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