proposition: Lemma nbhs_open_ereal_gt r (f : R -> R) : f r < r -> nbhs r%:E [set y | (f r)%:E < y]%E.
proof: Proof. move=> xfx; rewrite nbhsE /=; eexists; last by move=> y; exact. by split; [apply open_ereal_gt_ereal | rewrite /= lte_fin]. 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