Nuprl Lemma : es-is-interface-co-restrict

[Info,A:Type]. ∀[I:EClass(A)]. ∀[P:es:EO+(Info) ─→ E ─→ ℙ]. ∀[p:∀es:EO+(Info). ∀e:E.  Dec(P[es;e])]. ∀[es:EO+(Info)].
[e:E].
  uiff(↑e ∈b (I|¬p);(↑e ∈b I) ∧ P[es;e]))


Proof




Definitions occuring in Statement :  es-interface-co-restrict: (I|¬p) in-eclass: e ∈b X eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-E: E assert: b decidable: Dec(P) uiff: uiff(P;Q) uall: [x:A]. B[x] prop: so_apply: x[s1;s2] all: x:A. B[x] not: ¬A and: P ∧ Q function: x:A ─→ B[x] universe: Type
Lemmas :  all_wf es-E_wf event-ordering+_subtype decidable_wf bag_size_empty_lemma assert_witness false_wf assert_wf eq_int_wf bag-size_wf nat_wf not_wf equal_wf in-eclass_wf es-interface-subtype_rel2 event-ordering+_wf top_wf es-interface-co-restrict_wf eclass_wf

Latex:
\mforall{}[Info,A:Type].  \mforall{}[I:EClass(A)].  \mforall{}[P:es:EO+(Info)  {}\mrightarrow{}  E  {}\mrightarrow{}  \mBbbP{}].
\mforall{}[p:\mforall{}es:EO+(Info).  \mforall{}e:E.    Dec(P[es;e])].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].
    uiff(\muparrow{}e  \mmember{}\msubb{}  (I|\mneg{}p);(\muparrow{}e  \mmember{}\msubb{}  I)  \mwedge{}  (\mneg{}P[es;e]))



Date html generated: 2015_07_20-PM-03_29_24
Last ObjectModification: 2015_01_27-PM-10_17_46

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