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