proposition: Proposition underlying_Equalizer_arr_pr {w : C} (h : w --> x) (q : h · f = h · g) : underlying_Equalizer_arr h q · enriched_equalizer_cone_pr a = h.
proof: Proof. unfold underlying_Equalizer_arr, enriched_equalizer_cone_pr. use (invmaponpathsweq (make_weq _ (isweq_enriched_from_arr E _ _))) ; cbn. rewrite enriched_from_arr_comp. rewrite !enriched_from_to_arr. rewrite tensor_split. rewrite !assoc. rewrite <- tensor_linvunitor. rewrite !assoc'. refine (maponpaths (λ z, _ · z) _ @ EqualizerCommutes (is_equalizer_enriched_to_Equalizer Ha w) I_{V} (enriched_from_arr E h) _). cbn ; unfold postcomp_arr. rewrite !assoc'. apply maponpaths. do 2 apply maponpaths_2. refine (!_). apply enriched_from_to_arr. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.Limits.Equalizers