proposition: Lemma closed_eq (y : R) : closed [set x : R | x = y].
proof: Proof. rewrite [X in closed X](_ : (eq^~ _) = ~` (xpredC (eq_op^~ y))). by apply: open_closedC; exact: open_neq. by rewrite predeqE /setC => x /=; rewrite (rwP eqP); case: eqP; split. 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