Proposition make_positivity_l : (∏ {x y z : C} (f : x --> y) (g : y --> z), is_deterministic(f · g) -> f · ⟨g, identity _⟩ = ⟨f · g, f⟩) -> is_positive C. Proof. intros p. apply make_positivity_r. intros x y z f g d. apply cancel_braiding. rewrite !assoc', !pairing_sym_mon_braiding. apply p. 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.