rw [contract_ground, and_iff_right (inter_subset_left.trans diff_subset), diff_eq,
  diff_eq, inter_right_comm, inter_assoc, and_iff_right inter_subset_right,
  ← contract_inter_ground_eq, hI.contract_eq_contract_delete, diff_eq, inter_assoc]
case right
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
M : Matroid α
C I : Set α
hI : M.Basis I (C ∩ M.E)
⊢ C \ I ∩ M.E ⊆ (M ／ I).E ∧ C \ I ∩ M.E ⊆ C ∧ M ／ C = M ／ I ＼ (C \ I ∩ M.E)
no goals