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.

(* Specifications: *)
Lemma bin_lt_is_irreflexive : forall x : Qpositive, ~ bin_lt x x.
Lemma bin_lt_is_transitive : forall x y z : Qpositive, bin_lt x y -> bin_lt y z -> bin_lt x z.
Lemma bin_lt_is_order : is_order Qpositive bin_lt.
Lemma bin_eq_is_reflexive : forall x : Qpositive, bin_eq x x.
Lemma bin_eq_is_symmetric : forall x y : Qpositive, bin_eq x y -> bin_eq y x.
Lemma bin_eq_is_transitive : forall x y z : Qpositive, bin_eq x y -> bin_eq y z -> bin_eq x z.
Lemma bin_eq_is_equality : is_equality Qpositive bin_eq.
Lemma bin_lt_is_wf : wf_ind Qpositive bin_lt.
Lemma bin_lt_is_well_def_rht : is_well_def_rht Qpositive bin_lt bin_eq.