Nuprl Lemma : archive-consensus-accum-num
∀[V:Type]. ∀[A:Id List]. ∀[t:ℕ+]. ∀[f:(V List) ─→ V]. ∀[v0:V]. ∀[L:consensus-rcv(V;A) List]. ∀[v:V]. ∀[i:ℤ].
↑(fst(consensus-accum-num-state(t;f;v0;L))) supposing archive-condition(V;A;t;f;i;v;L)
Proof
Definitions occuring in Statement :
consensus-accum-num-state: consensus-accum-num-state(t;f;v0;L),
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+,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
function: x:A ─→ B[x],
int: ℤ,
universe: Type
Lemmas :
nil_wf,
nat_plus_subtype_nat,
archive-condition_wf,
less_than_wf,
not_wf,
list_wf,
list_ind_cons_lemma,
product_subtype_list,
list_ind_nil_lemma,
list-cases,
consensus-rcv_wf,
list_accum_nil_lemma,
id-deq_wf,
subtype_rel-deq,
Id_wf,
l_member_wf,
sq_stable__l_member,
decidable__equal_Id,
equal_wf,
set_wf,
consensus-accum-num-property1,
append_wf,
cons_wf,
consensus-accum-num-property2,
list_accum_append,
subtype_rel_list,
top_wf,
consensus-accum-num-state_wf,
bool_wf,
list_accum_cons_lemma,
isect_wf,
equal-wf-T-base,
votes-from-inning_wf,
subtract_wf,
le_wf,
length_wf,
remove-repeats_wf,
map_wf,
uall_wf,
assert_wf,
eq_int_wf,
equal-wf-base,
int_subtype_base,
length_of_nil_lemma,
zip_nil_lemma,
filter_wf5,
rcvd-inning-gt_wf,
equal-wf-base-T,
null_wf3,
values-for-distinct_wf,
zip_wf,
bnot_wf,
archive-condition-append-init,
and_wf,
pi2_wf,
pi1_wf_top,
subtype_rel_product,
subtype_top,
null_nil_lemma,
btrue_wf,
null_cons_lemma,
bfalse_wf,
btrue_neq_bfalse,
lt_int_wf,
archive-condition-append-vote,
le_int_wf,
length_of_cons_lemma,
zip_cons_cons_lemma,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
assert_of_lt_int,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
assert_of_null,
votes-from-inning-is-nil,
decidable__lt,
false_wf,
condition-implies-le,
add-associates,
minus-add,
minus-minus,
minus-one-mul,
add-swap,
zero-add,
add-commutes,
le_antisymmetry_iff,
less-iff-le,
add_functionality_wrt_le,
le-add-cancel-alt,
le-add-cancel,
le-add-cancel2,
map_nil_lemma,
remove_repeats_nil_lemma,
subtype_base_sq,
decidable__equal_int,
mapfilter-append,
filter_cons_lemma,
filter_nil_lemma,
append-nil,
mul-associates,
map_cons_lemma,
not-equal-2,
length-map,
less_than_transitivity1,
le_weakening,
less_than_irreflexivity,
le_antisymmetry
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[f:(V List) {}\mrightarrow{} V]. \mforall{}[v0:V]. \mforall{}[L:consensus-rcv(V;A) List]. \mforall{}[v:V].
\mforall{}[i:\mBbbZ{}].
\muparrow{}(fst(consensus-accum-num-state(t;f;v0;L))) supposing archive-condition(V;A;t;f;i;v;L)
Date html generated:
2015_07_17-AM-11_51_31
Last ObjectModification:
2015_07_16-AM-09_46_12
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