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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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(*i Some properties about pow and sum have been made with John Harrison i*)
(*i Some Lemmas (about pow and powerRZ) have been done by Laurent Thery i*)
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(**          Definition of the sum functions            *)
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Require Export ArithRing.
Require Export Rpow_def.
Require Export R_Ifp.
Require Export Rbasic_fun.
Require Export R_sqr.
Require Export SplitAbsolu.
Require Export SplitRmult.
Require Export ArithProp.
Local Open Scope nat_scope.
Local Open Scope R_scope.

(* Specifications: *)
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(** * Lemmas about factorial   *)
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Lemma INR_fact_neq_0 : forall n:nat, INR (fact n) <> 0.
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Lemma fact_simpl : forall n:nat, fact (S n) = (S n * fact n)%nat.
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Lemma simpl_fact :
forall n:nat, / INR (fact (S n)) * / / INR (fact n) = / INR (S n).