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




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: ⇐⇒ Q function: x:A ─→ B[x] universe: Type bag: bag(T)
Lemmas :  State-classrel State-comb-classrel-class classrel_wf State-comb_wf iff_wf State-class_wf iterated_classrel_wf es-E_wf event-ordering+_subtype eclass_wf event-ordering+_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-comb(init;f;X)(e)  \mLeftarrow{}{}\mRightarrow{}  iterated\_classrel(es;B;A;f;init;X;e;v))



Date html generated: 2015_07_22-PM-00_21_13
Last ObjectModification: 2015_01_28-AM-10_13_30

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