Nuprl Lemma : Memory-class-progress
[Info,B,A:Type].
R:B 
B 
. P:A B . f:A B B. init:Id bag(B). X:EClass(A). es:EO+(Info). e1,e2:E. v1,v2:B.
((a:A. s:B. Dec(P[a;s]))
Trans(B;x,y.R[x;y])
(s1,s2:B. SqStable(R[s1;s2]))
(a:A. e:E. s:B.
(e1 
loc e
(e <loc e2)
a 
X(e)
s Memory-class(f;init;X)(e)
((P[a;s] R[s;f a s]) 
((
P[a;s]) (s = (f a s))))))
single-valued-classrel(es;X;A)
single-valued-bag(init loc(e1);B)
v1 Memory-class(f;init;X)(e1)
v2 Memory-class(f;init;X)(e2)
(e1 <loc e2)
(
e:E. a:A. s:B. (e1 loc e (e <loc e2) s Memory-class(f;init;X)(e) a X(e) P[a;s]))
R[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,
trans: Trans(T;x,y.E[x; y]),
sq_stable: SqStable(P),
decidable: Dec(P),
uall: [x:A]. B[x],
prop: ,
so_apply: x[s1;s2],
all: x:A. B[x],
exists: x:A. B[x],
not: A,
implies: P Q,
and: P Q,
apply: f a,
function: x:A B[x],
universe: Type,
equal: s = t,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
prop: ,
implies: P Q,
so_apply: x[s1;s2],
member: t T,
so_lambda: 
x.t[x],
so_lambda: x y.t[x; y],
and: P Q,
iterated_classrel: v X*(f,init,e),
exists: x:A. B[x],
ycomb: Y,
squash: 
T,
ifthenelse: if b then t else f fi ,
or: P 
Q,
btrue: tt,
true: True,
es-le: e loc e' ,
bag-member: x bs,
guard: {T},
cand: A c B,
label: ...$L... t,
es-locl: (e <loc e'),
not: A,
assert: 
b,
bfalse: ff,
false: False,
classrel: v X(e),
iff: P 
Q,
so_apply: x[s],
uimplies: b supposing a,
decidable: Dec(P),
sq_type: SQType(T),
rev_implies: P Q,
single-valued-classrel: single-valued-classrel(es;X;T),
single-valued-bag: single-valued-bag(b;T),
trans: Trans(T;x,y.E[x; y]),
subtype: S 
T,
!hyp_hide: x
Lemmas :
Memory-classrel,
btrue_neq_bfalse,
exists_wf,
es-E_wf,
event-ordering+_inc,
and_wf,
es-le_wf,
es-locl_wf,
classrel_wf,
Memory-class_wf,
single-valued-bag_wf,
es-loc_wf,
single-valued-classrel_wf,
all_wf,
not_wf,
equal_wf,
sq_stable_wf,
trans_wf,
decidable_wf,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf,
es-locl-first,
assert_elim,
decidable__exists-single-valued-classrel,
subtype_base_sq,
bool_wf,
bool_subtype_base,
bag-member_wf,
or_wf,
es-first_wf,
es-pred_property,
assert_witness,
assert_wf,
iterated_classrel_wf,
iterated_classrel-single-val,
es-causl_transitivity2,
es-causle_weakening_eq,
es-causle_weakening_locl,
es-causl_irreflexivity,
es-le-loc,
not_assert_elim,
es-causle_wf,
iterated_classrel_progress,
es-pred_wf,
false_wf,
squash_wf,
true_wf,
es-pred-locl,
es-le_weakening,
es-pred-causl,
es-causl_weakening,
es-causle_weakening,
es-causl_wf,
decidable__exists-iterated-classrel-between3-sv,
implies-es-le-pred,
es-le-first,
ifthenelse_wf,
es-loc-pred,
es-locl-trichotomy,
es-locl_transitivity2,
es-le_weakening_eq,
es-locl_irreflexivity,
es-locl_transitivity1
\mforall{}[Info,B,A:Type].
\mforall{}R:B {}\mrightarrow{} B {}\mrightarrow{} \mBbbP{}. \mforall{}P:A {}\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{}s:B. Dec(P[a;s]))
{}\mRightarrow{} Trans(B;x,y.R[x;y])
{}\mRightarrow{} (\mforall{}s1,s2:B. SqStable(R[s1;s2]))
{}\mRightarrow{} (\mforall{}a:A. \mforall{}e:E. \mforall{}s:B.
(e1 \mleq{}loc e
{}\mRightarrow{} (e <loc e2)
{}\mRightarrow{} a \mmember{} X(e)
{}\mRightarrow{} s \mmember{} Memory-class(f;init;X)(e)
{}\mRightarrow{} ((P[a;s] {}\mRightarrow{} R[s;f a s]) \mwedge{} ((\mneg{}P[a;s]) {}\mRightarrow{} (s = (f a s))))))
{}\mRightarrow{} single-valued-classrel(es;X;A)
{}\mRightarrow{} single-valued-bag(init loc(e1);B)
{}\mRightarrow{} v1 \mmember{} Memory-class(f;init;X)(e1)
{}\mRightarrow{} v2 \mmember{} Memory-class(f;init;X)(e2)
{}\mRightarrow{} (e1 <loc e2)
{}\mRightarrow{} (\mexists{}e:E
\mexists{}a:A. \mexists{}s:B. (e1 \mleq{}loc e \mwedge{} (e <loc e2) \mwedge{} s \mmember{} Memory-class(f;init;X)(e) \mwedge{} a \mmember{} X(e) \mwedge{} P[a;s]))
{}\mRightarrow{} R[v1;v2])
Date html generated:
2012_01_23-PM-01_02_15
Last ObjectModification:
2012_01_21-PM-08_34_15
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