proposition: Lemma indexJg G H x : #|G :^ x : H :^ x| = #|G : H|.
proof: Proof. by rewrite -!divgI -conjIg !cardJg. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)