choose Is hIs using fun i ↦ M.exists_basis (Xs i) (hXE 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
inst✝ : Fintype ι
hXs : ∀ (i : ι), M.rFin (Xs i)
hXE : ∀ (i : ι), Xs i ⊆ M.E
hsum : ∑ i : ι, M.er (Xs i) = M.er (⋃ i, Xs i)
⊢ M.SkewFamily Xs
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
inst✝ : Fintype ι
hXs : ∀ (i : ι), M.rFin (Xs i)
hXE : ∀ (i : ι), Xs i ⊆ M.E
hsum : ∑ i : ι, M.er (Xs i) = M.er (⋃ i, Xs i)
Is : ι → Set α
hIs : ∀ (i : ι), M.Basis (Is i) (Xs i)
⊢ M.SkewFamily Xs