refine ContinuousLinearMap.ext ?_
𝕜 : Type u_1
𝕜' : Type u_2
F : Type u_3
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NontriviallyNormedField 𝕜'
inst✝⁴ : NormedAlgebra 𝕜 𝕜'
inst✝³ : NontriviallyNormedField F
inst✝² : NormedAlgebra 𝕜 F
inst✝¹ : NormedAlgebra 𝕜' F
inst✝ : IsScalarTower 𝕜 𝕜' F
x : 𝕜
g : 𝕜 → 𝕜'
f : 𝕜' → F
g' : 𝕜'
f' : F
hf : HasFDerivAt f (ContinuousLinearMap.smulRight 1 f') (g x)
hg : HasFDerivAt g (ContinuousLinearMap.smulRight 1 g') x
⊢ ContinuousLinearMap.comp (ContinuousLinearMap.restrictScalars 𝕜 (ContinuousLinearMap.smulRight 1 f'))
      (ContinuousLinearMap.smulRight 1 g') =
    ContinuousLinearMap.smulRight 1 (g' • f')
𝕜 : Type u_1
𝕜' : Type u_2
F : Type u_3
inst✝⁶ : NontriviallyNormedField 𝕜
inst✝⁵ : NontriviallyNormedField 𝕜'
inst✝⁴ : NormedAlgebra 𝕜 𝕜'
inst✝³ : NontriviallyNormedField F
inst✝² : NormedAlgebra 𝕜 F
inst✝¹ : NormedAlgebra 𝕜' F
inst✝ : IsScalarTower 𝕜 𝕜' F
x : 𝕜
g : 𝕜 → 𝕜'
f : 𝕜' → F
g' : 𝕜'
f' : F
hf : HasFDerivAt f (ContinuousLinearMap.smulRight 1 f') (g x)
hg : HasFDerivAt g (ContinuousLinearMap.smulRight 1 g') x
⊢ ∀ (x : 𝕜),
    (ContinuousLinearMap.comp (ContinuousLinearMap.restrictScalars 𝕜 (ContinuousLinearMap.smulRight 1 f'))
          (ContinuousLinearMap.smulRight 1 g'))
        x =
      (ContinuousLinearMap.smulRight 1 (g' • f')) x