In this paper we present the formalisation of the library which is an implementation of rational numbers as binary sequences for both lazy and strict computation. We use the representation also known as the Stern-Brocot representation for rational numbers. This formalisation uses advanced machinery of the theorem prover and applies recent developments in formalising general recursive functions. This formalisation highlights the rôle of type theory both as a tool to verify hand-written programs and as a tool to generate verified programs.