theorem
  a|^(m+1)+b|^(m+1) >= (a|^m+b|^m)*(a+b)/2
  proof
    A1: a|^(m+1)+b|^(m+1)=((a|^m+b|^m)*(a+b) + (a-b)*(a|^m-b|^m))/2 by Th9
    .= (a|^m+b|^m)*(a+b)/2 + (a-b)*(a|^m-b|^m)/2;
    (a|^m+b|^m)*(a+b) + (a-b)*(a|^m-b|^m) >= (a|^m+b|^m)*(a+b)
    by Th10,XREAL_1:31; then
    ((a|^m+b|^m)*(a+b) + (a-b)*(a|^m-b|^m))/2 >= ((a|^m+b|^m)*(a+b))/2
    by XREAL_1:72;
    hence thesis by A1;
  end;
