proposition: Lemma plus_comm : ∀ m k, (m ⊕ k) = (k ⊕ m).
proof: Proof. intros m k. move: ord_inj => Hordinj. unfold injective in Hordinj. apply Hordinj. destruct m. cbn. rewrite BinNat.N.lxor_comm. reflexivity. Qed.
imports: Relational(OrderEnrichedCategory GenericRulesSimple) mathcomp(all_ssreflect all_algebra reals distr fingroup.fingroup realsum ssrnat ssreflect ssrfun ssrbool ssrnum eqtype choice seq) Crypt(Axioms ChoiceAsOrd SubDistr Couplings UniformDistrLemmas FreeProbProg Theta_dens RulesStateProb UniformStateProb pkg_composition pkg_rhl Package Prelude) Coq(Utf8 Lia) extructures(ord fset fmap) Equations(Equations)