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.

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.