Nuprl Lemma : is-isometry_wf
∀[rv:InnerProductSpace]. ∀[f:Point ⟶ Point]. (is-isometry(rv;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
is-isometry: is-isometry(rv;f),
inner-product-space: InnerProductSpace,
ss-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
is-isometry: is-isometry(rv;f),
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
all: ∀x:A. B[x],
so_apply: x[s]
Lemmas referenced :
exists_wf,
ss-point_wf,
real-vector-space_subtype1,
inner-product-space_subtype,
subtype_rel_transitivity,
inner-product-space_wf,
real-vector-space_wf,
separation-space_wf,
rv-orthogonal_wf,
all_wf,
ss-eq_wf,
rv-add_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
because_Cache,
lambdaEquality,
productEquality,
dependent_functionElimination,
functionExtensionality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[f:Point {}\mrightarrow{} Point]. (is-isometry(rv;f) \mmember{} \mBbbP{})
Date html generated:
2017_10_04-PM-11_53_56
Last ObjectModification:
2017_03_23-PM-03_53_36
Theory : inner!product!spaces
Home
Index