(** ** 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.

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.