[{elements:[{"elem_id":12,items:[{"i_id":1,"type":"x"},{"i_id":2,"type":"y"},{"i_id":3,"type":"x"}]},{"elem_id":13,items:[{"i_id":4,"type":"x"},{"i_id":5,"type":"x"}]}]}]

db.collection.aggregate([{$unwind:"$elements"},{$match:{$expr:{$gt:[{$size:{$setIntersection:["$elements.items.type","$elements.items.type"]}},1]}}}])