theorem Th60:
  H * a * b = H * (a + b)
proof
  the carrier of H * a * b = carr(H * a) * b by Def6A
    .= (carr H * a) * b by Def6A
    .= carr H * (a + b) by Th47
    .= the carrier of H * (a + b) by Def6A;
  hence thesis by Th59;
end;
