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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