∀ (S : CategoryTheory.Functor Type u_1ᵒᵖ (Type u_1)) (α : Type u_1) (f : α → S.obj (Opposite.op PUnit.{u_1 + 1}))
  (β γ δ : Type u_1) (g₁ : δ ⟶ β) (g₂ : δ ⟶ γ) (f₁ : β ⟶ α) (f₂ : γ ⟶ α) (hf₁ : CategoryTheory.discretePresieve α f₁)
  (hf₂ : CategoryTheory.discretePresieve α f₂),
  CategoryTheory.CategoryStruct.comp g₁ f₁ = CategoryTheory.CategoryStruct.comp g₂ f₂ →
    ∀ (ε : Type u_1) (g : ε ⟶ δ) (x : ε),
      S.map g.op
          (S.map g₁.op
            ((fun x g hg => S.map (CategoryTheory.asHom fun x => PUnit.unit).op (f (g (Classical.choose hg)))) β f₁
              hf₁)) =
        S.map g.op
          (S.map g₂.op
            ((fun x g hg => S.map (CategoryTheory.asHom fun x => PUnit.unit).op (f (g (Classical.choose hg)))) γ f₂
              hf₂))