Nuprl Lemma : rsc4-agreement-property
[Cmd:ValueAllType]. [cmdeq:EqDecider(Cmd)]. [locs,clients:bag(Id)]. [coeff:{2...}]. [flrs:
]. [es:EO'].
((StandardAssumptions(rsc4_Main) es)
bag-no-repeats(Id;locs)
(bag-size(locs) = ((coeff * flrs) + flrs + 1))
any v1,v2 from rsc4_decided'base(Cmd) satisfy
((fst(v1)) = (fst(v2))) ((snd(v1)) = (snd(v2))))
Proof
Definitions occuring in Statement :
rsc4_stdma: StandardAssumptions(rsc4_Main),
rsc4_decided'base: rsc4_decided'base(Cmd),
Message: Message,
consistent-class: consistent-class,
event-ordering+: EO+(Info),
Id: Id,
int_upper: {i...},
nat: ,
uall: [x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
implies: P Q,
apply: f a,
product: x:A 
B[x],
multiply: n * m,
add: n + m,
natural_number: $n,
int: 
,
equal: s = t,
deq: EqDecider(T),
bag-no-repeats: bag-no-repeats(T;bs),
bag-size: bag-size(bs),
bag: bag(T),
vatype: ValueAllType
Definitions :
subtype: S 
T,
top: Top,
prop: 
,
all: x:A. B[x],
member: t 
T,
pi2: snd(t),
consistent-class: consistent-class,
implies: P Q,
vatype: ValueAllType,
uall: [x:A]. B[x],
so_lambda: 
x.t[x],
cand: A c
B,
exists: 
x:A. B[x],
and: P Q,
bag-size: bag-size(bs),
true: True,
squash: 
T,
bag-no-repeats: bag-no-repeats(T;bs),
guard: {T},
l_disjoint: l_disjoint(T;l1;l2),
l_exists: (xL. P[x]),
not: 
A,
false: False,
le: A 
B,
nat: ,
ge: i 
j ,
l_all: (xL.P[x]),
lelt: i j < k,
int_seg: {i..j
},
bag-append: as + bs,
bag-member: x bs,
Id: Id,
rev_implies: P 
Q,
iff: P Q,
bfalse: ff,
btrue: tt,
lt_int: i <z j,
bnot: 
b,
le_int: i z j,
ifthenelse: if b then t else f fi ,
ycomb: Y,
select: l[i],
name: Name,
es-header: es-header(es;e),
rsc4_headers_no_inputs: rsc4_headers_no_inputs(),
length: ||as||,
null: null(as),
assert: 
b,
uimplies: b supposing a,
sq_type: SQType(T),
pi1: fst(t),
int_upper: {i...},
or: P 
Q,
decidable: Dec(P),
so_apply: x[s],
uiff: uiff(P;Q),
sq_stable: SqStable(P),
sq_or: a b,
strongwellfounded: SWellFounded(R[x; y]),
possible-majority: possible-majority(T;eq;L;x),
deq: EqDecider(T),
rev_uimplies: rev_uimplies(P;Q),
l_member: (x l),
std-ma: StandardMessageAutomaton(X;hdrs),
message-constraint: message-constraint{i:l}(es;X;hdrs),
rsc4_stdma: StandardAssumptions(rsc4_Main),
msg-header: msg-header(m),
rsc4_retry'base: rsc4_retry'base(Cmd)
Lemmas :
valueall-type_wf,
deq_wf,
bag_wf,
int_upper_wf,
event-ordering+_wf,
Message_wf,
rsc4_stdma_wf,
bag-no-repeats_wf,
nat_wf,
Id_wf,
bag-size_wf,
event-ordering+_inc,
es-E_wf,
rsc4_decided'base_wf,
classrel_wf,
pi1_wf_top,
equal_wf,
rsc4-decided-property,
int_subtype_base,
subtype_base_sq,
decidable__equal_int,
decidable__equal_Id,
decidable__l_member,
l_member_wf,
decidable__l_exists_better-extract,
all_wf,
bag-member_wf,
bag_qinc,
append_wf,
bag-size-append,
no_repeats_wf,
no_repeats-append,
and_wf,
bag-member-list,
member_append,
bag-no-repeats-le-bag-size,
mul_bounds_1a,
rsc4-votes-consistent,
decidable__lt,
le_wf,
Id-valueall-type,
int-valueall-type,
product-valueall-type,
make-Msg_wf,
rsc4_main_wf,
rsc4-retry-property,
sq_stable__valueall-type,
rsc4-vote,
es-causl_wf,
es-causl-swellfnd,
less_than_wf,
ge_wf,
nat_properties,
count-all,
hd_wf,
poss-maj-property,
assert-deq,
select_wf,
lelt_wf,
id-deq_wf,
deq-member_wf,
filter-split-length,
bnot_wf,
filter_wf,
bag-append_wf,
no_repeats_filter,
member_filter,
assert-deq-member,
not_functionality_wrt_iff,
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
not_wf,
assert_wf,
bag-member-append,
member_filter_2,
atom2_subtype_base,
length_append,
true_wf,
squash_wf,
length_wf,
mul_preserves_le,
length-filter-le,
upto_wf,
int_seg_wf,
length-map,
filter-upto-length,
count-as-filter,
count_wf,
es-loc_wf,
exists_wf,
rsc4_headers_no_inputs_wf,
msg-header_wf,
name_wf,
select_member,
base-noloc-classrel-make-Msg,
hd_member,
false_wf
\mforall{}[Cmd:ValueAllType]. \mforall{}[cmdeq:EqDecider(Cmd)]. \mforall{}[locs,clients:bag(Id)]. \mforall{}[coeff:\{2...\}]. \mforall{}[flrs:\mBbbN{}].
\mforall{}[es:EO'].
((StandardAssumptions(rsc4\_Main) es)
{}\mRightarrow{} bag-no-repeats(Id;locs)
{}\mRightarrow{} (bag-size(locs) = ((coeff * flrs) + flrs + 1))
{}\mRightarrow{} any v1,v2 from rsc4\_decided'base(Cmd) satisfy
((fst(v1)) = (fst(v2))) {}\mRightarrow{} ((snd(v1)) = (snd(v2))))
Date html generated:
2012_02_20-PM-05_02_16
Last ObjectModification:
2012_02_02-PM-02_16_46
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