proposition: Lemma acts_qact_doms (H : {group rT}) : H \subset D -> [acts A, on H | to] -> qact_dom to H :=: A.
proof: Proof. move=> sHD aH; apply/eqP; rewrite eqEsubset; apply/andP. split; first exact: qact_dom_doms. apply/subsetP=> x Ax; rewrite qact_domE //; apply/gastabsP=> //. by move/gactsP: aH; move/(_ x Ax). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(automorphism quotient action gseries)