∀ {α : Type u_1} (M : Matroid α) (E : Set α) (IsBase Indep : Set α → Prop) (hE : E = M.E)
  (hB : ∀ (B : Set α), IsBase B ↔ M.IsBase B) (hI : ∀ (I : Set α), Indep I ↔ M.Indep I),
  (M.copy E IsBase Indep hE hB hI).E = E