lean2/tests/lean/induction1.lean.expected.out

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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)
(trans (Nat::add_zeror n) (symm (Nat::add_zerol n)))
(λ (m : ) (iH : n + m = m + n),
trans (trans (Nat::add_succr n m) (subst (refl (n + m + 1)) iH)) (symm (Nat::add_succl m n)))