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