∀ {Γ : Type u_1} {R : Type u_2} (κ : Cardinal.{u_1}) [inst : PartialOrder Γ] [inst_1 : AddCommMonoid Γ]
  [inst_2 : IsOrderedCancelAddMonoid Γ] [inst_3 : Ring R] [hκ : Fact (Cardinal.aleph0 ≤ κ)] {x : HahnSeries Γ R},
  (x ∈ HahnSeries.cardSuppLTSubring Γ R κ) = (x.cardSupp < κ)