Nuprl Lemma : defined-by-rec-comb-program

[Info:Type]. [B:{B:Type| valueall-type(B)} ]. [Ps:eclass-program{i:l}(Info) List].
  [F:k:||Ps||  bag(eclass-program-type(Ps[k]))  bag(B)  bag(B)]
    defined-class(rec-comb-program(F;B;Ps)) = F|k.defined-class(Ps[k]),(self)'| 
    supposing buf:bag(B). ((F (k.{}) buf) = {}) 
  supposing 0 < ||Ps||


Proof not projected




Definitions occuring in Statement :  rec-comb-program: rec-comb-program(F;B;Ps) defined-class: defined-class(prg) eclass-program-type: eclass-program-type(prg) eclass-program: eclass-program{i:l}(Info) rec-combined-class: f|X,(self)'| eclass: EClass(A[eo; e]) select: l[i] length: ||as|| int_seg: {i..j} uimplies: b supposing a uall: [x:A]. B[x] all: x:A. B[x] less_than: a < b set: {x:A| B[x]}  apply: f a lambda: x.A[x] function: x:A  B[x] list: type List natural_number: $n universe: Type equal: s = t empty-bag: {} bag: bag(T) valueall-type: valueall-type(T)
Definitions :  pi1: fst(t) fpf-dom: x  dom(f) fpf-cap: f(x)?z mk_fpf: mk_fpf(L;f) false: False not: A prop: le: A  B so_lambda: x.t[x] and: P  Q exists: x:A. B[x] implies: P  Q member: t  T rec-comb-program: rec-comb-program(F;B;Ps) defined-class: defined-class(prg) all: x:A. B[x] uimplies: b supposing a uall: [x:A]. B[x] so_lambda: x y.t[x; y] true: True squash: T ifthenelse: if b then t else f fi  btrue: tt bfalse: ff eclass-program-type: eclass-program-type(prg) rec-combined-class: f|X,(self)'| nat: ge: i  j  ycomb: Y eclass: EClass(A[eo; e]) dataflow-set-class: dataflow-set-class(x.P[x]) map: map(f;as) dataflow-history-val: dataflow-history-val(es;e;x.P[x]) es-le-before: loc(e) top: Top subtype: S  T length: ||as|| select: l[i] last: last(L) null: null(as) lt_int: i <z j assert: b le_int: i z j bnot: b data-stream: data-stream(P;L) append: as @ bs filter: filter(P;l) reduce: reduce(f;k;as) better-feedback-dataflow: better-feedback-dataflow(n;ds;F;s;x.P[x]) dataflow-out: dataflow-out(df;a) pi2: snd(t) guard: {T} rev_implies: P  Q iff: P  Q es-le: e loc e'  or: P  Q compose: f o g lelt: i  j < k so_apply: x[s] int_seg: {i..j} so_apply: x[s1;s2] bool: unit: Unit sq_stable: SqStable(P) eclass-program: eclass-program{i:l}(Info) decidable: Dec(P) strongwellfounded: SWellFounded(R[x; y]) es-locl: (e <loc e') uiff: uiff(P;Q) rev_uimplies: rev_uimplies(P;Q) sq_type: SQType(T) fpf-domain: fpf-domain(f) it: !hyp_hide: x
Lemmas :  less_than_wf length_wf int_seg_wf valueall-type_wf empty-bag_wf equal_wf bag_wf all_wf union-list2_wf top_wf Id_wf l_member_wf and_wf eclass-program_wf select_member select_wf member_map fpf_wf eclass-program-type_wf df-program-type_wf dataflow-program_wf fpf-trivial-subtype-top eclass-program-flows_wf fpf-domain_wf map_wf id-deq_wf member-union-list2 event-ordering+_wf event-ordering+_inc es-E_wf eclass_wf true_wf squash_wf deq-member_wf bool_wf iff_transitivity assert_wf iff_weakening_uiff eqtt_to_assert assert-deq-member bnot_wf not_wf eqff_to_assert assert_of_bnot not_functionality_wrt_iff fpf-ap_wf member-fpf-dom null-df-program_wf sq_stable__valueall-type dataflow_wf df-program-meaning_wf df-program-meaning_wf_null subtype_rel_self subtype_rel_bag sq_stable__subtype_rel subtype_rel_weakening ext-eq_weakening dataflow_subtype eclass-ext dataflow-set-class_wf ifthenelse_wf better-feedback-dataflow_wf length_wf_nat lt_int_wf bag-size_wf nat_wf constant-dataflow_wf rec-combined-class_wf es-loc_wf decidable__l_member decidable__equal_Id es-causl-swellfnd nat_properties ge_wf le_wf es-causl_wf primed-class-equal es-locl_wf prior-dataflow-set-class map_append_sq es-before_wf3 es-info_wf es-before_wf data-stream-append data-stream-cons last_append upto_wf eval-parallel-dataflow-property pi2_wf dataflow-ap_wf pi1_wf_top dataflow-out_wf false_wf iterate-dataflow_wf rec-dataflow_wf eval-parallel-dataflow_wf uiff_transitivity assert_of_lt_int data-stream_wf le_int_wf assert_functionality_wrt_uiff bnot_of_lt_int assert_of_le_int filter_wf last-cons null_wf3 assert_of_null not_functionality_wrt_uiff last_wf append_wf es-le-before_wf null-data-stream null-map es-le-before_wf2 es-le_wf es-le-before-not-null subtype_base_sq bool_subtype_base bfalse_wf length-data-stream length-map non_null_iff_length subtype_rel_list length_nil non_neg_length length_wf_nil length_cons length_append data-stream-null-df-program last-map primed-class-cases es-interface-top es-first_wf es-pred_wf es-pred-causl es-causle_weakening_locl es-causl_transitivity2 es-pred-locl es-locl_transitivity2 es-le_weakening es-le-loc es-loc-pred constant-data-stream length_upto map-map length-map-sq list_extensionality

\mforall{}[Info:Type].  \mforall{}[B:\{B:Type|  valueall-type(B)\}  ].  \mforall{}[Ps:eclass-program\{i:l\}(Info)  List].
    \mforall{}[F:k:\mBbbN{}||Ps||  {}\mrightarrow{}  bag(eclass-program-type(Ps[k]))  {}\mrightarrow{}  bag(B)  {}\mrightarrow{}  bag(B)]
        defined-class(rec-comb-program(F;B;Ps))  =  F|\mlambda{}k.defined-class(Ps[k]),(self)'| 
        supposing  \mforall{}buf:bag(B).  ((F  (\mlambda{}k.\{\})  buf)  =  \{\}) 
    supposing  0  <  ||Ps||


Date html generated: 2012_01_23-PM-12_33_44
Last ObjectModification: 2012_01_06-AM-11_11_15

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