Nuprl Lemma : is-interface-at
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[i:Id]. ∀[e:E]. uiff(↑e ∈b X@i;(loc(e) = i ∈ Id) ∧ (↑e ∈b X))
Proof
Definitions occuring in Statement :
es-interface-at: X@i,
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
top: Top,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
in-eclass: e ∈b X,
es-interface-at: X@i,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
eclass: EClass(A[eo; e]),
nat: ℕ,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
eq_int: (i =z j),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[i:Id]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} X@i;(loc(e) = i) \mwedge{} (\muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2016_05_16-PM-10_54_30
Last ObjectModification:
2015_12_29-AM-10_44_34
Theory : event-ordering
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