Nuprl Lemma : iterated-classrel_wf

[Info,A,S:Type]. ∀[init:Id ─→ bag(S)]. ∀[f:A ─→ S ─→ S]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:S].
  (iterated-classrel(es;S;A;f;init;X;e;v) ∈ ℙ)


Proof




Definitions occuring in Statement :  iterated-classrel: iterated-classrel(es;S;A;f;init;X;e;v) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-E: E Id: Id uall: [x:A]. B[x] prop: member: t ∈ T function: x:A ─→ B[x] universe: Type bag: bag(T)
Lemmas :  es-causl-swellfnd nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf int_seg_wf int_seg_subtype-nat decidable__le subtract_wf false_wf not-ge-2 less-iff-le condition-implies-le minus-one-mul zero-add minus-add minus-minus add-associates add-swap add-commutes add_functionality_wrt_le add-zero le-add-cancel decidable__equal_int subtype_rel-int_seg le_weakening int_seg_properties le_wf nat_wf zero-le-nat lelt_wf es-causl_wf exists_wf es-first_wf2 bool_wf eqtt_to_assert bag-member_wf es-loc_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot es-pred_wf es-pred-locl es-causl_weakening or_wf classrel_wf all_wf not_wf decidable__lt not-equal-2 le-add-cancel-alt not-le-2 sq_stable__le add-mul-special zero-mul es-E_wf event-ordering+_subtype event-ordering+_wf eclass_wf Id_wf bag_wf
\mforall{}[Info,A,S:Type].  \mforall{}[init:Id  {}\mrightarrow{}  bag(S)].  \mforall{}[f:A  {}\mrightarrow{}  S  {}\mrightarrow{}  S].  \mforall{}[X:EClass(A)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].
\mforall{}[v:S].
    (iterated-classrel(es;S;A;f;init;X;e;v)  \mmember{}  \mBbbP{})



Date html generated: 2015_07_17-PM-00_26_03
Last ObjectModification: 2015_01_27-PM-11_35_27

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