proposition: Proposition cartesian_semi_cart_tensor_pr2 (VC : category) (TV : Terminal VC) (VP : BinProducts VC) (expV : Exponentials VP) (V : sym_mon_closed_cat := sym_mon_closed_cartesian_cat VC VP TV expV) (x y : V) : semi_cart_tensor_pr2 (is_semicartesian_cartesian_monoidalcat VC VP TV) x y = BinProductPr2 _ _.
proof: Proof. unfold semi_cart_tensor_pr2 ; cbn. unfold monoidal_cat_tensor_mor, functoronmorphisms1 ; cbn. rewrite !assoc'. rewrite BinProductOfArrowsPr2. rewrite id_right. rewrite BinProductOfArrowsPr2. apply id_right. Qed.
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