Nuprl Lemma : es-fset-loc-iff
∀es:EO. ∀s:fset(E). ∀i:Id. (i ∈ locs(s) ⇐⇒ ∃e:E. ((loc(e) = i ∈ Id) ∧ e ∈ s))
Proof
Definitions occuring in Statement :
es-fset-loc: i ∈ locs(s),
es-eq: es-eq(es),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
fset-member: a ∈ s,
fset: fset(T),
Id: Id,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
es-fset-loc: i ∈ locs(s),
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
rev_implies: P ⇐ Q,
not: ¬A,
false: False,
so_lambda: λ2x.t[x],
so_apply: x[s],
or: P ∨ Q,
cons: [a / b],
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
exists: ∃x:A. B[x],
cand: A c∧ B,
bfalse: ff
Latex:
\mforall{}es:EO. \mforall{}s:fset(E). \mforall{}i:Id. (i \mmember{} locs(s) \mLeftarrow{}{}\mRightarrow{} \mexists{}e:E. ((loc(e) = i) \mwedge{} e \mmember{} s))
Date html generated:
2016_05_16-AM-10_14_24
Last ObjectModification:
2015_12_28-PM-09_25_23
Theory : new!event-ordering
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