proposition: Lemma mul_succ_l n m : S n * m = n * m + m.
proof: Proof. assert (succ_r : forall x y, x+S y = S(x+y)) by now intro x; induction x. assert (comm : forall x y, x+y = y+x). { intro x; induction x; simpl; auto. intros; rewrite succ_r; now f_equal. } now rewrite comm. Qed.
imports: NAxioms NProperties OrdersFacts DecidableClass