proposition: Lemma open_lt (y : R) : open [set x : R| x < y].
proof: Proof. move=> x /=; rewrite -subr_gt0 => yDx_gt0. exists (y - x) => // z. by rewrite /= ltr_distlC addrCA subrr addr0 => /andP[]. 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