Nuprl Lemma : es-E-interface_functionality-iff
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(Top)]. uiff(E(X) ⊆r E(Y);{∀[e:E]. ↑e ∈b Y supposing ↑e ∈b X})
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uiff: uiff(P;Q),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
guard: {T},
universe: Type
Definitions unfolded in proof :
guard: {T},
es-E-interface: E(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
sq_type: SQType(T),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(Top)].
uiff(E(X) \msubseteq{}r E(Y);\{\mforall{}[e:E]. \muparrow{}e \mmember{}\msubb{} Y supposing \muparrow{}e \mmember{}\msubb{} X\})
Date html generated:
2016_05_16-PM-02_51_37
Last ObjectModification:
2015_12_29-AM-11_21_42
Theory : event-ordering
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