Nuprl Lemma : cs-ref-map3-predecided
∀[V:Type]
∀L:ts-reachable(consensus-ts3(V)). ∀v:V.
((∀v':V. (¬(COMMITED[v'] ∈ L))) ∧ (CONSIDERING[v] ∈ L) ⇐⇒ cs-ref-map3(L) = PREDECIDED[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],
cs-considering: CONSIDERING[v],
consensus-state3: consensus-state3(T),
cs-predecided: PREDECIDED[v],
consensus-state2: consensus-state2(T),
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T,
ts-reachable: ts-reachable(ts)
Lemmas :
consensus-ts3-invariant1,
cs-ref-map3-decided,
ts-reachable_wf,
consensus-ts3_wf,
subtype_rel_wf,
ts-type_wf,
all_wf,
not_wf,
l_member_wf,
consensus-state3_wf,
cs-commited_wf,
cs-considering_wf,
equal_wf,
consensus-state2_wf,
cs-ref-map3_wf,
cs-predecided_wf,
filter_is_empty,
cs-is-committed_wf,
null_wf3,
filter_wf5,
subtype_rel_list,
top_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
list_wf,
bnot_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_null,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
cs-is-considering_wf,
uiff_wf,
true_wf,
uall_wf,
int_seg_wf,
select_wf,
sq_stable__le,
length_wf,
lelt_wf,
assert-cs-is-considering,
squash_wf,
false_wf,
filter_type,
set_wf,
list-cases,
nil_wf,
equal-wf-base,
product_subtype_list,
reduce_hd_cons_lemma,
cs-considered-val_wf,
cons_member,
member_filter,
cs-is-considering-implies,
iff_weakening_equal,
assert-cs-is-committed,
int_seg_subtype-nat,
less_than_wf,
btrue_wf,
and_wf,
isl_wf,
bfalse_wf,
btrue_neq_bfalse,
bool_cases,
subtype_base_sq,
bool_subtype_base,
ppcc-problem,
unit_wf2,
outl_wf
\mforall{}[V:Type]
\mforall{}L:ts-reachable(consensus-ts3(V)). \mforall{}v:V.
((\mforall{}v':V. (\mneg{}(COMMITED[v'] \mmember{} L))) \mwedge{} (CONSIDERING[v] \mmember{} L) \mLeftarrow{}{}\mRightarrow{} cs-ref-map3(L) = PREDECIDED[v])
Date html generated:
2015_07_17-AM-11_24_49
Last ObjectModification:
2015_02_04-PM-05_01_50
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