Nuprl Lemma : real-ball_wf
∀[n:ℕ]. ∀[r:ℝ]. (B(n;r) ∈ Type)
Proof
Definitions occuring in Statement :
real-ball: B(n;r),
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-ball: B(n;r),
prop: ℙ
Lemmas referenced :
real-vec_wf,
rleq_wf,
real-vec-norm_wf,
real_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
setEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[r:\mBbbR{}]. (B(n;r) \mmember{} Type)
Date html generated:
2019_10_30-AM-10_14_47
Last ObjectModification:
2019_06_28-PM-01_52_09
Theory : real!vectors
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