proposition: Lemma index_quotient : G :&: K \subset 'N(H) -> #|G / H : K / H| %| #|G : K|.
proof: Proof. exact: index_morphim. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)