∀ {α : Type u_2} {β : Type u_1} [inst : Lattice α] [inst_1 : Lattice β] [inst_2 : BoundedOrder α]
  [inst_3 : BoundedOrder β] (f : BoundedLatticeHom α β) (a b : α), f.toFun (a ⊓ b) = f.toFun a ⊓ f.toFun b