theorem Th35:
  denominator x <> {}
proof
  per cases;
  suppose
    x in omega;
    hence thesis by Def9,Lm4;
  end;
  suppose
A1: not x in omega;
    then ex i,j st x = [i,j] & i,j are_coprime & j <> {} & j <> 1 by
Th29;
    hence thesis by A1,Def9;
  end;
end;
