Nuprl Lemma : cs-ref-map3-decided
∀[V:Type]
∀L:ts-reachable(consensus-ts3(V)). ∀v:V. ((COMMITED[v] ∈ L) ⇐⇒ cs-ref-map3(L) = Decided[v] ∈ consensus-state2(V))
Proof
Definitions occuring in Statement :
cs-ref-map3: cs-ref-map3(L),
consensus-ts3: consensus-ts3(T),
cs-commited: COMMITED[v],
consensus-state3: consensus-state3(T),
consensus-state2: consensus-state2(T),
cs-decided: Decided[v],
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type,
equal: s = t ∈ T,
ts-reachable: ts-reachable(ts)
Lemmas :
filter_is_empty,
consensus-state3_wf,
cs-is-committed_wf,
null_wf3,
filter_wf5,
l_member_wf,
subtype_rel_list,
top_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
list_wf,
cs-is-considering_wf,
cs-commited_wf,
equal-wf-base-T,
consensus-state2_wf,
cs-decided_wf2,
uiff_wf,
true_wf,
uall_wf,
int_seg_wf,
length_wf,
not_wf,
select_wf,
sq_stable__le,
bnot_wf,
equal_wf,
cs-predecided_wf,
cs-considered-val_wf,
hd_wf,
filter_type,
listp_properties,
assert_of_lt_int,
list-cases,
length_of_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
length_wf_nat,
nat_wf,
decidable__lt,
false_wf,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
lt_int_wf,
cs-committed-val_wf,
nil_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_null,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
lelt_wf,
btrue_wf,
and_wf,
isl_wf,
bfalse_wf,
btrue_neq_bfalse,
squash_wf,
cs-considering_wf,
set_wf,
equal-wf-base,
reduce_hd_cons_lemma,
cons_member,
member_filter,
cs-is-committed-implies,
iff_weakening_equal
\mforall{}[V:Type]
\mforall{}L:ts-reachable(consensus-ts3(V)). \mforall{}v:V. ((COMMITED[v] \mmember{} L) \mLeftarrow{}{}\mRightarrow{} cs-ref-map3(L) = Decided[v])
Date html generated:
2015_07_17-AM-11_24_35
Last ObjectModification:
2015_02_04-PM-05_03_56
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