Nuprl Lemma : es-cut-exists

[Info:Type]
  ∀es:EO+(Info). ∀X:EClass(Top). ∀f:sys-antecedent(es;X). ∀s:fset(E(X)).
    ∃c:Cut(X;f). (s ⊆ c ∧ (∀[c':Cut(X;f)]. c ⊆ c' supposing s ⊆ c'))


Proof




Definitions occuring in Statement :  es-cut: Cut(X;f) sys-antecedent: sys-antecedent(es;Sys) es-E-interface: E(X) eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-eq: es-eq(es) f-subset: xs ⊆ ys fset: fset(T) uimplies: supposing a uall: [x:A]. B[x] top: Top all: x:A. B[x] exists: x:A. B[x] and: P ∧ Q universe: Type
Lemmas :  sys-antecedent-closure cons_wf es-interface-pred_wf nil_wf fset-closed_wf es-eq_wf-interface es-interface-pred_wf2 fset-member_witness fset-member_wf f-subset_wf es-cut_wf uall_wf isect_wf fset_wf es-E-interface_wf sys-antecedent_wf eclass_wf top_wf es-E_wf event-ordering+_subtype event-ordering+_wf sq_stable_from_decidable decidable__fset-closed

Latex:
\mforall{}[Info:Type]
    \mforall{}es:EO+(Info).  \mforall{}X:EClass(Top).  \mforall{}f:sys-antecedent(es;X).  \mforall{}s:fset(E(X)).
        \mexists{}c:Cut(X;f).  (s  \msubseteq{}  c  \mwedge{}  (\mforall{}[c':Cut(X;f)].  c  \msubseteq{}  c'  supposing  s  \msubseteq{}  c'))



Date html generated: 2015_07_21-PM-03_55_14
Last ObjectModification: 2015_01_27-PM-05_56_53

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