lean2/tests/lean/using_bug1.lean
Leonardo de Moura ba9a8f9d98 feat(frontends/lean): add 'show' expression syntax sugar
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-02-06 07:50:22 -08:00

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variables a b c d : Nat
axiom H : a + (b + c) = a + (b + d)
set_option pp::implicit true
using Nat
check add_succr a
theorem mul_zerol2 (a : Nat) : 0 * a = 0
:= induction_on a
(show 0 * 0 = 0, from mul_zeror 0)
(λ (n : Nat) (iH : 0 * n = 0),
calc 0 * (n + 1) = (0 * n) + 0 : mul_succr 0 n
... = 0 + 0 : { iH }
... = 0 : add_zeror 0)