Nuprl Lemma : realvec-ibs_wf
∀[n:ℕ]. ∀[p:ℝ^n]. (realvec-ibs(n;p) ∈ IBS)
Proof
Definitions occuring in Statement :
realvec-ibs: realvec-ibs(n;p),
incr-binary-seq: IBS,
real-vec: ℝ^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
realvec-ibs: realvec-ibs(n;p)
Lemmas referenced :
rless_ibs_wf,
int-to-real_wf,
real-vec-norm_wf,
real-vec_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[p:\mBbbR{}\^{}n]. (realvec-ibs(n;p) \mmember{} IBS)
Date html generated:
2019_10_30-AM-10_16_03
Last ObjectModification:
2019_06_28-PM-01_55_49
Theory : real!vectors
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