Nuprl Lemma : State-comb-invariant
[Info,A,S:Type]. [init:Id 
bag(S)]. [f:A S S]. [X:EClass(A)]. [es:EO+(Info)]. [P:S 
]. [e:E].
v:S
((s:S. SqStable(P[s]))
(s:S. (s 
init loc(e) P[s]))
(a:A. e':E. (e' 
loc e a X(e') (s:S. (s Memory-class(f;init;X)(e') P[s] P[f a s]))))
v State-comb(init;f;X)(e)
P[v])
Proof not projected
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
Memory-class: Memory-class(f;init;X),
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e loc e' ,
es-loc: loc(e),
es-E: E,
Id: Id,
sq_stable: SqStable(P),
uall: [x:A]. B[x],
prop: ,
so_apply: x[s],
all: x:A. B[x],
implies: 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],
prop: ,
all: x:A. B[x],
implies: P Q,
so_apply: x[s],
member: t T,
squash: T,
true: True,
so_lambda: 
x.t[x],
so_lambda: x y.t[x; y],
sq_stable: SqStable(P),
rev_implies: P 
Q,
and: P 
Q,
iff: P Q,
so_apply: x[s1;s2],
prior_iterated_classrel: s prior(X*(f,init,e)),
subtype: S 
T
Lemmas :
iterated_classrel_invariant3,
Memory-classrel,
prior_iterated_classrel_wf,
classrel_wf,
es-le_wf,
State-comb-classrel,
State-comb_wf,
all_wf,
es-E_wf,
event-ordering+_inc,
Memory-class_wf,
bag-member_wf,
es-loc_wf,
sq_stable_wf,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf
\mforall{}[Info,A,S:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(S)]. \mforall{}[f:A {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)].
\mforall{}[P:S {}\mrightarrow{} \mBbbP{}]. \mforall{}[e:E].
\mforall{}v:S
((\mforall{}s:S. SqStable(P[s]))
{}\mRightarrow{} (\mforall{}s:S. (s \mdownarrow{}\mmember{} init loc(e) {}\mRightarrow{} P[s]))
{}\mRightarrow{} (\mforall{}a:A. \mforall{}e':E.
(e' \mleq{}loc e {}\mRightarrow{} a \mmember{} X(e') {}\mRightarrow{} (\mforall{}s:S. (s \mmember{} Memory-class(f;init;X)(e') {}\mRightarrow{} P[s] {}\mRightarrow{} P[f a s]))))
{}\mRightarrow{} v \mmember{} State-comb(init;f;X)(e)
{}\mRightarrow{} P[v])
Date html generated:
2012_02_20-PM-03_09_30
Last ObjectModification:
2012_02_17-AM-10_00_09
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