  function decreaseAllowance(
    address spender,
    uint256 subtractedValue
  )
    public
    returns (bool)
  {
    require(spender != address(0));
    _allowed[msg.sender][spender] = (
      _allowed[msg.sender][spender].sub(subtractedValue));
    emit Approval(msg.sender, spender, _allowed[msg.sender][spender]);
    return true;
  }