reserve a,b for object, I,J for set;
reserve b for bag of I;
reserve R for asymmetric transitive non empty RelStr,
  a,b,c for bag of the carrier of R,
  x,y,z for Element of R;
reserve p for partition of b-'a, q for partition of b;
reserve J for set, m for bag of I;

theorem
  for a,b being Element of DershowitzMannaOrder R st a <= b
  holds b <> EmptyBag the carrier of R
  proof set DM = DershowitzMannaOrder R;
    set I = the carrier of R;
    set E = EmptyBag I;
    let a,b be Element of DM;
    assume Z0: a <= b;
    per cases;
    suppose a = E;
      hence b <> E by Z0;
    end;
    suppose
A1:   a <> E;
      E divides a by PRE_POLY:59;
      then [E,a] in DivOrder I c= the InternalRel of DM by A1,DO,Th16;
      hence thesis by Z0,ORDERS_2:def 5;
    end;
  end;
