proposition: Lemma nbhs_right_lt x z : x < z -> \forall y \near x^'+, y < z.
proof: Proof. move=> xz; exists (z - x) => //=; first by rewrite subr_gt0. by move=> y /= + xy; rewrite distrC ?ger0_norm ?subr_ge0 1?ltW// ltrD2r. 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