(* ratInverse only works correctly when the number is positive *)
Definition ratInverse (r : Rat) :=
  match r with
    | RatIntro n d =>
      match n with
        | O => RatIntro d (pos (S O))
        | S n' => RatIntro d (pos (S n'))
      end
  end.Fixpoint expRat r n :=
  match n with
    | O => rat1 
    | S n' => r * (expRat r n')
  end.

Lemma expRat_leRat_compat : forall n r1 r2, r1 <= r2 -> expRat r1 n <= expRat r2 n.