proposition: Lemma weak_equiv_preserves_binproducts_pr2 : weak_equiv_preserves_binproducts_map · # F (BinProductPr2 C BP) = g2.
proof: Proof. unfold weak_equiv_preserves_binproducts_map. rewrite assoc'. rewrite <- functor_comp. rewrite BinProductPr2Commutes. unfold f2; rewrite functor_on_fully_faithful_inv_hom. rewrite assoc. rewrite z_iso_after_z_iso_inv. apply id_left. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.catiso UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.PrecompEquivalence