proposition: Lemma Qlt_dec_Qpos : forall x y, {~ Qlt (Qpos y) (Qpos x)} + {Qlt (Qpos y) (Qpos x)}.
proof: Proof. intros x y; case Qpositive_le_dec with x y; intro H'; [left;intro H; inversion H; contradiction | right;unfold Qlt; constructor; trivial]. Qed.
imports: Coq(FunInd) QArithSternBrocot(Field_Theory_Q)