Theorems · Theorem · functional analysis

Orthonormal.equiv.congr_simp

∀ {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} {E' : Type u_7} [inst_3 : SeminormedAddCommGroup E'] [inst_4 : InnerProductSpace 𝕜 E']
  {v v_1 : Module.Basis ι 𝕜 E} (e_v : v = v_1) (hv : Orthonormal 𝕜 ⇑v) {v' v'_1 : Module.Basis ι' 𝕜 E'}
  (e_v' : v' = v'_1) (hv' : Orthonormal 𝕜 ⇑v') (e e_1 : ι ≃ ι'), e = e_1 → hv.equiv hv' e = ⋯.equiv ⋯ e_1

Defined in

Mathlib.Analysis.InnerProductSpace.Orthonormal

Cited by

0 results in Mathlib

Foundations

Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpaceSeminormedAddCommGroupInnerProductSpace