∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {X Y K : C} {f : X ⟶ Y} (i : K ⟶ X)
  (h :
    {A : C} →
      (k : A ⟶ X) → CategoryTheory.CategoryStruct.comp k f = 0 → { l // CategoryTheory.CategoryStruct.comp l i = k })
  [hi : CategoryTheory.Mono i] {A : C} (k : A ⟶ X) (hk : CategoryTheory.CategoryStruct.comp k f = 0) (m : A ⟶ K),
  CategoryTheory.CategoryStruct.comp m i = k → m = (fun {x} k hk => ↑(h k hk)) k hk