simp only [Set.empty_subset, true_and, Set.mem_setOf_eq, and_imp]
α : Type u_1
I✝ : Set α
M : Matroid α
A B : Set α
hA : A ⊆ B
hB : B ⊆ M.E
I : Set α
hI : (M.Indep I ∧ I ⊆ A) ∧ ∀ ⦃b : Set α⦄, M.Indep b → b ⊆ A → I ⊆ b → b ⊆ I
hI_indep : M.Indep I
hI_subset_A : I ⊆ A
right✝ : ∀ ⦃b : Set α⦄, M.Indep b → b ⊆ A → I ⊆ b → b ⊆ I
J : Set α
hJ : J ∈ maximals (fun x x_1 => x ⊆ x_1) {Y | M.Indep Y ∧ I ⊆ Y ∧ Y ⊆ B}
hIJ : I ⊆ J
⊢ I ∈
    {a |
      a ∈ {I' | M.Indep I' ∧ ∅ ⊆ I' ∧ I' ⊆ A} ∧
        ∀ ⦃b : Set α⦄,
          b ∈ {I' | M.Indep I' ∧ ∅ ⊆ I' ∧ I' ⊆ A} → (fun x x_1 => x ⊆ x_1) a b → (fun x x_1 => x ⊆ x_1) b a}
α : Type u_1
I✝ : Set α
M : Matroid α
A B : Set α
hA : A ⊆ B
hB : B ⊆ M.E
I : Set α
hI : (M.Indep I ∧ I ⊆ A) ∧ ∀ ⦃b : Set α⦄, M.Indep b → b ⊆ A → I ⊆ b → b ⊆ I
hI_indep : M.Indep I
hI_subset_A : I ⊆ A
right✝ : ∀ ⦃b : Set α⦄, M.Indep b → b ⊆ A → I ⊆ b → b ⊆ I
J : Set α
hJ : J ∈ maximals (fun x x_1 => x ⊆ x_1) {Y | M.Indep Y ∧ I ⊆ Y ∧ Y ⊆ B}
hIJ : I ⊆ J
⊢ (M.Indep I ∧ I ⊆ A) ∧ ∀ ⦃b : Set α⦄, M.Indep b → b ⊆ A → I ⊆ b → b ⊆ I