Nuprl Lemma : new_23_sig_quorum_state_eq1
∀Cmd:ValueAllType. ∀notify,propose:Atom List. ∀f:new_23_sig_headers_type{i:l}(Cmd;notify;propose). ∀es:EO+(Message(f)).
∀e:E. ∀n,r:ℤ.
(new_23_sig_QuorumStateFun(Cmd;notify;propose;f;<n, r>;es;e)
= <rev(mapfilter(λe.(snd(fst(msgval(e))));
λe.new_23_sig_vote_with_ballot_first(Cmd;notify;propose;f;es;e;n;r);
[es-init(es;e);e)))
, rev(mapfilter(λe.(snd(msgval(e)));
λe.new_23_sig_vote_with_ballot_first(Cmd;notify;propose;f;es;e;n;r);
[es-init(es;e);e)))
>
∈ (Cmd List × (Id List)))
Proof
Definitions occuring in Statement :
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_QuorumStateFun: new_23_sig_QuorumStateFun(Cmd;notify;propose;f;x;es;e),
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
es-info-body: msgval(e),
Message: Message(f),
event-ordering+: EO+(Info),
es-init: es-init(es;e),
es-closed-open-interval: [e;e'),
es-E: E,
Id: Id,
mapfilter: mapfilter(f;P;L),
reverse: rev(as),
list: T List,
vatype: ValueAllType,
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
lambda: λx.A[x],
pair: <a, b>,
product: x:A × B[x],
int: ℤ,
atom: Atom,
equal: s = t ∈ T
Lemmas :
es-causl-swellfnd,
event-ordering+_subtype,
Message_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
es-E_wf,
int_seg_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
decidable__assert,
es-first_wf2,
list_wf,
Id_wf,
new_23_sig_quorum_state_fun_eq,
reverse_wf,
mapfilter_wf,
es-closed-open-interval_wf,
es-init_wf,
new_23_sig_vote_with_ballot_first_wf,
assert_wf,
new_23_sig_vote_with_ballot_first-assert-type,
es-info-body_wf,
iff_weakening_equal,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
es-init-identity,
squash_wf,
true_wf,
event_ordering_wf,
nil_wf,
es-closed-open-interval-nil,
bool_cases_sqequal,
mapfilter_nil_lemma,
reverse_nil_lemma,
sqequal-tt-to-assert,
sqequal-ff-to-assert,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
subtype_base_sq,
bool_subtype_base,
member-eclass_wf,
new_23_sig_vote'base_wf,
es-pred_wf,
new_23_sig_add_to_quorum_wf,
es-loc_wf,
classfun-res_wf,
base-headers-msg-val-single-val,
cons_wf_listp,
cons_wf,
listp_wf,
subtype_rel_weakening,
ext-eq_weakening,
new_23_sig_QuorumStateFun_wf,
es-init-locl,
set_wf,
map_cons_lemma,
map_nil_lemma,
es-pred-locl,
es-causl_weakening,
append_wf,
es-closed-open-interval-decomp-last,
mapfilter-append,
mapfilter-singleton,
member-implies-classrel,
new_23_sig_vote_with_ballot-if-classrel,
new_23_sig_vote_with_ballot-assert-type,
pair-eta,
length_wf,
name_wf,
new_23_sig_headers_wf,
l_all_iff,
l_member_wf,
new_23_sig_headers_fun_wf,
cons_member,
equal-wf-base,
list_subtype_base,
atom_subtype_base,
name_eq_wf,
assert-name_eq,
sq_stable__no_repeats,
assert-bnot,
product-deq_wf,
int-deq_wf,
deq_wf,
pi1_wf_top,
top_wf,
es-interface-subtype_rel2,
event-ordering+_wf,
subtype_rel_product,
subtype_top,
subtype_rel_wf,
bnot_wf,
deq-member_wf,
id-deq_wf,
pi2_wf,
not_wf,
assert_elim,
and_wf,
bfalse_wf,
btrue_neq_bfalse,
assert-product-deq,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
assert-deq-member,
reverse_append,
reverse_singleton,
list_ind_cons_lemma,
list_ind_nil_lemma,
classfun-res-member-base,
es-init-elim2,
member-reverse,
member-mapfilter,
new_23_sig_vote_with_ballot_wf,
bl-all_wf,
new_23_sig_vote_with_ballot_and_id_wf,
l_all_wf2,
l_all_fwd,
new_23_sig_vote_with_ballot_first-assert,
new_23_sig_vote_with_ballot-assert-classrel,
classrel_wf,
new_23_sig_vote_with_ballot_and_id-if-classrel,
assert_of_band,
assert-bl-all,
l_all_functionality,
classfun-res-base-classrel,
equal-wf-base-T,
int_subtype_base,
new_23_sig_vote_with_ballot_first-not2,
l_exists_iff,
new_23_sig_vote_with_ballot_and_id-assert-classrel,
base-noloc-classrel,
append-nil,
classrel-implies-member,
append_nil_sq
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}notify,propose:Atom List. \mforall{}f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose).
\mforall{}es:EO+(Message(f)). \mforall{}e:E. \mforall{}n,r:\mBbbZ{}.
(new\_23\_sig\_QuorumStateFun(Cmd;notify;propose;f;<n, r>es;e)
= <rev(mapfilter(\mlambda{}e.(snd(fst(msgval(e))));
\mlambda{}e.new\_23\_sig\_vote\_with\_ballot\_first(Cmd;notify;propose;f;es;e;n;r);
[es-init(es;e);e)))
, rev(mapfilter(\mlambda{}e.(snd(msgval(e)));
\mlambda{}e.new\_23\_sig\_vote\_with\_ballot\_first(Cmd;notify;propose;f;es;e;n;r);
[es-init(es;e);e)))
>)
Date html generated:
2015_07_23-PM-04_03_00
Last ObjectModification:
2015_02_04-PM-04_04_33
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