lean2/tests/lean/apply_tac1.lean

24 lines
558 B
Text
Raw Normal View History

import tactic.
import Int.
variable f : Int -> Int -> Bool
variable P : Int -> Int -> Bool
axiom Ax1 (x y : Int) (H : P x y) : (f x y)
theorem T1 (a : Int) : (P a a) → (f a a).
apply Ax1.
exact.
done.
variable b : Int
axiom Ax2 (x : Int) : (f x b)
(*
simple_tac = Repeat(OrElse(assumption_tac(), apply_tac("Ax2"), apply_tac("Ax1")))
*)
theorem T2 (a : Int) : (P a a) → (f a a).
simple_tac.
done.
theorem T3 (a : Int) : (P a a) → (f a a).
Repeat (OrElse exact (apply Ax2) (apply Ax1)).
done.
print environment 2.