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 Th11:
  <* a *> |^ b = <* a |^ b *>
proof
A1: now
    let k be Nat;
    assume k in dom<* a *>;
    then k in {1} by FINSEQ_1:2,38;
    then
A2: k = 1 by TARSKI:def 1;
    hence <* a |^ b *>.k = a |^ b
      .= (<* a *>/.k) |^ b by A2,FINSEQ_4:16;
  end;
  len<* a |^ b *> = 1 by FINSEQ_1:40
    .= len<* a *> by FINSEQ_1:39;
  hence thesis by A1,Def1;
end;
