∀ {Γ : Type u_1} {R : Type u_2} {A : Type u_3} [inst : LinearOrder Γ] [inst_1 : AddCommMonoid Γ]
  [inst_2 : IsOrderedCancelAddMonoid Γ] [inst_3 : CommRing R] [inst_4 : BinomialRing R] [inst_5 : CommRing A]
  [inst_6 : Algebra R A] (x x_1 : HahnSeries Γ A),
  x = x_1 →
    ∀ (r r_1 : R),
      r = r_1 → HahnSeries.SummableFamily.binomialFamily x r = HahnSeries.SummableFamily.binomialFamily x_1 r_1