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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 (* This file was automatically generated: do not edit *********************)
19 (*#***********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
25 (* \VV/ **************************************************************)
27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
31 (*#***********************************************************************)
33 (*i $Id: MVT.v,v 1.10.2.1 2004/07/16 19:31:10 herbelin Exp $ i*)
35 include "Reals/Rbase.ma".
37 include "Reals/Rfunctions.ma".
39 include "Reals/Ranalysis1.ma".
41 include "Reals/Rtopology.ma".
44 Open Local Scope R_scope.
47 (* The Mean Value Theorem *)
49 inline procedural "cic:/Coq/Reals/MVT/MVT.con" as theorem.
53 inline procedural "cic:/Coq/Reals/MVT/MVT_cor1.con" as lemma.
55 inline procedural "cic:/Coq/Reals/MVT/MVT_cor2.con" as theorem.
57 inline procedural "cic:/Coq/Reals/MVT/MVT_cor3.con" as lemma.
59 inline procedural "cic:/Coq/Reals/MVT/Rolle.con" as lemma.
63 inline procedural "cic:/Coq/Reals/MVT/nonneg_derivative_1.con" as lemma.
67 inline procedural "cic:/Coq/Reals/MVT/nonpos_derivative_0.con" as lemma.
71 inline procedural "cic:/Coq/Reals/MVT/increasing_decreasing_opp.con" as lemma.
75 inline procedural "cic:/Coq/Reals/MVT/nonpos_derivative_1.con" as lemma.
79 inline procedural "cic:/Coq/Reals/MVT/positive_derivative.con" as lemma.
83 inline procedural "cic:/Coq/Reals/MVT/strictincreasing_strictdecreasing_opp.con" as lemma.
87 inline procedural "cic:/Coq/Reals/MVT/negative_derivative.con" as lemma.
91 inline procedural "cic:/Coq/Reals/MVT/null_derivative_0.con" as lemma.
95 inline procedural "cic:/Coq/Reals/MVT/increasing_decreasing.con" as lemma.
99 inline procedural "cic:/Coq/Reals/MVT/null_derivative_1.con" as lemma.
103 inline procedural "cic:/Coq/Reals/MVT/derive_increasing_interv_ax.con" as lemma.
107 inline procedural "cic:/Coq/Reals/MVT/derive_increasing_interv.con" as lemma.
111 inline procedural "cic:/Coq/Reals/MVT/derive_increasing_interv_var.con" as lemma.
117 inline procedural "cic:/Coq/Reals/MVT/IAF.con" as theorem.
119 inline procedural "cic:/Coq/Reals/MVT/IAF_var.con" as lemma.
121 (* If f has a null derivative in ]a,b[ and is continue in [a,b], *)
123 (* then f is constant on [a,b] *)
125 inline procedural "cic:/Coq/Reals/MVT/null_derivative_loc.con" as lemma.
127 (* Unicity of the antiderivative *)
129 inline procedural "cic:/Coq/Reals/MVT/antiderivative_Ucte.con" as lemma.