Nuprl Lemma : realvec-max-ibs_wf
∀[n:ℕ]. ∀[p:ℝ^n]. (realvec-max-ibs(n;p) ∈ IBS)
Proof
Definitions occuring in Statement :
realvec-max-ibs: realvec-max-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,
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
realvec-max-ibs: realvec-max-ibs(n;p)
Lemmas referenced :
int-to-real_wf,
int_seg_wf,
rless_ibs_wf,
mdist_wf,
real-vec_wf,
max-metric_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
lambdaEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
productElimination,
hypothesis,
universeIsType,
natural_numberEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[p:\mBbbR{}\^{}n]. (realvec-max-ibs(n;p) \mmember{} IBS)
Date html generated:
2019_10_30-AM-10_16_10
Last ObjectModification:
2019_07_03-PM-04_17_29
Theory : real!vectors
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