Nuprl Lemma : not-alle-lt
∀es:EO. ∀e':E. ∀[P:{e:E| loc(e) = loc(e') ∈ Id} ⟶ ℙ]. (∀e@loc(e').Dec(P[e]) ⇒ (¬∀e<e'.P[e] ⇐⇒ ∃e<e'.¬P[e]))
Proof
Definitions occuring in Statement :
alle-lt: ∀e<e'.P[e],
existse-before: ∃e<e'.P[e],
alle-at: ∀e@i.P[e],
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
implies: 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,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
not: ¬A,
false: False,
alle-at: ∀e@i.P[e],
decidable: Dec(P),
or: P ∨ Q,
alle-lt: ∀e<e'.P[e],
es-locl: (e <loc e'),
existse-before: ∃e<e'.P[e],
exists: ∃x:A. B[x],
cand: A c∧ B
Latex:
\mforall{}es:EO. \mforall{}e':E.
\mforall{}[P:\{e:E| loc(e) = loc(e')\} {}\mrightarrow{} \mBbbP{}]. (\mforall{}e@loc(e').Dec(P[e]) {}\mRightarrow{} (\mneg{}\mforall{}e<e'.P[e] \mLeftarrow{}{}\mRightarrow{} \mexists{}e<e'.\mneg{}P[e]))
Date html generated:
2016_05_16-AM-09_42_24
Last ObjectModification:
2015_12_28-PM-09_42_03
Theory : new!event-ordering
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