intros x x' y y' H' H'0; try assumption.
apply Trans with (addfraction_fun x' y).
apply addfraction_law_l; auto with algebra.
apply addfraction_law_r; auto with algebra.
Qed.

Lemma multfraction_dist_l :
forall x y z : fraction_set,
Equal (multfraction_fun x (addfraction_fun y z))
(addfraction_fun (multfraction_fun x y) (multfraction_fun x z)).