theorem
  [.a,b |^ a".] = [.b,a".]
proof
  thus [.a,b |^ a".] = a" * (b" |^ a") * a * (b |^ a") by GROUP_3:26
    .= a" * (a"" * (b" * a")) * a * (b |^ a") by GROUP_1:def 3
    .= (b" * a") * a * (b |^ a") by GROUP_3:1
    .= b" * (a"" * b * a") by GROUP_3:1
    .= [.b,a".] by Th16;
end;
