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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: Qsetoid.v,v 1.6 2004/04/06 15:46:05 lcf Exp $ *)
21 include "model/structures/Qsec.ma".
23 include "algebra/CSetoidFun.ma".
25 (*#* **Example of a setoid: [Q]
29 inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_irreflexive1.con" as lemma.
31 inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_symmetric1.con" as lemma.
33 inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_cotransitive1.con" as lemma.
35 inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_tight1.con" as lemma.
37 inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_is_apartness.con" as definition.
39 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Q_as_CSetoid.con" as definition.
44 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_wd.con" as lemma.
46 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_strext1.con" as lemma.
48 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_bin_fun.con" as definition.
50 (*#* It is associative and commutative.
53 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_assoc.con" as lemma.
55 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_commut1.con" as lemma.
60 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_wd.con" as lemma.
62 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_strext.con" as lemma.
64 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_is_fun.con" as definition.
66 (*#* ***Multiplication
69 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_wd.con" as lemma.
71 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_strext1.con" as lemma.
73 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_bin_fun.con" as definition.
75 (*#* It is associative and commutative.
78 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_assoc.con" as lemma.
80 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_commut.con" as lemma.
85 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qlt_strext.con" as lemma.
87 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qlt_is_CSetoid_relation.con" as definition.