Nuprl Lemma : loop-class-memory-exists

[Info,B:Type]. ∀[X:EClass(B ─→ B)]. ∀[init:Id ─→ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E].
  uiff(0 < #(init loc(e));↓∃v:B. v ∈ loop-class-memory(X;init)(e))


Proof




Definitions occuring in Statement :  loop-class-memory: loop-class-memory(X;init) classrel: v ∈ X(e) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-loc: loc(e) es-E: E Id: Id less_than: a < b uiff: uiff(P;Q) uall: [x:A]. B[x] exists: x:A. B[x] squash: T apply: a function: x:A ─→ B[x] natural_number: $n universe: Type bag-size: #(bs) bag: bag(T)
Lemmas :  es-causl-swellfnd nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf bag-size_wf es-loc_wf member-less_than squash_wf exists_wf classrel_wf loop-class-memory_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 equal_wf 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 Id_wf bag_wf eclass_wf decidable__assert es-first_wf2 es-p-local-pred_wf es-locl_wf btrue_neq_bfalse assert_elim es-locl-first eclass3_wf primed-class-opt-classrel bag-member-iff-size iff_weakening_equal es-loc-pred true_wf member-eclass_wf es-causl_weakening es-pred-locl es-pred_wf bag-member_wf not_wf all_wf eclass3-classrel assert-member-eclass es-causl_irreflexivity es-causle_weakening es-causl_transitivity2 es-locl_irreflexivity es-le_weakening_eq es-locl_transitivity2 es-pred_property es-le_weakening es-pred-loc-base and_wf

Latex:
\mforall{}[Info,B:Type].  \mforall{}[X:EClass(B  {}\mrightarrow{}  B)].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].
    uiff(0  <  \#(init  loc(e));\mdownarrow{}\mexists{}v:B.  v  \mmember{}  loop-class-memory(X;init)(e))



Date html generated: 2015_07_21-PM-02_34_40
Last ObjectModification: 2015_07_16-AM-09_42_36

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