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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.

Each creature with lifelink dealing combat damage causes a separate life-gaining event. For example, if two creatures you control with lifelink deal combat damage at the same time, Aerith Gainsborough's second ability will trigger twice. However, if a single creature you control with lifelink deals combat damage to multiple creatures, players, planeswalkers, and/or battles at the same time (perhaps because it has trample or was blocked by more than one creature), the ability will trigger only once.

If you gain an amount of life "for each" of something or "equal to the number" of something, that life is gained as one event and Aerith Gainsborough's second ability triggers only once.

In a Two-Headed Giant game, life gained by your teammate won't cause Aerith Gainsborough's second ability to trigger, even though it caused your team's life total to increase.

In the rare case where enough -1/-1 counters are put on Aerith Gainsborough at the same time to make its toughness 0 or less, the number of +1/+1 counters on it before it got those -1/-1 counters will be used to determine the value of X in Aerith Gainsborough's third ability. For example, if there are two +1/+1 counters on Aerith Gainsborough and it gets three -1/-1 counters, you'll put two +1/+1 counters on each legendary creature you control when Aerith Gainsborough's third ability resolves.

If Aerith Gainsborough is dealt lethal damage at the same time that you gain life, it will die before its second ability would resolve. Its last ability will use the number of counters that were on it when it was last on the battlefield.

Aerith Gainsborough's second ability triggers just once for each life-gaining event, whether it's 1 life from Al Bhed Salvagers or 3 life from Balamb T-Rexaur.