obtain ⟨I, hI⟩ := M.exists_basis' X
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
M : Matroid α
X : Set α
e f : α
⊢ M.ModularPair (M.cl (insert e X)) (M.cl (insert f X))
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
M : Matroid α
X : Set α
e f : α
I : Set α
hI : M.Basis' I X
⊢ M.ModularPair (M.cl (insert e X)) (M.cl (insert f X))