proposition: Lemma im_cyclem : cyclem (val u) a @* <[a]> = <[a]>.
proof: Proof. apply/morphim_fixP=> //; first exact: injm_cyclem. by rewrite morphim_cycle ?cycle_id ?cycleX. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice div) mathcomp(fintype bigop prime finset fingroup morphism) mathcomp(perm automorphism quotient gproduct ssralg) mathcomp(finalg zmodp poly)