2014-01-05 20:05:08 +00:00
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import Int.
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2014-01-05 18:32:47 +00:00
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(* import("tactic.lua") *)
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2014-01-05 20:05:08 +00:00
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variable f : Int -> Int -> Int
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2013-12-07 21:09:39 +00:00
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2014-01-05 18:32:47 +00:00
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(*
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2014-01-06 03:10:21 +00:00
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refl_tac = apply_tac("refl")
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congr_tac = apply_tac("congr")
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symm_tac = apply_tac("symm")
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trans_tac = apply_tac("trans")
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2013-12-07 21:09:39 +00:00
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unfold_homo_eq_tac = unfold_tac("eq")
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2013-12-26 23:54:53 +00:00
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auto = unfold_homo_eq_tac .. Repeat(OrElse(refl_tac, congr_tac, assumption_tac(), Then(symm_tac, assumption_tac(), now_tac())))
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2014-01-05 18:32:47 +00:00
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*)
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2013-12-07 21:09:39 +00:00
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2014-01-05 20:05:08 +00:00
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theorem T1 (a b c : Int) (H1 : a = b) (H2 : a = c) : (f (f a a) b) = (f (f b c) a).
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2013-12-26 23:54:53 +00:00
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auto.
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2013-12-07 21:09:39 +00:00
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done.
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2014-01-05 20:05:08 +00:00
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theorem T2 (a b c : Int) (H1 : a = b) (H2 : a = c) : (f (f a c)) = (f (f b a)).
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2013-12-26 23:54:53 +00:00
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auto.
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2013-12-07 21:09:39 +00:00
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done.
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2014-01-05 20:05:08 +00:00
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print environment 2.
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