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).

Lemma actpermM : {in D &, {morph actperm : a b / a * b}}.