theorem
  a|^m + b|^m <= c|^m implies ex x st a|^m + b|^m <= (a+x)|^m
  proof
    assume
    A1: a|^m +b|^m <= c|^m;
    then ex x st c = a + x by Th6,NAT_1:10;
    hence thesis by A1;
  end;
