proposition: Lemma orbit_act G a x: a \in G -> orbit to G (to x a) = orbit to G x.
proof: Proof. exact/orbit_act_in/subsetT. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)