simpa [extendBy_Indep, ModularCut.extIndep_iff_of_mem (mem_insert e I), heI, hI.indep,
  not_iff_not, ← hF.eq_cl_of_basis hI] using h_eq
case inr.intro
α : Type u_1
M✝ : Matroid α
I✝ J B F₀ F✝ F' X Y : Set α
e f : α
U✝ : M✝.ModularCut
M : Matroid α
he : e ∉ M.E
U U' : M.ModularCut
F : Set α
hF : M.Flat F
I : Set α
hI : M.Basis I F
heI : e ∉ I
h_eq : (M.extendBy e U).Indep (insert e I) = (M.extendBy e U').Indep (insert e I)
⊢ F ∈ ↑U ↔ F ∈ ↑U'
no goals