proposition: Lemma composition_of x y z g f : mor_of _ _ (f o g) = mor_of y z f o mor_of x y g.
proof: Proof. simpl. erewrite IsInitialMorphism_property_morphism_unique; [ reflexivity | ]. rewrite ?composition_of. repeat try_associativity_quick rewrite IsInitialMorphism_property_morphism_property. reflexivity. Qed.
imports: Category.Core Functor.Core NaturalTransformation.Core Functor.Identity Functor.Composition.Core Functor.Dual Category.Dual Adjoint.Core Adjoint.UnitCounit Adjoint.UnitCounitCoercions Adjoint.Dual UniversalProperties Comma.Dual InitialTerminalCategory.Core InitialTerminalCategory.Functors