Nuprl Lemma : iterated-classrel-single-val

[Info,A,S:Type]. ∀[init:Id ─→ bag(S)]. ∀[f:A ─→ S ─→ S]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v1,v2:S].
  (v1 v2 ∈ S) supposing 
     (iterated-classrel(es;S;A;f;init;X;e;v2) and 
     iterated-classrel(es;S;A;f;init;X;e;v1) and 
     single-valued-bag(init loc(e);S) and 
     single-valued-classrel(es;X;A))


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 uimplies: supposing a uall: [x:A]. B[x] apply: a function: x:A ─→ B[x] universe: Type equal: t ∈ T single-valued-bag: single-valued-bag(b;T) bag: bag(T)
Lemmas :  es-causl-swellfnd nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf iterated-classrel_wf single-valued-bag_wf es-loc_wf single-valued-classrel_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 es-first_wf2 bool_cases subtype_base_sq bool_wf bool_subtype_base eqtt_to_assert and_wf equal_wf eqff_to_assert assert_of_bnot es-pred_wf es-pred-locl es-causl_weakening squash_wf true_wf bag_wf es-pred-loc-base iff_weakening_equal decidable__lt not-equal-2 le-add-cancel-alt not-le-2 sq_stable__le add-mul-special zero-mul event-ordering+_subtype es-E_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].
\mforall{}[v1,v2:S].
    (v1  =  v2)  supposing 
          (iterated-classrel(es;S;A;f;init;X;e;v2)  and 
          iterated-classrel(es;S;A;f;init;X;e;v1)  and 
          single-valued-bag(init  loc(e);S)  and 
          single-valued-classrel(es;X;A))



Date html generated: 2015_07_17-PM-00_26_30
Last ObjectModification: 2015_02_04-PM-05_35_10

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