Nuprl Lemma : es-minimal-event
∀es:EO
∀[P:E ─→ ℙ]. ((∀e:E. Dec(P[e])) ⇒ (∀e:E. (P[e] ⇒ (∃m:E. (m ≤loc e ∧ P[m] ∧ (∀e':E. ((e' <loc m) ⇒ (¬P[e']))))))))
Proof
Definitions occuring in Statement :
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
event_ordering: EO,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x]
Lemmas :
exists_wf,
es-E_wf,
es-le_wf,
all_wf,
es-locl_wf,
not_wf,
es-causl_wf,
decidable_wf,
event_ordering_wf,
decidable__existse-before,
subtype_rel_dep_function,
Id_wf,
es-loc_wf,
subtype_rel_self,
set_wf,
equal_wf,
es-causl_weakening,
es-locl_transitivity1,
es-le_weakening,
es-le-self
\mforall{}es:EO
\mforall{}[P:E {}\mrightarrow{} \mBbbP{}]
((\mforall{}e:E. Dec(P[e]))
{}\mRightarrow{} (\mforall{}e:E. (P[e] {}\mRightarrow{} (\mexists{}m:E. (m \mleq{}loc e \mwedge{} P[m] \mwedge{} (\mforall{}e':E. ((e' <loc m) {}\mRightarrow{} (\mneg{}P[e']))))))))
Date html generated:
2015_07_17-AM-08_46_03
Last ObjectModification:
2015_01_27-PM-02_28_30
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