[{"_id":"p001","variations":[{"id":"v001","lots":[{"quantity":10,"size":"S"},{"quantity":15,"size":"M"}]},{"id":"v002","lots":[{"quantity":5,"size":"S"},{"quantity":20,"size":"M"},{"quantity":10,"size":"L"}]}]}]

db.collection.update({"_id":"p001"},{$inc:{"variations.$[v].lots.$[l].quantity":-1}},{arrayFilters:[{"v.id":"v002"},{"l.size":"S"},]})