∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {W : CategoryTheory.MorphismProperty C} {J : Type w}
  [inst_1 : LinearOrder J] [inst_2 : SuccOrder J] [inst_3 : OrderBot J] [inst_4 : WellFoundedLT J] {X Y : C} {f : X ⟶ Y}
  (toTransfiniteCompositionOfShape : CategoryTheory.TransfiniteCompositionOfShape J f)
  (map_mem : ∀ (j : J), ¬IsMax j → W (toTransfiniteCompositionOfShape.F.map (CategoryTheory.homOfLE ⋯)))
  (toTransfiniteCompositionOfShape_1 : CategoryTheory.TransfiniteCompositionOfShape J f)
  (map_mem_1 : ∀ (j : J), ¬IsMax j → W (toTransfiniteCompositionOfShape_1.F.map (CategoryTheory.homOfLE ⋯))),
  ({ toTransfiniteCompositionOfShape := toTransfiniteCompositionOfShape, map_mem := map_mem } =
      { toTransfiniteCompositionOfShape := toTransfiniteCompositionOfShape_1, map_mem := map_mem_1 }) =
    (toTransfiniteCompositionOfShape = toTransfiniteCompositionOfShape_1)