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(* 02110-1301 USA                                                     *)
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(*          Projet Coq - Calculus of Inductive Constructions V5.10           *)
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(*                                                                           *)
(*          Basic Category Theory: epic, monic, iso in SET                   *)
(*                                                                           *)
(*          Amokrane Saibi,  May 1994                                        *)
(*                                                                           *)
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Require Export SET.
Require Export CatProperty.
Require Export MapProperty.
Set Implicit Arguments.
Unset Strict Implicit.
(* Epic <-> Surj *)
SubClass SET_Epic_law (A B : Setoid) (f : Map A B) := Epic_law f.
SubClass SET_Monic_law (A B : Setoid) (f : Map A B) := Monic_law f.
Section set_epic_monic.
Variables (A B : Setoid) (f : Map A B).

Lemma Surj_epic : forall h : B -> A, Surj_law f h -> SET_Epic_law f.