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_lcoset_in A a x :
A \subset D -> a \in D ->
orbit to (a *: A) x = orbit to A (to x a).