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
  Lex(E)* = E^omega
proof
A1: now
    let x be object;
    assume x in E^omega;
    then reconsider a = x as Element of E^omega;
    a in Lex(E) |^ len a by Th73;
    hence x in Lex(E)* by Th41;
  end;
  for x being object st x in Lex(E)* holds x in E^omega;
  hence thesis by A1,TARSKI:2;
end;
