theorem Th9:
  w = u^v implies len u <= len w & len v <= len w
proof
  assume w = u^v;
  then len w = len u + len v by AFINSQ_1:17;
  then
  len w + len u >= len u + len v + 0 & len w + len v >= len u + len v + 0
  by XREAL_1:7;
  hence thesis by XREAL_1:6;
end;
