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
J X : Set α
hJF : M.Basis J F
hJX : M.Basis J X
e : α
heX : e ∈ X
⊢ M.Basis I (insert e I)
no goals