Nuprl Lemma : rv-orthogonal_wf
∀[rv:InnerProductSpace]. ∀f:Point ⟶ Point. (Orthogonal(f) ∈ ℙ)
Proof
Definitions occuring in Statement :
rv-orthogonal: Orthogonal(f),
inner-product-space: InnerProductSpace,
ss-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
rv-orthogonal: Orthogonal(f),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rv-mul_wf,
real_wf,
rv-ip_wf,
req_wf,
rv-add_wf,
ss-eq_wf,
separation-space_wf,
real-vector-space_wf,
inner-product-space_wf,
subtype_rel_transitivity,
inner-product-space_subtype,
real-vector-space_subtype1,
ss-point_wf,
all_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
dependent_functionElimination,
functionEquality,
functionExtensionality,
because_Cache,
lambdaEquality,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
lambdaFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}f:Point {}\mrightarrow{} Point. (Orthogonal(f) \mmember{} \mBbbP{})
Date html generated:
2016_11_08-AM-09_17_42
Last ObjectModification:
2016_10_31-PM-11_41_41
Theory : inner!product!spaces
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