Nuprl Lemma : interval-fun-real-fun
∀[a,b:ℝ]. ∀[f:[a, b] ⟶ℝ]. real-fun(f;a;b) supposing ∃J:Interval. interval-fun([a, b];J;x.f[x])
Proof
Definitions occuring in Statement :
interval-fun: interval-fun(I;J;x.f[x]),
real-fun: real-fun(f;a;b),
rfun: I ⟶ℝ,
rccint: [l, u],
interval: Interval,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
exists: ∃x:A. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
exists: ∃x:A. B[x],
interval-fun: interval-fun(I;J;x.f[x]),
and: P ∧ Q,
real-fun: real-fun(f;a;b),
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s],
prop: ℙ,
rfun: I ⟶ℝ,
so_lambda: λ2x.t[x],
label: ...$L... t
Latex:
\mforall{}[a,b:\mBbbR{}]. \mforall{}[f:[a, b] {}\mrightarrow{}\mBbbR{}]. real-fun(f;a;b) supposing \mexists{}J:Interval. interval-fun([a, b];J;x.f[x])
Date html generated:
2020_05_20-PM-00_25_35
Last ObjectModification:
2019_12_05-PM-05_52_26
Theory : reals
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