∀ {X : Type u_1} {Z : Type u_3} [inst : TopologicalSpace X] {C₀ C₁ C₂ : Set X} (h₀ : C₀ ⊆ C₁ ∪ C₂) (h₁ : IsClosed C₁)
  (h₂ : IsClosed C₂) (f₁ : LocallyConstant (↑C₁) Z) (f₂ : LocallyConstant (↑C₂) Z)
  [inst_1 : DecidablePred fun x => x ∈ C₁] (hf : ∀ (x : X) (hx : x ∈ C₁ ∩ C₂), f₁ ⟨x, ⋯⟩ = f₂ ⟨x, ⋯⟩),
  LocallyConstant.piecewise' h₀ h₁ h₂ f₁ f₂ hf =
    LocallyConstant.piecewise ⋯ ⋯ ⋯
      (LocallyConstant.comap { toFun := C₁.restrictPreimage Subtype.val, continuous_toFun := ⋯ } f₁)
      (LocallyConstant.comap { toFun := C₂.restrictPreimage Subtype.val, continuous_toFun := ⋯ } f₂) ⋯