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

Lemma afix_mod G S :
H \subset 'C(S | to) -> G \subset 'N_D(H) ->
'Fix_(S | mod_action)(G / H) = 'Fix_(S | to)(G).