### Nuprl Lemma : es-first-before

`∀es:EO. ∀i:Id. ∀e':E.`
`  ∀[P:{e:E| loc(e) = i ∈ Id}  ─→ ℙ]`
`    (∀e@i.Dec(P[e]) `` ∃e<e'.e is first@ i s.t.  e.P[e] `⇐⇒` ∃e<e'.P[e] supposing loc(e') = i ∈ Id)`

Proof

Definitions occuring in Statement :  es-first-at: `e is first@ i s.t.  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)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s]` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` implies: `P `` Q` set: `{x:A| B[x]} ` function: `x:A ─→ B[x]` equal: `s = t ∈ T`
Lemmas :  existse-before_wf Id_wf es-loc_wf es-E_wf es-first-at_wf equal_wf alle-at_wf decidable_wf event_ordering_wf es-locl_wf all_wf es-locl-wellfnd es-locl-first assert_elim btrue_neq_bfalse assert_wf es-first_wf2 decidable__existse-before es-pred_wf es-loc-pred existse-before-iff es-pred-locl es-pred-loc-base iff_weakening_equal
\mforall{}es:EO.  \mforall{}i:Id.  \mforall{}e':E.
\mforall{}[P:\{e:E|  loc(e)  =  i\}    {}\mrightarrow{}  \mBbbP{}]
(\mforall{}e@i.Dec(P[e])  {}\mRightarrow{}  \mexists{}e<e'.e  is  first@  i  s.t.    e.P[e]  \mLeftarrow{}{}\mRightarrow{}  \mexists{}e<e'.P[e]  supposing  loc(e')  =  i)

Date html generated: 2015_07_17-AM-09_05_33
Last ObjectModification: 2015_02_04-PM-06_27_47

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