intuition.
exists (ratSubtract r1 r2).
apply eqRat_symm.
apply ratSubtract_ratAdd_inverse_2.
trivial.
Qed.

Lemma ratSubtract_ratMult_le : forall r1 r2 r3 r4,
r1 <= r2 ->
r3 <= r4 ->
ratSubtract (r2 * r4) (r1 * r3) == (ratSubtract r2 r1) * r3 + (ratSubtract r4 r3) * r1 + (ratSubtract r2 r1) * (ratSubtract r4 r3).