proposition: Lemma ocitvP X : ocitv X <-> X = set0 \/ exists2 x, x.1 < x.2 & X = `]x.1, x.2]%classic.
proof: Proof. split=> [[x _ <-]|[->//|[x xlt ->]]]//. case: (boolP (x.1 < x.2)) => x12; first by right; exists x. by left; rewrite set_itv_ge. 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