feat: add a test replacing an axiom

Lean4CheckerTests/ReplaceAxiom.lean

@@ -0,0 +1,27 @@
+import Lean4CheckerTests.OpenPrivate
+
+/- Redefine `propext : False`. -/
+open Lean Elab Meta in
+open private Environment.mk from Lean.Environment in
+#eval modifyEnv (m := MetaM) fun env =>
+  let consts :=
+    { env.constants with
+        map₁ := env.constants.map₁.insert ``propext (.axiomInfo {
+          name := ``propext
+          type := .const ``False []
+          levelParams := []
+          isUnsafe := false
+        })
+    }
+  Environment.mk env.const2ModIdx consts env.extensions env.extraConstNames env.header
+
+theorem efsq : ∀ (x y z n : Nat),
+    0 < x → 0 < y → 0 < z → 2 < n →
+    x^n + y^n ≠ z^n := by
+  exfalso
+  exact propext
+
+/-- info: 'efsq' depends on axioms: [propext] -/
+#guard_msgs in
+-- 'efsq' depends on axioms: [propext]
+#print axioms efsq

test.sh

@@ -32,6 +32,14 @@ but it is expected to have type
 check_command "lake -q exe lean4checker Lean4CheckerTests.AddFalseConstructor" "lean4checker found a problem in Lean4CheckerTests.AddFalseConstructor
 uncaught exception: No such constructor False.intro"
 
+check_command "lake -q exe lean4checker Lean4CheckerTests.ReplaceAxiom" "lean4checker found a problem in Lean4CheckerTests.ReplaceAxiom
+uncaught exception: application type mismatch
+  False.elim @propext
+argument has type
+  ∀ {a b : Prop}, (a ↔ b) → a = b
+but function has type
+  False → ∀ (x y z n : Nat), 0 < x → 0 < y → 0 < z → 2 < n → x ^ n + y ^ n ≠ z ^ n"
+
 check_command "lake -q exe lean4checker --fresh Lean4CheckerTests.UseFalseConstructor" "uncaught exception: (kernel) unknown constant 'False.intro'"
 
 # The 'ReduceBool' test writes to a temporary file.