http://www.theguardian.com/politics/live/2016/jun/25/brexit-...
http://www.bbc.co.uk/news/uk-politics-eu-referendum-36629331
https://www.theguardian.com/uk-news/2016/jun/25/sturgeon-see... We knew all along that Scotland was strongly pro-EU.
http://www.bbc.co.uk/news/uk-scotland-scotland-politics-3561...
And that the only reason a bunch of people in Scotland voted to stay in the UK was because of promises about staying in EU.
If the question of post-Independence EU membership is resolved on the EU side I'd love to know, during the last referendum the EU was pretty clear there would be no automatic entry for Scotland. But whether that was true or politically driven... guess we'll find out.
There was a question last time about whether Scotland would automatically inherit EU membership or would have to apply for accession. IIRC, the EU wouldn't answer the question directly because Westminster refused to ask them. I'm guessing Nicola Sturgeon might be keen for this question to be cleared up.
I'm not claiming to have an answer one way or another there, but it seems a bit of a risk to just assume that.