∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {f g : CategoryTheory.ComposableArrows C 5}
  (app₀ : f.obj' 0 _proof_441✝ ≅ g.obj' 0 _proof_441✝¹) (app₁ : f.obj' 1 _proof_442✝ ≅ g.obj' 1 _proof_442✝¹)
  (app₂ : f.obj' 2 _proof_443✝ ≅ g.obj' 2 _proof_443✝¹) (app₃ : f.obj' 3 _proof_444✝ ≅ g.obj' 3 _proof_444✝¹)
  (app₄ : f.obj' 4 _proof_445✝ ≅ g.obj' 4 _proof_445✝¹) (app₅ : f.obj' 5 _proof_446✝ ≅ g.obj' 5 _proof_446✝¹)
  (w₀ :
    CategoryTheory.CategoryStruct.comp (f.map' 0 1 CategoryTheory.ComposableArrows.homMk₁._proof_4 _proof_442✝²)
        app₁.hom =
      CategoryTheory.CategoryStruct.comp app₀.hom
        (g.map' 0 1 CategoryTheory.ComposableArrows.homMk₁._proof_4 _proof_442✝³))
  (w₁ :
    CategoryTheory.CategoryStruct.comp (f.map' 1 2 _proof_238✝ _proof_443✝²) app₂.hom =
      CategoryTheory.CategoryStruct.comp app₁.hom (g.map' 1 2 _proof_238✝¹ _proof_443✝³))
  (w₂ :
    CategoryTheory.CategoryStruct.comp (f.map' 2 3 _proof_291✝ _proof_444✝²) app₃.hom =
      CategoryTheory.CategoryStruct.comp app₂.hom (g.map' 2 3 _proof_291✝¹ _proof_444✝³))
  (w₃ :
    CategoryTheory.CategoryStruct.comp (f.map' 3 4 _proof_356✝ _proof_445✝²) app₄.hom =
      CategoryTheory.CategoryStruct.comp app₃.hom (g.map' 3 4 _proof_356✝¹ _proof_445✝³))
  (w₄ :
    CategoryTheory.CategoryStruct.comp (f.map' 4 5 _proof_445✝⁴ _proof_446✝²) app₅.hom =
      CategoryTheory.CategoryStruct.comp app₄.hom (g.map' 4 5 _proof_445✝⁵ _proof_446✝³)),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.ComposableArrows.homMk₅ app₀.hom app₁.hom app₂.hom app₃.hom app₄.hom app₅.hom w₀ w₁ w₂ w₃ w₄)
      (CategoryTheory.ComposableArrows.homMk₅ app₀.inv app₁.inv app₂.inv app₃.inv app₄.inv app₅.inv ⋯ ⋯ ⋯ ⋯ ⋯) =
    CategoryTheory.CategoryStruct.id f