∀ {X : TopCat} (p₀ : ↑X) [inst : (U : TopologicalSpace.Opens ↑X) → Decidable (p₀ ∈ U)] {C : Type u_1}
  [inst_1 : CategoryTheory.Category.{u_3, u_1} C] [inst_2 : CategoryTheory.Limits.HasTerminal C] {a : C}
  (U : (TopologicalSpace.Opens ↑X)ᵒᵖ), p₀ ∈ Opposite.unop U → (if p₀ ∈ Opposite.unop U then a else ⊤_ C) = a