Nuprl Lemma : State-classrel2
∀[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)].
∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀[v:B]. (v ∈ State-class(init;f;X)(e)
⇐⇒ ↓iterated-classrel(es;B;A;f;init;X;e;v))
Proof
Definitions occuring in Statement :
State-class: State-class(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
,
squash: ↓T
,
function: x:A ─→ B[x]
,
universe: Type
,
bag: bag(T)
Lemmas :
squash_wf,
iterated-classrel_wf,
iterated-classrel-iff,
iterated_classrel_wf,
iff_wf,
State-classrel,
classrel_wf,
State-class_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf
Latex:
\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-class(init;f;X)(e) \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}iterated-classrel(es;B;A;f;init;X;e;v))
Date html generated:
2015_07_22-PM-00_20_21
Last ObjectModification:
2015_01_28-AM-10_13_22
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