intuition.
rewrite H.
rewrite <- (ratMult_1_r r2) at 2.
rewrite ratMult_assoc.
eapply ratMult_eqRat_compat.
intuition.
rewrite <- ratMult_num_den.
eapply num_dem_same_rat1.
rattac.
Qed.

Lemma ratMult_inverse_nat : forall r1 r2 n d (nzn : nz n),
r1 == r2 * (RatIntro n d) ->
r1 * (RatIntro d (natToPosnat nzn)) == r2.