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;
