∀ {Γ : Type u_1} {R : Type u_2} [inst : AddCommMonoid Γ] [inst_1 : PartialOrder Γ] [inst_2 : IsOrderedCancelAddMonoid Γ]
  [inst_3 : NonUnitalNonAssocSemiring R] (a b c : HahnSeries Γ R), a * (b + c) = a * b + a * c