∀ {ι : Type u_1} {σ : Type u_2} {A : Type u_3} [inst : AddMonoid ι] [inst_1 : Semiring A] [inst_2 : SetLike σ A]
  [inst_3 : AddSubmonoidClass σ A] {𝒜 : ι → σ} [inst_4 : DecidableEq ι] [inst_5 : GradedRing 𝒜]
  (x x_1 : HomogeneousSubsemiring 𝒜), x.carrier = x_1.carrier → x = x_1