∀ {α : Type u_1} (E : Set α) (Indep : Set α → Prop) (indep_empty : Indep ∅)
  (indep_subset : ∀ ⦃I J : Set α⦄, Indep J → I ⊆ J → Indep I)
  (indep_aug : ∀ ⦃I J : Set α⦄, Indep I → Indep J → I.encard < J.encard → ∃ e ∈ J, e ∉ I ∧ Indep (insert e I))
  (indep_bdd : ∃ n, ∀ (I : Set α), Indep I → I.encard ≤ ↑n) (subset_ground : ∀ (I : Set α), Indep I → I ⊆ E),
  (IndepMatroid.ofBddAugment E Indep indep_empty indep_subset indep_aug indep_bdd subset_ground).matroid.RankFinite