Nuprl Lemma : r-ap_wf
∀[I:Interval]. ∀[f:I ⟶ℝ]. ∀[x:ℝ]. f(x) ∈ ℝ supposing x ∈ I
Proof
Definitions occuring in Statement :
r-ap: f(x),
rfun: I ⟶ℝ,
i-member: r ∈ I,
interval: Interval,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
r-ap: f(x),
rfun: I ⟶ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
i-member_wf,
real_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
applyEquality,
hypothesisEquality,
dependent_set_memberEquality,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
setEquality
Latex:
\mforall{}[I:Interval]. \mforall{}[f:I {}\mrightarrow{}\mBbbR{}]. \mforall{}[x:\mBbbR{}]. f(x) \mmember{} \mBbbR{} supposing x \mmember{} I
Date html generated:
2016_05_18-AM-08_41_53
Last ObjectModification:
2015_12_27-PM-11_51_30
Theory : reals
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