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 Th60:
  A c= B* implies A* c= B*
proof
  assume
A1: A c= B*;
  thus thesis
  proof
    let x be object;
    assume x in A*;
    then consider n such that
A2: x in A |^ n by Th41;
    A |^ n c= B* by A1,Th59;
    hence thesis by A2;
  end;
end;
