theorem
  [.a,b,a.] = [.a |^ b,a.]
proof
  thus [.a,b,a.] = [.b,a.] * a" * [.a,b.] * a by Th22
    .= (a" |^ b) * (a" * b" * a * b) * a by GROUP_3:1
    .= (a |^ b)" * (a" * b" * a * b) * a by GROUP_3:26
    .= (a |^ b)" * (a" * b" * (a * b)) * a by GROUP_1:def 3
    .= (a |^ b)" * (a" * (b" * (a * b))) * a by GROUP_1:def 3
    .= (a |^ b)" * (a" * (a |^ b)) * a by GROUP_1:def 3
    .= [.a |^ b,a.] by Th16;
end;
