primorial_le_four_pow_bounded

((forall n. exists c. (((exists bcf_lt_gap_bpfpsp_central_exists_out_of_range. bcf_lt_gap_bpfpsp_central_exists_out_of_range + S (n + n) = n) /\ c = 0) \/ ((exists bcf_le_gap_bpfpsp_central_exists_in_range. bcf_le_gap_bpfpsp_central_exists_in_range + (n) = n + n) /\ (exists bcf_row_code_code_bpfpsp_central_exists bcf_row_code_scale_bpfpsp_central_exists bcf_row_scale_code_bpfpsp_central_exists bcf_row_scale_scale_bpfpsp_central_exists bcf_row_code_bpfpsp_central_exists bcf_row_scale_bpfpsp_central_exists. ((forall bcf_row_index_bpfpsp_central_exists_table. (exists bcf_lt_gap_bpfpsp_central_exists_table_row_bound. bcf_lt_gap_bpfpsp_central_exists_table_row_bound + S (bcf_row_index_bpfpsp_central_exists_table) = S (n + n)) -> exists bcf_row_code_bpfpsp_central_exists_table bcf_row_scale_bpfpsp_central_exists_table. ((((exists bcf_height_bpfpsp_central_exists_table_decoded_row_code. bcf_height_bpfpsp_central_exists_table_decoded_row_code + S (bcf_row_code_bpfpsp_central_exists_table) = S ((S (bcf_row_index_bpfpsp_central_exists_table)) * bcf_row_code_scale_bpfpsp_central_exists)) /\ exists bcf_quotient_bpfpsp_central_exists_table_decoded_row_code. bcf_row_code_code_bpfpsp_central_exists = bcf_quotient_bpfpsp_central_exists_table_decoded_row_code * S ((S (bcf_row_index_bpfpsp_central_exists_table)) * bcf_row_code_scale_bpfpsp_central_exists) + (bcf_row_code_bpfpsp_central_exists_table))) /\ ((((exists bcf_height_bpfpsp_central_exists_table_decoded_row_scale. bcf_height_bpfpsp_central_exists_table_decoded_row_scale + S (bcf_row_scale_bpfpsp_central_exists_table) = S ((S (bcf_row_index_bpfpsp_central_exists_table)) * bcf_row_scale_scale_bpfpsp_central_exists)) /\ exists bcf_quotient_bpfpsp_central_exists_table_decoded_row_scale. bcf_row_scale_code_bpfpsp_central_exists = bcf_quotient_bpfpsp_central_exists_table_decoded_row_scale * S ((S (bcf_row_index_bpfpsp_central_exists_table)) * bcf_row_scale_scale_bpfpsp_central_exists) + (bcf_row_scale_bpfpsp_central_exists_table))) /\ ((bcf_row_index_bpfpsp_central_exists_table = 0 /\ (forall bcf_index_bpfpsp_central_exists_table_zero_row. (exists bcf_lt_gap_bpfpsp_central_exists_table_zero_row_bound. bcf_lt_gap_bpfpsp_central_exists_table_zero_row_bound + S (bcf_index_bpfpsp_central_exists_table_zero_row) = S (n + n)) -> exists bcf_value_bpfpsp_central_exists_table_zero_row. ((((exists bcf_height_bpfpsp_central_exists_table_zero_row_entry. bcf_height_bpfpsp_central_exists_table_zero_row_entry + S (bcf_value_bpfpsp_central_exists_table_zero_row) = S ((S (bcf_index_bpfpsp_central_exists_table_zero_row)) * bcf_row_scale_bpfpsp_central_exists_table)) /\ exists bcf_quotient_bpfpsp_central_exists_table_zero_row_entry. bcf_row_code_bpfpsp_central_exists_table = bcf_quotient_bpfpsp_central_exists_table_zero_row_entry * S ((S (bcf_index_bpfpsp_central_exists_table_zero_row)) * bcf_row_scale_bpfpsp_central_exists_table) + (bcf_value_bpfpsp_central_exists_table_zero_row))) /\ ((bcf_index_bpfpsp_central_exists_table_zero_row = 0 /\ bcf_value_bpfpsp_central_exists_table_zero_row = 1) \/ exists bcf_predecessor_bpfpsp_central_exists_table_zero_row. bcf_index_bpfpsp_central_exists_table_zero_row = S bcf_predecessor_bpfpsp_central_exists_table_zero_row /\ bcf_value_bpfpsp_central_exists_table_zero_row = 0)))) \/ exists bcf_predecessor_bpfpsp_central_exists_table bcf_previous_code_bpfpsp_central_exists_table bcf_previous_scale_bpfpsp_central_exists_table. bcf_row_index_bpfpsp_central_exists_table = S bcf_predecessor_bpfpsp_central_exists_table /\ ((((exists bcf_height_bpfpsp_central_exists_table_decoded_previous_code. bcf_height_bpfpsp_central_exists_table_decoded_previous_code + S (bcf_previous_code_bpfpsp_central_exists_table) = S ((S (bcf_predecessor_bpfpsp_central_exists_table)) * bcf_row_code_scale_bpfpsp_central_exists)) /\ exists bcf_quotient_bpfpsp_central_exists_table_decoded_previous_code. bcf_row_code_code_bpfpsp_central_exists = bcf_quotient_bpfpsp_central_exists_table_decoded_previous_code * S ((S (bcf_predecessor_bpfpsp_central_exists_table)) * bcf_row_code_scale_bpfpsp_central_exists) + (bcf_previous_code_bpfpsp_central_exists_table))) /\ ((((exists bcf_height_bpfpsp_central_exists_table_decoded_previous_scale. bcf_height_bpfpsp_central_exists_table_decoded_previous_scale + S (bcf_previous_scale_bpfpsp_central_exists_table) = S ((S (bcf_predecessor_bpfpsp_central_exists_table)) * bcf_row_scale_scale_bpfpsp_central_exists)) /\ exists bcf_quotient_bpfpsp_central_exists_table_decoded_previous_scale. bcf_row_scale_code_bpfpsp_central_exists = bcf_quotient_bpfpsp_central_exists_table_decoded_previous_scale * S ((S (bcf_predecessor_bpfpsp_central_exists_table)) * bcf_row_scale_scale_bpfpsp_central_exists) + (bcf_previous_scale_bpfpsp_central_exists_table))) /\ (forall bcf_index_bpfpsp_central_exists_table_row_step. (exists bcf_lt_gap_bpfpsp_central_exists_table_row_step_bound. bcf_lt_gap_bpfpsp_central_exists_table_row_step_bound + S (bcf_index_bpfpsp_central_exists_table_row_step) = S (n + n)) -> exists bcf_value_bpfpsp_central_exists_table_row_step. ((((exists bcf_height_bpfpsp_central_exists_table_row_step_entry. bcf_height_bpfpsp_central_exists_table_row_step_entry + S (bcf_value_bpfpsp_central_exists_table_row_step) = S ((S (bcf_index_bpfpsp_central_exists_table_row_step)) * bcf_row_scale_bpfpsp_central_exists_table)) /\ exists bcf_quotient_bpfpsp_central_exists_table_row_step_entry. bcf_row_code_bpfpsp_central_exists_table = bcf_quotient_bpfpsp_central_exists_table_row_step_entry * S ((S (bcf_index_bpfpsp_central_exists_table_row_step)) * bcf_row_scale_bpfpsp_central_exists_table) + (bcf_value_bpfpsp_central_exists_table_row_step))) /\ ((bcf_index_bpfpsp_central_exists_table_row_step = 0 /\ bcf_value_bpfpsp_central_exists_table_row_step = 1) \/ exists bcf_predecessor_bpfpsp_central_exists_table_row_step bcf_left_bpfpsp_central_exists_table_row_step bcf_right_bpfpsp_central_exists_table_row_step. bcf_index_bpfpsp_central_exists_table_row_step = S bcf_predecessor_bpfpsp_central_exists_table_row_step /\ ((((exists bcf_height_bpfpsp_central_exists_table_row_step_previous_left. bcf_height_bpfpsp_central_exists_table_row_step_previous_left + S (bcf_left_bpfpsp_central_exists_table_row_step) = S ((S (bcf_predecessor_bpfpsp_central_exists_table_row_step)) * bcf_previous_scale_bpfpsp_central_exists_table)) /\ exists bcf_quotient_bpfpsp_central_exists_table_row_step_previous_left. bcf_previous_code_bpfpsp_central_exists_table = bcf_quotient_bpfpsp_central_exists_table_row_step_previous_left * S ((S (bcf_predecessor_bpfpsp_central_exists_table_row_step)) * bcf_previous_scale_bpfpsp_central_exists_table) + (bcf_left_bpfpsp_central_exists_table_row_step))) /\ ((((exists bcf_height_bpfpsp_central_exists_table_row_step_previous_right. bcf_height_bpfpsp_central_exists_table_row_step_previous_right + S (bcf_right_bpfpsp_central_exists_table_row_step) = S ((S (S (bcf_predecessor_bpfpsp_central_exists_table_row_step))) * bcf_previous_scale_bpfpsp_central_exists_table)) /\ exists bcf_quotient_bpfpsp_central_exists_table_row_step_previous_right. bcf_previous_code_bpfpsp_central_exists_table = bcf_quotient_bpfpsp_central_exists_table_row_step_previous_right * S ((S (S (bcf_predecessor_bpfpsp_central_exists_table_row_step))) * bcf_previous_scale_bpfpsp_central_exists_table) + (bcf_right_bpfpsp_central_exists_table_row_step))) /\ bcf_value_bpfpsp_central_exists_table_row_step = bcf_left_bpfpsp_central_exists_table_row_step + bcf_right_bpfpsp_central_exists_table_row_step))))))))))) /\ ((((exists bcf_height_bpfpsp_central_exists_decoded_row_code. bcf_height_bpfpsp_central_exists_decoded_row_code + S (bcf_row_code_bpfpsp_central_exists) = S ((S (n + n)) * bcf_row_code_scale_bpfpsp_central_exists)) /\ exists bcf_quotient_bpfpsp_central_exists_decoded_row_code. bcf_row_code_code_bpfpsp_central_exists = bcf_quotient_bpfpsp_central_exists_decoded_row_code * S ((S (n + n)) * bcf_row_code_scale_bpfpsp_central_exists) + (bcf_row_code_bpfpsp_central_exists))) /\ ((((exists bcf_height_bpfpsp_central_exists_decoded_row_scale. bcf_height_bpfpsp_central_exists_decoded_row_scale + S (bcf_row_scale_bpfpsp_central_exists) = S ((S (n + n)) * bcf_row_scale_scale_bpfpsp_central_exists)) /\ exists bcf_quotient_bpfpsp_central_exists_decoded_row_scale. bcf_row_scale_code_bpfpsp_central_exists = bcf_quotient_bpfpsp_central_exists_decoded_row_scale * S ((S (n + n)) * bcf_row_scale_scale_bpfpsp_central_exists) + (bcf_row_scale_bpfpsp_central_exists))) /\ (((exists bcf_height_bpfpsp_central_exists_decoded_value. bcf_height_bpfpsp_central_exists_decoded_value + S (c) = S ((S (n)) * bcf_row_scale_bpfpsp_central_exists)) /\ exists bcf_quotient_bpfpsp_central_exists_decoded_value. bcf_row_code_bpfpsp_central_exists = bcf_quotient_bpfpsp_central_exists_decoded_value * S ((S (n)) * bcf_row_scale_bpfpsp_central_exists) + (c)))))))))) /\ ((forall n k. exists c. (((exists bcf_lt_gap_bpfpsp_choose_exists_out_of_range. bcf_lt_gap_bpfpsp_choose_exists_out_of_range + S (n) = k) /\ c = 0) \/ ((exists bcf_le_gap_bpfpsp_choose_exists_in_range. bcf_le_gap_bpfpsp_choose_exists_in_range + (k) = n) /\ (exists bcf_row_code_code_bpfpsp_choose_exists bcf_row_code_scale_bpfpsp_choose_exists bcf_row_scale_code_bpfpsp_choose_exists bcf_row_scale_scale_bpfpsp_choose_exists bcf_row_code_bpfpsp_choose_exists bcf_row_scale_bpfpsp_choose_exists. ((forall bcf_row_index_bpfpsp_choose_exists_table. (exists bcf_lt_gap_bpfpsp_choose_exists_table_row_bound. bcf_lt_gap_bpfpsp_choose_exists_table_row_bound + S (bcf_row_index_bpfpsp_choose_exists_table) = S (n)) -> exists bcf_row_code_bpfpsp_choose_exists_table bcf_row_scale_bpfpsp_choose_exists_table. ((((exists bcf_height_bpfpsp_choose_exists_table_decoded_row_code. bcf_height_bpfpsp_choose_exists_table_decoded_row_code + S (bcf_row_code_bpfpsp_choose_exists_table) = S ((S (bcf_row_index_bpfpsp_choose_exists_table)) * bcf_row_code_scale_bpfpsp_choose_exists)) /\ exists bcf_quotient_bpfpsp_choose_exists_table_decoded_row_code. bcf_row_code_code_bpfpsp_choose_exists = bcf_quotient_bpfpsp_choose_exists_table_decoded_row_code * S ((S (bcf_row_index_bpfpsp_choose_exists_table)) * bcf_row_code_scale_bpfpsp_choose_exists) + (bcf_row_code_bpfpsp_choose_exists_table))) /\ ((((exists bcf_height_bpfpsp_choose_exists_table_decoded_row_scale. bcf_height_bpfpsp_choose_exists_table_decoded_row_scale + S (bcf_row_scale_bpfpsp_choose_exists_table) = S ((S (bcf_row_index_bpfpsp_choose_exists_table)) * bcf_row_scale_scale_bpfpsp_choose_exists)) /\ exists bcf_quotient_bpfpsp_choose_exists_table_decoded_row_scale. bcf_row_scale_code_bpfpsp_choose_exists = bcf_quotient_bpfpsp_choose_exists_table_decoded_row_scale * S ((S (bcf_row_index_bpfpsp_choose_exists_table)) * bcf_row_scale_scale_bpfpsp_choose_exists) + (bcf_row_scale_bpfpsp_choose_exists_table))) /\ ((bcf_row_index_bpfpsp_choose_exists_table = 0 /\ (forall bcf_index_bpfpsp_choose_exists_table_zero_row. (exists bcf_lt_gap_bpfpsp_choose_exists_table_zero_row_bound. bcf_lt_gap_bpfpsp_choose_exists_table_zero_row_bound + S (bcf_index_bpfpsp_choose_exists_table_zero_row) = S (n)) -> exists bcf_value_bpfpsp_choose_exists_table_zero_row. ((((exists bcf_height_bpfpsp_choose_exists_table_zero_row_entry. bcf_height_bpfpsp_choose_exists_table_zero_row_entry + S (bcf_value_bpfpsp_choose_exists_table_zero_row) = S ((S (bcf_index_bpfpsp_choose_exists_table_zero_row)) * bcf_row_scale_bpfpsp_choose_exists_table)) /\ exists bcf_quotient_bpfpsp_choose_exists_table_zero_row_entry. bcf_row_code_bpfpsp_choose_exists_table = bcf_quotient_bpfpsp_choose_exists_table_zero_row_entry * S ((S (bcf_index_bpfpsp_choose_exists_table_zero_row)) * bcf_row_scale_bpfpsp_choose_exists_table) + (bcf_value_bpfpsp_choose_exists_table_zero_row))) /\ ((bcf_index_bpfpsp_choose_exists_table_zero_row = 0 /\ bcf_value_bpfpsp_choose_exists_table_zero_row = 1) \/ exists bcf_predecessor_bpfpsp_choose_exists_table_zero_row. bcf_index_bpfpsp_choose_exists_table_zero_row = S bcf_predecessor_bpfpsp_choose_exists_table_zero_row /\ bcf_value_bpfpsp_choose_exists_table_zero_row = 0)))) \/ exists bcf_predecessor_bpfpsp_choose_exists_table bcf_previous_code_bpfpsp_choose_exists_table bcf_previous_scale_bpfpsp_choose_exists_table. bcf_row_index_bpfpsp_choose_exists_table = S bcf_predecessor_bpfpsp_choose_exists_table /\ ((((exists bcf_height_bpfpsp_choose_exists_table_decoded_previous_code. bcf_height_bpfpsp_choose_exists_table_decoded_previous_code + S (bcf_previous_code_bpfpsp_choose_exists_table) = S ((S (bcf_predecessor_bpfpsp_choose_exists_table)) * bcf_row_code_scale_bpfpsp_choose_exists)) /\ exists bcf_quotient_bpfpsp_choose_exists_table_decoded_previous_code. bcf_row_code_code_bpfpsp_choose_exists = bcf_quotient_bpfpsp_choose_exists_table_decoded_previous_code * S ((S (bcf_predecessor_bpfpsp_choose_exists_table)) * bcf_row_code_scale_bpfpsp_choose_exists) + (bcf_previous_code_bpfpsp_choose_exists_table))) /\ ((((exists bcf_height_bpfpsp_choose_exists_table_decoded_previous_scale. bcf_height_bpfpsp_choose_exists_table_decoded_previous_scale + S (bcf_previous_scale_bpfpsp_choose_exists_table) = S ((S (bcf_predecessor_bpfpsp_choose_exists_table)) * bcf_row_scale_scale_bpfpsp_choose_exists)) /\ exists bcf_quotient_bpfpsp_choose_exists_table_decoded_previous_scale. bcf_row_scale_code_bpfpsp_choose_exists = bcf_quotient_bpfpsp_choose_exists_table_decoded_previous_scale * S ((S (bcf_predecessor_bpfpsp_choose_exists_table)) * bcf_row_scale_scale_bpfpsp_choose_exists) + (bcf_previous_scale_bpfpsp_choose_exists_table))) /\ (forall bcf_index_bpfpsp_choose_exists_table_row_step. (exists bcf_lt_gap_bpfpsp_choose_exists_table_row_step_bound. bcf_lt_gap_bpfpsp_choose_exists_table_row_step_bound + S (bcf_index_bpfpsp_choose_exists_table_row_step) = S (n)) -> exists bcf_value_bpfpsp_choose_exists_table_row_step. ((((exists bcf_height_bpfpsp_choose_exists_table_row_step_entry. bcf_height_bpfpsp_choose_exists_table_row_step_entry + S (bcf_value_bpfpsp_choose_exists_table_row_step) = S ((S (bcf_index_bpfpsp_choose_exists_table_row_step)) * bcf_row_scale_bpfpsp_choose_exists_table)) /\ exists bcf_quotient_bpfpsp_choose_exists_table_row_step_entry. bcf_row_code_bpfpsp_choose_exists_table = bcf_quotient_bpfpsp_choose_exists_table_row_step_entry * S ((S (bcf_index_bpfpsp_choose_exists_table_row_step)) * bcf_row_scale_bpfpsp_choose_exists_table) + (bcf_value_bpfpsp_choose_exists_table_row_step))) /\ ((bcf_index_bpfpsp_choose_exists_table_row_step = 0 /\ bcf_value_bpfpsp_choose_exists_table_row_step = 1) \/ exists bcf_predecessor_bpfpsp_choose_exists_table_row_step bcf_left_bpfpsp_choose_exists_table_row_step bcf_right_bpfpsp_choose_exists_table_row_step. bcf_index_bpfpsp_choose_exists_table_row_step = S bcf_predecessor_bpfpsp_choose_exists_table_row_step /\ ((((exists bcf_height_bpfpsp_choose_exists_table_row_step_previous_left. bcf_height_bpfpsp_choose_exists_table_row_step_previous_left + S (bcf_left_bpfpsp_choose_exists_table_row_step) = S ((S (bcf_predecessor_bpfpsp_choose_exists_table_row_step)) * bcf_previous_scale_bpfpsp_choose_exists_table)) /\ exists bcf_quotient_bpfpsp_choose_exists_table_row_step_previous_left. bcf_previous_code_bpfpsp_choose_exists_table = bcf_quotient_bpfpsp_choose_exists_table_row_step_previous_left * S ((S (bcf_predecessor_bpfpsp_choose_exists_table_row_step)) * bcf_previous_scale_bpfpsp_choose_exists_table) + (bcf_left_bpfpsp_choose_exists_table_row_step))) /\ ((((exists bcf_height_bpfpsp_choose_exists_table_row_step_previous_right. bcf_height_bpfpsp_choose_exists_table_row_step_previous_right + S (bcf_right_bpfpsp_choose_exists_table_row_step) = S ((S (S (bcf_predecessor_bpfpsp_choose_exists_table_row_step))) * bcf_previous_scale_bpfpsp_choose_exists_table)) /\ exists bcf_quotient_bpfpsp_choose_exists_table_row_step_previous_right. bcf_previous_code_bpfpsp_choose_exists_table = bcf_quotient_bpfpsp_choose_exists_table_row_step_previous_right * S ((S (S (bcf_predecessor_bpfpsp_choose_exists_table_row_step))) * bcf_previous_scale_bpfpsp_choose_exists_table) + (bcf_right_bpfpsp_choose_exists_table_row_step))) /\ bcf_value_bpfpsp_choose_exists_table_row_step = bcf_left_bpfpsp_choose_exists_table_row_step + bcf_right_bpfpsp_choose_exists_table_row_step))))))))))) /\ ((((exists bcf_height_bpfpsp_choose_exists_decoded_row_code. bcf_height_bpfpsp_choose_exists_decoded_row_code + S (bcf_row_code_bpfpsp_choose_exists) = S ((S (n)) * bcf_row_code_scale_bpfpsp_choose_exists)) /\ exists bcf_quotient_bpfpsp_choose_exists_decoded_row_code. bcf_row_code_code_bpfpsp_choose_exists = bcf_quotient_bpfpsp_choose_exists_decoded_row_code * S ((S (n)) * bcf_row_code_scale_bpfpsp_choose_exists) + (bcf_row_code_bpfpsp_choose_exists))) /\ ((((exists bcf_height_bpfpsp_choose_exists_decoded_row_scale. bcf_height_bpfpsp_choose_exists_decoded_row_scale + S (bcf_row_scale_bpfpsp_choose_exists) = S ((S (n)) * bcf_row_scale_scale_bpfpsp_choose_exists)) /\ exists bcf_quotient_bpfpsp_choose_exists_decoded_row_scale. bcf_row_scale_code_bpfpsp_choose_exists = bcf_quotient_bpfpsp_choose_exists_decoded_row_scale * S ((S (n)) * bcf_row_scale_scale_bpfpsp_choose_exists) + (bcf_row_scale_bpfpsp_choose_exists))) /\ (((exists bcf_height_bpfpsp_choose_exists_decoded_value. bcf_height_bpfpsp_choose_exists_decoded_value + S (c) = S ((S (k)) * bcf_row_scale_bpfpsp_choose_exists)) /\ exists bcf_quotient_bpfpsp_choose_exists_decoded_value. bcf_row_code_bpfpsp_choose_exists = bcf_quotient_bpfpsp_choose_exists_decoded_value * S ((S (k)) * bcf_row_scale_bpfpsp_choose_exists) + (c)))))))))) /\ ((forall a l z. (exists bpr_code_bpfpsp_split_source bpr_scale_bpfpsp_split_source. ((forall bpr_index_bpfpsp_split_source_mask. (exists bpr_gap_bpfpsp_split_source_mask_bound. bpr_gap_bpfpsp_split_source_mask_bound + S (bpr_index_bpfpsp_split_source_mask) = a + l) -> exists bpr_value_bpfpsp_split_source_mask. ((((exists bpr_height_bpfpsp_split_source_mask_decoded. bpr_height_bpfpsp_split_source_mask_decoded + S (bpr_value_bpfpsp_split_source_mask) = S ((S (bpr_index_bpfpsp_split_source_mask)) * bpr_scale_bpfpsp_split_source)) /\ exists bpr_quotient_bpfpsp_split_source_mask_decoded. bpr_code_bpfpsp_split_source = bpr_quotient_bpfpsp_split_source_mask_decoded * S ((S (bpr_index_bpfpsp_split_source_mask)) * bpr_scale_bpfpsp_split_source) + (bpr_value_bpfpsp_split_source_mask))) /\ (((((~(S (bpr_index_bpfpsp_split_source_mask) = 1) /\ forall bpr_left_bpfpsp_split_source_mask_choice_prime bpr_right_bpfpsp_split_source_mask_choice_prime. S (bpr_index_bpfpsp_split_source_mask) = bpr_left_bpfpsp_split_source_mask_choice_prime * bpr_right_bpfpsp_split_source_mask_choice_prime -> bpr_left_bpfpsp_split_source_mask_choice_prime = 1 \/ bpr_right_bpfpsp_split_source_mask_choice_prime = 1)) /\ bpr_value_bpfpsp_split_source_mask = S (bpr_index_bpfpsp_split_source_mask)) \/ (~((~(S (bpr_index_bpfpsp_split_source_mask) = 1) /\ forall bpr_left_bpfpsp_split_source_mask_choice_prime bpr_right_bpfpsp_split_source_mask_choice_prime. S (bpr_index_bpfpsp_split_source_mask) = bpr_left_bpfpsp_split_source_mask_choice_prime * bpr_right_bpfpsp_split_source_mask_choice_prime -> bpr_left_bpfpsp_split_source_mask_choice_prime = 1 \/ bpr_right_bpfpsp_split_source_mask_choice_prime = 1)) /\ bpr_value_bpfpsp_split_source_mask = 1))))) /\ (exists ff_u_bpfpsp_split_source_product ff_v_bpfpsp_split_source_product. ((((exists ff_h_bpfpsp_split_source_product_start. ff_h_bpfpsp_split_source_product_start + S (1) = S ((S (0)) * ff_v_bpfpsp_split_source_product)) /\ exists ff_q_bpfpsp_split_source_product_start. ff_u_bpfpsp_split_source_product = ff_q_bpfpsp_split_source_product_start * S ((S (0)) * ff_v_bpfpsp_split_source_product) + (1))) /\ ((((exists ff_h_bpfpsp_split_source_product_terminal. ff_h_bpfpsp_split_source_product_terminal + S (z) = S ((S (a + l)) * ff_v_bpfpsp_split_source_product)) /\ exists ff_q_bpfpsp_split_source_product_terminal. ff_u_bpfpsp_split_source_product = ff_q_bpfpsp_split_source_product_terminal * S ((S (a + l)) * ff_v_bpfpsp_split_source_product) + (z))) /\ forall ff_i_bpfpsp_split_source_product. (exists ff_lt_bpfpsp_split_source_product_bound. ff_lt_bpfpsp_split_source_product_bound + S ff_i_bpfpsp_split_source_product = a + l) -> exists ff_p_bpfpsp_split_source_product ff_r_bpfpsp_split_source_product ff_s_bpfpsp_split_source_product. ((((exists ff_h_bpfpsp_split_source_product_factor. ff_h_bpfpsp_split_source_product_factor + S (ff_p_bpfpsp_split_source_product) = S ((S (ff_i_bpfpsp_split_source_product)) * bpr_scale_bpfpsp_split_source)) /\ exists ff_q_bpfpsp_split_source_product_factor. bpr_code_bpfpsp_split_source = ff_q_bpfpsp_split_source_product_factor * S ((S (ff_i_bpfpsp_split_source_product)) * bpr_scale_bpfpsp_split_source) + (ff_p_bpfpsp_split_source_product))) /\ ((((exists ff_h_bpfpsp_split_source_product_partial. ff_h_bpfpsp_split_source_product_partial + S (ff_r_bpfpsp_split_source_product) = S ((S (ff_i_bpfpsp_split_source_product)) * ff_v_bpfpsp_split_source_product)) /\ exists ff_q_bpfpsp_split_source_product_partial. ff_u_bpfpsp_split_source_product = ff_q_bpfpsp_split_source_product_partial * S ((S (ff_i_bpfpsp_split_source_product)) * ff_v_bpfpsp_split_source_product) + (ff_r_bpfpsp_split_source_product))) /\ ((((exists ff_h_bpfpsp_split_source_product_successor. ff_h_bpfpsp_split_source_product_successor + S (ff_s_bpfpsp_split_source_product) = S ((S (S ff_i_bpfpsp_split_source_product)) * ff_v_bpfpsp_split_source_product)) /\ exists ff_q_bpfpsp_split_source_product_successor. ff_u_bpfpsp_split_source_product = ff_q_bpfpsp_split_source_product_successor * S ((S (S ff_i_bpfpsp_split_source_product)) * ff_v_bpfpsp_split_source_product) + (ff_s_bpfpsp_split_source_product))) /\ ff_s_bpfpsp_split_source_product = ff_r_bpfpsp_split_source_product * ff_p_bpfpsp_split_source_product)))))))) -> exists x y. (exists bpr_code_bpfpsp_split_prefix bpr_scale_bpfpsp_split_prefix. ((forall bpr_index_bpfpsp_split_prefix_mask. (exists bpr_gap_bpfpsp_split_prefix_mask_bound. bpr_gap_bpfpsp_split_prefix_mask_bound + S (bpr_index_bpfpsp_split_prefix_mask) = a) -> exists bpr_value_bpfpsp_split_prefix_mask. ((((exists bpr_height_bpfpsp_split_prefix_mask_decoded. bpr_height_bpfpsp_split_prefix_mask_decoded + S (bpr_value_bpfpsp_split_prefix_mask) = S ((S (bpr_index_bpfpsp_split_prefix_mask)) * bpr_scale_bpfpsp_split_prefix)) /\ exists bpr_quotient_bpfpsp_split_prefix_mask_decoded. bpr_code_bpfpsp_split_prefix = bpr_quotient_bpfpsp_split_prefix_mask_decoded * S ((S (bpr_index_bpfpsp_split_prefix_mask)) * bpr_scale_bpfpsp_split_prefix) + (bpr_value_bpfpsp_split_prefix_mask))) /\ (((((~(S (bpr_index_bpfpsp_split_prefix_mask) = 1) /\ forall bpr_left_bpfpsp_split_prefix_mask_choice_prime bpr_right_bpfpsp_split_prefix_mask_choice_prime. S (bpr_index_bpfpsp_split_prefix_mask) = bpr_left_bpfpsp_split_prefix_mask_choice_prime * bpr_right_bpfpsp_split_prefix_mask_choice_prime -> bpr_left_bpfpsp_split_prefix_mask_choice_prime = 1 \/ bpr_right_bpfpsp_split_prefix_mask_choice_prime = 1)) /\ bpr_value_bpfpsp_split_prefix_mask = S (bpr_index_bpfpsp_split_prefix_mask)) \/ (~((~(S (bpr_index_bpfpsp_split_prefix_mask) = 1) /\ forall bpr_left_bpfpsp_split_prefix_mask_choice_prime bpr_right_bpfpsp_split_prefix_mask_choice_prime. S (bpr_index_bpfpsp_split_prefix_mask) = bpr_left_bpfpsp_split_prefix_mask_choice_prime * bpr_right_bpfpsp_split_prefix_mask_choice_prime -> bpr_left_bpfpsp_split_prefix_mask_choice_prime = 1 \/ bpr_right_bpfpsp_split_prefix_mask_choice_prime = 1)) /\ bpr_value_bpfpsp_split_prefix_mask = 1))))) /\ (exists ff_u_bpfpsp_split_prefix_product ff_v_bpfpsp_split_prefix_product. ((((exists ff_h_bpfpsp_split_prefix_product_start. ff_h_bpfpsp_split_prefix_product_start + S (1) = S ((S (0)) * ff_v_bpfpsp_split_prefix_product)) /\ exists ff_q_bpfpsp_split_prefix_product_start. ff_u_bpfpsp_split_prefix_product = ff_q_bpfpsp_split_prefix_product_start * S ((S (0)) * ff_v_bpfpsp_split_prefix_product) + (1))) /\ ((((exists ff_h_bpfpsp_split_prefix_product_terminal. ff_h_bpfpsp_split_prefix_product_terminal + S (x) = S ((S (a)) * ff_v_bpfpsp_split_prefix_product)) /\ exists ff_q_bpfpsp_split_prefix_product_terminal. ff_u_bpfpsp_split_prefix_product = ff_q_bpfpsp_split_prefix_product_terminal * S ((S (a)) * ff_v_bpfpsp_split_prefix_product) + (x))) /\ forall ff_i_bpfpsp_split_prefix_product. (exists ff_lt_bpfpsp_split_prefix_product_bound. ff_lt_bpfpsp_split_prefix_product_bound + S ff_i_bpfpsp_split_prefix_product = a) -> exists ff_p_bpfpsp_split_prefix_product ff_r_bpfpsp_split_prefix_product ff_s_bpfpsp_split_prefix_product. ((((exists ff_h_bpfpsp_split_prefix_product_factor. ff_h_bpfpsp_split_prefix_product_factor + S (ff_p_bpfpsp_split_prefix_product) = S ((S (ff_i_bpfpsp_split_prefix_product)) * bpr_scale_bpfpsp_split_prefix)) /\ exists ff_q_bpfpsp_split_prefix_product_factor. bpr_code_bpfpsp_split_prefix = ff_q_bpfpsp_split_prefix_product_factor * S ((S (ff_i_bpfpsp_split_prefix_product)) * bpr_scale_bpfpsp_split_prefix) + (ff_p_bpfpsp_split_prefix_product))) /\ ((((exists ff_h_bpfpsp_split_prefix_product_partial. ff_h_bpfpsp_split_prefix_product_partial + S (ff_r_bpfpsp_split_prefix_product) = S ((S (ff_i_bpfpsp_split_prefix_product)) * ff_v_bpfpsp_split_prefix_product)) /\ exists ff_q_bpfpsp_split_prefix_product_partial. ff_u_bpfpsp_split_prefix_product = ff_q_bpfpsp_split_prefix_product_partial * S ((S (ff_i_bpfpsp_split_prefix_product)) * ff_v_bpfpsp_split_prefix_product) + (ff_r_bpfpsp_split_prefix_product))) /\ ((((exists ff_h_bpfpsp_split_prefix_product_successor. ff_h_bpfpsp_split_prefix_product_successor + S (ff_s_bpfpsp_split_prefix_product) = S ((S (S ff_i_bpfpsp_split_prefix_product)) * ff_v_bpfpsp_split_prefix_product)) /\ exists ff_q_bpfpsp_split_prefix_product_successor. ff_u_bpfpsp_split_prefix_product = ff_q_bpfpsp_split_prefix_product_successor * S ((S (S ff_i_bpfpsp_split_prefix_product)) * ff_v_bpfpsp_split_prefix_product) + (ff_s_bpfpsp_split_prefix_product))) /\ ff_s_bpfpsp_split_prefix_product = ff_r_bpfpsp_split_prefix_product * ff_p_bpfpsp_split_prefix_product)))))))) /\ ((exists bpr_code_bpfpsp_split_interval bpr_scale_bpfpsp_split_interval. ((forall bpr_index_bpfpsp_split_interval_mask. (exists bpr_gap_bpfpsp_split_interval_mask_bound. bpr_gap_bpfpsp_split_interval_mask_bound + S (bpr_index_bpfpsp_split_interval_mask) = l) -> exists bpr_value_bpfpsp_split_interval_mask. ((((exists bpr_height_bpfpsp_split_interval_mask_decoded. bpr_height_bpfpsp_split_interval_mask_decoded + S (bpr_value_bpfpsp_split_interval_mask) = S ((S (bpr_index_bpfpsp_split_interval_mask)) * bpr_scale_bpfpsp_split_interval)) /\ exists bpr_quotient_bpfpsp_split_interval_mask_decoded. bpr_code_bpfpsp_split_interval = bpr_quotient_bpfpsp_split_interval_mask_decoded * S ((S (bpr_index_bpfpsp_split_interval_mask)) * bpr_scale_bpfpsp_split_interval) + (bpr_value_bpfpsp_split_interval_mask))) /\ (((((~(S (a + bpr_index_bpfpsp_split_interval_mask) = 1) /\ forall bpr_left_bpfpsp_split_interval_mask_choice_prime bpr_right_bpfpsp_split_interval_mask_choice_prime. S (a + bpr_index_bpfpsp_split_interval_mask) = bpr_left_bpfpsp_split_interval_mask_choice_prime * bpr_right_bpfpsp_split_interval_mask_choice_prime -> bpr_left_bpfpsp_split_interval_mask_choice_prime = 1 \/ bpr_right_bpfpsp_split_interval_mask_choice_prime = 1)) /\ bpr_value_bpfpsp_split_interval_mask = S (a + bpr_index_bpfpsp_split_interval_mask)) \/ (~((~(S (a + bpr_index_bpfpsp_split_interval_mask) = 1) /\ forall bpr_left_bpfpsp_split_interval_mask_choice_prime bpr_right_bpfpsp_split_interval_mask_choice_prime. S (a + bpr_index_bpfpsp_split_interval_mask) = bpr_left_bpfpsp_split_interval_mask_choice_prime * bpr_right_bpfpsp_split_interval_mask_choice_prime -> bpr_left_bpfpsp_split_interval_mask_choice_prime = 1 \/ bpr_right_bpfpsp_split_interval_mask_choice_prime = 1)) /\ bpr_value_bpfpsp_split_interval_mask = 1))))) /\ (exists ff_u_bpfpsp_split_interval_product ff_v_bpfpsp_split_interval_product. ((((exists ff_h_bpfpsp_split_interval_product_start. ff_h_bpfpsp_split_interval_product_start + S (1) = S ((S (0)) * ff_v_bpfpsp_split_interval_product)) /\ exists ff_q_bpfpsp_split_interval_product_start. ff_u_bpfpsp_split_interval_product = ff_q_bpfpsp_split_interval_product_start * S ((S (0)) * ff_v_bpfpsp_split_interval_product) + (1))) /\ ((((exists ff_h_bpfpsp_split_interval_product_terminal. ff_h_bpfpsp_split_interval_product_terminal + S (y) = S ((S (l)) * ff_v_bpfpsp_split_interval_product)) /\ exists ff_q_bpfpsp_split_interval_product_terminal. ff_u_bpfpsp_split_interval_product = ff_q_bpfpsp_split_interval_product_terminal * S ((S (l)) * ff_v_bpfpsp_split_interval_product) + (y))) /\ forall ff_i_bpfpsp_split_interval_product. (exists ff_lt_bpfpsp_split_interval_product_bound. ff_lt_bpfpsp_split_interval_product_bound + S ff_i_bpfpsp_split_interval_product = l) -> exists ff_p_bpfpsp_split_interval_product ff_r_bpfpsp_split_interval_product ff_s_bpfpsp_split_interval_product. ((((exists ff_h_bpfpsp_split_interval_product_factor. ff_h_bpfpsp_split_interval_product_factor + S (ff_p_bpfpsp_split_interval_product) = S ((S (ff_i_bpfpsp_split_interval_product)) * bpr_scale_bpfpsp_split_interval)) /\ exists ff_q_bpfpsp_split_interval_product_factor. bpr_code_bpfpsp_split_interval = ff_q_bpfpsp_split_interval_product_factor * S ((S (ff_i_bpfpsp_split_interval_product)) * bpr_scale_bpfpsp_split_interval) + (ff_p_bpfpsp_split_interval_product))) /\ ((((exists ff_h_bpfpsp_split_interval_product_partial. ff_h_bpfpsp_split_interval_product_partial + S (ff_r_bpfpsp_split_interval_product) = S ((S (ff_i_bpfpsp_split_interval_product)) * ff_v_bpfpsp_split_interval_product)) /\ exists ff_q_bpfpsp_split_interval_product_partial. ff_u_bpfpsp_split_interval_product = ff_q_bpfpsp_split_interval_product_partial * S ((S (ff_i_bpfpsp_split_interval_product)) * ff_v_bpfpsp_split_interval_product) + (ff_r_bpfpsp_split_interval_product))) /\ ((((exists ff_h_bpfpsp_split_interval_product_successor. ff_h_bpfpsp_split_interval_product_successor + S (ff_s_bpfpsp_split_interval_product) = S ((S (S ff_i_bpfpsp_split_interval_product)) * ff_v_bpfpsp_split_interval_product)) /\ exists ff_q_bpfpsp_split_interval_product_successor. ff_u_bpfpsp_split_interval_product = ff_q_bpfpsp_split_interval_product_successor * S ((S (S ff_i_bpfpsp_split_interval_product)) * ff_v_bpfpsp_split_interval_product) + (ff_s_bpfpsp_split_interval_product))) /\ ff_s_bpfpsp_split_interval_product = ff_r_bpfpsp_split_interval_product * ff_p_bpfpsp_split_interval_product)))))))) /\ z = x * y)) /\ ((forall n z c. (exists bpr_code_bpfpsp_even_interval bpr_scale_bpfpsp_even_interval. ((forall bpr_index_bpfpsp_even_interval_mask. (exists bpr_gap_bpfpsp_even_interval_mask_bound. bpr_gap_bpfpsp_even_interval_mask_bound + S (bpr_index_bpfpsp_even_interval_mask) = n) -> exists bpr_value_bpfpsp_even_interval_mask. ((((exists bpr_height_bpfpsp_even_interval_mask_decoded. bpr_height_bpfpsp_even_interval_mask_decoded + S (bpr_value_bpfpsp_even_interval_mask) = S ((S (bpr_index_bpfpsp_even_interval_mask)) * bpr_scale_bpfpsp_even_interval)) /\ exists bpr_quotient_bpfpsp_even_interval_mask_decoded. bpr_code_bpfpsp_even_interval = bpr_quotient_bpfpsp_even_interval_mask_decoded * S ((S (bpr_index_bpfpsp_even_interval_mask)) * bpr_scale_bpfpsp_even_interval) + (bpr_value_bpfpsp_even_interval_mask))) /\ (((((~(S (n + bpr_index_bpfpsp_even_interval_mask) = 1) /\ forall bpr_left_bpfpsp_even_interval_mask_choice_prime bpr_right_bpfpsp_even_interval_mask_choice_prime. S (n + bpr_index_bpfpsp_even_interval_mask) = bpr_left_bpfpsp_even_interval_mask_choice_prime * bpr_right_bpfpsp_even_interval_mask_choice_prime -> bpr_left_bpfpsp_even_interval_mask_choice_prime = 1 \/ bpr_right_bpfpsp_even_interval_mask_choice_prime = 1)) /\ bpr_value_bpfpsp_even_interval_mask = S (n + bpr_index_bpfpsp_even_interval_mask)) \/ (~((~(S (n + bpr_index_bpfpsp_even_interval_mask) = 1) /\ forall bpr_left_bpfpsp_even_interval_mask_choice_prime bpr_right_bpfpsp_even_interval_mask_choice_prime. S (n + bpr_index_bpfpsp_even_interval_mask) = bpr_left_bpfpsp_even_interval_mask_choice_prime * bpr_right_bpfpsp_even_interval_mask_choice_prime -> bpr_left_bpfpsp_even_interval_mask_choice_prime = 1 \/ bpr_right_bpfpsp_even_interval_mask_choice_prime = 1)) /\ bpr_value_bpfpsp_even_interval_mask = 1))))) /\ (exists ff_u_bpfpsp_even_interval_product ff_v_bpfpsp_even_interval_product. ((((exists ff_h_bpfpsp_even_interval_product_start. ff_h_bpfpsp_even_interval_product_start + S (1) = S ((S (0)) * ff_v_bpfpsp_even_interval_product)) /\ exists ff_q_bpfpsp_even_interval_product_start. ff_u_bpfpsp_even_interval_product = ff_q_bpfpsp_even_interval_product_start * S ((S (0)) * ff_v_bpfpsp_even_interval_product) + (1))) /\ ((((exists ff_h_bpfpsp_even_interval_product_terminal. ff_h_bpfpsp_even_interval_product_terminal + S (z) = S ((S (n)) * ff_v_bpfpsp_even_interval_product)) /\ exists ff_q_bpfpsp_even_interval_product_terminal. ff_u_bpfpsp_even_interval_product = ff_q_bpfpsp_even_interval_product_terminal * S ((S (n)) * ff_v_bpfpsp_even_interval_product) + (z))) /\ forall ff_i_bpfpsp_even_interval_product. (exists ff_lt_bpfpsp_even_interval_product_bound. ff_lt_bpfpsp_even_interval_product_bound + S ff_i_bpfpsp_even_interval_product = n) -> exists ff_p_bpfpsp_even_interval_product ff_r_bpfpsp_even_interval_product ff_s_bpfpsp_even_interval_product. ((((exists ff_h_bpfpsp_even_interval_product_factor. ff_h_bpfpsp_even_interval_product_factor + S (ff_p_bpfpsp_even_interval_product) = S ((S (ff_i_bpfpsp_even_interval_product)) * bpr_scale_bpfpsp_even_interval)) /\ exists ff_q_bpfpsp_even_interval_product_factor. bpr_code_bpfpsp_even_interval = ff_q_bpfpsp_even_interval_product_factor * S ((S (ff_i_bpfpsp_even_interval_product)) * bpr_scale_bpfpsp_even_interval) + (ff_p_bpfpsp_even_interval_product))) /\ ((((exists ff_h_bpfpsp_even_interval_product_partial. ff_h_bpfpsp_even_interval_product_partial + S (ff_r_bpfpsp_even_interval_product) = S ((S (ff_i_bpfpsp_even_interval_product)) * ff_v_bpfpsp_even_interval_product)) /\ exists ff_q_bpfpsp_even_interval_product_partial. ff_u_bpfpsp_even_interval_product = ff_q_bpfpsp_even_interval_product_partial * S ((S (ff_i_bpfpsp_even_interval_product)) * ff_v_bpfpsp_even_interval_product) + (ff_r_bpfpsp_even_interval_product))) /\ ((((exists ff_h_bpfpsp_even_interval_product_successor. ff_h_bpfpsp_even_interval_product_successor + S (ff_s_bpfpsp_even_interval_product) = S ((S (S ff_i_bpfpsp_even_interval_product)) * ff_v_bpfpsp_even_interval_product)) /\ exists ff_q_bpfpsp_even_interval_product_successor. ff_u_bpfpsp_even_interval_product = ff_q_bpfpsp_even_interval_product_successor * S ((S (S ff_i_bpfpsp_even_interval_product)) * ff_v_bpfpsp_even_interval_product) + (ff_s_bpfpsp_even_interval_product))) /\ ff_s_bpfpsp_even_interval_product = ff_r_bpfpsp_even_interval_product * ff_p_bpfpsp_even_interval_product)))))))) -> (((exists bcf_lt_gap_bpfpsp_even_central_out_of_range. bcf_lt_gap_bpfpsp_even_central_out_of_range + S (n + n) = n) /\ c = 0) \/ ((exists bcf_le_gap_bpfpsp_even_central_in_range. bcf_le_gap_bpfpsp_even_central_in_range + (n) = n + n) /\ (exists bcf_row_code_code_bpfpsp_even_central bcf_row_code_scale_bpfpsp_even_central bcf_row_scale_code_bpfpsp_even_central bcf_row_scale_scale_bpfpsp_even_central bcf_row_code_bpfpsp_even_central bcf_row_scale_bpfpsp_even_central. ((forall bcf_row_index_bpfpsp_even_central_table. (exists bcf_lt_gap_bpfpsp_even_central_table_row_bound. bcf_lt_gap_bpfpsp_even_central_table_row_bound + S (bcf_row_index_bpfpsp_even_central_table) = S (n + n)) -> exists bcf_row_code_bpfpsp_even_central_table bcf_row_scale_bpfpsp_even_central_table. ((((exists bcf_height_bpfpsp_even_central_table_decoded_row_code. bcf_height_bpfpsp_even_central_table_decoded_row_code + S (bcf_row_code_bpfpsp_even_central_table) = S ((S (bcf_row_index_bpfpsp_even_central_table)) * bcf_row_code_scale_bpfpsp_even_central)) /\ exists bcf_quotient_bpfpsp_even_central_table_decoded_row_code. bcf_row_code_code_bpfpsp_even_central = bcf_quotient_bpfpsp_even_central_table_decoded_row_code * S ((S (bcf_row_index_bpfpsp_even_central_table)) * bcf_row_code_scale_bpfpsp_even_central) + (bcf_row_code_bpfpsp_even_central_table))) /\ ((((exists bcf_height_bpfpsp_even_central_table_decoded_row_scale. bcf_height_bpfpsp_even_central_table_decoded_row_scale + S (bcf_row_scale_bpfpsp_even_central_table) = S ((S (bcf_row_index_bpfpsp_even_central_table)) * bcf_row_scale_scale_bpfpsp_even_central)) /\ exists bcf_quotient_bpfpsp_even_central_table_decoded_row_scale. bcf_row_scale_code_bpfpsp_even_central = bcf_quotient_bpfpsp_even_central_table_decoded_row_scale * S ((S (bcf_row_index_bpfpsp_even_central_table)) * bcf_row_scale_scale_bpfpsp_even_central) + (bcf_row_scale_bpfpsp_even_central_table))) /\ ((bcf_row_index_bpfpsp_even_central_table = 0 /\ (forall bcf_index_bpfpsp_even_central_table_zero_row. (exists bcf_lt_gap_bpfpsp_even_central_table_zero_row_bound. bcf_lt_gap_bpfpsp_even_central_table_zero_row_bound + S (bcf_index_bpfpsp_even_central_table_zero_row) = S (n + n)) -> exists bcf_value_bpfpsp_even_central_table_zero_row. ((((exists bcf_height_bpfpsp_even_central_table_zero_row_entry. bcf_height_bpfpsp_even_central_table_zero_row_entry + S (bcf_value_bpfpsp_even_central_table_zero_row) = S ((S (bcf_index_bpfpsp_even_central_table_zero_row)) * bcf_row_scale_bpfpsp_even_central_table)) /\ exists bcf_quotient_bpfpsp_even_central_table_zero_row_entry. bcf_row_code_bpfpsp_even_central_table = bcf_quotient_bpfpsp_even_central_table_zero_row_entry * S ((S (bcf_index_bpfpsp_even_central_table_zero_row)) * bcf_row_scale_bpfpsp_even_central_table) + (bcf_value_bpfpsp_even_central_table_zero_row))) /\ ((bcf_index_bpfpsp_even_central_table_zero_row = 0 /\ bcf_value_bpfpsp_even_central_table_zero_row = 1) \/ exists bcf_predecessor_bpfpsp_even_central_table_zero_row. bcf_index_bpfpsp_even_central_table_zero_row = S bcf_predecessor_bpfpsp_even_central_table_zero_row /\ bcf_value_bpfpsp_even_central_table_zero_row = 0)))) \/ exists bcf_predecessor_bpfpsp_even_central_table bcf_previous_code_bpfpsp_even_central_table bcf_previous_scale_bpfpsp_even_central_table. bcf_row_index_bpfpsp_even_central_table = S bcf_predecessor_bpfpsp_even_central_table /\ ((((exists bcf_height_bpfpsp_even_central_table_decoded_previous_code. bcf_height_bpfpsp_even_central_table_decoded_previous_code + S (bcf_previous_code_bpfpsp_even_central_table) = S ((S (bcf_predecessor_bpfpsp_even_central_table)) * bcf_row_code_scale_bpfpsp_even_central)) /\ exists bcf_quotient_bpfpsp_even_central_table_decoded_previous_code. bcf_row_code_code_bpfpsp_even_central = bcf_quotient_bpfpsp_even_central_table_decoded_previous_code * S ((S (bcf_predecessor_bpfpsp_even_central_table)) * bcf_row_code_scale_bpfpsp_even_central) + (bcf_previous_code_bpfpsp_even_central_table))) /\ ((((exists bcf_height_bpfpsp_even_central_table_decoded_previous_scale. bcf_height_bpfpsp_even_central_table_decoded_previous_scale + S (bcf_previous_scale_bpfpsp_even_central_table) = S ((S (bcf_predecessor_bpfpsp_even_central_table)) * bcf_row_scale_scale_bpfpsp_even_central)) /\ exists bcf_quotient_bpfpsp_even_central_table_decoded_previous_scale. bcf_row_scale_code_bpfpsp_even_central = bcf_quotient_bpfpsp_even_central_table_decoded_previous_scale * S ((S (bcf_predecessor_bpfpsp_even_central_table)) * bcf_row_scale_scale_bpfpsp_even_central) + (bcf_previous_scale_bpfpsp_even_central_table))) /\ (forall bcf_index_bpfpsp_even_central_table_row_step. (exists bcf_lt_gap_bpfpsp_even_central_table_row_step_bound. bcf_lt_gap_bpfpsp_even_central_table_row_step_bound + S (bcf_index_bpfpsp_even_central_table_row_step) = S (n + n)) -> exists bcf_value_bpfpsp_even_central_table_row_step. ((((exists bcf_height_bpfpsp_even_central_table_row_step_entry. bcf_height_bpfpsp_even_central_table_row_step_entry + S (bcf_value_bpfpsp_even_central_table_row_step) = S ((S (bcf_index_bpfpsp_even_central_table_row_step)) * bcf_row_scale_bpfpsp_even_central_table)) /\ exists bcf_quotient_bpfpsp_even_central_table_row_step_entry. bcf_row_code_bpfpsp_even_central_table = bcf_quotient_bpfpsp_even_central_table_row_step_entry * S ((S (bcf_index_bpfpsp_even_central_table_row_step)) * bcf_row_scale_bpfpsp_even_central_table) + (bcf_value_bpfpsp_even_central_table_row_step))) /\ ((bcf_index_bpfpsp_even_central_table_row_step = 0 /\ bcf_value_bpfpsp_even_central_table_row_step = 1) \/ exists bcf_predecessor_bpfpsp_even_central_table_row_step bcf_left_bpfpsp_even_central_table_row_step bcf_right_bpfpsp_even_central_table_row_step. bcf_index_bpfpsp_even_central_table_row_step = S bcf_predecessor_bpfpsp_even_central_table_row_step /\ ((((exists bcf_height_bpfpsp_even_central_table_row_step_previous_left. bcf_height_bpfpsp_even_central_table_row_step_previous_left + S (bcf_left_bpfpsp_even_central_table_row_step) = S ((S (bcf_predecessor_bpfpsp_even_central_table_row_step)) * bcf_previous_scale_bpfpsp_even_central_table)) /\ exists bcf_quotient_bpfpsp_even_central_table_row_step_previous_left. bcf_previous_code_bpfpsp_even_central_table = bcf_quotient_bpfpsp_even_central_table_row_step_previous_left * S ((S (bcf_predecessor_bpfpsp_even_central_table_row_step)) * bcf_previous_scale_bpfpsp_even_central_table) + (bcf_left_bpfpsp_even_central_table_row_step))) /\ ((((exists bcf_height_bpfpsp_even_central_table_row_step_previous_right. bcf_height_bpfpsp_even_central_table_row_step_previous_right + S (bcf_right_bpfpsp_even_central_table_row_step) = S ((S (S (bcf_predecessor_bpfpsp_even_central_table_row_step))) * bcf_previous_scale_bpfpsp_even_central_table)) /\ exists bcf_quotient_bpfpsp_even_central_table_row_step_previous_right. bcf_previous_code_bpfpsp_even_central_table = bcf_quotient_bpfpsp_even_central_table_row_step_previous_right * S ((S (S (bcf_predecessor_bpfpsp_even_central_table_row_step))) * bcf_previous_scale_bpfpsp_even_central_table) + (bcf_right_bpfpsp_even_central_table_row_step))) /\ bcf_value_bpfpsp_even_central_table_row_step = bcf_left_bpfpsp_even_central_table_row_step + bcf_right_bpfpsp_even_central_table_row_step))))))))))) /\ ((((exists bcf_height_bpfpsp_even_central_decoded_row_code. bcf_height_bpfpsp_even_central_decoded_row_code + S (bcf_row_code_bpfpsp_even_central) = S ((S (n + n)) * bcf_row_code_scale_bpfpsp_even_central)) /\ exists bcf_quotient_bpfpsp_even_central_decoded_row_code. bcf_row_code_code_bpfpsp_even_central = bcf_quotient_bpfpsp_even_central_decoded_row_code * S ((S (n + n)) * bcf_row_code_scale_bpfpsp_even_central) + (bcf_row_code_bpfpsp_even_central))) /\ ((((exists bcf_height_bpfpsp_even_central_decoded_row_scale. bcf_height_bpfpsp_even_central_decoded_row_scale + S (bcf_row_scale_bpfpsp_even_central) = S ((S (n + n)) * bcf_row_scale_scale_bpfpsp_even_central)) /\ exists bcf_quotient_bpfpsp_even_central_decoded_row_scale. bcf_row_scale_code_bpfpsp_even_central = bcf_quotient_bpfpsp_even_central_decoded_row_scale * S ((S (n + n)) * bcf_row_scale_scale_bpfpsp_even_central) + (bcf_row_scale_bpfpsp_even_central))) /\ (((exists bcf_height_bpfpsp_even_central_decoded_value. bcf_height_bpfpsp_even_central_decoded_value + S (c) = S ((S (n)) * bcf_row_scale_bpfpsp_even_central)) /\ exists bcf_quotient_bpfpsp_even_central_decoded_value. bcf_row_code_bpfpsp_even_central = bcf_quotient_bpfpsp_even_central_decoded_value * S ((S (n)) * bcf_row_scale_bpfpsp_even_central) + (c))))))))) -> (exists bcf_le_gap_bpfpsp_even_result. bcf_le_gap_bpfpsp_even_result + (z) = c)) /\ ((forall n z c. (exists bpr_code_bpfpsp_odd_interval bpr_scale_bpfpsp_odd_interval. ((forall bpr_index_bpfpsp_odd_interval_mask. (exists bpr_gap_bpfpsp_odd_interval_mask_bound. bpr_gap_bpfpsp_odd_interval_mask_bound + S (bpr_index_bpfpsp_odd_interval_mask) = n) -> exists bpr_value_bpfpsp_odd_interval_mask. ((((exists bpr_height_bpfpsp_odd_interval_mask_decoded. bpr_height_bpfpsp_odd_interval_mask_decoded + S (bpr_value_bpfpsp_odd_interval_mask) = S ((S (bpr_index_bpfpsp_odd_interval_mask)) * bpr_scale_bpfpsp_odd_interval)) /\ exists bpr_quotient_bpfpsp_odd_interval_mask_decoded. bpr_code_bpfpsp_odd_interval = bpr_quotient_bpfpsp_odd_interval_mask_decoded * S ((S (bpr_index_bpfpsp_odd_interval_mask)) * bpr_scale_bpfpsp_odd_interval) + (bpr_value_bpfpsp_odd_interval_mask))) /\ (((((~(S (S n + bpr_index_bpfpsp_odd_interval_mask) = 1) /\ forall bpr_left_bpfpsp_odd_interval_mask_choice_prime bpr_right_bpfpsp_odd_interval_mask_choice_prime. S (S n + bpr_index_bpfpsp_odd_interval_mask) = bpr_left_bpfpsp_odd_interval_mask_choice_prime * bpr_right_bpfpsp_odd_interval_mask_choice_prime -> bpr_left_bpfpsp_odd_interval_mask_choice_prime = 1 \/ bpr_right_bpfpsp_odd_interval_mask_choice_prime = 1)) /\ bpr_value_bpfpsp_odd_interval_mask = S (S n + bpr_index_bpfpsp_odd_interval_mask)) \/ (~((~(S (S n + bpr_index_bpfpsp_odd_interval_mask) = 1) /\ forall bpr_left_bpfpsp_odd_interval_mask_choice_prime bpr_right_bpfpsp_odd_interval_mask_choice_prime. S (S n + bpr_index_bpfpsp_odd_interval_mask) = bpr_left_bpfpsp_odd_interval_mask_choice_prime * bpr_right_bpfpsp_odd_interval_mask_choice_prime -> bpr_left_bpfpsp_odd_interval_mask_choice_prime = 1 \/ bpr_right_bpfpsp_odd_interval_mask_choice_prime = 1)) /\ bpr_value_bpfpsp_odd_interval_mask = 1))))) /\ (exists ff_u_bpfpsp_odd_interval_product ff_v_bpfpsp_odd_interval_product. ((((exists ff_h_bpfpsp_odd_interval_product_start. ff_h_bpfpsp_odd_interval_product_start + S (1) = S ((S (0)) * ff_v_bpfpsp_odd_interval_product)) /\ exists ff_q_bpfpsp_odd_interval_product_start. ff_u_bpfpsp_odd_interval_product = ff_q_bpfpsp_odd_interval_product_start * S ((S (0)) * ff_v_bpfpsp_odd_interval_product) + (1))) /\ ((((exists ff_h_bpfpsp_odd_interval_product_terminal. ff_h_bpfpsp_odd_interval_product_terminal + S (z) = S ((S (n)) * ff_v_bpfpsp_odd_interval_product)) /\ exists ff_q_bpfpsp_odd_interval_product_terminal. ff_u_bpfpsp_odd_interval_product = ff_q_bpfpsp_odd_interval_product_terminal * S ((S (n)) * ff_v_bpfpsp_odd_interval_product) + (z))) /\ forall ff_i_bpfpsp_odd_interval_product. (exists ff_lt_bpfpsp_odd_interval_product_bound. ff_lt_bpfpsp_odd_interval_product_bound + S ff_i_bpfpsp_odd_interval_product = n) -> exists ff_p_bpfpsp_odd_interval_product ff_r_bpfpsp_odd_interval_product ff_s_bpfpsp_odd_interval_product. ((((exists ff_h_bpfpsp_odd_interval_product_factor. ff_h_bpfpsp_odd_interval_product_factor + S (ff_p_bpfpsp_odd_interval_product) = S ((S (ff_i_bpfpsp_odd_interval_product)) * bpr_scale_bpfpsp_odd_interval)) /\ exists ff_q_bpfpsp_odd_interval_product_factor. bpr_code_bpfpsp_odd_interval = ff_q_bpfpsp_odd_interval_product_factor * S ((S (ff_i_bpfpsp_odd_interval_product)) * bpr_scale_bpfpsp_odd_interval) + (ff_p_bpfpsp_odd_interval_product))) /\ ((((exists ff_h_bpfpsp_odd_interval_product_partial. ff_h_bpfpsp_odd_interval_product_partial + S (ff_r_bpfpsp_odd_interval_product) = S ((S (ff_i_bpfpsp_odd_interval_product)) * ff_v_bpfpsp_odd_interval_product)) /\ exists ff_q_bpfpsp_odd_interval_product_partial. ff_u_bpfpsp_odd_interval_product = ff_q_bpfpsp_odd_interval_product_partial * S ((S (ff_i_bpfpsp_odd_interval_product)) * ff_v_bpfpsp_odd_interval_product) + (ff_r_bpfpsp_odd_interval_product))) /\ ((((exists ff_h_bpfpsp_odd_interval_product_successor. ff_h_bpfpsp_odd_interval_product_successor + S (ff_s_bpfpsp_odd_interval_product) = S ((S (S ff_i_bpfpsp_odd_interval_product)) * ff_v_bpfpsp_odd_interval_product)) /\ exists ff_q_bpfpsp_odd_interval_product_successor. ff_u_bpfpsp_odd_interval_product = ff_q_bpfpsp_odd_interval_product_successor * S ((S (S ff_i_bpfpsp_odd_interval_product)) * ff_v_bpfpsp_odd_interval_product) + (ff_s_bpfpsp_odd_interval_product))) /\ ff_s_bpfpsp_odd_interval_product = ff_r_bpfpsp_odd_interval_product * ff_p_bpfpsp_odd_interval_product)))))))) -> (((exists bcf_lt_gap_bpfpsp_odd_middle_out_of_range. bcf_lt_gap_bpfpsp_odd_middle_out_of_range + S (S (n + n)) = n) /\ c = 0) \/ ((exists bcf_le_gap_bpfpsp_odd_middle_in_range. bcf_le_gap_bpfpsp_odd_middle_in_range + (n) = S (n + n)) /\ (exists bcf_row_code_code_bpfpsp_odd_middle bcf_row_code_scale_bpfpsp_odd_middle bcf_row_scale_code_bpfpsp_odd_middle bcf_row_scale_scale_bpfpsp_odd_middle bcf_row_code_bpfpsp_odd_middle bcf_row_scale_bpfpsp_odd_middle. ((forall bcf_row_index_bpfpsp_odd_middle_table. (exists bcf_lt_gap_bpfpsp_odd_middle_table_row_bound. bcf_lt_gap_bpfpsp_odd_middle_table_row_bound + S (bcf_row_index_bpfpsp_odd_middle_table) = S (S (n + n))) -> exists bcf_row_code_bpfpsp_odd_middle_table bcf_row_scale_bpfpsp_odd_middle_table. ((((exists bcf_height_bpfpsp_odd_middle_table_decoded_row_code. bcf_height_bpfpsp_odd_middle_table_decoded_row_code + S (bcf_row_code_bpfpsp_odd_middle_table) = S ((S (bcf_row_index_bpfpsp_odd_middle_table)) * bcf_row_code_scale_bpfpsp_odd_middle)) /\ exists bcf_quotient_bpfpsp_odd_middle_table_decoded_row_code. bcf_row_code_code_bpfpsp_odd_middle = bcf_quotient_bpfpsp_odd_middle_table_decoded_row_code * S ((S (bcf_row_index_bpfpsp_odd_middle_table)) * bcf_row_code_scale_bpfpsp_odd_middle) + (bcf_row_code_bpfpsp_odd_middle_table))) /\ ((((exists bcf_height_bpfpsp_odd_middle_table_decoded_row_scale. bcf_height_bpfpsp_odd_middle_table_decoded_row_scale + S (bcf_row_scale_bpfpsp_odd_middle_table) = S ((S (bcf_row_index_bpfpsp_odd_middle_table)) * bcf_row_scale_scale_bpfpsp_odd_middle)) /\ exists bcf_quotient_bpfpsp_odd_middle_table_decoded_row_scale. bcf_row_scale_code_bpfpsp_odd_middle = bcf_quotient_bpfpsp_odd_middle_table_decoded_row_scale * S ((S (bcf_row_index_bpfpsp_odd_middle_table)) * bcf_row_scale_scale_bpfpsp_odd_middle) + (bcf_row_scale_bpfpsp_odd_middle_table))) /\ ((bcf_row_index_bpfpsp_odd_middle_table = 0 /\ (forall bcf_index_bpfpsp_odd_middle_table_zero_row. (exists bcf_lt_gap_bpfpsp_odd_middle_table_zero_row_bound. bcf_lt_gap_bpfpsp_odd_middle_table_zero_row_bound + S (bcf_index_bpfpsp_odd_middle_table_zero_row) = S (S (n + n))) -> exists bcf_value_bpfpsp_odd_middle_table_zero_row. ((((exists bcf_height_bpfpsp_odd_middle_table_zero_row_entry. bcf_height_bpfpsp_odd_middle_table_zero_row_entry + S (bcf_value_bpfpsp_odd_middle_table_zero_row) = S ((S (bcf_index_bpfpsp_odd_middle_table_zero_row)) * bcf_row_scale_bpfpsp_odd_middle_table)) /\ exists bcf_quotient_bpfpsp_odd_middle_table_zero_row_entry. bcf_row_code_bpfpsp_odd_middle_table = bcf_quotient_bpfpsp_odd_middle_table_zero_row_entry * S ((S (bcf_index_bpfpsp_odd_middle_table_zero_row)) * bcf_row_scale_bpfpsp_odd_middle_table) + (bcf_value_bpfpsp_odd_middle_table_zero_row))) /\ ((bcf_index_bpfpsp_odd_middle_table_zero_row = 0 /\ bcf_value_bpfpsp_odd_middle_table_zero_row = 1) \/ exists bcf_predecessor_bpfpsp_odd_middle_table_zero_row. bcf_index_bpfpsp_odd_middle_table_zero_row = S bcf_predecessor_bpfpsp_odd_middle_table_zero_row /\ bcf_value_bpfpsp_odd_middle_table_zero_row = 0)))) \/ exists bcf_predecessor_bpfpsp_odd_middle_table bcf_previous_code_bpfpsp_odd_middle_table bcf_previous_scale_bpfpsp_odd_middle_table. bcf_row_index_bpfpsp_odd_middle_table = S bcf_predecessor_bpfpsp_odd_middle_table /\ ((((exists bcf_height_bpfpsp_odd_middle_table_decoded_previous_code. bcf_height_bpfpsp_odd_middle_table_decoded_previous_code + S (bcf_previous_code_bpfpsp_odd_middle_table) = S ((S (bcf_predecessor_bpfpsp_odd_middle_table)) * bcf_row_code_scale_bpfpsp_odd_middle)) /\ exists bcf_quotient_bpfpsp_odd_middle_table_decoded_previous_code. bcf_row_code_code_bpfpsp_odd_middle = bcf_quotient_bpfpsp_odd_middle_table_decoded_previous_code * S ((S (bcf_predecessor_bpfpsp_odd_middle_table)) * bcf_row_code_scale_bpfpsp_odd_middle) + (bcf_previous_code_bpfpsp_odd_middle_table))) /\ ((((exists bcf_height_bpfpsp_odd_middle_table_decoded_previous_scale. bcf_height_bpfpsp_odd_middle_table_decoded_previous_scale + S (bcf_previous_scale_bpfpsp_odd_middle_table) = S ((S (bcf_predecessor_bpfpsp_odd_middle_table)) * bcf_row_scale_scale_bpfpsp_odd_middle)) /\ exists bcf_quotient_bpfpsp_odd_middle_table_decoded_previous_scale. bcf_row_scale_code_bpfpsp_odd_middle = bcf_quotient_bpfpsp_odd_middle_table_decoded_previous_scale * S ((S (bcf_predecessor_bpfpsp_odd_middle_table)) * bcf_row_scale_scale_bpfpsp_odd_middle) + (bcf_previous_scale_bpfpsp_odd_middle_table))) /\ (forall bcf_index_bpfpsp_odd_middle_table_row_step. (exists bcf_lt_gap_bpfpsp_odd_middle_table_row_step_bound. bcf_lt_gap_bpfpsp_odd_middle_table_row_step_bound + S (bcf_index_bpfpsp_odd_middle_table_row_step) = S (S (n + n))) -> exists bcf_value_bpfpsp_odd_middle_table_row_step. ((((exists bcf_height_bpfpsp_odd_middle_table_row_step_entry. bcf_height_bpfpsp_odd_middle_table_row_step_entry + S (bcf_value_bpfpsp_odd_middle_table_row_step) = S ((S (bcf_index_bpfpsp_odd_middle_table_row_step)) * bcf_row_scale_bpfpsp_odd_middle_table)) /\ exists bcf_quotient_bpfpsp_odd_middle_table_row_step_entry. bcf_row_code_bpfpsp_odd_middle_table = bcf_quotient_bpfpsp_odd_middle_table_row_step_entry * S ((S (bcf_index_bpfpsp_odd_middle_table_row_step)) * bcf_row_scale_bpfpsp_odd_middle_table) + (bcf_value_bpfpsp_odd_middle_table_row_step))) /\ ((bcf_index_bpfpsp_odd_middle_table_row_step = 0 /\ bcf_value_bpfpsp_odd_middle_table_row_step = 1) \/ exists bcf_predecessor_bpfpsp_odd_middle_table_row_step bcf_left_bpfpsp_odd_middle_table_row_step bcf_right_bpfpsp_odd_middle_table_row_step. bcf_index_bpfpsp_odd_middle_table_row_step = S bcf_predecessor_bpfpsp_odd_middle_table_row_step /\ ((((exists bcf_height_bpfpsp_odd_middle_table_row_step_previous_left. bcf_height_bpfpsp_odd_middle_table_row_step_previous_left + S (bcf_left_bpfpsp_odd_middle_table_row_step) = S ((S (bcf_predecessor_bpfpsp_odd_middle_table_row_step)) * bcf_previous_scale_bpfpsp_odd_middle_table)) /\ exists bcf_quotient_bpfpsp_odd_middle_table_row_step_previous_left. bcf_previous_code_bpfpsp_odd_middle_table = bcf_quotient_bpfpsp_odd_middle_table_row_step_previous_left * S ((S (bcf_predecessor_bpfpsp_odd_middle_table_row_step)) * bcf_previous_scale_bpfpsp_odd_middle_table) + (bcf_left_bpfpsp_odd_middle_table_row_step))) /\ ((((exists bcf_height_bpfpsp_odd_middle_table_row_step_previous_right. bcf_height_bpfpsp_odd_middle_table_row_step_previous_right + S (bcf_right_bpfpsp_odd_middle_table_row_step) = S ((S (S (bcf_predecessor_bpfpsp_odd_middle_table_row_step))) * bcf_previous_scale_bpfpsp_odd_middle_table)) /\ exists bcf_quotient_bpfpsp_odd_middle_table_row_step_previous_right. bcf_previous_code_bpfpsp_odd_middle_table = bcf_quotient_bpfpsp_odd_middle_table_row_step_previous_right * S ((S (S (bcf_predecessor_bpfpsp_odd_middle_table_row_step))) * bcf_previous_scale_bpfpsp_odd_middle_table) + (bcf_right_bpfpsp_odd_middle_table_row_step))) /\ bcf_value_bpfpsp_odd_middle_table_row_step = bcf_left_bpfpsp_odd_middle_table_row_step + bcf_right_bpfpsp_odd_middle_table_row_step))))))))))) /\ ((((exists bcf_height_bpfpsp_odd_middle_decoded_row_code. bcf_height_bpfpsp_odd_middle_decoded_row_code + S (bcf_row_code_bpfpsp_odd_middle) = S ((S (S (n + n))) * bcf_row_code_scale_bpfpsp_odd_middle)) /\ exists bcf_quotient_bpfpsp_odd_middle_decoded_row_code. bcf_row_code_code_bpfpsp_odd_middle = bcf_quotient_bpfpsp_odd_middle_decoded_row_code * S ((S (S (n + n))) * bcf_row_code_scale_bpfpsp_odd_middle) + (bcf_row_code_bpfpsp_odd_middle))) /\ ((((exists bcf_height_bpfpsp_odd_middle_decoded_row_scale. bcf_height_bpfpsp_odd_middle_decoded_row_scale + S (bcf_row_scale_bpfpsp_odd_middle) = S ((S (S (n + n))) * bcf_row_scale_scale_bpfpsp_odd_middle)) /\ exists bcf_quotient_bpfpsp_odd_middle_decoded_row_scale. bcf_row_scale_code_bpfpsp_odd_middle = bcf_quotient_bpfpsp_odd_middle_decoded_row_scale * S ((S (S (n + n))) * bcf_row_scale_scale_bpfpsp_odd_middle) + (bcf_row_scale_bpfpsp_odd_middle))) /\ (((exists bcf_height_bpfpsp_odd_middle_decoded_value. bcf_height_bpfpsp_odd_middle_decoded_value + S (c) = S ((S (n)) * bcf_row_scale_bpfpsp_odd_middle)) /\ exists bcf_quotient_bpfpsp_odd_middle_decoded_value. bcf_row_code_bpfpsp_odd_middle = bcf_quotient_bpfpsp_odd_middle_decoded_value * S ((S (n)) * bcf_row_scale_bpfpsp_odd_middle) + (c))))))))) -> (exists bcf_le_gap_bpfpsp_odd_result. bcf_le_gap_bpfpsp_odd_result + (z) = c)) /\ (forall n c q. (((exists bcf_lt_gap_bpfpsp_odd_upper_middle_out_of_range. bcf_lt_gap_bpfpsp_odd_upper_middle_out_of_range + S (S (n + n)) = n) /\ c = 0) \/ ((exists bcf_le_gap_bpfpsp_odd_upper_middle_in_range. bcf_le_gap_bpfpsp_odd_upper_middle_in_range + (n) = S (n + n)) /\ (exists bcf_row_code_code_bpfpsp_odd_upper_middle bcf_row_code_scale_bpfpsp_odd_upper_middle bcf_row_scale_code_bpfpsp_odd_upper_middle bcf_row_scale_scale_bpfpsp_odd_upper_middle bcf_row_code_bpfpsp_odd_upper_middle bcf_row_scale_bpfpsp_odd_upper_middle. ((forall bcf_row_index_bpfpsp_odd_upper_middle_table. (exists bcf_lt_gap_bpfpsp_odd_upper_middle_table_row_bound. bcf_lt_gap_bpfpsp_odd_upper_middle_table_row_bound + S (bcf_row_index_bpfpsp_odd_upper_middle_table) = S (S (n + n))) -> exists bcf_row_code_bpfpsp_odd_upper_middle_table bcf_row_scale_bpfpsp_odd_upper_middle_table. ((((exists bcf_height_bpfpsp_odd_upper_middle_table_decoded_row_code. bcf_height_bpfpsp_odd_upper_middle_table_decoded_row_code + S (bcf_row_code_bpfpsp_odd_upper_middle_table) = S ((S (bcf_row_index_bpfpsp_odd_upper_middle_table)) * bcf_row_code_scale_bpfpsp_odd_upper_middle)) /\ exists bcf_quotient_bpfpsp_odd_upper_middle_table_decoded_row_code. bcf_row_code_code_bpfpsp_odd_upper_middle = bcf_quotient_bpfpsp_odd_upper_middle_table_decoded_row_code * S ((S (bcf_row_index_bpfpsp_odd_upper_middle_table)) * bcf_row_code_scale_bpfpsp_odd_upper_middle) + (bcf_row_code_bpfpsp_odd_upper_middle_table))) /\ ((((exists bcf_height_bpfpsp_odd_upper_middle_table_decoded_row_scale. bcf_height_bpfpsp_odd_upper_middle_table_decoded_row_scale + S (bcf_row_scale_bpfpsp_odd_upper_middle_table) = S ((S (bcf_row_index_bpfpsp_odd_upper_middle_table)) * bcf_row_scale_scale_bpfpsp_odd_upper_middle)) /\ exists bcf_quotient_bpfpsp_odd_upper_middle_table_decoded_row_scale. bcf_row_scale_code_bpfpsp_odd_upper_middle = bcf_quotient_bpfpsp_odd_upper_middle_table_decoded_row_scale * S ((S (bcf_row_index_bpfpsp_odd_upper_middle_table)) * bcf_row_scale_scale_bpfpsp_odd_upper_middle) + (bcf_row_scale_bpfpsp_odd_upper_middle_table))) /\ ((bcf_row_index_bpfpsp_odd_upper_middle_table = 0 /\ (forall bcf_index_bpfpsp_odd_upper_middle_table_zero_row. (exists bcf_lt_gap_bpfpsp_odd_upper_middle_table_zero_row_bound. bcf_lt_gap_bpfpsp_odd_upper_middle_table_zero_row_bound + S (bcf_index_bpfpsp_odd_upper_middle_table_zero_row) = S (S (n + n))) -> exists bcf_value_bpfpsp_odd_upper_middle_table_zero_row. ((((exists bcf_height_bpfpsp_odd_upper_middle_table_zero_row_entry. bcf_height_bpfpsp_odd_upper_middle_table_zero_row_entry + S (bcf_value_bpfpsp_odd_upper_middle_table_zero_row) = S ((S (bcf_index_bpfpsp_odd_upper_middle_table_zero_row)) * bcf_row_scale_bpfpsp_odd_upper_middle_table)) /\ exists bcf_quotient_bpfpsp_odd_upper_middle_table_zero_row_entry. bcf_row_code_bpfpsp_odd_upper_middle_table = bcf_quotient_bpfpsp_odd_upper_middle_table_zero_row_entry * S ((S (bcf_index_bpfpsp_odd_upper_middle_table_zero_row)) * bcf_row_scale_bpfpsp_odd_upper_middle_table) + (bcf_value_bpfpsp_odd_upper_middle_table_zero_row))) /\ ((bcf_index_bpfpsp_odd_upper_middle_table_zero_row = 0 /\ bcf_value_bpfpsp_odd_upper_middle_table_zero_row = 1) \/ exists bcf_predecessor_bpfpsp_odd_upper_middle_table_zero_row. bcf_index_bpfpsp_odd_upper_middle_table_zero_row = S bcf_predecessor_bpfpsp_odd_upper_middle_table_zero_row /\ bcf_value_bpfpsp_odd_upper_middle_table_zero_row = 0)))) \/ exists bcf_predecessor_bpfpsp_odd_upper_middle_table bcf_previous_code_bpfpsp_odd_upper_middle_table bcf_previous_scale_bpfpsp_odd_upper_middle_table. bcf_row_index_bpfpsp_odd_upper_middle_table = S bcf_predecessor_bpfpsp_odd_upper_middle_table /\ ((((exists bcf_height_bpfpsp_odd_upper_middle_table_decoded_previous_code. bcf_height_bpfpsp_odd_upper_middle_table_decoded_previous_code + S (bcf_previous_code_bpfpsp_odd_upper_middle_table) = S ((S (bcf_predecessor_bpfpsp_odd_upper_middle_table)) * bcf_row_code_scale_bpfpsp_odd_upper_middle)) /\ exists bcf_quotient_bpfpsp_odd_upper_middle_table_decoded_previous_code. bcf_row_code_code_bpfpsp_odd_upper_middle = bcf_quotient_bpfpsp_odd_upper_middle_table_decoded_previous_code * S ((S (bcf_predecessor_bpfpsp_odd_upper_middle_table)) * bcf_row_code_scale_bpfpsp_odd_upper_middle) + (bcf_previous_code_bpfpsp_odd_upper_middle_table))) /\ ((((exists bcf_height_bpfpsp_odd_upper_middle_table_decoded_previous_scale. bcf_height_bpfpsp_odd_upper_middle_table_decoded_previous_scale + S (bcf_previous_scale_bpfpsp_odd_upper_middle_table) = S ((S (bcf_predecessor_bpfpsp_odd_upper_middle_table)) * bcf_row_scale_scale_bpfpsp_odd_upper_middle)) /\ exists bcf_quotient_bpfpsp_odd_upper_middle_table_decoded_previous_scale. bcf_row_scale_code_bpfpsp_odd_upper_middle = bcf_quotient_bpfpsp_odd_upper_middle_table_decoded_previous_scale * S ((S (bcf_predecessor_bpfpsp_odd_upper_middle_table)) * bcf_row_scale_scale_bpfpsp_odd_upper_middle) + (bcf_previous_scale_bpfpsp_odd_upper_middle_table))) /\ (forall bcf_index_bpfpsp_odd_upper_middle_table_row_step. (exists bcf_lt_gap_bpfpsp_odd_upper_middle_table_row_step_bound. bcf_lt_gap_bpfpsp_odd_upper_middle_table_row_step_bound + S (bcf_index_bpfpsp_odd_upper_middle_table_row_step) = S (S (n + n))) -> exists bcf_value_bpfpsp_odd_upper_middle_table_row_step. ((((exists bcf_height_bpfpsp_odd_upper_middle_table_row_step_entry. bcf_height_bpfpsp_odd_upper_middle_table_row_step_entry + S (bcf_value_bpfpsp_odd_upper_middle_table_row_step) = S ((S (bcf_index_bpfpsp_odd_upper_middle_table_row_step)) * bcf_row_scale_bpfpsp_odd_upper_middle_table)) /\ exists bcf_quotient_bpfpsp_odd_upper_middle_table_row_step_entry. bcf_row_code_bpfpsp_odd_upper_middle_table = bcf_quotient_bpfpsp_odd_upper_middle_table_row_step_entry * S ((S (bcf_index_bpfpsp_odd_upper_middle_table_row_step)) * bcf_row_scale_bpfpsp_odd_upper_middle_table) + (bcf_value_bpfpsp_odd_upper_middle_table_row_step))) /\ ((bcf_index_bpfpsp_odd_upper_middle_table_row_step = 0 /\ bcf_value_bpfpsp_odd_upper_middle_table_row_step = 1) \/ exists bcf_predecessor_bpfpsp_odd_upper_middle_table_row_step bcf_left_bpfpsp_odd_upper_middle_table_row_step bcf_right_bpfpsp_odd_upper_middle_table_row_step. bcf_index_bpfpsp_odd_upper_middle_table_row_step = S bcf_predecessor_bpfpsp_odd_upper_middle_table_row_step /\ ((((exists bcf_height_bpfpsp_odd_upper_middle_table_row_step_previous_left. bcf_height_bpfpsp_odd_upper_middle_table_row_step_previous_left + S (bcf_left_bpfpsp_odd_upper_middle_table_row_step) = S ((S (bcf_predecessor_bpfpsp_odd_upper_middle_table_row_step)) * bcf_previous_scale_bpfpsp_odd_upper_middle_table)) /\ exists bcf_quotient_bpfpsp_odd_upper_middle_table_row_step_previous_left. bcf_previous_code_bpfpsp_odd_upper_middle_table = bcf_quotient_bpfpsp_odd_upper_middle_table_row_step_previous_left * S ((S (bcf_predecessor_bpfpsp_odd_upper_middle_table_row_step)) * bcf_previous_scale_bpfpsp_odd_upper_middle_table) + (bcf_left_bpfpsp_odd_upper_middle_table_row_step))) /\ ((((exists bcf_height_bpfpsp_odd_upper_middle_table_row_step_previous_right. bcf_height_bpfpsp_odd_upper_middle_table_row_step_previous_right + S (bcf_right_bpfpsp_odd_upper_middle_table_row_step) = S ((S (S (bcf_predecessor_bpfpsp_odd_upper_middle_table_row_step))) * bcf_previous_scale_bpfpsp_odd_upper_middle_table)) /\ exists bcf_quotient_bpfpsp_odd_upper_middle_table_row_step_previous_right. bcf_previous_code_bpfpsp_odd_upper_middle_table = bcf_quotient_bpfpsp_odd_upper_middle_table_row_step_previous_right * S ((S (S (bcf_predecessor_bpfpsp_odd_upper_middle_table_row_step))) * bcf_previous_scale_bpfpsp_odd_upper_middle_table) + (bcf_right_bpfpsp_odd_upper_middle_table_row_step))) /\ bcf_value_bpfpsp_odd_upper_middle_table_row_step = bcf_left_bpfpsp_odd_upper_middle_table_row_step + bcf_right_bpfpsp_odd_upper_middle_table_row_step))))))))))) /\ ((((exists bcf_height_bpfpsp_odd_upper_middle_decoded_row_code. bcf_height_bpfpsp_odd_upper_middle_decoded_row_code + S (bcf_row_code_bpfpsp_odd_upper_middle) = S ((S (S (n + n))) * bcf_row_code_scale_bpfpsp_odd_upper_middle)) /\ exists bcf_quotient_bpfpsp_odd_upper_middle_decoded_row_code. bcf_row_code_code_bpfpsp_odd_upper_middle = bcf_quotient_bpfpsp_odd_upper_middle_decoded_row_code * S ((S (S (n + n))) * bcf_row_code_scale_bpfpsp_odd_upper_middle) + (bcf_row_code_bpfpsp_odd_upper_middle))) /\ ((((exists bcf_height_bpfpsp_odd_upper_middle_decoded_row_scale. bcf_height_bpfpsp_odd_upper_middle_decoded_row_scale + S (bcf_row_scale_bpfpsp_odd_upper_middle) = S ((S (S (n + n))) * bcf_row_scale_scale_bpfpsp_odd_upper_middle)) /\ exists bcf_quotient_bpfpsp_odd_upper_middle_decoded_row_scale. bcf_row_scale_code_bpfpsp_odd_upper_middle = bcf_quotient_bpfpsp_odd_upper_middle_decoded_row_scale * S ((S (S (n + n))) * bcf_row_scale_scale_bpfpsp_odd_upper_middle) + (bcf_row_scale_bpfpsp_odd_upper_middle))) /\ (((exists bcf_height_bpfpsp_odd_upper_middle_decoded_value. bcf_height_bpfpsp_odd_upper_middle_decoded_value + S (c) = S ((S (n)) * bcf_row_scale_bpfpsp_odd_upper_middle)) /\ exists bcf_quotient_bpfpsp_odd_upper_middle_decoded_value. bcf_row_code_bpfpsp_odd_upper_middle = bcf_quotient_bpfpsp_odd_upper_middle_decoded_value * S ((S (n)) * bcf_row_scale_bpfpsp_odd_upper_middle) + (c))))))))) -> (exists pa_b_bpfpsp_odd_upper_power pa_c_bpfpsp_odd_upper_power. ((forall pa_i_bpfpsp_odd_upper_power_repeat. (exists pa_lt_bpfpsp_odd_upper_power_repeat_bound. pa_lt_bpfpsp_odd_upper_power_repeat_bound + S pa_i_bpfpsp_odd_upper_power_repeat = n) -> (((exists pa_h_bpfpsp_odd_upper_power_repeat_decoded. pa_h_bpfpsp_odd_upper_power_repeat_decoded + S (4) = S ((S (pa_i_bpfpsp_odd_upper_power_repeat)) * pa_c_bpfpsp_odd_upper_power)) /\ exists pa_q_bpfpsp_odd_upper_power_repeat_decoded. pa_b_bpfpsp_odd_upper_power = pa_q_bpfpsp_odd_upper_power_repeat_decoded * S ((S (pa_i_bpfpsp_odd_upper_power_repeat)) * pa_c_bpfpsp_odd_upper_power) + (4)))) /\ (exists pa_u_bpfpsp_odd_upper_power_product pa_v_bpfpsp_odd_upper_power_product. ((((exists pa_h_bpfpsp_odd_upper_power_product_start. pa_h_bpfpsp_odd_upper_power_product_start + S (1) = S ((S (0)) * pa_v_bpfpsp_odd_upper_power_product)) /\ exists pa_q_bpfpsp_odd_upper_power_product_start. pa_u_bpfpsp_odd_upper_power_product = pa_q_bpfpsp_odd_upper_power_product_start * S ((S (0)) * pa_v_bpfpsp_odd_upper_power_product) + (1))) /\ ((((exists pa_h_bpfpsp_odd_upper_power_product_terminal. pa_h_bpfpsp_odd_upper_power_product_terminal + S (q) = S ((S (n)) * pa_v_bpfpsp_odd_upper_power_product)) /\ exists pa_q_bpfpsp_odd_upper_power_product_terminal. pa_u_bpfpsp_odd_upper_power_product = pa_q_bpfpsp_odd_upper_power_product_terminal * S ((S (n)) * pa_v_bpfpsp_odd_upper_power_product) + (q))) /\ forall pa_i_bpfpsp_odd_upper_power_product. (exists pa_lt_bpfpsp_odd_upper_power_product_bound. pa_lt_bpfpsp_odd_upper_power_product_bound + S pa_i_bpfpsp_odd_upper_power_product = n) -> exists pa_p_bpfpsp_odd_upper_power_product pa_r_bpfpsp_odd_upper_power_product pa_s_bpfpsp_odd_upper_power_product. ((((exists pa_h_bpfpsp_odd_upper_power_product_factor. pa_h_bpfpsp_odd_upper_power_product_factor + S (pa_p_bpfpsp_odd_upper_power_product) = S ((S (pa_i_bpfpsp_odd_upper_power_product)) * pa_c_bpfpsp_odd_upper_power)) /\ exists pa_q_bpfpsp_odd_upper_power_product_factor. pa_b_bpfpsp_odd_upper_power = pa_q_bpfpsp_odd_upper_power_product_factor * S ((S (pa_i_bpfpsp_odd_upper_power_product)) * pa_c_bpfpsp_odd_upper_power) + (pa_p_bpfpsp_odd_upper_power_product))) /\ ((((exists pa_h_bpfpsp_odd_upper_power_product_partial. pa_h_bpfpsp_odd_upper_power_product_partial + S (pa_r_bpfpsp_odd_upper_power_product) = S ((S (pa_i_bpfpsp_odd_upper_power_product)) * pa_v_bpfpsp_odd_upper_power_product)) /\ exists pa_q_bpfpsp_odd_upper_power_product_partial. pa_u_bpfpsp_odd_upper_power_product = pa_q_bpfpsp_odd_upper_power_product_partial * S ((S (pa_i_bpfpsp_odd_upper_power_product)) * pa_v_bpfpsp_odd_upper_power_product) + (pa_r_bpfpsp_odd_upper_power_product))) /\ ((((exists pa_h_bpfpsp_odd_upper_power_product_successor. pa_h_bpfpsp_odd_upper_power_product_successor + S (pa_s_bpfpsp_odd_upper_power_product) = S ((S (S pa_i_bpfpsp_odd_upper_power_product)) * pa_v_bpfpsp_odd_upper_power_product)) /\ exists pa_q_bpfpsp_odd_upper_power_product_successor. pa_u_bpfpsp_odd_upper_power_product = pa_q_bpfpsp_odd_upper_power_product_successor * S ((S (S pa_i_bpfpsp_odd_upper_power_product)) * pa_v_bpfpsp_odd_upper_power_product) + (pa_s_bpfpsp_odd_upper_power_product))) /\ pa_s_bpfpsp_odd_upper_power_product = pa_r_bpfpsp_odd_upper_power_product * pa_p_bpfpsp_odd_upper_power_product)))))))) -> (exists bcf_le_gap_bpfpsp_odd_upper_result. bcf_le_gap_bpfpsp_odd_upper_result + (c) = q))))))) -> (forall N n z q. (exists bcf_le_gap_bplfpb_index. bcf_le_gap_bplfpb_index + (n) = N) -> (exists bpr_code_bplfpb_primorial bpr_scale_bplfpb_primorial. ((forall bpr_index_bplfpb_primorial_mask. (exists bpr_gap_bplfpb_primorial_mask_bound. bpr_gap_bplfpb_primorial_mask_bound + S (bpr_index_bplfpb_primorial_mask) = n) -> exists bpr_value_bplfpb_primorial_mask. ((((exists bpr_height_bplfpb_primorial_mask_decoded. bpr_height_bplfpb_primorial_mask_decoded + S (bpr_value_bplfpb_primorial_mask) = S ((S (bpr_index_bplfpb_primorial_mask)) * bpr_scale_bplfpb_primorial)) /\ exists bpr_quotient_bplfpb_primorial_mask_decoded. bpr_code_bplfpb_primorial = bpr_quotient_bplfpb_primorial_mask_decoded * S ((S (bpr_index_bplfpb_primorial_mask)) * bpr_scale_bplfpb_primorial) + (bpr_value_bplfpb_primorial_mask))) /\ (((((~(S (bpr_index_bplfpb_primorial_mask) = 1) /\ forall bpr_left_bplfpb_primorial_mask_choice_prime bpr_right_bplfpb_primorial_mask_choice_prime. S (bpr_index_bplfpb_primorial_mask) = bpr_left_bplfpb_primorial_mask_choice_prime * bpr_right_bplfpb_primorial_mask_choice_prime -> bpr_left_bplfpb_primorial_mask_choice_prime = 1 \/ bpr_right_bplfpb_primorial_mask_choice_prime = 1)) /\ bpr_value_bplfpb_primorial_mask = S (bpr_index_bplfpb_primorial_mask)) \/ (~((~(S (bpr_index_bplfpb_primorial_mask) = 1) /\ forall bpr_left_bplfpb_primorial_mask_choice_prime bpr_right_bplfpb_primorial_mask_choice_prime. S (bpr_index_bplfpb_primorial_mask) = bpr_left_bplfpb_primorial_mask_choice_prime * bpr_right_bplfpb_primorial_mask_choice_prime -> bpr_left_bplfpb_primorial_mask_choice_prime = 1 \/ bpr_right_bplfpb_primorial_mask_choice_prime = 1)) /\ bpr_value_bplfpb_primorial_mask = 1))))) /\ (exists ff_u_bplfpb_primorial_product ff_v_bplfpb_primorial_product. ((((exists ff_h_bplfpb_primorial_product_start. ff_h_bplfpb_primorial_product_start + S (1) = S ((S (0)) * ff_v_bplfpb_primorial_product)) /\ exists ff_q_bplfpb_primorial_product_start. ff_u_bplfpb_primorial_product = ff_q_bplfpb_primorial_product_start * S ((S (0)) * ff_v_bplfpb_primorial_product) + (1))) /\ ((((exists ff_h_bplfpb_primorial_product_terminal. ff_h_bplfpb_primorial_product_terminal + S (z) = S ((S (n)) * ff_v_bplfpb_primorial_product)) /\ exists ff_q_bplfpb_primorial_product_terminal. ff_u_bplfpb_primorial_product = ff_q_bplfpb_primorial_product_terminal * S ((S (n)) * ff_v_bplfpb_primorial_product) + (z))) /\ forall ff_i_bplfpb_primorial_product. (exists ff_lt_bplfpb_primorial_product_bound. ff_lt_bplfpb_primorial_product_bound + S ff_i_bplfpb_primorial_product = n) -> exists ff_p_bplfpb_primorial_product ff_r_bplfpb_primorial_product ff_s_bplfpb_primorial_product. ((((exists ff_h_bplfpb_primorial_product_factor. ff_h_bplfpb_primorial_product_factor + S (ff_p_bplfpb_primorial_product) = S ((S (ff_i_bplfpb_primorial_product)) * bpr_scale_bplfpb_primorial)) /\ exists ff_q_bplfpb_primorial_product_factor. bpr_code_bplfpb_primorial = ff_q_bplfpb_primorial_product_factor * S ((S (ff_i_bplfpb_primorial_product)) * bpr_scale_bplfpb_primorial) + (ff_p_bplfpb_primorial_product))) /\ ((((exists ff_h_bplfpb_primorial_product_partial. ff_h_bplfpb_primorial_product_partial + S (ff_r_bplfpb_primorial_product) = S ((S (ff_i_bplfpb_primorial_product)) * ff_v_bplfpb_primorial_product)) /\ exists ff_q_bplfpb_primorial_product_partial. ff_u_bplfpb_primorial_product = ff_q_bplfpb_primorial_product_partial * S ((S (ff_i_bplfpb_primorial_product)) * ff_v_bplfpb_primorial_product) + (ff_r_bplfpb_primorial_product))) /\ ((((exists ff_h_bplfpb_primorial_product_successor. ff_h_bplfpb_primorial_product_successor + S (ff_s_bplfpb_primorial_product) = S ((S (S ff_i_bplfpb_primorial_product)) * ff_v_bplfpb_primorial_product)) /\ exists ff_q_bplfpb_primorial_product_successor. ff_u_bplfpb_primorial_product = ff_q_bplfpb_primorial_product_successor * S ((S (S ff_i_bplfpb_primorial_product)) * ff_v_bplfpb_primorial_product) + (ff_s_bplfpb_primorial_product))) /\ ff_s_bplfpb_primorial_product = ff_r_bplfpb_primorial_product * ff_p_bplfpb_primorial_product)))))))) -> (exists pa_b_bplfpb_power pa_c_bplfpb_power. ((forall pa_i_bplfpb_power_repeat. (exists pa_lt_bplfpb_power_repeat_bound. pa_lt_bplfpb_power_repeat_bound + S pa_i_bplfpb_power_repeat = n) -> (((exists pa_h_bplfpb_power_repeat_decoded. pa_h_bplfpb_power_repeat_decoded + S (4) = S ((S (pa_i_bplfpb_power_repeat)) * pa_c_bplfpb_power)) /\ exists pa_q_bplfpb_power_repeat_decoded. pa_b_bplfpb_power = pa_q_bplfpb_power_repeat_decoded * S ((S (pa_i_bplfpb_power_repeat)) * pa_c_bplfpb_power) + (4)))) /\ (exists pa_u_bplfpb_power_product pa_v_bplfpb_power_product. ((((exists pa_h_bplfpb_power_product_start. pa_h_bplfpb_power_product_start + S (1) = S ((S (0)) * pa_v_bplfpb_power_product)) /\ exists pa_q_bplfpb_power_product_start. pa_u_bplfpb_power_product = pa_q_bplfpb_power_product_start * S ((S (0)) * pa_v_bplfpb_power_product) + (1))) /\ ((((exists pa_h_bplfpb_power_product_terminal. pa_h_bplfpb_power_product_terminal + S (q) = S ((S (n)) * pa_v_bplfpb_power_product)) /\ exists pa_q_bplfpb_power_product_terminal. pa_u_bplfpb_power_product = pa_q_bplfpb_power_product_terminal * S ((S (n)) * pa_v_bplfpb_power_product) + (q))) /\ forall pa_i_bplfpb_power_product. (exists pa_lt_bplfpb_power_product_bound. pa_lt_bplfpb_power_product_bound + S pa_i_bplfpb_power_product = n) -> exists pa_p_bplfpb_power_product pa_r_bplfpb_power_product pa_s_bplfpb_power_product. ((((exists pa_h_bplfpb_power_product_factor. pa_h_bplfpb_power_product_factor + S (pa_p_bplfpb_power_product) = S ((S (pa_i_bplfpb_power_product)) * pa_c_bplfpb_power)) /\ exists pa_q_bplfpb_power_product_factor. pa_b_bplfpb_power = pa_q_bplfpb_power_product_factor * S ((S (pa_i_bplfpb_power_product)) * pa_c_bplfpb_power) + (pa_p_bplfpb_power_product))) /\ ((((exists pa_h_bplfpb_power_product_partial. pa_h_bplfpb_power_product_partial + S (pa_r_bplfpb_power_product) = S ((S (pa_i_bplfpb_power_product)) * pa_v_bplfpb_power_product)) /\ exists pa_q_bplfpb_power_product_partial. pa_u_bplfpb_power_product = pa_q_bplfpb_power_product_partial * S ((S (pa_i_bplfpb_power_product)) * pa_v_bplfpb_power_product) + (pa_r_bplfpb_power_product))) /\ ((((exists pa_h_bplfpb_power_product_successor. pa_h_bplfpb_power_product_successor + S (pa_s_bplfpb_power_product) = S ((S (S pa_i_bplfpb_power_product)) * pa_v_bplfpb_power_product)) /\ exists pa_q_bplfpb_power_product_successor. pa_u_bplfpb_power_product = pa_q_bplfpb_power_product_successor * S ((S (S pa_i_bplfpb_power_product)) * pa_v_bplfpb_power_product) + (pa_s_bplfpb_power_product))) /\ pa_s_bplfpb_power_product = pa_r_bplfpb_power_product * pa_p_bplfpb_power_product)))))))) -> (exists bcf_le_gap_bplfpb_result. bcf_le_gap_bplfpb_result + (z) = q))