Nuprl Lemma : archive-condition-innings
∀[V:Type]. ∀[A:Id List]. ∀[t:ℕ+]. ∀[f:(V List) ─→ V]. ∀[L1,L2:consensus-rcv(V;A) List]. ∀[n1,n2:ℤ]. ∀[v1,v2:V].
(n1 < n2) supposing (archive-condition(V;A;t;f;n2;v2;L2) and L1 < L2 and archive-condition(V;A;t;f;n1;v1;L1))
Proof
Definitions occuring in Statement :
archive-condition: archive-condition(V;A;t;f;n;v;L),
consensus-rcv: consensus-rcv(V;A),
Id: Id,
proper-iseg: L1 < L2,
list: T List,
nat_plus: ℕ+,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ─→ B[x],
int: ℤ,
universe: Type
Lemmas :
archive-condition_wf,
nat_plus_subtype_nat,
member-less_than,
proper-iseg_wf,
consensus-rcv_wf,
list_wf,
nat_plus_wf,
Id_wf,
squash_wf,
true_wf,
iff_weakening_equal,
proper-iseg-append-one,
length_wf_nat,
equal_wf,
nat_wf,
iseg_wf,
iseg_nil,
list-cases,
null_nil_lemma,
archive-condition-nil,
product_subtype_list,
null_cons_lemma,
decidable__lt,
member_append,
cons_wf,
nil_wf,
cons_member,
l_member_wf,
iseg_member,
member_filter,
rcvd-inning-gt_wf,
member_null,
filter_wf5,
assert_wf,
subtract_wf,
less_than_transitivity1,
le_weakening,
less_than_irreflexivity,
not_wf,
assert_of_lt_int,
less_than_wf,
condition-implies-le,
add-associates,
minus-one-mul,
add-commutes,
add-swap,
add_functionality_wrt_le,
le-add-cancel-alt,
le_wf,
length_wf,
values-for-distinct_wf,
id-deq_wf,
subtype_rel-deq,
sq_stable__l_member,
decidable__equal_Id,
set_wf,
votes-from-inning_wf,
consensus-rcv-crosses-threshold,
assert_functionality_wrt_uiff,
decidable__equal_int,
false_wf,
not-equal-2,
le-add-cancel,
minus-add,
minus-minus,
zero-add,
subtype_base_sq,
int_subtype_base,
iseg-mapfilter,
rcvd-inning-eq_wf,
rcvd-vote_wf,
remove-repeats_wf,
map_wf,
remove-repeats-l_contains,
iseg-l_contains,
iseg_map,
length-map
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[f:(V List) {}\mrightarrow{} V]. \mforall{}[L1,L2:consensus-rcv(V;A) List]. \mforall{}[n1,n2:\mBbbZ{}].
\mforall{}[v1,v2:V].
(n1 < n2) supposing
(archive-condition(V;A;t;f;n2;v2;L2) and
L1 < L2 and
archive-condition(V;A;t;f;n1;v1;L1))
Date html generated:
2015_07_17-AM-11_50_02
Last ObjectModification:
2015_02_04-PM-05_42_43
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