{ 
[V:Type]. [A:Id List]. [t:
]. [f:V List 
V]. [v0:V].
[L:consensus-rcv(V;A) List]. [v:V]. [i:
].
(fst(consensus-accum-num-state(t;f;v0;L)))
supposing archive-condition(V;A;t;f;i;v;L) }
{ Proof }
Definitions occuring in Statement :
consensus-accum-num-state: consensus-accum-num-state(t;f;v0;L),
archive-condition: archive-condition(V;A;t;f;n;v;L),
consensus-rcv: consensus-rcv(V;A),
Id: Id,
assert: b,
nat_plus: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
pi1: fst(t),
function: x:A B[x],
list: type List,
int: ,
universe: Type
Definitions :
top: Top,
strong-subtype: strong-subtype(A;B),
exists: 
x:A. B[x],
ge: i 
j ,
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
bool: 
,
l_member: (x 
l),
product: x:A 
B[x],
so_lambda: 
x.t[x],
consensus-accum-num-state: consensus-accum-num-state(t;f;v0;L),
pi1: fst(t),
true: True,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
assert: b,
natural_number: $n,
void: Void,
implies: P 
Q,
false: False,
not: 
A,
le: A 
B,
real: 
,
rationals: 
,
subtype: S T,
less_than: a < b,
nat: ,
prop: 
,
archive-condition: archive-condition(V;A;t;f;n;v;L),
uimplies: b supposing a,
int: ,
isect: 
x:A. B[x],
consensus-rcv: consensus-rcv(V;A),
set: {x:A| B[x]} ,
all: x:A. B[x],
function: x:A B[x],
uall: [x:A]. B[x],
nat_plus: ,
universe: Type,
member: t T,
Id: Id,
list: type List,
equal: s = t,
tactic: Error :tactic,
lambda: x.A[x],
guard: {T},
append: as @ bs,
cons: [car / cdr],
nil: [],
grp_car: |g|,
minus: -n,
or: P 
Q,
cs-rcv-vote: Vote[a;i;v],
let: let,
pi2: snd(t),
fpf-dom: x dom(f),
tl: tl(l),
hd: hd(l),
cs-initial-rcv: Init[v],
lt_int: i <z j,
le_int: i z j,
btrue: tt,
eq_atom: x =a y,
set_blt: a <
b,
grp_blt: a < b,
apply: f a,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$n(x;y),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_str: Error :eq_str,
eq_id: a = b,
eq_lnk: a = b,
bimplies: p q,
band: p q,
bor: p q,
eq_int: (i =
j),
bnot: b,
unit: Unit,
listp: A List,
combination: Combination(n;T),
int_nzero: 
,
limited-type: LimitedType,
sqequal: s ~ t,
so_lambda: x y.t[x; y],
values-for-distinct: values-for-distinct(eq;L),
null: null(as),
zip: zip(as;bs),
rcvd-inning-gt: i <z inning(r),
filter: filter(P;l),
map: map(f;as),
remove-repeats: remove-repeats(eq;L),
length: ||as||,
subtract: n - m,
votes-from-inning: votes-from-inning(i;L),
bfalse: ff,
pair: <a, b>,
multiply: n * m,
add: n + m,
consensus-accum-num: consensus-accum-num(num;f;s;r),
list_accum: list_accum(x,a.f[x; a];y;l),
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e],
union: left + right,
cand: A c B,
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
iff: P 
Q,
it: 
,
id-deq: IdDeq,
deq: EqDecider(T),
atom: Atom$n,
atom: Atom,
sq_type: SQType(T),
remove_repeats_nil: remove_repeats_nil{remove_repeats_nil_compseq_tag_def:o}(eq),
divides: b | a,
assoced: a ~ b,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
l_contains: A B,
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
l_exists: (xL. P[x]),
l_all: (xL.P[x]),
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
fset-member: a s,
f-subset: xs ys,
fset-closed: (s closed under fs),
l_disjoint: l_disjoint(T;l1;l2),
cs-not-completed: in state s, a has not completed inning i,
cs-archived: by state s, a archived v in inning i,
cs-passed: by state s, a passed inning i without archiving a value,
cs-inning-committed: in state s, inning i has committed v,
cs-inning-committable: in state s, inning i could commit v ,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
decidable: Dec(P),
rcv-vote?: rcv-vote?(x),
rcvd-inning-eq: inning(r) = i,
rcvd-vote: rcvd-vote(x),
spreadn: spread3,
mapfilter: mapfilter(f;P;L),
dstype: dstype(TypeNames; d; a),
fset: FSet{T},
string: Error :string,
IdLnk: IdLnk,
Knd: Knd,
MaName: MaName,
consensus-state3: consensus-state3(T)
Lemmas :
length-map,
append-nil,
rcvd-inning-eq_wf,
mapfilter-append,
decidable__equal_int,
int_subtype_base,
decidable__lt,
filter_wf_top,
assert_of_null,
atom2_subtype_base,
set_subtype_base,
product_subtype_base,
list_subtype_base,
subtype_base_sq,
votes-from-inning-is-nil,
pi2_wf,
subtype_rel_wf,
deq_wf,
id-deq_wf,
iff_wf,
strong-subtype-deq-subtype,
strong-subtype_wf,
strong-subtype-set3,
strong-subtype-self,
consensus-accum-num-property1,
append_wf,
consensus-accum-num-property2,
list_accum_append,
votes-from-inning_wf,
remove-repeats_wf,
length_wf1,
map_wf,
iff_weakening_uiff,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
not_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
eq_int_wf,
bnot_wf,
filter_wf,
rcvd-inning-gt_wf,
null_wf3,
values-for-distinct_wf,
zip_wf,
archive-condition-append-init,
length_wf_nat,
assert_of_lt_int,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
lt_int_wf,
nat_properties,
le_int_wf,
cs-rcv-vote_wf,
archive-condition-append-vote,
last_induction,
Id_wf,
l_member_wf,
member_wf,
bool_wf,
top_wf,
consensus-accum-num-state_wf,
pi1_wf_top,
true_wf,
pi1_wf,
ifthenelse_wf,
false_wf,
assert_wf,
assert_witness,
nat_plus_inc,
le_wf,
nat_plus_properties,
archive-condition_wf,
consensus-rcv_wf,
nat_plus_wf
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[f:V List {}\mrightarrow{} V]. \mforall{}[v0:V]. \mforall{}[L:consensus-rcv(V;A) List]. \mforall{}[v:V].
\mforall{}[i:\mBbbZ{}].
\muparrow{}(fst(consensus-accum-num-state(t;f;v0;L))) supposing archive-condition(V;A;t;f;i;v;L)
Date html generated:
2011_08_16-AM-10_14_36
Last ObjectModification:
2011_06_18-AM-09_06_33
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