Nuprl Lemma : consensus-accum-num-property2
∀[V:Type]
∀A:Id List. ∀t:ℕ+. ∀f:(V List) ─→ V. ∀v0:V. ∀L:consensus-rcv(V;A) List.
let b,i,as,vs,v = consensus-accum-num-state(t;f;v0;L) in
(((2 * t) + 1) ≤ ||remove-repeats(IdDeq;map(λp.(fst(p));votes-from-inning(i - 2;L)))||) supposing
((votes-from-inning(i - 1;L) = [] ∈ (({b:Id| (b ∈ A)} × V) List)) and
1 < i)
Proof
Definitions occuring in Statement :
consensus-accum-num-state: consensus-accum-num-state(t;f;v0;L),
votes-from-inning: votes-from-inning(i;L),
consensus-rcv: consensus-rcv(V;A),
id-deq: IdDeq,
Id: Id,
remove-repeats: remove-repeats(eq;L),
l_member: (x ∈ l),
map: map(f;as),
length: ||as||,
nil: [],
list: T List,
nat_plus: ℕ+,
less_than: a < b,
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e],
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
le: A ≤ B,
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
lambda: λx.A[x],
function: x:A ─→ B[x],
product: x:A × B[x],
multiply: n * m,
subtract: n - m,
add: n + m,
natural_number: $n,
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,
last_induction,
consensus-rcv_wf,
consensus-accum-num-state_wf,
nat_plus_subtype_nat,
bool_wf,
list_wf,
isect_wf,
less_than_wf,
equal-wf-T-base,
votes-from-inning_wf,
subtract_wf,
le_wf,
length_wf,
remove-repeats_wf,
map_wf,
mapfilter_nil_lemma,
map_nil_lemma,
remove_repeats_nil_lemma,
length_of_nil_lemma,
list_accum_append,
subtype_rel_list,
top_wf,
list_accum_cons_lemma,
list_accum_nil_lemma,
nat_plus_wf,
eq_int_wf,
equal-wf-base,
int_subtype_base,
assert_wf,
bnot_wf,
not_wf,
mapfilter-append,
append_is_nil,
append_wf,
cons_wf,
cs-initial-rcv_wf,
nil_wf,
lt_int_wf,
cs-rcv-vote_wf,
le_int_wf,
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,
map_append_sq,
remove-repeats-append-sq,
length-append,
non_neg_length,
length_wf_nat,
filter_wf5,
deq-member_wf,
filter_cons_lemma,
filter_nil_lemma,
map_cons_lemma,
null_nil_lemma,
btrue_wf,
and_wf,
null_wf3,
null_cons_lemma,
bfalse_wf,
btrue_neq_bfalse,
not-equal-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-mul-special,
zero-mul,
add-zero,
add-associates,
minus-minus,
add-commutes,
le-add-cancel,
bool_cases,
subtype_base_sq,
bool_subtype_base,
consensus-accum-num-property1,
rcvd-inning-gt_wf,
zip_wf,
values-for-distinct_wf,
unzip_zip,
list_subtype_base,
set_subtype_base,
atom2_subtype_base,
equal-wf-base-T,
le_weakening,
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.
let b,i,as,vs,v = consensus-accum-num-state(t;f;v0;L) in
(((2 * t) + 1) \mleq{} ||remove-repeats(IdDeq;map(\mlambda{}p.(fst(p));votes-from-inning(i
- 2;L)))||) supposing
((votes-from-inning(i - 1;L) = []) and
1 < i)
Date html generated:
2015_07_17-AM-11_50_46
Last ObjectModification:
2015_01_28-AM-00_47_02
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