The list chromatic number of the intersection of two generalized partition matroids

A famous theorem of Galvin states that the list chromatic number of the intersection of two partition matroids equals its chromatic number. Kiraly and Berczi et. al. conjectured that this equality holds for any two matroids. We prove this conjecture and a conjecture by Aharoni–Berger for any two generalized partition matroids.