∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {f g : CategoryTheory.ComposableArrows C 4}
  (app₀ app₀_1 : f.obj' 0 _proof_353✝ ⟶ g.obj' 0 _proof_353✝) (e_app₀ : app₀ = app₀_1)
  (app₁ app₁_1 : f.obj' 1 _proof_354✝ ⟶ g.obj' 1 _proof_354✝) (e_app₁ : app₁ = app₁_1)
  (app₂ app₂_1 : f.obj' 2 _proof_355✝ ⟶ g.obj' 2 _proof_355✝) (e_app₂ : app₂ = app₂_1)
  (app₃ app₃_1 : f.obj' 3 _proof_356✝ ⟶ g.obj' 3 _proof_356✝) (e_app₃ : app₃ = app₃_1)
  (app₄ app₄_1 : f.obj' 4 _proof_357✝ ⟶ g.obj' 4 _proof_357✝) (e_app₄ : app₄ = app₄_1)
  (w₀ :
    CategoryTheory.CategoryStruct.comp (f.map' 0 1 CategoryTheory.ComposableArrows.homMk₁._proof_4 _proof_354✝) app₁ =
      CategoryTheory.CategoryStruct.comp app₀ (g.map' 0 1 CategoryTheory.ComposableArrows.homMk₁._proof_4 _proof_354✝))
  (w₁ :
    CategoryTheory.CategoryStruct.comp (f.map' 1 2 _proof_238✝ _proof_355✝) app₂ =
      CategoryTheory.CategoryStruct.comp app₁ (g.map' 1 2 _proof_238✝ _proof_355✝))
  (w₂ :
    CategoryTheory.CategoryStruct.comp (f.map' 2 3 _proof_291✝ _proof_356✝) app₃ =
      CategoryTheory.CategoryStruct.comp app₂ (g.map' 2 3 _proof_291✝ _proof_356✝))
  (w₃ :
    CategoryTheory.CategoryStruct.comp (f.map' 3 4 _proof_356✝ _proof_357✝) app₄ =
      CategoryTheory.CategoryStruct.comp app₃ (g.map' 3 4 _proof_356✝ _proof_357✝)),
  CategoryTheory.ComposableArrows.homMk₄ app₀ app₁ app₂ app₃ app₄ w₀ w₁ w₂ w₃ =
    CategoryTheory.ComposableArrows.homMk₄ app₀_1 app₁_1 app₂_1 app₃_1 app₄_1 ⋯ ⋯ ⋯ ⋯