transcript: we improved the parser/lexer to read the scripts of the standard

[helm.git] / helm / software / matita / contribs / procedural / Coq / Arith / Div2.mma

diff --git a/helm/software/matita/contribs/procedural/Coq/Arith/Div2.mma b/helm/software/matita/contribs/procedural/Coq/Arith/Div2.mma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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: Div2.v,v 1.15 2003/11/29 17:28:28 herbelin Exp $ i*)
+
+include "Arith/Lt.ma".
+
+include "Arith/Plus.ma".
+
+include "Arith/Compare_dec.ma".
+
+include "Arith/Even.ma".
+
+(* UNEXPORTED
+Open Local Scope nat_scope.
+*)
+
+(* UNEXPORTED
+Implicit Type n : nat.
+*)
+
+(*#* Here we define [n/2] and prove some of its properties *)
+
+inline procedural "cic:/Coq/Arith/Div2/div2.con" as definition.
+
+(*#* Since [div2] is recursively defined on [0], [1] and [(S (S n))], it is
+    useful to prove the corresponding induction principle *)
+
+inline procedural "cic:/Coq/Arith/Div2/ind_0_1_SS.con" as lemma.
+
+(*#* [0 <n  =>  n/2 < n] *)
+
+inline procedural "cic:/Coq/Arith/Div2/lt_div2.con" as lemma.
+
+(* UNEXPORTED
+Hint Resolve lt_div2: arith.
+*)
+
+(*#* Properties related to the parity *)
+
+inline procedural "cic:/Coq/Arith/Div2/even_odd_div2.con" as lemma.
+
+(*#* Specializations *)
+
+inline procedural "cic:/Coq/Arith/Div2/even_div2.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Div2/div2_even.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Div2/odd_div2.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Div2/div2_odd.con" as lemma.
+
+(* UNEXPORTED
+Hint Resolve even_div2 div2_even odd_div2 div2_odd: arith.
+*)
+
+(*#* Properties related to the double ([2n]) *)
+
+inline procedural "cic:/Coq/Arith/Div2/double.con" as definition.
+
+(* UNEXPORTED
+Hint Unfold double: arith.
+*)
+
+inline procedural "cic:/Coq/Arith/Div2/double_S.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Div2/double_plus.con" as lemma.
+
+(* UNEXPORTED
+Hint Resolve double_S: arith.
+*)
+
+inline procedural "cic:/Coq/Arith/Div2/even_odd_double.con" as lemma.
+
+(*#* Specializations *)
+
+inline procedural "cic:/Coq/Arith/Div2/even_double.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Div2/double_even.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Div2/odd_double.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Div2/double_odd.con" as lemma.
+
+(* UNEXPORTED
+Hint Resolve even_double double_even odd_double double_odd: arith.
+*)
+
+(*#* Application: 
+    - if [n] is even then there is a [p] such that [n = 2p]
+    - if [n] is odd  then there is a [p] such that [n = 2p+1]
+
+    (Immediate: it is [n/2]) *)
+
+inline procedural "cic:/Coq/Arith/Div2/even_2n.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Div2/odd_S2n.con" as lemma.
+