∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] {f : X → Y → Z}
  {hf : ∀ (a : X) (b : Y) (c : X) (d : Y), Inseparable a c → Inseparable b d → f a b = f c d}
  {s : Set (SeparationQuotient X × SeparationQuotient Y)},
  ContinuousOn (Function.uncurry (SeparationQuotient.lift₂ f hf)) s =
    ContinuousOn (Function.uncurry f) (Prod.map SeparationQuotient.mk SeparationQuotient.mk ⁻¹' s)