Nuprl Lemma : real-vec-norm-nonneg
∀[n:ℕ]. ∀[x:ℝ^n]. (r0 ≤ ||x||)
Proof
Definitions occuring in Statement :
real-vec-norm: ||x||,
real-vec: ℝ^n,
rleq: x ≤ y,
int-to-real: r(n),
nat: ℕ,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-vec-norm: ||x||,
prop: ℙ,
rleq: x ≤ y,
rnonneg: rnonneg(x),
all: ∀x:A. B[x],
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
real: ℝ
Lemmas referenced :
rsqrt_nonneg,
dot-product-nonneg,
dot-product_wf,
rleq_wf,
int-to-real_wf,
less_than'_wf,
rsub_wf,
real-vec-norm_wf,
real_wf,
nat_plus_wf,
real-vec_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
productElimination,
independent_pairEquality,
because_Cache,
applyEquality,
setElimination,
rename,
minusEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x:\mBbbR{}\^{}n]. (r0 \mleq{} ||x||)
Date html generated:
2016_05_18-AM-09_48_39
Last ObjectModification:
2015_12_27-PM-11_11_36
Theory : reals
Home
Index