proposition: Lemma interval_is_interval (i : interval R) : is_interval [set` i].
proof: Proof. by case: i => -[[]a|[]] [[]b|[]] // x y /=; do ?[by rewrite ?itv_ge//]; move=> xi yi z; rewrite -[x <= z <= y]/(z \in `[x, y]); apply/subitvP; rewrite subitvE /Order.le/= ?(itvP xi, itvP yi). Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrint ssrnum finmap matrix) mathcomp(rat interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality set_interval Rstruct) ereal reals signed topology prodnormedzmodule