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| @[extern "add_one"] | |
| opaque addOne : UInt32 → UInt32 | |
| def specialAddOne : (x : Nat) → Nat := | |
| fun x => (addOne (UInt32.ofNat x)).toNat | |
| axiom specialAddOne_eq_add_one : ∀ x : Nat, specialAddOne x = x + 1 | |
| variable (a b c d e : Nat) | |
| variable (h1 : a = b) | |
| variable (h2 : b = specialAddOne c) | |
| --variable (h2 : b = c + 1) | |
| variable (h3 : c = d) | |
| variable (h4 : e = 1 + d) | |
| theorem T : a = e := | |
| calc | |
| a = b := h1 | |
| b = specialAddOne c := h2 | |
| specialAddOne c = c + 1 := specialAddOne_eq_add_one c | |
| c + 1 = d + 1 := congrArg Nat.succ h3 | |
| d + 1 = 1 + d := Nat.add_comm d 1 | |
| 1 + d = e := Eq.symm h4 |
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