Nuprl Lemma : real-vec-norm_wf
∀[n:ℕ]. ∀[x:ℝ^n]. (||x|| ∈ ℝ)
Proof
Definitions occuring in Statement :
real-vec-norm: ||x||,
real-vec: ℝ^n,
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-vec-norm: ||x||,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
rsqrt_wf,
dot-product-nonneg,
dot-product_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,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality,
natural_numberEquality,
applyEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x:\mBbbR{}\^{}n]. (||x|| \mmember{} \mBbbR{})
Date html generated:
2016_05_18-AM-09_48_15
Last ObjectModification:
2015_12_27-PM-11_12_00
Theory : reals
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