Nuprl Lemma : decidable__exists-last-classrel-between3
[Info,T:Type].
X:EClass(T). es:EO+(Info). 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 :
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,
squash: T,
implies: P Q,
and: P Q,
universe: Type
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
member: t T,
so_lambda: 
x y.t[x; y],
squash: T,
implies: P Q,
not: A,
nat: 
,
ge: i 
j ,
le: A B,
false: False,
true: True,
decidable: Dec(P),
exists: x:A. B[x],
and: P Q,
es-le: e loc e' ,
or: P 
Q,
cand: A c B,
guard: {T},
prop: 
,
so_lambda: x.t[x],
assert: 
b,
bfalse: ff,
ifthenelse: if b then t else f fi ,
label: ...$L... t,
so_apply: x[s1;s2],
iff: P 
Q,
strongwellfounded: SWellFounded(R[x; y]),
uimplies: b supposing a,
so_apply: x[s],
sq_type: SQType(T),
es-locl: (e <loc e'),
subtype: S 
T,
!hyp_hide: x
Lemmas :
decidable__equal_Id,
es-loc_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
eclass_wf,
es-locl-trichotomy,
es-causl-swellfnd,
nat_properties,
ge_wf,
less_than_wf,
nat_wf,
le_wf,
es-causl_wf,
decidable__exists_classrel,
es-locl_wf,
equal_wf,
Id_wf,
es-locl_transitivity2,
es-locl_irreflexivity,
es-le_wf,
squash_wf,
exists_wf,
classrel_wf,
all_wf,
not_wf,
and_wf,
es-pred_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
false_wf,
es-locl-first,
es-loc-pred,
es-pred-causl,
es-causl_weakening,
es-pred-locl,
es-locl_transitivity1,
es-le_weakening,
implies-es-le-pred,
es-pred_property,
es-le_weakening_eq,
es-causl_transitivity2,
es-causle_weakening,
es-causle_weakening_eq,
es-causl_irreflexivity,
es-causle_wf,
decidable_wf,
es-le-loc
\mforall{}[Info,T:Type].
\mforall{}X:EClass(T). \mforall{}es:EO+(Info). \mforall{}e1,e2:E.
Dec(\mexists{}e:E
((e1 <loc e)
\mwedge{} e \mleq{}loc e2
\mwedge{} (\mdownarrow{}\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_17_36
Last ObjectModification:
2012_01_18-AM-02_03_04
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