Proposition bayesian_inverse_eq_r {y : C} (f : x --> y) : p · f · ⟨identity _, bayesian_inverse f⟩ = p · ⟨f, identity _⟩. Proof. apply cancel_braiding. rewrite !assoc', !pairing_sym_mon_braiding, assoc. apply bayesian_inverse_eq_l. 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.