Nuprl Lemma : State-comb-classrel
[Info,B,A:Type]. [f:A 
B B]. [init:Id bag(B)].
X:EClass(A). es:EO+(Info). e:E. [v:B]. (v 
State-comb(init;f;X)(e) 
iterated_classrel(es;B;A;f;init;X;e;v))
Proof not projected
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
classrel: v X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
uall: [x:A]. B[x],
all: x:A. B[x],
iff: P Q,
function: x:A B[x],
universe: Type,
bag: bag(T)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
member: t T,
so_lambda: 
x y.t[x; y],
iff: P Q,
rev_implies: P Q,
implies: P Q,
and: P 
Q,
so_apply: x[s1;s2],
prop: 
,
subtype: S 
T
Lemmas :
State-classrel,
es-E_wf,
event-ordering+_inc,
eclass_wf,
event-ordering+_wf,
Id_wf,
bag_wf,
classrel_wf,
State-comb_wf,
State-class_wf,
iterated_classrel_wf,
iff_functionality_wrt_iff,
State-comb-classrel-class
\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{} State-comb(init;f;X)(e) \mLeftarrow{}{}\mRightarrow{} iterated\_classrel(es;B;A;f;init;X;e;v))
Date html generated:
2012_02_20-PM-03_07_35
Last ObjectModification:
2012_02_16-PM-03_32_19
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