(* Proof of lem_fun_vide_sig                                               *)
split;
[ exact lem_vide_application
| split;
[ exact lem_dom_vide | rewrite lem_img_vide; exact (lem_vide_is_inc a) ] ].
Qed.
(* End of proof of lem_fun_vide_sig                                        *)

(* Specifications: *)
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(* Quelques proprietes sur application, domaine et image                   *)
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Lemma lem_fun_and_dom :
forall f a b : E, fun_ f -> In (couple a b) f -> In a (dom f).