∀ {C₁ : Type u₁} {C₂ : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C₁]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] {W₁ : CategoryTheory.MorphismProperty C₁}
  {W₂ : CategoryTheory.MorphismProperty C₂} {E : Type u₅} [inst_2 : CategoryTheory.Category.{v₅, u₅} E]
  (F : CategoryTheory.Functor (C₁ × C₂) E) (hF : (W₁.prod W₂).IsInvertedBy F) [inst_3 : W₁.ContainsIdentities]
  [inst_4 : W₂.ContainsIdentities],
  CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prodLift F hF =
    CategoryTheory.Functor.uncurry.obj
      (CategoryTheory.Localization.Construction.lift
          (CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prodLift₁ F hF).flip ⋯).flip