proposition: Lemma seqDU_seqD F : nondecreasing_seq F -> seqDU F = seqD F.
proof: Proof. move=> ndF; rewrite funeqE => -[|n] /=; first by rewrite /seqDU big_ord0 setD0. rewrite /seqDU big_ord_recr /= setUC; congr (_ `\` _); apply/setUidPl. by rewrite -bigcup_mkord => + [k /= kn]; exact/subsetPset/ndF/ltnW. 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