My Digimon with this card in its digivolution cards attacked, an opponent's Digimon with digivolution cards was deleted in the battle, and after that battle, my opponent doesn't have any Digimon with digivolution cards. This Digimon gains <Piercing> from this card's inherited effect at such times, but does the <Piercing> trigger simultaneously?
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Official Ruling
Yes, it triggers. If an effect's trigger conditions are met when the effect is gained, that effect will trigger. In this case, your opponent no longer has Digimon with digivolution cards at the same timing as when your opponent's Digimon is deleted in battle, therefore you can activate <Piercing>.
Source: EX7-021 CrysPaledramon