proposition: Lemma closed_openC (D : set T) : closed D -> open (~` D).
proof: Proof. rewrite closedE openE => Dcl t nDt; apply: contrapT. by rewrite /interior nbhs_nearE => /Dcl. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed