proposition: Lemma sdprodJ A B x : (A ><| B) :^ x = A :^ x ><| B :^ x.
proof: Proof. rewrite /sdprod -conjIg sub_conjg conjs1g -pprodJ. by case: ifP => _ //; apply: imset0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)