Nuprl Lemma : Memory-classrel
[Info,B,A:Type]. [f:A 
B B]. [init:Id bag(B)].
X:EClass(A). es:EO+(Info). e:E.
[v:B]
(v 
Memory-class(f;init;X)(e) 
((
first(e)) 
v 
init loc(e)) 
((
first(e)) v X*(f,init,pred(e))))
Proof not projected
Definitions occuring in Statement :
Memory-class: Memory-class(f;init;X),
iterated_classrel: v X*(f,init,e),
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-pred: pred(e),
es-first: first(e),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: b,
uall: [x:A]. B[x],
all: x:A. B[x],
iff: P Q,
not: A,
or: P Q,
and: P Q,
apply: f a,
function: x:A B[x],
universe: Type,
bag-member: x bs,
bag: bag(T)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
or: P Q,
and: P Q,
assert: b,
bag-member: x bs,
not: A,
sq_stable: SqStable(P),
prop: 
,
implies: P Q,
member: t T,
cand: A c B,
btrue: tt,
ifthenelse: if b then t else f fi ,
true: True,
squash: T,
bfalse: ff,
guard: {T},
so_lambda: 
x y.t[x; y],
exists: 
x:A. B[x],
so_lambda: x.t[x],
iff: P Q,
rev_implies: P Q,
false: False,
bool: 
,
uimplies: b supposing a,
unit: Unit,
uiff: uiff(P;Q),
so_apply: x[s1;s2],
so_apply: x[s],
subtype: S 
T,
it: 
Lemmas :
sq_stable__iff,
classrel_wf,
Memory-class_wf,
or_wf,
assert_wf,
es-first_wf,
event-ordering+_inc,
bag-member_wf,
es-loc_wf,
not_wf,
iterated_classrel_wf,
es-pred_wf,
sq_stable__classrel,
bool_wf,
eqtt_to_assert,
true_wf,
squash_wf,
uiff_transitivity,
equal_wf,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
sq_stable__iterated_classrel,
false_wf,
es-E_wf,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf,
exists_wf,
all_wf,
iff_functionality_wrt_iff,
iff_weakening_uiff,
Memory-classrel1,
and_wf,
or_functionality_wrt_iff,
and_functionality_wrt_uiff3,
iterated-classrel-Memory-classrel
\mforall{}[Info,B,A:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
\mforall{}X:EClass(A). \mforall{}es:EO+(Info). \mforall{}e:E.
\mforall{}[v:B]
(v \mmember{} Memory-class(f;init;X)(e)
\mLeftarrow{}{}\mRightarrow{} ((\muparrow{}first(e)) \mwedge{} v \mdownarrow{}\mmember{} init loc(e)) \mvee{} ((\mneg{}\muparrow{}first(e)) \mwedge{} v \mmember{} X*(f,init,pred(e))))
Date html generated:
2012_01_23-PM-12_59_28
Last ObjectModification:
2012_01_11-PM-12_13_28
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