Nuprl Lemma : es-fset-at-property
∀es:EO. ∀i:Id. ∀s:fset(E).
((∀e:E. (e ∈ s ∧ (loc(e) = i ∈ Id) ⇐⇒ (e ∈ s@i))) ∧ no_repeats(E;s@i) ∧ sorted-by(λe,e'. e ≤loc e' ;s@i))
Proof
Definitions occuring in Statement :
es-fset-at: s@i,
es-le: e ≤loc e' ,
es-eq: es-eq(es),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
fset-member: a ∈ s,
fset: fset(T),
Id: Id,
sorted-by: sorted-by(R;L),
no_repeats: no_repeats(T;l),
l_member: (x ∈ l),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
lambda: λx.A[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
es-fset-at: s@i,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
pi1: fst(t)
Latex:
\mforall{}es:EO. \mforall{}i:Id. \mforall{}s:fset(E).
((\mforall{}e:E. (e \mmember{} s \mwedge{} (loc(e) = i) \mLeftarrow{}{}\mRightarrow{} (e \mmember{} s@i))) \mwedge{} no\_repeats(E;s@i) \mwedge{} sorted-by(\mlambda{}e,e'. e \mleq{}loc e' ;s@\000Ci))
Date html generated:
2016_05_16-AM-10_13_35
Last ObjectModification:
2015_12_28-PM-09_25_46
Theory : new!event-ordering
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