Nuprl Lemma : real-vec-norm_functionality
∀[n:ℕ]. ∀[x,y:ℝ^n]. ||x|| = ||y|| supposing req-vec(n;x;y)
Proof
Definitions occuring in Statement :
real-vec-norm: ||x||,
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
req: x = y,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
real-vec-norm: ||x||,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
real-vec-norm_wf,
req-vec_wf,
real-vec_wf,
nat_wf,
dot-product_functionality,
rsqrt_wf,
dot-product-nonneg,
dot-product_wf,
rleq_wf,
int-to-real_wf,
req_weakening,
req_functionality,
rsqrt_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
dependent_set_memberEquality,
natural_numberEquality,
applyEquality,
productElimination
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x,y:\mBbbR{}\^{}n]. ||x|| = ||y|| supposing req-vec(n;x;y)
Date html generated:
2016_05_18-AM-09_48_28
Last ObjectModification:
2015_12_27-PM-11_12_17
Theory : reals
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