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
Lemmas :
not_wf,
alle-lt_wf,
Id_wf,
es-loc_wf,
es-E_wf,
existse-before_wf,
alle-at_wf,
decidable_wf,
event_ordering_wf,
decidable__existse-before,
decidable__not,
equal_wf,
es-locl_wf
\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:
2015_07_17-AM-08_46_27
Last ObjectModification:
2015_01_27-PM-02_27_01
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