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)
Definitions unfolded in proof :
oar-consistency: oar-consistency(es;M;correct;OARDeliver),
oar-failure-model: oar-failure-model(orderers;f;correct),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
oar-deliver: oar-deliver(es;M;V;correct;orderers;f;OARDeliver),
guard: {T},
exists: ∃x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
not: ¬A,
uimplies: b supposing a,
cand: A c∧ B,
bag-size: #(bs),
uiff: uiff(P;Q),
l_intersection: l_intersection(eq;L1;L2),
iff: P ⇐⇒ Q,
top: Top,
es-E-interface: E(X),
false: False,
squash: ↓T,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
l_contains: A ⊆ B,
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
oar-crypto: oar-crypto(es;M;V;S;correct),
oar-order: oar-order(es;M;S;correct;orderers)
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:
2016_05_17-PM-00_56_06
Last ObjectModification:
2016_01_18-AM-07_43_56
Theory : event-logic-applications
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