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
  r < s & r < t implies ex t0 being Element of RAT+ st t0 <=' s & t0 <='
  t & r < t0
proof
  s <=' t & s <=' s or t <=' s & t <=' t;
  hence thesis;
end;
