fix: grind internalization (#11318)

This PR fixes a local declaration internalization in `grind` that was
exposed when using `grind -revert`. This bug was affecting a `grind`
proof in Mathlib.

src/Lean/Meta/Tactic/Grind/Main.lean

@@ -215,16 +215,7 @@ private def addHypotheses (goal : Goal) : GrindM Goal := GoalM.run' goal do
       | none => add r.expr localDecl.toExpr
       | some h => add r.expr <| mkApp4 (mkConst ``Eq.mp [0]) type r.expr h localDecl.toExpr
     else
-      /-
-      **Note**: We must internalize local variables because their types may be empty, and may not be
-      referenced anywhere else. Example:
-      ```
-      example (a : { x : Int // x < 0 ∧ x > 0 }) : False := by grind
-      ```
-      -/
-      let e ← shareCommon localDecl.toExpr
-      internalize e 0
-  processNewFacts
+      internalizeLocalDecl localDecl
 
 private def initCore (mvarId : MVarId) (params : Params) : GrindM Goal := do
   /-

src/Lean/Meta/Tactic/Grind/Types.lean

@@ -1288,6 +1288,23 @@ opaque internalize (e : Expr) (generation : Nat) (parent? : Option Expr := none)
 @[extern "lean_grind_process_new_facts"]
 opaque processNewFacts : GoalM Unit
 
+/--
+Internalizes a local declaration which is not a proposition.
+**Note**: We must internalize local variables because their types may be empty, and may not be
+referenced anywhere else. Example:
+```
+example (a : { x : Int // x < 0 ∧ x > 0 }) : False := by grind
+```
+`etaStruct` may also be applicable.
+-/
+def internalizeLocalDecl (localDecl : LocalDecl) : GoalM Unit := do
+  let e ← shareCommon localDecl.toExpr
+  internalize e 0
+  /-
+  **Note**: `internalize` may add new facts (e.g., `etaStruct` equality)
+  -/
+  processNewFacts
+
 /--
 Returns a proof that `a = b` if they have the same type. Otherwise, returns a proof of `a ≍ b`.
 It assumes `a` and `b` are in the same equivalence class.

tests/lean/run/grind_eta_struct_internalize.lean

@@ -0,0 +1,38 @@
+namespace List
+
+/-
+This example exposed a bug in the `grind` internalizer when `grind -revert`
+is used.
+-/
+
+variable {α : Type} {β : α → Type}
+
+def keys : List (Sigma β) → List α :=
+  map Sigma.fst
+
+@[grind =]
+theorem keys_cons {s} {l : List (Sigma β)} : (s :: l).keys = s.1 :: l.keys :=
+  rfl
+
+variable [DecidableEq α]
+
+def dlookup (a : α) : List (Sigma β) → Option (β a)
+  | [] => none
+  | ⟨a', b⟩ :: l => if h : a' = a then some (Eq.recOn h b) else dlookup a l
+
+@[grind =]
+theorem dlookup_cons_eq (l) (a : α) (b : β a) : dlookup a (⟨a, b⟩ :: l) = some b :=
+  dif_pos rfl
+
+@[grind =]
+theorem dlookup_cons_ne (l) {a} : ∀ s : Sigma β, a ≠ s.1 → dlookup a (s :: l) = dlookup a l
+  | ⟨_, _⟩, h => dif_neg h.symm
+
+@[grind =]
+theorem dlookup_isSome {a : α} {l : List (Sigma β)} : (dlookup a l).isSome ↔ a ∈ l.keys := by
+  induction l with
+  | nil => sorry
+  | cons s _ _ =>
+    by_cases a = s.fst
+    · grind
+    · sorry