proposition: Lemma sdprod_mul_proof (u v : sdT) : (u.1 * v.1, to u.2 v.1 * v.2) \in setX D R.
proof: Proof. case: u v => [[a x] /= /setXP[Da Rx]] [[b y] /= /setXP[Db Ry]]. by rewrite inE !groupM //= gact_stable. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)