### Nuprl Lemma : alle-at-iff

`∀es:EO. ∀i:Id.`
`  ∀[P:{e:E| loc(e) = i ∈ Id}  ─→ ℙ]`
`    (∀e@i.P[e] `⇐⇒` ∀e@i.P[e] supposing ↑first(e) ∧ ∀e@i.P[pred(e)] `` P[e] supposing ¬↑first(e))`

Proof

Definitions occuring in Statement :  alle-at: `∀e@i.P[e]` es-first: `first(e)` es-pred: `pred(e)` es-loc: `loc(e)` es-E: `E` event_ordering: `EO` Id: `Id` assert: `↑b` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s]` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` not: `¬A` implies: `P `` Q` and: `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 isect_wf assert_wf es-first_wf2 not_wf es-pred-loc-base iff_weakening_equal es-pred_wf event_ordering_wf assert_witness equal_wf all_wf es-locl_wf es-locl-wellfnd decidable__assert es-pred-locl
\mforall{}es:EO.  \mforall{}i:Id.
\mforall{}[P:\{e:E|  loc(e)  =  i\}    {}\mrightarrow{}  \mBbbP{}]
(\mforall{}e@i.P[e]  \mLeftarrow{}{}\mRightarrow{}  \mforall{}e@i.P[e]  supposing  \muparrow{}first(e)  \mwedge{}  \mforall{}e@i.P[pred(e)]  {}\mRightarrow{}  P[e]  supposing  \mneg{}\muparrow{}first(e))

Date html generated: 2015_07_17-AM-08_45_29
Last ObjectModification: 2015_02_04-AM-07_10_02

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