∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : Type w} {Φ : CategoryTheory.SmallObject.SuccStruct C}
  [inst_1 : LinearOrder J] [inst_2 : SuccOrder J] [inst_3 : OrderBot J]
  [inst_4 : CategoryTheory.Limits.HasIterationOfShape J C] [inst_5 : WellFoundedLT J] {j : J} (iter : Φ.Iteration j)
  {k l : J} (h : k ≤ l) (h' : l ≤ j), iter.mapObj iter h ⋯ h' ⋯ = iter.F.map (CategoryTheory.homOfLE h)