{ 
[V:Type]. [A:Id List]. [t:
]. [f:V List 
V].
[L1,L2:consensus-rcv(V;A) List]. [n1,n2:
]. [v1,v2:V].
(n1 < n2) supposing
(archive-condition(V;A;t;f;n2;v2;L2) and
L1 < L2 and
archive-condition(V;A;t;f;n1;v1;L1)) }
{ Proof }
Definitions occuring in Statement :
archive-condition: archive-condition(V;A;t;f;n;v;L),
consensus-rcv: consensus-rcv(V;A),
Id: Id,
nat_plus: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
less_than: a < b,
function: x:A B[x],
list: type List,
int: ,
universe: Type,
proper-iseg: L1 < L2
Definitions :
uall: [x:A]. B[x],
uimplies: b supposing a,
member: t 
T,
all: x:A. B[x],
top: Top,
subtype: S 
T,
prop: 
,
and: P 
Q,
le: A 
B,
not: 
A,
implies: P 
Q,
false: False,
or: P 
Q,
guard: {T},
squash: 
T,
true: True,
so_lambda: 
x.t[x],
votes-from-inning: votes-from-inning(i;L),
assert: 
b,
spreadn: spread3,
rcv-vote?: rcv-vote?(x),
bfalse: ff,
btrue: tt,
ifthenelse: if b then t else f fi ,
values-for-distinct: values-for-distinct(eq;L),
archive-condition: archive-condition(V;A;t;f;n;v;L),
exists: 
x:A. B[x],
iff: P 
Q,
null: null(as),
decidable: Dec(P),
rev_implies: P Q,
cs-rcv-vote: Vote[a;i;v],
rcvd-inning-gt: i <z inning(r),
band: p 
q,
rcvd-vote: rcvd-vote(x),
outr: outr(x),
nat_plus: ,
so_apply: x[s],
sq_type: SQType(T),
consensus-rcv: consensus-rcv(V;A),
rcvd-inning-eq: inning(r) =
i
Lemmas :
archive-condition_wf,
nat_plus_inc,
proper-iseg_wf,
consensus-rcv_wf,
nat_plus_wf,
Id_wf,
proper-iseg-append-one,
length_wf_nat,
top_wf,
nat_wf,
iseg_wf,
member_wf,
iseg_nil,
archive-condition-nil,
decidable__lt,
member_append,
cons_member,
l_member_wf,
iseg_member,
squash_wf,
true_wf,
member_filter,
rcvd-inning-gt_wf,
member_null,
filter_wf,
assert_wf,
not_wf,
iff_weakening_uiff,
lt_int_wf,
not_functionality_wrt_uiff,
assert_of_lt_int,
le_wf,
length_wf1,
values-for-distinct_wf,
id-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
strong-subtype-self,
votes-from-inning_wf,
consensus-rcv-crosses-threshold,
not_assert_elim,
null_wf3,
filter_wf_top,
subtype_base_sq,
bool_wf,
bool_subtype_base,
int_subtype_base,
iseg-mapfilter,
rcvd-inning-eq_wf,
rcvd-vote_wf,
remove-repeats_wf,
map_wf,
pi1_wf_top,
remove-repeats-l_contains,
iseg-l_contains,
iseg_map,
length-map
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[f:V List {}\mrightarrow{} V]. \mforall{}[L1,L2:consensus-rcv(V;A) List]. \mforall{}[n1,n2:\mBbbZ{}].
\mforall{}[v1,v2:V].
(n1 < n2) supposing
(archive-condition(V;A;t;f;n2;v2;L2) and
L1 < L2 and
archive-condition(V;A;t;f;n1;v1;L1))
Date html generated:
2011_08_16-AM-10_13_41
Last ObjectModification:
2011_06_18-AM-09_06_13
Home
Index