proposition: Lemma open_gt (y : R) : open [set x : R | x > y].
proof: Proof. move=> x /=; rewrite -subr_gt0 => xDy_gt0; exists (x - y) => // z. by rewrite /= ltr_distlC opprB 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