Nuprl Lemma : filter-vote-with-ballot-lemma
∀Cmd:{T:Type| valueall-type(T)} . ∀propose,notify:Atom List. ∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose).
∀es:EO+(Message(f)). ∀e:E. ∀n:ℤ. ∀e':E.
(filter(λa.new_23_sig_vote_with_ballot_first_alt(Cmd;notify;propose;f;es;e;e';n;0;a);[e, e'])
~ filter(λe'.new_23_sig_vote_with_ballot_first(Cmd;notify;propose;f;es.e;e';n;0);[e, e']))
Proof
Definitions occuring in Statement :
new_23_sig_vote_with_ballot_first_alt: new_23_sig_vote_with_ballot_first_alt(Cmd;notify;propose;f;es;e;e';n;r;a),
new_23_sig_vote_with_ballot_first: new_23_sig_vote_with_ballot_first(Cmd;notify;propose;f;es;e;n;r),
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
Message: Message(f),
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-interval: [e, e'],
es-E: E,
filter: filter(P;l),
list: T List,
valueall-type: valueall-type(T),
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
lambda: λx.A[x],
natural_number: $n,
int: ℤ,
atom: Atom,
universe: Type,
sqequal: s ~ t
Lemmas :
es-E_wf,
event-ordering+_subtype,
Message_wf,
subtype_rel_dep_function,
name_wf,
vatype_wf,
event-ordering+_wf,
new_23_sig_headers_type_wf,
list_wf,
valueall-type_wf,
filter-sq,
es-interval_wf,
l_member_wf,
new_23_sig_vote_with_ballot_first_alt_wf,
new_23_sig_vote_with_ballot_first_wf,
eo-forward_wf,
member-eo-forward-E,
member-es-interval,
equal_wf,
Id_wf,
es-loc_wf,
new_23_sig_vote_with_ballot_first-forward,
sq_stable_from_decidable,
es-le_wf,
decidable__es-le,
new_23_sig_vote_with_ballot_wf,
bool_wf,
eqtt_to_assert,
subtype_base_sq,
bool_subtype_base,
new_23_sig_vote_with_ballot-assert-type,
eqff_to_assert,
bool_cases_sqequal,
assert_wf,
set_wf,
assert-bl-all,
es-closed-open-interval_wf,
bnot_wf,
new_23_sig_vote_with_ballot_and_id_wf,
es-info-body_wf,
l_all_iff,
assert_of_bnot,
bl-exists_wf,
es-blocl_wf,
id-deq_wf,
deq_wf,
assert-bl-exists,
l_exists_iff,
new_23_sig_vote_with_ballot_and_id-snd,
member-es-closed-open-interval,
es-locl_transitivity2,
es-le_weakening,
eq_id_wf,
new_23_sig_vote_with_ballot_and_id-implies,
es-blocl-iff,
iff_transitivity,
iff_weakening_uiff,
assert_of_band,
assert-eq-id,
l_exists_wf,
not_wf,
bl-all_wf,
l_all_wf2,
l_all_functionality,
atom2_subtype_base,
member-eclass_wf,
new_23_sig_vote'base_wf,
equal-wf-base,
int_subtype_base,
eq_int_wf,
assert_of_eq_int,
member_wf
Latex:
\mforall{}Cmd:\{T:Type| valueall-type(T)\} . \mforall{}propose,notify:Atom List.
\mforall{}f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose). \mforall{}es:EO+(Message(f)). \mforall{}e:E. \mforall{}n:\mBbbZ{}. \mforall{}e':E.
(filter(\mlambda{}a.new\_23\_sig\_vote\_with\_ballot\_first\_alt(Cmd;notify;propose;f;es;e;e';n;0;a);[e, e'])
\msim{} filter(\mlambda{}e'.new\_23\_sig\_vote\_with\_ballot\_first(Cmd;notify;propose;f;es.e;e';n;0);[e, e']))
Date html generated:
2015_07_23-PM-04_03_22
Last ObjectModification:
2015_01_29-AM-08_49_03
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