Do references to the book of Jasher in the Bible prove that the book of Joshua was written after the death of Saul?

The book of Joshua references the book of Jasher (Joshua 10:13 ), as does 2 Samuel 1:18 . However, the quote from the book of Jasher in 2 Samuel 1:23 references both Saul and Jonathan, both of whom lived centuries after Joshua. Some Jews and Christians believe that Joshua wrote the book of Joshua, but since the book of Joshua mentions the book of Jasher, and the book of Jasher mentions Saul, logically it would seem to follow that the book of Joshua must have been written hundreds of years after the death of Joshua (i.e. sometime *after* the death of Saul). Such an account would seem to fit with the Deuteronomistic history proposed by Martin Noth . An alternate hypothesis offered by conservapedia suggests that the book of Jasher was written over the timespan of hundreds of years: > David's dirge at the death of Saul was recorded in [the book of > Jasher], indicating it was being maintained as a long-term record of > certain aspects of Israel's history. This explanation seems less likely to me, especially because the book of Jasher has been lost to time, and a book that was written over many hundreds of years would probably have increased the probability that it would have had greater distribution (and thus greater longevity) than other books written over a comparatively short time frame. Are there other explanations and/or documentation to support one timeframe or another for the chronological authorship of the books of Jasher and Joshua?