proposition: Theorem minus_n_n : forall n, n - n = 0.
proof: Proof. Admitted. Theorem add_comm : forall n m : nat, n + m = m + n. Admitted. Theorem mult_0_plus' : forall n m : nat, (n + 0 + 0) * m = n * m. Proof. intros n m. assert (H: n + 0 + 0 = n). { rewrite add_comm. simpl. rewrite add_comm. reflexivity. } rewrite -> H. reflexivity. Qed.