∀ {α : Type u_1} (E : Type u_2) (𝕜 : Type u_3) [inst : TopologicalSpace α] [inst_1 : DiscreteTopology α]
  [inst_2 : NontriviallyNormedField 𝕜] [inst_3 : NormedAddCommGroup E] [inst_4 : NormedSpace 𝕜 E]
  (f : ↥(lp (fun x => E) ⊤)),
  ‖{ toFun := AddEquiv.lpBCF.toFun, map_add' := ⋯, map_smul' := ⋯, invFun := AddEquiv.lpBCF.invFun, left_inv := ⋯,
          right_inv := ⋯ }
        f‖ =
    ‖f‖