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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