∀ {G : Type u_1} [inst : Group G] [inst_1 : DecidableEq G] {K : ℝ} {S : Finset G}
  (motive : (∃ A, A.Nonempty ∧ Finset.IsFragment✝ K S A) → Prop) (x : ∃ A, A.Nonempty ∧ Finset.IsFragment✝¹ K S A),
  (∀ (A : Finset G) (left : A.Nonempty) (hA : Finset.IsFragment✝² K S A), motive ⋯) → motive x