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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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Local Open Scope R_scope.
Local Ltac Tauto.intuition_solver ::= auto with rorders real.
(** * Preliminaries lemmas *)

(* begin hide *)
Lemma leftinv_is_rightinv : forall (f g:R->R),
(forall x y, x < y -> f x < f y) ->
(forall x, (comp f g) x = id x) ->
(forall x, (comp g f) x = id x).