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
  m <= n & <%>E in A implies (A |^ (m, n))* = (A*) |^ (m, n)
proof
  assume that
A1: m <= n and
A2: <%>E in A;
  (A |^ (m, n))* = (A |^ n)* & A* |^ (m, n) = A* |^ n by A1,A2,Th34,FLANG_1:48;
  hence thesis by A2,Th17;
end;
