chore: test for issue #9216 (#9238)

This PR adds a new test with the analysis for issue #9216.

Author: leodemoura

tests/lean/run/grind_9216.lean

@@ -0,0 +1,36 @@
+import Std.Data.HashSet
+
+open Std
+
+example (seen : HashSet Int) (xs : List Int) (x : Int) (h : ¬-x ∈ seen) :
+    (∃ a, a ∈ seen.insert x ∧ ∃ b, b ∈ xs ∧ a + b = 0) ↔
+    (∃ y, y ∈ xs ∧ x + y = 0) ∨ ∃ a, a ∈ seen ∧ ∃ b, b ∈ x :: xs ∧ a + b = 0 := by
+  -- In 4.22.0-rc2, this example used to work without the `simp only` because patterns containing `+` were being selected.
+  -- By unfolding `HashSet.mem_insert` before invoking `grind` we change the pattern that is selected. That is, `_ ∈ seen` is selected.
+  simp only [HashSet.mem_insert]
+  grind
+
+-- The example also works when we restore `HAdd.hAdd` priority.
+-- We say this example worked by "accident" before.
+attribute [local grind symbol default] HAdd.hAdd in
+example (seen : HashSet Int) (xs : List Int) (x : Int) (h : ¬-x ∈ seen) :
+    (∃ a, a ∈ seen.insert x ∧ ∃ b, b ∈ xs ∧ a + b = 0) ↔
+    (∃ y, y ∈ xs ∧ x + y = 0) ∨ ∃ a, a ∈ seen ∧ ∃ b, b ∈ x :: xs ∧ a + b = 0 := by
+  grind
+
+/-
+Here is an encoding trick used in the SMT community.
+Terms like `x + y` are rarely used in patterns because
+they generate too many instances, and because arithmetical
+terms are often normalized by SMT solvers. However, for E-matching,
+`+` is just another symbol. The E-matcher does not know that it is,
+for example, associative and commutative (AC).
+If you want to E-match against an arithmetical relation, you can
+introduce an auxiliary definition to make the pattern matching more effective.
+Example:
+-/
+@[grind] def IsAddInv (a b : Int) : Prop := a = -b
+example (seen : HashSet Int) (xs : List Int) (x : Int) (h : ¬-x ∈ seen) :
+    (∃ a, a ∈ seen.insert x ∧ ∃ b, b ∈ xs ∧ IsAddInv a b) ↔
+    (∃ y, y ∈ xs ∧ IsAddInv x y) ∨ ∃ a, a ∈ seen ∧ ∃ b, b ∈ x :: xs ∧ IsAddInv a b := by
+  grind