induction m.
rewrite mult_comm in H.
simpl in H;discriminate.
assert ((S n)<=((S n)*(S m))).
apply mult_lemma1;discriminate.
assert (((S n)*(S m))=((S m)+n*(S m))).
reflexivity.
rewrite H1 in H0.
rewrite H in H0.
assert ((S n)=1).
omega.
split;trivial.
inversion H2.
rewrite H4 in H.
simpl in H.
omega.
Qed.

(* Specifications: *)
Lemma plus_minus_lemma1 : forall (y x:nat),(x+y-y=x).
induction y;intros;rewrite plus_comm;simpl.