Nuprl Lemma : cs-possible-state-reachable
∀[V:Type]. ∀[A:Id List]. ∀[W:{a:Id| (a ∈ A)} List List]. ∀[v:V].
(∀[L:{a:Id| (a ∈ A)} List]
(<λa.<0, if a ∈b L) then 0 : v else ⊗ fi >, λa.mk_fpf(A;λb.<0, ff>)>
∈ ts-reachable(consensus-ts5(V;A;W)))) supposing
(two-intersection(A;W) and
1 < ||W||)
Proof
Definitions occuring in Statement :
consensus-ts5: consensus-ts5(V;A;W),
two-intersection: two-intersection(A;W),
mk_fpf: mk_fpf(L;f),
fpf-single: x : v,
fpf-empty: ⊗,
id-deq: IdDeq,
Id: Id,
deq-member: x ∈b L),
l_member: (x ∈ l),
length: ||as||,
list: T List,
ifthenelse: if b then t else f fi ,
bfalse: ff,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
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 :
two-intersection_wf,
less_than_wf,
length_wf,
list_wf,
l_member_wf,
Id_wf,
top_wf,
mk_fpf_wf,
fpf-empty_wf,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
fpf-single_wf,
assert-deq-member,
eqtt_to_assert,
bool_wf,
subtype_rel_list,
id-deq_wf,
deq-member_wf,
list_induction,
set_wf,
deq_member_nil_lemma,
rel_star_weakening,
consensus-rel-knowledge_wf,
fpf_wf,
deq_member_cons_lemma,
rel_star_transitivity,
bor_wf,
deq_wf,
iff_transitivity,
assert_wf,
or_wf,
iff_weakening_uiff,
assert_of_bor,
rel_rel_star,
decidable__l_member,
decidable__equal_set,
decidable__equal_Id,
assert_of_band,
bnot_thru_bor,
assert_of_bnot,
btrue_wf,
true_wf,
false_wf,
not_wf,
bnot_wf,
assert-eq-id,
eq_id_wf,
equal-wf-T-base,
subtype_rel_self,
subtype_rel_dep_function,
consensus-rel-knowledge-step_wf,
cs-knowledge_wf,
sq_stable__l_member,
subtype_rel-deq,
cs-inning_wf,
consensus-rel-knowledge-inning-step_wf,
consensus-rel-add-knowledge-step_wf,
nil_wf,
cons_wf,
l_member-settype,
int-deq_wf,
fpf-join_wf,
equal-wf-base-T,
cs-knowledge-precondition_wf,
btrue_neq_bfalse,
member-implies-null-eq-bfalse,
null_nil_lemma,
fpf-join-empty,
exists_wf,
equal-wf-base,
fpf-dom_wf,
all_wf,
length_of_cons_lemma,
product_subtype_list,
mk_fpf_ap_lemma,
length_of_nil_lemma,
list-cases,
assert_witness,
l_member-set,
list-subtype,
cons_member,
l_all_wf2,
l_all_iff,
and_wf,
ts-init_wf,
ts-rel_wf,
consensus-ts5_wf,
ts-type_wf,
rel_star_wf,
infix_ap_wf
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[W:\{a:Id| (a \mmember{} A)\} List List]. \mforall{}[v:V].
(\mforall{}[L:\{a:Id| (a \mmember{} A)\} List]
(<\mlambda{}a.ɘ, if a \mmember{}\msubb{} L) then 0 : v else \motimes{} fi >, \mlambda{}a.mk\_fpf(A;\mlambda{}b.ɘ, ff>)>
\mmember{} ts-reachable(consensus-ts5(V;A;W)))) supposing
(two-intersection(A;W) and
1 < ||W||)
Date html generated:
2015_07_17-AM-11_42_51
Last ObjectModification:
2015_07_16-AM-09_47_04
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