Fixpoint Qpositive_c (p q n : nat) {struct n} : Qpositive :=
  match n with
  | O => One
  | S n' =>
      match p - q with
      | O => match q - p with
             | O => One
             | v => dL (Qpositive_c p v n')
             end
      | v => nR (Qpositive_c v q n')
      end
  end.

Theorem Qpositive_c_equiv' : forall n p q n' p' q' : nat, 1 <= p -> 1 <= q -> 1 <= p' -> 1 <= q' -> p + q <= n -> p' + q' <= n' -> Qpositive_c p q n = Qpositive_c p' q' n' -> p * q' = p' * q.