helm/software/matita/contribs/procedural/CoRN/model/setoids/Nsetoid.mma

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  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 include "CoRN.ma".
  18
  19 (* $Id: Nsetoid.v,v 1.4 2004/04/06 15:46:04 lcf Exp $ *)
  20
  21 include "model/structures/Nsec.ma".
  22
  23 include "algebra/CSetoidFun.ma".
  24
  25 (*#* **Example of a setoid: [nat]
  26
  27 We will show that the natural numbers form a CSetoid.
  28 *)
  29
  30 inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_irreflexive.con" as lemma.
  31
  32 inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_symmetric.con" as lemma.
  33
  34 inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_cotransitive.con" as lemma.
  35
  36 inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_tight.con" as lemma.
  37
  38 inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_is_apartness.con" as definition.
  39
  40 inline procedural "cic:/CoRN/model/setoids/Nsetoid/nat_as_CSetoid.con" as definition.
  41
  42 (*#* ***Addition
  43 *)
  44
  45 inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_wd.con" as lemma.
  46
  47 inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_strext.con" as lemma.
  48
  49 inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_bin_fun.con" as definition.
  50
  51 (*#* It is associative and commutative.
  52 *)
  53
  54 inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_assoc.con" as lemma.
  55
  56 inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_commut.con" as lemma.
  57
  58 (*#* ***Multiplication
  59 *)
  60
  61 inline procedural "cic:/CoRN/model/setoids/Nsetoid/mult_strext.con" as lemma.
  62
  63 inline procedural "cic:/CoRN/model/setoids/Nsetoid/mult_as_bin_fun.con" as definition.
  64