König's lemma states that given an infinite tree, an infinite path exists, where of course by tree we mean a full binary tree. I found some examples in Logical Labyrinths by Smullyan where he discusses about immortal people having infinite descending chain of children ancestrally.
My question, what are some applications or examples of KL in real life? Also being a contrapositive of Brouwer's fan theorem, the weakened form has applications in logic especially in Heine-Borel theorem.
I just want to get a further intuitive understanding of the lemma when fleshed out in concrete examples.
Thank you. Please note I have already went over this site which gives an excellent account of it but I was looking for similar but different examples.