A proof of the theta operator conjecture

In the context of (generalized) Delta Conjecture and its compositional form, D'Adderio, Iraci, Vanden Wyngaerd recently stated a conjecture relating two symmetric function operators, Dk Θk. We prove this Theta Operator Conjecture, finding it as consequence five-term relation Mellit Garsia. As result, we find surprising ways writing operators. Even though deal specifically with between Θk our work introduces method for relations other plethystic operators which are important in area study.