Nuprl Lemma : OARcast_lemma1
∀[Info:Type]
∀es:EO+(Info). ∀M:Type. ∀V,S:EClass(Id × Atom1 × Id × ℕ × M). ∀correct:Id ─→ ℙ. ∀f:ℕ. ∀orderers:bag(Id).
∀OARDeliver:EClass(Id × ℕ × M).
(oar-deliver(es;M;V;correct;orderers;f;OARDeliver)
⇒ oar-order(es;M;S;correct;orderers)
⇒ oar-crypto(es;M;V;S;correct)
⇒ oar-failure-model(orderers;f;correct)
⇒ (∀m1,m2:M. Dec(m1 = m2 ∈ M))
⇒ oar-consistency(es;M;correct;OARDeliver))
Proof
Definitions occuring in Statement :
oar-consistency: oar-consistency(es;M;correct;OARDeliver),
oar-failure-model: oar-failure-model(orderers;f;correct),
oar-crypto: oar-crypto(es;M;V;S;correct),
oar-order: oar-order(es;M;S;correct;orderers),
oar-deliver: oar-deliver(es;M;V;correct;orderers;f;OARDeliver),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
nat: ℕ,
atom: Atom$n,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Lemmas :
es-loc_wf,
event-ordering+_subtype,
classrel_wf,
Id_wf,
nat_wf,
es-E_wf,
all_wf,
decidable_wf,
equal_wf,
bag-size_wf,
bag-no-repeats_wf,
not_wf,
exists_wf,
bag_wf,
less_than_wf,
bag-member_wf,
oar-crypto_wf,
oar-order_wf,
oar-deliver_wf,
eclass_wf,
event-ordering+_wf,
l_intersection_wf,
id-deq_wf,
list-subtype-bag,
subtype_rel_self,
bag-no-repeats-list,
no_repeats_filter,
deq-member_wf,
bag-member-list,
decidable__equal_Id,
member-intersection,
l_all_iff,
l_member_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
top_wf,
subtype_top,
es-le_wf,
bag_to_squash_list,
l_all_wf2,
es-locl_wf,
subtract_wf,
decidable__le,
false_wf,
not-le-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
le_wf,
list_wf,
length_wf,
no_repeats_wf,
l_intersection-size,
select_wf,
sq_stable__le,
int_seg_wf,
es-locl-trichotomy,
and_wf
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}M:Type. \mforall{}V,S:EClass(Id \mtimes{} Atom1 \mtimes{} Id \mtimes{} \mBbbN{} \mtimes{} M). \mforall{}correct:Id {}\mrightarrow{} \mBbbP{}. \mforall{}f:\mBbbN{}.
\mforall{}orderers:bag(Id). \mforall{}OARDeliver:EClass(Id \mtimes{} \mBbbN{} \mtimes{} M).
(oar-deliver(es;M;V;correct;orderers;f;OARDeliver)
{}\mRightarrow{} oar-order(es;M;S;correct;orderers)
{}\mRightarrow{} oar-crypto(es;M;V;S;correct)
{}\mRightarrow{} oar-failure-model(orderers;f;correct)
{}\mRightarrow{} (\mforall{}m1,m2:M. Dec(m1 = m2))
{}\mRightarrow{} oar-consistency(es;M;correct;OARDeliver))
Date html generated:
2015_07_23-PM-00_27_28
Last ObjectModification:
2015_01_29-AM-01_33_44
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