Canonical mod_action := Action modact_is_action.
Section Stabilizers.
Variable S : {set rT}.
Hypothesis cSH : H \subset 'C(S | to).
Let fixSH : S \subset 'Fix_to(D :&: H).

Lemma astab_mod : 'C(S | mod_action) = 'C(S | to) / H.
End Stabilizers.