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.
Canonical perm_action := Action aperm_is_action.

Lemma porbit_actperm (a : aT) :
a \in D -> porbit (actperm to a) =1 orbit to <[a]>.