Definition Q_eq_dec : forall x y : Q, {x = y} + {x <> y}.

Theorem Qpositive_le_sub_simpl_l : forall x y z : Qpositive, Qpositive_le x z -> Qpositive_le y z -> z <> x -> z <> y -> Qpositive_le (Qpositive_sub z x) (Qpositive_sub z y) -> Qpositive_le y x.