choose Js hJs using fun i ↦ (hIs i).subset_basis_of_subset (hIX i)
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
hIX : ∀ (i : ι), Is i ⊆ Xs i
hIs : ∀ (i : ι), M.Indep (Is i)
⊢ M.Indep (⋃ i, Is i)
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
hIX : ∀ (i : ι), Is i ⊆ Xs i
hIs : ∀ (i : ι), M.Indep (Is i)
Js : ι → Set α
hJs : ∀ (i : ι), M.Basis (Js i) (Xs i) ∧ Is i ⊆ Js i
⊢ M.Indep (⋃ i, Is i)