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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
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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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Theorem IAF :
forall (f:R -> R) (a b k:R) (pr:derivable f),
a <= b ->
(forall c:R, a <= c <= b -> derive_pt f c (pr c) <= k) ->
f b - f a <= k * (b - a).