∀ {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 B : Set α⦄, Indep I → ¬Maximal Indep I → Maximal Indep B → ∃ x ∈ B \ I, Indep (insert x I))
  (subset_ground : ∀ (I : Set α), Indep I → I ⊆ E) (h_bdd : ∃ n, ∀ (I : Set α), Indep I → I.encard ≤ ↑n),
  (IndepMatroid.ofBdd E Indep indep_empty indep_subset indep_aug subset_ground h_bdd).Indep = Indep