Nuprl Lemma : cs-ref-map-changed
[V:Type]
((v1,v2:V. Dec(v1 = v2))
{
v,v':V. (
(v = v'))}
(A:Id List. W:{a:Id| (a 
A)} List List.
(two-intersection(A;W)
(f:ConsensusState 
(consensus-state3(V) List)
(cs-ref-map-constraints(V;A;W;f)
(x,y:ts-reachable(consensus-ts4(V;A;W)).
((x ts-rel(consensus-ts4(V;A;W)) y)
(i:
(v:V
((in state x, inning i could commit v 
(in state y, inning i could commit v ))
((f y[i] = WITHDRAWN)
((f x[i] = INITIAL)
((f y[i] = INITIAL)
(v':V
((j:i. ((f x[j] = INITIAL)))
((f y[i] = CONSIDERING[v']) (f y[i] = COMMITED[v']))
(j:i. v'':V.
(((f x[j] = CONSIDERING[v'']) (f x[j] = COMMITED[v'']))
(v'' = v')))))))))) supposing
((i < ||f y||) and
(i < ||f x||))))))))))
Proof not projected
Definitions occuring in Statement :
cs-ref-map-constraints: cs-ref-map-constraints(V;A;W;f),
two-intersection: two-intersection(A;W),
cs-inning-committable: in state s, inning i could commit v ,
consensus-ts4: consensus-ts4(V;A;W),
consensus-state4: ConsensusState,
cs-commited: COMMITED[v],
cs-considering: CONSIDERING[v],
cs-withdrawn: WITHDRAWN,
cs-initial: INITIAL,
consensus-state3: consensus-state3(T),
Id: Id,
select: l[i],
length: ||as||,
int_seg: {i..j
},
nat: ,
decidable: Dec(P),
uimplies: b supposing a,
uall: [x:A]. B[x],
guard: {T},
infix_ap: x f y,
all: x:A. B[x],
exists: x:A. B[x],
not: A,
implies: P Q,
or: P Q,
and: P Q,
less_than: a < b,
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-reachable: ts-reachable(ts),
ts-rel: ts-rel(ts)
Definitions :
so_lambda: 
x.t[x],
prop: 
,
member: t T,
and: P Q,
uimplies: b supposing a,
infix_ap: x f y,
exists: x:A. B[x],
all: x:A. B[x],
implies: P Q,
uall: [x:A]. B[x],
false: False,
le: A 
B,
not: A,
or: P Q,
guard: {T},
cand: A c B,
cs-inning-committable: in state s, inning i could commit v ,
nat: ,
Id: Id,
cs-not-completed: in state s, a has not completed inning i,
true: True,
top: Top,
so_apply: x[s],
pi1: fst(t),
ts-type: ts-type(ts),
consensus-ts4: consensus-ts4(V;A;W),
ts-reachable: ts-reachable(ts),
iff: P 
Q,
cs-ref-map-constraints: cs-ref-map-constraints(V;A;W;f),
decidable: Dec(P),
int_seg: {i..j},
lelt: i j < k,
l_exists: (xL. P[x]),
pi2: snd(t),
ts-rel: ts-rel(ts),
rev_implies: P Q,
consensus-rel: CR[x,y],
sq_type: SQType(T),
ge: i 
j ,
uiff: uiff(P;Q)
Lemmas :
decidable_wf,
all_wf,
equal_wf,
exists_wf,
guard_wf,
Id_wf,
l_member_wf,
two-intersection_wf,
consensus-state4_wf,
cs-ref-map-constraints_wf,
ts-type_wf,
consensus-ts4_wf,
ts-reachable_wf,
ts-rel_wf,
nat_wf,
consensus-state3_wf,
length_wf,
less_than_wf,
not_wf,
cs-inning-committable_wf,
and_wf,
select_wf,
consensus-state3-cases,
decidable__cs-inning-two-committable,
decidable__cs-inning-committable-some,
cs-withdrawn_wf,
cs-commited_wf,
cs-considering_wf,
or_wf,
int_seg_wf,
cs-not-completed_wf,
decidable__cs-archived,
list-subtype,
cs-archived_wf,
decidable__l_exists_better-extract,
consensus-ts4-archived-invariant,
le_wf,
decidable__cs-not-completed,
decidable__equal_Id,
atom2_subtype_base,
subtype_base_sq,
top_wf,
cs-estimate_wf,
fpf-domain_wf,
nat_properties,
fpf-trivial-subtype-top,
int-deq_wf,
fpf-domain-join,
fpf-single_wf,
subtype-top,
subtype-fpf2,
not_functionality_wrt_iff,
cs-inning-committed-committable,
int_seg_properties
\mforall{}[V:Type]
((\mforall{}v1,v2:V. Dec(v1 = v2))
{}\mRightarrow{} \{\mexists{}v,v':V. (\mneg{}(v = v'))\}
{}\mRightarrow{} (\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List.
(two-intersection(A;W)
{}\mRightarrow{} (\mforall{}f:ConsensusState {}\mrightarrow{} (consensus-state3(V) List)
(cs-ref-map-constraints(V;A;W;f)
{}\mRightarrow{} (\mforall{}x,y:ts-reachable(consensus-ts4(V;A;W)).
((x ts-rel(consensus-ts4(V;A;W)) y)
{}\mRightarrow{} (\mforall{}i:\mBbbN{}
(\mforall{}v:V
((in state x, inning i could commit v
\mwedge{} (\mneg{}in state y, inning i could commit v ))
{}\mRightarrow{} ((f y[i] = WITHDRAWN)
\mvee{} ((f x[i] = INITIAL)
\mwedge{} ((f y[i] = INITIAL)
\mvee{} (\mexists{}v':V
((\mforall{}j:\mBbbN{}i. (\mneg{}(f x[j] = INITIAL)))
\mwedge{} ((f y[i] = CONSIDERING[v']) \mvee{} (f y[i] = COMMITED[v']))
\mwedge{} (\mforall{}j:\mBbbN{}i. \mforall{}v'':V.
(((f x[j] = CONSIDERING[v''])
\mvee{} (f x[j] = COMMITED[v'']))
{}\mRightarrow{} (v'' = v')))))))))) supposing
((i < ||f y||) and
(i < ||f x||))))))))))
Date html generated:
2012_01_23-PM-12_04_45
Last ObjectModification:
2011_12_13-AM-10_33_38
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