Nuprl Lemma : rv-0ip
∀[rv:InnerProductSpace]. ∀[x:Point(rv)]. (0 ⋅ x = r0)
Proof
Definitions occuring in Statement :
rv-ip: x ⋅ y,
inner-product-space: InnerProductSpace,
rv-0: 0,
req: x = y,
int-to-real: r(n),
uall: ∀[x:A]. B[x],
natural_number: $n
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,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rv-ip_wf,
rv-0_wf,
inner-product-space_subtype,
int-to-real_wf,
Error :ss-point_wf,
real-vector-space_subtype1,
subtype_rel_transitivity,
inner-product-space_wf,
real-vector-space_wf,
Error :separation-space_wf,
rv-ip0,
req_functionality,
rv-ip-symmetry,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
natural_numberEquality,
independent_functionElimination,
universeIsType,
instantiate,
independent_isectElimination,
isect_memberEquality_alt,
because_Cache,
isectIsTypeImplies,
inhabitedIsType,
productElimination
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[x:Point(rv)]. (0 \mcdot{} x = r0)
Date html generated:
2020_05_20-PM-01_11_04
Last ObjectModification:
2019_12_09-PM-11_53_19
Theory : inner!product!spaces
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