refine ⟨_, ?_, ?_, hB.basis_inter⟩
case intro
ι : Type u_1
α : Type u_2
M : Matroid α
B✝ I J X X' Y Y' F : Set α
Xs Ys Js Is : ι → Set α
i j : ι
e f : α
h : M.SkewFamily Xs
B : Set α
hB : M.ModularBase B Xs
⊢ ∃ Is, Pairwise (Disjoint on Is) ∧ M.Basis (⋃ i, Is i) (⋃ i, Xs i) ∧ ∀ (i : ι), M.Basis (Is i) (Xs i)
case intro.refine_1
ι : Type u_1
α : Type u_2
M : Matroid α
B✝ I J X X' Y Y' F : Set α
Xs Ys Js Is : ι → Set α
i j : ι
e f : α
h : M.SkewFamily Xs
B : Set α
hB : M.ModularBase B Xs
⊢ Pairwise (Disjoint on fun i => Xs i ∩ B)

case intro.refine_2
ι : Type u_1
α : Type u_2
M : Matroid α
B✝ I J X X' Y Y' F : Set α
Xs Ys Js Is : ι → Set α
i j : ι
e f : α
h : M.SkewFamily Xs
B : Set α
hB : M.ModularBase B Xs
⊢ M.Basis (⋃ i, Xs i ∩ B) (⋃ i, Xs i)