reserve x for set;
reserve a, b, c for Real;
reserve m, n, m1, m2 for Nat;
reserve k, l for Integer;
reserve p, q for Rational;
reserve s1, s2 for Real_Sequence;

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;
