theorem
  Th1: (A + B) `1 = A `1 + B `1 & (A + B) `2 = A `2 + B `2
proof
  A + B = |[((A `1) + (B `1)), ((A `2) + (B `2))]| by EUCLID:55;
  hence thesis by EUCLID:52;
end;
