This question is in response to an answer on another question. Due to my lack of reputation on this SE I couldn't comment on the answer.

Based on JonTheMon's answer to Can a continuous effect that gives haste wear off? , destroying a creature that gives Haste to an artifact creature would remove Haste from the newly summoned artifact creature. But then he goes on to say that the activated Tap ability would be allowed. How?

According to the official rules on Haste (http://mtg.wikia.com/wiki/Haste), tapping or untapping falls under the same rules as attacking.

If a creature has haste, it can attack even if it hasn't been controlled by
its controller continuously since his or her most recent turn began.

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 his or her most 
recent turn began.
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    You misunderstood. The answer states that he could tap it in response (while it still has haste, before Thopter Engineer dies). – Rainbolt Jul 30 '15 at 20:05
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    @Steve I think you might want to go read in the basic rules about how the stack works. Once the killing spell is played, it's not at all too late to activate an ability. The spell goes on the stack, then you activate the ability in response (as the answer says) so it goes on the stack on top of the spell, and resolves before the spell does. – Cascabel Jul 30 '15 at 20:18
  • In the current version of the basic rules the stack is discussed on page 10. – Cascabel Jul 30 '15 at 20:28
  • I've proposed as a duplicate a question that goes into a fair amount of detail about how the stack works and when you can do what. The answer to your specific question is an application of that, as mentioned in my first comment. – Cascabel Jul 30 '15 at 20:29