refine ⟨hI.modularFamily fun i ↦ ?_, fun i j hij ↦ ?_⟩
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
hI : M.Indep (⋃ i, Is i)
hdj : Pairwise (Disjoint on Is)
hIs : ∀ (i : ι), M.Basis (Is i) (Xs i)
⊢ M.SkewFamily Xs
case 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
hI : M.Indep (⋃ i, Is i)
hdj : Pairwise (Disjoint on Is)
hIs : ∀ (i : ι), M.Basis (Is i) (Xs i)
i : ι
⊢ M.Basis (Xs i ∩ ⋃ i, Is i) (Xs i)

case 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
hI : M.Indep (⋃ i, Is i)
hdj : Pairwise (Disjoint on Is)
hIs : ∀ (i : ι), M.Basis (Is i) (Xs i)
i j : ι
hij : i ≠ j
⊢ Xs i ∩ Xs j ⊆ M.cl ∅