Nuprl Lemma : last-event
∀es:EO. ∀e:E.
∀[P:{a:E| loc(a) = loc(e) ∈ Id} ⟶ ℙ]
((∀a:{a:E| loc(a) = loc(e) ∈ Id} . Dec(P[a]))
⇒ (∀e'≤e.¬P[e'] ∨ (∃e':E. (e' ≤loc e c∧ (P[e'] ∧ (∀e'':E. ((e' <loc e'') ⇒ e'' ≤loc e ⇒ (¬P[e'']))))))))
Proof
Definitions occuring in Statement :
alle-le: ∀e≤e'.P[e],
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
cand: A c∧ B,
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,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
existse-le: ∃e≤e'.P[e],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
alle-at: ∀e@i.P[e],
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
cand: A c∧ B,
and: P ∧ Q,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
es-locl: (e <loc e'),
alle-le: ∀e≤e'.P[e],
not: ¬A,
false: False,
exists: ∃x:A. B[x]
Latex:
\mforall{}es:EO. \mforall{}e:E.
\mforall{}[P:\{a:E| loc(a) = loc(e)\} {}\mrightarrow{} \mBbbP{}]
((\mforall{}a:\{a:E| loc(a) = loc(e)\} . Dec(P[a]))
{}\mRightarrow{} (\mforall{}e'\mleq{}e.\mneg{}P[e']
\mvee{} (\mexists{}e':E. (e' \mleq{}loc e c\mwedge{} (P[e'] \mwedge{} (\mforall{}e'':E. ((e' <loc e'') {}\mRightarrow{} e'' \mleq{}loc e {}\mRightarrow{} (\mneg{}P[e'']))))))))
Date html generated:
2016_05_16-AM-09_50_16
Last ObjectModification:
2015_12_28-PM-09_36_40
Theory : new!event-ordering
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