Nuprl Lemma : consensus-refinement4
∀[V:Type]
((∀v1,v2:V. Dec(v1 = v2 ∈ V))
⇒ (∃v,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);λs.(fst(s))))))
Proof
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,
l_member: (x ∈ l),
length: ||as||,
list: T List,
less_than: a < b,
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,
set: {x:A| B[x]} ,
lambda: λx.A[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
ts-refinement: ts-refinement(ts1;ts2;f)
Lemmas :
less_than_wf,
length_wf,
list_wf,
Id_wf,
l_member_wf,
two-intersection_wf,
exists_wf,
not_wf,
equal_wf,
all_wf,
decidable_wf,
list_induction,
l_contains_wf,
infix_ap_wf,
consensus-state4_wf,
rel_star_wf,
consensus-rel_wf,
fpf-empty_wf,
deq-member_wf,
id-deq_wf,
subtype_rel-deq,
sq_stable__l_member,
decidable__equal_Id,
set_wf,
list-set-type2,
bool_wf,
eqtt_to_assert,
assert-deq-member,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
nil_wf,
cons_wf,
rel_star_weakening,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
btrue_neq_bfalse,
l_contains_cons,
rel_star_transitivity,
deq_member_cons_lemma,
decidable__l_member,
bor_wf,
eq_id_wf,
iff_transitivity,
assert_wf,
or_wf,
iff_weakening_uiff,
assert_of_bor,
assert-eq-id,
fpf_wf,
ite_rw_true,
l_member_set2,
and_wf,
iff_weakening_equal,
rel_rel_star,
pi1_wf_top,
equal-wf-base,
cs-precondition_wf,
equal-wf-base-T,
fpf-join_wf,
fpf-single_wf,
int-deq_wf,
fpf-domain_wf,
subtype-fpf2,
top_wf,
l_contains_weakening,
l_member-set,
ts-reachable_wf,
consensus-ts5_wf,
subtype_rel_set,
subtype_rel_wf,
ts-type_wf,
ts-rel_wf,
subtype_rel_dep_function,
subtype_rel_self,
cs-inning_wf,
cs-estimate_wf,
consensus-state4-subtype,
cs-archive-blocked_wf,
le_wf,
int_subtype_base,
consensus-ts5-true-knowledge,
fpf-ap_wf,
fpf-dom_wf,
isect_wf,
subtype_rel_sum,
equal-wf-T-base,
true_wf,
false_wf,
decide_bfalse_lemma,
decidable__lt,
decidable__equal_int,
not-equal-2,
add_functionality_wrt_le,
add-associates,
add-commutes,
le-add-cancel,
add-swap,
less_than_transitivity2,
le_weakening,
less_than_transitivity1,
assert_functionality_wrt_uiff,
squash_wf,
deq_wf,
subtype_top,
member-less_than,
assert_witness,
consensus-ts5-archive-invariant,
member_wf,
ts-final_wf,
consensus-ts4_wf,
cs-possible-state-reachable,
list-subtype,
mk_fpf_wf,
bnot_wf,
pair_eta_rw,
assert_of_bnot
\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:
2015_07_17-AM-11_43_26
Last ObjectModification:
2015_07_16-AM-10_13_19
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