Nuprl Lemma : assert-test-msg-header-and-loc
∀[f:Name ⟶ Type]
∀msg:Message(f). ∀hdr:Name. ∀loc:Id.
uiff(↑test-msg-header-and-loc(msg;hdr;loc);(msg-header(msg) = hdr ∈ Name) ∧ (loc = (fst(msg-body(msg))) ∈ Id))
supposing hdr encodes Id × Top
Proof
Definitions occuring in Statement :
test-msg-header-and-loc: test-msg-header-and-loc(msg;hdr;loc),
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,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
all: ∀x:A. B[x],
and: P ∧ Q,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
test-msg-header-and-loc: test-msg-header-and-loc(msg;hdr;loc),
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,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]
\mforall{}msg:Message(f). \mforall{}hdr:Name. \mforall{}loc:Id.
uiff(\muparrow{}test-msg-header-and-loc(msg;hdr;loc);(msg-header(msg) = hdr)
\mwedge{} (loc = (fst(msg-body(msg)))))
supposing hdr encodes Id \mtimes{} Top
Date html generated:
2016_05_17-AM-08_52_34
Last ObjectModification:
2015_12_29-PM-02_55_28
Theory : messages
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