Nuprl Lemma : State-comb-mem
[Info,B,A:Type]. [R:A 
B B 
]. [f:A B B]. [init:Id bag(B)]. [X:EClass(A)]. [es:EO+(Info)].
[e1,e2:E].
v1,v2:B. a:A.
((a:A. s:B. e:E. (e1 
loc e 
e loc e2 a 
X(e) s Memory-class(f;init;X)(e) R[a;s;f a s]))
(a1,a2:A. s1,s2:B. e,e':E.
(e1 loc e
(e <loc e')
e' loc e2
a1 X(e)
s1 Memory-class(f;init;X)(e)
a2 X(e')
s2 State-comb(init;f;X)(pred(e'))
R[a1;s1;s2]
R[a1;s1;f a2 s2]))
(s1,s2:B. a:A. SqStable(R[a;s1;s2]))
single-valued-classrel(es;X;A)
single-valued-bag(init loc(e1);B)
e1 loc e2
a X(e1)
v1 Memory-class(f;init;X)(e1)
v2 State-comb(init;f;X)(e2)
R[a;v1;v2])
Proof not projected
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
Memory-class: Memory-class(f;init;X),
single-valued-classrel: single-valued-classrel(es;X;T),
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e loc e' ,
es-locl: (e <loc e'),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
Id: Id,
sq_stable: SqStable(P),
uall: [x:A]. B[x],
prop: ,
so_apply: x[s1;s2;s3],
all: x:A. B[x],
implies: P Q,
apply: f a,
function: x:A B[x],
universe: Type,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Definitions :
prior_iterated_classrel: s prior(X*(f,init,e)),
or: P 
Q,
and: P 
Q,
cand: A c B,
false: False,
guard: {T},
uall: [x:A]. B[x],
prop: ,
all: x:A. B[x],
implies: P Q,
so_apply: x[s1;s2;s3],
member: t T,
squash: 
T,
true: True,
so_lambda: 
x.t[x],
not: 
A,
assert: 
b,
bfalse: ff,
ifthenelse: if b then t else f fi ,
so_lambda: x y.t[x; y],
rev_implies: P 
Q,
iff: P Q,
sq_stable: SqStable(P),
so_apply: x[s],
uimplies: b supposing a,
sq_type: SQType(T),
so_apply: x[s1;s2],
subtype: S 
T
Lemmas :
not_wf,
assert_wf,
es-first_wf,
and_wf,
bag-member_wf,
Memory-classrel,
iterated_classrel_mem2,
prior_iterated_classrel_wf,
iterated_classrel_wf,
State-comb-classrel,
classrel_wf,
State-comb_wf,
Memory-class_wf,
es-le_wf,
event-ordering+_inc,
single-valued-bag_wf,
es-loc_wf,
single-valued-classrel_wf,
all_wf,
sq_stable_wf,
es-E_wf,
es-locl_wf,
es-pred_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
false_wf,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf,
es-locl-first
\mforall{}[Info,B,A:Type]. \mforall{}[R:A {}\mrightarrow{} B {}\mrightarrow{} 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{}[e1,e2:E].
\mforall{}v1,v2:B. \mforall{}a:A.
((\mforall{}a:A. \mforall{}s:B. \mforall{}e:E.
(e1 \mleq{}loc e {}\mRightarrow{} e \mleq{}loc e2 {}\mRightarrow{} a \mmember{} X(e) {}\mRightarrow{} s \mmember{} Memory-class(f;init;X)(e) {}\mRightarrow{} R[a;s;f a s]))
{}\mRightarrow{} (\mforall{}a1,a2:A. \mforall{}s1,s2:B. \mforall{}e,e':E.
(e1 \mleq{}loc e
{}\mRightarrow{} (e <loc e')
{}\mRightarrow{} e' \mleq{}loc e2
{}\mRightarrow{} a1 \mmember{} X(e)
{}\mRightarrow{} s1 \mmember{} Memory-class(f;init;X)(e)
{}\mRightarrow{} a2 \mmember{} X(e')
{}\mRightarrow{} s2 \mmember{} State-comb(init;f;X)(pred(e'))
{}\mRightarrow{} R[a1;s1;s2]
{}\mRightarrow{} R[a1;s1;f a2 s2]))
{}\mRightarrow{} (\mforall{}s1,s2:B. \mforall{}a:A. SqStable(R[a;s1;s2]))
{}\mRightarrow{} single-valued-classrel(es;X;A)
{}\mRightarrow{} single-valued-bag(init loc(e1);B)
{}\mRightarrow{} e1 \mleq{}loc e2
{}\mRightarrow{} a \mmember{} X(e1)
{}\mRightarrow{} v1 \mmember{} Memory-class(f;init;X)(e1)
{}\mRightarrow{} v2 \mmember{} State-comb(init;f;X)(e2)
{}\mRightarrow{} R[a;v1;v2])
Date html generated:
2012_02_20-PM-03_10_57
Last ObjectModification:
2012_02_17-PM-02_30_51
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