Nuprl Lemma : member-es-interface-events
∀[Info:Type]. ∀es:EO+(Info). ∀X:EClass(Top). ∀L:E List. ∀e:E(X). ((e ∈ eclass-events(es;X;L)) ⇐⇒ (e ∈ L))
Proof
Definitions occuring in Statement :
eclass-events: eclass-events(es;X;L),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
es-E-interface: E(X),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
eclass-events: eclass-events(es;X;L),
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B,
sq_type: SQType(T),
guard: {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:EClass(Top). \mforall{}L:E List. \mforall{}e:E(X). ((e \mmember{} eclass-events(es;X;L)) \mLeftarrow{}{}\mRightarrow{} (e \mmember{} L))
Date html generated:
2016_05_16-PM-11_01_09
Last ObjectModification:
2015_12_29-AM-10_42_15
Theory : event-ordering
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