Section unique_mor_d.
Variables (d : D) (f g : Thi2_v --> d).
(* equalizer de f et g *)
Definition Thi2_D_E_fg := Build_Equalizer2 (D_complete (F_fg f g)) Elt1.
Definition Thi2_c := E1_ob Thi2_D_E_fg.
Definition Thi2_e1 := E1_mor Thi2_D_E_fg.
(* s : w -> c *)
Definition Thi2_p_j := Proj1 Thi2_D_prod (SSC1_i SSC1_D Thi2_c).
Definition Thi2_f_c := SSC1_f SSC1_D Thi2_c.
Definition Thi2_s := Thi2_p_j o Thi2_f_c.
(* s o e1 o e : w -> w *)
(* ainsi que Id(w) : w -> w *)
(* comme e est l'equalizer des fle`ches de C(w,w), on a: e o s o e1 o e = e o Id (w) *)
(* ((e o s) o e1) = (Id v) *)

Lemma Thi2_e1_RightInv : RIso_law Thi2_e1 (Thi2_e o Thi2_s).