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
  a<=-1 & n is odd implies n-root a <= -1 & a <= n-root a
proof
  assume that
A1: a<=-1 and
A2: n is odd;
A3: n>=1 & -a>=1 by A1,A2,ABIAN:12,XREAL_1:25;
then A4: n-root (-a) >= 1 by Th18;
A5: -a >= n-root (-a) by A3,Th18;
A6: - n-root (-a) <= -1 by A4,XREAL_1:24;
 a <= - n-root (-a) by A5,XREAL_1:25;
  hence thesis by A2,A6,Th10;
end;
