proposition: Lemma iso_to_isProduct : isProduct _ _ _ Y (λ j, i · ProductPr _ _ P j).
proof: Proof. intros W f. use unique_exists. - exact ((ProductArrow _ _ P f) · (z_iso_inv_from_z_iso i)). - abstract exact (iso_to_isProduct_comm W f). - abstract (intro; apply impred_isaprop; intro; apply C). - abstract (intros y0 T; exact (iso_to_isProduct_unique W f y0 T)). Defined.
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.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.ProductCategory UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.Combinatorics.StandardFiniteSets