Nuprl Lemma : es-info-make-Msg-iff
∀[f:Name ⟶ Type]. ∀[es:EO+(Message(f))]. ∀[e:E]. ∀[hdr:Name]. ∀[v:f hdr].
uiff(make-Msg(hdr;v) = info(e) ∈ Message(f);msg-authentic(info(e)) = ff
∧ (header(e) = hdr ∈ Name)
∧ (msg-body(info(e)) = v ∈ (f hdr)))
Proof
Definitions occuring in Statement :
make-Msg: make-Msg(hdr;val),
es-header: header(e),
msg-body: msg-body(msg),
msg-authentic: msg-authentic(m),
Message: Message(f),
es-info: info(e),
event-ordering+: EO+(Info),
es-E: E,
name: Name,
bfalse: ff,
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],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
msg-type: msg-type(msg;f),
es-header: header(e),
make-Msg: make-Msg(hdr;val),
msg-body: msg-body(msg),
msg-header: msg-header(m),
cand: A c∧ B,
Message: Message(f),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
false: False,
msg-authentic: msg-authentic(m),
pi1: fst(t),
rev_implies: P ⇐ Q,
msg-msg: msg-msg(m),
pi2: snd(t),
make-basicMsg: make-basicMsg(hdr;val),
basicMessage: basicMessage(f),
top: Top
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[es:EO+(Message(f))]. \mforall{}[e:E]. \mforall{}[hdr:Name]. \mforall{}[v:f hdr].
uiff(make-Msg(hdr;v) = info(e);msg-authentic(info(e)) = ff
\mwedge{} (header(e) = hdr)
\mwedge{} (msg-body(info(e)) = v))
Date html generated:
2016_05_17-AM-08_58_33
Last ObjectModification:
2016_01_17-PM-08_32_58
Theory : messages
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