A proof of the compositional Delta conjecture

We prove a compositional refinement of the Delta conjecture (rise version) of Haglund, Remmel and Wilson (2018) for ${\mathrm{\Delta }}_{e_{n-k-1}}^{\mathrm{\prime }}{e}_n$ which was stated by D’Adderio, Iraci and Vanden Wyngaerd (2020) in terms of Theta operators.