intuition.
unfold ratDistance, maxRat, minRat.
destruct (bleRat r1 r2); trivial.
Qed.

Lemma rat_distance_of_difference : forall r1 r2 r3 r4 d1 d2,
r2 <= r1 ->
r4 <= r3 ->
ratDistance r1 r3 <= d1 ->
ratDistance r2 r4 <= d2 ->
ratDistance (ratSubtract r1 r2) (ratSubtract r3 r4) <= (d1 + d2).