SignedNonsingularHornerRoot(pb,pc,nb,nc,a,l,m,p)

exists hsc_vp_secondwave hsc_dp_secondwave hsc_vn_secondwave hsc_dn_secondwave. ((((exists ff_u_hd_hpl_sph_hsc_secondwave_pair_positive ff_v_hd_hpl_sph_hsc_secondwave_pair_positive ff_d_hd_hpl_sph_hsc_secondwave_pair_positive ff_e_hd_hpl_sph_hsc_secondwave_pair_positive. ((((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_start. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_start + S (0) = S ((S (0)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_positive)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_start. ff_u_hd_hpl_sph_hsc_secondwave_pair_positive = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_start * S ((S (0)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_positive) + (0))) /\ ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_terminal. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_terminal + S (hsc_vp_secondwave) = S ((S (l)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_positive)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_terminal. ff_u_hd_hpl_sph_hsc_secondwave_pair_positive = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_terminal * S ((S (l)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_positive) + (hsc_vp_secondwave))) /\ forall ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps. (exists ph_bound_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps. ph_bound_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps + S ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps = l) -> exists ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps. ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps_coefficient. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps_coefficient + S (ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps) = S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps)) * pc)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps_coefficient. pb = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps_coefficient * S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps)) * pc) + (ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps))) /\ ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps_before. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps_before + S (ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps) = S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_positive)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps_before. ff_u_hd_hpl_sph_hsc_secondwave_pair_positive = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps_before * S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_positive) + (ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps))) /\ ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps_after. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps_after + S (ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps) = S ((S (S ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_positive)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps_after. ff_u_hd_hpl_sph_hsc_secondwave_pair_positive = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps_after * S ((S (S ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_positive) + (ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps))) /\ ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps = ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps * a + ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_value_steps)))))) /\ (((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_start. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_start + S (0) = S ((S (0)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_positive)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_start. ff_d_hd_hpl_sph_hsc_secondwave_pair_positive = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_start * S ((S (0)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_positive) + (0))) /\ ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_terminal. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_terminal + S (hsc_dp_secondwave) = S ((S (l)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_positive)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_terminal. ff_d_hd_hpl_sph_hsc_secondwave_pair_positive = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_terminal * S ((S (l)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_positive) + (hsc_dp_secondwave))) /\ forall ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps. (exists ph_bound_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps. ph_bound_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps + S ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps = l) -> exists ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps. ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps_coefficient. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps_coefficient + S (ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps) = S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_positive)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps_coefficient. ff_u_hd_hpl_sph_hsc_secondwave_pair_positive = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps_coefficient * S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_positive) + (ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps))) /\ ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps_before. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps_before + S (ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps) = S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_positive)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps_before. ff_d_hd_hpl_sph_hsc_secondwave_pair_positive = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps_before * S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_positive) + (ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps))) /\ ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps_after. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps_after + S (ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps) = S ((S (S ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_positive)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps_after. ff_d_hd_hpl_sph_hsc_secondwave_pair_positive = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps_after * S ((S (S ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_positive) + (ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps))) /\ ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps = ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps * a + ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_positive_body_derivative_steps)))))))) /\ (exists ff_u_hd_hpl_sph_hsc_secondwave_pair_negative ff_v_hd_hpl_sph_hsc_secondwave_pair_negative ff_d_hd_hpl_sph_hsc_secondwave_pair_negative ff_e_hd_hpl_sph_hsc_secondwave_pair_negative. ((((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_start. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_start + S (0) = S ((S (0)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_negative)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_start. ff_u_hd_hpl_sph_hsc_secondwave_pair_negative = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_start * S ((S (0)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_negative) + (0))) /\ ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_terminal. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_terminal + S (hsc_vn_secondwave) = S ((S (l)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_negative)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_terminal. ff_u_hd_hpl_sph_hsc_secondwave_pair_negative = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_terminal * S ((S (l)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_negative) + (hsc_vn_secondwave))) /\ forall ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps. (exists ph_bound_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps. ph_bound_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps + S ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps = l) -> exists ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps. ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps_coefficient. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps_coefficient + S (ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps) = S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps)) * nc)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps_coefficient. nb = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps_coefficient * S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps)) * nc) + (ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps))) /\ ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps_before. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps_before + S (ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps) = S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_negative)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps_before. ff_u_hd_hpl_sph_hsc_secondwave_pair_negative = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps_before * S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_negative) + (ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps))) /\ ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps_after. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps_after + S (ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps) = S ((S (S ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_negative)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps_after. ff_u_hd_hpl_sph_hsc_secondwave_pair_negative = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps_after * S ((S (S ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_negative) + (ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps))) /\ ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps = ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps * a + ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_value_steps)))))) /\ (((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_start. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_start + S (0) = S ((S (0)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_negative)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_start. ff_d_hd_hpl_sph_hsc_secondwave_pair_negative = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_start * S ((S (0)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_negative) + (0))) /\ ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_terminal. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_terminal + S (hsc_dn_secondwave) = S ((S (l)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_negative)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_terminal. ff_d_hd_hpl_sph_hsc_secondwave_pair_negative = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_terminal * S ((S (l)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_negative) + (hsc_dn_secondwave))) /\ forall ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps. (exists ph_bound_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps. ph_bound_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps + S ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps = l) -> exists ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps. ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps_coefficient. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps_coefficient + S (ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps) = S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_negative)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps_coefficient. ff_u_hd_hpl_sph_hsc_secondwave_pair_negative = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps_coefficient * S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps)) * ff_v_hd_hpl_sph_hsc_secondwave_pair_negative) + (ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps))) /\ ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps_before. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps_before + S (ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps) = S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_negative)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps_before. ff_d_hd_hpl_sph_hsc_secondwave_pair_negative = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps_before * S ((S (ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_negative) + (ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps))) /\ ((((exists fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps_after. fs_h_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps_after + S (ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps) = S ((S (S ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_negative)) /\ exists fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps_after. ff_d_hd_hpl_sph_hsc_secondwave_pair_negative = fs_q_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps_after * S ((S (S ff_i_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps)) * ff_e_hd_hpl_sph_hsc_secondwave_pair_negative) + (ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps))) /\ ff_current_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps = ff_previous_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps * a + ff_coefficient_ph_hd_hpl_sph_hsc_secondwave_pair_negative_body_derivative_steps)))))))))) /\ ((exists hgcrt_mod_left_hpl_hsc_secondwave_root hgcrt_mod_right_hpl_hsc_secondwave_root. hsc_vp_secondwave + m * hgcrt_mod_left_hpl_hsc_secondwave_root = hsc_vn_secondwave + m * hgcrt_mod_right_hpl_hsc_secondwave_root) /\ (~(exists hgcrt_mod_left_hpl_hsc_secondwave hgcrt_mod_right_hpl_hsc_secondwave. hsc_dp_secondwave + p * hgcrt_mod_left_hpl_hsc_secondwave = hsc_dn_secondwave + p * hgcrt_mod_right_hpl_hsc_secondwave))))

The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.