Lemma morphim_actm :
  {in D, forall a (S : {set rT}), S \subset R -> acrT.Definition act_morph to x := forall a b, to x (a * b) = to (to x a) b.Record action := Action {act :> rT -> aT -> rT; _ : is_action act}.Record action := Action {act :> rT -> aT -> rT; _ : is_action act}.Record action := Action {act :> rT -> aT -> rT; _ : is_action act}.Notation "[ 'faithful' A , 'on' S | to ]" := (faithful A S to)
  (at level 0, format "[ 'faithful'  A ,  'on'  S  |  to ]") : form_scope.

(* Specifications: *)
Lemma is_total_action : is_action setT to.