∀ {α : Type u_1} [inst : UniformSpace α] (U : SetRel α α)
  (motive :
    (x : α × α) →
      x ∈
          Prod.map SeparationQuotient.mk SeparationQuotient.mk ⁻¹'
            (Prod.map SeparationQuotient.mk SeparationQuotient.mk '' id U) →
        Prop)
  (x : α × α)
  (x_1 :
    x ∈
      Prod.map SeparationQuotient.mk SeparationQuotient.mk ⁻¹'
        (Prod.map SeparationQuotient.mk SeparationQuotient.mk '' id U)),
  (∀ (x₁ x₂ : α)
      (x :
        (x₁, x₂) ∈
          Prod.map SeparationQuotient.mk SeparationQuotient.mk ⁻¹'
            (Prod.map SeparationQuotient.mk SeparationQuotient.mk '' id U)),
      motive (x₁, x₂) x) →
    motive x x_1