elim H.
elim mult_comm; elim mult_comm with (S x) a.
apply lt_mult_n_Sn; assumption.
intros.
apply lt_trans with (a * m).
assumption.
elim mult_comm; elim mult_comm with (S m) a.
apply lt_mult_n_Sn; assumption.
Qed.
Hint Resolve lt_mult_cst.

(* Specifications: *)
Lemma lt_mult_csts : forall a b c d : nat, a < b -> c < d -> a * c < b * d.
intros.