have hF : M.Flat F := by
  refine' ⟨fun J X hJF hJX e heX ↦ (_ : M.Basis _ _), hIF.subset_ground⟩
  exact (hIF.basis_of_basis_of_subset_of_subset (hJX.basis_union hJF) hJF.subset
    (hIF.subset.trans subset_union_right)).basis_subset (subset_insert _ _)
    (insert_subset (Or.inl heX) (hIF.subset.trans subset_union_right))
α : Type u_1
ι : Type u_2
M : Matroid α
F✝ I J X Y B C R : Set α
e f x y : α
hI : M.Indep I
F : Set α := {x | M.Basis I (insert x I)}
hIF : M.Basis I F
⊢ M.cl I = F
α : Type u_1
ι : Type u_2
M : Matroid α
F✝ I J X Y B C R : Set α
e f x y : α
hI : M.Indep I
F : Set α := {x | M.Basis I (insert x I)}
hIF : M.Basis I F
hF : M.Flat F
⊢ M.cl I = F