Nuprl Lemma : bind-class-locally-programmable

[Info:{Info:Type| Info} ]
  A,B:{T:Type| valueall-type(T)} .
    [X:EClass(A)]. [Y:A  EClass(B)].
      (NormalLProgrammable(A;X)  (a:A. NormalLProgrammable(B;Y[a]))  NormalLProgrammable(B;X >a> Y[a]))


Proof not projected




Definitions occuring in Statement :  normal-locally-programmable: NormalLProgrammable(A;X),  bind-class: X >x> Y[x],  eclass: EClass(A[eo; e]),  uall: [x:A]. B[x],  so_apply: x[s],  all: x:A. B[x],  squash: T,  implies: P  Q,  set: {x:A| B[x]} ,  function: x:A  B[x],  universe: Type,  valueall-type: valueall-type(T)
Definitions :  so_lambda: x y.t[x; y],  true: True,  and: P  Q,  so_lambda: x.t[x],  prop: ,  member: t  T,  exists: x:A. B[x],  local-program-at: local-program-at{i:l}(Info;A;X;dfp;x),  sq_exists: x:{A| B[x]},  so_apply: x[s],  normal-locally-programmable: NormalLProgrammable(A;X),  implies: P  Q,  all: x:A. B[x],  squash: T,  uall: [x:A]. B[x],  ifthenelse: if b then t else f fi ,  bfalse: ff,  top: Top,  assert: b,  not: A,  subtype: S  T,  spreadn: spread4,  pi1: fst(t),  df-program-type: df-program-type(dfp),  bind-df-program: bind-df-program,  bind-class: X >x> Y[x],  rev_implies: P  Q,  iff: P  Q,  es-le-before: loc(e),  suptype: suptype(S; T),  false: False,  le: A  B,  let: let,  bind-dataflow-aux: bind-dataflow-aux(P;dfs;a.Q[a]),  pi2: snd(t),  guard: {T},  or: P  Q,  es-le: e loc e' ,  rev_subtype_rel: A r B,  rev_uimplies: rev_uimplies(P;Q),  nat: ,  ycomb: Y,  bag-map: bag-map(f;bs),  bag-combine: xbs.f[x],  map: map(f;as),  reduce: reduce(f;k;as),  concat: concat(ll),  bag-union: bag-union(bbs),  btrue: tt,  es-before: before(e),  compose: f o g,  lt_int: i <z j,  le_int: i z j,  select: l[i],  bnot: b,  length: ||as||,  null: null(as),  last: last(L),  so_apply: x[s1;s2],  sq_stable: SqStable(P),  uimplies: b supposing a,  sq_type: SQType(T),  dataflow-program: DataflowProgram(A),  lelt: i  j < k,  int_seg: {i..j},  uiff: uiff(P;Q),  unit: Unit,  bool: ,  eclass: EClass(A[eo; e]),  single-bag: {x},  bag-append: as + bs,  empty-bag: {},  it:
Lemmas :  squash_wf,  valueall-type_wf,  event-ordering+_wf,  eclass_wf,  normal-locally-programmable_wf,  bind-class_wf,  df-program-type_wf,  subtype_rel-equal,  sq_stable__valueall-type,  bind-df-program_wf,  equal_wf,  es-E_wf,  event-ordering+_inc,  es-loc_wf,  local-program-at_wf,  all_wf,  dataflow-program_wf,  Id_wf,  sq_exists_wf,  bfalse_wf,  false_wf,  bool_subtype_base,  bool_wf,  subtype_base_sq,  es-le-before-not-null,  es-le_wf,  es-le-before_wf2,  null-map,  top_wf,  null-data-stream,  es-le-before_wf,  es-info_wf,  map_wf,  bag_wf,  last_wf,  not_wf,  assert_wf,  null_wf3,  data-stream_wf,  true_wf,  dataflow_wf,  bind-df-program-meaning,  dataflow_subtype,  df-program-meaning_wf,  decidable__es-le,  sq_stable_from_decidable,  member-eo-forward-E,  eo-forward_wf,  es-le-loc,  bag-combine_wf,  subtype_rel_self,  list-subtype-bag,  eo-forward-loc,  bind-dataflow_wf,  eo-forward-info,  iterate-bind-dataflow,  eo-forward-E-subtype,  iterate-dataflow_wf,  dataflow-ap_wf,  pi2_wf,  es-before_wf,  select_wf,  firstn_wf,  nth_tl_wf,  bag_qinc,  upto_wf,  length_wf,  int_seg_wf,  bag-map_wf,  bag-map-append,  and_wf,  es-locl_wf,  es-le_weakening,  subtype_rel_dep_function,  bag-combine-append-left,  subtype_rel_sets,  subtype_rel_bag,  es-before_wf3,  ext-eq_weakening,  ext-eq_inversion,  subtype_rel_weakening,  subtype_rel_functionality_wrt_implies,  bag-append_wf,  length_wf_nat,  map_length,  non_neg_length,  map-as-map-upto,  map-id,  bag-combine-map,  decidable__es-locl,  firstn-before,  le_wf,  firstn_map,  select-map,  eo-forward-before,  nth_tl-es-before,  es-ble_wf,  filter_wf,  select_member,  member-es-before,  nth_tl_map,  length-map,  bag-combine-assoc,  assert_of_bnot,  eqff_to_assert,  bnot_wf,  uiff_transitivity,  eqtt_to_assert,  eo-forward-first-trivial,  btrue_wf,  bag-append-empty,  bag-map-map,  last_append,  not_functionality_wrt_uiff,  append_is_nil,  assert_of_null,  append_wf,  last-data-stream,  map_append_sq,  assert_of_lt_int,  bnot_of_le_int,  assert_functionality_wrt_uiff,  less_than_wf,  lt_int_wf,  firstn_all,  assert_of_le_int,  le_int_wf,  firstn-append,  length_append

\mforall{}[Info:\{Info:Type|  \mdownarrow{}Info\}  ]
    \mforall{}A,B:\{T:Type|  valueall-type(T)\}  .
        \mforall{}[X:EClass(A)].  \mforall{}[Y:A  {}\mrightarrow{}  EClass(B)].
            (NormalLProgrammable(A;X)
            {}\mRightarrow{}  (\mforall{}a:A.  NormalLProgrammable(B;Y[a]))
            {}\mRightarrow{}  NormalLProgrammable(B;X  >a>  Y[a]))


Date html generated: 2012_01_23-PM-12_32_18
Last ObjectModification: 2012_01_06-AM-10_23_01

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