The paper reports on a formalization of a proof of wellfoundedness of the higher-order recursive path ordering (HORPO) in the proof checker Coq. The development is axiom-free and fully constructive. Three substantive parts that could be used also in other developments are the formalizations of the simply-typed lambda calculus, of finite multisets and of the multiset ordering. The Coq code consists of more than 1000 lemmas and 300 definitions.