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
h : M.ModularFamily Xs
A : Set ι
⊢ M.ModularPair (⋃ i ∈ A, Xs i) (⋃ i ∈ Aᶜ, Xs i)
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
h : M.ModularFamily Xs
A : Set ι
⊢ ∃ I, M.Indep I ∧ M.Basis ((⋃ i ∈ A, Xs i) ∩ I) (⋃ i ∈ A, Xs i) ∧ M.Basis ((⋃ i ∈ Aᶜ, Xs i) ∩ I) (⋃ i ∈ Aᶜ, Xs i)