proposition: Lemma left_unitor_id_is_right_unitor_id {C : prebicategory} {a : C} : left_unitor_2mor (identity1 a) = right_unitor_2mor (identity1 a).
proof: Proof. apply whisker_right_id_inj. use (pre_comp_with_z_iso_is_inj (associator _ _ _)). intermediate_path (left_unitor_2mor ((identity1 a) ;1; (identity1 a))). apply pathsinv0. apply kelly_left. intermediate_path (whisker_left (identity1 a) (left_unitor (identity1 a))). apply pathsinv0. apply left_unitor_on_id. apply (triangle_axiom (identity1 a) (identity1 a)). Defined.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Categories.StandardCategories UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.Equivalences.Core UniMath.Bicategories.WkCatEnrichment.prebicategory UniMath.Bicategories.WkCatEnrichment.Notations