Nuprl Lemma : rv-ip-sub
∀[rv:InnerProductSpace]. ∀[x,y,z:Point]. (x - y ⋅ z = (x ⋅ z - y ⋅ z))
Proof
Definitions occuring in Statement :
rv-sub: x - y,
rv-ip: x ⋅ y,
inner-product-space: InnerProductSpace,
ss-point: Point,
rsub: x - y,
req: x = y,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
rev_uimplies: rev_uimplies(P;Q),
and: P ∧ Q,
uiff: uiff(P;Q),
rsub: x - y,
uimplies: b supposing a,
guard: {T},
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
rv-sub: x - y,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rv-ip-minus,
radd_functionality,
rv-ip-add,
req_transitivity,
req_functionality,
req_weakening,
rminus_wf,
radd_wf,
rv-minus_wf,
rv-add_wf,
separation-space_wf,
real-vector-space_wf,
inner-product-space_wf,
subtype_rel_transitivity,
real-vector-space_subtype1,
ss-point_wf,
rsub_wf,
inner-product-space_subtype,
rv-sub_wf,
rv-ip_wf,
req_witness
Rules used in proof :
productElimination,
because_Cache,
isect_memberEquality,
independent_isectElimination,
instantiate,
independent_functionElimination,
sqequalRule,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[x,y,z:Point]. (x - y \mcdot{} z = (x \mcdot{} z - y \mcdot{} z))
Date html generated:
2016_11_08-AM-09_15_37
Last ObjectModification:
2016_10_31-PM-03_28_54
Theory : inner!product!spaces
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