Nuprl Lemma : es-fset-at-loc
∀es:EO. ∀i:Id. ∀s:fset(E).
∃L:E List. ((∀e:E. (e ∈ s ∧ (loc(e) = i ∈ Id) ⇐⇒ (e ∈ L))) ∧ no_repeats(E;L) ∧ sorted-by(λe,e'. e ≤loc e' ;L))
Proof
Definitions occuring in Statement :
es-le: e ≤loc e' ,
es-eq: es-eq(es),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
fset-member: a ∈ s,
fset: fset(T),
sorted-by: sorted-by(R;L),
no_repeats: no_repeats(T;l),
l_member: (x ∈ l),
list: T List,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
lambda: λx.A[x],
equal: s = t ∈ T
Lemmas :
fset-to-list,
es-loc_wf,
es-eq_wf,
subtype_rel-deq,
equal_wf,
set_wf,
es-le_wf,
decidable__es-le,
es-le-linorder,
sorted-by-exists2,
decidable__equal_set,
decidable__es-E-equal,
fset_wf,
es-E_wf,
Id_wf,
event_ordering_wf,
fset-filter_wf2,
eq_id_wf,
fset-subtype,
assert_wf,
subtype_rel_sets,
assert-eq-id,
subtype_rel_list,
fset-member_wf,
l_member_wf,
no_repeats-settype,
all_wf,
iff_wf,
no_repeats_wf,
sorted-by_wf,
member-fset-filter,
l_all_iff,
l_member-settype,
select_wf,
sq_stable__le
\mforall{}es:EO. \mforall{}i:Id. \mforall{}s:fset(E).
\mexists{}L:E List
((\mforall{}e:E. (e \mmember{} s \mwedge{} (loc(e) = i) \mLeftarrow{}{}\mRightarrow{} (e \mmember{} L))) \mwedge{} no\_repeats(E;L) \mwedge{} sorted-by(\mlambda{}e,e'. e \mleq{}loc e' ;L))
Date html generated:
2015_07_17-AM-09_00_26
Last ObjectModification:
2015_01_27-PM-01_04_38
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