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
  a > 0 implies a #Q l = a #Z l
proof
  assume a > 0;
  then a #Z l > 0 by Th39;
  then
A1: a #Z l = 1-Root (a #Z l) |^ 1 by Def2;
  denominator l=1 by RAT_1:17;
  hence a #Q l = 1-Root (a #Z l) by RAT_1:17
    .= a #Z l by A1;
end;
