Proof assistants are computer systems that allows a user to do mathematics on a computer helping with the development of formal proof by human-machine collaboration, however most of them only work with strictly positive types, this restriction limits the number of problem that can be formalized. This is perhaps the reason why verification of programs that use positive (and negative) types is uncommon. Hence, we use the programming logic created by Bove, Dybjer and Sicard- Ram´ırez that accept positive types to formalize the termination of a breadth-first search in a binary tree using continuations data type which is positive.