proposition: Lemma oppe_continuous (R : realFieldType) : continuous (-%E : \bar R -> \bar R).
proof: Proof. move=> x S /= xS; apply nbhsNKe; rewrite image_preimage //. by rewrite predeqE => y; split => // _; exists (- y) => //; rewrite oppeK. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(fsbigop cardinality set_interval) reals signed topology constructive_ereal