reserve x, x1, x2, y, y1, y2, z, z1, z2 for object, X, X1, X2 for set;
reserve E for non empty set;
reserve e for Element of E;
reserve u, u9, u1, u2, v, v1, v2, w, w1, w2 for Element of E^omega;
reserve F, F1, F2 for Subset of E^omega;
reserve i, k, l, n for Nat;

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;
