intros x' y' H1; red in |- *; intros H2; elim H1.
inversion H2.
apply not_Qpositive_le_Qpositive_le'; auto with *.
intros x' y' H1; red in |- *; intros H2; elim H1.
inversion H2; apply not_Qpositive_le_Qpositive_le'; auto.
unfold not in |- *; intros x' H1; inversion H1.
unfold not in |- *; intros x' y' H1; inversion H1.
unfold not in |- *; intros x' H1; inversion H1.
Qed.

Theorem Qgt_trans : forall x y z : Q, Qgt x y -> Qgt y z -> Qgt x z.
intros x y z H; elim H; auto with *.