theorem Th20:
  a>=0 & a<1 & n>=1 implies a <= n-root a & n-root a < 1
proof
  assume that
A1: a>=0 and
A2: a<1 and
A3: n>=1;
  a <= n -Root a & n -Root a < 1 by A1,A2,A3,PREPOWER:30;
  hence thesis by A1,A3,Def1;
end;
