proposition: Lemma is_interval_bigcup_ointsub U q : is_interval (bigcup_ointsub U q).
proof: Proof. move=> /= a b [A [[oA iA AU] Aq] Aa] [B [[oB iB BU] Bq] Bb] c /andP[ac cb]. have [cq|cq|->] := ltgtP c (ratr q); last by exists A. - by exists A => //; apply: (iA a (ratr q)) => //; rewrite ac (ltW cq). - by exists B => //; apply: (iB (ratr q) b) => //; rewrite cb (ltW cq). 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