s d (m : morphism C s d) : CO d o F _1 m = F'' _1 m o CO s := (associativity _ _ _ _ _ _ _ _) @ ap (fun x => _ o x) (commutes T _ _ m) @ (associativity_sym _ _ _ _ _ _ _ _) @ ap (fun x => x o _) (commutes T' _ _ m) @ (associativity _ _ _ _ _ _ _ _).
Require Import Category.Core Functor.Core Functor.Composition.Core NaturalTransformation.Core.