Nuprl Lemma : Accum-classrel-Memory
[Info,B,A:Type]. [f:A 
B B]. [init:Id bag(B)]. [X:EClass(A)]. [es:EO+(Info)]. [e:E]. [v:B].
(v 
Accum-class(f;init;X)(e) 
a:A. b:B. (a X(e) 
b Memory-class(f;init;X)(e) (v = (f a b))))
Proof not projected
Definitions occuring in Statement :
Memory-class: Memory-class(f;init;X),
Accum-class: Accum-class(f;init;X),
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
uall: [x:A]. B[x],
exists: x:A. B[x],
iff: P Q,
squash: T,
and: P Q,
apply: f a,
function: x:A B[x],
universe: Type,
equal: s = t,
bag: bag(T)
Definitions :
eclass: EClass(A[eo; e]),
iff: P Q,
squash: T,
exists: x:A. B[x],
and: P Q,
top: Top,
member: t T,
so_lambda: 
x.t[x],
implies: P Q,
rev_implies: P Q,
true: True,
so_lambda: x y.t[x; y],
uall: [x:A]. B[x],
prop: 
,
so_apply: x[s],
all: x:A. B[x],
so_apply: x[s1;s2],
classrel: v X(e),
subtype: S 
T
Lemmas :
Accum-classrel-Memory-sq,
bag-member_wf,
lifting-2_wf,
Memory-class_wf,
squash_wf,
exists_wf,
and_wf,
equal_wf,
classrel_wf,
Accum-class_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf,
iff_functionality_wrt_iff,
iff_weakening_uiff,
bag-member-lifting-2
\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].
(v \mmember{} Accum-class(f;init;X)(e)
\mLeftarrow{}{}\mRightarrow{} \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))))
Date html generated:
2012_01_23-PM-12_57_40
Last ObjectModification:
2012_01_11-AM-11_57_14
Home
Index