Definition TotalAction := Action is_total_action.Definition morph_act rT rT' (to : action D rT) (to' : action D' rT') f fA :=
  forall x a, f (to x a) = to' (f x) (fA a).Section RawGroupAction.Section InternalGroupAction.Notation "to ^*" := (setact to) (at level 2, format "to ^*") : fun_scope.(at level 8, format "''C_' ( | to ) [ a ]") : group_scope.
Notation "''C_' ( G | to ) [ a ]" := 'C_(G | to)([set a])
  (at level 8, format "''C_' ( G  |  to ) [ a ]") : group_scope.

Lemma act_inj : left_injective to.