∀ {R : Type u_1} [inst : Semiring R] {E : Type u_2} {F : Type u_4} {F' : Type u_5} [inst_1 : TopologicalSpace E]
  [inst_2 : AddCommMonoid E] [inst_3 : Module R E] [inst_4 : TopologicalSpace F] [inst_5 : AddCommMonoid F]
  [inst_6 : Module R F] [inst_7 : TopologicalSpace F'] [inst_8 : AddCommMonoid F'] [inst_9 : Module R F']
  {f : E →L[R] F} {g : F ≃L[R] F'}, f.HasLeftInverse → ((↑g).comp f).HasLeftInverse