Nuprl Lemma : real-vec-dist_wf
∀[n:ℕ]. ∀[x,y:ℝ^n]. (d(x;y) ∈ {d:ℝ| r0 ≤ d} )
Proof
Definitions occuring in Statement :
real-vec-dist: d(x;y),
real-vec: ℝ^n,
rleq: x ≤ y,
int-to-real: r(n),
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-vec-dist: d(x;y),
prop: ℙ
Lemmas referenced :
real-vec-norm-nonneg,
real-vec-sub_wf,
real-vec-norm_wf,
rleq_wf,
int-to-real_wf,
real-vec_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x,y:\mBbbR{}\^{}n]. (d(x;y) \mmember{} \{d:\mBbbR{}| r0 \mleq{} d\} )
Date html generated:
2016_10_26-AM-10_24_37
Last ObjectModification:
2016_09_14-PM-06_28_59
Theory : reals
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