∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} C] {J : CategoryTheory.Precoverage C}
  {motive : (X : C) → (a : CategoryTheory.Sieve X) → J.Saturate X a → Prop} {X : C} {a : CategoryTheory.Sieve X}
  (t : J.Saturate X a),
  (∀ (X : C) (a : CategoryTheory.Sieve X) (t : J.Saturate X a),
      CategoryTheory.Precoverage.Saturate.below t → motive X a t) →
    motive X a t