Nuprl Lemma : prior-classrel
[T,Info:Type]. [X:EClass(T)]. [es:EO+(Info)]. [e:E]. [v:T].
uiff(v 
Prior(X)(e);
e':E. (((last(
e'.0 <z bag-size(X es e')) e) = (inl e' )) 
v X(e')))
Proof not projected
Definitions occuring in Statement :
primed-class: Prior(X),
es-local-pred: last(P),
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
lt_int: i <z j,
uiff: uiff(P;Q),
uall: [x:A]. B[x],
top: Top,
exists: x:A. B[x],
squash: T,
and: P Q,
apply: f a,
lambda: x.A[x],
inl: inl x ,
union: left + right,
natural_number: $n,
universe: Type,
equal: s = t,
bag-size: bag-size(bs)
Definitions :
so_lambda: 
x y.t[x; y],
implies: P 
Q,
sq_exists: x:{A| B[x]},
or: P 
Q,
cand: A c B,
so_lambda: x.t[x],
subtype: S 
T,
all: x:A. B[x],
bag-member: x bs,
prop: 
,
true: True,
member: t T,
uimplies: b supposing a,
top: Top,
and: P Q,
exists: x:A. B[x],
squash: T,
classrel: v X(e),
uiff: uiff(P;Q),
eclass: EClass(A[eo; e]),
primed-class: Prior(X),
so_apply: x[s1;s2],
nat: 
,
so_apply: x[s],
uall: [x:A]. B[x],
false: False,
sq_stable: SqStable(P)
Lemmas :
equal_wf,
and_wf,
eclass_wf,
event-ordering+_wf,
or_wf,
sq_exists_wf,
not_wf,
all_wf,
assert_wf,
es-locl_wf,
nat_wf,
bag-size_wf,
lt_int_wf,
es-local-pred_wf,
top_wf,
event-ordering+_inc,
es-E_wf,
exists_wf,
squash_wf,
primed-class_wf,
classrel_wf,
bag-member_wf,
empty-bag_wf,
bag-member-empty,
sq_stable__bag-member
\mforall{}[T,Info:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:T].
uiff(v \mmember{} Prior(X)(e);\mdownarrow{}\mexists{}e':E. (((last(\mlambda{}e'.0 <z bag-size(X es e')) e) = (inl e' )) \mwedge{} v \mmember{} X(e')))
Date html generated:
2012_01_23-PM-01_11_59
Last ObjectModification:
2011_12_05-PM-12_36_44
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