rw [cl_eq_self, inter_eq_self_of_subset_left Fsub]
case F_flat
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
Fsub : F ⊆ M.E
I : Set α
hI : (C.extension e).Basis I F
hI' : M.Basis I F
⊢ (C.extension e).cl F ∩ M.E = F
no goals