exact rFin.indep_of_encard_le_er
  ((rFin.iUnion hXs).subset (iUnion_mono (fun i ↦ (hIs i).subset)))
  ((encard_iUnion_le _).trans hsum.le)
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
Is : ι → Set α
hIs : ∀ (i : ι), M.Basis (Is i) (Xs i)
hsum : ∑ x : ι, (Is x).encard = M.er (⋃ i, Is i)
⊢ M.Indep (⋃ i, Is i)
no goals