proposition: Lemma lt_in_itv bl br x : x \in Interval bl br -> bl < br.
proof: Proof. by case/andP; apply/le_lt_trans. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(div fintype bigop order ssralg finset fingroup) mathcomp(ssrnum)