Nuprl Lemma : m-set_wf
∀[X:Type]. ∀[d:metric(X)]. ∀[A:X ⟶ ℙ]. (m-set(X;d;x.A[x]) ∈ ℙ)
Proof
Definitions occuring in Statement :
m-set: m-set(X;d;x.A[x]),
metric: metric(X),
uall: ∀[x:A]. B[x],
prop: ℙ,
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,
m-set: m-set(X;d;x.A[x]),
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s]
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[A:X {}\mrightarrow{} \mBbbP{}]. (m-set(X;d;x.A[x]) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-11_54_55
Last ObjectModification:
2020_01_12-PM-00_29_15
Theory : reals
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