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 Th64:
  A c= B* implies A |^ (m, n) c= B*
proof
  assume
A1: A c= B*;
  thus thesis
  proof
    let x be object;
    assume x in A |^ (m, n);
    then consider mn such that
    m <= mn and
    mn <= n and
A2: x in A |^ mn by Th19;
    A |^ mn c= B* by A1,FLANG_1:59;
    hence thesis by A2;
  end;
end;
