∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f f₁ : 𝕜 → F} {f' : F} {x : 𝕜} {s t : Set 𝕜},
  HasDerivWithinAt f f' s x → (∀ x ∈ t, f₁ x = f x) → f₁ x = f x → t ⊆ s → HasDerivWithinAt f₁ f' t x