{α : Type u_1} →
  {E : Set α} →
    E.Finite →
      (Indep : Set α → Prop) →
        Indep ∅ →
          (∀ ⦃I J : Set α⦄, Indep J → I ⊆ J → Indep I) →
            (∀ ⦃I J : Set α⦄, Indep I → Indep J → I.ncard < J.ncard → ∃ e ∈ J, e ∉ I ∧ Indep (insert e I)) →
              (∀ ⦃I : Set α⦄, Indep I → I ⊆ E) → IndepMatroid α