Nuprl Lemma : assert-has-header-and-in-locs
∀[f:Name ⟶ Type]
∀msg:Message(f). ∀hdr:Name. ∀locs:bag(Id).
↑has-header-and-in-locs(msg;hdr;locs) ⇐⇒ (msg-header(msg) = hdr ∈ Name) ∧ fst(msg-body(msg)) ↓∈ locs
supposing hdr encodes Id × Top
Proof
Definitions occuring in Statement :
has-header-and-in-locs: has-header-and-in-locs(msg;hdr;locs),
encodes-msg-type: hdr encodes T,
msg-body: msg-body(msg),
msg-header: msg-header(m),
Message: Message(f),
Id: Id,
name: Name,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T,
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
has-header-and-in-locs: has-header-and-in-locs(msg;hdr;locs),
member: t ∈ T,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
encodes-msg-type: hdr encodes T,
msg-type: msg-type(msg;f),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bag-member: x ↓∈ bs,
squash: ↓T,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]
\mforall{}msg:Message(f). \mforall{}hdr:Name. \mforall{}locs:bag(Id).
\muparrow{}has-header-and-in-locs(msg;hdr;locs) \mLeftarrow{}{}\mRightarrow{} (msg-header(msg) = hdr) \mwedge{} fst(msg-body(msg)) \mdownarrow{}\mmember{} locs
supposing hdr encodes Id \mtimes{} Top
Date html generated:
2016_05_17-AM-08_53_05
Last ObjectModification:
2016_01_17-PM-08_35_27
Theory : messages
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