theorem Th24:
  a |^ g |^ h = a |^ (g * h)
proof
  thus a |^ g |^ h = h" * (g" * a) * g * h by GROUP_1:def 3
    .= h" * g" * a * g * h by GROUP_1:def 3
    .= (g * h)" * a * g * h by GROUP_1:17
    .= a |^ (g * h) by GROUP_1:def 3;
end;
