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;
