(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
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Require Export Relation_Definitions.
Require Export Relation_Operators.
Require Export Operators_Properties.

(* Specifications: *)
Lemma inverse_image_of_equivalence :
forall (A B:Type) (f:A -> B) (r:relation B),
equivalence B r -> equivalence A (fun x y:A => r (f x) (f y)).
Lemma inverse_image_of_eq :
forall (A B:Type) (f:A -> B), equivalence A (fun x y:A => f x = f y).