proposition: Lemma setU_seqD F : nondecreasing_seq F -> forall n, F n.+1 = F n `|` seqD F n.+1.
proof: Proof. move=> ndF n; rewrite /seqD funeqE => x; rewrite propeqE; split. by move=> ?; have [?|?] := pselect (F n x); [left | right]. by move=> -[|[]//]; move: x; exact/subsetPset/ndF. 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