Nuprl Lemma : m-open-set
∀[X:Type]. ∀[d:metric(X)]. ∀[A:X ⟶ ℙ]. (m-open(X;d;x.A[x]) ⇒ m-set(X;d;x.A[x]))
Proof
Definitions occuring in Statement :
m-set: m-set(X;d;x.A[x]),
m-open: m-open(X;d;x.A[x]),
metric: metric(X),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
m-open: m-open(X;d;x.A[x]),
m-set: m-set(X;d;x.A[x]),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
exists: ∃x:A. B[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
nat_plus: ℕ+,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
uiff: uiff(P;Q),
decidable: Dec(P),
or: P ∨ Q,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[A:X {}\mrightarrow{} \mBbbP{}]. (m-open(X;d;x.A[x]) {}\mRightarrow{} m-set(X;d;x.A[x]))
Date html generated:
2020_05_20-AM-11_55_13
Last ObjectModification:
2020_01_12-PM-00_36_38
Theory : reals
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