rw [←diff_singleton_eq_self e_not_mem, diff_singleton_subset_iff, ←cl_eq_self, ←(C.extension_ground)]
case Fsub
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_eq : C.extension e ↾ M.E = M
e_not_mem : e ∉ F
⊢ F ⊆ M.E
case Fsub
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_eq : C.extension e ↾ M.E = M
e_not_mem : e ∉ F
⊢ (C.extension e).cl F ⊆ (C.extension e).E