End equalizer_limit_def.
Coercion Equalizer2_to_Equalizer : Equalizer2 >-> Equalizer.
(* cas particuliers *)
(* de deux morhismes *)
Section equaz_fg.
Variables (C : Category) (a b : C) (f g : a --> b).
Definition K_fg (i : TwoElts) := match i with
| Elt1 => f
| Elt2 => g
end.
Definition J_fg := PA K_fg.
Definition F_fg := FPA K_fg.
SubClass Equalizer1_fg := Equalizer1 K_fg.

(* Specifications: *)
Lemma Prf_law1_fg :
forall (r : C) (h : r --> a), h o f =_S h o g -> Equalizer_eq K_fg h.