proposition: Lemma not_Qeq_inf : forall x y : Q, x <> y -> {Qlt x y} + {Qlt y x}.
proof: Proof. intros x y Hxy; destruct (Q_le_lt_dec x y) as [H|H]; try tauto; left; destruct (Qle_lt_eq_dec _ _ H) as [H'|H']; trivial; contradiction. Qed.
imports: Coq(FunInd) QArithSternBrocot(Field_Theory_Q)