Nuprl Lemma : alle-between1-not-first-since
∀[es:EO]. ∀[e1:E]. ∀[e2:{e:E| loc(e) = loc(e1) ∈ Id} ]. ∀[p:{e:E| loc(e) = loc(e1) ∈ Id} ─→ ℙ].
uiff(∀e∈[e1,e2).¬e = first e ≥ e1.p[e];∀e∈[e1,e2).¬p[e])
Proof
Definitions occuring in Statement :
es-first-since: e2 = first e ≥ e1.P[e],
alle-between1: ∀e∈[e1,e2).P[e],
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
not: ¬A,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
es-le_wf,
es-locl_wf,
not_wf,
es-le-loc,
Id_wf,
es-loc_wf,
es-E_wf,
all_wf,
es-locl-wellfnd,
es-locl_transitivity2,
es-le_weakening,
es-first-since_wf
\mforall{}[es:EO]. \mforall{}[e1:E]. \mforall{}[e2:\{e:E| loc(e) = loc(e1)\} ]. \mforall{}[p:\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}].
uiff(\mforall{}e\mmember{}[e1,e2).\mneg{}e = first e \mgeq{} e1.p[e];\mforall{}e\mmember{}[e1,e2).\mneg{}p[e])
Date html generated:
2015_07_17-AM-08_53_17
Last ObjectModification:
2015_01_27-PM-01_19_25
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