Understanding Correctness of Bidirectional Dijkstra
I came across these slides where on slide 23 another proof is given, however the idea of this proof is the same as in the slides of my original post.



But this still doesn't show, why $dist(s,v)$ and $dist(w,t)$ need to be less than $top_f$ and $top_b$ respectively.

EDIT: Note that with this proof $dist(s,v) \leq top_f$ and $dist(w,t) \leq top_b$ hold, since both vertices have already been settled. I'm in doubt, whether the original statement $dist(s,v) &lt; top_f$ and $dist(w,t) &lt; top_b$ is actually correct and therefore I'm marking this question as 'answered'. However if anyone finds an explanation, feel free to answer!