rw [modularPair_iff]
ι : Type u_1
α : Type u_2
M : Matroid α
B I J X X' Y Y' F : Set α
Xs Ys Js Is : ι → Set α
i j : ι
e f : α
⊢ M.ModularPair X Y ↔ ∃ I J, M.Basis I X ∧ M.Basis J Y ∧ M.Indep (I ∪ J)
ι : Type u_1
α : Type u_2
M : Matroid α
B I J X X' Y Y' F : Set α
Xs Ys Js Is : ι → Set α
i j : ι
e f : α
⊢ (∃ I, M.Indep I ∧ M.Basis (X ∩ I) X ∧ M.Basis (Y ∩ I) Y) ↔ ∃ I J, M.Basis I X ∧ M.Basis J Y ∧ M.Indep (I ∪ J)