chore: avoid runtime array bounds checks

.github/workflows/check-prelude.yml

@@ -14,7 +14,6 @@ jobs:
           sparse-checkout: |
             src/Lean
             src/Std
-            src/lake/Lake
       - name: Check Prelude
         run: |
           failed_files=""
@@ -22,7 +21,7 @@ jobs:
             if ! grep -q "^prelude$" "$file"; then
               failed_files="$failed_files$file\n"
             fi
-          done < <(find src/Lean src/Std src/lake/Lake -name '*.lean' -print0)
+          done < <(find src/Lean src/Std -name '*.lean' -print0)
           if [ -n "$failed_files" ]; then
             echo -e "The following files should use 'prelude':\n$failed_files"
             exit 1

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

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

.github/workflows/pr-release.yml

@@ -34,7 +34,7 @@ jobs:
       - name: Download artifact from the previous workflow.
         if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
         id: download-artifact
-        uses: dawidd6/action-download-artifact@v7 # https://github.com/marketplace/actions/download-workflow-artifact
+        uses: dawidd6/action-download-artifact@v6 # https://github.com/marketplace/actions/download-workflow-artifact
         with:
           run_id: ${{ github.event.workflow_run.id }}
           path: artifacts
@@ -111,7 +111,7 @@ jobs:
 
       - name: 'Setup jq'
         if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
-        uses: dcarbone/install-jq-action@v3.0.1
+        uses: dcarbone/install-jq-action@v2.1.0
 
       # Check that the most recently nightly coincides with 'git merge-base HEAD master'
       - name: Check merge-base and nightly-testing-YYYY-MM-DD

RELEASES.md

@@ -8,15 +8,10 @@ This file contains work-in-progress notes for the upcoming release, as well as p
 Please check the [releases](https://github.com/leanprover/lean4/releases) page for the current status
 of each version.
 
-v4.16.0
-----------
-
-Development in progress.
-
 v4.15.0
 ----------
 
-Release candidate, release notes will be copied from the branch `releases/v4.15.0` once completed.
+Development in progress.
 
 v4.14.0
 ----------
@@ -93,7 +88,7 @@ v4.13.0
   * [#4768](https://github.com/leanprover/lean4/pull/4768) fixes a parse error when `..` appears with a `.` on the next line
 
 * Metaprogramming
-  * [#3090](https://github.com/leanprover/lean4/pull/3090) handles level parameters in `Meta.evalExpr` (@eric-wieser)
+  * [#3090](https://github.com/leanprover/lean4/pull/3090) handles level parameters in `Meta.evalExpr` (@eric-wieser)  
   * [#5401](https://github.com/leanprover/lean4/pull/5401) instance for `Inhabited (TacticM α)` (@alexkeizer)
   * [#5412](https://github.com/leanprover/lean4/pull/5412) expose Kernel.check for debugging purposes
   * [#5556](https://github.com/leanprover/lean4/pull/5556) improves the "invalid projection" type inference error in `inferType`.

debug.log

@@ -0,0 +1 @@
+[0829/202002.254:ERROR:crashpad_client_win.cc(868)] not connected

doc/dev/bootstrap.md

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

doc/examples/interp.lean

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

doc/examples/tc.lean

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

doc/examples/test_single.sh

@@ -1,4 +1,4 @@
 #!/usr/bin/env bash
 source ../../tests/common.sh
 
-exec_check_raw lean -Dlinter.all=false "$f"
+exec_check lean -Dlinter.all=false "$f"

script/mathlib-bench

@@ -1,12 +0,0 @@
-#! /bin/env bash
-# Open a Mathlib4 PR for benchmarking a given Lean 4 PR
-
-set -euo pipefail
-
-[ $# -eq 1 ] || (echo "usage: $0 <lean4 PR #>"; exit 1)
-
-LEAN_PR=$1
-PR_RESPONSE=$(gh api repos/leanprover-community/mathlib4/pulls -X POST -f head=lean-pr-testing-$LEAN_PR -f base=nightly-testing -f title="leanprover/lean4#$LEAN_PR benchmarking" -f draft=true -f body="ignore me")
-PR_NUMBER=$(echo "$PR_RESPONSE" | jq '.number')
-echo "opened https://github.com/leanprover-community/mathlib4/pull/$PR_NUMBER"
-gh api repos/leanprover-community/mathlib4/issues/$PR_NUMBER/comments -X POST -f body="!bench" > /dev/null

src/CMakeLists.txt

@@ -10,7 +10,7 @@ endif()
 include(ExternalProject)
 project(LEAN CXX C)
 set(LEAN_VERSION_MAJOR 4)
-set(LEAN_VERSION_MINOR 16)
+set(LEAN_VERSION_MINOR 15)
 set(LEAN_VERSION_PATCH 0)
 set(LEAN_VERSION_IS_RELEASE 0)  # This number is 1 in the release revision, and 0 otherwise.
 set(LEAN_SPECIAL_VERSION_DESC "" CACHE STRING "Additional version description like 'nightly-2018-03-11'")
@@ -51,8 +51,6 @@ option(LLVM               "LLVM"               OFF)
 option(USE_GITHASH        "GIT_HASH"           ON)
 # When ON we install LICENSE files to CMAKE_INSTALL_PREFIX
 option(INSTALL_LICENSE "INSTALL_LICENSE" ON)
-# When ON we install a copy of cadical
-option(INSTALL_CADICAL "Install a copy of cadical" ON)
 # When ON thread storage is automatically finalized, it assumes platform support pthreads.
 # This option is important when using Lean as library that is invoked from a different programming language (e.g., Haskell).
 option(AUTO_THREAD_FINALIZATION "AUTO_THREAD_FINALIZATION" ON)
@@ -122,7 +120,7 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
     # From https://emscripten.org/docs/compiling/WebAssembly.html#backends:
     # > The simple and safe thing is to pass all -s flags at both compile and link time.
     set(EMSCRIPTEN_SETTINGS "-s ALLOW_MEMORY_GROWTH=1 -fwasm-exceptions -pthread -flto")
-    string(APPEND LEANC_EXTRA_CC_FLAGS " -pthread")
+    string(APPEND LEANC_EXTRA_FLAGS " -pthread")
     string(APPEND LEAN_EXTRA_CXX_FLAGS " -D LEAN_EMSCRIPTEN ${EMSCRIPTEN_SETTINGS}")
     string(APPEND LEAN_EXTRA_LINKER_FLAGS " ${EMSCRIPTEN_SETTINGS}")
 endif()
@@ -157,11 +155,11 @@ if ((${MULTI_THREAD} MATCHES "ON") AND (${CMAKE_SYSTEM_NAME} MATCHES "Darwin"))
 endif ()
 
 # We want explicit stack probes in huge Lean stack frames for robust stack overflow detection
-string(APPEND LEANC_EXTRA_CC_FLAGS " -fstack-clash-protection")
+string(APPEND LEANC_EXTRA_FLAGS " -fstack-clash-protection")
 
 # This makes signed integer overflow guaranteed to match 2's complement.
 string(APPEND CMAKE_CXX_FLAGS " -fwrapv")
-string(APPEND LEANC_EXTRA_CC_FLAGS " -fwrapv")
+string(APPEND LEANC_EXTRA_FLAGS " -fwrapv")
 
 if(NOT MULTI_THREAD)
   message(STATUS "Disabled multi-thread support, it will not be safe to run multiple threads in parallel")
@@ -451,7 +449,7 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Linux")
     string(APPEND TOOLCHAIN_SHARED_LINKER_FLAGS " -Wl,-Bsymbolic")
   endif()
   string(APPEND CMAKE_CXX_FLAGS " -fPIC -ftls-model=initial-exec")
-  string(APPEND LEANC_EXTRA_CC_FLAGS " -fPIC")
+  string(APPEND LEANC_EXTRA_FLAGS " -fPIC")
   string(APPEND TOOLCHAIN_SHARED_LINKER_FLAGS " -Wl,-rpath=\\$$ORIGIN/..:\\$$ORIGIN")
   string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libLake.a.export -Wl,--no-whole-archive")
   string(APPEND CMAKE_EXE_LINKER_FLAGS " -Wl,-rpath=\\\$ORIGIN/../lib:\\\$ORIGIN/../lib/lean")
@@ -464,7 +462,7 @@ elseif(${CMAKE_SYSTEM_NAME} MATCHES "Darwin")
   string(APPEND CMAKE_EXE_LINKER_FLAGS " -Wl,-rpath,@executable_path/../lib -Wl,-rpath,@executable_path/../lib/lean")
 elseif(${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
   string(APPEND CMAKE_CXX_FLAGS " -fPIC")
-  string(APPEND LEANC_EXTRA_CC_FLAGS " -fPIC")
+  string(APPEND LEANC_EXTRA_FLAGS " -fPIC")
 elseif(${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 ${CMAKE_BINARY_DIR}/lib/temp/libLake.a.export -Wl,--no-whole-archive")
 endif()
@@ -479,7 +477,7 @@ if(NOT(${CMAKE_SYSTEM_NAME} MATCHES "Windows") AND NOT(${CMAKE_SYSTEM_NAME} MATC
   string(APPEND CMAKE_EXE_LINKER_FLAGS " -rdynamic")
   # hide all other symbols
   string(APPEND CMAKE_CXX_FLAGS " -fvisibility=hidden -fvisibility-inlines-hidden")
-  string(APPEND LEANC_EXTRA_CC_FLAGS " -fvisibility=hidden")
+  string(APPEND LEANC_EXTRA_FLAGS " -fvisibility=hidden")
 endif()
 
 # On Windows, add bcrypt for random number generation
@@ -544,10 +542,9 @@ include_directories(${CMAKE_BINARY_DIR}/include)  # config.h etc., "public" head
 string(TOUPPER "${CMAKE_BUILD_TYPE}" uppercase_CMAKE_BUILD_TYPE)
 string(APPEND LEANC_OPTS " ${CMAKE_CXX_FLAGS_${uppercase_CMAKE_BUILD_TYPE}}")
 
-# Do embed flag for finding system headers and libraries in dev builds
+# Do embed flag for finding system libraries in dev builds
 if(CMAKE_OSX_SYSROOT AND NOT LEAN_STANDALONE)
-  string(APPEND LEANC_EXTRA_CC_FLAGS " ${CMAKE_CXX_SYSROOT_FLAG}${CMAKE_OSX_SYSROOT}")
-  string(APPEND LEAN_EXTRA_LINKER_FLAGS " ${CMAKE_CXX_SYSROOT_FLAG}${CMAKE_OSX_SYSROOT}")
+  string(APPEND LEANC_EXTRA_FLAGS " ${CMAKE_CXX_SYSROOT_FLAG}${CMAKE_OSX_SYSROOT}")
 endif()
 
 add_subdirectory(initialize)
@@ -619,7 +616,7 @@ else()
     OUTPUT_NAME leancpp)
 endif()
 
-if((${STAGE} GREATER 0) AND CADICAL AND INSTALL_CADICAL)
+if((${STAGE} GREATER 0) AND CADICAL)
   add_custom_target(copy-cadical
     COMMAND cmake -E copy_if_different "${CADICAL}" "${CMAKE_BINARY_DIR}/bin/cadical${CMAKE_EXECUTABLE_SUFFIX}")
   add_dependencies(leancpp copy-cadical)
@@ -741,7 +738,7 @@ file(COPY ${LEAN_SOURCE_DIR}/bin/leanmake DESTINATION ${CMAKE_BINARY_DIR}/bin)
 
 install(DIRECTORY "${CMAKE_BINARY_DIR}/bin/" USE_SOURCE_PERMISSIONS DESTINATION bin)
 
-if (${STAGE} GREATER 0 AND CADICAL AND INSTALL_CADICAL)
+if (${STAGE} GREATER 0 AND CADICAL)
   install(PROGRAMS "${CADICAL}" DESTINATION bin)
 endif()
 

src/Init/Data.lean

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

src/Init/Data/Array.lean

@@ -19,6 +19,3 @@ import Init.Data.Array.GetLit
 import Init.Data.Array.MapIdx
 import Init.Data.Array.Set
 import Init.Data.Array.Monadic
-import Init.Data.Array.FinRange
-import Init.Data.Array.Perm
-import Init.Data.Array.Find

src/Init/Data/Array/Attach.lean

@@ -251,7 +251,7 @@ theorem getElem?_attach {xs : Array α} {i : Nat} :
 theorem getElem_attachWith {xs : Array α} {P : α → Prop} {H : ∀ a ∈ xs, P a}
     {i : Nat} (h : i < (xs.attachWith P H).size) :
     (xs.attachWith P H)[i] = ⟨xs[i]'(by simpa using h), H _ (getElem_mem (by simpa using h))⟩ :=
-  getElem_pmap _ _ h
+  getElem_pmap ..
 
 @[simp]
 theorem getElem_attach {xs : Array α} {i : Nat} (h : i < xs.attach.size) :

src/Init/Data/Array/Basic.lean

@@ -13,7 +13,6 @@ import Init.Data.ToString.Basic
 import Init.GetElem
 import Init.Data.List.ToArray
 import Init.Data.Array.Set
-
 universe u v w
 
 /-! ### Array literal syntax -/
@@ -166,15 +165,15 @@ This will perform the update destructively provided that `a` has a reference
 count of 1 when called.
 -/
 @[extern "lean_array_fswap"]
-def swap (a : Array α) (i j : @& Nat) (hi : i < a.size := by get_elem_tactic) (hj : j < a.size := by get_elem_tactic) : Array α :=
+def swap (a : Array α) (i j : @& Fin a.size) : Array α :=
   let v₁ := a[i]
   let v₂ := a[j]
   let a'  := a.set i v₂
-  a'.set j v₁ (Nat.lt_of_lt_of_eq hj (size_set a i v₂ _).symm)
+  a'.set j v₁ (Nat.lt_of_lt_of_eq j.isLt (size_set a i v₂ _).symm)
 
-@[simp] theorem size_swap (a : Array α) (i j : Nat) {hi hj} : (a.swap i j hi hj).size = a.size := by
+@[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[j]).set j a[i]
-    (Nat.lt_of_lt_of_eq hj (size_set a i a[j] _).symm)).size = a.size
+    (Nat.lt_of_lt_of_eq j.isLt (size_set a i a[j] _).symm)).size = a.size
   rw [size_set, size_set]
 
 /--
@@ -184,14 +183,12 @@ This will perform the update destructively provided that `a` has a reference
 count of 1 when called.
 -/
 @[extern "lean_array_swap"]
-def swapIfInBounds (a : Array α) (i j : @& Nat) : Array α :=
+def swap! (a : Array α) (i j : @& Nat) : Array α :=
   if h₁ : i < a.size then
-  if h₂ : j < a.size then swap a i j
+  if h₂ : j < a.size then swap a ⟨i, h₁⟩ ⟨j, h₂⟩
   else a
   else a
 
-@[deprecated swapIfInBounds (since := "2024-11-24")] abbrev swap! := @swapIfInBounds
-
 /-! ### GetElem instance for `USize`, backed by `uget` -/
 
 instance : GetElem (Array α) USize α fun xs i => i.toNat < xs.size where
@@ -236,7 +233,7 @@ def ofFn {n} (f : Fin n → α) : Array α := go 0 (mkEmpty n) where
 
 /-- The array `#[0, 1, ..., n - 1]`. -/
 def range (n : Nat) : Array Nat :=
-  ofFn fun (i : Fin n) => i
+  n.fold (flip Array.push) (mkEmpty n)
 
 def singleton (v : α) : Array α :=
   mkArray 1 v
@@ -252,7 +249,7 @@ def get? (a : Array α) (i : Nat) : Option α :=
 def back? (a : Array α) : Option α :=
   a[a.size - 1]?
 
-@[inline] def swapAt (a : Array α) (i : Nat) (v : α) (hi : i < a.size := by get_elem_tactic) : α × Array α :=
+@[inline] def swapAt (a : Array α) (i : Fin a.size) (v : α) : α × Array α :=
   let e := a[i]
   let a := a.set i v
   (e, a)
@@ -260,7 +257,7 @@ def back? (a : Array α) : Option α :=
 @[inline]
 def swapAt! (a : Array α) (i : Nat) (v : α) : α × Array α :=
   if h : i < a.size then
-    swapAt a i v
+    swapAt a ⟨i, h⟩ v
   else
     have : Inhabited (α × Array α) := ⟨(v, a)⟩
     panic! ("index " ++ toString i ++ " out of bounds")
@@ -474,10 +471,6 @@ def findSomeM? {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f
     | _      => pure ⟨⟩
   return none
 
-/--
-Note that the universe level is contrained to `Type` here,
-to avoid having to have the predicate live in `p : α → m (ULift Bool)`.
--/
 @[inline]
 def findM? {α : Type} {m : Type → Type} [Monad m] (p : α → m Bool) (as : Array α) : m (Option α) := do
   for a in as do
@@ -589,12 +582,8 @@ def zipWithIndex (arr : Array α) : Array (α × Nat) :=
   arr.mapIdx fun i a => (a, i)
 
 @[inline]
-def find? {α : Type u} (p : α → Bool) (as : Array α) : Option α :=
-  Id.run do
-    for a in as do
-      if p a then
-        return a
-    return none
+def find? {α : Type} (p : α → Bool) (as : Array α) : Option α :=
+  Id.run <| as.findM? p
 
 @[inline]
 def findSome? {α : Type u} {β : Type v} (f : α → Option β) (as : Array α) : Option β :=
@@ -624,15 +613,8 @@ def findIdx? {α : Type u} (p : α → Bool) (as : Array α) : Option Nat :=
     decreasing_by simp_wf; decreasing_trivial_pre_omega
   loop 0
 
-@[inline]
-def findFinIdx? {α : Type u} (p : α → Bool) (as : Array α) : Option (Fin as.size) :=
-  let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
-  loop (j : Nat) :=
-    if h : j < as.size then
-      if p as[j] then some ⟨j, h⟩ else loop (j + 1)
-    else none
-    decreasing_by simp_wf; decreasing_trivial_pre_omega
-  loop 0
+def getIdx? [BEq α] (a : Array α) (v : α) : Option Nat :=
+  a.findIdx? fun a => a == v
 
 @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
 def indexOfAux [BEq α] (a : Array α) (v : α) (i : Nat) : Option (Fin a.size) :=
@@ -645,10 +627,6 @@ decreasing_by simp_wf; decreasing_trivial_pre_omega
 def indexOf? [BEq α] (a : Array α) (v : α) : Option (Fin a.size) :=
   indexOfAux a v 0
 
-@[deprecated indexOf? (since := "2024-11-20")]
-def getIdx? [BEq α] (a : Array α) (v : α) : Option Nat :=
-  a.findIdx? fun a => a == v
-
 @[inline]
 def any (as : Array α) (p : α → Bool) (start := 0) (stop := as.size) : Bool :=
   Id.run <| as.anyM p start stop
@@ -757,7 +735,7 @@ where
   loop (as : Array α) (i : Nat) (j : Fin as.size) :=
     if h : i < j then
       have := termination h
-      let as := as.swap i j (Nat.lt_trans h j.2)
+      let as := as.swap ⟨i, Nat.lt_trans h j.2⟩ j
       have : j-1 < as.size := by rw [size_swap]; exact Nat.lt_of_le_of_lt (Nat.pred_le _) j.2
       loop as (i+1) ⟨j-1, this⟩
     else
@@ -788,63 +766,49 @@ def takeWhile (p : α → Bool) (as : Array α) : Array α :=
     decreasing_by simp_wf; decreasing_trivial_pre_omega
   go 0 #[]
 
-/--
-Remove the element at a given index from an array without a runtime bounds checks,
-using a `Nat` index and a tactic-provided bound.
+/-- Remove the element at a given index from an array without bounds checks, using a `Fin` index.
 
-This function takes worst case O(n) time because
-it has to backshift all elements at positions greater than `i`.-/
+  This function takes worst case O(n) time because
+  it has to backshift all elements at positions greater than `i`.-/
 @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
-def eraseIdx (a : Array α) (i : Nat) (h : i < a.size := by get_elem_tactic) : Array α :=
-  if h' : i + 1 < a.size then
-    let a' := a.swap (i + 1) i
-    a'.eraseIdx (i + 1) (by simp [a', h'])
+def feraseIdx (a : Array α) (i : Fin a.size) : Array α :=
+  if h : i.val + 1 < a.size then
+    let a' := a.swap ⟨i.val + 1, h⟩ i
+    let i' : Fin a'.size := ⟨i.val + 1, by simp [a', h]⟩
+    a'.feraseIdx i'
   else
     a.pop
-termination_by a.size - i
-decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ h
+termination_by a.size - i.val
+decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ i.isLt
 
 -- This is required in `Lean.Data.PersistentHashMap`.
-@[simp] theorem size_eraseIdx (a : Array α) (i : Nat) (h) : (a.eraseIdx i h).size = a.size - 1 := by
-  induction a, i, h using Array.eraseIdx.induct with
-  | @case1 a i h h' a' ih =>
-    unfold eraseIdx
-    simp [h', a', ih]
-  | case2 a i h h' =>
-    unfold eraseIdx
-    simp [h']
+@[simp] theorem size_feraseIdx (a : Array α) (i : Fin a.size) : (a.feraseIdx i).size = a.size - 1 := by
+  induction a, i using Array.feraseIdx.induct with
+  | @case1 a i h a' _ ih =>
+    unfold feraseIdx
+    simp [h, a', ih]
+  | case2 a i h =>
+    unfold feraseIdx
+    simp [h]
 
 /-- Remove the element at a given index from an array, or do nothing if the index is out of bounds.
 
   This function takes worst case O(n) time because
   it has to backshift all elements at positions greater than `i`.-/
-def eraseIdxIfInBounds (a : Array α) (i : Nat) : Array α :=
-  if h : i < a.size then a.eraseIdx i h else a
-
-/-- Remove the element at a given index from an array, or panic if the index is out of bounds.
-
-This function takes worst case O(n) time because
-it has to backshift all elements at positions greater than `i`. -/
-def eraseIdx! (a : Array α) (i : Nat) : Array α :=
-  if h : i < a.size then a.eraseIdx i h else panic! "invalid index"
+def eraseIdx (a : Array α) (i : Nat) : Array α :=
+  if h : i < a.size then a.feraseIdx ⟨i, h⟩ else a
 
 def erase [BEq α] (as : Array α) (a : α) : Array α :=
   match as.indexOf? a with
   | none   => as
-  | some i => as.eraseIdx i
-
-/-- Erase the first element that satisfies the predicate `p`. -/
-def eraseP (as : Array α) (p : α → Bool) : Array α :=
-  match as.findIdx? p with
-  | none   => as
-  | some i => as.eraseIdxIfInBounds i
+  | some i => as.feraseIdx i
 
 /-- Insert element `a` at position `i`. -/
-@[inline] def insertIdx (as : Array α) (i : Nat) (a : α) (_ : i ≤ as.size := by get_elem_tactic) : Array α :=
+@[inline] def insertAt (as : Array α) (i : Fin (as.size + 1)) (a : α) : Array α :=
   let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
   loop (as : Array α) (j : Fin as.size) :=
-    if i < j then
-      let j' : Fin as.size := ⟨j-1, Nat.lt_of_le_of_lt (Nat.pred_le _) j.2⟩
+    if i.1 < j then
+      let j' := ⟨j-1, Nat.lt_of_le_of_lt (Nat.pred_le _) j.2⟩
       let as := as.swap j' j
       loop as ⟨j', by rw [size_swap]; exact j'.2⟩
     else
@@ -854,23 +818,12 @@ def eraseP (as : Array α) (p : α → Bool) : Array α :=
   let as := as.push a
   loop as ⟨j, size_push .. ▸ j.lt_succ_self⟩
 
-@[deprecated insertIdx (since := "2024-11-20")] abbrev insertAt := @insertIdx
-
 /-- Insert element `a` at position `i`. Panics if `i` is not `i ≤ as.size`. -/
-def insertIdx! (as : Array α) (i : Nat) (a : α) : Array α :=
+def insertAt! (as : Array α) (i : Nat) (a : α) : Array α :=
   if h : i ≤ as.size then
-    insertIdx as i a
+    insertAt as ⟨i, Nat.lt_succ_of_le h⟩ a
   else panic! "invalid index"
 
-@[deprecated insertIdx! (since := "2024-11-20")] abbrev insertAt! := @insertIdx!
-
-/-- Insert element `a` at position `i`, or do nothing if `as.size < i`. -/
-def insertIdxIfInBounds (as : Array α) (i : Nat) (a : α) : Array α :=
-  if h : i ≤ as.size then
-    insertIdx as i a
-  else
-    as
-
 @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
 def isPrefixOfAux [BEq α] (as bs : Array α) (hle : as.size ≤ bs.size) (i : Nat) : Bool :=
   if h : i < as.size then
@@ -894,12 +847,12 @@ def isPrefixOf [BEq α] (as bs : Array α) : Bool :=
     false
 
 @[semireducible, specialize] -- This is otherwise irreducible because it uses well-founded recursion.
-def zipWithAux (as : Array α) (bs : Array β) (f : α → β → γ) (i : Nat) (cs : Array γ) : Array γ :=
+def zipWithAux (f : α → β → γ) (as : Array α) (bs : Array β) (i : Nat) (cs : Array γ) : Array γ :=
   if h : i < as.size then
     let a := as[i]
     if h : i < bs.size then
       let b := bs[i]
-      zipWithAux as bs f (i+1) <| cs.push <| f a b
+      zipWithAux f as bs (i+1) <| cs.push <| f a b
     else
       cs
   else
@@ -907,23 +860,11 @@ def zipWithAux (as : Array α) (bs : Array β) (f : α → β → γ) (i : Nat)
 decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 @[inline] def zipWith (as : Array α) (bs : Array β) (f : α → β → γ) : Array γ :=
-  zipWithAux as bs f 0 #[]
+  zipWithAux f as bs 0 #[]
 
 def zip (as : Array α) (bs : Array β) : Array (α × β) :=
   zipWith as bs Prod.mk
 
-def zipWithAll (as : Array α) (bs : Array β) (f : Option α → Option β → γ) : Array γ :=
-  go as bs 0 #[]
-where go (as : Array α) (bs : Array β) (i : Nat) (cs : Array γ) :=
-  if i < max as.size bs.size then
-    let a := as[i]?
-    let b := bs[i]?
-    go as bs (i+1) (cs.push (f a b))
-  else
-    cs
-  termination_by max as.size bs.size - i
-  decreasing_by simp_wf; decreasing_trivial_pre_omega
-
 def unzip (as : Array (α × β)) : Array α × Array β :=
   as.foldl (init := (#[], #[])) fun (as, bs) (a, b) => (as.push a, bs.push b)
 

src/Init/Data/Array/BinSearch.lean

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

src/Init/Data/Array/Bootstrap.lean

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

src/Init/Data/Array/DecidableEq.lean

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

src/Init/Data/Array/FinRange.lean

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

src/Init/Data/Array/InsertionSort.lean

@@ -6,7 +6,7 @@ Authors: Leonardo de Moura
 prelude
 import Init.Data.Array.Basic
 
-@[inline] def Array.insertionSort (a : Array α) (lt : α → α → Bool := by exact (· < ·)) : Array α :=
+@[inline] def Array.insertionSort (a : Array α) (lt : α → α → Bool) : Array α :=
   traverse a 0 a.size
 where
   @[specialize] traverse (a : Array α) (i : Nat) (fuel : Nat) : Array α :=
@@ -23,6 +23,6 @@ where
     | j'+1 =>
       have h' : j' < a.size := by subst j; exact Nat.lt_trans (Nat.lt_succ_self _) h
       if lt a[j] a[j'] then
-        swapLoop (a.swap j j') j' (by rw [size_swap]; assumption; done)
+        swapLoop (a.swap ⟨j, h⟩ ⟨j', h'⟩) j' (by rw [size_swap]; assumption; done)
       else
         a

src/Init/Data/Array/Lemmas.lean

@@ -21,14 +21,15 @@ import Init.TacticsExtra
 ## Theorems about `Array`.
 -/
 
-
-/-! ### Preliminaries about `Array` needed for `List.toArray` lemmas.
-
-This section contains only the bare minimum lemmas about `Array`
-that we need to write lemmas about `List.toArray`.
--/
 namespace Array
 
+@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l := by
+  simp [mem_def]
+
+@[simp] theorem getElem_mk {xs : List α} {i : Nat} (h : i < xs.length) : (Array.mk xs)[i] = xs[i] := rfl
+
+theorem getElem_eq_getElem_toList {a : Array α} (h : i < a.size) : a[i] = a.toList[i] := rfl
+
 theorem getElem?_eq_getElem {a : Array α} {i : Nat} (h : i < a.size) : a[i]? = some a[i] :=
   getElem?_pos ..
 
@@ -38,34 +39,96 @@ theorem getElem?_eq_getElem {a : Array α} {i : Nat} (h : i < a.size) : a[i]? =
   · rw [getElem?_neg a i h]
     simp_all
 
-@[simp] theorem get_eq_getElem (a : Array α) (i : Nat) (h) : a.get i h = a[i] := rfl
+@[simp] theorem none_eq_getElem?_iff {a : Array α} {i : Nat} : none = a[i]? ↔ a.size ≤ i := by
+  simp [eq_comm (a := none)]
+
+theorem getElem?_eq {a : Array α} {i : Nat} :
+    a[i]? = if h : i < a.size then some a[i] else none := by
+  split
+  · simp_all [getElem?_eq_getElem]
+  · simp_all
+
+theorem getElem?_eq_some_iff {a : Array α} : a[i]? = some b ↔ ∃ h : i < a.size, a[i] = b := by
+  simp [getElem?_eq]
+
+theorem some_eq_getElem?_iff {a : Array α} : some b = a[i]? ↔ ∃ h : i < a.size, a[i] = b := by
+  rw [eq_comm, getElem?_eq_some_iff]
+
+theorem getElem?_eq_getElem?_toList (a : Array α) (i : Nat) : a[i]? = a.toList[i]? := by
+  rw [getElem?_eq]
+  split <;> simp_all
+
+theorem getElem_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_getElem_toList, List.concat_eq_append, List.getElem_append_left, h]
+
+@[simp] theorem getElem_push_eq (a : Array α) (x : α) : (a.push x)[a.size] = x := by
+  simp only [push, getElem_eq_getElem_toList, List.concat_eq_append]
+  rw [List.getElem_append_right] <;> simp [getElem_eq_getElem_toList, Nat.zero_lt_one]
+
+theorem getElem_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
+  by_cases h' : i < a.size
+  · simp [getElem_push_lt, h']
+  · simp at h
+    simp [getElem_push_lt, Nat.le_antisymm (Nat.le_of_lt_succ h) (Nat.ge_of_not_lt h')]
+
+@[deprecated getElem_push (since := "2024-10-21")] abbrev get_push := @getElem_push
+@[deprecated getElem_push_lt (since := "2024-10-21")] abbrev get_push_lt := @getElem_push_lt
+@[deprecated getElem_push_eq (since := "2024-10-21")] abbrev get_push_eq := @getElem_push_eq
+
+@[simp] theorem mem_push {a : Array α} {x y : α} : x ∈ a.push y ↔ x ∈ a ∨ x = y := by
+  simp [mem_def]
+
+theorem mem_push_self {a : Array α} {x : α} : x ∈ a.push x :=
+  mem_push.2 (Or.inr rfl)
+
+theorem mem_push_of_mem {a : Array α} {x : α} (y : α) (h : x ∈ a) : x ∈ a.push y :=
+  mem_push.2 (Or.inl h)
+
+theorem getElem_of_mem {a} {l : Array α} (h : a ∈ l) : ∃ (n : Nat) (h : n < l.size), l[n]'h = a := by
+  cases l
+  simp [List.getElem_of_mem (by simpa using h)]
+
+theorem getElem?_of_mem {a} {l : Array α} (h : a ∈ l) : ∃ n : Nat, l[n]? = some a :=
+  let ⟨n, _, e⟩ := getElem_of_mem h; ⟨n, e ▸ getElem?_eq_getElem _⟩
+
+theorem mem_of_getElem? {l : Array α} {n : Nat} {a : α} (e : l[n]? = some a) : a ∈ l :=
+  let ⟨_, e⟩ := getElem?_eq_some_iff.1 e; e ▸ getElem_mem ..
+
+theorem mem_iff_getElem {a} {l : Array α} : a ∈ l ↔ ∃ (n : Nat) (h : n < l.size), l[n]'h = a :=
+  ⟨getElem_of_mem, fun ⟨_, _, e⟩ => e ▸ getElem_mem ..⟩
+
+theorem mem_iff_getElem? {a} {l : Array α} : a ∈ l ↔ ∃ n : Nat, l[n]? = some a := by
+  simp [getElem?_eq_some_iff, mem_iff_getElem]
+
+theorem forall_getElem {l : Array α} {p : α → Prop} :
+    (∀ (n : Nat) h, p (l[n]'h)) ↔ ∀ a, a ∈ l → p a := by
+  cases l; simp [List.forall_getElem]
 
 @[simp] theorem get!_eq_getElem! [Inhabited α] (a : Array α) (i : Nat) : a.get! i = a[i]! := by
   simp [getElem!_def, get!, getD]
   split <;> rename_i h
   · simp [getElem?_eq_getElem h]
+    rfl
   · simp [getElem?_eq_none_iff.2 (by simpa using h)]
 
-@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l := by
-  simp [mem_def]
+theorem singleton_inj : #[a] = #[b] ↔ a = b := by
+  simp
+
+theorem singleton_eq_toArray_singleton (a : α) : #[a] = [a].toArray := rfl
 
 end Array
 
+namespace List
+
+open Array
+
 /-! ### Lemmas about `List.toArray`.
 
 We prefer to pull `List.toArray` outwards.
 -/
-namespace List
-
-open Array
-
-theorem toArray_inj {a b : List α} (h : a.toArray = b.toArray) : a = b := by
-  cases a with
-  | nil => simpa using h
-  | cons a as =>
-    cases b with
-    | nil => simp at h
-    | cons b bs => simpa using h
 
 @[simp] theorem size_toArrayAux {a : List α} {b : Array α} :
     (a.toArrayAux b).size = b.size + a.length := by
@@ -230,13 +293,7 @@ theorem findRevM?_toArray [Monad m] [LawfulMonad m] (f : α → m Bool) (l : Lis
 
 @[simp] theorem find?_toArray (f : α → Bool) (l : List α) :
     l.toArray.find? f = l.find? f := by
-  rw [Array.find?]
-  simp only [Id.run, Id, Id.pure_eq, Id.bind_eq, forIn_toArray]
-  induction l with
-  | nil => simp
-  | cons a l ih =>
-    simp only [forIn_cons, Id.pure_eq, Id.bind_eq, find?]
-    by_cases f a <;> simp_all
+  rw [Array.find?, ← findM?_id, findM?_toArray, Id.run]
 
 theorem isPrefixOfAux_toArray_succ [BEq α] (l₁ l₂ : List α) (hle : l₁.length ≤ l₂.length) (i : Nat) :
     Array.isPrefixOfAux l₁.toArray l₂.toArray hle (i + 1) =
@@ -286,8 +343,8 @@ theorem isPrefixOfAux_toArray_zero [BEq α] (l₁ l₂ : List α) (hle : l₁.le
         rw [ih]
         simp_all
 
-theorem zipWithAux_toArray_succ (as : List α) (bs : List β) (f : α → β → γ) (i : Nat) (cs : Array γ) :
-    zipWithAux as.toArray bs.toArray f (i + 1) cs = zipWithAux as.tail.toArray bs.tail.toArray f i cs := by
+theorem zipWithAux_toArray_succ (f : α → β → γ) (as : List α) (bs : List β) (i : Nat) (cs : Array γ) :
+    zipWithAux f as.toArray bs.toArray (i + 1) cs = zipWithAux f as.tail.toArray bs.tail.toArray i cs := by
   rw [zipWithAux]
   conv => rhs; rw [zipWithAux]
   simp only [size_toArray, getElem_toArray, length_tail, getElem_tail]
@@ -298,8 +355,8 @@ theorem zipWithAux_toArray_succ (as : List α) (bs : List β) (f : α → β →
       rw [dif_neg (by omega)]
   · rw [dif_neg (by omega)]
 
-theorem zipWithAux_toArray_succ' (as : List α) (bs : List β) (f : α → β → γ) (i : Nat) (cs : Array γ) :
-    zipWithAux as.toArray bs.toArray f (i + 1) cs = zipWithAux (as.drop (i+1)).toArray (bs.drop (i+1)).toArray f 0 cs := by
+theorem zipWithAux_toArray_succ' (f : α → β → γ) (as : List α) (bs : List β) (i : Nat) (cs : Array γ) :
+    zipWithAux f as.toArray bs.toArray (i + 1) cs = zipWithAux f (as.drop (i+1)).toArray (bs.drop (i+1)).toArray 0 cs := by
   induction i generalizing as bs cs with
   | zero => simp [zipWithAux_toArray_succ]
   | succ i ih =>
@@ -307,7 +364,7 @@ theorem zipWithAux_toArray_succ' (as : List α) (bs : List β) (f : α → β
     simp
 
 theorem zipWithAux_toArray_zero (f : α → β → γ) (as : List α) (bs : List β) (cs : Array γ) :
-    zipWithAux as.toArray bs.toArray f 0 cs = cs ++ (List.zipWith f as bs).toArray := by
+    zipWithAux f as.toArray bs.toArray 0 cs = cs ++ (List.zipWith f as bs).toArray := by
   rw [Array.zipWithAux]
   match as, bs with
   | [], _ => simp
@@ -315,7 +372,7 @@ theorem zipWithAux_toArray_zero (f : α → β → γ) (as : List α) (bs : List
   | a :: as, b :: bs =>
     simp [zipWith_cons_cons, zipWithAux_toArray_succ', zipWithAux_toArray_zero, push_append_toArray]
 
-@[simp] theorem zipWith_toArray (as : List α) (bs : List β) (f : α → β → γ) :
+@[simp] theorem zipWith_toArray (f : α → β → γ) (as : List α) (bs : List β) :
     Array.zipWith as.toArray bs.toArray f = (List.zipWith f as bs).toArray := by
   rw [Array.zipWith]
   simp [zipWithAux_toArray_zero]
@@ -324,286 +381,10 @@ theorem zipWithAux_toArray_zero (f : α → β → γ) (as : List α) (bs : List
     Array.zip as.toArray bs.toArray = (List.zip as bs).toArray := by
   simp [Array.zip, zipWith_toArray, zip]
 
-theorem zipWithAll_go_toArray (as : List α) (bs : List β) (f : Option α → Option β → γ) (i : Nat) (cs : Array γ) :
-    zipWithAll.go f as.toArray bs.toArray i cs = cs ++ (List.zipWithAll f (as.drop i) (bs.drop i)).toArray := by
-  unfold zipWithAll.go
-  split <;> rename_i h
-  · rw [zipWithAll_go_toArray]
-    simp at h
-    simp only [getElem?_toArray, push_append_toArray]
-    if ha : i < as.length then
-      if hb : i < bs.length then
-        rw [List.drop_eq_getElem_cons ha, List.drop_eq_getElem_cons hb]
-        simp only [ha, hb, getElem?_eq_getElem, zipWithAll_cons_cons]
-      else
-        simp only [Nat.not_lt] at hb
-        rw [List.drop_eq_getElem_cons ha]
-        rw [(drop_eq_nil_iff (l := bs)).mpr (by omega), (drop_eq_nil_iff (l := bs)).mpr (by omega)]
-        simp only [zipWithAll_nil, map_drop, map_cons]
-        rw [getElem?_eq_getElem ha]
-        rw [getElem?_eq_none hb]
-    else
-      if hb : i < bs.length then
-        simp only [Nat.not_lt] at ha
-        rw [List.drop_eq_getElem_cons hb]
-        rw [(drop_eq_nil_iff (l := as)).mpr (by omega), (drop_eq_nil_iff (l := as)).mpr (by omega)]
-        simp only [nil_zipWithAll, map_drop, map_cons]
-        rw [getElem?_eq_getElem hb]
-        rw [getElem?_eq_none ha]
-      else
-        omega
-  · simp only [size_toArray, Nat.not_lt] at h
-    rw [drop_eq_nil_of_le (by omega), drop_eq_nil_of_le (by omega)]
-    simp
-  termination_by max as.length bs.length - i
-  decreasing_by simp_wf; decreasing_trivial_pre_omega
-
-@[simp] theorem zipWithAll_toArray (f : Option α → Option β → γ) (as : List α) (bs : List β) :
-    Array.zipWithAll as.toArray bs.toArray f = (List.zipWithAll f as bs).toArray := by
-  simp [Array.zipWithAll, zipWithAll_go_toArray]
-
-@[simp] theorem toArray_appendList (l₁ l₂ : List α) :
-    l₁.toArray ++ l₂ = (l₁ ++ l₂).toArray := by
-  apply ext'
-  simp
-
-@[simp] theorem pop_toArray (l : List α) : l.toArray.pop = l.dropLast.toArray := by
-  apply ext'
-  simp
-
-theorem takeWhile_go_succ (p : α → Bool) (a : α) (l : List α) (i : Nat) :
-    takeWhile.go p (a :: l).toArray (i+1) r = takeWhile.go p l.toArray i r := by
-  rw [takeWhile.go, takeWhile.go]
-  simp only [size_toArray, length_cons, Nat.add_lt_add_iff_right, Array.get_eq_getElem,
-    getElem_toArray, getElem_cons_succ]
-  split
-  rw [takeWhile_go_succ]
-  rfl
-
-theorem takeWhile_go_toArray (p : α → Bool) (l : List α) (i : Nat) :
-    Array.takeWhile.go p l.toArray i r = r ++ (takeWhile p (l.drop i)).toArray := by
-  induction l generalizing i r with
-  | nil => simp [takeWhile.go]
-  | cons a l ih =>
-    rw [takeWhile.go]
-    cases i with
-    | zero =>
-      simp [takeWhile_go_succ, ih, takeWhile_cons]
-      split <;> simp
-    | succ i =>
-      simp only [size_toArray, length_cons, Nat.add_lt_add_iff_right, Array.get_eq_getElem,
-        getElem_toArray, getElem_cons_succ, drop_succ_cons]
-      split <;> rename_i h₁
-      · rw [takeWhile_go_succ, ih]
-        rw [← getElem_cons_drop_succ_eq_drop h₁, takeWhile_cons]
-        split <;> simp_all
-      · simp_all [drop_eq_nil_of_le]
-
-@[simp] theorem takeWhile_toArray (p : α → Bool) (l : List α) :
-    l.toArray.takeWhile p = (l.takeWhile p).toArray := by
-  simp [Array.takeWhile, takeWhile_go_toArray]
-
 end List
 
-
 namespace Array
 
-/-! ## Preliminaries -/
-
-/-! ### toList -/
-
-theorem toList_inj {a b : Array α} (h : a.toList = b.toList) : a = b := by
-  cases a; cases b; simpa using h
-
-/-! ### empty -/
-
-@[simp] theorem empty_eq {xs : Array α} : #[] = xs ↔ xs = #[] := by
-  cases xs <;> simp
-
-/-! ### size -/
-
-theorem eq_empty_of_size_eq_zero (h : l.size = 0) : l = #[] := by
-  cases l
-  simp_all
-
-theorem ne_empty_of_size_eq_add_one (h : l.size = n + 1) : l ≠ #[] := by
-  cases l
-  simpa using List.ne_nil_of_length_eq_add_one h
-
-theorem ne_empty_of_size_pos (h : 0 < l.size) : l ≠ #[] := by
-  cases l
-  simpa using List.ne_nil_of_length_pos h
-
-@[simp] theorem size_eq_zero : l.size = 0 ↔ l = #[] :=
-  ⟨eq_empty_of_size_eq_zero, fun h => h ▸ rfl⟩
-
-theorem size_pos_of_mem {a : α} {l : Array α} (h : a ∈ l) : 0 < l.size := by
-  cases l
-  simp only [mem_toArray] at h
-  simpa using List.length_pos_of_mem h
-
-theorem exists_mem_of_size_pos {l : Array α} (h : 0 < l.size) : ∃ a, a ∈ l := by
-  cases l
-  simpa using List.exists_mem_of_length_pos h
-
-theorem size_pos_iff_exists_mem {l : Array α} : 0 < l.size ↔ ∃ a, a ∈ l :=
-  ⟨exists_mem_of_size_pos, fun ⟨_, h⟩ => size_pos_of_mem h⟩
-
-theorem exists_mem_of_size_eq_add_one {l : Array α} (h : l.size = n + 1) : ∃ a, a ∈ l := by
-  cases l
-  simpa using List.exists_mem_of_length_eq_add_one h
-
-theorem size_pos {l : Array α} : 0 < l.size ↔ l ≠ #[] :=
-  Nat.pos_iff_ne_zero.trans (not_congr size_eq_zero)
-
-theorem size_eq_one {l : Array α} : l.size = 1 ↔ ∃ a, l = #[a] := by
-  cases l
-  simpa using List.length_eq_one
-
-/-! ### push -/
-
-theorem push_ne_empty {a : α} {xs : Array α} : xs.push a ≠ #[] := by
-  cases xs
-  simp
-
-@[simp] theorem push_ne_self {a : α} {xs : Array α} : xs.push a ≠ xs := by
-  cases xs
-  simp
-
-@[simp] theorem ne_push_self {a : α} {xs : Array α} : xs ≠ xs.push a := by
-  rw [ne_eq, eq_comm]
-  simp
-
-theorem back_eq_of_push_eq {a b : α} {xs ys : Array α} (h : xs.push a = ys.push b) : a = b := by
-  cases xs
-  cases ys
-  simp only [List.push_toArray, mk.injEq] at h
-  replace h := List.append_inj_right' h (by simp)
-  simpa using h
-
-theorem pop_eq_of_push_eq {a b : α} {xs ys : Array α} (h : xs.push a = ys.push b) : xs = ys := by
-  cases xs
-  cases ys
-  simp at h
-  replace h := List.append_inj_left' h (by simp)
-  simp [h]
-
-theorem push_inj_left {a : α} {xs ys : Array α} : xs.push a = ys.push a ↔ xs = ys :=
-  ⟨pop_eq_of_push_eq, fun h => by simp [h]⟩
-
-theorem push_inj_right {a b : α} {xs : Array α} : xs.push a = xs.push b ↔ a = b :=
-  ⟨back_eq_of_push_eq, fun h => by simp [h]⟩
-
-theorem push_eq_push {a b : α} {xs ys : Array α} : xs.push a = ys.push b ↔ a = b ∧ xs = ys := by
-  constructor
-  · intro h
-    exact ⟨back_eq_of_push_eq h, pop_eq_of_push_eq h⟩
-  · rintro ⟨rfl, rfl⟩
-    rfl
-
-theorem exists_push_of_ne_empty {xs : Array α} (h : xs ≠ #[]) :
-    ∃ (ys : Array α) (a : α), xs = ys.push a := by
-  rcases xs with ⟨xs⟩
-  simp only [ne_eq, mk.injEq] at h
-  exact ⟨(xs.take (xs.length - 1)).toArray, xs.getLast h, by simp⟩
-
-theorem ne_empty_iff_exists_push {xs : Array α} :
-    xs ≠ #[] ↔ ∃ (ys : Array α) (a : α), xs = ys.push a :=
-  ⟨exists_push_of_ne_empty, fun ⟨_, _, eq⟩ => eq.symm ▸ push_ne_empty⟩
-
-theorem exists_push_of_size_pos {xs : Array α} (h : 0 < xs.size) :
-    ∃ (ys : Array α) (a : α), xs = ys.push a := by
-  replace h : xs ≠ #[] := size_pos.mp h
-  exact exists_push_of_ne_empty h
-
-theorem size_pos_iff_exists_push {xs : Array α} :
-    0 < xs.size ↔ ∃ (ys : Array α) (a : α), xs = ys.push a :=
-  ⟨exists_push_of_size_pos, fun ⟨_, _, eq⟩ => by simp [eq]⟩
-
-theorem exists_push_of_size_eq_add_one {xs : Array α} (h : xs.size = n + 1) :
-    ∃ (ys : Array α) (a : α), xs = ys.push a :=
-  exists_push_of_size_pos (by simp [h])
-
-/-! ## L[i] and L[i]? -/
-
-@[deprecated List.getElem_toArray (since := "2024-11-29")]
-theorem getElem_mk {xs : List α} {i : Nat} (h : i < xs.length) : (Array.mk xs)[i] = xs[i] := rfl
-
-theorem getElem_eq_getElem_toList {a : Array α} (h : i < a.size) : a[i] = a.toList[i] := rfl
-
-@[simp] theorem none_eq_getElem?_iff {a : Array α} {i : Nat} : none = a[i]? ↔ a.size ≤ i := by
-  simp [eq_comm (a := none)]
-
-theorem getElem?_eq {a : Array α} {i : Nat} :
-    a[i]? = if h : i < a.size then some a[i] else none := by
-  split
-  · simp_all [getElem?_eq_getElem]
-  · simp_all
-
-theorem getElem?_eq_some_iff {a : Array α} : a[i]? = some b ↔ ∃ h : i < a.size, a[i] = b := by
-  simp [getElem?_eq]
-
-theorem some_eq_getElem?_iff {a : Array α} : some b = a[i]? ↔ ∃ h : i < a.size, a[i] = b := by
-  rw [eq_comm, getElem?_eq_some_iff]
-
-theorem getElem?_eq_getElem?_toList (a : Array α) (i : Nat) : a[i]? = a.toList[i]? := by
-  rw [getElem?_eq]
-  split <;> simp_all
-
-theorem getElem_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_getElem_toList, List.concat_eq_append, List.getElem_append_left, h]
-
-@[simp] theorem getElem_push_eq (a : Array α) (x : α) : (a.push x)[a.size] = x := by
-  simp only [push, getElem_eq_getElem_toList, List.concat_eq_append]
-  rw [List.getElem_append_right] <;> simp [getElem_eq_getElem_toList, Nat.zero_lt_one]
-
-theorem getElem_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
-  by_cases h' : i < a.size
-  · simp [getElem_push_lt, h']
-  · simp at h
-    simp [getElem_push_lt, Nat.le_antisymm (Nat.le_of_lt_succ h) (Nat.ge_of_not_lt h')]
-
-@[deprecated getElem_push (since := "2024-10-21")] abbrev get_push := @getElem_push
-@[deprecated getElem_push_lt (since := "2024-10-21")] abbrev get_push_lt := @getElem_push_lt
-@[deprecated getElem_push_eq (since := "2024-10-21")] abbrev get_push_eq := @getElem_push_eq
-
-@[simp] theorem mem_push {a : Array α} {x y : α} : x ∈ a.push y ↔ x ∈ a ∨ x = y := by
-  simp [mem_def]
-
-theorem mem_push_self {a : Array α} {x : α} : x ∈ a.push x :=
-  mem_push.2 (Or.inr rfl)
-
-theorem mem_push_of_mem {a : Array α} {x : α} (y : α) (h : x ∈ a) : x ∈ a.push y :=
-  mem_push.2 (Or.inl h)
-
-theorem getElem_of_mem {a} {l : Array α} (h : a ∈ l) : ∃ (n : Nat) (h : n < l.size), l[n]'h = a := by
-  cases l
-  simp [List.getElem_of_mem (by simpa using h)]
-
-theorem getElem?_of_mem {a} {l : Array α} (h : a ∈ l) : ∃ n : Nat, l[n]? = some a :=
-  let ⟨n, _, e⟩ := getElem_of_mem h; ⟨n, e ▸ getElem?_eq_getElem _⟩
-
-theorem mem_of_getElem? {l : Array α} {n : Nat} {a : α} (e : l[n]? = some a) : a ∈ l :=
-  let ⟨_, e⟩ := getElem?_eq_some_iff.1 e; e ▸ getElem_mem ..
-
-theorem mem_iff_getElem {a} {l : Array α} : a ∈ l ↔ ∃ (n : Nat) (h : n < l.size), l[n]'h = a :=
-  ⟨getElem_of_mem, fun ⟨_, _, e⟩ => e ▸ getElem_mem ..⟩
-
-theorem mem_iff_getElem? {a} {l : Array α} : a ∈ l ↔ ∃ n : Nat, l[n]? = some a := by
-  simp [getElem?_eq_some_iff, mem_iff_getElem]
-
-theorem forall_getElem {l : Array α} {p : α → Prop} :
-    (∀ (n : Nat) h, p (l[n]'h)) ↔ ∀ a, a ∈ l → p a := by
-  cases l; simp [List.forall_getElem]
-
-theorem singleton_inj : #[a] = #[b] ↔ a = b := by
-  simp
-
-theorem singleton_eq_toArray_singleton (a : α) : #[a] = [a].toArray := rfl
-
 @[simp] theorem singleton_def (v : α) : singleton v = #[v] := rfl
 
 -- This is a duplicate of `List.toArray_toList`.
@@ -677,11 +458,6 @@ where
   simp only [← length_toList]
   simp
 
-@[simp] theorem mapM_empty [Monad m] (f : α → m β) : mapM f #[] = pure #[] := by
-  rw [mapM, mapM.map]; rfl
-
-@[simp] theorem map_empty (f : α → β) : map f #[] = #[] := mapM_empty f
-
 @[simp] theorem appendList_nil (arr : Array α) : arr ++ ([] : List α) = arr := Array.ext' (by simp)
 
 @[simp] theorem appendList_cons (arr : Array α) (a : α) (l : List α) :
@@ -721,6 +497,8 @@ theorem size_uset (a : Array α) (v i h) : (uset a i v h).size = a.size := by si
 
 /-! # get -/
 
+@[simp] theorem get_eq_getElem (a : Array α) (i : Nat) (h) : a.get i h = a[i] := rfl
+
 theorem getElem?_lt
     (a : Array α) {i : Nat} (h : i < a.size) : a[i]? = some a[i] := dif_pos h
 
@@ -735,10 +513,10 @@ theorem getElem?_len_le (a : Array α) {i : Nat} (h : a.size ≤ i) : a[i]? = no
 theorem getD_get? (a : Array α) (i : Nat) (d : α) :
   Option.getD a[i]? d = if p : i < a.size then a[i]'p else d := by
   if h : i < a.size then
-    simp [setIfInBounds, h, getElem?_def]
+    simp [setD, h, getElem?_def]
   else
     have p : i ≥ a.size := Nat.le_of_not_gt h
-    simp [setIfInBounds, getElem?_len_le _ p, h]
+    simp [setD, getElem?_len_le _ p, h]
 
 @[simp] theorem getD_eq_get? (a : Array α) (n d) : a.getD n d = (a[n]?).getD d := by
   simp only [getD, get_eq_getElem, get?_eq_getElem?]; split <;> simp [getD_get?, *]
@@ -774,32 +552,31 @@ theorem getElem_set (a : Array α) (i : Nat) (h' : i < a.size) (v : α) (j : Nat
     (ne : i ≠ j) : (a.set i v)[j]? = a[j]? := by
   by_cases h : j < a.size <;> simp [getElem?_lt, getElem?_ge, Nat.ge_of_not_lt, ne, h]
 
-/-! # setIfInBounds -/
+/-! # setD -/
 
-@[simp] theorem set!_is_setIfInBounds : @set! = @setIfInBounds := rfl
+@[simp] theorem set!_is_setD : @set! = @setD := rfl
 
-@[simp] theorem size_setIfInBounds (a : Array α) (index : Nat) (val : α) :
-    (Array.setIfInBounds a index val).size = a.size := by
+@[simp] theorem size_setD (a : Array α) (index : Nat) (val : α) :
+    (Array.setD a index val).size = a.size := by
   if h : index < a.size  then
-    simp [setIfInBounds, h]
+    simp [setD, h]
   else
-    simp [setIfInBounds, h]
+    simp [setD, h]
 
-@[simp] theorem getElem_setIfInBounds_eq (a : Array α) {i : Nat} (v : α) (h : _) :
-    (setIfInBounds a i v)[i]'h = v := by
+@[simp] theorem getElem_setD_eq (a : Array α) {i : Nat} (v : α) (h : _) :
+    (setD a i v)[i]'h = v := by
   simp at h
-  simp only [setIfInBounds, h, ↓reduceDIte, getElem_set_eq]
+  simp only [setD, h, ↓reduceDIte, getElem_set_eq]
 
 @[simp]
-theorem getElem?_setIfInBounds_eq (a : Array α) {i : Nat} (p : i < a.size) (v : α) :
-    (a.setIfInBounds i v)[i]? = some v := by
+theorem getElem?_setD_eq (a : Array α) {i : Nat} (p : i < a.size) (v : α) : (a.setD i v)[i]? = some v := by
   simp [getElem?_lt, p]
 
 /-- Simplifies a normal form from `get!` -/
-@[simp] theorem getD_get?_setIfInBounds (a : Array α) (i : Nat) (v d : α) :
-    Option.getD (setIfInBounds a i v)[i]? d = if i < a.size then v else d := by
+@[simp] theorem getD_get?_setD (a : Array α) (i : Nat) (v d : α) :
+    Option.getD (setD a i v)[i]? d = if i < a.size then v else d := by
   by_cases h : i < a.size <;>
-    simp [setIfInBounds, Nat.not_lt_of_le, h,  getD_get?]
+    simp [setD, Nat.not_lt_of_le, h,  getD_get?]
 
 /-! # ofFn -/
 
@@ -844,20 +621,7 @@ theorem getElem?_ofFn (f : Fin n → α) (i : Nat) :
     (ofFn f)[i]? = if h : i < n then some (f ⟨i, h⟩) else none := by
   simp [getElem?_def]
 
-@[simp] theorem ofFn_zero (f : Fin 0 → α) : ofFn f = #[] := rfl
-
-theorem ofFn_succ (f : Fin (n+1) → α) :
-    ofFn f = (ofFn (fun (i : Fin n) => f i.castSucc)).push (f ⟨n, by omega⟩) := by
-  ext i h₁ h₂
-  · simp
-  · simp [getElem_push]
-    split <;> rename_i h₃
-    · rfl
-    · congr
-      simp at h₁ h₂
-      omega
-
-/-! # mkArray -/
+/-- # mkArray -/
 
 @[simp] theorem size_mkArray (n : Nat) (v : α) : (mkArray n v).size = n :=
   List.length_replicate ..
@@ -873,7 +637,7 @@ theorem getElem?_mkArray (n : Nat) (v : α) (i : Nat) :
     (mkArray n v)[i]? = if i < n then some v else none := by
   simp [getElem?_def]
 
-/-! # mem -/
+/-- # mem -/
 
 @[simp] theorem mem_toList {a : α} {l : Array α} : a ∈ l.toList ↔ a ∈ l := mem_def.symm
 
@@ -895,7 +659,7 @@ theorem not_mem_nil (a : α) : ¬ a ∈ #[] := nofun
     (x ∈ if p then l else #[]) ↔ p ∧ x ∈ l := by
   split <;> simp_all
 
-/-! # get lemmas -/
+/-- # get lemmas -/
 
 theorem lt_of_getElem {x : α} {a : Array α} {idx : Nat} {hidx : idx < a.size} (_ : a[idx] = x) :
     idx < a.size :=
@@ -991,32 +755,32 @@ theorem get_set (a : Array α) (i : Nat) (hi : i < a.size) (j : Nat) (hj : j < a
     (h : i ≠ j) : (a.set i v)[j]'(by simp [*]) = a[j] := by
   simp only [set, getElem_eq_getElem_toList, List.getElem_set_ne h]
 
-theorem getElem_setIfInBounds (a : Array α) (i : Nat) (v : α) (h : i < (setIfInBounds a i v).size) :
-    (setIfInBounds a i v)[i] = v := by
+theorem getElem_setD (a : Array α) (i : Nat) (v : α) (h : i < (setD a i v).size) :
+    (setD a i v)[i] = v := by
   simp at h
-  simp only [setIfInBounds, h, ↓reduceDIte, getElem_set_eq]
+  simp only [setD, h, ↓reduceDIte, getElem_set_eq]
 
 theorem set_set (a : Array α) (i : Nat) (h) (v v' : α) :
     (a.set i v h).set i v' (by simp [h]) = a.set i v' := by simp [set, List.set_set]
 
 private theorem fin_cast_val (e : n = n') (i : Fin n) : e ▸ i = ⟨i.1, e ▸ i.2⟩ := by cases e; rfl
 
-theorem swap_def (a : Array α) (i j : Nat) (hi hj) :
-    a.swap i j hi hj = (a.set i a[j]).set j a[i] (by simpa using hj) := by
+theorem swap_def (a : Array α) (i j : Fin a.size) :
+    a.swap i j = (a.set i a[j]).set j a[i] := by
   simp [swap, fin_cast_val]
 
-@[simp] theorem toList_swap (a : Array α) (i j : Nat) (hi hj) :
-    (a.swap i j hi hj).toList = (a.toList.set i a[j]).set j a[i] := by simp [swap_def]
+@[simp] theorem toList_swap (a : Array α) (i j : Fin a.size) :
+    (a.swap i j).toList = (a.toList.set i a[j]).set j a[i] := by simp [swap_def]
 
-theorem getElem?_swap (a : Array α) (i j : Nat) (hi hj) (k : Nat) : (a.swap i j hi hj)[k]? =
-    if j = k then some a[i] else if i = k then some a[j] else a[k]? := by
+theorem getElem?_swap (a : Array α) (i j : Fin a.size) (k : Nat) : (a.swap i j)[k]? =
+    if j = k then some a[i.1] else if i = k then some a[j.1] else a[k]? := by
   simp [swap_def, get?_set, ← getElem_fin_eq_getElem_toList]
 
-@[simp] theorem swapAt_def (a : Array α) (i : Nat) (v : α) (hi) :
-    a.swapAt i v hi = (a[i], a.set i v) := rfl
+@[simp] theorem swapAt_def (a : Array α) (i : Fin a.size) (v : α) :
+    a.swapAt i v = (a[i.1], a.set i v) := rfl
 
-@[simp] theorem size_swapAt (a : Array α) (i : Nat) (v : α) (hi) :
-    (a.swapAt i v hi).2.size = a.size := by simp [swapAt_def]
+@[simp] theorem size_swapAt (a : Array α) (i : Fin a.size) (v : α) :
+    (a.swapAt i v).2.size = a.size := by simp [swapAt_def]
 
 @[simp]
 theorem swapAt!_def (a : Array α) (i : Nat) (v : α) (h : i < a.size) :
@@ -1039,6 +803,11 @@ theorem swapAt!_def (a : Array α) (i : Nat) (v : α) (h : i < a.size) :
     a.pop[i] = a[i]'(Nat.lt_of_lt_of_le (a.size_pop ▸ hi) (Nat.sub_le _ _)) :=
   List.getElem_dropLast ..
 
+theorem eq_empty_of_size_eq_zero {as : Array α} (h : as.size = 0) : as = #[] := by
+  apply ext
+  · simp [h]
+  · intros; contradiction
+
 theorem eq_push_pop_back!_of_size_ne_zero [Inhabited α] {as : Array α} (h : as.size ≠ 0) :
     as = as.pop.push as.back! := by
   apply ext
@@ -1058,10 +827,8 @@ theorem eq_push_of_size_ne_zero {as : Array α} (h : as.size ≠ 0) :
 
 theorem size_eq_length_toList (as : Array α) : as.size = as.toList.length := rfl
 
-@[simp] theorem size_swapIfInBounds (a : Array α) (i j) :
-    (a.swapIfInBounds i j).size = a.size := by unfold swapIfInBounds; split <;> (try split) <;> simp [size_swap]
-
-@[deprecated size_swapIfInBounds (since := "2024-11-24")] abbrev size_swap! := @size_swapIfInBounds
+@[simp] theorem size_swap! (a : Array α) (i j) :
+    (a.swap! i j).size = a.size := by unfold swap!; split <;> (try split) <;> simp [size_swap]
 
 @[simp] theorem size_reverse (a : Array α) : a.reverse.size = a.size := by
   let rec go (as : Array α) (i j) : (reverse.loop as i j).size = as.size := by
@@ -1073,10 +840,16 @@ theorem size_eq_length_toList (as : Array α) : as.size = as.toList.length := rf
   simp only [reverse]; split <;> simp [go]
 
 @[simp] theorem size_range {n : Nat} : (range n).size = n := by
-  induction n <;> simp [range]
+  unfold range
+  induction n with
+  | zero      => simp [Nat.fold]
+  | succ k ih =>
+    rw [Nat.fold, flip]
+    simp only [mkEmpty_eq, size_push] at *
+    omega
 
 @[simp] theorem toList_range (n : Nat) : (range n).toList = List.range n := by
-  apply List.ext_getElem <;> simp [range]
+  induction n <;> simp_all [range, Nat.fold, flip, List.range_succ]
 
 @[simp]
 theorem getElem_range {n : Nat} {x : Nat} (h : x < (Array.range n).size) : (Array.range n)[x] = x := by
@@ -1272,34 +1045,6 @@ theorem foldr_congr {as bs : Array α} (h₀ : as = bs) {f g : α → β → β}
     as.foldr f a start stop = bs.foldr g b start' stop' := by
   congr
 
-theorem foldl_eq_foldlM (f : β → α → β) (b) (l : Array α) :
-    l.foldl f b = l.foldlM (m := Id) f b := by
-  cases l
-  simp [List.foldl_eq_foldlM]
-
-theorem foldr_eq_foldrM (f : α → β → β) (b) (l : Array α) :
-    l.foldr f b = l.foldrM (m := Id) f b := by
-  cases l
-  simp [List.foldr_eq_foldrM]
-
-@[simp] theorem id_run_foldlM (f : β → α → Id β) (b) (l : Array α) :
-    Id.run (l.foldlM f b) = l.foldl f b := (foldl_eq_foldlM f b l).symm
-
-@[simp] theorem id_run_foldrM (f : α → β → Id β) (b) (l : Array α) :
-    Id.run (l.foldrM f b) = l.foldr f b := (foldr_eq_foldrM f b l).symm
-
-theorem foldl_hom (f : α₁ → α₂) (g₁ : α₁ → β → α₁) (g₂ : α₂ → β → α₂) (l : Array β) (init : α₁)
-    (H : ∀ x y, g₂ (f x) y = f (g₁ x y)) : l.foldl g₂ (f init) = f (l.foldl g₁ init) := by
-  cases l
-  simp
-  rw [List.foldl_hom _ _ _ _ _ H]
-
-theorem foldr_hom (f : β₁ → β₂) (g₁ : α → β₁ → β₁) (g₂ : α → β₂ → β₂) (l : Array α) (init : β₁)
-    (H : ∀ x y, g₂ x (f y) = f (g₁ x y)) : l.foldr g₂ (f init) = f (l.foldr g₁ init) := by
-  cases l
-  simp
-  rw [List.foldr_hom _ _ _ _ _ H]
-
 /-! ### map -/
 
 @[simp] theorem mem_map {f : α → β} {l : Array α} : b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b := by
@@ -1555,18 +1300,6 @@ theorem getElem?_append {as bs : Array α} {n : Nat} :
   · exact getElem?_append_left h
   · exact getElem?_append_right (by simpa using h)
 
-@[simp] theorem toArray_eq_append_iff {xs : List α} {as bs : Array α} :
-    xs.toArray = as ++ bs ↔ xs = as.toList ++ bs.toList := by
-  cases as
-  cases bs
-  simp
-
-@[simp] theorem append_eq_toArray_iff {as bs : Array α} {xs : List α} :
-    as ++ bs = xs.toArray ↔ as.toList ++ bs.toList = xs := by
-  cases as
-  cases bs
-  simp
-
 /-! ### flatten -/
 
 @[simp] theorem toList_flatten {l : Array (Array α)} :
@@ -1863,30 +1596,28 @@ instance [DecidableEq α] (a : α) (as : Array α) : Decidable (a ∈ as) :=
 
 open Fin
 
-@[simp] theorem getElem_swap_right (a : Array α) {i j : Nat} {hi hj} :
-    (a.swap i j hi hj)[j]'(by simpa using hj) = a[i] := by
+@[simp] theorem getElem_swap_right (a : Array α) {i j : Fin a.size} : (a.swap i j)[j.1] = a[i] := by
   simp [swap_def, getElem_set]
 
-@[simp] theorem getElem_swap_left (a : Array α) {i j : Nat} {hi hj} :
-    (a.swap i j hi hj)[i]'(by simpa using hi) = a[j] := by
+@[simp] theorem getElem_swap_left (a : Array α) {i j : Fin a.size} : (a.swap i j)[i.1] = a[j] := by
   simp +contextual [swap_def, getElem_set]
 
-@[simp] theorem getElem_swap_of_ne (a : Array α) {i j : Nat} {hi hj} (hp : p < a.size)
-    (hi' : p ≠ i) (hj' : p ≠ j) : (a.swap i j hi hj)[p]'(a.size_swap .. |>.symm ▸ hp) = a[p] := by
-  simp [swap_def, getElem_set, hi'.symm, hj'.symm]
+@[simp] theorem getElem_swap_of_ne (a : Array α) {i j : Fin a.size} (hp : p < a.size)
+    (hi : p ≠ i) (hj : p ≠ j) : (a.swap i j)[p]'(a.size_swap .. |>.symm ▸ hp) = a[p] := by
+  simp [swap_def, getElem_set, hi.symm, hj.symm]
 
-theorem getElem_swap' (a : Array α) (i j : Nat) {hi hj} (k : Nat) (hk : k < a.size) :
-    (a.swap i j hi hj)[k]'(by simp_all) = if k = i then a[j] else if k = j then a[i] else a[k] := by
+theorem getElem_swap' (a : Array α) (i j : Fin a.size) (k : Nat) (hk : k < a.size) :
+    (a.swap i j)[k]'(by simp_all) = if k = i then a[j] else if k = j then a[i] else a[k] := by
   split
   · simp_all only [getElem_swap_left]
   · split <;> simp_all
 
-theorem getElem_swap (a : Array α) (i j : Nat) {hi hj}(k : Nat) (hk : k < (a.swap i j).size) :
-    (a.swap i j hi hj)[k] = if k = i then a[j] else if k = j then a[i] else a[k]'(by simp_all) := by
+theorem getElem_swap (a : Array α) (i j : Fin a.size) (k : Nat) (hk : k < (a.swap i j).size) :
+    (a.swap i j)[k] = if k = i then a[j] else if k = j then a[i] else a[k]'(by simp_all) := by
   apply getElem_swap'
 
-@[simp] theorem swap_swap (a : Array α) {i j : Nat} (hi hj) :
-    (a.swap i j hi hj).swap i j ((a.size_swap ..).symm ▸ hi) ((a.size_swap ..).symm ▸ hj) = a := by
+@[simp] theorem swap_swap (a : Array α) {i j : Fin a.size} :
+    (a.swap i j).swap ⟨i.1, (a.size_swap ..).symm ▸ i.2⟩ ⟨j.1, (a.size_swap ..).symm ▸ j.2⟩ = a := by
   apply ext
   · simp only [size_swap]
   · intros
@@ -1895,7 +1626,7 @@ theorem getElem_swap (a : Array α) (i j : Nat) {hi hj}(k : Nat) (hk : k < (a.sw
     · simp_all
     · split <;> simp_all
 
-theorem swap_comm (a : Array α) {i j : Nat} {hi hj} : a.swap i j hi hj = a.swap j i hj hi := by
+theorem swap_comm (a : Array α) {i j : Fin a.size} : a.swap i j = a.swap j i := by
   apply ext
   · simp only [size_swap]
   · intros
@@ -1906,9 +1637,9 @@ theorem swap_comm (a : Array α) {i j : Nat} {hi hj} : a.swap i j hi hj = a.swap
 
 /-! ### eraseIdx -/
 
-theorem eraseIdx_eq_eraseIdxIfInBounds {a : Array α} {i : Nat} (h : i < a.size) :
-    a.eraseIdx i h = a.eraseIdxIfInBounds i := by
-  simp [eraseIdxIfInBounds, h]
+theorem feraseIdx_eq_eraseIdx {a : Array α} {i : Fin a.size} :
+    a.feraseIdx i = a.eraseIdx i.1 := by
+  simp [eraseIdx]
 
 /-! ### isPrefixOf -/
 
@@ -1930,20 +1661,6 @@ theorem eraseIdx_eq_eraseIdxIfInBounds {a : Array α} {i : Nat} (h : i < a.size)
     (Array.zip as bs).toList = List.zip as.toList bs.toList := by
   simp [zip, toList_zipWith, List.zip]
 
-@[simp] theorem toList_zipWithAll (f : Option α → Option β → γ) (as : Array α) (bs : Array β) :
-    (Array.zipWithAll as bs f).toList = List.zipWithAll f as.toList bs.toList := by
-  cases as
-  cases bs
-  simp
-
-@[simp] theorem size_zipWith (as : Array α) (bs : Array β) (f : α → β → γ) :
-    (as.zipWith bs f).size = min as.size bs.size := by
-  rw [size_eq_length_toList, toList_zipWith, List.length_zipWith]
-
-@[simp] theorem size_zip (as : Array α) (bs : Array β) :
-    (as.zip bs).size = min as.size bs.size :=
-  as.size_zipWith bs Prod.mk
-
 /-! ### findSomeM?, findM?, findSome?, find? -/
 
 @[simp] theorem findSomeM?_toList [Monad m] [LawfulMonad m] (p : α → m (Option β)) (as : Array α) :
@@ -2003,6 +1720,11 @@ Our goal is to have `simp` "pull `List.toArray` outwards" as much as possible.
   apply ext'
   simp
 
+@[simp] theorem toArray_appendList (l₁ l₂ : List α) :
+    l₁.toArray ++ l₂ = (l₁ ++ l₂).toArray := by
+  apply ext'
+  simp
+
 @[simp] theorem set_toArray (l : List α) (i : Fin l.toArray.size) (a : α) :
     l.toArray.set i a = (l.set i a).toArray := by
   apply ext'
@@ -2013,10 +1735,10 @@ Our goal is to have `simp` "pull `List.toArray` outwards" as much as possible.
   apply ext'
   simp
 
-@[simp] theorem setIfInBounds_toArray (l : List α) (i : Nat) (a : α) :
-    l.toArray.setIfInBounds i a  = (l.set i a).toArray := by
+@[simp] theorem setD_toArray (l : List α) (i : Nat) (a : α) :
+    l.toArray.setD i a  = (l.set i a).toArray := by
   apply ext'
-  simp only [setIfInBounds]
+  simp only [setD]
   split
   · simp
   · simp_all [List.set_eq_of_length_le]
@@ -2061,8 +1783,12 @@ theorem all_toArray (p : α → Bool) (l : List α) : l.toArray.all p = l.all p
   subst h
   rw [all_toList]
 
-@[simp] theorem swap_toArray (l : List α) (i j : Nat) {hi hj}:
-    l.toArray.swap i j hi hj = ((l.set i l[j]).set j l[i]).toArray := by
+@[simp] theorem swap_toArray (l : List α) (i j : Fin l.toArray.size) :
+    l.toArray.swap i j = ((l.set i l[j]).set j l[i]).toArray := by
+  apply ext'
+  simp
+
+@[simp] theorem pop_toArray (l : List α) : l.toArray.pop = l.dropLast.toArray := by
   apply ext'
   simp
 
@@ -2111,15 +1837,48 @@ theorem filterMap_toArray (f : α → Option β) (l : List α) :
 @[simp] theorem toArray_ofFn (f : Fin n → α) : (ofFn f).toArray = Array.ofFn f := by
   ext <;> simp
 
-@[simp] theorem eraseIdx_toArray (l : List α) (i : Nat) (h : i < l.toArray.size) :
-    l.toArray.eraseIdx i h = (l.eraseIdx i).toArray := by
-  rw [Array.eraseIdx]
-  split <;> rename_i h'
-  · rw [eraseIdx_toArray]
+theorem takeWhile_go_succ (p : α → Bool) (a : α) (l : List α) (i : Nat) :
+    takeWhile.go p (a :: l).toArray (i+1) r = takeWhile.go p l.toArray i r := by
+  rw [takeWhile.go, takeWhile.go]
+  simp only [size_toArray, length_cons, Nat.add_lt_add_iff_right, Array.get_eq_getElem,
+    getElem_toArray, getElem_cons_succ]
+  split
+  rw [takeWhile_go_succ]
+  rfl
+
+theorem takeWhile_go_toArray (p : α → Bool) (l : List α) (i : Nat) :
+    Array.takeWhile.go p l.toArray i r = r ++ (takeWhile p (l.drop i)).toArray := by
+  induction l generalizing i r with
+  | nil => simp [takeWhile.go]
+  | cons a l ih =>
+    rw [takeWhile.go]
+    cases i with
+    | zero =>
+      simp [takeWhile_go_succ, ih, takeWhile_cons]
+      split <;> simp
+    | succ i =>
+      simp only [size_toArray, length_cons, Nat.add_lt_add_iff_right, Array.get_eq_getElem,
+        getElem_toArray, getElem_cons_succ, drop_succ_cons]
+      split <;> rename_i h₁
+      · rw [takeWhile_go_succ, ih]
+        rw [← getElem_cons_drop_succ_eq_drop h₁, takeWhile_cons]
+        split <;> simp_all
+      · simp_all [drop_eq_nil_of_le]
+
+@[simp] theorem takeWhile_toArray (p : α → Bool) (l : List α) :
+    l.toArray.takeWhile p = (l.takeWhile p).toArray := by
+  simp [Array.takeWhile, takeWhile_go_toArray]
+
+@[simp] theorem feraseIdx_toArray (l : List α) (i : Fin l.toArray.size) :
+    l.toArray.feraseIdx i = (l.eraseIdx i).toArray := by
+  rw [feraseIdx]
+  split <;> rename_i h
+  · rw [feraseIdx_toArray]
     simp only [swap_toArray, Fin.getElem_fin, toList_toArray, mk.injEq]
     rw [eraseIdx_set_gt (by simp), eraseIdx_set_eq]
     simp
-  · simp at h h'
+  · rcases i with ⟨i, w⟩
+    simp at h w
     have t : i = l.length - 1 := by omega
     simp [t]
 termination_by l.length - i
@@ -2129,9 +1888,9 @@ decreasing_by
   simp
   omega
 
-@[simp] theorem eraseIdxIfInBounds_toArray (l : List α) (i : Nat) :
-    l.toArray.eraseIdxIfInBounds i = (l.eraseIdx i).toArray := by
-  rw [Array.eraseIdxIfInBounds]
+@[simp] theorem eraseIdx_toArray (l : List α) (i : Nat) :
+    l.toArray.eraseIdx i = (l.eraseIdx i).toArray := by
+  rw [Array.eraseIdx]
   split
   · simp
   · simp_all [eraseIdx_eq_self.2]
@@ -2150,13 +1909,13 @@ namespace Array
     (as.takeWhile p).toList = as.toList.takeWhile p := by
   induction as; simp
 
-@[simp] theorem toList_eraseIdx (as : Array α) (i : Nat) (h : i < as.size) :
-    (as.eraseIdx i h).toList = as.toList.eraseIdx i := by
+@[simp] theorem toList_feraseIdx (as : Array α) (i : Fin as.size) :
+    (as.feraseIdx i).toList = as.toList.eraseIdx i.1 := by
   induction as
   simp
 
-@[simp] theorem toList_eraseIdxIfInBounds (as : Array α) (i : Nat) :
-    (as.eraseIdxIfInBounds i).toList = as.toList.eraseIdx i := by
+@[simp] theorem toList_eraseIdx (as : Array α) (i : Nat) :
+    (as.eraseIdx i).toList = as.toList.eraseIdx i := by
   induction as
   simp
 
@@ -2210,20 +1969,6 @@ theorem foldr_filterMap (f : α → Option β) (g : β → γ → γ) (l : Array
   simp [List.foldr_filterMap]
   rfl
 
-theorem foldl_map' (g : α → β) (f : α → α → α) (f' : β → β → β) (a : α) (l : Array α)
-    (h : ∀ x y, f' (g x) (g y) = g (f x y)) :
-    (l.map g).foldl f' (g a) = g (l.foldl f a) := by
-  cases l
-  simp
-  rw [List.foldl_map' _ _ _ _ _ h]
-
-theorem foldr_map' (g : α → β) (f : α → α → α) (f' : β → β → β) (a : α) (l : List α)
-    (h : ∀ x y, f' (g x) (g y) = g (f x y)) :
-    (l.map g).foldr f' (g a) = g (l.foldr f a) := by
-  cases l
-  simp
-  rw [List.foldr_map' _ _ _ _ _ h]
-
 /-! ### flatten -/
 
 @[simp] theorem flatten_empty : flatten (#[] : Array (Array α)) = #[] := rfl
@@ -2346,8 +2091,6 @@ theorem toArray_concat {as : List α} {x : α} :
 
 @[deprecated back!_toArray (since := "2024-10-31")] abbrev back_toArray := @back!_toArray
 
-@[deprecated setIfInBounds_toArray (since := "2024-11-24")] abbrev setD_toArray := @setIfInBounds_toArray
-
 end List
 
 namespace Array
@@ -2493,11 +2236,4 @@ abbrev get_swap' := @getElem_swap'
 @[deprecated eq_push_pop_back!_of_size_ne_zero (since := "2024-10-31")]
 abbrev eq_push_pop_back_of_size_ne_zero := @eq_push_pop_back!_of_size_ne_zero
 
-@[deprecated set!_is_setIfInBounds (since := "2024-11-24")] abbrev set_is_setIfInBounds := @set!_is_setIfInBounds
-@[deprecated size_setIfInBounds (since := "2024-11-24")] abbrev size_setD := @size_setIfInBounds
-@[deprecated getElem_setIfInBounds_eq (since := "2024-11-24")] abbrev getElem_setD_eq := @getElem_setIfInBounds_eq
-@[deprecated getElem?_setIfInBounds_eq (since := "2024-11-24")] abbrev get?_setD_eq := @getElem?_setIfInBounds_eq
-@[deprecated getD_get?_setIfInBounds (since := "2024-11-24")] abbrev getD_setD := @getD_get?_setIfInBounds
-@[deprecated getElem_setIfInBounds (since := "2024-11-24")] abbrev getElem_setD := @getElem_setIfInBounds
-
 end Array

src/Init/Data/Array/Perm.lean

@@ -1,65 +0,0 @@
-/-
-Copyright (c) 2024 Lean FRO. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison
--/
-prelude
-import Init.Data.List.Nat.Perm
-import Init.Data.Array.Lemmas
-
-namespace Array
-
-open List
-
-/--
-`Perm as bs` asserts that `as` and `bs` are permutations of each other.
-
-This is a wrapper around `List.Perm`, and for now has much less API.
-For more complicated verification, use `perm_iff_toList_perm` and the `List` API.
--/
-def Perm (as bs : Array α) : Prop :=
-  as.toList ~ bs.toList
-
-@[inherit_doc] scoped infixl:50 " ~ " => Perm
-
-theorem perm_iff_toList_perm {as bs : Array α} : as ~ bs ↔ as.toList ~ bs.toList := Iff.rfl
-
-@[simp] theorem perm_toArray (as bs : List α) : as.toArray ~ bs.toArray ↔ as ~ bs := by
-  simp [perm_iff_toList_perm]
-
-@[simp, refl] protected theorem Perm.refl (l : Array α) : l ~ l := by
-  cases l
-  simp
-
-protected theorem Perm.rfl {l : List α} : l ~ l := .refl _
-
-theorem Perm.of_eq {l₁ l₂ : Array α} (h : l₁ = l₂) : l₁ ~ l₂ := h ▸ .rfl
-
-protected theorem Perm.symm {l₁ l₂ : Array α} (h : l₁ ~ l₂) : l₂ ~ l₁ := by
-  cases l₁; cases l₂
-  simp only [perm_toArray] at h
-  simpa using h.symm
-
-protected theorem Perm.trans {l₁ l₂ l₃ : Array α} (h₁ : l₁ ~ l₂) (h₂ : l₂ ~ l₃) : l₁ ~ l₃ := by
-  cases l₁; cases l₂; cases l₃
-  simp only [perm_toArray] at h₁ h₂
-  simpa using h₁.trans h₂
-
-instance : Trans (Perm (α := α)) (Perm (α := α)) (Perm (α := α)) where
-  trans h₁ h₂ := Perm.trans h₁ h₂
-
-theorem perm_comm {l₁ l₂ : Array α} : l₁ ~ l₂ ↔ l₂ ~ l₁ := ⟨Perm.symm, Perm.symm⟩
-
-theorem Perm.push (x y : α) {l₁ l₂ : Array α} (p : l₁ ~ l₂) :
-    (l₁.push x).push y ~ (l₂.push y).push x := by
-  cases l₁; cases l₂
-  simp only [perm_toArray] at p
-  simp only [push_toArray, List.append_assoc, singleton_append, perm_toArray]
-  exact p.append (Perm.swap' _ _ Perm.nil)
-
-theorem swap_perm {as : Array α} {i j : Nat} (h₁ : i < as.size) (h₂ : j < as.size) :
-    as.swap i j ~ as := by
-  simp only [swap, perm_iff_toList_perm, toList_set]
-  apply set_set_perm
-
-end Array

src/Init/Data/Array/QSort.lean

@@ -4,46 +4,46 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura
 -/
 prelude
-import Init.Data.Vector.Basic
+import Init.Data.Array.Basic
 import Init.Data.Ord
 
 namespace Array
+-- TODO: remove the [Inhabited α] parameters as soon as we have the tactic framework for automating proof generation and using Array.fget
 
-private def qpartition {n} (as : Vector α n) (lt : α → α → Bool) (lo hi : Nat)
-    (hlo : lo < n := by omega) (hhi : hi < n := by omega) : {n : Nat // lo ≤ n} × Vector α n :=
+def qpartition (as : Array α) (lt : α → α → Bool) (lo hi : Nat) : Nat × Array α :=
+  if h : as.size = 0 then (0, as) else have : Inhabited α := ⟨as[0]'(by revert h; cases as.size <;> simp)⟩ -- TODO: remove
   let mid := (lo + hi) / 2
-  let as  := if lt as[mid] as[lo] then as.swap lo mid else as
-  let as  := if lt as[hi]  as[lo] then as.swap lo hi  else as
-  let as  := if lt as[mid] as[hi] then as.swap mid hi else as
-  let pivot := as[hi]
-  let rec loop (as : Vector α n) (i j : Nat)
-      (ilo : lo ≤ i := by omega) (jh : j < n := by omega) (w : i ≤ j := by omega) :=
+  let as  := if lt (as.get! mid) (as.get! lo) then as.swap! lo mid else as
+  let as  := if lt (as.get! hi)  (as.get! lo) then as.swap! lo hi  else as
+  let as  := if lt (as.get! mid) (as.get! hi) then as.swap! mid hi else as
+  let pivot := as.get! hi
+  let rec loop (as : Array α) (i j : Nat) :=
     if h : j < hi then
-      if lt as[j] pivot then
-        loop (as.swap i j) (i+1) (j+1)
+      if lt (as.get! j) pivot then
+        let as := as.swap! i j
+        loop as (i+1) (j+1)
       else
         loop as i (j+1)
     else
-      (⟨i, ilo⟩, as.swap i hi)
+      let as := as.swap! i hi
+      (i, as)
+    termination_by hi - j
+    decreasing_by all_goals simp_wf; decreasing_trivial_pre_omega
   loop as lo lo
 
-@[inline] def qsort (as : Array α) (lt : α → α → Bool := by exact (· < ·))
-    (low := 0) (high := as.size - 1) : Array α :=
-  let rec @[specialize] sort {n} (as : Vector α n) (lo hi : Nat)
-      (hlo : lo < n := by omega) (hhi : hi < n := by omega) :=
-    if h₁ : lo < hi then
-      let ⟨⟨mid, hmid⟩, as⟩ := qpartition as lt lo hi
-      if h₂ : mid ≥ hi then
-        as
+@[inline] partial def qsort (as : Array α) (lt : α → α → Bool) (low := 0) (high := as.size - 1) : Array α :=
+  let rec @[specialize] sort (as : Array α) (low high : Nat) :=
+    if low < high then
+      let p := qpartition as lt low high;
+      -- TODO: fix `partial` support in the equation compiler, it breaks if we use `let (mid, as) := partition as lt low high`
+      let mid := p.1
+      let as  := p.2
+      if mid >= high then as
       else
-        sort (sort as lo mid) (mid+1) hi
+        let as := sort as low mid
+        sort as (mid+1) high
     else as
-  if h : as.size = 0 then
-    as
-  else
-    let low := min low (as.size - 1)
-    let high := min high (as.size - 1)
-    sort ⟨as, rfl⟩ low high |>.toArray
+  sort as low high
 
 set_option linter.unusedVariables.funArgs false in
 /--

src/Init/Data/Array/Set.lean

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

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

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

src/Init/Data/BitVec/Bitblast.lean

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

src/Init/Data/BitVec/Lemmas.lean

@@ -269,10 +269,6 @@ theorem ofBool_eq_iff_eq : ∀ {b b' : Bool}, BitVec.ofBool b = BitVec.ofBool b'
   getLsbD (x#'lt) i = x.testBit i := by
   simp [getLsbD, BitVec.ofNatLt]
 
-@[simp] theorem getMsbD_ofNatLt {n x i : Nat} (h : x < 2^n) :
-    getMsbD (x#'h) i = (decide (i < n) && x.testBit (n - 1 - i)) := by
-  simp [getMsbD, getLsbD]
-
 @[simp, bv_toNat] theorem toNat_ofNat (x w : Nat) : (BitVec.ofNat w x).toNat = x % 2^w := by
   simp [BitVec.toNat, BitVec.ofNat, Fin.ofNat']
 
@@ -565,10 +561,6 @@ theorem zeroExtend_eq_setWidth {v : Nat} {x : BitVec w} :
   else
     simp [n_le_i, toNat_ofNat]
 
-@[simp] theorem toInt_setWidth (x : BitVec w) :
-    (x.setWidth v).toInt = Int.bmod x.toNat (2^v) := by
-  simp [toInt_eq_toNat_bmod, toNat_setWidth, Int.emod_bmod]
-
 theorem setWidth'_eq {x : BitVec w} (h : w ≤ v) : x.setWidth' h = x.setWidth v := by
   apply eq_of_toNat_eq
   rw [toNat_setWidth, toNat_setWidth']
@@ -763,10 +755,6 @@ 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 getMsbD_allOnes : (allOnes v).getMsbD i = decide (i < v) := by
-  simp [allOnes]
-  omega
-
 @[simp] theorem getElem_allOnes (i : Nat) (h : i < v) : (allOnes v)[i] = true := by
   simp [getElem_eq_testBit_toNat, h]
 
@@ -784,12 +772,6 @@ theorem extractLsb'_eq_extractLsb {w : Nat} (x : BitVec w) (start len : Nat) (h
 @[simp] theorem toNat_or (x y : BitVec v) :
     BitVec.toNat (x ||| y) = BitVec.toNat x ||| BitVec.toNat y := rfl
 
-@[simp] theorem toInt_or (x y : BitVec w) :
-    BitVec.toInt (x ||| y) = Int.bmod (BitVec.toNat x ||| BitVec.toNat y) (2^w) := by
-  rw_mod_cast [Int.bmod_def, BitVec.toInt, toNat_or, Nat.mod_eq_of_lt
-    (Nat.or_lt_two_pow (BitVec.isLt x) (BitVec.isLt y))]
-  omega
-
 @[simp] theorem toFin_or (x y : BitVec v) :
     BitVec.toFin (x ||| y) = BitVec.toFin x ||| BitVec.toFin y := by
   apply Fin.eq_of_val_eq
@@ -857,12 +839,6 @@ instance : Std.LawfulCommIdentity (α := BitVec n) (· ||| · ) (0#n) where
 @[simp] theorem toNat_and (x y : BitVec v) :
     BitVec.toNat (x &&& y) = BitVec.toNat x &&& BitVec.toNat y := rfl
 
-@[simp] theorem toInt_and (x y : BitVec w) :
-    BitVec.toInt (x &&& y) = Int.bmod (BitVec.toNat x &&& BitVec.toNat y) (2^w) := by
-  rw_mod_cast [Int.bmod_def, BitVec.toInt, toNat_and, Nat.mod_eq_of_lt
-    (Nat.and_lt_two_pow x.toNat (BitVec.isLt y))]
-  omega
-
 @[simp] theorem toFin_and (x y : BitVec v) :
     BitVec.toFin (x &&& y) = BitVec.toFin x &&& BitVec.toFin y := by
   apply Fin.eq_of_val_eq
@@ -930,12 +906,6 @@ instance : Std.LawfulCommIdentity (α := BitVec n) (· &&& · ) (allOnes n) wher
 @[simp] theorem toNat_xor (x y : BitVec v) :
     BitVec.toNat (x ^^^ y) = BitVec.toNat x ^^^ BitVec.toNat y := rfl
 
-@[simp] theorem toInt_xor (x y : BitVec w) :
-    BitVec.toInt (x ^^^ y) = Int.bmod (BitVec.toNat x ^^^ BitVec.toNat y) (2^w) := by
-  rw_mod_cast [Int.bmod_def, BitVec.toInt, toNat_xor, Nat.mod_eq_of_lt
-    (Nat.xor_lt_two_pow (BitVec.isLt x) (BitVec.isLt y))]
-  omega
-
 @[simp] theorem toFin_xor (x y : BitVec v) :
     BitVec.toFin (x ^^^ y) = BitVec.toFin x ^^^ BitVec.toFin y := by
   apply Fin.eq_of_val_eq
@@ -1013,13 +983,6 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
           _ ≤ 2 ^ i := Nat.pow_le_pow_of_le_right Nat.zero_lt_two w
       · simp
 
-@[simp] theorem toInt_not {x : BitVec w} :
-    (~~~x).toInt = Int.bmod (2^w - 1 - x.toNat) (2^w) := by
-  rw_mod_cast [BitVec.toInt, BitVec.toNat_not, Int.bmod_def]
-  simp [show ((2^w : Nat) : Int) - 1 - x.toNat = ((2^w - 1 - x.toNat) : Nat) by omega]
-  rw_mod_cast [Nat.mod_eq_of_lt (by omega)]
-  omega
-
 @[simp] theorem ofInt_negSucc_eq_not_ofNat {w n : Nat} :
     BitVec.ofInt w (Int.negSucc n) = ~~~.ofNat w n := by
   simp only [BitVec.ofInt, Int.toNat, Int.ofNat_eq_coe, toNat_eq, toNat_ofNatLt, toNat_not,
@@ -1044,10 +1007,6 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
 @[simp] theorem getLsbD_not {x : BitVec v} : (~~~x).getLsbD i = (decide (i < v) && ! x.getLsbD i) := by
   by_cases h' : i < v <;> simp_all [not_def]
 
-@[simp] theorem getMsbD_not {x : BitVec v} :
-    (~~~x).getMsbD i = (decide (i < v) && ! x.getMsbD i) := by
-  by_cases h' : i < v <;> simp_all [not_def]
-
 @[simp] theorem getElem_not {x : BitVec w} {i : Nat} (h : i < w) : (~~~x)[i] = !x[i] := by
   simp only [getElem_eq_testBit_toNat, toNat_not]
   rw [← Nat.sub_add_eq, Nat.add_comm 1]
@@ -1316,61 +1275,6 @@ theorem toNat_ushiftRight_lt (x : BitVec w) (n : Nat) (hn : n ≤ w) :
     · apply hn
   · apply Nat.pow_pos (by decide)
 
-
-/-- Shifting right by `n`, which is larger than the bitwidth `w` produces `0. -/
-theorem ushiftRight_eq_zero {x : BitVec w} {n : Nat} (hn : w ≤ n) :
-    x >>> n = 0#w := by
-  simp only [toNat_eq, toNat_ushiftRight, toNat_ofNat, Nat.zero_mod]
-  have : 2^w ≤ 2^n := Nat.pow_le_pow_of_le Nat.one_lt_two hn
-  rw [Nat.shiftRight_eq_div_pow, Nat.div_eq_of_lt (by omega)]
-
-
-/--
-Unsigned shift right by at least one bit makes the interpretations of the bitvector as an `Int` or `Nat` agree,
-because it makes the value of the bitvector less than or equal to `2^(w-1)`.
--/
-theorem toInt_ushiftRight_of_lt {x : BitVec w} {n : Nat} (hn : 0 < n) :
-    (x >>> n).toInt = x.toNat >>> n := by
-  rw [toInt_eq_toNat_cond]
-  simp only [toNat_ushiftRight, ite_eq_left_iff, Nat.not_lt]
-  intros h
-  by_cases hn : n ≤ w
-  · have h1 := Nat.mul_lt_mul_of_pos_left (toNat_ushiftRight_lt x n hn) Nat.two_pos
-    simp only [toNat_ushiftRight, Nat.zero_lt_succ, Nat.mul_lt_mul_left] at h1
-    have : 2 ^ (w - n).succ ≤ 2^ w := Nat.pow_le_pow_of_le (by decide) (by omega)
-    have := show 2 * x.toNat >>> n < 2 ^ w by
-      omega
-    omega
-  · have : x.toNat >>> n = 0 := by
-      apply Nat.shiftRight_eq_zero
-      have : 2^w ≤ 2^n := Nat.pow_le_pow_of_le (by decide) (by omega)
-      omega
-    simp [this] at h
-    omega
-
-/--
-Unsigned shift right by at least one bit makes the interpretations of the bitvector as an `Int` or `Nat` agree,
-because it makes the value of the bitvector less than or equal to `2^(w-1)`.
-In the case when `n = 0`, then the shift right value equals the integer interpretation.
--/
-@[simp]
-theorem toInt_ushiftRight {x : BitVec w} {n : Nat} :
-    (x >>> n).toInt = if n = 0 then x.toInt else x.toNat >>> n := by
-  by_cases hn : n = 0
-  · simp [hn]
-  · rw [toInt_ushiftRight_of_lt (by omega), toInt_eq_toNat_cond]
-    simp [hn]
-
-@[simp]
-theorem toFin_uShiftRight {x : BitVec w} {n : Nat} :
-    (x >>> n).toFin = x.toFin / (Fin.ofNat' (2^w) (2^n)) := by
-  apply Fin.eq_of_val_eq
-  by_cases hn : n < w
-  · simp [Nat.shiftRight_eq_div_pow, Nat.mod_eq_of_lt (Nat.pow_lt_pow_of_lt Nat.one_lt_two hn)]
-  · simp only [Nat.not_lt] at hn
-    rw [ushiftRight_eq_zero (by omega)]
-    simp [Nat.dvd_iff_mod_eq_zero.mp (Nat.pow_dvd_pow 2 hn)]
-
 @[simp]
 theorem getMsbD_ushiftRight {x : BitVec w} {i n : Nat} :
     (x >>> n).getMsbD i = (decide (i < w) && (!decide (i < n) && x.getMsbD (i - n))) := by
@@ -1576,12 +1480,6 @@ theorem getLsbD_sshiftRight' {x y: BitVec w} {i : Nat} :
       (!decide (w ≤ i) && if y.toNat + i < w then x.getLsbD (y.toNat + i) else x.msb) := by
   simp only [BitVec.sshiftRight', BitVec.getLsbD_sshiftRight]
 
-@[simp]
-theorem getElem_sshiftRight' {x y : BitVec w} {i : Nat} (h : i < w) :
-    (x.sshiftRight' y)[i] =
-      (!decide (w ≤ i) && if y.toNat + i < w then x.getLsbD (y.toNat + i) else x.msb) := by
-  simp only [← getLsbD_eq_getElem, BitVec.sshiftRight', BitVec.getLsbD_sshiftRight]
-
 @[simp]
 theorem getMsbD_sshiftRight' {x y: BitVec w} {i : Nat} :
     (x.sshiftRight y.toNat).getMsbD i = (decide (i < w) && if i < y.toNat then x.msb else x.getMsbD (i - y.toNat)) := by
@@ -1674,82 +1572,6 @@ theorem signExtend_eq_setWidth_of_lt (x : BitVec w) {v : Nat} (hv : v ≤ w):
 theorem signExtend_eq (x : BitVec w) : x.signExtend w = x := by
   rw [signExtend_eq_setWidth_of_lt _ (Nat.le_refl _), setWidth_eq]
 
-/-- Sign extending to a larger bitwidth depends on the msb.
-If the msb is false, then the result equals the original value.
-If the msb is true, then we add a value of `(2^v - 2^w)`, which arises from the sign extension. -/
-private theorem toNat_signExtend_of_le (x : BitVec w) {v : Nat} (hv : w ≤ v) :
-    (x.signExtend v).toNat = x.toNat + if x.msb then 2^v - 2^w else 0 := by
-  apply Nat.eq_of_testBit_eq
-  intro i
-  have ⟨k, hk⟩ := Nat.exists_eq_add_of_le hv
-  rw [hk, testBit_toNat, getLsbD_signExtend, Nat.pow_add, ← Nat.mul_sub_one, Nat.add_comm (x.toNat)]
-  by_cases hx : x.msb
-  · simp only [hx, Bool.if_true_right, ↓reduceIte,
-      Nat.testBit_mul_pow_two_add _ x.isLt,
-      testBit_toNat, Nat.testBit_two_pow_sub_one]
-    -- Case analysis on i being in the intervals [0..w), [w..w + k), [w+k..∞)
-    have hi : i < w ∨ (w ≤ i ∧ i < w + k) ∨ w + k ≤ i := by omega
-    rcases hi with hi | hi | hi
-    · simp [hi]; omega
-    · simp [hi]; omega
-    · simp [hi, show ¬ (i < w + k) by omega, show ¬ (i < w) by omega]
-      omega
-  · simp only [hx, Bool.if_false_right,
-      Bool.false_eq_true, ↓reduceIte, Nat.zero_add, testBit_toNat]
-    have hi : i < w ∨ (w ≤ i ∧ i < w + k) ∨ w + k ≤ i := by omega
-    rcases hi with hi | hi | hi
-    · simp [hi]; omega
-    · simp [hi]
-    · simp [hi, show ¬ (i < w + k) by omega, show ¬ (i < w) by omega, getLsbD_ge x i (by omega)]
-
-/-- Sign extending to a larger bitwidth depends on the msb.
-If the msb is false, then the result equals the original value.
-If the msb is true, then we add a value of `(2^v - 2^w)`, which arises from the sign extension. -/
-theorem toNat_signExtend (x : BitVec w) {v : Nat} :
-    (x.signExtend v).toNat = (x.setWidth v).toNat + if x.msb then 2^v - 2^w else 0 := by
-  by_cases h : v ≤ w
-  · have : 2^v ≤ 2^w := Nat.pow_le_pow_of_le_right Nat.two_pos h
-    simp [signExtend_eq_setWidth_of_lt x h, toNat_setWidth, Nat.sub_eq_zero_of_le this]
-  · have : 2^w ≤ 2^v := Nat.pow_le_pow_of_le_right Nat.two_pos (by omega)
-    rw [toNat_signExtend_of_le x (by omega), toNat_setWidth, Nat.mod_eq_of_lt (by omega)]
-
-/-
-If the current width `w` is smaller than the extended width `v`,
-then the value when interpreted as an integer does not change.
--/
-theorem toInt_signExtend_of_lt {x : BitVec w} (hv : w < v):
-    (x.signExtend v).toInt = x.toInt := by
-  simp only [toInt_eq_msb_cond, toNat_signExtend]
-  have : (x.signExtend v).msb = x.msb := by
-    rw [msb_eq_getLsbD_last, getLsbD_eq_getElem (Nat.sub_one_lt_of_lt hv)]
-    simp [getElem_signExtend, Nat.le_sub_one_of_lt hv]
-  have H : 2^w ≤ 2^v := Nat.pow_le_pow_of_le_right (by omega) (by omega)
-  simp only [this, toNat_setWidth, Int.natCast_add, Int.ofNat_emod, Int.natCast_mul]
-  by_cases h : x.msb
-  <;> norm_cast
-  <;> simp [h, Nat.mod_eq_of_lt (Nat.lt_of_lt_of_le x.isLt H)]
-  omega
-
-/-
-If the current width `w` is larger than the extended width `v`,
-then the value when interpreted as an integer is truncated,
-and we compute a modulo by `2^v`.
--/
-theorem toInt_signExtend_of_le {x : BitVec w} (hv : v ≤ w) :
-    (x.signExtend v).toInt = Int.bmod x.toNat (2^v) := by
-  simp [signExtend_eq_setWidth_of_lt _ hv]
-
-/-
-Interpreting the sign extension of `(x : BitVec w)` to width `v`
-computes `x % 2^v` (where `%` is the balanced mod).
--/
-theorem toInt_signExtend (x : BitVec w) :
-    (x.signExtend v).toInt = Int.bmod x.toNat (2^(min v w)) := by
-  by_cases hv : v ≤ w
-  · simp [toInt_signExtend_of_le hv, Nat.min_eq_left hv]
-  · simp only [Nat.not_le] at hv
-    rw [toInt_signExtend_of_lt hv, Nat.min_eq_right (by omega), toInt_eq_toNat_bmod]
-
 /-! ### append -/
 
 theorem append_def (x : BitVec v) (y : BitVec w) :
@@ -2057,46 +1879,6 @@ theorem getElem_concat (x : BitVec w) (b : Bool) (i : Nat) (h : i < w + 1) :
     (concat x b)[i + 1] = x[i] := by
   simp [getElem_concat, h, getLsbD_eq_getElem]
 
-@[simp]
-theorem getMsbD_concat {i w : Nat} {b : Bool} {x : BitVec w} :
-    (x.concat b).getMsbD i = if i < w then x.getMsbD i else decide (i = w) && b := by
-  simp only [getMsbD_eq_getLsbD, Nat.add_sub_cancel, getLsbD_concat]
-  by_cases h₀ : i = w
-  · simp [h₀]
-  · by_cases h₁ : i < w
-    · simp [h₀, h₁, show ¬ w - i = 0 by omega, show i < w + 1 by omega, Nat.sub_sub, Nat.add_comm]
-    · simp only [show w - i = 0 by omega, ↓reduceIte, h₁, h₀, decide_false, Bool.false_and,
-        Bool.and_eq_false_imp, decide_eq_true_eq]
-      intro
-      omega
-
-@[simp]
-theorem msb_concat {w : Nat} {b : Bool} {x : BitVec w} :
-    (x.concat b).msb = if 0 < w then x.msb else b := by
-  simp only [BitVec.msb, getMsbD_eq_getLsbD, Nat.zero_lt_succ, decide_true, Nat.add_one_sub_one,
-    Nat.sub_zero, Bool.true_and]
-  by_cases h₀ : 0 < w
-  · simp only [Nat.lt_add_one, getLsbD_eq_getElem, getElem_concat, h₀, ↓reduceIte, decide_true,
-      Bool.true_and, ite_eq_right_iff]
-    intro
-    omega
-  · simp [h₀, show w = 0 by omega]
-
-@[simp] theorem toInt_concat (x : BitVec w) (b : Bool) :
-    (concat x b).toInt = if w = 0 then -b.toInt else x.toInt * 2 + b.toInt := by
-  simp only [BitVec.toInt, toNat_concat]
-  cases w
-  · cases b <;> simp [eq_nil x]
-  · cases b <;> simp <;> omega
-
-@[simp] theorem toFin_concat (x : BitVec w) (b : Bool) :
-    (concat x b).toFin = Fin.mk (x.toNat * 2 + b.toNat) (by
-      have := Bool.toNat_lt b
-      simp [← Nat.two_pow_pred_add_two_pow_pred, Bool.toNat_lt b]
-      omega
-    ) := by
-  simp [← Fin.val_inj]
-
 @[simp] theorem not_concat (x : BitVec w) (b : Bool) : ~~~(concat x b) = concat (~~~x) !b := by
   ext i; cases i using Fin.succRecOn <;> simp [*, Nat.succ_lt_succ]
 
@@ -2112,10 +1894,6 @@ theorem msb_concat {w : Nat} {b : Bool} {x : BitVec w} :
     (concat x a) ^^^ (concat y b) = concat (x ^^^ y) (a ^^ b) := by
   ext i; cases i using Fin.succRecOn <;> simp
 
-@[simp] theorem zero_concat_false : concat 0#w false = 0#(w + 1) := by
-  ext
-  simp [getLsbD_concat]
-
 /-! ### shiftConcat -/
 
 theorem getLsbD_shiftConcat (x : BitVec w) (b : Bool) (i : Nat) :
@@ -2161,6 +1939,35 @@ theorem toNat_shiftConcat_lt_of_lt {x : BitVec w} {b : Bool} {k : Nat}
   have := Bool.toNat_lt b
   omega
 
+@[simp] theorem zero_concat_false : concat 0#w false = 0#(w + 1) := by
+  ext
+  simp [getLsbD_concat]
+
+@[simp]
+theorem getMsbD_concat {i w : Nat} {b : Bool} {x : BitVec w} :
+    (x.concat b).getMsbD i = if i < w then x.getMsbD i else decide (i = w) && b := by
+  simp only [getMsbD_eq_getLsbD, Nat.add_sub_cancel, getLsbD_concat]
+  by_cases h₀ : i = w
+  · simp [h₀]
+  · by_cases h₁ : i < w
+    · simp [h₀, h₁, show ¬ w - i = 0 by omega, show i < w + 1 by omega, Nat.sub_sub, Nat.add_comm]
+    · simp only [show w - i = 0 by omega, ↓reduceIte, h₁, h₀, decide_false, Bool.false_and,
+        Bool.and_eq_false_imp, decide_eq_true_eq]
+      intro
+      omega
+
+@[simp]
+theorem msb_concat {w : Nat} {b : Bool} {x : BitVec w} :
+    (x.concat b).msb = if 0 < w then x.msb else b := by
+  simp only [BitVec.msb, getMsbD_eq_getLsbD, Nat.zero_lt_succ, decide_true, Nat.add_one_sub_one,
+    Nat.sub_zero, Bool.true_and]
+  by_cases h₀ : 0 < w
+  · simp only [Nat.lt_add_one, getLsbD_eq_getElem, getElem_concat, h₀, ↓reduceIte, decide_true,
+      Bool.true_and, ite_eq_right_iff]
+    intro
+    omega
+  · simp [h₀, show w = 0 by omega]
+
 /-! ### add -/
 
 theorem add_def {n} (x y : BitVec n) : x + y = .ofNat n (x.toNat + y.toNat) := rfl
@@ -2831,6 +2638,12 @@ theorem getElem_rotateLeft {x : BitVec w} {r i : Nat} (h : i < w) :
       if h' : i < r % w then x[(w - (r % w) + i)] else x[i - (r % w)] := by
   simp [← BitVec.getLsbD_eq_getElem, h]
 
+/-- If `w ≤ x < 2 * w`, then `x % w = x - w` -/
+theorem mod_eq_sub_of_le_of_lt {x w : Nat} (x_le : w ≤ x) (x_lt : x < 2 * w) :
+    x % w = x - w := by
+  rw [Nat.mod_eq_sub_mod, Nat.mod_eq_of_lt (by omega)]
+  omega
+
 theorem getMsbD_rotateLeftAux_of_lt {x : BitVec w} {r : Nat} {i : Nat} (hi : i < w - r) :
     (x.rotateLeftAux r).getMsbD i = x.getMsbD (r + i) := by
   rw [rotateLeftAux, getMsbD_or]
@@ -2840,20 +2653,6 @@ theorem getMsbD_rotateLeftAux_of_ge {x : BitVec w} {r : Nat} {i : Nat} (hi : i
     (x.rotateLeftAux r).getMsbD i = (decide (i < w) && x.getMsbD (i - (w - r))) := by
   simp [rotateLeftAux, getMsbD_or, show i + r ≥ w by omega, show ¬i < w - r by omega]
 
-/--
-If a number `w * n ≤ i < w * (n + 1)`, then `i - w * n` equals `i % w`.
-This is true by subtracting `w * n` from the inequality, giving
-`0 ≤ i - w * n < w`, which uniquely identifies `i % w`.
--/
-private theorem Nat.sub_mul_eq_mod_of_lt_of_le (hlo : w * n ≤ i) (hhi : i < w * (n + 1)) :
-    i - w * n = i % w := by
-  rw [Nat.mod_def]
-  congr
-  symm
-  apply Nat.div_eq_of_lt_le
-    (by rw [Nat.mul_comm]; omega)
-    (by rw [Nat.mul_comm]; omega)
-
 /-- When `r < w`, we give a formula for `(x.rotateLeft r).getMsbD i`. -/
 theorem getMsbD_rotateLeft_of_lt {n w : Nat} {x : BitVec w} (hi : r < w):
     (x.rotateLeft r).getMsbD n = (decide (n < w) && x.getMsbD ((r + n) % w)) := by
@@ -2866,8 +2665,8 @@ theorem getMsbD_rotateLeft_of_lt {n w : Nat} {x : BitVec w} (hi : r < w):
       by_cases h₁ : n < w + 1
       · simp only [h₁, decide_true, Bool.true_and]
         have h₂ : (r + n) < 2 * (w + 1) := by omega
+        rw [mod_eq_sub_of_le_of_lt (by omega) (by omega)]
         congr 1
-        rw [← Nat.sub_mul_eq_mod_of_lt_of_le (n := 1) (by omega) (by omega), Nat.mul_one]
         omega
       · simp [h₁]
 
@@ -3184,6 +2983,20 @@ theorem replicate_succ_eq {x : BitVec w} :
     (x ++ replicate n x).cast (by rw [Nat.mul_succ]; omega) := by
   simp [replicate]
 
+/--
+If a number `w * n ≤ i < w * (n + 1)`, then `i - w * n` equals `i % w`.
+This is true by subtracting `w * n` from the inequality, giving
+`0 ≤ i - w * n < w`, which uniquely identifies `i % w`.
+-/
+private theorem Nat.sub_mul_eq_mod_of_lt_of_le (hlo : w * n ≤ i) (hhi : i < w * (n + 1)) :
+    i - w * n = i % w := by
+  rw [Nat.mod_def]
+  congr
+  symm
+  apply Nat.div_eq_of_lt_le
+    (by rw [Nat.mul_comm]; omega)
+    (by rw [Nat.mul_comm]; omega)
+
 @[simp]
 theorem getLsbD_replicate {n w : Nat} (x : BitVec w) :
     (x.replicate n).getLsbD i =
@@ -3289,11 +3102,6 @@ theorem toInt_neg_of_ne_intMin {x : BitVec w} (rs : x ≠ intMin w) :
   have := @Nat.two_pow_pred_mul_two w (by omega)
   split <;> split <;> omega
 
-theorem toInt_neg_eq_ite {x : BitVec w} :
-    (-x).toInt = if x = intMin w then x.toInt else -(x.toInt) := by
-  by_cases hx : x = intMin w <;>
-    simp [hx, neg_intMin, toInt_neg_of_ne_intMin]
-
 theorem msb_intMin {w : Nat} : (intMin w).msb = decide (0 < w) := by
   simp only [msb_eq_decide, toNat_intMin, decide_eq_decide]
   by_cases h : 0 < w <;> simp_all
@@ -3416,84 +3224,13 @@ theorem toNat_abs {x : BitVec w} : x.abs.toNat = if x.msb then 2^w - x.toNat els
   · simp [h]
 
 theorem getLsbD_abs {i : Nat} {x : BitVec w} :
-    getLsbD x.abs i = if x.msb then getLsbD (-x) i else getLsbD x i := by
-  by_cases h : x.msb <;> simp [BitVec.abs, h]
-
-theorem getElem_abs {i : Nat} {x : BitVec w} (h : i < w) :
-    x.abs[i] = if x.msb then (-x)[i] else x[i] := by
+   getLsbD x.abs i = if x.msb then getLsbD (-x) i else getLsbD x i := by
   by_cases h : x.msb <;> simp [BitVec.abs, h]
 
 theorem getMsbD_abs {i : Nat} {x : BitVec w} :
     getMsbD (x.abs) i = if x.msb then getMsbD (-x) i else getMsbD x i := by
   by_cases h : x.msb <;> simp [BitVec.abs, h]
 
-/-
-The absolute value of `x : BitVec w` is naively a case split on the sign of `x`.
-However, recall that when `x = intMin w`, `-x = x`.
-Thus, the full value of `abs x` is computed by the case split:
-- If `x : BitVec w` is `intMin`, then its absolute value is also `intMin w`, and
-  thus `toInt` will equal `intMin.toInt`.
-- Otherwise, if `x` is negative, then `x.abs.toInt = (-x).toInt`.
-- If `x` is positive, then it is equal to `x.abs.toInt = x.toInt`.
--/
-theorem toInt_abs_eq_ite {x : BitVec w} :
-  x.abs.toInt =
-    if x = intMin w then (intMin w).toInt
-    else if x.msb then -x.toInt
-    else x.toInt := by
-  by_cases hx : x = intMin w
-  · simp [hx]
-  · simp [hx]
-    by_cases hx₂ : x.msb
-    · simp [hx₂, abs_eq, toInt_neg_of_ne_intMin hx]
-    · simp [hx₂, abs_eq]
-
-
-
-/-
-The absolute value of `x : BitVec w` is a case split on the sign of `x`, when `x ≠ intMin w`.
-This is a variant of `toInt_abs_eq_ite`.
--/
-theorem toInt_abs_eq_ite_of_ne_intMin {x : BitVec w} (hx : x ≠ intMin w) :
-  x.abs.toInt = if x.msb then -x.toInt else x.toInt := by
-  simp [toInt_abs_eq_ite, hx]
-
-
-/--
-The absolute value of `x : BitVec w`, interpreted as an integer, is a case split:
-- When `x = intMin w`, then `x.abs = intMin w`
-- Otherwise, `x.abs.toInt` equals the absolute value (`x.toInt.natAbs`).
-
-This is a simpler version of `BitVec.toInt_abs_eq_ite`, which hides a case split on `x.msb`.
--/
-theorem toInt_abs_eq_natAbs {x : BitVec w} : x.abs.toInt =
-    if x = intMin w then (intMin w).toInt else x.toInt.natAbs := by
-  rw [toInt_abs_eq_ite]
-  by_cases hx : x = intMin w
-  · simp [hx]
-  · simp [hx]
-    by_cases h : x.msb
-    · simp only [h, ↓reduceIte]
-      have : x.toInt < 0 := by
-        rw [toInt_neg_iff]
-        have := msb_eq_true_iff_two_mul_ge.mp h
-        omega
-      omega
-    · simp only [h, Bool.false_eq_true, ↓reduceIte]
-      have : 0 ≤ x.toInt := by
-        rw [toInt_pos_iff]
-        exact msb_eq_false_iff_two_mul_lt.mp (by simp [h])
-      omega
-
-/-
-The absolute value of `(x : BitVec w)`, when interpreted as an integer,
-is the absolute value of `x.toInt` when `(x ≠ intMin)`.
--/
-theorem toInt_abs_eq_natAbs_of_ne_intMin {x : BitVec w} (hx : x ≠ intMin w) :
-    x.abs.toInt = x.toInt.natAbs := by
-  simp [toInt_abs_eq_natAbs, hx]
-
-
 /-! ### Decidable quantifiers -/
 
 theorem forall_zero_iff {P : BitVec 0 → Prop} :

src/Init/Data/Bool.lean

@@ -384,15 +384,6 @@ theorem toNat_lt (b : Bool) : b.toNat < 2 :=
 @[simp] theorem toNat_eq_one  {b : Bool} : b.toNat = 1 ↔ b = true := by
   cases b <;> simp
 
-/-! ## toInt -/
-
-/-- convert a `Bool` to an `Int`, `false -> 0`, `true -> 1` -/
-def toInt (b : Bool) : Int := cond b 1 0
-
-@[simp] theorem toInt_false : false.toInt = 0 := rfl
-
-@[simp] theorem toInt_true : true.toInt = 1 := rfl
-
 /-! ### ite -/
 
 @[simp] theorem if_true_left  (p : Prop) [h : Decidable p] (f : Bool) :

src/Init/Data/ByteArray/Basic.lean

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

src/Init/Data/Channel.lean

@@ -8,8 +8,6 @@ import Init.Data.Queue
 import Init.System.Promise
 import Init.System.Mutex
 
-set_option linter.deprecated false
-
 namespace IO
 
 /--
@@ -17,7 +15,6 @@ Internal state of an `Channel`.
 
 We maintain the invariant that at all times either `consumers` or `values` is empty.
 -/
-@[deprecated "Use Std.Channel.State from Std.Sync.Channel instead" (since := "2024-12-02")]
 structure Channel.State (α : Type) where
   values : Std.Queue α := ∅
   consumers : Std.Queue (Promise (Option α)) := ∅
@@ -30,14 +27,12 @@ FIFO channel with unbounded buffer, where `recv?` returns a `Task`.
 A channel can be closed.  Once it is closed, all `send`s are ignored, and
 `recv?` returns `none` once the queue is empty.
 -/
-@[deprecated "Use Std.Channel from Std.Sync.Channel instead" (since := "2024-12-02")]
 def Channel (α : Type) : Type := Mutex (Channel.State α)
 
 instance : Nonempty (Channel α) :=
   inferInstanceAs (Nonempty (Mutex _))
 
 /-- Creates a new `Channel`. -/
-@[deprecated "Use Std.Channel.new from Std.Sync.Channel instead" (since := "2024-12-02")]
 def Channel.new : BaseIO (Channel α) :=
   Mutex.new {}
 
@@ -46,7 +41,6 @@ Sends a message on an `Channel`.
 
 This function does not block.
 -/
-@[deprecated "Use Std.Channel.send from Std.Sync.Channel instead" (since := "2024-12-02")]
 def Channel.send (ch : Channel α) (v : α) : BaseIO Unit :=
   ch.atomically do
     let st ← get
@@ -60,7 +54,6 @@ def Channel.send (ch : Channel α) (v : α) : BaseIO Unit :=
 /--
 Closes an `Channel`.
 -/
-@[deprecated "Use Std.Channel.close from Std.Sync.Channel instead" (since := "2024-12-02")]
 def Channel.close (ch : Channel α) : BaseIO Unit :=
   ch.atomically do
     let st ← get
@@ -74,7 +67,6 @@ Every message is only received once.
 
 Returns `none` if the channel is closed and the queue is empty.
 -/
-@[deprecated "Use Std.Channel.recv? from Std.Sync.Channel instead" (since := "2024-12-02")]
 def Channel.recv? (ch : Channel α) : BaseIO (Task (Option α)) :=
   ch.atomically do
     let st ← get
@@ -93,7 +85,6 @@ def Channel.recv? (ch : Channel α) : BaseIO (Task (Option α)) :=
 
 Note that if this function is called twice, each `forAsync` only gets half the messages.
 -/
-@[deprecated "Use Std.Channel.forAsync from Std.Sync.Channel instead" (since := "2024-12-02")]
 partial def Channel.forAsync (f : α → BaseIO Unit) (ch : Channel α)
     (prio : Task.Priority := .default) : BaseIO (Task Unit) := do
   BaseIO.bindTask (prio := prio) (← ch.recv?) fun
@@ -105,13 +96,11 @@ Receives all currently queued messages from the channel.
 
 Those messages are dequeued and will not be returned by `recv?`.
 -/
-@[deprecated "Use Std.Channel.recvAllCurrent from Std.Sync.Channel instead" (since := "2024-12-02")]
 def Channel.recvAllCurrent (ch : Channel α) : BaseIO (Array α) :=
   ch.atomically do
     modifyGet fun st => (st.values.toArray, { st with values := ∅ })
 
 /-- Type tag for synchronous (blocking) operations on a `Channel`. -/
-@[deprecated "Use Std.Channel.Sync from Std.Sync.Channel instead" (since := "2024-12-02")]
 def Channel.Sync := Channel
 
 /--
@@ -121,7 +110,6 @@ For example, `ch.sync.recv?` blocks until the next message,
 and `for msg in ch.sync do ...` iterates synchronously over the channel.
 These functions should only be used in dedicated threads.
 -/
-@[deprecated "Use Std.Channel.sync from Std.Sync.Channel instead" (since := "2024-12-02")]
 def Channel.sync (ch : Channel α) : Channel.Sync α := ch
 
 /--
@@ -130,11 +118,9 @@ Synchronously receives a message from the channel.
 Every message is only received once.
 Returns `none` if the channel is closed and the queue is empty.
 -/
-@[deprecated "Use Std.Channel.Sync.recv? from Std.Sync.Channel instead" (since := "2024-12-02")]
 def Channel.Sync.recv? (ch : Channel.Sync α) : BaseIO (Option α) := do
   IO.wait (← Channel.recv? ch)
 
-@[deprecated "Use Std.Channel.Sync.forIn from Std.Sync.Channel instead" (since := "2024-12-02")]
 private partial def Channel.Sync.forIn [Monad m] [MonadLiftT BaseIO m]
     (ch : Channel.Sync α) (f : α → β → m (ForInStep β)) : β → m β := fun b => do
   match ← ch.recv? with

src/Init/Data/Fin/Basic.lean

@@ -36,6 +36,12 @@ def succ : Fin n → Fin (n + 1)
 
 variable {n : Nat}
 
+/--
+Returns `a` modulo `n + 1` as a `Fin n.succ`.
+-/
+protected def ofNat {n : Nat} (a : Nat) : Fin (n + 1) :=
+  ⟨a % (n+1), Nat.mod_lt _ (Nat.zero_lt_succ _)⟩
+
 /--
 Returns `a` modulo `n` as a `Fin n`.
 
@@ -44,12 +50,9 @@ The assumption `NeZero n` 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)⟩
 
-/--
-Returns `a` modulo `n + 1` as a `Fin n.succ`.
--/
-@[deprecated Fin.ofNat' (since := "2024-11-27")]
-protected def ofNat {n : Nat} (a : Nat) : Fin (n + 1) :=
-  ⟨a % (n+1), Nat.mod_lt _ (Nat.zero_lt_succ _)⟩
+-- 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
 
 private theorem mlt {b : Nat} : {a : Nat} → a < n → b % n < n
   | 0,   h => Nat.mod_lt _ h

src/Init/Data/Fin/Fold.lean

@@ -13,17 +13,17 @@ namespace Fin
 /-- Folds over `Fin n` from the left: `foldl 3 f x = f (f (f x 0) 1) 2`. -/
 @[inline] def foldl (n) (f : α → Fin n → α) (init : α) : α := loop init 0 where
   /-- Inner loop for `Fin.foldl`. `Fin.foldl.loop n f x i = f (f (f x i) ...) (n-1)`  -/
-  @[semireducible, specialize] loop (x : α) (i : Nat) : α :=
+  loop (x : α) (i : Nat) : α :=
     if h : i < n then loop (f x ⟨i, h⟩) (i+1) else x
   termination_by n - i
+  decreasing_by decreasing_trivial_pre_omega
 
 /-- Folds over `Fin n` from the right: `foldr 3 f x = f 0 (f 1 (f 2 x))`. -/
-@[inline] def foldr (n) (f : Fin n → α → α) (init : α) : α := loop n (Nat.le_refl n) init where
+@[inline] def foldr (n) (f : Fin n → α → α) (init : α) : α := loop ⟨n, Nat.le_refl n⟩ init where
   /-- Inner loop for `Fin.foldr`. `Fin.foldr.loop n f i x = f 0 (f ... (f (i-1) x))`  -/
-  @[specialize] loop : (i : _) → i ≤ n → α → α
-  | 0, _, x => x
-  | i+1, h, x => loop i (Nat.le_of_lt h) (f ⟨i, h⟩ x)
-  termination_by structural i => i
+  loop : {i // i ≤ n} → α → α
+  | ⟨0, _⟩, x => x
+  | ⟨i+1, h⟩, x => loop ⟨i, Nat.le_of_lt h⟩ (f ⟨i, h⟩ x)
 
 /--
 Folds a monadic function over `Fin n` from left to right:
@@ -47,7 +47,7 @@ Fin.foldlM n f x₀ = do
     pure xₙ
   ```
   -/
-  @[semireducible, specialize] loop (x : α) (i : Nat) : m α := do
+  loop (x : α) (i : Nat) : m α := do
     if h : i < n then f x ⟨i, h⟩ >>= (loop · (i+1)) else pure x
   termination_by n - i
   decreasing_by decreasing_trivial_pre_omega
@@ -76,7 +76,7 @@ Fin.foldrM n f xₙ = do
     pure x₀
   ```
   -/
-  @[semireducible, specialize] loop : {i // i ≤ n} → α → m α
+  loop : {i // i ≤ n} → α → m α
   | ⟨0, _⟩, x => pure x
   | ⟨i+1, h⟩, x => f ⟨i, h⟩ x >>= loop ⟨i, Nat.le_of_lt h⟩
 
@@ -125,7 +125,7 @@ theorem foldrM_loop [Monad m] [LawfulMonad m] (f : Fin (n+1) → α → m α) (x
   | zero =>
     rw [foldrM_loop_zero, foldrM_loop_succ, pure_bind]
     conv => rhs; rw [←bind_pure (f 0 x)]
-    congr; funext
+    congr; funext; exact foldrM_loop_zero ..
   | succ i ih =>
     rw [foldrM_loop_succ, foldrM_loop_succ, bind_assoc]
     congr; funext; exact ih ..
@@ -176,19 +176,17 @@ theorem foldl_eq_foldlM (f : α → Fin n → α) (x) :
 /-! ### foldr -/
 
 theorem foldr_loop_zero (f : Fin n → α → α) (x) :
-    foldr.loop n f 0 (Nat.zero_le _) x = x := by
+    foldr.loop n f ⟨0, Nat.zero_le _⟩ x = x := by
   rw [foldr.loop]
 
 theorem foldr_loop_succ (f : Fin n → α → α) (x) (h : i < n) :
-    foldr.loop n f (i+1) h x = foldr.loop n f i (Nat.le_of_lt h) (f ⟨i, h⟩ x) := by
+    foldr.loop n f ⟨i+1, h⟩ x = foldr.loop n f ⟨i, Nat.le_of_lt h⟩ (f ⟨i, h⟩ x) := by
   rw [foldr.loop]
 
 theorem foldr_loop (f : Fin (n+1) → α → α) (x) (h : i+1 ≤ n+1) :
-    foldr.loop (n+1) f (i+1) h x =
-      f 0 (foldr.loop n (fun j => f j.succ) i (Nat.le_of_succ_le_succ h) x) := by
-  induction i generalizing x with
-  | zero => simp [foldr_loop_succ, foldr_loop_zero]
-  | succ i ih => rw [foldr_loop_succ, ih]; rfl
+    foldr.loop (n+1) f ⟨i+1, h⟩ x =
+      f 0 (foldr.loop n (fun j => f j.succ) ⟨i, Nat.le_of_succ_le_succ h⟩ x) := by
+  induction i generalizing x <;> simp [foldr_loop_zero, foldr_loop_succ, *]
 
 @[simp] theorem foldr_zero (f : Fin 0 → α → α) (x) : foldr 0 f x = x :=
   foldr_loop_zero ..

src/Init/Data/Float.lean

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

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

@@ -34,8 +34,4 @@ theorem shiftRight_eq_div_pow (m : Int) (n : Nat) :
 theorem zero_shiftRight (n : Nat) : (0 : Int) >>> n = 0 := by
   simp [Int.shiftRight_eq_div_pow]
 
-@[simp]
-theorem shiftRight_zero (n : Int) : n >>> 0 = n := by
-  simp [Int.shiftRight_eq_div_pow]
-
 end Int

src/Init/Data/Int/DivModLemmas.lean

@@ -125,7 +125,7 @@ theorem eq_one_of_mul_eq_one_right {a b : Int} (H : 0 ≤ a) (H' : a * b = 1) :
   eq_one_of_dvd_one H ⟨b, H'.symm⟩
 
 theorem eq_one_of_mul_eq_one_left {a b : Int} (H : 0 ≤ b) (H' : a * b = 1) : b = 1 :=
-  eq_one_of_mul_eq_one_right (b := a) H <| by rw [Int.mul_comm, H']
+  eq_one_of_mul_eq_one_right H <| by rw [Int.mul_comm, H']
 
 /-! ### *div zero  -/
 

src/Init/Data/List.lean

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

src/Init/Data/List/Basic.lean

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

src/Init/Data/List/BasicAux.lean

@@ -155,8 +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' : i < (as ++ bs).length} :
-    (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 =>

src/Init/Data/List/Count.lean

@@ -162,10 +162,6 @@ theorem countP_filterMap (p : β → Bool) (f : α → Option β) (l : List α)
 
 @[deprecated countP_flatten (since := "2024-10-14")] abbrev countP_join := @countP_flatten
 
-theorem countP_flatMap (p : β → Bool) (l : List α) (f : α → List β) :
-    countP p (l.flatMap f) = sum (map (countP p ∘ f) l) := by
-  rw [List.flatMap, countP_flatten, map_map]
-
 @[simp] theorem countP_reverse (l : List α) : countP p l.reverse = countP p l := by
   simp [countP_eq_length_filter, filter_reverse]
 
@@ -330,9 +326,6 @@ theorem count_filterMap {α} [BEq β] (b : β) (f : α → Option β) (l : List
   · simp
   · simp
 
-theorem count_flatMap {α} [BEq β] (l : List α) (f : α → List β) (x : β) :
-    count x (l.flatMap f) = sum (map (count x ∘ f) l) := countP_flatMap _ _ _
-
 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/FinRange.lean

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

src/Init/Data/List/Lemmas.lean

@@ -83,12 +83,44 @@ open Nat
 @[simp] theorem nil_eq {α} {xs : List α} : [] = xs ↔ xs = [] := by
   cases xs <;> simp
 
+/-! ### cons -/
+
+theorem cons_ne_nil (a : α) (l : List α) : a :: l ≠ [] := nofun
+
+@[simp]
+theorem cons_ne_self (a : α) (l : List α) : a :: l ≠ l := mt (congrArg length) (Nat.succ_ne_self _)
+
+@[simp] theorem ne_cons_self {a : α} {l : List α} : l ≠ a :: l := by
+  rw [ne_eq, eq_comm]
+  simp
+
+theorem head_eq_of_cons_eq (H : h₁ :: t₁ = h₂ :: t₂) : h₁ = h₂ := (cons.inj H).1
+
+theorem tail_eq_of_cons_eq (H : h₁ :: t₁ = h₂ :: t₂) : t₁ = t₂ := (cons.inj H).2
+
+theorem cons_inj_right (a : α) {l l' : List α} : a :: l = a :: l' ↔ l = l' :=
+  ⟨tail_eq_of_cons_eq, congrArg _⟩
+
+@[deprecated (since := "2024-06-15")] abbrev cons_inj := @cons_inj_right
+
+theorem cons_eq_cons {a b : α} {l l' : List α} : a :: l = b :: l' ↔ a = b ∧ l = l' :=
+  List.cons.injEq .. ▸ .rfl
+
+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
 
 theorem ne_nil_of_length_eq_add_one (_ : length l = n + 1) : l ≠ [] := fun _ => nomatch l
 
+@[deprecated ne_nil_of_length_eq_add_one (since := "2024-06-16")]
+abbrev ne_nil_of_length_eq_succ := @ne_nil_of_length_eq_add_one
+
 theorem ne_nil_of_length_pos (_ : 0 < length l) : l ≠ [] := fun _ => nomatch l
 
 @[simp] theorem length_eq_zero : length l = 0 ↔ l = [] :=
@@ -124,36 +156,6 @@ theorem length_pos {l : List α} : 0 < length l ↔ l ≠ [] :=
 theorem length_eq_one {l : List α} : length l = 1 ↔ ∃ a, l = [a] :=
   ⟨fun h => match l, h with | [_], _ => ⟨_, rfl⟩, fun ⟨_, h⟩ => by simp [h]⟩
 
-/-! ### cons -/
-
-theorem cons_ne_nil (a : α) (l : List α) : a :: l ≠ [] := nofun
-
-@[simp]
-theorem cons_ne_self (a : α) (l : List α) : a :: l ≠ l := mt (congrArg length) (Nat.succ_ne_self _)
-
-@[simp] theorem ne_cons_self {a : α} {l : List α} : l ≠ a :: l := by
-  rw [ne_eq, eq_comm]
-  simp
-
-theorem head_eq_of_cons_eq (H : h₁ :: t₁ = h₂ :: t₂) : h₁ = h₂ := (cons.inj H).1
-
-theorem tail_eq_of_cons_eq (H : h₁ :: t₁ = h₂ :: t₂) : t₁ = t₂ := (cons.inj H).2
-
-theorem cons_inj_right (a : α) {l l' : List α} : a :: l = a :: l' ↔ l = l' :=
-  ⟨tail_eq_of_cons_eq, congrArg _⟩
-
-theorem cons_eq_cons {a b : α} {l l' : List α} : a :: l = b :: l' ↔ a = b ∧ l = l' :=
-  List.cons.injEq .. ▸ .rfl
-
-theorem exists_cons_of_ne_nil : ∀ {l : List α}, l ≠ [] → ∃ b L, l = b :: L
-  | c :: l', _ => ⟨c, l', rfl⟩
-
-theorem ne_nil_iff_exists_cons {l : List α} : l ≠ [] ↔ ∃ b L, l = b :: L :=
-  ⟨exists_cons_of_ne_nil, fun ⟨_, _, eq⟩ => eq.symm ▸ cons_ne_nil _ _⟩
-
-theorem singleton_inj {α : Type _} {a b : α} : [a] = [b] ↔ a = b := by
-  simp
-
 /-! ## L[i] and L[i]? -/
 
 /-! ### `get` and `get?`.
@@ -161,29 +163,57 @@ theorem singleton_inj {α : Type _} {a b : α} : [a] = [b] ↔ a = b := by
 We simplify `l.get i` to `l[i.1]'i.2` and `l.get? i` to `l[i]?`.
 -/
 
-@[simp] theorem get_eq_getElem (l : List α) (i : Fin l.length) : l.get i = l[i.1]'i.2 := rfl
+theorem get_cons_zero : get (a::l) (0 : Fin (l.length + 1)) = a := rfl
 
-theorem get?_eq_none : ∀ {l : List α} {n}, length l ≤ n → l.get? n = none
+theorem get_cons_succ {as : List α} {h : i + 1 < (a :: as).length} :
+  (a :: as).get ⟨i+1, h⟩ = as.get ⟨i, Nat.lt_of_succ_lt_succ h⟩ := rfl
+
+theorem get_cons_succ' {as : List α} {i : Fin as.length} :
+  (a :: as).get i.succ = as.get i := rfl
+
+@[deprecated (since := "2024-07-09")]
+theorem get_cons_cons_one : (a₁ :: a₂ :: as).get (1 : Fin (as.length + 2)) = a₂ := rfl
+
+theorem get_mk_zero : ∀ {l : List α} (h : 0 < l.length), l.get ⟨0, h⟩ = l.head (length_pos.mp h)
+  | _::_, _ => rfl
+
+theorem get?_zero (l : List α) : l.get? 0 = l.head? := by cases l <;> rfl
+
+theorem get?_len_le : ∀ {l : List α} {n}, length l ≤ n → l.get? n = none
   | [], _, _ => rfl
-  | _ :: l, _+1, h => get?_eq_none (l := l) <| Nat.le_of_succ_le_succ h
+  | _ :: l, _+1, h => get?_len_le (l := l) <| Nat.le_of_succ_le_succ h
 
 theorem get?_eq_get : ∀ {l : List α} {n} (h : n < l.length), l.get? n = some (get l ⟨n, h⟩)
   | _ :: _, 0, _ => rfl
   | _ :: l, _+1, _ => get?_eq_get (l := l) _
 
-theorem get?_eq_some_iff : l.get? n = some a ↔ ∃ h, get l ⟨n, h⟩ = a :=
+theorem get?_eq_some : l.get? n = some a ↔ ∃ h, get l ⟨n, h⟩ = a :=
   ⟨fun e =>
-    have : n < length l := Nat.gt_of_not_le fun hn => by cases get?_eq_none hn ▸ e
+    have : n < length l := Nat.gt_of_not_le fun hn => by cases get?_len_le hn ▸ e
     ⟨this, by rwa [get?_eq_get this, Option.some.injEq] at e⟩,
   fun ⟨_, e⟩ => e ▸ get?_eq_get _⟩
 
-theorem get?_eq_none_iff : l.get? n = none ↔ length l ≤ n :=
-  ⟨fun e => Nat.ge_of_not_lt (fun h' => by cases e ▸ get?_eq_some_iff.2 ⟨h', rfl⟩), get?_eq_none⟩
+theorem get?_eq_none : l.get? n = none ↔ length l ≤ n :=
+  ⟨fun e => Nat.ge_of_not_lt (fun h' => by cases e ▸ get?_eq_some.2 ⟨h', rfl⟩), get?_len_le⟩
 
 @[simp] theorem get?_eq_getElem? (l : List α) (i : Nat) : l.get? i = l[i]? := by
-  simp only [getElem?_def]; split
+  simp only [getElem?, decidableGetElem?]; split
   · exact (get?_eq_get ‹_›)
-  · exact (get?_eq_none_iff.2 <| Nat.not_lt.1 ‹_›)
+  · exact (get?_eq_none.2 <| Nat.not_lt.1 ‹_›)
+
+@[simp] theorem get_eq_getElem (l : List α) (i : Fin l.length) : l.get i = l[i.1]'i.2 := rfl
+
+theorem getElem?_eq_some {l : List α} : l[i]? = some a ↔ ∃ h : i < l.length, l[i]'h = a := by
+  simpa using get?_eq_some
+
+/--
+If one has `l.get i` in an expression (with `i : Fin l.length`) and `h : l = l'`,
+`rw [h]` will give a "motive it not type correct" error, as it cannot rewrite the
+`i : Fin l.length` to `Fin l'.length` directly. The theorem `get_of_eq` can be used to make
+such a rewrite, with `rw [get_of_eq h]`.
+-/
+theorem get_of_eq {l l' : List α} (h : l = l') (i : Fin l.length) :
+    get l i = get l' ⟨i, h ▸ i.2⟩ := by cases h; rfl
 
 /-! ### getD
 
@@ -194,29 +224,42 @@ Because of this, there is only minimal API for `getD`.
 @[simp] theorem getD_eq_getElem?_getD (l) (n) (a : α) : getD l n a = (l[n]?).getD a := by
   simp [getD]
 
+@[deprecated getD_eq_getElem?_getD (since := "2024-06-12")]
+theorem getD_eq_get? : ∀ l n (a : α), getD l n a = (get? l n).getD a := by simp
+
 /-! ### get!
 
 We simplify `l.get! n` to `l[n]!`.
 -/
 
+theorem get!_of_get? [Inhabited α] : ∀ {l : List α} {n}, get? l n = some a → get! l n = a
+  | _a::_, 0, rfl => rfl
+  | _::l, _+1, e => get!_of_get? (l := l) e
+
 theorem get!_eq_getD [Inhabited α] : ∀ (l : List α) n, l.get! n = l.getD n default
   | [], _      => rfl
   | _a::_, 0   => rfl
   | _a::l, n+1 => get!_eq_getD l n
 
+theorem get!_len_le [Inhabited α] : ∀ {l : List α} {n}, length l ≤ n → l.get! n = (default : α)
+  | [], _, _ => rfl
+  | _ :: l, _+1, h => get!_len_le (l := l) <| Nat.le_of_succ_le_succ h
+
 @[simp] theorem get!_eq_getElem! [Inhabited α] (l : List α) (n) : l.get! n = l[n]! := by
   simp [get!_eq_getD]
   rfl
 
-/-! ### getElem!
+/-! ### getElem! -/
 
-We simplify `l[n]!` to `(l[n]?).getD default`.
--/
+@[simp] theorem getElem!_nil [Inhabited α] {n : Nat} : ([] : List α)[n]! = default := rfl
 
-@[simp] theorem getElem!_eq_getElem?_getD [Inhabited α] (l : List α) (n : Nat) :
-    l[n]! = (l[n]?).getD (default : α) := by
-  simp only [getElem!_def]
-  split <;> simp_all
+@[simp] theorem getElem!_cons_zero [Inhabited α] {l : List α} : (a::l)[0]! = a := by
+  rw [getElem!_pos] <;> simp
+
+@[simp] theorem getElem!_cons_succ [Inhabited α] {l : List α} : (a::l)[n+1]! = l[n]! := by
+  by_cases h : n < l.length
+  · rw [getElem!_pos, getElem!_pos] <;> simp_all [Nat.succ_lt_succ_iff]
+  · rw [getElem!_neg, getElem!_neg] <;> simp_all [Nat.succ_lt_succ_iff]
 
 /-! ### getElem? and getElem -/
 
@@ -224,19 +267,23 @@ We simplify `l[n]!` to `(l[n]?).getD default`.
   simp only [getElem?_def, h, ↓reduceDIte]
 
 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_iff, get_eq_getElem]
+  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_iff]
+  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) :
+    l[i]? = if h : i < l.length then some l[i] else none := by
+  split <;> simp_all
+
 @[simp] theorem some_getElem_eq_getElem?_iff {α} (xs : List α) (i : Nat) (h : i < xs.length) :
     (some xs[i] = xs[i]?) ↔ True := by
   simp [h]
@@ -253,6 +300,9 @@ theorem getElem_eq_getElem?_get (l : List α) (i : Nat) (h : i < l.length) :
     l[i] = l[i]?.get (by simp [getElem?_eq_getElem, h]) := by
   simp [getElem_eq_iff]
 
+@[deprecated getElem_eq_getElem?_get (since := "2024-09-04")] abbrev getElem_eq_getElem? :=
+  @getElem_eq_getElem?_get
+
 @[simp] theorem getElem?_nil {n : Nat} : ([] : List α)[n]? = none := rfl
 
 theorem getElem?_cons_zero {l : List α} : (a::l)[0]? = some a := by simp
@@ -264,6 +314,11 @@ theorem getElem?_cons_zero {l : List α} : (a::l)[0]? = some a := by simp
 theorem getElem?_cons : (a :: l)[i]? = if i = 0 then some a else l[i-1]? := by
   cases i <;> simp
 
+theorem getElem?_len_le : ∀ {l : List α} {n}, length l ≤ n → l[n]? = none
+  | [], _, _ => rfl
+  | _ :: l, _+1, h => by
+    rw [getElem?_cons_succ, getElem?_len_le (l := l) <| Nat.le_of_succ_le_succ h]
+
 /--
 If one has `l[i]` in an expression and `h : l = l'`,
 `rw [h]` will give a "motive it not type correct" error, as it cannot rewrite the
@@ -277,10 +332,20 @@ theorem getElem_of_eq {l l' : List α} (h : l = l') {i : Nat} (w : i < l.length)
   match i, h with
   | 0, _ => rfl
 
+@[deprecated getElem_singleton (since := "2024-06-12")]
+theorem get_singleton (a : α) (n : Fin 1) : get [a] n = a := by simp
+
 theorem getElem_zero {l : List α} (h : 0 < l.length) : l[0] = l.head (length_pos.mp h) :=
   match l, h with
   | _ :: _, _ => rfl
 
+theorem getElem!_of_getElem? [Inhabited α] : ∀ {l : List α} {n : Nat}, l[n]? = some a → l[n]! = a
+  | _a::_, 0, _ => by
+    rw [getElem!_pos] <;> simp_all
+  | _::l, _+1, e => by
+    simp at e
+    simp_all [getElem!_of_getElem? (l := l) e]
+
 @[ext] theorem ext_getElem? {l₁ l₂ : List α} (h : ∀ n : Nat, l₁[n]? = l₂[n]?) : l₁ = l₂ :=
   ext_get? fun n => by simp_all
 
@@ -291,7 +356,11 @@ theorem ext_getElem {l₁ l₂ : List α} (hl : length l₁ = length l₂)
       simp_all [getElem?_eq_getElem]
     else by
       have h₁ := Nat.le_of_not_lt h₁
-      rw [getElem?_eq_none h₁, getElem?_eq_none]; rwa [← hl]
+      rw [getElem?_len_le h₁, getElem?_len_le]; rwa [← hl]
+
+theorem ext_get {l₁ l₂ : List α} (hl : length l₁ = length l₂)
+    (h : ∀ n h₁ h₂, get l₁ ⟨n, h₁⟩ = get l₂ ⟨n, h₂⟩) : l₁ = l₂ :=
+  ext_getElem hl (by simp_all)
 
 @[simp] theorem getElem_concat_length : ∀ (l : List α) (a : α) (i) (_ : i = l.length) (w), (l ++ [a])[i]'w = a
   | [], a, _, h, _ => by subst h; simp
@@ -300,11 +369,19 @@ theorem ext_getElem {l₁ l₂ : List α} (hl : length l₁ = length l₂)
 theorem getElem?_concat_length (l : List α) (a : α) : (l ++ [a])[l.length]? = some a := by
   simp
 
-theorem isSome_getElem? {l : List α} {n : Nat} : l[n]?.isSome ↔ n < l.length := by
-  simp
+@[deprecated getElem?_concat_length (since := "2024-06-12")]
+theorem get?_concat_length (l : List α) (a : α) : (l ++ [a]).get? l.length = some a := by simp
 
-theorem isNone_getElem? {l : List α} {n : Nat} : l[n]?.isNone ↔ l.length ≤ n := by
-  simp
+@[simp] theorem isSome_getElem? {l : List α} {n : Nat} : l[n]?.isSome ↔ n < l.length := by
+  by_cases h : n < l.length
+  · simp_all
+  · simp [h]
+    simp_all
+
+@[simp] theorem isNone_getElem? {l : List α} {n : Nat} : l[n]?.isNone ↔ l.length ≤ n := by
+  by_cases h : n < l.length
+  · simp_all
+  · simp [h]
 
 /-! ### mem -/
 
@@ -416,19 +493,42 @@ theorem getElem_of_mem : ∀ {a} {l : List α}, a ∈ l → ∃ (n : Nat) (h : n
   | _, _ :: _, .head .. => ⟨0, Nat.succ_pos _, rfl⟩
   | _, _ :: _, .tail _ m => let ⟨n, h, e⟩ := getElem_of_mem m; ⟨n+1, Nat.succ_lt_succ h, e⟩
 
-theorem getElem?_of_mem {a} {l : List α} (h : a ∈ l) : ∃ n : Nat, l[n]? = some a := by
-  let ⟨n, _, e⟩ := getElem_of_mem h
-  exact ⟨n, e ▸ getElem?_eq_getElem _⟩
+theorem get_of_mem {a} {l : List α} (h : a ∈ l) : ∃ n, get l n = a := by
+  obtain ⟨n, h, e⟩ := getElem_of_mem h
+  exact ⟨⟨n, h⟩, e⟩
+
+theorem getElem?_of_mem {a} {l : List α} (h : a ∈ l) : ∃ n : Nat, l[n]? = some a :=
+  let ⟨n, _, e⟩ := getElem_of_mem h; ⟨n, e ▸ getElem?_eq_getElem _⟩
+
+theorem get?_of_mem {a} {l : List α} (h : a ∈ l) : ∃ n, l.get? n = some a :=
+  let ⟨⟨n, _⟩, e⟩ := get_of_mem h; ⟨n, e ▸ get?_eq_get _⟩
+
+theorem get_mem : ∀ (l : List α) n, get l n ∈ l
+  | _ :: _, ⟨0, _⟩ => .head ..
+  | _ :: l, ⟨_+1, _⟩ => .tail _ (get_mem l ..)
 
 theorem mem_of_getElem? {l : List α} {n : Nat} {a : α} (e : l[n]? = some a) : a ∈ l :=
   let ⟨_, e⟩ := getElem?_eq_some_iff.1 e; e ▸ getElem_mem ..
 
+@[deprecated mem_of_getElem? (since := "2024-09-06")] abbrev getElem?_mem := @mem_of_getElem?
+
+theorem mem_of_get? {l : List α} {n a} (e : l.get? n = some a) : a ∈ l :=
+  let ⟨_, e⟩ := get?_eq_some.1 e; e ▸ get_mem ..
+
+@[deprecated mem_of_get? (since := "2024-09-06")] abbrev get?_mem := @mem_of_get?
+
 theorem mem_iff_getElem {a} {l : List α} : a ∈ l ↔ ∃ (n : Nat) (h : n < l.length), l[n]'h = a :=
   ⟨getElem_of_mem, fun ⟨_, _, e⟩ => e ▸ getElem_mem ..⟩
 
+theorem mem_iff_get {a} {l : List α} : a ∈ l ↔ ∃ n, get l n = a :=
+  ⟨get_of_mem, fun ⟨_, e⟩ => e ▸ get_mem ..⟩
+
 theorem mem_iff_getElem? {a} {l : List α} : a ∈ l ↔ ∃ n : Nat, l[n]? = some a := by
   simp [getElem?_eq_some_iff, mem_iff_getElem]
 
+theorem mem_iff_get? {a} {l : List α} : a ∈ l ↔ ∃ n, l.get? n = some a := by
+  simp [getElem?_eq_some_iff, Fin.exists_iff, mem_iff_get]
+
 theorem forall_getElem {l : List α} {p : α → Prop} :
     (∀ (n : Nat) h, p (l[n]'h)) ↔ ∀ a, a ∈ l → p a := by
   induction l with
@@ -479,6 +579,18 @@ theorem isEmpty_iff_length_eq_zero {l : List α} : l.isEmpty ↔ l.length = 0 :=
 
 /-! ### any / all -/
 
+theorem any_beq [BEq α] [LawfulBEq α] {l : List α} : (l.any fun x => a == x) ↔ a ∈ l := by
+  induction l <;> simp_all
+
+theorem any_beq' [BEq α] [LawfulBEq α] {l : List α} : (l.any fun x => x == a) ↔ a ∈ l := by
+  induction l <;> simp_all [eq_comm (a := a)]
+
+theorem all_bne [BEq α] [LawfulBEq α] {l : List α} : (l.all fun x => a != x) ↔ a ∉ l := by
+  induction l <;> simp_all
+
+theorem all_bne' [BEq α] [LawfulBEq α] {l : List α} : (l.all fun x => x != a) ↔ a ∉ l := by
+  induction l <;> simp_all [eq_comm (a := a)]
+
 theorem any_eq {l : List α} : l.any p = decide (∃ x, x ∈ l ∧ p x) := by induction l <;> simp [*]
 
 theorem all_eq {l : List α} : l.all p = decide (∀ x, x ∈ l → p x) := by induction l <;> simp [*]
@@ -503,18 +615,6 @@ theorem decide_forall_mem {l : List α} {p : α → Prop} [DecidablePred p] :
 @[simp] theorem all_eq_false {l : List α} : l.all p = false ↔ ∃ x, x ∈ l ∧ ¬p x := by
   simp [all_eq]
 
-theorem any_beq [BEq α] [LawfulBEq α] {l : List α} : (l.any fun x => a == x) ↔ a ∈ l := by
-  simp
-
-theorem any_beq' [BEq α] [LawfulBEq α] {l : List α} : (l.any fun x => x == a) ↔ a ∈ l := by
-  simp
-
-theorem all_bne [BEq α] [LawfulBEq α] {l : List α} : (l.all fun x => a != x) ↔ a ∉ l := by
-  induction l <;> simp_all
-
-theorem all_bne' [BEq α] [LawfulBEq α] {l : List α} : (l.all fun x => x != a) ↔ a ∉ l := by
-  induction l <;> simp_all [eq_comm (a := a)]
-
 /-! ### set -/
 
 -- As `List.set` is defined in `Init.Prelude`, we write the basic simplification lemmas here.
@@ -532,10 +632,19 @@ theorem all_bne' [BEq α] [LawfulBEq α] {l : List α} : (l.all fun x => x != a)
   | _ :: _, 0 => by simp
   | _ :: l, i + 1 => by simp [getElem_set_self]
 
+@[deprecated getElem_set_self (since := "2024-09-04")] abbrev getElem_set_eq := @getElem_set_self
+
+@[deprecated getElem_set_self (since := "2024-06-12")]
+theorem get_set_eq {l : List α} {i : Nat} {a : α} (h : i < (l.set i a).length) :
+    (l.set i a).get ⟨i, h⟩ = a := by
+  simp
+
 @[simp] theorem getElem?_set_self {l : List α} {i : Nat} {a : α} (h : i < l.length) :
     (l.set i a)[i]? = some a := by
   simp_all [getElem?_eq_some_iff]
 
+@[deprecated getElem?_set_self (since := "2024-09-04")] abbrev getElem?_set_eq := @getElem?_set_self
+
 /-- This differs from `getElem?_set_self` by monadically mapping `Function.const _ a` over the `Option`
 returned by `l[i]?`. -/
 theorem getElem?_set_self' {l : List α} {i : Nat} {a : α} :
@@ -557,6 +666,12 @@ theorem getElem?_set_self' {l : List α} {i : Nat} {a : α} :
     have g : i ≠ j := h ∘ congrArg (· + 1)
     simp [getElem_set_ne g]
 
+@[deprecated getElem_set_ne (since := "2024-06-12")]
+theorem get_set_ne {l : List α} {i j : Nat} (h : i ≠ j) {a : α}
+    (hj : j < (l.set i a).length) :
+    (l.set i a).get ⟨j, hj⟩ = l.get ⟨j, by simp at hj; exact hj⟩ := by
+  simp [h]
+
 @[simp] theorem getElem?_set_ne {l : List α} {i j : Nat} (h : i ≠ j) {a : α}  :
     (l.set i a)[j]? = l[j]? := by
   by_cases hj : j < (l.set i a).length
@@ -571,6 +686,11 @@ theorem getElem_set {l : List α} {m n} {a} (h) :
   else
     simp [h]
 
+@[deprecated getElem_set (since := "2024-06-12")]
+theorem get_set {l : List α} {m n} {a : α} (h) :
+    (set l m a).get ⟨n, h⟩ = if m = n then a else l.get ⟨n, length_set .. ▸ h⟩ := by
+  simp [getElem_set]
+
 theorem getElem?_set {l : List α} {i j : Nat} {a : α} :
     (l.set i a)[j]? = if i = j then if i < l.length then some a else none else l[j]? := by
   if h : i = j then
@@ -590,14 +710,6 @@ theorem getElem?_set' {l : List α} {i j : Nat} {a : α} :
   · simp only [getElem?_set_self', Option.map_eq_map, ↓reduceIte, *]
   · simp only [ne_eq, not_false_eq_true, getElem?_set_ne, ↓reduceIte, *]
 
-@[simp] theorem set_getElem_self {as : List α} {i : Nat} (h : i < as.length) :
-    as.set i as[i] = as := by
-  apply ext_getElem
-  · simp
-  · intro n h₁ h₂
-    rw [getElem_set]
-    split <;> simp_all
-
 theorem set_eq_of_length_le {l : List α} {n : Nat} (h : l.length ≤ n) {a : α} :
     l.set n a = l := by
   induction l generalizing n with
@@ -612,6 +724,8 @@ theorem set_eq_of_length_le {l : List α} {n : Nat} (h : l.length ≤ n) {a : α
 @[simp] theorem set_eq_nil_iff {l : List α} (n : Nat) (a : α) : l.set n a = [] ↔ l = [] := by
   cases l <;> cases n <;> simp [set]
 
+@[deprecated set_eq_nil_iff (since := "2024-09-05")] abbrev set_eq_nil := @set_eq_nil_iff
+
 theorem set_comm (a b : α) : ∀ {n m : Nat} (l : List α), n ≠ m →
     (l.set n a).set m b = (l.set m b).set n a
   | _, _, [], _ => by simp
@@ -677,24 +791,6 @@ theorem mem_or_eq_of_mem_set : ∀ {l : List α} {n : Nat} {a b : α}, a ∈ l.s
     · intro a
       simp
 
-@[simp] theorem beq_nil_iff [BEq α] {l : List α} : (l == []) = l.isEmpty := by
-  cases l <;> rfl
-
-@[simp] theorem nil_beq_iff [BEq α] {l : List α} : ([] == l) = l.isEmpty := by
-  cases l <;> rfl
-
-@[simp] theorem cons_beq_cons [BEq α] {a b : α} {l₁ l₂ : List α} :
-    (a :: l₁ == b :: l₂) = (a == b && l₁ == l₂) := rfl
-
-theorem length_eq_of_beq [BEq α] {l₁ l₂ : List α} (h : l₁ == l₂) : l₁.length = l₂.length :=
-  match l₁, l₂ with
-  | [], [] => rfl
-  | [], _ :: _ => by simp [beq_nil_iff] at h
-  | _ :: _, [] => by simp [nil_beq_iff] at h
-  | a :: l₁, b :: l₂ => by
-    simp at h
-    simpa [Nat.add_one_inj]using length_eq_of_beq h.2
-
 /-! ### Lexicographic ordering -/
 
 protected theorem lt_irrefl [LT α] (lt_irrefl : ∀ x : α, ¬x < x) (l : List α) : ¬l < l := by
@@ -760,12 +856,6 @@ theorem foldr_eq_foldrM (f : α → β → β) (b) (l : List α) :
     l.foldr f b = l.foldrM (m := Id) f b := by
   induction l <;> simp [*, foldr]
 
-@[simp] theorem id_run_foldlM (f : β → α → Id β) (b) (l : List α) :
-    Id.run (l.foldlM f b) = l.foldl f b := (foldl_eq_foldlM f b l).symm
-
-@[simp] theorem id_run_foldrM (f : α → β → Id β) (b) (l : List α) :
-    Id.run (l.foldrM f b) = l.foldr f b := (foldr_eq_foldrM f b l).symm
-
 /-! ### foldl and foldr -/
 
 @[simp] theorem foldr_cons_eq_append (l : List α) : l.foldr cons l' = l ++ l' := by
@@ -950,7 +1040,7 @@ theorem getLast_eq_getElem : ∀ (l : List α) (h : l ≠ []),
   | _ :: _ :: _, _ => by
     simp [getLast, get, Nat.succ_sub_succ, getLast_eq_getElem]
 
-theorem getElem_length_sub_one_eq_getLast (l : List α) (h : l.length - 1 < l.length) :
+theorem getElem_length_sub_one_eq_getLast (l : List α) (h) :
     l[l.length - 1] = getLast l (by cases l; simp at h; simp) := by
   rw [← getLast_eq_getElem]
 
@@ -1078,8 +1168,7 @@ theorem head_eq_getElem (l : List α) (h : l ≠ []) : head l h = l[0]'(length_p
   | nil => simp at h
   | cons _ _ => simp
 
-theorem getElem_zero_eq_head (l : List α) (h : 0 < l.length) :
-    l[0] = head l (by simpa [length_pos] using h) := by
+theorem getElem_zero_eq_head (l : List α) (h) : l[0] = head l (by simpa [length_pos] using h) := by
   cases l with
   | nil => simp at h
   | cons _ _ => simp
@@ -1671,7 +1760,7 @@ theorem filterMap_eq_cons_iff {l} {b} {bs} :
 @[simp] theorem cons_append_fun (a : α) (as : List α) :
     (fun bs => ((a :: as) ++ bs)) = fun bs => a :: (as ++ bs) := rfl
 
-theorem getElem_append {l₁ l₂ : List α} (n : Nat) (h : n < (l₁ ++ l₂).length) :
+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']
@@ -1711,7 +1800,7 @@ theorem getElem_append_right' (l₁ : List α) {l₂ : List α} {n : Nat} (hn :
     l₂[n] = (l₁ ++ l₂)[n + l₁.length]'(by simpa [Nat.add_comm] using Nat.add_lt_add_left hn _) := by
   rw [getElem_append_right] <;> simp [*, le_add_left]
 
-@[deprecated "Deprecated without replacement." (since := "2024-06-12")]
+@[deprecated (since := "2024-06-12")]
 theorem get_append_right_aux {l₁ l₂ : List α} {n : Nat}
   (h₁ : l₁.length ≤ n) (h₂ : n < (l₁ ++ l₂).length) : n - l₁.length < l₂.length := by
   rw [length_append] at h₂
@@ -1728,7 +1817,7 @@ theorem getElem_of_append {l : List α} (eq : l = l₁ ++ a :: l₂) (h : l₁.l
   rw [← getElem?_eq_getElem, eq, getElem?_append_right (h ▸ Nat.le_refl _), h]
   simp
 
-@[deprecated "Deprecated without replacement." (since := "2024-06-12")]
+@[deprecated (since := "2024-06-12")]
 theorem get_of_append_proof {l : List α}
     (eq : l = l₁ ++ a :: l₂) (h : l₁.length = n) : n < length l := eq ▸ h ▸ by simp_arith
 
@@ -2213,11 +2302,6 @@ theorem flatMap_def (l : List α) (f : α → List β) : l.flatMap f = flatten (
 
 @[simp] theorem flatMap_id (l : List (List α)) : List.flatMap l id = l.flatten := by simp [flatMap_def]
 
-@[simp]
-theorem length_flatMap (l : List α) (f : α → List β) :
-    length (l.flatMap f) = sum (map (length ∘ f) l) := by
-  rw [List.flatMap, length_flatten, map_map]
-
 @[simp] theorem mem_flatMap {f : α → List β} {b} {l : List α} : b ∈ l.flatMap f ↔ ∃ a, a ∈ l ∧ b ∈ f a := by
   simp [flatMap_def, mem_flatten]
   exact ⟨fun ⟨_, ⟨a, h₁, rfl⟩, h₂⟩ => ⟨a, h₁, h₂⟩, fun ⟨a, h₁, h₂⟩ => ⟨_, ⟨a, h₁, rfl⟩, h₂⟩⟩
@@ -2874,7 +2958,7 @@ are often used for theorems about `Array.pop`.
 @[simp] theorem getElem_dropLast : ∀ (xs : List α) (i : Nat) (h : i < xs.dropLast.length),
     xs.dropLast[i] = xs[i]'(Nat.lt_of_lt_of_le h (length_dropLast .. ▸ Nat.pred_le _))
   | _::_::_, 0, _ => rfl
-  | _::_::_, i+1, h => getElem_dropLast _ i (Nat.add_one_lt_add_one_iff.mp h)
+  | _::_::_, i+1, _ => getElem_dropLast _ i _
 
 @[deprecated getElem_dropLast (since := "2024-06-12")]
 theorem get_dropLast (xs : List α) (i : Fin xs.dropLast.length) :
@@ -3249,10 +3333,10 @@ theorem any_eq_not_all_not (l : List α) (p : α → Bool) : l.any p = !l.all (!
 theorem all_eq_not_any_not (l : List α) (p : α → Bool) : l.all p = !l.any (!p .) := by
   simp only [not_any_eq_all_not, Bool.not_not]
 
-@[simp] theorem any_map {l : List α} {p : β → Bool} : (l.map f).any p = l.any (p ∘ f) := by
+@[simp] theorem any_map {l : List α} {p : α → Bool} : (l.map f).any p = l.any (p ∘ f) := by
   induction l with simp | cons _ _ ih => rw [ih]
 
-@[simp] theorem all_map {l : List α} {p : β → Bool} : (l.map f).all p = l.all (p ∘ f) := by
+@[simp] theorem all_map {l : List α} {p : α → Bool} : (l.map f).all p = l.all (p ∘ f) := by
   induction l with simp | cons _ _ ih => rw [ih]
 
 @[simp] theorem any_filter {l : List α} {p q : α → Bool} :
@@ -3337,137 +3421,17 @@ theorem all_eq_not_any_not (l : List α) (p : α → Bool) : l.all p = !l.any (!
     (l.insert a).all f = (f a && l.all f) := by
   simp [all_eq]
 
-/-! ### Legacy lemmas about `get`, `get?`, and `get!`.
-
-Hopefully these should not be needed, in favour of lemmas about `xs[i]`, `xs[i]?`, and `xs[i]!`,
-to which these simplify.
-
-We may consider deprecating or downstreaming these lemmas.
--/
-
-theorem get_cons_zero : get (a::l) (0 : Fin (l.length + 1)) = a := rfl
-
-theorem get_cons_succ {as : List α} {h : i + 1 < (a :: as).length} :
-  (a :: as).get ⟨i+1, h⟩ = as.get ⟨i, Nat.lt_of_succ_lt_succ h⟩ := rfl
-
-theorem get_cons_succ' {as : List α} {i : Fin as.length} :
-  (a :: as).get i.succ = as.get i := rfl
-
-theorem get_mk_zero : ∀ {l : List α} (h : 0 < l.length), l.get ⟨0, h⟩ = l.head (length_pos.mp h)
-  | _::_, _ => rfl
-
-theorem get?_zero (l : List α) : l.get? 0 = l.head? := by cases l <;> rfl
-
-/--
-If one has `l.get i` in an expression (with `i : Fin l.length`) and `h : l = l'`,
-`rw [h]` will give a "motive is not type correct" error, as it cannot rewrite the
-`i : Fin l.length` to `Fin l'.length` directly. The theorem `get_of_eq` can be used to make
-such a rewrite, with `rw [get_of_eq h]`.
--/
-theorem get_of_eq {l l' : List α} (h : l = l') (i : Fin l.length) :
-    get l i = get l' ⟨i, h ▸ i.2⟩ := by cases h; rfl
-
-theorem get!_of_get? [Inhabited α] : ∀ {l : List α} {n}, get? l n = some a → get! l n = a
-  | _a::_, 0, rfl => rfl
-  | _::l, _+1, e => get!_of_get? (l := l) e
-
-theorem get!_len_le [Inhabited α] : ∀ {l : List α} {n}, length l ≤ n → l.get! n = (default : α)
-  | [], _, _ => rfl
-  | _ :: l, _+1, h => get!_len_le (l := l) <| Nat.le_of_succ_le_succ h
-
-theorem getElem!_nil [Inhabited α] {n : Nat} : ([] : List α)[n]! = default := rfl
-
-theorem getElem!_cons_zero [Inhabited α] {l : List α} : (a::l)[0]! = a := by
-  rw [getElem!_pos] <;> simp
-
-theorem getElem!_cons_succ [Inhabited α] {l : List α} : (a::l)[n+1]! = l[n]! := by
-  by_cases h : n < l.length
-  · rw [getElem!_pos, getElem!_pos] <;> simp_all [Nat.succ_lt_succ_iff]
-  · rw [getElem!_neg, getElem!_neg] <;> simp_all [Nat.succ_lt_succ_iff]
-
-theorem getElem!_of_getElem? [Inhabited α] : ∀ {l : List α} {n : Nat}, l[n]? = some a → l[n]! = a
-  | _a::_, 0, _ => by
-    rw [getElem!_pos] <;> simp_all
-  | _::l, _+1, e => by
-    simp at e
-    simp_all [getElem!_of_getElem? (l := l) e]
-
-theorem ext_get {l₁ l₂ : List α} (hl : length l₁ = length l₂)
-    (h : ∀ n h₁ h₂, get l₁ ⟨n, h₁⟩ = get l₂ ⟨n, h₂⟩) : l₁ = l₂ :=
-  ext_getElem hl (by simp_all)
-
-theorem get_of_mem {a} {l : List α} (h : a ∈ l) : ∃ n, get l n = a := by
-  obtain ⟨n, h, e⟩ := getElem_of_mem h
-  exact ⟨⟨n, h⟩, e⟩
-
-theorem get?_of_mem {a} {l : List α} (h : a ∈ l) : ∃ n, l.get? n = some a :=
-  let ⟨⟨n, _⟩, e⟩ := get_of_mem h; ⟨n, e ▸ get?_eq_get _⟩
-
-theorem get_mem : ∀ (l : List α) n, get l n ∈ l
-  | _ :: _, ⟨0, _⟩ => .head ..
-  | _ :: l, ⟨_+1, _⟩ => .tail _ (get_mem l ..)
-
-theorem mem_of_get? {l : List α} {n a} (e : l.get? n = some a) : a ∈ l :=
-  let ⟨_, e⟩ := get?_eq_some_iff.1 e; e ▸ get_mem ..
-
-theorem mem_iff_get {a} {l : List α} : a ∈ l ↔ ∃ n, get l n = a :=
-  ⟨get_of_mem, fun ⟨_, e⟩ => e ▸ get_mem ..⟩
-
-theorem mem_iff_get? {a} {l : List α} : a ∈ l ↔ ∃ n, l.get? n = some a := by
-  simp [getElem?_eq_some_iff, Fin.exists_iff, mem_iff_get]
-
 /-! ### Deprecations -/
 
-@[deprecated getD_eq_getElem?_getD (since := "2024-06-12")]
-theorem getD_eq_get? : ∀ l n (a : α), getD l n a = (get? l n).getD a := by simp
-@[deprecated getElem_singleton (since := "2024-06-12")]
-theorem get_singleton (a : α) (n : Fin 1) : get [a] n = a := by simp
-@[deprecated getElem?_concat_length (since := "2024-06-12")]
-theorem get?_concat_length (l : List α) (a : α) : (l ++ [a]).get? l.length = some a := by simp
-@[deprecated getElem_set_self (since := "2024-06-12")]
-theorem get_set_eq {l : List α} {i : Nat} {a : α} (h : i < (l.set i a).length) :
-    (l.set i a).get ⟨i, h⟩ = a := by
-  simp
-@[deprecated getElem_set_ne (since := "2024-06-12")]
-theorem get_set_ne {l : List α} {i j : Nat} (h : i ≠ j) {a : α}
-    (hj : j < (l.set i a).length) :
-    (l.set i a).get ⟨j, hj⟩ = l.get ⟨j, by simp at hj; exact hj⟩ := by
-  simp [h]
-@[deprecated getElem_set (since := "2024-06-12")]
-theorem get_set {l : List α} {m n} {a : α} (h) :
-    (set l m a).get ⟨n, h⟩ = if m = n then a else l.get ⟨n, length_set .. ▸ h⟩ := by
-  simp [getElem_set]
-@[deprecated cons_inj_right (since := "2024-06-15")] abbrev cons_inj := @cons_inj_right
-@[deprecated ne_nil_of_length_eq_add_one (since := "2024-06-16")]
-abbrev ne_nil_of_length_eq_succ := @ne_nil_of_length_eq_add_one
-
-@[deprecated "Deprecated without replacement." (since := "2024-07-09")]
-theorem get_cons_cons_one : (a₁ :: a₂ :: as).get (1 : Fin (as.length + 2)) = a₂ := rfl
-
-@[deprecated filter_flatten (since := "2024-08-26")]
-theorem join_map_filter (p : α → Bool) (l : List (List α)) :
-    (l.map (filter p)).flatten = (l.flatten).filter p := by
-  rw [filter_flatten]
-
-@[deprecated getElem_eq_getElem?_get (since := "2024-09-04")] abbrev getElem_eq_getElem? :=
-  @getElem_eq_getElem?_get
-@[deprecated flatten_eq_nil_iff (since := "2024-09-05")] abbrev join_eq_nil := @flatten_eq_nil_iff
-@[deprecated flatten_ne_nil_iff (since := "2024-09-05")] abbrev join_ne_nil := @flatten_ne_nil_iff
-@[deprecated flatten_eq_cons_iff (since := "2024-09-05")] abbrev join_eq_cons_iff := @flatten_eq_cons_iff
-@[deprecated flatten_eq_cons_iff (since := "2024-09-05")] abbrev join_eq_cons := @flatten_eq_cons_iff
-@[deprecated flatten_eq_append_iff (since := "2024-09-05")] abbrev join_eq_append := @flatten_eq_append_iff
-@[deprecated mem_of_getElem? (since := "2024-09-06")] abbrev getElem?_mem := @mem_of_getElem?
-@[deprecated mem_of_get? (since := "2024-09-06")] abbrev get?_mem := @mem_of_get?
-@[deprecated getElem_set_self (since := "2024-09-04")] abbrev getElem_set_eq := @getElem_set_self
-@[deprecated getElem?_set_self (since := "2024-09-04")] abbrev getElem?_set_eq := @getElem?_set_self
-@[deprecated set_eq_nil_iff (since := "2024-09-05")] abbrev set_eq_nil := @set_eq_nil_iff
 
 @[deprecated flatten_nil (since := "2024-10-14")] abbrev join_nil := @flatten_nil
 @[deprecated flatten_cons (since := "2024-10-14")] abbrev join_cons := @flatten_cons
 @[deprecated length_flatten (since := "2024-10-14")] abbrev length_join := @length_flatten
 @[deprecated flatten_singleton (since := "2024-10-14")] abbrev join_singleton := @flatten_singleton
 @[deprecated mem_flatten (since := "2024-10-14")] abbrev mem_join := @mem_flatten
+@[deprecated flatten_eq_nil_iff (since := "2024-09-05")] abbrev join_eq_nil := @flatten_eq_nil_iff
 @[deprecated flatten_eq_nil_iff (since := "2024-10-14")] abbrev join_eq_nil_iff := @flatten_eq_nil_iff
+@[deprecated flatten_ne_nil_iff (since := "2024-09-05")] abbrev join_ne_nil := @flatten_ne_nil_iff
 @[deprecated flatten_ne_nil_iff (since := "2024-10-14")] abbrev join_ne_nil_iff := @flatten_ne_nil_iff
 @[deprecated exists_of_mem_flatten (since := "2024-10-14")] abbrev exists_of_mem_join := @exists_of_mem_flatten
 @[deprecated mem_flatten_of_mem (since := "2024-10-14")] abbrev mem_join_of_mem := @mem_flatten_of_mem
@@ -3481,9 +3445,16 @@ theorem join_map_filter (p : α → Bool) (l : List (List α)) :
 @[deprecated filter_flatten (since := "2024-10-14")] abbrev filter_join := @filter_flatten
 @[deprecated flatten_filter_not_isEmpty (since := "2024-10-14")] abbrev join_filter_not_isEmpty := @flatten_filter_not_isEmpty
 @[deprecated flatten_filter_ne_nil (since := "2024-10-14")] abbrev join_filter_ne_nil := @flatten_filter_ne_nil
+@[deprecated filter_flatten (since := "2024-08-26")]
+theorem join_map_filter (p : α → Bool) (l : List (List α)) :
+    (l.map (filter p)).flatten = (l.flatten).filter p := by
+  rw [filter_flatten]
 @[deprecated flatten_append (since := "2024-10-14")] abbrev join_append := @flatten_append
 @[deprecated flatten_concat (since := "2024-10-14")] abbrev join_concat := @flatten_concat
 @[deprecated flatten_flatten (since := "2024-10-14")] abbrev join_join := @flatten_flatten
+@[deprecated flatten_eq_cons_iff (since := "2024-09-05")] abbrev join_eq_cons_iff := @flatten_eq_cons_iff
+@[deprecated flatten_eq_cons_iff (since := "2024-09-05")] abbrev join_eq_cons := @flatten_eq_cons_iff
+@[deprecated flatten_eq_append_iff (since := "2024-09-05")] abbrev join_eq_append := @flatten_eq_append_iff
 @[deprecated flatten_eq_append_iff (since := "2024-10-14")] abbrev join_eq_append_iff := @flatten_eq_append_iff
 @[deprecated eq_iff_flatten_eq (since := "2024-10-14")] abbrev eq_iff_join_eq := @eq_iff_flatten_eq
 @[deprecated flatten_replicate_nil (since := "2024-10-14")] abbrev join_replicate_nil := @flatten_replicate_nil
@@ -3518,18 +3489,4 @@ theorem join_map_filter (p : α → Bool) (l : List (List α)) :
 @[deprecated any_flatMap (since := "2024-10-16")] abbrev any_bind := @any_flatMap
 @[deprecated all_flatMap (since := "2024-10-16")] abbrev all_bind := @all_flatMap
 
-@[deprecated get?_eq_none (since := "2024-11-29")] abbrev get?_len_le := @get?_eq_none
-@[deprecated getElem?_eq_some_iff (since := "2024-11-29")]
-abbrev getElem?_eq_some := @getElem?_eq_some_iff
-@[deprecated get?_eq_some_iff (since := "2024-11-29")]
-abbrev get?_eq_some := @get?_eq_some_iff
-@[deprecated LawfulGetElem.getElem?_def (since := "2024-11-29")]
-theorem getElem?_eq (l : List α) (i : Nat) :
-    l[i]? = if h : i < l.length then some l[i] else none :=
-  getElem?_def _ _
-@[deprecated getElem?_eq_none (since := "2024-11-29")] abbrev getElem?_len_le := @getElem?_eq_none
-
-
-
-
 end List

src/Init/Data/List/MapIdx.lean

@@ -87,8 +87,8 @@ theorem mapFinIdx_eq_ofFn {as : List α} {f : Fin as.length → α → β} :
   apply ext_getElem <;> simp
 
 @[simp] theorem getElem?_mapFinIdx {l : List α} {f : Fin l.length → α → β} {i : Nat} :
-    (l.mapFinIdx f)[i]? = l[i]?.pbind fun x m => f ⟨i, by simp [getElem?_eq_some_iff] at m; exact m.1⟩ x := by
-  simp only [getElem?_def, length_mapFinIdx, getElem_mapFinIdx]
+    (l.mapFinIdx f)[i]? = l[i]?.pbind fun x m => f ⟨i, by simp [getElem?_eq_some] at m; exact m.1⟩ x := by
+  simp only [getElem?_eq, length_mapFinIdx, getElem_mapFinIdx]
   split <;> simp
 
 @[simp]
@@ -126,8 +126,7 @@ theorem mapFinIdx_singleton {a : α} {f : Fin 1 → α → β} :
 
 theorem mapFinIdx_eq_enum_map {l : List α} {f : Fin l.length → α → β} :
     l.mapFinIdx f = l.enum.attach.map
-      fun ⟨⟨i, x⟩, m⟩ =>
-        f ⟨i, by rw [mk_mem_enum_iff_getElem?, getElem?_eq_some_iff] at m; exact m.1⟩ x := by
+      fun ⟨⟨i, x⟩, m⟩ => f ⟨i, by rw [mk_mem_enum_iff_getElem?, getElem?_eq_some] at m; exact m.1⟩ x := by
   apply ext_getElem <;> simp
 
 @[simp]
@@ -236,7 +235,7 @@ theorem getElem?_mapIdx_go : ∀ {l : List α} {arr : Array β} {i : Nat},
     (mapIdx.go f l arr)[i]? =
       if h : i < arr.size then some arr[i] else Option.map (f i) l[i - arr.size]?
   | [], arr, i => by
-    simp only [mapIdx.go, Array.toListImpl_eq, getElem?_def, Array.length_toList,
+    simp only [mapIdx.go, Array.toListImpl_eq, getElem?_eq, Array.length_toList,
       Array.getElem_eq_getElem_toList, length_nil, Nat.not_lt_zero, ↓reduceDIte, Option.map_none']
   | a :: l, arr, i => by
     rw [mapIdx.go, getElem?_mapIdx_go]

src/Init/Data/List/Nat.lean

@@ -15,4 +15,3 @@ import Init.Data.List.Nat.Find
 import Init.Data.List.Nat.BEq
 import Init.Data.List.Nat.Modify
 import Init.Data.List.Nat.InsertIdx
-import Init.Data.List.Nat.Perm

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

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

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

@@ -1,54 +0,0 @@
-/-
-Copyright (c) 2024 Lean FRO. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison
--/
-prelude
-import Init.Data.List.Nat.TakeDrop
-import Init.Data.List.Perm
-
-namespace List
-
-/-- Helper lemma for `set_set_perm`-/
-private theorem set_set_perm' {as : List α} {i j : Nat} (h₁ : i < as.length) (h₂ : i + j < as.length)
-    (hj : 0 < j) :
-    (as.set i as[i + j]).set (i + j) as[i] ~ as := by
-  have : as =
-      as.take i ++ as[i] :: (as.take (i + j)).drop (i + 1) ++ as[i + j] :: as.drop (i + j + 1) := by
-    simp only [getElem_cons_drop, append_assoc, cons_append]
-    rw [← drop_append_of_le_length]
-    · simp
-    · simp; omega
-  conv => lhs; congr; congr; rw [this]
-  conv => rhs; rw [this]
-  rw [set_append_left _ _ (by simp; omega)]
-  rw [set_append_right _ _ (by simp; omega)]
-  rw [set_append_right _ _ (by simp; omega)]
-  simp only [length_append, length_take, length_set, length_cons, length_drop]
-  rw [(show i - min i as.length = 0 by omega)]
-  rw [(show i + j - (min i as.length + (min (i + j) as.length - (i + 1) + 1)) = 0 by omega)]
-  simp only [set_cons_zero]
-  simp only [append_assoc]
-  apply Perm.append_left
-  apply cons_append_cons_perm
-
-theorem set_set_perm {as : List α} {i j : Nat} (h₁ : i < as.length) (h₂ : j < as.length) :
-    (as.set i as[j]).set j as[i] ~ as := by
-  if h₃ : i = j then
-    simp [h₃]
-  else
-    if h₃ : i < j then
-      let j' := j - i
-      have t : j = i + j' := by omega
-      generalize j' = j' at t
-      subst t
-      exact set_set_perm' _ _ (by omega)
-    else
-      rw [set_comm _ _ _ (by omega)]
-      let i' := i - j
-      have t : i = j + i' := by omega
-      generalize i' = i' at t
-      subst t
-      apply set_set_perm' _ _ (by omega)
-
-end List

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

@@ -345,7 +345,7 @@ theorem drop_append {l₁ l₂ : List α} (i : Nat) : drop (l₁.length + i) (l
   rw [drop_append_eq_append_drop, drop_eq_nil_of_le] <;>
     simp [Nat.add_sub_cancel_left, Nat.le_add_right]
 
-theorem set_eq_take_append_cons_drop (l : List α) (n : Nat) (a : α) :
+theorem set_eq_take_append_cons_drop {l : List α} {n : Nat} {a : α} :
     l.set n a = if n < l.length then l.take n ++ a :: l.drop (n + 1) else l := by
   split <;> rename_i h
   · ext1 m

src/Init/Data/List/Perm.lean

@@ -39,9 +39,6 @@ protected theorem Perm.symm {l₁ l₂ : List α} (h : l₁ ~ l₂) : l₂ ~ l
   | swap => exact swap ..
   | trans _ _ ih₁ ih₂ => exact trans ih₂ ih₁
 
-instance : Trans (Perm (α := α)) (Perm (α := α)) (Perm (α := α)) where
-  trans h₁ h₂ := Perm.trans h₁ h₂
-
 theorem perm_comm {l₁ l₂ : List α} : l₁ ~ l₂ ↔ l₂ ~ l₁ := ⟨Perm.symm, Perm.symm⟩
 
 theorem Perm.swap' (x y : α) {l₁ l₂ : List α} (p : l₁ ~ l₂) : y :: x :: l₁ ~ x :: y :: l₂ :=
@@ -105,7 +102,7 @@ theorem perm_append_comm : ∀ {l₁ l₂ : List α}, l₁ ++ l₂ ~ l₂ ++ l
   | _ :: _, _ => (perm_append_comm.cons _).trans perm_middle.symm
 
 theorem perm_append_comm_assoc (l₁ l₂ l₃ : List α) :
-    (l₁ ++ (l₂ ++ l₃)) ~ (l₂ ++ (l₁ ++ l₃)) := by
+    Perm (l₁ ++ (l₂ ++ l₃)) (l₂ ++ (l₁ ++ l₃)) := by
   simpa only [List.append_assoc] using perm_append_comm.append_right _
 
 theorem concat_perm (l : List α) (a : α) : concat l a ~ a :: l := by simp
@@ -136,7 +133,7 @@ theorem Perm.nil_eq {l : List α} (p : [] ~ l) : [] = l := p.symm.eq_nil.symm
 
 theorem not_perm_nil_cons (x : α) (l : List α) : ¬[] ~ x :: l := (nomatch ·.symm.eq_nil)
 
-theorem not_perm_cons_nil {l : List α} {a : α} : ¬((a::l) ~ []) :=
+theorem not_perm_cons_nil {l : List α} {a : α} : ¬(Perm (a::l) []) :=
   fun h => by simpa using h.length_eq
 
 theorem Perm.isEmpty_eq {l l' : List α} (h : Perm l l') : l.isEmpty = l'.isEmpty := by
@@ -481,15 +478,6 @@ theorem Perm.flatten {l₁ l₂ : List (List α)} (h : l₁ ~ l₂) : l₁.flatt
 
 @[deprecated Perm.flatten (since := "2024-10-14")] abbrev Perm.join := @Perm.flatten
 
-theorem cons_append_cons_perm {a b : α} {as bs : List α} :
-    a :: as ++ b :: bs ~ b :: as ++ a :: bs := by
-  suffices [[a], as, [b], bs].flatten ~ [[b], as, [a], bs].flatten by simpa
-  apply Perm.flatten
-  calc
-    [[a], as, [b], bs] ~ [as, [a], [b], bs] := Perm.swap as [a] _
-    _ ~ [as, [b], [a], bs] := Perm.cons _ (Perm.swap [b] [a] _)
-    _ ~ [[b], as, [a], bs] := Perm.swap [b] as _
-
 theorem Perm.flatMap_right {l₁ l₂ : List α} (f : α → List β) (p : l₁ ~ l₂) : l₁.flatMap f ~ l₂.flatMap f :=
   (p.map _).flatten
 

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

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

src/Init/Data/List/Sublist.lean

@@ -835,13 +835,13 @@ theorem isPrefix_iff : l₁ <+: l₂ ↔ ∀ i (h : i < l₁.length), l₂[i]? =
       simpa using ⟨0, by simp⟩
     | cons b l₂ =>
       simp only [cons_append, cons_prefix_cons, ih]
-      rw (occs := [2]) [← Nat.and_forall_add_one]
+      rw (occs := .pos [2]) [← Nat.and_forall_add_one]
       simp [Nat.succ_lt_succ_iff, eq_comm]
 
 theorem isPrefix_iff_getElem {l₁ l₂ : List α} :
     l₁ <+: l₂ ↔ ∃ (h : l₁.length ≤ l₂.length), ∀ x (hx : x < l₁.length),
       l₁[x] = l₂[x]'(Nat.lt_of_lt_of_le hx h) where
-  mp h := ⟨h.length_le, fun _ h' ↦ h.getElem h'⟩
+  mp h := ⟨h.length_le, fun _ _ ↦ h.getElem _⟩
   mpr h := by
     obtain ⟨hl, h⟩ := h
     induction l₂ generalizing l₁ with

src/Init/Data/List/TakeDrop.lean

@@ -65,13 +65,13 @@ theorem lt_length_of_take_ne_self {l : List α} {n} (h : l.take n ≠ l) : n < l
 theorem getElem_cons_drop : ∀ (l : List α) (i : Nat) (h : i < l.length),
     l[i] :: drop (i + 1) l = drop i l
   | _::_, 0, _ => rfl
-  | _::_, i+1, h => getElem_cons_drop _ i (Nat.add_one_lt_add_one_iff.mp h)
+  | _::_, i+1, _ => getElem_cons_drop _ i _
 
 @[deprecated getElem_cons_drop (since := "2024-06-12")]
 theorem get_cons_drop (l : List α) (i) : get l i :: drop (i + 1) l = drop i l := by
   simp
 
-theorem drop_eq_getElem_cons {n} {l : List α} (h : n < l.length) : drop n l = l[n] :: drop (n + 1) l :=
+theorem drop_eq_getElem_cons {n} {l : List α} (h) : drop n l = l[n] :: drop (n + 1) l :=
   (getElem_cons_drop _ n h).symm
 
 @[deprecated drop_eq_getElem_cons (since := "2024-06-12")]
@@ -192,24 +192,6 @@ theorem take_concat_get (l : List α) (i : Nat) (h : i < l.length) :
   Eq.symm <| (append_left_inj _).1 <| (take_append_drop (i+1) l).trans <| by
     rw [concat_eq_append, append_assoc, singleton_append, getElem_cons_drop_succ_eq_drop, take_append_drop]
 
-@[simp] theorem take_append_getElem (l : List α) (i : Nat) (h : i < l.length) :
-    (l.take i) ++ [l[i]] = l.take (i+1) := by
-  simpa using take_concat_get l i h
-
-@[simp] theorem take_append_getLast (l : List α) (h : l ≠ []) :
-    (l.take (l.length - 1)) ++ [l.getLast h] = l := by
-  rw [getLast_eq_getElem]
-  cases l
-  · contradiction
-  · simp
-
-@[simp] theorem take_append_getLast? (l : List α) :
-    (l.take (l.length - 1)) ++ l.getLast?.toList = l := by
-  match l with
-  | [] => simp
-  | x :: xs =>
-    simpa using take_append_getLast (x :: xs) (by simp)
-
 @[deprecated take_succ_cons (since := "2024-07-25")]
 theorem take_cons_succ : (a::as).take (i+1) = a :: as.take i := rfl
 
@@ -242,7 +224,7 @@ theorem take_succ {l : List α} {n : Nat} : l.take (n + 1) = l.take n ++ l[n]?.t
     · simp only [take, Option.toList, getElem?_cons_zero, nil_append]
     · simp only [take, hl, getElem?_cons_succ, cons_append]
 
-@[deprecated "Deprecated without replacement." (since := "2024-07-25")]
+@[deprecated (since := "2024-07-25")]
 theorem drop_sizeOf_le [SizeOf α] (l : List α) (n : Nat) : sizeOf (l.drop n) ≤ sizeOf l := by
   induction l generalizing n with
   | nil => rw [drop_nil]; apply Nat.le_refl

src/Init/Data/Nat.lean

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

src/Init/Data/Nat/Basic.lean

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

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

@@ -71,9 +71,6 @@ theorem shiftRight_eq_div_pow (m : Nat) : ∀ n, m >>> n = m / 2 ^ n
     rw [shiftRight_add, shiftRight_eq_div_pow m k]
     simp [Nat.div_div_eq_div_mul, ← Nat.pow_succ, shiftRight_succ]
 
-theorem shiftRight_eq_zero (m n : Nat) (hn : m < 2^n) : m >>> n = 0 := by
-  simp [Nat.shiftRight_eq_div_pow, Nat.div_eq_of_lt hn]
-
 /-!
 ### testBit
 We define an operation for testing individual bits in the binary representation

src/Init/Data/Nat/Control.lean

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

src/Init/Data/Nat/Dvd.lean

@@ -39,9 +39,9 @@ protected theorem dvd_add_iff_right {k m n : Nat} (h : k ∣ m) : k ∣ n ↔ k
 protected theorem dvd_add_iff_left {k m n : Nat} (h : k ∣ n) : k ∣ m ↔ k ∣ m + n := by
   rw [Nat.add_comm]; exact Nat.dvd_add_iff_right h
 
-theorem dvd_mod_iff {k m n : Nat} (h: k ∣ n) : k ∣ m % n ↔ k ∣ m := by
-  have := Nat.dvd_add_iff_left (m := m % n) <| Nat.dvd_trans h <| Nat.dvd_mul_right n (m / n)
-  rwa [mod_add_div] at this
+theorem dvd_mod_iff {k m n : Nat} (h: k ∣ n) : k ∣ m % n ↔ k ∣ m :=
+  have := Nat.dvd_add_iff_left <| Nat.dvd_trans h <| Nat.dvd_mul_right n (m / n)
+  by rwa [mod_add_div] at this
 
 theorem le_of_dvd {m n : Nat} (h : 0 < n) : m ∣ n → m ≤ n
   | ⟨k, e⟩ => by
@@ -92,7 +92,7 @@ protected theorem div_mul_cancel {n m : Nat} (H : n ∣ m) : m / n * n = m := by
   rw [Nat.mul_comm, Nat.mul_div_cancel' H]
 
 @[simp] theorem mod_mod_of_dvd (a : Nat) (h : c ∣ b) : a % b % c = a % c := by
-  rw (occs := [2]) [← mod_add_div a b]
+  rw (occs := .pos [2]) [← mod_add_div a b]
   have ⟨x, h⟩ := h
   subst h
   rw [Nat.mul_assoc, add_mul_mod_self_left]

src/Init/Data/Nat/Fold.lean

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

src/Init/Data/Nat/Lemmas.lean

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

src/Init/Data/NeZero.lean

@@ -36,7 +36,3 @@ theorem neZero_iff {n : R} : NeZero n ↔ n ≠ 0 :=
 
 @[simp] theorem neZero_zero_iff_false {α : Type _} [Zero α] : NeZero (0 : α) ↔ False :=
   ⟨fun _ ↦ NeZero.ne (0 : α) rfl, fun h ↦ h.elim⟩
-
-instance {p : Prop} [Decidable p] {n m : Nat} [NeZero n] [NeZero m] :
-    NeZero (if p then n else m) := by
-  split <;> infer_instance

src/Init/Data/Sum/Basic.lean

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

src/Init/Data/UInt/Basic.lean

@@ -246,12 +246,6 @@ instance (a b : UInt64) : Decidable (a ≤ b) := UInt64.decLe a b
 instance : Max UInt64 := maxOfLe
 instance : Min UInt64 := minOfLe
 
-theorem usize_size_le : USize.size ≤ 18446744073709551616 := by
-  cases usize_size_eq <;> next h => rw [h]; decide
-
-theorem le_usize_size : 4294967296 ≤ USize.size := by
-  cases usize_size_eq <;> next h => rw [h]; decide
-
 @[extern "lean_usize_mul"]
 def USize.mul (a b : USize) : USize := ⟨a.toBitVec * b.toBitVec⟩
 @[extern "lean_usize_div"]
@@ -270,39 +264,10 @@ def USize.xor (a b : USize) : USize := ⟨a.toBitVec ^^^ b.toBitVec⟩
 def USize.shiftLeft (a b : USize) : USize := ⟨a.toBitVec <<< (mod b (USize.ofNat System.Platform.numBits)).toBitVec⟩
 @[extern "lean_usize_shift_right"]
 def USize.shiftRight (a b : USize) : USize := ⟨a.toBitVec >>> (mod b (USize.ofNat System.Platform.numBits)).toBitVec⟩
-/--
-Upcast a `Nat` less than `2^32` to a `USize`.
-This is lossless because `USize.size` is either `2^32` or `2^64`.
-This function is overridden with a native implementation.
--/
-@[extern "lean_usize_of_nat"]
-def USize.ofNat32 (n : @& Nat) (h : n < 4294967296) : USize :=
-  USize.ofNatCore n (Nat.lt_of_lt_of_le h le_usize_size)
-@[extern "lean_uint8_to_usize"]
-def UInt8.toUSize (a : UInt8) : USize :=
-  USize.ofNat32 a.toBitVec.toNat (Nat.lt_trans a.toBitVec.isLt (by decide))
-@[extern "lean_usize_to_uint8"]
-def USize.toUInt8 (a : USize) : UInt8 := a.toNat.toUInt8
-@[extern "lean_uint16_to_usize"]
-def UInt16.toUSize (a : UInt16) : USize :=
-  USize.ofNat32 a.toBitVec.toNat (Nat.lt_trans a.toBitVec.isLt (by decide))
-@[extern "lean_usize_to_uint16"]
-def USize.toUInt16 (a : USize) : UInt16 := a.toNat.toUInt16
 @[extern "lean_uint32_to_usize"]
 def UInt32.toUSize (a : UInt32) : USize := USize.ofNat32 a.toBitVec.toNat a.toBitVec.isLt
 @[extern "lean_usize_to_uint32"]
 def USize.toUInt32 (a : USize) : UInt32 := a.toNat.toUInt32
-/-- Converts a `UInt64` to a `USize` by reducing modulo `USize.size`. -/
-@[extern "lean_uint64_to_usize"]
-def UInt64.toUSize (a : UInt64) : USize := a.toNat.toUSize
-/--
-Upcast a `USize` to a `UInt64`.
-This is lossless because `USize.size` is either `2^32` or `2^64`.
-This function is overridden with a native implementation.
--/
-@[extern "lean_usize_to_uint64"]
-def USize.toUInt64 (a : USize) : UInt64 :=
-  UInt64.ofNatCore a.toBitVec.toNat (Nat.lt_of_lt_of_le a.toBitVec.isLt usize_size_le)
 
 instance : Mul USize       := ⟨USize.mul⟩
 instance : Mod USize       := ⟨USize.mod⟩

src/Init/Data/UInt/BasicAux.lean

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

src/Init/Data/UInt/Bitwise.lean

@@ -1,39 +1,25 @@
 /-
 Copyright (c) 2024 Lean FRO, LLC. All Rights Reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Markus Himmel, Mac Malone
+Authors: Markus Himmel
 -/
 prelude
-import Init.Data.UInt.Lemmas
+import Init.Data.UInt.Basic
 import Init.Data.Fin.Bitwise
 import Init.Data.BitVec.Lemmas
 
 set_option hygiene false in
-macro "declare_bitwise_uint_theorems" typeName:ident bits:term:arg : command =>
+macro "declare_bitwise_uint_theorems" typeName:ident : command =>
 `(
 namespace $typeName
 
-@[simp] protected theorem toBitVec_and (a b : $typeName) : (a &&& b).toBitVec = a.toBitVec &&& b.toBitVec := rfl
-@[simp] protected theorem toBitVec_or (a b : $typeName) : (a ||| b).toBitVec = a.toBitVec ||| b.toBitVec := rfl
-@[simp] protected theorem toBitVec_xor (a b : $typeName) : (a ^^^ b).toBitVec = a.toBitVec ^^^ b.toBitVec := rfl
-@[simp] protected theorem toBitVec_shiftLeft (a b : $typeName) : (a <<< b).toBitVec = a.toBitVec <<< (b.toBitVec % $bits) := rfl
-@[simp] protected theorem toBitVec_shiftRight (a b : $typeName) : (a >>> b).toBitVec = a.toBitVec >>> (b.toBitVec % $bits) := rfl
-
-@[simp] protected theorem toNat_and (a b : $typeName) : (a &&& b).toNat = a.toNat &&& b.toNat := by simp [toNat]
-@[simp] protected theorem toNat_or (a b : $typeName) : (a ||| b).toNat = a.toNat ||| b.toNat := by simp [toNat]
-@[simp] protected theorem toNat_xor (a b : $typeName) : (a ^^^ b).toNat = a.toNat ^^^ b.toNat := by simp [toNat]
-@[simp] protected theorem toNat_shiftLeft (a b : $typeName) : (a <<< b).toNat = a.toNat <<< (b.toNat % $bits) % 2 ^ $bits := by simp [toNat]
-@[simp] protected theorem toNat_shiftRight (a b : $typeName) : (a >>> b).toNat = a.toNat >>> (b.toNat % $bits) := by simp [toNat]
-
-open $typeName (toNat_and) in
-@[deprecated toNat_and (since := "2024-11-28")]
-protected theorem and_toNat (a b : $typeName) : (a &&& b).toNat = a.toNat &&& b.toNat := BitVec.toNat_and ..
+@[simp] protected theorem and_toNat (a b : $typeName) : (a &&& b).toNat = a.toNat &&& b.toNat := BitVec.toNat_and ..
 
 end $typeName
 )
 
-declare_bitwise_uint_theorems UInt8 8
-declare_bitwise_uint_theorems UInt16 16
-declare_bitwise_uint_theorems UInt32 32
-declare_bitwise_uint_theorems UInt64 64
-declare_bitwise_uint_theorems USize System.Platform.numBits
+declare_bitwise_uint_theorems UInt8
+declare_bitwise_uint_theorems UInt16
+declare_bitwise_uint_theorems UInt32
+declare_bitwise_uint_theorems UInt64
+declare_bitwise_uint_theorems USize

src/Init/Data/UInt/Lemmas.lean

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura, François G. Dorais, Mario Carneiro, Mac Malone
+Authors: Leonardo de Moura
 -/
 prelude
 import Init.Data.UInt.Basic
@@ -9,205 +9,129 @@ import Init.Data.Fin.Lemmas
 import Init.Data.BitVec.Lemmas
 import Init.Data.BitVec.Bitblast
 
-open Lean in
 set_option hygiene false in
-macro "declare_uint_theorems" typeName:ident bits:term:arg : command => do
-  let mut cmds ← Syntax.getArgs <$> `(
-  namespace $typeName
+macro "declare_uint_theorems" typeName:ident : command =>
+`(
+namespace $typeName
 
-  theorem zero_def : (0 : $typeName) = ⟨0⟩ := rfl
-  theorem one_def : (1 : $typeName) = ⟨1⟩ := rfl
-  theorem sub_def (a b : $typeName) : a - b = ⟨a.toBitVec - b.toBitVec⟩ := rfl
-  theorem mul_def (a b : $typeName) : a * b = ⟨a.toBitVec * b.toBitVec⟩ := rfl
-  theorem mod_def (a b : $typeName) : a % b = ⟨a.toBitVec % b.toBitVec⟩ := rfl
-  theorem add_def (a b : $typeName) : a + b = ⟨a.toBitVec + b.toBitVec⟩ := rfl
+instance : Inhabited $typeName where
+  default := 0
 
-  @[simp] theorem toNat_mk : (mk a).toNat = a.toNat := rfl
+theorem zero_def : (0 : $typeName) = ⟨0⟩ := rfl
+theorem one_def : (1 : $typeName) = ⟨1⟩ := rfl
+theorem sub_def (a b : $typeName) : a - b = ⟨a.toBitVec - b.toBitVec⟩ := rfl
+theorem mul_def (a b : $typeName) : a * b = ⟨a.toBitVec * b.toBitVec⟩ := rfl
+theorem mod_def (a b : $typeName) : a % b = ⟨a.toBitVec % b.toBitVec⟩ := rfl
+theorem add_def (a b : $typeName) : a + b = ⟨a.toBitVec + b.toBitVec⟩ := rfl
 
-  @[simp] theorem toNat_ofNat {n : Nat} : (ofNat n).toNat = n % 2 ^ $bits := BitVec.toNat_ofNat ..
+@[simp] theorem mk_toBitVec_eq : ∀ (a : $typeName), mk a.toBitVec = a
+  | ⟨_, _⟩ => rfl
 
-  @[simp] theorem toNat_ofNatCore {n : Nat} {h : n < size} : (ofNatCore n h).toNat = n := BitVec.toNat_ofNatLt ..
+theorem toBitVec_eq_of_lt {a : Nat} : a < size → (ofNat a).toBitVec.toNat = a :=
+  Nat.mod_eq_of_lt
 
-  @[simp] theorem val_val_eq_toNat (x : $typeName) : x.val.val = x.toNat := rfl
+theorem toNat_ofNat_of_lt {n : Nat} (h : n < size) : (ofNat n).toNat = n := by
+  rw [toNat, toBitVec_eq_of_lt h]
 
-  theorem toNat_toBitVec_eq_toNat (x : $typeName) : x.toBitVec.toNat = x.toNat := rfl
+theorem le_def {a b : $typeName} : a ≤ b ↔ a.toBitVec ≤ b.toBitVec := .rfl
 
-  @[simp] theorem mk_toBitVec_eq : ∀ (a : $typeName), mk a.toBitVec = a
-    | ⟨_, _⟩ => rfl
+theorem lt_def {a b : $typeName} : a < b ↔ a.toBitVec < b.toBitVec := .rfl
 
-  theorem toBitVec_eq_of_lt {a : Nat} : a < size → (ofNat a).toBitVec.toNat = a :=
-    Nat.mod_eq_of_lt
+@[simp] protected theorem not_le {a b : $typeName} : ¬ a ≤ b ↔ b < a := by simp [le_def, lt_def]
 
-  theorem toNat_ofNat_of_lt {n : Nat} (h : n < size) : (ofNat n).toNat = n := by
-    rw [toNat, toBitVec_eq_of_lt h]
+@[simp] protected theorem not_lt {a b : $typeName} : ¬ a < b ↔ b ≤ a := by simp [le_def, lt_def]
 
-  theorem le_def {a b : $typeName} : a ≤ b ↔ a.toBitVec ≤ b.toBitVec := .rfl
+@[simp] protected theorem le_refl (a : $typeName) : a ≤ a := by simp [le_def]
 
-  theorem lt_def {a b : $typeName} : a < b ↔ a.toBitVec < b.toBitVec := .rfl
+@[simp] protected theorem lt_irrefl (a : $typeName) : ¬ a < a := by simp
 
-  theorem le_iff_toNat_le {a b : $typeName} : a ≤ b ↔ a.toNat ≤ b.toNat := .rfl
+protected theorem le_trans {a b c : $typeName} : a ≤ b → b ≤ c → a ≤ c := BitVec.le_trans
 
-  theorem lt_iff_toNat_lt {a b : $typeName} : a < b ↔ a.toNat < b.toNat := .rfl
+protected theorem lt_trans {a b c : $typeName} : a < b → b < c → a < c := BitVec.lt_trans
 
-  @[simp] protected theorem not_le {a b : $typeName} : ¬ a ≤ b ↔ b < a := by simp [le_def, lt_def]
+protected theorem le_total (a b : $typeName) : a ≤ b ∨ b ≤ a := BitVec.le_total ..
 
-  @[simp] protected theorem not_lt {a b : $typeName} : ¬ a < b ↔ b ≤ a := by simp [le_def, lt_def]
+protected theorem lt_asymm {a b : $typeName} : a < b → ¬ b < a := BitVec.lt_asymm
 
-  @[simp] protected theorem le_refl (a : $typeName) : a ≤ a := by simp [le_def]
+protected theorem toBitVec_eq_of_eq {a b : $typeName} (h : a = b) : a.toBitVec = b.toBitVec := h ▸ rfl
 
-  @[simp] protected theorem lt_irrefl (a : $typeName) : ¬ a < a := by simp
+protected theorem eq_of_toBitVec_eq {a b : $typeName} (h : a.toBitVec = b.toBitVec) : a = b := by
+  cases a; cases b; simp_all
 
-  protected theorem le_trans {a b c : $typeName} : a ≤ b → b ≤ c → a ≤ c := BitVec.le_trans
+open $typeName (eq_of_toBitVec_eq) in
+protected theorem eq_of_val_eq {a b : $typeName} (h : a.val = b.val) : a = b := by
+  rcases a with ⟨⟨_⟩⟩; rcases b with ⟨⟨_⟩⟩; simp_all [val]
 
-  protected theorem lt_trans {a b c : $typeName} : a < b → b < c → a < c := BitVec.lt_trans
+open $typeName (toBitVec_eq_of_eq) in
+protected theorem ne_of_toBitVec_ne {a b : $typeName} (h : a.toBitVec ≠ b.toBitVec) : a ≠ b :=
+  fun h' => absurd (toBitVec_eq_of_eq h') h
 
-  protected theorem le_total (a b : $typeName) : a ≤ b ∨ b ≤ a := BitVec.le_total ..
+open $typeName (ne_of_toBitVec_ne) in
+protected theorem ne_of_lt {a b : $typeName} (h : a < b) : a ≠ b := by
+  apply ne_of_toBitVec_ne
+  apply BitVec.ne_of_lt
+  simpa [lt_def] using h
 
-  protected theorem lt_asymm {a b : $typeName} : a < b → ¬ b < a := BitVec.lt_asymm
+@[simp] protected theorem toNat_zero : (0 : $typeName).toNat = 0 := Nat.zero_mod _
 
-  protected theorem toBitVec_eq_of_eq {a b : $typeName} (h : a = b) : a.toBitVec = b.toBitVec := h ▸ rfl
+@[simp] protected theorem toNat_mod (a b : $typeName) : (a % b).toNat = a.toNat % b.toNat := BitVec.toNat_umod ..
 
-  protected theorem eq_of_toBitVec_eq {a b : $typeName} (h : a.toBitVec = b.toBitVec) : a = b := by
-    cases a; cases b; simp_all
+@[simp] protected theorem toNat_div (a b : $typeName) : (a / b).toNat = a.toNat / b.toNat := BitVec.toNat_udiv  ..
 
-  open $typeName (eq_of_toBitVec_eq toBitVec_eq_of_eq) in
-  protected theorem toBitVec_inj {a b : $typeName} : a.toBitVec = b.toBitVec ↔ a = b :=
-    Iff.intro eq_of_toBitVec_eq toBitVec_eq_of_eq
+@[simp] protected theorem toNat_sub_of_le (a b : $typeName) : b ≤ a → (a - b).toNat = a.toNat - b.toNat := BitVec.toNat_sub_of_le
 
-  open $typeName (eq_of_toBitVec_eq) in
-  protected theorem eq_of_val_eq {a b : $typeName} (h : a.val = b.val) : a = b := by
-    rcases a with ⟨⟨_⟩⟩; rcases b with ⟨⟨_⟩⟩; simp_all [val]
+protected theorem toNat_lt_size (a : $typeName) : a.toNat < size := a.toBitVec.isLt
 
-  open $typeName (eq_of_val_eq) in
-  protected theorem val_inj {a b : $typeName} : a.val = b.val ↔ a = b :=
-    Iff.intro eq_of_val_eq (congrArg val)
+open $typeName (toNat_mod toNat_lt_size) in
+protected theorem toNat_mod_lt {m : Nat} : ∀ (u : $typeName), m > 0 → toNat (u % ofNat m) < m := by
+  intro u h1
+  by_cases h2 : m < size
+  · rw [toNat_mod, toNat_ofNat_of_lt h2]
+    apply Nat.mod_lt _ h1
+  · apply Nat.lt_of_lt_of_le
+    · apply toNat_lt_size
+    · simpa using h2
 
-  open $typeName (toBitVec_eq_of_eq) in
-  protected theorem ne_of_toBitVec_ne {a b : $typeName} (h : a.toBitVec ≠ b.toBitVec) : a ≠ b :=
-    fun h' => absurd (toBitVec_eq_of_eq h') h
+open $typeName (toNat_mod_lt) in
+set_option linter.deprecated false in
+@[deprecated toNat_mod_lt (since := "2024-09-24")]
+protected theorem modn_lt {m : Nat} : ∀ (u : $typeName), m > 0 → toNat (u % m) < m := by
+  intro u
+  simp only [(· % ·)]
+  simp only [gt_iff_lt, toNat, modn, Fin.modn_val, BitVec.natCast_eq_ofNat, BitVec.toNat_ofNat,
+    Nat.reducePow]
+  rw [Nat.mod_eq_of_lt]
+  · apply Nat.mod_lt
+  · apply Nat.lt_of_le_of_lt
+    · apply Nat.mod_le
+    · apply Fin.is_lt
 
-  open $typeName (ne_of_toBitVec_ne) in
-  protected theorem ne_of_lt {a b : $typeName} (h : a < b) : a ≠ b := by
-    apply ne_of_toBitVec_ne
-    apply BitVec.ne_of_lt
-    simpa [lt_def] using h
+protected theorem mod_lt (a : $typeName) {b : $typeName} : 0 < b → a % b < b := by
+  simp only [lt_def, mod_def]
+  apply BitVec.umod_lt
 
-  @[simp] protected theorem toNat_zero : (0 : $typeName).toNat = 0 := Nat.zero_mod _
+protected theorem toNat.inj : ∀ {a b : $typeName}, a.toNat = b.toNat → a = b
+  | ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
 
-  @[simp] protected theorem toNat_add (a b : $typeName) : (a + b).toNat = (a.toNat + b.toNat) % 2 ^ $bits := BitVec.toNat_add ..
+@[simp] protected theorem ofNat_one : ofNat 1 = 1 := rfl
 
-  protected theorem toNat_sub (a b : $typeName) : (a - b).toNat = (2 ^ $bits - b.toNat + a.toNat) % 2 ^ $bits := BitVec.toNat_sub  ..
+@[simp]
+theorem val_ofNat (n : Nat) : val (no_index (OfNat.ofNat n)) = OfNat.ofNat n := rfl
 
-  @[simp] protected theorem toNat_mul (a b : $typeName) : (a * b).toNat = a.toNat * b.toNat % 2 ^ $bits := BitVec.toNat_mul  ..
+@[simp]
+theorem toBitVec_ofNat (n : Nat) : toBitVec (no_index (OfNat.ofNat n)) = BitVec.ofNat _ n := rfl
 
-  @[simp] protected theorem toNat_mod (a b : $typeName) : (a % b).toNat = a.toNat % b.toNat := BitVec.toNat_umod ..
+@[simp]
+theorem mk_ofNat (n : Nat) : mk (BitVec.ofNat _ n) = OfNat.ofNat n := rfl
 
-  @[simp] protected theorem toNat_div (a b : $typeName) : (a / b).toNat = a.toNat / b.toNat := BitVec.toNat_udiv  ..
+end $typeName
+)
 
-  @[simp] protected theorem toNat_sub_of_le (a b : $typeName) : b ≤ a → (a - b).toNat = a.toNat - b.toNat := BitVec.toNat_sub_of_le
-
-  protected theorem toNat_lt_size (a : $typeName) : a.toNat < size := a.toBitVec.isLt
-
-  open $typeName (toNat_mod toNat_lt_size) in
-  protected theorem toNat_mod_lt {m : Nat} : ∀ (u : $typeName), m > 0 → toNat (u % ofNat m) < m := by
-    intro u h1
-    by_cases h2 : m < size
-    · rw [toNat_mod, toNat_ofNat_of_lt h2]
-      apply Nat.mod_lt _ h1
-    · apply Nat.lt_of_lt_of_le
-      · apply toNat_lt_size
-      · simpa using h2
-
-  open $typeName (toNat_mod_lt) in
-  set_option linter.deprecated false in
-  @[deprecated toNat_mod_lt (since := "2024-09-24")]
-  protected theorem modn_lt {m : Nat} : ∀ (u : $typeName), m > 0 → toNat (u % m) < m := by
-    intro u
-    simp only [(· % ·)]
-    simp only [gt_iff_lt, toNat, modn, Fin.modn_val, BitVec.natCast_eq_ofNat, BitVec.toNat_ofNat,
-      Nat.reducePow]
-    rw [Nat.mod_eq_of_lt]
-    · apply Nat.mod_lt
-    · apply Nat.lt_of_le_of_lt
-      · apply Nat.mod_le
-      · apply Fin.is_lt
-
-  protected theorem mod_lt (a : $typeName) {b : $typeName} : 0 < b → a % b < b := by
-    simp only [lt_def, mod_def]
-    apply BitVec.umod_lt
-
-  protected theorem toNat.inj : ∀ {a b : $typeName}, a.toNat = b.toNat → a = b
-    | ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
-
-  protected theorem toNat_inj : ∀ {a b : $typeName}, a.toNat = b.toNat ↔ a = b :=
-    Iff.intro toNat.inj (congrArg toNat)
-
-  open $typeName (toNat_inj) in
-  protected theorem le_antisymm_iff {a b : $typeName} : a = b ↔ a ≤ b ∧ b ≤ a :=
-    toNat_inj.symm.trans Nat.le_antisymm_iff
-
-  open $typeName (le_antisymm_iff) in
-  protected theorem le_antisymm {a b : $typeName} (h₁ : a ≤ b) (h₂ : b ≤ a) : a = b :=
-    le_antisymm_iff.2 ⟨h₁, h₂⟩
-
-  @[simp] protected theorem ofNat_one : ofNat 1 = 1 := rfl
-
-  @[simp] protected theorem ofNat_toNat {x : $typeName} : ofNat x.toNat = x := by
-    apply toNat.inj
-    simp [Nat.mod_eq_of_lt x.toNat_lt_size]
-
-  @[simp]
-  theorem val_ofNat (n : Nat) : val (no_index (OfNat.ofNat n)) = OfNat.ofNat n := rfl
-
-  @[simp]
-  theorem toBitVec_ofNat (n : Nat) : toBitVec (no_index (OfNat.ofNat n)) = BitVec.ofNat _ n := rfl
-
-  @[simp]
-  theorem mk_ofNat (n : Nat) : mk (BitVec.ofNat _ n) = OfNat.ofNat n := rfl
-
-  )
-  if let some nbits := bits.raw.isNatLit? then
-    if nbits > 8 then
-      cmds := cmds.push <| ←
-        `(@[simp] theorem toNat_toUInt8 (x : $typeName) : x.toUInt8.toNat = x.toNat % 2 ^ 8 := rfl)
-    if nbits < 16 then
-      cmds := cmds.push <| ←
-        `(@[simp] theorem toNat_toUInt16 (x : $typeName) : x.toUInt16.toNat = x.toNat := rfl)
-    else if nbits > 16 then
-      cmds := cmds.push <| ←
-        `(@[simp] theorem toNat_toUInt16 (x : $typeName) : x.toUInt16.toNat = x.toNat % 2 ^ 16 := rfl)
-    if nbits < 32 then
-      cmds := cmds.push <| ←
-        `(@[simp] theorem toNat_toUInt32 (x : $typeName) : x.toUInt32.toNat = x.toNat := rfl)
-    else if nbits > 32 then
-      cmds := cmds.push <| ←
-        `(@[simp] theorem toNat_toUInt32 (x : $typeName) : x.toUInt32.toNat = x.toNat % 2 ^ 32 := rfl)
-    if nbits ≤ 32 then
-      cmds := cmds.push <| ←
-        `(@[simp] theorem toNat_toUSize (x : $typeName) : x.toUSize.toNat = x.toNat := rfl)
-    else
-      cmds := cmds.push <| ←
-        `(@[simp] theorem toNat_toUSize (x : $typeName) : x.toUSize.toNat = x.toNat % 2 ^ System.Platform.numBits := rfl)
-    if nbits < 64 then
-      cmds := cmds.push <| ←
-        `(@[simp] theorem toNat_toUInt64 (x : $typeName) : x.toUInt64.toNat = x.toNat := rfl)
-  cmds := cmds.push <| ← `(end $typeName)
-  return ⟨mkNullNode cmds⟩
-
-declare_uint_theorems UInt8 8
-declare_uint_theorems UInt16 16
-declare_uint_theorems UInt32 32
-declare_uint_theorems UInt64 64
-declare_uint_theorems USize System.Platform.numBits
-
-@[simp] theorem USize.toNat_ofNat32 {n : Nat} {h : n < 4294967296} : (ofNat32 n h).toNat = n := rfl
-
-@[simp] theorem USize.toNat_toUInt32 (x : USize) : x.toUInt32.toNat = x.toNat % 2 ^ 32  := rfl
-
-@[simp] theorem USize.toNat_toUInt64 (x : USize) : x.toUInt64.toNat = x.toNat := rfl
-
-theorem USize.toNat_ofNat_of_lt_32 {n : Nat} (h : n < 4294967296) : toNat (ofNat n) = n :=
-  toNat_ofNat_of_lt (Nat.lt_of_lt_of_le h le_usize_size)
+declare_uint_theorems UInt8
+declare_uint_theorems UInt16
+declare_uint_theorems UInt32
+declare_uint_theorems UInt64
+declare_uint_theorems USize
 
 theorem UInt32.toNat_lt_of_lt {n : UInt32} {m : Nat} (h : m < size) : n < ofNat m → n.toNat < m := by
   simp [lt_def, BitVec.lt_def, UInt32.toNat, toBitVec_eq_of_lt h]
@@ -221,22 +145,22 @@ theorem UInt32.toNat_le_of_le {n : UInt32} {m : Nat} (h : m < size) : n ≤ ofNa
 theorem UInt32.le_toNat_of_le {n : UInt32} {m : Nat} (h : m < size) : ofNat m ≤ n → m ≤ n.toNat := by
   simp [le_def, BitVec.le_def, UInt32.toNat, toBitVec_eq_of_lt h]
 
-@[deprecated UInt8.toNat_zero (since := "2024-06-23")] protected abbrev UInt8.zero_toNat := @UInt8.toNat_zero
-@[deprecated UInt8.toNat_div (since := "2024-06-23")] protected abbrev UInt8.div_toNat := @UInt8.toNat_div
-@[deprecated UInt8.toNat_mod (since := "2024-06-23")] protected abbrev UInt8.mod_toNat := @UInt8.toNat_mod
+@[deprecated (since := "2024-06-23")] protected abbrev UInt8.zero_toNat := @UInt8.toNat_zero
+@[deprecated (since := "2024-06-23")] protected abbrev UInt8.div_toNat := @UInt8.toNat_div
+@[deprecated (since := "2024-06-23")] protected abbrev UInt8.mod_toNat := @UInt8.toNat_mod
 
-@[deprecated UInt16.toNat_zero (since := "2024-06-23")] protected abbrev UInt16.zero_toNat := @UInt16.toNat_zero
-@[deprecated UInt16.toNat_div (since := "2024-06-23")] protected abbrev UInt16.div_toNat := @UInt16.toNat_div
-@[deprecated UInt16.toNat_mod (since := "2024-06-23")] protected abbrev UInt16.mod_toNat := @UInt16.toNat_mod
+@[deprecated (since := "2024-06-23")] protected abbrev UInt16.zero_toNat := @UInt16.toNat_zero
+@[deprecated (since := "2024-06-23")] protected abbrev UInt16.div_toNat := @UInt16.toNat_div
+@[deprecated (since := "2024-06-23")] protected abbrev UInt16.mod_toNat := @UInt16.toNat_mod
 
-@[deprecated UInt32.toNat_zero (since := "2024-06-23")] protected abbrev UInt32.zero_toNat := @UInt32.toNat_zero
-@[deprecated UInt32.toNat_div (since := "2024-06-23")] protected abbrev UInt32.div_toNat := @UInt32.toNat_div
-@[deprecated UInt32.toNat_mod (since := "2024-06-23")] protected abbrev UInt32.mod_toNat := @UInt32.toNat_mod
+@[deprecated (since := "2024-06-23")] protected abbrev UInt32.zero_toNat := @UInt32.toNat_zero
+@[deprecated (since := "2024-06-23")] protected abbrev UInt32.div_toNat := @UInt32.toNat_div
+@[deprecated (since := "2024-06-23")] protected abbrev UInt32.mod_toNat := @UInt32.toNat_mod
 
-@[deprecated UInt64.toNat_zero (since := "2024-06-23")] protected abbrev UInt64.zero_toNat := @UInt64.toNat_zero
-@[deprecated UInt64.toNat_div (since := "2024-06-23")] protected abbrev UInt64.div_toNat := @UInt64.toNat_div
-@[deprecated UInt64.toNat_mod (since := "2024-06-23")] protected abbrev UInt64.mod_toNat := @UInt64.toNat_mod
+@[deprecated (since := "2024-06-23")] protected abbrev UInt64.zero_toNat := @UInt64.toNat_zero
+@[deprecated (since := "2024-06-23")] protected abbrev UInt64.div_toNat := @UInt64.toNat_div
+@[deprecated (since := "2024-06-23")] protected abbrev UInt64.mod_toNat := @UInt64.toNat_mod
 
-@[deprecated USize.toNat_zero (since := "2024-06-23")] protected abbrev USize.zero_toNat := @USize.toNat_zero
-@[deprecated USize.toNat_div (since := "2024-06-23")] protected abbrev USize.div_toNat := @USize.toNat_div
-@[deprecated USize.toNat_mod (since := "2024-06-23")] protected abbrev USize.mod_toNat := @USize.toNat_mod
+@[deprecated (since := "2024-06-23")] protected abbrev USize.zero_toNat := @USize.toNat_zero
+@[deprecated (since := "2024-06-23")] protected abbrev USize.div_toNat := @USize.toNat_div
+@[deprecated (since := "2024-06-23")] protected abbrev USize.mod_toNat := @USize.toNat_mod

src/Init/Data/Vector.lean

@@ -1,7 +0,0 @@
-/-
-Copyright (c) 2024 Lean FRO. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kim Morrison
--/
-prelude
-import Init.Data.Vector.Basic

src/Init/Data/Vector/Basic.lean

@@ -1,256 +0,0 @@
-/-
-Copyright (c) 2024 Shreyas Srinivas. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Shreyas Srinivas, François G. Dorais, Kim Morrison
--/
-
-prelude
-import Init.Data.Array.Lemmas
-
-/-!
-# Vectors
-
-`Vector α n` is a thin wrapper around `Array α` for arrays of fixed size `n`.
--/
-
-/-- `Vector α n` is an `Array α` with size `n`. -/
-structure Vector (α : Type u) (n : Nat) extends Array α where
-  /-- Array size. -/
-  size_toArray : toArray.size = n
-deriving Repr, DecidableEq
-
-attribute [simp] Vector.size_toArray
-
-/-- Convert `xs : Array α` to `Vector α xs.size`. -/
-abbrev Array.toVector (xs : Array α) : Vector α xs.size := .mk xs rfl
-
-namespace Vector
-
-/-- Syntax for `Vector α n` -/
-syntax "#v[" withoutPosition(sepBy(term, ", ")) "]" : term
-
-open Lean in
-macro_rules
-  | `(#v[ $elems,* ]) => `(Vector.mk (n := $(quote elems.getElems.size)) #[$elems,*] rfl)
-
-/-- Custom eliminator for `Vector α n` through `Array α` -/
-@[elab_as_elim]
-def elimAsArray {motive : Vector α n → Sort u}
-    (mk : ∀ (a : Array α) (ha : a.size = n), motive ⟨a, ha⟩) :
-    (v : Vector α n) → motive v
-  | ⟨a, ha⟩ => mk a ha
-
-/-- Custom eliminator for `Vector α n` through `List α` -/
-@[elab_as_elim]
-def elimAsList {motive : Vector α n → Sort u}
-    (mk : ∀ (a : List α) (ha : a.length = n), motive ⟨⟨a⟩, ha⟩) :
-    (v : Vector α n) → motive v
-  | ⟨⟨a⟩, ha⟩ => mk a ha
-
-/-- Make an empty vector with pre-allocated capacity. -/
-@[inline] def mkEmpty (capacity : Nat) : Vector α 0 := ⟨.mkEmpty capacity, rfl⟩
-
-/-- Makes a vector of size `n` with all cells containing `v`. -/
-@[inline] def mkVector (n) (v : α) : Vector α n := ⟨mkArray n v, by simp⟩
-
-/-- Returns a vector of size `1` with element `v`. -/
-@[inline] def singleton (v : α) : Vector α 1 := ⟨#[v], rfl⟩
-
-instance [Inhabited α] : Inhabited (Vector α n) where
-  default := mkVector n default
-
-/-- Get an element of a vector using a `Fin` index. -/
-@[inline] def get (v : Vector α n) (i : Fin n) : α :=
-  v.toArray[(i.cast v.size_toArray.symm).1]
-
-/-- Get an element of a vector using a `USize` index and a proof that the index is within bounds. -/
-@[inline] def uget (v : Vector α n) (i : USize) (h : i.toNat < n) : α :=
-  v.toArray.uget i (v.size_toArray.symm ▸ h)
-
-instance : GetElem (Vector α n) Nat α fun _ i => i < n where
-  getElem x i h := get x ⟨i, h⟩
-
-/--
-Get an element of a vector using a `Nat` index. Returns the given default value if the index is out
-of bounds.
--/
-@[inline] def getD (v : Vector α n) (i : Nat) (default : α) : α := v.toArray.getD i default
-
-/-- The last element of a vector. Panics if the vector is empty. -/
-@[inline] def back! [Inhabited α] (v : Vector α n) : α := v.toArray.back!
-
-/-- The last element of a vector, or `none` if the array is empty. -/
-@[inline] def back? (v : Vector α n) : Option α := v.toArray.back?
-
-/-- The last element of a non-empty vector. -/
-@[inline] def back [NeZero n] (v : Vector α n) : α :=
-  -- TODO: change to just `v[n]`
-  have : Inhabited α := ⟨v[0]'(Nat.pos_of_neZero n)⟩
-  v.back!
-
-/-- The first element of a non-empty vector.  -/
-@[inline] def head [NeZero n] (v : Vector α n) := v[0]'(Nat.pos_of_neZero n)
-
-/-- Push an element `x` to the end of a vector. -/
-@[inline] def push (x : α) (v : Vector α n)  : Vector α (n + 1) :=
-  ⟨v.toArray.push x, by simp⟩
-
-/-- Remove the last element of a vector. -/
-@[inline] def pop (v : Vector α n) : Vector α (n - 1) :=
-  ⟨Array.pop v.toArray, by simp⟩
-
-/--
-Set an element in a vector using a `Nat` index, with a tactic provided proof that the index is in
-bounds.
-
-This will perform the update destructively provided that the vector has a reference count of 1.
--/
-@[inline] def set (v : Vector α n) (i : Nat) (x : α) (h : i < n := by get_elem_tactic): Vector α n :=
-  ⟨v.toArray.set i x (by simp [*]), by simp⟩
-
-/--
-Set an element in a vector using a `Nat` index. Returns the vector unchanged if the index is out of
-bounds.
-
-This will perform the update destructively provided that the vector has a reference count of 1.
--/
-@[inline] def setIfInBounds (v : Vector α n) (i : Nat) (x : α) : Vector α n :=
-  ⟨v.toArray.setIfInBounds i x, by simp⟩
-
-/--
-Set an element in a vector using a `Nat` index. Panics if the index is out of bounds.
-
-This will perform the update destructively provided that the vector has a reference count of 1.
--/
-@[inline] def set! (v : Vector α n) (i : Nat) (x : α) : Vector α n :=
-  ⟨v.toArray.set! i x, by simp⟩
-
-/-- Append two vectors. -/
-@[inline] def append (v : Vector α n) (w : Vector α m) : Vector α (n + m) :=
-  ⟨v.toArray ++ w.toArray, by simp⟩
-
-instance : HAppend (Vector α n) (Vector α m) (Vector α (n + m)) where
-  hAppend := append
-
-/-- Creates a vector from another with a provably equal length. -/
-@[inline] protected def cast (h : n = m) (v : Vector α n) : Vector α m :=
-  ⟨v.toArray, by simp [*]⟩
-
-/--
-Extracts the slice of a vector from indices `start` to `stop` (exclusive). If `start ≥ stop`, the
-result is empty. If `stop` is greater than the size of the vector, the size is used instead.
--/
-@[inline] def extract (v : Vector α n) (start stop : Nat) : Vector α (min stop n - start) :=
-  ⟨v.toArray.extract start stop, by simp⟩
-
-/-- Maps elements of a vector using the function `f`. -/
-@[inline] def map (f : α → β) (v : Vector α n) : Vector β n :=
-  ⟨v.toArray.map f, by simp⟩
-
-/-- Maps corresponding elements of two vectors of equal size using the function `f`. -/
-@[inline] def zipWith (a : Vector α n) (b : Vector β n) (f : α → β → φ) : Vector φ n :=
-  ⟨Array.zipWith a.toArray b.toArray f, by simp⟩
-
-/-- The vector of length `n` whose `i`-th element is `f i`. -/
-@[inline] def ofFn (f : Fin n → α) : Vector α n :=
-  ⟨Array.ofFn f, by simp⟩
-
-/--
-Swap two elements of a vector using `Fin` indices.
-
-This will perform the update destructively provided that the vector has a reference count of 1.
--/
-@[inline] def swap (v : Vector α n) (i j : Nat)
-    (hi : i < n := by get_elem_tactic) (hj : j < n := by get_elem_tactic) : Vector α n :=
-  ⟨v.toArray.swap i j (by simpa using hi) (by simpa using hj), by simp⟩
-
-/--
-Swap two elements of a vector using `Nat` indices. Panics if either index is out of bounds.
-
-This will perform the update destructively provided that the vector has a reference count of 1.
--/
-@[inline] def swapIfInBounds (v : Vector α n) (i j : Nat) : Vector α n :=
-  ⟨v.toArray.swapIfInBounds i j, by simp⟩
-
-/--
-Swaps an element of a vector with a given value using a `Fin` index. The original value is returned
-along with the updated vector.
-
-This will perform the update destructively provided that the vector has a reference count of 1.
--/
-@[inline] def swapAt (v : Vector α n) (i : Nat) (x : α) (hi : i < n := by get_elem_tactic) :
-    α × Vector α n :=
-  let a := v.toArray.swapAt i x (by simpa using hi)
-  ⟨a.fst, a.snd, by simp [a]⟩
-
-/--
-Swaps an element of a vector with a given value using a `Nat` index. Panics if the index is out of
-bounds. The original value is returned along with the updated vector.
-
-This will perform the update destructively provided that the vector has a reference count of 1.
--/
-@[inline] def swapAt! (v : Vector α n) (i : Nat) (x : α) : α × Vector α n :=
-  let a := v.toArray.swapAt! i x
-  ⟨a.fst, a.snd, by simp [a]⟩
-
-/-- The vector `#v[0,1,2,...,n-1]`. -/
-@[inline] def range (n : Nat) : Vector Nat n := ⟨Array.range n, by simp⟩
-
-/--
-Extract the first `m` elements of a vector. If `m` is greater than or equal to the size of the
-vector then the vector is returned unchanged.
--/
-@[inline] def take (v : Vector α n) (m : Nat) : Vector α (min m n) :=
-  ⟨v.toArray.take m, by simp⟩
-
-/--
-Deletes the first `m` elements of a vector. If `m` is greater than or equal to the size of the
-vector then the empty vector is returned.
--/
-@[inline] def drop (v : Vector α n) (m : Nat) : Vector α (n - m) :=
-  ⟨v.toArray.extract m v.size, by simp⟩
-
-/--
-Compares two vectors of the same size using a given boolean relation `r`. `isEqv v w r` returns
-`true` if and only if `r v[i] w[i]` is true for all indices `i`.
--/
-@[inline] def isEqv (v w : Vector α n) (r : α → α → Bool) : Bool :=
-  Array.isEqvAux v.toArray w.toArray (by simp) r n (by simp)
-
-instance [BEq α] : BEq (Vector α n) where
-  beq a b := isEqv a b (· == ·)
-
-/-- Reverse the elements of a vector. -/
-@[inline] def reverse (v : Vector α n) : Vector α n :=
-  ⟨v.toArray.reverse, by simp⟩
-
-/-- Delete an element of a vector using a `Nat` index and a tactic provided proof. -/
-@[inline] def eraseIdx (v : Vector α n) (i : Nat) (h : i < n := by get_elem_tactic) :
-    Vector α (n-1) :=
-  ⟨v.toArray.eraseIdx i (v.size_toArray.symm ▸ h), by simp [Array.size_eraseIdx]⟩
-
-/-- Delete an element of a vector using a `Nat` index. Panics if the index is out of bounds. -/
-@[inline] def eraseIdx! (v : Vector α n) (i : Nat) : Vector α (n-1) :=
-  if _ : i < n then
-    v.eraseIdx i
-  else
-    have : Inhabited (Vector α (n-1)) := ⟨v.pop⟩
-    panic! "index out of bounds"
-
-/-- Delete the first element of a vector. Returns the empty vector if the input vector is empty. -/
-@[inline] def tail (v : Vector α n) : Vector α (n-1) :=
-  if _ : 0 < n then
-    v.eraseIdx 0
-  else
-    v.cast (by omega)
-
-/--
-Finds the first index of a given value in a vector using `==` for comparison. Returns `none` if the
-no element of the index matches the given value.
--/
-@[inline] def indexOf? [BEq α] (v : Vector α n) (x : α) : Option (Fin n) :=
-  (v.toArray.indexOf? x).map (Fin.cast v.size_toArray)
-
-/-- Returns `true` when `v` is a prefix of the vector `w`. -/
-@[inline] def isPrefixOf [BEq α] (v : Vector α m) (w : Vector α n) : Bool :=
-  v.toArray.isPrefixOf w.toArray

src/Init/Data/Vector/Lemmas.lean

@@ -1,294 +0,0 @@
-/-
-Copyright (c) 2024 Shreyas Srinivas. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Shreyas Srinivas, Francois Dorais
--/
-prelude
-import Init.Data.Vector.Basic
-
-/-!
-## Vectors
-Lemmas about `Vector α n`
--/
-
-namespace Array
-
-theorem toVector_inj {a b : Array α} (h₁ : a.size = b.size) (h₂ : a.toVector.cast h₁ = b.toVector) : a = b := by
-  ext i ih₁ ih₂
-  · exact h₁
-  · simpa using congrArg (fun a => a[i]) h₂
-
-end Array
-
-namespace Vector
-
-@[simp] theorem getElem_mk {data : Array α} {size : data.size = n} {i : Nat} (h : i < n) :
-    (Vector.mk data size)[i] = data[i] := rfl
-
-@[simp] theorem getElem_toArray {α n} (xs : Vector α n) (i : Nat) (h : i < xs.toArray.size) :
-    xs.toArray[i] = xs[i]'(by simpa using h) := by
-  cases xs
-  simp
-
-@[simp] theorem getElem_ofFn {α n} (f : Fin n → α) (i : Nat) (h : i < n) :
-    (Vector.ofFn f)[i] = f ⟨i, by simpa using h⟩ := by
-  simp [ofFn]
-
-/-- The empty vector maps to the empty vector. -/
-@[simp]
-theorem map_empty (f : α → β) : map f #v[] = #v[] := by
-  rw [map, mk.injEq]
-  exact Array.map_empty f
-
-theorem toArray_inj : ∀ {v w : Vector α n}, v.toArray = w.toArray → v = w
-  | {..}, {..}, rfl => rfl
-
-/-- A vector of length `0` is the empty vector. -/
-protected theorem eq_empty (v : Vector α 0) : v = #v[] := by
-  apply Vector.toArray_inj
-  apply Array.eq_empty_of_size_eq_zero v.2
-
-/--
-`Vector.ext` is an extensionality theorem.
-Vectors `a` and `b` are equal to each other if their elements are equal for each valid index.
--/
-@[ext]
-protected theorem ext {a b : Vector α n} (h : (i : Nat) → (_ : i < n) → a[i] = b[i]) : a = b := by
-  apply Vector.toArray_inj
-  apply Array.ext
-  · rw [a.size_toArray, b.size_toArray]
-  · intro i hi _
-    rw [a.size_toArray] at hi
-    exact h i hi
-
-@[simp] theorem push_mk {data : Array α} {size : data.size = n} {x : α} :
-    (Vector.mk data size).push x =
-      Vector.mk (data.push x) (by simp [size, Nat.succ_eq_add_one]) := rfl
-
-@[simp] theorem pop_mk {data : Array α} {size : data.size = n} :
-    (Vector.mk data size).pop = Vector.mk data.pop (by simp [size]) := rfl
-
-@[simp] theorem getElem_push_last {v : Vector α n} {x : α} : (v.push x)[n] = x := by
-  rcases v with ⟨data, rfl⟩
-  simp
-
-@[simp] theorem getElem_push_lt {v : Vector α n} {x : α} {i : Nat} (h : i < n) :
-    (v.push x)[i] = v[i] := by
-  rcases v with ⟨data, rfl⟩
-  simp [Array.getElem_push_lt, h]
-
-@[simp] theorem getElem_pop {v : Vector α n} {i : Nat} (h : i < n - 1) : (v.pop)[i] = v[i] := by
-  rcases v with ⟨data, rfl⟩
-  simp
-
-/--
-Variant of `getElem_pop` that will sometimes fire when `getElem_pop` gets stuck because of
-defeq issues in the implicit size argument.
--/
-@[simp] theorem getElem_pop' (v : Vector α (n + 1)) (i : Nat) (h : i < n + 1 - 1) :
-    @getElem (Vector α n) Nat α (fun _ i => i < n) instGetElemNatLt v.pop i h = v[i] :=
-  getElem_pop h
-
-@[simp] theorem push_pop_back (v : Vector α (n + 1)) : v.pop.push v.back = v := by
-  ext i
-  by_cases h : i < n
-  · simp [h]
-  · replace h : i = v.size - 1 := by rw [size_toArray]; omega
-    subst h
-    simp [pop, back, back!, ← Array.eq_push_pop_back!_of_size_ne_zero]
-
-
-/-! ### mk lemmas -/
-
-theorem toArray_mk (a : Array α) (h : a.size = n) : (Vector.mk a h).toArray = a := rfl
-
-@[simp] theorem allDiff_mk [BEq α] (a : Array α) (h : a.size = n) :
-    (Vector.mk a h).allDiff = a.allDiff := rfl
-
-@[simp] theorem mk_append_mk (a b : Array α) (ha : a.size = n) (hb : b.size = m) :
-    Vector.mk a ha ++ Vector.mk b hb = Vector.mk (a ++ b) (by simp [ha, hb]) := rfl
-
-@[simp] theorem back!_mk [Inhabited α] (a : Array α) (h : a.size = n) :
-    (Vector.mk a h).back! = a.back! := rfl
-
-@[simp] theorem back?_mk (a : Array α) (h : a.size = n) :
-    (Vector.mk a h).back? = a.back? := rfl
-
-@[simp] theorem drop_mk (a : Array α) (h : a.size = n) (m) :
-    (Vector.mk a h).drop m = Vector.mk (a.extract m a.size) (by simp [h]) := rfl
-
-@[simp] theorem eraseIdx_mk (a : Array α) (h : a.size = n) (i) (h') :
-    (Vector.mk a h).eraseIdx i h' = Vector.mk (a.eraseIdx i) (by simp [h]) := rfl
-
-@[simp] theorem eraseIdx!_mk (a : Array α) (h : a.size = n) (i) (hi : i < n) :
-    (Vector.mk a h).eraseIdx! i = Vector.mk (a.eraseIdx i) (by simp [h, hi]) := by
-  simp [Vector.eraseIdx!, hi]
-
-@[simp] theorem extract_mk (a : Array α) (h : a.size = n) (start stop) :
-    (Vector.mk a h).extract start stop = Vector.mk (a.extract start stop) (by simp [h]) := rfl
-
-@[simp] theorem indexOf?_mk [BEq α] (a : Array α) (h : a.size = n) (x : α) :
-    (Vector.mk a h).indexOf? x = (a.indexOf? x).map (Fin.cast h) := rfl
-
-@[simp] theorem mk_isEqv_mk (r : α → α → Bool) (a b : Array α) (ha : a.size = n) (hb : b.size = n) :
-    Vector.isEqv (Vector.mk a ha) (Vector.mk b hb) r = Array.isEqv a b r := by
-  simp [Vector.isEqv, Array.isEqv, ha, hb]
-
-@[simp] theorem mk_isPrefixOf_mk [BEq α] (a b : Array α) (ha : a.size = n) (hb : b.size = m) :
-    (Vector.mk a ha).isPrefixOf (Vector.mk b hb) = a.isPrefixOf b := rfl
-
-@[simp] theorem map_mk (a : Array α) (h : a.size = n) (f : α → β) :
-    (Vector.mk a h).map f = Vector.mk (a.map f) (by simp [h]) := rfl
-
-@[simp] theorem reverse_mk (a : Array α) (h : a.size = n) :
-    (Vector.mk a h).reverse = Vector.mk a.reverse (by simp [h]) := rfl
-
-@[simp] theorem set_mk (a : Array α) (h : a.size = n) (i x w) :
-    (Vector.mk a h).set i x = Vector.mk (a.set i x) (by simp [h]) := rfl
-
-@[simp] theorem set!_mk (a : Array α) (h : a.size = n) (i x) :
-    (Vector.mk a h).set! i x = Vector.mk (a.set! i x) (by simp [h]) := rfl
-
-@[simp] theorem setIfInBounds_mk (a : Array α) (h : a.size = n) (i x) :
-    (Vector.mk a h).setIfInBounds i x = Vector.mk (a.setIfInBounds i x) (by simp [h]) := rfl
-
-@[simp] theorem swap_mk (a : Array α) (h : a.size = n) (i j) (hi hj) :
-    (Vector.mk a h).swap i j = Vector.mk (a.swap i j) (by simp [h]) :=
-  rfl
-
-@[simp] theorem swapIfInBounds_mk (a : Array α) (h : a.size = n) (i j) :
-    (Vector.mk a h).swapIfInBounds i j = Vector.mk (a.swapIfInBounds i j) (by simp [h]) := rfl
-
-@[simp] theorem swapAt_mk (a : Array α) (h : a.size = n) (i x) (hi) :
-    (Vector.mk a h).swapAt i x =
-      ((a.swapAt i x).fst, Vector.mk (a.swapAt i x).snd (by simp [h])) :=
-  rfl
-
-@[simp] theorem swapAt!_mk (a : Array α) (h : a.size = n) (i x) : (Vector.mk a h).swapAt! i x =
-    ((a.swapAt! i x).fst, Vector.mk (a.swapAt! i x).snd (by simp [h])) := rfl
-
-@[simp] theorem take_mk (a : Array α) (h : a.size = n) (m) :
-    (Vector.mk a h).take m = Vector.mk (a.take m) (by simp [h]) := rfl
-
-@[simp] theorem mk_zipWith_mk (f : α → β → γ) (a : Array α) (b : Array β)
-      (ha : a.size = n) (hb : b.size = n) : zipWith (Vector.mk a ha) (Vector.mk b hb) f =
-        Vector.mk (Array.zipWith a b f) (by simp [ha, hb]) := rfl
-
-/-! ### toArray lemmas -/
-
-@[simp] theorem toArray_append (a : Vector α m) (b : Vector α n) :
-    (a ++ b).toArray = a.toArray ++ b.toArray := rfl
-
-@[simp] theorem toArray_drop (a : Vector α n) (m) :
-    (a.drop m).toArray = a.toArray.extract m a.size := rfl
-
-@[simp] theorem toArray_empty : (#v[] : Vector α 0).toArray = #[] := rfl
-
-@[simp] theorem toArray_mkEmpty (cap) :
-    (Vector.mkEmpty (α := α) cap).toArray = Array.mkEmpty cap := rfl
-
-@[simp] theorem toArray_eraseIdx (a : Vector α n) (i) (h) :
-    (a.eraseIdx i h).toArray = a.toArray.eraseIdx i (by simp [h]) := rfl
-
-@[simp] theorem toArray_eraseIdx! (a : Vector α n) (i) (hi : i < n) :
-    (a.eraseIdx! i).toArray = a.toArray.eraseIdx! i := by
-  cases a; simp_all [Array.eraseIdx!]
-
-@[simp] theorem toArray_extract (a : Vector α n) (start stop) :
-    (a.extract start stop).toArray = a.toArray.extract start stop := rfl
-
-@[simp] theorem toArray_map (f : α → β) (a : Vector α n) :
-    (a.map f).toArray = a.toArray.map f := rfl
-
-@[simp] theorem toArray_ofFn (f : Fin n → α) : (Vector.ofFn f).toArray = Array.ofFn f := rfl
-
-@[simp] theorem toArray_pop (a : Vector α n) : a.pop.toArray = a.toArray.pop := rfl
-
-@[simp] theorem toArray_push (a : Vector α n) (x) : (a.push x).toArray = a.toArray.push x := rfl
-
-@[simp] theorem toArray_range : (Vector.range n).toArray = Array.range n := rfl
-
-@[simp] theorem toArray_reverse (a : Vector α n) : a.reverse.toArray = a.toArray.reverse := rfl
-
-@[simp] theorem toArray_set (a : Vector α n) (i x h) :
-    (a.set i x).toArray = a.toArray.set i x (by simpa using h):= rfl
-
-@[simp] theorem toArray_set! (a : Vector α n) (i x) :
-    (a.set! i x).toArray = a.toArray.set! i x := rfl
-
-@[simp] theorem toArray_setIfInBounds (a : Vector α n) (i x) :
-    (a.setIfInBounds i x).toArray = a.toArray.setIfInBounds i x := rfl
-
-@[simp] theorem toArray_singleton (x : α) : (Vector.singleton x).toArray = #[x] := rfl
-
-@[simp] theorem toArray_swap (a : Vector α n) (i j) (hi hj) : (a.swap i j).toArray =
-    a.toArray.swap i j (by simp [hi, hj]) (by simp [hi, hj]) := rfl
-
-@[simp] theorem toArray_swapIfInBounds (a : Vector α n) (i j) :
-    (a.swapIfInBounds i j).toArray = a.toArray.swapIfInBounds i j := rfl
-
-@[simp] theorem toArray_swapAt (a : Vector α n) (i x h) :
-    ((a.swapAt i x).fst, (a.swapAt i x).snd.toArray) =
-      ((a.toArray.swapAt i x (by simpa using h)).fst,
-        (a.toArray.swapAt i x (by simpa using h)).snd) := rfl
-
-@[simp] theorem toArray_swapAt! (a : Vector α n) (i x) :
-    ((a.swapAt! i x).fst, (a.swapAt! i x).snd.toArray) =
-      ((a.toArray.swapAt! i x).fst, (a.toArray.swapAt! i x).snd) := rfl
-
-@[simp] theorem toArray_take (a : Vector α n) (m) : (a.take m).toArray = a.toArray.take m := rfl
-
-@[simp] theorem toArray_zipWith (f : α → β → γ) (a : Vector α n) (b : Vector β n) :
-    (Vector.zipWith a b f).toArray = Array.zipWith a.toArray b.toArray f := rfl
-
-/-! ### toList lemmas -/
-
-theorem length_toList {α n} (xs : Vector α n) : xs.toList.length = n := by simp
-
-theorem getElem_toList {α n} (xs : Vector α n) (i : Nat) (h : i < xs.toList.length) :
-    xs.toList[i] = xs[i]'(by simpa using h) := by simp
-
-theorem toList_inj {a b : Vector α n} (h : a.toList = b.toList) : a = b := by
-  rcases a with ⟨⟨a⟩, ha⟩
-  rcases b with ⟨⟨b⟩, hb⟩
-  simpa using h
-
-/-! ### Decidable quantifiers. -/
-
-theorem forall_zero_iff {P : Vector α 0 → Prop} :
-    (∀ v, P v) ↔ P #v[] := by
-  constructor
-  · intro h
-    apply h
-  · intro h v
-    obtain (rfl : v = #v[]) := (by ext i h; simp at h)
-    apply h
-
-theorem forall_cons_iff {P : Vector α (n + 1) → Prop} :
-    (∀ v : Vector α (n + 1), P v) ↔ (∀ (x : α) (v : Vector α n), P (v.push x)) := by
-  constructor
-  · intro h _ _
-    apply h
-  · intro h v
-    have w : v = v.pop.push v.back := by simp
-    rw [w]
-    apply h
-
-instance instDecidableForallVectorZero (P : Vector α 0 → Prop) :
-    ∀ [Decidable (P #v[])], Decidable (∀ v, P v)
-  | .isTrue h => .isTrue fun ⟨v, s⟩ => by
-    obtain (rfl : v = .empty) := (by ext i h₁ h₂; exact s; cases h₂)
-    exact h
-  | .isFalse h => .isFalse (fun w => h (w _))
-
-instance instDecidableForallVectorSucc (P : Vector α (n+1) → Prop)
-    [Decidable (∀ (x : α) (v : Vector α n), P (v.push x))] : Decidable (∀ v, P v) :=
-  decidable_of_iff' (∀ x (v : Vector α n), P (v.push x)) forall_cons_iff
-
-instance instDecidableExistsVectorZero (P : Vector α 0 → Prop) [Decidable (P #v[])] :
-    Decidable (∃ v, P v) :=
-  decidable_of_iff (¬ ∀ v, ¬ P v) Classical.not_forall_not
-
-instance instDecidableExistsVectorSucc (P : Vector α (n+1) → Prop)
-    [Decidable (∀ (x : α) (v : Vector α n), ¬ P (v.push x))] : Decidable (∃ v, P v) :=
-  decidable_of_iff (¬ ∀ v, ¬ P v) Classical.not_forall_not

src/Init/GetElem.lean

@@ -172,16 +172,6 @@ theorem getElem!_neg [GetElem? cont idx elem dom] [LawfulGetElem cont idx elem d
   simp only [getElem?_def] at h ⊢
   split <;> simp_all
 
-@[simp] theorem isNone_getElem? [GetElem? cont idx elem dom] [LawfulGetElem cont idx elem dom]
-    (c : cont) (i : idx) [Decidable (dom c i)] : c[i]?.isNone = ¬dom c i := by
-  simp only [getElem?_def]
-  split <;> simp_all
-
-@[simp] theorem isSome_getElem? [GetElem? cont idx elem dom] [LawfulGetElem cont idx elem dom]
-    (c : cont) (i : idx) [Decidable (dom c i)] : c[i]?.isSome = dom c i := by
-  simp only [getElem?_def]
-  split <;> simp_all
-
 namespace Fin
 
 instance instGetElemFinVal [GetElem cont Nat elem dom] : GetElem cont (Fin n) elem fun xs i => dom xs i where
@@ -216,12 +206,12 @@ instance : GetElem (List α) Nat α fun as i => i < as.length where
 @[simp] theorem getElem_cons_zero (a : α) (as : List α) (h : 0 < (a :: as).length) : getElem (a :: as) 0 h = a := by
   rfl
 
-@[deprecated getElem_cons_zero (since := "2024-06-12")] abbrev cons_getElem_zero := @getElem_cons_zero
+@[deprecated (since := "2024-06-12")] abbrev cons_getElem_zero := @getElem_cons_zero
 
 @[simp] theorem getElem_cons_succ (a : α) (as : List α) (i : Nat) (h : i + 1 < (a :: as).length) : getElem (a :: as) (i+1) h = getElem as i (Nat.lt_of_succ_lt_succ h) := by
   rfl
 
-@[deprecated getElem_cons_succ (since := "2024-06-12")] abbrev cons_getElem_succ := @getElem_cons_succ
+@[deprecated (since := "2024-06-12")] abbrev cons_getElem_succ := @getElem_cons_succ
 
 @[simp] theorem getElem_mem : ∀ {l : List α} {n} (h : n < l.length), l[n]'h ∈ l
   | _ :: _, 0, _ => .head ..
@@ -231,10 +221,9 @@ theorem getElem_cons_drop_succ_eq_drop {as : List α} {i : Nat} (h : i < as.leng
     as[i] :: as.drop (i+1) = as.drop i :=
   match as, i with
   | _::_, 0   => rfl
-  | _::_, i+1 => getElem_cons_drop_succ_eq_drop (i := i) (Nat.add_one_lt_add_one_iff.mp h)
+  | _::_, i+1 => getElem_cons_drop_succ_eq_drop (i := i) _
 
-@[deprecated getElem_cons_drop_succ_eq_drop (since := "2024-11-05")]
-abbrev get_drop_eq_drop := @getElem_cons_drop_succ_eq_drop
+@[deprecated (since := "2024-11-05")] abbrev get_drop_eq_drop := @getElem_cons_drop_succ_eq_drop
 
 end List
 

src/Init/MetaTypes.lean

@@ -224,8 +224,7 @@ structure Config where
   -/
   index             : Bool := true
   /--
-  If `implicitDefEqProofs := true`, `simp` does not create proof terms when the
-  input and output terms are definitionally equal.
+  This option does not have any effect (yet).
   -/
   implicitDefEqProofs : Bool := true
   deriving Inhabited, BEq
@@ -250,25 +249,12 @@ def neutralConfig : Simp.Config := {
   zetaDelta         := false
 }
 
-structure NormCastConfig extends Simp.Config where
-    zeta := false
-    beta := false
-    eta  := false
-    proj := false
-    iota := false
-
 end Simp
 
-/-- Configuration for which occurrences that match an expression should be rewritten. -/
 inductive Occurrences where
-  /-- All occurrences should be rewritten. -/
   | all
-  /-- A list of indices for which occurrences should be rewritten. -/
   | pos (idxs : List Nat)
-  /-- A list of indices for which occurrences should not be rewritten. -/
   | neg (idxs : List Nat)
   deriving Inhabited, BEq
 
-instance : Coe (List Nat) Occurrences := ⟨.pos⟩
-
 end Lean.Meta

src/Init/Notation.lean

@@ -48,10 +48,6 @@ def tactic : Category := {}
 For example, `let x ← e` is a `doElem`, and a `do` block consists of a list of `doElem`s. -/
 def doElem : Category := {}
 
-/-- `structInstFieldDecl` is the syntax category for value declarations for fields in structure instance notation.
-For example, the `:= 1` and `| 0 => 0 | n + 1 => n` in `{ x := 1, f | 0 => 0 | n + 1 => n }` are in the `structInstFieldDecl` class. -/
-def structInstFieldDecl : Category := {}
-
 /-- `level` is a builtin syntax category for universe levels.
 This is the `u` in `Sort u`: it can contain `max` and `imax`, addition with
 constants, and variables. -/
@@ -75,9 +71,9 @@ def prio : Category := {}
 
 /-- `prec` is a builtin syntax category for precedences. A precedence is a value
 that expresses how tightly a piece of syntax binds: for example `1 + 2 * 3` is
-parsed as `1 + (2 * 3)` because `*` has a higher precedence than `+`.
+parsed as `1 + (2 * 3)` because `*` has a higher pr0ecedence than `+`.
 Higher numbers denote higher precedence.
-In addition to literals like `37`, there are some special named precedence levels:
+In addition to literals like `37`, there are some special named priorities:
 * `arg` for the precedence of function arguments
 * `max` for the highest precedence used in term parsers (not actually the maximum possible value)
 * `lead` for the precedence of terms not supposed to be used as arguments

src/Init/Omega/IntList.lean

@@ -32,9 +32,13 @@ theorem get_map {xs : IntList} (h : f 0 = 0) : get (xs.map f) i = f (xs.get i) :
   cases xs[i]? <;> simp_all
 
 theorem get_of_length_le {xs : IntList} (h : xs.length ≤ i) : xs.get i = 0 := by
-  rw [get, List.get?_eq_none_iff.mpr h]
+  rw [get, List.get?_eq_none.mpr h]
   rfl
 
+-- theorem lt_length_of_get_nonzero {xs : IntList} (h : xs.get i ≠ 0) : i < xs.length := by
+--   revert h
+--   simpa using mt get_of_length_le
+
 /-- Like `List.set`, but right-pad with zeroes as necessary first. -/
 def set (xs : IntList) (i : Nat) (y : Int) : IntList :=
   match xs, i with

src/Init/Prelude.lean

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

src/Init/ShareCommon.lean

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

src/Init/SimpLemmas.lean

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

src/Init/Syntax.lean

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

src/Init/System/IO.lean

@@ -462,16 +462,6 @@ Note that it is the caller's job to remove the file after use.
 -/
 @[extern "lean_io_create_tempfile"] opaque createTempFile : IO (Handle × FilePath)
 
-/--
-Creates a temporary directory in the most secure manner possible. There are no race conditions in the
-directory’s creation. The directory is readable and writable only by the creating user ID.
-
-Returns the new directory's path.
-
-It is the caller's job to remove the directory after use.
--/
-@[extern "lean_io_create_tempdir"] opaque createTempDir : IO FilePath
-
 end FS
 
 @[extern "lean_io_getenv"] opaque getEnv (var : @& String) : BaseIO (Option String)
@@ -484,6 +474,17 @@ namespace FS
 def withFile (fn : FilePath) (mode : Mode) (f : Handle → IO α) : IO α :=
   Handle.mk fn mode >>= f
 
+/--
+Like `createTempFile` but also takes care of removing the file after usage.
+-/
+def withTempFile [Monad m] [MonadFinally m] [MonadLiftT IO m] (f : Handle → FilePath → m α) :
+    m α := do
+  let (handle, path) ← createTempFile
+  try
+    f handle path
+  finally
+    removeFile path
+
 def Handle.putStrLn (h : Handle) (s : String) : IO Unit :=
   h.putStr (s.push '\n')
 
@@ -674,10 +675,8 @@ def appDir : IO FilePath := do
     | throw <| IO.userError s!"System.IO.appDir: unexpected filename '{p}'"
   FS.realPath p
 
-namespace FS
-
 /-- Create given path and all missing parents as directories. -/
-partial def createDirAll (p : FilePath) : IO Unit := do
+partial def FS.createDirAll (p : FilePath) : IO Unit := do
   if ← p.isDir then
     return ()
   if let some parent := p.parent then
@@ -694,7 +693,7 @@ partial def createDirAll (p : FilePath) : IO Unit := do
 /--
   Fully remove given directory by deleting all contained files and directories in an unspecified order.
   Fails if any contained entry cannot be deleted or was newly created during execution. -/
-partial def removeDirAll (p : FilePath) : IO Unit := do
+partial def FS.removeDirAll (p : FilePath) : IO Unit := do
   for ent in (← p.readDir) do
     if (← ent.path.isDir : Bool) then
       removeDirAll ent.path
@@ -702,32 +701,6 @@ partial def removeDirAll (p : FilePath) : IO Unit := do
       removeFile ent.path
   removeDir p
 
-/--
-Like `createTempFile`, but also takes care of removing the file after usage.
--/
-def withTempFile [Monad m] [MonadFinally m] [MonadLiftT IO m] (f : Handle → FilePath → m α) :
-    m α := do
-  let (handle, path) ← createTempFile
-  try
-    f handle path
-  finally
-    removeFile path
-
-/--
-Like `createTempDir`, but also takes care of removing the directory after usage.
-
-All files in the directory are recursively deleted, regardless of how or when they were created.
--/
-def withTempDir [Monad m] [MonadFinally m] [MonadLiftT IO m] (f : FilePath → m α) :
-    m α := do
-  let path ← createTempDir
-  try
-    f path
-  finally
-    removeDirAll path
-
-end FS
-
 namespace Process
 
 /-- Returns the current working directory of the calling process. -/
@@ -959,36 +932,3 @@ syntax "println! " (interpolatedStr(term) <|> term) : term
 macro_rules
   | `(println! $msg:interpolatedStr) => `((IO.println (s! $msg) : IO Unit))
   | `(println! $msg:term)            => `((IO.println $msg : IO Unit))
-
-/--
-  Marks given value and its object graph closure as multi-threaded if currently
-  marked single-threaded. This will make reference counter updates atomic and
-  thus more costly. It can still be useful to do eagerly when the value will be
-  shared between threads later anyway and there is available time budget to mark
-  it now. -/
-@[extern "lean_runtime_mark_multi_threaded"]
-def Runtime.markMultiThreaded (a : α) : BaseIO α := return a
-
-/--
-Marks given value and its object graph closure as persistent. This will remove
-reference counter updates but prevent the closure from being deallocated until
-the end of the process! It can still be useful to do eagerly when the value
-will be marked persistent later anyway and there is available time budget to
-mark it now or it would be unnecessarily marked multi-threaded in between.
-
-This function is only safe to use on objects (in the full closure) which are
-not used concurrently or which are already persistent.
--/
-@[extern "lean_runtime_mark_persistent"]
-unsafe def Runtime.markPersistent (a : α) : BaseIO α := return a
-
-set_option linter.unusedVariables false in
-/--
-Discards the passed owned reference. This leads to `a` any any object reachable from it never being
-freed. This can be a useful optimization for eliding deallocation time of big object graphs that are
-kept alive close to the end of the process anyway (in which case calling `Runtime.markPersistent`
-would be similarly costly to deallocation). It is still considered a safe operation as it cannot
-lead to undefined behavior.
--/
-@[extern "lean_runtime_forget"]
-def Runtime.forget (a : α) : BaseIO Unit := return

src/Init/System/Mutex.lean

@@ -7,9 +7,6 @@ prelude
 import Init.System.IO
 import Init.Control.StateRef
 
-
-set_option linter.deprecated false
-
 namespace IO
 
 private opaque BaseMutexImpl : NonemptyType.{0}
@@ -19,13 +16,12 @@ Mutual exclusion primitive (a lock).
 
 If you want to guard shared state, use `Mutex α` instead.
 -/
-@[deprecated "Use Std.BaseMutex from Std.Sync.Mutex instead" (since := "2024-12-02")]
 def BaseMutex : Type := BaseMutexImpl.type
 
 instance : Nonempty BaseMutex := BaseMutexImpl.property
 
 /-- Creates a new `BaseMutex`. -/
-@[extern "lean_io_basemutex_new", deprecated "Use Std.BaseMutex.new from Std.Sync.Mutex instead" (since := "2024-12-02")]
+@[extern "lean_io_basemutex_new"]
 opaque BaseMutex.new : BaseIO BaseMutex
 
 /--
@@ -34,7 +30,7 @@ Locks a `BaseMutex`.  Waits until no other thread has locked the mutex.
 The current thread must not have already locked the mutex.
 Reentrant locking is undefined behavior (inherited from the C++ implementation).
 -/
-@[extern "lean_io_basemutex_lock", deprecated "Use Std.BaseMutex.lock from Std.Sync.Mutex instead" (since := "2024-12-02")]
+@[extern "lean_io_basemutex_lock"]
 opaque BaseMutex.lock (mutex : @& BaseMutex) : BaseIO Unit
 
 /--
@@ -43,35 +39,33 @@ Unlocks a `BaseMutex`.
 The current thread must have already locked the mutex.
 Unlocking an unlocked mutex is undefined behavior (inherited from the C++ implementation).
 -/
-@[extern "lean_io_basemutex_unlock", deprecated "Use Std.BaseMutex.unlock from Std.Sync.Mutex instead" (since := "2024-12-02")]
+@[extern "lean_io_basemutex_unlock"]
 opaque BaseMutex.unlock (mutex : @& BaseMutex) : BaseIO Unit
 
 private opaque CondvarImpl : NonemptyType.{0}
 
 /-- Condition variable. -/
-@[deprecated "Use Std.Condvar from Std.Sync.Mutex instead" (since := "2024-12-02")]
 def Condvar : Type := CondvarImpl.type
 
 instance : Nonempty Condvar := CondvarImpl.property
 
 /-- Creates a new condition variable. -/
-@[extern "lean_io_condvar_new", deprecated "Use Std.Condvar.new from Std.Sync.Mutex instead" (since := "2024-12-02")]
+@[extern "lean_io_condvar_new"]
 opaque Condvar.new : BaseIO Condvar
 
 /-- Waits until another thread calls `notifyOne` or `notifyAll`. -/
-@[extern "lean_io_condvar_wait", deprecated "Use Std.Condvar.wait from Std.Sync.Mutex instead" (since := "2024-12-02")]
+@[extern "lean_io_condvar_wait"]
 opaque Condvar.wait (condvar : @& Condvar) (mutex : @& BaseMutex) : BaseIO Unit
 
 /-- Wakes up a single other thread executing `wait`. -/
-@[extern "lean_io_condvar_notify_one", deprecated "Use Std.Condvar.notifyOne from Std.Sync.Mutex instead" (since := "2024-12-02")]
+@[extern "lean_io_condvar_notify_one"]
 opaque Condvar.notifyOne (condvar : @& Condvar) : BaseIO Unit
 
 /-- Wakes up all other threads executing `wait`. -/
-@[extern "lean_io_condvar_notify_all", deprecated "Use Std.Condvar.notifyAll from Std.Sync.Mutex instead" (since := "2024-12-02")]
+@[extern "lean_io_condvar_notify_all"]
 opaque Condvar.notifyAll (condvar : @& Condvar) : BaseIO Unit
 
 /-- Waits on the condition variable until the predicate is true. -/
-@[deprecated "Use Std.Condvar.waitUntil from Std.Sync.Mutex instead" (since := "2024-12-02")]
 def Condvar.waitUntil [Monad m] [MonadLift BaseIO m]
     (condvar : Condvar) (mutex : BaseMutex) (pred : m Bool) : m Unit := do
   while !(← pred) do
@@ -84,7 +78,6 @@ The type `Mutex α` is similar to `IO.Ref α`,
 except that concurrent accesses are guarded by a mutex
 instead of atomic pointer operations and busy-waiting.
 -/
-@[deprecated "Use Std.Mutex from Std.Sync.Mutex instead" (since := "2024-12-02")]
 structure Mutex (α : Type) where private mk ::
   private ref : IO.Ref α
   mutex : BaseMutex
@@ -93,7 +86,6 @@ structure Mutex (α : Type) where private mk ::
 instance : CoeOut (Mutex α) BaseMutex where coe := Mutex.mutex
 
 /-- Creates a new mutex. -/
-@[deprecated "Use Std.Mutex.new from Std.Sync.Mutex instead" (since := "2024-12-02")]
 def Mutex.new (a : α) : BaseIO (Mutex α) :=
   return { ref := ← mkRef a, mutex := ← BaseMutex.new }
 
@@ -102,11 +94,9 @@ def Mutex.new (a : α) : BaseIO (Mutex α) :=
 with outside monad `m`.
 The action has access to the state `α` of the mutex (via `get` and `set`).
 -/
-@[deprecated "Use Std.AtomicT from Std.Sync.Mutex instead" (since := "2024-12-02")]
 abbrev AtomicT := StateRefT' IO.RealWorld
 
 /-- `mutex.atomically k` runs `k` with access to the mutex's state while locking the mutex. -/
-@[deprecated "Use Std.Mutex.atomically from Std.Sync.Mutex instead" (since := "2024-12-02")]
 def Mutex.atomically [Monad m] [MonadLiftT BaseIO m] [MonadFinally m]
     (mutex : Mutex α) (k : AtomicT α m β) : m β := do
   try
@@ -120,7 +110,6 @@ def Mutex.atomically [Monad m] [MonadLiftT BaseIO m] [MonadFinally m]
 waiting on `condvar` until `pred` returns true.
 Both `k` and `pred` have access to the mutex's state.
 -/
-@[deprecated "Use Std.Mutex.atomicallyOnce from Std.Sync.Mutex instead" (since := "2024-12-02")]
 def Mutex.atomicallyOnce [Monad m] [MonadLiftT BaseIO m] [MonadFinally m]
     (mutex : Mutex α) (condvar : Condvar)
     (pred : AtomicT α m Bool) (k : AtomicT α m β) : m β :=

src/Init/System/Platform.lean

@@ -23,14 +23,5 @@ def isEmscripten : Bool := getIsEmscripten ()
 /-- The LLVM target triple of the current platform. Empty if missing at Lean compile time. -/
 def target : String := getTarget ()
 
-theorem numBits_pos : 0 < numBits := by
-  cases numBits_eq <;> next h => simp [h]
-
-theorem le_numBits : 32 ≤ numBits := by
-  cases numBits_eq <;> next h => simp [h]
-
-theorem numBits_le : numBits ≤ 64 := by
-  cases numBits_eq <;> next h => simp [h]
-
 end Platform
 end System

src/Init/Tactics.lean

@@ -428,11 +428,11 @@ macro "infer_instance" : tactic => `(tactic| exact inferInstance)
 /--
 `+opt` is short for `(opt := true)`. It sets the `opt` configuration option to `true`.
 -/
-syntax posConfigItem := " +" noWs ident
+syntax posConfigItem := "+" noWs ident
 /--
 `-opt` is short for `(opt := false)`. It sets the `opt` configuration option to `false`.
 -/
-syntax negConfigItem := " -" noWs ident
+syntax negConfigItem := "-" noWs ident
 /--
 `(opt := val)` sets the `opt` configuration option to `val`.
 
@@ -1309,7 +1309,7 @@ macro "bv_omega" : tactic => `(tactic| (try simp only [bv_toNat] at *) <;> omega
 syntax (name := acNf0) "ac_nf0" (location)? : tactic
 
 /-- Implementation of `norm_cast` (the full `norm_cast` calls `trivial` afterwards). -/
-syntax (name := normCast0) "norm_cast0" optConfig (location)? : tactic
+syntax (name := normCast0) "norm_cast0" (location)? : tactic
 
 /-- `assumption_mod_cast` is a variant of `assumption` that solves the goal
 using a hypothesis. Unlike `assumption`, it first pre-processes the goal and
@@ -1318,7 +1318,7 @@ in more situations.
 
 Concretely, it runs `norm_cast` on the goal. For each local hypothesis `h`, it also
 normalizes `h` with `norm_cast` and tries to use that to close the goal. -/
-macro "assumption_mod_cast" cfg:optConfig : tactic => `(tactic| norm_cast0 $cfg at * <;> assumption)
+macro "assumption_mod_cast" : tactic => `(tactic| norm_cast0 at * <;> assumption)
 
 /--
 The `norm_cast` family of tactics is used to normalize certain coercions (*casts*) in expressions.
@@ -1355,9 +1355,26 @@ their operation, to make them more flexible about the expressions they accept
 
 See also `push_cast`, which moves casts inwards rather than lifting them outwards.
 -/
-macro "norm_cast" cfg:optConfig loc:(location)? : tactic =>
-  `(tactic| norm_cast0 $cfg $[$loc]? <;> try trivial)
+macro "norm_cast" loc:(location)? : tactic =>
+  `(tactic| norm_cast0 $[$loc]? <;> try trivial)
 
+/--
+`ac_nf` normalizes equalities up to application of an associative and commutative operator.
+- `ac_nf` normalizes all hypotheses and the goal target of the goal.
+- `ac_nf at l` normalizes at location(s) `l`, where `l` is either `*` or a
+  list of hypotheses in the local context. In the latter case, a turnstile `⊢` or `|-`
+  can also be used, to signify the target of the goal.
+```
+instance : Associative (α := Nat) (.+.) := ⟨Nat.add_assoc⟩
+instance : Commutative (α := Nat) (.+.) := ⟨Nat.add_comm⟩
+
+example (a b c d : Nat) : a + b + c + d = d + (b + c) + a := by
+ ac_nf
+ -- goal: a + (b + (c + d)) = a + (b + (c + d))
+```
+-/
+macro "ac_nf" loc:(location)? : tactic =>
+  `(tactic| ac_nf0 $[$loc]? <;> try trivial)
 
 /--
 `push_cast` rewrites the goal to move certain coercions (*casts*) inward, toward the leaf nodes.
@@ -1400,24 +1417,6 @@ syntax (name := pushCast) "push_cast" optConfig (discharger)? (&" only")?
 -/
 syntax (name := normCastAddElim) "norm_cast_add_elim" ident : command
 
-/--
-`ac_nf` normalizes equalities up to application of an associative and commutative operator.
-- `ac_nf` normalizes all hypotheses and the goal target of the goal.
-- `ac_nf at l` normalizes at location(s) `l`, where `l` is either `*` or a
-  list of hypotheses in the local context. In the latter case, a turnstile `⊢` or `|-`
-  can also be used, to signify the target of the goal.
-```
-instance : Associative (α := Nat) (.+.) := ⟨Nat.add_assoc⟩
-instance : Commutative (α := Nat) (.+.) := ⟨Nat.add_comm⟩
-
-example (a b c d : Nat) : a + b + c + d = d + (b + c) + a := by
- ac_nf
- -- goal: a + (b + (c + d)) = a + (b + (c + d))
-```
--/
-macro "ac_nf" loc:(location)? : tactic =>
-  `(tactic| ac_nf0 $[$loc]? <;> try trivial)
-
 /--
 * `symm` applies to a goal whose target has the form `t ~ u` where `~` is a symmetric relation,
   that is, a relation which has a symmetry lemma tagged with the attribute [symm].

src/Init/Util.lean

@@ -79,3 +79,21 @@ def withPtrEq {α : Type u} (a b : α) (k : Unit → Bool) (h : a = b → k () =
 
 @[implemented_by withPtrAddrUnsafe]
 def withPtrAddr {α : Type u} {β : Type v} (a : α) (k : USize → β) (h : ∀ u₁ u₂, k u₁ = k u₂) : β := k 0
+
+/--
+  Marks given value and its object graph closure as multi-threaded if currently
+  marked single-threaded. This will make reference counter updates atomic and
+  thus more costly. It can still be useful to do eagerly when the value will be
+  shared between threads later anyway and there is available time budget to mark
+  it now. -/
+@[extern "lean_runtime_mark_multi_threaded"]
+def Runtime.markMultiThreaded (a : α) : α := a
+
+/--
+  Marks given value and its object graph closure as persistent. This will remove
+  reference counter updates but prevent the closure from being deallocated until
+  the end of the process! It can still be useful to do eagerly when the value
+  will be marked persistent later anyway and there is available time budget to
+  mark it now or it would be unnecessarily marked multi-threaded in between. -/
+@[extern "lean_runtime_mark_persistent"]
+def Runtime.markPersistent (a : α) : α := a

src/Lean/Compiler/IR/Borrow.lean

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

src/Lean/Compiler/IR/Boxing.lean

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

src/Lean/Compiler/IR/ElimDeadBranches.lean

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

src/Lean/Compiler/IR/EmitC.lean

@@ -108,9 +108,9 @@ def emitFnDeclAux (decl : Decl) (cppBaseName : String) (isExternal : Bool) : M U
     if ps.size > closureMaxArgs && isBoxedName decl.name then
       emit "lean_object**"
     else
-      ps.size.forM fun i _ => do
+      ps.size.forM fun i => do
         if i > 0 then emit ", "
-        emit (toCType ps[i].ty)
+        emit (toCType ps[i]!.ty)
     emit ")"
   emitLn ";"
 
@@ -321,22 +321,20 @@ def emitSSet (x : VarId) (n : Nat) (offset : Nat) (y : VarId) (t : IRType) : M U
 
 def emitJmp (j : JoinPointId) (xs : Array Arg) : M Unit := do
   let ps ← getJPParams j
-  if h : xs.size = ps.size then
-    xs.size.forM fun i _ => do
-      let p := ps[i]
-      let x := xs[i]
-      emit p.x; emit " = "; emitArg x; emitLn ";"
-    emit "goto "; emit j; emitLn ";"
-  else
-    do throw "invalid goto"
+  unless xs.size == ps.size do throw "invalid goto"
+  xs.size.forM fun i => do
+    let p := ps[i]!
+    let x := xs[i]!
+    emit p.x; emit " = "; emitArg x; emitLn ";"
+  emit "goto "; emit j; emitLn ";"
 
 def emitLhs (z : VarId) : M Unit := do
   emit z; emit " = "
 
 def emitArgs (ys : Array Arg) : M Unit :=
-  ys.size.forM fun i _ => do
+  ys.size.forM fun i => do
     if i > 0 then emit ", "
-    emitArg ys[i]
+    emitArg ys[i]!
 
 def emitCtorScalarSize (usize : Nat) (ssize : Nat) : M Unit := do
   if usize == 0 then emit ssize
@@ -348,8 +346,8 @@ def emitAllocCtor (c : CtorInfo) : M Unit := do
   emitCtorScalarSize c.usize c.ssize; emitLn ");"
 
 def emitCtorSetArgs (z : VarId) (ys : Array Arg) : M Unit :=
-  ys.size.forM fun i _ => do
-    emit "lean_ctor_set("; emit z; emit ", "; emit i; emit ", "; emitArg ys[i]; emitLn ");"
+  ys.size.forM fun i => do
+    emit "lean_ctor_set("; emit z; emit ", "; emit i; emit ", "; emitArg ys[i]!; emitLn ");"
 
 def emitCtor (z : VarId) (c : CtorInfo) (ys : Array Arg) : M Unit := do
   emitLhs z;
@@ -360,7 +358,7 @@ def emitCtor (z : VarId) (c : CtorInfo) (ys : Array Arg) : M Unit := do
 
 def emitReset (z : VarId) (n : Nat) (x : VarId) : M Unit := do
   emit "if (lean_is_exclusive("; emit x; emitLn ")) {";
-  n.forM fun i _ => do
+  n.forM fun i => do
     emit " lean_ctor_release("; emit x; emit ", "; emit i; emitLn ");"
   emit " "; emitLhs z; emit x; emitLn ";";
   emitLn "} else {";
@@ -401,12 +399,12 @@ def emitSimpleExternalCall (f : String) (ps : Array Param) (ys : Array Arg) : M
   emit f; emit "("
   -- We must remove irrelevant arguments to extern calls.
   discard <| ys.size.foldM
-    (fun i _ (first : Bool) =>
+    (fun i (first : Bool) =>
       if ps[i]!.ty.isIrrelevant then
         pure first
       else do
         unless first do emit ", "
-        emitArg ys[i]
+        emitArg ys[i]!
         pure false)
     true
   emitLn ");"
@@ -433,8 +431,8 @@ def emitPartialApp (z : VarId) (f : FunId) (ys : Array Arg) : M Unit := do
   let decl ← getDecl f
   let arity := decl.params.size;
   emitLhs z; emit "lean_alloc_closure((void*)("; emitCName f; emit "), "; emit arity; emit ", "; emit ys.size; emitLn ");";
-  ys.size.forM fun i _ => do
-    let y := ys[i]
+  ys.size.forM fun i => do
+    let y := ys[i]!
     emit "lean_closure_set("; emit z; emit ", "; emit i; emit ", "; emitArg y; emitLn ");"
 
 def emitApp (z : VarId) (f : VarId) (ys : Array Arg) : M Unit :=
@@ -546,36 +544,34 @@ That is, we have
 -/
 def overwriteParam (ps : Array Param) (ys : Array Arg) : Bool :=
   let n := ps.size;
-  n.any fun i _ =>
-    let p := ps[i]
-    (i+1, n).anyI fun j _ _ => paramEqArg p ys[j]!
+  n.any fun i =>
+    let p := ps[i]!
+    (i+1, n).anyI fun j => paramEqArg p ys[j]!
 
 def emitTailCall (v : Expr) : M Unit :=
   match v with
   | Expr.fap _ ys => do
     let ctx ← read
     let ps := ctx.mainParams
-    if h : ps.size = ys.size then
-      if overwriteParam ps ys then
-        emitLn "{"
-        ps.size.forM fun i _ => do
-          let p := ps[i]
-          let y := ys[i]
-          unless paramEqArg p y do
-            emit (toCType p.ty); emit " _tmp_"; emit i; emit " = "; emitArg y; emitLn ";"
-        ps.size.forM fun i _ => do
-          let p := ps[i]
-          let y := ys[i]
-          unless paramEqArg p y do emit p.x; emit " = _tmp_"; emit i; emitLn ";"
-        emitLn "}"
-      else
-        ys.size.forM fun i _ => do
-          let p := ps[i]
-          let y := ys[i]
-          unless paramEqArg p y do emit p.x; emit " = "; emitArg y; emitLn ";"
-      emitLn "goto _start;"
+    unless ps.size == ys.size do throw "invalid tail call"
+    if overwriteParam ps ys then
+      emitLn "{"
+      ps.size.forM fun i => do
+        let p := ps[i]!
+        let y := ys[i]!
+        unless paramEqArg p y do
+          emit (toCType p.ty); emit " _tmp_"; emit i; emit " = "; emitArg y; emitLn ";"
+      ps.size.forM fun i => do
+        let p := ps[i]!
+        let y := ys[i]!
+        unless paramEqArg p y do emit p.x; emit " = _tmp_"; emit i; emitLn ";"
+      emitLn "}"
     else
-      throw "invalid tail call"
+      ys.size.forM fun i => do
+        let p := ps[i]!
+        let y := ys[i]!
+        unless paramEqArg p y do emit p.x; emit " = "; emitArg y; emitLn ";"
+    emitLn "goto _start;"
   | _ => throw "bug at emitTailCall"
 
 mutual
@@ -658,16 +654,16 @@ def emitDeclAux (d : Decl) : M Unit := do
         if xs.size > closureMaxArgs && isBoxedName d.name then
           emit "lean_object** _args"
         else
-          xs.size.forM fun i _ => do
+          xs.size.forM fun i => do
             if i > 0 then emit ", "
-            let x := xs[i]
+            let x := xs[i]!
             emit (toCType x.ty); emit " "; emit x.x
         emit ")"
       else
         emit ("_init_" ++ baseName ++ "()")
       emitLn " {";
       if xs.size > closureMaxArgs && isBoxedName d.name then
-        xs.size.forM fun i _ => do
+        xs.size.forM fun i => do
           let x := xs[i]!
           emit "lean_object* "; emit x.x; emit " = _args["; emit i; emitLn "];"
       emitLn "_start:";

src/Lean/Compiler/IR/EmitLLVM.lean

@@ -571,9 +571,9 @@ def emitAllocCtor (builder : LLVM.Builder llvmctx)
 
 def emitCtorSetArgs (builder : LLVM.Builder llvmctx)
     (z : VarId) (ys : Array Arg) : M llvmctx Unit := do
-  ys.size.forM fun i _ => do
+  ys.size.forM fun i => do
     let zv ← emitLhsVal builder z
-    let (_yty, yv) ← emitArgVal builder ys[i]
+    let (_yty, yv) ← emitArgVal builder ys[i]!
     let iv ← constIntUnsigned i
     callLeanCtorSet builder zv iv yv
     emitLhsSlotStore builder z zv
@@ -702,8 +702,8 @@ def emitPartialApp (builder : LLVM.Builder llvmctx) (z : VarId) (f : FunId) (ys
                                     (← constIntUnsigned arity)
                                     (← constIntUnsigned ys.size)
   LLVM.buildStore builder zval zslot
-  ys.size.forM fun i _ => do
-    let (yty, yslot) ← emitArgSlot_ builder ys[i]
+  ys.size.forM fun i => do
+    let (yty, yslot) ← emitArgSlot_ builder ys[i]!
     let yval ← LLVM.buildLoad2 builder yty yslot
     callLeanClosureSetFn builder zval (← constIntUnsigned i) yval
 
@@ -922,7 +922,7 @@ def emitReset (builder : LLVM.Builder llvmctx) (z : VarId) (n : Nat) (x : VarId)
   buildIfThenElse_ builder "isExclusive" isExclusive
    (fun builder => do
      let xv ← emitLhsVal builder x
-     n.forM fun i _ => do
+     n.forM fun i => do
          callLeanCtorRelease builder xv (← constIntUnsigned i)
      emitLhsSlotStore builder z xv
      return ShouldForwardControlFlow.yes

src/Lean/Compiler/IR/ExpandResetReuse.lean

@@ -134,15 +134,15 @@ abbrev M := ReaderT Context (StateM Nat)
   modifyGet fun n => ({ idx := n }, n + 1)
 
 def releaseUnreadFields (y : VarId) (mask : Mask) (b : FnBody) : M FnBody :=
-  mask.size.foldM (init := b) fun i _ b =>
-    match mask[i] with
+  mask.size.foldM (init := b) fun i b =>
+    match mask.get! i with
     | some _ => pure b -- code took ownership of this field
     | none   => do
       let fld ← mkFresh
       pure (FnBody.vdecl fld IRType.object (Expr.proj i y) (FnBody.dec fld 1 true false b))
 
 def setFields (y : VarId) (zs : Array Arg) (b : FnBody) : FnBody :=
-  zs.size.fold (init := b) fun i _ b => FnBody.set y i zs[i] b
+  zs.size.fold (init := b) fun i b => FnBody.set y i (zs.get! i) b
 
 /-- Given `set x[i] := y`, return true iff `y := proj[i] x` -/
 def isSelfSet (ctx : Context) (x : VarId) (i : Nat) (y : Arg) : Bool :=

src/Lean/Compiler/IR/RC.lean

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

src/Lean/Compiler/LCNF/Basic.lean

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

src/Lean/Compiler/LCNF/ElimDeadBranches.lean

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

src/Lean/Compiler/LCNF/InferType.lean

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

src/Lean/Compiler/LCNF/PassManager.lean

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

src/Lean/Compiler/LCNF/ToLCNF.lean

@@ -593,14 +593,6 @@ where
       let minor ← visit minor
       mkOverApplication minor args arity
 
-  visitHEqRec (e : Expr) : M Arg :=
-    let arity := 7
-    etaIfUnderApplied e arity do
-      let args := e.getAppArgs
-      let minor := if e.isAppOf ``HEq.rec || e.isAppOf ``HEq.ndrec then args[3]! else args[6]!
-      let minor ← visit minor
-      mkOverApplication minor args arity
-
   visitFalseRec (e : Expr) : M Arg :=
     let arity := 2
     etaIfUnderApplied e arity do
@@ -677,8 +669,6 @@ where
         visitCtor 3 e
       else if declName == ``Eq.casesOn || declName == ``Eq.rec || declName == ``Eq.ndrec then
         visitEqRec e
-      else if declName == ``HEq.casesOn || declName == ``HEq.rec || declName == ``HEq.ndrec then
-        visitHEqRec e
       else if declName == ``And.rec || declName == ``Iff.rec then
         visitAndIffRecCore e (minorPos := 3)
       else if declName == ``And.casesOn || declName == ``Iff.casesOn then

src/Lean/Compiler/Specialize.lean

@@ -33,7 +33,7 @@ private def elabSpecArgs (declName : Name) (args : Array Syntax) : MetaM (Array
           result := result.push idx
       else
         let argName := arg.getId
-        if let some idx := argNames.indexOf? argName then
+        if let some idx := argNames.getIdx? argName then
           if result.contains idx then throwErrorAt arg "invalid specialization argument name `{argName}`, it has already been specified as a specialization candidate"
           result := result.push idx
         else

src/Lean/CoreM.lean

@@ -11,7 +11,6 @@ import Lean.ResolveName
 import Lean.Elab.InfoTree.Types
 import Lean.MonadEnv
 import Lean.Elab.Exception
-import Lean.Language.Basic
 
 namespace Lean
 register_builtin_option diagnostics : Bool := {
@@ -31,19 +30,6 @@ register_builtin_option maxHeartbeats : Nat := {
   descr := "maximum amount of heartbeats per command. A heartbeat is number of (small) memory allocations (in thousands), 0 means no limit"
 }
 
-register_builtin_option Elab.async : Bool := {
-  defValue := false
-  descr := "perform elaboration using multiple threads where possible\
-    \n\
-    \nThis option defaults to `false` but (when not explicitly set) is overridden to `true` in \
-      `Lean.Language.Lean.process` as used by the cmdline driver and language server. \
-      Metaprogramming users driving elaboration directly via e.g. \
-      `Lean.Elab.Command.elabCommandTopLevel` can opt into asynchronous elaboration by setting \
-      this option but then are responsible for processing messages and other data not only in the \
-      resulting command state but also from async tasks in `Lean.Command.Context.snap?` and \
-      `Lean.Command.State.snapshotTasks`."
-}
-
 /--
 If the `diagnostics` option is not already set, gives a message explaining this option.
 Begins with a `\n`, so an error message can look like `m!"some error occurred{useDiagnosticMsg}"`.
@@ -86,13 +72,6 @@ structure State where
   messages        : MessageLog     := {}
   /-- Info tree. We have the info tree here because we want to update it while adding attributes. -/
   infoState       : Elab.InfoState := {}
-  /--
-  Snapshot trees of asynchronous subtasks. As these are untyped and reported only at the end of the
-  command's main elaboration thread, they are only useful for basic message log reporting; for
-  incremental reporting and reuse within a long-running elaboration thread, types rooted in
-  `CommandParsedSnapshot` need to be adjusted.
-  -/
-  snapshotTasks : Array (Language.SnapshotTask Language.SnapshotTree) := #[]
   deriving Nonempty
 
 /-- Context for the CoreM monad. -/
@@ -201,8 +180,7 @@ instance : Elab.MonadInfoTree CoreM where
   modifyInfoState f := modify fun s => { s with infoState := f s.infoState }
 
 @[inline] def modifyCache (f : Cache → Cache) : CoreM Unit :=
-  modify fun ⟨env, next, ngen, trace, cache, messages, infoState, snaps⟩ =>
-   ⟨env, next, ngen, trace, f cache, messages, infoState, snaps⟩
+  modify fun ⟨env, next, ngen, trace, cache, messages, infoState⟩ => ⟨env, next, ngen, trace, f cache, messages, infoState⟩
 
 @[inline] def modifyInstLevelTypeCache (f : InstantiateLevelCache → InstantiateLevelCache) : CoreM Unit :=
   modifyCache fun ⟨c₁, c₂⟩ => ⟨f c₁, c₂⟩
@@ -364,7 +342,9 @@ Returns the current log and then resets its messages while adjusting `MessageLog
 for incremental reporting during elaboration of a single command.
 -/
 def getAndEmptyMessageLog : CoreM MessageLog :=
-  modifyGet fun s => (s.messages, { s with messages := s.messages.markAllReported })
+  modifyGet fun s => (s.messages, { s with
+    messages.unreported := {}
+    messages.hadErrors  := s.messages.hasErrors })
 
 instance : MonadLog CoreM where
   getRef      := getRef
@@ -375,83 +355,13 @@ instance : MonadLog CoreM where
     if (← read).suppressElabErrors then
       -- discard elaboration errors, except for a few important and unlikely misleading ones, on
       -- parse error
-      unless msg.data.hasTag (· matches `Elab.synthPlaceholder | `Tactic.unsolvedGoals | `trace) do
+      unless msg.data.hasTag (· matches `Elab.synthPlaceholder | `Tactic.unsolvedGoals) do
         return
 
     let ctx ← read
     let msg := { msg with data := MessageData.withNamingContext { currNamespace := ctx.currNamespace, openDecls := ctx.openDecls } msg.data };
     modify fun s => { s with messages := s.messages.add msg }
 
-/--
-Includes a given task (such as from `wrapAsyncAsSnapshot`) in the overall snapshot tree for this
-command's elaboration, making its result available to reporting and the language server. The
-reporter will not know about this snapshot tree node until the main elaboration thread for this
-command has finished so this function is not useful for incremental reporting within a longer
-elaboration thread but only for tasks that outlive it such as background kernel checking or proof
-elaboration.
--/
-def logSnapshotTask (task : Language.SnapshotTask Language.SnapshotTree) : CoreM Unit :=
-  modify fun s => { s with snapshotTasks := s.snapshotTasks.push task }
-
-/-- Wraps the given action for use in `EIO.asTask` etc., discarding its final monadic state. -/
-def wrapAsync (act : Unit → CoreM α) : CoreM (EIO Exception α) := do
-  let st ← get
-  let ctx ← read
-  let heartbeats := (← IO.getNumHeartbeats) - ctx.initHeartbeats
-  return withCurrHeartbeats (do
-      -- include heartbeats since start of elaboration in new thread as well such that forking off
-      -- an action doesn't suddenly allow it to succeed from a lower heartbeat count
-      IO.addHeartbeats heartbeats.toUInt64
-      act () : CoreM _)
-    |>.run' ctx st
-
-/-- Option for capturing output to stderr during elaboration. -/
-register_builtin_option stderrAsMessages : Bool := {
-  defValue := true
-  group    := "server"
-  descr    := "(server) capture output to the Lean stderr channel (such as from `dbg_trace`) during elaboration of a command as a diagnostic message"
-}
-
-open Language in
-/--
-Wraps the given action for use in `BaseIO.asTask` etc., discarding its final state except for
-`logSnapshotTask` tasks, which are reported as part of the returned tree.
--/
-def wrapAsyncAsSnapshot (act : Unit → CoreM Unit) (desc : String := by exact decl_name%.toString) :
-    CoreM (BaseIO SnapshotTree) := do
-  let t ← wrapAsync fun _ => do
-    IO.FS.withIsolatedStreams (isolateStderr := stderrAsMessages.get (← getOptions)) do
-      let tid ← IO.getTID
-      -- reset trace state and message log so as not to report them twice
-      modify fun st => { st with messages := st.messages.markAllReported, traceState := { tid } }
-      try
-        withTraceNode `Elab.async (fun _ => return desc) do
-          act ()
-      catch e =>
-        logError e.toMessageData
-      finally
-        addTraceAsMessages
-      get
-  let ctx ← readThe Core.Context
-  return do
-    match (← t.toBaseIO) with
-    | .ok (output, st) =>
-      let mut msgs := st.messages
-      if !output.isEmpty then
-        msgs := msgs.add {
-          fileName := ctx.fileName
-          severity := MessageSeverity.information
-          pos      := ctx.fileMap.toPosition <| ctx.ref.getPos?.getD 0
-          data     := output
-        }
-      return .mk {
-        desc
-        diagnostics := (← Language.Snapshot.Diagnostics.ofMessageLog msgs)
-        traces := st.traceState
-      } st.snapshotTasks
-    -- interrupt or abort exception as `try catch` above should have caught any others
-    | .error _ => default
-
 end Core
 
 export Core (CoreM mkFreshUserName checkSystem withCurrHeartbeats)

src/Lean/Data/HashMap.lean

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

src/Lean/Data/PersistentArray.lean

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

src/Lean/Data/PersistentHashMap.lean

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

src/Lean/Elab.lean

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

src/Lean/Elab/App.lean

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

src/Lean/Elab/BuiltinCommand.lean

@@ -211,7 +211,7 @@ private def replaceBinderAnnotation (binder : TSyntax ``Parser.Term.bracketedBin
         else
           `(bracketedBinderF| {$id $[: $ty?]?})
       for id in ids.reverse do
-        if let some idx := binderIds.findFinIdx? fun binderId => binderId.raw.isIdent && binderId.raw.getId == id.raw.getId then
+        if let some idx := binderIds.findIdx? fun binderId => binderId.raw.isIdent && binderId.raw.getId == id.raw.getId then
           binderIds := binderIds.eraseIdx idx
           modifiedVarDecls := true
           varDeclsNew := varDeclsNew.push (← mkBinder id explicit)
@@ -488,9 +488,6 @@ where
     let mut lines : Array MessageData := #[]
     let decls ← getOptionDecls
     for (name, val) in opts do
-      -- `#guard_msgs` sets this option internally, we don't want it to end up in its output
-      if name == `Elab.async then
-        continue
       let (isSet, isUnknown) :=
         match decls.find? name with
         | some decl => (decl.defValue != val, false)

src/Lean/Elab/Command.lean

@@ -84,7 +84,6 @@ structure State where
   ngen           : NameGenerator := {}
   infoState      : InfoState := {}
   traceState     : TraceState := {}
-  snapshotTasks  : Array (Language.SnapshotTask Language.SnapshotTree) := #[]
   deriving Nonempty
 
 structure Context where
@@ -101,7 +100,7 @@ structure Context where
   (mutual) defs and contained tactics, in which case the `DynamicSnapshot` is a
   `HeadersParsedSnapshot`.
 
-  Definitely resolved in `Lean.Elab.Command.elabCommandTopLevel`.
+  Definitely resolved in `Language.Lean.process.doElab`.
 
   Invariant: if the bundle's `old?` is set, the context and state at the beginning of current and
   old elaboration are identical.
@@ -115,7 +114,8 @@ structure Context where
   -/
   suppressElabErrors : Bool := false
 
-abbrev CommandElabM := ReaderT Context $ StateRefT State $ EIO Exception
+abbrev CommandElabCoreM (ε) := ReaderT Context $ StateRefT State $ EIO ε
+abbrev CommandElabM := CommandElabCoreM Exception
 abbrev CommandElab  := Syntax → CommandElabM Unit
 structure Linter where
   run : Syntax → CommandElabM Unit
@@ -198,6 +198,36 @@ instance : AddErrorMessageContext CommandElabM where
     let msg ← addMacroStack msg ctx.macroStack
     return (ref, msg)
 
+def mkMessageAux (ctx : Context) (ref : Syntax) (msgData : MessageData) (severity : MessageSeverity) : Message :=
+  let pos := ref.getPos?.getD ctx.cmdPos
+  let endPos := ref.getTailPos?.getD pos
+  mkMessageCore ctx.fileName ctx.fileMap msgData severity pos endPos
+
+private def addTraceAsMessagesCore (ctx : Context) (log : MessageLog) (traceState : TraceState) : MessageLog := Id.run do
+  if traceState.traces.isEmpty then return log
+  let mut traces : Std.HashMap (String.Pos × String.Pos) (Array MessageData) := ∅
+  for traceElem in traceState.traces do
+    let ref := replaceRef traceElem.ref ctx.ref
+    let pos := ref.getPos?.getD 0
+    let endPos := ref.getTailPos?.getD pos
+    traces := traces.insert (pos, endPos) <| traces.getD (pos, endPos) #[] |>.push traceElem.msg
+  let mut log := log
+  let traces' := traces.toArray.qsort fun ((a, _), _) ((b, _), _) => a < b
+  for ((pos, endPos), traceMsg) in traces' do
+    let data := .tagged `trace <| .joinSep traceMsg.toList "\n"
+    log := log.add <| mkMessageCore ctx.fileName ctx.fileMap data .information pos endPos
+  return log
+
+private def addTraceAsMessages : CommandElabM Unit := do
+  let ctx ← read
+  -- do not add trace messages if `trace.profiler.output` is set as it would be redundant and
+  -- pretty printing the trace messages is expensive
+  if trace.profiler.output.get? (← getOptions) |>.isNone then
+    modify fun s => { s with
+      messages          := addTraceAsMessagesCore ctx s.messages s.traceState
+      traceState.traces := {}
+    }
+
 private def runCore (x : CoreM α) : CommandElabM α := do
   let s ← get
   let ctx ← read
@@ -223,7 +253,6 @@ private def runCore (x : CoreM α) : CommandElabM α := do
     nextMacroScope := s.nextMacroScope
     infoState.enabled := s.infoState.enabled
     traceState := s.traceState
-    snapshotTasks := s.snapshotTasks
   }
   let (ea, coreS) ← liftM x
   modify fun s => { s with
@@ -232,7 +261,6 @@ private def runCore (x : CoreM α) : CommandElabM α := do
     ngen              := coreS.ngen
     infoState.trees   := s.infoState.trees.append coreS.infoState.trees
     traceState.traces := coreS.traceState.traces.map fun t => { t with ref := replaceRef t.ref ctx.ref }
-    snapshotTasks     := coreS.snapshotTasks
     messages          := s.messages ++ coreS.messages
   }
   return ea
@@ -240,6 +268,10 @@ private def runCore (x : CoreM α) : CommandElabM α := do
 def liftCoreM (x : CoreM α) : CommandElabM α := do
   MonadExcept.ofExcept (← runCore (observing x))
 
+private def ioErrorToMessage (ctx : Context) (ref : Syntax) (err : IO.Error) : Message :=
+  let ref := getBetterRef ref ctx.macroStack
+  mkMessageAux ctx ref (toString err) MessageSeverity.error
+
 @[inline] def liftIO {α} (x : IO α) : CommandElabM α := do
   let ctx ← read
   IO.toEIO (fun (ex : IO.Error) => Exception.error ctx.ref ex.toString) x
@@ -262,8 +294,9 @@ instance : MonadLog CommandElabM where
   logMessage msg := do
     if (← read).suppressElabErrors then
       -- discard elaboration errors on parse error
-      unless msg.data.hasTag (· matches `trace) do
-        return
+      -- NOTE: unlike `CoreM`'s `logMessage`, we do not currently have any command-level errors that
+      -- we want to allowlist
+      return
     let currNamespace ← getCurrNamespace
     let openDecls ← getOpenDecls
     let msg := { msg with data := MessageData.withNamingContext { currNamespace := currNamespace, openDecls := openDecls } msg.data }
@@ -287,75 +320,7 @@ def runLinters (stx : Syntax) : CommandElabM Unit := do
               | Exception.internal _ _ =>
                 logException ex
             finally
-              -- TODO: it would be good to preserve even more state (#4363) but preserving info
-              -- trees currently breaks from linters adding context-less info nodes
-              modify fun s => { savedState with messages := s.messages, traceState := s.traceState }
-
-/--
-Catches and logs exceptions occurring in `x`. Unlike `try catch` in `CommandElabM`, this function
-catches interrupt exceptions as well and thus is intended for use at the top level of elaboration.
-Interrupt and abort exceptions are caught but not logged.
--/
-@[inline] def withLoggingExceptions (x : CommandElabM Unit) : CommandElabM Unit := fun ctx ref =>
-  EIO.catchExceptions (withLogging x ctx ref) (fun _ => pure ())
-
-@[inherit_doc Core.wrapAsync]
-def wrapAsync (act : Unit → CommandElabM α) : CommandElabM (EIO Exception α) := do
-  return act () |>.run (← read) |>.run' (← get)
-
-open Language in
-@[inherit_doc Core.wrapAsyncAsSnapshot]
--- `CoreM` and `CommandElabM` are too different to meaningfully share this code
-def wrapAsyncAsSnapshot (act : Unit → CommandElabM Unit)
-    (desc : String := by exact decl_name%.toString) :
-    CommandElabM (BaseIO SnapshotTree) := do
-  let t ← wrapAsync fun _ => do
-    IO.FS.withIsolatedStreams (isolateStderr := Core.stderrAsMessages.get (← getOptions)) do
-      let tid ← IO.getTID
-      -- reset trace state and message log so as not to report them twice
-      modify fun st => { st with messages := st.messages.markAllReported, traceState := { tid } }
-      try
-        withTraceNode `Elab.async (fun _ => return desc) do
-          act ()
-      catch e =>
-        logError e.toMessageData
-      finally
-        addTraceAsMessages
-      get
-  let ctx ← read
-  return do
-    match (← t.toBaseIO) with
-    | .ok (output, st) =>
-      let mut msgs := st.messages
-      if !output.isEmpty then
-        msgs := msgs.add {
-          fileName := ctx.fileName
-          severity := MessageSeverity.information
-          pos      := ctx.fileMap.toPosition <| ctx.ref.getPos?.getD 0
-          data     := output
-        }
-      return .mk {
-        desc
-        diagnostics := (← Language.Snapshot.Diagnostics.ofMessageLog msgs)
-        traces := st.traceState
-      } st.snapshotTasks
-    -- interrupt or abort exception as `try catch` above should have caught any others
-    | .error _ => default
-
-@[inherit_doc Core.logSnapshotTask]
-def logSnapshotTask (task : Language.SnapshotTask Language.SnapshotTree) : CommandElabM Unit :=
-  modify fun s => { s with snapshotTasks := s.snapshotTasks.push task }
-
-def runLintersAsync (stx : Syntax) : CommandElabM Unit := do
-  if !Elab.async.get (← getOptions) then
-    withoutModifyingEnv do
-      runLinters stx
-    return
-
-  -- We only start one task for all linters for now as most linters are fast and we simply want
-  -- to unblock elaboration of the next command
-  let lintAct ← wrapAsyncAsSnapshot fun _ => runLinters stx
-  logSnapshotTask { range? := none, task := (← BaseIO.asTask lintAct) }
+              modify fun s => { savedState with messages := s.messages }
 
 protected def getCurrMacroScope : CommandElabM Nat  := do pure (← read).currMacroScope
 protected def getMainModule     : CommandElabM Name := do pure (← getEnv).mainModule
@@ -560,18 +525,19 @@ def elabCommandTopLevel (stx : Syntax) : CommandElabM Unit := withRef stx do pro
     -- rather than engineer a general solution.
     unless (stx.find? (·.isOfKind ``Lean.guardMsgsCmd)).isSome do
       withLogging do
-        runLintersAsync stx
+        runLinters stx
   finally
-    -- Make sure `snap?` is definitely resolved; we do not use it for reporting as `#guard_msgs` may
-    -- be the caller of this function and add new messages and info trees
-    if let some snap := (← read).snap? then
-      snap.new.resolve default
-
     -- note the order: first process current messages & info trees, then add back old messages & trees,
     -- then convert new traces to messages
     let mut msgs := (← get).messages
     for tree in (← getInfoTrees) do
       trace[Elab.info] (← tree.format)
+    if (← isTracingEnabledFor `Elab.snapshotTree) then
+      if let some snap := (← read).snap? then
+        -- We can assume that the root command snapshot is not involved in parallelism yet, so this
+        -- should be true iff the command supports incrementality
+        if (← IO.hasFinished snap.new.result) then
+          liftCoreM <| Language.ToSnapshotTree.toSnapshotTree snap.new.result.get |>.trace
     modify fun st => { st with
       messages := initMsgs ++ msgs
       infoState := { st.infoState with trees := initInfoTrees ++ st.infoState.trees }
@@ -702,6 +668,14 @@ def runTermElabM (elabFn : Array Expr → TermElabM α) : CommandElabM α := do
           Term.addAutoBoundImplicits' xs someType fun xs _ =>
             Term.withoutAutoBoundImplicit <| elabFn xs
 
+/--
+Catches and logs exceptions occurring in `x`. Unlike `try catch` in `CommandElabM`, this function
+catches interrupt exceptions as well and thus is intended for use at the top level of elaboration.
+Interrupt and abort exceptions are caught but not logged.
+-/
+@[inline] def withLoggingExceptions (x : CommandElabM Unit) : CommandElabCoreM Empty Unit := fun ctx ref =>
+  EIO.catchExceptions (withLogging x ctx ref) (fun _ => pure ())
+
 private def liftAttrM {α} (x : AttrM α) : CommandElabM α := do
   liftCoreM x