Nuprl Lemma : simple-comb-1-concat-classrel

[Info,B,C:Type]. ∀[f:B ─→ bag(C)]. ∀[X:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
  uiff(v ∈ f@|X|(e);↓∃b:B. (v ↓∈ b ∧ b ∈ X(e)))


Proof




Definitions occuring in Statement :  simple-comb-1: F|X| classrel: v ∈ X(e) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-E: E uiff: uiff(P;Q) uall: [x:A]. B[x] exists: x:A. B[x] squash: T and: P ∧ Q apply: a function: x:A ─→ B[x] universe: Type concat-lifting-1: f@ bag-member: x ↓∈ bs bag: bag(T)
Lemmas :  simple-comb1-concat-classrel bag-member_wf classrel_wf simple-comb_wf false_wf le_wf select_wf cons_wf nil_wf sq_stable__le length_wf length_nil non_neg_length length_wf_nil length_cons length_wf_nat int_seg_wf es-interface-subtype_rel2 es-E_wf event-ordering+_subtype subtype_rel-equal select-cons-hd decidable__le not-le-2 less-iff-le condition-implies-le add-commutes minus-add minus-zero zero-add add_functionality_wrt_le add-associates le-add-cancel2 concat-lifting1_wf lelt_wf bag_wf squash_wf exists_wf event-ordering+_wf eclass_wf

Latex:
\mforall{}[Info,B,C:Type].  \mforall{}[f:B  {}\mrightarrow{}  bag(C)].  \mforall{}[X:EClass(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].  \mforall{}[v:C].
    uiff(v  \mmember{}  f@|X|(e);\mdownarrow{}\mexists{}b:B.  (v  \mdownarrow{}\mmember{}  f  b  \mwedge{}  b  \mmember{}  X(e)))



Date html generated: 2015_07_22-PM-00_10_55
Last ObjectModification: 2015_01_28-AM-11_41_25

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