helm/software/matita/contribs/procedural/CoRN/algebra/CVectorSpace.mma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 include "CoRN.ma".
  18
  19 (* $Id: CVectorSpace.v,v 1.4 2004/04/23 10:00:54 lcf Exp $ *)
  20
  21 (*#* printing ['] %{'}% #'# *)
  22
  23 include "algebra/CFields.ma".
  24
  25 (*#*
  26 * Vector Spaces
  27
  28 Obsolete but maintained.
  29 *)
  30
  31 (* begin hide *)
  32
  33 (* UNEXPORTED
  34 Set Implicit Arguments.
  35 *)
  36
  37 (* UNEXPORTED
  38 Unset Strict Implicit.
  39 *)
  40
  41 (* end hide *)
  42
  43 inline procedural "cic:/CoRN/algebra/CVectorSpace/VSpace.ind".
  44
  45 (* COERCION
  46 cic:/matita/CoRN-Procedural/algebra/CVectorSpace/vs_vs.con
  47 *)
  48
  49 (* begin hide *)
  50
  51 (* UNEXPORTED
  52 Set Strict Implicit.
  53 *)
  54
  55 (* UNEXPORTED
  56 Unset Implicit Arguments.
  57 *)
  58
  59 (* end hide *)
  60
  61 (* UNEXPORTED
  62 Hint Resolve vs_assoc vs_unit vs_distl vs_distr: algebra.
  63 *)
  64
  65 (* UNEXPORTED
  66 Implicit Arguments vs_op [F v].
  67 *)
  68
  69 (* NOTATION
  70 Infix "[']" := vs_op (at level 30, no associativity).
  71 *)
  72
  73 (*#*
  74 %\begin{convention}%
  75 Let [F] be a fiels and let [V] be a vector space over [F]
  76 %\end{convention}%
  77 *)
  78
  79 (* UNEXPORTED
  80 Section VS_basics
  81 *)
  82
  83 (* UNEXPORTED
  84 cic:/CoRN/algebra/CVectorSpace/VS_basics/F.var
  85 *)
  86
  87 (* UNEXPORTED
  88 cic:/CoRN/algebra/CVectorSpace/VS_basics/V.var
  89 *)
  90
  91 inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_zero.con" as lemma.
  92
  93 inline procedural "cic:/CoRN/algebra/CVectorSpace/zero_vs_op.con" as lemma.
  94
  95 (* UNEXPORTED
  96 Hint Resolve vs_op_zero zero_vs_op: algebra.
  97 *)
  98
  99 inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_V.con" as lemma.
 100
 101 inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_S.con" as lemma.
 102
 103 (* UNEXPORTED
 104 Hint Resolve vs_op_inv_V vs_op_inv_S: algebra.
 105 *)
 106
 107 inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_inv_assoc.con" as lemma.
 108
 109 (* UNEXPORTED
 110 Hint Resolve vs_inv_assoc: algebra.
 111 *)
 112
 113 inline procedural "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_l.con" as lemma.
 114
 115 inline procedural "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_r.con" as lemma.
 116
 117 (* note this is the same proof as mult_resp_ap_zero *)
 118
 119 inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_rht.con" as lemma.
 120
 121 inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_zero.con" as lemma.
 122
 123 inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_lft.con" as lemma.
 124
 125 (* UNEXPORTED
 126 End VS_basics
 127 *)
 128
 129 (* UNEXPORTED
 130 Hint Resolve vs_op_zero zero_vs_op: algebra.
 131 *)
 132