Section set_diese1_tau_def.
Variable i : J.
(* (h(x)i)(Elt) =  tau(i)(x) *)
Definition SET_diese1_tau_fun (a : Single) :=
match a with
| Elt => tau i x
end.
Canonical Structure SET_diese1_tau := Build_Map SET_diese1_tau_map_law.
End set_diese1_tau_def.
(* h(x) : DElta({*}) -> F *)
Definition SET_diese1 : SET_lim := Build_Cone SET_diese1_tau_cone_law.
End set_diese1_def.
Canonical Structure SET_diese := Build_Map0'' SET_diese_map_law.
End set_diese.
(* universalite' *)

Lemma SET_coUAlaw2 :
forall (X : SET) (tau : Cone X F) (g : Map0'' X SET_lim),
(forall (i : J) (x : X), tau i x =_S SET_lcone_tau i (g x)) ->
forall x : X, g x =_S'' SET_diese tau x.