proposition: Corollary proj_left_right_diagonal {x y} : proj_left ⨂ proj_right ∘ ∆(x ⨂ y) ≈ id[x ⨂ y].
proof: Proof. rewrite <- bimap_id_left_right. rewrite <- comp_assoc. rewrite proj_left_id_diagonal. rewrite comp_assoc. unfold proj_right. rewrite bimap_comp_id_left. rewrite <- !comp_assoc. rewrite (comp_assoc _ tensor_assoc). rewrite to_tensor_assoc_natural. normal. rewrite <- comp_assoc. rewrite eliminate_right_diagonal. normal. rewrite <- triangle_identity. normal. rewrite iso_to_from. normal; reflexivity. Qed.
imports: Category.Lib Category.Theory.Category Category.Theory.Morphisms Category.Theory.Isomorphism Category.Theory.Functor Category.Functor.Bifunctor Category.Structure.Monoidal.Proofs Category.Structure.Monoidal.Cartesian