intuition.
eapply leRat_trans.
2:{
eapply eqRat_impl_leRat.
eapply eqRat_symm.
eapply H.
}
apply ratAdd_any_leRat_r.
apply leRat_refl.
Qed.

Lemma ratSubtract_leRat_r : forall r1 r2 r3,
r1 <= r2 ->
ratSubtract r3 r2 <= ratSubtract r3 r1.