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 astab_norm S : 'N(S | to) \subset 'N('C(S | to)).