reserve E, x, y, X for set;
reserve A, B, C for Subset of E^omega;
reserve a, b for Element of E^omega;
reserve i, k, l, kl, m, n, mn for Nat;

theorem
  A c= C |^ k & B c= C |^ l implies A ^^ B c= C |^ (k + l)
proof
  assume A c= C |^ k & B c= C |^ l;
  then A ^^ B c= (C |^ k) ^^ (C |^ l) by FLANG_1:17;
  hence thesis by FLANG_1:33;
end;
