Nuprl Lemma : iterated-classrel-exists-iff

[Info,A,S:Type]. ∀[init:Id ─→ bag(S)].
  ∀f:A ─→ S ─→ S. ∀X:EClass(A). ∀es:EO+(Info). ∀e:E.
    (single-valued-classrel(es;X;A)  (∃s:S. s ↓∈ init loc(e) ⇐⇒ ∃v:S. iterated-classrel(es;S;A;f;init;X;e;v)))


Proof




Definitions occuring in Statement :  iterated-classrel: iterated-classrel(es;S;A;f;init;X;e;v) single-valued-classrel: single-valued-classrel(es;X;T) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-loc: loc(e) es-E: E Id: Id uall: [x:A]. B[x] all: x:A. B[x] exists: x:A. B[x] iff: ⇐⇒ Q implies:  Q apply: a function: x:A ─→ B[x] universe: Type bag-member: x ↓∈ bs bag: bag(T)
Lemmas :  iterated-classrel-exists exists_wf bag-member_wf es-loc_wf event-ordering+_subtype es-causl-swellfnd less_than_transitivity1 less_than_irreflexivity int_seg_wf decidable__equal_int subtype_rel-int_seg false_wf le_weakening subtract_wf int_seg_properties le_wf nat_wf zero-le-nat lelt_wf es-causl_wf es-first_wf2 bool_cases subtype_base_sq bool_wf bool_subtype_base eqtt_to_assert eqff_to_assert assert_of_bnot es-pred_wf es-pred-locl es-causl_weakening iterated-classrel_wf squash_wf true_wf bag_wf es-pred-loc-base es-E_wf iff_weakening_equal equal_wf all_wf int_seg_subtype-nat decidable__lt not-equal-2 condition-implies-le minus-add minus-minus minus-one-mul add-swap add-commutes add-associates add_functionality_wrt_le zero-add le-add-cancel-alt less-iff-le le-add-cancel set_wf less_than_wf primrec-wf2 decidable__le not-le-2 sq_stable__le add-zero add-mul-special zero-mul single-valued-classrel_wf event-ordering+_wf eclass_wf Id_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.
        (single-valued-classrel(es;X;A)
        {}\mRightarrow{}  (\mexists{}s:S.  s  \mdownarrow{}\mmember{}  init  loc(e)  \mLeftarrow{}{}\mRightarrow{}  \mexists{}v:S.  iterated-classrel(es;S;A;f;init;X;e;v)))



Date html generated: 2015_07_17-PM-00_26_46
Last ObjectModification: 2015_02_04-PM-05_34_44

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