Nuprl Lemma : disjoint-union-comb-classrel-weak
[Info,A,B:Type]. [X:EClass(A)]. [Y:EClass(B)]. [es:EO+(Info)]. [e:E]. [v:A + B].
(v 
X (+) Y(e) 
((
isl(v)) 
outl(v) X(e)) 
((
isl(v)) outr(v) Y(e)))
Proof not projected
Definitions occuring in Statement :
disjoint-union-comb: X (+) Y,
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
outr: outr(x),
outl: outl(x),
isl: isl(x),
assert: b,
uall: [x:A]. B[x],
iff: P Q,
not: A,
squash: T,
or: P Q,
and: P Q,
union: left + right,
universe: Type
Definitions :
iff: P Q,
classrel: v X(e),
squash: T,
or: P Q,
and: P Q,
assert: b,
isl: isl(x),
outl: outl(x),
outr: outr(x),
member: t T,
implies: P Q,
rev_implies: P Q,
true: True,
prop: 
,
btrue: tt,
bfalse: ff,
ifthenelse: if b then t else f fi ,
cand: A c B,
bag-member: x bs,
exists: 
x:A. B[x],
so_lambda: 
x.t[x],
so_lambda: x y.t[x; y],
not: A,
uall: [x:A]. B[x],
uiff: uiff(P;Q),
uimplies: b supposing a,
false: False,
so_apply: x[s],
all: x:A. B[x],
so_apply: x[s1;s2],
subtype: S 
T
Lemmas :
disjoint-union-comb-classrel,
squash_wf,
or_wf,
true_wf,
classrel_wf,
not_wf,
exists_wf,
and_wf,
equal_wf,
bag_wf,
bag_qinc,
l_member_wf,
false_wf,
disjoint-union-comb_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
eclass_wf
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:A + B].
(v \mmember{} X (+) Y(e) \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}((\muparrow{}isl(v)) \mwedge{} outl(v) \mmember{} X(e)) \mvee{} ((\mneg{}\muparrow{}isl(v)) \mwedge{} outr(v) \mmember{} Y(e)))
Date html generated:
2012_01_23-PM-01_25_49
Last ObjectModification:
2012_01_11-PM-07_58_40
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