Problem with where active record

Controller.rb

class ApplicationController < ActionController::Base
  def get_brands(limit = nil)
    @brands = cache("#{sub_menu_cache_key}:brand_list")  do
      @brands = Brand.joins(:products => [:sales]).merge(Sale.active).merge(Product.with_stock).to_sql
    end
  end
end


#ActiveRecord::ConfigurationError: Association named 'inventory_items' was not found; perhaps you misspelled it?

Product.rb

class Product < ActiveRecord::Base
  scope :with_stock, where("inventory_items.in_stock - inventory_items.in_carts - inventory_items.processing > 0 AND inventory_items.deleted = ?", false).joins(:inventory_items)
end