Nuprl Lemma : hdf-ap-only-headers2
∀[f:Name ⟶ Type]
∀hdrs:Name List. ∀X:{X:msg-interface-hdf(f)| hdf-only-headers(f;hdrs;X)} . ∀m:Message(f). ∀mi:Interface.
(mi ↓∈ snd(X(m)) ⇒ (msg-header(mi.msg) ∈ hdrs))
Proof
Definitions occuring in Statement :
hdf-only-headers: hdf-only-headers(f;hdrs;X),
msg-interface-hdf: msg-interface-hdf(f),
msg-interface-message: mi.msg,
msg-interface: Interface,
msg-header: msg-header(m),
Message: Message(f),
hdf-ap: X(a),
name: Name,
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
pi2: snd(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type,
bag-member: x ↓∈ bs
Definitions unfolded in proof :
msg-interface-hdf: msg-interface-hdf(f),
hdf-only-headers: hdf-only-headers(f;hdrs;X),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
msg-interface: Interface,
so_apply: x[s],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
false: False,
subtype_rel: A ⊆r B,
guard: {T}
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]
\mforall{}hdrs:Name List. \mforall{}X:\{X:msg-interface-hdf(f)| hdf-only-headers(f;hdrs;X)\} . \mforall{}m:Message(f).
\mforall{}mi:Interface.
(mi \mdownarrow{}\mmember{} snd(X(m)) {}\mRightarrow{} (msg-header(mi.msg) \mmember{} hdrs))
Date html generated:
2016_05_17-AM-09_02_39
Last ObjectModification:
2015_12_29-PM-02_50_30
Theory : messages
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