proposition: Lemma gactsP (G : {set rT}) : reflect {acts A, on G | to} [acts A, on G | to].
proof: Proof. apply: (iffP idP) => [nGA x|nGA]; first exact: acts_act. apply/subsetP=> a Aa /[!inE]; rewrite Aa. by apply/subsetP=> x; rewrite inE nGA. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(automorphism quotient action gseries)