 reserve o,o1,o2 for object;
 reserve n for Ordinal;
 reserve R,L for non degenerated comRing;
 reserve b for bag of 1;

theorem Th11:
   (NBag1)*(BagN1) = id(Bags 1)
   proof
     for o st o in dom((NBag1)*(BagN1)) holds
       ((NBag1)*(BagN1)).o = (id(Bags 1)).o
     proof
       let o;
       assume o in dom ((NBag1)*(BagN1)); then
       reconsider b = o as Element of Bags 1;
A1:    BagN1.o = b.0 by Def2;
       ((NBag1)*(BagN1)).o = (NBag1).(b.0) by A1,FUNCT_2:15
       .= 1-->b.0 by Def1 .= (id(Bags 1)).o by Th5;
       hence thesis;
     end;
     hence thesis by FUNCT_2:def 1;
   end;
