Nuprl Lemma : Threshold-Combinator-locally-programmable

S:{S:'| valueall-type(S)} 
  [A:']
    B:{B:'| valueall-type(B)} 
      [X:EClass'(A)]
        R:A  S  . init_state:Id  bag(S). accum:A  S  S. f:Id  A  S  bag(B).
          (NormalLProgrammable'(A;X)  NormalLProgrammable'(B;Threshold-Combinator(R;X;init_state;accum;f)))


Proof not projected




Definitions occuring in Statement :  Threshold-Combinator: Threshold-Combinator(R;X;init_state;accum;f) Message: Message normal-locally-programmable: NormalLProgrammable(A;X) eclass: EClass(A[eo; e]) Id: Id bool: uall: [x:A]. B[x] all: x:A. B[x] implies: P  Q set: {x:A| B[x]}  function: x:A  B[x] universe: Type bag: bag(T) valueall-type: valueall-type(T)
Definitions :  all: x:A. B[x] uall: [x:A]. B[x] eclass: EClass(A[eo; e]) implies: P  Q Threshold-Combinator: Threshold-Combinator(R;X;init_state;accum;f) let: let member: t  T or: P  Q squash: T and: P  Q concat-lifting-loc-2: f@Loc ifthenelse: if b then t else f fi  guard: {T} concat-lifting2-loc: concat-lifting2-loc(f;abag;bbag;loc) concat-lifting-loc: concat-lifting-loc(n;bags;loc;f) select: l[i] concat-lifting: concat-lifting(n;f;bags) concat-lifting-list: concat-lifting-list(n;bags) lifting-gen-list-rev: lifting-gen-list-rev(n;bags) ycomb: Y eq_int: (i = j) btrue: tt bfalse: ff le_int: i z j bnot: b lt_int: i <z j true: True prop: so_lambda: x.t[x] cand: A c B so_apply: x[s] subtype: S  T
Lemmas :  simple-loc-comb-2-nlp concat-lifting-loc-2_wf ifthenelse_wf bag_wf empty-bag_wf Id_wf primed-class-opt_wf Accum-class_wf normal-locally-programmable_wf Message_wf bool_wf event-ordering+_wf es-E_wf event-ordering+_inc valueall-type_wf squash_wf all_wf equal_wf Accum-class-locally-programmable primed-class-opt-nlp

\mforall{}S:\{S:\mBbbU{}'|  valueall-type(S)\} 
    \mforall{}[A:\mBbbU{}']
        \mforall{}B:\{B:\mBbbU{}'|  valueall-type(B)\} 
            \mforall{}[X:EClass'(A)]
                \mforall{}R:A  {}\mrightarrow{}  S  {}\mrightarrow{}  \mBbbB{}.  \mforall{}init$_{state}$:Id  {}\mrightarrow{}  bag(S).  \mforall{}accum:A  {}\mrightarrow{}  S  {}\mrightarrow{}  S.  \mforall{}f:Id  \000C{}\mrightarrow{}  A  {}\mrightarrow{}  S  {}\mrightarrow{}  bag(B).
                    (NormalLProgrammable'(A;X)
                    {}\mRightarrow{}  NormalLProgrammable'(B;Threshold-Combinator(R;X;init$_{state}$;accu\000Cm;f)))


Date html generated: 2012_01_23-PM-01_05_26
Last ObjectModification: 2011_12_30-PM-08_13_11

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