refine' ⟨B', hB'.1, fun i ↦ _⟩
case intro.intro.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
R B : Set α
hBb : (M ↾ R).Base B
hB : ∀ (i : ι), (M ↾ R).Basis (Xs i ∩ B) (Xs i)
B' : Set α
hB' : M.Base B' ∧ B ⊆ B'
⊢ M.ModularFamily fun i => Xs i ∩ M.E
case intro.intro.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
R B : Set α
hBb : (M ↾ R).Base B
hB : ∀ (i : ι), (M ↾ R).Basis (Xs i ∩ B) (Xs i)
B' : Set α
hB' : M.Base B' ∧ B ⊆ B'
i : ι
⊢ M.Basis ((fun i => Xs i ∩ M.E) i ∩ B') ((fun i => Xs i ∩ M.E) i)