∀ {C : Type u_1} [inst : Preorder C] {J : Type u_2} [inst_1 : CategoryTheory.Category.{u_3, u_2} J]
  (F : CategoryTheory.Functor J C) (motive : (∃ x, IsGLB (Set.range F.obj) x) → Prop)
  (x : ∃ x, IsGLB (Set.range F.obj) x), (∀ (w : C) (h : IsGLB (Set.range F.obj) w), motive ⋯) → motive x