intuition.
unfold ratInverse.
destruct r1. destruct r2.
destruct n.
exfalso.
eapply H.
eapply rat_num_0.
destruct n0.
exfalso.
eapply rat_num_nz.
2:{
rewrite rat_num_0 in H0.
eauto.
}
omega.
eapply eqRat_flip.
eapply H0.
Qed.

Lemma ratSubtract_ratAdd_distr : forall r1 r2 r3,
ratSubtract r1 (r2 + r3) == ratSubtract (ratSubtract r1 r2) r3.