Nuprl Lemma : consensus-rcv-crosses-size
∀[V:Type]. ∀[A:Id List]. ∀[t:ℕ+]. ∀[n:ℤ]. ∀[L:consensus-rcv(V;A) List]. ∀[r:consensus-rcv(V;A)].
(||remove-repeats(IdDeq;map(λp.(fst(p));votes-from-inning(n;L @ [r])))|| = ((2 * t) + 1) ∈ ℤ) supposing
((((2 * t) + 1) ≤ ||values-for-distinct(IdDeq;votes-from-inning(n;L @ [r]))||) and
(||values-for-distinct(IdDeq;votes-from-inning(n;L))|| ≤ (2 * t)))
Proof
Definitions occuring in Statement :
votes-from-inning: votes-from-inning(i;L),
consensus-rcv: consensus-rcv(V;A),
id-deq: IdDeq,
Id: Id,
values-for-distinct: values-for-distinct(eq;L),
remove-repeats: remove-repeats(eq;L),
map: map(f;as),
length: ||as||,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
nat_plus: ℕ+,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
le: A ≤ B,
lambda: λx.A[x],
multiply: n * m,
add: n + m,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
length-map,
remove-repeats_wf,
map_wf,
mapfilter-append,
map_append_sq,
le_wf,
length_wf,
values-for-distinct_wf,
Id_wf,
l_member_wf,
id-deq_wf,
subtype_rel-deq,
sq_stable__l_member,
decidable__equal_Id,
equal_wf,
set_wf,
votes-from-inning_wf,
append_wf,
consensus-rcv_wf,
cons_wf,
nil_wf,
list_wf,
nat_plus_wf,
filter_cons_lemma,
filter_nil_lemma,
map_nil_lemma,
subtype_rel_list,
top_wf,
condition-implies-le,
minus-add,
minus-one-mul,
mul-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-associates,
le-add-cancel,
eq_int_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
equal-wf-base-T,
int_subtype_base,
map_cons_lemma,
bnot_wf,
not_wf,
append-nil,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
remove-repeats-append-one
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[n:\mBbbZ{}]. \mforall{}[L:consensus-rcv(V;A) List]. \mforall{}[r:consensus-rcv(V;A)].
(||remove-repeats(IdDeq;map(\mlambda{}p.(fst(p));votes-from-inning(n;L @ [r])))||
= ((2 * t) + 1)) supposing
((((2 * t) + 1) \mleq{} ||values-for-distinct(IdDeq;votes-from-inning(n;L @ [r]))||) and
(||values-for-distinct(IdDeq;votes-from-inning(n;L))|| \mleq{} (2 * t)))
Date html generated:
2015_07_17-AM-11_49_37
Last ObjectModification:
2015_01_28-AM-00_43_44
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