proposition: Lemma ocitvI : setI_closed ocitv.
proof: Proof. move=> _ _ [a _ <-] [b _ <-]; rewrite -set_itvI/=. rewrite /Order.meet/= /Order.meet /Order.join/= ?(andbF, orbF)/= ?(meetEtotal, joinEtotal). by rewrite -negb_or le_total/=. Qed.
imports: mathcomp(all_ssreflect ssralg ssrnum ssrint interval) mathcomp(finmap fingroup perm rat) HB(structures) mathcomp.classical(mathcomp_extra boolp classical_sets) mathcomp.classical(functions fsbigop cardinality) reals ereal signed topology numfun normedtype sequences esum real_interval measure realfun