BinaryExecutionPowerInvariant(d,s,a,m,n,r)

Hygienic expanded first-order definition

exists ff_exponent_be_transport. ((exists ff_u_ph_be_transport_horner ff_v_ph_be_transport_horner. ((((exists fs_h_ph_be_transport_horner_body_start. fs_h_ph_be_transport_horner_body_start + S (0) = S ((S (0)) * ff_v_ph_be_transport_horner)) /\ exists fs_q_ph_be_transport_horner_body_start. ff_u_ph_be_transport_horner = fs_q_ph_be_transport_horner_body_start * S ((S (0)) * ff_v_ph_be_transport_horner) + (0))) /\ ((((exists fs_h_ph_be_transport_horner_body_terminal. fs_h_ph_be_transport_horner_body_terminal + S (ff_exponent_be_transport) = S ((S (n)) * ff_v_ph_be_transport_horner)) /\ exists fs_q_ph_be_transport_horner_body_terminal. ff_u_ph_be_transport_horner = fs_q_ph_be_transport_horner_body_terminal * S ((S (n)) * ff_v_ph_be_transport_horner) + (ff_exponent_be_transport))) /\ forall ff_i_ph_be_transport_horner_body_steps. (exists ph_bound_be_transport_horner_body_steps. ph_bound_be_transport_horner_body_steps + S ff_i_ph_be_transport_horner_body_steps = n) -> exists ff_coefficient_ph_be_transport_horner_body_steps ff_previous_ph_be_transport_horner_body_steps ff_current_ph_be_transport_horner_body_steps. ((((exists fs_h_ph_be_transport_horner_body_steps_coefficient. fs_h_ph_be_transport_horner_body_steps_coefficient + S (ff_coefficient_ph_be_transport_horner_body_steps) = S ((S (ff_i_ph_be_transport_horner_body_steps)) * s)) /\ exists fs_q_ph_be_transport_horner_body_steps_coefficient. d = fs_q_ph_be_transport_horner_body_steps_coefficient * S ((S (ff_i_ph_be_transport_horner_body_steps)) * s) + (ff_coefficient_ph_be_transport_horner_body_steps))) /\ ((((exists fs_h_ph_be_transport_horner_body_steps_before. fs_h_ph_be_transport_horner_body_steps_before + S (ff_previous_ph_be_transport_horner_body_steps) = S ((S (ff_i_ph_be_transport_horner_body_steps)) * ff_v_ph_be_transport_horner)) /\ exists fs_q_ph_be_transport_horner_body_steps_before. ff_u_ph_be_transport_horner = fs_q_ph_be_transport_horner_body_steps_before * S ((S (ff_i_ph_be_transport_horner_body_steps)) * ff_v_ph_be_transport_horner) + (ff_previous_ph_be_transport_horner_body_steps))) /\ ((((exists fs_h_ph_be_transport_horner_body_steps_after. fs_h_ph_be_transport_horner_body_steps_after + S (ff_current_ph_be_transport_horner_body_steps) = S ((S (S ff_i_ph_be_transport_horner_body_steps)) * ff_v_ph_be_transport_horner)) /\ exists fs_q_ph_be_transport_horner_body_steps_after. ff_u_ph_be_transport_horner = fs_q_ph_be_transport_horner_body_steps_after * S ((S (S ff_i_ph_be_transport_horner_body_steps)) * ff_v_ph_be_transport_horner) + (ff_current_ph_be_transport_horner_body_steps))) /\ ff_current_ph_be_transport_horner_body_steps = ff_previous_ph_be_transport_horner_body_steps * 2 + ff_coefficient_ph_be_transport_horner_body_steps)))))) /\ (exists ff_power_binary_be_transport_power. ((exists ff_b_binary_be_transport_power_value ff_c_binary_be_transport_power_value. ((forall ff_i_binary_be_transport_power_value_repeat. (exists ff_lt_binary_be_transport_power_value_repeat_bound. ff_lt_binary_be_transport_power_value_repeat_bound + S ff_i_binary_be_transport_power_value_repeat = ff_exponent_be_transport) -> (((exists ff_h_binary_be_transport_power_value_repeat_decoded. ff_h_binary_be_transport_power_value_repeat_decoded + S (a) = S ((S (ff_i_binary_be_transport_power_value_repeat)) * ff_c_binary_be_transport_power_value)) /\ exists ff_q_binary_be_transport_power_value_repeat_decoded. ff_b_binary_be_transport_power_value = ff_q_binary_be_transport_power_value_repeat_decoded * S ((S (ff_i_binary_be_transport_power_value_repeat)) * ff_c_binary_be_transport_power_value) + (a)))) /\ (exists ff_u_binary_be_transport_power_value_product ff_v_binary_be_transport_power_value_product. ((((exists ff_h_binary_be_transport_power_value_product_start. ff_h_binary_be_transport_power_value_product_start + S (1) = S ((S (0)) * ff_v_binary_be_transport_power_value_product)) /\ exists ff_q_binary_be_transport_power_value_product_start. ff_u_binary_be_transport_power_value_product = ff_q_binary_be_transport_power_value_product_start * S ((S (0)) * ff_v_binary_be_transport_power_value_product) + (1))) /\ ((((exists ff_h_binary_be_transport_power_value_product_terminal. ff_h_binary_be_transport_power_value_product_terminal + S (ff_power_binary_be_transport_power) = S ((S (ff_exponent_be_transport)) * ff_v_binary_be_transport_power_value_product)) /\ exists ff_q_binary_be_transport_power_value_product_terminal. ff_u_binary_be_transport_power_value_product = ff_q_binary_be_transport_power_value_product_terminal * S ((S (ff_exponent_be_transport)) * ff_v_binary_be_transport_power_value_product) + (ff_power_binary_be_transport_power))) /\ forall ff_i_binary_be_transport_power_value_product. (exists ff_lt_binary_be_transport_power_value_product_bound. ff_lt_binary_be_transport_power_value_product_bound + S ff_i_binary_be_transport_power_value_product = ff_exponent_be_transport) -> exists ff_p_binary_be_transport_power_value_product ff_r_binary_be_transport_power_value_product ff_s_binary_be_transport_power_value_product. ((((exists ff_h_binary_be_transport_power_value_product_factor. ff_h_binary_be_transport_power_value_product_factor + S (ff_p_binary_be_transport_power_value_product) = S ((S (ff_i_binary_be_transport_power_value_product)) * ff_c_binary_be_transport_power_value)) /\ exists ff_q_binary_be_transport_power_value_product_factor. ff_b_binary_be_transport_power_value = ff_q_binary_be_transport_power_value_product_factor * S ((S (ff_i_binary_be_transport_power_value_product)) * ff_c_binary_be_transport_power_value) + (ff_p_binary_be_transport_power_value_product))) /\ ((((exists ff_h_binary_be_transport_power_value_product_partial. ff_h_binary_be_transport_power_value_product_partial + S (ff_r_binary_be_transport_power_value_product) = S ((S (ff_i_binary_be_transport_power_value_product)) * ff_v_binary_be_transport_power_value_product)) /\ exists ff_q_binary_be_transport_power_value_product_partial. ff_u_binary_be_transport_power_value_product = ff_q_binary_be_transport_power_value_product_partial * S ((S (ff_i_binary_be_transport_power_value_product)) * ff_v_binary_be_transport_power_value_product) + (ff_r_binary_be_transport_power_value_product))) /\ ((((exists ff_h_binary_be_transport_power_value_product_successor. ff_h_binary_be_transport_power_value_product_successor + S (ff_s_binary_be_transport_power_value_product) = S ((S (S ff_i_binary_be_transport_power_value_product)) * ff_v_binary_be_transport_power_value_product)) /\ exists ff_q_binary_be_transport_power_value_product_successor. ff_u_binary_be_transport_power_value_product = ff_q_binary_be_transport_power_value_product_successor * S ((S (S ff_i_binary_be_transport_power_value_product)) * ff_v_binary_be_transport_power_value_product) + (ff_s_binary_be_transport_power_value_product))) /\ ff_s_binary_be_transport_power_value_product = ff_r_binary_be_transport_power_value_product * ff_p_binary_be_transport_power_value_product)))))))) /\ (((exists ff_gap_binary_be_transport_power_residue. ff_gap_binary_be_transport_power_residue + S (r) = m) /\ (exists ff_left_binary_be_transport_power_residue_congruence ff_right_binary_be_transport_power_residue_congruence. (ff_power_binary_be_transport_power) + m * ff_left_binary_be_transport_power_residue_congruence = (r) + m * ff_right_binary_be_transport_power_residue_congruence))))))

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

Direct definition dependencies

Definitions depending on this notation

Checked theorems using this definition