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We study a derivative method allowing to prove termination of computations on regular expressions. A Coq formalisation of a canonical non-deterministic finite automaton construction on a regular expression is presented. The correctness of the functional definitions is formally verified in Coq using the libraries and the smallscale reflection tools of Ssreflect. We propose to extend the proofs further, and this is a work in progress, to study termination of containment and equivalence in termsdoi:10.1145/2103776.2103784 dblp:conf/plpv/Komendantsky12 fatcat:3rvy5sdllff55ddcpl2y7fli7u