premise: Libya's case against Britain and the US concerns the dispute over their demand for extradition of Libyans charged with blowing up a Pan Am jet over Lockerbie in 1988.
hypothesis: Libya wants the Libyans that blew up the plane back back in their country.
reason: The statement "Libya wants the Libyans that blew up the plane back back in their country" is definitely correct because their major issue with Britain and the US is that those countries would not extradite those involved back to Libya.