proposition: Lemma gact_stable : {acts D, on R | to}.
proof: Proof. apply: acts_act; apply/subsetP=> a Da; rewrite !inE Da. apply/subsetP=> x; rewrite inE; apply: contraLR => R'xa. by rewrite -(actKin to Da x) gact_out ?groupV. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)