Nuprl Lemma : decidable__exists-last-classrel-between3-sv
[Info,T:Type].
X:EClass(T). es:EO+(Info).
(single-valued-classrel(es;X;T)
(e1,e2:E.
Dec(
e:E
((e1 <loc e)
e 
loc e2
(v:T. v 
X(e))
(e'':E. ((e <loc e'') e'' loc e2 (x:T. (
x X(e'')))))))))
Proof not projected
Definitions occuring in Statement :
single-valued-classrel: single-valued-classrel(es;X;T),
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e loc e' ,
es-locl: (e <loc e'),
es-E: E,
decidable: Dec(P),
uall: [x:A]. B[x],
all: x:A. B[x],
exists: x:A. B[x],
not: A,
implies: P Q,
and: P Q,
universe: Type
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
implies: P Q,
decidable: Dec(P),
member: t T,
so_lambda: 
x y.t[x; y],
exists: x:A. B[x],
and: P Q,
not: A,
or: P 
Q,
false: False,
prop: 
,
so_lambda: x.t[x],
squash: 
T,
guard: {T},
true: True,
so_apply: x[s1;s2],
so_apply: x[s],
subtype: S 
T
Lemmas :
decidable__exists-last-classrel-between3,
es-E_wf,
event-ordering+_inc,
single-valued-classrel_wf,
event-ordering+_wf,
eclass_wf,
decidable__exists-single-valued-classrel,
classrel_wf,
es-le_wf,
es-locl_wf,
and_wf,
exists_wf,
all_wf,
not_wf,
squash_wf
\mforall{}[Info,T:Type].
\mforall{}X:EClass(T). \mforall{}es:EO+(Info).
(single-valued-classrel(es;X;T)
{}\mRightarrow{} (\mforall{}e1,e2:E.
Dec(\mexists{}e:E
((e1 <loc e)
\mwedge{} e \mleq{}loc e2
\mwedge{} (\mexists{}v:T. v \mmember{} X(e))
\mwedge{} (\mforall{}e'':E. ((e <loc e'') {}\mRightarrow{} e'' \mleq{}loc e2 {}\mRightarrow{} (\mforall{}x:T. (\mneg{}x \mmember{} X(e'')))))))))
Date html generated:
2012_01_23-PM-12_19_03
Last ObjectModification:
2012_01_18-AM-02_06_06
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