proposition: Lemma dlet_eq0 (f : T -> U) mu y : {in dinsupp mu, forall x, f x != y} -> (\dlet_(x <- mu) dunit (f x)) y = 0.
proof: Proof. move=> h; unlock dlet => /=; apply/psum_eq0 => x. case/boolP: (x \in dinsupp mu) => [|/dinsuppPn->]; last by rewrite mul0r. by move/h; rewrite dunit1E => /negbTE ->; rewrite mulr0. Qed.
imports: mathcomp(all_ssreflect all_algebra) mathcomp.classical(boolp classical_sets mathcomp_extra) xfinmap ereal reals discrete topology realseq realsum