Nuprl Lemma : base-disjoint-classrel
∀A,B:Type. ∀f:Name ⟶ Type. ∀es:EO+(Message(f)). ∀hdr1,hdr2:Name.
((¬(hdr1 = hdr2 ∈ Name)) ⇒ hdr1 encodes A ⇒ hdr2 encodes B ⇒ disjoint-classrel(es;A;Base(hdr1);B;Base(hdr2)))
Proof
Definitions occuring in Statement :
base-headers-msg-val: Base(hdr),
encodes-msg-type: hdr encodes T,
Message: Message(f),
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
event-ordering+: EO+(Info),
name: Name,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
member: t ∈ T,
uall: ∀[x:A]. B[x],
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
not: ¬A,
false: False,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
name: Name,
sq_type: SQType(T),
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
encodes-msg-type: hdr encodes T
Latex:
\mforall{}A,B:Type. \mforall{}f:Name {}\mrightarrow{} Type. \mforall{}es:EO+(Message(f)). \mforall{}hdr1,hdr2:Name.
((\mneg{}(hdr1 = hdr2))
{}\mRightarrow{} hdr1 encodes A
{}\mRightarrow{} hdr2 encodes B
{}\mRightarrow{} disjoint-classrel(es;A;Base(hdr1);B;Base(hdr2)))
Date html generated:
2016_05_17-AM-09_33_59
Last ObjectModification:
2015_12_29-PM-04_00_16
Theory : classrel!lemmas
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