proposition: Lemma sdprod_context G K H : K ><| H = G -> [/\ K <| G, H \subset G, K * H = G, H \subset 'N(K) & K :&: H = 1].
proof: Proof. case/sdprodP=> _ <- nKH tiKH. by rewrite /normal mulG_subl mulG_subr mulG_subG normG. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)