rewrite mult_assoc_reverse.
rewrite mult_assoc_reverse.
replace (c * b) with (b * c); auto with arith.
Qed. Hint Resolve mult_permute.
(* Lemma plus_n_n : (n:nat)((plus n n)=(mult n (S (S O)))). Intro. Rewrite -> mult_sym. Simpl. Replace (plus n O) with (plus O n);Auto with arith. Qed. Hints Resolve plus_n_n. *)

Lemma plus_O_O : forall n m : nat, n + m = 0 -> n = 0.
simple induction n. intros. trivial with arith.