test: test case for #10775

Author: nomeata

tests/lean/run/issue10775.lean

@@ -0,0 +1,132 @@
+set_option linter.unusedVariables false
+
+opaque R : (n m : Int) → Type
+
+axiom mkR : Nat → R n m
+
+noncomputable def d : ∀ (n m : Int), R n m
+  | .ofNat n, .ofNat m => mkR 0
+  | .negSucc n, .negSucc m => mkR 0
+  | .negSucc 0, .ofNat 0 => mkR 0
+  | .ofNat _, .negSucc _ => mkR 0
+  | .negSucc _, .ofNat _ => mkR 0
+
+/--
+error: unsolved goals
+case refine_1
+⊢ ∀ (n m : Nat), ¬↑n + 1 = ↑m → mkR 0 = mkR 0
+
+case refine_2
+⊢ ∀ (n m : Nat), ¬Int.negSucc n + 1 = Int.negSucc m → mkR 0 = mkR 0
+
+case refine_3
+⊢ ¬0 = 0 → mkR 0 = mkR 0
+
+case refine_4
+⊢ ∀ (a a_1 : Nat), ¬↑a + 1 = Int.negSucc a_1 → mkR 0 = mkR 0
+
+case refine_5
+⊢ ∀ (a a_1 : Nat), (a = 0 → a_1 = 0 → False) → ¬Int.negSucc a + 1 = ↑a_1 → mkR 0 = mkR 0
+-/
+#guard_msgs in
+example : (n m : Int) → (hnm : n + 1 ≠ m) → d n m = mkR 0 := by
+  refine d.fun_cases_unfolding (motive := fun n m r => (n + 1 ≠ m) → r = mkR 0)
+    ?_ ?_ ?_ ?_ ?_ <;> dsimp
+
+/--
+error: unsolved goals
+case case1
+n✝ m✝ : Nat
+hnm : Int.ofNat n✝ + 1 ≠ Int.ofNat m✝
+⊢ d (Int.ofNat n✝) (Int.ofNat m✝) = mkR 0
+
+case case2
+n✝ m✝ : Nat
+hnm : Int.negSucc n✝ + 1 ≠ Int.negSucc m✝
+⊢ d (Int.negSucc n✝) (Int.negSucc m✝) = mkR 0
+
+case case3
+hnm : Int.negSucc 0 + 1 ≠ Int.ofNat 0
+⊢ d (Int.negSucc 0) (Int.ofNat 0) = mkR 0
+
+case case4
+a✝¹ a✝ : Nat
+hnm : Int.ofNat a✝¹ + 1 ≠ Int.negSucc a✝
+⊢ d (Int.ofNat a✝¹) (Int.negSucc a✝) = mkR 0
+
+case case5
+a✝¹ a✝ : Nat
+x✝ : a✝¹ = 0 → a✝ = 0 → False
+hnm : Int.negSucc a✝¹ + 1 ≠ Int.ofNat a✝
+⊢ d (Int.negSucc a✝¹) (Int.ofNat a✝) = mkR 0
+-/
+#guard_msgs in
+example : (n m : Int) → (hnm : n + 1 ≠ m) → d n m = mkR 0 := by
+  intros n m hnm
+  fun_cases d
+
+-- set_option trace.Elab.induction true in
+
+/--
+error: unsolved goals
+case case1
+n✝ m✝ : Nat
+hnm : Int.ofNat n✝ + 1 ≠ Int.ofNat m✝
+⊢ d (Int.ofNat n✝) (Int.ofNat m✝) = mkR 0
+
+case case2
+n✝ m✝ : Nat
+hnm : Int.negSucc n✝ + 1 ≠ Int.negSucc m✝
+⊢ d (Int.negSucc n✝) (Int.negSucc m✝) = mkR 0
+
+case case3
+hnm : Int.negSucc 0 + 1 ≠ Int.ofNat 0
+⊢ d (Int.negSucc 0) (Int.ofNat 0) = mkR 0
+
+case case4
+a✝¹ a✝ : Nat
+hnm : Int.ofNat a✝¹ + 1 ≠ Int.negSucc a✝
+⊢ d (Int.ofNat a✝¹) (Int.negSucc a✝) = mkR 0
+
+case case5
+a✝¹ a✝ : Nat
+x✝ : a✝¹ = 0 → a✝ = 0 → False
+hnm : Int.negSucc a✝¹ + 1 ≠ Int.ofNat a✝
+⊢ d (Int.negSucc a✝¹) (Int.ofNat a✝) = mkR 0
+-/
+#guard_msgs(pass trace, all) in
+example : (n m : Int) → (hnm : n + 1 ≠ m) → d n m = mkR 0 := by
+  intros n m hnm
+  cases n, m using d.fun_cases_unfolding
+
+/--
+error: unsolved goals
+case case1
+n✝ m✝ : Nat
+hnm : Int.ofNat n✝ + 1 ≠ Int.ofNat m✝
+⊢ mkR 0 = mkR 0
+
+case case2
+n✝ m✝ : Nat
+hnm : Int.negSucc n✝ + 1 ≠ Int.negSucc m✝
+⊢ mkR 0 = mkR 0
+
+case case3
+hnm : Int.negSucc 0 + 1 ≠ Int.ofNat 0
+⊢ mkR 0 = mkR 0
+
+case case4
+a✝¹ a✝ : Nat
+hnm : Int.ofNat a✝¹ + 1 ≠ Int.negSucc a✝
+⊢ mkR 0 = mkR 0
+
+case case5
+a✝¹ a✝ : Nat
+x✝ : a✝¹ = 0 → a✝ = 0 → False
+hnm : Int.negSucc a✝¹ + 1 ≠ Int.ofNat a✝
+⊢ mkR 0 = mkR 0
+-/
+#guard_msgs(pass trace, all) in
+example : (n m : Int) → (hnm : n + 1 ≠ m) → d n m = mkR 0 := by
+  intros n m hnm
+  induction n, m using d.fun_cases_unfolding