proposition: Lemma ereal_mem_Interval (r : R) (a b : itv_bound R) : (a < r%:E < b)%E -> r \in Interval a b.
proof: Proof. move: a b => [[]a|[]] [[]b|[]] //=; rewrite ?lte_fin ?in_itv //= => /andP[] //; by do ?[move->|move/ltW|move=>_]. 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