End ActpermOrbits.
Section RestrictPerm.
Variables (T : finType) (S : {set T}).
Definition restr_perm := actperm (<[subxx 'N(S | 'P)]>).
Canonical restr_perm_morphism := [morphism of restr_perm].

Lemma restr_permE : {in 'N(S | 'P) & S, forall p, restr_perm p =1 p}.