proposition: Lemma orderXdiv a n : n %| #[a] -> #[a ^+ n] = #[a] %/ n.
proof: Proof. by case/dvdnP=> q defq; rewrite orderXgcd {2}defq gcdnC gcdnMl. 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)