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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 *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Npossetoid".
21 (* $Id: Npossetoid.v,v 1.3 2004/04/06 15:46:04 lcf Exp $ *)
23 include "model/setoids/Nsetoid.ma".
25 include "model/structures/Npossec.ma".
27 include "algebra/CSetoidFun.ma".
29 (*#* **Example of a setoid: [Npos]
32 The positive natural numbers [Npos] will be defined as a subsetoid of the
36 inline "cic:/CoRN/model/setoids/Npossetoid/Npos.con".
38 inline "cic:/CoRN/model/setoids/Npossetoid/NposP.con".
40 (*#* One and two are elements of it.
43 inline "cic:/CoRN/model/setoids/Npossetoid/ONEpos.con".
45 inline "cic:/CoRN/model/setoids/Npossetoid/TWOpos.con".
47 (*#* ***Addition and multiplication
48 Because addition and multiplication preserve positivity, we can define
49 them on this subsetoid.
52 inline "cic:/CoRN/model/setoids/Npossetoid/plus_resp_Npos.con".
54 inline "cic:/CoRN/model/setoids/Npossetoid/Npos_plus.con".
56 inline "cic:/CoRN/model/setoids/Npossetoid/mult_resp_Npos.con".
58 inline "cic:/CoRN/model/setoids/Npossetoid/Npos_mult.con".
60 (*#* The addition has no right unit on this set.
63 inline "cic:/CoRN/model/setoids/Npossetoid/no_rht_unit_Npos1.con".
65 (*#* And the multiplication doesn't have an inverse, because there can't be an
69 inline "cic:/CoRN/model/setoids/Npossetoid/no_inverse_Nposmult1.con".