We give a verified implementation of a procedure for simplifying formulas of intuitionistic propositional logic, relying on a particular contractionfree sequent calculus for this logic. We apply this procedure to simplify the output given by a verified program for computing propositional quantifiers of such formulas, developed by the the first-and second-named authors in earlier work. This also allows us to simplify and improve the efficiency of that program, as well as the proof of its correctness.