Nuprl Lemma : es-maximal-event
∀es:EO
∀[P:E ⟶ ℙ]
((∀e:E. Dec(P[e]))
⇒ (∀e:E
((∃m:E. (m ≤loc e ∧ P[m] ∧ (∀e':E. ((m <loc e') ⇒ e' ≤loc e ⇒ (¬P[e'])))))
∨ (∀e':E. (e' ≤loc e ⇒ (¬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,
or: P ∨ Q,
and: P ∧ Q,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
or: P ∨ Q,
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
guard: {T},
decidable: Dec(P),
cand: A c∧ B,
not: ¬A,
false: False,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
btrue: tt,
es-le: e ≤loc e' ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}es:EO
\mforall{}[P:E {}\mrightarrow{} \mBbbP{}]
((\mforall{}e:E. Dec(P[e]))
{}\mRightarrow{} (\mforall{}e:E
((\mexists{}m:E. (m \mleq{}loc e \mwedge{} P[m] \mwedge{} (\mforall{}e':E. ((m <loc e') {}\mRightarrow{} e' \mleq{}loc e {}\mRightarrow{} (\mneg{}P[e'])))))
\mvee{} (\mforall{}e':E. (e' \mleq{}loc e {}\mRightarrow{} (\mneg{}P[e']))))))
Date html generated:
2016_05_16-AM-09_29_25
Last ObjectModification:
2015_12_28-PM-09_53_04
Theory : new!event-ordering
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