Nuprl Lemma : rv-isometry-id
∀[rv:InnerProductSpace]. Isometry(λx.x)
Proof
Definitions occuring in Statement :
rv-isometry: Isometry(f),
inner-product-space: InnerProductSpace,
uall: ∀[x:A]. B[x],
lambda: λx.A[x]
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
rv-isometry: Isometry(f),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
req_weakening,
separation-space_wf,
real-vector-space_wf,
inner-product-space_wf,
subtype_rel_transitivity,
real-vector-space_subtype1,
ss-point_wf,
rv-ip_wf,
rmul_wf,
req_wf,
int-to-real_wf,
rleq_wf,
real_wf,
inner-product-space_subtype,
rv-sub_wf,
rv-norm_wf,
req_witness
Rules used in proof :
independent_isectElimination,
instantiate,
independent_functionElimination,
natural_numberEquality,
productEquality,
setEquality,
rename,
setElimination,
lambdaEquality,
because_Cache,
hypothesis,
applyEquality,
extract_by_obid,
hypothesisEquality,
thin,
isectElimination,
isect_memberEquality,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[rv:InnerProductSpace]. Isometry(\mlambda{}x.x)
Date html generated:
2016_11_08-AM-09_20_35
Last ObjectModification:
2016_11_02-PM-11_44_33
Theory : inner!product!spaces
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