Nuprl Lemma : interval-fun-maps-compact
∀I,J:Interval. ∀f:I ⟶ℝ. (interval-fun(I;J;x.f[x]) ⇒ maps-compact(I;J;x.f[x]))
Proof
Definitions occuring in Statement :
interval-fun: interval-fun(I;J;x.f[x]),
maps-compact: maps-compact(I;J;x.f[x]),
rfun: I ⟶ℝ,
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]),
member: t ∈ T,
uall: ∀[x:A]. B[x],
sq_stable: SqStable(P),
squash: ↓T,
interval-fun: interval-fun(I;J;x.f[x]),
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
label: ...$L... t,
rfun: I ⟶ℝ,
so_apply: x[s],
interval: Interval,
rccint: [l, u],
rocint: (l, u],
rcoint: [l, u),
rooint: (l, u),
cand: A c∧ B,
subinterval: I ⊆ J ,
top: Top,
guard: {T},
i-member: r ∈ I,
rev_uimplies: rev_uimplies(P;Q),
rge: x ≥ y,
uiff: uiff(P;Q),
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A,
true: True,
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla)
Latex:
\mforall{}I,J:Interval. \mforall{}f:I {}\mrightarrow{}\mBbbR{}. (interval-fun(I;J;x.f[x]) {}\mRightarrow{} maps-compact(I;J;x.f[x]))
Date html generated:
2020_05_20-PM-00_26_05
Last ObjectModification:
2019_12_05-PM-06_56_32
Theory : reals
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