### Nuprl Lemma : decidable__existse-between1

`∀es:EO. ∀e1,e2:E.`
`  ∀[P:{e:E| loc(e) = loc(e1) ∈ Id}  ─→ ℙ]. ∀e@loc(e1).Dec(P[e]) `` Dec(∃e∈[e1,e2).P[e]) supposing loc(e2) = loc(e1) ∈ Id`

Proof

Definitions occuring in Statement :  existse-between1: `∃e∈[e1,e2).P[e]` alle-at: `∀e@i.P[e]` es-loc: `loc(e)` es-E: `E` event_ordering: `EO` Id: `Id` decidable: `Dec(P)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s]` all: `∀x:A. B[x]` implies: `P `` Q` set: `{x:A| B[x]} ` function: `x:A ─→ B[x]` equal: `s = t ∈ T`
Lemmas :  alle-at_wf Id_wf es-loc_wf es-E_wf decidable_wf equal_wf event_ordering_wf decidable__existse-before es-le_wf decidable__and decidable__es-le es-locl_wf es-le-loc not_wf exists_wf
\mforall{}es:EO.  \mforall{}e1,e2:E.
\mforall{}[P:\{e:E|  loc(e)  =  loc(e1)\}    {}\mrightarrow{}  \mBbbP{}]
\mforall{}e@loc(e1).Dec(P[e])  {}\mRightarrow{}  Dec(\mexists{}e\mmember{}[e1,e2).P[e])  supposing  loc(e2)  =  loc(e1)

Date html generated: 2015_07_17-AM-08_47_33
Last ObjectModification: 2015_01_27-PM-02_28_06

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