proposition: Lemma associativity x1 x2 x3 x4 (m1 : morphism x1 x2) (m2 : morphism x2 x3) (m3 : morphism x3 x4) : compose (compose m3 m2) m1 = compose m3 (compose m2 m1).
proof: Proof. refine (@path_morphism' _ A B S T _ _ (compose (compose m3 m2) m1) (compose m3 (compose m2 m1)) (Category.Core.associativity _ _ _ _ _ _ _ _) (Category.Core.associativity _ _ _ _ _ _ _ _) _). simpl. apply associativity_helper. - exact (p_composition_of_coherent_for_rewrite _ _ _ _ _ _ _ _). - exact (p_composition_of_coherent_inverse_for_rewrite _ _ _ _ _ _ _ _). Defined.
imports: Functor.Core NaturalTransformation.Core Category.Strict Functor.Composition.Core NaturalTransformation.Paths NaturalTransformation.Composition.Core Category.Morphisms FunctorCategory.Core Pseudofunctor.Core Pseudofunctor.RewriteLaws NaturalTransformation.Composition.Laws FunctorCategory.Morphisms HoTT.Tactics