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 :=
    forall::intro
        (λ n : ℕ,
           Induction ◂ (λ x : ℕ, n + x == x + n) ◂ (Nat::add::zeror n ⋈ symm (Nat::add::zerol n)) ◂
           forall::intro
               (λ m : ℕ,
                  discharge
                      (λ iH : n + m = m + n,
                         Nat::add::succr n m ⋈ subst (refl (n + m + 1)) iH ⋈ symm (Nat::add::succl m n))))