∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : CompleteSpace E] {F : Type u_3} [inst_4 : NormedAddCommGroup F]
  [inst_5 : NormedSpace 𝕜 F] [inst_6 : CompleteSpace F] (f : E → F) (f' : E →L[𝕜] F) {a : E}
  (hf : HasStrictFDerivAt f f' a) (hf' : (↑f').range = ⊤) (hker : (↑f').ker.ClosedComplemented),
  HasStrictFDerivAt.implicitFunctionDataOfComplemented f f' hf hf' hker =
    { leftFun := f, leftDeriv := f', rightFun := fun x => (Classical.choose hker) (x - a),
      rightDeriv := Classical.choose hker, pt := a, hasStrictFDerivAt_leftFun := hf, hasStrictFDerivAt_rightFun := ⋯,
      range_leftDeriv := hf', range_rightDeriv := ⋯, isCompl_ker := ⋯ }