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

theorem Th5:
   for b be bag of 1 holds b = 1 --> b.0
   proof
     let b be bag of 1;
     for o st o in dom b holds b.o = (1 --> b.0).o
     proof
       let o;
       assume
A1:    o in dom b; then
       o = 0 by CARD_1:49, TARSKI:def 1;
       hence thesis by A1,FUNCOP_1:7;
     end;
     hence thesis by PARTFUN1:def 2;
   end;
