Nuprl Lemma : sublevelset_wf
∀[I:Interval]. ∀[f:I ⟶ℝ]. ∀[c:ℝ]. (sublevelset(I;f;c) ∈ ℝ ⟶ ℙ)
Proof
Definitions occuring in Statement :
sublevelset: sublevelset(I;f;c),
rfun: I ⟶ℝ,
interval: Interval,
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sublevelset: sublevelset(I;f;c),
prop: ℙ,
and: P ∧ Q,
uimplies: b supposing a
Lemmas referenced :
i-member_wf,
rleq_wf,
r-ap_wf,
real_wf,
rfun_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I:Interval]. \mforall{}[f:I {}\mrightarrow{}\mBbbR{}]. \mforall{}[c:\mBbbR{}]. (sublevelset(I;f;c) \mmember{} \mBbbR{} {}\mrightarrow{} \mBbbP{})
Date html generated:
2016_05_18-AM-08_50_59
Last ObjectModification:
2015_12_27-PM-11_43_20
Theory : reals
Home
Index