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 Th35:
  <%>E in A & n > 0 implies A c= A |^ n
proof
  assume that
A1: <%>E in A and
A2: n > 0;
  consider m such that
A3: m + 1 = n by A2,NAT_1:6;
  <%>E in A |^ m by A1,Th30;
  then A c= A |^ m ^^ A by Th16;
  hence thesis by A3,Th23;
end;
