Nuprl Lemma : consensus-safety1
V:Type
((v1,v2:V. Dec(v1 = v2))
{
v,v':V. (
(v = v'))}
(L:V List. Dec(v:V. ((v 
L))))
(A:Id List. W:{a:Id| (a A)} List List.
((||W|| 
1 )
two-intersection(A;W)
(f:ConsensusState 
consensus-state1(V)
((v:V. s:ts-reachable(consensus-ts4(V;A;W)).
((f s) = Decided[v] 
i:
. in state s, inning i has committed v))
ts-refinement(consensus-ts1(V);consensus-ts4(V;A;W);f))))))
Proof not projected
Definitions occuring in Statement :
two-intersection: two-intersection(A;W),
cs-inning-committed: in state s, inning i has committed v,
consensus-ts4: consensus-ts4(V;A;W),
consensus-state4: ConsensusState,
consensus-ts1: consensus-ts1(T),
cs-decided: Decided[v],
consensus-state1: consensus-state1(V),
Id: Id,
length: ||as||,
nat: ,
decidable: Dec(P),
guard: {T},
ge: i j ,
all: x:A. B[x],
exists: x:A. B[x],
iff: P Q,
not: A,
implies: P Q,
and: P Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A B[x],
list: type List,
natural_number: $n,
universe: Type,
equal: s = t,
l_member: (x l),
ts-refinement: ts-refinement(ts1;ts2;f),
ts-reachable: ts-reachable(ts)
Definitions :
all: x:A. B[x],
implies: P Q,
exists: x:A. B[x],
ge: i j ,
member: t T,
prop: 
,
so_lambda: 
x.t[x],
consensus-ts3: consensus-ts3(T),
consensus-ts2: consensus-ts2(T),
consensus-ts1: consensus-ts1(T),
cs-is-decided: cs-is-decided(x),
cs-undecided: UNDECIDED,
consensus-state1: consensus-state1(V),
ts-type: ts-type(ts),
pi1: fst(t),
consensus-state2: consensus-state2(T),
top: Top,
subtype: S 
T,
consensus-ts4: consensus-ts4(V;A;W),
bfalse: ff,
btrue: tt,
ifthenelse: if b then t else f fi ,
and: P Q,
compose: f o g,
suptype: suptype(S; T),
rev_implies: P Q,
squash: 
T,
iff: P Q,
true: True,
false: False,
cand: A c B,
le: A 
B,
l_member: (x l),
not: A,
cs-decided: Decided[v],
isl: isl(x),
assert: 
b,
uall: [x:A]. B[x],
uimplies: b supposing a,
so_apply: x[s],
guard: {T},
unit: Unit,
bool: 
,
ts-reachable: ts-reachable(ts),
uiff: uiff(P;Q),
or: P 
Q,
cs-ambivalent: AMBIVALENT,
cs-predecided: PREDECIDED[v],
nat: ,
cs-ref-map-constraints: cs-ref-map-constraints(V;A;W;f),
cs-archived: by state s, a archived v in inning i,
l_all: (xL.P[x]),
one-intersection: one-intersection(A;W),
cs-inning-committed: in state s, inning i has committed v,
it: 
Lemmas :
consensus-refinement3,
consensus-ts4-ref-map,
consensus-refinement2,
consensus-refinement1,
two-intersection_wf,
ge_wf,
length_wf,
Id_wf,
l_member_wf,
all_wf,
decidable_wf,
exists_wf,
not_wf,
guard_wf,
equal_wf,
ts-refinement-composition,
consensus-ts1_wf,
consensus-ts2_wf,
consensus-ts3_wf,
cs-ref-map3_wf,
consensus-state3_wf,
ifthenelse_wf,
isl_wf,
top_wf,
consensus-ts4_wf,
compose_wf,
assert_of_bnot,
eqff_to_assert,
bnot_wf,
assert_wf,
iff_transitivity,
eqtt_to_assert,
bool_wf,
ts-reachable_wf,
ts-type_wf,
ts-refinement-reachable,
consensus-state4_wf,
cs-is-decided_wf,
uiff_transitivity,
consensus-state2-cases,
cs-decided_wf2,
consensus-state2_wf,
true_wf,
squash_wf,
cs-inning-committed_wf,
nat_wf,
cs-decided_wf,
consensus-state1_wf,
cs-ref-map3-decided,
cs-inning_wf,
le_wf,
consensus-ts4-estimate-domain,
two-intersection-one-intersection,
select_wf,
cs-commited_wf,
cs-undecided_wf,
ts-refinement_wf,
iff_wf
\mforall{}V:Type
((\mforall{}v1,v2:V. Dec(v1 = v2))
{}\mRightarrow{} \{\mexists{}v,v':V. (\mneg{}(v = v'))\}
{}\mRightarrow{} (\mforall{}L:V List. Dec(\mexists{}v:V. (\mneg{}(v \mmember{} L))))
{}\mRightarrow{} (\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List.
((||W|| \mgeq{} 1 )
{}\mRightarrow{} two-intersection(A;W)
{}\mRightarrow{} (\mexists{}f:ConsensusState {}\mrightarrow{} consensus-state1(V)
((\mforall{}v:V. \mforall{}s:ts-reachable(consensus-ts4(V;A;W)).
((f s) = Decided[v] \mLeftarrow{}{}\mRightarrow{} \mexists{}i:\mBbbN{}. in state s, inning i has committed v))
\mwedge{} ts-refinement(consensus-ts1(V);consensus-ts4(V;A;W);f))))))
Date html generated:
2012_01_23-PM-12_05_37
Last ObjectModification:
2011_12_31-AM-11_10_21
Home
Index