proposition: Lemma le_sum S1 S2 : summable S1 -> summable S2 -> (S1 <=1 S2) -> sum S1 <= sum S2.
proof: Proof. move=> smS1 smS2 leS; rewrite /sum lerB //. apply/le_psum/summable_fpos => // x. by rewrite ge0_fpos /= le_fpos. apply/le_psum/summable_fneg => // x. rewrite -!fposN ge0_fpos le_fpos // => y. by rewrite lerN2. Qed.
imports: mathcomp(all_ssreflect all_algebra) mathcomp.classical(boolp) xfinmap ereal reals discrete realseq mathcomp.classical(classical_sets functions mathcomp_extra) topology