obtain ⟨B, hB⟩ := h
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
h : M.ModularPair X Y
⊢ ∃ I, M.Basis I (X ∪ Y) ∧ M.Basis (I ∩ X) X ∧ M.Basis (I ∩ Y) Y ∧ M.Basis (I ∩ X ∩ Y) (X ∩ Y)
case 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
B : Set α
hB : M.ModularBase B fun i => bif i then X else Y
⊢ ∃ I, M.Basis I (X ∪ Y) ∧ M.Basis (I ∩ X) X ∧ M.Basis (I ∩ Y) Y ∧ M.Basis (I ∩ X ∩ Y) (X ∩ Y)