∀ {L : FirstOrder.Language} {ι : Type v} [inst : Preorder ι] (G : ι → Type w) [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] {n : ℕ} {R : L.Relations n} {i : ι}
  {x : Fin n → G i},
  (FirstOrder.Language.Structure.RelMap R fun a => ⟦FirstOrder.Language.Structure.Sigma.mk f i (x a)⟧) =
    FirstOrder.Language.Structure.RelMap R x