Nuprl Lemma : committed-inning0-reachable
[V:Type]. [A:Id List]. [W:{a:Id| (a 
A)} List List].
[v:V]. (
a.<0, 0 : v> ts-reachable(consensus-ts4(V;A;W))) supposing ||W|| 
1
Proof not projected
Definitions occuring in Statement :
consensus-ts4: consensus-ts4(V;A;W),
fpf-single: x : v,
Id: Id,
length: ||as||,
uimplies: b supposing a,
uall: [x:A]. B[x],
ge: i j ,
member: t T,
set: {x:A| B[x]} ,
lambda: x.A[x],
pair: <a, b>,
list: type List,
natural_number: $n,
universe: Type,
l_member: (x l),
ts-reachable: ts-reachable(ts)
Definitions :
prop: 
,
so_lambda: 
x.t[x],
pi2: snd(t),
pi1: fst(t),
ts-init: ts-init(ts),
ts-rel: ts-rel(ts),
infix_ap: x f y,
consensus-state4: ConsensusState,
ts-type: ts-type(ts),
consensus-ts4: consensus-ts4(V;A;W),
ts-reachable: ts-reachable(ts),
member: t T,
uimplies: b supposing a,
uall: [x:A]. B[x],
implies: P 
Q,
all: x:A. B[x],
btrue: tt,
bfalse: ff,
reduce: reduce(f;k;as),
deq-member: deq-member(eq;x;L),
ifthenelse: if b then t else f fi ,
eqof: eqof(d),
guard: {T},
bor: p 
q,
Id: Id,
top: Top,
cand: A c
B,
fpf-domain: fpf-domain(f),
or: P Q,
cs-estimate: Estimate(s;a),
cs-inning: Inning(s;a),
and: P Q,
exists: 
x:A. B[x],
fpf-empty: 
,
consensus-rel: CR[x,y],
fpf-single: x : v,
not: 
A,
cs-precondition: state s may consider v in inning i,
false: False,
null: null(as),
assert: 
b,
le: A 
B,
so_apply: x[s],
iff: P 
Q,
unit: Unit,
bool: 
,
decidable: Dec(P),
uiff: uiff(P;Q),
sq_type: SQType(T),
l_contains: A 
B,
ge: i j ,
rev_implies: P Q,
ycomb: Y,
length: ||as||,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
it: 
,
eq_id: a = b
Lemmas :
l_member_wf,
Id_wf,
length_wf,
ge_wf,
fpf-empty_wf,
consensus-rel_wf,
consensus-state4_wf,
rel_star_wf,
fpf-single_wf,
l_contains_wf,
not_functionality_wrt_iff,
assert_of_bnot,
eqff_to_assert,
assert-deq-member,
eqtt_to_assert,
iff_weakening_uiff,
iff_transitivity,
not_wf,
bnot_wf,
assert_wf,
bool_wf,
id-deq_wf,
deq-member_wf,
rel_star_weakening,
nil_member,
l_contains_cons,
eqof_wf,
bor_wf,
fpf_wf,
ifthenelse_wf,
rel_star_transitivity,
decidable__equal_Id,
decidable__l_member,
eq_id_wf,
not_functionality_wrt_uiff,
assert-eq-id,
equal_wf,
uiff_transitivity,
atom2_subtype_base,
subtype_base_sq,
rel_rel_star,
list-set-type2,
strong-subtype-self,
strong-subtype-set3,
strong-subtype-deq-subtype,
or_wf,
top_wf,
pi1_wf_top,
all_wf,
int-deq_wf,
fpf-join_wf,
cs-precondition_wf,
exists_wf,
l_contains_weakening,
false_wf,
cs-archive-blocked_wf,
le_wf,
hd_wf,
hd_member,
fpf-join-empty
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[W:\{a:Id| (a \mmember{} A)\} List List].
\mforall{}[v:V]. (\mlambda{}a.ɘ, 0 : v> \mmember{} ts-reachable(consensus-ts4(V;A;W))) supposing ||W|| \mgeq{} 1
Date html generated:
2012_01_23-PM-12_04_28
Last ObjectModification:
2011_12_14-PM-06_21_18
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