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)
Lemmas :
msg-body_wf2,
Id_wf,
top_wf,
subtype_rel-equal,
msg-type_wf,
iff_weakening_equal,
subtype_rel_transitivity,
assert_wf,
bag-deq-member_wf,
id-deq_wf,
assert-bag-deq-member,
assert_witness,
name_wf,
bag-member_wf,
false_wf,
msg-header_wf
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:
2015_07_21-PM-04_50_11
Last ObjectModification:
2015_02_04-PM-05_08_58
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