helm/software/matita/contribs/procedural/CoRN/algebra/CAbMonoids.mma

   1 (**************************************************************************)
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   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  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" as definition.
  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 (* UNEXPORTED
  43 cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/AbMonoid_Axioms/M.var
  44 *)
  45
  46 (*#*
  47 %\begin{convention}% Let [M] be an abelian monoid.
  48 %\end{convention}%
  49 *)
  50
  51 inline procedural "cic:/CoRN/algebra/CAbMonoids/CAbMonoid_is_CAbMonoid.con" as lemma.
  52
  53 inline procedural "cic:/CoRN/algebra/CAbMonoids/cam_commutes.con" as lemma.
  54
  55 inline procedural "cic:/CoRN/algebra/CAbMonoids/cam_commutes_unfolded.con" as lemma.
  56
  57 (* UNEXPORTED
  58 End AbMonoid_Axioms
  59 *)
  60
  61 (* UNEXPORTED
  62 Section SubCAbMonoids
  63 *)
  64
  65 (*#*
  66 ** Subgroups of an Abelian Monoid
  67 *)
  68
  69 (* UNEXPORTED
  70 cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/M.var
  71 *)
  72
  73 (* UNEXPORTED
  74 cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/P.var
  75 *)
  76
  77 (* UNEXPORTED
  78 cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/Punit.var
  79 *)
  80
  81 (* UNEXPORTED
  82 cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/op_pres_P.var
  83 *)
  84
  85 (*#*
  86 %\begin{convention}%
  87 Let [M] be an Abelian Monoid and [P] be a ([CProp]-valued) predicate on [M]
  88 that contains [Zero] and is closed under [[+]] and [[--]].
  89 %\end{convention}%
  90 *)
  91
  92 inline procedural "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/subcrr.con" "Abelian_Monoids__SubCAbMonoids__" as definition.
  93
  94 inline procedural "cic:/CoRN/algebra/CAbMonoids/isabgrp_scrr.con" as lemma.
  95
  96 inline procedural "cic:/CoRN/algebra/CAbMonoids/Build_SubCAbMonoid.con" as definition.
  97
  98 (* UNEXPORTED
  99 End SubCAbMonoids
 100 *)
 101
 102 (* UNEXPORTED
 103 End Abelian_Monoids
 104 *)
 105
 106 (* UNEXPORTED
 107 Hint Resolve cam_commutes_unfolded: algebra.
 108 *)
 109