proposition: Proposition exp_eta_alt {x y z : C} (f : z --> exp x y) : f = exp_lam_alt (BinProductOfArrows C _ _ f (identity x) · exp_eval_alt x y).
proof: Proof. refine (exp_eta _ @ _). unfold exp_lam_alt. apply maponpaths. unfold exp_eval_alt. rewrite !assoc. apply maponpaths_2. rewrite !assoc'. rewrite BinProductOfArrows_swap. rewrite !assoc. rewrite prod_swap_swap. rewrite id_left. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.catiso UniMath.CategoryTheory.CategoryEquality UniMath.CategoryTheory.Core.Univalence