Nuprl Lemma : alle-lt-iff
∀es:EO. ∀e':E.
∀[P:{e:E| loc(e) = loc(e') ∈ Id} ─→ ℙ]. (∀e<e'.P[e] ⇐⇒ P[pred(e')] ∧ ∀e<pred(e').P[e] supposing ¬↑first(e'))
Proof
Definitions occuring in Statement :
alle-lt: ∀e<e'.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,
and: P ∧ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
assert_wf,
es-first_wf2,
es-pred_wf,
es-pred-locl,
es-locl_transitivity2,
es-le_weakening,
es-locl_wf,
es-E_wf,
not_wf,
all_wf,
Id_wf,
es-loc_wf,
isect_wf,
es-pred-loc-base,
iff_weakening_equal,
es-loc-pred,
es-locl-iff,
equal_wf,
and_wf,
member_wf
\mforall{}es:EO. \mforall{}e':E.
\mforall{}[P:\{e:E| loc(e) = loc(e')\} {}\mrightarrow{} \mBbbP{}]
(\mforall{}e<e'.P[e] \mLeftarrow{}{}\mRightarrow{} P[pred(e')] \mwedge{} \mforall{}e<pred(e').P[e] supposing \mneg{}\muparrow{}first(e'))
Date html generated:
2015_07_17-AM-08_46_22
Last ObjectModification:
2015_02_04-PM-05_55_41
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