feat: List.replicate lemmas

not a fix, unfortunately, just recording the test.

.github/PULL_REQUEST_TEMPLATE.md

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

.github/workflows/ci.yml

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

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

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

src/Init/Core.lean

@@ -817,14 +817,12 @@ variable {a b c d : Prop}
 theorem iff_iff_implies_and_implies {a b : Prop} : (a ↔ b) ↔ (a → b) ∧ (b → a) :=
   Iff.intro (fun h => And.intro h.mp h.mpr) (fun h => Iff.intro h.left h.right)
 
-theorem Iff.refl (a : Prop) : a ↔ a :=
+@[refl] theorem Iff.refl (a : Prop) : a ↔ a :=
   Iff.intro (fun h => h) (fun h => h)
 
 protected theorem Iff.rfl {a : Prop} : a ↔ a :=
   Iff.refl a
 
-macro_rules | `(tactic| rfl) => `(tactic| exact Iff.rfl)
-
 theorem Iff.of_eq (h : a = b) : a ↔ b := h ▸ Iff.rfl
 
 theorem Iff.trans (h₁ : a ↔ b) (h₂ : b ↔ c) : a ↔ c :=

src/Init/Data/BitVec/Lemmas.lean

@@ -1667,6 +1667,14 @@ protected theorem lt_of_le_ne {x y : BitVec n} : x ≤ y → ¬ x = y → x < y
   simp only [lt_def, le_def, BitVec.toNat_eq]
   apply Nat.lt_of_le_of_ne
 
+protected theorem ne_of_lt {x y : BitVec n} : x < y → x ≠ y := by
+  simp only [lt_def, ne_eq, toNat_eq]
+  apply Nat.ne_of_lt
+
+protected theorem umod_lt (x : BitVec n) {y : BitVec n} : 0 < y → x.umod y < y := by
+  simp only [ofNat_eq_ofNat, lt_def, toNat_ofNat, Nat.zero_mod, umod, toNat_ofNatLt]
+  apply Nat.mod_lt
+
 /-! ### ofBoolList -/
 
 @[simp] theorem getMsbD_ofBoolListBE : (ofBoolListBE bs).getMsbD i = bs.getD i false := by
@@ -2038,4 +2046,20 @@ theorem getLsbD_intMax (w : Nat) : (intMax w).getLsbD i = decide (i + 1 < w) :=
   · simp [h]
   · rw [Nat.sub_add_cancel (Nat.two_pow_pos (w - 1)), Nat.two_pow_pred_mod_two_pow (by omega)]
 
+
+/-! ### Non-overflow theorems -/
+
+/--
+If `y ≤ x`, then the subtraction `(x - y)` does not overflow.
+Thus, `(x - y).toNat = x.toNat - y.toNat`
+-/
+theorem toNat_sub_of_le {x y : BitVec n} (h : y ≤ x) :
+    (x - y).toNat = x.toNat - y.toNat := by
+  simp only [toNat_sub]
+  rw [BitVec.le_def] at h
+  by_cases h' : x.toNat = y.toNat
+  · rw [h', Nat.sub_self, Nat.sub_add_cancel (by omega), Nat.mod_self]
+  · have : 2 ^ n - y.toNat + x.toNat = 2 ^ n + (x.toNat - y.toNat) := by omega
+    rw [this, Nat.add_mod_left, Nat.mod_eq_of_lt (by omega)]
+
 end BitVec

src/Init/Data/Int/DivMod.lean

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

src/Init/Data/Int/DivModLemmas.lean

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

src/Init/Data/List/Count.lean

@@ -119,12 +119,12 @@ theorem countP_filter (l : List α) :
     countP p (filter q l) = countP (fun a => p a && q a) l := by
   simp only [countP_eq_length_filter, filter_filter]
 
-@[simp] theorem countP_true {l : List α} : (l.countP fun _ => true) = l.length := by
-  rw [countP_eq_length]
+@[simp] theorem countP_true : (countP fun (_ : α) => true) = length := by
+  funext l
   simp
 
-@[simp] theorem countP_false {l : List α} : (l.countP fun _ => false) = 0 := by
-  rw [countP_eq_zero]
+@[simp] theorem countP_false : (countP fun (_ : α) => false) = Function.const _ 0 := by
+  funext l
   simp
 
 @[simp] theorem countP_map (p : β → Bool) (f : α → β) :

src/Init/Data/List/Lemmas.lean

@@ -572,17 +572,25 @@ theorem any_eq {l : List α} : l.any p = decide (∃ x, x ∈ l ∧ p x) := by i
 
 theorem all_eq {l : List α} : l.all p = decide (∀ x, x ∈ l → p x) := by induction l <;> simp [*]
 
-@[simp] theorem any_decide {l : List α} {p : α → Prop} [DecidablePred p] :
-    l.any p = decide (∃ x, x ∈ l ∧ p x) := by
+theorem decide_exists_mem {l : List α} {p : α → Prop} [DecidablePred p] :
+    decide (∃ x, x ∈ l ∧ p x) = l.any p := by
   simp [any_eq]
 
-@[simp] theorem all_decide {l : List α} {p : α → Prop} [DecidablePred p] :
-    l.all p = decide (∀ x, x ∈ l → p x) := by
+theorem decide_forall_mem {l : List α} {p : α → Prop} [DecidablePred p] :
+    decide (∀ x, x ∈ l → p x) = l.all p := by
   simp [all_eq]
 
-@[simp] theorem any_eq_true {l : List α} : l.any p = true ↔ ∃ x, x ∈ l ∧ p x := by simp [any_eq]
+@[simp] theorem any_eq_true {l : List α} : l.any p = true ↔ ∃ x, x ∈ l ∧ p x := by
+  simp only [any_eq, decide_eq_true_eq]
 
-@[simp] theorem all_eq_true {l : List α} : l.all p = true ↔ ∀ x, x ∈ l → p x := by simp [all_eq]
+@[simp] theorem all_eq_true {l : List α} : l.all p = true ↔ ∀ x, x ∈ l → p x := by
+  simp only [all_eq, decide_eq_true_eq]
+
+@[simp] theorem any_eq_false {l : List α} : l.any p = false ↔ ∀ x, x ∈ l → ¬p x := by
+  simp [any_eq]
+
+@[simp] theorem all_eq_false {l : List α} : l.all p = false ↔ ∃ x, x ∈ l ∧ ¬p x := by
+  simp [all_eq]
 
 /-! ### set -/
 
@@ -1044,6 +1052,9 @@ theorem tail_eq_tailD (l) : @tail α l = tailD l [] := by cases l <;> rfl
 
 theorem tail_eq_tail? (l) : @tail α l = (tail? l).getD [] := by simp [tail_eq_tailD]
 
+theorem mem_of_mem_tail {a : α} {l : List α} (h : a ∈ tail l) : a ∈ l := by
+  induction l <;> simp_all
+
 /-! ## Basic operations -/
 
 /-! ### map -/
@@ -2312,6 +2323,47 @@ theorem bind_replicate {β} (f : α → List β) : (replicate n a).bind f = (rep
 @[simp] theorem isEmpty_replicate : (replicate n a).isEmpty = decide (n = 0) := by
   cases n <;> simp [replicate_succ]
 
+/-- Every list is either empty, a non-empty `replicate`, or begins with a non-empty `replicate`
+followed by a different element. -/
+theorem eq_replicate_or_eq_replicate_append_cons {α : Type _} (l : List α) :
+    (l = []) ∨ (∃ n a, l = replicate n a ∧ 0 < n) ∨
+      (∃ n a b l', l = replicate n a ++ b :: l' ∧ 0 < n ∧ a ≠ b) := by
+  induction l with
+  | nil => simp
+  | cons x l ih =>
+    right
+    rcases ih with rfl | ⟨n, a, rfl, h⟩ | ⟨n, a, b, l', rfl, h⟩
+    · left
+      exact ⟨1, x, rfl, by decide⟩
+    · by_cases h' : x = a
+      · subst h'
+        left
+        exact ⟨n + 1, x, rfl, by simp⟩
+      · right
+        refine ⟨1, x, a, replicate (n - 1) a, ?_, by decide, h'⟩
+        match n with | n + 1 => simp [replicate_succ]
+    · right
+      by_cases h' : x = a
+      · subst h'
+        refine ⟨n + 1, x, b, l', by simp [replicate_succ], by simp, h.2⟩
+      · refine ⟨1, x, a, replicate (n - 1) a ++ b :: l', ?_, by decide, h'⟩
+        match n with | n + 1 => simp [replicate_succ]
+
+/-- An induction principle for lists based on contiguous runs of identical elements. -/
+-- A `Sort _` valued version would require a different design. (And associated `@[simp]` lemmas.)
+theorem replicateRecOn {α : Type _} {p : List α → Prop} (m : List α)
+    (h0 : p []) (hr : ∀ a n, 0 < n → p (replicate n a))
+    (hi : ∀ a b n l, a ≠ b → 0 < n → p (b :: l) → p (replicate n a ++ b :: l)) : p m := by
+  rcases eq_replicate_or_eq_replicate_append_cons m with
+    rfl | ⟨n, a, rfl, hn⟩ | ⟨n, a, b, l', w, hn, h⟩
+  · exact h0
+  · exact hr _ _ hn
+  · have : (b :: l').length < m.length := by
+      simpa [w] using Nat.lt_add_of_pos_left hn
+    subst w
+    exact hi _ _ _ _ h hn (replicateRecOn (b :: l') h0 hr hi)
+termination_by m.length
+
 /-! ### reverse -/
 
 @[simp] theorem length_reverse (as : List α) : (as.reverse).length = as.length := by

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

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

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

@@ -38,7 +38,7 @@ namespace List.MergeSort.Internal
 /--
 `O(min |l| |r|)`. Merge two lists using `le` as a switch.
 -/
-def mergeTR (le : α → α → Bool) (l₁ l₂ : List α) : List α :=
+def mergeTR (l₁ l₂ : List α) (le : α → α → Bool) : List α :=
   go l₁ l₂ []
 where go : List α → List α → List α → List α
   | [], l₂, acc => reverseAux acc l₂
@@ -49,7 +49,7 @@ where go : List α → List α → List α → List α
     else
       go (x :: xs) ys (y :: acc)
 
-theorem mergeTR_go_eq : mergeTR.go le l₁ l₂ acc = acc.reverse ++ merge le l₁ l₂ := by
+theorem mergeTR_go_eq : mergeTR.go le l₁ l₂ acc = acc.reverse ++ merge l₁ l₂ le := by
   induction l₁ generalizing l₂ acc with
   | nil => simp [mergeTR.go, merge, reverseAux_eq]
   | cons x l₁ ih₁ =>
@@ -97,14 +97,14 @@ This version uses the tail-recurive `mergeTR` function as a subroutine.
 This is not the final version we use at runtime, as `mergeSortTR₂` is faster.
 This definition is useful as an intermediate step in proving the `@[csimp]` lemma for `mergeSortTR₂`.
 -/
-def mergeSortTR (le : α → α → Bool) (l : List α) : List α :=
+def mergeSortTR (l : List α) (le : α → α → Bool := by exact fun a b => a ≤ b) : List α :=
   run ⟨l, rfl⟩
 where run : {n : Nat} → { l : List α // l.length = n } → List α
   | 0, ⟨[], _⟩ => []
   | 1, ⟨[a], _⟩ => [a]
   | n+2, xs =>
     let (l, r) := splitInTwo xs
-    mergeTR le (run l) (run r)
+    mergeTR (run l) (run r) le
 
 /--
 Split a list in two equal parts, reversing the first part.
@@ -130,7 +130,7 @@ Faster version of `mergeSortTR`, which avoids unnecessary list reversals.
 -- Per the benchmark in `tests/bench/mergeSort/`
 -- (which averages over 4 use cases: already sorted lists, reverse sorted lists, almost sorted lists, and random lists),
 -- for lists of length 10^6, `mergeSortTR₂` is about 20% faster than `mergeSortTR`.
-def mergeSortTR₂ (le : α → α → Bool) (l : List α) : List α :=
+def mergeSortTR₂ (l : List α) (le : α → α → Bool := by exact fun a b => a ≤ b) : List α :=
   run ⟨l, rfl⟩
 where
   run : {n : Nat} → { l : List α // l.length = n } → List α
@@ -138,13 +138,13 @@ where
   | 1, ⟨[a], _⟩ => [a]
   | n+2, xs =>
     let (l, r) := splitRevInTwo xs
-    mergeTR le (run' l) (run r)
+    mergeTR (run' l) (run r) le
   run' : {n : Nat} → { l : List α // l.length = n } → List α
   | 0, ⟨[], _⟩ => []
   | 1, ⟨[a], _⟩ => [a]
   | n+2, xs =>
     let (l, r) := splitRevInTwo' xs
-    mergeTR le (run' r) (run l)
+    mergeTR (run' r) (run l) le
 
 theorem splitRevInTwo'_fst (l : { l : List α // l.length = n }) :
     (splitRevInTwo' l).1 = ⟨(splitInTwo ⟨l.1.reverse, by simpa using l.2⟩).2.1, by have := l.2; simp; omega⟩ := by
@@ -166,7 +166,7 @@ theorem splitRevInTwo_snd (l : { l : List α // l.length = n }) :
     (splitRevInTwo l).2 = ⟨(splitInTwo l).2.1, by have := l.2; simp; omega⟩ := by
   simp only [splitRevInTwo, splitRevAt_eq, reverse_take, splitInTwo_snd]
 
-theorem mergeSortTR_run_eq_mergeSort : {n : Nat} → (l : { l : List α // l.length = n }) → mergeSortTR.run le l = mergeSort le l.1
+theorem mergeSortTR_run_eq_mergeSort : {n : Nat} → (l : { l : List α // l.length = n }) → mergeSortTR.run le l = mergeSort l.1 le
   | 0, ⟨[], _⟩
   | 1, ⟨[a], _⟩ => by simp [mergeSortTR.run, mergeSort]
   | n+2, ⟨a :: b :: l, h⟩ => by
@@ -183,7 +183,7 @@ theorem mergeSort_eq_mergeSortTR : @mergeSort = @mergeSortTR := by
 -- This mutual block is unfortunately quite slow to elaborate.
 set_option maxHeartbeats 400000 in
 mutual
-theorem mergeSortTR₂_run_eq_mergeSort : {n : Nat} → (l : { l : List α // l.length = n }) → mergeSortTR₂.run le l = mergeSort le l.1
+theorem mergeSortTR₂_run_eq_mergeSort : {n : Nat} → (l : { l : List α // l.length = n }) → mergeSortTR₂.run le l = mergeSort l.1 le
   | 0, ⟨[], _⟩
   | 1, ⟨[a], _⟩ => by simp [mergeSortTR₂.run, mergeSort]
   | n+2, ⟨a :: b :: l, h⟩ => by
@@ -195,7 +195,7 @@ theorem mergeSortTR₂_run_eq_mergeSort : {n : Nat} → (l : { l : List α // l.
     rw [reverse_reverse]
 termination_by n => n
 
-theorem mergeSortTR₂_run'_eq_mergeSort : {n : Nat} → (l : { l : List α // l.length = n }) → (w : l' = l.1.reverse) → mergeSortTR₂.run' le l = mergeSort le l'
+theorem mergeSortTR₂_run'_eq_mergeSort : {n : Nat} → (l : { l : List α // l.length = n }) → (w : l' = l.1.reverse) → mergeSortTR₂.run' le l = mergeSort l' le
   | 0, ⟨[], _⟩, w
   | 1, ⟨[a], _⟩, w => by simp_all [mergeSortTR₂.run', mergeSort]
   | n+2, ⟨a :: b :: l, h⟩, w => by

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

@@ -23,11 +23,6 @@ import Init.Data.Bool
 
 namespace List
 
--- We enable this instance locally so we can write `Pairwise le` instead of `Pairwise (le · ·)` everywhere.
-attribute [local instance] boolRelToRel
-
-variable {le : α → α → Bool}
-
 /-! ### splitInTwo -/
 
 @[simp] theorem splitInTwo_fst (l : { l : List α // l.length = n }) :
@@ -89,6 +84,8 @@ theorem splitInTwo_fst_le_splitInTwo_snd {l : { l : List α // l.length = n }} (
 
 /-! ### enumLE -/
 
+variable {le : α → α → Bool}
+
 theorem enumLE_trans (trans : ∀ a b c, le a b → le b c → le a c)
     (a b c : Nat × α) : enumLE le a b → enumLE le b c → enumLE le a c := by
   simp only [enumLE]
@@ -129,7 +126,7 @@ theorem enumLE_total (total : ∀ a b, !le a b → le b a)
 /-! ### merge -/
 
 theorem merge_stable : ∀ (xs ys) (_ : ∀ x y, x ∈ xs → y ∈ ys → x.1 ≤ y.1),
-    (merge (enumLE le) xs ys).map (·.2) = merge le (xs.map (·.2)) (ys.map (·.2))
+    (merge xs ys (enumLE le)).map (·.2) = merge (xs.map (·.2)) (ys.map (·.2)) le
   | [], ys, _ => by simp [merge]
   | xs, [], _ => by simp [merge]
   | (i, x) :: xs, (j, y) :: ys, h => by
@@ -147,7 +144,7 @@ theorem merge_stable : ∀ (xs ys) (_ : ∀ x y, x ∈ xs → y ∈ ys → x.1
 The elements of `merge le xs ys` are exactly the elements of `xs` and `ys`.
 -/
 -- We subsequently prove that `mergeSort_perm : merge le xs ys ~ xs ++ ys`.
-theorem mem_merge {a : α} {xs ys : List α} : a ∈ merge le xs ys ↔ a ∈ xs ∨ a ∈ ys := by
+theorem mem_merge {a : α} {xs ys : List α} : a ∈ merge xs ys le ↔ a ∈ xs ∨ a ∈ ys := by
   induction xs generalizing ys with
   | nil => simp [merge]
   | cons x xs ih =>
@@ -161,6 +158,9 @@ theorem mem_merge {a : α} {xs ys : List α} : a ∈ merge le xs ys ↔ a ∈ xs
         apply or_congr_left
         simp only [or_comm (a := a = y), or_assoc]
 
+-- We enable this instance locally so we can write `Pairwise le` instead of `Pairwise (le · ·)` everywhere.
+attribute [local instance] boolRelToRel
+
 /--
 If the ordering relation `le` is transitive and total (i.e. `le a b ∨ le b a` for all `a, b`)
 then the `merge` of two sorted lists is sorted.
@@ -168,7 +168,7 @@ then the `merge` of two sorted lists is sorted.
 theorem sorted_merge
     (trans : ∀ (a b c : α), le a b → le b c → le a c)
     (total : ∀ (a b : α), !le a b → le b a)
-    (l₁ l₂ : List α) (h₁ : l₁.Pairwise le) (h₂ : l₂.Pairwise le) : (merge le l₁ l₂).Pairwise le := by
+    (l₁ l₂ : List α) (h₁ : l₁.Pairwise le) (h₂ : l₂.Pairwise le) : (merge l₁ l₂ le).Pairwise le := by
   induction l₁ generalizing l₂ with
   | nil => simpa only [merge]
   | cons x l₁ ih₁ =>
@@ -195,7 +195,7 @@ theorem sorted_merge
         · exact ih₂ h₂.tail
 
 theorem merge_of_le : ∀ {xs ys : List α} (_ : ∀ a b, a ∈ xs → b ∈ ys → le a b),
-    merge le xs ys = xs ++ ys
+    merge xs ys le = xs ++ ys
   | [], ys, _
   | xs, [], _ => by simp [merge]
   | x :: xs, y :: ys, h => by
@@ -206,7 +206,7 @@ theorem merge_of_le : ∀ {xs ys : List α} (_ : ∀ a b, a ∈ xs → b ∈ ys
     · exact h x y (mem_cons_self _ _) (mem_cons_self _ _)
 
 variable (le) in
-theorem merge_perm_append : ∀ {xs ys : List α}, merge le xs ys ~ xs ++ ys
+theorem merge_perm_append : ∀ {xs ys : List α}, merge xs ys le ~ xs ++ ys
   | [], ys => by simp [merge]
   | xs, [] => by simp [merge]
   | x :: xs, y :: ys => by
@@ -222,24 +222,23 @@ theorem merge_perm_append : ∀ {xs ys : List α}, merge le xs ys ~ xs ++ ys
 
 @[simp] theorem mergeSort_singleton (a : α) : [a].mergeSort r = [a] := by rw [List.mergeSort]
 
-variable (le) in
-theorem mergeSort_perm : ∀ (l : List α), mergeSort le l ~ l
-  | [] => by simp [mergeSort]
-  | [a] => by simp [mergeSort]
-  | a :: b :: xs => by
+theorem mergeSort_perm : ∀ (l : List α) (le), mergeSort l le ~ l
+  | [], _ => by simp [mergeSort]
+  | [a], _ => by simp [mergeSort]
+  | a :: b :: xs, le => by
     simp only [mergeSort]
     have : (splitInTwo ⟨a :: b :: xs, rfl⟩).1.1.length < xs.length + 1 + 1 := by simp [splitInTwo_fst]; omega
     have : (splitInTwo ⟨a :: b :: xs, rfl⟩).2.1.length < xs.length + 1 + 1 := by simp [splitInTwo_snd]; omega
     exact (merge_perm_append le).trans
-      (((mergeSort_perm _).append (mergeSort_perm _)).trans
+      (((mergeSort_perm _ _).append (mergeSort_perm _ _)).trans
         (Perm.of_eq (splitInTwo_fst_append_splitInTwo_snd _)))
 termination_by l => l.length
 
-@[simp] theorem mergeSort_length (l : List α) : (mergeSort le l).length = l.length :=
-  (mergeSort_perm le l).length_eq
+@[simp] theorem mergeSort_length (l : List α) : (mergeSort l le).length = l.length :=
+  (mergeSort_perm l le).length_eq
 
-@[simp] theorem mem_mergeSort {a : α} {l : List α} : a ∈ mergeSort le l ↔ a ∈ l :=
-  (mergeSort_perm le l).mem_iff
+@[simp] theorem mem_mergeSort {a : α} {l : List α} : a ∈ mergeSort l le ↔ a ∈ l :=
+  (mergeSort_perm l le).mem_iff
 
 /--
 The result of `mergeSort` is sorted,
@@ -251,7 +250,7 @@ The comparison function need not be irreflexive, i.e. `le a b` and `le b a` is a
 theorem sorted_mergeSort
     (trans : ∀ (a b c : α), le a b → le b c → le a c)
     (total : ∀ (a b : α), !le a b → le b a) :
-    (l : List α) → (mergeSort le l).Pairwise le
+    (l : List α) → (mergeSort l le).Pairwise le
   | [] => by simp [mergeSort]
   | [a] => by simp [mergeSort]
   | a :: b :: xs => by
@@ -268,7 +267,7 @@ termination_by l => l.length
 /--
 If the input list is already sorted, then `mergeSort` does not change the list.
 -/
-theorem mergeSort_of_sorted : ∀ {l : List α} (_ : Pairwise le l), mergeSort le l = l
+theorem mergeSort_of_sorted : ∀ {l : List α} (_ : Pairwise le l), mergeSort l le = l
   | [], _ => by simp [mergeSort]
   | [a], _ => by simp [mergeSort]
   | a :: b :: xs, h => by
@@ -294,10 +293,10 @@ See also:
 * `pair_sublist_mergeSort`: if `[a, b] <+ l` and `le a b`, then `[a, b] <+ mergeSort le l`)
 -/
 theorem mergeSort_enum {l : List α} :
-    (mergeSort (enumLE le) (l.enum)).map (·.2) = mergeSort le l :=
+    (mergeSort (l.enum) (enumLE le)).map (·.2) = mergeSort l le :=
   go 0 l
 where go : ∀ (i : Nat) (l : List α),
-    (mergeSort (enumLE le) (l.enumFrom i)).map (·.2) = mergeSort le l
+    (mergeSort (l.enumFrom i) (enumLE le)).map (·.2) = mergeSort l le
   | _, []
   | _, [a] => by simp [mergeSort]
   | _, a :: b :: xs => by
@@ -320,24 +319,24 @@ theorem mergeSort_cons {le : α → α → Bool}
     (trans : ∀ (a b c : α), le a b → le b c → le a c)
     (total : ∀ (a b : α), !le a b → le b a)
     (a : α) (l : List α) :
-    ∃ l₁ l₂, mergeSort le (a :: l) = l₁ ++ a :: l₂ ∧ mergeSort le l = l₁ ++ l₂ ∧
+    ∃ l₁ l₂, mergeSort (a :: l) le = l₁ ++ a :: l₂ ∧ mergeSort l le = l₁ ++ l₂ ∧
       ∀ b, b ∈ l₁ → !le a b := by
   rw [← mergeSort_enum]
   rw [enum_cons]
   have nd : Nodup ((a :: l).enum.map (·.1)) := by rw [enum_map_fst]; exact nodup_range _
-  have m₁ : (0, a) ∈ mergeSort (enumLE le) ((a :: l).enum) :=
+  have m₁ : (0, a) ∈ mergeSort ((a :: l).enum) (enumLE le) :=
     mem_mergeSort.mpr (mem_cons_self _ _)
   obtain ⟨l₁, l₂, h⟩ := append_of_mem m₁
   have s := sorted_mergeSort (enumLE_trans trans) (enumLE_total total) ((a :: l).enum)
   rw [h] at s
-  have p := mergeSort_perm (enumLE le) ((a :: l).enum)
+  have p := mergeSort_perm ((a :: l).enum) (enumLE le)
   rw [h] at p
   refine ⟨l₁.map (·.2), l₂.map (·.2), ?_, ?_, ?_⟩
   · simpa using congrArg (·.map (·.2)) h
   · rw [← mergeSort_enum.go 1, ← map_append]
     congr 1
-    have q : mergeSort (enumLE le) (enumFrom 1 l) ~ l₁ ++ l₂ :=
-      (mergeSort_perm (enumLE le) (enumFrom 1 l)).trans
+    have q : mergeSort (enumFrom 1 l) (enumLE le) ~ l₁ ++ l₂ :=
+      (mergeSort_perm (enumFrom 1 l) (enumLE le)).trans
         (p.symm.trans perm_middle).cons_inv
     apply Perm.eq_of_sorted (le := enumLE le)
     · rintro ⟨i, a⟩ ⟨j, b⟩  ha hb
@@ -379,7 +378,7 @@ theorem sublist_mergeSort
     (trans : ∀ (a b c : α), le a b → le b c → le a c)
     (total : ∀ (a b : α), !le a b → le b a) :
     ∀ {c : List α} (_ : c.Pairwise le) (_ : c <+ l),
-    c <+ mergeSort le l
+    c <+ mergeSort l le
   | _, _, .slnil => nil_sublist _
   | c, hc, @Sublist.cons _ _ l a h => by
     obtain ⟨l₁, l₂, h₁, h₂, -⟩ := mergeSort_cons trans total a l
@@ -409,7 +408,7 @@ then `[a, b]` is still a sublist of `mergeSort le l`.
 theorem pair_sublist_mergeSort
     (trans : ∀ (a b c : α), le a b → le b c → le a c)
     (total : ∀ (a b : α), !le a b → le b a)
-    (hab : le a b) (h : [a, b] <+ l) : [a, b] <+ mergeSort le l :=
+    (hab : le a b) (h : [a, b] <+ l) : [a, b] <+ mergeSort l le :=
   sublist_mergeSort trans total (pairwise_pair.mpr hab) h
 
 @[deprecated (since := "2024-09-02")] abbrev mergeSort_stable_pair := @pair_sublist_mergeSort

src/Init/Data/Nat/Basic.lean

@@ -514,6 +514,10 @@ protected theorem add_lt_add_left {n m : Nat} (h : n < m) (k : Nat) : k + n < k
 protected theorem add_lt_add_right {n m : Nat} (h : n < m) (k : Nat) : n + k < m + k :=
   Nat.add_comm k m ▸ Nat.add_comm k n ▸ Nat.add_lt_add_left h k
 
+protected theorem lt_add_of_pos_left (h : 0 < k) : n < k + n := by
+  rw [Nat.add_comm]
+  exact Nat.add_lt_add_left h n
+
 protected theorem lt_add_of_pos_right (h : 0 < k) : n < n + k :=
   Nat.add_lt_add_left h n
 

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

@@ -476,16 +476,20 @@ theorem and_lt_two_pow (x : Nat) {y n : Nat} (right : y < 2^n) : (x &&& y) < 2^n
           exact pow_le_pow_of_le_right Nat.zero_lt_two i_ge_n
   simp [testBit_and, yf]
 
-@[simp] theorem and_pow_two_is_mod (x n : Nat) : x &&& (2^n-1) = x % 2^n := by
+@[simp] theorem and_pow_two_sub_one_eq_mod (x n : Nat) : x &&& 2^n - 1 = x % 2^n := by
   apply eq_of_testBit_eq
   intro i
   simp only [testBit_and, testBit_mod_two_pow]
   cases testBit x i <;> simp
 
-theorem and_pow_two_identity {x : Nat} (lt : x < 2^n) : x &&& 2^n-1 = x := by
-  rw [and_pow_two_is_mod]
+@[deprecated and_pow_two_sub_one_eq_mod (since := "2024-09-11")] abbrev and_pow_two_is_mod := @and_pow_two_sub_one_eq_mod
+
+theorem and_pow_two_sub_one_of_lt_two_pow {x : Nat} (lt : x < 2^n) : x &&& 2^n - 1 = x := by
+  rw [and_pow_two_sub_one_eq_mod]
   apply Nat.mod_eq_of_lt lt
 
+@[deprecated and_pow_two_sub_one_of_lt_two_pow (since := "2024-09-11")] abbrev and_two_pow_identity := @and_pow_two_sub_one_of_lt_two_pow
+
 @[simp] theorem and_mod_two_eq_one : (a &&& b) % 2 = 1 ↔ a % 2 = 1 ∧ b % 2 = 1 := by
   simp only [mod_two_eq_one_iff_testBit_zero]
   rw [testBit_and]

src/Init/Data/Nat/Lemmas.lean

@@ -84,9 +84,6 @@ protected theorem add_lt_add_of_lt_of_le {a b c d : Nat} (hlt : a < b) (hle : c
     a + c < b + d :=
   Nat.lt_of_le_of_lt (Nat.add_le_add_left hle _) (Nat.add_lt_add_right hlt _)
 
-protected theorem lt_add_of_pos_left : 0 < k → n < k + n := by
-  rw [Nat.add_comm]; exact Nat.lt_add_of_pos_right
-
 protected theorem pos_of_lt_add_right (h : n < n + k) : 0 < k :=
   Nat.lt_of_add_lt_add_left h
 
@@ -577,6 +574,15 @@ theorem mul_mod (a b n : Nat) : a * b % n = (a % n) * (b % n) % n := by
 theorem add_mod (a b n : Nat) : (a + b) % n = ((a % n) + (b % n)) % n := by
   rw [add_mod_mod, mod_add_mod]
 
+@[simp] theorem self_sub_mod (n k : Nat) [NeZero k] : (n - k) % n = n - k := by
+  cases n with
+  | zero => simp
+  | succ n =>
+    rw [mod_eq_of_lt]
+    cases k with
+    | zero => simp_all
+    | succ k => omega
+
 /-! ### pow -/
 
 theorem pow_succ' {m n : Nat} : m ^ n.succ = m * m ^ n := by

src/Init/Data/Option/Lemmas.lean

@@ -13,7 +13,7 @@ namespace Option
 
 theorem mem_iff {a : α} {b : Option α} : a ∈ b ↔ b = some a := .rfl
 
-@[simp] theorem mem_some {a b : α} : a ∈ some b ↔ a = b := by simp [mem_iff, eq_comm]
+@[simp] theorem mem_some {a b : α} : a ∈ some b ↔ b = a := by simp [mem_iff]
 
 theorem mem_some_self (a : α) : a ∈ some a := mem_some.2 rfl
 
@@ -432,6 +432,38 @@ section ite
     (x ∈ if p then l else none) ↔ p ∧ x ∈ l := by
   split <;> simp_all
 
+@[simp] theorem dite_none_left_eq_some {p : Prop} [Decidable p] {b : ¬p → Option β} :
+    (if h : p then none else b h) = some a ↔ ∃ h, b h = some a := by
+  split <;> simp_all
+
+@[simp] theorem dite_none_right_eq_some {p : Prop} [Decidable p] {b : p → Option α} :
+    (if h : p then b h else none) = some a ↔ ∃ h, b h = some a := by
+  split <;> simp_all
+
+@[simp] theorem some_eq_dite_none_left {p : Prop} [Decidable p] {b : ¬p → Option β} :
+    some a = (if h : p then none else b h) ↔ ∃ h, some a = b h := by
+  split <;> simp_all
+
+@[simp] theorem some_eq_dite_none_right {p : Prop} [Decidable p] {b : p → Option α} :
+    some a = (if h : p then b h else none) ↔ ∃ h, some a = b h := by
+  split <;> simp_all
+
+@[simp] theorem ite_none_left_eq_some {p : Prop} [Decidable p] {b : Option β} :
+    (if p then none else b) = some a ↔ ¬ p ∧ b = some a := by
+  split <;> simp_all
+
+@[simp] theorem ite_none_right_eq_some {p : Prop} [Decidable p] {b : Option α} :
+    (if p then b else none) = some a ↔ p ∧ b = some a := by
+  split <;> simp_all
+
+@[simp] theorem some_eq_ite_none_left {p : Prop} [Decidable p] {b : Option β} :
+    some a = (if p then none else b) ↔ ¬ p ∧ some a = b := by
+  split <;> simp_all
+
+@[simp] theorem some_eq_ite_none_right {p : Prop} [Decidable p] {b : Option α} :
+    some a = (if p then b else none) ↔ p ∧ some a = b := by
+  split <;> simp_all
+
 @[simp] theorem isSome_dite {p : Prop} [Decidable p] {b : p → β} :
     (if h : p then some (b h) else none).isSome = true ↔ p := by
   split <;> simpa

src/Lean/Data/Rat.lean

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

src/Lean/Elab/InheritDoc.lean

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

src/Lean/Elab/Match.lean

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

src/Lean/Environment.lean

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

src/Lean/Language/Lean.lean

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

src/Lean/Meta/Tactic/FunInd.lean

@@ -438,9 +438,11 @@ def buildInductionCase (oldIH newIH : FVarId) (isRecCall : Expr → Option Expr)
   let mvar ← mkFreshExprSyntheticOpaqueMVar goal (tag := `hyp)
   let mut mvarId := mvar.mvarId!
   mvarId ← assertIHs IHs mvarId
+  trace[Meta.FunInd] "Goal before cleanup:{mvarId}"
   for fvarId in toClear do
     mvarId ← mvarId.clear fvarId
   mvarId ← mvarId.cleanup (toPreserve := toPreserve)
+  trace[Meta.FunInd] "Goal after cleanup (toClear := {toClear.map mkFVar}) (toPreserve := {toPreserve.map mkFVar}):{mvarId}"
   modify (·.push mvarId)
   let mvar ← instantiateMVars mvar
   pure mvar

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

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

src/Lean/Parser/Basic.lean

@@ -145,7 +145,7 @@ def errorAtSavedPosFn (msg : String) (delta : Bool) : ParserFn := fun c s =>
 /-- Generate an error at the position saved with the `withPosition` combinator.
    If `delta == true`, then it reports at saved position+1.
    This useful to make sure a parser consumed at least one character.  -/
-def errorAtSavedPos (msg : String) (delta : Bool) : Parser := {
+@[builtin_doc] def errorAtSavedPos (msg : String) (delta : Bool) : Parser := {
   fn := errorAtSavedPosFn msg delta
 }
 
@@ -271,7 +271,7 @@ def orelseFn (p q : ParserFn) : ParserFn :=
   NOTE: In order for the pretty printer to retrace an `orelse`, `p` must be a call to `node` or some other parser
   producing a single node kind. Nested `orelse` calls are flattened for this, i.e. `(node k1 p1 <|> node k2 p2) <|> ...`
   is fine as well. -/
-def orelse (p q : Parser) : Parser where
+@[builtin_doc] def orelse (p q : Parser) : Parser where
   info := orelseInfo p.info q.info
   fn   := orelseFn p.fn q.fn
 
@@ -295,7 +295,7 @@ This is important for the `p <|> q` combinator, because it is not backtracking,
 `p` fails after consuming some tokens. To get backtracking behavior, use `atomic(p) <|> q` instead.
 
 This parser has the same arity as `p` - it produces the same result as `p`. -/
-def atomic : Parser → Parser := withFn atomicFn
+@[builtin_doc] def atomic : Parser → Parser := withFn atomicFn
 
 /-- Information about the state of the parse prior to the failing parser's execution -/
 structure RecoveryContext where
@@ -335,7 +335,7 @@ state immediately after the failure.
 
 The interactions between <|> and `recover'` are subtle, especially for syntactic
 categories that admit user extension. Consider avoiding it in these cases. -/
-def recover' (parser : Parser) (handler : RecoveryContext → Parser) : Parser where
+@[builtin_doc] def recover' (parser : Parser) (handler : RecoveryContext → Parser) : Parser where
   info := parser.info
   fn := recoverFn parser.fn fun s => handler s |>.fn
 
@@ -347,7 +347,7 @@ If `handler` fails itself, then no recovery is performed.
 
 The interactions between <|> and `recover` are subtle, especially for syntactic
 categories that admit user extension. Consider avoiding it in these cases. -/
-def recover (parser handler : Parser) : Parser := recover' parser fun _ => handler
+@[builtin_doc] def recover (parser handler : Parser) : Parser := recover' parser fun _ => handler
 
 def optionalFn (p : ParserFn) : ParserFn := fun c s =>
   let iniSz  := s.stackSize
@@ -378,7 +378,7 @@ position to the original state on success. So for example `lookahead("=>")` will
 next token is `"=>"`, without actually consuming this token.
 
 This parser has arity 0 - it does not capture anything. -/
-def lookahead : Parser → Parser := withFn lookaheadFn
+@[builtin_doc] def lookahead : Parser → Parser := withFn lookaheadFn
 
 def notFollowedByFn (p : ParserFn) (msg : String) : ParserFn := fun c s =>
   let iniSz  := s.stackSize
@@ -394,7 +394,7 @@ def notFollowedByFn (p : ParserFn) (msg : String) : ParserFn := fun c s =>
 if `p` succeeds then it fails with the message `"unexpected foo"`.
 
 This parser has arity 0 - it does not capture anything. -/
-def notFollowedBy (p : Parser) (msg : String) : Parser where
+@[builtin_doc] def notFollowedBy (p : Parser) (msg : String) : Parser where
   fn := notFollowedByFn p.fn msg
 
 partial def manyAux (p : ParserFn) : ParserFn := fun c s => Id.run do
@@ -1143,7 +1143,7 @@ def checkWsBeforeFn (errorMsg : String) : ParserFn := fun _ s =>
 For example, the parser `"foo" ws "+"` parses `foo +` or `foo/- -/+` but not `foo+`.
 
 This parser has arity 0 - it does not capture anything. -/
-def checkWsBefore (errorMsg : String := "space before") : Parser where
+@[builtin_doc] def checkWsBefore (errorMsg : String := "space before") : Parser where
   info := epsilonInfo
   fn   := checkWsBeforeFn errorMsg
 
@@ -1160,7 +1160,7 @@ def checkLinebreakBeforeFn (errorMsg : String) : ParserFn := fun _ s =>
 (The line break may be inside a comment.)
 
 This parser has arity 0 - it does not capture anything. -/
-def checkLinebreakBefore (errorMsg : String := "line break") : Parser where
+@[builtin_doc] def checkLinebreakBefore (errorMsg : String := "line break") : Parser where
   info := epsilonInfo
   fn   := checkLinebreakBeforeFn errorMsg
 
@@ -1180,7 +1180,7 @@ This is almost the same as `"foo+"`, but using this parser will make `foo+` a to
 problems for the use of `"foo"` and `"+"` as separate tokens in other parsers.
 
 This parser has arity 0 - it does not capture anything. -/
-def checkNoWsBefore (errorMsg : String := "no space before") : Parser := {
+@[builtin_doc] def checkNoWsBefore (errorMsg : String := "no space before") : Parser := {
   info := epsilonInfo
   fn   := checkNoWsBeforeFn errorMsg
 }
@@ -1430,7 +1430,7 @@ position (see `withPosition`). This can be used to do whitespace sensitive synta
 a `by` block or `do` block, where all the lines have to line up.
 
 This parser has arity 0 - it does not capture anything. -/
-def checkColEq (errorMsg : String := "checkColEq") : Parser where
+@[builtin_doc] def checkColEq (errorMsg : String := "checkColEq") : Parser where
   fn := checkColEqFn errorMsg
 
 def checkColGeFn (errorMsg : String) : ParserFn := fun c s =>
@@ -1449,7 +1449,7 @@ certain indentation scope. For example it is used in the lean grammar for `else
 that the `else` is not less indented than the `if` it matches with.
 
 This parser has arity 0 - it does not capture anything. -/
-def checkColGe (errorMsg : String := "checkColGe") : Parser where
+@[builtin_doc] def checkColGe (errorMsg : String := "checkColGe") : Parser where
   fn := checkColGeFn errorMsg
 
 def checkColGtFn (errorMsg : String) : ParserFn := fun c s =>
@@ -1473,7 +1473,7 @@ Here, the `revert` tactic is followed by a list of `colGt ident`, because otherw
 interpret `exact` as an identifier and try to revert a variable named `exact`.
 
 This parser has arity 0 - it does not capture anything. -/
-def checkColGt (errorMsg : String := "checkColGt") : Parser where
+@[builtin_doc] def checkColGt (errorMsg : String := "checkColGt") : Parser where
   fn := checkColGtFn errorMsg
 
 def checkLineEqFn (errorMsg : String) : ParserFn := fun c s =>
@@ -1491,7 +1491,7 @@ different lines. For example, `else if` is parsed using `lineEq` to ensure that
 are on the same line.
 
 This parser has arity 0 - it does not capture anything. -/
-def checkLineEq (errorMsg : String := "checkLineEq") : Parser where
+@[builtin_doc] def checkLineEq (errorMsg : String := "checkLineEq") : Parser where
   fn := checkLineEqFn errorMsg
 
 /-- `withPosition(p)` runs `p` while setting the "saved position" to the current position.
@@ -1507,7 +1507,7 @@ The saved position is only available in the read-only state, which is why this i
 after the `withPosition(..)` block the saved position will be restored to its original value.
 
 This parser has the same arity as `p` - it just forwards the results of `p`. -/
-def withPosition : Parser → Parser := withFn fun f c s =>
+@[builtin_doc] def withPosition : Parser → Parser := withFn fun f c s =>
     adaptCacheableContextFn ({ · with savedPos? := s.pos }) f c s
 
 def withPositionAfterLinebreak : Parser → Parser := withFn fun f c s =>
@@ -1519,7 +1519,7 @@ parsers like `colGt` will have no effect. This is usually used by bracketing con
 `(...)` so that the user can locally override whitespace sensitivity.
 
 This parser has the same arity as `p` - it just forwards the results of `p`. -/
-def withoutPosition (p : Parser) : Parser :=
+@[builtin_doc] def withoutPosition (p : Parser) : Parser :=
   adaptCacheableContext ({ · with savedPos? := none }) p
 
 /-- `withForbidden tk p` runs `p` with `tk` as a "forbidden token". This means that if the token
@@ -1529,7 +1529,7 @@ stop there, making `tk` effectively a lowest-precedence operator. This is used f
 would be treated as an application.
 
 This parser has the same arity as `p` - it just forwards the results of `p`. -/
-def withForbidden (tk : Token) (p : Parser) : Parser :=
+@[builtin_doc] def withForbidden (tk : Token) (p : Parser) : Parser :=
   adaptCacheableContext ({ · with forbiddenTk? := tk }) p
 
 /-- `withoutForbidden(p)` runs `p` disabling the "forbidden token" (see `withForbidden`), if any.
@@ -1537,7 +1537,7 @@ This is usually used by bracketing constructs like `(...)` because there is no p
 inside these nested constructs.
 
 This parser has the same arity as `p` - it just forwards the results of `p`. -/
-def withoutForbidden (p : Parser) : Parser :=
+@[builtin_doc] def withoutForbidden (p : Parser) : Parser :=
   adaptCacheableContext ({ · with forbiddenTk? := none }) p
 
 def eoiFn : ParserFn := fun c s =>
@@ -1692,7 +1692,7 @@ def termParser (prec : Nat := 0) : Parser :=
 -- ==================
 
 /-- Fail if previous token is immediately followed by ':'. -/
-def checkNoImmediateColon : Parser := {
+@[builtin_doc] def checkNoImmediateColon : Parser := {
   fn := fun c s =>
     let prev := s.stxStack.back
     if checkTailNoWs prev then
@@ -1756,7 +1756,7 @@ def unicodeSymbol (sym asciiSym : String) : Parser :=
   Define parser for `$e` (if `anonymous == true`) and `$e:name`.
   `kind` is embedded in the antiquotation's kind, and checked at syntax `match` unless `isPseudoKind` is true.
   Antiquotations can be escaped as in `$$e`, which produces the syntax tree for `$e`. -/
-def mkAntiquot (name : String) (kind : SyntaxNodeKind) (anonymous := true) (isPseudoKind := false) : Parser :=
+@[builtin_doc] def mkAntiquot (name : String) (kind : SyntaxNodeKind) (anonymous := true) (isPseudoKind := false) : Parser :=
   let kind := kind ++ (if isPseudoKind then `pseudo else .anonymous) ++ `antiquot
   let nameP := node `antiquotName <| checkNoWsBefore ("no space before ':" ++ name ++ "'") >> symbol ":" >> nonReservedSymbol name
   -- if parsing the kind fails and `anonymous` is true, check that we're not ignoring a different
@@ -1781,7 +1781,7 @@ def withAntiquotFn (antiquotP p : ParserFn) (isCatAntiquot := false) : ParserFn
     p c s
 
 /-- Optimized version of `mkAntiquot ... <|> p`. -/
-def withAntiquot (antiquotP p : Parser) : Parser := {
+@[builtin_doc] def withAntiquot (antiquotP p : Parser) : Parser := {
   fn := withAntiquotFn antiquotP.fn p.fn
   info := orelseInfo antiquotP.info p.info
 }
@@ -1791,7 +1791,7 @@ def withoutInfo (p : Parser) : Parser := {
 }
 
 /-- Parse `$[p]suffix`, e.g. `$[p],*`. -/
-def mkAntiquotSplice (kind : SyntaxNodeKind) (p suffix : Parser) : Parser :=
+@[builtin_doc] def mkAntiquotSplice (kind : SyntaxNodeKind) (p suffix : Parser) : Parser :=
   let kind := kind ++ `antiquot_scope
   leadingNode kind maxPrec <| atomic <|
     setExpected [] "$" >>
@@ -1808,7 +1808,7 @@ private def withAntiquotSuffixSpliceFn (kind : SyntaxNodeKind) (suffix : ParserF
   s.mkNode (kind ++ `antiquot_suffix_splice) (s.stxStack.size - 2)
 
 /-- Parse `suffix` after an antiquotation, e.g. `$x,*`, and put both into a new node. -/
-def withAntiquotSuffixSplice (kind : SyntaxNodeKind) (p suffix : Parser) : Parser where
+@[builtin_doc] def withAntiquotSuffixSplice (kind : SyntaxNodeKind) (p suffix : Parser) : Parser where
   info := andthenInfo p.info suffix.info
   fn c s :=
     let s := p.fn c s

src/Lean/Parser/Command.lean

@@ -78,7 +78,7 @@ All modifiers are optional, and have to come in the listed order.
 `nestedDeclModifiers` is the same as `declModifiers`, but attributes are printed
 on the same line as the declaration. It is used for declarations nested inside other syntax,
 such as inductive constructors, structure projections, and `let rec` / `where` definitions. -/
-def declModifiers (inline : Bool) := leading_parser
+@[builtin_doc] def declModifiers (inline : Bool) := leading_parser
   optional docComment >>
   optional (Term.«attributes» >> if inline then skip else ppDedent ppLine) >>
   optional visibility >>
@@ -86,13 +86,16 @@ def declModifiers (inline : Bool) := leading_parser
   optional «unsafe» >>
   optional («partial» <|> «nonrec»)
 /-- `declId` matches `foo` or `foo.{u,v}`: an identifier possibly followed by a list of universe names -/
-def declId           := leading_parser
+-- @[builtin_doc] -- FIXME: suppress the hover
+def declId := leading_parser
   ident >> optional (".{" >> sepBy1 (recover ident (skipUntil (fun c => c.isWhitespace || c ∈ [',', '}']))) ", " >> "}")
 /-- `declSig` matches the signature of a declaration with required type: a list of binders and then `: type` -/
-def declSig          := leading_parser
+-- @[builtin_doc] -- FIXME: suppress the hover
+def declSig := leading_parser
   many (ppSpace >> (Term.binderIdent <|> Term.bracketedBinder)) >> Term.typeSpec
 /-- `optDeclSig` matches the signature of a declaration with optional type: a list of binders and then possibly `: type` -/
-def optDeclSig       := leading_parser
+-- @[builtin_doc] -- FIXME: suppress the hover
+def optDeclSig := leading_parser
   many (ppSpace >> (Term.binderIdent <|> Term.bracketedBinder)) >> Term.optType
 /-- Right-hand side of a `:=` in a declaration, a term. -/
 def declBody : Parser :=
@@ -141,11 +144,11 @@ def whereStructInst  := leading_parser
 * a sequence of `| pat => expr` (a declaration by equations), shorthand for a `match`
 * `where` and then a sequence of `field := value` initializers, shorthand for a structure constructor
 -/
-def declVal          :=
+@[builtin_doc] def declVal :=
   -- Remark: we should not use `Term.whereDecls` at `declVal`
   -- because `Term.whereDecls` is defined using `Term.letRecDecl` which may contain attributes.
   -- Issue #753 shows an example that fails to be parsed when we used `Term.whereDecls`.
-  withAntiquot (mkAntiquot "declVal" `Lean.Parser.Command.declVal (isPseudoKind := true)) <|
+  withAntiquot (mkAntiquot "declVal" decl_name% (isPseudoKind := true)) <|
     declValSimple <|> declValEqns <|> whereStructInst
 def «abbrev»         := leading_parser
   "abbrev " >> declId >> ppIndent optDeclSig >> declVal
@@ -193,9 +196,10 @@ inductive List (α : Type u) where
 ```
 A list of elements of type `α` is either the empty list, `nil`,
 or an element `head : α` followed by a list `tail : List α`.
-For more information about [inductive types](https://lean-lang.org/theorem_proving_in_lean4/inductive_types.html).
+See [Inductive types](https://lean-lang.org/theorem_proving_in_lean4/inductive_types.html)
+for more information.
 -/
-def «inductive»      := leading_parser
+@[builtin_doc] def «inductive» := leading_parser
   "inductive " >> recover declId skipUntilWsOrDelim >> ppIndent optDeclSig >> optional (symbol " :=" <|> " where") >>
   many ctor >> optional (ppDedent ppLine >> computedFields) >> optDeriving
 def classInductive   := leading_parser
@@ -544,7 +548,7 @@ def openSimple       := leading_parser
 def openScoped       := leading_parser
   " scoped" >> many1 (ppSpace >> checkColGt >> ident)
 /-- `openDecl` is the body of an `open` declaration (see `open`) -/
-def openDecl         :=
+@[builtin_doc] def openDecl :=
   withAntiquot (mkAntiquot "openDecl" `Lean.Parser.Command.openDecl (isPseudoKind := true)) <|
     openHiding <|> openRenaming <|> openOnly <|> openSimple <|> openScoped
 /-- Makes names from other namespaces visible without writing the namespace prefix.

src/Lean/Parser/Do.lean

@@ -30,7 +30,7 @@ def doSeqBracketed := leading_parser
 do elements that take blocks. It can either have the form `"{" (doElem ";"?)* "}"` or
 `many1Indent (doElem ";"?)`, where `many1Indent` ensures that all the items are at
 the same or higher indentation level as the first line. -/
-def doSeq          :=
+@[builtin_doc] def doSeq :=
   withAntiquot (mkAntiquot "doSeq" decl_name% (isPseudoKind := true)) <|
     doSeqBracketed <|> doSeqIndent
 /-- `termBeforeDo` is defined as `withForbidden("do", term)`, which will parse a term but

src/Lean/Parser/Extra.lean

@@ -31,7 +31,7 @@ it to parse correctly. `ident?` will not work; one must write `(ident)?` instead
 This parser has arity 1: it produces a `nullKind` node containing either zero arguments
 (for the `none` case) or the list of arguments produced by `p`.
 (In particular, if `p` has arity 0 then the two cases are not differentiated!) -/
-@[run_builtin_parser_attribute_hooks] def optional (p : Parser) : Parser :=
+@[run_builtin_parser_attribute_hooks, builtin_doc] def optional (p : Parser) : Parser :=
   optionalNoAntiquot (withAntiquotSpliceAndSuffix `optional p (symbol "?"))
 
 /-- The parser `many(p)`, or `p*`, repeats `p` until it fails, and returns the list of results.
@@ -41,7 +41,7 @@ automatically replaced by `group(p)` to ensure that it produces exactly 1 value.
 
 This parser has arity 1: it produces a `nullKind` node containing one argument for each
 invocation of `p` (or `group(p)`). -/
-@[run_builtin_parser_attribute_hooks] def many (p : Parser) : Parser :=
+@[run_builtin_parser_attribute_hooks, builtin_doc] def many (p : Parser) : Parser :=
   manyNoAntiquot (withAntiquotSpliceAndSuffix `many p (symbol "*"))
 
 /-- The parser `many1(p)`, or `p+`, repeats `p` until it fails, and returns the list of results.
@@ -56,7 +56,7 @@ automatically replaced by `group(p)` to ensure that it produces exactly 1 value.
 
 This parser has arity 1: it produces a `nullKind` node containing one argument for each
 invocation of `p` (or `group(p)`). -/
-@[run_builtin_parser_attribute_hooks] def many1 (p : Parser) : Parser :=
+@[run_builtin_parser_attribute_hooks, builtin_doc] def many1 (p : Parser) : Parser :=
   many1NoAntiquot (withAntiquotSpliceAndSuffix `many p (symbol "*"))
 
 /-- The parser `ident` parses a single identifier, possibly with namespaces, such as `foo` or
@@ -70,18 +70,18 @@ using disallowed characters in identifiers such as `«foo.bar».baz` or `«hello
 
 This parser has arity 1: it produces a `Syntax.ident` node containing the parsed identifier.
 You can use `TSyntax.getId` to extract the name from the resulting syntax object. -/
-@[run_builtin_parser_attribute_hooks] def ident : Parser :=
+@[run_builtin_parser_attribute_hooks, builtin_doc] def ident : Parser :=
   withAntiquot (mkAntiquot "ident" identKind) identNoAntiquot
 
 -- `optional (checkNoWsBefore >> "." >> checkNoWsBefore >> ident)`
 -- can never fully succeed but ensures that the identifier
 -- produces a partial syntax that contains the dot.
 -- The partial syntax is sometimes useful for dot-auto-completion.
-@[run_builtin_parser_attribute_hooks] def identWithPartialTrailingDot :=
+@[run_builtin_parser_attribute_hooks, builtin_doc] def identWithPartialTrailingDot :=
   ident >> optional (checkNoWsBefore >> "." >> checkNoWsBefore >> ident)
 
 -- `ident` and `rawIdent` produce the same syntax tree, so we reuse the antiquotation kind name
-@[run_builtin_parser_attribute_hooks] def rawIdent : Parser :=
+@[run_builtin_parser_attribute_hooks, builtin_doc] def rawIdent : Parser :=
   withAntiquot (mkAntiquot "ident" identKind) rawIdentNoAntiquot
 
 /-- The parser `hygieneInfo` parses no text, but captures the current macro scope information
@@ -96,7 +96,7 @@ for more information about macro hygiene.
 
 This parser has arity 1: it produces a `Syntax.ident` node containing the parsed identifier.
 You can use `TSyntax.getHygieneInfo` to extract the name from the resulting syntax object. -/
-@[run_builtin_parser_attribute_hooks] def hygieneInfo : Parser :=
+@[run_builtin_parser_attribute_hooks, builtin_doc] def hygieneInfo : Parser :=
   withAntiquot (mkAntiquot "hygieneInfo" hygieneInfoKind (anonymous := false)) hygieneInfoNoAntiquot
 
 /-- The parser `num` parses a numeric literal in several bases:
@@ -109,7 +109,7 @@ You can use `TSyntax.getHygieneInfo` to extract the name from the resulting synt
 This parser has arity 1: it produces a `numLitKind` node containing an atom with the text of the
 literal.
 You can use `TSyntax.getNat` to extract the number from the resulting syntax object. -/
-@[run_builtin_parser_attribute_hooks] def numLit : Parser :=
+@[run_builtin_parser_attribute_hooks, builtin_doc] def numLit : Parser :=
   withAntiquot (mkAntiquot "num" numLitKind) numLitNoAntiquot
 
 /-- The parser `scientific` parses a scientific-notation literal, such as `1.3e-24`.
@@ -117,7 +117,7 @@ You can use `TSyntax.getNat` to extract the number from the resulting syntax obj
 This parser has arity 1: it produces a `scientificLitKind` node containing an atom with the text
 of the literal.
 You can use `TSyntax.getScientific` to extract the parts from the resulting syntax object. -/
-@[run_builtin_parser_attribute_hooks] def scientificLit : Parser :=
+@[run_builtin_parser_attribute_hooks, builtin_doc] def scientificLit : Parser :=
   withAntiquot (mkAntiquot "scientific" scientificLitKind) scientificLitNoAntiquot
 
 /-- The parser `str` parses a string literal, such as `"foo"` or `"\r\n"`. Strings can contain
@@ -127,7 +127,7 @@ Newlines in a string are interpreted literally.
 This parser has arity 1: it produces a `strLitKind` node containing an atom with the raw
 literal (including the quote marks and without interpreting the escapes).
 You can use `TSyntax.getString` to decode the string from the resulting syntax object. -/
-@[run_builtin_parser_attribute_hooks] def strLit : Parser :=
+@[run_builtin_parser_attribute_hooks, builtin_doc] def strLit : Parser :=
   withAntiquot (mkAntiquot "str" strLitKind) strLitNoAntiquot
 
 /-- The parser `char` parses a character literal, such as `'a'` or `'\n'`. Character literals can
@@ -138,7 +138,7 @@ like `∈`, but must evaluate to a single unicode codepoint, so `'♥'` is allow
 This parser has arity 1: it produces a `charLitKind` node containing an atom with the raw
 literal (including the quote marks and without interpreting the escapes).
 You can use `TSyntax.getChar` to decode the string from the resulting syntax object. -/
-@[run_builtin_parser_attribute_hooks] def charLit : Parser :=
+@[run_builtin_parser_attribute_hooks, builtin_doc] def charLit : Parser :=
   withAntiquot (mkAntiquot "char" charLitKind) charLitNoAntiquot
 
 /-- The parser `name` parses a name literal like `` `foo``. The syntax is the same as for identifiers
@@ -147,7 +147,7 @@ You can use `TSyntax.getChar` to decode the string from the resulting syntax obj
 This parser has arity 1: it produces a `nameLitKind` node containing the raw literal
 (including the backquote).
 You can use `TSyntax.getName` to extract the name from the resulting syntax object. -/
-@[run_builtin_parser_attribute_hooks] def nameLit : Parser :=
+@[run_builtin_parser_attribute_hooks, builtin_doc] def nameLit : Parser :=
   withAntiquot (mkAntiquot "name" nameLitKind) nameLitNoAntiquot
 
 /-- The parser `group(p)` parses the same thing as `p`, but it wraps the results in a `groupKind`
@@ -156,7 +156,7 @@ node.
 This parser always has arity 1, even if `p` does not. Parsers like `p*` are automatically
 rewritten to `group(p)*` if `p` does not have arity 1, so that the results from separate invocations
 of `p` can be differentiated. -/
-@[run_builtin_parser_attribute_hooks, inline] def group (p : Parser) : Parser :=
+@[run_builtin_parser_attribute_hooks, builtin_doc, inline] def group (p : Parser) : Parser :=
   node groupKind p
 
 /-- The parser `many1Indent(p)` is equivalent to `withPosition((colGe p)+)`. This has the effect of
@@ -165,7 +165,7 @@ the same or more than the first parse.
 
 This parser has arity 1, and returns a list of the results from `p`.
 `p` is "auto-grouped" if it is not arity 1. -/
-@[run_builtin_parser_attribute_hooks, inline] def many1Indent (p : Parser) : Parser :=
+@[run_builtin_parser_attribute_hooks, builtin_doc, inline] def many1Indent (p : Parser) : Parser :=
   withPosition $ many1 (checkColGe "irrelevant" >> p)
 
 /-- The parser `manyIndent(p)` is equivalent to `withPosition((colGe p)*)`. This has the effect of
@@ -174,14 +174,14 @@ the same or more than the first parse.
 
 This parser has arity 1, and returns a list of the results from `p`.
 `p` is "auto-grouped" if it is not arity 1. -/
-@[run_builtin_parser_attribute_hooks, inline] def manyIndent (p : Parser) : Parser :=
+@[run_builtin_parser_attribute_hooks, builtin_doc, inline] def manyIndent (p : Parser) : Parser :=
   withPosition $ many (checkColGe "irrelevant" >> p)
 
-@[inline] def sepByIndent (p : Parser) (sep : String) (psep : Parser := symbol sep) (allowTrailingSep : Bool := false) : Parser :=
+@[builtin_doc, inline] def sepByIndent (p : Parser) (sep : String) (psep : Parser := symbol sep) (allowTrailingSep : Bool := false) : Parser :=
   let p := withAntiquotSpliceAndSuffix `sepBy p (symbol "*")
   withPosition $ sepBy (checkColGe "irrelevant" >> p) sep (psep <|> checkColEq "irrelevant" >> checkLinebreakBefore >> pushNone) allowTrailingSep
 
-@[inline] def sepBy1Indent (p : Parser) (sep : String) (psep : Parser := symbol sep) (allowTrailingSep : Bool := false) : Parser :=
+@[builtin_doc, inline] def sepBy1Indent (p : Parser) (sep : String) (psep : Parser := symbol sep) (allowTrailingSep : Bool := false) : Parser :=
   let p := withAntiquotSpliceAndSuffix `sepBy p (symbol "*")
   withPosition $ sepBy1 (checkColGe "irrelevant" >> p) sep (psep <|> checkColEq "irrelevant" >> checkLinebreakBefore >> pushNone) allowTrailingSep
 
@@ -205,32 +205,33 @@ def sepByIndent.formatter (p : Formatter) (_sep : String) (pSep : Formatter) : F
 
 attribute [run_builtin_parser_attribute_hooks] sepByIndent sepBy1Indent
 
-@[run_builtin_parser_attribute_hooks] abbrev notSymbol (s : String) : Parser :=
+@[run_builtin_parser_attribute_hooks, builtin_doc] abbrev notSymbol (s : String) : Parser :=
   notFollowedBy (symbol s) s
 
 /-- No-op parser combinator that annotates subtrees to be ignored in syntax patterns. -/
-@[inline, run_builtin_parser_attribute_hooks] def patternIgnore : Parser → Parser := node `patternIgnore
+@[run_builtin_parser_attribute_hooks, builtin_doc, inline]
+def patternIgnore : Parser → Parser := node `patternIgnore
 
 /-- No-op parser that advises the pretty printer to emit a non-breaking space. -/
-@[inline] def ppHardSpace : Parser := skip
+@[builtin_doc, inline] def ppHardSpace : Parser := skip
 /-- No-op parser that advises the pretty printer to emit a space/soft line break. -/
-@[inline] def ppSpace : Parser := skip
+@[builtin_doc, inline] def ppSpace : Parser := skip
 /-- No-op parser that advises the pretty printer to emit a hard line break. -/
-@[inline] def ppLine : Parser := skip
+@[builtin_doc, inline] def ppLine : Parser := skip
 /-- No-op parser combinator that advises the pretty printer to emit a `Format.fill` node. -/
-@[inline] def ppRealFill : Parser → Parser := id
+@[builtin_doc, inline] def ppRealFill : Parser → Parser := id
 /-- No-op parser combinator that advises the pretty printer to emit a `Format.group` node. -/
-@[inline] def ppRealGroup : Parser → Parser := id
+@[builtin_doc, inline] def ppRealGroup : Parser → Parser := id
 /-- No-op parser combinator that advises the pretty printer to indent the given syntax without grouping it. -/
-@[inline] def ppIndent : Parser → Parser := id
+@[builtin_doc, inline] def ppIndent : Parser → Parser := id
 /--
   No-op parser combinator that advises the pretty printer to group and indent the given syntax.
   By default, only syntax categories are grouped. -/
-@[inline] def ppGroup (p : Parser) : Parser := ppRealFill (ppIndent p)
+@[builtin_doc, inline] def ppGroup (p : Parser) : Parser := ppRealFill (ppIndent p)
 /--
   No-op parser combinator that advises the pretty printer to dedent the given syntax.
   Dedenting can in particular be used to counteract automatic indentation. -/
-@[inline] def ppDedent : Parser → Parser := id
+@[builtin_doc, inline] def ppDedent : Parser → Parser := id
 
 /--
   No-op parser combinator that allows the pretty printer to omit the group and
@@ -242,19 +243,19 @@ attribute [run_builtin_parser_attribute_hooks] sepByIndent sepBy1Indent
     trivial
   ```
 -/
-@[inline] def ppAllowUngrouped : Parser := skip
+@[builtin_doc, inline] def ppAllowUngrouped : Parser := skip
 
 /--
   No-op parser combinator that advises the pretty printer to dedent the given syntax,
   if it was grouped by the category parser.
   Dedenting can in particular be used to counteract automatic indentation. -/
-@[inline] def ppDedentIfGrouped : Parser → Parser := id
+@[builtin_doc, inline] def ppDedentIfGrouped : Parser → Parser := id
 
 /--
   No-op parser combinator that prints a line break.
   The line break is soft if the combinator is followed
   by an ungrouped parser (see ppAllowUngrouped), otherwise hard. -/
-@[inline] def ppHardLineUnlessUngrouped : Parser := skip
+@[builtin_doc, inline] def ppHardLineUnlessUngrouped : Parser := skip
 
 end Parser
 

src/Lean/Parser/StrInterpolation.lean

@@ -68,7 +68,7 @@ This parser has arity 1, and returns a `interpolatedStrKind` with an odd number
 alternating between chunks of literal text and results from `p`. The literal chunks contain
 uninterpreted substrings of the input. For example, `"foo\n{2 + 2}"` would have three arguments:
 an atom `"foo\n{`, the parsed `2 + 2` term, and then the atom `}"`. -/
-def interpolatedStr (p : Parser) : Parser :=
+@[builtin_doc] def interpolatedStr (p : Parser) : Parser :=
   withAntiquot (mkAntiquot "interpolatedStr" interpolatedStrKind) $ interpolatedStrNoAntiquot p
 
 end Lean.Parser

src/Lean/Parser/Term.lean

@@ -24,6 +24,7 @@ a regular comment (that is, as whitespace); it is parsed and forms part of the s
 
 A `docComment` node contains a `/--` atom and then the remainder of the comment, `foo -/` in this
 example. Use `TSyntax.getDocString` to extract the body text from a doc string syntax node. -/
+-- @[builtin_doc] -- FIXME: suppress the hover
 def docComment := leading_parser
   ppDedent $ "/--" >> ppSpace >> commentBody >> ppLine
 end Command
@@ -49,7 +50,7 @@ example := by
   skip
 ```
 is legal, but `by skip skip` is not - it must be written as `by skip; skip`. -/
-@[run_builtin_parser_attribute_hooks]
+@[run_builtin_parser_attribute_hooks, builtin_doc]
 def sepByIndentSemicolon (p : Parser) : Parser :=
   sepByIndent p "; " (allowTrailingSep := true)
 
@@ -62,7 +63,7 @@ example := by
   skip
 ```
 is legal, but `by skip skip` is not - it must be written as `by skip; skip`. -/
-@[run_builtin_parser_attribute_hooks]
+@[run_builtin_parser_attribute_hooks, builtin_doc]
 def sepBy1IndentSemicolon (p : Parser) : Parser :=
   sepBy1Indent p "; " (allowTrailingSep := true)
 
@@ -70,22 +71,22 @@ builtin_initialize
   register_parser_alias sepByIndentSemicolon
   register_parser_alias sepBy1IndentSemicolon
 
-def tacticSeq1Indented : Parser := leading_parser
+@[builtin_doc] def tacticSeq1Indented : Parser := leading_parser
   sepBy1IndentSemicolon tacticParser
 /-- The syntax `{ tacs }` is an alternative syntax for `· tacs`.
 It runs the tactics in sequence, and fails if the goal is not solved. -/
-def tacticSeqBracketed : Parser := leading_parser
+@[builtin_doc] def tacticSeqBracketed : Parser := leading_parser
   "{" >> sepByIndentSemicolon tacticParser >> ppDedent (ppLine >> "}")
 
 /-- A sequence of tactics in brackets, or a delimiter-free indented sequence of tactics.
 Delimiter-free indentation is determined by the *first* tactic of the sequence. -/
-def tacticSeq := leading_parser
+@[builtin_doc] def tacticSeq := leading_parser
   tacticSeqBracketed <|> tacticSeq1Indented
 
 /-- Same as [`tacticSeq`] but requires delimiter-free tactic sequence to have strict indentation.
 The strict indentation requirement only apply to *nested* `by`s, as top-level `by`s do not have a
 position set. -/
-def tacticSeqIndentGt := withAntiquot (mkAntiquot "tacticSeq" ``tacticSeq) <| node ``tacticSeq <|
+@[builtin_doc] def tacticSeqIndentGt := withAntiquot (mkAntiquot "tacticSeq" ``tacticSeq) <| node ``tacticSeq <|
   tacticSeqBracketed <|> (checkColGt "indented tactic sequence" >> tacticSeq1Indented)
 
 /- Raw sequence for quotation and grouping -/
@@ -206,7 +207,7 @@ def fromTerm   := leading_parser
 def showRhs := fromTerm <|> byTactic'
 /-- A `sufficesDecl` represents everything that comes after the `suffices` keyword:
 an optional `x :`, then a term `ty`, then `from val` or `by tac`. -/
-def sufficesDecl := leading_parser
+@[builtin_doc] def sufficesDecl := leading_parser
   (atomic (group (binderIdent >> " : ")) <|> hygieneInfo) >> termParser >> ppSpace >> showRhs
 @[builtin_term_parser] def «suffices» := leading_parser:leadPrec
   withPosition ("suffices " >> sufficesDecl) >> optSemicolon termParser
@@ -272,7 +273,7 @@ open Lean.PrettyPrinter Parenthesizer Syntax.MonadTraverser in
 Explicit binder, like `(x y : A)` or `(x y)`.
 Default values can be specified using `(x : A := v)` syntax, and tactics using `(x : A := by tac)`.
 -/
-def explicitBinder (requireType := false) := leading_parser ppGroup <|
+@[builtin_doc] def explicitBinder (requireType := false) := leading_parser ppGroup <|
   "(" >> withoutPosition (many1 binderIdent >> binderType requireType >> optional (binderTactic <|> binderDefault)) >> ")"
 /--
 Implicit binder, like `{x y : A}` or `{x y}`.
@@ -283,7 +284,7 @@ by unification.
 
 In `@` explicit mode, implicit binders behave like explicit binders.
 -/
-def implicitBinder (requireType := false) := leading_parser ppGroup <|
+@[builtin_doc] def implicitBinder (requireType := false) := leading_parser ppGroup <|
   "{" >> withoutPosition (many1 binderIdent >> binderType requireType) >> "}"
 def strictImplicitLeftBracket := atomic (group (symbol "{" >> "{")) <|> "⦃"
 def strictImplicitRightBracket := atomic (group (symbol "}" >> "}")) <|> "⦄"
@@ -300,7 +301,7 @@ and `h hs` has type `p y`.
 In contrast, if `h' : ∀ {x : A}, x ∈ s → p x`, then `h` by itself elaborates to have type `?m ∈ s → p ?m`
 with `?m` a fresh metavariable.
 -/
-def strictImplicitBinder (requireType := false) := leading_parser ppGroup <|
+@[builtin_doc] def strictImplicitBinder (requireType := false) := leading_parser ppGroup <|
   strictImplicitLeftBracket >> many1 binderIdent >>
   binderType requireType >> strictImplicitRightBracket
 /--
@@ -310,7 +311,7 @@ and solved for by typeclass inference for the specified class `C`.
 In `@` explicit mode, if `_` is used for an an instance-implicit parameter, then it is still solved for by typeclass inference;
 use `(_)` to inhibit this and have it be solved for by unification instead, like an implicit argument.
 -/
-def instBinder := leading_parser ppGroup <|
+@[builtin_doc] def instBinder := leading_parser ppGroup <|
   "[" >> withoutPosition (optIdent >> termParser) >> "]"
 /-- A `bracketedBinder` matches any kind of binder group that uses some kind of brackets:
 * An explicit binder like `(x y : A)`
@@ -318,7 +319,7 @@ def instBinder := leading_parser ppGroup <|
 * A strict implicit binder, `⦃y z : A⦄` or its ASCII alternative `{{y z : A}}`
 * An instance binder `[A]` or `[x : A]` (multiple variables are not allowed here)
 -/
-def bracketedBinder (requireType := false) :=
+@[builtin_doc] def bracketedBinder (requireType := false) :=
   withAntiquot (mkAntiquot "bracketedBinder" decl_name% (isPseudoKind := true)) <|
     explicitBinder requireType <|> strictImplicitBinder requireType <|>
     implicitBinder requireType <|> instBinder
@@ -366,7 +367,7 @@ def matchAlts (rhsParser : Parser := termParser) : Parser :=
 
 /-- `matchDiscr` matches a "match discriminant", either `h : tm` or `tm`, used in `match` as
 `match h1 : e1, e2, h3 : e3 with ...`. -/
-def matchDiscr := leading_parser
+@[builtin_doc] def matchDiscr := leading_parser
   optional (atomic (ident >> " : ")) >> termParser
 
 def trueVal  := leading_parser nonReservedSymbol "true"
@@ -497,7 +498,7 @@ def letEqnsDecl := leading_parser (withAnonymousAntiquot := false)
 `let pat := e` (where `pat` is an arbitrary term) or `let f | pat1 => e1 | pat2 => e2 ...`
 (a pattern matching declaration), except for the `let` keyword itself.
 `let rec` declarations are not handled here. -/
-def letDecl     := leading_parser (withAnonymousAntiquot := false)
+@[builtin_doc] def letDecl := leading_parser (withAnonymousAntiquot := false)
   -- Remark: we disable anonymous antiquotations here to make sure
   -- anonymous antiquotations (e.g., `$x`) are not `letDecl`
   notFollowedBy (nonReservedSymbol "rec") "rec" >>
@@ -556,7 +557,7 @@ def haveEqnsDecl := leading_parser (withAnonymousAntiquot := false)
 /-- `haveDecl` matches the body of a have declaration: `have := e`, `have f x1 x2 := e`,
 `have pat := e` (where `pat` is an arbitrary term) or `have f | pat1 => e1 | pat2 => e2 ...`
 (a pattern matching declaration), except for the `have` keyword itself. -/
-def haveDecl     := leading_parser (withAnonymousAntiquot := false)
+@[builtin_doc] def haveDecl := leading_parser (withAnonymousAntiquot := false)
   haveIdDecl <|> (ppSpace >> letPatDecl) <|> haveEqnsDecl
 @[builtin_term_parser] def «have» := leading_parser:leadPrec
   withPosition ("have" >> haveDecl) >> optSemicolon termParser
@@ -570,7 +571,7 @@ def haveDecl     := leading_parser (withAnonymousAntiquot := false)
 def «scoped» := leading_parser "scoped "
 def «local»  := leading_parser "local "
 /-- `attrKind` matches `("scoped" <|> "local")?`, used before an attribute like `@[local simp]`. -/
-def attrKind := leading_parser optional («scoped» <|> «local»)
+@[builtin_doc] def attrKind := leading_parser optional («scoped» <|> «local»)
 def attrInstance     := ppGroup $ leading_parser attrKind >> attrParser
 
 def attributes       := leading_parser
@@ -607,13 +608,13 @@ If omitted, a termination argument will be inferred. If written as `termination_
 the inferrred termination argument will be suggested.
 
 -/
-def terminationBy := leading_parser
+@[builtin_doc] def terminationBy := leading_parser
   "termination_by " >>
   optional (nonReservedSymbol "structural ") >>
   optional (atomic (many (ppSpace >> Term.binderIdent) >> " => ")) >>
   termParser
 
-@[inherit_doc terminationBy]
+@[inherit_doc terminationBy, builtin_doc]
 def terminationBy? := leading_parser
   "termination_by?"
 
@@ -626,13 +627,13 @@ By default, the tactic `decreasing_tactic` is used.
 Forces the use of well-founded recursion and is hence incompatible with
 `termination_by structural`.
 -/
-def decreasingBy := leading_parser
+@[builtin_doc] def decreasingBy := leading_parser
   ppDedent ppLine >> "decreasing_by " >> Tactic.tacticSeqIndentGt
 
 /--
 Termination hints are `termination_by` and `decreasing_by`, in that order.
 -/
-def suffix := leading_parser
+@[builtin_doc] def suffix := leading_parser
   optional (ppDedent ppLine >> (terminationBy? <|> terminationBy)) >> optional decreasingBy
 
 end Termination
@@ -640,9 +641,10 @@ namespace Term
 
 /-- `letRecDecl` matches the body of a let-rec declaration: a doc comment, attributes, and then
 a let declaration without the `let` keyword, such as `/-- foo -/ @[simp] bar := 1`. -/
-def letRecDecl       := leading_parser
+@[builtin_doc] def letRecDecl := leading_parser
   optional Command.docComment >> optional «attributes» >> letDecl >> Termination.suffix
 /-- `letRecDecls` matches `letRecDecl,+`, a comma-separated list of let-rec declarations (see `letRecDecl`). -/
+-- @[builtin_doc] -- FIXME: suppress the hover
 def letRecDecls      := leading_parser
   sepBy1 letRecDecl ", "
 @[builtin_term_parser]

src/Lean/Parser/Types.lean

@@ -7,6 +7,7 @@ prelude
 import Lean.Data.Trie
 import Lean.Syntax
 import Lean.Message
+import Lean.DocString.Extension
 
 namespace Lean.Parser
 
@@ -428,7 +429,7 @@ def withCacheFn (parserName : Name) (p : ParserFn) : ParserFn := fun c s => Id.r
     panic! s!"withCacheFn: unexpected stack growth {s.stxStack.raw}"
   { s with cache.parserCache := s.cache.parserCache.insert key ⟨s.stxStack.back, s.lhsPrec, s.pos, s.errorMsg⟩ }
 
-@[inherit_doc withCacheFn]
+@[inherit_doc withCacheFn, builtin_doc]
 def withCache (parserName : Name) : Parser → Parser := withFn (withCacheFn parserName)
 
 def ParserFn.run (p : ParserFn) (ictx : InputContext) (pmctx : ParserModuleContext) (tokens : TokenTable) (s : ParserState) : ParserState :=

src/Lean/Server/Completion.lean

@@ -666,6 +666,50 @@ private def tacticCompletion (params : CompletionParams) (ctx : ContextInfo) : I
       }, 1)
     return some { items := sortCompletionItems items, isIncomplete := true }
 
+/--
+If there are `Info`s that contain `hoverPos` and have a nonempty `LocalContext`,
+yields the closest one of those `Info`s.
+Otherwise, yields the closest `Info` that contains `hoverPos` and has an empty `LocalContext`.
+-/
+private def findClosestInfoWithLocalContextAt?
+    (hoverPos : String.Pos)
+    (infoTree : InfoTree)
+    : Option (ContextInfo × Info) :=
+  infoTree.visitM (m := Id) (postNode := choose) |>.join
+where
+  choose
+      (ctx : ContextInfo)
+      (info : Info)
+      (_ : PersistentArray InfoTree)
+      (childValues : List (Option (Option (ContextInfo × Info))))
+      : Option (ContextInfo × Info) :=
+    let bestChildValue := childValues.map (·.join) |>.foldl (init := none) fun v best =>
+      if isBetter v best then
+        v
+      else
+        best
+    if info.occursInOrOnBoundary hoverPos && isBetter (ctx, info) bestChildValue then
+      (ctx, info)
+    else
+      bestChildValue
+
+  isBetter (a b : Option (ContextInfo × Info)) : Bool :=
+    match a, b with
+    | none,   none   => false
+    | some _, none   => true
+    | none,   some _ => false
+    | some (_, ia), some (_, ib) =>
+      if !ia.lctx.isEmpty && ib.lctx.isEmpty then
+        true
+      else if ia.lctx.isEmpty && !ib.lctx.isEmpty then
+        false
+      else if ia.isSmaller ib then
+        true
+      else if ib.isSmaller ia then
+        false
+      else
+        false
+
 private def findCompletionInfoAt?
     (fileMap  : FileMap)
     (hoverPos : String.Pos)
@@ -675,9 +719,32 @@ private def findCompletionInfoAt?
   match infoTree.foldInfo (init := none) (choose hoverLine) with
   | some (hoverInfo, ctx, Info.ofCompletionInfo info) =>
     some (hoverInfo, ctx, info)
-  | _ =>
-    -- TODO try to extract id from `fileMap` and some `ContextInfo` from `InfoTree`
-    none
+  | _ => do
+    -- No completion info => Attempt providing identifier completions
+    let some (ctx, info) := findClosestInfoWithLocalContextAt? hoverPos infoTree
+      | none
+    let some stack := info.stx.findStack? (·.getRange?.any (·.contains hoverPos (includeStop := true)))
+      | none
+    let stack := stack.dropWhile fun (stx, _) => !(stx matches `($_:ident) || stx matches `($_:ident.))
+    let some (stx, _) := stack.head?
+      | none
+    let isDotIdCompletion := stack.any fun (stx, _) => stx matches `(.$_:ident)
+    if isDotIdCompletion then
+      -- An identifier completion is never useful in a dotId completion context.
+      none
+    let some (id, danglingDot) :=
+        match stx with
+        | `($id:ident) => some (id.getId, false)
+        | `($id:ident.) => some (id.getId, true)
+        | _ => none
+      | none
+    let tailPos := stx.getTailPos?.get!
+    let hoverInfo :=
+      if hoverPos < tailPos then
+        HoverInfo.inside (tailPos - hoverPos).byteIdx
+      else
+        HoverInfo.after
+    some (hoverInfo, ctx, .id stx id danglingDot info.lctx none)
 where
   choose
       (hoverLine : Nat)

src/Lean/Server/InfoUtils.lean

@@ -141,10 +141,12 @@ def Info.stx : Info → Syntax
   | ofOmissionInfo i       => i.stx
 
 def Info.lctx : Info → LocalContext
-  | Info.ofTermInfo i     => i.lctx
-  | Info.ofFieldInfo i    => i.lctx
-  | Info.ofOmissionInfo i => i.lctx
-  | _                     => LocalContext.empty
+  | .ofTermInfo i           => i.lctx
+  | .ofFieldInfo i          => i.lctx
+  | .ofOmissionInfo i       => i.lctx
+  | .ofMacroExpansionInfo i => i.lctx
+  | .ofCompletionInfo i     => i.lctx
+  | _                       => LocalContext.empty
 
 def Info.pos? (i : Info) : Option String.Pos :=
   i.stx.getPos? (canonicalOnly := true)

src/Std/Data/DHashMap/Basic.lean

@@ -152,6 +152,18 @@ variable {β : Type v}
 
 end
 
+@[inline, inherit_doc Raw.getKey?] def getKey? (m : DHashMap α β) (a : α) : Option α :=
+  Raw₀.getKey? ⟨m.1, m.2.size_buckets_pos⟩ a
+
+@[inline, inherit_doc Raw.getKey] def getKey (m : DHashMap α β) (a : α) (h : a ∈ m) : α :=
+  Raw₀.getKey ⟨m.1, m.2.size_buckets_pos⟩ a h
+
+@[inline, inherit_doc Raw.getKey!] def getKey! [Inhabited α] (m : DHashMap α β) (a : α) : α :=
+  Raw₀.getKey! ⟨m.1, m.2.size_buckets_pos⟩ a
+
+@[inline, inherit_doc Raw.getKeyD] def getKeyD (m : DHashMap α β) (a : α) (fallback : α) : α :=
+  Raw₀.getKeyD ⟨m.1, m.2.size_buckets_pos⟩ a fallback
+
 @[inline, inherit_doc Raw.size] def size (m : DHashMap α β) : Nat :=
   m.1.size
 

src/Std/Data/DHashMap/Internal/AssocList/Basic.lean

@@ -102,16 +102,31 @@ def getCast [BEq α] [LawfulBEq α] (a : α) : (l : AssocList α β) → l.conta
   | cons k v es, h => if hka : k == a then cast (congrArg β (eq_of_beq hka)) v
       else es.getCast a (by rw [← h, contains, Bool.of_not_eq_true hka, Bool.false_or])
 
+/-- Internal implementation detail of the hash map -/
+def getKey [BEq α] (a : α) : (l : AssocList α β) → l.contains a → α
+  | cons k _ es, h => if hka : k == a then k
+      else es.getKey a (by rw [← h, contains, Bool.of_not_eq_true hka, Bool.false_or])
+
 /-- Internal implementation detail of the hash map -/
 def getCast! [BEq α] [LawfulBEq α] (a : α) [Inhabited (β a)] : AssocList α β → β a
   | nil => panic! "key is not present in hash table"
   | cons k v es => if h : k == a then cast (congrArg β (eq_of_beq h)) v else es.getCast! a
 
+/-- Internal implementation detail of the hash map -/
+def getKey? [BEq α] (a : α) : AssocList α β → Option α
+  | nil => none
+  | cons k _ es => if k == a then some k else es.getKey? a
+
 /-- Internal implementation detail of the hash map -/
 def get! {β : Type v} [BEq α] [Inhabited β] (a : α) : AssocList α (fun _ => β) → β
   | nil => panic! "key is not present in hash table"
   | cons k v es => bif k == a then v else es.get! a
 
+/-- Internal implementation detail of the hash map -/
+def getKey! [BEq α] [Inhabited α] (a : α) : AssocList α β → α
+  | nil => panic! "key is not present in hash table"
+  | cons k _ es => if k == a then k else es.getKey! a
+
 /-- Internal implementation detail of the hash map -/
 def getCastD [BEq α] [LawfulBEq α] (a : α) (fallback : β a) : AssocList α β → β a
   | nil => fallback
@@ -123,6 +138,11 @@ def getD {β : Type v} [BEq α] (a : α) (fallback : β) : AssocList α (fun _ =
   | nil => fallback
   | cons k v es => bif k == a then v else es.getD a fallback
 
+/-- Internal implementation detail of the hash map -/
+def getKeyD [BEq α] (a : α) (fallback : α) : AssocList α β → α
+  | nil => fallback
+  | cons k _ es => if k == a then k else es.getKeyD a fallback
+
 /-- Internal implementation detail of the hash map -/
 def replace [BEq α] (a : α) (b : β a) : AssocList α β → AssocList α β
   | nil => nil

src/Std/Data/DHashMap/Internal/AssocList/Lemmas.lean

@@ -112,6 +112,32 @@ theorem get!_eq {β : Type v} [BEq α] [Inhabited β] {l : AssocList α (fun _ =
   · simp_all [get!, List.getValue!, List.getValue!, List.getValue?_cons,
       Bool.apply_cond Option.get!]
 
+@[simp]
+theorem getKey?_eq [BEq α] {l : AssocList α β} {a : α} :
+    l.getKey? a = List.getKey? a l.toList := by
+  induction l <;> simp_all [getKey?]
+
+@[simp]
+theorem getKey_eq [BEq α] {l : AssocList α β} {a : α} {h} :
+    l.getKey a h = List.getKey a l.toList (contains_eq.symm.trans h) := by
+  induction l
+  · simp [contains] at h
+  · next k v t ih => simp only [getKey, toList_cons, List.getKey_cons, ih]
+
+@[simp]
+theorem getKeyD_eq [BEq α] {l : AssocList α β} {a fallback : α} :
+    l.getKeyD a fallback = List.getKeyD a l.toList fallback := by
+  induction l
+  · simp [getKeyD, List.getKeyD]
+  · simp_all [getKeyD, List.getKeyD, Bool.apply_cond (fun x => Option.getD x fallback)]
+
+@[simp]
+theorem getKey!_eq [BEq α] [Inhabited α] {l : AssocList α β} {a : α} :
+    l.getKey! a = List.getKey! a l.toList := by
+  induction l
+  · simp [getKey!, List.getKey!]
+  · simp_all [getKey!, List.getKey!, Bool.apply_cond Option.get!]
+
 @[simp]
 theorem toList_replace [BEq α] {l : AssocList α β} {a : α} {b : β a} :
     (l.replace a b).toList = replaceEntry a b l.toList := by

src/Std/Data/DHashMap/Internal/Defs.lean

@@ -100,9 +100,9 @@ Here is a summary of the steps required to add and verify a new operation:
   * Connect the implementation on lists and associative lists in `Internal.AssocList.Lemmas` via a
     lemma `AssocList.operation_eq`.
 3. Write the model implementation
-  * Write the model implementation `Raw₀.operationₘ` in `Internal.List.Model`
+  * Write the model implementation `Raw₀.operationₘ` in `Internal.Model`
   * Prove that the model implementation is equal to the actual implementation in
-    `Internal.List.Model` via a lemma `operation_eq_operationₘ`.
+    `Internal.Model` via a lemma `operation_eq_operationₘ`.
 4. Verify the model implementation
   * In `Internal.WF`, prove `operationₘ_eq_List.operation` (for access operations) or
     `wfImp_operationₘ` and `toListModel_operationₘ`
@@ -121,18 +121,18 @@ Here is a summary of the steps required to add and verify a new operation:
     might also have to prove that your list operation is invariant under permutation and add that to
     the tactic.
 7. State and prove the user-facing lemmas
-  * Restate all of your lemmas for `DHashMap.Raw` in `DHashMap.Lemmas` and prove them using the
+  * Restate all of your lemmas for `DHashMap.Raw` in `DHashMap.RawLemmas` and prove them using the
     provided tactic after hooking in your `operation_eq` and `operation_val` from step 5.
   * Restate all of your lemmas for `DHashMap` in `DHashMap.Lemmas` and prove them by reducing to
     `Raw₀`.
-  * Restate all of your lemmas for `HashMap.Raw` in `HashMap.Lemmas` and prove them by reducing to
+  * Restate all of your lemmas for `HashMap.Raw` in `HashMap.RawLemmas` and prove them by reducing to
     `DHashMap.Raw`.
   * Restate all of your lemmas for `HashMap` in `HashMap.Lemmas` and prove them by reducing to
     `DHashMap`.
-  * Restate all of your lemmas for `HashSet.Raw` in `HashSet.Lemmas` and prove them by reducing to
-    `DHashSet.Raw`.
+  * Restate all of your lemmas for `HashSet.Raw` in `HashSet.RawLemmas` and prove them by reducing to
+    `HashMap.Raw`.
   * Restate all of your lemmas for `HashSet` in `HashSet.Lemmas` and prove them by reducing to
-    `DHashSet`.
+    `HashMap`.
 
 This sounds like a lot of work (and it is if you have to add a lot of user-facing lemmas), but the
 framework is set up in such a way that each step is really easy and the proofs are all really short
@@ -420,6 +420,30 @@ variable {β : Type v}
 
 end
 
+/-- Internal implementation detail of the hash map -/
+@[inline] def getKey? [BEq α] [Hashable α] (m : Raw₀ α β) (a : α) : Option α :=
+  let ⟨⟨_, buckets⟩, h⟩ := m
+  let ⟨i, h⟩ := mkIdx buckets.size h (hash a)
+  buckets[i].getKey? a
+
+/-- Internal implementation detail of the hash map -/
+@[inline] def getKey [BEq α] [Hashable α] (m : Raw₀ α β) (a : α) (hma : m.contains a) : α :=
+  let ⟨⟨_, buckets⟩, h⟩ := m
+  let idx := mkIdx buckets.size h (hash a)
+  buckets[idx.1].getKey a hma
+
+/-- Internal implementation detail of the hash map -/
+@[inline] def getKeyD [BEq α] [Hashable α] (m : Raw₀ α β) (a : α) (fallback : α) : α :=
+  let ⟨⟨_, buckets⟩, h⟩ := m
+  let idx := mkIdx buckets.size h (hash a)
+  buckets[idx.1].getKeyD a fallback
+
+/-- Internal implementation detail of the hash map -/
+@[inline] def getKey! [BEq α] [Hashable α] [Inhabited α] (m : Raw₀ α β) (a : α) : α :=
+  let ⟨⟨_, buckets⟩, h⟩ := m
+  let idx := mkIdx buckets.size h (hash a)
+  buckets[idx.1].getKey! a
+
 end Raw₀
 
 /-- Internal implementation detail of the hash map -/

src/Std/Data/DHashMap/Internal/List/Associative.lean

@@ -526,6 +526,111 @@ theorem getValue!_eq_getValueD_default [BEq α] [Inhabited β] {l : List ((_ :
 
 end
 
+/-- Internal implementation detail of the hash map -/
+def getKey? [BEq α] (a : α) : List ((a : α) × β a) → Option α
+  | [] => none
+  | ⟨k, _⟩ :: l => bif k == a then some k else getKey? a l
+
+@[simp] theorem getKey?_nil [BEq α] {a : α} :
+    getKey? a ([] : List ((a : α) × β a)) = none := rfl
+
+@[simp] theorem getKey?_cons [BEq α] {l : List ((a : α) × β a)} {k a : α} {v : β k} :
+    getKey? a (⟨k, v⟩ :: l) = bif k == a then some k else getKey? a l := rfl
+
+theorem getKey?_cons_of_true [BEq α] {l : List ((a : α) × β a)} {k a : α} {v : β k} (h : k == a) :
+    getKey? a (⟨k, v⟩ :: l) = some k := by
+  simp [h]
+
+theorem getKey?_cons_of_false [BEq α] {l : List ((a : α) × β a)} {k a : α} {v : β k}
+    (h : (k == a) = false) : getKey? a (⟨k, v⟩ :: l) = getKey? a l := by
+  simp [h]
+
+theorem getKey?_eq_getEntry? [BEq α] {l : List ((a : α) × β a)} {a : α} :
+    getKey? a l = (getEntry? a l).map (·.1) := by
+  induction l using assoc_induction
+  · simp
+  · next k v l ih =>
+    cases h : k == a
+    · rw [getEntry?_cons_of_false h, getKey?_cons_of_false h, ih]
+    · rw [getEntry?_cons_of_true h, getKey?_cons_of_true h, Option.map_some']
+
+theorem containsKey_eq_isSome_getKey? [BEq α] {l : List ((a : α) × β a)} {a : α} :
+    containsKey a l = (getKey? a l).isSome := by
+  simp [containsKey_eq_isSome_getEntry?, getKey?_eq_getEntry?]
+
+/-- Internal implementation detail of the hash map -/
+def getKey [BEq α] (a : α) (l : List ((a : α) × β a)) (h : containsKey a l) : α :=
+  (getKey? a l).get <| containsKey_eq_isSome_getKey?.symm.trans h
+
+theorem getKey?_eq_some_getKey [BEq α] {l : List ((a : α) × β a)} {a : α} (h : containsKey a l) :
+    getKey? a l = some (getKey a l h) := by
+  simp [getKey]
+
+theorem getKey_cons [BEq α] {l : List ((a : α) × β a)} {k a : α} {v : β k} {h} :
+    getKey a (⟨k, v⟩ :: l) h = if h' : k == a then k
+      else getKey a l (containsKey_of_containsKey_cons (k := k) h (Bool.eq_false_iff.2 h')) := by
+  rw [← Option.some_inj, ← getKey?_eq_some_getKey, getKey?_cons, apply_dite Option.some,
+    cond_eq_if]
+  split
+  · rfl
+  · exact getKey?_eq_some_getKey _
+
+/-- Internal implementation detail of the hash map -/
+def getKeyD [BEq α] (a : α) (l : List ((a : α) × β a)) (fallback : α) : α :=
+  (getKey? a l).getD fallback
+
+@[simp]
+theorem getKeyD_nil [BEq α] {a fallback : α} :
+  getKeyD a ([] : List ((a : α) × β a)) fallback = fallback := rfl
+
+theorem getKeyD_eq_getKey? [BEq α] {l : List ((a : α) × β a)} {a fallback : α} :
+  getKeyD a l fallback = (getKey? a l).getD fallback := rfl
+
+theorem getKeyD_eq_fallback [BEq α] [EquivBEq α] {l : List ((a : α) × β a)} {a fallback : α}
+    (h : containsKey a l = false) : getKeyD a l fallback = fallback := by
+  rw [containsKey_eq_isSome_getKey?, Bool.eq_false_iff, ne_eq,
+    Option.not_isSome_iff_eq_none] at h
+  rw [getKeyD_eq_getKey?, h, Option.getD_none]
+
+theorem getKey_eq_getKeyD [BEq α] [EquivBEq α] {l : List ((a : α) × β a)} {a fallback : α}
+    (h : containsKey a l = true) :
+    getKey a l h = getKeyD a l fallback := by
+  rw [getKeyD_eq_getKey?, getKey, Option.get_eq_getD]
+
+theorem getKey?_eq_some_getKeyD [BEq α] [EquivBEq α] {l : List ((a : α) × β a)} {a fallback : α}
+    (h : containsKey a l = true) :
+    getKey? a l = some (getKeyD a l fallback) := by
+  rw [getKey?_eq_some_getKey h, getKey_eq_getKeyD]
+
+/-- Internal implementation detail of the hash map -/
+def getKey! [BEq α] [Inhabited α] (a : α) (l : List ((a : α) × β a)) : α :=
+  (getKey? a l).get!
+
+@[simp]
+theorem getKey!_nil [BEq α] [Inhabited α] {a : α} :
+    getKey! a ([] : List ((a : α) × β a)) = default := rfl
+
+theorem getKey!_eq_getKey? [BEq α] [Inhabited α] {l : List ((a : α) × β a)} {a : α} :
+    getKey! a l = (getKey? a l).get! := rfl
+
+theorem getKey!_eq_default [BEq α] [Inhabited α] {l : List ((a : α) × β a)} {a : α}
+    (h : containsKey a l = false) : getKey! a l = default := by
+  rw [containsKey_eq_isSome_getKey?, Bool.eq_false_iff, ne_eq,
+    Option.not_isSome_iff_eq_none] at h
+  rw [getKey!_eq_getKey?, h, Option.get!_none]
+
+theorem getKey_eq_getKey! [BEq α] [Inhabited α] {l : List ((a : α) × β a)} {a : α}
+    (h : containsKey a l = true) : getKey a l h = getKey! a l := by
+  rw [getKey!_eq_getKey?, getKey, Option.get_eq_get!]
+
+theorem getKey?_eq_some_getKey! [BEq α] [Inhabited α] {l : List ((a : α) × β a)} {a : α}
+    (h : containsKey a l = true) :
+    getKey? a l = some (getKey! a l) := by
+  rw [getKey?_eq_some_getKey h, getKey_eq_getKey!]
+
+theorem getKey!_eq_getKeyD_default [BEq α] [EquivBEq α] [Inhabited α] {l : List ((a : α) × β a)}
+    {a : α} : getKey! a l = getKeyD a l default := rfl
+
 /-- Internal implementation detail of the hash map -/
 def replaceEntry [BEq α] (k : α) (v : β k) : List ((a : α) × β a) → List ((a : α) × β a)
   | [] => []
@@ -643,6 +748,18 @@ theorem getValueCast?_replaceEntry [BEq α] [LawfulBEq α] {l : List ((a : α)
     · rw [Option.dmap_congr (getEntry?_replaceEntry_of_false (Bool.eq_false_iff.2 h)),
         getValueCast?_eq_getEntry?]
 
+theorem getKey?_replaceEntry [BEq α] [PartialEquivBEq α] {l : List ((a : α) × β a)} {a k : α}
+    {v : β k} : getKey? a (replaceEntry k v l) =
+      if containsKey k l ∧ k == a then some k else getKey? a l := by
+  rw [getKey?_eq_getEntry?]
+  split
+  · next h => simp [getEntry?_replaceEntry_of_true h.1 h.2]
+  · next h =>
+    simp only [Decidable.not_and_iff_or_not_not] at h
+    rcases h with h|h
+    · rw [getEntry?_replaceEntry_of_containsKey_eq_false (Bool.eq_false_iff.2 h), getKey?_eq_getEntry?]
+    · rw [getEntry?_replaceEntry_of_false (Bool.eq_false_iff.2 h), getKey?_eq_getEntry?]
+
 @[simp]
 theorem containsKey_replaceEntry [BEq α] [PartialEquivBEq α] {l : List ((a : α) × β a)} {a k : α}
     {v : β k} : containsKey a (replaceEntry k v l) = containsKey a l := by
@@ -974,6 +1091,39 @@ theorem getValueD_insertEntry_self {β : Type v} [BEq α] [EquivBEq α] {l : Lis
     {k : α} {fallback v : β} : getValueD k (insertEntry k v l) fallback = v := by
   simp [getValueD_insertEntry, BEq.refl]
 
+theorem getKey?_insertEntry [BEq α] [PartialEquivBEq α] {l : List ((a : α) × β a)} {k a : α}
+    {v : β k} : getKey? a (insertEntry k v l) = if k == a then some k else getKey? a l := by
+  cases hl : containsKey k l
+  · simp [insertEntry_of_containsKey_eq_false hl]
+  · rw [insertEntry_of_containsKey hl, getKey?_replaceEntry, hl]
+    split <;> simp_all
+
+theorem getKey?_insertEntry_self [BEq α] [EquivBEq α] {l : List ((a : α) × β a)} {k : α}
+    {v : β k} : getKey? k (insertEntry k v l) = some k := by
+  simp [getKey?_insertEntry]
+
+theorem getKey?_eq_none [BEq α] [PartialEquivBEq α] {l : List ((a : α) × β a)} {a : α}
+    (h : containsKey a l = false) : getKey? a l = none := by
+  rwa [← Option.not_isSome_iff_eq_none, ← containsKey_eq_isSome_getKey?, Bool.not_eq_true]
+
+theorem getKey!_insertEntry [BEq α] [EquivBEq α] [Inhabited α]  {l : List ((a : α) × β a)}
+    {k a : α} {v : β k} : getKey! a (insertEntry k v l) =
+      if k == a then k else getKey! a l := by
+  simp [getKey!_eq_getKey?, getKey?_insertEntry, apply_ite Option.get!]
+
+theorem getKey!_insertEntry_self [BEq α] [EquivBEq α] [Inhabited α] {l : List ((a : α) × β a)}
+    {k : α} {v : β k} : getKey! k (insertEntry k v l) = k := by
+  rw [getKey!_insertEntry, if_pos BEq.refl]
+
+theorem getKeyD_insertEntry [BEq α] [EquivBEq α] {l : List ((a : α) × β a)} {k a fallback : α}
+    {v : β k} : getKeyD a (insertEntry k v l) fallback =
+      if k == a then k else getKeyD a l fallback := by
+  simp [getKeyD_eq_getKey?, getKey?_insertEntry, apply_ite (fun x => Option.getD x fallback)]
+
+theorem getKeyD_insertEntry_self [BEq α] [EquivBEq α] {l : List ((a : α) × β a)} {k fallback : α}
+    {v : β k} : getKeyD k (insertEntry k v l) fallback = k := by
+  rw [getKeyD_insertEntry, if_pos BEq.refl]
+
 @[local simp]
 theorem containsKey_insertEntry [BEq α] [PartialEquivBEq α] {l : List ((a : α) × β a)} {k a : α}
     {v : β k} : containsKey a (insertEntry k v l) = ((k == a) || containsKey a l) := by
@@ -1017,6 +1167,17 @@ theorem getValue_insertEntry_self {β : Type v} [BEq α] [EquivBEq α] {l : List
     {v : β} : getValue k (insertEntry k v l) containsKey_insertEntry_self = v := by
   simp [getValue_insertEntry]
 
+theorem getKey_insertEntry [BEq α] [EquivBEq α] {l : List ((a : α) × β a)} {k a : α}
+    {v : β k} {h} : getKey a (insertEntry k v l) h =
+    if h' : k == a then k
+    else getKey a l (containsKey_of_containsKey_insertEntry h (Bool.eq_false_iff.2 h')) := by
+  rw [← Option.some_inj, ← getKey?_eq_some_getKey, apply_dite Option.some, getKey?_insertEntry]
+  simp only [← getKey?_eq_some_getKey, dite_eq_ite]
+
+theorem getKey_insertEntry_self [BEq α] [EquivBEq α] {l : List ((a : α) × β a)} {k : α}
+    {v : β k} : getKey k (insertEntry k v l) containsKey_insertEntry_self = k := by
+  simp [getKey_insertEntry]
+
 /-- Internal implementation detail of the hash map -/
 def insertEntryIfNew [BEq α] (k : α) (v : β k) (l : List ((a : α) × β a)) : List ((a : α) × β a) :=
   bif containsKey k l then l else ⟨k, v⟩ :: l
@@ -1135,6 +1296,32 @@ theorem getValueD_insertEntryIfNew {β : Type v} [BEq α] [PartialEquivBEq α] {
   simp [getValueD_eq_getValue?, getValue?_insertEntryIfNew,
     apply_ite (fun x => Option.getD x fallback)]
 
+theorem getKey?_insertEntryIfNew [BEq α] [PartialEquivBEq α] {l : List ((a : α) × β a)} {k a : α}
+    {v : β k} : getKey? a (insertEntryIfNew k v l) =
+      if k == a ∧ containsKey k l = false then some k else getKey? a l := by
+  cases h : containsKey k l
+  · rw [insertEntryIfNew_of_containsKey_eq_false h]
+    split <;> simp_all
+  · simp [insertEntryIfNew_of_containsKey h]
+
+theorem getKey_insertEntryIfNew [BEq α] [PartialEquivBEq α] {l : List ((a : α) × β a)}
+    {k a : α} {v : β k} {h} : getKey a (insertEntryIfNew k v l) h =
+    if h' : k == a ∧ containsKey k l = false then k
+    else getKey a l (containsKey_of_containsKey_insertEntryIfNew' h h') := by
+  rw [← Option.some_inj, ← getKey?_eq_some_getKey, apply_dite Option.some,
+    getKey?_insertEntryIfNew, ← dite_eq_ite]
+  simp [← getKey?_eq_some_getKey]
+
+theorem getKey!_insertEntryIfNew [BEq α] [PartialEquivBEq α] [Inhabited α]
+    {l : List ((a : α) × β a)} {k a : α} {v : β k} : getKey! a (insertEntryIfNew k v l) =
+      if k == a ∧ containsKey k l = false then k else getKey! a l := by
+  simp [getKey!_eq_getKey?, getKey?_insertEntryIfNew, apply_ite Option.get!]
+
+theorem getKeyD_insertEntryIfNew [BEq α] [PartialEquivBEq α] {l : List ((a : α) × β a)}
+    {k a fallback : α} {v : β k} : getKeyD a (insertEntryIfNew k v l) fallback =
+      if k == a ∧ containsKey k l = false then k else getKeyD a l fallback := by
+  simp [getKeyD_eq_getKey?, getKey?_insertEntryIfNew, apply_ite (fun x => Option.getD x fallback)]
+
 theorem length_insertEntryIfNew [BEq α] {l : List ((a : α) × β a)} {k : α} {v : β k} :
     (insertEntryIfNew k v l).length = if containsKey k l then l.length else l.length + 1 := by
   simp [insertEntryIfNew, Bool.apply_cond List.length]
@@ -1253,6 +1440,36 @@ theorem getValue?_eraseKey [BEq α] [PartialEquivBEq α] {l : List ((_ : α) ×
 
 end
 
+theorem getKey?_eraseKey [BEq α] [PartialEquivBEq α] {l : List ((a : α) × β a)} {k a : α}
+    (hl : DistinctKeys l) :
+    getKey? a (eraseKey k l) = if k == a then none else getKey? a l := by
+  rw [getKey?_eq_getEntry?, getEntry?_eraseKey hl]
+  by_cases h : k == a
+  . simp [h]
+  . simp [h, getKey?_eq_getEntry?]
+
+theorem getKey?_eraseKey_self [BEq α] [PartialEquivBEq α] {l : List ((a : α) × β a)} {k : α}
+    (hl : DistinctKeys l) : getKey? k (eraseKey k l) = none := by
+  simp [getKey?_eq_getEntry?, getEntry?_eraseKey_self hl]
+
+theorem getKey!_eraseKey [BEq α] [PartialEquivBEq α] [Inhabited α] {l : List ((a : α) × β a)}
+    {k a : α} (hl : DistinctKeys l) :
+    getKey! a (eraseKey k l) = if k == a then default else getKey! a l := by
+  simp [getKey!_eq_getKey?, getKey?_eraseKey hl, apply_ite Option.get!]
+
+theorem getKey!_eraseKey_self [BEq α] [PartialEquivBEq α] [Inhabited α]  {l : List ((a : α) × β a)}
+    {k : α} (hl : DistinctKeys l) : getKey! k (eraseKey k l) = default := by
+  simp [getKey!_eq_getKey?, getKey?_eraseKey_self hl]
+
+theorem getKeyD_eraseKey [BEq α] [PartialEquivBEq α] {l : List ((a : α) × β a)} {k a fallback : α}
+    (hl : DistinctKeys l) :
+    getKeyD a (eraseKey k l) fallback = if k == a then fallback else getKeyD a l fallback := by
+  simp [getKeyD_eq_getKey?, getKey?_eraseKey hl, apply_ite (fun x => Option.getD x fallback)]
+
+theorem getKeyD_eraseKey_self [BEq α] [PartialEquivBEq α] {l : List ((a : α) × β a)}
+    {k fallback : α} (hl : DistinctKeys l) : getKeyD k (eraseKey k l) fallback = fallback := by
+  simp [getKeyD_eq_getKey?, getKey?_eraseKey_self hl]
+
 theorem containsKey_eraseKey_self [BEq α] [PartialEquivBEq α] {l : List ((a : α) × β a)} {k : α}
     (h : DistinctKeys l) : containsKey k (eraseKey k l) = false := by
   simp [containsKey_eq_isSome_getEntry?, getEntry?_eraseKey_self h]
@@ -1340,6 +1557,13 @@ theorem getValue_eraseKey {β : Type v} [BEq α] [PartialEquivBEq α] {l : List
   rw [← Option.some_inj, ← getValue?_eq_some_getValue, getValue?_eraseKey hl, h.1]
   simp [← getValue?_eq_some_getValue]
 
+theorem getKey_eraseKey [BEq α] [EquivBEq α] {l : List ((a : α) × β a)} {k a : α} {h}
+    (hl : DistinctKeys l) : getKey a (eraseKey k l) h =
+      getKey a l (containsKey_of_containsKey_eraseKey hl h) := by
+  rw [containsKey_eraseKey hl, Bool.and_eq_true, Bool.not_eq_true'] at h
+  rw [← Option.some_inj, ← getKey?_eq_some_getKey, getKey?_eraseKey hl, h.1]
+  simp [← getKey?_eq_some_getKey]
+
 theorem getEntry?_of_perm [BEq α] [PartialEquivBEq α] {l l' : List ((a : α) × β a)} {a : α}
     (hl : DistinctKeys l) (h : Perm l l') : getEntry? a l = getEntry? a l' := by
   induction h
@@ -1412,6 +1636,26 @@ theorem getValueD_of_perm [BEq α] [PartialEquivBEq α] {l l' : List ((_ : α)
 
 end
 
+theorem getKey?_of_perm [BEq α] [PartialEquivBEq α] {l l' : List ((a : α) × β a)} {a : α}
+    (hl : DistinctKeys l) (h : Perm l l') : getKey? a l = getKey? a l' := by
+  rw [getKey?_eq_getEntry?, getKey?_eq_getEntry?, getEntry?_of_perm hl h]
+
+theorem getKey_of_perm [BEq α] [PartialEquivBEq α] {l l' : List ((a : α) × β a)} {a : α} {h'}
+    (hl : DistinctKeys l) (h : Perm l l') :
+    getKey a l h' = getKey a l' ((containsKey_of_perm h).symm.trans h') := by
+  rw [← Option.some_inj, ← getKey?_eq_some_getKey, ← getKey?_eq_some_getKey,
+    getKey?_of_perm hl h]
+
+theorem getKey!_of_perm [BEq α] [PartialEquivBEq α] [Inhabited α] {l l' : List ((a : α) × β a)}
+    {a : α} (hl : DistinctKeys l) (h : Perm l l') :
+    getKey! a l = getKey! a l' := by
+  simp only [getKey!_eq_getKey?, getKey?_of_perm hl h]
+
+theorem getKeyD_of_perm [BEq α] [PartialEquivBEq α] {l l' : List ((a : α) × β a)} {a fallback : α}
+    (hl : DistinctKeys l) (h : Perm l l') :
+    getKeyD a l fallback = getKeyD a l' fallback := by
+  simp only [getKeyD_eq_getKey?, getKey?_of_perm hl h]
+
 theorem perm_cons_getEntry [BEq α] {l : List ((a : α) × β a)} {a : α} (h : containsKey a l) :
     ∃ l', Perm l (getEntry a l h :: l') := by
   induction l using assoc_induction
@@ -1521,6 +1765,18 @@ theorem getValueCast_append_of_containsKey_eq_false [BEq α] [LawfulBEq α]
   rw [← Option.some_inj, ← getValueCast?_eq_some_getValueCast, ← getValueCast?_eq_some_getValueCast,
     getValueCast?_append_of_containsKey_eq_false hl']
 
+theorem getKey?_append_of_containsKey_eq_false [BEq α] [PartialEquivBEq α]
+    {l l' : List ((a : α) × β a)} {a : α} (hl' : containsKey a l' = false) :
+    getKey? a (l ++ l') = getKey? a l := by
+  simp [getKey?_eq_getEntry?, getEntry?_eq_none.2 hl']
+
+theorem getKey_append_of_containsKey_eq_false [BEq α] [PartialEquivBEq α]
+    {l l' : List ((a : α) × β a)} {a : α} {h} (hl' : containsKey a l' = false) :
+    getKey a (l ++ l') h =
+      getKey a l ((containsKey_append_of_not_contains_right hl').symm.trans h) := by
+  rw [← Option.some_inj, ← getKey?_eq_some_getKey, ← getKey?_eq_some_getKey,
+    getKey?_append_of_containsKey_eq_false hl']
+
 theorem replaceEntry_append_of_containsKey_left [BEq α] {l l' : List ((a : α) × β a)} {k : α}
     {v : β k} (h : containsKey k l) : replaceEntry k v (l ++ l') = replaceEntry k v l ++ l' := by
   induction l using assoc_induction

src/Std/Data/DHashMap/Internal/Model.lean

@@ -262,6 +262,10 @@ def consₘ [BEq α] [Hashable α] (m : Raw₀ α β) (a : α) (b : β a) : Raw
 def get?ₘ [BEq α] [LawfulBEq α] [Hashable α] (m : Raw₀ α β) (a : α) : Option (β a) :=
   (bucket m.1.buckets m.2 a).getCast? a
 
+/-- Internal implementation detail of the hash map -/
+def getKey?ₘ [BEq α] [Hashable α] (m : Raw₀ α β) (a : α) : Option α :=
+  (bucket m.1.buckets m.2 a).getKey? a
+
 /-- Internal implementation detail of the hash map -/
 def containsₘ [BEq α] [Hashable α] (m : Raw₀ α β) (a : α) : Bool :=
   (bucket m.1.buckets m.2 a).contains a
@@ -278,6 +282,18 @@ def getDₘ [BEq α] [LawfulBEq α] [Hashable α] (m : Raw₀ α β) (a : α) (f
 def get!ₘ [BEq α] [LawfulBEq α] [Hashable α] (m : Raw₀ α β) (a : α) [Inhabited (β a)] : β a :=
   (m.get?ₘ a).get!
 
+/-- Internal implementation detail of the hash map -/
+def getKeyₘ [BEq α] [Hashable α] (m : Raw₀ α β) (a : α) (h : m.containsₘ a) : α :=
+  (bucket m.1.buckets m.2 a).getKey a h
+
+/-- Internal implementation detail of the hash map -/
+def getKeyDₘ [BEq α] [Hashable α] (m : Raw₀ α β) (a : α) (fallback : α) : α :=
+  (m.getKey?ₘ a).getD fallback
+
+/-- Internal implementation detail of the hash map -/
+def getKey!ₘ [BEq α] [Hashable α] [Inhabited α] (m : Raw₀ α β) (a : α) : α :=
+  (m.getKey?ₘ a).get!
+
 /-- Internal implementation detail of the hash map -/
 def insertₘ [BEq α] [Hashable α] (m : Raw₀ α β) (a : α) (b : β a) : Raw₀ α β :=
   if m.containsₘ a then m.replaceₘ a b else Raw₀.expandIfNecessary (m.consₘ a b)
@@ -348,6 +364,20 @@ theorem get!_eq_get!ₘ [BEq α] [LawfulBEq α] [Hashable α] (m : Raw₀ α β)
     get! m a = get!ₘ m a := by
   simp [get!, get!ₘ, get?ₘ, List.getValueCast!_eq_getValueCast?, bucket]
 
+theorem getKey?_eq_getKey?ₘ [BEq α] [Hashable α] (m : Raw₀ α β) (a : α) :
+    getKey? m a = getKey?ₘ m a := rfl
+
+theorem getKey_eq_getKeyₘ [BEq α] [Hashable α] (m : Raw₀ α β) (a : α) (h : m.contains a) :
+    getKey m a h = getKeyₘ m a h := rfl
+
+theorem getKeyD_eq_getKeyDₘ [BEq α] [Hashable α] (m : Raw₀ α β) (a fallback : α) :
+    getKeyD m a fallback = getKeyDₘ m a fallback := by
+  simp [getKeyD, getKeyDₘ, getKey?ₘ, List.getKeyD_eq_getKey?, bucket]
+
+theorem getKey!_eq_getKey!ₘ [BEq α] [Hashable α] [Inhabited α] (m : Raw₀ α β) (a : α) :
+    getKey! m a = getKey!ₘ m a := by
+  simp [getKey!, getKey!ₘ, getKey?ₘ, List.getKey!_eq_getKey?, bucket]
+
 theorem contains_eq_containsₘ [BEq α] [Hashable α] (m : Raw₀ α β) (a : α) :
     m.contains a = m.containsₘ a := rfl
 

src/Std/Data/DHashMap/Internal/Raw.lean

@@ -135,6 +135,37 @@ theorem get!_val [BEq α] [Hashable α] [LawfulBEq α] {m : Raw₀ α β} {a :
     m.val.get! a = m.get! a := by
   simp [Raw.get!, m.2]
 
+theorem getKey?_eq [BEq α] [Hashable α] {m : Raw α β} (h : m.WF) {a : α} :
+    m.getKey? a = Raw₀.getKey? ⟨m, h.size_buckets_pos⟩ a := by
+  simp [Raw.getKey?, h.size_buckets_pos]
+
+theorem getKey?_val [BEq α] [Hashable α] {m : Raw₀ α β} {a : α} :
+    m.val.getKey? a = m.getKey? a := by
+  simp [Raw.getKey?, m.2]
+
+theorem getKey_eq [BEq α] [Hashable α] {m : Raw α β} {a : α} {h : a ∈ m} :
+    m.getKey a h = Raw₀.getKey ⟨m, by change dite .. = true at h; split at h <;> simp_all⟩ a
+      (by change dite .. = true at h; split at h <;> simp_all) := rfl
+
+theorem getKey_val [BEq α] [Hashable α] {m : Raw₀ α β} {a : α} {h : a ∈ m.val}  :
+    m.val.getKey a h = m.getKey a (contains_val (m := m) ▸ h) := rfl
+
+theorem getKeyD_eq [BEq α] [Hashable α] {m : Raw α β} (h : m.WF) {a fallback : α} :
+    m.getKeyD a fallback = Raw₀.getKeyD ⟨m, h.size_buckets_pos⟩ a fallback := by
+  simp [Raw.getKeyD, h.size_buckets_pos]
+
+theorem getKeyD_val [BEq α] [Hashable α] {m : Raw₀ α β} {a fallback : α} :
+    m.val.getKeyD a fallback = m.getKeyD a fallback := by
+  simp [Raw.getKeyD, m.2]
+
+theorem getKey!_eq [BEq α] [Hashable α] [Inhabited α] {m : Raw α β} (h : m.WF) {a : α} :
+    m.getKey! a = Raw₀.getKey! ⟨m, h.size_buckets_pos⟩ a := by
+  simp [Raw.getKey!, h.size_buckets_pos]
+
+theorem getKey!_val [BEq α] [Hashable α] [Inhabited α] {m : Raw₀ α β} {a : α} :
+    m.val.getKey! a = m.getKey! a := by
+  simp [Raw.getKey!, m.2]
+
 theorem erase_eq [BEq α] [Hashable α] {m : Raw α β} (h : m.WF) {a : α} :
     m.erase a = Raw₀.erase ⟨m, h.size_buckets_pos⟩ a := by
   simp [Raw.erase, h.size_buckets_pos]

src/Std/Data/DHashMap/Internal/RawLemmas.lean

@@ -83,7 +83,8 @@ private def queryNames : Array Name :=
   #[``contains_eq_containsKey, ``Raw.isEmpty_eq_isEmpty, ``Raw.size_eq_length,
     ``get?_eq_getValueCast?, ``Const.get?_eq_getValue?, ``get_eq_getValueCast,
     ``Const.get_eq_getValue, ``get!_eq_getValueCast!, ``getD_eq_getValueCastD,
-    ``Const.get!_eq_getValue!, ``Const.getD_eq_getValueD]
+    ``Const.get!_eq_getValue!, ``Const.getD_eq_getValueD, ``getKey?_eq_getKey?,
+    ``getKey_eq_getKey, ``getKeyD_eq_getKeyD, ``getKey!_eq_getKey!]
 
 private def modifyNames : Array Name :=
   #[``toListModel_insert, ``toListModel_erase, ``toListModel_insertIfNew]
@@ -93,7 +94,8 @@ private def congrNames : MacroM (Array (TSyntax `term)) := do
     ← `(_root_.List.Perm.length_eq), ← `(getValueCast?_of_perm _),
     ← `(getValue?_of_perm _), ← `(getValue_of_perm _), ← `(getValueCast_of_perm _),
     ← `(getValueCast!_of_perm _), ← `(getValueCastD_of_perm _), ← `(getValue!_of_perm _),
-    ← `(getValueD_of_perm _) ]
+    ← `(getValueD_of_perm _), ← `(getKey?_of_perm _), ← `(getKey_of_perm _), ← `(getKeyD_of_perm _),
+    ← `(getKey!_of_perm _)]
 
 /-- Internal implementation detail of the hash map -/
 scoped syntax "simp_to_model" ("using" term)? : tactic
@@ -535,6 +537,147 @@ theorem getD_congr [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {a b : α} {fa
 
 end Const
 
+@[simp]
+theorem getKey?_empty {a : α} {c} : (empty c : Raw₀ α β).getKey? a = none := by
+  simp [getKey?]
+
+theorem getKey?_of_isEmpty [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {a : α} :
+    m.1.isEmpty = true → m.getKey? a = none := by
+  simp_to_model; empty
+
+theorem getKey?_insert [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {a k : α} {v : β k} :
+    (m.insert k v).getKey? a = if k == a then some k else m.getKey? a := by
+  simp_to_model using List.getKey?_insertEntry
+
+theorem getKey?_insert_self [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {k : α} {v : β k} :
+    (m.insert k v).getKey? k = some k := by
+  simp_to_model using List.getKey?_insertEntry_self
+
+theorem contains_eq_isSome_getKey? [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {a : α} :
+    m.contains a = (m.getKey? a).isSome := by
+  simp_to_model using List.containsKey_eq_isSome_getKey?
+
+theorem getKey?_eq_none [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {a : α} :
+    m.contains a = false → m.getKey? a = none := by
+  simp_to_model using List.getKey?_eq_none
+
+theorem getKey?_erase [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {k a : α} :
+    (m.erase k).getKey? a = if k == a then none else m.getKey? a := by
+  simp_to_model using List.getKey?_eraseKey
+
+theorem getKey?_erase_self [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {k : α} :
+    (m.erase k).getKey? k = none := by
+  simp_to_model using List.getKey?_eraseKey_self
+
+theorem getKey_insert [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {k a : α} {v : β k} {h₁} :
+    (m.insert k v).getKey a h₁ =
+      if h₂ : k == a then
+        k
+      else
+        m.getKey a (contains_of_contains_insert _ h h₁ (Bool.eq_false_iff.2 h₂)) := by
+  simp_to_model using List.getKey_insertEntry
+
+theorem getKey_insert_self [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {k : α} {v : β k} :
+    (m.insert k v).getKey k (contains_insert_self _ h) = k := by
+  simp_to_model using List.getKey_insertEntry_self
+
+@[simp]
+theorem getKey_erase [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {k a : α} {h'} :
+    (m.erase k).getKey a h' = m.getKey a (contains_of_contains_erase _ h h') := by
+  simp_to_model using List.getKey_eraseKey
+
+theorem getKey?_eq_some_getKey [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {a : α} {h} :
+    m.getKey? a = some (m.getKey a h) := by
+  simp_to_model using List.getKey?_eq_some_getKey
+
+theorem getKey!_empty {a : α} [Inhabited α] {c} :
+    (empty c : Raw₀ α β).getKey! a = default := by
+  simp [getKey!, empty]
+
+theorem getKey!_of_isEmpty [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.1.WF) {a : α} :
+    m.1.isEmpty = true → m.getKey! a = default := by
+  simp_to_model; empty;
+
+theorem getKey!_insert [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.1.WF) {k a : α}
+    {v : β k} :
+    (m.insert k v).getKey! a = if k == a then k else m.getKey! a := by
+  simp_to_model using List.getKey!_insertEntry
+
+theorem getKey!_insert_self [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.1.WF) {a : α}
+    {b : β a} : (m.insert a b).getKey! a = a := by
+  simp_to_model using List.getKey!_insertEntry_self
+
+theorem getKey!_eq_default [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.1.WF) {a : α} :
+    m.contains a = false → m.getKey! a = default := by
+  simp_to_model using List.getKey!_eq_default
+
+theorem getKey!_erase [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.1.WF) {k a : α} :
+    (m.erase k).getKey! a = if k == a then default else m.getKey! a := by
+  simp_to_model using List.getKey!_eraseKey
+
+theorem getKey!_erase_self [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.1.WF) {k : α} :
+    (m.erase k).getKey! k = default := by
+  simp_to_model using List.getKey!_eraseKey_self
+
+theorem getKey?_eq_some_getKey! [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.1.WF) {a : α} :
+    m.contains a = true → m.getKey? a = some (m.getKey! a) := by
+  simp_to_model using List.getKey?_eq_some_getKey!
+
+theorem getKey!_eq_get!_getKey? [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.1.WF) {a : α} :
+    m.getKey! a = (m.getKey? a).get! := by
+  simp_to_model using List.getKey!_eq_getKey?
+
+theorem getKey_eq_getKey! [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.1.WF) {a : α} {h} :
+    m.getKey a h = m.getKey! a := by
+  simp_to_model using List.getKey_eq_getKey!
+
+theorem getKeyD_empty {a : α} {fallback : α} {c} :
+    (empty c : Raw₀ α β).getKeyD a fallback = fallback := by
+  simp [getKeyD, empty]
+
+theorem getKeyD_of_isEmpty [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {a fallback : α} :
+    m.1.isEmpty = true → m.getKeyD a fallback = fallback := by
+  simp_to_model; empty
+
+theorem getKeyD_insert [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {k a fallback : α} {v : β k} :
+    (m.insert k v).getKeyD a fallback =
+      if k == a then k else m.getKeyD a fallback := by
+  simp_to_model using List.getKeyD_insertEntry
+
+theorem getKeyD_insert_self [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {a fallback : α}
+    {b : β a} :
+    (m.insert a b).getKeyD a fallback = a := by
+  simp_to_model using List.getKeyD_insertEntry_self
+
+theorem getKeyD_eq_fallback [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {a fallback : α} :
+    m.contains a = false → m.getKeyD a fallback = fallback := by
+  simp_to_model using List.getKeyD_eq_fallback
+
+theorem getKeyD_erase [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {k a fallback : α} :
+    (m.erase k).getKeyD a fallback = if k == a then fallback else m.getKeyD a fallback := by
+  simp_to_model using List.getKeyD_eraseKey
+
+theorem getKeyD_erase_self [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {k fallback : α} :
+    (m.erase k).getKeyD k fallback = fallback := by
+  simp_to_model using List.getKeyD_eraseKey_self
+
+theorem getKey?_eq_some_getKeyD [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {a fallback : α} :
+    m.contains a = true → m.getKey? a = some (m.getKeyD a fallback) := by
+  simp_to_model using List.getKey?_eq_some_getKeyD
+
+theorem getKeyD_eq_getD_getKey? [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {a fallback : α} :
+    m.getKeyD a fallback = (m.getKey? a).getD fallback := by
+  simp_to_model using List.getKeyD_eq_getKey?
+
+theorem getKey_eq_getKeyD [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {a fallback : α} {h} :
+    m.getKey a h = m.getKeyD a fallback := by
+  simp_to_model using List.getKey_eq_getKeyD
+
+theorem getKey!_eq_getKeyD_default [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.1.WF)
+    {a : α} :
+    m.getKey! a = m.getKeyD a default := by
+  simp_to_model using List.getKey!_eq_getKeyD_default
+
 theorem isEmpty_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {k : α} {v : β k} :
     (m.insertIfNew k v).1.isEmpty = false := by
   simp_to_model using List.isEmpty_insertEntryIfNew
@@ -620,6 +763,29 @@ theorem getD_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {k a :
 
 end Const
 
+theorem getKey?_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {k a : α} {v : β k} :
+    (m.insertIfNew k v).getKey? a =
+      if k == a ∧ m.contains k = false then some k else m.getKey? a := by
+  simp_to_model using List.getKey?_insertEntryIfNew
+
+theorem getKey_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {k a : α} {v : β k} {h₁} :
+    (m.insertIfNew k v).getKey a h₁ =
+      if h₂ : k == a ∧ m.contains k = false then k
+      else m.getKey a (contains_of_contains_insertIfNew' _ h h₁ h₂) := by
+  simp_to_model using List.getKey_insertEntryIfNew
+
+theorem getKey!_insertIfNew [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.1.WF) {k a : α}
+    {v : β k} :
+    (m.insertIfNew k v).getKey! a =
+      if k == a ∧ m.contains k = false then k else m.getKey! a := by
+  simp_to_model using List.getKey!_insertEntryIfNew
+
+theorem getKeyD_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.1.WF) {k a fallback : α}
+    {v : β k} :
+    (m.insertIfNew k v).getKeyD a fallback =
+      if k == a ∧ m.contains k = false then k else m.getKeyD a fallback := by
+  simp_to_model using List.getKeyD_insertEntryIfNew
+
 @[simp]
 theorem getThenInsertIfNew?_fst [LawfulBEq α] {k : α} {v : β k} :
     (m.getThenInsertIfNew? k v).1 = m.get? k := by

src/Std/Data/DHashMap/Internal/WF.lean

@@ -233,6 +233,47 @@ theorem getD_eq_getValueCastD [BEq α] [Hashable α] [LawfulBEq α] {m : Raw₀
     m.getD a fallback = getValueCastD a (toListModel m.1.buckets) fallback := by
   rw [getD_eq_getDₘ, getDₘ_eq_getValueCastD hm]
 
+theorem getKey?ₘ_eq_getKey? [BEq α] [Hashable α] [EquivBEq α] [LawfulHashable α] {m : Raw₀ α β}
+    (hm : Raw.WFImp m.1) {a : α} :
+    m.getKey?ₘ a = List.getKey? a (toListModel m.1.buckets) :=
+  apply_bucket hm AssocList.getKey?_eq List.getKey?_of_perm List.getKey?_append_of_containsKey_eq_false
+
+theorem getKey?_eq_getKey? [BEq α] [Hashable α] [EquivBEq α] [LawfulHashable α] {m : Raw₀ α β}
+    (hm : Raw.WFImp m.1) {a : α} :
+    m.getKey? a = List.getKey? a (toListModel m.1.buckets) := by
+  rw [getKey?_eq_getKey?ₘ, getKey?ₘ_eq_getKey? hm]
+
+theorem getKeyₘ_eq_getKey [BEq α] [Hashable α] [EquivBEq α] [LawfulHashable α] {m : Raw₀ α β}
+    (hm : Raw.WFImp m.1) {a : α} {h : m.contains a} :
+    m.getKeyₘ a h = List.getKey a (toListModel m.1.buckets) (contains_eq_containsKey hm ▸ h) :=
+  apply_bucket_with_proof hm a AssocList.getKey List.getKey AssocList.getKey_eq
+    List.getKey_of_perm List.getKey_append_of_containsKey_eq_false
+
+theorem getKey_eq_getKey [BEq α] [Hashable α] [EquivBEq α] [LawfulHashable α] {m : Raw₀ α β}
+    (hm : Raw.WFImp m.1) {a : α} {h : m.contains a} :
+    m.getKey a h = List.getKey a (toListModel m.1.buckets) (contains_eq_containsKey hm ▸ h) := by
+  rw [getKey_eq_getKeyₘ, getKeyₘ_eq_getKey hm]
+
+theorem getKey!ₘ_eq_getKey! [BEq α] [Hashable α] [EquivBEq α] [LawfulHashable α] [Inhabited α]
+    {m : Raw₀ α β} (hm : Raw.WFImp m.1) {a : α} :
+    m.getKey!ₘ a = List.getKey! a (toListModel m.1.buckets) := by
+  rw [getKey!ₘ, getKey?ₘ_eq_getKey? hm, List.getKey!_eq_getKey?]
+
+theorem getKey!_eq_getKey! [BEq α] [Hashable α] [EquivBEq α] [LawfulHashable α] [Inhabited α]
+    {m : Raw₀ α β} (hm : Raw.WFImp m.1) {a : α} :
+    m.getKey! a = List.getKey! a (toListModel m.1.buckets) := by
+  rw [getKey!_eq_getKey!ₘ, getKey!ₘ_eq_getKey! hm]
+
+theorem getKeyDₘ_eq_getKeyD [BEq α] [Hashable α] [EquivBEq α] [LawfulHashable α] {m : Raw₀ α β}
+    (hm : Raw.WFImp m.1) {a fallback : α} :
+    m.getKeyDₘ a fallback = List.getKeyD a (toListModel m.1.buckets) fallback := by
+  rw [getKeyDₘ, getKey?ₘ_eq_getKey? hm, List.getKeyD_eq_getKey?]
+
+theorem getKeyD_eq_getKeyD [BEq α] [Hashable α] [EquivBEq α] [LawfulHashable α] {m : Raw₀ α β}
+    (hm : Raw.WFImp m.1) {a fallback : α} :
+    m.getKeyD a fallback = List.getKeyD a (toListModel m.1.buckets) fallback := by
+  rw [getKeyD_eq_getKeyDₘ, getKeyDₘ_eq_getKeyD hm]
+
 section
 
 variable {β : Type v}

src/Std/Data/DHashMap/Lemmas.lean

@@ -599,6 +599,189 @@ theorem getD_congr [EquivBEq α] [LawfulHashable α] {a b : α} {fallback : β}
 
 end Const
 
+@[simp]
+theorem getKey?_empty {a : α} {c} : (empty c : DHashMap α β).getKey? a = none :=
+  Raw₀.getKey?_empty
+
+@[simp]
+theorem getKey?_emptyc {a : α} : (∅ : DHashMap α β).getKey? a = none :=
+  Raw₀.getKey?_empty
+
+theorem getKey?_of_isEmpty [EquivBEq α] [LawfulHashable α] {a : α} :
+    m.isEmpty = true → m.getKey? a = none :=
+  Raw₀.getKey?_of_isEmpty ⟨m.1, _⟩ m.2
+
+theorem getKey?_insert [EquivBEq α] [LawfulHashable α] {a k : α} {v : β k} :
+    (m.insert k v).getKey? a = if k == a then some k else m.getKey? a :=
+  Raw₀.getKey?_insert ⟨m.1, _⟩ m.2
+
+@[simp]
+theorem getKey?_insert_self [EquivBEq α] [LawfulHashable α] {k : α} {v : β k} :
+    (m.insert k v).getKey? k = some k :=
+  Raw₀.getKey?_insert_self ⟨m.1, _⟩ m.2
+
+theorem contains_eq_isSome_getKey? [EquivBEq α] [LawfulHashable α] {a : α} :
+    m.contains a = (m.getKey? a).isSome :=
+  Raw₀.contains_eq_isSome_getKey? ⟨m.1, _⟩ m.2
+
+theorem getKey?_eq_none_of_contains_eq_false [EquivBEq α] [LawfulHashable α] {a : α} :
+    m.contains a = false → m.getKey? a = none :=
+  Raw₀.getKey?_eq_none ⟨m.1, _⟩ m.2
+
+theorem getKey?_eq_none [EquivBEq α] [LawfulHashable α] {a : α} : ¬a ∈ m → m.getKey? a = none := by
+  simpa [mem_iff_contains] using getKey?_eq_none_of_contains_eq_false
+
+theorem getKey?_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
+    (m.erase k).getKey? a = if k == a then none else m.getKey? a :=
+  Raw₀.getKey?_erase ⟨m.1, _⟩ m.2
+
+@[simp]
+theorem getKey?_erase_self [EquivBEq α] [LawfulHashable α] {k : α} : (m.erase k).getKey? k = none :=
+  Raw₀.getKey?_erase_self ⟨m.1, _⟩ m.2
+
+theorem getKey_insert [EquivBEq α] [LawfulHashable α] {k a : α} {v : β k} {h₁} :
+    (m.insert k v).getKey a h₁ =
+      if h₂ : k == a then
+        k
+      else
+        m.getKey a (mem_of_mem_insert h₁ (Bool.eq_false_iff.2 h₂)) :=
+  Raw₀.getKey_insert ⟨m.1, _⟩ m.2
+
+@[simp]
+theorem getKey_insert_self [EquivBEq α] [LawfulHashable α] {k : α} {v : β k} :
+    (m.insert k v).getKey k mem_insert_self = k :=
+  Raw₀.getKey_insert_self ⟨m.1, _⟩ m.2
+
+@[simp]
+theorem getKey_erase [EquivBEq α] [LawfulHashable α] {k a : α} {h'} :
+    (m.erase k).getKey a h' = m.getKey a (mem_of_mem_erase h') :=
+  Raw₀.getKey_erase ⟨m.1, _⟩ m.2
+
+theorem getKey?_eq_some_getKey [EquivBEq α] [LawfulHashable α] {a : α}
+    {h} :
+    m.getKey? a = some (m.getKey a h) :=
+  Raw₀.getKey?_eq_some_getKey ⟨m.1, _⟩ m.2
+
+@[simp]
+theorem getKey!_empty [Inhabited α] {a : α} {c} :
+    (empty c : DHashMap α β).getKey! a = default :=
+  Raw₀.getKey!_empty
+
+@[simp]
+theorem getKey!_emptyc [Inhabited α] {a : α} :
+    (∅ : DHashMap α β).getKey! a = default :=
+  getKey!_empty
+
+theorem getKey!_of_isEmpty [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
+    m.isEmpty = true → m.getKey! a = default :=
+  Raw₀.getKey!_of_isEmpty ⟨m.1, _⟩ m.2
+
+theorem getKey!_insert [EquivBEq α] [LawfulHashable α] [Inhabited α] {k a : α} {v : β k} :
+    (m.insert k v).getKey! a =
+      if k == a then k else m.getKey! a :=
+  Raw₀.getKey!_insert ⟨m.1, _⟩ m.2
+
+@[simp]
+theorem getKey!_insert_self [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} {b : β a} :
+    (m.insert a b).getKey! a = a :=
+  Raw₀.getKey!_insert_self ⟨m.1, _⟩ m.2
+
+theorem getKey!_eq_default_of_contains_eq_false [EquivBEq α] [LawfulHashable α] [Inhabited α]
+    {a : α} :
+    m.contains a = false → m.getKey! a = default :=
+  Raw₀.getKey!_eq_default ⟨m.1, _⟩ m.2
+
+theorem getKey!_eq_default [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
+    ¬a ∈ m → m.getKey! a = default := by
+  simpa [mem_iff_contains] using getKey!_eq_default_of_contains_eq_false
+
+theorem getKey!_erase [EquivBEq α] [LawfulHashable α] [Inhabited α] {k a : α} :
+    (m.erase k).getKey! a = if k == a then default else m.getKey! a :=
+  Raw₀.getKey!_erase ⟨m.1, _⟩ m.2
+
+@[simp]
+theorem getKey!_erase_self [EquivBEq α] [LawfulHashable α] [Inhabited α] {k : α} :
+    (m.erase k).getKey! k = default :=
+  Raw₀.getKey!_erase_self ⟨m.1, _⟩ m.2
+
+theorem getKey?_eq_some_getKey!_of_contains [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
+    m.contains a = true → m.getKey? a = some (m.getKey! a) :=
+  Raw₀.getKey?_eq_some_getKey! ⟨m.1, _⟩ m.2
+
+theorem getKey?_eq_some_getKey! [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
+    a ∈ m → m.getKey? a = some (m.getKey! a) := by
+  simpa [mem_iff_contains] using getKey?_eq_some_getKey!_of_contains
+
+theorem getKey!_eq_get!_getKey? [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
+    m.getKey! a = (m.getKey? a).get! :=
+  Raw₀.getKey!_eq_get!_getKey? ⟨m.1, _⟩ m.2
+
+theorem getKey_eq_getKey! [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} {h} :
+    m.getKey a h = m.getKey! a :=
+  Raw₀.getKey_eq_getKey! ⟨m.1, _⟩ m.2
+
+@[simp]
+theorem getKeyD_empty {a fallback : α} {c} :
+    (empty c : DHashMap α β).getKeyD a fallback = fallback :=
+  Raw₀.getKeyD_empty
+
+@[simp]
+theorem getKeyD_emptyc {a fallback : α} :
+    (∅ : DHashMap α β).getKeyD a fallback = fallback :=
+  getKeyD_empty
+
+theorem getKeyD_of_isEmpty [EquivBEq α] [LawfulHashable α] {a fallback : α} :
+    m.isEmpty = true → m.getKeyD a fallback = fallback :=
+  Raw₀.getKeyD_of_isEmpty ⟨m.1, _⟩ m.2
+
+theorem getKeyD_insert [EquivBEq α] [LawfulHashable α] {k a fallback : α} {v : β k} :
+    (m.insert k v).getKeyD a fallback =
+      if k == a then k else m.getKeyD a fallback :=
+  Raw₀.getKeyD_insert ⟨m.1, _⟩ m.2
+
+@[simp]
+theorem getKeyD_insert_self [EquivBEq α] [LawfulHashable α] {k fallback : α} {v : β k} :
+    (m.insert k v).getKeyD k fallback = k :=
+  Raw₀.getKeyD_insert_self ⟨m.1, _⟩ m.2
+
+theorem getKeyD_eq_fallback_of_contains_eq_false [EquivBEq α] [LawfulHashable α] {a : α}
+    {fallback : α} :
+    m.contains a = false → m.getKeyD a fallback = fallback :=
+  Raw₀.getKeyD_eq_fallback ⟨m.1, _⟩ m.2
+
+theorem getKeyD_eq_fallback [EquivBEq α] [LawfulHashable α] {a fallback : α} :
+    ¬a ∈ m → m.getKeyD a fallback = fallback := by
+  simpa [mem_iff_contains] using getKeyD_eq_fallback_of_contains_eq_false
+
+theorem getKeyD_erase [EquivBEq α] [LawfulHashable α] {k a fallback : α} :
+    (m.erase k).getKeyD a fallback = if k == a then fallback else m.getKeyD a fallback :=
+  Raw₀.getKeyD_erase ⟨m.1, _⟩ m.2
+
+@[simp]
+theorem getKeyD_erase_self [EquivBEq α] [LawfulHashable α] {k fallback : α} :
+    (m.erase k).getKeyD k fallback = fallback :=
+  Raw₀.getKeyD_erase_self ⟨m.1, _⟩ m.2
+
+theorem getKey?_eq_some_getKeyD_of_contains [EquivBEq α] [LawfulHashable α] {a fallback : α} :
+    m.contains a = true → m.getKey? a = some (m.getKeyD a fallback) :=
+  Raw₀.getKey?_eq_some_getKeyD ⟨m.1, _⟩ m.2
+
+theorem getKey?_eq_some_getKeyD [EquivBEq α] [LawfulHashable α] {a fallback : α} :
+    a ∈ m → m.getKey? a = some (m.getKeyD a fallback) := by
+  simpa [mem_iff_contains] using getKey?_eq_some_getKeyD_of_contains
+
+theorem getKeyD_eq_getD_getKey? [EquivBEq α] [LawfulHashable α] {a fallback : α} :
+    m.getKeyD a fallback = (m.getKey? a).getD fallback :=
+  Raw₀.getKeyD_eq_getD_getKey? ⟨m.1, _⟩ m.2
+
+theorem getKey_eq_getKeyD [EquivBEq α] [LawfulHashable α] {a fallback : α} {h} :
+    m.getKey a h = m.getKeyD a fallback :=
+  Raw₀.getKey_eq_getKeyD ⟨m.1, _⟩ m.2
+
+theorem getKey!_eq_getKeyD_default [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
+    m.getKey! a = m.getKeyD a default :=
+  Raw₀.getKey!_eq_getKeyD_default ⟨m.1, _⟩ m.2
+
 @[simp]
 theorem isEmpty_insertIfNew [EquivBEq α] [LawfulHashable α] {k : α} {v : β k} :
     (m.insertIfNew k v).isEmpty = false :=
@@ -706,6 +889,29 @@ theorem getD_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {fallback
 
 end Const
 
+theorem getKey?_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {v : β k} :
+    getKey? (m.insertIfNew k v) a = if k == a ∧ ¬k ∈ m then some k else getKey? m a := by
+  simp [mem_iff_contains, contains_insertIfNew]
+  exact Raw₀.getKey?_insertIfNew ⟨m.1, _⟩ m.2
+
+theorem getKey_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {v : β k} {h₁} :
+    getKey (m.insertIfNew k v) a h₁ =
+      if h₂ : k == a ∧ ¬k ∈ m then k else getKey m a (mem_of_mem_insertIfNew' h₁ h₂) := by
+  simp [mem_iff_contains, contains_insertIfNew]
+  exact Raw₀.getKey_insertIfNew ⟨m.1, _⟩ m.2
+
+theorem getKey!_insertIfNew [EquivBEq α] [LawfulHashable α] [Inhabited α] {k a : α} {v : β k} :
+    getKey! (m.insertIfNew k v) a = if k == a ∧ ¬k ∈ m then k else getKey! m a := by
+  simp [mem_iff_contains, contains_insertIfNew]
+  exact Raw₀.getKey!_insertIfNew ⟨m.1, _⟩ m.2
+
+theorem getKeyD_insertIfNew [EquivBEq α] [LawfulHashable α] {k a fallback : α} {v : β k} :
+    getKeyD (m.insertIfNew k v) a fallback =
+      if k == a ∧ ¬k ∈ m then k else getKeyD m a fallback := by
+  simp [mem_iff_contains, contains_insertIfNew]
+  exact Raw₀.getKeyD_insertIfNew ⟨m.1, _⟩ m.2
+
+
 @[simp]
 theorem getThenInsertIfNew?_fst [LawfulBEq α] {k : α} {v : β k} :
     (m.getThenInsertIfNew? k v).1 = m.get? k :=

src/Std/Data/DHashMap/Raw.lean

@@ -237,6 +237,41 @@ returned map has a new value inserted.
 
 end
 
+/--
+Checks if a mapping for the given key exists and returns the key if it does, otherwise `none`.
+The result in the `some` case is guaranteed to be pointer equal to the key in the map.
+-/
+@[inline] def getKey? [BEq α] [Hashable α] (m : Raw α β) (a : α) : Option α :=
+  if h : 0 < m.buckets.size then
+    Raw₀.getKey? ⟨m, h⟩ a
+  else none -- will never happen for well-formed inputs
+
+/--
+Retrieves the key from the mapping that matches `a`. Ensures that such a mapping exists by
+requiring a proof of `a ∈ m`. The result is guaranteed to be pointer equal to the key in the map.
+-/
+@[inline] def getKey [BEq α] [Hashable α] (m : Raw α β) (a : α) (h : a ∈ m) : α :=
+  Raw₀.getKey ⟨m, by change dite .. = true at h; split at h <;> simp_all⟩ a
+    (by change dite .. = true at h; split at h <;> simp_all)
+
+/--
+Checks if a mapping for the given key exists and returns the key if it does, otherwise `fallback`.
+If a mapping exists the result is guaranteed to be pointer equal to the key in the map.
+-/
+@[inline] def getKeyD [BEq α] [Hashable α] (m : Raw α β) (a : α) (fallback : α) : α :=
+  if h : 0 < m.buckets.size then
+    Raw₀.getKeyD ⟨m, h⟩ a fallback
+  else fallback -- will never happen for well-formed inputs
+
+/--
+Checks if a mapping for the given key exists and returns the key if it does, otherwise panics.
+If no panic occurs the result is guaranteed to be pointer equal to the key in the map.
+-/
+@[inline] def getKey! [BEq α] [Hashable α] [Inhabited α] (m : Raw α β) (a : α) : α :=
+  if h : 0 < m.buckets.size then
+    Raw₀.getKey! ⟨m, h⟩ a
+  else default -- will never happen for well-formed inputs
+
 /--
 Returns `true` if the hash map contains no mappings.
 

src/Std/Data/DHashMap/RawLemmas.lean

@@ -54,7 +54,11 @@ private def baseNames : Array Name :=
     ``contains_eq, ``contains_val,
     ``get_eq, ``get_val,
     ``getD_eq, ``getD_val,
-    ``get!_eq, ``get!_val]
+    ``get!_eq, ``get!_val,
+    ``getKey?_eq, ``getKey?_val,
+    ``getKey_eq, ``getKey_val,
+    ``getKey!_eq, ``getKey!_val,
+    ``getKeyD_eq, ``getKeyD_val]
 
 /-- Internal implementation detail of the hash map -/
 scoped syntax "simp_to_raw" ("using" term)? : tactic
@@ -661,6 +665,194 @@ theorem getD_congr [EquivBEq α] [LawfulHashable α] (h : m.WF) {a b : α} {fall
 
 end Const
 
+@[simp]
+theorem getKey?_empty {a : α} {c} :
+    (empty c : Raw α β).getKey? a = none := by
+  simp_to_raw using Raw₀.getKey?_empty
+
+@[simp]
+theorem getKey?_emptyc {a : α} : (∅ : Raw α β).getKey? a = none :=
+  getKey?_empty
+
+theorem getKey?_of_isEmpty [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
+    m.isEmpty = true → m.getKey? a = none := by
+  simp_to_raw using Raw₀.getKey?_of_isEmpty ⟨m, _⟩
+
+theorem getKey?_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {a k : α} {v : β k} :
+    (m.insert k v).getKey? a = if k == a then some k else m.getKey? a := by
+  simp_to_raw using Raw₀.getKey?_insert
+
+@[simp]
+theorem getKey?_insert_self [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} {v : β k} :
+    (m.insert k v).getKey? k = some k := by
+  simp_to_raw using Raw₀.getKey?_insert_self
+
+theorem contains_eq_isSome_getKey? [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
+    m.contains a = (m.getKey? a).isSome := by
+  simp_to_raw using Raw₀.contains_eq_isSome_getKey?
+
+theorem getKey?_eq_none_of_contains_eq_false [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
+    m.contains a = false → m.getKey? a = none := by
+  simp_to_raw using Raw₀.getKey?_eq_none
+
+theorem getKey?_eq_none [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
+    ¬a ∈ m → m.getKey? a = none := by
+  simpa [mem_iff_contains] using getKey?_eq_none_of_contains_eq_false h
+
+theorem getKey?_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
+    (m.erase k).getKey? a = if k == a then none else m.getKey? a := by
+  simp_to_raw using Raw₀.getKey?_erase
+
+@[simp]
+theorem getKey?_erase_self [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} :
+    (m.erase k).getKey? k = none := by
+  simp_to_raw using Raw₀.getKey?_erase_self
+
+theorem getKey_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} {v : β k} {h₁} :
+    (m.insert k v).getKey a h₁ =
+      if h₂ : k == a then
+        k
+      else
+        m.getKey a (mem_of_mem_insert h h₁ (Bool.eq_false_iff.2 h₂)) := by
+  simp_to_raw using Raw₀.getKey_insert ⟨m, _⟩
+
+@[simp]
+theorem getKey_insert_self [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} {v : β k} :
+    (m.insert k v).getKey k (mem_insert_self h) = k := by
+  simp_to_raw using Raw₀.getKey_insert_self ⟨m, _⟩
+
+@[simp]
+theorem getKey_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} {h'} :
+    (m.erase a).getKey k h' = m.getKey k (mem_of_mem_erase h h') := by
+  simp_to_raw using Raw₀.getKey_erase ⟨m, _⟩
+
+theorem getKey?_eq_some_getKey [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} {h} :
+    m.getKey? a = some (m.getKey a h) := by
+  simp_to_raw using Raw₀.getKey?_eq_some_getKey
+
+@[simp]
+theorem getKey!_empty [Inhabited α] {a : α} {c} :
+    (empty c : Raw α β).getKey! a = default := by
+  simp_to_raw using Raw₀.getKey!_empty
+
+@[simp]
+theorem getKey!_emptyc [Inhabited α] {a : α} :
+    (∅ : Raw α β).getKey! a = default :=
+  getKey!_empty
+
+theorem getKey!_of_isEmpty [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {a : α} :
+    m.isEmpty = true → m.getKey! a = default := by
+  simp_to_raw using Raw₀.getKey!_of_isEmpty ⟨m, _⟩
+
+theorem getKey!_insert [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {k a : α} {v : β k} :
+    (m.insert k v).getKey! a = if k == a then k else m.getKey! a := by
+  simp_to_raw using Raw₀.getKey!_insert
+
+@[simp]
+theorem getKey!_insert_self [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {k : α}
+    {v : β k} :
+    (m.insert k v).getKey! k = k := by
+  simp_to_raw using Raw₀.getKey!_insert_self
+
+theorem getKey!_eq_default_of_contains_eq_false [EquivBEq α] [LawfulHashable α] [Inhabited α]
+    (h : m.WF) {a : α} :
+    m.contains a = false → m.getKey! a = default := by
+  simp_to_raw using Raw₀.getKey!_eq_default
+
+theorem getKey!_eq_default [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {a : α}:
+    ¬a ∈ m → m.getKey! a = default := by
+  simpa [mem_iff_contains] using getKey!_eq_default_of_contains_eq_false h
+
+theorem getKey!_erase [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {k a : α} :
+    (m.erase k).getKey! a = if k == a then default else m.getKey! a := by
+  simp_to_raw using Raw₀.getKey!_erase
+
+@[simp]
+theorem getKey!_erase_self [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {k : α} :
+    (m.erase k).getKey! k = default := by
+  simp_to_raw using Raw₀.getKey!_erase_self
+
+theorem getKey?_eq_some_getKey!_of_contains [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF)
+    {a : α} :
+    m.contains a = true → m.getKey? a = some (m.getKey! a) := by
+  simp_to_raw using Raw₀.getKey?_eq_some_getKey!
+
+theorem getKey?_eq_some_getKey! [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {a : α} :
+    a ∈ m → m.getKey? a = some (m.getKey! a) := by
+  simpa [mem_iff_contains] using getKey?_eq_some_getKey!_of_contains h
+
+theorem getKey!_eq_get!_getKey? [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {a : α} :
+    m.getKey! a = (m.getKey? a).get! := by
+  simp_to_raw using Raw₀.getKey!_eq_get!_getKey?
+
+theorem getKey_eq_getKey! [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {a : α} {h} :
+    m.getKey a h = m.getKey! a := by
+  simp_to_raw using Raw₀.getKey_eq_getKey!
+
+@[simp]
+theorem getKeyD_empty {a fallback : α} {c} :
+    (empty c : Raw α β).getKeyD a fallback = fallback := by
+  simp_to_raw using Raw₀.getKeyD_empty
+
+@[simp]
+theorem getKeyD_emptyc {a fallback : α} :
+    (∅ : Raw α β).getKeyD a fallback = fallback :=
+  getKeyD_empty
+
+theorem getKeyD_of_isEmpty [EquivBEq α] [LawfulHashable α] (h : m.WF) {a fallback : α} :
+    m.isEmpty = true → m.getKeyD a fallback = fallback := by
+  simp_to_raw using Raw₀.getKeyD_of_isEmpty ⟨m, _⟩
+
+theorem getKeyD_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a fallback : α} {v : β k} :
+    (m.insert k v).getKeyD a fallback =
+      if k == a then k else m.getKeyD a fallback := by
+  simp_to_raw using Raw₀.getKeyD_insert
+
+@[simp]
+theorem getKeyD_insert_self [EquivBEq α] [LawfulHashable α] (h : m.WF) {a fallback : α} {b : β a} :
+    (m.insert a b).getKeyD a fallback = a := by
+  simp_to_raw using Raw₀.getKeyD_insert_self
+
+theorem getKeyD_eq_fallback_of_contains_eq_false [EquivBEq α] [LawfulHashable α] (h : m.WF)
+    {a fallback : α} :
+    m.contains a = false → m.getKeyD a fallback = fallback := by
+  simp_to_raw using Raw₀.getKeyD_eq_fallback
+
+theorem getKeyD_eq_fallback [EquivBEq α] [LawfulHashable α] (h : m.WF) {a fallback : α} :
+    ¬a ∈ m → m.getKeyD a fallback = fallback := by
+  simpa [mem_iff_contains] using getKeyD_eq_fallback_of_contains_eq_false h
+
+theorem getKeyD_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a fallback : α} :
+    (m.erase k).getKeyD a fallback = if k == a then fallback else m.getKeyD a fallback := by
+  simp_to_raw using Raw₀.getKeyD_erase
+
+@[simp]
+theorem getKeyD_erase_self [EquivBEq α] [LawfulHashable α] (h : m.WF) {k fallback : α} :
+    (m.erase k).getKeyD k fallback = fallback := by
+  simp_to_raw using Raw₀.getKeyD_erase_self
+
+theorem getKey?_eq_some_getKeyD_of_contains [EquivBEq α] [LawfulHashable α] (h : m.WF)
+    {a fallback : α} :
+    m.contains a = true → m.getKey? a = some (m.getKeyD a fallback) := by
+  simp_to_raw using Raw₀.getKey?_eq_some_getKeyD
+
+theorem getKey?_eq_some_getKeyD [EquivBEq α] [LawfulHashable α] (h : m.WF) {a fallback : α} :
+    a ∈ m → m.getKey? a = some (m.getKeyD a fallback) := by
+  simpa [mem_iff_contains] using getKey?_eq_some_getKeyD_of_contains h
+
+theorem getKeyD_eq_getD_getKey? [EquivBEq α] [LawfulHashable α] (h : m.WF) {a fallback : α} :
+    m.getKeyD a fallback = (m.getKey? a).getD fallback := by
+  simp_to_raw using Raw₀.getKeyD_eq_getD_getKey?
+
+theorem getKey_eq_getKeyD [EquivBEq α] [LawfulHashable α] (h : m.WF) {a fallback : α} {h} :
+    m.getKey a h = m.getKeyD a fallback := by
+  simp_to_raw using Raw₀.getKey_eq_getKeyD
+
+theorem getKey!_eq_getKeyD_default [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF)
+    {a : α} :
+    m.getKey! a = m.getKeyD a default := by
+  simp_to_raw using Raw₀.getKey!_eq_getKeyD_default
+
 @[simp]
 theorem isEmpty_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} {v : β k} :
     (m.insertIfNew k v).isEmpty = false := by
@@ -774,6 +966,30 @@ theorem getD_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α}
 
 end Const
 
+theorem getKey?_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} {v : β k} :
+    getKey? (m.insertIfNew k v) a = if k == a ∧ ¬k ∈ m then some k else getKey? m a := by
+  simp only [mem_iff_contains, Bool.not_eq_true]
+  simp_to_raw using Raw₀.getKey?_insertIfNew
+
+theorem getKey_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} {v : β k} {h₁} :
+    getKey (m.insertIfNew k v) a h₁ =
+      if h₂ : k == a ∧ ¬k ∈ m then k else getKey m a (mem_of_mem_insertIfNew' h h₁ h₂) := by
+  simp only [mem_iff_contains, Bool.not_eq_true]
+  simp_to_raw using Raw₀.getKey_insertIfNew ⟨m, _⟩
+
+theorem getKey!_insertIfNew [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {k a : α}
+    {v : β k} :
+    getKey! (m.insertIfNew k v) a = if k == a ∧ ¬k ∈ m then k else getKey! m a := by
+  simp only [mem_iff_contains, Bool.not_eq_true]
+  simp_to_raw using Raw₀.getKey!_insertIfNew
+
+theorem getKeyD_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a fallback : α}
+    {v : β k} :
+    getKeyD (m.insertIfNew k v) a fallback =
+      if k == a ∧ ¬k ∈ m then k else getKeyD m a fallback := by
+  simp only [mem_iff_contains, Bool.not_eq_true]
+  simp_to_raw using Raw₀.getKeyD_insertIfNew
+
 @[simp]
 theorem getThenInsertIfNew?_fst [LawfulBEq α] (h : m.WF) {k : α} {v : β k} :
     (m.getThenInsertIfNew? k v).1 = m.get? k := by

src/Std/Data/HashMap/Basic.lean

@@ -160,6 +160,18 @@ instance [BEq α] [Hashable α] : GetElem? (HashMap α β) α β (fun m a => a
   getElem? m a := m.get? a
   getElem! m a := m.get! a
 
+@[inline, inherit_doc DHashMap.getKey?] def getKey? (m : HashMap α β) (a : α) : Option α :=
+  DHashMap.getKey? m.inner a
+
+@[inline, inherit_doc DHashMap.getKey] def getKey (m : HashMap α β) (a : α) (h : a ∈ m) : α :=
+  DHashMap.getKey m.inner a h
+
+@[inline, inherit_doc DHashMap.getKeyD] def getKeyD (m : HashMap α β) (a : α) (fallback : α) : α :=
+  DHashMap.getKeyD m.inner a fallback
+
+@[inline, inherit_doc DHashMap.getKey!] def getKey! [Inhabited α] (m : HashMap α β) (a : α) : α :=
+  DHashMap.getKey! m.inner a
+
 @[inline, inherit_doc DHashMap.erase] def erase (m : HashMap α β) (a : α) :
     HashMap α β :=
   ⟨m.inner.erase a⟩

src/Std/Data/HashMap/Lemmas.lean

@@ -391,6 +391,178 @@ theorem getD_congr [EquivBEq α] [LawfulHashable α] {a b : α} {fallback : β}
     m.getD a fallback = m.getD b fallback :=
   DHashMap.Const.getD_congr hab
 
+@[simp]
+theorem getKey?_empty {a : α} {c} : (empty c : HashMap α β).getKey? a = none :=
+  DHashMap.getKey?_empty
+
+@[simp]
+theorem getKey?_emptyc {a : α} : (∅ : HashMap α β).getKey? a = none :=
+  DHashMap.getKey?_emptyc
+
+theorem getKey?_of_isEmpty [EquivBEq α] [LawfulHashable α] {a : α} :
+    m.isEmpty = true → m.getKey? a = none :=
+  DHashMap.getKey?_of_isEmpty
+
+theorem getKey?_insert [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} :
+    (m.insert k v).getKey? a = if k == a then some k else m.getKey? a :=
+  DHashMap.getKey?_insert
+
+@[simp]
+theorem getKey?_insert_self [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
+    (m.insert k v).getKey? k = some k :=
+  DHashMap.getKey?_insert_self
+
+theorem contains_eq_isSome_getKey? [EquivBEq α] [LawfulHashable α] {a : α} :
+    m.contains a = (m.getKey? a).isSome :=
+  DHashMap.contains_eq_isSome_getKey?
+
+theorem getKey?_eq_none_of_contains_eq_false [EquivBEq α] [LawfulHashable α] {a : α} :
+    m.contains a = false → m.getKey? a = none :=
+  DHashMap.getKey?_eq_none_of_contains_eq_false
+
+theorem getKey?_eq_none [EquivBEq α] [LawfulHashable α] {a : α} : ¬a ∈ m → m.getKey? a = none :=
+  DHashMap.getKey?_eq_none
+
+theorem getKey?_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
+    (m.erase k).getKey? a = if k == a then none else m.getKey? a :=
+  DHashMap.getKey?_erase
+
+@[simp]
+theorem getKey?_erase_self [EquivBEq α] [LawfulHashable α] {k : α} : (m.erase k).getKey? k = none :=
+  DHashMap.getKey?_erase_self
+
+theorem getKey_insert [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} {h₁} :
+    (m.insert k v)[a]'h₁ =
+      if h₂ : k == a then v else m[a]'(mem_of_mem_insert h₁ (Bool.eq_false_iff.2 h₂)) :=
+  DHashMap.Const.get_insert (h₁ := h₁)
+
+@[simp]
+theorem getKey_insert_self [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
+    (m.insert k v).getKey k mem_insert_self = k :=
+  DHashMap.getKey_insert_self
+
+@[simp]
+theorem getKey_erase [EquivBEq α] [LawfulHashable α] {k a : α} {h'} :
+    (m.erase k).getKey a h' = m.getKey a (mem_of_mem_erase h') :=
+  DHashMap.getKey_erase (h' := h')
+
+theorem getKey?_eq_some_getKey [EquivBEq α] [LawfulHashable α] {a : α} {h' : a ∈ m} :
+    m.getKey? a = some (m.getKey a h') :=
+  @DHashMap.getKey?_eq_some_getKey _ _ _ _ _ _ _ _ h'
+
+@[simp]
+theorem getKey!_empty [Inhabited α] {a : α} {c} : (empty c : HashMap α β).getKey! a = default :=
+  DHashMap.getKey!_empty
+
+@[simp]
+theorem getKey!_emptyc [Inhabited α] {a : α} : (∅ : HashMap α β).getKey! a = default :=
+  DHashMap.getKey!_emptyc
+
+theorem getKey!_of_isEmpty [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
+    m.isEmpty = true → m.getKey! a = default :=
+  DHashMap.getKey!_of_isEmpty
+
+theorem getKey!_insert [EquivBEq α] [LawfulHashable α] [Inhabited α] {k a : α} {v : β} :
+    (m.insert k v).getKey! a = if k == a then k else m.getKey! a :=
+  DHashMap.getKey!_insert
+
+@[simp]
+theorem getKey!_insert_self [EquivBEq α] [LawfulHashable α] [Inhabited α] {k : α} {v : β} :
+    (m.insert k v).getKey! k = k :=
+  DHashMap.getKey!_insert_self
+
+theorem getKey!_eq_default_of_contains_eq_false [EquivBEq α] [LawfulHashable α] [Inhabited α]
+    {a : α} : m.contains a = false → m.getKey! a = default :=
+  DHashMap.getKey!_eq_default_of_contains_eq_false
+
+theorem getKey!_eq_default [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
+    ¬a ∈ m → m.getKey! a = default :=
+  DHashMap.getKey!_eq_default
+
+theorem getKey!_erase [EquivBEq α] [LawfulHashable α] [Inhabited α] {k a : α} :
+    (m.erase k).getKey! a = if k == a then default else m.getKey! a :=
+  DHashMap.getKey!_erase
+
+@[simp]
+theorem getKey!_erase_self [EquivBEq α] [LawfulHashable α] [Inhabited α] {k : α} :
+    (m.erase k).getKey! k = default :=
+  DHashMap.getKey!_erase_self
+
+theorem getKey?_eq_some_getKey!_of_contains [EquivBEq α] [LawfulHashable α] [Inhabited α]
+    {a : α} : m.contains a = true → m.getKey? a = some (m.getKey! a) :=
+  DHashMap.getKey?_eq_some_getKey!_of_contains
+
+theorem getKey?_eq_some_getKey! [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
+    a ∈ m → m.getKey? a = some (m.getKey! a) :=
+  DHashMap.getKey?_eq_some_getKey!
+
+theorem getKey!_eq_get!_getKey? [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
+    m.getKey! a = (m.getKey? a).get! :=
+  DHashMap.getKey!_eq_get!_getKey?
+
+theorem getKey_eq_getKey! [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} {h'} :
+    m.getKey a h' = m.getKey! a :=
+  @DHashMap.getKey_eq_getKey! _ _ _ _ _ _ _ _ _ h'
+
+@[simp]
+theorem getKeyD_empty {a : α} {fallback : α} {c} :
+    (empty c : HashMap α β).getKeyD a fallback = fallback :=
+  DHashMap.getKeyD_empty
+
+@[simp]
+theorem getKeyD_emptyc {a : α} {fallback : α} : (∅ : HashMap α β).getKeyD a fallback = fallback :=
+  DHashMap.getKeyD_empty
+
+theorem getKeyD_of_isEmpty [EquivBEq α] [LawfulHashable α] {a : α} {fallback : α} :
+    m.isEmpty = true → m.getKeyD a fallback = fallback :=
+  DHashMap.getKeyD_of_isEmpty
+
+theorem getKeyD_insert [EquivBEq α] [LawfulHashable α] {k a fallback : α} {v : β} :
+    (m.insert k v).getKeyD a fallback = if k == a then k else m.getKeyD a fallback :=
+  DHashMap.getKeyD_insert
+
+@[simp]
+theorem getKeyD_insert_self [EquivBEq α] [LawfulHashable α] {k fallback : α} {v : β} :
+   (m.insert k v).getKeyD k fallback = k :=
+  DHashMap.getKeyD_insert_self
+
+theorem getKeyD_eq_fallback_of_contains_eq_false [EquivBEq α] [LawfulHashable α] {a : α}
+    {fallback : α} : m.contains a = false → m.getKeyD a fallback = fallback :=
+  DHashMap.getKeyD_eq_fallback_of_contains_eq_false
+
+theorem getKeyD_eq_fallback [EquivBEq α] [LawfulHashable α] {a : α} {fallback : α} :
+    ¬a ∈ m → m.getKeyD a fallback = fallback :=
+  DHashMap.getKeyD_eq_fallback
+
+theorem getKeyD_erase [EquivBEq α] [LawfulHashable α] {k a : α} {fallback : α} :
+    (m.erase k).getKeyD a fallback = if k == a then fallback else m.getKeyD a fallback :=
+  DHashMap.getKeyD_erase
+
+@[simp]
+theorem getKeyD_erase_self [EquivBEq α] [LawfulHashable α] {k : α} {fallback : α} :
+    (m.erase k).getKeyD k fallback = fallback :=
+  DHashMap.getKeyD_erase_self
+
+theorem getKey?_eq_some_getKeyD_of_contains [EquivBEq α] [LawfulHashable α] {a : α} {fallback : α} :
+    m.contains a = true → m.getKey? a = some (m.getKeyD a fallback) :=
+  DHashMap.getKey?_eq_some_getKeyD_of_contains
+
+theorem getKey?_eq_some_getKeyD [EquivBEq α] [LawfulHashable α] {a : α} {fallback : α} :
+    a ∈ m → m.getKey? a = some (m.getKeyD a fallback) :=
+  DHashMap.getKey?_eq_some_getKeyD
+
+theorem getKeyD_eq_getD_getKey? [EquivBEq α] [LawfulHashable α] {a : α} {fallback : α} :
+    m.getKeyD a fallback = (m.getKey? a).getD fallback :=
+  DHashMap.getKeyD_eq_getD_getKey?
+
+theorem getKey_eq_getKeyD [EquivBEq α] [LawfulHashable α] {a : α} {fallback : α} {h'} :
+    m.getKey a h' = m.getKeyD a fallback :=
+  @DHashMap.getKey_eq_getKeyD _ _ _ _ _ _ _ _ _ h'
+
+theorem getKey!_eq_getKeyD_default [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
+    m.getKey! a = m.getKeyD a default :=
+  DHashMap.getKey!_eq_getKeyD_default
+
 @[simp]
 theorem isEmpty_insertIfNew [EquivBEq α] [LawfulHashable α] {k : α} {v : β} :
     (m.insertIfNew k v).isEmpty = false :=
@@ -464,6 +636,23 @@ theorem getD_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {fallback
       if k == a ∧ ¬k ∈ m then v else m.getD a fallback :=
   DHashMap.Const.getD_insertIfNew
 
+theorem getKey?_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} :
+    getKey? (m.insertIfNew k v) a = if k == a ∧ ¬k ∈ m then some k else getKey? m a :=
+  DHashMap.getKey?_insertIfNew
+
+theorem getKey_insertIfNew [EquivBEq α] [LawfulHashable α] {k a : α} {v : β} {h₁} :
+    getKey (m.insertIfNew k v) a h₁ =
+      if h₂ : k == a ∧ ¬k ∈ m then k else getKey m a (mem_of_mem_insertIfNew' h₁ h₂) :=
+  DHashMap.getKey_insertIfNew
+
+theorem getKey!_insertIfNew [EquivBEq α] [LawfulHashable α] [Inhabited α] {k a : α} {v : β} :
+    getKey! (m.insertIfNew k v) a = if k == a ∧ ¬k ∈ m then k else getKey! m a :=
+  DHashMap.getKey!_insertIfNew
+
+theorem getKeyD_insertIfNew [EquivBEq α] [LawfulHashable α] {k a fallback : α} {v : β} :
+    getKeyD (m.insertIfNew k v) a fallback = if k == a ∧ ¬k ∈ m then k else getKeyD m a fallback :=
+  DHashMap.getKeyD_insertIfNew
+
 @[simp]
 theorem getThenInsertIfNew?_fst {k : α} {v : β} : (getThenInsertIfNew? m k v).1 = get? m k :=
   DHashMap.Const.getThenInsertIfNew?_fst

src/Std/Data/HashMap/Raw.lean

@@ -138,6 +138,22 @@ instance [BEq α] [Hashable α] : GetElem? (Raw α β) α β (fun m a => a ∈ m
   getElem? m a := m.get? a
   getElem! m a := m.get! a
 
+@[inline, inherit_doc DHashMap.Raw.getKey?] def getKey? [BEq α] [Hashable α] (m : Raw α β) (a : α) :
+    Option α :=
+  DHashMap.Raw.getKey? m.inner a
+
+@[inline, inherit_doc DHashMap.Raw.getKey] def getKey [BEq α] [Hashable α] (m : Raw α β) (a : α)
+    (h : a ∈ m) : α :=
+  DHashMap.Raw.getKey m.inner a h
+
+@[inline, inherit_doc DHashMap.Raw.getKeyD] def getKeyD [BEq α] [Hashable α] (m : Raw α β) (a : α)
+    (fallback : α) : α :=
+  DHashMap.Raw.getKeyD m.inner a fallback
+
+@[inline, inherit_doc DHashMap.Raw.getKey!] def getKey! [BEq α] [Hashable α] [Inhabited α]
+    (m : Raw α β) (a : α) : α :=
+  DHashMap.Raw.getKey! m.inner a
+
 @[inline, inherit_doc DHashMap.Raw.erase] def erase [BEq α] [Hashable α] (m : Raw α β)
     (a : α) : Raw α β :=
   ⟨m.inner.erase a⟩

src/Std/Data/HashMap/RawLemmas.lean

@@ -400,6 +400,181 @@ theorem getD_congr [EquivBEq α] [LawfulHashable α] (h : m.WF) {a b : α} {fall
     (hab : a == b) : m.getD a fallback = m.getD b fallback :=
   DHashMap.Raw.Const.getD_congr h.out hab
 
+@[simp]
+theorem getKey?_empty {a : α} {c} : (empty c : Raw α β).getKey? a = none :=
+  DHashMap.Raw.getKey?_empty
+
+@[simp]
+theorem getKey?_emptyc {a : α} : (∅ : Raw α β).getKey? a = none :=
+  DHashMap.Raw.getKey?_emptyc
+
+theorem getKey?_of_isEmpty [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
+    m.isEmpty = true → m.getKey? a = none :=
+  DHashMap.Raw.getKey?_of_isEmpty h.out
+
+theorem getKey?_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} {v : β} :
+    (m.insert k v).getKey? a = if k == a then some k else m.getKey? a :=
+  DHashMap.Raw.getKey?_insert h.out
+
+@[simp]
+theorem getKey?_insert_self [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} {v : β} :
+    (m.insert k v).getKey? k = some k :=
+  DHashMap.Raw.getKey?_insert_self h.out
+
+theorem contains_eq_isSome_getKey? [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
+    m.contains a = (m.getKey? a).isSome :=
+  DHashMap.Raw.contains_eq_isSome_getKey? h.out
+
+theorem getKey?_eq_none_of_contains_eq_false [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
+    m.contains a = false → m.getKey? a = none :=
+  DHashMap.Raw.getKey?_eq_none_of_contains_eq_false h.out
+
+theorem getKey?_eq_none [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
+    ¬a ∈ m → m.getKey? a = none :=
+  DHashMap.Raw.getKey?_eq_none h.out
+
+theorem getKey?_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
+    (m.erase k).getKey? a = if k == a then none else m.getKey? a :=
+  DHashMap.Raw.getKey?_erase h.out
+
+@[simp]
+theorem getKey?_erase_self [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} :
+    (m.erase k).getKey? k = none :=
+  DHashMap.Raw.getKey?_erase_self h.out
+
+theorem getKey_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} {v : β} {h₁} :
+    (m.insert k v).getKey a h₁ =
+      if h₂ : k == a then k else m.getKey a (mem_of_mem_insert h h₁ (Bool.eq_false_iff.2 h₂)) :=
+  DHashMap.Raw.getKey_insert (h₁ := h₁) h.out
+
+@[simp]
+theorem getKey_insert_self [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} {v : β} :
+    (m.insert k v).getKey k (mem_insert_self h) = k :=
+  DHashMap.Raw.getKey_insert_self h.out
+
+@[simp]
+theorem getKey_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} {h'} :
+    (m.erase k).getKey a h' = m.getKey a (mem_of_mem_erase h h') :=
+  DHashMap.Raw.getKey_erase (h' := h') h.out
+
+theorem getKey?_eq_some_getKey [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} {h' : a ∈ m} :
+    m.getKey? a = some (m.getKey a h') :=
+  @DHashMap.Raw.getKey?_eq_some_getKey _ _ _ _ _ _ _ h.out _ h'
+
+@[simp]
+theorem getKey!_empty [Inhabited α] {a : α} {c} : (empty c : Raw α β).getKey! a = default :=
+  DHashMap.Raw.getKey!_empty
+
+@[simp]
+theorem getKey!_emptyc [Inhabited α] {a : α} : (∅ : Raw α β).getKey! a = default :=
+  DHashMap.Raw.getKey!_emptyc
+
+theorem getKey!_of_isEmpty [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {a : α} :
+    m.isEmpty = true → m.getKey! a = default :=
+  DHashMap.Raw.getKey!_of_isEmpty h.out
+
+theorem getKey!_insert [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {k a : α} {v : β} :
+    (m.insert k v).getKey! a = if k == a then k else m.getKey! a :=
+  DHashMap.Raw.getKey!_insert h.out
+
+@[simp]
+theorem getKey!_insert_self [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {k : α}
+    {v : β} : (m.insert k v).getKey! k = k :=
+  DHashMap.Raw.getKey!_insert_self h.out
+
+theorem getKey!_eq_default_of_contains_eq_false [EquivBEq α] [LawfulHashable α] [Inhabited α]
+    (h : m.WF) {a : α} : m.contains a = false → m.getKey! a = default :=
+  DHashMap.Raw.getKey!_eq_default_of_contains_eq_false h.out
+
+theorem getKey!_eq_default [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {a : α} :
+    ¬a ∈ m → m.getKey! a = default :=
+  DHashMap.Raw.getKey!_eq_default h.out
+
+theorem getKey!_erase [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {k a : α} :
+    (m.erase k).getKey! a = if k == a then default else m.getKey! a :=
+  DHashMap.Raw.getKey!_erase h.out
+
+@[simp]
+theorem getKey!_erase_self [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {k : α} :
+    (m.erase k).getKey! k = default :=
+  DHashMap.Raw.getKey!_erase_self h.out
+
+theorem getKey?_eq_some_getKey!_of_contains [EquivBEq α] [LawfulHashable α] [Inhabited α]
+    (h : m.WF) {a : α} : m.contains a = true → m.getKey? a = some (m.getKey! a) :=
+  DHashMap.Raw.getKey?_eq_some_getKey!_of_contains h.out
+
+theorem getKey?_eq_some_getKey! [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {a : α} :
+    a ∈ m → m.getKey? a = some (m.getKey! a) :=
+  DHashMap.Raw.getKey?_eq_some_getKey! h.out
+
+theorem getKey!_eq_get!_getKey? [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {a : α} :
+    m.getKey! a = (m.getKey? a).get! :=
+  DHashMap.Raw.getKey!_eq_get!_getKey? h.out
+
+theorem getKey_eq_getKey! [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {a : α} {h'} :
+    m.getKey a h' = m.getKey! a :=
+  DHashMap.Raw.getKey_eq_getKey! h.out
+
+@[simp]
+theorem getKeyD_empty {a fallback : α} {c} :
+    (empty c : Raw α β).getKeyD a fallback = fallback :=
+  DHashMap.Raw.getKeyD_empty
+
+@[simp]
+theorem getKeyD_emptyc {a fallback : α} : (∅ : Raw α β).getKeyD a fallback = fallback :=
+  DHashMap.Raw.getKeyD_empty
+
+theorem getKeyD_of_isEmpty [EquivBEq α] [LawfulHashable α] (h : m.WF) {a fallback : α} :
+    m.isEmpty = true → m.getKeyD a fallback = fallback :=
+  DHashMap.Raw.getKeyD_of_isEmpty h.out
+
+theorem getKeyD_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a fallback : α} {v : β} :
+    (m.insert k v).getKeyD a fallback = if k == a then k else m.getKeyD a fallback :=
+  DHashMap.Raw.getKeyD_insert h.out
+
+@[simp]
+theorem getKeyD_insert_self [EquivBEq α] [LawfulHashable α] (h : m.WF) {k fallback : α} {v : β} :
+   (m.insert k v).getKeyD k fallback = k :=
+  DHashMap.Raw.getKeyD_insert_self h.out
+
+theorem getKeyD_eq_fallback_of_contains_eq_false [EquivBEq α] [LawfulHashable α] (h : m.WF)
+    {a fallback : α} : m.contains a = false → m.getKeyD a fallback = fallback :=
+  DHashMap.Raw.getKeyD_eq_fallback_of_contains_eq_false h.out
+
+theorem getKeyD_eq_fallback [EquivBEq α] [LawfulHashable α] (h : m.WF) {a fallback : α} :
+    ¬a ∈ m → m.getKeyD a fallback = fallback :=
+  DHashMap.Raw.getKeyD_eq_fallback h.out
+
+theorem getKeyD_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a fallback : α} :
+    (m.erase k).getKeyD a fallback = if k == a then fallback else m.getKeyD a fallback :=
+  DHashMap.Raw.getKeyD_erase h.out
+
+@[simp]
+theorem getKeyD_erase_self [EquivBEq α] [LawfulHashable α] (h : m.WF) {k fallback : α} :
+    (m.erase k).getKeyD k fallback = fallback :=
+  DHashMap.Raw.getKeyD_erase_self h.out
+
+theorem getKey?_eq_some_getKeyD_of_contains [EquivBEq α] [LawfulHashable α] (h : m.WF)
+    {a fallback : α} : m.contains a = true → m.getKey? a = some (m.getKeyD a fallback) :=
+  DHashMap.Raw.getKey?_eq_some_getKeyD_of_contains h.out
+
+theorem getKey?_eq_some_getKeyD [EquivBEq α] [LawfulHashable α] (h : m.WF) {a fallback : α} :
+    a ∈ m → m.getKey? a = some (m.getKeyD a fallback) :=
+  DHashMap.Raw.getKey?_eq_some_getKeyD h.out
+
+theorem getKeyD_eq_getD_getKey? [EquivBEq α] [LawfulHashable α] (h : m.WF) {a fallback : α} :
+    m.getKeyD a fallback = (m.getKey? a).getD fallback :=
+  DHashMap.Raw.getKeyD_eq_getD_getKey? h.out
+
+theorem getKey_eq_getKeyD [EquivBEq α] [LawfulHashable α] (h : m.WF) {a fallback : α} {h'} :
+    m.getKey a h' = m.getKeyD a fallback :=
+  @DHashMap.Raw.getKey_eq_getKeyD _ _ _ _ _ _ _ h.out _ _ h'
+
+theorem getKey!_eq_getKeyD_default [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF)
+    {a : α} :
+    m.getKey! a = m.getKeyD a default :=
+  DHashMap.Raw.getKey!_eq_getKeyD_default h.out
+
 @[simp]
 theorem isEmpty_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} {v : β} :
     (m.insertIfNew k v).isEmpty = false :=
@@ -473,6 +648,24 @@ theorem getD_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α}
       if k == a ∧ ¬k ∈ m then v else m.getD a fallback :=
   DHashMap.Raw.Const.getD_insertIfNew h.out
 
+theorem getKey?_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} {v : β} :
+    (m.insertIfNew k v).getKey? a = if k == a ∧ ¬k ∈ m then some k else m.getKey? a :=
+  DHashMap.Raw.getKey?_insertIfNew h.out
+
+theorem getKey_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} {v : β} {h₁} :
+    (m.insertIfNew k v).getKey a h₁ =
+      if h₂ : k == a ∧ ¬k ∈ m then k else m.getKey a (mem_of_mem_insertIfNew' h h₁ h₂) :=
+  DHashMap.Raw.getKey_insertIfNew h.out
+
+theorem getKey!_insertIfNew [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {k a : α} {v : β} :
+    (m.insertIfNew k v).getKey! a = if k == a ∧ ¬k ∈ m then k else m.getKey! a :=
+  DHashMap.Raw.getKey!_insertIfNew h.out
+
+theorem getKeyD_insertIfNew [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a fallback : α} {v : β} :
+    (m.insertIfNew k v).getKeyD a fallback = if k == a ∧ ¬k ∈ m then k else m.getKeyD a fallback :=
+  DHashMap.Raw.getKeyD_insertIfNew h.out
+
+
 @[simp]
 theorem getThenInsertIfNew?_fst (h : m.WF) {k : α} {v : β} :
     (getThenInsertIfNew? m k v).1 = get? m k :=

src/Std/Data/HashSet/Basic.lean

@@ -112,6 +112,34 @@ instance [BEq α] [Hashable α] {m : HashSet α} {a : α} : Decidable (a ∈ m)
 @[inline] def size (m : HashSet α) : Nat :=
   m.inner.size
 
+/--
+Checks if given key is contained and returns the key if it is, otherwise `none`.
+The result in the `some` case is guaranteed to be pointer equal to the key in the set.
+-/
+@[inline] def get? (m : HashSet α) (a : α) : Option α :=
+  m.inner.getKey? a
+
+/--
+Retrieves the key from the set that matches `a`. Ensures that such a key exists by requiring a proof
+of `a ∈ m`. The result is guaranteed to be pointer equal to the key in the set.
+-/
+@[inline] def get [BEq α] [Hashable α] (m : HashSet α) (a : α) (h : a ∈ m) : α :=
+  m.inner.getKey a h
+
+/--
+Checks if given key is contained and returns the key if it is, otherwise `fallback`.
+If they key is contained the result is guaranteed to be pointer equal to the key in the set.
+-/
+@[inline] def getD [BEq α] [Hashable α] (m : HashSet α) (a : α) (fallback : α) : α :=
+  m.inner.getKeyD a fallback
+
+/--
+Checks if given key is contained and returns the key if it is, otherwise panics.
+If no panic occurs the result is guaranteed to be pointer equal to the key in the set.
+-/
+@[inline] def get! [BEq α] [Hashable α] [Inhabited α] (m : HashSet α) (a : α) : α :=
+  m.inner.getKey! a
+
 /--
 Returns `true` if the hash set contains no elements.
 

src/Std/Data/HashSet/Lemmas.lean

@@ -106,6 +106,18 @@ theorem mem_of_mem_insert [EquivBEq α] [LawfulHashable α] {k a : α} :
     a ∈ m.insert k → (k == a) = false → a ∈ m :=
   HashMap.mem_of_mem_insertIfNew
 
+/-- This is a restatement of `contains_insert` that is written to exactly match the proof
+obligation in the statement of `get_insert`. -/
+theorem contains_of_contains_insert' [EquivBEq α] [LawfulHashable α] {k a : α} :
+    (m.insert k).contains a → ¬((k == a) ∧ m.contains k = false) → m.contains a :=
+  HashMap.contains_of_contains_insertIfNew'
+
+/-- This is a restatement of `mem_insert` that is written to exactly match the proof obligation
+in the statement of `get_insert`. -/
+theorem mem_of_mem_insert' [EquivBEq α] [LawfulHashable α] {k a : α} :
+    a ∈ m.insert k → ¬((k == a) ∧ ¬k ∈ m) → a ∈ m :=
+  DHashMap.mem_of_mem_insertIfNew'
+
 @[simp]
 theorem contains_insert_self [EquivBEq α] [LawfulHashable α] {k : α}  : (m.insert k).contains k :=
   HashMap.contains_insertIfNew_self
@@ -177,6 +189,158 @@ theorem size_le_size_erase [EquivBEq α] [LawfulHashable α] {k : α} :
     m.size ≤ (m.erase k).size + 1 :=
   HashMap.size_le_size_erase
 
+@[simp]
+theorem get?_empty {a : α} {c} : (empty c : HashSet α).get? a = none :=
+  HashMap.getKey?_empty
+
+@[simp]
+theorem get?_emptyc {a : α} : (∅ : HashSet α).get? a = none :=
+  HashMap.getKey?_emptyc
+
+theorem get?_of_isEmpty [EquivBEq α] [LawfulHashable α] {a : α} :
+    m.isEmpty = true → m.get? a = none :=
+  HashMap.getKey?_of_isEmpty
+
+theorem get?_insert [EquivBEq α] [LawfulHashable α] {k a : α} :
+    (m.insert k).get? a = if k == a ∧ ¬k ∈ m then some k else m.get? a :=
+  HashMap.getKey?_insertIfNew
+
+theorem contains_eq_isSome_get? [EquivBEq α] [LawfulHashable α] {a : α} :
+    m.contains a = (m.get? a).isSome :=
+  HashMap.contains_eq_isSome_getKey?
+
+theorem get?_eq_none_of_contains_eq_false [EquivBEq α] [LawfulHashable α] {a : α} :
+    m.contains a = false → m.get? a = none :=
+  HashMap.getKey?_eq_none_of_contains_eq_false
+
+theorem get?_eq_none [EquivBEq α] [LawfulHashable α] {a : α} : ¬a ∈ m → m.get? a = none :=
+  HashMap.getKey?_eq_none
+
+theorem get?_erase [EquivBEq α] [LawfulHashable α] {k a : α} :
+    (m.erase k).get? a = if k == a then none else m.get? a :=
+  HashMap.getKey?_erase
+
+@[simp]
+theorem get?_erase_self [EquivBEq α] [LawfulHashable α] {k : α} : (m.erase k).get? k = none :=
+  HashMap.getKey?_erase_self
+
+theorem get_insert [EquivBEq α] [LawfulHashable α] {k a : α} {h₁} :
+    (m.insert k).get a h₁ =
+      if h₂ : k == a ∧ ¬k ∈ m then k else m.get a (mem_of_mem_insert' h₁ h₂) :=
+  HashMap.getKey_insertIfNew (h₁ := h₁)
+
+@[simp]
+theorem get_erase [EquivBEq α] [LawfulHashable α] {k a : α} {h'} :
+    (m.erase k).get a h' = m.get a (mem_of_mem_erase h') :=
+  HashMap.getKey_erase (h' := h')
+
+theorem get?_eq_some_get [EquivBEq α] [LawfulHashable α] {a : α} {h' : a ∈ m} :
+    m.get? a = some (m.get a h') :=
+  @HashMap.getKey?_eq_some_getKey _ _ _ _ _ _ _ _ h'
+
+@[simp]
+theorem get!_empty [Inhabited α] {a : α} {c} : (empty c : HashSet α).get! a = default :=
+  HashMap.getKey!_empty
+
+@[simp]
+theorem get!_emptyc [Inhabited α] {a : α} : (∅ : HashSet α).get! a = default :=
+  HashMap.getKey!_emptyc
+
+theorem get!_of_isEmpty [Inhabited α] [EquivBEq α] [LawfulHashable α] {a : α} :
+    m.isEmpty = true → m.get! a = default :=
+  HashMap.getKey!_of_isEmpty
+
+theorem get!_insert [Inhabited α] [EquivBEq α] [LawfulHashable α] {k a : α} :
+    (m.insert k).get! a = if k == a ∧ ¬k ∈ m then k else m.get! a :=
+  HashMap.getKey!_insertIfNew
+
+theorem get!_eq_default_of_contains_eq_false [Inhabited α] [EquivBEq α] [LawfulHashable α] {a : α} :
+    m.contains a = false → m.get! a = default :=
+  HashMap.getKey!_eq_default_of_contains_eq_false
+
+theorem get!_eq_default [Inhabited α] [EquivBEq α] [LawfulHashable α] {a : α} :
+    ¬a ∈ m → m.get! a = default :=
+  HashMap.getKey!_eq_default
+
+theorem get!_erase [Inhabited α] [EquivBEq α] [LawfulHashable α] {k a : α} :
+    (m.erase k).get! a = if k == a then default else m.get! a :=
+  HashMap.getKey!_erase
+
+@[simp]
+theorem get!_erase_self [Inhabited α] [EquivBEq α] [LawfulHashable α] {k : α} :
+    (m.erase k).get! k = default :=
+  HashMap.getKey!_erase_self
+
+theorem get?_eq_some_get!_of_contains [EquivBEq α] [LawfulHashable α] [Inhabited α]
+    {a : α} : m.contains a = true → m.get? a = some (m.get! a) :=
+  HashMap.getKey?_eq_some_getKey!_of_contains
+
+theorem get?_eq_some_get! [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
+    a ∈ m → m.get? a = some (m.get! a) :=
+  HashMap.getKey?_eq_some_getKey!
+
+theorem get!_eq_get!_get? [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
+    m.get! a = (m.get? a).get! :=
+  HashMap.getKey!_eq_get!_getKey?
+
+theorem get_eq_get! [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} {h'} :
+    m.get a h' = m.get! a :=
+  HashMap.getKey_eq_getKey!
+
+@[simp]
+theorem getD_empty {a fallback : α} {c} : (empty c : HashSet α).getD a fallback = fallback :=
+  HashMap.getKeyD_empty
+
+@[simp]
+theorem getD_emptyc {a fallback : α} : (∅ : HashSet α).getD a fallback = fallback :=
+  HashMap.getKeyD_emptyc
+
+theorem getD_of_isEmpty [EquivBEq α] [LawfulHashable α] {a fallback : α} :
+    m.isEmpty = true → m.getD a fallback = fallback :=
+  HashMap.getKeyD_of_isEmpty
+
+theorem getD_insert [EquivBEq α] [LawfulHashable α] {k a fallback : α} :
+    (m.insert k).getD a fallback = if k == a ∧ ¬k ∈ m then k else m.getD a fallback :=
+  HashMap.getKeyD_insertIfNew
+
+theorem getD_eq_fallback_of_contains_eq_false [EquivBEq α] [LawfulHashable α]
+    {a fallback : α} :
+    m.contains a = false → m.getD a fallback = fallback :=
+  HashMap.getKeyD_eq_fallback_of_contains_eq_false
+
+theorem getD_eq_fallback [EquivBEq α] [LawfulHashable α] {a fallback : α} :
+    ¬a ∈ m → m.getD a fallback = fallback :=
+  HashMap.getKeyD_eq_fallback
+
+theorem getD_erase [EquivBEq α] [LawfulHashable α] {k a fallback : α} :
+    (m.erase k).getD a fallback = if k == a then fallback else m.getD a fallback :=
+  HashMap.getKeyD_erase
+
+@[simp]
+theorem getD_erase_self [EquivBEq α] [LawfulHashable α] {k fallback : α} :
+    (m.erase k).getD k fallback = fallback :=
+  HashMap.getKeyD_erase_self
+
+theorem get?_eq_some_getD_of_contains [EquivBEq α] [LawfulHashable α] {a fallback : α} :
+    m.contains a = true → m.get? a = some (m.getD a fallback) :=
+  HashMap.getKey?_eq_some_getKeyD_of_contains
+
+theorem get?_eq_some_getD [EquivBEq α] [LawfulHashable α] {a fallback : α} :
+    a ∈ m → m.get? a = some (m.getD a fallback) :=
+  HashMap.getKey?_eq_some_getKeyD
+
+theorem getD_eq_getD_get? [EquivBEq α] [LawfulHashable α] {a fallback : α} :
+    m.getD a fallback = (m.get? a).getD fallback :=
+  HashMap.getKeyD_eq_getD_getKey?
+
+theorem get_eq_getD [EquivBEq α] [LawfulHashable α] {a fallback : α} {h'} :
+    m.get a h' = m.getD a fallback :=
+  @HashMap.getKey_eq_getKeyD _ _ _ _ _ _ _ _ _ h'
+
+theorem get!_eq_getD_default [EquivBEq α] [LawfulHashable α] [Inhabited α] {a : α} :
+    m.get! a = m.getD a default :=
+  HashMap.getKey!_eq_getKeyD_default
+
 @[simp]
 theorem containsThenInsert_fst {k : α} : (m.containsThenInsert k).1 = m.contains k :=
   HashMap.containsThenInsertIfNew_fst

src/Std/Data/HashSet/Raw.lean

@@ -14,7 +14,7 @@ set with unbundled well-formedness invariant.
 
 This version is safe to use in nested inductive types. The well-formedness predicate is
 available as `Std.Data.HashSet.Raw.WF` and we prove in this file that all operations preserve
-well-formedness. When in doubt, prefer `HashSet` over `DHashSet.Raw`.
+well-formedness. When in doubt, prefer `HashSet` over `HashSet.Raw`.
 
 Lemmas about the operations on `Std.Data.HashSet.Raw` are available in the module
 `Std.Data.HashSet.RawLemmas`.
@@ -113,6 +113,34 @@ instance [BEq α] [Hashable α] {m : Raw α} {a : α} : Decidable (a ∈ m) :=
 @[inline] def size (m : Raw α) : Nat :=
   m.inner.size
 
+/--
+Checks if given key is contained and returns the key if it is, otherwise `none`.
+The result in the `some` case is guaranteed to be pointer equal to the key in the map.
+-/
+@[inline] def get? [BEq α] [Hashable α] (m : Raw α) (a : α) : Option α :=
+  m.inner.getKey? a
+
+/--
+Retrieves the key from the set that matches `a`. Ensures that such a key exists by requiring a proof
+of `a ∈ m`. The result is guaranteed to be pointer equal to the key in the set.
+-/
+@[inline] def get [BEq α] [Hashable α] (m : Raw α) (a : α) (h : a ∈ m) : α :=
+  m.inner.getKey a h
+
+/--
+Checks if given key is contained and returns the key if it is, otherwise `fallback`.
+If they key is contained the result is guaranteed to be pointer equal to the key in the set.
+-/
+@[inline] def getD [BEq α] [Hashable α] (m : Raw α) (a : α) (fallback : α) : α :=
+  m.inner.getKeyD a fallback
+
+/--
+Checks if given key is contained and returns the key if it is, otherwise panics.
+If no panic occurs the result is guaranteed to be pointer equal to the key in the set.
+-/
+@[inline] def get! [BEq α] [Hashable α] [Inhabited α] (m : Raw α) (a : α) : α :=
+  m.inner.getKey! a
+
 /--
 Returns `true` if the hash set contains no elements.
 

src/Std/Data/HashSet/RawLemmas.lean

@@ -122,6 +122,18 @@ theorem mem_of_mem_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α
     a ∈ m.insert k → (k == a) = false → a ∈ m :=
   HashMap.Raw.mem_of_mem_insertIfNew h.out
 
+/-- This is a restatement of `contains_insert` that is written to exactly match the proof
+obligation in the statement of `get_insert`. -/
+theorem contains_of_contains_insert' [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
+    (m.insert k).contains a → ¬((k == a) ∧ m.contains k = false) → m.contains a :=
+  HashMap.Raw.contains_of_contains_insertIfNew' h.out
+
+/-- This is a restatement of `mem_insert` that is written to exactly match the proof obligation
+in the statement of `get_insertIfNew`. -/
+theorem mem_of_mem_insert' [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
+    a ∈ m.insert k → ¬((k == a) ∧ ¬k ∈ m) → a ∈ m :=
+  HashMap.Raw.mem_of_mem_insertIfNew' h.out
+
 @[simp]
 theorem contains_insert_self [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} :
     (m.insert k).contains k :=
@@ -186,6 +198,162 @@ theorem size_le_size_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α}
     m.size ≤ (m.erase k).size + 1 :=
   HashMap.Raw.size_le_size_erase h.out
 
+@[simp]
+theorem get?_empty {a : α} {c} : (empty c : Raw α).get? a = none :=
+  HashMap.Raw.getKey?_empty
+
+@[simp]
+theorem get?_emptyc {a : α} : (∅ : Raw α).get? a = none :=
+  HashMap.Raw.getKey?_emptyc
+
+theorem get?_of_isEmpty [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
+    m.isEmpty = true → m.get? a = none :=
+  HashMap.Raw.getKey?_of_isEmpty h.out
+
+theorem get?_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
+    (m.insert k).get? a = if k == a ∧ ¬k ∈ m then some k else m.get? a :=
+  HashMap.Raw.getKey?_insertIfNew h.out
+
+theorem contains_eq_isSome_get? [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
+    m.contains a = (m.get? a).isSome :=
+  HashMap.Raw.contains_eq_isSome_getKey? h.out
+
+theorem get?_eq_none_of_contains_eq_false [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
+    m.contains a = false → m.get? a = none :=
+  HashMap.Raw.getKey?_eq_none_of_contains_eq_false h.out
+
+theorem get?_eq_none [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
+    ¬a ∈ m → m.get? a = none :=
+  HashMap.Raw.getKey?_eq_none h.out
+
+theorem get?_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
+    (m.erase k).get? a = if k == a then none else m.get? a :=
+  HashMap.Raw.getKey?_erase h.out
+
+theorem get_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} {h₁} :
+    (m.insert k).get a h₁ =
+      if h₂ : k == a ∧ ¬k ∈ m then k else m.get a (mem_of_mem_insert' h h₁ h₂) :=
+  HashMap.Raw.getKey_insertIfNew (h₁ := h₁) h.out
+
+@[simp]
+theorem get_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} {h'} :
+    (m.erase k).get a h' = m.get a (mem_of_mem_erase h h') :=
+  HashMap.Raw.getKey_erase (h' := h') h.out
+
+theorem get?_eq_some_get [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} {h' : a ∈ m} :
+    m.get? a = some (m.get a h') :=
+  @HashMap.Raw.getKey?_eq_some_getKey _ _ _ _ _ _ _ h.out _ h'
+
+@[simp]
+theorem get?_erase_self [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} :
+    (m.erase k).get? k = none :=
+  HashMap.Raw.getKey?_erase_self h.out
+
+@[simp]
+theorem get!_empty [Inhabited α] {a : α} {c} : (empty c : Raw α).get! a = default :=
+  HashMap.Raw.getKey!_empty
+
+@[simp]
+theorem get!_emptyc [Inhabited α] {a : α} : (∅ : Raw α).get! a = default :=
+  HashMap.Raw.getKey!_emptyc
+
+theorem get!_of_isEmpty [Inhabited α] [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
+    m.isEmpty = true → m.get! a = default :=
+  HashMap.Raw.getKey!_of_isEmpty h.out
+
+theorem get!_insert [Inhabited α] [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
+    (m.insert k).get! a = if k == a ∧ ¬k ∈ m then k else m.get! a :=
+  HashMap.Raw.getKey!_insertIfNew h.out
+
+theorem get!_eq_default_of_contains_eq_false [Inhabited α] [EquivBEq α] [LawfulHashable α]
+    (h : m.WF) {a : α} :
+    m.contains a = false → m.get! a = default :=
+  HashMap.Raw.getKey!_eq_default_of_contains_eq_false h.out
+
+theorem get!_eq_default [Inhabited α] [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} :
+    ¬a ∈ m → m.get! a = default :=
+  HashMap.Raw.getKey!_eq_default h.out
+
+theorem get!_erase [Inhabited α] [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a : α} :
+    (m.erase k).get! a = if k == a then default else m.get! a :=
+  HashMap.Raw.getKey!_erase h.out
+
+@[simp]
+theorem get!_erase_self [Inhabited α] [EquivBEq α] [LawfulHashable α] (h : m.WF) {k : α} :
+    (m.erase k).get! k = default :=
+  HashMap.Raw.getKey!_erase_self h.out
+
+theorem get?_eq_some_get!_of_contains [EquivBEq α] [LawfulHashable α] [Inhabited α]
+    (h : m.WF) {a : α} : m.contains a = true → m.get? a = some (m.get! a) :=
+  HashMap.Raw.getKey?_eq_some_getKey!_of_contains h.out
+
+theorem get?_eq_some_get! [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {a : α} :
+    a ∈ m → m.get? a = some (m.get! a) :=
+  HashMap.Raw.getKey?_eq_some_getKey! h.out
+
+theorem get!_eq_get!_get? [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {a : α} :
+    m.get! a = (m.get? a).get! :=
+  HashMap.Raw.getKey!_eq_get!_getKey? h.out
+
+theorem get_eq_get! [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF) {a : α} {h'} :
+    m.get a h' = m.get! a :=
+  HashMap.Raw.getKey_eq_getKey! h.out
+
+@[simp]
+theorem getD_empty {a fallback : α} {c} : (empty c : Raw α).getD a fallback = fallback :=
+  HashMap.Raw.getKeyD_empty
+
+@[simp]
+theorem getD_emptyc {a fallback : α} : (∅ : Raw α).getD a fallback = fallback :=
+  HashMap.Raw.getKeyD_emptyc
+
+theorem getD_of_isEmpty [EquivBEq α] [LawfulHashable α] (h : m.WF) {a fallback : α} :
+    m.isEmpty = true → m.getD a fallback = fallback :=
+  HashMap.Raw.getKeyD_of_isEmpty h.out
+
+theorem getD_insert [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a fallback : α} :
+    (m.insert k).getD a fallback = if k == a ∧ ¬k ∈ m then k else m.getD a fallback :=
+  HashMap.Raw.getKeyD_insertIfNew h.out
+
+theorem getD_eq_fallback_of_contains_eq_false [EquivBEq α] [LawfulHashable α] (h : m.WF)
+    {a fallback : α} :
+    m.contains a = false → m.getD a fallback = fallback :=
+  HashMap.Raw.getKeyD_eq_fallback_of_contains_eq_false h.out
+
+theorem getD_eq_fallback [EquivBEq α] [LawfulHashable α] (h : m.WF) {a fallback : α} :
+    ¬a ∈ m → m.getD a fallback = fallback :=
+  HashMap.Raw.getKeyD_eq_fallback h.out
+
+theorem getD_erase [EquivBEq α] [LawfulHashable α] (h : m.WF) {k a fallback : α} :
+    (m.erase k).getD a fallback = if k == a then fallback else m.getD a fallback :=
+  HashMap.Raw.getKeyD_erase h.out
+
+@[simp]
+theorem getD_erase_self [EquivBEq α] [LawfulHashable α] (h : m.WF) {k fallback : α} :
+    (m.erase k).getD k fallback = fallback :=
+  HashMap.Raw.getKeyD_erase_self h.out
+
+theorem get?_eq_some_getD_of_contains [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α}
+    {fallback : α} : m.contains a = true → m.get? a = some (m.getD a fallback) :=
+  HashMap.Raw.getKey?_eq_some_getKeyD_of_contains h.out
+
+theorem get?_eq_some_getD [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} {fallback : α} :
+    a ∈ m → m.get? a = some (m.getD a fallback) :=
+  HashMap.Raw.getKey?_eq_some_getKeyD h.out
+
+theorem getD_eq_getD_get? [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} {fallback : α} :
+    m.getD a fallback = (m.get? a).getD fallback :=
+  HashMap.Raw.getKeyD_eq_getD_getKey? h.out
+
+theorem get_eq_getD [EquivBEq α] [LawfulHashable α] (h : m.WF) {a : α} {fallback : α} {h'} :
+    m.get a h' = m.getD a fallback :=
+  @HashMap.Raw.getKey_eq_getKeyD _ _ _ _ _ _ _ h.out _ _ h'
+
+theorem get!_eq_getD_default [EquivBEq α] [LawfulHashable α] [Inhabited α] (h : m.WF)
+    {a : α} :
+    m.get! a = m.getD a default :=
+  HashMap.Raw.getKey!_eq_getKeyD_default h.out
+
 @[simp]
 theorem containsThenInsert_fst (h : m.WF) {k : α} : (m.containsThenInsert k).1 = m.contains k :=
   HashMap.Raw.containsThenInsertIfNew_fst h.out

tests/lean/interactive/completionFallback.lean

@@ -0,0 +1,31 @@
+-- When the elaborator doesn't provide `CompletionInfo`, try to provide identifier completions.
+-- As of when this test case was written, the elaborator did not provide `CompletionInfo` in these cases.
+
+-- https://github.com/leanprover/lean4/issues/5172
+
+inductive Direction where
+  | up
+  | right
+  | down
+  | left
+deriving Repr
+
+def angle (d: Direction) :=
+  match d with
+  | Direction. => 90
+            --^ textDocument/completion
+  | Direction.right => 0
+  | Direction.down => 270
+  | Direction.left => 180
+
+-- Ensure that test is stable when changes to the `And` namespace are made.
+structure CustomAnd (a b : Prop) : Prop where
+  ha : a
+  hb : b
+
+example : p ∨ (q ∧ r) → CustomAnd (p ∨ q) (p ∨ r) := by
+  intro h
+  cases h with
+  | inl hp => apply CustomAnd. (Or.intro_left q hp) (Or.intro_left r hp)
+                            --^ textDocument/completion
+  | inr hqr => apply CustomAnd.mk (Or.intro_right p hqr.left) (Or.intro_right p hqr.right)

tests/lean/interactive/completionFallback.lean.expected.out

@@ -0,0 +1,80 @@
+{"textDocument": {"uri": "file:///completionFallback.lean"},
+ "position": {"line": 14, "character": 14}}
+{"items":
+ [{"sortText": "0",
+   "label": "down",
+   "kind": 4,
+   "data":
+   {"params":
+    {"textDocument": {"uri": "file:///completionFallback.lean"},
+     "position": {"line": 14, "character": 14}},
+    "id": {"const": {"declName": "Direction.down"}}}},
+  {"sortText": "1",
+   "label": "left",
+   "kind": 4,
+   "data":
+   {"params":
+    {"textDocument": {"uri": "file:///completionFallback.lean"},
+     "position": {"line": 14, "character": 14}},
+    "id": {"const": {"declName": "Direction.left"}}}},
+  {"sortText": "2",
+   "label": "noConfusionType",
+   "kind": 3,
+   "data":
+   {"params":
+    {"textDocument": {"uri": "file:///completionFallback.lean"},
+     "position": {"line": 14, "character": 14}},
+    "id": {"const": {"declName": "Direction.noConfusionType"}}}},
+  {"sortText": "3",
+   "label": "right",
+   "kind": 4,
+   "data":
+   {"params":
+    {"textDocument": {"uri": "file:///completionFallback.lean"},
+     "position": {"line": 14, "character": 14}},
+    "id": {"const": {"declName": "Direction.right"}}}},
+  {"sortText": "4",
+   "label": "toCtorIdx",
+   "kind": 3,
+   "data":
+   {"params":
+    {"textDocument": {"uri": "file:///completionFallback.lean"},
+     "position": {"line": 14, "character": 14}},
+    "id": {"const": {"declName": "Direction.toCtorIdx"}}}},
+  {"sortText": "5",
+   "label": "up",
+   "kind": 4,
+   "data":
+   {"params":
+    {"textDocument": {"uri": "file:///completionFallback.lean"},
+     "position": {"line": 14, "character": 14}},
+    "id": {"const": {"declName": "Direction.up"}}}}],
+ "isIncomplete": true}
+{"textDocument": {"uri": "file:///completionFallback.lean"},
+ "position": {"line": 28, "character": 30}}
+{"items":
+ [{"sortText": "0",
+   "label": "ha",
+   "kind": 5,
+   "data":
+   {"params":
+    {"textDocument": {"uri": "file:///completionFallback.lean"},
+     "position": {"line": 28, "character": 30}},
+    "id": {"const": {"declName": "CustomAnd.ha"}}}},
+  {"sortText": "1",
+   "label": "hb",
+   "kind": 5,
+   "data":
+   {"params":
+    {"textDocument": {"uri": "file:///completionFallback.lean"},
+     "position": {"line": 28, "character": 30}},
+    "id": {"const": {"declName": "CustomAnd.hb"}}}},
+  {"sortText": "2",
+   "label": "mk",
+   "kind": 4,
+   "data":
+   {"params":
+    {"textDocument": {"uri": "file:///completionFallback.lean"},
+     "position": {"line": 28, "character": 30}},
+    "id": {"const": {"declName": "CustomAnd.mk"}}}}],
+ "isIncomplete": true}

tests/lean/interactive/fieldCompletion.lean

@@ -1,8 +0,0 @@
-import Lean
-
-open Lean Elab
-
-def f (s : DefView) : DefView := {
-  m
- --^ textDocument/completion
-}

tests/lean/interactive/fieldCompletion.lean.expected.out

@@ -1,3 +0,0 @@
-{"textDocument": {"uri": "file:///fieldCompletion.lean"},
- "position": {"line": 5, "character": 3}}
-{"items": [], "isIncomplete": true}

tests/lean/interactive/hoverException.lean.expected.out

@@ -1,3 +1,8 @@
 {"textDocument": {"uri": "file:///hoverException.lean"},
  "position": {"line": 2, "character": 14}}
-null
+{"range":
+ {"start": {"line": 2, "character": 7}, "end": {"line": 2, "character": 18}},
+ "contents":
+ {"value":
+  "Explicit binder, like `(x y : A)` or `(x y)`.\nDefault values can be specified using `(x : A := v)` syntax, and tactics using `(x : A := by tac)`.\n",
+  "kind": "markdown"}}

tests/lean/interactive/incrementalCommand.lean

@@ -81,3 +81,16 @@ where
          --^ sync
          --^ insert: " "
          --^ collectDiagnostics
+
+/-!
+A reuse bug led to deletions after the header skipping a prefix of the next command on further edits
+-/
+-- RESET
+--asdf
+--^ delete: "a"
+--^ sync
+def f := 1  -- used to raise "unexpected identifier" after edit below because we would start parsing
+            -- on "ef"
+def g := 2
+   --^ insert: "g"
+   --^ collectDiagnostics

tests/lean/interactive/incrementalCommand.lean.expected.out

@@ -33,3 +33,4 @@ w
    "message": "tactic 'assumption' failed\n⊢ False",
    "fullRange":
    {"start": {"line": 2, "character": 2}, "end": {"line": 2, "character": 9}}}]}
+{"version": 3, "uri": "file:///incrementalCommand.lean", "diagnostics": []}

tests/lean/linterUnusedVariables.lean

@@ -250,8 +250,9 @@ example [ord : Ord β] (f : α → β) (x y : α) : Ordering := compare (f x) (f
 example {α β} [ord : Ord β] (f : α → β) (x y : α) : Ordering := compare (f x) (f y)
 example {h : Decidable True} (t e : α) : ite True t e = t := if_pos trivial
 
-@[unused_variables_ignore_fn]
-def ignoreEverything : Lean.Linter.IgnoreFunction :=
-  fun _ _ _ => true
-
-def ignored (x : Nat) := 0
+/-!
+The wildcard pattern introduces a copy of `x` that should not be linted as it is in an
+inaccessible annotation.
+-/
+example : (x = y) → y = x
+  | .refl _ => .refl _

tests/lean/run/issue5347.lean

@@ -0,0 +1,19 @@
+def f (x: Nat): Option Nat :=
+  if x > 10 then some 0 else none
+
+def test (x: Nat): Nat :=
+  match f x, x with
+  | some k, _ => k
+  | none, 0 => 0
+  | none, n + 1 => test n
+
+-- set_option trace.Meta.FunInd true
+
+-- At the time of writing, the induction princpile misses the `f x = some k` assumptions:
+
+/--
+info: test.induct (motive : Nat → Prop) (case1 : ∀ (x : Nat), motive x) (case2 : motive 0)
+  (case3 : ∀ (n : Nat), motive n → motive n.succ) (x : Nat) : motive x
+-/
+#guard_msgs in
+#check test.induct

tests/lean/run/mergeSort.lean

@@ -1,25 +1,62 @@
 open List MergeSort Internal
 
+-- If we omit the comparator, it is filled by the autoparam `fun a b => a ≤ b`
 unseal mergeSort merge in
-example : mergeSort (· ≤ ·) [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5] = [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9] :=
+example : mergeSort [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5] = [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9] :=
   rfl
 
 unseal mergeSort merge in
-example : mergeSort (fun x y => x/10 ≤ y/10) [3, 100 + 1, 4, 100 + 1, 5, 100 + 9, 2, 10 + 6, 5, 10 + 3, 5] = [3, 4, 5, 2, 5, 5, 16, 13, 101, 101, 109] :=
+example : mergeSort [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5] (· ≤ ·) = [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9] :=
+  rfl
+
+unseal mergeSort merge in
+example : mergeSort [3, 100 + 1, 4, 100 + 1, 5, 100 + 9, 2, 10 + 6, 5, 10 + 3, 5] (fun x y => x/10 ≤ y/10) = [3, 4, 5, 2, 5, 5, 16, 13, 101, 101, 109] :=
   rfl
 
 unseal mergeSortTR.run mergeTR.go in
-example : mergeSortTR (· ≤ ·) [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5] = [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9] :=
+example : mergeSortTR [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5] = [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9] :=
   rfl
 
 unseal mergeSortTR.run mergeTR.go in
-example : mergeSortTR (fun x y => x/10 ≤ y/10) [3, 100 + 1, 4, 100 + 1, 5, 100 + 9, 2, 10 + 6, 5, 10 + 3, 5] = [3, 4, 5, 2, 5, 5, 16, 13, 101, 101, 109] :=
+example : mergeSortTR [3, 100 + 1, 4, 100 + 1, 5, 100 + 9, 2, 10 + 6, 5, 10 + 3, 5] (fun x y => x/10 ≤ y/10) = [3, 4, 5, 2, 5, 5, 16, 13, 101, 101, 109] :=
   rfl
 
 unseal mergeSortTR₂.run mergeTR.go in
-example : mergeSortTR₂ (· ≤ ·) [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5] = [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9] :=
+example : mergeSortTR₂ [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5] = [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9] :=
   rfl
 
 unseal mergeSortTR₂.run mergeTR.go in
-example : mergeSortTR₂ (fun x y => x/10 ≤ y/10) [3, 100 + 1, 4, 100 + 1, 5, 100 + 9, 2, 10 + 6, 5, 10 + 3, 5] = [3, 4, 5, 2, 5, 5, 16, 13, 101, 101, 109] :=
+example : mergeSortTR₂ [3, 100 + 1, 4, 100 + 1, 5, 100 + 9, 2, 10 + 6, 5, 10 + 3, 5] (fun x y => x/10 ≤ y/10) = [3, 4, 5, 2, 5, 5, 16, 13, 101, 101, 109] :=
   rfl
+
+/-!
+# Behaviour of mergeSort when the comparator is not provided, but typeclasses are missing.
+-/
+
+inductive NoLE
+| mk : NoLE
+
+/--
+error: failed to synthesize
+  LE NoLE
+Additional diagnostic information may be available using the `set_option diagnostics true` command.
+-/
+#guard_msgs in
+example : mergeSort [NoLE.mk] = [NoLE.mk] := sorry
+
+inductive UndecidableLE
+| mk : UndecidableLE
+
+instance : LE UndecidableLE where
+  le := fun _ _ => true
+
+/--
+error: type mismatch
+  a ≤ b
+has type
+  Prop : Type
+but is expected to have type
+  Bool : Type
+-/
+#guard_msgs in
+example : mergeSort [UndecidableLE.mk] = [UndecidableLE.mk] := sorry

tests/lean/run/mergeSortCPDT.lean

@@ -6,7 +6,7 @@ def List.insert' (p : α → α → Bool) (a : α) (bs : List α) : List α :=
 def List.merge' (p : α → α → Bool) (as bs : List α) : List α :=
   match as with
   | [] => bs
-  | a :: as' => insert' p a (merge p as' bs)
+  | a :: as' => insert' p a (merge' p as' bs)
 
 def List.split (as : List α) : List α × List α :=
   match as with

tests/lean/run/variable.lean

@@ -138,6 +138,7 @@ variable [ToString α] in
 omit [ToString α] in
 theorem t13 (a : α) : toString a = toString a := rfl
 
+set_option pp.mvars false in
 /--
 error: application type mismatch
   ToString True
@@ -146,7 +147,7 @@ argument
 has type
   Prop : Type
 but is expected to have type
-  Type ?u.1758 : Type (?u.1758 + 1)
+  Type _ : Type (_ + 1)
 -/
 #guard_msgs in
 omit [ToString True]

tests/lean/stdio.lean

@@ -10,7 +10,7 @@ out.putStrLn "print stdout"
 let err ← IO.getStderr;
 (err.putStr "print stderr" : IO Unit)
 
-open usingIO IO
+open IO
 
 def test : IO Unit := do
 FS.withFile "stdout1.txt" IO.FS.Mode.write $ fun h₁ => do