helm/software/matita/contribs/procedural/CoRN/algebra/CSetoidInc.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: CSetoidInc.v,v 1.3 2004/04/22 14:49:43 lcf Exp $ *)
  20
  21 (*#* printing included %\ensuremath{\subseteq}% #&sube;# *)
  22
  23 include "algebra/CSetoidFun.ma".
  24
  25 (* UNEXPORTED
  26 Section inclusion
  27 *)
  28
  29 (*#* ** Inclusion
  30
  31 Let [S] be a setoid, and [P], [Q], [R] be predicates on [S]. *)
  32
  33 (* UNEXPORTED
  34 cic:/CoRN/algebra/CSetoidInc/inclusion/S.var
  35 *)
  36
  37 inline procedural "cic:/CoRN/algebra/CSetoidInc/included.con" as definition.
  38
  39 (* UNEXPORTED
  40 Section Basics
  41 *)
  42
  43 (* UNEXPORTED
  44 cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/P.var
  45 *)
  46
  47 (* UNEXPORTED
  48 cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/Q.var
  49 *)
  50
  51 (* UNEXPORTED
  52 cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/R.var
  53 *)
  54
  55 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_refl.con" as lemma.
  56
  57 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_trans.con" as lemma.
  58
  59 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj.con" as lemma.
  60
  61 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj'.con" as lemma.
  62
  63 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj''.con" as lemma.
  64
  65 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj_lft.con" as lemma.
  66
  67 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj_rht.con" as lemma.
  68
  69 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_extend.con" as lemma.
  70
  71 (* UNEXPORTED
  72 End Basics
  73 *)
  74
  75 (*#*
  76 %\begin{convention}% Let [I,R:S->CProp] and [F G:(PartFunct S)], and denote
  77 by [P] and [Q], respectively, the domains of [F] and [G].
  78 %\end{convention}%
  79 *)
  80
  81 (* UNEXPORTED
  82 cic:/CoRN/algebra/CSetoidInc/inclusion/F.var
  83 *)
  84
  85 (* UNEXPORTED
  86 cic:/CoRN/algebra/CSetoidInc/inclusion/G.var
  87 *)
  88
  89 (* begin hide *)
  90
  91 inline procedural "cic:/CoRN/algebra/CSetoidInc/inclusion/P.con" "inclusion__" as definition.
  92
  93 inline procedural "cic:/CoRN/algebra/CSetoidInc/inclusion/Q.con" "inclusion__" as definition.
  94
  95 (* end hide *)
  96
  97 (* UNEXPORTED
  98 cic:/CoRN/algebra/CSetoidInc/inclusion/R.var
  99 *)
 100
 101 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_FComp.con" as lemma.
 102
 103 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_FComp'.con" as lemma.
 104
 105 (* UNEXPORTED
 106 End inclusion
 107 *)
 108
 109 (* UNEXPORTED
 110 Implicit Arguments included [S].
 111 *)
 112
 113 (* UNEXPORTED
 114 Hint Resolve included_refl included_FComp : included.
 115 *)
 116
 117 (* UNEXPORTED
 118 Hint Immediate included_trans included_FComp' : included.
 119 *)
 120