simp_rw [Basis, mem_maximals_setOf_iff, hI.contract_indep_iff, and_iff_right hdj.1,
  and_iff_right h.indep, contract_ground, subset_diff, and_iff_left hdj.2,
  and_iff_left (subset_union_left.trans h.subset_ground), and_imp,
  and_iff_right
    (Disjoint.subset_left_of_subset_union (subset_union_left.trans h.subset) hdj.1)]
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
h : M.Basis (J ∪ I) (X ∪ I)
hdj : Disjoint J I ∧ Disjoint X I
hI : M.Indep I
⊢ (M ／ I).Basis J 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
h : M.Basis (J ∪ I) (X ∪ I)
hdj : Disjoint J I ∧ Disjoint X I
hI : M.Indep I
⊢ ∀ ⦃y : Set α⦄, Disjoint y I → M.Indep (y ∪ I) → y ⊆ X → J ⊆ y → J = y