Section s_equaz_def.
Variables (A B : Setoid) (I : Type) (f : I -> Map A B).
Definition S_equaz_pred (a : A) := forall i j : I, f i a =_S f j a.
Canonical Structure S_equaz_constr := Build_Setoid_pred S_equaz_reg.
Definition S_equaz_ob := SubSetoid S_equaz_constr.
Definition S_equaz_mor := RestrictedMap (Id_map A) S_equaz_constr.

Lemma S_equaz_law1 : Equalizer_law1 f S_equaz_mor.