proposition: Lemma closed_bigsetU (T : topologicalType) (I : eqType) (s : seq I) (F : I -> set T) : (forall x, x \in s -> closed (F x)) -> closed (\big[setU/set0]_(x <- s) F x).
proof: Proof. move=> scF; rewrite big_seq. by elim/big_ind : _ => //; [exact: closed0|exact: closedU]. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed