proposition: Lemma open_neq (y : R) : open [set x : R | x != y].
proof: Proof. rewrite (_ : mkset _ = [set x | x < y] `|` [set x | x > y]); first exact: openU. rewrite predeqE => x /=; rewrite eq_le !leNgt negb_and !negbK orbC. by symmetry; apply (rwP orP). 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