Nuprl Lemma : State-class-es-sv1

[Info,A,B:Type]. [es:EO+(Info)]. [f:A  B  B]. [X:EClass(A)]. [init:Id  bag(B)].
  (es-sv-class(es;State-class(init;f;X))) supposing ((l:Id. (bag-size(init l)  1)) and es-sv-class(es;X))


Proof not projected




Definitions occuring in Statement :  State-class: State-class(init;f;X) es-sv-class: es-sv-class(es;X) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) Id: Id uimplies: b supposing a uall: [x:A]. B[x] le: A  B all: x:A. B[x] apply: f a function: x:A  B[x] natural_number: $n universe: Type bag-size: bag-size(bs) bag: bag(T)
Definitions :  lifting-2: lifting-2(f) lifting2: lifting2(f;abag;bbag) lifting-gen-rev: lifting-gen-rev(n;f;bags) lifting-gen-list-rev: lifting-gen-list-rev(n;bags) eq_int: (i = j) top: Top all: x:A. B[x] le: A  B simple-comb-2: F|X, Y| ifthenelse: if b then t else f fi  select: l[i] nat: int_seg: {i..j} implies: P  Q not: A false: False length: ||as|| lelt: i  j < k and: P  Q ge: i  j  label: ...$L... t ycomb: Y guard: {T} le_int: i z j bnot: b lt_int: i <z j bfalse: ff btrue: tt subtype: S  T suptype: suptype(S; T) State-class: State-class(init;f;X) member: t  T so_lambda: x.t[x] so_lambda: x y.t[x; y] uimplies: b supposing a prop: decidable: Dec(P) or: P  Q sq_type: SQType(T) bool: unit: Unit uiff: uiff(P;Q) uall: [x:A]. B[x] so_apply: x[s] so_apply: x[s1;s2] it: eclass: EClass(A[eo; e])
Lemmas :  bag-size-one bag-combine-single-left bag-only_wf2 single-valued-bag-if-le1 bag-combine_wf single-bag_wf bag-size-zero bag-combine-empty-left and_wf Memory-class-es-sv subtype_rel_bag top_wf simple-comb-es-sv select_wf length_wf length_nil length_wf_nil length_cons non_neg_length length_wf_nat int_seg_wf decidable__equal_int subtype_base_sq int_subtype_base Memory-class_wf bag-null_wf lelt_wf bool_wf uiff_transitivity equal_wf assert_wf empty-bag_wf eqtt_to_assert assert-bag-null bnot_wf not_wf eqff_to_assert assert_of_bnot not_functionality_wrt_uiff lifting-2_wf bag-size_wf State-class_wf nat_wf es-E_wf event-ordering+_inc all_wf Id_wf le_wf es-sv-class_wf bag_wf eclass_wf event-ordering+_wf

\mforall{}[Info,A,B:Type].  \mforall{}[es:EO+(Info)].  \mforall{}[f:A  {}\mrightarrow{}  B  {}\mrightarrow{}  B].  \mforall{}[X:EClass(A)].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].
    (es-sv-class(es;State-class(init;f;X)))  supposing 
          ((\mforall{}l:Id.  (bag-size(init  l)  \mleq{}  1))  and 
          es-sv-class(es;X))


Date html generated: 2012_02_20-PM-03_04_37
Last ObjectModification: 2012_02_16-PM-03_55_46

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