Nuprl Lemma : disjoint-union-classrel-ite-weak2
[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) (w:A. (w X(e)))))
Proof not projected
Definitions occuring in Statement :
disjoint-union-class: 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),
bnot: b,
assert: b,
uall: [x:A]. B[x],
all: 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,
squash: T,
or: P Q,
and: P Q,
all: x:A. B[x],
member: t T,
implies: P Q,
rev_implies: P Q,
true: True,
prop: 
,
cand: A c B,
so_lambda: 
x y.t[x; y],
uall: [x:A]. B[x],
uiff: uiff(P;Q),
uimplies: b supposing a,
so_apply: x[s1;s2],
subtype: S 
T
Lemmas :
disjoint-union-classrel-ite2,
squash_wf,
assert_wf,
isl_wf,
classrel_wf,
outl_wf,
bnot_wf,
outr_wf,
not_wf,
disjoint-union-class_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{} ((\muparrow{}\mneg{}\msubb{}isl(v)) \mwedge{} outr(v) \mmember{} Y(e) \mwedge{} (\mforall{}w:A. (\mneg{}w \mmember{} X(e)))))
Date html generated:
2011_10_20-PM-03_39_03
Last ObjectModification:
2011_09_27-AM-10_24_41
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