Definition t := R.Definition eq := @eq R.Definition eqb := Reqb.Definition eqb_eq := Reqb_eq.Module R_as_DT <: UsualDecidableTypeFull := Make_UDTF R_as_UBE.(** Note that the last module fulfills by subtyping many other
    interfaces, such as [DecidableType] or [EqualityType]. *)



(** Note that [R_as_DT] can also be seen as a [DecidableType]
    and a [DecidableTypeOrig]. *)



(** * OrderedType structure for binary integers *)



Definition Rcompare x y :=
 match total_order_T x y with
  | inleft (left _) => Lt
  | inleft (right _) => Eq
  | inright _ => Gt
 end.

Lemma Rcompare_spec : forall x y, CompareSpec (x=y) (x<y) (y<x) (Rcompare x y).