matita/contribs/CoRN-Decl/algebra/CVectorSpace.ma

   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 set "baseuri" "cic:/matita/CoRN-Decl/algebra/CVectorSpace".
  18
  19 include "CoRN.ma".
  20
  21 (* $Id: CVectorSpace.v,v 1.4 2004/04/23 10:00:54 lcf Exp $ *)
  22
  23 (*#* printing ['] %{'}% #'# *)
  24
  25 include "algebra/CFields.ma".
  26
  27 (*#*
  28 * Vector Spaces
  29
  30 Obsolete but maintained.
  31 *)
  32
  33 (* begin hide *)
  34
  35 (* UNEXPORTED
  36 Set Implicit Arguments.
  37 *)
  38
  39 (* UNEXPORTED
  40 Unset Strict Implicit.
  41 *)
  42
  43 (* end hide *)
  44
  45 inline "cic:/CoRN/algebra/CVectorSpace/VSpace.ind".
  46
  47 coercion cic:/matita/CoRN-Decl/algebra/CVectorSpace/vs_vs.con 0 (* compounds *).
  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 alias id "F" = "cic:/CoRN/algebra/CVectorSpace/VS_basics/F.var".
  84
  85 alias id "V" = "cic:/CoRN/algebra/CVectorSpace/VS_basics/V.var".
  86
  87 inline "cic:/CoRN/algebra/CVectorSpace/vs_op_zero.con".
  88
  89 inline "cic:/CoRN/algebra/CVectorSpace/zero_vs_op.con".
  90
  91 (* UNEXPORTED
  92 Hint Resolve vs_op_zero zero_vs_op: algebra.
  93 *)
  94
  95 inline "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_V.con".
  96
  97 inline "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_S.con".
  98
  99 (* UNEXPORTED
 100 Hint Resolve vs_op_inv_V vs_op_inv_S: algebra.
 101 *)
 102
 103 inline "cic:/CoRN/algebra/CVectorSpace/vs_inv_assoc.con".
 104
 105 (* UNEXPORTED
 106 Hint Resolve vs_inv_assoc: algebra.
 107 *)
 108
 109 inline "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_l.con".
 110
 111 inline "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_r.con".
 112
 113 (* note this is the same proof as mult_resp_ap_zero *)
 114
 115 inline "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_rht.con".
 116
 117 inline "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_zero.con".
 118
 119 inline "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_lft.con".
 120
 121 (* UNEXPORTED
 122 End VS_basics
 123 *)
 124
 125 (* UNEXPORTED
 126 Hint Resolve vs_op_zero zero_vs_op: algebra.
 127 *)
 128