proposition: Proposition equalizer_enriched_from_underlying_map_inv₁ (h : I_{ V} --> E ⦃ w, a ⦄) : equalizer_enriched_from_underlying_map (h · equalizer_enriched_to_equalizer EqV a w) = h.
proof: Proof. unfold equalizer_enriched_from_underlying_map. refine (_ @ enriched_from_to_arr E h). apply maponpaths. use (isEqualizerInsEq eq_a). etrans. { apply (EqualizerCommutes (make_Equalizer _ _ _ _ eq_a)). } unfold enriched_equalizer_cone_pr. rewrite (enriched_to_arr_comp E). apply maponpaths. rewrite tensor_split. rewrite !assoc. rewrite <- tensor_linvunitor. rewrite enriched_from_to_arr. rewrite !assoc'. apply maponpaths. unfold equalizer_enriched_to_equalizer. rewrite EqualizerCommutes. rewrite !assoc. apply idpath. 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