Nuprl Lemma : consensus-refinement4
[V:Type]
((v1,v2:V. Dec(v1 = v2))
(
v,v':V. (
(v = v')))
(A:Id List. W:{a:Id| (a 
A)} List List.
(((1 < ||W||) 
two-intersection(A;W))
ts-refinement(consensus-ts4(V;A;W);consensus-ts5(V;A;W);
s.(fst(s))))))
Proof not projected
Definitions occuring in Statement :
consensus-ts5: consensus-ts5(V;A;W),
two-intersection: two-intersection(A;W),
consensus-ts4: consensus-ts4(V;A;W),
Id: Id,
length: ||as||,
decidable: Dec(P),
uall: [x:A]. B[x],
pi1: fst(t),
all: x:A. B[x],
exists: x:A. B[x],
not: A,
implies: P Q,
and: P Q,
less_than: a < b,
set: {x:A| B[x]} ,
lambda: x.A[x],
list: type List,
natural_number: $n,
universe: Type,
equal: s = t,
l_member: (x l),
ts-refinement: ts-refinement(ts1;ts2;f)
Definitions :
uall: [x:A]. B[x],
implies: P Q,
all: x:A. B[x],
and: P Q,
ts-refinement: ts-refinement(ts1;ts2;f),
member: t T,
prop: 
,
so_lambda: 
x.t[x],
consensus-ts4: consensus-ts4(V;A;W),
ts-rel: ts-rel(ts),
ts-init: ts-init(ts),
pi1: fst(t),
consensus-ts5: consensus-ts5(V;A;W),
pi2: snd(t),
btrue: tt,
bfalse: ff,
reduce: reduce(f;k;as),
deq-member: deq-member(eq;x;L),
ifthenelse: if b then t else f fi ,
consensus-state4: ConsensusState,
eqof: eqof(d),
guard: {T},
bor: p 
q,
Id: Id,
exists: x:A. B[x],
infix_ap: x f y,
consensus-rel: CR[x,y],
fpf-empty: 
,
cs-inning: Inning(s;a),
cs-estimate: Estimate(s;a),
or: P Q,
fpf-domain: fpf-domain(f),
cand: A c B,
top: Top,
ts-type: ts-type(ts),
true: True,
uimplies: b supposing a,
squash: 
T,
subtype: S 
T,
cs-knowledge: Knowledge(x;a),
iff: P 
Q,
rev_implies: P Q,
so_apply: x[s],
unit: Unit,
bool: 
,
false: False,
decidable: Dec(P),
uiff: uiff(P;Q),
sq_type: SQType(T),
not: A,
l_contains: A B,
consensus-rel-add-knowledge-step: consensus-rel-add-knowledge-step(V;A;W;x1;x2;y1;y2;a),
consensus-rel-knowledge-archive-step: consensus-rel-knowledge-archive-step(V;A;W;x1;x2;y1;y2;a),
consensus-rel-knowledge-inning-step: consensus-rel-knowledge-inning-step(V;A;W;x1;x2;y1;y2;a),
consensus-rel-knowledge-step: consensus-rel-knowledge-step(V;A;W;x1;x2;y1;y2;a),
consensus-rel-knowledge: consensus-rel-knowledge(V;A;W;x;y),
ts-reachable: ts-reachable(ts),
cs-knowledge-precondition: may consider v in inning i based on knowledge (s),
le: A 
B,
it: 
,
eq_id: a = b
Lemmas :
and_wf,
less_than_wf,
length_wf,
Id_wf,
l_member_wf,
two-intersection_wf,
exists_wf,
not_wf,
equal_wf,
all_wf,
decidable_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,
bnot_wf,
assert_wf,
bool_wf,
id-deq_wf,
deq-member_wf,
consensus-rel_wf,
fpf-empty_wf,
consensus-state4_wf,
rel_star_weakening,
nil_member,
l_contains_cons,
rel_star_transitivity,
ifthenelse_wf,
fpf_wf,
bor_wf,
eqof_wf,
decidable__l_member,
decidable__equal_Id,
eq_id_wf,
not_functionality_wrt_uiff,
assert-eq-id,
uiff_transitivity,
atom2_subtype_base,
subtype_base_sq,
rel_rel_star,
pi1_wf_top,
top_wf,
or_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
strong-subtype-self,
list-set-type2,
cs-precondition_wf,
fpf-join_wf,
fpf-single_wf,
int-deq_wf,
band_wf,
assert_of_bor,
or_functionality_wrt_iff,
assert_functionality_wrt_uiff,
bnot_thru_bor,
assert_of_band,
and_functionality_wrt_iff,
l_contains_weakening,
rel_star_wf,
ts-type_wf,
ts-reachable_wf,
consensus-ts5_wf,
ts-rel_wf,
subtype-top,
subtype-fpf2,
cs-estimate_wf,
fpf-domain_wf,
cs-inning_wf,
int_subtype_base,
false_wf,
assert_witness,
subtype_rel_simple_product,
subtype_rel_self,
subtype_rel_function,
fpf-dom_wf,
le_wf,
fpf-ap_wf,
consensus-ts5-true-knowledge,
true_wf,
squash_wf,
member_wf,
Error :pi2_wf,
pair_wf,
mk_fpf_wf,
pair_eta_rw
\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.
(((1 < ||W||) \mwedge{} two-intersection(A;W))
{}\mRightarrow{} ts-refinement(consensus-ts4(V;A;W);consensus-ts5(V;A;W);\mlambda{}s.(fst(s))))))
Date html generated:
2012_01_23-PM-12_06_45
Last ObjectModification:
2011_12_31-AM-11_09_42
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