reserve A,B,C for Ordinal;
reserve a,b,c,d for natural Ordinal;
reserve l,m,n for natural Ordinal;
reserve i,j,k for Element of omega;
reserve x,y,z for Element of RAT+;
reserve i,j,k for natural Ordinal;
reserve r,s,t for Element of RAT+;

theorem
  not ex y being object st [{},y] in RAT+
proof
  given y being object such that
A1: [{},y] in RAT+;
  consider i,j being Element of omega such that
A2: [{},y] = [i,j] and
A3: i,j are_coprime and
  j <> {} and
A4: j <> 1 by A1,Th29,Th32;
  i = {} by A2,XTUPLE_0:1;
  hence thesis by A3,A4,Th3;
end;
