscrs header indVal
+      let alts ← mkAlts indVal fun ctor args userNames => do
+        let ctorStr := ctor.name.eraseMacroScopes.getString!
+        match args, userNames with
+        | #[], _ => ``(toJson $(quote ctorStr))
+        | #[(x, t)], none => ``(mkObj [($(quote ctorStr), $(← mkToJson x t))])
+        | xs, none =>
+          let xs ← xs.mapM fun (x, t) => mkToJson x t
+          ``(mkObj [($(quote ctorStr), Json.arr #[$[$xs:term],*])])
+        | xs, some userNames =>
+          let xs ← xs.mapIdxM fun idx (x, t) => do
+            `(($(quote userNames[idx]!.eraseMacroScopes.getString!), $(← mkToJson x t)))
+          ``(mkObj [($(quote ctorStr), mkObj [$[$xs:term],*])])
+      let auxTerm ← `(match $[$discrs],* with $alts:matchAlt*)
+      let auxCmd ←
+        if ctx.usePartial then
+          let letDecls ← mkLocalInstanceLetDecls ctx ``ToJson header.argNames
+          let auxTerm ← mkLet letDecls auxTerm
+          `(private partial def $toJsonFuncId:ident $header.binders:bracketedBinder* : Json := $auxTerm)
+        else
+          `(private def $toJsonFuncId:ident $header.binders:bracketedBinder* : Json := $auxTerm)
+      return #[auxCmd] ++ (← mkInstanceCmds ctx ``ToJson #[declName])
+    cmds.forM elabCommand
+    return true
 
 where
   mkAlts
     (indVal : InductiveVal)
-    (rhs : ConstructorVal → Array (Ident × Expr) → Option (Array Name) → TermElabM Term): TermElabM (Array (TSyntax ``matchAlt)) := do
-      let mut alts := #[]
-      for ctorName in indVal.ctors do
-        let ctorInfo ← getConstInfoCtor ctorName
-        let alt ← forallTelescopeReducing ctorInfo.type fun xs _ => do
-          let mut patterns := #[]
-          -- add `_` pattern for indices
-          for _ in [:indVal.numIndices] do
-            patterns := patterns.push (← `(_))
-          let mut ctorArgs := #[]
-          -- add `_` for inductive parameters, they are inaccessible
-          for _ in [:indVal.numParams] do
-            ctorArgs := ctorArgs.push (← `(_))
-          -- bound constructor arguments and their types
-          let mut binders := #[]
-          let mut userNames := #[]
-          for i in [:ctorInfo.numFields] do
-            let x := xs[indVal.numParams + i]!
-            let localDecl ← x.fvarId!.getDecl
-            if !localDecl.userName.hasMacroScopes then
-              userNames := userNames.push localDecl.userName
-            let a := mkIdent (← mkFreshUserName `a)
-            binders := binders.push (a, localDecl.type)
-            ctorArgs := ctorArgs.push a
-          patterns := patterns.push (← `(@$(mkIdent ctorInfo.name):ident $ctorArgs:term*))
-          let rhs ← rhs ctorInfo binders (if userNames.size == binders.size then some userNames else none)
-          `(matchAltExpr| | $[$patterns:term],* => $rhs:term)
-        alts := alts.push alt
-      return alts
+    (rhs : ConstructorVal → Array (Ident × Expr) → Option (Array Name) → TermElabM Term) : TermElabM (Array (TSyntax ``matchAlt)) := do
+  indVal.ctors.toArray.mapM fun ctor => do
+    let ctorInfo ← getConstInfoCtor ctor
+    forallTelescopeReducing ctorInfo.type fun xs _ => do
+      let mut patterns := #[]
+      -- add `_` pattern for indices
+      for _ in [:indVal.numIndices] do
+        patterns := patterns.push (← `(_))
+      let mut ctorArgs := #[]
+      -- add `_` for inductive parameters, they are inaccessible
+      for _ in [:indVal.numParams] do
+        ctorArgs := ctorArgs.push (← `(_))
+      -- bound constructor arguments and their types
+      let mut binders := #[]
+      let mut userNames := #[]
+      for i in [:ctorInfo.numFields] do
+        let x := xs[indVal.numParams + i]!
+        let localDecl ← x.fvarId!.getDecl
+        if !localDecl.userName.hasMacroScopes then
+          userNames := userNames.push localDecl.userName
+        let a := mkIdent (← mkFreshUserName `a)
+        binders := binders.push (a, localDecl.type)
+        ctorArgs := ctorArgs.push a
+      patterns := patterns.push (← `(@$(mkIdent ctorInfo.name):ident $ctorArgs:term*))
+      let rhs ← rhs ctorInfo binders (if userNames.size == binders.size then some userNames else none)
+      `(matchAltExpr| | $[$patterns:term],* => $rhs:term)
 
-def mkFromJsonBodyForStruct (indName : Name) : TermElabM Term := do
-  let fields := getStructureFieldsFlattened (← getEnv) indName (includeSubobjectFields := false)
-  let getters ← fields.mapM (fun field => do
-    let getter ← `(getObjValAs? json _ $(Prod.snd <| ← mkJsonField field))
-    let getter ← `(doElem| Except.mapError (fun s => (toString $(quote indName)) ++ "." ++ (toString $(quote field)) ++ ": " ++ s) <| $getter)
-    return getter
-  )
-  let fields := fields.map mkIdent
-  `(do
-    $[let $fields:ident ← $getters]*
-    return { $[$fields:ident := $(id fields)],* })
+def mkFromJsonInstance (declName : Name) : CommandElabM Bool := do
+  if isStructure (← getEnv) declName then
+    let cmds ← liftTermElabM do
+      let ctx ← mkContext "fromJson" declName
+      let header ← mkHeader ``FromJson 0 ctx.typeInfos[0]!
+      let fields := getStructureFieldsFlattened (← getEnv) declName (includeSubobjectFields := false)
+      let getters ← fields.mapM (fun field => do
+        let getter ← `(getObjValAs? j _ $(Prod.snd <| ← mkJsonField field))
+        let getter ← `(doElem| Except.mapError (fun s => (toString $(quote declName)) ++ "." ++ (toString $(quote field)) ++ ": " ++ s) <| $getter)
+        return getter
+      )
+      let fields := fields.map mkIdent
+      let cmd ← `(private def $(mkIdent ctx.auxFunNames[0]!):ident $header.binders:bracketedBinder* (j : Json)
+        : Except String $(← mkInductiveApp ctx.typeInfos[0]! header.argNames) := do
+        $[let $fields:ident ← $getters]*
+        return { $[$fields:ident := $(id fields)],* })
+      return #[cmd] ++ (← mkInstanceCmds ctx ``FromJson #[declName])
+    cmds.forM elabCommand
+    return true
+  else
+    let indVal ← getConstInfoInduct declName
+    let cmds ← liftTermElabM do
+      let ctx ← mkContext "fromJson" declName
+      let header ← mkHeader ``FromJson 0 ctx.typeInfos[0]!
+      let fromJsonFuncId := mkIdent ctx.auxFunNames[0]!
+      let alts ← mkAlts indVal fromJsonFuncId
+      let mut auxTerm ← alts.foldrM (fun xs x => `(Except.orElseLazy $xs (fun _ => $x))) (← `(Except.error "no inductive constructor matched"))
+      if ctx.usePartial then
+        let letDecls ← mkLocalInstanceLetDecls ctx ``FromJson header.argNames
+        auxTerm ← mkLet letDecls auxTerm
+      -- FromJson is not structurally recursive even non-nested recursive inductives,
+      -- so we also use `partial` then.
+      let auxCmd ←
+        if ctx.usePartial || indVal.isRec then
+          `(private partial def $fromJsonFuncId:ident $header.binders:bracketedBinder* (json : Json)
+                : Except String $(← mkInductiveApp ctx.typeInfos[0]! header.argNames) :=
+              $auxTerm)
+        else
+          `(private def $fromJsonFuncId:ident $header.binders:bracketedBinder* (json : Json)
+                : Except String $(← mkInductiveApp ctx.typeInfos[0]! header.argNames) :=
+              $auxTerm)
+      return #[auxCmd] ++ (← mkInstanceCmds ctx ``FromJson #[declName])
+    cmds.forM elabCommand
+    return true
 
-def mkFromJsonBodyForInduct (ctx : Context) (indName : Name) : TermElabM Term := do
-  let indVal ← getConstInfoInduct indName
-  let alts ← mkAlts indVal
-  let auxTerm ← alts.foldrM (fun xs x => `(Except.orElseLazy $xs (fun _ => $x))) (← `(Except.error "no inductive constructor matched"))
-  `($auxTerm)
 where
-  mkAlts (indVal : InductiveVal) : TermElabM (Array Term) := do
-  let mut alts := #[]
-  for ctorName in indVal.ctors do
-    let ctorInfo ← getConstInfoCtor ctorName
-    let alt ← do forallTelescopeReducing ctorInfo.type fun xs _ => do
-        let mut binders   := #[]
+  mkAlts (indVal : InductiveVal) (fromJsonFuncId : Ident) : TermElabM (Array Term) := do
+  let alts ←
+    indVal.ctors.toArray.mapM fun ctor => do
+      let ctorInfo ← getConstInfoCtor ctor
+      forallTelescopeReducing ctorInfo.type fun xs _ => do
+        let mut binders := #[]
         let mut userNames := #[]
         for i in [:ctorInfo.numFields] do
           let x := xs[indVal.numParams + i]!
@@ -126,7 +162,7 @@ where
             userNames := userNames.push localDecl.userName
           let a := mkIdent (← mkFreshUserName `a)
           binders := binders.push (a, localDecl.type)
-        let fromJsonFuncId := mkIdent ctx.auxFunNames[0]!
+
         -- Return syntax to parse `id`, either via `FromJson` or recursively
         -- if `id`'s type is the type we're deriving for.
         let mkFromJson (idx : Nat) (type : Expr) : TermElabM (TSyntax ``doExpr) :=
@@ -139,111 +175,23 @@ where
         else
           ``(none)
         let stx ←
-          `((Json.parseTagged json $(quote ctorName.eraseMacroScopes.getString!) $(quote ctorInfo.numFields) $(quote userNamesOpt)).bind
+          `((Json.parseTagged json $(quote ctor.eraseMacroScopes.getString!) $(quote ctorInfo.numFields) $(quote userNamesOpt)).bind
             (fun jsons => do
               $[let $identNames:ident ← $fromJsons:doExpr]*
-              return $(mkIdent ctorName):ident $identNames*))
+              return $(mkIdent ctor):ident $identNames*))
         pure (stx, ctorInfo.numFields)
-      alts := alts.push alt
   -- the smaller cases, especially the ones without fields are likely faster
-  let alts' := alts.qsort (fun (_, x) (_, y) => x < y)
-  return alts'.map Prod.fst
-
-def mkToJsonBody (ctx : Context) (header : Header) (e : Expr): TermElabM Term := do
-  let indName := e.getAppFn.constName!
-  if isStructure (← getEnv) indName then
-    mkToJsonBodyForStruct header indName
-  else
-    mkToJsonBodyForInduct ctx header indName
-
-def mkToJsonAuxFunction (ctx : Context) (i : Nat) : TermElabM Command := do
-  let auxFunName := ctx.auxFunNames[i]!
-  let header     ←  mkToJsonHeader ctx.typeInfos[i]!
-  let binders    := header.binders
-  Term.elabBinders binders fun _ => do
-  let type       ← Term.elabTerm header.targetType none
-  let mut body   ← mkToJsonBody ctx header type
-  if ctx.usePartial then
-    let letDecls ← mkLocalInstanceLetDecls ctx ``ToJson header.argNames
-    body ← mkLet letDecls body
-    `(private partial def $(mkIdent auxFunName):ident $binders:bracketedBinder* : Json := $body:term)
-  else
-    `(private def $(mkIdent auxFunName):ident $binders:bracketedBinder* : Json := $body:term)
-
-def mkFromJsonBody (ctx : Context) (e : Expr) : TermElabM Term := do
-  let indName := e.getAppFn.constName!
-  if isStructure (← getEnv) indName then
-    mkFromJsonBodyForStruct indName
-  else
-    mkFromJsonBodyForInduct ctx indName
-
-def mkFromJsonAuxFunction (ctx : Context) (i : Nat) : TermElabM Command := do
-  let auxFunName := ctx.auxFunNames[i]!
-  let indval     := ctx.typeInfos[i]!
-  let header     ←  mkFromJsonHeader indval --TODO fix header info
-  let binders    := header.binders
-  Term.elabBinders binders fun _ => do
-  let type ← Term.elabTerm header.targetType none
-  let mut body ← mkFromJsonBody ctx type
-  if ctx.usePartial || indval.isRec then
-    let letDecls ← mkLocalInstanceLetDecls ctx ``FromJson header.argNames
-    body ← mkLet letDecls body
-    `(private partial def $(mkIdent auxFunName):ident $binders:bracketedBinder* : Except String $(← mkInductiveApp ctx.typeInfos[i]! header.argNames) := $body:term)
-  else
-    `(private def $(mkIdent auxFunName):ident $binders:bracketedBinder* : Except String $(← mkInductiveApp ctx.typeInfos[i]! header.argNames) := $body:term)
-
-
-def mkToJsonMutualBlock (ctx : Context) : TermElabM Command := do
-  let mut auxDefs := #[]
-  for i in [:ctx.typeInfos.size] do
-    auxDefs := auxDefs.push (← mkToJsonAuxFunction ctx i)
-  `(mutual
-     $auxDefs:command*
-    end)
-
-def mkFromJsonMutualBlock (ctx : Context) : TermElabM Command := do
-  let mut auxDefs := #[]
-  for i in [:ctx.typeInfos.size] do
-    auxDefs := auxDefs.push (← mkFromJsonAuxFunction ctx i)
-  `(mutual
-     $auxDefs:command*
-    end)
-
-private def mkToJsonInstance (declName : Name) : TermElabM (Array Command) := do
-  let ctx ← mkContext "toJson" declName
-  let cmds := #[← mkToJsonMutualBlock ctx] ++ (← mkInstanceCmds ctx ``ToJson #[declName])
-  trace[Elab.Deriving.toJson] "\n{cmds}"
-  return cmds
-
-private def mkFromJsonInstance (declName : Name) : TermElabM (Array Command) := do
-  let ctx ← mkContext "fromJson" declName
-  let cmds := #[← mkFromJsonMutualBlock ctx] ++ (← mkInstanceCmds ctx ``FromJson #[declName])
-  trace[Elab.Deriving.fromJson] "\n{cmds}"
-  return cmds
+  let alts := alts.qsort (fun (_, x) (_, y) => x < y)
+  return alts.map Prod.fst
 
 def mkToJsonInstanceHandler (declNames : Array Name) : CommandElabM Bool := do
-  if (← declNames.allM isInductive) && declNames.size > 0 then
-    for declName in declNames do
-      let cmds ← liftTermElabM <| mkToJsonInstance declName
-      cmds.forM elabCommand
-    return true
-  else
-    return false
+  declNames.foldlM (fun b n => andM (pure b) (mkToJsonInstance n)) true
 
 def mkFromJsonInstanceHandler (declNames : Array Name) : CommandElabM Bool := do
-  if (← declNames.allM isInductive) && declNames.size > 0 then
-    for declName in declNames do
-      let cmds ← liftTermElabM <| mkFromJsonInstance declName
-      cmds.forM elabCommand
-    return true
-  else
-    return false
+  declNames.foldlM (fun b n => andM (pure b) (mkFromJsonInstance n)) true
 
 builtin_initialize
   registerDerivingHandler ``ToJson mkToJsonInstanceHandler
   registerDerivingHandler ``FromJson mkFromJsonInstanceHandler
 
-  registerTraceClass `Elab.Deriving.toJson
-  registerTraceClass `Elab.Deriving.fromJson
-
 end Lean.Elab.Deriving.FromToJson

src/Lean/Elab/InfoTree/Main.lean

@@ -183,7 +183,7 @@ def UserWidgetInfo.format (info : UserWidgetInfo) : Format :=
   f!"UserWidget {info.id}\n{Std.ToFormat.format <| info.props.run' {}}"
 
 def FVarAliasInfo.format (info : FVarAliasInfo) : Format :=
-  f!"FVarAlias {info.userName.eraseMacroScopes}: {info.id.name} -> {info.baseId.name}"
+  f!"FVarAlias {info.userName.eraseMacroScopes}"
 
 def FieldRedeclInfo.format (ctx : ContextInfo) (info : FieldRedeclInfo) : Format :=
   f!"FieldRedecl @ {formatStxRange ctx info.stx}"

src/Lean/Elab/InheritDoc.lean

@@ -21,7 +21,7 @@ builtin_initialize
         let some id := id?
           | throwError "invalid `[inherit_doc]` attribute, could not infer doc source"
         let declName ← Elab.realizeGlobalConstNoOverloadWithInfo id
-        if (← findSimpleDocString? (← getEnv) decl (includeBuiltin := false)).isSome then
+        if (← findSimpleDocString? (← getEnv) decl).isSome then
           logWarning m!"{← mkConstWithLevelParams decl} already has a doc string"
         let some doc ← findSimpleDocString? (← getEnv) declName
           | logWarningAt id m!"{← mkConstWithLevelParams declName} does not have a doc string"

src/Lean/Elab/Match.lean

@@ -643,7 +643,7 @@ where
     | .proj _ _ b       => return p.updateProj! (← go b)
     | .mdata k b        =>
       if inaccessible? p |>.isSome then
-        return mkMData k (← withReader (fun _ => true) (go b))
+        return mkMData k (← withReader (fun _ => false) (go b))
       else if let some (stx, p) := patternWithRef? p then
         Elab.withInfoContext' (go p) fun p => do
           /- If `p` is a free variable and we are not inside of an "inaccessible" pattern, this `p` is a binder. -/

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

@@ -599,7 +599,7 @@ partial def solve {m} {α} [Monad m] (measures : Array α)
             all_le := false
             break
       -- No progress here? Try the next measure
-      if !(has_lt && all_le) then continue
+      if not (has_lt && all_le) then continue
       -- We found a suitable measure, remove it from the list (mild optimization)
       let measures' := measures.eraseIdx measureIdx
       return ← go measures' todo (acc.push measure)

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

@@ -41,9 +41,9 @@ def lratChecker (cfg : TacticContext) (bvExpr : BVLogicalExpr) : MetaM Expr := d
 
 @[inherit_doc Lean.Parser.Tactic.bvCheck]
 def bvCheck (g : MVarId) (cfg : TacticContext) : MetaM Unit := do
-  let unsatProver : UnsatProver := fun reflectionResult _ => do
+  let unsatProver : UnsatProver := fun bvExpr _ => do
     withTraceNode `sat (fun _ => return "Preparing LRAT reflection term") do
-      let proof ← lratChecker cfg reflectionResult.bvExpr
+      let proof ← lratChecker cfg bvExpr
       return ⟨proof, ""⟩
   let _ ← closeWithBVReflection g unsatProver
   return ()

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

@@ -74,111 +74,19 @@ def reconstructCounterExample (var2Cnf : Std.HashMap BVBit Nat) (assignment : Ar
     finalMap := finalMap.push (atomExpr, ⟨BitVec.ofNat currentBit value⟩)
   return finalMap
 
-structure ReflectionResult where
-  bvExpr : BVLogicalExpr
-  proveFalse : Expr → M Expr
-  unusedHypotheses : Std.HashSet FVarId
-
 structure UnsatProver.Result where
   proof : Expr
   lratCert : LratCert
 
-abbrev UnsatProver := ReflectionResult → Std.HashMap Nat Expr → MetaM UnsatProver.Result
+abbrev UnsatProver := BVLogicalExpr → Std.HashMap Nat Expr → MetaM UnsatProver.Result
 
-/--
-Contains values that will be used to diagnose spurious counter examples.
--/
-structure DiagnosisInput where
-  unusedHypotheses : Std.HashSet FVarId
-  atomsAssignment : Std.HashMap Nat Expr
-
-/--
-The result of a spurious counter example diagnosis.
--/
-structure Diagnosis where
-  uninterpretedSymbols : Std.HashSet Expr := {}
-  unusedRelevantHypotheses : Std.HashSet FVarId := {}
-
-abbrev DiagnosisM : Type → Type := ReaderT DiagnosisInput <| StateRefT Diagnosis MetaM
-
-namespace DiagnosisM
-
-def run (x : DiagnosisM Unit) (unusedHypotheses : Std.HashSet FVarId)
-    (atomsAssignment : Std.HashMap Nat Expr) : MetaM Diagnosis := do
-  let (_, issues) ← ReaderT.run x { unusedHypotheses, atomsAssignment } |>.run {}
-  return issues
-
-def unusedHyps : DiagnosisM (Std.HashSet FVarId) := do
-  return (← read).unusedHypotheses
-
-def atomsAssignment : DiagnosisM (Std.HashMap Nat Expr) := do
-  return (← read).atomsAssignment
-
-def addUninterpretedSymbol (e : Expr) : DiagnosisM Unit :=
-  modify fun s => { s with uninterpretedSymbols := s.uninterpretedSymbols.insert e }
-
-def addUnusedRelevantHypothesis (fvar : FVarId) : DiagnosisM Unit :=
-  modify fun s => { s with unusedRelevantHypotheses := s.unusedRelevantHypotheses.insert fvar }
-
-def checkRelevantHypsUsed (fvar : FVarId) : DiagnosisM Unit := do
-  for hyp in ← unusedHyps do
-    if (← hyp.getType).containsFVar fvar then
-      addUnusedRelevantHypothesis hyp
-
-/--
-Diagnose spurious counter examples, currently this checks:
-- Whether uninterpreted symbols were used
-- Whether all hypotheses which contain any variable that was bitblasted were included
--/
-def diagnose : DiagnosisM Unit := do
-  for (_, expr) in ← atomsAssignment do
-    match_expr expr with
-    | BitVec.ofBool x =>
-      match x with
-      | .fvar fvarId => checkRelevantHypsUsed fvarId
-      | _ => addUninterpretedSymbol expr
-    | _ =>
-      match expr with
-      | .fvar fvarId => checkRelevantHypsUsed fvarId
-      | _ => addUninterpretedSymbol expr
-
-end DiagnosisM
-
-def uninterpretedExplainer (d : Diagnosis) : Option MessageData := do
-  guard !d.uninterpretedSymbols.isEmpty
-  let symList := d.uninterpretedSymbols.toList
-  return m!"It abstracted the following unsupported expressions as opaque variables: {symList}"
-
-def unusedRelevantHypothesesExplainer (d : Diagnosis) : Option MessageData := do
-  guard !d.unusedRelevantHypotheses.isEmpty
-  let hypList := d.unusedRelevantHypotheses.toList.map mkFVar
-  return m!"The following potentially relevant hypotheses could not be used: {hypList}"
-
-def explainers : List (Diagnosis → Option MessageData) :=
-  [uninterpretedExplainer, unusedRelevantHypothesesExplainer]
-
-def explainCounterExampleQuality (unusedHypotheses : Std.HashSet FVarId)
-    (atomsAssignment : Std.HashMap Nat Expr) : MetaM MessageData := do
-  let diagnosis ← DiagnosisM.run DiagnosisM.diagnose unusedHypotheses atomsAssignment
-  let folder acc explainer := if let some m := explainer diagnosis then acc.push m else acc
-  let explanations := explainers.foldl (init := #[]) folder
-
-  if explanations.isEmpty then
-    return m!"The prover found a counterexample, consider the following assignment:\n"
-  else
-    let mut err := m!"The prover found a potentially spurious counterexample:\n"
-    err := err ++ explanations.foldl (init := m!"") (fun acc exp => acc ++ m!"- " ++ exp ++ m!"\n")
-    err := err ++ m!"Consider the following assignment:\n"
-    return err
-
-def lratBitblaster (cfg : TacticContext) (reflectionResult : ReflectionResult)
+def lratBitblaster (cfg : TacticContext) (bv : BVLogicalExpr)
     (atomsAssignment : Std.HashMap Nat Expr) :
     MetaM UnsatProver.Result := do
-  let bvExpr := reflectionResult.bvExpr
   let entry ←
     withTraceNode `bv (fun _ => return "Bitblasting BVLogicalExpr to AIG") do
       -- lazyPure to prevent compiler lifting
-      IO.lazyPure (fun _ => bvExpr.bitblast)
+      IO.lazyPure (fun _ => bv.bitblast)
   let aigSize := entry.aig.decls.size
   trace[Meta.Tactic.bv] s!"AIG has {aigSize} nodes."
 
@@ -200,25 +108,18 @@ def lratBitblaster (cfg : TacticContext) (reflectionResult : ReflectionResult)
 
   match res with
   | .ok cert =>
-    let proof ← cert.toReflectionProof cfg bvExpr ``verifyBVExpr ``unsat_of_verifyBVExpr_eq_true
+    let proof ← cert.toReflectionProof cfg bv ``verifyBVExpr ``unsat_of_verifyBVExpr_eq_true
     return ⟨proof, cert⟩
   | .error assignment =>
     let reconstructed := reconstructCounterExample map assignment aigSize atomsAssignment
-    let mut error ← explainCounterExampleQuality reflectionResult.unusedHypotheses atomsAssignment
+    let mut error := m!"The prover found a potential counterexample, consider the following assignment:\n"
     for (var, value) in reconstructed do
       error := error ++ m!"{var} = {value.bv}\n"
     throwError error
 
-
-def reflectBV (g : MVarId) : M ReflectionResult := g.withContext do
-  let hyps ← getPropHyps
-  let mut sats := #[]
-  let mut unusedHypotheses := {}
-  for hyp in hyps do
-    if let some reflected ← SatAtBVLogical.of (mkFVar hyp) then
-      sats := sats.push reflected
-    else
-      unusedHypotheses := unusedHypotheses.insert hyp
+def reflectBV (g : MVarId) : M (BVLogicalExpr × (Expr → M Expr)) := g.withContext do
+  let hyps ← getLocalHyps
+  let sats ← hyps.filterMapM SatAtBVLogical.of
   if sats.size = 0 then
     let mut error := "None of the hypotheses are in the supported BitVec fragment.\n"
     error := error ++ "There are two potential fixes for this:\n"
@@ -227,32 +128,27 @@ def reflectBV (g : MVarId) : M ReflectionResult := g.withContext do
     error := error ++ "   Consider expressing it in terms of different operations that are better supported."
     throwError error
   let sat := sats.foldl (init := SatAtBVLogical.trivial) SatAtBVLogical.and
-  return {
-    bvExpr := sat.bvExpr,
-    proveFalse := sat.proveFalse,
-    unusedHypotheses := unusedHypotheses
-  }
-
+  return (sat.bvExpr, sat.proveFalse)
 
 def closeWithBVReflection (g : MVarId) (unsatProver : UnsatProver) :
     MetaM LratCert := M.run do
   g.withContext do
-    let reflectionResult ←
+    let (bvLogicalExpr, f) ←
       withTraceNode `bv (fun _ => return "Reflecting goal into BVLogicalExpr") do
         reflectBV g
-    trace[Meta.Tactic.bv] "Reflected bv logical expression: {reflectionResult.bvExpr}"
+    trace[Meta.Tactic.bv] "Reflected bv logical expression: {bvLogicalExpr}"
 
     let atomsPairs := (← getThe State).atoms.toList.map (fun (expr, _, ident) => (ident, expr))
     let atomsAssignment := Std.HashMap.ofList atomsPairs
-    let ⟨bvExprUnsat, cert⟩ ← unsatProver reflectionResult atomsAssignment
-    let proveFalse ← reflectionResult.proveFalse bvExprUnsat
+    let ⟨bvExprUnsat, cert⟩ ← unsatProver bvLogicalExpr atomsAssignment
+    let proveFalse ← f bvExprUnsat
     g.assign proveFalse
     return cert
 
 def bvUnsat (g : MVarId) (cfg : TacticContext) : MetaM LratCert := M.run do
-  let unsatProver : UnsatProver := fun reflectionResult atomsAssignment => do
+  let unsatProver : UnsatProver := fun bvExpr atomsAssignment => do
     withTraceNode `bv (fun _ => return "Preparing LRAT reflection term") do
-      lratBitblaster cfg reflectionResult atomsAssignment
+      lratBitblaster cfg bvExpr atomsAssignment
   closeWithBVReflection g unsatProver
 
 structure Result where

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

@@ -56,7 +56,7 @@ partial def of (t : Expr) : M (Option ReifiedBVLogical) := do
     let expr := mkApp2 (mkConst ``BoolExpr.const) (mkConst ``BVPred) (toExpr Bool.false)
     let proof := return mkRefl (mkConst ``Bool.false)
     return some ⟨boolExpr, proof, expr⟩
-  | Bool.not subExpr =>
+  | not subExpr =>
     let some sub ← of subExpr | return none
     let boolExpr := .not sub.bvExpr
     let expr := mkApp2 (mkConst ``BoolExpr.not) (mkConst ``BVPred) sub.expr
@@ -65,9 +65,9 @@ partial def of (t : Expr) : M (Option ReifiedBVLogical) := do
       let subProof ← sub.evalsAtAtoms
       return mkApp3 (mkConst ``Std.Tactic.BVDecide.Reflect.Bool.not_congr) subExpr subEvalExpr subProof
     return some ⟨boolExpr, proof, expr⟩
-  | Bool.or lhsExpr rhsExpr => gateReflection lhsExpr rhsExpr .or ``Std.Tactic.BVDecide.Reflect.Bool.or_congr
-  | Bool.and lhsExpr rhsExpr => gateReflection lhsExpr rhsExpr .and ``Std.Tactic.BVDecide.Reflect.Bool.and_congr
-  | Bool.xor lhsExpr rhsExpr => gateReflection lhsExpr rhsExpr .xor ``Std.Tactic.BVDecide.Reflect.Bool.xor_congr
+  | or lhsExpr rhsExpr => gateReflection lhsExpr rhsExpr .or ``Std.Tactic.BVDecide.Reflect.Bool.or_congr
+  | and lhsExpr rhsExpr => gateReflection lhsExpr rhsExpr .and ``Std.Tactic.BVDecide.Reflect.Bool.and_congr
+  | xor lhsExpr rhsExpr => gateReflection lhsExpr rhsExpr .xor ``Std.Tactic.BVDecide.Reflect.Bool.xor_congr
   | BEq.beq α _ lhsExpr rhsExpr =>
     match_expr α with
     | Bool => gateReflection lhsExpr rhsExpr .beq ``Std.Tactic.BVDecide.Reflect.Bool.beq_congr

src/Lean/Elab/Tactic/Conv/Unfold.lean

@@ -12,13 +12,7 @@ open Meta
 
 @[builtin_tactic Lean.Parser.Tactic.Conv.unfold] def evalUnfold : Tactic := fun stx => withMainContext do
   for declNameId in stx[1].getArgs do
-    let e ← elabTermForApply declNameId (mayPostpone := false)
-    match e with
-    | .const declName _ =>
-      applySimpResult (← unfold (← getLhs) declName)
-    | .fvar declFVarId =>
-      let lhs ← instantiateMVars (← getLhs)
-      changeLhs (← Meta.zetaDeltaFVars lhs #[declFVarId])
-    | _ => throwErrorAt declNameId m!"'unfold' conv tactic failed, expression {e} is not a global or local constant"
+    let declName ← realizeGlobalConstNoOverloadWithInfo declNameId
+    applySimpResult (← unfold (← getLhs) declName)
 
 end Lean.Elab.Tactic.Conv

src/Lean/Elab/Tactic/ElabTerm.lean

@@ -405,8 +405,7 @@ private partial def blameDecideReductionFailure (inst : Expr) : MetaM Expr := do
     if r.isAppOf ``isTrue then
       -- Success!
       -- While we have a proof from reduction, we do not embed it in the proof term,
-      -- and instead we let the kernel recompute it during type checking from the following more
-      -- efficient term. The kernel handles the unification `e =?= true` specially.
+      -- and instead we let the kernel recompute it during type checking from the following more efficient term.
       let rflPrf ← mkEqRefl (toExpr true)
       return mkApp3 (Lean.mkConst ``of_decide_eq_true) expectedType s rflPrf
     else

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

@@ -422,11 +422,10 @@ partial def addFact (p : MetaProblem) (h : Expr) : OmegaM (MetaProblem × Nat) :
     trace[omega] "adding fact: {t}"
     match t with
     | .forallE _ x y _ =>
-      if ← pure t.isArrow <&&> isProp x <&&> isProp y then
+      if (← isProp x) && (← isProp y) then
         p.addFact (mkApp4 (.const ``Decidable.not_or_of_imp []) x y
           (.app (.const ``Classical.propDecidable []) x) h)
       else
-        trace[omega] "rejecting forall: it's not an arrow, or not propositional"
         return (p, 0)
     | .app _ _ =>
       match_expr t with

src/Lean/Elab/Tactic/Unfold.lean

@@ -17,25 +17,14 @@ def unfoldLocalDecl (declName : Name) (fvarId : FVarId) : TacticM Unit := do
 def unfoldTarget (declName : Name) : TacticM Unit := do
   replaceMainGoal [← Meta.unfoldTarget (← getMainGoal) declName]
 
-def zetaDeltaLocalDecl (declFVarId : FVarId) (fvarId : FVarId) : TacticM Unit := do
-  replaceMainGoal [← Meta.zetaDeltaLocalDecl (← getMainGoal) fvarId declFVarId]
-
-def zetaDeltaTarget (declFVarId : FVarId) : TacticM Unit := do
-  replaceMainGoal [← Meta.zetaDeltaTarget (← getMainGoal) declFVarId]
-
 /-- "unfold " ident+ (location)? -/
 @[builtin_tactic Lean.Parser.Tactic.unfold] def evalUnfold : Tactic := fun stx => do
   let loc := expandOptLocation stx[2]
   for declNameId in stx[1].getArgs do
     go declNameId loc
 where
-  go (declNameId : Syntax) (loc : Location) : TacticM Unit := withMainContext do
-    let e ← elabTermForApply declNameId (mayPostpone := false)
-    match e with
-    | .const declName _ =>
-      withLocation loc (unfoldLocalDecl declName) (unfoldTarget declName) (throwTacticEx `unfold · m!"did not unfold '{declName}'")
-    | .fvar declFVarId =>
-      withLocation loc (zetaDeltaLocalDecl declFVarId) (zetaDeltaTarget declFVarId) (throwTacticEx `unfold · m!"did not unfold '{e}'")
-    | _ => withRef declNameId <| throwTacticEx `unfold (← getMainGoal) m!"expression {e} is not a global or local constant"
+  go (declNameId : Syntax) (loc : Location) : TacticM Unit := do
+    let declName ← realizeGlobalConstNoOverloadWithInfo declNameId
+    withLocation loc (unfoldLocalDecl declName) (unfoldTarget declName) (throwTacticEx `unfold · m!"did not unfold '{declName}'")
 
 end Lean.Elab.Tactic

src/Lean/Elab/Term.lean

@@ -1439,7 +1439,7 @@ def resolveLocalName (n : Name) : TermElabM (Option (Expr × List String)) := do
     let localDecl? := lctx.decls.findSomeRev? fun localDecl? => do
       let localDecl ← localDecl?
       if localDecl.isAuxDecl then
-        guard (!skipAuxDecl)
+        guard (not skipAuxDecl)
         if let some fullDeclName := auxDeclToFullName.find? localDecl.fvarId then
           matchAuxRecDecl? localDecl fullDeclName givenNameView
         else
@@ -1497,7 +1497,7 @@ def resolveLocalName (n : Name) : TermElabM (Option (Expr × List String)) := do
       foo := 10
     ```
     -/
-    match findLocalDecl? givenNameView (skipAuxDecl := globalDeclFound && !projs.isEmpty) with
+    match findLocalDecl? givenNameView (skipAuxDecl := globalDeclFound && not projs.isEmpty) with
     | some decl => return some (decl.toExpr, projs)
     | none => match n with
       | .str pre s => loop pre (s::projs) globalDeclFoundNext

src/Lean/Environment.lean

@@ -1016,15 +1016,7 @@ private def registerNamePrefixes : Environment → Name → Environment
 
 @[export lean_environment_add]
 private def add (env : Environment) (cinfo : ConstantInfo) : Environment :=
-  let name := cinfo.name
-  let env := match name with
-    | .str _ s =>
-      if s.get 0 == '_' then
-        -- Do not register namespaces that only contain internal declarations.
-        env
-      else
-        registerNamePrefixes env name
-    | _ => env
+  let env := registerNamePrefixes env cinfo.name
   env.addAux cinfo
 
 @[export lean_display_stats]

src/Lean/Language/Lean.lean

@@ -322,8 +322,7 @@ where
           stx := newStx
           diagnostics := old.diagnostics
           cancelTk? := ctx.newCancelTk
-          result? := some {
-            parserState := newParserState
+          result? := some { oldSuccess with
             processedSnap := (← oldSuccess.processedSnap.bindIO (sync := true) fun oldProcessed => do
               if let some oldProcSuccess := oldProcessed.result? then
                 -- also wait on old command parse snapshot as parsing is cheap and may allow for
@@ -331,11 +330,8 @@ where
                 oldProcSuccess.firstCmdSnap.bindIO (sync := true) fun oldCmd => do
                   let prom ← IO.Promise.new
                   let _ ← IO.asTask (parseCmd oldCmd newParserState oldProcSuccess.cmdState prom ctx)
-                  return .pure {
-                    diagnostics := oldProcessed.diagnostics
-                    result? := some {
-                      cmdState := oldProcSuccess.cmdState
-                      firstCmdSnap := { range? := none, task := prom.result } } }
+                  return .pure { oldProcessed with result? := some { oldProcSuccess with
+                    firstCmdSnap := { range? := none, task := prom.result } } }
               else
                 return .pure oldProcessed) } }
       else return old

src/Lean/Linter/UnusedVariables.lean

@@ -447,10 +447,7 @@ def unusedVariables : Linter where
     let fvarAliases : Std.HashMap FVarId FVarId := s.fvarAliases.fold (init := {}) fun m id baseId =>
       m.insert id (followAliases s.fvarAliases baseId)
 
-    let getCanonVar (id : FVarId) : FVarId := fvarAliases.getD id id
-
     -- Collect all non-alias fvars corresponding to `fvarUses` by resolving aliases in the list.
-    -- Unlike `s.fvarUses`, `fvarUsesRef` is guaranteed to contain no aliases.
     let fvarUsesRef ← IO.mkRef <| fvarAliases.fold (init := s.fvarUses) fun fvarUses id baseId =>
       if fvarUses.contains id then fvarUses.insert baseId else fvarUses
 
@@ -464,7 +461,7 @@ def unusedVariables : Linter where
       let fvarUses ← fvarUsesRef.get
       -- If any of the `fvar`s corresponding to this declaration is (an alias of) a variable in
       -- `fvarUses`, then it is used
-      if aliases.any fun id => fvarUses.contains (getCanonVar id) then continue
+      if aliases.any fun id => fvarUses.contains (fvarAliases.getD id id) then continue
       -- If this is a global declaration then it is (potentially) used after the command
       if s.constDecls.contains range then continue
 
@@ -496,12 +493,10 @@ def unusedVariables : Linter where
       if !initializedMVars then
         -- collect additional `fvarUses` from tactic assignments
         visitAssignments (← IO.mkRef {}) fvarUsesRef s.assignments
-        -- Resolve potential aliases again to preserve `fvarUsesRef` invariant
-        fvarUsesRef.modify fun fvarUses => fvarUses.fold (·.insert <| getCanonVar ·) {}
         initializedMVars := true
         let fvarUses ← fvarUsesRef.get
         -- Redo the initial check because `fvarUses` could be bigger now
-        if aliases.any fun id => fvarUses.contains (getCanonVar id) then continue
+        if aliases.any fun id => fvarUses.contains (fvarAliases.getD id id) then continue
 
       -- If we made it this far then the variable is unused and not ignored
       unused := unused.push (declStx, userName)

src/Lean/Meta/Basic.lean

@@ -560,72 +560,16 @@ def useEtaStruct (inductName : Name) : MetaM Bool := do
   | .all  => return true
   | .notClasses => return !isClass (← getEnv) inductName
 
-/-!
-WARNING: The following 4 constants are a hack for simulating forward declarations.
-They are defined later using the `export` attribute. This is hackish because we
-have to hard-code the true arity of these definitions here, and make sure the C names match.
-We have used another hack based on `IO.Ref`s in the past, it was safer but less efficient.
--/
+/-! WARNING: The following 4 constants are a hack for simulating forward declarations.
+   They are defined later using the `export` attribute. This is hackish because we
+   have to hard-code the true arity of these definitions here, and make sure the C names match.
+   We have used another hack based on `IO.Ref`s in the past, it was safer but less efficient. -/
 
-/--
-Reduces an expression to its *weak head normal form*.
-This is when the "head" of the top-level expression has been fully reduced.
-The result may contain subexpressions that have not been reduced.
-
-See `Lean.Meta.whnfImp` for the implementation.
--/
+/-- Reduces an expression to its Weak Head Normal Form.
+This is when the topmost expression has been fully reduced,
+but may contain subexpressions which have not been reduced. -/
 @[extern 6 "lean_whnf"] opaque whnf : Expr → MetaM Expr
-/--
-Returns the inferred type of the given expression. Assumes the expression is type-correct.
-
-The type inference algorithm does not do general type checking.
-Type inference only looks at subterms that are necessary for determining an expression's type,
-and as such if `inferType` succeeds it does *not* mean the term is type-correct.
-If an expression is sufficiently ill-formed that it prevents `inferType` from computing a type,
-then it will fail with a type error.
-
-For typechecking during elaboration, see `Lean.Meta.check`.
-(Note that we do not guarantee that the elaborator typechecker is as correct or as efficient as
-the kernel typechecker. The kernel typechecker is invoked when a definition is added to the environment.)
-
-Here are examples of type-incorrect terms for which `inferType` succeeds:
-```lean
-import Lean
-
-open Lean Meta
-
-/--
-`@id.{1} Bool Nat.zero`.
-In general, the type of `@id α x` is `α`.
--/
-def e1 : Expr := mkApp2 (.const ``id [1]) (.const ``Bool []) (.const ``Nat.zero [])
-#eval inferType e1
--- Lean.Expr.const `Bool []
-#eval check e1
--- error: application type mismatch
-
-/--
-`let x : Int := Nat.zero; true`.
-In general, the type of `let x := v; e`, if `e` does not reference `x`, is the type of `e`.
--/
-def e2 : Expr := .letE `x (.const ``Int []) (.const ``Nat.zero []) (.const ``true []) false
-#eval inferType e2
--- Lean.Expr.const `Bool []
-#eval check e2
--- error: invalid let declaration
-```
-Here is an example of a type-incorrect term that makes `inferType` fail:
-```lean
-/--
-`Nat.zero Nat.zero`
--/
-def e3 : Expr := .app (.const ``Nat.zero []) (.const ``Nat.zero [])
-#eval inferType e3
--- error: function expected
-```
-
-See `Lean.Meta.inferTypeImp` for the implementation of `inferType`.
--/
+/-- Returns the inferred type of the given expression, or fails if it is not type-correct. -/
 @[extern 6 "lean_infer_type"] opaque inferType : Expr → MetaM Expr
 @[extern 7 "lean_is_expr_def_eq"] opaque isExprDefEqAux : Expr → Expr → MetaM Bool
 @[extern 7 "lean_is_level_def_eq"] opaque isLevelDefEqAux : Level → Level → MetaM Bool

src/Lean/Meta/Check.lean

@@ -82,7 +82,7 @@ where
         return (a, b)
       else if a.getAppNumArgs != b.getAppNumArgs then
         return (a, b)
-      else if !(← isDefEq a.getAppFn b.getAppFn) then
+      else if not (← isDefEq a.getAppFn b.getAppFn) then
         return (a, b)
       else
         let fType ← inferType a.getAppFn

src/Lean/Meta/DiscrTree.lean

@@ -211,7 +211,7 @@ private def ignoreArg (a : Expr) (i : Nat) (infos : Array ParamInfo) : MetaM Boo
     if info.isInstImplicit then
       return true
     else if info.isImplicit || info.isStrictImplicit then
-      return !(← isType a)
+      return not (← isType a)
     else
       isProof a
   else

src/Lean/Meta/ExprDefEq.lean

@@ -418,7 +418,7 @@ This method assumes that for any `xs[i]` and `xs[j]` where `i < j`, we have that
 where the index is the position in the local context.
 -/
 private partial def mkLambdaFVarsWithLetDeps (xs : Array Expr) (v : Expr) : MetaM (Option Expr) := do
-  if !(← hasLetDeclsInBetween) then
+  if not (← hasLetDeclsInBetween) then
     mkLambdaFVars xs v (etaReduce := true)
   else
     let ys ← addLetDeps

src/Lean/Meta/LazyDiscrTree.lean

@@ -77,7 +77,7 @@ private def ignoreArg (a : Expr) (i : Nat) (infos : Array ParamInfo) : MetaM Boo
     if info.isInstImplicit then
       return true
     else if info.isImplicit || info.isStrictImplicit then
-      return !(← isType a)
+      return not (← isType a)
     else
       isProof a
   else

src/Lean/Meta/Match/MatcherApp/Transform.lean

@@ -199,8 +199,9 @@ Performs a possibly type-changing transformation to a `MatcherApp`.
 If `useSplitter` is true, the matcher is replaced with the splitter.
 NB: Not all operations on `MatcherApp` can handle one `matcherName` is a splitter.
 
-If `addEqualities` is true, then equalities connecting the discriminant to the parameters of the
-alternative (like in `match h : x with …`) are be added, if not already there.
+The array `addEqualities`, if provided, indicates for which of the discriminants an equality
+connecting the discriminant to the parameters of the alternative (like in `match h : x with …`)
+should be added (if it is isn't already there).
 
 This function works even if the the type of alternatives do *not* fit the inferred type. This
 allows you to post-process the `MatcherApp` with `MatcherApp.inferMatchType`, which will
@@ -211,13 +212,20 @@ def transform
     [AddMessageContext n] [MonadOptions n]
     (matcherApp : MatcherApp)
     (useSplitter := false)
-    (addEqualities : Bool := false)
+    (addEqualities : Array Bool := mkArray matcherApp.discrs.size false)
     (onParams : Expr → n Expr := pure)
     (onMotive : Array Expr → Expr → n Expr := fun _ e => pure e)
     (onAlt : Expr → Expr → n Expr := fun _ e => pure e)
     (onRemaining : Array Expr → n (Array Expr) := pure) :
     n MatcherApp := do
 
+  if addEqualities.size != matcherApp.discrs.size then
+    throwError "MatcherApp.transform: addEqualities has wrong size"
+
+  -- Do not add equalities when the matcher already does so
+  let addEqualities := Array.zipWith addEqualities matcherApp.discrInfos fun b di =>
+    if di.hName?.isSome then false else b
+
   -- We also handle CasesOn applications here, and need to treat them specially in a
   -- few places.
   -- TODO: Expand MatcherApp with the necessary fields to make this more uniform
@@ -233,26 +241,17 @@ def transform
   let params' ← matcherApp.params.mapM onParams
   let discrs' ← matcherApp.discrs.mapM onParams
 
-  let (motive', uElim, addHEqualities) ← lambdaTelescope matcherApp.motive fun motiveArgs motiveBody => do
+
+  let (motive', uElim) ← lambdaTelescope matcherApp.motive fun motiveArgs motiveBody => do
     unless motiveArgs.size == matcherApp.discrs.size do
       throwError "unexpected matcher application, motive must be lambda expression with #{matcherApp.discrs.size} arguments"
     let mut motiveBody' ← onMotive motiveArgs motiveBody
 
-    -- Prepend `(x = e) →` or `(HEq x e) → ` to the motive when an equality is requested
-    -- and not already present, and remember whether we added an Eq or a HEq
-    let mut addHEqualities : Array (Option Bool) := #[]
-    for arg in motiveArgs, discr in discrs', di in matcherApp.discrInfos do
-      if addEqualities && di.hName?.isNone then
-        if ← isProof arg then
-          addHEqualities := addHEqualities.push none
-        else
-          let heq ← mkEqHEq discr arg
-          motiveBody' ← liftMetaM <| mkArrow heq motiveBody'
-          addHEqualities := addHEqualities.push heq.isHEq
-      else
-        addHEqualities := addHEqualities.push none
+    -- Prepend (x = e) → to the motive when an equality is requested
+    for arg in motiveArgs, discr in discrs', b in addEqualities do if b then
+      motiveBody' ← liftMetaM <| mkArrow (← mkEq discr arg) motiveBody'
 
-    return (← mkLambdaFVars motiveArgs motiveBody', ← getLevel motiveBody', addHEqualities)
+    return (← mkLambdaFVars motiveArgs motiveBody', ← getLevel motiveBody')
 
   let matcherLevels ← match matcherApp.uElimPos? with
     | none     => pure matcherApp.matcherLevels
@@ -262,14 +261,15 @@ def transform
   -- (and count them along the way)
   let mut remaining' := #[]
   let mut extraEqualities : Nat := 0
-  for discr in discrs'.reverse, b in addHEqualities.reverse do
-    match b with
-    | none => pure ()
-    | some is_heq =>
-        remaining' := remaining'.push (← (if is_heq then mkHEqRefl else mkEqRefl) discr)
-        extraEqualities := extraEqualities + 1
+  for discr in discrs'.reverse, b in addEqualities.reverse do if b then
+    remaining' := remaining'.push (← mkEqRefl discr)
+    extraEqualities := extraEqualities + 1
 
   if useSplitter && !isCasesOn then
+    -- We replace the matcher with the splitter
+    let matchEqns ← Match.getEquationsFor matcherApp.matcherName
+    let splitter := matchEqns.splitterName
+
     let aux1 := mkAppN (mkConst matcherApp.matcherName matcherLevels.toList) params'
     let aux1 := mkApp aux1 motive'
     let aux1 := mkAppN aux1 discrs'
@@ -278,10 +278,6 @@ def transform
       check aux1
     let origAltTypes ← inferArgumentTypesN matcherApp.alts.size aux1
 
-    -- We replace the matcher with the splitter
-    let matchEqns ← Match.getEquationsFor matcherApp.matcherName
-    let splitter := matchEqns.splitterName
-
     let aux2 := mkAppN (mkConst splitter matcherLevels.toList) params'
     let aux2 := mkApp aux2 motive'
     let aux2 := mkAppN aux2 discrs'

src/Lean/Meta/Tactic/FunInd.lean

@@ -8,6 +8,7 @@ prelude
 import Lean.Meta.Basic
 import Lean.Meta.Match.MatcherApp.Transform
 import Lean.Meta.Check
+import Lean.Meta.Tactic.Cleanup
 import Lean.Meta.Tactic.Subst
 import Lean.Meta.Injective -- for elimOptParam
 import Lean.Meta.ArgsPacker
@@ -401,51 +402,19 @@ def assertIHs (vals : Array Expr) (mvarid : MVarId) : MetaM MVarId := do
     mvarid ← mvarid.assert (.mkSimple s!"ih{i+1}") (← inferType v) v
   return mvarid
 
+
 /--
-Goal cleanup:
-Substitutes equations (with `substVar`) to remove superfluous varialbes, and clears unused
-let bindings.
-
-Substitutes from the outside in so that the inner-bound variable name wins, but does a first pass
-looking only at variables with names with macro scope, so that preferably they disappear.
-
-Careful to only touch the context after the motives (given by the index) as the motive could depend
-on anything before, and `substVar` would happily drop equations about these fixed parameters.
+Substitutes equations, but makes sure to only substitute variables introduced after the motives
+(given by the index) as the motive could depend on anything before, and `substVar` would happily
+drop equations about these fixed parameters.
 -/
-partial def cleanupAfter (mvarId : MVarId) (index : Nat) : MetaM MVarId := do
-  let mvarId ← go mvarId index true
-  let mvarId ← go mvarId index false
-  return mvarId
-where
-  go (mvarId : MVarId) (index : Nat) (firstPass : Bool) : MetaM MVarId := do
-    if let some mvarId ← cleanupAfter? mvarId index firstPass then
-      go mvarId index firstPass
-    else
-      return mvarId
-
-  allHeqToEq (mvarId : MVarId) (index : Nat) : MetaM MVarId :=
-    mvarId.withContext do
-      let mut mvarId := mvarId
-      for localDecl in (← getLCtx) do
-        if localDecl.index > index then
-          let (_, mvarId') ← heqToEq mvarId localDecl.fvarId
-          mvarId := mvarId'
-      return mvarId
-
-  cleanupAfter? (mvarId : MVarId) (index : Nat) (firstPass : Bool)  : MetaM (Option MVarId) := do
-    mvarId.withContext do
-      for localDecl in (← getLCtx) do
-        if localDecl.index > index && (!firstPass || localDecl.userName.hasMacroScopes) then
-          if localDecl.isLet then
-            if let some mvarId' ← observing? <| mvarId.clear localDecl.fvarId then
-              return some mvarId'
-          if let some mvarId' ← substVar? mvarId localDecl.fvarId then
-            -- After substituting, some HEq might turn into Eqs, and we want to be able to substitute
-            -- them as well
-            let mvarId' ← allHeqToEq mvarId' index
-            return some mvarId'
-      return none
-
+def substVarAfter (mvarId : MVarId) (index : Nat) : MetaM MVarId := do
+  mvarId.withContext do
+    let mut mvarId := mvarId
+    for localDecl in (← getLCtx) do
+      if localDecl.index > index then
+        mvarId ← trySubstVar mvarId localDecl.fvarId
+    return mvarId
 
 /--
 Second helper monad collecting the cases as mvars
@@ -460,7 +429,7 @@ def M2.branch {α} (act : M2 α) : M2 α :=
 
 
 /-- Base case of `buildInductionBody`: Construct a case for the final induction hypthesis.  -/
-def buildInductionCase (oldIH newIH : FVarId) (isRecCall : Expr → Option Expr) (toClear : Array FVarId)
+def buildInductionCase (oldIH newIH : FVarId) (isRecCall : Expr → Option Expr) (toClear toPreserve : Array FVarId)
     (goal : Expr)  (e : Expr) : M2 Expr := do
   let _e' ← foldAndCollect oldIH newIH isRecCall e
   let IHs : Array Expr ← M.ask
@@ -469,9 +438,9 @@ def buildInductionCase (oldIH newIH : FVarId) (isRecCall : Expr → Option Expr)
   let mvar ← mkFreshExprSyntheticOpaqueMVar goal (tag := `hyp)
   let mut mvarId := mvar.mvarId!
   mvarId ← assertIHs IHs mvarId
-  trace[Meta.FunInd] "Goal before cleanup:{mvarId}"
   for fvarId in toClear do
     mvarId ← mvarId.clear fvarId
+  mvarId ← mvarId.cleanup (toPreserve := toPreserve)
   modify (·.push mvarId)
   let mvar ← instantiateMVars mvar
   pure mvar
@@ -486,7 +455,7 @@ Like `mkLambdaFVars (usedOnly := true)`, but
 The result `r` can be applied with `r.beta (maskArray mask args)`.
 
 We use this when generating the functional induction principle to refine the goal through a `match`,
-here `xs` are the discriminants of the `match`.
+here `xs` are the discriminans of the `match`.
 We do not expect non-trivial discriminants to appear in the goal (and if they do, the user will
 get a helpful equality into the context).
 -/
@@ -516,7 +485,7 @@ Builds an expression of type `goal` by replicating the expression `e` into its t
 where it calls `buildInductionCase`. Collects the cases of the final induction hypothesis
 as `MVars` as it goes.
 -/
-partial def buildInductionBody (toClear : Array FVarId) (goal : Expr)
+partial def buildInductionBody (toClear toPreserve : Array FVarId) (goal : Expr)
     (oldIH newIH : FVarId) (isRecCall : Expr → Option Expr) (e : Expr) : M2 Expr := do
 
   -- if-then-else cause case split:
@@ -525,10 +494,10 @@ partial def buildInductionBody (toClear : Array FVarId) (goal : Expr)
     let c' ← foldAndCollect oldIH newIH isRecCall c
     let h' ← foldAndCollect oldIH newIH isRecCall h
     let t' ← withLocalDecl `h .default c' fun h => M2.branch do
-      let t' ← buildInductionBody toClear goal oldIH newIH isRecCall t
+      let t' ← buildInductionBody toClear (toPreserve.push h.fvarId!) goal oldIH newIH isRecCall t
       mkLambdaFVars #[h] t'
     let f' ← withLocalDecl `h .default (mkNot c') fun h => M2.branch do
-      let f' ← buildInductionBody toClear goal oldIH newIH isRecCall f
+      let f' ← buildInductionBody toClear (toPreserve.push h.fvarId!) goal oldIH newIH isRecCall f
       mkLambdaFVars #[h] f'
     let u ← getLevel goal
     return mkApp5 (mkConst ``dite [u]) goal c' h' t' f'
@@ -537,11 +506,11 @@ partial def buildInductionBody (toClear : Array FVarId) (goal : Expr)
     let h' ← foldAndCollect oldIH newIH isRecCall h
     let t' ← withLocalDecl `h .default c' fun h => M2.branch do
       let t ← instantiateLambda t #[h]
-      let t' ← buildInductionBody toClear goal oldIH newIH isRecCall t
+      let t' ← buildInductionBody toClear (toPreserve.push h.fvarId!) goal oldIH newIH isRecCall t
       mkLambdaFVars #[h] t'
     let f' ← withLocalDecl `h .default (mkNot c') fun h => M2.branch do
       let f ← instantiateLambda f #[h]
-      let f' ← buildInductionBody toClear goal oldIH newIH isRecCall f
+      let f' ← buildInductionBody toClear (toPreserve.push h.fvarId!) goal oldIH newIH isRecCall f
       mkLambdaFVars #[h] f'
     let u ← getLevel goal
     return mkApp5 (mkConst ``dite [u]) goal c' h' t' f'
@@ -552,8 +521,8 @@ partial def buildInductionBody (toClear : Array FVarId) (goal : Expr)
   match_expr goal with
   | And goal₁ goal₂ => match_expr e with
     | PProd.mk _α _β e₁ e₂ =>
-      let e₁' ← buildInductionBody toClear goal₁ oldIH newIH isRecCall e₁
-      let e₂' ← buildInductionBody toClear goal₂ oldIH newIH isRecCall e₂
+      let e₁' ← buildInductionBody toClear toPreserve goal₁ oldIH newIH isRecCall e₁
+      let e₂' ← buildInductionBody toClear toPreserve goal₂ oldIH newIH isRecCall e₂
       return mkApp4 (.const ``And.intro []) goal₁ goal₂ e₁' e₂'
     | _ =>
       throwError "Goal is PProd, but expression is:{indentExpr e}"
@@ -572,14 +541,14 @@ partial def buildInductionBody (toClear : Array FVarId) (goal : Expr)
     -- so we need to replace that IH
     if matcherApp.remaining.size == 1 && matcherApp.remaining[0]!.isFVarOf oldIH then
       let matcherApp' ← matcherApp.transform (useSplitter := true)
-        (addEqualities := true)
+        (addEqualities := mask.map not)
         (onParams := (foldAndCollect oldIH newIH isRecCall ·))
         (onMotive := fun xs _body => pure (absMotiveBody.beta (maskArray mask xs)))
         (onAlt := fun expAltType alt => M2.branch do
           removeLamda alt fun oldIH' alt => do
             forallBoundedTelescope expAltType (some 1) fun newIH' goal' => do
               let #[newIH'] := newIH' | unreachable!
-              let alt' ← buildInductionBody (toClear.push newIH'.fvarId!) goal' oldIH' newIH'.fvarId! isRecCall alt
+              let alt' ← buildInductionBody (toClear.push newIH'.fvarId!) toPreserve goal' oldIH' newIH'.fvarId! isRecCall alt
               mkLambdaFVars #[newIH'] alt')
         (onRemaining := fun _ => pure #[.fvar newIH])
       return matcherApp'.toExpr
@@ -591,34 +560,32 @@ partial def buildInductionBody (toClear : Array FVarId) (goal : Expr)
       let (mask, absMotiveBody) ← mkLambdaFVarsMasked matcherApp.discrs goal
 
       let matcherApp' ← matcherApp.transform (useSplitter := true)
-        (addEqualities := true)
+        (addEqualities := mask.map not)
         (onParams := (foldAndCollect oldIH newIH isRecCall ·))
         (onMotive := fun xs _body => pure (absMotiveBody.beta (maskArray mask xs)))
         (onAlt := fun expAltType alt => M2.branch do
-          buildInductionBody toClear expAltType oldIH newIH isRecCall alt)
+          buildInductionBody toClear toPreserve expAltType oldIH newIH isRecCall alt)
       return matcherApp'.toExpr
 
   if let .letE n t v b _ := e then
     let t' ← foldAndCollect oldIH newIH isRecCall t
     let v' ← foldAndCollect oldIH newIH isRecCall v
     return ← withLetDecl n t' v' fun x => M2.branch do
-      let b' ← buildInductionBody toClear goal oldIH newIH isRecCall (b.instantiate1 x)
+      let b' ← buildInductionBody toClear toPreserve goal oldIH newIH isRecCall (b.instantiate1 x)
       mkLetFVars #[x] b'
 
   if let some (n, t, v, b) := e.letFun? then
     let t' ← foldAndCollect oldIH newIH isRecCall t
     let v' ← foldAndCollect oldIH newIH isRecCall v
     return ← withLocalDecl n .default t' fun x => M2.branch do
-      let b' ← buildInductionBody toClear goal oldIH newIH isRecCall (b.instantiate1 x)
+      let b' ← buildInductionBody toClear toPreserve goal oldIH newIH isRecCall (b.instantiate1 x)
       mkLetFun x v' b'
 
-  liftM <| buildInductionCase oldIH newIH isRecCall toClear goal e
+  liftM <| buildInductionCase oldIH newIH isRecCall toClear toPreserve goal e
 
 /--
-Given an expression `e` with metavariables `mvars`
-* performs more cleanup:
-  * removes unused let-expressions after index `index`
-  * tries to substitute variables after index `index`
+Given an expression `e` with metavariables
+* collects all these meta-variables,
 * lifts them to the current context by reverting all local declarations after index `index`
 * introducing a local variable for each of the meta variable
 * assigning that local variable to the mvar
@@ -636,7 +603,7 @@ do not handle delayed assignemnts correctly.
 def abstractIndependentMVars (mvars : Array MVarId) (index : Nat) (e : Expr) : MetaM Expr := do
   trace[Meta.FunInd] "abstractIndependentMVars, to revert after {index}, original mvars: {mvars}"
   let mvars ← mvars.mapM fun mvar => do
-    let mvar ← cleanupAfter mvar index
+    let mvar ← substVarAfter mvar index
     mvar.withContext do
       let fvarIds := (← getLCtx).foldl (init := #[]) (start := index+1) fun fvarIds decl => fvarIds.push decl.fvarId
       let (_, mvar) ← mvar.revert fvarIds
@@ -693,7 +660,7 @@ def deriveUnaryInduction (name : Name) : MetaM Name := do
             let body ← instantiateLambda body targets
             removeLamda body fun oldIH body => do
               let body ← instantiateLambda body extraParams
-              let body' ← buildInductionBody #[genIH.fvarId!] goal oldIH genIH.fvarId! isRecCall body
+              let body' ← buildInductionBody #[genIH.fvarId!] #[] goal oldIH genIH.fvarId! isRecCall body
               if body'.containsFVar oldIH then
                 throwError m!"Did not fully eliminate {mkFVar oldIH} from induction principle body:{indentExpr body}"
               mkLambdaFVars (targets.push genIH) (← mkLambdaFVars extraParams body')
@@ -1003,7 +970,7 @@ def deriveInductionStructural (names : Array Name) (numFixed : Nat) : MetaM Unit
                 removeLamda body fun oldIH body => do
                   trace[Meta.FunInd] "replacing {Expr.fvar oldIH} with {genIH}"
                   let body ← instantiateLambda body extraParams
-                  let body' ← buildInductionBody #[genIH.fvarId!] goal oldIH genIH.fvarId! isRecCall body
+                  let body' ← buildInductionBody #[genIH.fvarId!] #[] goal oldIH genIH.fvarId! isRecCall body
                   if body'.containsFVar oldIH then
                     throwError m!"Did not fully eliminate {mkFVar oldIH} from induction principle body:{indentExpr body}"
                   mkLambdaFVars (targets.push genIH) (← mkLambdaFVars extraParams body')

src/Lean/Meta/Tactic/Simp/BuiltinSimprocs/BitVec.lean

@@ -51,7 +51,7 @@ Helper function for reducing homogenous binary bitvector operators.
   else
     return .continue
 
-/-- Simplification procedure for `setWidth`, `zeroExtend` and `signExtend` on `BitVec`s. -/
+/-- Simplification procedure for `zeroExtend` and `signExtend` on `BitVec`s. -/
 @[inline] def reduceExtend (declName : Name)
     (op : {n : Nat} → (m : Nat) → BitVec n → BitVec m) (e : Expr) : SimpM DStep := do
   unless e.isAppOfArity declName 3 do return .continue
@@ -253,13 +253,13 @@ builtin_dsimproc [simp, seval] reduceSLT (BitVec.slt _ _) :=
 builtin_dsimproc [simp, seval] reduceSLE (BitVec.sle _ _) :=
   reduceBoolPred ``BitVec.sle 3 BitVec.sle
 
-/-- Simplification procedure for `setWidth'` on `BitVec`s. -/
-builtin_dsimproc [simp, seval] reduceSetWidth' (setWidth' _ _) := fun e => do
-  let_expr setWidth' _ w _ v ← e | return .continue
+/-- Simplification procedure for `zeroExtend'` on `BitVec`s. -/
+builtin_dsimproc [simp, seval] reduceZeroExtend' (zeroExtend' _ _) := fun e => do
+  let_expr zeroExtend' _ w _ v ← e | return .continue
   let some v ← fromExpr? v | return .continue
   let some w ← Nat.fromExpr? w | return .continue
   if h : v.n ≤ w then
-    return .done <| toExpr (v.value.setWidth' h)
+    return .done <| toExpr (v.value.zeroExtend' h)
   else
     return .continue
 
@@ -285,9 +285,6 @@ builtin_dsimproc [simp, seval] reduceReplicate (replicate _ _) := fun e => do
   let some i ← Nat.fromExpr? i | return .continue
   return .done <| toExpr (v.value.replicate i)
 
-/-- Simplification procedure for `setWidth` on `BitVec`s. -/
-builtin_dsimproc [simp, seval] reduceSetWidth (setWidth _ _) := reduceExtend ``setWidth setWidth
-
 /-- Simplification procedure for `zeroExtend` on `BitVec`s. -/
 builtin_dsimproc [simp, seval] reduceZeroExtend (zeroExtend _ _) := reduceExtend ``zeroExtend zeroExtend
 

src/Lean/Meta/Tactic/Simp/BuiltinSimprocs/Fin.lean

@@ -77,9 +77,8 @@ builtin_dsimproc [simp, seval] reduceFinMk (Fin.mk _ _)  := fun e => do
   let_expr Fin.mk n v _ ← e | return .continue
   let some n ← evalNat n |>.run | return .continue
   let some v ← getNatValue? v | return .continue
-  if h : n ≠ 0 then
-    have : NeZero n := ⟨h⟩
-    return .done <| toExpr (Fin.ofNat' n v)
+  if h : n > 0 then
+    return .done <| toExpr (Fin.ofNat' v h)
   else
     return .continue
 

src/Lean/Meta/Tactic/Simp/BuiltinSimprocs/Int.lean

@@ -71,8 +71,8 @@ builtin_dsimproc [simp, seval] reduceMul ((_ * _ : Int)) := reduceBin ``HMul.hMu
 builtin_dsimproc [simp, seval] reduceSub ((_ - _ : Int)) := reduceBin ``HSub.hSub 6 (· - ·)
 builtin_dsimproc [simp, seval] reduceDiv ((_ / _ : Int)) := reduceBin ``HDiv.hDiv 6 (· / ·)
 builtin_dsimproc [simp, seval] reduceMod ((_ % _ : Int)) := reduceBin ``HMod.hMod 6 (· % ·)
-builtin_dsimproc [simp, seval] reduceTDiv (tdiv  _ _) := reduceBin ``Int.div 2 Int.tdiv
-builtin_dsimproc [simp, seval] reduceTMod (tmod  _ _) := reduceBin ``Int.mod 2 Int.tmod
+builtin_dsimproc [simp, seval] reduceTDiv (div  _ _) := reduceBin ``Int.div 2 Int.div
+builtin_dsimproc [simp, seval] reduceTMod (mod  _ _) := reduceBin ``Int.mod 2 Int.mod
 builtin_dsimproc [simp, seval] reduceFDiv (fdiv _ _) := reduceBin ``Int.fdiv 2 Int.fdiv
 builtin_dsimproc [simp, seval] reduceFMod (fmod _ _) := reduceBin ``Int.fmod 2 Int.fmod
 builtin_dsimproc [simp, seval] reduceBdiv (bdiv _ _) := reduceBinIntNatOp ``bdiv bdiv

src/Lean/Meta/Tactic/Unfold.lean

@@ -43,16 +43,4 @@ def unfoldLocalDecl (mvarId : MVarId) (fvarId : FVarId) (declName : Name) : Meta
   let some (_, mvarId) ← applySimpResultToLocalDecl mvarId fvarId r (mayCloseGoal := false) | unreachable!
   return mvarId
 
-def zetaDeltaTarget (mvarId : MVarId) (declFVarId : FVarId) : MetaM MVarId := mvarId.withContext do
-  let target ← instantiateMVars (← mvarId.getType)
-  let target' ← Meta.zetaDeltaFVars target #[declFVarId]
-  if target' == target then throwError "tactic 'unfold' failed to unfold '{Expr.fvar declFVarId}' at{indentExpr target}"
-  mvarId.replaceTargetDefEq target'
-
-def zetaDeltaLocalDecl (mvarId : MVarId) (fvarId : FVarId) (declFVarId : FVarId) : MetaM MVarId := mvarId.withContext do
-  let type ← fvarId.getType
-  let type' ← Meta.zetaDeltaFVars (← instantiateMVars type) #[declFVarId]
-  if type' == type then throwError "tactic 'unfold' failed to unfold '{Expr.fvar fvarId}' at{indentExpr type}"
-  mvarId.replaceLocalDeclDefEq fvarId type'
-
 end Lean.Meta