Nuprl Lemma : rsc4-agreement
[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 Base([notify];
Cmd) satisfy
((fst(v1)) = (fst(v2))) ((snd(v1)) = (snd(v2))))
Proof
Definitions occuring in Statement :
rsc4_stdma: StandardAssumptions(rsc4_Main),
base-headers-msg-val: Base(hdr;typ),
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],
cons: [car / cdr],
nil: [],
multiply: n * m,
add: n + m,
natural_number: $n,
int: ,
token: "$token",
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 :
prop: 
,
uall: [x:A]. B[x],
top: Top,
subtype: S 
T,
or: P 
Q,
true: True,
so_lambda: 
x.t[x],
squash: 
T,
name: Name,
es-header: es-header(es;e),
rsc4_headers_no_inputs: rsc4_headers_no_inputs(),
all: x:A. B[x],
member: t 
T,
rsc4_decided'base: rsc4_decided'base(Cmd),
implies: P Q,
consistent-class: consistent-class,
vatype: ValueAllType,
cand: A c
B,
rev_implies: P 
Q,
iff: P Q,
sq_stable: SqStable(P),
so_apply: x[s],
uiff: uiff(P;Q),
uimplies: b supposing a,
exists: 
x:A. B[x],
and: P Q,
std-ma: StandardMessageAutomaton(X;hdrs),
message-constraint: message-constraint{i:l}(es;X;hdrs),
rsc4_stdma: StandardAssumptions(rsc4_Main),
nat: ,
int_upper: {i...},
msg-header: msg-header(m)
Lemmas :
vatype_wf,
deq_wf,
bag_wf,
int_upper_wf,
event-ordering+_wf,
rsc4_stdma_wf,
bag-no-repeats_wf,
nat_wf,
bag-size_wf,
es-E_wf,
base-headers-msg-val_wf,
pi1_wf_top,
equal_wf,
Message_wf,
event-ordering+_inc,
rsc4-notify,
es-loc_wf,
rsc4_main_wf,
Id_wf,
classrel_wf,
es-causl_wf,
and_wf,
exists_wf,
squash_wf,
rsc4_headers_no_inputs_wf,
msg-header_wf,
l_member_wf,
name_wf,
cons_member,
valueall-type_wf,
sq_stable__valueall-type,
int-valueall-type,
product-valueall-type,
base-noloc-classrel-make-Msg,
rsc4-agreement-property
\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 Base([notify];\mBbbZ{} \mtimes{} Cmd) satisfy
((fst(v1)) = (fst(v2))) {}\mRightarrow{} ((snd(v1)) = (snd(v2))))
Date html generated:
2012_02_20-PM-05_03_02
Last ObjectModification:
2012_02_02-PM-02_16_50
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