Lemma union_mpl_correct_wrt_sign_invar_1 : forall (s0 s1 : state) (pa : pre_ad) (sigma : signature), state_correct_wrt_sign_with_offset s0 sigma pa -> state_correct_wrt_sign_with_offset s1 sigma pa -> state_correct_wrt_sign_with_offset (union_mpl s0 s1) sigma pa.