Section Category_comp.
Variable C : category.
Definition comp_hom (a b c : C) (g : Hom b c) (f : Hom a b) :=
Hom_comp a b c (couple g f).
intros a b c x x' y y' H' H'0; try assumption.
unfold comp_hom in |- *; auto with algebra.
Qed.

Lemma comp_hom_assoc :
forall (a b c d : C) (f : Hom a b) (g : Hom b c) (h : Hom c d),
Equal (comp_hom (comp_hom h g) f) (comp_hom h (comp_hom g f)).