proposition: Lemma divg_indexS G H : H \subset G -> #|G| %/ #|G : H| = #|H|.
proof: Proof. by move/Lagrange <-; rewrite mulnK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)