Nuprl Lemma : is-interface-pair
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(Top)]. ∀[e:E]. (e ∈b (X,Y) ~ e ∈b X ∧b e ∈b Y)
Proof
Definitions occuring in Statement :
es-interface-pair: (X,Y),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
band: p ∧b q,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
in-eclass: e ∈b X,
es-interface-pair: (X,Y),
eclass-compose2: eclass-compose2(f;X;Y),
member: t ∈ T,
uall: ∀[x:A]. B[x],
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,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
top: Top,
eq_int: (i =z j),
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(Top)]. \mforall{}[e:E]. (e \mmember{}\msubb{} (X,Y) \msim{} e \mmember{}\msubb{} X \mwedge{}\msubb{} e \mmember{}\msubb{} Y)
Date html generated:
2016_05_17-AM-07_13_05
Last ObjectModification:
2015_12_29-AM-00_03_58
Theory : event-ordering
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