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
  ex s st r < s
proof
  take s = r+one;
  s+{} = s by Th50;
  then
A1: r <> s by Th62;
  r <=' s;
  hence thesis by A1,Th66;
end;
