apply C.inter ha hb (modularPair_iff.2 ⟨(insert a (insert b X)), hI, _⟩)
α : Type u_1
M : Matroid α
I B : Set α
Ys Xs : Set (Set α)
a b : α
X : Set α
C : M.ModularCut
hI : M.Indep (insert a (insert b X))
ha : M.cl (insert a X) ∈ C
hb : M.cl (insert b X) ∈ C
hne : a ≠ b
⊢ M.cl (insert a X) ∩ M.cl (insert b X) ∈ C
α : Type u_1
M : Matroid α
I B : Set α
Ys Xs : Set (Set α)
a b : α
X : Set α
C : M.ModularCut
hI : M.Indep (insert a (insert b X))
ha : M.cl (insert a X) ∈ C
hb : M.cl (insert b X) ∈ C
hne : a ≠ b
⊢ M.Basis (M.cl (insert a X) ∩ insert a (insert b X)) (M.cl (insert a X)) ∧
    M.Basis (M.cl (insert b X) ∩ insert a (insert b X)) (M.cl (insert b X))