proposition: Lemma fsume_le0 (I : choiceType) (P : set I) (F : I -> \bar R) : (forall t, P t -> F t <= 0) -> \sum_(i \in P) F i <= 0.
proof: Proof. move=> PF; case: finite_supportP; rewrite ?big_nil// => X XP F0 _. by rewrite big_seq_cond big_mkcondr sume_le0// => i /XP/PF. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(fsbigop cardinality set_interval) reals signed topology constructive_ereal