proposition: Lemma Z_to_Qlt : forall x y : Z, (x < y)%Z -> Qlt x y.
proof: Proof. intros x y H. apply Qlt_Zero_Qminus. generalize (Z.lt_gt _ _ H); clear H; intro H. case (Zcompare_Gt_spec _ _ H). intros p Hp. rewrite <- Z_to_Qminus. unfold Zminus in |- *. rewrite Hp. unfold Z_to_Q in |- *. apply Qlt_zero_pos. Qed.
imports: Coq(FunInd) QArithSternBrocot(Field_Theory_Q)