reserve x,y for set,
  k,n for Nat,
  i for Integer,
  G for Group,
  a,b,c ,d,e for Element of G,
  A,B,C,D for Subset of G,
  H,H1,H2,H3,H4 for Subgroup of G ,
  N1,N2 for normal Subgroup of G,
  F,F1,F2 for FinSequence of the carrier of G,
  I,I1,I2 for FinSequence of INT;

theorem Th10:
  (<*> the carrier of G) |^ a = {}
proof
  len((<*> the carrier of G) |^ a) = len <*> the carrier of G by Def1
    .= 0;
  hence thesis;
end;
