theorem Th22:
  dom l2 = cod l1 implies (l2*l1)`2 = l2`2*l1`2 & dom(l2*l1) = dom
  l1 & cod(l2*l1) = cod l2
proof
  assume dom l2 = cod l1;
  then [[dom l1,cod l2],l2`2*l1`2] = l2*l1 by Def10
    .= [[dom(l2*l1),cod(l2*l1)],(l2*l1)`2] by Th20;
  hence thesis by Lm2,XTUPLE_0:1;
end;
