proposition: Corollary proj_left_braid {x y} : proj_left ∘ braid ≈ @proj_right _ _ _ x y.
proof: Proof. unfold proj_left, proj_right. rewrite <- proj_right_left_diagonal. normal. rewrite eliminate_comp. rewrite unit_right_eliminate. 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