Proposition positivity_l {ispos : is_positive C} {x y z : C} (f : x --> y) (g : y --> z) : is_deterministic(f · g) -> f · ⟨g, identity _⟩ = ⟨f · g, f⟩. Proof. intros det. apply cancel_braiding. rewrite !assoc', !pairing_sym_mon_braiding. use positivity_r; assumption. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.MarkovCategories.MarkovCategory. Require Import UniMath.CategoryTheory.MarkovCategories.Determinism. Require Import UniMath.CategoryTheory.MarkovCategories.AlmostSurely. Require Import UniMath.CategoryTheory.MarkovCategories.Univalence. Import MonoidalNotations.