Nuprl Lemma : es-is-filter-image
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B:Type]. ∀[f:A ⟶ bag(B)]. ∀[X:EClass(A)]. ∀[e:E].
uiff(↑e ∈b f[X];(↑e ∈b X) ∧ (#(f X(e)) = 1 ∈ ℤ))
Proof
Definitions occuring in Statement :
es-filter-image: f[X],
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T,
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
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,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
assert: ↑b,
true: True,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ,
rev_uimplies: rev_uimplies(P;Q),
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(A)]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} f[X];(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\#(f X(e)) = 1))
Date html generated:
2016_05_16-PM-10_27_40
Last ObjectModification:
2016_01_17-PM-07_24_37
Theory : event-ordering
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