Nuprl Lemma : cs-ref-map3-ambivalent
∀[V:Type]. ∀[L:ts-reachable(consensus-ts3(V))].
uiff((∀[v:V]. (¬(COMMITED[v] ∈ L))) ∧ (∀[v:V]. (¬(CONSIDERING[v] ∈ L)));cs-ref-map3(L)
= AMBIVALENT
∈ 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-ambivalent: AMBIVALENT,
consensus-state2: consensus-state2(T),
l_member: (x ∈ l),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T,
ts-reachable: ts-reachable(ts)
Lemmas :
uall_wf,
not_wf,
l_member_wf,
consensus-state3_wf,
cs-considering_wf,
cs-commited_wf,
equal-wf-T-base,
ts-reachable_wf,
consensus-ts3_wf,
subtype_rel_wf,
ts-type_wf,
consensus-ts3-invariant1,
cs-ref-map3-decided,
cs-ref-map3-predecided,
consensus-state2_wf,
cs-ref-map3_wf,
filter_is_empty,
cs-is-committed_wf,
null_wf3,
filter_wf5,
subtype_rel_list,
top_wf,
bool_wf,
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,
cs-ambivalent_wf,
uiff_wf,
true_wf,
int_seg_wf,
select_wf,
sq_stable__le,
length_wf,
false_wf,
assert-cs-is-considering,
int_seg_subtype-nat,
less_than_wf,
assert-cs-is-committed,
btrue_wf,
and_wf,
equal_wf,
isl_wf,
bfalse_wf,
btrue_neq_bfalse,
ppcc-problem,
unit_wf2,
iff_weakening_equal
\mforall{}[V:Type]. \mforall{}[L:ts-reachable(consensus-ts3(V))].
uiff((\mforall{}[v:V]. (\mneg{}(COMMITED[v] \mmember{} L))) \mwedge{} (\mforall{}[v:V]. (\mneg{}(CONSIDERING[v] \mmember{} L)));cs-ref-map3(L)
= AMBIVALENT)
Date html generated:
2015_07_17-AM-11_24_59
Last ObjectModification:
2015_02_04-PM-05_01_39
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