proposition: Lemma indexgI G H : #|G : G :&: H| = #|G : H|.
proof: Proof. by rewrite -divgI divgS ?subsetIl. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)