obtain ⟨I, hI⟩ := (loopyOn E).exists_basis' X
α : Type u_1
ι : Type u_2
M N : Matroid α
I B X✝ X' Y Y' Z R : Set α
n : ℕ∞
e f : α
E✝ E X : Set α
⊢ (loopyOn E).er X = 0
case intro
α : Type u_1
ι : Type u_2
M N : Matroid α
I✝ B X✝ X' Y Y' Z R : Set α
n : ℕ∞
e f : α
E✝ E X I : Set α
hI : (loopyOn E).Basis' I X
⊢ (loopyOn E).er X = 0