∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {i₀ i₁ i₂ i₃ i₄ : C} (f₁ : i₀ ⟶ i₁) (f₂ : i₁ ⟶ i₂)
  (f₃ : i₂ ⟶ i₃) (f₄ : i₃ ⟶ i₄) (f₂₃ : i₁ ⟶ i₃) (f₃₄ : i₂ ⟶ i₄),
  CategoryTheory.CategoryStruct.comp f₂ f₃ = f₂₃ →
    CategoryTheory.CategoryStruct.comp f₃ f₄ = f₃₄ →
      CategoryTheory.CategoryStruct.comp
          ((CategoryTheory.ComposableArrows.mk₃ f₁ f₂ f₃₄).map' 1 2 _proof_238✝ _proof_291✝) f₃ =
        CategoryTheory.CategoryStruct.comp
          (CategoryTheory.CategoryStruct.id ((CategoryTheory.ComposableArrows.mk₃ f₁ f₂ f₃₄).obj' 1 _proof_290✝))
          ((CategoryTheory.ComposableArrows.mk₃ f₁ f₂₃ f₄).map' 1 2 _proof_238✝¹ _proof_291✝¹)