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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.

You can look at a randomly discarded card before deciding where it goes.

The ability replaces the normal discard action with a discard action that puts the card on the library instead of the graveyard.

The discard triggers anything else that triggers on discards.

The ability applies any time a spell or ability has you discard as part of its effect. It does not matter if you or your opponent control the spell or ability. The discard is forced because it is an effect.

You can't use the Library of Leng ability to place a discarded card on top of your library when you discard a card as a cost, because costs aren't effects.

If more than one card is discarded due to a single effect, the Library allows you to decide whether or not to use it on each of the cards. You get to decide the order the cards are placed on the library if more than one goes there.

This effect has no effect on the cards being put into the graveyard from a library, because they are not "discarded".

Since the card goes directly to the library, the card is not revealed unless the spell or ability requiring the discard specifically says it is.

If multiple effects modify your hand size, apply them in timestamp order. For example, if you put Null Profusion (an enchantment that says your maximum hand size is two) onto the battlefield and then put Library of Leng onto the battlefield, you'll have no maximum hand size. However, if those permanents entered in the opposite order, your maximum hand size would be two.