proposition: Proposition equalizer_enriched_from_underlying_map_inv₂ (h : I_{ V} --> EqV _ _ (postcomp_arr E w f) (postcomp_arr E w g)) : equalizer_enriched_from_underlying_map h · equalizer_enriched_to_equalizer EqV a w = h.
proof: Proof. unfold equalizer_enriched_from_underlying_map. use (isEqualizerInsEq (pr22 (EqV _ _ _ _))). unfold equalizer_enriched_to_equalizer. rewrite !assoc'. rewrite EqualizerCommutes. rewrite enriched_from_arr_postcomp. refine (_ @ enriched_from_to_arr E _). apply maponpaths. apply (EqualizerCommutes (make_Equalizer _ _ _ _ eq_a)). 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