Nuprl Lemma : archive-condition-append-init
∀[V:Type]
∀A:Id List. ∀t:ℕ. ∀f:(V List) ─→ V. ∀L:consensus-rcv(V;A) List. ∀n:ℤ. ∀v,v2:V.
(archive-condition(V;A;t;f;n;v;L @ [Init[v2]])
⇐⇒ {(L = [] ∈ (consensus-rcv(V;A) List)) ∧ (n = 0 ∈ ℤ) ∧ (v2 = v ∈ V)})
Proof
Definitions occuring in Statement :
archive-condition: archive-condition(V;A;t;f;n;v;L),
cs-initial-rcv: Init[v],
consensus-rcv: consensus-rcv(V;A),
Id: Id,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
guard: {T},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
exists_wf,
list_wf,
consensus-rcv_wf,
append_wf,
cons_wf,
cs-initial-rcv_wf,
nil_wf,
length_wf,
length-append,
or_wf,
equal-wf-T-base,
length_of_nil_lemma,
equal-wf-base,
int_subtype_base,
le_wf,
Id_wf,
l_member_wf,
equal_wf,
cs-rcv-vote_wf,
less_than_wf,
values-for-distinct_wf,
id-deq_wf,
subtype_rel-deq,
sq_stable__l_member,
decidable__equal_Id,
set_wf,
votes-from-inning_wf,
subtract_wf,
assert_wf,
null_wf3,
filter_wf5,
rcvd-inning-gt_wf,
subtype_rel_list,
top_wf,
nat_wf,
general-append-cancellation,
length_of_cons_lemma,
hd_wf,
listp_properties,
assert_of_lt_int,
list-cases,
cons_neq_nil,
product_subtype_list,
length_wf_nat,
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,
lt_int_wf,
reduce_hd_cons_lemma,
tl_wf,
reduce_tl_cons_lemma,
and_wf,
outl_wf,
isl_wf,
bfalse_wf,
btrue_wf,
btrue_neq_bfalse,
mul-associates,
add-swap,
le_antisymmetry_iff,
mapfilter-append,
append-nil,
filter_cons_lemma,
filter_nil_lemma,
map_nil_lemma,
squash_wf,
true_wf,
le_weakening2,
list_ind_nil_lemma
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}t:\mBbbN{}. \mforall{}f:(V List) {}\mrightarrow{} V. \mforall{}L:consensus-rcv(V;A) List. \mforall{}n:\mBbbZ{}. \mforall{}v,v2:V.
(archive-condition(V;A;t;f;n;v;L @ [Init[v2]]) \mLeftarrow{}{}\mRightarrow{} \{(L = []) \mwedge{} (n = 0) \mwedge{} (v2 = v)\})
Date html generated:
2015_07_17-AM-11_48_27
Last ObjectModification:
2015_01_28-AM-00_45_54
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