In this paper Claim 1 states that x and y are smallest probability and there is optimal code tree in which this two characters are siblings at the maximum depth. In proof to that claim, author starts with tree T which has b and c at the maximum depth of tree. I can't understand why tree T is called optimal, because if x and y have smallest probabilities, then tree T cannot be optimal because Hoffman algorithm won't build such tree. I think my problem here is with understanding what optimal tree means.
If someone comes from CSLR this is about lemma 16.2 and proof to that.