Nuprl Lemma : m-open_wf
∀[X:Type]. ∀[d:metric(X)]. ∀[A:X ⟶ ℙ]. (m-open(X;d;x.A[x]) ∈ ℙ)
Proof
Definitions occuring in Statement :
m-open: m-open(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-open: m-open(X;d;x.A[x]),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
uimplies: b supposing a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[A:X {}\mrightarrow{} \mBbbP{}]. (m-open(X;d;x.A[x]) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-11_54_17
Last ObjectModification:
2020_01_12-PM-00_44_55
Theory : reals
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