2014-07-31 21:36:13 +00:00
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import logic
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inductive nat : Type :=
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2014-08-22 22:46:10 +00:00
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zero : nat,
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succ : nat → nat
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2014-07-31 21:36:13 +00:00
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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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axiom add_right_comm (n m k : nat) : n + m + k = n + k + m
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print "==========================="
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theorem bug (a b c d : nat) : a + b + c + d = a + c + b + d
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:= subst (add_right_comm _ _ _) (refl (a + b + c + d))
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