Nuprl Lemma : Message-eta
∀[f:Name ⟶ Type]. ∀[m:Message(f)].
(m
= if msg-authentic(m) then make-Authentic-Msg(msg-header(m);msg-body(m)) else make-Msg(msg-header(m);msg-body(m)) fi
∈ Message(f))
Proof
Definitions occuring in Statement :
make-Authentic-Msg: make-Authentic-Msg(hdr;val),
make-Msg: make-Msg(hdr;val),
msg-body: msg-body(msg),
msg-header: msg-header(m),
msg-authentic: msg-authentic(m),
Message: Message(f),
name: Name,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
Message: Message(f),
basicMessage: basicMessage(f),
make-Msg: make-Msg(hdr;val),
make-Authentic-Msg: make-Authentic-Msg(hdr;val),
msg-body: msg-body(msg),
msg-header: msg-header(m),
msg-authentic: msg-authentic(m),
pi1: fst(t),
msg-msg: msg-msg(m),
pi2: snd(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
make-basicMsg: make-basicMsg(hdr;val),
subtype_rel: A ⊆r B,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[m:Message(f)].
(m
= if msg-authentic(m)
then make-Authentic-Msg(msg-header(m);msg-body(m))
else make-Msg(msg-header(m);msg-body(m))
fi )
Date html generated:
2016_05_17-AM-08_58_12
Last ObjectModification:
2015_12_29-PM-02_52_17
Theory : messages
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