18 lines
490 B
Text
18 lines
490 B
Text
opaque f (x y : Nat) : Nat
|
|
opaque g (x : Nat) : Nat
|
|
|
|
theorem ex1 (x : Nat) (h₁ : f x x = g x) (h₂ : g x = x) : f x (f x x) = x := by
|
|
simp
|
|
simp [*]
|
|
|
|
theorem ex2 (x : Nat) (h₁ : f x x = g x) (h₂ : g x = x) : f x (f x x) = x := by
|
|
simp [*]
|
|
|
|
axiom g_ax (x : Nat) : g x = 0
|
|
|
|
theorem ex3 (x y : Nat) (h₁ : f x x = g x) (h₂ : f x x < 5) : f x x + f x x = 0 := by
|
|
simp [*] at *
|
|
trace_state
|
|
have aux₁ : f x x = g x := h₁
|
|
have aux₂ : g x < 5 := h₂
|
|
simp [g_ax]
|