# When the other filters change, update this filter to remove rows that
  # are filtered out by the other filters' criteria. (We also add in the
  # currently selected values for this filter, so that changing other
  # filters does not cause this filter's selected values to be unselected;
  # while that behavior might make sense logically, it's a poor user
  # experience.)
  observeEvent(choice_filter(), {
    current_values <- input$filter_value

    updateSelectInput(session, "filter_value",
      choices = sort(levels(c(current_values, df()[choice_filter(),col_num,drop=TRUE]))),
      selected = current_values
    )
  })