proposition: Corollary proj_left_natural {x y z w} (f : x ~> y) (g : z ~> w) : proj_left ∘ f ⨂ g ≈ f ∘ proj_left.
proof: Proof. unfold proj_left. rewrite comp_assoc. rewrite to_unit_right_natural. normal. rewrite eliminate_comp. reflexivity. Qed.
imports: Category.Lib Category.Theory.Category Category.Theory.Isomorphism Category.Theory.Functor Category.Functor.Bifunctor Category.Structure.Monoidal Category.Structure.Monoidal.Proofs Category.Structure.Monoidal.Semicartesian