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

  Set: pp::colors
  Set: pp::unicode
  Imported 'macros'
  Using: Nat
  Assumed: Induction
  Proved: Comm1
  Proved: Comm2
theorem Comm2 : ∀ n m : ℕ, n + m = m + n :=
    λ n : ℕ,
      Induction
          (λ x : ℕ, n + x == x + n)
          (Nat::add_zeror n ⋈ symm (Nat::add_zerol n))
          (λ (m : ℕ) (iH : n + m = m + n),
             Nat::add_succr n m ⋈ subst (refl (n + m + 1)) iH ⋈ symm (Nat::add_succl m n))