2014-08-01 16:37:23 +00:00
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import standard
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2014-07-26 17:36:21 +00:00
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using eq_proofs
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inductive nat : Type :=
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| zero : nat
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| succ : nat → nat
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definition add (x y : nat) : nat := nat_rec x (λn r, succ r) y
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infixl `+`:65 := add
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definition mul (n m : nat) := nat_rec zero (fun m x, x + n) m
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infixl `*`:75 := mul
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axiom mul_zero_right (n : nat) : n * zero = zero
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variable P : nat → Prop
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print "==========================="
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theorem tst (n : nat) (H : P (n * zero)) : P zero
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:= subst (mul_zero_right _) H
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