proposition: Lemma sup_int_approxRN_lty : M < +oo.
proof: Proof. rewrite /sup_int_approxRN; have [m hm] := int_approxRN_ub. rewrite (@le_lt_trans _ _ m%:E)// ?ltey// ub_ereal_sup// => x IGx. by apply: hm; rewrite inE. 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