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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 *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 (* This file was automatically generated: do not edit *********************)
19 (* $Id: Nsetoid.v,v 1.4 2004/04/06 15:46:04 lcf Exp $ *)
21 include "model/structures/Nsec.ma".
23 include "algebra/CSetoidFun.ma".
25 (*#* **Example of a setoid: [nat]
27 We will show that the natural numbers form a CSetoid.
30 inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_irreflexive.con" as lemma.
32 inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_symmetric.con" as lemma.
34 inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_cotransitive.con" as lemma.
36 inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_tight.con" as lemma.
38 inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_is_apartness.con" as definition.
40 inline procedural "cic:/CoRN/model/setoids/Nsetoid/nat_as_CSetoid.con" as definition.
45 inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_wd.con" as lemma.
47 inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_strext.con" as lemma.
49 inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_bin_fun.con" as definition.
51 (*#* It is associative and commutative.
54 inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_assoc.con" as lemma.
56 inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_commut.con" as lemma.
58 (*#* ***Multiplication
61 inline procedural "cic:/CoRN/model/setoids/Nsetoid/mult_strext.con" as lemma.
63 inline procedural "cic:/CoRN/model/setoids/Nsetoid/mult_as_bin_fun.con" as definition.