∀ (L : FirstOrder.Language) (ι : Type u_2) [inst : Preorder ι] (G : ι → Type u_3) [inst_1 : (i : ι) → L.Structure (G i)]
  (f : (i j : ι) → i ≤ j → L.Embedding (G i) (G j)) [inst_2 : IsDirectedOrder ι]
  [inst_3 : DirectedSystem G fun i j h => ⇑(f i j h)] [inst_4 : Nonempty ι] {P : Type u_1} [inst_5 : L.Structure P]
  (g : (i : ι) → L.Embedding (G i) P) (Hg : ∀ (i j : ι) (hij : i ≤ j) (x : G i), (g j) ((f i j hij) x) = (g i) x)
  {n : ℕ} (F : L.Functions n) (x : Fin n → FirstOrder.Language.DirectLimit G f),
  Quotient.lift (fun x => (g x.fst) x.snd) ⋯ (FirstOrder.Language.Structure.funMap F x) =
    FirstOrder.Language.Structure.funMap F (Quotient.lift (fun x => (g x.fst) x.snd) ⋯ ∘ x)