--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
+
+(* \VV/ *************************************************************)
+
+(* // * This file is distributed under the terms of the *)
+
+(* * GNU Lesser General Public License Version 2.1 *)
+
+(*#**********************************************************************)
+
+(*i $Id: Rprod.v,v 1.10 2003/11/29 17:28:38 herbelin Exp $ i*)
+
+include "Arith/Compare.ma".
+
+include "Reals/Rbase.ma".
+
+include "Reals/Rfunctions.ma".
+
+include "Reals/Rseries.ma".
+
+include "Reals/PartSum.ma".
+
+include "Reals/Binomial.ma".
+
+(* UNEXPORTED
+Open Local Scope R_scope.
+*)
+
+(* TT Ak; 1<=k<=N *)
+
+inline procedural "cic:/Coq/Reals/Rprod/prod_f_SO.con" as definition.
+
+(*#*********)
+
+inline procedural "cic:/Coq/Reals/Rprod/prod_SO_split.con" as lemma.
+
+(*#*********)
+
+inline procedural "cic:/Coq/Reals/Rprod/prod_SO_pos.con" as lemma.
+
+(*#*********)
+
+inline procedural "cic:/Coq/Reals/Rprod/prod_SO_Rle.con" as lemma.
+
+(* Application to factorial *)
+
+inline procedural "cic:/Coq/Reals/Rprod/fact_prodSO.con" as lemma.
+
+inline procedural "cic:/Coq/Reals/Rprod/le_n_2n.con" as lemma.
+
+(* We prove that (N!)²<=(2N-k)!*k! forall k in [|O;2N|] *)
+
+inline procedural "cic:/Coq/Reals/Rprod/RfactN_fact2N_factk.con" as lemma.
+
+(*#*********)
+
+inline procedural "cic:/Coq/Reals/Rprod/INR_fact_lt_0.con" as lemma.
+
+(* We have the following inequality : (C 2N k) <= (C 2N N) forall k in [|O;2N|] *)
+
+inline procedural "cic:/Coq/Reals/Rprod/C_maj.con" as lemma.
+