proposition: Lemma app_inj_2 {A} (l1 k1 l2 k2 : list A) : length l2 = length k2 → l1 ++ l2 = k1 ++ k2 → l1 = k1 ∧ l2 = k2.
proof: Proof. intros ? Hl. apply app_inj_1; auto. apply (f_equal length) in Hl. rewrite !app_length in Hl. lia. Qed.
imports: stdpp(options)