lean2/tests/lean/tactic13.lean
Leonardo de Moura 7726ccad28 chore(builtin): rename nat, int and real modules to Nat, Int and Real.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-01 13:52:25 -08:00

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Import Int.
(** import("tactic.lua") **)
Variable f : Int -> Int -> Int
(**
refl_tac = apply_tac("Refl")
congr_tac = apply_tac("Congr")
symm_tac = apply_tac("Symm")
trans_tac = apply_tac("Trans")
unfold_homo_eq_tac = unfold_tac("eq")
auto = unfold_homo_eq_tac .. Repeat(OrElse(refl_tac, congr_tac, assumption_tac(), Then(symm_tac, assumption_tac(), now_tac())))
**)
Theorem T1 (a b c : Int) (H1 : a = b) (H2 : a = c) : (f (f a a) b) = (f (f b c) a).
auto.
done.
Theorem T2 (a b c : Int) (H1 : a = b) (H2 : a = c) : (f (f a c)) = (f (f b a)).
auto.
done.
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