Nuprl Lemma : primed-class-opt-classrel
[T,Info:Type]. [X:EClass(T)]. [init:Id 
bag(T)]. [es:EO+(Info)]. [e:E]. [v:T].
uiff(v 
Prior(X)?init(e);
(
e':E. ((es-p-local-pred(es;
e'.(w:T. w X(e'))) e e') 
v X(e')))
((e':E. ((e' <loc e) 
(w:T. (
w X(e'))))) v init loc(e)))
Proof not projected
Definitions occuring in Statement :
primed-class-opt: Prior(X)?b,
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-p-local-pred: es-p-local-pred(es;P),
es-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: [x:A]. B[x],
all: x:A. B[x],
exists: x:A. B[x],
not: A,
squash: T,
implies: P Q,
or: P Q,
and: P Q,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
universe: Type,
bag-member: x bs,
bag: bag(T)
Definitions :
eclass: EClass(A[eo; e]),
classrel: v X(e),
primed-class-opt: Prior(X)?b,
or: P Q,
and: P Q,
all: x:A. B[x],
implies: P Q,
member: t T,
prop: 
,
so_lambda: 
x.t[x],
uimplies: b supposing a,
assert: 
b,
can-apply: can-apply(f;x),
do-apply: do-apply(f;x),
subtype: S 
T,
suptype: suptype(S; T),
isl: isl(x),
outl: outl(x),
sq_exists: x:{A| B[x]},
btrue: tt,
bfalse: ff,
ifthenelse: if b then t else f fi ,
cand: A c B,
so_lambda: x y.t[x; y],
squash: T,
bag-member: x bs,
true: True,
uiff: uiff(P;Q),
exists: x:A. B[x],
not: A,
es-p-local-pred: es-p-local-pred(es;P),
false: False,
guard: {T},
uall: [x:A]. B[x],
nat: 
,
so_apply: x[s],
so_apply: x[s1;s2],
rev_uimplies: rev_uimplies(P;Q),
sq_stable: SqStable(P),
es-locl: (e <loc e'),
iff: P 
Q,
lt_int: i <z j,
bag-size: bag-size(bs),
empty-bag: {},
length: ||as||,
ycomb: Y
Lemmas :
lt_int_wf,
bag-size_wf,
nat_wf,
bool_wf,
squash_wf,
exists_wf,
bag-member_wf,
es-E_wf,
es-local-pred-cases,
es-locl_wf,
es-local-pred_wf,
or_wf,
sq_exists_wf,
and_wf,
assert_wf,
all_wf,
not_wf,
true_wf,
es-first_wf,
event-ordering+_inc,
es-pred_wf,
isl_wf,
outl_wf,
isect_wf,
false_wf,
equal_wf,
classrel_wf,
primed-class-opt_wf,
es-p-local-pred_wf,
es-loc_wf,
event-ordering+_wf,
Id_wf,
bag_wf,
eclass_wf,
bag-member-iff-size,
assert_of_lt_int,
sq_stable__bag-member,
es-locl-trichotomy,
empty-bag-iff-no-member
\mforall{}[T,Info:Type]. \mforall{}[X:EClass(T)]. \mforall{}[init:Id {}\mrightarrow{} bag(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:T].
uiff(v \mmember{} Prior(X)?init(
e);\mdownarrow{}(\mexists{}e':E. ((es-p-local-pred(es;\mlambda{}e'.(\mdownarrow{}\mexists{}w:T. w \mmember{} X(e'))) e e') \mwedge{} v \mmember{} X(e')))
\mvee{} ((\mforall{}e':E. ((e' <loc e) {}\mRightarrow{} (\mforall{}w:T. (\mneg{}w \mmember{} X(e'))))) \mwedge{} v \mdownarrow{}\mmember{} init loc(e)))
Date html generated:
2012_01_23-PM-12_55_19
Last ObjectModification:
2012_01_13-AM-10_33_56
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