Proposition conditional_eq {a x y : C} (f : a --> x ⊗ y) : f = copy a · (f · proj1 · copy x) #⊗ identity a · mon_lassociator _ _ _ · identity x #⊗ (conditional f). Proof. exact (pr2 (pr2 C a x y f)). 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.InformationFlowAxioms. Require Import UniMath.CategoryTheory.MarkovCategories.AlmostSurely. Import MonoidalNotations.