Structure > UA : Type :=
{UA_ob : A; UA_mor : b --> G UA_ob; Prf_IsUA :> IsUA UA_mor}.
(*** rewrite rules ***)

Lemma UA_diag :
forall (u : UA) (a' : A) (f : b --> G a'),
UA_mor u o FMor G (UA_diese u f) =_S f.