Theorem Comma_Hom_compose_assoc {a b c d : Comma_Obj} (h : Comma_Hom a b) (h' : Comma_Hom b c) (h'' : Comma_Hom c d) : Comma_Hom_compose h (Comma_Hom_compose h' h'') = Comma_Hom_compose (Comma_Hom_compose h h') h''.