intuition.
rewrite <- ratMult_1_r.
erewrite <- (ratInverse_prod_1 H).
rewrite (ratMult_comm (ratInverse r1)).
rewrite <- ratMult_assoc.
eapply leRat_trans.
eapply ratMult_leRat_compat.
eapply H0.
eapply leRat_refl.
rewrite ratMult_assoc.
rewrite (ratMult_comm r1).
rewrite ratInverse_prod_1.
rewrite ratMult_1_r.
intuition.
intuition.
Qed.

Lemma ratMult_eq_rat1 : forall n1 n2 (nz1 : nz n1)(nz2 : nz n2),
(n1 / n2) * (n2 / n1) == 1.