Nuprl Lemma : proper-maps-compact
∀I,J:Interval. ∀f:I ⟶ℝ. (iproper(J) ⇒ maps-compact(I;J;x.f[x]) ⇒ maps-compact-proper(I;J;x.f[x]))
Proof
Definitions occuring in Statement :
maps-compact-proper: maps-compact-proper(I;J;x.f[x]),
maps-compact: maps-compact(I;J;x.f[x]),
rfun: I ⟶ℝ,
iproper: iproper(I),
interval: Interval,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
maps-compact: maps-compact(I;J;x.f[x]),
maps-compact-proper: maps-compact-proper(I;J;x.f[x]),
member: t ∈ T,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
exists: ∃x:A. B[x],
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
so_apply: x[s],
rfun: I ⟶ℝ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
label: ...$L... t,
sq_stable: SqStable(P),
squash: ↓T,
guard: {T}
Latex:
\mforall{}I,J:Interval. \mforall{}f:I {}\mrightarrow{}\mBbbR{}.
(iproper(J) {}\mRightarrow{} maps-compact(I;J;x.f[x]) {}\mRightarrow{} maps-compact-proper(I;J;x.f[x]))
Date html generated:
2020_05_20-PM-00_26_28
Last ObjectModification:
2020_01_08-AM-10_39_24
Theory : reals
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