proposition: Lemma sup_itv a b x : (a < BSide b x)%O -> sup [set` Interval a (BSide b x)] = x.
proof: Proof. by case: a => [b' y|[]]; rewrite ?bnd_simp//= => /sup_itv_bounded->. Qed.
imports: mathcomp(all_ssreflect ssralg ssrnum ssrint interval) mathcomp(finmap fingroup perm rat) mathcomp(mathcomp_extra boolp classical_sets functions) HB(structures) reals ereal signed topology normedtype sequences