Nuprl Lemma : es-local-pred_wf
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[P:E ─→ 𝔹].
(last(P) ∈ e:E ─→ ((∃e':{E| ((e' <loc e) ∧ (↑(P e')) ∧ (∀e'':E. ((e' <loc e'') ⇒ (e'' <loc e) ⇒ (¬↑(P e'')))))})
∨ (¬(∃e':{E| ((e' <loc e) ∧ (↑(P e')))}))))
Proof
Definitions occuring in Statement :
es-local-pred: last(P),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
sq_exists: ∃x:{A| B[x]},
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
member: t ∈ T,
apply: f a,
function: x:A ─→ B[x],
universe: Type
Lemmas :
es-local-pred_wf2,
es-E_wf,
event-ordering+_subtype,
bool_wf,
event-ordering+_wf,
subtype_rel_dep_function,
es-locl_wf,
subtype_rel_self,
set_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[P:E {}\mrightarrow{} \mBbbB{}].
(last(P) \mmember{} e:E {}\mrightarrow{} ((\mexists{}e':\{E| ((e' <loc e)
\mwedge{} (\muparrow{}(P e'))
\mwedge{} (\mforall{}e'':E. ((e' <loc e'') {}\mRightarrow{} (e'' <loc e) {}\mRightarrow{} (\mneg{}\muparrow{}(P e'')))))\})
\mvee{} (\mneg{}(\mexists{}e':\{E| ((e' <loc e) \mwedge{} (\muparrow{}(P e')))\}))))
Date html generated:
2015_07_20-PM-03_57_20
Last ObjectModification:
2015_01_27-PM-09_54_53
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