∀ {X Y : Type u_1} (f : X ⟶ Y) (a b : Set Y),
  { toFun := ⇑(CompleteLatticeHom.setPreimage f), map_sup' := ⋯, map_inf' := ⋯ }.toFun (a ⊓ b) =
    { toFun := ⇑(CompleteLatticeHom.setPreimage f), map_sup' := ⋯, map_inf' := ⋯ }.toFun a ⊓
      { toFun := ⇑(CompleteLatticeHom.setPreimage f), map_sup' := ⋯, map_inf' := ⋯ }.toFun b