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 *********************)
19 (* $Id: CSetoidInc.v,v 1.3 2004/04/22 14:49:43 lcf Exp $ *)
21 (*#* printing included %\ensuremath{\subseteq}% #⊆# *)
23 include "algebra/CSetoidFun.ma".
31 Let [S] be a setoid, and [P], [Q], [R] be predicates on [S]. *)
34 cic:/CoRN/algebra/CSetoidInc/inclusion/S.var
37 inline procedural "cic:/CoRN/algebra/CSetoidInc/included.con" as definition.
44 cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/P.var
48 cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/Q.var
52 cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/R.var
55 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_refl.con" as lemma.
57 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_trans.con" as lemma.
59 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj.con" as lemma.
61 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj'.con" as lemma.
63 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj''.con" as lemma.
65 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj_lft.con" as lemma.
67 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj_rht.con" as lemma.
69 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_extend.con" as lemma.
76 %\begin{convention}% Let [I,R:S->CProp] and [F G:(PartFunct S)], and denote
77 by [P] and [Q], respectively, the domains of [F] and [G].
82 cic:/CoRN/algebra/CSetoidInc/inclusion/F.var
86 cic:/CoRN/algebra/CSetoidInc/inclusion/G.var
91 inline procedural "cic:/CoRN/algebra/CSetoidInc/inclusion/P.con" "inclusion__" as definition.
93 inline procedural "cic:/CoRN/algebra/CSetoidInc/inclusion/Q.con" "inclusion__" as definition.
98 cic:/CoRN/algebra/CSetoidInc/inclusion/R.var
101 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_FComp.con" as lemma.
103 inline procedural "cic:/CoRN/algebra/CSetoidInc/included_FComp'.con" as lemma.
110 Implicit Arguments included [S].
114 Hint Resolve included_refl included_FComp : included.
118 Hint Immediate included_trans included_FComp' : included.