Nuprl Lemma : rsc4-validity-property
[Cmd:ValueAllType]. [cmdeq:EqDecider(Cmd)]. [locs,clients:bag(Id)]. [coeff:{2...}]. [flrs:
]. [es:EO'].
((StandardAssumptions(rsc4_Main) es)
for every d in rsc4_decided'base(Cmd) there is an
earlier p in rsc4_propose'base(Cmd) such that
d = p)
Proof
Definitions occuring in Statement :
rsc4_stdma: StandardAssumptions(rsc4_Main),
rsc4_propose'base: rsc4_propose'base(Cmd),
rsc4_decided'base: rsc4_decided'base(Cmd),
Message: Message,
causal-class-relation: causal-class-relation,
event-ordering+: EO+(Info),
Id: Id,
int_upper: {i...},
nat: ,
uall: [x:A]. B[x],
implies: P Q,
apply: f a,
product: x:A 
B[x],
natural_number: $n,
int: 
,
equal: s = t,
deq: EqDecider(T),
bag: bag(T),
vatype: ValueAllType
Definitions :
cand: A c
B,
bfalse: ff,
btrue: tt,
lt_int: i <z j,
bnot: 
b,
le_int: i 
z j,
ifthenelse: if b then t else f fi ,
lelt: i j < k,
ycomb: Y,
length: ||as||,
int_seg: {i..j
},
select: l[i],
so_lambda: 
x.t[x],
name: Name,
es-header: es-header(es;e),
rsc4_headers_no_inputs: rsc4_headers_no_inputs(),
true: True,
prop: 
,
false: False,
not: A,
le: A B,
ge: i 
j ,
pi2: snd(t),
pi1: fst(t),
exists: 
x:A. B[x],
squash: 
T,
and: P Q,
all: x:A. B[x],
member: t 
T,
causal-class-relation: causal-class-relation,
implies: P Q,
nat: ,
vatype: ValueAllType,
uall: [x:A]. B[x],
rsc4_QuorumState: rsc4_QuorumState(Cmd),
or: P 
Q,
guard: {T},
label: ...$L... t,
es-causle: e c e',
rsc4_propose'base: rsc4_propose'base(Cmd),
uiff: uiff(P;Q),
rsc4_vote'base: rsc4_vote'base(Cmd),
top: Top,
iff: P 
Q,
sq_or: a b,
sq_stable: SqStable(P),
so_apply: x[s],
uimplies: b supposing a,
std-ma: StandardMessageAutomaton(X;hdrs),
message-constraint: message-constraint{i:l}(es;X;hdrs),
strongwellfounded: SWellFounded(R[x; y]),
rsc4_retry'base: rsc4_retry'base(Cmd),
rsc4_decided'base: rsc4_decided'base(Cmd),
rsc4_stdma: StandardAssumptions(rsc4_Main),
int_upper: {i...},
sq_type: SQType(T),
rsc4_newvote: rsc4_newvote(Cmd),
l_member: (x l),
es-locl: (e <loc e'),
subtype: S 
T,
msg-header: msg-header(m),
!hyp_hide: x
Lemmas :
deq_wf,
bag_wf,
int_upper_wf,
event-ordering+_wf,
es-E_wf,
rsc4_stdma_wf,
rsc4_propose'base_wf,
equal_wf,
es-causle_wf,
eo-forward_wf,
rsc4_QuorumState_wf,
rsc4_retry'base_wf,
rsc4-retry,
rsc4_vote'base_wf,
rsc4-vote,
Id-valueall-type,
rsc4_decided'base_wf,
Message_wf,
event-ordering+_inc,
rsc4-decided,
es-loc_wf,
rsc4_main_wf,
Id_wf,
classrel_wf,
and_wf,
exists_wf,
squash_wf,
rsc4_headers_no_inputs_wf,
msg-header_wf,
l_member_wf,
lelt_wf,
name_wf,
select_member,
valueall-type_wf,
sq_stable__valueall-type,
int-valueall-type,
product-valueall-type,
base-noloc-classrel-make-Msg,
es-causl_wf,
le_wf,
nat_wf,
less_than_wf,
ge_wf,
nat_properties,
es-causl-swellfnd,
or_wf,
cons_member,
poss-maj-member,
int_subtype_base,
subtype_base_sq,
assert-deq-member,
not_functionality_wrt_iff,
assert_of_bnot,
assert_of_eq_int,
and_functionality_wrt_uiff,
uiff_transitivity,
and_functionality_wrt_iff,
assert_of_band,
iff_weakening_uiff,
iff_transitivity,
decidable__es-le,
es-le_wf,
sq_stable_from_decidable,
es-le-causle,
es-causle_weakening,
es-causl_transitivity2,
not_wf,
id-deq_wf,
deq-member_wf,
bnot_wf,
eq_int_wf,
band_wf,
assert_wf,
eo-forward-E-subtype,
subtype_rel_set,
base-headers-msg-val_wf,
es-causle-le,
member-eo-forward-E,
rsc4_quorum_invariant,
eo-forward-base-classrel,
and_functionality_wrt_uiff3,
exists_functionality_wrt_iff,
squash_functionality_wrt_uiff,
eo-forward-locl,
select_wf,
es-locl_wf,
es-causl_weakening
\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{} for every d in rsc4\_decided'base(Cmd) there is an
earlier p in rsc4\_propose'base(Cmd) such that
d = p)
Date html generated:
2012_02_20-PM-05_02_53
Last ObjectModification:
2012_02_02-PM-02_16_48
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