proposition: Proposition indexed_cat_lunitor {x y : C} (f : x --> y) (xx : Φ x) : identity ((Φ $ f) xx) = # (Φ $ f) (indexed_cat_id Φ x xx) · indexed_cat_comp Φ (identity x) f xx · idtoiso (maponpaths (λ g, (Φ $ g) xx) (id_left f)).
proof: Proof. exact (pr122 Φ x y f xx). Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations