End equal_one_mor.
Definition Comp_One_mor (a : One_ob) :=
let () as x
return
(forall b c : One_ob,
One_mor_setoid x b -> One_mor_setoid b c -> One_mor_setoid x c) :=
a in
fun b c =>
let () as x
return
(One_mor_setoid Obone b ->
One_mor_setoid b x -> One_mor_setoid Obone x) := c in
fun _ _ => Id_Obone.

(* Specifications: *)
Lemma Comp_One_mor_congl : Congl_law Comp_One_mor.
Lemma Comp_One_mor_congr : Congr_law Comp_One_mor.
Definition Comp_One := Build_Comp Comp_One_mor_congl Comp_One_mor_congr.
Lemma Assoc_One : Assoc_law Comp_One.
Definition Id_One (a : One_ob) : One_mor_setoid a a :=
let () as x return (One_mor x x) := a in Id_Obone.
Lemma Idl_One : Idl_law Comp_One Id_One.
Lemma Idr_One : Idr_law Comp_One Id_One.
Canonical Structure One := Build_Category Assoc_One Idl_One Idr_One.