Nuprl Lemma : es-filter-image-val2
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[f:A ⟶ bag(Top)]. ∀[X:EClass(A)]. ∀[e:E].
f[X](e) ~ only(f X(e)) supposing ↑e ∈b f[X]
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,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
sqequal: s ~ t,
bag-only: only(bs),
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[f:A {}\mrightarrow{} bag(Top)]. \mforall{}[X:EClass(A)]. \mforall{}[e:E].
f[X](e) \msim{} only(f X(e)) supposing \muparrow{}e \mmember{}\msubb{} f[X]
Date html generated:
2016_05_16-PM-10_28_20
Last ObjectModification:
2015_12_29-AM-11_05_14
Theory : event-ordering
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