∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} [inst : L.Structure M] [inst_1 : L.Structure N] {ι : Type u_3}
  {f : L.Hom M N},
  Function.Surjective ⇑f →
    ∀ (S : ι → L.Substructure N),
      FirstOrder.Language.Substructure.map f (⨆ i, FirstOrder.Language.Substructure.comap f (S i)) = ⨆ i, S i