It's always amusing to see "markwillstar" call other answers "ludicrous" and then proceed to give an answer that is even more ludicrous and factually wrong. Sorry but Anakin/Vader didn't "know" what he was "supposed" to do or for that matter care about the Prophecy and what it meant. In hind sight it is easy to see that Anakin was destine to fall to the dark side but while it was happening it wasn't seen. It wasn't until he was on the verge of death that he understood that he had to die also to fulfill the Prophecy.
In the context of your question Leia doesn't count ... she is NOT a Jedi, yes, she is Force sensitive and will finally complete her training as a Jedi ... 25 years after the events of ep VI.
Another thing about the "Prophecy" ... it never said anything about destroying the Sith ... at least when it was first "foreseen" and talked about ... it was just bring balance to the Force. Through the years the "destroy the Sith" was added on because that's what most of the Jedi thought "bring balance to the Force" would mean. In truth the word "balance" should have scared the hell out of the Jedi ... how do you bring balance to anything by destroying only one side ... you're smarter than the Jedi because you saw it but they didn't. In order to bring "balance" to the Force BOTH the Jedi and Sith Orders had to be destroyed.
At the end of ep III there was a "balance" of sort ... there were two Sith, Palpatine & Vader, and two Jedi, Yoda and Obi-Wan. If you read the novel version of ep III near the end of the duel between Yoda and Palpatine the "shroud of the dark side" lifted and Yoda saw the future. He saw that he was not the one who would defeat Palpatine ... he saw that he would be the one to train the person who would defeat Palpatine. That was the reason he didn't continue the fight with Palpatine ... he knew that he couldn't beat him.
There was always a small part of Anakin left inside the darkness that Vader was but it was dormant because it had nothing to live for. Anakin thought he had killed his wife and his children. Once he knew that Luke was his son that little piece of Anakin came alive ... that was the "conflict" that Luke felt in Vader. While Luke was being "fried" by Palpatine who did he call out to for help ... not Vader ... not Anakin ... he called out for help from his father. At that moment the little piece of Anakin inside Vader grabbed onto a power that can not be defeated ... the love a father has for his son ... with that the brilliant presence of Anakin Skywalker flooded back into the light side of the Force "destroying" the Sith Lord Darth Vader. He then destroyed the Sith Lord Darth Sidious but the Prophecy wasn't yet fulfilled. When Anakin died in his sons arms the Prophecy was fulfilled. This left the Force in balance and left his son to build a new Jedi Order from the ashes of the old.
With Luke left and no Sith it would seem to mean that balance wasn't achieved but it was. What was causing the imbalance to the Force was the rise of Palpatine's Sith Order, the Rule of Two so in essence when that Sith Order was destroyed and the Old Jedi Order destroyed the slate was clean. If you read the books of the EU you'll find that there were other Sith in the galaxy that had been driven into hiding by Palpatine & Vader's power.
In the end it is one of those "certain point of view" things that will have SW fans debating it forever.
Balance was achieved and Anakin Skywalker WAS the chosen one ... not Luke as another said here. That's just how things work in the world of Lucas ... paper thin reasons for things that he didn't think complete through when he wrote them.
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