Nuprl Lemma : m-open-cover_wf
∀[X:Type]. ∀[d:metric(X)]. ∀[I:Type]. ∀[A:I ⟶ X ⟶ ℙ]. (m-open-cover(X;d;I;i,x.A[i;x]) ∈ ℙ)
Proof
Definitions occuring in Statement :
m-open-cover: m-open-cover(X;d;I;i,x.A[i; x]),
metric: metric(X),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
m-open-cover: m-open-cover(X;d;I;i,x.A[i; x]),
prop: ℙ,
and: P ∧ Q,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
so_apply: x[s],
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[I:Type]. \mforall{}[A:I {}\mrightarrow{} X {}\mrightarrow{} \mBbbP{}]. (m-open-cover(X;d;I;i,x.A[i;x]) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-11_55_52
Last ObjectModification:
2020_01_12-PM-00_44_44
Theory : reals
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