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;
reserve r, u for Real,
  k for Nat;

theorem
  k>=n & r >= 1 implies r |^ k >= r |^ n
proof
  assume that
A1: k>=n and
A2: r >= 1;
  consider m be Nat such that
A3: k = n + m by A1,NAT_1:10;
A4: r |^ k = r |^ n * r |^ m by A3,NEWTON:8;
  r |^ n >= 1 by A2,Th11;
  hence thesis by A2,A4,Th11,XREAL_1:151;
end;
