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
  [.b,a,a.] = ([.b,a".] * [.b,a.]) |^ a
proof
  thus [.b,a,a.] = [.a,b.] * a" * [.b,a.] * a by Th22
    .= (a" * (b" * (a * b))) * a" * [.b,a.] * a by Th16
    .= (a" * ((b" * (a"" * b))) * a") * [.b,a.] * a
    .= (a" * (((b" * (a"" * b))) * a")) * [.b,a.] * a by GROUP_1:def 3
    .= a" * [.b,a".] * [.b,a.] * a by Th16
    .= ([.b,a".] * [.b,a.]) |^ a by GROUP_1:def 3;
end;
