proposition: Lemma indexSg G H K : H \subset K -> K \subset G -> #|K : H| %| #|G : H|.
proof: Proof. move=> sHK sKG; rewrite -(@dvdn_pmul2l #|H|) ?cardG_gt0 //. by rewrite !Lagrange ?(cardSg, subset_trans sHK). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)