Nuprl Lemma : new_23_sig_agreement
∀[Cmd:ValueAllType]. ∀[eq:EqDecider(Cmd)]. ∀[reps,clients:bag(Id)]. ∀[coeff:{2...}]. ∀[flrs:ℕ].
∀[propose,notify:Atom List]. ∀[slots:set-sig{i:l}(ℤ)]. ∀[f:new_23_sig_headers_type{i:l}(Cmd;notify;propose)].
∀[es:EO+(Message(f))].
(new_23_sig_message-constraint{i:l}(Cmd;clients;eq;coeff;flrs;notify;propose;reps;slots;f)
⇒ bag-no-repeats(Id;reps)
⇒ (#(reps) = ((coeff * flrs) + flrs + 1) ∈ ℤ)
⇒ any v1,v2 from new_23_sig_decided'base(Cmd;notify;propose;f) satisfy
((fst(v1)) = (fst(v2)) ∈ ℤ) ⇒ ((snd(v1)) = (snd(v2)) ∈ Cmd))
Proof
Definitions occuring in Statement :
new_23_sig_message-constraint: new_23_sig_message-constraint{i:l}(Cmd;clients;cmdeq;coeff;flrs;notify;propose;reps;slots;f),
new_23_sig_decided'base: new_23_sig_decided'base(Cmd;notify;propose;f),
new_23_sig_headers_type: new_23_sig_headers_type{i:l}(Cmd;notify;propose),
Message: Message(f),
consistent-class: consistent-class,
event-ordering+: EO+(Info),
Id: Id,
deq: EqDecider(T),
list: T List,
int_upper: {i...},
nat: ℕ,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
implies: P ⇒ Q,
product: x:A × B[x],
multiply: n * m,
add: n + m,
natural_number: $n,
int: ℤ,
atom: Atom,
equal: s = t ∈ T,
bag-no-repeats: bag-no-repeats(T;bs),
bag-size: #(bs),
bag: bag(T),
set-sig: set-sig{i:l}(Item)
Definitions :
assert: ↑b,
ifthenelse: if b then t else f fi ,
deq-member: x ∈b L),
reduce: reduce(f;k;as),
new_23_sig_headers_internal: new_23_sig_headers_internal(),
cons: [a / b],
bor: p ∨bq,
list-deq: list-deq(eq),
band: p ∧b q,
atom-deq: AtomDeq,
eq_atom: x =a y,
btrue: tt,
nil: [],
it: ⋅,
null: null(as),
true: True,
member: t ∈ T
Lemmas :
int_seg_wf,
length_wf,
name_wf,
new_23_sig_headers_wf,
l_all_iff,
l_member_wf,
equal_wf,
new_23_sig_headers_fun_wf,
cons_member,
cons_wf,
cons_wf_listp,
listp_wf,
nil_wf,
equal-wf-base,
list_subtype_base,
atom_subtype_base,
iff_weakening_equal,
name_eq_wf,
bool_wf,
eqtt_to_assert,
assert-name_eq,
sq_stable__no_repeats,
squash_wf,
true_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
int_subtype_base,
new_23_sig_decided_property,
classrel_wf,
new_23_sig_decided'base_wf,
es-E_wf,
event-ordering+_subtype,
bag-size_wf,
Id_wf,
nat_wf,
bag-no-repeats_wf,
new_23_sig_message-constraint_wf,
Message_wf,
subtype_rel_dep_function,
vatype_wf,
event-ordering+_wf,
new_23_sig_headers_type_wf,
set-sig_wf,
list_wf,
int_upper_wf,
bag_wf,
deq_wf,
valueall-type_wf,
decidable__equal_int,
decidable__l_exists_better-extract,
decidable__l_member,
decidable__equal_Id,
append_wf,
list-subtype-bag,
subtype_rel_self,
bag-member_wf,
all_wf,
bag-size-append,
no_repeats-append,
l_exists_iff,
no_repeats_wf,
bag-member-list,
member_append,
exists_wf,
msg-interface_wf,
new_23_sig_main_wf,
mk-msg-interface_wf,
make-Msg_wf,
subtype_rel_product,
subtype_rel_transitivity,
subtype_rel_weakening,
ext-eq_weakening,
sq_stable__bag-member,
bfalse_wf,
new_23_sig-vote,
bag-no-repeats-le-bag-size,
mul_bounds_1a,
subtract_wf,
new_23_sig_votes_consistent,
int_upper_subtype_nat,
false_wf,
le_wf,
decidable__lt,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
decidable__le,
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,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
es-causl-swellfnd,
non_neg_length,
length_wf_nat,
es-causl_wf,
zero-le-nat,
add-mul-special,
zero-mul,
not-equal-2,
le-add-cancel-alt,
lelt_wf,
not-le-2,
sq_stable__le,
base-noloc-classrel,
and_wf,
new_23_sig_retry_property,
poss-maj-property,
hd_wf,
count-all,
assert_wf,
safe-assert-deq,
select_wf,
filter-split-length,
deq-member_wf,
id-deq_wf,
bag-append_wf,
filter_wf5,
bnot_wf,
no_repeats_filter,
member_filter,
not_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
assert-deq-member,
bag-member-append,
member_filter_2,
length_append,
subtype_rel_list,
top_wf,
mul_preserves_le,
count-as-filter,
filter-upto-length,
length-map-sq,
filter_wf_top,
upto_wf,
length-filter-le,
new_23_sig_headers_internal_wf,
es-info-mk-msg,
event-ordering+_cumulative,
es-info-auth_wf,
es-info-body_wf,
es-info-type_wf,
make-msg-interface_wf,
pair-eta,
pi1_wf_top,
subtype_top,
mk-msg_wf,
list-cases,
length_of_nil_lemma,
null_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
null_cons_lemma,
le_antisymmetry_iff,
le-add-cancel2,
hd_member
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[eq:EqDecider(Cmd)]. \mforall{}[reps,clients:bag(Id)]. \mforall{}[coeff:\{2...\}]. \mforall{}[flrs:\mBbbN{}].
\mforall{}[propose,notify:Atom List]. \mforall{}[slots:set-sig\{i:l\}(\mBbbZ{})].
\mforall{}[f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose)]. \mforall{}[es:EO+(Message(f))].
(new\_23\_sig\_message-constraint\{i:l\}(Cmd;clients;eq;coeff;flrs;notify;propose;reps;slots;f)
{}\mRightarrow{} bag-no-repeats(Id;reps)
{}\mRightarrow{} (\#(reps) = ((coeff * flrs) + flrs + 1))
{}\mRightarrow{} any v1,v2 from new\_23\_sig\_decided'base(Cmd;notify;propose;f) satisfy
((fst(v1)) = (fst(v2))) {}\mRightarrow{} ((snd(v1)) = (snd(v2))))
Date html generated:
2015_07_23-PM-04_00_04
Last ObjectModification:
2015_02_04-PM-04_11_43
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