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(*         *      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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(** Author: Bruno Barras *)
Section Inverse_Image.
Variables A B : Type.
Variable R : B -> B -> Prop.
Variable f : A -> B.
Let Rof (x y:A) : Prop := R (f x) (f y).
Remark Acc_lemma : forall y:B, Acc R y -> forall x:A, y = f x -> Acc Rof x.

(* Specifications: *)
Lemma Acc_inverse_image : forall x:A, Acc R (f x) -> Acc Rof x.
Theorem wf_inverse_image : well_founded R -> well_founded Rof.
Variable F : A -> B -> Prop.