### 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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