Nuprl Lemma : es-is-prior-interface
∀[Info:Type]. ∀es:EO+(Info). ∀X:EClass(Top). ∀e:E. (↑e ∈b prior(X) ⇐⇒ ∃e':E. ((e' <loc e) ∧ (↑e' ∈b X)))
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
universe: Type
Lemmas :
is-prior-interface,
assert_wf,
in-eclass_wf,
es-prior-interface_wf0,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_top,
es-E-interface-property,
assert_witness,
exists_wf,
es-locl_wf,
eclass_wf
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} prior(X) \mLeftarrow{}{}\mRightarrow{} \mexists{}e':E. ((e' <loc e) \mwedge{} (\muparrow{}e' \mmember{}\msubb{} X)))
Date html generated:
2015_07_21-PM-02_44_43
Last ObjectModification:
2015_01_27-PM-09_42_07
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