HasteHaste is a static ability.
If a creature has haste, it can attack even if it hasn’t been controlled by its controller continuously since their most recent turn began. (See rule 302.6.)
If a creature has haste, its controller can activate its activated abilities whose cost includes the tap symbol or the untap symbol even if that creature hasn’t been controlled by that player continuously since their most recent turn began. (See rule 302.6.)
Multiple instances of haste on the same creature are redundant. (CR 702.10)
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castTo cast a spell is to take it from the zone it’s in (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect. A player may cast a spell if they have priority. See rule 601, “Casting Spells.”
To cast a card is to cast it as a spell. (CR 701.5) an instant or sorcery spell that targets only a single opponent or a single permanent an opponent controls this turn, for each other opponent, choose that player or a permanent they control, copy that spell, and the copy targets the chosen player or permanent.