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 Th47:
  p = 0 implies a #Q p = 1
proof
  reconsider i = 0 as Integer;
  assume that
A1: p=0;
  numerator(p)=0 by A1,RAT_1:14;
  hence a #Q p = 1 -Root (a #Z i) by A1,RAT_1:19
    .= 1 -Root 1 by Th34
    .= 1 by Th21;
end;
