Nuprl Lemma : existse-before-iff
∀es:EO. ∀e':E.
∀[P:{e:E| loc(e) = loc(e') ∈ Id} ⟶ ℙ]. (∃e<e'.P[e] ⇐⇒ (¬↑first(e')) c∧ (P[pred(e')] ∨ ∃e<pred(e').P[e]))
Proof
Definitions occuring in Statement :
existse-before: ∃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,
uall: ∀[x:A]. B[x],
cand: A c∧ B,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
or: P ∨ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
cand: A c∧ B,
not: ¬A,
false: False,
existse-before: ∃e<e'.P[e],
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
es-E: E,
es-base-E: es-base-E(es),
uimplies: b supposing a,
guard: {T},
or: P ∨ Q,
label: ...$L... t,
subtype_rel: A ⊆r B,
es-locl: (e <loc e')
Latex:
\mforall{}es:EO. \mforall{}e':E.
\mforall{}[P:\{e:E| loc(e) = loc(e')\} {}\mrightarrow{} \mBbbP{}]
(\mexists{}e<e'.P[e] \mLeftarrow{}{}\mRightarrow{} (\mneg{}\muparrow{}first(e')) c\mwedge{} (P[pred(e')] \mvee{} \mexists{}e<pred(e').P[e]))
Date html generated:
2016_05_16-AM-09_41_17
Last ObjectModification:
2015_12_28-PM-09_42_57
Theory : new!event-ordering
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