rwa [← inter_eq_iInter] at hi
case intro.refine_2
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
hi : M.Basis ((⋂ i, bif i then X else Y) ∩ B) (⋂ i, bif i then X else Y)
⊢ M.Basis (X ∩ Y ∩ B) (X ∩ Y)
no goals