binary_execution_step_power_invariant

Exact expanded first-order arithmetic statement

forall a h e m r d s. (exists ff_power_binary_previous_power. ((exists ff_b_binary_previous_power_value ff_c_binary_previous_power_value. ((forall ff_i_binary_previous_power_value_repeat. (exists ff_lt_binary_previous_power_value_repeat_bound. ff_lt_binary_previous_power_value_repeat_bound + S ff_i_binary_previous_power_value_repeat = h) -> (((exists ff_h_binary_previous_power_value_repeat_decoded. ff_h_binary_previous_power_value_repeat_decoded + S (a) = S ((S (ff_i_binary_previous_power_value_repeat)) * ff_c_binary_previous_power_value)) /\ exists ff_q_binary_previous_power_value_repeat_decoded. ff_b_binary_previous_power_value = ff_q_binary_previous_power_value_repeat_decoded * S ((S (ff_i_binary_previous_power_value_repeat)) * ff_c_binary_previous_power_value) + (a)))) /\ (exists ff_u_binary_previous_power_value_product ff_v_binary_previous_power_value_product. ((((exists ff_h_binary_previous_power_value_product_start. ff_h_binary_previous_power_value_product_start + S (1) = S ((S (0)) * ff_v_binary_previous_power_value_product)) /\ exists ff_q_binary_previous_power_value_product_start. ff_u_binary_previous_power_value_product = ff_q_binary_previous_power_value_product_start * S ((S (0)) * ff_v_binary_previous_power_value_product) + (1))) /\ ((((exists ff_h_binary_previous_power_value_product_terminal. ff_h_binary_previous_power_value_product_terminal + S (ff_power_binary_previous_power) = S ((S (h)) * ff_v_binary_previous_power_value_product)) /\ exists ff_q_binary_previous_power_value_product_terminal. ff_u_binary_previous_power_value_product = ff_q_binary_previous_power_value_product_terminal * S ((S (h)) * ff_v_binary_previous_power_value_product) + (ff_power_binary_previous_power))) /\ forall ff_i_binary_previous_power_value_product. (exists ff_lt_binary_previous_power_value_product_bound. ff_lt_binary_previous_power_value_product_bound + S ff_i_binary_previous_power_value_product = h) -> exists ff_p_binary_previous_power_value_product ff_r_binary_previous_power_value_product ff_s_binary_previous_power_value_product. ((((exists ff_h_binary_previous_power_value_product_factor. ff_h_binary_previous_power_value_product_factor + S (ff_p_binary_previous_power_value_product) = S ((S (ff_i_binary_previous_power_value_product)) * ff_c_binary_previous_power_value)) /\ exists ff_q_binary_previous_power_value_product_factor. ff_b_binary_previous_power_value = ff_q_binary_previous_power_value_product_factor * S ((S (ff_i_binary_previous_power_value_product)) * ff_c_binary_previous_power_value) + (ff_p_binary_previous_power_value_product))) /\ ((((exists ff_h_binary_previous_power_value_product_partial. ff_h_binary_previous_power_value_product_partial + S (ff_r_binary_previous_power_value_product) = S ((S (ff_i_binary_previous_power_value_product)) * ff_v_binary_previous_power_value_product)) /\ exists ff_q_binary_previous_power_value_product_partial. ff_u_binary_previous_power_value_product = ff_q_binary_previous_power_value_product_partial * S ((S (ff_i_binary_previous_power_value_product)) * ff_v_binary_previous_power_value_product) + (ff_r_binary_previous_power_value_product))) /\ ((((exists ff_h_binary_previous_power_value_product_successor. ff_h_binary_previous_power_value_product_successor + S (ff_s_binary_previous_power_value_product) = S ((S (S ff_i_binary_previous_power_value_product)) * ff_v_binary_previous_power_value_product)) /\ exists ff_q_binary_previous_power_value_product_successor. ff_u_binary_previous_power_value_product = ff_q_binary_previous_power_value_product_successor * S ((S (S ff_i_binary_previous_power_value_product)) * ff_v_binary_previous_power_value_product) + (ff_s_binary_previous_power_value_product))) /\ ff_s_binary_previous_power_value_product = ff_r_binary_previous_power_value_product * ff_p_binary_previous_power_value_product)))))))) /\ (((exists ff_gap_binary_previous_power_residue. ff_gap_binary_previous_power_residue + S (r) = m) /\ (exists ff_left_binary_previous_power_residue_congruence ff_right_binary_previous_power_residue_congruence. (ff_power_binary_previous_power) + m * ff_left_binary_previous_power_residue_congruence = (r) + m * ff_right_binary_previous_power_residue_congruence))))) -> ((((d = 0) \/ (d = 1)) /\ e = (h + h) + d)) -> ((((d = 0) /\ (((exists ff_gap_binary_step_square. ff_gap_binary_step_square + S (s) = m) /\ (exists ff_left_binary_step_square_congruence ff_right_binary_step_square_congruence. (r * r) + m * ff_left_binary_step_square_congruence = (s) + m * ff_right_binary_step_square_congruence)))) \/ ((d = 1) /\ (((exists ff_gap_binary_step_multiply. ff_gap_binary_step_multiply + S (s) = m) /\ (exists ff_left_binary_step_multiply_congruence ff_right_binary_step_multiply_congruence. ((r * r) * a) + m * ff_left_binary_step_multiply_congruence = (s) + m * ff_right_binary_step_multiply_congruence)))))) -> (exists ff_power_binary_current_power. ((exists ff_b_binary_current_power_value ff_c_binary_current_power_value. ((forall ff_i_binary_current_power_value_repeat. (exists ff_lt_binary_current_power_value_repeat_bound. ff_lt_binary_current_power_value_repeat_bound + S ff_i_binary_current_power_value_repeat = e) -> (((exists ff_h_binary_current_power_value_repeat_decoded. ff_h_binary_current_power_value_repeat_decoded + S (a) = S ((S (ff_i_binary_current_power_value_repeat)) * ff_c_binary_current_power_value)) /\ exists ff_q_binary_current_power_value_repeat_decoded. ff_b_binary_current_power_value = ff_q_binary_current_power_value_repeat_decoded * S ((S (ff_i_binary_current_power_value_repeat)) * ff_c_binary_current_power_value) + (a)))) /\ (exists ff_u_binary_current_power_value_product ff_v_binary_current_power_value_product. ((((exists ff_h_binary_current_power_value_product_start. ff_h_binary_current_power_value_product_start + S (1) = S ((S (0)) * ff_v_binary_current_power_value_product)) /\ exists ff_q_binary_current_power_value_product_start. ff_u_binary_current_power_value_product = ff_q_binary_current_power_value_product_start * S ((S (0)) * ff_v_binary_current_power_value_product) + (1))) /\ ((((exists ff_h_binary_current_power_value_product_terminal. ff_h_binary_current_power_value_product_terminal + S (ff_power_binary_current_power) = S ((S (e)) * ff_v_binary_current_power_value_product)) /\ exists ff_q_binary_current_power_value_product_terminal. ff_u_binary_current_power_value_product = ff_q_binary_current_power_value_product_terminal * S ((S (e)) * ff_v_binary_current_power_value_product) + (ff_power_binary_current_power))) /\ forall ff_i_binary_current_power_value_product. (exists ff_lt_binary_current_power_value_product_bound. ff_lt_binary_current_power_value_product_bound + S ff_i_binary_current_power_value_product = e) -> exists ff_p_binary_current_power_value_product ff_r_binary_current_power_value_product ff_s_binary_current_power_value_product. ((((exists ff_h_binary_current_power_value_product_factor. ff_h_binary_current_power_value_product_factor + S (ff_p_binary_current_power_value_product) = S ((S (ff_i_binary_current_power_value_product)) * ff_c_binary_current_power_value)) /\ exists ff_q_binary_current_power_value_product_factor. ff_b_binary_current_power_value = ff_q_binary_current_power_value_product_factor * S ((S (ff_i_binary_current_power_value_product)) * ff_c_binary_current_power_value) + (ff_p_binary_current_power_value_product))) /\ ((((exists ff_h_binary_current_power_value_product_partial. ff_h_binary_current_power_value_product_partial + S (ff_r_binary_current_power_value_product) = S ((S (ff_i_binary_current_power_value_product)) * ff_v_binary_current_power_value_product)) /\ exists ff_q_binary_current_power_value_product_partial. ff_u_binary_current_power_value_product = ff_q_binary_current_power_value_product_partial * S ((S (ff_i_binary_current_power_value_product)) * ff_v_binary_current_power_value_product) + (ff_r_binary_current_power_value_product))) /\ ((((exists ff_h_binary_current_power_value_product_successor. ff_h_binary_current_power_value_product_successor + S (ff_s_binary_current_power_value_product) = S ((S (S ff_i_binary_current_power_value_product)) * ff_v_binary_current_power_value_product)) /\ exists ff_q_binary_current_power_value_product_successor. ff_u_binary_current_power_value_product = ff_q_binary_current_power_value_product_successor * S ((S (S ff_i_binary_current_power_value_product)) * ff_v_binary_current_power_value_product) + (ff_s_binary_current_power_value_product))) /\ ff_s_binary_current_power_value_product = ff_r_binary_current_power_value_product * ff_p_binary_current_power_value_product)))))))) /\ (((exists ff_gap_binary_current_power_residue. ff_gap_binary_current_power_residue + S (s) = m) /\ (exists ff_left_binary_current_power_residue_congruence ff_right_binary_current_power_residue_congruence. (ff_power_binary_current_power) + m * ff_left_binary_current_power_residue_congruence = (s) + m * ff_right_binary_current_power_residue_congruence)))))