obtain (e_mem | e_not_mem) := em (e ∈ F ∧ F \ {e} ∈ C)
case refine'_1
α : Type u_1
M : Matroid α
I B : Set α
Ys Xs : Set (Set α)
F : Set α
C : M.ModularCut
hC : C.Nonempty
e : α
he : e ∉ M.E
cl_eq_self : (C.extension e).cl F = F
⊢ M.Flat F ∧ F ∉ C ∨ e ∈ F ∧ F \ {e} ∈ C
case refine'_1.inl
α : Type u_1
M : Matroid α
I B : Set α
Ys Xs : Set (Set α)
F : Set α
C : M.ModularCut
hC : C.Nonempty
e : α
he : e ∉ M.E
cl_eq_self : (C.extension e).cl F = F
e_mem : e ∈ F ∧ F \ {e} ∈ C
⊢ M.Flat F ∧ F ∉ C ∨ e ∈ F ∧ F \ {e} ∈ C

case refine'_1.inr
α : Type u_1
M : Matroid α
I B : Set α
Ys Xs : Set (Set α)
F : Set α
C : M.ModularCut
hC : C.Nonempty
e : α
he : e ∉ M.E
cl_eq_self : (C.extension e).cl F = F
e_not_mem : ¬(e ∈ F ∧ F \ {e} ∈ C)
⊢ M.Flat F ∧ F ∉ C ∨ e ∈ F ∧ F \ {e} ∈ C