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In this example, I have an Elemental HERO Woodsman with 2000 DEF facedown, and a Compulsory Evacuation Device Trap Card facedown. If my opponent attacks with a monster that has 2100 ATK, would I be able to reveal my Elemental HERO Woodsman, then play Compulsory Evacuation Device in order to stop the attack from destroying my monster?
Flipping of the monster happens during the damage step.
During the damage step, only 2 types of cards or effects can be activated:
Cards that change the atk or def value of a monster
Cards that negate the activation of a card or effect (simply negating the effect won't do)
Compulsory Evacuation Device falls under neither category, so cannot be activated at this point. If you want to use it, you'll have to do so before the damage step, and before you monster is flipped face up.