Nuprl Lemma : decidable__exists-iterated-classrel

[Info,A,S:Type].
  ∀init:Id ─→ bag(S). ∀f:A ─→ S ─→ S. ∀X:EClass(A). ∀es:EO+(Info). ∀e:E.
    (single-valued-classrel(es;X;A)
     single-valued-bag(init loc(e);S)
     Dec(∃v:S. iterated-classrel(es;S;A;f;init;X;e;v)))


Proof




Definitions occuring in Statement :  iterated-classrel: iterated-classrel(es;S;A;f;init;X;e;v) single-valued-classrel: single-valued-classrel(es;X;T) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-loc: loc(e) es-E: E Id: Id decidable: Dec(P) uall: [x:A]. B[x] all: x:A. B[x] exists: x:A. B[x] implies:  Q apply: a function: x:A ─→ B[x] universe: Type single-valued-bag: single-valued-bag(b;T) bag: bag(T)
Lemmas :  decidable__exists-single-valued-bag iterated-classrel-exists not_wf exists_wf iterated-classrel_wf iterated-classrel-exists-iff single-valued-bag_wf es-loc_wf event-ordering+_subtype single-valued-classrel_wf es-E_wf event-ordering+_wf eclass_wf Id_wf bag_wf
\mforall{}[Info,A,S:Type].
    \mforall{}init:Id  {}\mrightarrow{}  bag(S).  \mforall{}f:A  {}\mrightarrow{}  S  {}\mrightarrow{}  S.  \mforall{}X:EClass(A).  \mforall{}es:EO+(Info).  \mforall{}e:E.
        (single-valued-classrel(es;X;A)
        {}\mRightarrow{}  single-valued-bag(init  loc(e);S)
        {}\mRightarrow{}  Dec(\mexists{}v:S.  iterated-classrel(es;S;A;f;init;X;e;v)))



Date html generated: 2015_07_17-PM-00_26_55
Last ObjectModification: 2015_01_27-PM-11_34_13

Home Index