∀ {R : Type u_2} [inst : Ring R] {R₂ : Type u_3} [inst_1 : Ring R₂] {M : Type u_1} [inst_2 : TopologicalSpace M]
  [inst_3 : AddCommGroup M] {M₂ : Type u_4} [inst_4 : TopologicalSpace M₂] [inst_5 : AddCommGroup M₂]
  [inst_6 : Module R M] [inst_7 : Module R₂ M₂] {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} [inst_8 : RingHomInvPair σ₁₂ σ₂₁]
  [inst_9 : IsTopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂) (f₂ : M₂ →SL[σ₂₁] M),
  Function.RightInverse ⇑f₂ ⇑f₁ → ∀ (x : M), (ContinuousLinearMap.id R M - f₂.comp f₁) x ∈ (↑f₁).ker