∀ {Γ : Type u_1} {R : Type u_2} [inst : AddCommMonoid Γ] [inst_1 : PartialOrder Γ] {Γ' : Type u_3}
  [inst_2 : AddCommMonoid Γ'] [inst_3 : PartialOrder Γ'] [inst_4 : NonAssocSemiring R] (f : Γ →+ Γ')
  (hfi : Function.Injective ⇑f) (hf : ∀ (g g' : Γ), f g ≤ f g' ↔ g ≤ g') (x y : HahnSeries Γ R),
  HahnSeries.embDomain { toFun := ⇑f, inj' := hfi, map_rel_iff' := ⋯ } (x + y) =
    HahnSeries.embDomain { toFun := ⇑f, inj' := hfi, map_rel_iff' := ⋯ } x +
      HahnSeries.embDomain { toFun := ⇑f, inj' := hfi, map_rel_iff' := ⋯ } y