∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : HomotopicalAlgebra.ModelCategory C] {X Y : C}
  [inst_2 : HomotopicalAlgebra.IsCofibrant X] [inst_3 : HomotopicalAlgebra.IsCofibrant Y]
  [inst_4 : HomotopicalAlgebra.IsFibrant X] [inst_5 : HomotopicalAlgebra.IsFibrant Y] (f : X ⟶ Y),
  HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight.symm
      (HomotopicalAlgebra.BifibrantObject.toHoCat.map (HomotopicalAlgebra.BifibrantObject.homMk f)) =
    HomotopicalAlgebra.RightHomotopyClass.mk f