Nuprl Lemma : consensus-refinement5
∀[V:Type]
∀A:Id List. ∀W:{a:Id| (a ∈ A)} List List.
((1 < ||W|| ∧ two-intersection(A;W))
⇒ ts-refinement(consensus-ts5(V;A;W);consensus-ts6(V;A;W);λs.cs-events-to-state(A; s)))
Proof
Definitions occuring in Statement :
consensus-ts6: consensus-ts6(V;A;W),
cs-events-to-state: cs-events-to-state(A; s),
consensus-ts5: consensus-ts5(V;A;W),
two-intersection: two-intersection(A;W),
Id: Id,
l_member: (x ∈ l),
length: ||as||,
list: T List,
less_than: a < b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
lambda: λx.A[x],
natural_number: $n,
universe: Type,
ts-refinement: ts-refinement(ts1;ts2;f)
Lemmas :
less_than_wf,
length_wf,
list_wf,
Id_wf,
l_member_wf,
two-intersection_wf,
rel_star_weakening,
fpf_wf,
top_wf,
fpf-empty_wf,
mk_fpf_wf,
consensus-rel-knowledge_wf,
consensus-event-cases,
rel_rel_star,
consensus-state4_wf,
consensus-state5_wf,
cs-events-to-state_wf,
consensus-accum-state_wf,
squash_wf,
true_wf,
consensus-event_wf,
iff_weakening_equal,
equal-wf-base-T,
int_subtype_base,
not_wf,
equal_wf,
set_wf,
length_wf_nat,
nat_wf,
append_wf,
cons_wf,
nil_wf,
list_accum_append,
subtype_rel_list,
list_accum_wf,
inning-event_wf,
consensus-accum_wf,
list_accum_cons_lemma,
list_accum_nil_lemma,
or_wf,
consensus-rel-knowledge-archive-step_wf,
consensus-rel-add-knowledge-step_wf,
consensus-rel-knowledge-step_wf,
cs-knowledge-precondition_wf,
fpf-join_wf,
fpf-single_wf,
int-deq_wf,
fpf-domain_wf,
subtype-fpf2,
consensus-rel-knowledge-inning-step_wf,
infix_ap_wf,
ts-reachable_wf,
consensus-ts6_wf,
subtype_rel_set,
subtype_rel_wf,
ts-type_wf,
ts-rel_wf,
subtype_rel_dep_function,
subtype_rel_self,
int_seg_properties,
id-deq_wf,
deq_wf,
assert_wf,
fpf-dom_wf,
all_wf,
fpf-ap_wf,
le_wf,
exists_wf,
ts-final_wf,
consensus-state6_wf,
rel_star_wf,
ts-init_wf,
consensus-ts5_wf,
archive-event_wf,
list_induction,
deq-member_wf,
bool_wf,
eqtt_to_assert,
assert-deq-member,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
deq_member_nil_lemma,
rel_star_transitivity,
deq_member_cons_lemma,
decidable__l_member,
decidable__equal_Id,
equal-wf-T-base,
eq_id_wf,
assert-eq-id,
bnot_wf,
false_wf,
btrue_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
assert_of_bor,
bnot_thru_bor,
assert_of_band,
atom2_subtype_base,
l_member-settype,
consensus-event-constraint_wf,
one-consensus-event_wf,
bor_wf,
consensus-message_wf,
int_seg_wf,
unit_wf2,
fpf_ap_pair_lemma,
list-cases,
length_of_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
cons_member,
l_member-set,
sq_stable__l_member,
assert_witness,
equal-wf-base,
l_all_iff,
l_all_wf2,
ppcc-problem,
btrue_neq_bfalse,
list_ind_cons_lemma,
list_ind_nil_lemma,
list-subtype,
ite_rw_true,
pair_eta_rw,
fpf-join-empty
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List.
((1 < ||W|| \mwedge{} two-intersection(A;W))
{}\mRightarrow{} ts-refinement(consensus-ts5(V;A;W);consensus-ts6(V;A;W);\mlambda{}s.cs-events-to-state(A; s)))
Date html generated:
2015_07_17-AM-11_45_56
Last ObjectModification:
2015_07_16-AM-10_13_31
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