proposition: Theorem mul_add_distr_r : ∀ n m p, (n + m) * p = n * p + m * p.
proof: Proof. intros n m p. destruct n as [n| ]; [ simpl | reflexivity ]. destruct p as [p| ]; [ simpl | destruct m; reflexivity ]. destruct m; [ simpl | reflexivity ]. rewrite Nat.mul_add_distr_r; reflexivity. Qed.
imports: Utf8 Compare_dec NPeano Misc