proposition: Lemma morphpre_groupset M : group_set (f @*^-1 M).
proof: Proof. apply/group_setP; split=> [|x y]; rewrite !inE ?(morph1, group1) //. by case/andP=> Dx Mfx /andP[Dy Mfy]; rewrite morphM ?groupM. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype finfun bigop finset fingroup)