reserve x,y,X,Y for set,
  k,l,n for Nat,
  i,i1,i2,i3,j for Integer,
  G for Group,
  a,b,c,d for Element of G,
  A,B,C for Subset of G,
  H,H1,H2, H3 for Subgroup of G,
  h for Element of H,
  F,F1,F2 for FinSequence of the carrier of G,
  I,I1,I2 for FinSequence of INT;

theorem Th21:
  (<*> the carrier of G) |^ (<*> INT) = {}
proof
  len <*> the carrier of G = 0;
  then len((<*> the carrier of G) |^ (<*> INT)) = 0 by Def3;
  hence thesis;
end;
