binomial_legendre_valuation_balance

Statement with defined notation

forall p a b c e A B D. ((~(p = 1) /\ forall frm_prime_left_kmvblvb_prime frm_prime_right_kmvblvb_prime. p = frm_prime_left_kmvblvb_prime * frm_prime_right_kmvblvb_prime -> frm_prime_left_kmvblvb_prime = 1 \/ frm_prime_right_kmvblvb_prime = 1)) -> (((exists bcf_lt_gap_kmvblvb_choose_out_of_range. bcf_lt_gap_kmvblvb_choose_out_of_range + S (a + b) = a) /\ c = 0) \/ ((exists bcf_le_gap_kmvblvb_choose_in_range. bcf_le_gap_kmvblvb_choose_in_range + (a) = a + b) /\ (exists bcf_row_code_code_kmvblvb_choose bcf_row_code_scale_kmvblvb_choose bcf_row_scale_code_kmvblvb_choose bcf_row_scale_scale_kmvblvb_choose bcf_row_code_kmvblvb_choose bcf_row_scale_kmvblvb_choose. ((forall bcf_row_index_kmvblvb_choose_table. (exists bcf_lt_gap_kmvblvb_choose_table_row_bound. bcf_lt_gap_kmvblvb_choose_table_row_bound + S (bcf_row_index_kmvblvb_choose_table) = S (a + b)) -> exists bcf_row_code_kmvblvb_choose_table bcf_row_scale_kmvblvb_choose_table. ((((exists bcf_height_kmvblvb_choose_table_decoded_row_code. bcf_height_kmvblvb_choose_table_decoded_row_code + S (bcf_row_code_kmvblvb_choose_table) = S ((S (bcf_row_index_kmvblvb_choose_table)) * bcf_row_code_scale_kmvblvb_choose)) /\ exists bcf_quotient_kmvblvb_choose_table_decoded_row_code. bcf_row_code_code_kmvblvb_choose = bcf_quotient_kmvblvb_choose_table_decoded_row_code * S ((S (bcf_row_index_kmvblvb_choose_table)) * bcf_row_code_scale_kmvblvb_choose) + (bcf_row_code_kmvblvb_choose_table))) /\ ((((exists bcf_height_kmvblvb_choose_table_decoded_row_scale. bcf_height_kmvblvb_choose_table_decoded_row_scale + S (bcf_row_scale_kmvblvb_choose_table) = S ((S (bcf_row_index_kmvblvb_choose_table)) * bcf_row_scale_scale_kmvblvb_choose)) /\ exists bcf_quotient_kmvblvb_choose_table_decoded_row_scale. bcf_row_scale_code_kmvblvb_choose = bcf_quotient_kmvblvb_choose_table_decoded_row_scale * S ((S (bcf_row_index_kmvblvb_choose_table)) * bcf_row_scale_scale_kmvblvb_choose) + (bcf_row_scale_kmvblvb_choose_table))) /\ ((bcf_row_index_kmvblvb_choose_table = 0 /\ (forall bcf_index_kmvblvb_choose_table_zero_row. (exists bcf_lt_gap_kmvblvb_choose_table_zero_row_bound. bcf_lt_gap_kmvblvb_choose_table_zero_row_bound + S (bcf_index_kmvblvb_choose_table_zero_row) = S (a + b)) -> exists bcf_value_kmvblvb_choose_table_zero_row. ((((exists bcf_height_kmvblvb_choose_table_zero_row_entry. bcf_height_kmvblvb_choose_table_zero_row_entry + S (bcf_value_kmvblvb_choose_table_zero_row) = S ((S (bcf_index_kmvblvb_choose_table_zero_row)) * bcf_row_scale_kmvblvb_choose_table)) /\ exists bcf_quotient_kmvblvb_choose_table_zero_row_entry. bcf_row_code_kmvblvb_choose_table = bcf_quotient_kmvblvb_choose_table_zero_row_entry * S ((S (bcf_index_kmvblvb_choose_table_zero_row)) * bcf_row_scale_kmvblvb_choose_table) + (bcf_value_kmvblvb_choose_table_zero_row))) /\ ((bcf_index_kmvblvb_choose_table_zero_row = 0 /\ bcf_value_kmvblvb_choose_table_zero_row = 1) \/ exists bcf_predecessor_kmvblvb_choose_table_zero_row. bcf_index_kmvblvb_choose_table_zero_row = S bcf_predecessor_kmvblvb_choose_table_zero_row /\ bcf_value_kmvblvb_choose_table_zero_row = 0)))) \/ exists bcf_predecessor_kmvblvb_choose_table bcf_previous_code_kmvblvb_choose_table bcf_previous_scale_kmvblvb_choose_table. bcf_row_index_kmvblvb_choose_table = S bcf_predecessor_kmvblvb_choose_table /\ ((((exists bcf_height_kmvblvb_choose_table_decoded_previous_code. bcf_height_kmvblvb_choose_table_decoded_previous_code + S (bcf_previous_code_kmvblvb_choose_table) = S ((S (bcf_predecessor_kmvblvb_choose_table)) * bcf_row_code_scale_kmvblvb_choose)) /\ exists bcf_quotient_kmvblvb_choose_table_decoded_previous_code. bcf_row_code_code_kmvblvb_choose = bcf_quotient_kmvblvb_choose_table_decoded_previous_code * S ((S (bcf_predecessor_kmvblvb_choose_table)) * bcf_row_code_scale_kmvblvb_choose) + (bcf_previous_code_kmvblvb_choose_table))) /\ ((((exists bcf_height_kmvblvb_choose_table_decoded_previous_scale. bcf_height_kmvblvb_choose_table_decoded_previous_scale + S (bcf_previous_scale_kmvblvb_choose_table) = S ((S (bcf_predecessor_kmvblvb_choose_table)) * bcf_row_scale_scale_kmvblvb_choose)) /\ exists bcf_quotient_kmvblvb_choose_table_decoded_previous_scale. bcf_row_scale_code_kmvblvb_choose = bcf_quotient_kmvblvb_choose_table_decoded_previous_scale * S ((S (bcf_predecessor_kmvblvb_choose_table)) * bcf_row_scale_scale_kmvblvb_choose) + (bcf_previous_scale_kmvblvb_choose_table))) /\ (forall bcf_index_kmvblvb_choose_table_row_step. (exists bcf_lt_gap_kmvblvb_choose_table_row_step_bound. bcf_lt_gap_kmvblvb_choose_table_row_step_bound + S (bcf_index_kmvblvb_choose_table_row_step) = S (a + b)) -> exists bcf_value_kmvblvb_choose_table_row_step. ((((exists bcf_height_kmvblvb_choose_table_row_step_entry. bcf_height_kmvblvb_choose_table_row_step_entry + S (bcf_value_kmvblvb_choose_table_row_step) = S ((S (bcf_index_kmvblvb_choose_table_row_step)) * bcf_row_scale_kmvblvb_choose_table)) /\ exists bcf_quotient_kmvblvb_choose_table_row_step_entry. bcf_row_code_kmvblvb_choose_table = bcf_quotient_kmvblvb_choose_table_row_step_entry * S ((S (bcf_index_kmvblvb_choose_table_row_step)) * bcf_row_scale_kmvblvb_choose_table) + (bcf_value_kmvblvb_choose_table_row_step))) /\ ((bcf_index_kmvblvb_choose_table_row_step = 0 /\ bcf_value_kmvblvb_choose_table_row_step = 1) \/ exists bcf_predecessor_kmvblvb_choose_table_row_step bcf_left_kmvblvb_choose_table_row_step bcf_right_kmvblvb_choose_table_row_step. bcf_index_kmvblvb_choose_table_row_step = S bcf_predecessor_kmvblvb_choose_table_row_step /\ ((((exists bcf_height_kmvblvb_choose_table_row_step_previous_left. bcf_height_kmvblvb_choose_table_row_step_previous_left + S (bcf_left_kmvblvb_choose_table_row_step) = S ((S (bcf_predecessor_kmvblvb_choose_table_row_step)) * bcf_previous_scale_kmvblvb_choose_table)) /\ exists bcf_quotient_kmvblvb_choose_table_row_step_previous_left. bcf_previous_code_kmvblvb_choose_table = bcf_quotient_kmvblvb_choose_table_row_step_previous_left * S ((S (bcf_predecessor_kmvblvb_choose_table_row_step)) * bcf_previous_scale_kmvblvb_choose_table) + (bcf_left_kmvblvb_choose_table_row_step))) /\ ((((exists bcf_height_kmvblvb_choose_table_row_step_previous_right. bcf_height_kmvblvb_choose_table_row_step_previous_right + S (bcf_right_kmvblvb_choose_table_row_step) = S ((S (S (bcf_predecessor_kmvblvb_choose_table_row_step))) * bcf_previous_scale_kmvblvb_choose_table)) /\ exists bcf_quotient_kmvblvb_choose_table_row_step_previous_right. bcf_previous_code_kmvblvb_choose_table = bcf_quotient_kmvblvb_choose_table_row_step_previous_right * S ((S (S (bcf_predecessor_kmvblvb_choose_table_row_step))) * bcf_previous_scale_kmvblvb_choose_table) + (bcf_right_kmvblvb_choose_table_row_step))) /\ bcf_value_kmvblvb_choose_table_row_step = bcf_left_kmvblvb_choose_table_row_step + bcf_right_kmvblvb_choose_table_row_step))))))))))) /\ ((((exists bcf_height_kmvblvb_choose_decoded_row_code. bcf_height_kmvblvb_choose_decoded_row_code + S (bcf_row_code_kmvblvb_choose) = S ((S (a + b)) * bcf_row_code_scale_kmvblvb_choose)) /\ exists bcf_quotient_kmvblvb_choose_decoded_row_code. bcf_row_code_code_kmvblvb_choose = bcf_quotient_kmvblvb_choose_decoded_row_code * S ((S (a + b)) * bcf_row_code_scale_kmvblvb_choose) + (bcf_row_code_kmvblvb_choose))) /\ ((((exists bcf_height_kmvblvb_choose_decoded_row_scale. bcf_height_kmvblvb_choose_decoded_row_scale + S (bcf_row_scale_kmvblvb_choose) = S ((S (a + b)) * bcf_row_scale_scale_kmvblvb_choose)) /\ exists bcf_quotient_kmvblvb_choose_decoded_row_scale. bcf_row_scale_code_kmvblvb_choose = bcf_quotient_kmvblvb_choose_decoded_row_scale * S ((S (a + b)) * bcf_row_scale_scale_kmvblvb_choose) + (bcf_row_scale_kmvblvb_choose))) /\ (((exists bcf_height_kmvblvb_choose_decoded_value. bcf_height_kmvblvb_choose_decoded_value + S (c) = S ((S (a)) * bcf_row_scale_kmvblvb_choose)) /\ exists bcf_quotient_kmvblvb_choose_decoded_value. bcf_row_code_kmvblvb_choose = bcf_quotient_kmvblvb_choose_decoded_value * S ((S (a)) * bcf_row_scale_kmvblvb_choose) + (c))))))))) -> (((exists bpv_gap_kmvblvb_value_exponent_bound. bpv_gap_kmvblvb_value_exponent_bound + e = c) /\ (exists bpv_result_kmvblvb_value_selected. ((exists ff_b_kmvblvb_value_selected_power ff_c_kmvblvb_value_selected_power. ((forall ff_i_kmvblvb_value_selected_power_repeat. (exists ff_lt_kmvblvb_value_selected_power_repeat_bound. ff_lt_kmvblvb_value_selected_power_repeat_bound + S ff_i_kmvblvb_value_selected_power_repeat = e) -> (((exists ff_h_kmvblvb_value_selected_power_repeat_decoded. ff_h_kmvblvb_value_selected_power_repeat_decoded + S (p) = S ((S (ff_i_kmvblvb_value_selected_power_repeat)) * ff_c_kmvblvb_value_selected_power)) /\ exists ff_q_kmvblvb_value_selected_power_repeat_decoded. ff_b_kmvblvb_value_selected_power = ff_q_kmvblvb_value_selected_power_repeat_decoded * S ((S (ff_i_kmvblvb_value_selected_power_repeat)) * ff_c_kmvblvb_value_selected_power) + (p)))) /\ (exists ff_u_kmvblvb_value_selected_power_product ff_v_kmvblvb_value_selected_power_product. ((((exists ff_h_kmvblvb_value_selected_power_product_start. ff_h_kmvblvb_value_selected_power_product_start + S (1) = S ((S (0)) * ff_v_kmvblvb_value_selected_power_product)) /\ exists ff_q_kmvblvb_value_selected_power_product_start. ff_u_kmvblvb_value_selected_power_product = ff_q_kmvblvb_value_selected_power_product_start * S ((S (0)) * ff_v_kmvblvb_value_selected_power_product) + (1))) /\ ((((exists ff_h_kmvblvb_value_selected_power_product_terminal. ff_h_kmvblvb_value_selected_power_product_terminal + S (bpv_result_kmvblvb_value_selected) = S ((S (e)) * ff_v_kmvblvb_value_selected_power_product)) /\ exists ff_q_kmvblvb_value_selected_power_product_terminal. ff_u_kmvblvb_value_selected_power_product = ff_q_kmvblvb_value_selected_power_product_terminal * S ((S (e)) * ff_v_kmvblvb_value_selected_power_product) + (bpv_result_kmvblvb_value_selected))) /\ forall ff_i_kmvblvb_value_selected_power_product. (exists ff_lt_kmvblvb_value_selected_power_product_bound. ff_lt_kmvblvb_value_selected_power_product_bound + S ff_i_kmvblvb_value_selected_power_product = e) -> exists ff_p_kmvblvb_value_selected_power_product ff_r_kmvblvb_value_selected_power_product ff_s_kmvblvb_value_selected_power_product. ((((exists ff_h_kmvblvb_value_selected_power_product_factor. ff_h_kmvblvb_value_selected_power_product_factor + S (ff_p_kmvblvb_value_selected_power_product) = S ((S (ff_i_kmvblvb_value_selected_power_product)) * ff_c_kmvblvb_value_selected_power)) /\ exists ff_q_kmvblvb_value_selected_power_product_factor. ff_b_kmvblvb_value_selected_power = ff_q_kmvblvb_value_selected_power_product_factor * S ((S (ff_i_kmvblvb_value_selected_power_product)) * ff_c_kmvblvb_value_selected_power) + (ff_p_kmvblvb_value_selected_power_product))) /\ ((((exists ff_h_kmvblvb_value_selected_power_product_partial. ff_h_kmvblvb_value_selected_power_product_partial + S (ff_r_kmvblvb_value_selected_power_product) = S ((S (ff_i_kmvblvb_value_selected_power_product)) * ff_v_kmvblvb_value_selected_power_product)) /\ exists ff_q_kmvblvb_value_selected_power_product_partial. ff_u_kmvblvb_value_selected_power_product = ff_q_kmvblvb_value_selected_power_product_partial * S ((S (ff_i_kmvblvb_value_selected_power_product)) * ff_v_kmvblvb_value_selected_power_product) + (ff_r_kmvblvb_value_selected_power_product))) /\ ((((exists ff_h_kmvblvb_value_selected_power_product_successor. ff_h_kmvblvb_value_selected_power_product_successor + S (ff_s_kmvblvb_value_selected_power_product) = S ((S (S ff_i_kmvblvb_value_selected_power_product)) * ff_v_kmvblvb_value_selected_power_product)) /\ exists ff_q_kmvblvb_value_selected_power_product_successor. ff_u_kmvblvb_value_selected_power_product = ff_q_kmvblvb_value_selected_power_product_successor * S ((S (S ff_i_kmvblvb_value_selected_power_product)) * ff_v_kmvblvb_value_selected_power_product) + (ff_s_kmvblvb_value_selected_power_product))) /\ ff_s_kmvblvb_value_selected_power_product = ff_r_kmvblvb_value_selected_power_product * ff_p_kmvblvb_value_selected_power_product)))))))) /\ (exists bpv_factor_kmvblvb_value_selected_divides. c = bpv_result_kmvblvb_value_selected * bpv_factor_kmvblvb_value_selected_divides)))) /\ forall bpv_candidate_kmvblvb_value. (exists bpv_gap_kmvblvb_value_candidate_bound. bpv_gap_kmvblvb_value_candidate_bound + bpv_candidate_kmvblvb_value = c) -> (exists bpv_result_kmvblvb_value_candidate. ((exists ff_b_kmvblvb_value_candidate_power ff_c_kmvblvb_value_candidate_power. ((forall ff_i_kmvblvb_value_candidate_power_repeat. (exists ff_lt_kmvblvb_value_candidate_power_repeat_bound. ff_lt_kmvblvb_value_candidate_power_repeat_bound + S ff_i_kmvblvb_value_candidate_power_repeat = bpv_candidate_kmvblvb_value) -> (((exists ff_h_kmvblvb_value_candidate_power_repeat_decoded. ff_h_kmvblvb_value_candidate_power_repeat_decoded + S (p) = S ((S (ff_i_kmvblvb_value_candidate_power_repeat)) * ff_c_kmvblvb_value_candidate_power)) /\ exists ff_q_kmvblvb_value_candidate_power_repeat_decoded. ff_b_kmvblvb_value_candidate_power = ff_q_kmvblvb_value_candidate_power_repeat_decoded * S ((S (ff_i_kmvblvb_value_candidate_power_repeat)) * ff_c_kmvblvb_value_candidate_power) + (p)))) /\ (exists ff_u_kmvblvb_value_candidate_power_product ff_v_kmvblvb_value_candidate_power_product. ((((exists ff_h_kmvblvb_value_candidate_power_product_start. ff_h_kmvblvb_value_candidate_power_product_start + S (1) = S ((S (0)) * ff_v_kmvblvb_value_candidate_power_product)) /\ exists ff_q_kmvblvb_value_candidate_power_product_start. ff_u_kmvblvb_value_candidate_power_product = ff_q_kmvblvb_value_candidate_power_product_start * S ((S (0)) * ff_v_kmvblvb_value_candidate_power_product) + (1))) /\ ((((exists ff_h_kmvblvb_value_candidate_power_product_terminal. ff_h_kmvblvb_value_candidate_power_product_terminal + S (bpv_result_kmvblvb_value_candidate) = S ((S (bpv_candidate_kmvblvb_value)) * ff_v_kmvblvb_value_candidate_power_product)) /\ exists ff_q_kmvblvb_value_candidate_power_product_terminal. ff_u_kmvblvb_value_candidate_power_product = ff_q_kmvblvb_value_candidate_power_product_terminal * S ((S (bpv_candidate_kmvblvb_value)) * ff_v_kmvblvb_value_candidate_power_product) + (bpv_result_kmvblvb_value_candidate))) /\ forall ff_i_kmvblvb_value_candidate_power_product. (exists ff_lt_kmvblvb_value_candidate_power_product_bound. ff_lt_kmvblvb_value_candidate_power_product_bound + S ff_i_kmvblvb_value_candidate_power_product = bpv_candidate_kmvblvb_value) -> exists ff_p_kmvblvb_value_candidate_power_product ff_r_kmvblvb_value_candidate_power_product ff_s_kmvblvb_value_candidate_power_product. ((((exists ff_h_kmvblvb_value_candidate_power_product_factor. ff_h_kmvblvb_value_candidate_power_product_factor + S (ff_p_kmvblvb_value_candidate_power_product) = S ((S (ff_i_kmvblvb_value_candidate_power_product)) * ff_c_kmvblvb_value_candidate_power)) /\ exists ff_q_kmvblvb_value_candidate_power_product_factor. ff_b_kmvblvb_value_candidate_power = ff_q_kmvblvb_value_candidate_power_product_factor * S ((S (ff_i_kmvblvb_value_candidate_power_product)) * ff_c_kmvblvb_value_candidate_power) + (ff_p_kmvblvb_value_candidate_power_product))) /\ ((((exists ff_h_kmvblvb_value_candidate_power_product_partial. ff_h_kmvblvb_value_candidate_power_product_partial + S (ff_r_kmvblvb_value_candidate_power_product) = S ((S (ff_i_kmvblvb_value_candidate_power_product)) * ff_v_kmvblvb_value_candidate_power_product)) /\ exists ff_q_kmvblvb_value_candidate_power_product_partial. ff_u_kmvblvb_value_candidate_power_product = ff_q_kmvblvb_value_candidate_power_product_partial * S ((S (ff_i_kmvblvb_value_candidate_power_product)) * ff_v_kmvblvb_value_candidate_power_product) + (ff_r_kmvblvb_value_candidate_power_product))) /\ ((((exists ff_h_kmvblvb_value_candidate_power_product_successor. ff_h_kmvblvb_value_candidate_power_product_successor + S (ff_s_kmvblvb_value_candidate_power_product) = S ((S (S ff_i_kmvblvb_value_candidate_power_product)) * ff_v_kmvblvb_value_candidate_power_product)) /\ exists ff_q_kmvblvb_value_candidate_power_product_successor. ff_u_kmvblvb_value_candidate_power_product = ff_q_kmvblvb_value_candidate_power_product_successor * S ((S (S ff_i_kmvblvb_value_candidate_power_product)) * ff_v_kmvblvb_value_candidate_power_product) + (ff_s_kmvblvb_value_candidate_power_product))) /\ ff_s_kmvblvb_value_candidate_power_product = ff_r_kmvblvb_value_candidate_power_product * ff_p_kmvblvb_value_candidate_power_product)))))))) /\ (exists bpv_factor_kmvblvb_value_candidate_divides. c = bpv_result_kmvblvb_value_candidate * bpv_factor_kmvblvb_value_candidate_divides))) -> (exists bpv_gap_kmvblvb_value_maximal. bpv_gap_kmvblvb_value_maximal + bpv_candidate_kmvblvb_value = e)) -> (exists bls_code_kmvblvb_total bls_scale_kmvblvb_total. ((forall bls_index_kmvblvb_total_prefix. (exists bls_gap_kmvblvb_total_prefix_bound. bls_gap_kmvblvb_total_prefix_bound + S (bls_index_kmvblvb_total_prefix) = ((a + b))) -> exists bls_power_kmvblvb_total_prefix bls_quotient_kmvblvb_total_prefix bls_remainder_kmvblvb_total_prefix. ((exists bpvi_b_bls_kmvblvb_total_prefix_power bpvi_c_bls_kmvblvb_total_prefix_power. ((forall bpvi_i_bls_kmvblvb_total_prefix_power. (exists bpvi_repeat_gap_bls_kmvblvb_total_prefix_power. bpvi_repeat_gap_bls_kmvblvb_total_prefix_power + S bpvi_i_bls_kmvblvb_total_prefix_power = S bls_index_kmvblvb_total_prefix) -> (((exists bpvi_h_bls_kmvblvb_total_prefix_power_repeat. bpvi_h_bls_kmvblvb_total_prefix_power_repeat + S (p) = S ((S (bpvi_i_bls_kmvblvb_total_prefix_power)) * bpvi_c_bls_kmvblvb_total_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_total_prefix_power_repeat. bpvi_b_bls_kmvblvb_total_prefix_power = bpvi_q_bls_kmvblvb_total_prefix_power_repeat * S ((S (bpvi_i_bls_kmvblvb_total_prefix_power)) * bpvi_c_bls_kmvblvb_total_prefix_power) + (p)))) /\ (exists bpvi_u_bls_kmvblvb_total_prefix_power bpvi_v_bls_kmvblvb_total_prefix_power. ((((exists bpvi_h_bls_kmvblvb_total_prefix_power_start. bpvi_h_bls_kmvblvb_total_prefix_power_start + S (1) = S ((S (0)) * bpvi_v_bls_kmvblvb_total_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_total_prefix_power_start. bpvi_u_bls_kmvblvb_total_prefix_power = bpvi_q_bls_kmvblvb_total_prefix_power_start * S ((S (0)) * bpvi_v_bls_kmvblvb_total_prefix_power) + (1))) /\ ((((exists bpvi_h_bls_kmvblvb_total_prefix_power_terminal. bpvi_h_bls_kmvblvb_total_prefix_power_terminal + S (bls_power_kmvblvb_total_prefix) = S ((S (S bls_index_kmvblvb_total_prefix)) * bpvi_v_bls_kmvblvb_total_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_total_prefix_power_terminal. bpvi_u_bls_kmvblvb_total_prefix_power = bpvi_q_bls_kmvblvb_total_prefix_power_terminal * S ((S (S bls_index_kmvblvb_total_prefix)) * bpvi_v_bls_kmvblvb_total_prefix_power) + (bls_power_kmvblvb_total_prefix))) /\ forall bpvi_j_bls_kmvblvb_total_prefix_power. (exists bpvi_product_gap_bls_kmvblvb_total_prefix_power. bpvi_product_gap_bls_kmvblvb_total_prefix_power + S bpvi_j_bls_kmvblvb_total_prefix_power = S bls_index_kmvblvb_total_prefix) -> exists bpvi_factor_bls_kmvblvb_total_prefix_power bpvi_partial_bls_kmvblvb_total_prefix_power bpvi_successor_bls_kmvblvb_total_prefix_power. ((((exists bpvi_h_bls_kmvblvb_total_prefix_power_factor. bpvi_h_bls_kmvblvb_total_prefix_power_factor + S (bpvi_factor_bls_kmvblvb_total_prefix_power) = S ((S (bpvi_j_bls_kmvblvb_total_prefix_power)) * bpvi_c_bls_kmvblvb_total_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_total_prefix_power_factor. bpvi_b_bls_kmvblvb_total_prefix_power = bpvi_q_bls_kmvblvb_total_prefix_power_factor * S ((S (bpvi_j_bls_kmvblvb_total_prefix_power)) * bpvi_c_bls_kmvblvb_total_prefix_power) + (bpvi_factor_bls_kmvblvb_total_prefix_power))) /\ ((((exists bpvi_h_bls_kmvblvb_total_prefix_power_partial. bpvi_h_bls_kmvblvb_total_prefix_power_partial + S (bpvi_partial_bls_kmvblvb_total_prefix_power) = S ((S (bpvi_j_bls_kmvblvb_total_prefix_power)) * bpvi_v_bls_kmvblvb_total_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_total_prefix_power_partial. bpvi_u_bls_kmvblvb_total_prefix_power = bpvi_q_bls_kmvblvb_total_prefix_power_partial * S ((S (bpvi_j_bls_kmvblvb_total_prefix_power)) * bpvi_v_bls_kmvblvb_total_prefix_power) + (bpvi_partial_bls_kmvblvb_total_prefix_power))) /\ ((((exists bpvi_h_bls_kmvblvb_total_prefix_power_successor. bpvi_h_bls_kmvblvb_total_prefix_power_successor + S (bpvi_successor_bls_kmvblvb_total_prefix_power) = S ((S (S bpvi_j_bls_kmvblvb_total_prefix_power)) * bpvi_v_bls_kmvblvb_total_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_total_prefix_power_successor. bpvi_u_bls_kmvblvb_total_prefix_power = bpvi_q_bls_kmvblvb_total_prefix_power_successor * S ((S (S bpvi_j_bls_kmvblvb_total_prefix_power)) * bpvi_v_bls_kmvblvb_total_prefix_power) + (bpvi_successor_bls_kmvblvb_total_prefix_power))) /\ bpvi_successor_bls_kmvblvb_total_prefix_power = bpvi_partial_bls_kmvblvb_total_prefix_power * bpvi_factor_bls_kmvblvb_total_prefix_power)))))))) /\ ((((exists ff_h_bls_kmvblvb_total_prefix_quotient_entry. ff_h_bls_kmvblvb_total_prefix_quotient_entry + S (bls_quotient_kmvblvb_total_prefix) = S ((S (bls_index_kmvblvb_total_prefix)) * bls_scale_kmvblvb_total)) /\ exists ff_q_bls_kmvblvb_total_prefix_quotient_entry. bls_code_kmvblvb_total = ff_q_bls_kmvblvb_total_prefix_quotient_entry * S ((S (bls_index_kmvblvb_total_prefix)) * bls_scale_kmvblvb_total) + (bls_quotient_kmvblvb_total_prefix))) /\ (((a + b) = bls_power_kmvblvb_total_prefix * bls_quotient_kmvblvb_total_prefix + bls_remainder_kmvblvb_total_prefix /\ exists bls_remainder_gap_kmvblvb_total_prefix_division. bls_remainder_gap_kmvblvb_total_prefix_division + S (bls_remainder_kmvblvb_total_prefix) = bls_power_kmvblvb_total_prefix))))) /\ (exists ff_u_bls_kmvblvb_total_sum ff_v_bls_kmvblvb_total_sum. ((((exists ff_h_bls_kmvblvb_total_sum_start. ff_h_bls_kmvblvb_total_sum_start + S (0) = S ((S (0)) * ff_v_bls_kmvblvb_total_sum)) /\ exists ff_q_bls_kmvblvb_total_sum_start. ff_u_bls_kmvblvb_total_sum = ff_q_bls_kmvblvb_total_sum_start * S ((S (0)) * ff_v_bls_kmvblvb_total_sum) + (0))) /\ ((((exists ff_h_bls_kmvblvb_total_sum_terminal. ff_h_bls_kmvblvb_total_sum_terminal + S (A) = S ((S ((a + b))) * ff_v_bls_kmvblvb_total_sum)) /\ exists ff_q_bls_kmvblvb_total_sum_terminal. ff_u_bls_kmvblvb_total_sum = ff_q_bls_kmvblvb_total_sum_terminal * S ((S ((a + b))) * ff_v_bls_kmvblvb_total_sum) + (A))) /\ forall ff_i_bls_kmvblvb_total_sum. (exists ff_lt_bls_kmvblvb_total_sum_bound. ff_lt_bls_kmvblvb_total_sum_bound + S ff_i_bls_kmvblvb_total_sum = (a + b)) -> exists ff_a_bls_kmvblvb_total_sum ff_r_bls_kmvblvb_total_sum ff_s_bls_kmvblvb_total_sum. ((((exists ff_h_bls_kmvblvb_total_sum_summand. ff_h_bls_kmvblvb_total_sum_summand + S (ff_a_bls_kmvblvb_total_sum) = S ((S (ff_i_bls_kmvblvb_total_sum)) * bls_scale_kmvblvb_total)) /\ exists ff_q_bls_kmvblvb_total_sum_summand. bls_code_kmvblvb_total = ff_q_bls_kmvblvb_total_sum_summand * S ((S (ff_i_bls_kmvblvb_total_sum)) * bls_scale_kmvblvb_total) + (ff_a_bls_kmvblvb_total_sum))) /\ ((((exists ff_h_bls_kmvblvb_total_sum_partial. ff_h_bls_kmvblvb_total_sum_partial + S (ff_r_bls_kmvblvb_total_sum) = S ((S (ff_i_bls_kmvblvb_total_sum)) * ff_v_bls_kmvblvb_total_sum)) /\ exists ff_q_bls_kmvblvb_total_sum_partial. ff_u_bls_kmvblvb_total_sum = ff_q_bls_kmvblvb_total_sum_partial * S ((S (ff_i_bls_kmvblvb_total_sum)) * ff_v_bls_kmvblvb_total_sum) + (ff_r_bls_kmvblvb_total_sum))) /\ ((((exists ff_h_bls_kmvblvb_total_sum_successor. ff_h_bls_kmvblvb_total_sum_successor + S (ff_s_bls_kmvblvb_total_sum) = S ((S (S ff_i_bls_kmvblvb_total_sum)) * ff_v_bls_kmvblvb_total_sum)) /\ exists ff_q_bls_kmvblvb_total_sum_successor. ff_u_bls_kmvblvb_total_sum = ff_q_bls_kmvblvb_total_sum_successor * S ((S (S ff_i_bls_kmvblvb_total_sum)) * ff_v_bls_kmvblvb_total_sum) + (ff_s_bls_kmvblvb_total_sum))) /\ ff_s_bls_kmvblvb_total_sum = ff_r_bls_kmvblvb_total_sum + ff_a_bls_kmvblvb_total_sum)))))))) -> (exists bls_code_kmvblvb_left bls_scale_kmvblvb_left. ((forall bls_index_kmvblvb_left_prefix. (exists bls_gap_kmvblvb_left_prefix_bound. bls_gap_kmvblvb_left_prefix_bound + S (bls_index_kmvblvb_left_prefix) = (a)) -> exists bls_power_kmvblvb_left_prefix bls_quotient_kmvblvb_left_prefix bls_remainder_kmvblvb_left_prefix. ((exists bpvi_b_bls_kmvblvb_left_prefix_power bpvi_c_bls_kmvblvb_left_prefix_power. ((forall bpvi_i_bls_kmvblvb_left_prefix_power. (exists bpvi_repeat_gap_bls_kmvblvb_left_prefix_power. bpvi_repeat_gap_bls_kmvblvb_left_prefix_power + S bpvi_i_bls_kmvblvb_left_prefix_power = S bls_index_kmvblvb_left_prefix) -> (((exists bpvi_h_bls_kmvblvb_left_prefix_power_repeat. bpvi_h_bls_kmvblvb_left_prefix_power_repeat + S (p) = S ((S (bpvi_i_bls_kmvblvb_left_prefix_power)) * bpvi_c_bls_kmvblvb_left_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_left_prefix_power_repeat. bpvi_b_bls_kmvblvb_left_prefix_power = bpvi_q_bls_kmvblvb_left_prefix_power_repeat * S ((S (bpvi_i_bls_kmvblvb_left_prefix_power)) * bpvi_c_bls_kmvblvb_left_prefix_power) + (p)))) /\ (exists bpvi_u_bls_kmvblvb_left_prefix_power bpvi_v_bls_kmvblvb_left_prefix_power. ((((exists bpvi_h_bls_kmvblvb_left_prefix_power_start. bpvi_h_bls_kmvblvb_left_prefix_power_start + S (1) = S ((S (0)) * bpvi_v_bls_kmvblvb_left_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_left_prefix_power_start. bpvi_u_bls_kmvblvb_left_prefix_power = bpvi_q_bls_kmvblvb_left_prefix_power_start * S ((S (0)) * bpvi_v_bls_kmvblvb_left_prefix_power) + (1))) /\ ((((exists bpvi_h_bls_kmvblvb_left_prefix_power_terminal. bpvi_h_bls_kmvblvb_left_prefix_power_terminal + S (bls_power_kmvblvb_left_prefix) = S ((S (S bls_index_kmvblvb_left_prefix)) * bpvi_v_bls_kmvblvb_left_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_left_prefix_power_terminal. bpvi_u_bls_kmvblvb_left_prefix_power = bpvi_q_bls_kmvblvb_left_prefix_power_terminal * S ((S (S bls_index_kmvblvb_left_prefix)) * bpvi_v_bls_kmvblvb_left_prefix_power) + (bls_power_kmvblvb_left_prefix))) /\ forall bpvi_j_bls_kmvblvb_left_prefix_power. (exists bpvi_product_gap_bls_kmvblvb_left_prefix_power. bpvi_product_gap_bls_kmvblvb_left_prefix_power + S bpvi_j_bls_kmvblvb_left_prefix_power = S bls_index_kmvblvb_left_prefix) -> exists bpvi_factor_bls_kmvblvb_left_prefix_power bpvi_partial_bls_kmvblvb_left_prefix_power bpvi_successor_bls_kmvblvb_left_prefix_power. ((((exists bpvi_h_bls_kmvblvb_left_prefix_power_factor. bpvi_h_bls_kmvblvb_left_prefix_power_factor + S (bpvi_factor_bls_kmvblvb_left_prefix_power) = S ((S (bpvi_j_bls_kmvblvb_left_prefix_power)) * bpvi_c_bls_kmvblvb_left_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_left_prefix_power_factor. bpvi_b_bls_kmvblvb_left_prefix_power = bpvi_q_bls_kmvblvb_left_prefix_power_factor * S ((S (bpvi_j_bls_kmvblvb_left_prefix_power)) * bpvi_c_bls_kmvblvb_left_prefix_power) + (bpvi_factor_bls_kmvblvb_left_prefix_power))) /\ ((((exists bpvi_h_bls_kmvblvb_left_prefix_power_partial. bpvi_h_bls_kmvblvb_left_prefix_power_partial + S (bpvi_partial_bls_kmvblvb_left_prefix_power) = S ((S (bpvi_j_bls_kmvblvb_left_prefix_power)) * bpvi_v_bls_kmvblvb_left_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_left_prefix_power_partial. bpvi_u_bls_kmvblvb_left_prefix_power = bpvi_q_bls_kmvblvb_left_prefix_power_partial * S ((S (bpvi_j_bls_kmvblvb_left_prefix_power)) * bpvi_v_bls_kmvblvb_left_prefix_power) + (bpvi_partial_bls_kmvblvb_left_prefix_power))) /\ ((((exists bpvi_h_bls_kmvblvb_left_prefix_power_successor. bpvi_h_bls_kmvblvb_left_prefix_power_successor + S (bpvi_successor_bls_kmvblvb_left_prefix_power) = S ((S (S bpvi_j_bls_kmvblvb_left_prefix_power)) * bpvi_v_bls_kmvblvb_left_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_left_prefix_power_successor. bpvi_u_bls_kmvblvb_left_prefix_power = bpvi_q_bls_kmvblvb_left_prefix_power_successor * S ((S (S bpvi_j_bls_kmvblvb_left_prefix_power)) * bpvi_v_bls_kmvblvb_left_prefix_power) + (bpvi_successor_bls_kmvblvb_left_prefix_power))) /\ bpvi_successor_bls_kmvblvb_left_prefix_power = bpvi_partial_bls_kmvblvb_left_prefix_power * bpvi_factor_bls_kmvblvb_left_prefix_power)))))))) /\ ((((exists ff_h_bls_kmvblvb_left_prefix_quotient_entry. ff_h_bls_kmvblvb_left_prefix_quotient_entry + S (bls_quotient_kmvblvb_left_prefix) = S ((S (bls_index_kmvblvb_left_prefix)) * bls_scale_kmvblvb_left)) /\ exists ff_q_bls_kmvblvb_left_prefix_quotient_entry. bls_code_kmvblvb_left = ff_q_bls_kmvblvb_left_prefix_quotient_entry * S ((S (bls_index_kmvblvb_left_prefix)) * bls_scale_kmvblvb_left) + (bls_quotient_kmvblvb_left_prefix))) /\ ((a = bls_power_kmvblvb_left_prefix * bls_quotient_kmvblvb_left_prefix + bls_remainder_kmvblvb_left_prefix /\ exists bls_remainder_gap_kmvblvb_left_prefix_division. bls_remainder_gap_kmvblvb_left_prefix_division + S (bls_remainder_kmvblvb_left_prefix) = bls_power_kmvblvb_left_prefix))))) /\ (exists ff_u_bls_kmvblvb_left_sum ff_v_bls_kmvblvb_left_sum. ((((exists ff_h_bls_kmvblvb_left_sum_start. ff_h_bls_kmvblvb_left_sum_start + S (0) = S ((S (0)) * ff_v_bls_kmvblvb_left_sum)) /\ exists ff_q_bls_kmvblvb_left_sum_start. ff_u_bls_kmvblvb_left_sum = ff_q_bls_kmvblvb_left_sum_start * S ((S (0)) * ff_v_bls_kmvblvb_left_sum) + (0))) /\ ((((exists ff_h_bls_kmvblvb_left_sum_terminal. ff_h_bls_kmvblvb_left_sum_terminal + S (B) = S ((S (a)) * ff_v_bls_kmvblvb_left_sum)) /\ exists ff_q_bls_kmvblvb_left_sum_terminal. ff_u_bls_kmvblvb_left_sum = ff_q_bls_kmvblvb_left_sum_terminal * S ((S (a)) * ff_v_bls_kmvblvb_left_sum) + (B))) /\ forall ff_i_bls_kmvblvb_left_sum. (exists ff_lt_bls_kmvblvb_left_sum_bound. ff_lt_bls_kmvblvb_left_sum_bound + S ff_i_bls_kmvblvb_left_sum = a) -> exists ff_a_bls_kmvblvb_left_sum ff_r_bls_kmvblvb_left_sum ff_s_bls_kmvblvb_left_sum. ((((exists ff_h_bls_kmvblvb_left_sum_summand. ff_h_bls_kmvblvb_left_sum_summand + S (ff_a_bls_kmvblvb_left_sum) = S ((S (ff_i_bls_kmvblvb_left_sum)) * bls_scale_kmvblvb_left)) /\ exists ff_q_bls_kmvblvb_left_sum_summand. bls_code_kmvblvb_left = ff_q_bls_kmvblvb_left_sum_summand * S ((S (ff_i_bls_kmvblvb_left_sum)) * bls_scale_kmvblvb_left) + (ff_a_bls_kmvblvb_left_sum))) /\ ((((exists ff_h_bls_kmvblvb_left_sum_partial. ff_h_bls_kmvblvb_left_sum_partial + S (ff_r_bls_kmvblvb_left_sum) = S ((S (ff_i_bls_kmvblvb_left_sum)) * ff_v_bls_kmvblvb_left_sum)) /\ exists ff_q_bls_kmvblvb_left_sum_partial. ff_u_bls_kmvblvb_left_sum = ff_q_bls_kmvblvb_left_sum_partial * S ((S (ff_i_bls_kmvblvb_left_sum)) * ff_v_bls_kmvblvb_left_sum) + (ff_r_bls_kmvblvb_left_sum))) /\ ((((exists ff_h_bls_kmvblvb_left_sum_successor. ff_h_bls_kmvblvb_left_sum_successor + S (ff_s_bls_kmvblvb_left_sum) = S ((S (S ff_i_bls_kmvblvb_left_sum)) * ff_v_bls_kmvblvb_left_sum)) /\ exists ff_q_bls_kmvblvb_left_sum_successor. ff_u_bls_kmvblvb_left_sum = ff_q_bls_kmvblvb_left_sum_successor * S ((S (S ff_i_bls_kmvblvb_left_sum)) * ff_v_bls_kmvblvb_left_sum) + (ff_s_bls_kmvblvb_left_sum))) /\ ff_s_bls_kmvblvb_left_sum = ff_r_bls_kmvblvb_left_sum + ff_a_bls_kmvblvb_left_sum)))))))) -> (exists bls_code_kmvblvb_right bls_scale_kmvblvb_right. ((forall bls_index_kmvblvb_right_prefix. (exists bls_gap_kmvblvb_right_prefix_bound. bls_gap_kmvblvb_right_prefix_bound + S (bls_index_kmvblvb_right_prefix) = (b)) -> exists bls_power_kmvblvb_right_prefix bls_quotient_kmvblvb_right_prefix bls_remainder_kmvblvb_right_prefix. ((exists bpvi_b_bls_kmvblvb_right_prefix_power bpvi_c_bls_kmvblvb_right_prefix_power. ((forall bpvi_i_bls_kmvblvb_right_prefix_power. (exists bpvi_repeat_gap_bls_kmvblvb_right_prefix_power. bpvi_repeat_gap_bls_kmvblvb_right_prefix_power + S bpvi_i_bls_kmvblvb_right_prefix_power = S bls_index_kmvblvb_right_prefix) -> (((exists bpvi_h_bls_kmvblvb_right_prefix_power_repeat. bpvi_h_bls_kmvblvb_right_prefix_power_repeat + S (p) = S ((S (bpvi_i_bls_kmvblvb_right_prefix_power)) * bpvi_c_bls_kmvblvb_right_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_right_prefix_power_repeat. bpvi_b_bls_kmvblvb_right_prefix_power = bpvi_q_bls_kmvblvb_right_prefix_power_repeat * S ((S (bpvi_i_bls_kmvblvb_right_prefix_power)) * bpvi_c_bls_kmvblvb_right_prefix_power) + (p)))) /\ (exists bpvi_u_bls_kmvblvb_right_prefix_power bpvi_v_bls_kmvblvb_right_prefix_power. ((((exists bpvi_h_bls_kmvblvb_right_prefix_power_start. bpvi_h_bls_kmvblvb_right_prefix_power_start + S (1) = S ((S (0)) * bpvi_v_bls_kmvblvb_right_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_right_prefix_power_start. bpvi_u_bls_kmvblvb_right_prefix_power = bpvi_q_bls_kmvblvb_right_prefix_power_start * S ((S (0)) * bpvi_v_bls_kmvblvb_right_prefix_power) + (1))) /\ ((((exists bpvi_h_bls_kmvblvb_right_prefix_power_terminal. bpvi_h_bls_kmvblvb_right_prefix_power_terminal + S (bls_power_kmvblvb_right_prefix) = S ((S (S bls_index_kmvblvb_right_prefix)) * bpvi_v_bls_kmvblvb_right_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_right_prefix_power_terminal. bpvi_u_bls_kmvblvb_right_prefix_power = bpvi_q_bls_kmvblvb_right_prefix_power_terminal * S ((S (S bls_index_kmvblvb_right_prefix)) * bpvi_v_bls_kmvblvb_right_prefix_power) + (bls_power_kmvblvb_right_prefix))) /\ forall bpvi_j_bls_kmvblvb_right_prefix_power. (exists bpvi_product_gap_bls_kmvblvb_right_prefix_power. bpvi_product_gap_bls_kmvblvb_right_prefix_power + S bpvi_j_bls_kmvblvb_right_prefix_power = S bls_index_kmvblvb_right_prefix) -> exists bpvi_factor_bls_kmvblvb_right_prefix_power bpvi_partial_bls_kmvblvb_right_prefix_power bpvi_successor_bls_kmvblvb_right_prefix_power. ((((exists bpvi_h_bls_kmvblvb_right_prefix_power_factor. bpvi_h_bls_kmvblvb_right_prefix_power_factor + S (bpvi_factor_bls_kmvblvb_right_prefix_power) = S ((S (bpvi_j_bls_kmvblvb_right_prefix_power)) * bpvi_c_bls_kmvblvb_right_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_right_prefix_power_factor. bpvi_b_bls_kmvblvb_right_prefix_power = bpvi_q_bls_kmvblvb_right_prefix_power_factor * S ((S (bpvi_j_bls_kmvblvb_right_prefix_power)) * bpvi_c_bls_kmvblvb_right_prefix_power) + (bpvi_factor_bls_kmvblvb_right_prefix_power))) /\ ((((exists bpvi_h_bls_kmvblvb_right_prefix_power_partial. bpvi_h_bls_kmvblvb_right_prefix_power_partial + S (bpvi_partial_bls_kmvblvb_right_prefix_power) = S ((S (bpvi_j_bls_kmvblvb_right_prefix_power)) * bpvi_v_bls_kmvblvb_right_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_right_prefix_power_partial. bpvi_u_bls_kmvblvb_right_prefix_power = bpvi_q_bls_kmvblvb_right_prefix_power_partial * S ((S (bpvi_j_bls_kmvblvb_right_prefix_power)) * bpvi_v_bls_kmvblvb_right_prefix_power) + (bpvi_partial_bls_kmvblvb_right_prefix_power))) /\ ((((exists bpvi_h_bls_kmvblvb_right_prefix_power_successor. bpvi_h_bls_kmvblvb_right_prefix_power_successor + S (bpvi_successor_bls_kmvblvb_right_prefix_power) = S ((S (S bpvi_j_bls_kmvblvb_right_prefix_power)) * bpvi_v_bls_kmvblvb_right_prefix_power)) /\ exists bpvi_q_bls_kmvblvb_right_prefix_power_successor. bpvi_u_bls_kmvblvb_right_prefix_power = bpvi_q_bls_kmvblvb_right_prefix_power_successor * S ((S (S bpvi_j_bls_kmvblvb_right_prefix_power)) * bpvi_v_bls_kmvblvb_right_prefix_power) + (bpvi_successor_bls_kmvblvb_right_prefix_power))) /\ bpvi_successor_bls_kmvblvb_right_prefix_power = bpvi_partial_bls_kmvblvb_right_prefix_power * bpvi_factor_bls_kmvblvb_right_prefix_power)))))))) /\ ((((exists ff_h_bls_kmvblvb_right_prefix_quotient_entry. ff_h_bls_kmvblvb_right_prefix_quotient_entry + S (bls_quotient_kmvblvb_right_prefix) = S ((S (bls_index_kmvblvb_right_prefix)) * bls_scale_kmvblvb_right)) /\ exists ff_q_bls_kmvblvb_right_prefix_quotient_entry. bls_code_kmvblvb_right = ff_q_bls_kmvblvb_right_prefix_quotient_entry * S ((S (bls_index_kmvblvb_right_prefix)) * bls_scale_kmvblvb_right) + (bls_quotient_kmvblvb_right_prefix))) /\ ((b = bls_power_kmvblvb_right_prefix * bls_quotient_kmvblvb_right_prefix + bls_remainder_kmvblvb_right_prefix /\ exists bls_remainder_gap_kmvblvb_right_prefix_division. bls_remainder_gap_kmvblvb_right_prefix_division + S (bls_remainder_kmvblvb_right_prefix) = bls_power_kmvblvb_right_prefix))))) /\ (exists ff_u_bls_kmvblvb_right_sum ff_v_bls_kmvblvb_right_sum. ((((exists ff_h_bls_kmvblvb_right_sum_start. ff_h_bls_kmvblvb_right_sum_start + S (0) = S ((S (0)) * ff_v_bls_kmvblvb_right_sum)) /\ exists ff_q_bls_kmvblvb_right_sum_start. ff_u_bls_kmvblvb_right_sum = ff_q_bls_kmvblvb_right_sum_start * S ((S (0)) * ff_v_bls_kmvblvb_right_sum) + (0))) /\ ((((exists ff_h_bls_kmvblvb_right_sum_terminal. ff_h_bls_kmvblvb_right_sum_terminal + S (D) = S ((S (b)) * ff_v_bls_kmvblvb_right_sum)) /\ exists ff_q_bls_kmvblvb_right_sum_terminal. ff_u_bls_kmvblvb_right_sum = ff_q_bls_kmvblvb_right_sum_terminal * S ((S (b)) * ff_v_bls_kmvblvb_right_sum) + (D))) /\ forall ff_i_bls_kmvblvb_right_sum. (exists ff_lt_bls_kmvblvb_right_sum_bound. ff_lt_bls_kmvblvb_right_sum_bound + S ff_i_bls_kmvblvb_right_sum = b) -> exists ff_a_bls_kmvblvb_right_sum ff_r_bls_kmvblvb_right_sum ff_s_bls_kmvblvb_right_sum. ((((exists ff_h_bls_kmvblvb_right_sum_summand. ff_h_bls_kmvblvb_right_sum_summand + S (ff_a_bls_kmvblvb_right_sum) = S ((S (ff_i_bls_kmvblvb_right_sum)) * bls_scale_kmvblvb_right)) /\ exists ff_q_bls_kmvblvb_right_sum_summand. bls_code_kmvblvb_right = ff_q_bls_kmvblvb_right_sum_summand * S ((S (ff_i_bls_kmvblvb_right_sum)) * bls_scale_kmvblvb_right) + (ff_a_bls_kmvblvb_right_sum))) /\ ((((exists ff_h_bls_kmvblvb_right_sum_partial. ff_h_bls_kmvblvb_right_sum_partial + S (ff_r_bls_kmvblvb_right_sum) = S ((S (ff_i_bls_kmvblvb_right_sum)) * ff_v_bls_kmvblvb_right_sum)) /\ exists ff_q_bls_kmvblvb_right_sum_partial. ff_u_bls_kmvblvb_right_sum = ff_q_bls_kmvblvb_right_sum_partial * S ((S (ff_i_bls_kmvblvb_right_sum)) * ff_v_bls_kmvblvb_right_sum) + (ff_r_bls_kmvblvb_right_sum))) /\ ((((exists ff_h_bls_kmvblvb_right_sum_successor. ff_h_bls_kmvblvb_right_sum_successor + S (ff_s_bls_kmvblvb_right_sum) = S ((S (S ff_i_bls_kmvblvb_right_sum)) * ff_v_bls_kmvblvb_right_sum)) /\ exists ff_q_bls_kmvblvb_right_sum_successor. ff_u_bls_kmvblvb_right_sum = ff_q_bls_kmvblvb_right_sum_successor * S ((S (S ff_i_bls_kmvblvb_right_sum)) * ff_v_bls_kmvblvb_right_sum) + (ff_s_bls_kmvblvb_right_sum))) /\ ff_s_bls_kmvblvb_right_sum = ff_r_bls_kmvblvb_right_sum + ff_a_bls_kmvblvb_right_sum)))))))) -> A = (B + D) + e

Every purple notation token opens its conservative definition. This reading surface never changes the unchanged intuitionistic kernel or confers checked-use authority.

Definitions used by this theorem

In the theorem statement

In local proof propositions

Proof neighborhood

Direct theorem prerequisites

Direct theorem dependents

Definition-aware tactic body

Only propositions whose conservative expansion has been checked for exact first-order equivalence are compacted. Every changed line retains its immutable exact replay command.