proposition: Lemma leR_sumR r P f g : (forall i, P i -> f i <= g i) -> \sum_(i <- r | P i) f i <= \sum_(i <- r | P i) g i.
proof: Proof. move=> leE12. elim/big_ind2: _ => //. exact: Rle_refl. by move=> m1 m2 n1 n2; Lra.lra. Qed.
imports: mathcomp(all_ssreflect ssralg ssrnum) Reals mathcomp(lra) mathcomp(Rstruct)