Nuprl Lemma : mapfilter-class_wf
∀[Info,A,B:Type]. ∀[P:A ⟶ 𝔹]. ∀[f:A ⟶ B]. ∀[X:EClass(A)]. ((f[v] where v from X such that P[v]) ∈ EClass(B))
Proof
Definitions occuring in Statement :
mapfilter-class: (f[v] where v from X such that P[v]),
eclass: EClass(A[eo; e]),
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mapfilter-class: (f[v] where v from X such that P[v]),
so_apply: x[s],
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[X:EClass(A)].
((f[v] where v from X such that P[v]) \mmember{} EClass(B))
Date html generated:
2016_05_16-PM-10_29_00
Last ObjectModification:
2015_12_29-AM-11_04_44
Theory : event-ordering
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