Section ActsSetop.
Variables (A : {set aT}) (S T : {set rT}).
Hypotheses (AactS : [acts A, on S | to]) (AactT : [acts A, on T | to]).
Definition orbit_transversal A S := transversal (orbit to A @: S) S.
Canonical astab_group S := group (group_set_astab S).
Canonical astabs_group S := group (group_set_astabs S).

Lemma act_reprK :
{in rcosets 'C_G[x | to] G, cancel (to x \o repr) (amove to G x)}.