Nuprl Lemma : Accum-class-invariant
[Info,B,A:Type].
P:B 
. f:A B B. init:Id bag(B). X:EClass(A). es:EO+(Info). e:E. v:B.
((s:B. SqStable(P[s]))
(a:A. e':E. (e' 
loc e a 
X(e') (s:B. (P[s] P[f a s]))))
(v:B. (v 
init loc(e) P[v]))
v Accum-class(f;init;X)(e)
P[v])
Proof not projected
Definitions occuring in Statement :
Accum-class: Accum-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],
all: x:A. B[x],
prop: ,
implies: P Q,
so_apply: x[s],
es-le: e loc e' ,
squash: T,
member: t T,
true: True,
or: P 
Q,
guard: {T},
so_lambda: 
x.t[x],
so_lambda: x y.t[x; y],
sq_stable: SqStable(P),
exists: 
x:A. B[x],
and: P 
Q,
iff: P 
Q,
so_apply: x[s1;s2],
subtype: S 
T
Lemmas :
Accum-classrel-Memory,
Memory-class-invariant,
es-le_weakening,
event-ordering+_inc,
classrel_wf,
es-locl_wf,
Accum-class_wf,
all_wf,
bag-member_wf,
es-loc_wf,
es-E_wf,
es-le_wf,
sq_stable_wf,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf
\mforall{}[Info,B,A:Type].
\mforall{}P:B {}\mrightarrow{} \mBbbP{}. \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.
((\mforall{}s:B. SqStable(P[s]))
{}\mRightarrow{} (\mforall{}a:A. \mforall{}e':E. (e' \mleq{}loc e {}\mRightarrow{} a \mmember{} X(e') {}\mRightarrow{} (\mforall{}s:B. (P[s] {}\mRightarrow{} P[f a s]))))
{}\mRightarrow{} (\mforall{}v:B. (v \mdownarrow{}\mmember{} init loc(e) {}\mRightarrow{} P[v]))
{}\mRightarrow{} v \mmember{} Accum-class(f;init;X)(e)
{}\mRightarrow{} P[v])
Date html generated:
2012_02_20-PM-03_01_16
Last ObjectModification:
2012_02_03-AM-01_22_38
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