Nuprl Lemma : Memory-loc-classrel-single-val

[Info,B,A:Type].
  ∀f:Id ─→ A ─→ B ─→ B. ∀init:Id ─→ bag(B). ∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀v:B.
    (uiff(v ∈ Memory-loc-class(f;init;X)(e);prior-iterated-classrel(es;A;B;v;X;f loc(e);init;e))) supposing 
       (single-valued-classrel(es;X;A) and 
       single-valued-bag(init loc(e);B))


Proof




Definitions occuring in Statement :  Memory-loc-class: Memory-loc-class(f;init;X) prior-iterated-classrel: prior-iterated-classrel(es;A;S;s;X;f;init;e) single-valued-classrel: single-valued-classrel(es;X;T) classrel: v ∈ X(e) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-loc: loc(e) es-E: E Id: Id uiff: uiff(P;Q) uimplies: supposing a uall: [x:A]. B[x] all: x:A. B[x] apply: a function: x:A ─→ B[x] universe: Type single-valued-bag: single-valued-bag(b;T) bag: bag(T)
Lemmas :  bag-member_wf es-loc_wf event-ordering+_subtype classrel_wf es-E_wf Memory-loc-class_wf prior-iterated-classrel_wf single-valued-classrel_wf single-valued-bag_wf event-ordering+_wf eclass_wf Id_wf bag_wf Memory-classrel-loc Memory-classrel-single-val

Latex:
\mforall{}[Info,B,A:Type].
    \mforall{}f:Id  {}\mrightarrow{}  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.
        (uiff(v  \mmember{}  Memory-loc-class(f;init;X)(
                            e);prior-iterated-classrel(es;A;B;v;X;f  loc(e);init;e)))  supposing 
              (single-valued-classrel(es;X;A)  and 
              single-valued-bag(init  loc(e);B))



Date html generated: 2015_07_22-PM-00_12_46
Last ObjectModification: 2015_01_28-AM-11_39_42

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