(**************************************************************************)
(*       ___                                                              *)
(*      ||M||                                                             *)
(*      ||A||       A project by Andrea Asperti                           *)
(*      ||T||                                                             *)
(*      ||I||       Developers:                                           *)
(*      ||T||         The HELM team.                                      *)
(*      ||A||         http://helm.cs.unibo.it                             *)
(*      \   /                                                             *)
(*       \ /        This file is distributed under the terms of the       *)
(*        v         GNU General Public License Version 2                  *)
(*                                                                        *)
(**************************************************************************)

(* This file was automatically generated: do not edit *********************)

include "Coq.ma".

(*#***********************************************************************)

(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)

(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)

(*   \VV/  **************************************************************)

(*    //   *      This file is distributed under the terms of the       *)

(*         *       GNU Lesser General Public License Version 2.1        *)

(*#***********************************************************************)

(*i $Id: Rpower.v,v 1.17.2.1 2004/07/16 19:31:13 herbelin Exp $ i*)

(*i Due to L.Thery i*)

(*#***********************************************************)

(* Definitions of log and Rpower : R->R->R; main properties *)

(*#***********************************************************)

include "Reals/Rbase.ma".

include "Reals/Rfunctions.ma".

include "Reals/SeqSeries.ma".

include "Reals/Rtrigo.ma".

include "Reals/Ranalysis1.ma".

include "Reals/Exp_prop.ma".

include "Reals/Rsqrt_def.ma".

include "Reals/R_sqrt.ma".

include "Reals/MVT.ma".

include "Reals/Ranalysis4.ma".

(* UNEXPORTED
Open Local Scope R_scope.
*)

inline procedural "cic:/Coq/Reals/Rpower/P_Rmin.con" as lemma.

inline procedural "cic:/Coq/Reals/Rpower/exp_le_3.con" as lemma.

(*#*****************************************************************)

(*                        Properties of  Exp                      *)

(*#*****************************************************************)

inline procedural "cic:/Coq/Reals/Rpower/exp_increasing.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/exp_lt_inv.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/exp_ineq1.con" as lemma.

inline procedural "cic:/Coq/Reals/Rpower/ln_exists1.con" as lemma.

(*#*********)

inline procedural "cic:/Coq/Reals/Rpower/ln_exists.con" as lemma.

(* Definition of log R+* -> R *)

inline procedural "cic:/Coq/Reals/Rpower/Rln.con" as definition.

(* Extension on R *)

inline procedural "cic:/Coq/Reals/Rpower/ln.con" as definition.

inline procedural "cic:/Coq/Reals/Rpower/exp_ln.con" as lemma.

inline procedural "cic:/Coq/Reals/Rpower/exp_inv.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/exp_Ropp.con" as theorem.

(*#*****************************************************************)

(*                        Properties of  Ln                       *)

(*#*****************************************************************)

inline procedural "cic:/Coq/Reals/Rpower/ln_increasing.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/ln_exp.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/ln_1.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/ln_lt_inv.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/ln_inv.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/ln_mult.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/ln_Rinv.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/ln_continue.con" as theorem.

(*#*****************************************************************)

(*                        Definition of  Rpower                   *)

(*#*****************************************************************)

inline procedural "cic:/Coq/Reals/Rpower/Rpower.con" as definition.

(* NOTATION
Infix Local "^R" := Rpower (at level 30, right associativity) : R_scope.
*)

(*#*****************************************************************)

(*                        Properties of  Rpower                   *)

(*#*****************************************************************)

inline procedural "cic:/Coq/Reals/Rpower/Rpower_plus.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/Rpower_mult.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/Rpower_O.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/Rpower_1.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/Rpower_pow.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/Rpower_lt.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/Rpower_sqrt.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/Rpower_Ropp.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/Rle_Rpower.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/ln_lt_2.con" as theorem.

(*#*************************************)

(* Differentiability of Ln and Rpower *)

(*#*************************************)

inline procedural "cic:/Coq/Reals/Rpower/limit1_ext.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/limit1_imp.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/Rinv_Rdiv.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/Dln.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/derivable_pt_lim_ln.con" as lemma.

inline procedural "cic:/Coq/Reals/Rpower/D_in_imp.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/D_in_ext.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/Dpower.con" as theorem.

inline procedural "cic:/Coq/Reals/Rpower/derivable_pt_lim_power.con" as theorem.