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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
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(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
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Local Open Scope R_scope.

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Lemma formule :
forall (x h l1 l2:R) (f1 f2:R -> R),
h <> 0 ->
f2 x <> 0 ->
f2 (x + h) <> 0 ->
(f1 (x + h) / f2 (x + h) - f1 x / f2 x) / h -
(l1 * f2 x - l2 * f1 x) / Rsqr (f2 x) =
/ f2 (x + h) * ((f1 (x + h) - f1 x) / h - l1) +
l1 / (f2 x * f2 (x + h)) * (f2 x - f2 (x + h)) -
f1 x / (f2 x * f2 (x + h)) * ((f2 (x + h) - f2 x) / h - l2) +
l2 * f1 x / (Rsqr (f2 x) * f2 (x + h)) * (f2 (x + h) - f2 x).