∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.CategoryWithCofibrations C]
  [inst_2 : CategoryTheory.Limits.HasInitial C] [inst_3 : HomotopicalAlgebra.CategoryWithFibrations C]
  [inst_4 : CategoryTheory.Limits.HasTerminal C] [inst_5 : HomotopicalAlgebra.CategoryWithWeakEquivalences C] {X Y : C}
  [inst_6 : HomotopicalAlgebra.IsCofibrant X] [inst_7 : HomotopicalAlgebra.IsFibrant X]
  [inst_8 : HomotopicalAlgebra.IsCofibrant Y] [inst_9 : HomotopicalAlgebra.IsFibrant Y] (f : X ⟶ Y),
  HomotopicalAlgebra.WeakEquivalence (HomotopicalAlgebra.BifibrantObject.homMk f) = HomotopicalAlgebra.WeakEquivalence f