choose_upper_eq_transport

Exact expanded PA statement

forall n m k z. n = m -> (((exists bcf_lt_gap_bcuet_source_out_of_range. bcf_lt_gap_bcuet_source_out_of_range + S (n) = k) /\ z = 0) \/ ((exists bcf_le_gap_bcuet_source_in_range. bcf_le_gap_bcuet_source_in_range + (k) = n) /\ (exists bcf_row_code_code_bcuet_source bcf_row_code_scale_bcuet_source bcf_row_scale_code_bcuet_source bcf_row_scale_scale_bcuet_source bcf_row_code_bcuet_source bcf_row_scale_bcuet_source. ((forall bcf_row_index_bcuet_source_table. (exists bcf_lt_gap_bcuet_source_table_row_bound. bcf_lt_gap_bcuet_source_table_row_bound + S (bcf_row_index_bcuet_source_table) = S (n)) -> exists bcf_row_code_bcuet_source_table bcf_row_scale_bcuet_source_table. ((((exists bcf_height_bcuet_source_table_decoded_row_code. bcf_height_bcuet_source_table_decoded_row_code + S (bcf_row_code_bcuet_source_table) = S ((S (bcf_row_index_bcuet_source_table)) * bcf_row_code_scale_bcuet_source)) /\ exists bcf_quotient_bcuet_source_table_decoded_row_code. bcf_row_code_code_bcuet_source = bcf_quotient_bcuet_source_table_decoded_row_code * S ((S (bcf_row_index_bcuet_source_table)) * bcf_row_code_scale_bcuet_source) + (bcf_row_code_bcuet_source_table))) /\ ((((exists bcf_height_bcuet_source_table_decoded_row_scale. bcf_height_bcuet_source_table_decoded_row_scale + S (bcf_row_scale_bcuet_source_table) = S ((S (bcf_row_index_bcuet_source_table)) * bcf_row_scale_scale_bcuet_source)) /\ exists bcf_quotient_bcuet_source_table_decoded_row_scale. bcf_row_scale_code_bcuet_source = bcf_quotient_bcuet_source_table_decoded_row_scale * S ((S (bcf_row_index_bcuet_source_table)) * bcf_row_scale_scale_bcuet_source) + (bcf_row_scale_bcuet_source_table))) /\ ((bcf_row_index_bcuet_source_table = 0 /\ (forall bcf_index_bcuet_source_table_zero_row. (exists bcf_lt_gap_bcuet_source_table_zero_row_bound. bcf_lt_gap_bcuet_source_table_zero_row_bound + S (bcf_index_bcuet_source_table_zero_row) = S (n)) -> exists bcf_value_bcuet_source_table_zero_row. ((((exists bcf_height_bcuet_source_table_zero_row_entry. bcf_height_bcuet_source_table_zero_row_entry + S (bcf_value_bcuet_source_table_zero_row) = S ((S (bcf_index_bcuet_source_table_zero_row)) * bcf_row_scale_bcuet_source_table)) /\ exists bcf_quotient_bcuet_source_table_zero_row_entry. bcf_row_code_bcuet_source_table = bcf_quotient_bcuet_source_table_zero_row_entry * S ((S (bcf_index_bcuet_source_table_zero_row)) * bcf_row_scale_bcuet_source_table) + (bcf_value_bcuet_source_table_zero_row))) /\ ((bcf_index_bcuet_source_table_zero_row = 0 /\ bcf_value_bcuet_source_table_zero_row = 1) \/ exists bcf_predecessor_bcuet_source_table_zero_row. bcf_index_bcuet_source_table_zero_row = S bcf_predecessor_bcuet_source_table_zero_row /\ bcf_value_bcuet_source_table_zero_row = 0)))) \/ exists bcf_predecessor_bcuet_source_table bcf_previous_code_bcuet_source_table bcf_previous_scale_bcuet_source_table. bcf_row_index_bcuet_source_table = S bcf_predecessor_bcuet_source_table /\ ((((exists bcf_height_bcuet_source_table_decoded_previous_code. bcf_height_bcuet_source_table_decoded_previous_code + S (bcf_previous_code_bcuet_source_table) = S ((S (bcf_predecessor_bcuet_source_table)) * bcf_row_code_scale_bcuet_source)) /\ exists bcf_quotient_bcuet_source_table_decoded_previous_code. bcf_row_code_code_bcuet_source = bcf_quotient_bcuet_source_table_decoded_previous_code * S ((S (bcf_predecessor_bcuet_source_table)) * bcf_row_code_scale_bcuet_source) + (bcf_previous_code_bcuet_source_table))) /\ ((((exists bcf_height_bcuet_source_table_decoded_previous_scale. bcf_height_bcuet_source_table_decoded_previous_scale + S (bcf_previous_scale_bcuet_source_table) = S ((S (bcf_predecessor_bcuet_source_table)) * bcf_row_scale_scale_bcuet_source)) /\ exists bcf_quotient_bcuet_source_table_decoded_previous_scale. bcf_row_scale_code_bcuet_source = bcf_quotient_bcuet_source_table_decoded_previous_scale * S ((S (bcf_predecessor_bcuet_source_table)) * bcf_row_scale_scale_bcuet_source) + (bcf_previous_scale_bcuet_source_table))) /\ (forall bcf_index_bcuet_source_table_row_step. (exists bcf_lt_gap_bcuet_source_table_row_step_bound. bcf_lt_gap_bcuet_source_table_row_step_bound + S (bcf_index_bcuet_source_table_row_step) = S (n)) -> exists bcf_value_bcuet_source_table_row_step. ((((exists bcf_height_bcuet_source_table_row_step_entry. bcf_height_bcuet_source_table_row_step_entry + S (bcf_value_bcuet_source_table_row_step) = S ((S (bcf_index_bcuet_source_table_row_step)) * bcf_row_scale_bcuet_source_table)) /\ exists bcf_quotient_bcuet_source_table_row_step_entry. bcf_row_code_bcuet_source_table = bcf_quotient_bcuet_source_table_row_step_entry * S ((S (bcf_index_bcuet_source_table_row_step)) * bcf_row_scale_bcuet_source_table) + (bcf_value_bcuet_source_table_row_step))) /\ ((bcf_index_bcuet_source_table_row_step = 0 /\ bcf_value_bcuet_source_table_row_step = 1) \/ exists bcf_predecessor_bcuet_source_table_row_step bcf_left_bcuet_source_table_row_step bcf_right_bcuet_source_table_row_step. bcf_index_bcuet_source_table_row_step = S bcf_predecessor_bcuet_source_table_row_step /\ ((((exists bcf_height_bcuet_source_table_row_step_previous_left. bcf_height_bcuet_source_table_row_step_previous_left + S (bcf_left_bcuet_source_table_row_step) = S ((S (bcf_predecessor_bcuet_source_table_row_step)) * bcf_previous_scale_bcuet_source_table)) /\ exists bcf_quotient_bcuet_source_table_row_step_previous_left. bcf_previous_code_bcuet_source_table = bcf_quotient_bcuet_source_table_row_step_previous_left * S ((S (bcf_predecessor_bcuet_source_table_row_step)) * bcf_previous_scale_bcuet_source_table) + (bcf_left_bcuet_source_table_row_step))) /\ ((((exists bcf_height_bcuet_source_table_row_step_previous_right. bcf_height_bcuet_source_table_row_step_previous_right + S (bcf_right_bcuet_source_table_row_step) = S ((S (S (bcf_predecessor_bcuet_source_table_row_step))) * bcf_previous_scale_bcuet_source_table)) /\ exists bcf_quotient_bcuet_source_table_row_step_previous_right. bcf_previous_code_bcuet_source_table = bcf_quotient_bcuet_source_table_row_step_previous_right * S ((S (S (bcf_predecessor_bcuet_source_table_row_step))) * bcf_previous_scale_bcuet_source_table) + (bcf_right_bcuet_source_table_row_step))) /\ bcf_value_bcuet_source_table_row_step = bcf_left_bcuet_source_table_row_step + bcf_right_bcuet_source_table_row_step))))))))))) /\ ((((exists bcf_height_bcuet_source_decoded_row_code. bcf_height_bcuet_source_decoded_row_code + S (bcf_row_code_bcuet_source) = S ((S (n)) * bcf_row_code_scale_bcuet_source)) /\ exists bcf_quotient_bcuet_source_decoded_row_code. bcf_row_code_code_bcuet_source = bcf_quotient_bcuet_source_decoded_row_code * S ((S (n)) * bcf_row_code_scale_bcuet_source) + (bcf_row_code_bcuet_source))) /\ ((((exists bcf_height_bcuet_source_decoded_row_scale. bcf_height_bcuet_source_decoded_row_scale + S (bcf_row_scale_bcuet_source) = S ((S (n)) * bcf_row_scale_scale_bcuet_source)) /\ exists bcf_quotient_bcuet_source_decoded_row_scale. bcf_row_scale_code_bcuet_source = bcf_quotient_bcuet_source_decoded_row_scale * S ((S (n)) * bcf_row_scale_scale_bcuet_source) + (bcf_row_scale_bcuet_source))) /\ (((exists bcf_height_bcuet_source_decoded_value. bcf_height_bcuet_source_decoded_value + S (z) = S ((S (k)) * bcf_row_scale_bcuet_source)) /\ exists bcf_quotient_bcuet_source_decoded_value. bcf_row_code_bcuet_source = bcf_quotient_bcuet_source_decoded_value * S ((S (k)) * bcf_row_scale_bcuet_source) + (z))))))))) -> (((exists bcf_lt_gap_bcuet_target_out_of_range. bcf_lt_gap_bcuet_target_out_of_range + S (m) = k) /\ z = 0) \/ ((exists bcf_le_gap_bcuet_target_in_range. bcf_le_gap_bcuet_target_in_range + (k) = m) /\ (exists bcf_row_code_code_bcuet_target bcf_row_code_scale_bcuet_target bcf_row_scale_code_bcuet_target bcf_row_scale_scale_bcuet_target bcf_row_code_bcuet_target bcf_row_scale_bcuet_target. ((forall bcf_row_index_bcuet_target_table. (exists bcf_lt_gap_bcuet_target_table_row_bound. bcf_lt_gap_bcuet_target_table_row_bound + S (bcf_row_index_bcuet_target_table) = S (m)) -> exists bcf_row_code_bcuet_target_table bcf_row_scale_bcuet_target_table. ((((exists bcf_height_bcuet_target_table_decoded_row_code. bcf_height_bcuet_target_table_decoded_row_code + S (bcf_row_code_bcuet_target_table) = S ((S (bcf_row_index_bcuet_target_table)) * bcf_row_code_scale_bcuet_target)) /\ exists bcf_quotient_bcuet_target_table_decoded_row_code. bcf_row_code_code_bcuet_target = bcf_quotient_bcuet_target_table_decoded_row_code * S ((S (bcf_row_index_bcuet_target_table)) * bcf_row_code_scale_bcuet_target) + (bcf_row_code_bcuet_target_table))) /\ ((((exists bcf_height_bcuet_target_table_decoded_row_scale. bcf_height_bcuet_target_table_decoded_row_scale + S (bcf_row_scale_bcuet_target_table) = S ((S (bcf_row_index_bcuet_target_table)) * bcf_row_scale_scale_bcuet_target)) /\ exists bcf_quotient_bcuet_target_table_decoded_row_scale. bcf_row_scale_code_bcuet_target = bcf_quotient_bcuet_target_table_decoded_row_scale * S ((S (bcf_row_index_bcuet_target_table)) * bcf_row_scale_scale_bcuet_target) + (bcf_row_scale_bcuet_target_table))) /\ ((bcf_row_index_bcuet_target_table = 0 /\ (forall bcf_index_bcuet_target_table_zero_row. (exists bcf_lt_gap_bcuet_target_table_zero_row_bound. bcf_lt_gap_bcuet_target_table_zero_row_bound + S (bcf_index_bcuet_target_table_zero_row) = S (m)) -> exists bcf_value_bcuet_target_table_zero_row. ((((exists bcf_height_bcuet_target_table_zero_row_entry. bcf_height_bcuet_target_table_zero_row_entry + S (bcf_value_bcuet_target_table_zero_row) = S ((S (bcf_index_bcuet_target_table_zero_row)) * bcf_row_scale_bcuet_target_table)) /\ exists bcf_quotient_bcuet_target_table_zero_row_entry. bcf_row_code_bcuet_target_table = bcf_quotient_bcuet_target_table_zero_row_entry * S ((S (bcf_index_bcuet_target_table_zero_row)) * bcf_row_scale_bcuet_target_table) + (bcf_value_bcuet_target_table_zero_row))) /\ ((bcf_index_bcuet_target_table_zero_row = 0 /\ bcf_value_bcuet_target_table_zero_row = 1) \/ exists bcf_predecessor_bcuet_target_table_zero_row. bcf_index_bcuet_target_table_zero_row = S bcf_predecessor_bcuet_target_table_zero_row /\ bcf_value_bcuet_target_table_zero_row = 0)))) \/ exists bcf_predecessor_bcuet_target_table bcf_previous_code_bcuet_target_table bcf_previous_scale_bcuet_target_table. bcf_row_index_bcuet_target_table = S bcf_predecessor_bcuet_target_table /\ ((((exists bcf_height_bcuet_target_table_decoded_previous_code. bcf_height_bcuet_target_table_decoded_previous_code + S (bcf_previous_code_bcuet_target_table) = S ((S (bcf_predecessor_bcuet_target_table)) * bcf_row_code_scale_bcuet_target)) /\ exists bcf_quotient_bcuet_target_table_decoded_previous_code. bcf_row_code_code_bcuet_target = bcf_quotient_bcuet_target_table_decoded_previous_code * S ((S (bcf_predecessor_bcuet_target_table)) * bcf_row_code_scale_bcuet_target) + (bcf_previous_code_bcuet_target_table))) /\ ((((exists bcf_height_bcuet_target_table_decoded_previous_scale. bcf_height_bcuet_target_table_decoded_previous_scale + S (bcf_previous_scale_bcuet_target_table) = S ((S (bcf_predecessor_bcuet_target_table)) * bcf_row_scale_scale_bcuet_target)) /\ exists bcf_quotient_bcuet_target_table_decoded_previous_scale. bcf_row_scale_code_bcuet_target = bcf_quotient_bcuet_target_table_decoded_previous_scale * S ((S (bcf_predecessor_bcuet_target_table)) * bcf_row_scale_scale_bcuet_target) + (bcf_previous_scale_bcuet_target_table))) /\ (forall bcf_index_bcuet_target_table_row_step. (exists bcf_lt_gap_bcuet_target_table_row_step_bound. bcf_lt_gap_bcuet_target_table_row_step_bound + S (bcf_index_bcuet_target_table_row_step) = S (m)) -> exists bcf_value_bcuet_target_table_row_step. ((((exists bcf_height_bcuet_target_table_row_step_entry. bcf_height_bcuet_target_table_row_step_entry + S (bcf_value_bcuet_target_table_row_step) = S ((S (bcf_index_bcuet_target_table_row_step)) * bcf_row_scale_bcuet_target_table)) /\ exists bcf_quotient_bcuet_target_table_row_step_entry. bcf_row_code_bcuet_target_table = bcf_quotient_bcuet_target_table_row_step_entry * S ((S (bcf_index_bcuet_target_table_row_step)) * bcf_row_scale_bcuet_target_table) + (bcf_value_bcuet_target_table_row_step))) /\ ((bcf_index_bcuet_target_table_row_step = 0 /\ bcf_value_bcuet_target_table_row_step = 1) \/ exists bcf_predecessor_bcuet_target_table_row_step bcf_left_bcuet_target_table_row_step bcf_right_bcuet_target_table_row_step. bcf_index_bcuet_target_table_row_step = S bcf_predecessor_bcuet_target_table_row_step /\ ((((exists bcf_height_bcuet_target_table_row_step_previous_left. bcf_height_bcuet_target_table_row_step_previous_left + S (bcf_left_bcuet_target_table_row_step) = S ((S (bcf_predecessor_bcuet_target_table_row_step)) * bcf_previous_scale_bcuet_target_table)) /\ exists bcf_quotient_bcuet_target_table_row_step_previous_left. bcf_previous_code_bcuet_target_table = bcf_quotient_bcuet_target_table_row_step_previous_left * S ((S (bcf_predecessor_bcuet_target_table_row_step)) * bcf_previous_scale_bcuet_target_table) + (bcf_left_bcuet_target_table_row_step))) /\ ((((exists bcf_height_bcuet_target_table_row_step_previous_right. bcf_height_bcuet_target_table_row_step_previous_right + S (bcf_right_bcuet_target_table_row_step) = S ((S (S (bcf_predecessor_bcuet_target_table_row_step))) * bcf_previous_scale_bcuet_target_table)) /\ exists bcf_quotient_bcuet_target_table_row_step_previous_right. bcf_previous_code_bcuet_target_table = bcf_quotient_bcuet_target_table_row_step_previous_right * S ((S (S (bcf_predecessor_bcuet_target_table_row_step))) * bcf_previous_scale_bcuet_target_table) + (bcf_right_bcuet_target_table_row_step))) /\ bcf_value_bcuet_target_table_row_step = bcf_left_bcuet_target_table_row_step + bcf_right_bcuet_target_table_row_step))))))))))) /\ ((((exists bcf_height_bcuet_target_decoded_row_code. bcf_height_bcuet_target_decoded_row_code + S (bcf_row_code_bcuet_target) = S ((S (m)) * bcf_row_code_scale_bcuet_target)) /\ exists bcf_quotient_bcuet_target_decoded_row_code. bcf_row_code_code_bcuet_target = bcf_quotient_bcuet_target_decoded_row_code * S ((S (m)) * bcf_row_code_scale_bcuet_target) + (bcf_row_code_bcuet_target))) /\ ((((exists bcf_height_bcuet_target_decoded_row_scale. bcf_height_bcuet_target_decoded_row_scale + S (bcf_row_scale_bcuet_target) = S ((S (m)) * bcf_row_scale_scale_bcuet_target)) /\ exists bcf_quotient_bcuet_target_decoded_row_scale. bcf_row_scale_code_bcuet_target = bcf_quotient_bcuet_target_decoded_row_scale * S ((S (m)) * bcf_row_scale_scale_bcuet_target) + (bcf_row_scale_bcuet_target))) /\ (((exists bcf_height_bcuet_target_decoded_value. bcf_height_bcuet_target_decoded_value + S (z) = S ((S (k)) * bcf_row_scale_bcuet_target)) /\ exists bcf_quotient_bcuet_target_decoded_value. bcf_row_code_bcuet_target = bcf_quotient_bcuet_target_decoded_value * S ((S (k)) * bcf_row_scale_bcuet_target) + (z)))))))))