Definition numerator r :=
  match r with
    | RatIntro n d => n
  end.

(* Specifications: *)
Lemma ratDistance_le_max_triv : forall r1 r2, ratDistance r1 r2 <= maxRat r1 r2.
Lemma ratAdd_2_ratMax : forall r1 r2, (r1 + r2 <= 2 / 1 * (maxRat r1 r2))%rat.
Theorem rat_num_not_le : forall (d1 d2 : posnat), (RatIntro 1 d1 <= RatIntro 1 d2)%rat -> d1 < d2 -> False.
Lemma rat_le_1_if : forall n d, RatIntro n d <= 1 -> (n <= d)%nat.
Theorem ratFraction_le_1 : forall r1 r2, r1 <= r2 -> r1 * (ratInverse r2) <= 1.
Theorem ratFraction_ge_1_inv : forall r1 r2, 1 <= r1 * (ratInverse r2) -> r2 <= r1.