reserve x for set;
reserve a, b, c, d, e for Real;
reserve m, n, m1, m2 for Nat;
reserve k, l for Integer;
reserve p for Rational;

theorem Th7:
  a>=0 & n>=1 implies n-root a >= 0
proof
  assume that
A1: a>=0 and
A2: n>=1;
 now per cases by A1;
    suppose
A3:   a>0;
   n-root a = n -Root a by A1,A2,Def1;
      hence thesis by A2,A3,PREPOWER:def 2;
    end;
    suppose
A4:   a=0;
   n-root a = n -Root a by A1,A2,Def1
        .= 0 by A2,A4,PREPOWER:def 2;
      hence thesis;
    end;
  end;
  hence thesis;
end;
