Karn's Sylex enters tapped.
Players can't pay life to
castTo cast a spell is to take it from the zone it’s in (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect. A player may cast a spell if they have priority. See rule 601, “Casting Spells.”
To cast a card is to cast it as a spell. (CR 701.5) spells or to
activateTo activate an activated ability is to put it onto the stack and pay its costs, so that it will eventually resolve and have its effect. Only an object’s controller (or its owner, if it doesn’t have a controller) can activate its activated ability unless the object specifically says otherwise. A player may activate an ability if they have priority. See rule 602, “Activating Activated Abilities.” (CR 701.2) abilities that aren't mana abilities.
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ExileTo exile an object, move it to the exile zone from wherever it is. See rule 406, “Exile.” (CR 701.13) Karn's Sylex:
DestroyThe only ways a permanent can be destroyed are as a result of an effect that uses the word “destroy” or as a result of the state-based actions that check for lethal damage (see rule 704.5g) or damage from a source with deathtouch (see rule 704.5h). If a permanent is put into its owner’s graveyard for any other reason, it hasn’t been “destroyed.”
A regeneration effect replaces a destruction event. See rule 701.19, “Regenerate.” (CR 701.8) each nonland permanent with mana value X or less.
ActivateTo activate an activated ability is to put it onto the stack and pay its costs, so that it will eventually resolve and have its effect. Only an object’s controller (or its owner, if it doesn’t have a controller) can activate its activated ability unless the object specifically says otherwise. A player may activate an ability if they have priority. See rule 602, “Activating Activated Abilities.” (CR 701.2) only as a sorcery.