∀ {F : Type u_1} {α : Type u_2} {β : Type u_3} [inst : Lattice α] [inst_1 : Lattice β] [inst_2 : FunLike F α β]
  [inst_3 : OrderBot α] [inst_4 : OrderBot β] [BotHomClass F α β] [InfHomClass F α β] {a b : α} (f : F),
  Disjoint a b → Disjoint (f a) (f b)