∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] [inst_1 : CompleteLattice β] (f : CompleteLatticeHom α β)
  {L : CompleteSublattice α} {b : β}, b ∈ CompleteSublattice.map f L ↔ ∃ a ∈ L, f a = b