proposition: Lemma binproduct_of_isos {C : category} {x1 x2 y1 y2 : C} (p : BinProduct _ x1 x2) (i1 : z_iso x1 y1) (i2 : z_iso x2 y2) : BinProduct _ y1 y2.
proof: Proof. use make_BinProduct. - exact p. - exact (BinProductPr1 _ p · i1). - exact (BinProductPr2 _ p · i2). - use (isbinproduct_of_isos p (z_iso_inv i1) (z_iso_inv i2) (identity_z_iso p)) ; rewrite id_left; rewrite assoc'; rewrite z_iso_inv_after_z_iso; now rewrite id_right. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.FunctorCategory UniMath.Combinatorics.StandardFiniteSets