(** NB: This file is here only for compatibility with earlier version of
     [FSets] and [FMap]. Please use [Structures/Orders.v] directly now. *)

(** * Ordered types *)

Inductive Compare (X : Type) (lt eq : X -> X -> Prop) (x y : X) : Type :=
  | LT : lt x y -> Compare lt eq x y
  | EQ : eq x y -> Compare lt eq x y
  | GT : lt y x -> Compare lt eq x y.(** NB: This file is here only for compatibility with earlier version of
     [FSets] and [FMap]. Please use [Structures/Orders.v] directly now. *)

(** * Ordered types *)

Inductive Compare (X : Type) (lt eq : X -> X -> Prop) (x y : X) : Type :=
  | LT : lt x y -> Compare lt eq x y
  | EQ : eq x y -> Compare lt eq x y
  | GT : lt y x -> Compare lt eq x y.(** NB: This file is here only for compatibility with earlier version of
     [FSets] and [FMap]. Please use [Structures/Orders.v] directly now. *)

(** * Ordered types *)

Inductive Compare (X : Type) (lt eq : X -> X -> Prop) (x y : X) : Type :=
  | LT : lt x y -> Compare lt eq x y
  | EQ : eq x y -> Compare lt eq x y
  | GT : lt y x -> Compare lt eq x y.(** NB: This file is here only for compatibility with earlier version of
     [FSets] and [FMap]. Please use [Structures/Orders.v] directly now. *)

(** * Ordered types *)

Inductive Compare (X : Type) (lt eq : X -> X -> Prop) (x y : X) : Type :=
  | LT : lt x y -> Compare lt eq x y
  | EQ : eq x y -> Compare lt eq x y
  | GT : lt y x -> Compare lt eq x y.Definition eq_dec : forall x y : t, {eq x y} + {~ eq x y}.#[global]
  Instance eq_equiv : Equivalence eq.

Lemma lt_antirefl : forall x, ~ lt x x.