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If an ability would produce one or more mana of an undefined type, it produces no mana instead.

Some abilities produce mana based on the type of mana another permanent or permanents “could produce.” The type of mana a permanent could produce at any time includes any type of mana that an ability of that permanent would produce if the ability were to resolve at that time, taking into account any applicable replacement effects in any possible order. Ignore whether any costs of the ability could or could not be paid. If that permanent wouldn’t produce any mana under these conditions, or no type of mana can be defined this way, there’s no type of mana it could produce.

To “tap [a permanent] for mana” is to activate a mana ability of that permanent that includes the {T} symbol in its activation cost. See rule 605, “Mana Abilities.”

An ability that triggers whenever a permanent “is tapped for mana” or is tapped for mana of a specified type triggers whenever such a mana ability resolves and produces mana or the specified type of mana.

A replacement effect that applies if a permanent “is tapped for mana” or tapped for mana of a specific type and/or amount modifies the mana production event while such an ability is resolving and producing mana or the specified type and/or amount of mana.

If an object’s enters-the-battlefield triggered ability or replacement effect refers to X, and the spell that became that object as it resolved had a value of X chosen for any of its costs, the value of X for that ability is the same as the value of X for that spell, although the value of X for that permanent is 0. This is an exception to rule 107.3i.

The tap symbol is {T}. The tap symbol in an activation cost means “Tap this permanent.” A permanent that’s already tapped can’t be tapped again to pay the cost. A creature’s activated ability with the tap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The untap symbol is {Q}. The untap symbol in an activation cost means “Untap this permanent.” A permanent that’s already untapped can’t be untapped again to pay the cost. A creature’s activated ability with the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

Any cards drawn prior to Sylvan Library’s ability resolving, including in your upkeep or in response to Sylvan Library’s triggered ability, can be chosen to be put back using this effect. Sylvan Library’s controller is responsible for keeping these cards distinguishable in hand, such as by keeping them separate from cards that began the turn in hand.

If you choose to draw two cards, then replace one or more of those draws with some other effect, the rest of Sylvan Library’s ability still happens. If you’ve actually drawn only one card that turn, you must choose that card and either pay 4 life or put it on top of your library. If you haven’t actually drawn any cards that turn, the rest of the ability has no effect.

If you control other triggered abilities that allow you to draw cards during your draw step, you can choose to order Sylvan Library’s ability before or after those abilities. Triggered abilities controlled by other players will resolve before triggered abilities you control.

If you control more than one Sylvan Library, the triggered ability of each will resolve in sequence. You don’t get to draw all the cards at once and then put them all back at once.

You always perform your normal draw before this ability. The normal draw occurs before anything can be placed on the stack during a player’s draw step.

You can put back zero, one, or two cards.

It’s not possible to take any actions between drawing the cards and choosing two cards. You can’t cast the cards you drew to avoid having two cards to choose.