∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice α] [inst_1 : ConditionallyCompleteLattice β]
  {l : α → β} {u : β → α}, GaloisConnection l u → ∀ {s : Set β}, s.Nonempty → BddBelow s → u (sInf s) = ⨅ x, u ↑x