intros H'; inversion H'.
intros n H'; rewrite mult_comm; simpl in |- *; auto with arith.
Qed.
(*********************************************************************** ********************************************************************** ********************************************************************** FACTORIAL*)
Fixpoint factorial (n : nat) : nat :=
match n with
| O => 1
| S n' => n * factorial n'
end.
(*********************************************************************** ********************************************************************** ********************************************************************** POWER*)
Fixpoint power (x n : nat) {struct n} : nat :=
match n with
| O => 1
| S n' => x * power x n'
end.

(* Specifications: *)
Lemma power_SO : forall x : nat, power 1 x = 1.
Lemma power_lt_O : forall x n : nat, 0 < x -> 0 < power x n.
simple induction n; simpl in |- *; auto with arith.