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

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  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 include "CoRN.ma".
  20
  21 (* $Id: CSemiGroups.v,v 1.8 2004/04/22 14:49:43 lcf Exp $ *)
  22
  23 (*#* printing [+] %\ensuremath+% #+# *)
  24
  25 (*#* printing {+} %\ensuremath+% #+# *)
  26
  27 include "algebra/CSetoidInc.ma".
  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 coercion cic:/matita/CoRN-Decl/algebra/CSemiGroups/csg_crr.con 0 (* compounds *).
  41
  42 (*#*
  43 %\begin{nameconvention}%
  44 In the %{\em %names%}% of lemmas, we will denote [[+]] with [plus].
  45 %\end{nameconvention}%
  46 *)
  47
  48 (* UNEXPORTED
  49 Implicit Arguments csg_op [c].
  50 *)
  51
  52 (* NOTATION
  53 Infix "[+]" := csg_op (at level 50, left associativity).
  54 *)
  55
  56 (* End_SpecReals *)
  57
  58 (*#* **Semigroup axioms
  59 The axiomatic properties of a semi group.
  60
  61 %\begin{convention}% Let [G] be a semi-group.
  62 %\end{convention}%
  63 *)
  64
  65 (* UNEXPORTED
  66 Section CSemiGroup_axioms
  67 *)
  68
  69 alias id "G" = "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_axioms/G.var".
  70
  71 inline "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_is_CSemiGroup.con".
  72
  73 inline "cic:/CoRN/algebra/CSemiGroups/plus_assoc.con".
  74
  75 (* UNEXPORTED
  76 End CSemiGroup_axioms
  77 *)
  78
  79 (* Begin_SpecReals *)
  80
  81 (*#* **Semigroup basics
  82
  83 %\begin{convention}%
  84 Let [G] be a semi-group.
  85 %\end{convention}%
  86 *)
  87
  88 (* UNEXPORTED
  89 Section CSemiGroup_basics
  90 *)
  91
  92 alias id "G" = "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_basics/G.var".
  93
  94 (* End_SpecReals *)
  95
  96 inline "cic:/CoRN/algebra/CSemiGroups/plus_assoc_unfolded.con".
  97
  98 (* UNEXPORTED
  99 End CSemiGroup_basics
 100 *)
 101
 102 (* End_SpecReals *)
 103
 104 (* UNEXPORTED
 105 Hint Resolve plus_assoc_unfolded: algebra.
 106 *)
 107
 108 (*#* **Functional operations
 109 We can also define a similar addition operator, which will be denoted by [{+}], on partial functions.
 110
 111 %\begin{convention}% Whenever possible, we will denote the functional construction corresponding to an algebraic operation by the same symbol enclosed in curly braces.
 112 %\end{convention}%
 113
 114 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.
 115
 116 %\begin{convention}% Let [G:CSemiGroup] and [F,F':(PartFunct G)] and denote by [P] and [Q], respectively, the predicates characterizing their domains.
 117 %\end{convention}%
 118 *)
 119
 120 (* UNEXPORTED
 121 Section Part_Function_Plus
 122 *)
 123
 124 alias id "G" = "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/G.var".
 125
 126 alias id "F" = "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/F.var".
 127
 128 alias id "F'" = "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/F'.var".
 129
 130 (* begin hide *)
 131
 132 inline "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/P.con" "Part_Function_Plus__".
 133
 134 inline "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/Q.con" "Part_Function_Plus__".
 135
 136 (* end hide *)
 137
 138 inline "cic:/CoRN/algebra/CSemiGroups/part_function_plus_strext.con".
 139
 140 inline "cic:/CoRN/algebra/CSemiGroups/Fplus.con".
 141
 142 (*#*
 143 %\begin{convention}% Let [R:G->CProp].
 144 %\end{convention}%
 145 *)
 146
 147 alias id "R" = "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/R.var".
 148
 149 inline "cic:/CoRN/algebra/CSemiGroups/included_FPlus.con".
 150
 151 inline "cic:/CoRN/algebra/CSemiGroups/included_FPlus'.con".
 152
 153 inline "cic:/CoRN/algebra/CSemiGroups/included_FPlus''.con".
 154
 155 (* UNEXPORTED
 156 End Part_Function_Plus
 157 *)
 158
 159 (* UNEXPORTED
 160 Implicit Arguments Fplus [G].
 161 *)
 162
 163 (* NOTATION
 164 Infix "{+}" := Fplus (at level 50, left associativity).
 165 *)
 166
 167 (* UNEXPORTED
 168 Hint Resolve included_FPlus : included.
 169 *)
 170
 171 (* UNEXPORTED
 172 Hint Immediate included_FPlus' included_FPlus'' : included.
 173 *)
 174
 175 (*#* **Subsemigroups
 176 %\begin{convention}%
 177 Let [csg] a semi-group and [P] a non-empty
 178 predicate on the semi-group which is preserved by [[+]].
 179 %\end{convention}%
 180 *)
 181
 182 (* UNEXPORTED
 183 Section SubCSemiGroups
 184 *)
 185
 186 alias id "csg" = "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/csg.var".
 187
 188 alias id "P" = "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/P.var".
 189
 190 alias id "op_pres_P" = "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/op_pres_P.var".
 191
 192 inline "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/subcrr.con" "SubCSemiGroups__".
 193
 194 inline "cic:/CoRN/algebra/CSemiGroups/Build_SubCSemiGroup.con".
 195
 196 (* UNEXPORTED
 197 End SubCSemiGroups
 198 *)
 199