Module DSO_to_OT (O:DecStrOrder) <: OrderedType :=
  O <+ Compare2EqBool <+ HasEqBool2Dec.Definition le x y := x<y \/ x==y.

(* Specifications: *)
Lemma le_lteq : forall x y, le x y <-> x<y \/ x==y.
Lemma lt_total : forall x y, x<y \/ x==y \/ y<x.