proposition: Lemma lee_sum_nneg_ord (f : nat -> \bar R) (P : pred nat) : (forall n, P n -> 0 <= f n) -> {homo (fun n => \sum_(i < n | P i) (f i)) : i j / (i <= j)%N >-> i <= j}.
proof: Proof. move=> f0 i j le_ij; rewrite (big_ord_widen_cond j) // big_mkcondr /=. by rewrite lee_sum // => k ?; case: ifP => // _; exact: f0. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra) signed