rw [← dual_inj, contract_dual_eq_dual_delete, delete_dual_eq_dual_contract, eq_comm,
  contract_eq_delete_of_subset_coloops]
α : Type u_1
M M' N : Matroid α
e f : α
I J R B X Y Z K C C₁ C₂ : Set α
hX : X ⊆ M.cl ∅
⊢ M ／ X = M ＼ X
α : Type u_1
M M' N : Matroid α
e f : α
I J R B X Y Z K C C₁ C₂ : Set α
hX : X ⊆ M.cl ∅
⊢ X ⊆ M✶✶.cl ∅