rw [restrict_indep_iff, and_iff_right (hK.indep.diff I), diff_subset_iff, union_comm Y,
  ← union_assoc]
α : Type u_1
M : Matroid α
B B' I I' J K✝ X Y✝ : Set α
hI : M.Indep I
hI' : M.Indep I'
hII' : M.cl I = M.cl I'
hJ : M.Indep J
K : Set α
hK : M.Basis K (I ∪ J)
hIK : I ⊆ K
hsk : M.Skew (M.cl I) (K \ I)
hdj : Disjoint (M.cl I) (K \ I)
hb : ∀ ⦃B : Set α⦄, M.Basis B (M.cl I) → (M ／ (K \ I)).Basis B (B ∪ J \ (K \ I)) ∧ K \ I ⊆ B ∪ J
hb' : ∀ ⦃B : Set α⦄, M.Basis B (M.cl I) → (B ∩ J).encard + (M ／ (K \ I) ↾ (B ∪ J \ (K \ I)))✶.erk = (J \ (K \ I)).encard
Y : Set α
⊢ (M ↾ (Y ∪ J)).Indep (K \ I)
α : Type u_1
M : Matroid α
B B' I I' J K✝ X Y✝ : Set α
hI : M.Indep I
hI' : M.Indep I'
hII' : M.cl I = M.cl I'
hJ : M.Indep J
K : Set α
hK : M.Basis K (I ∪ J)
hIK : I ⊆ K
hsk : M.Skew (M.cl I) (K \ I)
hdj : Disjoint (M.cl I) (K \ I)
hb : ∀ ⦃B : Set α⦄, M.Basis B (M.cl I) → (M ／ (K \ I)).Basis B (B ∪ J \ (K \ I)) ∧ K \ I ⊆ B ∪ J
hb' : ∀ ⦃B : Set α⦄, M.Basis B (M.cl I) → (B ∩ J).encard + (M ／ (K \ I) ↾ (B ∪ J \ (K \ I)))✶.erk = (J \ (K \ I)).encard
Y : Set α
⊢ K ⊆ I ∪ J ∪ Y