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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.

Because Alhammarret’s Archive is legendary, it’s unlikely that one player will control two. However, if that happens, life gained by that player will be multiplied by four. Three Archives will multiply that life gain by eight, and so on.

If two or more replacement effects would apply to a card-drawing event, the player drawing the card chooses the order in which to apply them.

If an effect would set your life total to a specific number that’s higher than your current life total, that effect would cause you to gain life equal to the difference. Alhammarret’s Archive will then double the amount of life that effect would cause you to gain. For example, if you have 3 life and an effect says that your life total “becomes 10,” your life total will actually become 17.

In a Two-Headed Giant game, only the controller of Alhammarret’s Archive is affected by it. If that player’s teammate gains life, Alhammarret’s Archive will have no effect, even when that life gain is applied to the team’s shared life total.

Similarly, the effects of the last abilities of multiple Archives are cumulative. If you control two, you’ll draw four times the number of cards, and so on.