proposition: Lemma bounded_funD (T : Type) (R : realFieldType) (a b : T -> R) : bounded_fun a -> bounded_fun b -> bounded_fun (a \+ b).
proof: Proof. move=> [M [Mreal Ma]] [N [Nreal Nb]]. rewrite /bounded_fun/bounded_near; near=> x => y /= _. rewrite (le_trans (ler_normD _ _))// [x]splitr. by rewrite lerD// (Ma, Nb)// ltr_pdivlMr//; near: x; apply: nbhs_pinfty_gt; rewrite ?rpredM ?rpred_nat. Unshelve. all: by end_near. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrint ssrnum finmap matrix) mathcomp(rat interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality set_interval Rstruct) ereal reals signed topology prodnormedzmodule