rw [union_comm, cl_union_eq_of_subset_coloops _ (inter_subset_right.trans hK),
  union_diff_distrib, diff_eq_empty.mpr inter_subset_right, union_empty, eq_comm,
  sdiff_eq_self_iff_disjoint, disjoint_iff_forall_ne]
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 X : Set α
hK : K ⊆ M✶.cl ∅
⊢ M.cl (X \ K) = M.cl (X ∩ K ∪ X \ K) \ K
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 X : Set α
hK : K ⊆ M✶.cl ∅
⊢ ∀ ⦃a : α⦄, a ∈ K → ∀ ⦃b : α⦄, b ∈ M.cl (X \ K) → a ≠ b