{X : Type u_1} →
  {Z : Type u_3} →
    [inst : TopologicalSpace X] →
      {C₁ C₂ : Set X} →
        IsClosed C₁ →
          IsClosed C₂ →
            C₁ ∪ C₂ = Set.univ →
              (f : LocallyConstant (↑C₁) Z) →
                (g : LocallyConstant (↑C₂) Z) →
                  (∀ (x : X) (hx : x ∈ C₁ ∩ C₂), f ⟨x, ⋯⟩ = g ⟨x, ⋯⟩) →
                    [DecidablePred fun x => x ∈ C₁] → LocallyConstant X Z