  On the one hand, ordered completion is a fundamental technique in equational
theorem proving that is employed by automated tools. On the other hand, their
complexity makes such tools inherently error prone. As a remedy to this
situation we give an Isabelle/HOL formalization of ordered rewriting and
completion that comes with a formally verified certifier for ordered completion
proofs. By validating generated proof certificates, our certifier increases the
reliability of ordered completion tools.
