Section RestrictActionTheory.
Variables (aT : finGroupType) (D : {set aT}) (rT : finType).
Variables (to : action D rT).
Variables (A : {set aT}) (sAD : A \subset D).
Canonical morph_action := Action mact_is_action.
Canonical comp_action := Action comp_is_action.

Lemma afix_comp (A : {set gT}) :
A \subset B -> 'Fix_comp_action(A) = 'Fix_to(f @* A).