Nuprl Lemma : es-is-interface-map
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:Top]. ∀[e:E].
(e ∈b es-interface-map(f;X) ~ e ∈b X ∧b (#(f X(e) e) =z 1))
Proof
Definitions occuring in Statement :
es-interface-map: es-interface-map(f;X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
band: p ∧b q,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
natural_number: $n,
universe: Type,
sqequal: s ~ t,
bag-size: #(bs)
Definitions unfolded in proof :
eclass-val: X(e),
in-eclass: e ∈b X,
es-interface-map: es-interface-map(f;X),
let: let,
eclass: EClass(A[eo; e]),
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,
nat: ℕ,
ifthenelse: if b then t else f fi ,
band: p ∧b q,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
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{}[f:Top]. \mforall{}[e:E].
(e \mmember{}\msubb{} es-interface-map(f;X) \msim{} e \mmember{}\msubb{} X \mwedge{}\msubb{} (\#(f X(e) e) =\msubz{} 1))
Date html generated:
2016_05_16-PM-10_33_15
Last ObjectModification:
2015_12_29-AM-10_59_32
Theory : event-ordering
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