Nuprl Lemma : alle-at-not-first
∀es:EO. ∀i:Id. ∀[P:{e:E| loc(e) = i ∈ Id} ─→ ℙ]. (∀e@i.P[e] ⇒ ∀e@i.P[pred(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],
not: ¬A,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
assert_wf,
es-first_wf2,
not_wf,
equal_wf,
es-loc_wf,
alle-at_wf,
Id_wf,
es-E_wf,
event_ordering_wf,
es-pred_wf,
es-pred-loc-base,
iff_weakening_equal
\mforall{}es:EO. \mforall{}i:Id. \mforall{}[P:\{e:E| loc(e) = i\} {}\mrightarrow{} \mBbbP{}]. (\mforall{}e@i.P[e] {}\mRightarrow{} \mforall{}e@i.P[pred(e)] supposing \mneg{}\muparrow{}first(e))
Date html generated:
2015_07_17-AM-08_45_32
Last ObjectModification:
2015_02_04-PM-05_55_49
Home
Index