End ModAction.
Notation "to %% H" := (mod_action to H) : action_scope.
Section ActPerm.
(* Morphism to permutations induced by an action. *)
Variables (aT : finGroupType) (D : {set aT}) (rT : finType).
Variable to : action D rT.
Definition actperm a := perm (act_inj to a).

(* Specifications: *)
Lemma actpermM : {in D &, {morph actperm : a b / a * b}}.
End ActPerm.