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 Th28:
  [.a,b".] = [.b,a.] |^ b"
proof
  thus [.a,b".] = a" * b * a * b" .= 1_G * (a" * b * a * b") by GROUP_1:def 4
    .= (b"" * b") * (a" * b * a * b") by GROUP_1:def 5
    .= (b"" * b") * (a" * b * a) * b" by GROUP_1:def 3
    .= b"" * (b" * (a" * b * a)) * b" by GROUP_1:def 3
    .= [.b,a.] |^ b" by Th16;
end;
