lean2/tests/lean/induction1.lean.expected.out
Leonardo de Moura 048151487e feat(kernel): use Pi as forall/implication
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-08 00:38:39 -08:00

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Set: pp::colors
Set: pp::unicode
Imported 'macros'
Using: Nat
Assumed: Induction
Proved: Comm1
Proved: Comm2
theorem Comm2 : ∀ n m : , n + m = m + n :=
λ n : ,
Induction
(λ x : , n + x == x + n)
(Nat::add::zeror n ⋈ symm (Nat::add::zerol n))
(λ (m : ) (iH : n + m = m + n),
Nat::add::succr n m ⋈ subst (refl (n + m + 1)) iH ⋈ symm (Nat::add::succl m n))