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