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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 an effect puts Vizier of Remedies onto the battlefield with one or more -1/-1 counters on it, its effect won’t apply. This is because you must control Vizier of Remedies before the creature begins to enter the battlefield for its effect to apply. The same is true of any creatures entering the battlefield with -1/-1 counters on them at the same time as Vizier of Remedies enters the battlefield.

If multiple creatures with wither and/or infect deal damage to a creature at once, Vizier of Remedies causes only one counter fewer to be put on that creature. Its effect doesn’t apply separately for each creature dealing damage.

“Put on a creature you control” includes that creature entering the battlefield with -1/-1 counters on it. If a creature would enter the battlefield under your control with a number of -1/-1 counters on it while you control Vizier of Remedies, it enters with that many counters minus one.

Each additional Vizier of Remedies you control will decrease the number of -1/-1 counters put on a creature by one.

If a creature you control is dealt damage by a source with wither or infect, that much damage is dealt, but one fewer -1/-1 counter is put on your creature. For example, if a 2/2 creature with lifelink and infect is blocked by Vizier of Remedies, the first creature’s controller gains 2 life and puts one -1/-1 counter on Vizier of Remedies.