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
  <%>E in A & n > 0 implies A? c= A |^ n
proof
  assume that
A1: <%>E in A and
A2: n > 0;
  <%>E in A |^ n by A1,FLANG_1:30;
  then
A3: {<%>E} c= A |^ n by ZFMISC_1:31;
  A c= A |^ n by A1,A2,FLANG_1:35;
  then {<%>E} \/ A c= A |^ n by A3,XBOOLE_1:8;
  hence thesis by Th76;
end;
