rw [← contract_inter_ground_eq, Dep, hI.contract_indep_iff,
  and_iff_left (hCK.mono_left inter_subset_left), contract_ground, subset_diff,
  and_iff_left (hCK.symm.mono_right inter_subset_left), and_iff_left hK.subset_ground]
case intro
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
hK : M.Circuit K
hCK : Disjoint C K
I : Set α
hI : M.Basis I (C ∩ M.E)
⊢ (M ／ C).Dep K
case intro
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
hK : M.Circuit K
hCK : Disjoint C K
I : Set α
hI : M.Basis I (C ∩ M.E)
⊢ ¬M.Indep (K ∪ I)