Nuprl Lemma : iterated-classrel-Memory-classrel
[Info,B,A:Type]. [f:A 
B B]. [init:Id bag(B)].
X:EClass(A). es:EO+(Info). e:E.
[v:B]
uiff(v 
X*(f,init,e);
(
a:A. b:B. (a X(e) 
b Memory-class(f;init;X)(e) (v = (f a b))))
((a:A. (
a X(e))) v Memory-class(f;init;X)(e)))
Proof not projected
Definitions occuring in Statement :
Memory-class: Memory-class(f;init;X),
iterated_classrel: v X*(f,init,e),
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: [x:A]. B[x],
all: x:A. B[x],
exists: x:A. B[x],
not: A,
squash: T,
or: P Q,
and: P Q,
apply: f a,
function: x:A B[x],
universe: Type,
equal: s = t,
bag: bag(T)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
iterated_classrel: v X*(f,init,e),
squash: T,
or: P Q,
and: P Q,
not: A,
prop: 
,
implies: P 
Q,
member: t T,
so_lambda: 
x.t[x],
cand: A c B,
true: True,
nat: 
,
ge: i 
j ,
le: A 
B,
false: False,
ycomb: Y,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
so_lambda: x y.t[x; y],
uiff: uiff(P;Q),
exists: x:A. B[x],
uimplies: b supposing a,
guard: {T},
assert: 
b,
rev_implies: P 
Q,
iff: P Q,
sq_stable: SqStable(P),
so_apply: x[s],
strongwellfounded: SWellFounded(R[x; y]),
bool: 
,
unit: Unit,
so_apply: x[s1;s2],
rev_uimplies: rev_uimplies(P;Q),
it: 
,
subtype: S 
T
Lemmas :
sq_stable__uiff,
iterated_classrel_wf,
squash_wf,
or_wf,
exists_wf,
classrel_wf,
Memory-class_wf,
all_wf,
not_wf,
sq_stable__iterated_classrel,
sq_stable__squash,
es-causl-swellfnd,
nat_properties,
ge_wf,
less_than_wf,
nat_wf,
le_wf,
es-causl_wf,
es-first_wf,
bool_wf,
eqtt_to_assert,
uiff_transitivity,
equal_wf,
assert_wf,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf,
bag-member_wf,
es-loc_wf,
and_wf,
Memory-classrel1,
true_wf,
es-pred_wf,
member_wf,
es-pred-causl,
uiff_functionality_wrt_uiff2,
iff_weakening_uiff,
squash_functionality_wrt_uiff,
exists_functionality_wrt_iff,
and_functionality_wrt_uiff2,
false_wf
\mforall{}[Info,B,A:Type]. \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]
uiff(v \mmember{} X*(f,init,e);\mdownarrow{}(\mexists{}a:A
\mexists{}b:B. (a \mmember{} X(e) \mwedge{} b \mmember{} Memory-class(f;init;X)(e) \mwedge{} (v = (f a b))))
\mvee{} ((\mforall{}a:A. (\mneg{}a \mmember{} X(e))) \mwedge{} v \mmember{} Memory-class(f;init;X)(e)))
Date html generated:
2012_01_23-PM-12_58_52
Last ObjectModification:
2012_01_11-PM-12_08_48
Home
Index