intuition.
unfold ratSubtract, ratAdd.
rattac.
arithNormalize.
rewrite minus_plus_assoc.
f_equal.
f_equal.
do 5 arithSimplify.
do 5 arithSimplify.
unfold natToPosnat, posnatToNat in *.
eapply mult_le_compat; trivial.
eapply mult_le_compat; trivial.
eapply mult_le_compat; trivial.
rewrite <- (mult_assoc).
rewrite (mult_comm x).
rewrite mult_assoc.
rewrite <- (mult_assoc n3).
rewrite (mult_comm x).
rewrite mult_assoc.
eapply mult_le_compat; trivial.
Qed.

Lemma eqRat_ratMult_same_r : forall r1 r2 r3,
~r1 == 0 ->
r2 * r1 == r3 * r1 ->
r2 == r3.