matita/contribs/CoRN-Decl/model/monoids/Zmonoid.ma

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  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Zmonoid".
  18
  19 include "CoRN.ma".
  20
  21 (* $Id: Zmonoid.v,v 1.6 2004/04/08 08:20:33 lcf Exp $ *)
  22
  23 include "model/semigroups/Zsemigroup.ma".
  24
  25 include "algebra/CMonoids.ma".
  26
  27 (*#* **Examples of monoids: $\langle$#&lang;#[Z],[[+]]$\rangle$#&rang;# and $\langle$#&lang;#[Z],[[*]]$\rangle$#&rang;#
  28 ***$\langle$#&lang;#[Z],[[+]]$\rangle$#&rang;#
  29 We use the addition [ZERO] (defined in the standard library) as the
  30 unit of monoid:
  31 *)
  32
  33 inline "cic:/CoRN/model/monoids/Zmonoid/ZERO_as_rht_unit.con".
  34
  35 inline "cic:/CoRN/model/monoids/Zmonoid/ZERO_as_lft_unit.con".
  36
  37 inline "cic:/CoRN/model/monoids/Zmonoid/Z_is_CMonoid.con".
  38
  39 inline "cic:/CoRN/model/monoids/Zmonoid/Z_as_CMonoid.con".
  40
  41 (*#* The term [Z_as_CMonoid] is of type [CMonoid]. Hence we have proven that [Z] is a constructive monoid.
  42
  43 ***$\langle$#&lang;#[Z],[[*]]$\rangle$#&rang;#
  44 As the multiplicative unit we should use [`1`], which is [(POS xH)] in
  45 the representation we have for integers.
  46 *)
  47
  48 inline "cic:/CoRN/model/monoids/Zmonoid/ONE_as_rht_unit.con".
  49
  50 inline "cic:/CoRN/model/monoids/Zmonoid/ONE_as_lft_unit.con".
  51
  52 inline "cic:/CoRN/model/monoids/Zmonoid/Z_mul_is_CMonoid.con".
  53
  54 inline "cic:/CoRN/model/monoids/Zmonoid/Z_mul_as_CMonoid.con".
  55
  56 (*#* The term [Z_mul_as_CMonoid] is another term of type [CMonoid]. *)
  57