exact ⟨fun ⟨B, ⟨hBI, hdj⟩, hJB⟩ ↦
  ⟨disjoint_of_subset_left hJB hdj, _, hBI, hJB.trans subset_union_left,
    subset_union_right⟩,
  fun ⟨hdj, B, hB, hJB, hIB⟩ ↦ ⟨B \ I,⟨by simpa [union_eq_self_of_subset_right hIB],
    disjoint_sdiff_left⟩, subset_diff.2 ⟨hJB, hdj⟩ ⟩⟩
α : Type u_1
M M' N : Matroid α
e f : α
I J R B X Y Z K C C₁ C₂ : Set α
hI : M.Indep I
⊢ (∃ B, (M.Base (B ∪ I) ∧ Disjoint B I) ∧ J ⊆ B) ↔ Disjoint J I ∧ ∃ B, M.Base B ∧ J ⊆ B ∧ I ⊆ B
no goals