helm/software/matita/contribs/CoRN-Decl/algebra/CSemiGroups.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   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/CSemiGroups".
  18
  19 (* $Id: CSemiGroups.v,v 1.8 2004/04/22 14:49:43 lcf Exp $ *)
  20
  21 (*#* printing [+] %\ensuremath+% #+# *)
  22
  23 (*#* printing {+} %\ensuremath+% #+# *)
  24
  25 (* INCLUDE
  26 CSetoidInc
  27 *)
  28
  29 (* Begin_SpecReals *)
  30
  31 (*#* *Semigroups
  32
  33 **Definition of the notion of semigroup
  34 *)
  35
  36 inline cic:/CoRN/algebra/CSemiGroups/is_CSemiGroup.con.
  37
  38 inline cic:/CoRN/algebra/CSemiGroups/CSemiGroup.ind.
  39
  40 (*#*
  41 %\begin{nameconvention}%
  42 In the %{\em %names%}% of lemmas, we will denote [[+]] with [plus].
  43 %\end{nameconvention}%
  44 *)
  45
  46 (* UNEXPORTED
  47 Implicit Arguments csg_op [c].
  48 *)
  49
  50 (* End_SpecReals *)
  51
  52 (*#* **Semigroup axioms
  53 The axiomatic properties of a semi group.
  54
  55 %\begin{convention}% Let [G] be a semi-group.
  56 %\end{convention}%
  57 *)
  58
  59 (* UNEXPORTED
  60 Section CSemiGroup_axioms.
  61 *)
  62
  63 inline cic:/CoRN/algebra/CSemiGroups/G.var.
  64
  65 inline cic:/CoRN/algebra/CSemiGroups/CSemiGroup_is_CSemiGroup.con.
  66
  67 inline cic:/CoRN/algebra/CSemiGroups/plus_assoc.con.
  68
  69 (* UNEXPORTED
  70 End CSemiGroup_axioms.
  71 *)
  72
  73 (* Begin_SpecReals *)
  74
  75 (*#* **Semigroup basics
  76
  77 %\begin{convention}%
  78 Let [G] be a semi-group.
  79 %\end{convention}%
  80 *)
  81
  82 (* UNEXPORTED
  83 Section CSemiGroup_basics.
  84 *)
  85
  86 inline cic:/CoRN/algebra/CSemiGroups/G.var.
  87
  88 (* End_SpecReals *)
  89
  90 inline cic:/CoRN/algebra/CSemiGroups/plus_assoc_unfolded.con.
  91
  92 (* UNEXPORTED
  93 End CSemiGroup_basics.
  94 *)
  95
  96 (* End_SpecReals *)
  97
  98 (* UNEXPORTED
  99 Hint Resolve plus_assoc_unfolded: algebra.
 100 *)
 101
 102 (*#* **Functional operations
 103 We can also define a similar addition operator, which will be denoted by [{+}], on partial functions.
 104
 105 %\begin{convention}% Whenever possible, we will denote the functional construction corresponding to an algebraic operation by the same symbol enclosed in curly braces.
 106 %\end{convention}%
 107
 108 At this stage, we will always consider automorphisms; we %{\em %could%}% treat this in a more general setting, but we feel that it wouldn't really be a useful effort.
 109
 110 %\begin{convention}% Let [G:CSemiGroup] and [F,F':(PartFunct G)] and denote by [P] and [Q], respectively, the predicates characterizing their domains.
 111 %\end{convention}%
 112 *)
 113
 114 (* UNEXPORTED
 115 Section Part_Function_Plus.
 116 *)
 117
 118 inline cic:/CoRN/algebra/CSemiGroups/G.var.
 119
 120 inline cic:/CoRN/algebra/CSemiGroups/F.var.
 121
 122 inline cic:/CoRN/algebra/CSemiGroups/F'.var.
 123
 124 (* begin hide *)
 125
 126 inline cic:/CoRN/algebra/CSemiGroups/P.con.
 127
 128 inline cic:/CoRN/algebra/CSemiGroups/Q.con.
 129
 130 (* end hide *)
 131
 132 inline cic:/CoRN/algebra/CSemiGroups/part_function_plus_strext.con.
 133
 134 inline cic:/CoRN/algebra/CSemiGroups/Fplus.con.
 135
 136 (*#*
 137 %\begin{convention}% Let [R:G->CProp].
 138 %\end{convention}%
 139 *)
 140
 141 inline cic:/CoRN/algebra/CSemiGroups/R.var.
 142
 143 inline cic:/CoRN/algebra/CSemiGroups/included_FPlus.con.
 144
 145 inline cic:/CoRN/algebra/CSemiGroups/included_FPlus'.con.
 146
 147 inline cic:/CoRN/algebra/CSemiGroups/included_FPlus''.con.
 148
 149 (* UNEXPORTED
 150 End Part_Function_Plus.
 151 *)
 152
 153 (* UNEXPORTED
 154 Implicit Arguments Fplus [G].
 155 *)
 156
 157 (* UNEXPORTED
 158 Hint Resolve included_FPlus : included.
 159 *)
 160
 161 (* UNEXPORTED
 162 Hint Immediate included_FPlus' included_FPlus'' : included.
 163 *)
 164
 165 (*#* **Subsemigroups
 166 %\begin{convention}%
 167 Let [csg] a semi-group and [P] a non-empty
 168 predicate on the semi-group which is preserved by [[+]].
 169 %\end{convention}%
 170 *)
 171
 172 (* UNEXPORTED
 173 Section SubCSemiGroups.
 174 *)
 175
 176 inline cic:/CoRN/algebra/CSemiGroups/csg.var.
 177
 178 inline cic:/CoRN/algebra/CSemiGroups/P.var.
 179
 180 inline cic:/CoRN/algebra/CSemiGroups/op_pres_P.var.
 181
 182 inline cic:/CoRN/algebra/CSemiGroups/subcrr.con.
 183
 184 inline cic:/CoRN/algebra/CSemiGroups/Build_SubCSemiGroup.con.
 185
 186 (* UNEXPORTED
 187 End SubCSemiGroups.
 188 *)
 189