Nuprl Lemma : member-interface-part
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[g:⋂es:EO+(Info). (E(X) ⟶ Id)]. ∀[es:EO+(Info)]. ∀[e:E(X)]. (e ∈ E((X|g=g e)))
Proof
Definitions occuring in Statement :
es-interface-part: (X|g=i),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
top: Top,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
prop: ℙ,
true: True,
btrue: tt,
ifthenelse: if b then t else f fi ,
assert: ↑b,
guard: {T},
implies: P ⇒ Q,
all: ∀x:A. B[x],
sq_type: SQType(T),
cand: A c∧ B,
uimplies: b supposing a,
rev_uimplies: rev_uimplies(P;Q),
and: P ∧ Q,
uiff: uiff(P;Q),
subtype_rel: A ⊆r B,
es-E-interface: E(X),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[g:\mcap{}es:EO+(Info). (E(X) {}\mrightarrow{} Id)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E(X)].
(e \mmember{} E((X|g=g e)))
Date html generated:
2016_05_17-AM-08_09_32
Last ObjectModification:
2015_12_28-PM-11_13_11
Theory : event-ordering
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