We present a Coq library that allows for readily proving that a function is computable in polynomial time. It is based on quasi-interpretations that, in combination with termination ordering, provide a characterisation of the class \textsc{fp} of functions computable in polynomial time. At the heart of this formalisation is a proof of soundness and extensional completeness. Compared to the original paper proof, we had to fill a lot of not so trivial details that were left to the reader and fix a few glitches. To demonstrate the usability of our library, we apply it to the modular exponentiation.