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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          *)
(*         *     (see LICENSE file for the text of the license)         *)
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Local Open Scope R_scope.

Lemma derive_pt_inv :
forall (f:R -> R) (x:R) (pr:derivable_pt f x) (na:f x <> 0),
derive_pt (/ f) x (derivable_pt_inv f x na pr) =
- derive_pt f x pr / Rsqr (f x).