The Battle Master fighter has access to a number of maneuvers that add a superiority die to the damage roll. For instance, the Trip Attack maneuver says (PHB, p. 74):
When you hit a creature with a weapon attack, you can expend one superiority die to attempt to knock the target down. You add the superiority die to the attack’s damage roll, and if the target is Large or smaller, it must make a Strength saving throw. On a failed save, you knock the target prone.
The Critical Hits rule states (PHB, p. 196):
When you score a critical hit, you get to roll extra dice for the attack’s damage against the target. Roll all of the attack’s damage dice twice and add them together. Then add any relevant modifiers as normal. [...] If the attack involves other damage dice, such as from the rogue’s Sneak Attack feature, you roll those dice twice as well.
During our game, the fighter PC rolled a critical hit. He then wanted to use a superiority die to use the Trip Attack maneuver to trip the enemy. Based on the above rules, is the damage from the superiority die also doubled?
I'm assuming the answer is yes based on the last statement in the Critical Hits section, but I wanted to confirm.