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

theorem Th43:
   for B be Subset of Bags 1 holds card(B) = card((BagN1).:B)
   proof
     let B be Subset of Bags 1;
     reconsider F = (BagN1)|B as Function;
A1:  rng F = (BagN1).:B by RELAT_1:115;
     dom F = B by FUNCT_2:def 1;
     hence thesis by CARD_1:5, A1,WELLORD2:def 4;
   end;
