have hu := hB.basis_iUnion
case intro.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
B : Set α
hB : M.ModularBase B fun i => bif i then X else Y
⊢ M.Basis ((X ∪ Y) ∩ B) (X ∪ Y)
case intro.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
B : Set α
hB : M.ModularBase B fun i => bif i then X else Y
hu : M.Basis ((⋃ i, bif i then X else Y) ∩ B) (⋃ i, bif i then X else Y)
⊢ M.Basis ((X ∪ Y) ∩ B) (X ∪ Y)