Nuprl Lemma : Message-extensionality
∀[f:Name ⟶ Type]. ∀[m1,m2:Message(f)].
uiff(m1 = m2 ∈ Message(f);msg-authentic(m1) = msg-authentic(m2)
∧ (msg-header(m1) = msg-header(m2) ∈ Name)
∧ (msg-body(m1) = msg-body(m2) ∈ (f msg-header(m1))))
Proof
Definitions occuring in Statement :
msg-body: msg-body(msg),
msg-header: msg-header(m),
msg-authentic: msg-authentic(m),
Message: Message(f),
name: Name,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
prop: ℙ,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
rev_implies: P ⇐ Q,
squash: ↓T,
msg-type: msg-type(msg;f),
Message: Message(f),
basicMessage: basicMessage(f),
msg-body: msg-body(msg),
msg-header: msg-header(m),
msg-msg: msg-msg(m),
pi2: snd(t),
pi1: fst(t),
msg-authentic: msg-authentic(m),
subtype_rel: A ⊆r B
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[m1,m2:Message(f)].
uiff(m1 = m2;msg-authentic(m1) = msg-authentic(m2)
\mwedge{} (msg-header(m1) = msg-header(m2))
\mwedge{} (msg-body(m1) = msg-body(m2)))
Date html generated:
2016_05_17-AM-08_50_46
Last ObjectModification:
2016_01_17-PM-08_35_17
Theory : messages
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