Nuprl Lemma : es-interface-val-restrict-sq

[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].
  (I|p)(e) I(e) supposing ↑e ∈b (I|p)


Proof




Definitions occuring in Statement :  es-interface-restrict: (I|p) eclass-val: X(e) in-eclass: e ∈b X eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-E: E assert: b decidable: Dec(P) uimplies: supposing a uall: [x:A]. B[x] prop: so_apply: x[s1;s2] all: x:A. B[x] function: x:A ─→ B[x] universe: Type sqequal: t
Lemmas :  all_wf es-E_wf event-ordering+_subtype decidable_wf assert_wf eq_int_wf bag-size_wf nat_wf bag_size_empty_lemma false_wf equal_wf in-eclass_wf es-interface-restrict_wf top_wf es-interface-subtype_rel2 event-ordering+_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].
    (I|p)(e)  \msim{}  I(e)  supposing  \muparrow{}e  \mmember{}\msubb{}  (I|p)



Date html generated: 2015_07_20-PM-03_29_52
Last ObjectModification: 2015_01_27-PM-10_18_32

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