rw [← union_indep_iff_indep_of_subset_coloops hK, diff_union_self,
  union_indep_iff_indep_of_subset_coloops hK]
α : Type u_1
β : Type u_2
M N : Matroid α
e f : α
B L L' I X Y Z F C K : Set α
hK : K ⊆ M✶.cl ∅
⊢ M.Indep (I \ K) ↔ M.Indep I
no goals