intuition.
rattac.
rewrite mult_0_l in e.
unfold posnatToNat in *.
simpl in *.
rewrite mult_1_r in e.
apply mult_is_O in e.
intuition; subst.
left.
apply rat_num_0.
right.
apply rat_num_0.
rewrite <- (ratMult_0_l r2).
eapply ratMult_eqRat_compat; intuition.
rewrite <- (ratMult_0_r r1).
eapply ratMult_eqRat_compat; intuition.
Qed.

Theorem ratMult_nz : forall r1 r2,
(~r1 * r2 == 0) <->
(~r1 == 0) /\ (~r2 == 0).