Can I resolve the portion of the effect following "After" in this card's [When Digivolving] [When Attacking] effect even if I don't fulfill the "by doing X" condition?
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No, you can't. You can only resolve the portion following "After" in this card's [When Digivolving] [When Attacking] effect if you trash the top card of your security stack or trash the bottom face-down card from under any of your Tamers.
Source: EX13-032 Chirinmon