Definition Z4_as_well_ordering :=
  Build_well_ordering Z4 Z4_lt Z4_eq Z4_lt_is_order Z4_eq_is_equality
    Z4_lt_is_wf Z4_lt_is_well_def_rht.

Lemma bin_lt_is_transitive : forall x y z : Qpositive, bin_lt x y -> bin_lt y z -> bin_lt x z.