Nuprl Lemma : es-first-at-exists2
∀es:EO. ∀i:Id.
∀[P:{e:E| loc(e) = i ∈ Id} ─→ ℙ]
((∀e:{e:E| loc(e) = i ∈ Id} . Dec(P[e]))
⇒ (∀e:E. (∃e'≤e.e' is first@ i s.t. e'.P[e']) supposing ((¬∀e'≤e.¬P[e']) and (loc(e) = i ∈ Id))))
Proof
Definitions occuring in Statement :
es-first-at: e is first@ i s.t. e.P[e],
alle-le: ∀e≤e'.P[e],
existse-le: ∃e≤e'.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],
not: ¬A,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
es-le-loc,
es-first-at-exists,
es-le_transitivity,
es-le_wf,
es-first-at_wf,
Id_wf,
es-loc_wf,
es-E_wf
\mforall{}es:EO. \mforall{}i:Id.
\mforall{}[P:\{e:E| loc(e) = i\} {}\mrightarrow{} \mBbbP{}]
((\mforall{}e:\{e:E| loc(e) = i\} . Dec(P[e]))
{}\mRightarrow{} (\mforall{}e:E. (\mexists{}e'\mleq{}e.e' is first@ i s.t. e'.P[e']) supposing ((\mneg{}\mforall{}e'\mleq{}e.\mneg{}P[e']) and (loc(e) = i))))
Date html generated:
2015_07_17-AM-08_50_07
Last ObjectModification:
2015_01_27-PM-02_26_12
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