proposition: Lemma dlet_additive (f : T -> {distr U / R}) z : (forall x, mu x = mu1 x + mu2 x) -> (\dlet_(x <- mu) f x) z = (\dlet_(x <- mu1) f x) z + (\dlet_(x <- mu2) f x) z.
proof: Proof. move=> muD; rewrite !dletE -psumD /=. by move=> x; rewrite mulr_ge0. by move=> x; rewrite mulr_ge0. by apply/summable_mlet. by apply/summable_mlet. by apply/eq_psum=> x /=; rewrite -mulrDl -muD. Qed.
imports: mathcomp(all_ssreflect all_algebra) mathcomp.classical(boolp classical_sets mathcomp_extra) xfinmap ereal reals discrete topology realseq realsum