Nuprl Lemma : es-interface-conditional-domain-iff

∀[Info:Type]. ∀es:EO+(Info). ∀[A:Type]. ∀X,Y:EClass(A). ∀e:E.  (↑e ∈b [X?Y] ⇐⇒ (↑e ∈b X) ∨ (↑e ∈b Y))


Proof




Definitions occuring in Statement :  cond-class: [X?Y],  in-eclass: e ∈b X,  eclass: EClass(A[eo; e]),  event-ordering+: EO+(Info),  es-E: E,  assert: ↑b,  uall: ∀[x:A]. B[x],  all: ∀x:A. B[x],  iff: P ⇐⇒ Q,  or: P ∨ Q,  universe: Type
Lemmas :  es-E_wf,  event-ordering+_subtype,  eclass_wf,  event-ordering+_wf,  assert_functionality_wrt_uiff,  in-eclass_wf,  cond-class_wf,  top_wf,  es-interface-subtype_rel2,  bor_wf,  es-interface-conditional-domain,  assert_wf,  iff_wf,  or_wf,  assert_of_bor
\mforall{}[Info:Type]
    \mforall{}es:EO+(Info).  \mforall{}[A:Type].  \mforall{}X,Y:EClass(A).  \mforall{}e:E.    (\muparrow{}e  \mmember{}\msubb{}  [X?Y]  \mLeftarrow{}{}\mRightarrow{}  (\muparrow{}e  \mmember{}\msubb{}  X)  \mvee{}  (\muparrow{}e  \mmember{}\msubb{}  Y))



Date html generated: 2015_07_17-PM-00_51_26
Last ObjectModification: 2015_01_27-PM-11_01_03

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