∀ {ι : Type u_1} {𝕜 : Type u_2} [inst : RCLike 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : InnerProductSpace 𝕜 E] (b₁ b₂ : E ≃ₗᵢ[𝕜] ↥(lp (fun i => 𝕜) 2)),
  (fun b i => b.repr.symm (lp.single 2 i 1)) { repr := b₁ } =
      (fun b i => b.repr.symm (lp.single 2 i 1)) { repr := b₂ } →
    { repr := b₁ } = { repr := b₂ }