Nuprl Lemma : consensus-refinement3
[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.
two-intersection(A;W)
(f:ConsensusState 
(consensus-state3(V) List)
(cs-ref-map-constraints(V;A;W;f) ts-refinement(consensus-ts3(V);consensus-ts4(V;A;W);f)))
supposing ||W|| 
1 ))
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),
consensus-ts4: consensus-ts4(V;A;W),
consensus-state4: ConsensusState,
consensus-ts3: consensus-ts3(T),
consensus-state3: consensus-state3(T),
Id: Id,
length: ||as||,
decidable: Dec(P),
uimplies: b supposing a,
uall: [x:A]. B[x],
guard: {T},
ge: i j ,
all: x:A. B[x],
exists: x:A. B[x],
not: A,
implies: P Q,
set: {x:A| B[x]} ,
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)
Definitions :
true: True,
squash: 
T,
or: P 
Q,
so_lambda: 
x.t[x],
prop: 
,
false: False,
le: A 
B,
member: t T,
ge: i j ,
uimplies: b supposing a,
not: A,
exists: x:A. B[x],
all: x:A. B[x],
implies: P Q,
uall: [x:A]. B[x],
infix_ap: x f y,
and: P 
Q,
ts-refinement: ts-refinement(ts1;ts2;f),
pi1: fst(t),
consensus-ts4: consensus-ts4(V;A;W),
ts-type: ts-type(ts),
consensus-ts3: consensus-ts3(T),
nat: 
,
ycomb: Y,
pi2: snd(t),
ts-init: ts-init(ts),
length: ||as||,
subtype: S 
T,
top: Top,
int_iseg: {i...j},
ts-rel: ts-rel(ts),
guard: {T},
cand: A c B,
lelt: i j < k,
iff: P 
Q,
rev_implies: P Q,
int_seg: {i..j
},
cs-estimate: Estimate(s;a),
cs-inning: Inning(s;a),
ts-final: ts-final(ts),
consensus-state4: ConsensusState,
btrue: tt,
bfalse: ff,
lt_int: i <z j,
bnot: 
b,
le_int: i z j,
ifthenelse: if b then t else f fi ,
select: l[i],
fpf-ap: f(x),
fpf-domain: fpf-domain(f),
cs-archived: by state s, a archived v in inning i,
cs-inning-committed: in state s, inning i has committed v,
fpf-single: x : v,
null: null(as),
assert: 
b,
sq_stable: SqStable(P),
so_apply: x[s],
l_all: (xL.P[x]),
two-intersection: two-intersection(A;W),
ts-reachable: ts-reachable(ts),
cs-ref-map-constraints: cs-ref-map-constraints(V;A;W;f),
decidable: Dec(P),
sq_type: SQType(T),
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
last: last(L)
Lemmas :
decidable__equal_Id,
decidable__l_member,
sq_stable_from_decidable,
cons_member,
equal_wf,
guard_wf,
not_wf,
exists_wf,
decidable_wf,
all_wf,
ge_wf,
two-intersection_wf,
consensus-state3_wf,
consensus-state4_wf,
cs-ref-map-constraints_wf,
l_member_wf,
Id_wf,
length_wf,
consensus-ts3_wf,
ts-final_wf,
ts-type_wf,
ts-reachable_wf,
consensus-ts4_wf,
ts-rel_wf,
rel_star_weakening,
subtype_rel_self,
ts-init_wf,
nat_wf,
decidable__lt,
le_wf,
length_cons,
top_wf,
length_wf_nat,
non_neg_length,
cs-ref-map-changed,
cs-ref-map-unchanged,
cs-ref-map-step,
decidable__le,
two-intersection-one-intersection,
decidable__cs-committed-change,
firstn_wf,
rel_star_transitivity,
and_wf,
length_firstn_eq,
cs-commited_wf,
cs-considering_wf,
cs-withdrawn_wf,
or_wf,
select_wf,
int_seg_wf,
rel_rel_star,
append_wf,
int_subtype_base,
set_subtype_base,
subtype_base_sq,
last-lemma-sq,
assert_of_null,
null_wf3,
assert_wf,
not_functionality_wrt_uiff,
member_wf,
cs-inning-committable_wf,
decidable__cs-inning-committable,
less_than_wf,
squash_wf,
decidable__equal_int,
list_extensionality,
lelt_wf,
select_append_back,
true_wf,
select_firstn,
length_firstn,
committed-inning0-reachable,
fpf_wf,
fpf-single_wf,
property-from-l_member,
hd_member,
hd_wf,
false_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.
two-intersection(A;W)
{}\mRightarrow{} (\mforall{}f:ConsensusState {}\mrightarrow{} (consensus-state3(V) List)
(cs-ref-map-constraints(V;A;W;f)
{}\mRightarrow{} ts-refinement(consensus-ts3(V);consensus-ts4(V;A;W);f)))
supposing ||W|| \mgeq{} 1 ))
Date html generated:
2012_01_23-PM-12_05_25
Last ObjectModification:
2011_12_14-PM-05_52_13
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