∀ {α : Type u_1} (E E_1 : Set α) (e_E : E = E_1) (Indep Indep_1 : Set α → Prop) (e_Indep : Indep = Indep_1)
  (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) (indep_bdd : ∃ n, ∀ (I : Set α), Indep I → I.encard ≤ ↑n),
  IndepMatroid.ofBdd E Indep indep_empty indep_subset indep_aug subset_ground indep_bdd =
    IndepMatroid.ofBdd E_1 Indep_1 ⋯ ⋯ ⋯ ⋯ ⋯