proposition: Proposition is_cartesian_cartesian_monoidalcat : is_cartesian cartesian_monoidalcat.
proof: Proof. refine (is_semicartesian_cartesian_monoidalcat ,, _). intros x y ; cbn. use (isBinProduct_eq_arrow _ _ (pr2 (CP x y))). - abstract (unfold semi_cart_tensor_pr1 ; cbn ; unfold monoidal_cat_tensor_mor ; unfold functoronmorphisms1 ; cbn ; rewrite !assoc' ; rewrite BinProductOfArrowsPr1 ; rewrite id_right ; rewrite BinProductOfArrowsPr1 ; rewrite id_right ; apply idpath). - abstract (unfold semi_cart_tensor_pr2 ; cbn ; unfold monoidal_cat_tensor_mor ; unfold functoronmorphisms1 ; cbn ; rewrite !assoc' ; rewrite BinProductOfArrowsPr2 ; rewrite id_right ; rewrite BinProductOfArrowsPr2 ; rewrite id_right ; apply idpath). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Cartesian UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.Closed UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Adjunctions.Core