Nuprl Lemma : Inorm_wf
∀[I:{I:Interval| icompact(I)} ]. ∀[f:I ⟶ℝ]. ∀[mc:f[x] continuous for x ∈ I]. (||f[x]||_I ∈ ℝ)
Proof
Definitions occuring in Statement :
Inorm: ||f[x]||_I,
continuous: f[x] continuous for x ∈ I,
icompact: icompact(I),
rfun: I ⟶ℝ,
interval: Interval,
real: ℝ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
Inorm: ||f[x]||_I,
prop: ℙ,
so_lambda: λ2x.t[x],
label: ...$L... t,
rfun: I ⟶ℝ,
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
range-sup_wf,
icompact_wf,
rabs_wf,
real_wf,
i-member_wf,
continuous-abs-subtype,
continuous_wf,
rfun_wf,
set_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
setElimination,
thin,
rename,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
dependent_set_memberEquality,
because_Cache,
hypothesis,
hypothesisEquality,
lambdaEquality,
applyEquality,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I:\{I:Interval| icompact(I)\} ]. \mforall{}[f:I {}\mrightarrow{}\mBbbR{}]. \mforall{}[mc:f[x] continuous for x \mmember{} I]. (||f[x]||\_I \mmember{} \mBbbR{})
Date html generated:
2016_05_18-AM-09_17_06
Last ObjectModification:
2015_12_27-PM-11_26_04
Theory : reals
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