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(*         *      The Rocq Prover / The Rocq Development Team           *)
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(*         *     GNU Lesser General Public License Version 2.1          *)
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(** * Examples of Ordered Type structures. *)
(** First, a particular case of [OrderedType] where the equality is the usual one of Coq. *)
Module Type UsualOrderedType.
Parameter Inline t : Type.
Definition eq := @eq t.
Parameter Inline lt : t -> t -> Prop.
Definition eq_refl := @eq_refl t.
Definition eq_sym := @eq_sym t.
Definition eq_trans := @eq_trans t.

Axiom lt_trans : forall x y z : t, lt x y -> lt y z -> lt x z.