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

theorem
   for R holds (0_(1,R))*NBag1 = 0_.R
   proof
     let R;
     for o st o in dom ((0_(1,R))*NBag1) holds ((0_(1,R))*NBag1).o = (0_.R).o
     proof
       let o;
       assume
A1:    o in dom ((0_(1,R))*NBag1); then
       reconsider m = o as Element of NAT;
A2:    NBag1.o = 1 --> m by Def1;
       reconsider b = (NBag1).o as Element of Bags 1 by A2,PRE_POLY:def 12;
       ((0_(1,R))*NBag1).o = (0_(1,R)).b by A1,FUNCT_2:15
       .= (0_.R).m .= (0_.R).o;
       hence thesis;
     end;
     hence thesis by FUNCT_2:def 1;
   end;
