Nuprl Lemma : rv-norm-sub
∀[rv:InnerProductSpace]. ∀[x,y:Point(rv)]. (||x - y|| = ||y - x||)
Proof
Definitions occuring in Statement :
rv-norm: ||x||,
rv-sub: x - y,
inner-product-space: InnerProductSpace,
req: x = y,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
rv-norm-difference-symmetry,
req_witness,
rv-norm_wf,
rv-sub_wf,
inner-product-space_subtype,
Error :ss-point_wf,
real-vector-space_subtype1,
subtype_rel_transitivity,
inner-product-space_wf,
real-vector-space_wf,
Error :separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
lambdaEquality_alt,
setElimination,
rename,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
because_Cache,
independent_functionElimination,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType,
instantiate,
independent_isectElimination
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[x,y:Point(rv)]. (||x - y|| = ||y - x||)
Date html generated:
2020_05_20-PM-01_11_33
Last ObjectModification:
2019_12_09-PM-11_48_25
Theory : inner!product!spaces
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