unfold minRat in *.
intuition.
case_eq (bleRat r1 r2); intuition.
eapply bleRat_total.
trivial.
Qed.

(* Specifications: *)
Lemma ratDistance_ge_difference: forall r1 r2 d,
ratDistance r1 r2 <= d ->
ratSubtract r1 d <= r2.