proposition: Lemma scale_ball_set0 (k : R) : k *` set0 = set0 :> set R.
proof: Proof. by rewrite /scale_ball is_ball0// radius0/= mulr0 ball0. 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