theorem Th29:
  a>=1 & n>=1 implies n -Root a >= 1 & a >= n -Root a
proof
  assume that
A1: a>=1 and
A2: n>=1;
  n -Root a >= n -Root 1 by A1,A2,Th27;
  hence n -Root a >= 1 by A2,Th20;
  n -Root a <= n -Root (a |^ n) by A1,A2,Th12,Th27;
  hence thesis by A1,A2,Lm2;
end;
