proposition: Lemma sup_int_approxRN_ge0 : 0 <= sup_int_approxRN.
proof: Proof. rewrite -(ereal_sup1 0) le_ereal_sup// sub1set inE. exists (fun=> 0); last exact: integral0. by split => //; [exact: integrable0|move=> E; rewrite integral0]. Qed.
imports: mathcomp(all_ssreflect ssralg ssrnum ssrint interval) mathcomp(finmap fingroup perm rat) mathcomp(mathcomp_extra boolp classical_sets cardinality) mathcomp(functions fsbigop set_interval) HB(structures) reals ereal signed topology numfun normedtype sequences esum measure realfun lebesgue_measure lebesgue_integral