∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type v} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [CompleteSpace 𝕜] [LocallyCompactSpace 𝕜], IsCompactOperator id ↔ FiniteDimensional 𝕜 E