have hI' : I ∈ {J : Set α | J ⊆ I ∧ e ∈ M.cl J} := ⟨rfl.subset, he.1⟩
α : Type u_1
M : Matroid α
C C' I X K C₁ C₂ R : Set α
e f x y : α
hI : M.Indep I
he : e ∈ M.cl I \ I
hu : M.Indep (⋃₀ {J | J ⊆ I ∧ e ∈ M.cl J})
⊢ ¬M.Indep (insert e (⋂₀ {J | J ⊆ I ∧ e ∈ M.cl J})) ∧
    ∀ e_1 ∈ insert e (⋂₀ {J | J ⊆ I ∧ e ∈ M.cl J}), M.Indep (insert e (⋂₀ {J | J ⊆ I ∧ e ∈ M.cl J}) \ {e_1})
α : Type u_1
M : Matroid α
C C' I X K C₁ C₂ R : Set α
e f x y : α
hI : M.Indep I
he : e ∈ M.cl I \ I
hu : M.Indep (⋃₀ {J | J ⊆ I ∧ e ∈ M.cl J})
hI' : I ∈ {J | J ⊆ I ∧ e ∈ M.cl J}
⊢ ¬M.Indep (insert e (⋂₀ {J | J ⊆ I ∧ e ∈ M.cl J})) ∧
    ∀ e_1 ∈ insert e (⋂₀ {J | J ⊆ I ∧ e ∈ M.cl J}), M.Indep (insert e (⋂₀ {J | J ⊆ I ∧ e ∈ M.cl J}) \ {e_1})