proposition: Lemma triangle_identity {a b c : C} (f : C ⟦ a, b ⟧) (g : C ⟦ b, c ⟧) : id2 f ⋆ lunitor g = lassociator f (identity b) g • (runitor f ⋆ id2 g).
proof: Proof. unfold hcomp at 2. rewrite vassocr. rewrite runitor_rwhisker. rewrite hcomp_hcomp'. unfold hcomp'. apply maponpaths. rewrite lwhisker_id2. apply id2_rwhisker. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.HorizontalComposition UniMath.Bicategories.WkCatEnrichment.prebicategory UniMath.Bicategories.WkCatEnrichment.Notations UniMath.Bicategories.Core.Bicat