proposition: Lemma closed_ge (y : R) : closed [set x : R | y <= x].
proof: Proof. rewrite (_ : mkset _ = ~` [set x | x < y]); first exact: open_closedC. by rewrite predeqE => x /=; rewrite leNgt; split => /negP. 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