intuition.
apply eqRat_symm.
eapply eqRat_trans.
2:{
apply ratSubtract_ratAdd_assoc.
trivial.
}
apply eqRat_symm.
apply ratSubtract_ratAdd_inverse.
Qed.

Lemma leRat_difference_exists : forall r1 r2,
r2 <= r1 ->
exists r3, r1 == r2 + r3.