Definition ratHalf(r : Rat) :=
  r * (1 / 2).

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).