proposition: Lemma indexg_gt1 G H : (#|G : H| > 1) = ~~ (G \subset H).
proof: Proof. by rewrite -indexg_eq1 eqn_leq indexg_gt0 andbT -ltnNge. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)