∀ {J : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} J] (j₁ j₂ : J)
  (hj₁ : CategoryTheory.ConnectedComponents.objectProperty (Quotient.mk'' j₂) j₁) (l : List J)
  (hf : ∀ a ∈ l, CategoryTheory.Zigzag a j₂),
  ¬(j₁ :: l).length - 1 = 0 →
    ({ obj := j₁, property := ⋯ } :: List.pmap (fun x h => { obj := x, property := ⋯ }) l ⋯).length - 2 <
      (List.pmap (fun x h => { obj := x, property := ⋯ }) l ⋯).length