Nuprl Lemma : message-cmp-zero
∀[f:Name ⟶ Type]. ∀[hdrs:Name List]. ∀[mcmp:hdr:Name ⟶ comparison(f hdr)]. ∀[x,y:{m:Message(f)|
(msg-header(m) ∈ hdrs)} ].
uiff((message-cmp(hdrs;mcmp) x y) = 0 ∈ ℤ;msg-authentic(x) = msg-authentic(y)
∧ (msg-header(x) = msg-header(y) ∈ Name)
∧ ((mcmp msg-header(x) msg-body(x) msg-body(y)) = 0 ∈ ℤ))
Proof
Definitions occuring in Statement :
message-cmp: message-cmp(hdrs;mcmp),
msg-body: msg-body(msg),
msg-header: msg-header(m),
msg-authentic: msg-authentic(m),
Message: Message(f),
name: Name,
comparison: comparison(T),
l_member: (x ∈ l),
list: T List,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
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,
comparison: comparison(T),
all: ∀x:A. B[x],
msg-type: msg-type(msg;f),
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
message-cmp: message-cmp(hdrs;mcmp),
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B,
msg-header: msg-header(m),
pi1: fst(t),
msg-msg: msg-msg(m),
pi2: snd(t),
msg-body-cmp: msg-body-cmp(mcmp),
compare-fun: compare-fun(cmp;f),
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[hdrs:Name List]. \mforall{}[mcmp:hdr:Name {}\mrightarrow{} comparison(f hdr)]. \mforall{}[x,y:\{m:Message(f)|
(msg-header(m)
\mmember{} hdrs)\} ].
uiff((message-cmp(hdrs;mcmp) x y) = 0;msg-authentic(x) = msg-authentic(y)
\mwedge{} (msg-header(x) = msg-header(y))
\mwedge{} ((mcmp msg-header(x) msg-body(x) msg-body(y)) = 0))
Date html generated:
2016_05_17-AM-09_03_37
Last ObjectModification:
2016_01_17-PM-08_34_59
Theory : messages
Home
Index