proposition: Lemma cvg_has_sup u_ : cvgn u_ -> has_sup (u_ @` setT).
proof: Proof. move/cvg_has_ub; rewrite -/(_ @` _) -(image_comp u_ normr setT). by move=> /has_ub_image_norm uM; split => //; exists (u_ 0%N), 0%N. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum matrix) mathcomp(interval rat) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(set_interval) reals ereal signed topology normedtype landau