∀ {C₀ : Type u₀} {C : Type u} [inst : CategoryTheory.Category.{v₀, u₀} C₀] [inst_1 : CategoryTheory.Category.{v, u} C]
  {F : CategoryTheory.Functor C₀ C} {S : C} (self : F.PreOneHypercoverDenseData S) ⦃i₁ i₂ : self.I₀⦄
  (j : self.I₁ i₁ i₂),
  CategoryTheory.CategoryStruct.comp (F.map (self.p₁ j)) (self.f i₁) =
    CategoryTheory.CategoryStruct.comp (F.map (self.p₂ j)) (self.f i₂)