∀ {α : Type u_1} (M : Matroid α) (X : Set α) (motive : (∃ J, M.IsBasis J X ∧ ∅ ⊆ J) → Prop)
  (x : ∃ J, M.IsBasis J X ∧ ∅ ⊆ J), (∀ (w : Set α) (hI : M.IsBasis w X) (right : ∅ ⊆ w), motive ⋯) → motive x