proposition: Lemma HallJ G H x : x \in G -> Hall G (H :^ x) = Hall G H.
proof: Proof. by move=> Gx; rewrite /Hall -!divgI -{1 3}(conjGid Gx) conjSg -conjIg !cardJg. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(fintype bigop finset prime fingroup morphism) mathcomp(gfunctor automorphism quotient action gproduct) mathcomp(cyclic)