Nuprl Lemma : archive-condition-one-one
∀[V:Type]. ∀[A:Id List]. ∀[t:ℕ+]. ∀[f:(V List) ─→ V]. ∀[L:consensus-rcv(V;A) List]. ∀[n1,n2:ℤ]. ∀[v1,v2:V].
({(n1 = n2 ∈ ℤ) ∧ (v1 = v2 ∈ V)}) supposing
(archive-condition(V;A;t;f;n2;v2;L) and
archive-condition(V;A;t;f;n1;v1;L))
Proof
Definitions occuring in Statement :
archive-condition: archive-condition(V;A;t;f;n;v;L),
consensus-rcv: consensus-rcv(V;A),
Id: Id,
list: T List,
nat_plus: ℕ+,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
and: P ∧ Q,
function: x:A ─→ B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
id-deq_wf,
subtype_rel-deq,
Id_wf,
l_member_wf,
sq_stable__l_member,
decidable__equal_Id,
equal_wf,
set_wf,
length_wf_nat,
nat_wf,
archive-condition_wf,
general-append-cancellation,
cons_wf,
nil_wf,
length-singleton,
length_wf,
length_of_cons_lemma,
length_of_nil_lemma,
hd_wf,
listp_properties,
assert_of_lt_int,
consensus-rcv_wf,
list-cases,
cons_neq_nil,
product_subtype_list,
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,
assert_wf,
lt_int_wf,
reduce_hd_cons_lemma,
tl_wf,
reduce_tl_cons_lemma,
or_wf,
equal-wf-T-base,
cs-initial-rcv_wf,
equal-wf-base,
int_subtype_base,
le_wf,
exists_wf,
cs-rcv-vote_wf,
less_than_wf,
values-for-distinct_wf,
votes-from-inning_wf,
subtract_wf,
null_wf3,
filter_wf5,
rcvd-inning-gt_wf,
subtype_rel_list,
top_wf,
le_weakening2,
nat_plus_subtype_nat,
list_wf,
nat_plus_wf,
filter_nil_lemma,
list_ind_nil_lemma,
null_nil_lemma,
true_wf,
bfalse_wf,
and_wf,
isl_wf,
btrue_wf,
btrue_neq_bfalse,
outl_wf,
not_wf,
null_cons_lemma,
length-map,
filter_cons_lemma,
map_nil_lemma,
remove_repeats_nil_lemma,
remove-repeats_wf,
map_wf,
rcvd-inning-eq_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
map_cons_lemma,
remove_repeats_cons_lemma,
eqff_to_assert,
assert_of_bnot,
append_wf,
vote-crosses-threshold,
squash_wf,
deq_wf,
iff_weakening_equal,
consensus-rcv-crosses-threshold,
list_ind_cons_lemma,
set_subtype_base,
decidable__equal_int,
not-equal-2,
le_antisymmetry_iff,
minus-minus,
add-swap,
le-add-cancel-alt
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[f:(V List) {}\mrightarrow{} V]. \mforall{}[L:consensus-rcv(V;A) List]. \mforall{}[n1,n2:\mBbbZ{}].
\mforall{}[v1,v2:V].
(\{(n1 = n2) \mwedge{} (v1 = v2)\}) supposing
(archive-condition(V;A;t;f;n2;v2;L) and
archive-condition(V;A;t;f;n1;v1;L))
Date html generated:
2015_07_17-AM-11_49_50
Last ObjectModification:
2015_02_04-PM-05_47_46
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