Nuprl Lemma : rv-isometry_wf
∀[rv:InnerProductSpace]. ∀[f:Point ⟶ Point]. (Isometry(f) ∈ ℙ)
Proof
Definitions occuring in Statement :
rv-isometry: Isometry(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 :
so_apply: x[s],
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
rv-isometry: Isometry(f),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rmul_wf,
int-to-real_wf,
rleq_wf,
real_wf,
rv-ip_wf,
rv-sub_wf,
rv-norm_wf,
req_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,
uall_wf
Rules used in proof :
isect_memberEquality,
functionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
natural_numberEquality,
productEquality,
setEquality,
rename,
setElimination,
functionExtensionality,
because_Cache,
lambdaEquality,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[f:Point {}\mrightarrow{} Point]. (Isometry(f) \mmember{} \mBbbP{})
Date html generated:
2016_11_08-AM-09_18_15
Last ObjectModification:
2016_11_02-PM-08_41_39
Theory : inner!product!spaces
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