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
  (A /\ B) |^ n c= (A |^ n) /\ (B |^ n)
proof
  (A /\ B) |^ n c= A |^ n & (A /\ B) |^ n c= B |^ n by Th37,XBOOLE_1:17;
  hence thesis by XBOOLE_1:19;
end;
