+-comm : (x y : ℕ) → x + y ≡ y + x
+-comm zero y rewrite (+zero {y}) = refl
+-comm (suc x) y = let open ≡-Reasoning in
  begin
  suc (x + y) ≡⟨⟩
  suc (x + y) ≡⟨ cong suc (+-comm x y) ⟩
  suc (y + x) ≡⟨ sym (+-suc {y} {x}) ⟩
  y + suc x ∎

-- +-suc : {x y : ℕ} → x + suc y ≡ suc (x + y)
-- +-suc {zero} {y} = refl
-- +-suc {suc x} {y} = cong suc (+-suc {x} {y})