∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.ModelCategory C] {X Y : C}
  [inst_2 : HomotopicalAlgebra.IsCofibrant X] [inst_3 : HomotopicalAlgebra.IsFibrant Y] (f : X ⟶ Y),
  HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass.symm (HomotopicalAlgebra.RightHomotopyClass.mk f) =
    HomotopicalAlgebra.LeftHomotopyClass.mk f