∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'} {l : ℕ} {v : α → M} {xs : Fin l → M}
  (t₁ t₂ : L.Term (α ⊕ Fin l)),
  (t₁.bdEqual t₂).Realize v xs =
    (FirstOrder.Language.Term.realize (Sum.elim v xs) t₁ = FirstOrder.Language.Term.realize (Sum.elim v xs) t₂)