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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.

If the spell has damage divided as it was cast, the division can't be changed (although the targets receiving that damage still can). The same is true of spells that distribute counters.

The copy is created on the stack, so it's not "cast." Abilities that trigger when a player casts a spell won't trigger.

If a spell has {X} in its mana cost, include the value chosen for that X when determining the mana value of that spell.

The copy will have the same targets as the spell it's copying unless you choose new ones. You may change any number of the targets, including all of them or none of them. If, for one of the targets, you can't choose a new legal target, then it remains unchanged (even if the current target is illegal).

If the spell that's copied is modal (that is, it says "Choose one —" or the like), the copy will have the same mode. A different mode can't be chosen.

If the spell that's copied has an X whose value was determined as it was cast (like Banefire does), the copy will have the same value of X.

If you copy a spell, you control the copy. It will resolve before the original spell does.

League Guildmage's second ability can copy any instant or sorcery spell you control, not just one with targets.

The controller of a copy can't choose to pay any alternative or additional costs for the copy. However, effects based on any alternative or additional costs that were paid for the original spell are copied as though those same costs were paid for the copy.