reserve E, x, y, X for set;
reserve A, B, C for Subset of E^omega;
reserve a, a1, a2, b for Element of E^omega;
reserve i, k, l, m, n for Nat;

theorem
  A c= B* implies A |^.. n c= B*
proof
  assume
A1: A c= B*;
  let x be object;
  assume x in A |^.. n;
  then consider k such that
  k >= n and
A2: x in A |^ k by Th2;
  A |^ k c= B* by A1,FLANG_1:59;
  hence thesis by A2;
end;
