(** ** From OrderedType to OrderedTypeOrig. *)
Module Backport_OT (O:OrderedType) <: OrderedTypeOrig.
Include Backport_DT O. (* Provides : t eq eq_refl eq_sym eq_trans eq_dec *)
Definition lt := O.lt.

(* Specifications: *)
Lemma lt_not_eq : forall x y, lt x y -> ~eq x y.
Lemma lt_trans : Transitive lt.
#[global]
Instance lt_strorder : StrictOrder lt.
Lemma lt_eq : forall x y z, lt x y -> eq y z -> lt x z.
Lemma eq_lt : forall x y z, eq x y -> lt y z -> lt x z.
#[global]
Instance lt_compat : Proper (eq==>eq==>iff) lt.