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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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11 (* v GNU General Public License Version 2 *)
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15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/algebra/CAbMonoids".
21 include "algebra/CMonoids.ma".
24 Section Abelian_Monoids
29 Now we introduce commutativity and add some results.
32 inline "cic:/CoRN/algebra/CAbMonoids/is_CAbMonoid.con".
34 inline "cic:/CoRN/algebra/CAbMonoids/CAbMonoid.ind".
36 coercion cic:/matita/CoRN-Decl/algebra/CAbMonoids/cam_crr.con 0 (* compounds *).
39 Section AbMonoid_Axioms
42 alias id "M" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/AbMonoid_Axioms/M.var".
45 %\begin{convention}% Let [M] be an abelian monoid.
49 inline "cic:/CoRN/algebra/CAbMonoids/CAbMonoid_is_CAbMonoid.con".
51 inline "cic:/CoRN/algebra/CAbMonoids/cam_commutes.con".
53 inline "cic:/CoRN/algebra/CAbMonoids/cam_commutes_unfolded.con".
64 ** Subgroups of an Abelian Monoid
67 alias id "M" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/M.var".
69 alias id "P" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/P.var".
71 alias id "Punit" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/Punit.var".
73 alias id "op_pres_P" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/op_pres_P.var".
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 [[--]].
82 inline "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/subcrr.con" "Abelian_Monoids__SubCAbMonoids__".
84 inline "cic:/CoRN/algebra/CAbMonoids/isabgrp_scrr.con".
86 inline "cic:/CoRN/algebra/CAbMonoids/Build_SubCAbMonoid.con".
97 Hint Resolve cam_commutes_unfolded: algebra.