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: ⇐⇒ 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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