Nuprl Lemma : loop-class-memory-single-val

[Info,B:Type]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(B ─→ B)]. ∀[es:EO+(Info)].
  (single-valued-classrel(es;loop-class-memory(X;init);B)) supposing 
     ((∀l:Id. single-valued-bag(init l;B)) and 
     single-valued-classrel(es;X;B ─→ B))


Proof




Definitions occuring in Statement :  loop-class-memory: loop-class-memory(X;init) single-valued-classrel: single-valued-classrel(es;X;T) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) Id: Id uimplies: supposing a uall: [x:A]. B[x] all: x:A. B[x] apply: a function: x:A ─→ B[x] universe: Type single-valued-bag: single-valued-bag(b;T) bag: bag(T)
Lemmas :  es-causl-swellfnd event-ordering+_subtype nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf classrel_wf loop-class-memory_wf es-E_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 loop-class-memory-classrel es-first_wf2 bool_cases subtype_base_sq bool_wf bool_subtype_base eqtt_to_assert eqff_to_assert assert_of_bnot member-eclass_wf es-pred_wf es-loc_wf es-pred-locl es-causl_weakening equal_wf decidable__lt not-equal-2 le-add-cancel-alt not-le-2 sq_stable__le add-mul-special zero-mul all_wf Id_wf single-valued-bag_wf single-valued-classrel_wf event-ordering+_wf eclass_wf bag_wf

Latex:
\mforall{}[Info,B:Type].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].  \mforall{}[X:EClass(B  {}\mrightarrow{}  B)].  \mforall{}[es:EO+(Info)].
    (single-valued-classrel(es;loop-class-memory(X;init);B))  supposing 
          ((\mforall{}l:Id.  single-valued-bag(init  l;B))  and 
          single-valued-classrel(es;X;B  {}\mrightarrow{}  B))



Date html generated: 2015_07_21-PM-02_36_42
Last ObjectModification: 2015_01_27-PM-09_43_58

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