Section ActsSetop.
Variables (A : {set aT}) (S T : {set rT}).
Hypotheses (AactS : [acts A, on S | to]) (AactT : [acts A, on T | to]).

Lemma orbit_in_transl G x y z :
G \subset D -> y \in orbit to G x ->
(y \in orbit to G z) = (x \in orbit to G z).