∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : HomotopicalAlgebra.ModelCategory C] {X Y : C}
  {f g : X ⟶ Y} (h : HomotopicalAlgebra.RightHomotopyRel f g) (Q : HomotopicalAlgebra.Cylinder X)
  (h_1 : ⋯.choose.RightHomotopy f g),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.coprod.desc (CategoryTheory.CategoryStruct.comp f ⋯.choose.ι) h_1.h) ⋯.choose.p₀ =
    CategoryTheory.CategoryStruct.comp Q.i (CategoryTheory.CategoryStruct.comp Q.π f)