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 Th49:
  for n be Nat st 0 <= a holds a #Q n = a |^ n
proof
  let n be Nat;
A1: denominator n=1 by RAT_1:17;
A2: numerator n=n by RAT_1:17;
  assume 0 <= a;
  hence a #Q n = a #Z n by A1,A2,Lm5,Th21
    .= a |^ n by Th36;
end;
