{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {D : Type u_2} →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        {G : CategoryTheory.Functor C D} →
          {J : CategoryTheory.GrothendieckTopology C} →
            {K : CategoryTheory.GrothendieckTopology D} →
              {motive : G.IsCocontinuous J K → Sort u} →
                (t : G.IsCocontinuous J K) →
                  ((cover_lift :
                        ∀ {U : C} {S : CategoryTheory.Sieve (G.obj U)},
                          S ∈ K (G.obj U) → CategoryTheory.Sieve.functorPullback G S ∈ J U) →
                      motive ⋯) →
                    motive t