Theorems · Theorem · functional analysis

Orthonormal.equiv_trans

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {ι : Type u_4} {ι' : Type u_5} {ι'' : Type u_6} {E' : Type u_7} [inst_3 : SeminormedAddCommGroup E']
  [inst_4 : InnerProductSpace 𝕜 E'] {E'' : Type u_8} [inst_5 : SeminormedAddCommGroup E'']
  [inst_6 : InnerProductSpace 𝕜 E''] {v : Module.Basis ι 𝕜 E} (hv : Orthonormal 𝕜 ⇑v) {v' : Module.Basis ι' 𝕜 E'}
  (hv' : Orthonormal 𝕜 ⇑v') (e : ι ≃ ι') {v'' : Module.Basis ι'' 𝕜 E''} (hv'' : Orthonormal 𝕜 ⇑v'') (e' : ι' ≃ ι''),
  (hv.equiv hv' e).trans (hv'.equiv hv'' e') = hv.equiv hv'' (e.trans e')

Defined in

Mathlib.Analysis.InnerProductSpace.Orthonormal

Cited by

0 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpaceSeminormedAddCommGroupInnerProductSpaceSeminormedAddCommGroupInnerProductSpace