1 (**************************************************************************)
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 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Nsetoid".
21 (* $Id: Nsetoid.v,v 1.4 2004/04/06 15:46:04 lcf Exp $ *)
23 include "model/structures/Nsec.ma".
25 include "algebra/CSetoidFun.ma".
27 (*#* **Example of a setoid: [nat]
29 We will show that the natural numbers form a CSetoid.
32 inline "cic:/CoRN/model/setoids/Nsetoid/ap_nat_irreflexive.con".
34 inline "cic:/CoRN/model/setoids/Nsetoid/ap_nat_symmetric.con".
36 inline "cic:/CoRN/model/setoids/Nsetoid/ap_nat_cotransitive.con".
38 inline "cic:/CoRN/model/setoids/Nsetoid/ap_nat_tight.con".
40 inline "cic:/CoRN/model/setoids/Nsetoid/ap_nat_is_apartness.con".
42 inline "cic:/CoRN/model/setoids/Nsetoid/nat_as_CSetoid.con".
47 inline "cic:/CoRN/model/setoids/Nsetoid/plus_wd.con".
49 inline "cic:/CoRN/model/setoids/Nsetoid/plus_strext.con".
51 inline "cic:/CoRN/model/setoids/Nsetoid/plus_is_bin_fun.con".
53 (*#* It is associative and commutative.
56 inline "cic:/CoRN/model/setoids/Nsetoid/plus_is_assoc.con".
58 inline "cic:/CoRN/model/setoids/Nsetoid/plus_is_commut.con".
60 (*#* ***Multiplication
63 inline "cic:/CoRN/model/setoids/Nsetoid/mult_strext.con".
65 inline "cic:/CoRN/model/setoids/Nsetoid/mult_as_bin_fun.con".