∀ {α : Type u} {g : Set (Set α)} {motive : (a : Set α) → Filter.GenerateSets g a → Prop} {s t : Set α}
  (a : Filter.GenerateSets g s) (a_1 : s ⊆ t), Filter.GenerateSets.below a → motive s a → Filter.GenerateSets.below ⋯