Section CoEqualizer.
Context (C : Category) {A B : PreSheaf C} (f g : (A –≻ B)%nattrans).

Lemma equalizer_morph_com_simplified
(a : C)
(x y : (B _o)%object a)
(H : CoEq_rel (Trans f a) (Trans g a) x y)
:
Equalizer.Type_Cat_CoEq_obligation_1 (Trans f a) (Trans g a) y =
Equalizer.Type_Cat_CoEq_obligation_1 (Trans f a) (Trans g a) x
.