Nuprl Lemma : consensus-ts4-ref-map
[V:Type]
((
v,v':V. (
(v = v')))
(v,v':V. Dec(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)))))
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-state4: ConsensusState,
consensus-state3: consensus-state3(T),
Id: Id,
decidable: Dec(P),
uall: [x:A]. B[x],
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,
universe: Type,
equal: s = t,
l_member: (x l)
Definitions :
pi1: fst(t),
rev_implies: P 
Q,
cand: A c
B,
so_lambda: 
x.t[x],
prop: 
,
member: t T,
iff: P Q,
and: P Q,
cs-ref-map-constraints: cs-ref-map-constraints(V;A;W;f),
all: x:A. B[x],
exists: x:A. B[x],
implies: P Q,
uall: [x:A]. B[x],
subtype: S 
T,
top: Top,
false: False,
not: A,
le: A 
B,
nat: 
,
true: True,
ycomb: Y,
length: ||as||,
map: map(f;as),
l_exists: (xL. P[x]),
l_all: (xL.P[x]),
uimplies: b supposing a,
squash: 
T,
lelt: i j < k,
int_seg: {i..j
},
so_apply: x[s],
guard: {T},
or: P 
Q,
decidable: Dec(P),
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
null: null(as),
assert: 
b,
uiff: uiff(P;Q),
sq_stable: SqStable(P),
sq_type: SQType(T)
Lemmas :
and_wf,
cs-considering_wf,
cs-inning-committed_wf,
cs-commited_wf,
cs-withdrawn_wf,
cs-inning-committable_wf,
cs-initial_wf,
iff_wf,
consensus-state3_wf,
consensus-state4_wf,
not_wf,
exists_wf,
equal_wf,
decidable_wf,
all_wf,
l_member_wf,
Id_wf,
two-intersection_wf,
consensus-ts4-ref-map1,
top_wf,
null_wf3,
decidable__assert,
nat_wf,
cs-inning_wf,
nat_properties,
le_wf,
nil_member,
list-subtype,
map_wf,
length_wf_nat,
non_neg_length,
length_wf,
length-map,
imax-list-ub,
imax-list-lb,
imax-list_wf,
member_map,
less_than_wf,
uiff_wf,
uall_wf,
isect_wf,
decidable__lt,
decidable__equal_Id,
decidable__l_member,
sq_stable_from_decidable,
l_member-set,
upto_wf,
int_seg_wf,
length_upto,
select-map,
int_subtype_base,
subtype_base_sq,
select_upto,
select_wf
\mforall{}[V:Type]
((\mexists{}v,v':V. (\mneg{}(v = v')))
{}\mRightarrow{} (\mforall{}v,v':V. Dec(v = v'))
{}\mRightarrow{} (\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List.
(two-intersection(A;W)
{}\mRightarrow{} (\mexists{}f:ConsensusState {}\mrightarrow{} (consensus-state3(V) List). cs-ref-map-constraints(V;A;W;f)))))
Date html generated:
2012_01_23-PM-12_04_16
Last ObjectModification:
2011_12_14-PM-06_48_20
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