reserve E, x, y, X for set;
reserve A, B, C, D for Subset of E^omega;
reserve a, a1, a2, b, c, c1, c2, d, ab, bc for Element of E^omega;
reserve e for Element of E;
reserve i, j, k, l, n, n1, n2, m for Nat;

theorem Th5:
  for p, q being XFinSequence holds a = p ^ q implies p is Element
  of E^omega & q is Element of E^omega
proof
  let p, q be XFinSequence;
  assume a = p ^ q;
  then p is XFinSequence of E & q is XFinSequence of E by AFINSQ_1:31;
  hence thesis by AFINSQ_1:def 7;
end;
