Definition Z8_as_well_ordering :=
  Build_well_ordering Z8 Z8_lt Z8_eq Z8_lt_is_order Z8_eq_is_equality
    Z8_lt_is_wf Z8_lt_is_well_def_rht.Definition Qpositive2 := (Qpositive * Qpositive)%type.Definition bin2_lt (x y : Qpositive2) :=
  let (p1, p2) := x in let (p1', p2) := y in bin_lt p1 p1'.Definition bin2_eq (x y : Qpositive2) :=
  let (p1, p2) := x in let (p1', p2) := y in p1 = p1'.

Lemma bin2_eq_is_transitive : forall x y z : Qpositive2, bin2_eq x y -> bin2_eq y z -> bin2_eq x z.