Nuprl Lemma : interface-cmp-zero
∀[f:Name ⟶ Type]. ∀[locs:Id List]. ∀[hdrs:Name List]. ∀[mcmp:hdr:Name ⟶ comparison(f hdr)].
∀[x,y:Interface(to locs, with hdrs)].
(((interface-cmp(mcmp;locs;hdrs) x y) = 0 ∈ ℤ)
⇒ {(x.delay = y.delay ∈ ℤ)
∧ (x.dst = y.dst ∈ Id)
∧ msg-authentic(x.msg) = msg-authentic(y.msg)
∧ (msg-header(x.msg) = msg-header(y.msg) ∈ Name)
∧ ((mcmp msg-header(x.msg) msg-body(x.msg) msg-body(y.msg)) = 0 ∈ ℤ)})
Proof
Definitions occuring in Statement :
interface-cmp: interface-cmp(mcmp;locs;hdrs),
constrained-msg-interface: Interface(to locs, with hdrs),
msg-interface-delay: mi.delay,
msg-interface-message: mi.msg,
msg-interface-destination: mi.dst,
msg-body: msg-body(msg),
msg-header: msg-header(m),
msg-authentic: msg-authentic(m),
Id: Id,
name: Name,
comparison: comparison(T),
list: T List,
bool: 𝔹,
uall: ∀[x:A]. B[x],
guard: {T},
implies: P ⇒ Q,
and: P ∧ Q,
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],
member: t ∈ T,
implies: P ⇒ Q,
constrained-msg-interface: Interface(to locs, with hdrs),
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
comparison: comparison(T),
all: ∀x:A. B[x],
guard: {T},
interface-cmp: interface-cmp(mcmp;locs;hdrs),
uiff: uiff(P;Q),
int-minus-comparison: int-minus-comparison(f),
compare-fun: compare-fun(cmp;f),
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
or: P ∨ Q,
false: False,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
msg-interface-destination: mi.dst,
pi1: fst(t),
pi2: snd(t)
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[locs:Id List]. \mforall{}[hdrs:Name List]. \mforall{}[mcmp:hdr:Name {}\mrightarrow{} comparison(f hdr)].
\mforall{}[x,y:Interface(to locs, with hdrs)].
(((interface-cmp(mcmp;locs;hdrs) x y) = 0)
{}\mRightarrow{} \{(x.delay = y.delay)
\mwedge{} (x.dst = y.dst)
\mwedge{} msg-authentic(x.msg) = msg-authentic(y.msg)
\mwedge{} (msg-header(x.msg) = msg-header(y.msg))
\mwedge{} ((mcmp msg-header(x.msg) msg-body(x.msg) msg-body(y.msg)) = 0)\})
Date html generated:
2016_05_17-AM-09_03_52
Last ObjectModification:
2016_01_17-PM-08_34_02
Theory : messages
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