∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : TopologicalSpace M] [inst_1 : TopologicalSpace M₂]
  [inst_2 : Semiring R] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : AddCommMonoid M₂]
  [inst_6 : Module R M₂] (e : M ≃L[R] M₂) (f : M →L[R] M₂), f.inverse = (Ring.inverse ((↑e.symm).comp f)).comp ↑e.symm