proposition: Lemma divg_index G H : #|G| %/ #|G : H| = #|G :&: H|.
proof: Proof. by rewrite -(LagrangeI G H) mulnK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)