∀ {J : Type w} [inst : CategoryTheory.SmallCategory J] {κ : Cardinal.{w}} [inst_1 : Fact κ.IsRegular] {ι : Type w}
  (D : ι → CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.DiagramWithUniqueTerminal J κ)
  (hι : HasCardinalLT ι κ) {m : J} (u : (i : ι) → (D i).top ⟶ m) (a : J),
  (CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₂ D hι u).P a = ((∃ a_1, (D a_1).P a) ∨ m = a)