have ex_basis : (extension C e).Basis' I X
case intro
α : Type u_1
M : Matroid α
I✝ B : Set α
Ys Xs : Set (Set α)
e : α
X : Set α
C : M.ModularCut
he : e ∉ M.E
hX : M.cl X ∈ C
I : Set α
hI : M.Basis' I X
⊢ (C.extension e).cl X = insert e (M.cl X)
case ex_basis
α : Type u_1
M : Matroid α
I✝ B : Set α
Ys Xs : Set (Set α)
e : α
X : Set α
C : M.ModularCut
he : e ∉ M.E
hX : M.cl X ∈ C
I : Set α
hI : M.Basis' I X
⊢ (C.extension e).Basis' I X

case intro
α : Type u_1
M : Matroid α
I✝ B : Set α
Ys Xs : Set (Set α)
e : α
X : Set α
C : M.ModularCut
he : e ∉ M.E
hX : M.cl X ∈ C
I : Set α
hI : M.Basis' I X
ex_basis : (C.extension e).Basis' I X
⊢ (C.extension e).cl X = insert e (M.cl X)