obtain (he | he) := em' (e ∈ M.E)
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 (M.cl I))) (M.cl (insert f (M.cl I)))
case intro.inl
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
he : e ∉ M.E
⊢ M.ModularPair (M.cl (insert e (M.cl I))) (M.cl (insert f (M.cl I)))

case intro.inr
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
he : e ∈ M.E
⊢ M.ModularPair (M.cl (insert e (M.cl I))) (M.cl (insert f (M.cl I)))