{ 
[V:Type]
A:Id List. W:{a:Id| (a 
A)} List List. ws:{a:Id| (a A)} List.
x:ConsensusState. i:
.
((ws W)
x
((
x,y.CR(in ws)[x, y] )^*)
(a.<if deq-member(IdDeq;a;ws) then i else Inning(x;a) fi
, Estimate(x;a)
>)
supposing (aws.Inning(x;a) < i)) }
{ Proof }
Definitions occuring in Statement :
consensus-rel-mod: CR(in ws)[x, y] ,
cs-estimate: Estimate(s;a),
cs-inning: Inning(s;a),
consensus-state4: ConsensusState,
id-deq: IdDeq,
Id: Id,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: [x:A]. B[x],
infix_ap: x f y,
all: x:A. B[x],
implies: P Q,
less_than: a < b,
set: {x:A| B[x]} ,
lambda: x.A[x],
pair: <a, b>,
list: type List,
int: ,
universe: Type,
l_all: (xL.P[x]),
l_member: (x l),
rel_star: R^*,
deq-member: deq-member(eq;x;L)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
implies: P Q,
uimplies: b supposing a,
l_all: (xL.P[x]),
member: t T,
prop: 
,
ge: i 
j ,
le: A 
B,
not: 
A,
false: False,
consensus-state4: ConsensusState,
ifthenelse: if b then t else f fi ,
band: p 
q,
deq-member: deq-member(eq;x;L),
top: Top,
subtype: S 
T,
reduce: reduce(f;k;as),
bfalse: ff,
cs-inning: Inning(s;a),
cs-estimate: Estimate(s;a),
pi1: fst(t),
pi2: snd(t),
so_lambda: 
x.t[x],
l_member: (x l),
decidable: Dec(P),
cand: A c B,
and: P Q,
or: P 
Q,
exists: 
x:A. B[x],
infix_ap: x f y,
int_seg: {i..j
},
lelt: i j < k,
btrue: tt,
Id: Id,
nat: 
,
squash: 
T,
true: True,
rev_implies: P 
Q,
iff: P Q,
consensus-rel-mod: CR(in ws)[x, y] ,
so_apply: x[s],
bool: 
,
unit: Unit,
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
it: 
Lemmas :
l_member_wf,
Id_wf,
cs-inning_wf,
consensus-state4_wf,
nat_wf,
nat_properties,
ge_wf,
first0,
top_wf,
rel_star_weakening,
cs-estimate_wf,
consensus-rel-mod_wf,
fpf_wf,
pi1_wf_top,
rel_star_transitivity,
ifthenelse_wf,
band_wf,
deq-member_wf,
id-deq_wf,
firstn_wf,
length_wf1,
select_wf,
not_wf,
decidable__cand,
decidable__lt,
decidable__l_member,
decidable__equal_Id,
rel_star_wf,
eq_id_wf,
select_member,
le_wf,
bool_wf,
iff_weakening_uiff,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert-eq-id,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
subtype_base_sq,
atom2_subtype_base,
bor_wf,
iff_transitivity,
assert_of_band,
and_functionality_wrt_iff,
assert-deq-member,
assert_functionality_wrt_uiff,
bnot_thru_band,
assert_of_bor,
or_functionality_wrt_iff,
not_functionality_wrt_iff,
member_firstn,
squash_wf,
true_wf,
firstn_decomp,
deq-member-append,
eqof_wf,
bfalse_wf,
member_singleton,
bor_ff_simp,
l_member_set2,
int_subtype_base,
fpf-domain_wf,
subtype-fpf2,
subtype-top,
cs-precondition_wf,
fpf-join_wf,
fpf-single_wf,
int-deq_wf,
rel_rel_star,
decidable__equal_int,
length_wf_nat,
firstn_all
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List. \mforall{}ws:\{a:Id| (a \mmember{} A)\} List. \mforall{}x:ConsensusState. \mforall{}i:\mBbbZ{}.
((ws \mmember{} W)
{}\mRightarrow{} x
rel\_star(ConsensusState; \mlambda{}x,y.CR(in ws)[x, y] )
(\mlambda{}a.<if deq-member(IdDeq;a;ws) then i else Inning(x;a) fi , Estimate(x;a)>)
supposing (\mforall{}a\mmember{}ws.Inning(x;a) < i))
Date html generated:
2011_08_16-AM-10_07_01
Last ObjectModification:
2011_06_18-AM-09_01_27
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