suffices ∀ X ⊆ M.E, M.conn X (M.E \ X) = M✶.conn X (M.E \ X) by
  rw [conn_eq_conn_inter_ground_left, M✶.conn_eq_conn_inter_ground_left,
    show M.E \ X = M.E \ (X ∩ M.E) by simp, this _ inter_subset_right, dual_ground]
α : Type u_1
M✝ : Matroid α
B B' I I' J K X✝ Y : Set α
M : Matroid α
X : Set α
⊢ M.conn X (M.E \ X) = M✶.conn X (M.E \ X)
α : Type u_1
M✝ : Matroid α
B B' I I' J K X✝ Y : Set α
M : Matroid α
X : Set α
⊢ ∀ X ⊆ M.E, M.conn X (M.E \ X) = M✶.conn X (M.E \ X)