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 Th72:
  <%>E in A & k <= n & l <= n implies A |^ (k, n) = A |^ (l, n)
proof
  assume that
A1: <%>E in A and
A2: k <= n and
A3: l <= n;
  thus A |^ (k, n) = A |^ n by A1,A2,Th34
    .= A |^ (l, n) by A1,A3,Th34;
end;
