∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (a a_1 : D), (CategoryTheory.Join.right a = CategoryTheory.Join.right a_1) = (a = a_1)