intuition.
unfold ratDistance.
eauto using ratSubtract_eqRat_compat, maxRat_eqRat_compat, minRat_eqRat_compat.
Qed.
Add Parametric Morphism : ratDistance
with signature (eqRat ==> eqRat ==> eqRat)
as ratDistance_eqRat_mor.
intuition.
eapply ratDistance_eqRat_compat; trivial.
Qed.

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