Nuprl Lemma : sq_stable__rv-orthogonal
∀[rv:InnerProductSpace]. ∀f:Point ⟶ Point. SqStable(Orthogonal(f))
Proof
Definitions occuring in Statement :
rv-orthogonal: Orthogonal(f),
inner-product-space: InnerProductSpace,
ss-point: Point,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
function: x:A ⟶ B[x]
Definitions unfolded in proof :
false: False,
not: ¬A,
ss-eq: x ≡ y,
sq_stable: SqStable(P),
implies: P ⇒ Q,
so_apply: x[s],
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
rv-orthogonal: Orthogonal(f)
Lemmas referenced :
squash_wf,
req_witness,
ss-sep_wf,
sq_stable__req,
sq_stable__ss-eq,
sq_stable__all,
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,
sq_stable__and
Rules used in proof :
voidElimination,
independent_pairEquality,
productElimination,
dependent_functionElimination,
functionEquality,
independent_functionElimination,
isect_memberEquality,
functionExtensionality,
productEquality,
because_Cache,
lambdaEquality,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
lambdaFormation,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}f:Point {}\mrightarrow{} Point. SqStable(Orthogonal(f))
Date html generated:
2016_11_08-AM-09_17_45
Last ObjectModification:
2016_11_03-AM-11_49_32
Theory : inner!product!spaces
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