Nuprl Lemma : iterated_classrel_invariant2
[Info,A,S:Type]. [init:Id 
bag(S)]. [f:A S S]. [X:EClass(A)].
es:EO+(Info)
[P:S 
]
((s:S. SqStable(P[s]))
(e:E. v:S.
((s:S. (s 
init loc(e) P[s]))
(a:A. e':E. (e' 
loc e a X(e') (s:S. (P[s] P[f a s]))))
v X*(f,init,e)
P[v])))
Proof not projected
Definitions occuring in Statement :
iterated_classrel: v X*(f,init,e),
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],
member: t T,
nat: 
,
ge: i 
j ,
le: A B,
not: 
A,
false: False,
squash: T,
true: True,
so_lambda: 
x.t[x],
so_lambda: x y.t[x; y],
es-le: e loc e' ,
or: P 
Q,
guard: {T},
and: P 
Q,
sq_stable: SqStable(P),
iterated_classrel: v X*(f,init,e),
strongwellfounded: SWellFounded(R[x; y]),
exists: 
x:A. B[x],
ycomb: Y,
so_apply: x[s1;s2],
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
sq_type: SQType(T),
uimplies: b supposing a,
uiff: uiff(P;Q),
subtype: S 
T
Lemmas :
es-causl-swellfnd,
event-ordering+_inc,
nat_properties,
ge_wf,
less_than_wf,
nat_wf,
le_wf,
es-causl_wf,
iterated_classrel_wf,
all_wf,
es-E_wf,
es-le_wf,
classrel_wf,
bag-member_wf,
es-loc_wf,
equal_wf,
sq_stable_wf,
eclass_wf,
event-ordering+_wf,
Id_wf,
bag_wf,
es-first_wf,
bool_wf,
assert_wf,
bnot_wf,
not_wf,
bool_cases,
subtype_base_sq,
bool_subtype_base,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
es-locl_wf,
and_wf,
member_wf,
es-pred_wf,
es-pred-causl,
es-pred-locl,
es-locl_transitivity1,
es-le_weakening,
es-loc-pred
\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{}s:S. SqStable(P[s]))
{}\mRightarrow{} (\mforall{}e:E. \mforall{}v:S.
((\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. (P[s] {}\mRightarrow{} P[f a s]))))
{}\mRightarrow{} v \mmember{} X*(f,init,e)
{}\mRightarrow{} P[v])))
Date html generated:
2012_01_23-PM-12_20_35
Last ObjectModification:
2012_01_20-PM-03_55_55
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