proposition: Theorem power_of_mult : forall n x y, (x * y) ^ n == x ^ n * y ^ n.
proof: Proof. induction n;simpl. - intros;rewrite Eone_left;auto. reflexivity. - intros; rewrite IHn; repeat rewrite Eop_assoc. rewrite <- (Eop_assoc x y (power x n)); rewrite (Eop_comm y (power x n)). repeat rewrite Eop_assoc;reflexivity. Qed.
imports: ZArith Div2 Recdef Relations Morphisms Monoid_def Arith Lia