helm/software/matita/contribs/CoRN-Procedural/algebra/CAbMonoids.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 include "algebra/CMonoids.ma".
  20
  21 (* UNEXPORTED
  22 Section Abelian_Monoids
  23 *)
  24
  25 (*#*
  26 * Abelian Monoids
  27 Now we introduce commutativity and add some results.
  28 *)
  29
  30 inline procedural "cic:/CoRN/algebra/CAbMonoids/is_CAbMonoid.con".
  31
  32 inline procedural "cic:/CoRN/algebra/CAbMonoids/CAbMonoid.ind".
  33
  34 (* COERCION
  35 cic:/matita/CoRN-Procedural/algebra/CAbMonoids/cam_crr.con
  36 *)
  37
  38 (* UNEXPORTED
  39 Section AbMonoid_Axioms
  40 *)
  41
  42 alias id "M" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/AbMonoid_Axioms/M.var".
  43
  44 (*#*
  45 %\begin{convention}% Let [M] be an abelian monoid.
  46 %\end{convention}%
  47 *)
  48
  49 inline procedural "cic:/CoRN/algebra/CAbMonoids/CAbMonoid_is_CAbMonoid.con".
  50
  51 inline procedural "cic:/CoRN/algebra/CAbMonoids/cam_commutes.con".
  52
  53 inline procedural "cic:/CoRN/algebra/CAbMonoids/cam_commutes_unfolded.con".
  54
  55 (* UNEXPORTED
  56 End AbMonoid_Axioms
  57 *)
  58
  59 (* UNEXPORTED
  60 Section SubCAbMonoids
  61 *)
  62
  63 (*#*
  64 ** Subgroups of an Abelian Monoid
  65 *)
  66
  67 alias id "M" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/M.var".
  68
  69 alias id "P" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/P.var".
  70
  71 alias id "Punit" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/Punit.var".
  72
  73 alias id "op_pres_P" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/op_pres_P.var".
  74
  75 (*#*
  76 %\begin{convention}%
  77 Let [M] be an Abelian Monoid and [P] be a ([CProp]-valued) predicate on [M]
  78 that contains [Zero] and is closed under [[+]] and [[--]].
  79 %\end{convention}%
  80 *)
  81
  82 inline procedural "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/subcrr.con" "Abelian_Monoids__SubCAbMonoids__".
  83
  84 inline procedural "cic:/CoRN/algebra/CAbMonoids/isabgrp_scrr.con".
  85
  86 inline procedural "cic:/CoRN/algebra/CAbMonoids/Build_SubCAbMonoid.con".
  87
  88 (* UNEXPORTED
  89 End SubCAbMonoids
  90 *)
  91
  92 (* UNEXPORTED
  93 End Abelian_Monoids
  94 *)
  95
  96 (* UNEXPORTED
  97 Hint Resolve cam_commutes_unfolded: algebra.
  98 *)
  99