∀ {α : Type u_1} {M : Matroid α} (motive : (∃ x, M.IsCircuit x ∧ x.Subsingleton) → Prop)
  (x : ∃ x, M.IsCircuit x ∧ x.Subsingleton),
  (∀ (C : Set α) (hC : M.IsCircuit C) (hCs : C.Subsingleton), motive ⋯) → motive x