helm/software/matita/contribs/procedural/CoRN/model/monoids/Zmonoid.mma

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