simp only [truncate_indep_iff', and_congr_right_iff]
α : Type u_1
M : Matroid α
E I B : Set α
k : ℕ∞
inst✝ : M.RkPos
⊢ M.truncate.Indep I ↔ M.Indep I ∧ ¬M.Base I
α : Type u_1
M : Matroid α
E I B : Set α
k : ℕ∞
inst✝ : M.RkPos
⊢ M.Indep I → (M.Base I → I = ∅ ↔ ¬M.Base I)