Nuprl Lemma : Memory-class-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 Memory-class(f;init;X)(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 Memory-class(f;init;X)(e2)
R[a;v1;v2])
Proof not projected
Definitions occuring in Statement :
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-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 :
so_lambda: 
x y.t[x; y],
so_lambda: x.t[x],
member: t T,
so_apply: x[s1;s2;s3],
implies: P Q,
prop: ,
all: x:A. B[x],
uall: [x:A]. B[x],
cand: A c
B,
true: True,
squash: 
T,
and: P Q,
or: P 
Q,
prior_iterated_classrel: s prior(X*(f,init,e)),
bag-member: x bs,
ifthenelse: if b then t else f fi ,
bfalse: ff,
not: 
A,
assert: 
b,
false: False,
guard: {T},
uimplies: b supposing a,
so_apply: x[s1;s2],
so_apply: x[s],
iff: P 
Q,
sq_type: SQType(T),
rev_implies: P Q,
subtype: S 
T
Lemmas :
assert_elim,
es-locl-first,
bag_wf,
Id_wf,
eclass_wf,
event-ordering+_wf,
es-le_wf,
es-E_wf,
sq_stable_wf,
all_wf,
single-valued-classrel_wf,
es-loc_wf,
single-valued-bag_wf,
event-ordering+_inc,
es-locl_wf,
Memory-class_wf,
classrel_wf,
btrue_neq_bfalse,
Memory-classrel,
implies-es-le-pred,
assert_wf,
not_wf,
es-first_wf,
assert_witness,
false_wf,
bool_subtype_base,
bool_wf,
subtype_base_sq,
iterated_classrel_wf,
prior_iterated_classrel_wf,
es-pred_wf,
iterated_classrel_mem2,
es-locl_transitivity1,
es-pred-locl,
equal_wf,
bag-member_wf,
and_wf
\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 <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' <loc e2)
{}\mRightarrow{} a1 \mmember{} X(e)
{}\mRightarrow{} s1 \mmember{} Memory-class(f;init;X)(e)
{}\mRightarrow{} a2 \mmember{} X(e')
{}\mRightarrow{} s2 \mmember{} Memory-class(f;init;X)(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 <loc e2)
{}\mRightarrow{} a \mmember{} X(e1)
{}\mRightarrow{} v1 \mmember{} Memory-class(f;init;X)(e1)
{}\mRightarrow{} v2 \mmember{} Memory-class(f;init;X)(e2)
{}\mRightarrow{} R[a;v1;v2])
Date html generated:
2012_02_20-PM-02_54_40
Last ObjectModification:
2012_01_24-AM-10_25_56
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