∀ {G : Type u_1} {H : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup H] {K : Type u_3} [inst_2 : AddGroup K]
  (f : AddMonoid.Coprod G H →+ K), f.range = (f.comp AddMonoid.Coprod.inl).range ⊔ (f.comp AddMonoid.Coprod.inr).range