SubClass Equalizer1 := Limit FPA.
(* The Type I must be non empty *)
Structure Equalizer2 : Type :=  {Prf_equalizer1 :> Equalizer1; Witness : I}.
Variable l : Equalizer2.
Definition E1_ob := Lim l.
Definition E1_mor : E1_ob --> a := Limiting_cone l PA1.

Lemma Prf_E1_law1 : Equalizer_law1 k E1_mor.
Section e1_diese_def.