Nuprl Lemma : committed-inning0-reachable
∀[V:Type]. ∀[A:Id List]. ∀[W:{a:Id| (a ∈ A)} List List].
∀[v:V]. (λa.<0, 0 : v> ∈ ts-reachable(consensus-ts4(V;A;W))) supposing ||W|| ≥ 1
Proof
Definitions occuring in Statement :
consensus-ts4: consensus-ts4(V;A;W),
fpf-single: x : v,
Id: Id,
l_member: (x ∈ l),
length: ||as||,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
ge: i ≥ j ,
member: t ∈ T,
set: {x:A| B[x]} ,
lambda: λx.A[x],
pair: <a, b>,
natural_number: $n,
universe: Type,
ts-reachable: ts-reachable(ts)
Lemmas :
list_induction,
l_contains_wf,
infix_ap_wf,
consensus-state4_wf,
rel_star_wf,
consensus-rel_wf,
fpf-empty_wf,
l_member_wf,
deq-member_wf,
id-deq_wf,
subtype_rel-deq,
Id_wf,
sq_stable__l_member,
decidable__equal_Id,
equal_wf,
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,
list_wf,
btrue_neq_bfalse,
member-implies-null-eq-bfalse,
btrue_wf,
null_nil_lemma,
rel_star_weakening,
l_contains_cons,
rel_star_transitivity,
deq_member_cons_lemma,
decidable__l_member,
assert-eq-id,
assert_of_bor,
iff_weakening_uiff,
or_wf,
assert_wf,
iff_transitivity,
eq_id_wf,
bor_wf,
iff_weakening_equal,
and_wf,
l_member_set2,
ite_rw_true,
fpf_wf,
rel_rel_star,
not_wf,
pi1_wf_top,
int-deq_wf,
fpf-single_wf,
fpf-join_wf,
equal-wf-base-T,
cs-precondition_wf,
exists_wf,
equal-wf-base,
all_wf,
top_wf,
subtype-fpf2,
fpf-domain_wf,
l_contains_weakening,
l_member-set,
subtype_rel_dep_function,
subtype_rel_self,
less_than_wf,
fpf-join-empty,
cs-archive-blocked_wf,
le_wf,
hd_wf,
false_wf,
null_cons_lemma,
product_subtype_list,
length_of_nil_lemma,
list-cases,
hd_member
\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:
2015_07_17-AM-11_32_49
Last ObjectModification:
2015_07_16-AM-09_48_21
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